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GAMMA Users Guide

1. block_1D BLK 50 create a data block double x y theta declare needed variables double a b declare needed variables for int 1 0 1 lt 50 i loop through 50 points fill up block with Prolate Cycloid a 1 b 2 theta PI 1 4 0 P1 49 0 angles span pi to 3pi x a theta b sin theta x a theta b sin theta here a 1 b 2 y a b cos theta y a b cos theta BLK i complex x y FM_scatter FM mif BLK 0 1 14 5 A output FrameMaker mif plot file You can set the symbol type to use in the figure either in the function call or afterwards in FrameMaker 4 5 6 2D Contour Plots 2D contour plots are produced for FrameMaker with function FM_contour Each contour is an in dividual graphic object which can be manipulated For example the negative contours can selec tively changed to dashed lines Overall plot height amp width can be set within FrameMaker Scott Smith Copyright S A Smith May 22 1998 GAMMA Plotting 39 Users Manual Plotting Figures 4 2 oS _ soso NONBRAGe Soo beste Cave The example plot has be altered within FrameMaker and the 1D plots added Thsi program made it include lt gamma h gt main matrix mx 101 101 create a 101x101 matrix for data row_vector BLK1 101 BLK2 101 create two 1D data blocks of length 101 BLK1 sinc 101 50 10 use provided window sinc function BLK2 sin_square 101 50 us
2. line or ask for them filename spin_system sys Declare spin system sys sys read filename Read system from filename int t2pts Number of points in FID query_parameter argc argv Get number of points 2 n tNumber of acquisition points t2pts char J query_parameter argc argv Get number of points 3 An tStrong or Weak Coupling s w J Determine the Isotope Detection Type int isoset 0 String Isotype sys symbol 0 Get isotope type of first spin if sys heteronuclear Check if system is heteronuclear isoset while isoset lt 0 cout lt lt n tWhich Isotope Type cin gt gt Isotype for int k 0 k lt sys spins k if Isotype sys symbol k isoset k break Tilo Levante Scott Smith May 22 1998 GAMMA NMR Simulations 66 NMR Examples One Pulse General 5 6 if isoset lt 0 cout lt lt n tSystem Contains No Spin of That Type Set Up Spectral Parameters double offset sys center isoset Find the center of the system sys offsetShifts offset isoset Offset the rotating frame double NyqF sys Nyquist Approximate Nyquist frequency double dt 1 0 2 0 NyqF Dwell time quadrature detection double sw 2 0 NyqF Total Spectal width Nyquist Set Variables block_1D data t2pts Storage for the FID Spectrum gen_op sigma sigma_eq sys Set density matrix equilibrium gen
3. Read in Parameters String filename Name of spin system file query_parameter argc argv Get filename from command 1 n tSpin system filename line or ask for them filename spin_system sys Declare spin system sys Tilo Levante Scott Smith May 22 1998 GAMMA NMR Simulations NMR Examples 56 One Ideal Pulse Homonuclear Spin System 5 5 sys read filename int t2pts query_parameter argc argv 2 n tNumber of acquisition points t2pts char J query_parameter argc argv 3 n tStrong or Weak Coupling s w J Determine the Isotope Detection Type int isoset 0 String Isotype sys symbol 0 if sys heteronuclear isoset while isoset lt 0 cout lt lt n tWhich Isotope Type cin gt gt Isotype for int k 0 k lt sys spins k if Isotype sys symbol k isoset k break if isoset lt 0 Read system from filename Number of points in FID Get number of points Get number of points Get isotope type of first spin Check if system is heteronuclear cout lt lt n tSystem Contains No Spin of That Type Set Up Spectral Parameters double offset sys center isoset sys offsetShifts offset isoset double NyqF sys Nyquist double dt 1 0 2 0 NyqF double sw 2 0 NyqF Find the center of the system Offset the rotating frame Approximate Nyquist frequency Dwel
4. lt mx cols j Put i s in the first row mx put complexi 0 j mx put complex 2 3 1 2 Set lt 3lmxl4 gt to 2 31 FM_Mat_Plot FM mif mx Output FrameMaker mmf file Here is the output from the program the contents of file FM mif read by FrameMaker Scott Smith Copyright S A Smith May 22 1998 GAMMA Plotting 46 Users Manual Plotting Figures 4 2 Those familiar with FrameMaker should not that the result of this function is a graphical object whereas the result of the previous function goes into an equation Scott Smith Copyright S A Smith May 22 1998 GAMMA Plotting 47 Users Manual Plotting Figures 4 2 4 6 Felix 4 6 1 Description GAMMA has some knowledge of the Felix NMR processing program It contains a class for per forming I O to and from Felix files and to the older FTNMR Scott Smith Copyright S A Smith May 22 1998 GAMMA NMR Simulations 48 NMR Examples NMR Simulation Sections 5 1 5 NMR Simulations If you have been following diligently through this book you now know how to build C programs and GAMMA programs You also know how to weild the GAMMA supplied data types as well as the wide variety of functions supplied We combine all of that knowledge in this section and em bark on some NMR simulations 5 1 NMR Simulation Sections Single Pulse Acquisition Simulations page 48 3 4 1 Description page 28 3 4 2 1D Plots page 28 FrameMaker Output to FrameMaker
5. n n tAxes in Hz 0 or PPM 1 cin gt gt inPPM cout lt lt An if inPPM For PPM adjust plot limits If 1f sys Omega rt rt sys Omega exponential_multiply data 8 Apodize the FID data FFT data Fourier transform the FID FM_1D filename data 14 5 1f rt Write spectrum to a FrameMaker file break case 2 Felix output Felix filename data Output FID in Felix format cout lt lt n t tParameters Needed for Felix Data Workupin Tilo Levante Scott Smith May 22 1998 GAMMA NMR Simulations 68 NMR Examples One Pulse General 5 6 cout lt lt n tTo set OMEGA sf lt lt sys Omega isoset cout lt lt n tTo set spectral width sw lt lt 2 NyqF cout lt lt n tTo set offset no zf ref lt lt t2pts 2 lt lt lt lt offset cout lt lt n tTo set axis in Hertz ax 2 lt lt mu break case 3 NMRi filename data Output FID in NMRi format break case 4 MATLAB filename spectrum data Output FID in MatLab format cout lt lt n t t MATLAB Spectrum is Internally Named spectrum break cout lt lt An 5 6 3 Discussion Read in Parameters Following the output of the program description an arbitrary spin sys tem is read in from an external file specified Afterwards the number of points in the FID is inter actively set Because it is useful to examine the weak coupling case the us
6. GAMMA Classes 19 Users Manual Isotropic Spin Systems 2 5 formation to the spin operator functions and this sets the stage for building spin Hamiltonians and ultimately for applying pulses delays and acquisitions to the sample Consider the high resolution isotropic NMR Hamiltonian It is given by spins spins spins H Y 9t 1 Lil i 1 i j gt i We have already seen that we can readily make J spin operators for each spin in the system A line of code might be where sys is the spin system spin_op Iz0 Fz sys 0 Iz for the 1st spin Without much thought ei ILI I I I id j we know we can readily make the spin op iz jz ix jx erators required for scalar coupled spin pairs Here is a code line that would partially suffice spin_op IOI1 Fz sys 0 Fz sys 1 Iz1 Iz2 for the 1st spin pair Fx sys 0 Fx sys 1 Fy sys 0 Fy sys 1 If we stretch out imaginations we can just put in a loop over the number of spins and the number of spin pairs and do a summation The code C code would look like int i j for 1 0 i lt sys spins i Add in the chemical shift contributions here for 1 1 j lt sys spins j Add in the scalar coupling contributions here However we still lack some important information particularly the chemical shifts of all the system spins and the scalar couplings between the system spin pairs One solution would be to just add this isotropic information directly into the
7. Tilo Levante Scott Smith May 22 1998 GAMMA NMR Simulations 58 NMR Examples One Ideal Pulse Homonuclear Spin System 3 5 case 1 FrameMaker output default double If rt double inPPM 2 If offset sw 2 0 Set plot limits in Hertz rt offset sw 2 0 while inPPM lt 0 Il inPPM gt 1 Querie for Hertz or PPM axis cout lt lt n n tAxes in Hz 0 or PPM 1 cin gt gt inPPM cout lt lt An if inPPM For PPM adjust plot limits If 1f sys Omega rt rt sys Omega exponential_multiply data 8 Apodize the FID data FFT data Fourier transform the FID FM_1D filename data 14 5 1f rt Write spectrum to a FrameMaker file break case 2 Felix output Felix filename data Output FID in Felix format cout lt lt n t tParameters Needed for Felix Data Workupin cout lt lt n tTo set OMEGA sf lt lt sys Omega isoset cout lt lt n tTo set spectral width sw lt lt 2 NyqF cout lt lt n tTo set offset no zf ref lt lt t2pts 2 lt lt lt lt offset cout lt lt n tTo set axis in Hertz ax 2 lt lt Ann break case 3 NMRi filename data Output FID in NMRi format break case 4 MATLAB filename spectrum data Output FID in MatLab format cout lt lt n t tMATLAB Spectrum is Internally Named spectrum break cout lt lt An Tilo Levante Scott Smith Ma
8. 1998 GAMMA Classes 21 Users Manual Isotropic Spin Systems 2 5 J O 1 1 22 0 Scalar coupling Hz v 0 1 1200 Shift of spin 1 Hz PPM 1 1 0 Shift of spin 2 PPM Omega 1 600 00 Spec Freq in MHz 1H based Remember you can have any number of spins in a spin system and virtually any spin isotope Now UI run the program with this file lgammal gt a out sosi sys Matrix GAMMA 6 x 6 Diagonal Matrix 589 00 0 00 600 00 0 00 611 00 0 00 589 00 0 00 600 00 0 00 611 00 0 00 Basis Default Basis 6 x 6 Identity Matrix O K that is pretty uneventful The Hamiltonian is diagonal because the scalar coupling in hetero nuclear The GAMMA function Ho knows that from the system and automatically sets weak scalar coupling Let me rerun after switching the deuterium to carbon replacing 2H by 13C in the file sosi sys Now here is the output lgammal1 gt a out sosi sys Matrix GAMMA 4 x 4 Full Matrix 594 50 0 00 0 00 0 00 0 00 0 00 0 00 0 00 0 00 0 00 605 50 0 00 11 00 0 00 0 00 0 00 0 00 0 00 11 00 0 00 594 50 0 00 0 00 0 00 0 00 0 00 0 00 0 00 0 00 0 00 605 50 0 00 Basis Default Basis 4 x 4 Identity Matrix Still dull but at least we have off diagonals Note how although the GAMMA program has noth ing specific about the input system the output Hamiltonian automatically adjusts depending upon the system used We will lat
9. 1H Spin Isotope Type Iso 6 2 1H Spin Isotope Type Iso 7 2 1H Spin Isotope Type PPM 0 1 4 27 Chemical Shifts in PPM PPM 1 1 3 47 Chemical Shifts in PPM PPM 2 1 3 6 Chemical Shifts in PPM PPM 3 1 3 89 Chemical Shifts in PPM PPM 4 1 3 63 Chemical Shifts in PPM PPM 5 1 3 76 Chemical Shifts in PPM PPM 6 1 3 71 Chemical Shifts in PPM PPM 7 1 3 54 Chemical Shifts in PPM J 0 1 1 7 8 Coupling Constants in Hz J 1 2 1 8 2 Coupling Constants in Hz J 2 3 1 3 71 Coupling Constants in Hz J 3 4 1 4 0 Coupling Constants in Hz J 4 5 1 10 5 Coupling Constants in Hz J 5 6 1 1055 Coupling Constants in Hz J 6 7 1 15 Coupling Constants in Hz Omega 1 400 Spectrometer Frequency in MHz 1H based 5 4 6 Results 8 Spin System The second example was done with One_pulse 2 0ne_pulse 2a sys 0 0025 1024 6000 5000 4000 3000 2000 1000 200 UI Mi d 5 5 One Ideal Pulse Homonuclear Spin System For the next example of a single pulse experiment simulation we present a more complicated pro gram which will work on any input spin system The pulse sequence is again shown below with density matrices labeled to coincide with the program code Tilo Levante Scott Smith May 22 1998 GAMMA NMR Simulations 55 NMR Examples One Ideal Pulse Homonuclear Spin System 5 5 Acquire di Wu Oo ei O ty The spin system acquisition size
10. IH Spectrum Tilo Levante Scott Smith May 22 1998 GAMMA NMR Simulations 64 NMR Examples One Pulse General 5 6 5 6 One Pulse General 5 6 1 Description Inp the previous example we put together a general GAMMA program to simulate a simple 1D experiment using ideal pulses and ignoring relaxation In many experiments the effects of relax ation and finite length pulses are well apparent and cannot be ignored We now turn our attention to adding in the effects of relaxation during the acquisiton period For the moment we continue to apply a single Ideal pulse but we slightly modify the previous simulation to include relaxation effects Again the simulation code is long soas to accomodate any input spin system The pulse sequence is again shown below with density matrices labeled to coincide with the program code Acquire gl Wu On OG O t2 The spin system acquisition size isotope to be detected and output format at will all be specified by the user interactively Following this the spin system shifts will be offset to the center of the spectrum so the simulation occurs in an optimal rotating frame All spectral parameters such as the spectral width and dwell time will be determined automatically The equilibrium density matrix Op can be generated directly from the specified spin system This density matrix is then
11. MIF page 30 3 5 1 Description page 30 5 2 NMR Simulation Figures 5 3 Single Pulse Acquisition Simulations The simplest NMR experiment one can simulate is that of a single pulse experiment A pulse is applied to the system with subsequent FID acquisition The pulse sequence is depicted in the fol lowing diagram Simple Pulse Acquisition Sequence Acquire di Even with this simple experiment there are several tradeoffs between computational simplicty 1 Do not confuse computational ease with programming ease The intent of GAMMA is to make complicat ed simulations relatively easy to produce In many instances the more computationally intensive simula tions are produced from GAMMA programs which are not significantly more complex Tilo Levante Scott Smith May 22 1998 GAMMA NMR Simulations 49 NMR Examples Single Pulse Acquisition Simulations 5 3 and simulation accuracy which one may wish to consider Below is again the pulse sequence di agram with GAMMA provided simulation possibilities listed for each of the two steps Single Pulse Experiment Simulation Possibilities Step 1 Step 2 Pulse Acquisition A Ideal B Real No Relaxation No Relaxation C Real Relaxation D Shaped No Relaxation Jl Relaxation E Shaped Relaxation For the application of any pulse in GAMMA users may opt to apply what we call an ideal pulse An ideal pulse affects all spins of a particular isotope equal
12. the operator log will be known to both integers and doubles and so on Now we must convert this program code into an executable That is done by using the gamma script which invokes the C compiler links any required C libraries and links to the GAMMA platform We still use noesy gt to be the prompt that the computer we are working on uses and we will assume the file containing this program code is called dbl cc note that the cc is often manda tory when using the C compiler Here we go noesy gt gamma dbl cc GAMMA Other Messages noesy gt Your actual response may vary depending on your GAMMA version and your computer type The command gamma acting on dbl cc or any C program will produce an executable that has a default name called a out To run the program noesy gt a out Output From Program noesy gt I won t include the output of this run the program isn t meant to do anything constructive It is only to show what a simple C program using doubles will look like Scott Smith Copyright S A Smith May 22 1998 GAMMA Classes 12 Users Manual Matrices and Vectors 22 2 2 Matrices and Vectors Let us now jump up a level in abstraction yet remain focused on mathematical manipulations GAMMA provides data types matrix row_vector and col_vector to handle matrices row vectors and column vectors respectively What does that mean It means that you are free to manipulate these objects in yourGAMMA
13. to other I O libraries However GAMMA has modules which interface to some of the more common plotting and manipulation programs 4 1 Plotting Sections Overview Overview of producing graphical output page 29 Gnuplot Output to Interactive plots with Gnuplot ASCII page 31 4 4 1 Description page 31 4 4 2 1D Plots page 31 FrameMaker Output to FrameMaker MIF page 33 4 5 1 Description page 33 4 5 2 1D Plots page 33 4 5 4 xy Plane Plots page 36 4 5 5 Scatter Plots page 37 4 5 6 2D Contour Plots page 38 4 5 7 2D Stack Plots page 40 4 5 8 3D Sphere Plots page 42 4 5 9 Histograms page 43 4 5 10 Matrix Output page 44 4 5 11 Matrix Plots page 45 Felix Output Input of Felix formatted data sets page 47 4 2 Plotting Figures GAMMA Supported I O page 29 GAMMA I O Methodology page 30 Scott Smith Copyright S A Smith May 22 1998 GAMMA Plotting 29 Users Manual Plotting Figures 4 2 4 3 Overview GAMMA provides interfaces between itself and the formats supported by several useful software packages This scheme is depicted in the following diagram GAMMA Supported I O Mor DL ef IN NMRi Figure 19 1 Some of the programs with which GAMMA can easily interact There are other prgrams that also have been used with GAMMA those that come to mind at the moment are Sig maPlot Deltagraph and XMGR These take ASCII input and need no special interface GAMMA has the ability to read and write data in the formats used by the
14. 0 Fz sys 1 Dipolar Hamiltonian component Since according to the previous program demonstrating class spin_sys the Hilbert space is 34 for the test sys defined spin system all our output operators will be 34x34 arrays too big to do a screen capture and have on this page So I m going to use a smaller spin system defined in my test sys Here is the one I will use instead just tritium instead of vanadium Scott Smith Copyright S A Smith May 22 1998 GAMMA Classes 18 Users Manual Isotropic Spin Systems 2 5 SysName 2 3Spins Name of the Spin System NSpins 0 3 Number of Spins in the System Iso 0 2 13C Spin Isotope Type Iso 1 2 2H Spin Isotope Type Iso 2 2 3H Spin Isotope Type I m also going to use a GAMMA FrameMaker function so I can bring them right into this docu ment Rather than use the function cout lt lt spin_op as is shown in the above program I will sub stitute in FM_Matrix file mif spin_op Those of you who don t use FrameMaker don t need to worry about this suffice it to say that the following matrices are one in the same as the ones that would appear on screen if you ran the program with the 3 spin CDV system used previously ex cept they would show up on screen as diagonal and Hermitian arrays 20000 lo1141 0 0 0 10 0000000 0 0 0 0 010000000000 00 0 141 0 0010 0 0 001000000000 00 0 1 1410001 0 0 0 000000000000 00 0 0 0 141000 1 0 0 00
15. 55 DISCUSSION E 59 Dab EE 59 Kante A dd 60 One Pulse General sera ris 64 D scrip gn eebe eege 64 Programi E 65 May 22 1998 GAMMA Table of Contents iv Users Guide 5 6 3 DISCUSSION Mustaine 68 5 6 4 IR E EE E 69 5 6 5 Results aan deeg ee ee ee Memes 70 5 7 L I E EE 74 5 8 One Pulse Fimte Length iaa 74 5 8 1 A O E OO 75 5 8 2 IR EE e e WEE He 5 8 3 RESU S gt EE Batted SAB aut ice lode He May 22 1998 GAMMA Introduction Users Manual Basics of C Programs 1 1 1 Introduction THIS DOCUMENT ASSUMES THAT THE READER HAS A WORKING VERSION OFT GAMMA is a computational environment designed to simplify the simulation of magnetic reso nance MR phenomena It accomplishes this by allowing users to write C programs using the objects that are commonly used to describe MR Thus GAMMA programs are C programs buth they make use of quantities such as spin systems pulses delays Hamiltonians and the like This document describes the basics of using GAMMA and writing GAMMA programs It will be biased towards simulations of nuclear magnetic resonance NMR problems as well as towards use in a Unix environment It also assumes that the reader is familiar with some editor and that the GAM MA platform has been successfully installed 1 1 Basics of C Programs The purpose of GAMMA is to allow you the user to write your own programs easily and efficient ly In this regard it is similar to programs such as MATLAB
16. Igammal gt so don t let that worry you GAMMA is not limited to the number of spins in a spin system and has a internal knowledge of most spin isotopes To learn more about GAMMA s spin system s and isotopes see their chapters in the GAMMA CLASS DOCUMENTATION 2 4 Spin Operators Having learned about basic spin systems we shall start learning to use something which is funda mental to the mathematical treatment of magnetic resonance a spin operator GAMMA provides the user with a wide variety of functions that return spin operators operators based on spin angular momentum that reside in a composite spin space These functions almost invariably take a GAM MA spin system as a function argument 2 4 1 GAMMA Spin Operators Construction Functions Output To keep things simple the following program will just read in the system file test sys rather than ask the user for it include lt gamma h gt main Spin_sys sys System sys sys read test sys System reads itself from file test sys spin_op FZ Fz sys Here is Fz for the system cout lt lt nSystem Total Fz Op lt lt FZ Have a look at Fz for the system cout lt lt nSystem F Here is F for the system output lt lt Fx sys complexi Fy sys to the screen cout lt lt AnSystem F lt lt Fp sys This is also F by a easier way double dij 134 7 Dipolar coupling value gen op HD dij Fz sys
17. Manual Plotting Figures 4 2 Ninety Ideal Pulse On A 4 Spin Proton System Have your GAMMA program fill up a row vector with the simulated data points you wish to plot Then make a function call to FM_1D with the row vector and an output file name given as argu ments The output file can be read by FrameMaker Please note that GAMMA takes no time to make pretty output you can do the cosmetic work within FrameMaker Here is a simple example include lt gamma h gt main row_vector vx 101 1 dim data block or use row_vector double x y for int i 0 i lt 101 i Fill up data block x double i 50 y x x x 125000 cubical parabolic in imaginaries x x x 2500 parabolic into reals vx put complex x y i FM_1D FM mif vx 10 5 50 50 1 output FM mif with both plots When compiled and run it will produce a file called FM mif When that file is subsequently read by FrameMaker the following plots will appear The one on the left has been left except for resiz ing as GAMMA produced the one on the right has been cosmetically enhanced just to show what you can do to the plot in FrameMaker Scott Smith Copyright S A Smith May 22 1998 GAMMA Plotting 35 Users Manual Plotting Figures 4 2 l 1 Wow I can do anything 0 8 I want to with this plot now 0 5 0 6 0 0 4 0 2 0 5 0 1 40 20 0 20 40 4 5 3 Multiple 1D Plots You can easily output several plot
18. Numbers 2 1 2 Classes In the previous chapter of this document you learned the basics of constructing and compiling sim ple C programs In this chapter we shall start writing simple programs which use the objects which are defined both in C and in GAMMA The programs herein will highlight some of the features of using GAMMA classes BUT to take full advantage of them you should look at the GAMMA CLASS DOCUMENTATION There will be a chapter for each class type and a full list of the functions and operators defined for them 2 1 Double Precision Numbers Consider the data type double intrinsic in C Such variables are used to track floating point numbers with double precision accuracy We bring this up here so that those who are new to C can see how to utilize double precision numbers in their programs Subsequently data types sup plied by GAMMA will be used with similar lines of code Variables of type double have the following data type properties 1 A double precision number may be declared anywhere in a program 2 An array of double precision numbers can be readily declared and accessed with 3 Double precision numbers come with their own functions exp lt lt 4 Double precision numbers have a defined algebra 5 Double precision number have the ability to interact with other data types int double Other intrinsic data types such as integers strings have similar characteristics In GAMMA sti
19. SEQUENCE AND DATA WORKUP apply a PI 2 y pulse perform an acquisition write FID to a FrameMaker file with size 5 14 cm Fourier transform the FID for plot widths May 22 1998 GAMMA NMR Simulations 76 NMR Examples One Pulse Finite Length 5 8 FM_1D One_pulse 3 FFTmif write spectrum to a FrameMaker file data 14 5 lim lim with size 5 14 cm 5 8 2 Discussion Set Parameters The spin system used was a simple two spin system read in from the disk file One_pulse 3 sys The dwell time is set to 0 005 called t2dt which sets the resulting spectral width to 100 This will insure the shift frequencies in sys are covered The number of points in the acquisition is set to 1K Declare Needed Variables Many of these steps both declare a variable and set it at the same time The first line specifies a general operator sigma0 which is initialized to the equilibrium den sity matrix Similarly the operator H is declared and set to the liquid NMR Hamiltonian with strong coupling The detection operator is declared and set to F A 1 dimensional data block is set up to contain t2pts points An unscaled dipolar relaxation superoperator is set in the next line Fol lowing this a working density matrix is declared The last line of this section declares and sets an acquisition a parameter which facilitates computation of acquisitions Apply Pulse Sequence and Data Workup The pulse sequence is very short
20. an operator gen_op in a single step Rather than writing a subroutine to make a dipolar relaxation matrix there is a simple function which will return it as a superoperator super_op contains a Magnetic Rather than looping over the points of an acquisi tion there are functions which will fill a data block with the FID points And so on You don t have to use these functions in your GAMMA programs just as you are not required to use GAMMA data types in your C programs But the idea is that once you are used to them you can focus your programming efforts on new and exciting things rather than spending a week to program in a 90 pulse 3 1 Hamiltonians This document already made use of the function which provides the isotropic Hamiltonian Ho It is just a sum of the isotropic shift Hamiltonian and the isotropic scalar coupling Hamiltonian That s all we d ever need for NMR simulations if we always dealt with small molecules in nicely liquid systems where relaxation didn t concern us But the fact is that we do deal strongly relaxting systems large molecules powder samples liquid crystals etc If we want to do simulations on those we do we do then we ll need some other Hamiltonians at our disposal Remember you can just build any Hamiltonian you wish by adding and multiplying together spin operators The Hamiltonian functions provided are just the ones so common that we don t want to have to think about th
21. and then we ll do something with GAMMA 1 Include statements are used to tell the C compiler about specific files it should know about These may be header files filename h files that indicate how to interface with var ious functions and data types whose code has already been compiled and will be included in a library or they may be files of C code filename cc Include statements begin with Scott Smith Copyright S A Smith May 22 1998 GAMMA Introduction Users Manual Basics of C Programs 1 1 a and the filename will be encased either with brackets to indicate it is in a searched di rectory e g include lt filename h gt or in quotes indicating it is in the local directory e g include filename cc 2 Subroutines or functions which are in the file containing the main source code will nor mally reside after the include statements but before the main program The main program will see only routines which are above it in the file Functions and subroutine may also exist in separate files included as indicated in the previous paragraph 3 Interactive programs may be written either by allowing the main function to accept argu ments or by use of standard input Our simple programs have already used the include statement so that they have been able to use GAMMA but haven t If you wish to include other programs and modules you will have to ex periment that s really beyond the level of this
22. can manipulate the Hamiltonians because they are just operators gen_op Note For Anisotropic Hamitonians See Spatial amp Spin Tensors and the Rank 2 Interactions 3 2 Ideal Pulses This the the stuff to know about if you don t care about artifacts from pulse offsets pulse power and pulse lengths Ideal pulses are perfect and the easiest way to generate transverse magnetization You might think of these pulses as being infinitly short and with just the power to get the pulse an gle you need They actually can do the impossible you can even do perfect spin specific pulses im possible to do experimentally if two spins have overlapping transitions There are lots of function in GAMMA that do ideal pulses any angle any phase any selectifity But you MUST know that these functions come in two flavors 1 Those that operate directly on the spin system density operator 2 Those that produce pulse propagators that can be used repeatedly in a simulation If you just need a quick pulse in some simulation just a function that does a direct pulse on the sys tem If you are doing some long and involved multi dimensional experiment simulations where the same pulse is repeately applied then use the latter it will conserve both CPU time and memory use If you don t know which to use don t bother they both do the same thing if applied in your GAM MA program correctly Here s some code to demonstrate these things include l
23. lt n tA Default Three Spin System n Write sys to standard output lt lt sys The program just declares a spin system and then the system writes itself to standard output We Il compile and run the program taking sys1 cc to be the name of the file containing the above code noesy gt gamma sysl cc GAMMA Other Messages noesy gt a out A Default Three Spin System System Spin 0 1 2 Scott Smith Copyright S A Smith May 22 1998 GAMMA Classes 14 Users Manual Basic Spin Systems 2 3 Isotope 1H 1H 1H Momentum 1 2 1 2 1 2 noesy gt Because we have not specified any details other than that the system contains 3 spins GAMMA automatically uses a default isotope of 1H Also note that there is a standard output function lt lt defined for a spin system In effect the system knows how to display itself to the screen as do dou bles integers matrices and most of the data types in GAMMA 2 32 GAMMA Base Spin System Member Functions Info Access File Input Now wel get a bit more fancy with our basic spin system Since in C we have control over what functions are available to these type of variables lets consider some that might be useful 1 Set Retrieve the number of spins 2 Set Retrieve a spin s particular isotope type 3 Read Write spin system to disk 4 Get the system Hilbert space dimension 5 Obtains a spins angular momentum and or gyromagnetic ratio nN All of these are intrinsic
24. programs in the figure Thus GAMMA may be used to directly produce data in a format specific to any of these or used to swap data between the different programs This allows the user to take advantage of any data processing provided in these programs and any additional program which perform data conversions on them Keep in mind that GAMMA itself has only rudimentary abilities for graphical display and signal processing It would be foolish to compete with professional and or establish public domain pro grams that performs such tasks well Furthermore it is difficult to support all plotting and terminal devices there are plently of excellent software packages on the market which already perform this duty Our aim is simply to provide a means of reading and writing data files in the formats utilized Scott Smith Copyright S A Smith May 22 1998 GAMMA Plotting 30 Users Manual Plotting Figures 4 2 by such programs A nice consequence of supporting multiple formats is that GAMMA may also be used to perform format conversions GAMMA T O Methodology Row Vector class row_vec Simulation Matrix class matrix Result s L Coordinate Vector class coord_vec Data To Be Plotted is Contained k In One Of These GAMMA Types NMRi Figure 19 2 Some of the programs with which GAMMA can easily interact We should mention that there are currently NO direct plots from GAMMA to the screen NOR direct output to any specialized printi
25. properties of any spin system and therefore available to GAMMA pro grams at any time Have a look at the following variation of the previous program I m gonna make it more sophisticated now that you know a bit of C and GAMMA include lt gamma h gt main spin_sys sys System sys sys read test sys System reads itself from file test sys cout lt lt sys Have a look at the system cout lt lt n2nd spin Iz lt lt sys qn 1 Here is Iz of the 2nd spin cout lt lt nIst spin is lt lt sys element 0 This is the Ist spin type cout lt lt nSystem Hilbert space is lt lt sys HSO This is the spin Hilbert space if sys homonuclear Tell us if it homo hetero nuclear cout lt lt nSystem is Homonuclear else cout lt lt nSystem is Heteronuclear The above code may seem cryptic to those used C and FORTRAN programs because it makes use of member functions Rather that making use of the function sin on the variable x via sin x the Scott Smith Copyright S A Smith May 22 1998 Classes 15 Basic Spin Systems 2 3 GAMMA Users Manual member function use of sine might be written x sin i e the function is attached to the data type by a single period In the above code the spin_sys member functions read qn element HS and homonuclear are used It ll take some getting used to but once you familiarize yourself with this synt
26. read the system from That can be done crudely by use of code such as Spin_sys sys String filename cout lt lt n n tWhich file cin gt gt filename Scott Smith Copyright S A Smith System sys A string for the filename Ask the user for a filename Get the filename from user May 22 1998 GAMMA Classes 16 Users Manual Basic Spin Systems 2 3 sys read filename System reads itself from file test sys substituted in the previous program UI use a more sophisticated approach because its something that is nice to use once you take the time to learn it Here s a rewrite of the previous program start include lt gamma h gt main int argc char argv Spin_sys sys System sys sys ask_read argc argv 1 Ask for and or Read system cout lt lt sys Have a look at the system ded Rest of the program here The key concepts here are 1 The change to the main program to take an integer and an array of strings and 2 Use of the member function ask_read to have the spin system ask the user which file it should read itself from The former is standard in C and C you don t need to understand it you can just always write you main program statement in such a manner What that does is provide the program with argc the number of arguments given on the command line when the program is run and argv the argu ments given on the command line The latter is just
27. treated by a 90 degree pulse along the y axis and propagated in time without relaxation effects while the FID is computed The detection operator necessary for determining the FID will be set to F_ for the entire spin system The is equivalent to a operator which samples by xy magnetization Use of F_as the detection operator in combination with a pulse along the y axis produces a properly phased spectrum In this simulation the FID does decay during the acquistion due to relaxation effects For our test spin system these effects will decay the FID to zero before the acquistion is complete However if relaxation is not strong enough depending upon the effects included cor relation times internuclear distances etc it may still be necessary to apodize prior to Fourier transformation The code is written to be clear and concise Although efficient it is not the most computationally efficient 1 The spin system size is not limited by GAMMA but is ultimately limited by the computer running the pro gram and its associated memory Tilo Levante Scott Smith May 22 1998 GAMMA NMR Simulations 65 NMR Examples One Pulse General 5 6 5 6 2 Program include lt gamma h gt main int argc char argv cout lt lt n n t t tGAMMA 1D NMR Simulation Programinin Read in Parameters String filename Name of spin system file query_parameter argc argv Get filename from command 1 n tSpin system filename
28. two step se quences and two program lines The first step makes use of the function Iypuls which takes 6p the equilibrium density matrix and applies a 90 pulse along the y axis to it The resulting density ma trix is set equal to sigma The next step ia analogous to the function FID used in previous simula tions of this chapter Here we are utilizing the acquire ACQ previously set The parameters indicate how the acquisition takes place filling the block data with the points as relaxation is in effect In order to explicitly see the decaying FID the next step writes the acquisition to the FrameMaker file One_pulse 3 FIDmif The data is then Fourier transformed and put out to a sec ond FrameMaker file called One_pulse 3 FFT mif 5 8 3 Results The two FrameMaker files from the simulation are reproduced below scaled and annotated Tilo Levante Scott Smith May 22 1998 GAMMA NMR Simulations 77 NMR Examples One Pulse Finite Length 5 8 1 FID Decaying 0 Under Dipolar Relaxation 1 0 l 2 Seconds 3 4 5 100 Fourier Transform of the Above FID 50 100 50 0 50 Hertz Tilo Levante Scott Smith May 22 1998 Users Guide Appendix r GAMMA GAMMA Users Guide Users Guide Dee d ee ee e ee E tee e ee Ehe e ee E ee ee e E A EI r GAMMA Users Guide GAMMA Users Guide A GAMMA Users Guide
29. 0 2 19F Spin Isotope Type Iso 1 2 1H Spin Isotope Type Iso 2 2 1H Spin Isotope Type Iso 3 2 1H Spin Isotope Type Iso 4 2 1H Spin Isotope Type Omega 1 300 00 1H Spectrometer Frequency MHz v 0 1 110 0 Chemical Shift Hz v 1 1 2175 0 Chemical Shift Hz v 2 1 2175 0 Chemical Shift Hz v 3 1 231350 Chemical Shift Hz v 4 1 2313 0 Chemical Shift Hz J 0 1 1 9 10 Coupling Constants in Hz J 0 2 1 9 10 Coupling Constants in Hz J 0 3 1 53 90 Coupling Constants in Hz J 0 4 1 5 50 Coupling Constants in Hz J 1 2 1 2 62 Coupling Constants in Hz J 1 3 1 8 60 Coupling Constants in Hz J 1 4 1 0 50 Coupling Constants in Hz J 2 3 1 0 50 Coupling Constants in Hz J 2 4 1 8 60 Coupling Constants in Hz J 3 4 1 2 50 Coupling Constants in Hz 5 5 4 Results The program was compiled with the command gamma One_pulse 3 cc o One_pulse 3 This takes the gamma library and links to the program One_pulse 3 cc during compilation The o option specifies the name of the final executable program in this instance called One_pulse 3 Had the o option not been used o One_pulse 3 left out the executable program is automatically given the name a out The compiled program can be executed with the command One_pulse 3 Since we have given the executable the name One_pulse 3 it is run by entering that name Below is the full computer interaction which took place to produce the flu
30. 0 1 3 0 19 0000110011000 0 A 9 OCOCR TTI OR LILO 002 Here is a simple example of how this is done include lt gamma h gt main matrix mx 3 4 complex0 Make a 3x4 array filled with zero for int i 0 i lt mx rows i Put 6 s in the first column mx put 6 1 0 for int j 0 j lt mx cols j Put i s in the first row mx put complexi 0 j mx put complex 2 3 1 2 Set lt 3lmxl4 gt to 2 31 Scott Smith Copyright S A Smith May 22 1998 GAMMA Plotting 45 Users Manual Plotting Figures 4 2 FM_Matrix FM mmf mx Output FrameMaker mmf file Here is the output from the program the contents of file FM mmf read by FrameMaker ase dez le 6 0 2 3 i 0 60 0 o 4 5 11 Matrix Plots While the previous function is great for putting matrices into your documents remember cout lt lt mx will print any array to the screen often the arrays in GAMMA programs are just too darn big to look at Every once in a while we just need a graphical representation of which elements are non zero rather than what the actual elements are For that purpose you can use the function PM Mat Plot For an example we ll just reuse the previous program but with the EM Mat Plot function instead of FM_Matrix include lt gamma h gt main matrix mx 3 4 complex0 Make a 3x4 array filled with zero for int i 0 i lt mx rows i Put 6 s in the first column mx put 6 i 0 for int j 0
31. 0000000000 000 0 0 1000 0 1 0 Fe 00000 100000 0 si nto e 0 0 0000 0 0 1 000000100000 000 0 0 0 01141 0 0 0 000000000000 000 0 0 0000140 0 000000000000 000 0 0 0000 1 141 0 000000000 100 000 0 0 0000 0 0 141 0000000000 10 000 0 0 0000 0 0 1 0000000000 0 2 00 0 0 0 0000 0 0 0 Note also that I cheated on the last line of the program and used GAMMA class gen_op the general quantum mechanical operator class We ll get back to that later I just wanted to show those who know the math how one can build up various Hamiltonians Of course there are functions in GAM MA for doing such things in 1 step but you can build up ANY spin Hamiltonians you like and manipulate them in whatever way you need To find out which spin operators are available by simple function calls see the GAMMA MR Li brary DOCUMENTATION You ll find that all commonly used spin operators are there including spin rotation operators Users can build up any such operators if there is no function to do so To see how GAMMA spin operators are constructed and their functionality see the GAMMA CLASS DOCUMENTATION 2 5 Isotropic Spin Systems The last two sections have shown how basic spin systems variables of class spin_sys are defined and in turn are used to produce spin operators in a completely generalized manner Spin systems are containers of information about the spin isotopes in a sample The system provides that in Scott Smith Copyright S A Smith May 22 1998
32. 1 i loop through and fill up the matrix for int j 0 j lt 101 j mx i j vx 1 vx j FM_stack stack mif mx 0 02 0 02 1 output the FrameMaker mif plot file The output file stack mif can be read into FrameMaker and below are some of the manipulations that can be subsequently performed Scott Smith Copyright S A Smith May 22 1998 GAMMA Plotting 41 Users Manual Plotting Figures 4 2 Original Plot Specific Line Highlighted AR a ae v v Positive in plane amp negative Specific Line Isolated Rescaled Original Plot Hidden Lines now Visible Rotated Scott Smith Copyright S A Smith May 22 1998 GAMMA Plotting 42 Users Manual Plotting Figures 4 2 4 5 8 3D Sphere Plots Three dimensional sphere plots are produced for FrameMaker with the function FM_sphere This is real handy for making 3 dimensional plots of trajectories for example Unlike other FM functions this function takes a vector of coordinates class coord_vec which are assumed to be in Cartesian space There function allows the user to orient the sphere and to plot either with vectors from the origin to the points with a line connecting points or just with the points plotted individually As with all other FM function the user can fully manipulate the plot within FrameMaker after it is output by GAMMA Here is a simple example program include lt gamma h gt main coord_vec data1 500 Dec
33. FID Spectrum gen_op sigma sigma_eq sys Set density matrix equilibrim gen_op H Hcs sys HJ sys Set the Hamiltonian gen_op detect Fm sys Set detection operator to F Pulse Sequence Data Workup sigma Iypuls sys sigma 90 Apply a PI 2 y pulse FID sigma detect H dt t2pts data Calculate the FID after the pulse NMRIi One_pulse 2 dat data Write data in NMRi format exponential_multiply data 8 Apodize the FID data FFT data Fourier transform the FID FM_1D One_pulse 2 mif Write spectrum to FrameMaker file data 14 5 0 5 dt 0 5 dt with frames of the size 5 14 cm 5 4 2 Discussion Read in Parameters Note that in the program start main there are now two arguments argc and argv This is a means by which programs in C and C can take parameters supplied directly from the command line at run time Three parameters are asked for using GAMMA s function query_parameter the spin system filename the dwell time and the number of points in the ac quisition When the program is run values for these can be given directly or if not given the program will automatically ask for them If the values are given the program will not ask for them The spin system is then read in from the file Set Variables The first line here creates a data block of the proper size The density matrix is declared and set to equilibrium Another general operator H is specified and initialized t
34. GAMMA Users Guide f Author Dr Scott A Smith Tilo Levante Date May 22 1998 Nun Users Guide Chapters rte e e EE 5 Ci o od 10 Nasn tic Respaldo Library sucias 25 Proti ii ee ee eg 28 NMR Simao iS 48 GAMMA Table of Contents ii Users Guide Users Guide Table of Contents e EE 1 1 Basics of C e 5 1 1 1 Basic C Program Hello Cruel World ooooconnnccnocccoccconanonanononcnononannnonn corn ncnnns 5 1 1 2 Basic C Program Comments Spacing Executable Name 6 1 1 3 Basic C Program Includes Subroutines Running Interactive oo 7 e WEE EES 208 2 1 Double Precision Numbers eseeggeeutesgeere Eege geg 10 2 1 1 Basic C Program Using Doubles rusia ie 10 2 2 Matrices and VECTO S iria 12 2 2 1 Basic GAMMA Program Using Matrices amp Vectors ooooccoccconccnocnnonncconcnnnnos 12 2 3 Basico Spin Systems ta 13 2 3 1 GAMMA Base Spin System Primitive Construction Standard Output 13 2 3 2 GAMMA Base Spin System Member Functions Info Access File Input 14 2 3 3 GAMMA Base Spin System Interactive ooooonccnoncconncconnconcnonnncnnnccnnnnnna conan 15 2 4 Spin Operators reia 17 2 4 1 GAMMA Spin Operators Construction Functions Output oo eee 17 2 5 Isotropic Spin Systems taa 18 2 5 1 GAMMA Isotropic Spin System Interactive NMR Hamiltonian 20 2 9 2 GAMMA Isotropic Spin System Access Functions ooccccoccccconcninonccinnnccnonnnos 22 2 6 General e 23 2 6 1 GAMMA Operators Hamiltoni
35. Mathematica MAPLE etc However GAMMA programs are C programs and that implies that 1 You have a full computer language at your disposal with all its flexibility and added librar ies 2 You will have to gain some rudimentary knowledge of programming in C There is a learning curve associated with GAMMA but we hope you will find that small relative to what you will gain in ability 1 1 1 Basic C Program Hello Cruel World We begin by writing a GAMMA actually a C program A simple program would be the fol lowing include lt gamma h gt main cout lt lt n tHello World n The first line is a compiler directive to include the GAMMA platform You can have several lines such as this to include more libraries as desired In this program GAMMA isn t providing anything so the line could be left out 1 The author was a steadfast FORTRAN user until the GAMMA project began Some can argue that he still doesn t know how to program in C and barely manages in C but he now avoids FORTRAN unless its shoved in his face Given that a slow learner such as him can manage in C you should be able to as well Scott Smith Copyright S A Smith May 22 1998 GAMMA Introduction Users Manual Basics of C Programs 1 1 The next line declares that the main part of the program is following enclosed by the brackets OA These brackets must both be present and any code associated with main must reside
36. Number of acquisition points 2048 Strong or Weak Coupling s w s Which Isotope Type 19F Please Choose an Output Format 1 FrameMaker 2 Felix 3 NMRi 4 MatLab Output Type 2 Output File Name Please Include any Extension Felix 1D Files Normally Use a dat Extension Remember Felix reads only lower case names pfphe dat Parameters Needed for Felix Data Workup To set OMEGA sf 282 282 Tilo Levante Scott Smith May 22 1998 GAMMA NMR Simulations 71 NMR Examples One Pulse General 5 6 To set spectral width sw 32 12 To set offset no zf ref 1024 110 To set axis in Hertz ax 2 Icosy gt Alternatively this program will accept input directly on the command line Below is the full com puter interaction which took place to produce the protom spectrum now the information is input directly Again user response typed in from the keyboard and followed by a return is printed in bold face italics lcosy gt One_pulse 3 pfPHE sys 2048 s GAMMA 1D NMR Simulation Program Which Isotope Type IH Please Choose an Output Format 1 FrameMaker 2 Felix 3 NMRi 4 MatLab Output Type 2 Output File Name Please Include any Extension Felix 1D Files Normally Use a dat Extension Remember Felix reads only lower case names hpfphe dat Parameters Needed for Felix Data Workup To set OMEGA sf 300 To set spectral width sw 274 12 To set offset no zf ref 1024 2244 To set axis in Hertz ax 2 Icosy gt These two runs produce
37. Please Include any Extension Tilo Levante Scott Smith May 22 1998 GAMMA NMR Simulations 62 NMR Examples One Ideal Pulse Homonuclear Spin System 5 5 Felix 1D Files Normally Use a dat Extension Remember Felix reads only lower case names hpfphe dat Parameters Needed for Felix Data Workup To set OMEGA sf 300 To set spectral width sw 274 12 To set offset no zf ref 1024 2244 To set axis in Hertz ax 2 Icosy gt These two runs produced the Felix files pfphe dat and hpfphe dat respectively These are shown on the following page using the felix commands given below Fluorine Spectrum Proton Spectrum re pfphe dat re hpfphe dat sf 282 282 sf 300 sw 32 12 sw 274 12 ref 1024 110 ref 1024 2244 ax 2 ax 2 Ib 0 1 Ib 0 1 em em ft ft dr dr hdv pfphe hpgl hdv hpfphe hpgl hpm 32 hpm 32 hcp hcp The last three commands in both workups create hpgl plot output files These were then converted into FrameMaker MIF files and incorporated into this document in FrameMaker 1 A conversion program of this type is supplied with the program FrameMaker For those who use FrameMaker but do not have the conversion program there is a currently crude GAMMA program which does the job called hp2mif cc included with the example files here Tilo Levante Scott Smith May 22 1998 GAMMA NMR Simulations 63 NMR Examples One Ideal Pulse Homonuclear Spin System 5 5 Ir Spectrum
38. _op H if J w H Hcs sys HJw sys Set the weak coupling Hamiltonian else H Hcs sys HJwh sys Set the strong coupling Hamiltonian gen_op detect Fm sys Isotype Set detection operator to F Pulse Sequence sigma lypuls sys sigma Isotype 90 Apply an PI 2 y pulse FID sigma detect H dt t2pts data Calculate the FID after the pulse Spectral Output Format amp File Selection int type 0 Select an output format while type lt 0 Il type gt 4 cout lt lt n tPlease Choose an Output Format cout lt lt n n t t1 FrameMaker cout lt lt n t t2 Felix cout lt lt n t t3 NMRI cout lt lt n t t4 MatLab cout lt lt n n tOutput Type Tilo Levante Scott Smith May 22 1998 GAMMA NMR Simulations 67 NMR Examples One Pulse General 5 6 cin gt gt type cout lt lt An cout lt lt n tOutput File Name Please Include any Extension if type 2 cout lt lt n tFelix 1D Files Normally Use a dat Extension cout lt lt n t Remember Felix reads only lower case names cin gt gt filename Spectral Output cout lt lt mn switch type case FrameMaker output default double If rt double inPPM 2 If offset sw 2 0 Set plot limits in Hertz rt offset sw 2 0 while inPPM lt 0 Il inPPM gt 1 Querie for Hertz or PPM axis cout lt lt
39. allowed Tilo Levante Scott Smith May 22 1998 GAMMA NMR Simulations 69 NMR Examples One Pulse General 5 6 Spectral Output In this section the simulated FID is written to an output file For FrameMaker output the FID is apodized and Fourier Transformed before output since that program has not FFT capabilities Because Felix currently has problems accepting data into its parameter block the pa rameters needed to reference the spectrum are output if this format is specified For MATLAB out put there may be several matrices stored in each MAT file These each have an internal MATLAB data name which is set to spectrum here 5 6 4 Data 5 Spin System This program is general and may take any spin system For demonstation we here use the input spin system file One_pulse 3 sys which contains a p fluorophenyl spin system This is a hetero nuclear system containing 5 spin 1 2 species SysName 2 p_fluoro_PHE Name of the Spin System NSpins 0 5 Number of Spins in the System Iso 0 2 19F Spin Isotope Type Iso 2 1H Spin Isotope Type Iso 2 2 1H Spin Isotope Type Iso 3 2 1H Spin Isotope Type Iso 4 2 1H Spin Isotope Type Omega 1 300 00 1H Spectrometer Frequency MHz v 0 1 110 0 Chemical Shift Hz vd 1 2175 0 Chemical Shift Hz vQ 1 2175 0 Chemical Shift Hz v 3 1 2313 0 Chemical Shift Hz v 4 1 2313 0 Chemical Shift Hz J 0 1 1 9 10 Coup
40. amming before using GAMMA for anything in teresting A few key points to remember 1 On Intel based PC s running Windows the executable file is a exe rather than a out Scott Smith Copyright S A Smith May 22 1998 GAMMA Introduction Users Manual Basics of C Programs 1 1 1 Blank spaces are ignored it doesn t matter if there is 1 or 20 or none Thus there is no col umn alignment of code code may span multiple lines i e multiple lines before a or on a single line 66 9499 S there may be multiple 2 Comments in C may be either in the typical C fashion i e anything between and is taken as a comment or by use of a anything past on that line is a comment 3 The output executable can be named anything you like by using o outfile during compi lation of your program Now we can start by writing a GAMMA actually a C program A simple program would be the following include lt gamma h gt Include the GAMMA library Iddee Here s the same program again O main cout lt lt n tHello World n j A Output the message Assuming that this file is named hellol cc we shall compile and name the output executable again noesy gt gamma hellol cc o again GAMMA Other Messages noesy gt To run the program noesy gt again Hello World noesy gt 1 1 3 Basic C Program Includes Subroutines Running Interactive Three more basic areas
41. ans Propagators Density Operators 23 3 Magnetic Resoance Library oooncnnncnnnnnonnnnnnnnnononooooooooo 29 3 1 Hamiltonians E 25 3 2 Ideal A A 26 4 Plotting SOCHSHSSHSHSSSHSHSHSHSHSHSHSHSHSHSHSSHSHSHSHSHSSHSSHSHSSSHSHSHSSSHSHSSHSHSHSSHSSHSSSHSSESSSHSSSSSsSeeseeeeseeee 28 4 1 Plotting EEN 28 May 22 1998 GAMMA Table of Contents 111 Users Guide 4 2 Plotting Figures naaa 28 4 3 O e E E T 29 4 4 E 31 4 4 1 Sek e 31 4 4 2 TD PIOUS mad 31 4 5 ME E 33 4 5 1 DEEN egener eegene 33 4 5 2 ID PIOUS EE 33 4 5 3 Multiple 1D Ee cs 35 4 5 4 o eege 36 4 5 5 Scatter PIOUS sl id 37 4 5 6 O 38 4 5 7 2D Stack PIOUS ras 40 4 5 8 SLMS ele 42 4 5 9 Histograms 2951 43 4 5 10 Matix Cute eet 44 4 5 11 A OE A RS E RS 45 4 6 A LE Uno o leases async 47 4 6 1 IR et e EEN 47 e NME SUR CONS EE eo 5 1 5 2 5 3 5 4 5 4 1 5 4 2 5 4 3 5 4 4 5 4 5 5 4 6 5 5 5 5 1 5 5 2 5 5 3 5 5 4 5 6 5 6 1 5 6 2 NMR Simulation Sections E 48 NMR Simulation Figures cat 48 Single Pulse Acquisition Simulations ooconnoooccnonooccnononncnnnonancnonanancnnnn 48 Ideal 90 Pulse 4 8 N Homonuclear Spin Systems ceeeeeees 50 Programo A O A 50 LEE E 51 Example Data 4 Spin System 52 Re s lts 4 Spin System deenen 52 Example Data 8 Spin System seenen eegen ei 53 Results Spin System serrera aier E AE A ES 54 One Ideal Pulse Homonuclear Spin System coooocccnnnncccnnnoocncnnonannnnnnns 54 a A E EEA E
42. ax you ll start to like it However there may be both member and non member functions de fined for a particular data type but that is simple you just need to look up the function and its usage Pay particular attention to the fact that this program DOES NOT contain any information about the spin system it is system independent although I do ask for information on the Ist two spins so the program would give an error if the system doesn t have at least two spins When the program is run it will look for a file test sys that contains information that defines the system Here is an example of such a file This is a Example of A File Containing A Basic GAMMA Spin System SysName 2 CDV NSpins 0 3 Name of the Spin System Number of Spins in the System Iso 0 2 13C Spin Isotope Type Iso 1 2 2H Spin Isotope Type Iso 2 2 51V Spin Isotope Type If I compile the program and the above system information is in a file test sys here will be the program output System CDV Spin 0 1 2 Isotope 13C 2H 51V Momentum 1 2 1 7 2 2nd spin Iz 1 Ist spin is C System Hilbert space is 48 If you use a different test sys file you will of course get different results 2 3 3 GAMMA Base Spin System Interactive Suppose now that you like the above program very much but rather than having it always read the file test sys to get the spin system you would like it to ask you for which file to
43. be tween them The only line of code is just to write Hello World to standard output A few things to note 1 Standard output your screen by default is called cout 1113 2 The operator lt lt is one that the object itself the stuff enclosed in about a String knows all 3 The special combinations n and t are a page break and tab respectively when in a String 4 Every code line must end with a semicolon except things enclosed in Now we must convert this program code into an executable That is done by using the gamma script which invokes the C compiler links any C libraries and links to the GAMMA platform We sill use noesy gt to be the prompt that the computer we are working on uses and we will assume the program is called hello cc note that the cc is often mandatory when using the C compiler Here we go noesy gt gamma hello cc GAMMA Other Messages noesy gt Your actual response may vary depending on your GAMMA version and your computer type The command gamma acting on hello cc or any C program will produce an executable that has a default name called a out To run the program noesy gt a out Hello World noesy gt That s it if this worked you have completed compilation of your first C program and compila tion your GAMMA programs will be very similar 1 1 2 Basic C Program Comments Spacing Executable Name We ll will cover a few of the basics of C progr
44. d the Felix files pfphe dat and hpfphe dat respectively These are shown Tilo Levante Scott Smith May 22 1998 GAMMA NMR Examples NMR Simulations One Pulse General 72 5 6 on the following page using the felix commands given below Fluorine Spectrum re pfphe dat sf 282 282 sw 32 12 ref 1024 110 ax 2 Ib 0 1 em ft dr hdv pfphe hpgl hpm 32 hcp Proton Spectrum re hpfphe dat sf 300 sw 274 12 ref 1024 2244 ax 2 Ib 0 1 em ft dr hdv hpfphe hpgl hpm 32 hcp The last three commands in both workups create hpgl plot output files These were then converted into FrameMaker MIF files and incorporated into this document in FrameMaker 1 A conversion program of this type is supplied with the program FrameMaker For those who use FrameMaker but do not have the conversion program there is a currently crude GAMMA program which does the job called hp2mif cc included with the example files here Tilo Levante Scott Smith May 22 1998 GAMMA NMR Simulations 73 NMR Examples One Pulse General 5 6 Ir Spectrum 124 120 136 LS 108 104 100 96 Hz IH Spectrum A M 2360 2320 2280 2210 2200 7160 2120 Hz Tilo Levante Scott Smith May 22 1998 GAMMA NMR Simulations 74 NMR Examples One RF Pulse 5 7 5 7 One RF Pulse This example is another implementation of the one pulse experiment simulation on a two spin sys tem The pulse sequence is shown below with density matrices labeled
45. data in real asc during pro gram execution It first makes an ASCII gnuplot load file called real gnu then runs gnuplot us ing the commands in the load file The following figure is roughly the plot that appears on the screen when you run the program What I ve done here is re run gnuplot after program completion plotted the real asc file then output the plot into this document using Gnuplots MIF output 500 1000 1500 2000 2500 3000 3500 4000 4500 There are a couple of very nice Gnuplot features worth mentioning First and foremost is that it is a program in public domain Not only does the user not have to pay for it one has access to the entire source code and it runs on almost all common computer architectures Second Gnuplot has many different output formats That means that you can get your figures in PostScript MIF as was done here for FrameMaker LaTex PBM even GIF Scott Smith Copyright S A Smith May 22 1998 GAMMA Plotting 33 Users Manual Plotting Figures 4 2 4 5 FrameMaker 4 5 1 Description page 33 4 5 2 1D Plots page 33 4 5 4 xy Plane Plots page 36 4 5 5 Scatter Plots page 37 4 5 6 2D Contour Plots page 38 4 5 7 2D Stack Plots page 40 4 5 8 3D Sphere Plots page 42 4 5 9 Histograms page 43 4 5 10 Matrix Output page 44 4 5 11 Matrix Plots page 45 4 5 1 Description GAMMA provides functions for generation of figures suitable for direct use in FrameMaker see http www fra
46. e provided window sin squared function for int 1 0 1 lt 101 i loop through and fill up the matrix for int j 0 j lt 101 j mx i j BLK1 BLK2 j FM_contour contour mif mx 05 10 05 create file FM contour file contour mif You can just use the computer to remove your T1 noise now Read your spectrum F1xF2 into a GAMMA matrix output the contour plot into FrameMaker Edit As You Wish removing artifacts you don t want anyone to see no more white out Print to A Tranparency Too Easy Scott Smith Copyright S A Smith May 22 1998 GAMMA Plotting 40 Users Manual Plotting Figures 4 2 4 5 7 2D Stack Plots Two dimensional stack plots are produced for FrameMaker with the function FM_stack The func tion is called with a GAMMA matrix as an input argument The function automatically used a hidden line algorithm which can be removed in FrameMaker and the user may set the skew Each plotted row is an individual graphic object which can be ma nipulated For example a particular slice in the plot below was selectively shaded The overall plot height and width can be altered as well within FrameMaker Here is a simple program the one that produced the plot above include lt gamma h gt main matrix mx 101 101 create a 101x101 matrix for data block_1D vx 100 create a 1D data block of length 101 vx sinc 101 50 10 use provided window sinc function for int 1 0 i lt 10
47. ector vx 360 create a data block double x y theta declare needed variables for int 1 0 i lt 360 i loop through 360 degrees fill up block with Astroid theta 1 2 0 PI 360 0 also called a Hypercycloid of four cusps x cos theta x a cos theta 3 here a 1 y sin theta y a sin theta 3 here a 1 Scott Smith Copyright S A Smith May 22 1998 GAMMA Plotting 37 Users Manual Plotting Figures 4 2 X x x x SY TY vx put complex x y 1 FM_xyPlot astroid mif BLK output FrameMaker mif plot file When compiled and run it will produce a file called astroid mif When that file is subsequently read by FrameMaker the following plot on the left will appear The one on the right is just a copy that ve jerked with within FrameMaker 0 5 4 5 5 Scatter Plots Scatter plots can be generated for FrameMaker with the function FM_scatter These are similar to plots produced with the function FM_xyPlot except that the plots are not connected and can be in dividually plotted with symbols or characters I forget why I even wrote this function now Perhaps I used it to have my point plotted on top of a theoretical curve by blending a graphic like the one above with another one with a continuous line Here s the code for the one above Scott Smith Copyright S A Smith May 22 1998 GAMMA Plotting 38 Users Manual Plotting Figures 4 2 include lt gamma h gt main
48. em 3 1 1 Isotropic NMR First well make some isotropic ones good for liquid NMR simulations Remember the key here is to use a spin_system a spin system that internally knows about isotropic shifts isotropic scalar couplings isotope types gyromagnetic ratios include lt gamma h gt main spin_system sys Here is a spin system empty though sys read ABMX sys Set the system from ASCII file ABMX sys gen op H Ho sys Our friend the isotropic NMR Ham gen_op H_S Hcs sys Just the shift part of Ho Scott Smith Copyright S A Smith May 22 1998 GAMMA Magnetic Resoance Library 26 Users Manual Ideal Pulses 3 2 gen_op H_SL Hcs_lab sys Shift in the lab frame big s here gen_op H_J HJ sys Isotropic scalar coupling STRONG gen_op H_JW HJw sys Isotrpic scalar coupling WEAK gen_op H_JWH HJwh sys Isotropic scalar coupling Weak Hetero gen_op H1 H_S H_JWH Same as H above gen op HZ Hz sys Zeeman Hamiltonian big s if in a field gen op HZI Hz sys 2H Zeeman Hamiltonian for any deuteriums gen op HQ HQsec sys 2 e6 0 Quad Ham wQ 2 MHz 1st spin We could go on but I think you might be a bored as I am Have a look in the GAMMA MR Library Documentation for all the Hamiltonian functions The really important part of all of this is only that you have simple likes of code to get some need Hamiltonians Even better you
49. er deal with Hamiltonians and operators operators being the return data type from function Ho that is why the output talks about a basis Scott Smith Copyright S A Smith May 22 1998 GAMMA Classes 22 Users Manual Isotropic Spin Systems 2 5 2 5 2 GAMMA Isotropic Spin System Access Functions Now you know about isotropic systems how they do everything base spin systems do and how readily they may be used in GAMMA programs Now think how you might run a program that loops through a set of similar spin systems perhaps fitting some results to spin system parameters or watching the effects of strong coupling a two spins shifts mover closer together To do that you Il need full access to the spin system information i e be able to set chemical shifts coupling constants isotope types etc within your GAMMA programs Not a problem The next program illustrates a couple of these abilities include lt gamma h gt main int argc char argv spin_system sys 4 A system of 4spins all 1H cout lt lt sys Lets have a look at it sys 1sotope 2 31P Set the 3rd spin to phosphorous sys Omega 900 0 Set field for 900 MHz proton yeah sys PPM 7 2 0 Set Ist spin shift to 7 2 PPM sys J O 1 11 0 Set J12 to be 11 Hz cout lt lt sys Lets have another look Here s the output from this little ditty a out sosi sys Spin 0 1 2 3 Isotope 1H 1H 1H 1H Momentum 1 2 1 2 1 2 1 2 Sh
50. er is then allowed to specify weak or strong coupling Determine the Isotope Detected A check is made to see if the input spin system is homo nuclear or heteronuclear If heteronuclear the user must choose the isotope type to be detected Set Up Spectral Parameters Here all chemical shifts for spins of the isotope type being detected may be altered so as to be referenced to an optimal rotating frame Following this a Nyquist frequency is chosen and both the dwell time and spectral width set Set Variables A 1D data block is declared to hold the simulated FID A general operator is declared and set to the equilibrium density matrix Another general operator is declared and set to be either the strong or weak coupling isotropic Hamiltonian Finally a general operator is declared and set to hold the detection operator Pulse Sequence The pulse sequence is very short a two step sequence is performed with two program lines The first step makes use of the function Iypuls which takes 69 the equilibrium den sity matrix and applies a 90 pulse along the y axis to it The resulting density matrix is set equal to sigma The next function FID propagates sigma with the Hamiltonian H while filling up the data block The detector the number of points and the dwell time are also parameters used as ar guments for this function Spectral Output Format amp File Selection The user is prompted to specify an output type Currently four formats are
51. fects of dipole dipole relaxation while the FID is computed The detection operator necessary for determining the FID will be set to F_ for the entire spin system The is equivalent to a operator which samples xy magnetization F_ in combination with a pulse along the y axis produces a properly phased spectrum In this simulation the FID does decay somewhat as shown in the pulse sequence diagram on its own via relaxation processes Thus no apodization is utilized during the spectral workup 5 8 1 Program include lt gamma h gt main spin_system sys sys read One_pulse 3 sys double t2dt 0 005 int t2pts 1024 gen op sigma0 sigma_eq sys gen op H Hcs sys HJ sys gen_op detect Fm sys block_1D data t2pts super_op R RDDExtNrw sys H gen_op sigma acquire ACQ detect H t2dt sigma Iypuls sys sigma0 90 ACQ sigma sigma0 R data FM_1D One_pulse 3 FIDmif data 14 5 0 t2pts 1 t2dt data FFT data double lim 1 0 2 0 t2dt Tilo Levante Scott Smith SET PARAMETERS Set up a spin system Read system in from disk Dwell time 100 Hz Number of increments DECLARE NEEDED VARIABLES set equilibrium density matrix sys set Hamiltonian to shift J set the detection operator to F storage for the FID Spectrum dipolar relaxation superoperator working density matrix set up an acquisiton PULSE
52. gnuplot is started and the appropriate com mands issued to read the file created by the GAMMA program 442 1D Plots The simplest type of plot is a 1D plot created from a data vector with the function GP_1D With this function the horizontal axis is the point index of vector and the vertical axis contains the data value This program demonstrates how to have a 1D plot sent interactively to the screen using gnuplot Note that in order for it to work the system command gnuplot must be known to the user running the program include lt gamma h gt Include GAMMA itself main int N 4096 We ll plot this many points row_vector data N Here s a vector of points double rval ival More temporaries for int 1 0 i lt N i Now we ll fill up the vector putting a cosine into the rval cos 33 33 double 1 double N 1 real part data put rval 1 GP_1D real asc data 0 Write real points to ASCII file GP_1Dplot real gnu real asc This will plot points in real asc cout lt lt nin Keep the screen nice The call to the function GP_1D produces an ASCII file called real asc that is usable by the Gn Scott Smith Copyright S A Smith May 22 1998 GAMMA Plotting 32 Users Manual Plotting Figures 4 2 uplot program It will contain the cosine function which was put into the row_vector data The call to the function GP_1Dplot will make a plot on the screen of the
53. he Spin System NSpins 0 4 Number of Spins in the System Iso 0 2 1H Spin Isotope Type Iso 1 2 1H Spin Isotope Type Iso 2 2 1H Spin Isotope Type Iso 3 2 1H Spin Isotope Type v 0 1 200 0 Chemical Shifts in Hz v 1 1 40 0 Chemical Shifts in Hz v 2 1 10 0 Chemical Shifts in Hz v 3 1 200 0 Chemical Shifts in Hz 0 1 1 5 0 Coupling Constants in Hz J 0 2 1 0 0 Coupling Constants in Hz J 0 3 1 0 0 Coupling Constants in Hz J 1 2 1 10 0 Coupling Constants in Hz J 1 3 1 0 0 Coupling Constants in Hz J 2 3 1 8 0 Coupling Constants in Hz Omega 1 400 Spectrometer Frequency in MHz 1H based 5 4 4 Results 4 Spin System The program was compiled with the command gamma One_pulse 2 cc o One_pulse 2 This takes the gamma library and links to the program One_pulse 2 cc during compilation The o option specifies the name of the final executable program in this instance called One_pulse 2 Had the o option not been used o One_pulse 2 left out the executable program is automatically Tilo Levante Scott Smith May 22 1998 GAMMA NMR Simulations 53 NMR Examples Ideal 90 Pulse 4 8 N Homonuclear Spin Systems 5 4 given the name a out The compiled program was called with One_pulse 2 One_pulse 2 sys 0 002 1024 Since we have given the executable the name One_pulse 2 it is run by entering that name The pro gram having been given all
54. if vx bins output FrameMaker mif plot file I colored some of the boxes in FrameMaker after reading the file FM mif into that program Per haps one of the nicer uses of this function is to make cool plots of your pulse shape functions Once again we see the typical scheme for getting plotted output from GAMMA We do something to fill some array in this case a row vector with some simulated data we wish to plot Then one or more of the plot functions is called with the array as one of the arguments 4 5 10 Matrix Output Matrices can be output for FrameMaker equations with the function FM_matrix For example the following double commutation superoperators given below were incorporated directly from GAM MA into this document D D D D T3 KD T3 vi 1 IT kD T3 AD 1 2000011001100000 2000011001100000 0 3 10000 1000 10000 0 1 10000 1000 10 00 0 0 130000 1000 100 00 0 1 10000 1000 10 00 0 000 40000000000 0 0 0000000000000000 0000 1000 1100 00 11 10 0000 3000 1000 0 1 1 0 10000 2 100 100000 1 10000 2 100 100 0 HI EE E E EE EE EE ENER 1 10000 12000 10000 1 1 0 1 100003000 10000 1 0 1 10000 1000 10000 166 0 OY 4 OO 0 10 O 00 1 10 16 0 000 1000 30000 1 10 10000 1000 2 10000 1 10000 1000 2 10 0001 100000 100 1 20000 1 10000 0 100 1200001 0 1 10000 100 0 300 0 0 0 1 10000 1000 10 00 0 0 00 000006 00 000 0 0 00000000000 0 40 0 0 0000 1000 10000 1 10 0000 1000 100 0 0 3 10 0000 1000 10000 1 1 0 0000 1000 10 0 0
55. ifts 0 00 0 00 0 00 0 00 J Values Hz Spin 0 0 00 0 00 0 00 Spin 1 0 00 0 00 Spin 2 0 00 Spin 0 1 2 3 Isotope 1H 1H 31P 1H Momentum 1 2 1 2 1 2 1 2 Shifts 648K 0 00 0 00 0 00 PPM 720 0 00 0 00 0 00 Scott Smith Copyright S A Smith May 22 1998 GAMMA Classes 23 Users Manual General Operators 2 6 J Values Hz Spin 0 11 00 0 00 0 00 Spin 1 0 00 0 00 Spin 2 0 00 Omega 900 00M 900 00 M 364 33 M 900 00 M Ho hum Lets move on vou get your fill of spin systems as you go through this document See the GAMMA CLASS DOCUMENTATION for all of the spin_system functions and what param eters are important in external ASCII files that may be used to define them 2 6 General Operators Often magnetic resonance problems are described in terms of operators whether spin operators as we have already seen product operators single transition operators even Hamiltonian opera tors To handle generalized quantum mechanical operators GAMMA contains class gen_op In the same way that GAMMA contains a battery of function to construct common spin operators GAM MA contains a variety of functions that construct common general operators An example of that was the function Ho that was used in an earlier program 2 6 1 GAMMA Operators Hamiltonians Propagators Density Operators To demonstrate the use of GAMMA operators we ll approach a simple equation often encountered in NMR the evolution of the spin syste
56. isotope to be detected and output format at will all be specified by the user interactively Following this the spin system shifts will be offset to the center of the spectrum so the simulation occurs in an optimal rotating frame All spectral parameters such as the spectral width and dwell time will be determined automatically The equilibrium density matrix Oy can be generated directly from the specified spin system This density matrix is then treated by a 90 degree pulse along the y axis and propagated in time without relaxation effects while the FID is computed The detection operator necessary for determining the FID will be set to F_ for the entire spin system The is equivalent to a operator which samples by xy magnetization Use of F_as the detection operator in combination with a pulse along the y axis produces a properly phased spectrum Again we must mention that the FID does not decay as shown in the pulse sequence diagram For that relaxation effects must be included or the FID apodized Since we here ignore relaxation ef fects it is assumed the user will apply some apodization in the spectral workup prior to Fourier transformation done automatically for FrameMaker output Also the code is written to be clear and concise Although efficient it is not the most computationally efficient 5 5 1 Program include lt gamma h gt main int argc char argv cout lt lt n n t t tGAMMA 1D NMR Simulation Programinin
57. l time quadrature detection Total Spectal width Nyquist Set Variables Tilo Levante Scott Smith May 22 1998 GAMMA NMR Simulations 57 NMR Examples One Ideal Pulse Homonuclear Spin System 5 5 block_1D data t2pts Storage for the FID Spectrum gen_op sigma sigma_eq sys Set density matrix equilibrium gen_op H if J wi H Hcs sys HJ w sys Set the weak coupling Hamiltonian else H Hcs sys HJwh sys Set the strong coupling Hamiltonian gen_op detect Fm sys Isotype Set detection operator to F Pulse Sequence sigma lypuls sys sigma Isotype 90 Apply an PI 2 y pulse FID sigma detect H dt t2pts data Calculate the FID after the pulse Spectral Output Format amp File Selection int type 0 Select an output format while type lt 0 Il type gt Au cout lt lt n tPlease Choose an Output Format cout lt lt n n t t1 FrameMaker cout lt lt n t t2 Felix cout lt lt n t t3 NMRi cout lt lt n t t4 MatLab cout lt lt n n tOutput Type cin gt gt type cout lt lt An cout lt lt n tOutput File Name Please Include any Extension if type 2 cout lt lt n tFelix 1D Files Normally Use a dat Extension cout lt lt n t Remember Felix reads only lower case names cin gt gt filename Spectral Output cout lt lt An switch type
58. lare a 500 point coordinate vector coord_vec data2 500 A second coordinate vector double xx yy ZZ Declare needed variables double theta Declare an angle variable for int i 0 1 lt 500 i Fill datal with a spiral theta 1 6 0 PI 499 0 xx 3 0 cos theta yy 3 0 sin theta ZZ 3 0 6 1 499 datal put xx yy ZZ 1 data2 datal rotate 90 90 0 Set 2nd coordinate vector to rotated datal Scott Smith Copyright S A Smith May 22 1998 GAMMA Plotting 43 Users Manual Plotting Figures 4 2 FM_sphere FM_sph2a mif datal 0 Output FrameMaker file FM_sph2a mif FM_sphere FM_sph2b mif data2 1 Output FrameMaker file FM_sph2b mif The program will produce two plot files FM_sph2a mif and FM_sp h2b mif which are shown be low I marked the points in red within FrameMaker after the fact 4 5 9 Histograms Histogram plots can be generated for FrameMaker with the function FM_histogram 0 8 0 6 0 4 0 2 0 10 20 30 40 50 Here is a little program that illustrates how to make FrameMaker histograms in a GAMMA pro gram include lt gamma h gt main row_vector vx 51 create a data block row_vector vx1 Gaussian 51 25 3 fill up data with Gaussian Scott Smith Copyright S A Smith May 22 1998 GAMMA Plotting 44 Users Manual Plotting Figures 4 2 for int i 0 1 lt 51 i vx i complex i Re vx1 1 FM_histogram FM m
59. ling Constants in Hz J 0 2 1 9 10 Coupling Constants in Hz J 0 3 1 5 50 Coupling Constants in Hz J 0 4 1 5 50 Coupling Constants in Hz J 1 2 G1 22 62 Coupling Constants in Hz J 1 3 1 8 60 Coupling Constants in Hz 1 4 1 0 50 Coupling Constants in Hz J 2 3 1 0 50 Coupling Constants in Hz J 2 4 1 8 60 Coupling Constants in Hz J 3 4 1 2 50 Coupling Constants in Hz Tilo Levante Scott Smith May 22 1998 GAMMA NMR Simulations 70 NMR Examples One Pulse General 5 6 5 6 5 Results The program was compiled with the command gamma One_pulse 3 cc o One_pulse 3 This takes the gamma library and links to the program One_pulse 3 cc during compilation The o option specifies the name of the final executable program in this instance called One_pulse 3 Had the o option not been used o One_pulse 3 left out the executable program is automatically given the name a out The compiled program can be executed with the command One_pulse 3 Since we have given the executable the name One_pulse 3 it is run by entering that name Below is the full computer interaction which took place to produce the fluorine spectrum The prompt Icosy gt is just the computer prompt and will vary from machine to machine User response typed in from the keyboard and followed by a return is printed in bold face italics lcosy gt One_pulse 3 GAMMA 1D NMR Simulation Program Spin system filename One_pulse 3 sys
60. ll more data types are defined and also have such features matrices operators tensors In the next sections we ll look at some simple programs with double then simple programs using GAMMA defined non intrinsic data types 2 1 1 Basic C Program Using Doubles We begin by writing a GAMMA actually a C program A simple program would be the fol lowing include lt gamma h gt main double x This is an empty double double y 5 0 This is double y of value 5 cout lt lt nValue y is lt lt y lt lt An Print value of y to standard out x 12 4 y exp 1 07 Set double x to some value xarr 10 This is an array of doubles Scott Smith Copyright S A Smith May 22 1998 GAMMA Classes 11 Users Manual Double Precision Numbers 2 1 for int i 0 1 lt 10 i A loop to fill up xarr xarr i x i y cout lt lt nThe Ist array value is Print the first array value lt lt xarr 0 cout lt lt nThe last array value is Print the last array value lt lt xarr 9 double tanx tan x Here is the tangent of x Again wel emphasize what the intrinsic class double means 1 All doubles have a well defined interface Not to much worry about multiplying and adding them one knows exactly what to expect 2 They have a set of functions which apply to them and perhaps to other types as well Thus the operator lt lt is known to both doubles and Strings
61. ly and occurs instantaneously This would be suitable when one is not particularly concerned with the effects of relaxation pulse shape or pulse length phasing problems Being the easiest to implement computationally it might also be used when one desires the most rapid simulation When the pulse itself is of concern one may apply either a square pulse of finite length which we call a real pulse or an individually tailored shaped pulse Although these take use more com puter time the simulation becomes more realistic Real pulses have user specified lengths and strengths so may be used for frequency selection spin locking etc The same is true for shaped pulses but then users have the additional ability to specify the pulse waveform in the time domain Another level of complexity involves the treatment of relaxation both while the rf field is applied and during the FID acquisition This is not applicable to ideal pulses as they are infinitely short During the application of real and shaped pulse application and during acquisition steps which are of finite length appreciable relaxation may occur This of course depends upon input relax ation strengths and step times Inclusion of relaxation effects will always increase program exe cution time and should only be used when of true concern or for comparison with analogous experiments without relaxation Normally it is the relaxtion during the FID acquisition that is most important as thi
62. m during a delay under a constant Hamiltonian The spin system will be embodied by a density operator and we ll use the isotropic NMR Hamiltonian for our constant Hamiltonian Here is the math solution to the Liouville equation under constant H an external file and then build and output the isotropic Hamiltonian to the screen Here goes include lt gamma h gt main int argc char argv spin_system sys System sys sys ask_read argc argv 1 Ask for and or Read system gen_op sigma Fx sys Start with pure x magnetization gen_op H Ho sys Have a look at Ho double t 1 23 Set time for 1 23 seconds gen_op sigmal evolve sigma H t Evolve sigma under H for time t You are very close to a 1D NMR simulation In this example the operator sigma is used to represent the state of the spin system following a perfect 90y pulse pure X magnetization The operator H is set to the isotropic NMR Hamiltonian and then a new density operator sigmal is made by evolv ing sigma under the Hamiltonian H for a time t using the function evolve Scott Smith Copyright S A Smith May 22 1998 GAMMA Classes 24 Users Manual General Operators 2 6 That might be too cryptic for some since the function evolve does hide the underlying mathematics just as the functions Ho and Fx hide the mathematics behind themselves But that is only for con venience there is nothing preventing the user from doing the step by
63. me com The GAMMA functions are handed data typically a matrix or vector and produce disk files in MIF Maker Interchange Format format or in the MML Maker Mathematical Language format Plots or data structures are then seen by simply opening the file with FrameMaker Such output may then be graphically manipulated and or incorporated as part of a document and data such a matrices placed into FrameMaker equations Plots produced in this man ner can be printed on a laserprinter in PostScript colorized to make transparencies converted into HTML etc One important point to realize is that these FrameMaker files are not changeable into other formats with any GAMMA based code If your data is valuable and you wish to use it again in GAMMA it should be stored to disk in one of the other formats so that GAMMA can retreive and manipulate it once again There are some FrameMaker and public domain programs which can convert FrameMaker files to other formats but they must be obtained independently from GAMMA To see all specifics regarding these functions look in the GAMMA FrameMaker Documentation 4 5 2 1D Plots The simplest type of plot is a 1D plot created from a data vector with the function FM_1D With this function the horizontal axis is the point index of vector and the vertical axis contains the data value An example would be the simulated NMR spectrum shown below Scott Smith Copyright S A Smith May 22 1998 GAMMA Plotting 34 Users
64. needed parameters will run to completion without asking questions to the user The program writes two files one data file with the FID in the format of the NMRi pro gram and the other processed spectrum file in FrameMaker format the later is below 250 200 150 100 d orl uM 200 100 0 100 200 An alternative way of running the program is to let it prompt the user for needed information The following is a second way of achieving the same results One_pulse 2 Spin system filename One_pulse 2 sys Dwell time 0 002 Number of points 1024 Since the parameters were not supplied on the command line which executed the program One_pulse 2 sys the program responds by asking the user to supply them The results are of course identical to that as when the parameters are given on the command line 5 4 5 Example Data 8 Spin System The second spin system file One_pulse 2a sys contains SysName 2 galact Name of the Spin System galactose NSpins 0 8 Number of Spins in the System Iso 0 2 TH Spin Isotope Type Iso 1 2 1H Spin Isotope Type Iso 2 2 1H Spin Isotope Type Iso 3 2 1H Spin Isotope Type Iso 4 2 1H Spin Isotope Type Tilo Levante Scott Smith May 22 1998 GAMMA NMR Simulations 54 NMR Examples One Ideal Pulse Homonuclear Spin System 5 5 Iso 5 2
65. ng and plotting devices There are many ways to do indirect plots so that your programs will interactively display print and or plot These are just GAMMA programs which output their data into one or more of the supported formats then call the associated program s from within the GAMMA program having it perform the visual and or hardcopy output In particular see the Gnuplot section for pro grams which plot to screen interactively Scott Smith Copyright S A Smith May 22 1998 GAMMA Plotting 31 Users Manual Plotting Figures 4 2 4 4 Gnuplot 4 4 1 Description One way to have your plots appear on the screen during the course of a GAMMA simulation is to have your program output its data into a file that is compatible with the Gnuplot program and then call Gnuplot from within your program while it is running Alternatively you can use Gnuplot to view results of GAMMA simulations after program completion Typically the GAMMA program files a vector or matrix full of simulated data Then one of the numerous gnuplot functions provided in GAMMA is called with the vector or matrix as one of the function arguments The gnuplot function writes out the data to an external file in a format which is readable with gnuplot If the plot is desired to be viewed during program execution then another call is made to the system either using other GAMMA gnuplot functions or with explicit code To view the plot using gnuplot after program completion
66. o it The resulting density matrix is set equal to sigma The next function FID propagates sigma with the Hamiltonian H while filling up the data block The detector the number of points and the dwell time are also parameters used as ar guments for this function Spectral Output Format amp File Selection The user is prompted to specify an output type Currently four formats are allowed Spectral Output In this section the simulated FID is written to an output file For FrameMaker output the FID is apodized and Fourier Transformed before output since that program has not FFT capabilities Because Felix currently has problems accepting data into its parameter block the pa rameters needed to reference the spectrum are output if this format is specified For MATLAB out put there may be several matrices stored in each MAT file These each have an internal MATLAB data name which is set to spectrum here 5 5 3 Data 5 Spin System This program is general and may take any spin system For demonstation we here use the input spin system file One_pulse 3 sys which contains a p fluorophenyl spin system This is a hetero nuclear system containing 5 spin 1 2 species SysName 2 p_fluoro_PHE Name of the Spin System NSpins CO 2 Number of Spins in the System Tilo Levante Scott Smith May 22 1998 GAMMA NMR Simulations 60 NMR Examples One Ideal Pulse Homonuclear Spin System 5 5 Tso
67. o the liq uid NMR Hamiltonian with strong homonuclear coupling The detection operator is declared and set to F 1 FORTRAN programmers may find this unfamiliar territory In C and C the program itself is structured as any other routine it has a name main its code is encased in brackets OI and it may take arguments Tilo Levante Scott Smith May 22 1998 GAMMA NMR Simulations 52 NMR Examples Ideal 90 Pulse 4 8 N Homonuclear Spin Systems 5 4 Pulse Sequence Data Workup The pulse sequence is very short two steps and two pro gram lines The first step makes use of the function Iypuls which takes on the equilibrium density matrix and applies a 90 pulse along the y axis to it The resulting density matrix is set equal to sigma The next function FID propagates sigma under the active Hamiltonian H while filling up the data block The detector the number of points and the dwell time are also parameters used as arguments for this function Following this the FID is sent out to a file One_pulse 2 dat in NMR1 compatible format The FID is then internally manipulated by an exponential multiplication Fou rier transformation and finally an output to the file One_pulse 2 mif in FrameMaker format I left in a line to output the unprocessed FID to an NMRi compatible file for those who use that software 5 4 3 Example Data 4 Spin System The first spin system file One_pulse 2 sys contains SysName 2 antamanide Name of t
68. orine spectrum The prompt lcosy gt is just the computer prompt and will vary from machine to machine User response typed in from the keyboard and followed by a return is printed in bold face italics lcosy gt One_pulse 3 GAMMA 1D NMR Simulation Program Spin system filename One_pulse 3 sys Tilo Levante Scott Smith May 22 1998 GAMMA NMR Simulations 61 NMR Examples One Ideal Pulse Homonuclear Spin System 5 5 Number of acquisition points 2048 Strong or Weak Coupling s w s Which Isotope Type 19F Please Choose an Output Format 1 FrameMaker 2 Felix 3 NMRi 4 MatLab Output Type 2 Output File Name Please Include any Extension Felix 1D Files Normally Use a dat Extension Remember Felix reads only lower case names pfphe dat Parameters Needed for Felix Data Workup To set OMEGA sf 282 282 To set spectral width sw 32 12 To set offset no zf ref 1024 110 To set axis in Hertz ax 2 Icosy gt Alternatively this program will accept input directly on the command line Below is the full com puter interaction which took place to produce the protom spectrum now the information is input directly Again user response typed in from the keyboard and followed by a return is printed in bold face italics lcosy gt One_pulse 3 pfPHE sys 2048 s GAMMA 1D NMR Simulation Program Which Isotope Type 1H Please Choose an Output Format 1 FrameMaker 2 Felix 3 NMRi 4 MatLab Output Type 2 Output File Name
69. part of class spin_sys in GAMMA If the 1st argument via the 1 in the call is provided when the program is executed then sys will use that value as the filename it should use to read itself If no 1st argument is provided then the system will ask the user for a filename Don t spend too much time worrying about the details here You lI learn this stuff with experience Below is the above program run both with and without a spin system file name on the command line Pm leaving out the code following cout lt lt sys for brevity Here is the program executable named a out run when the name test sys is supplied on the command line lgammal gt a out test sys System CDV Spin 0 1 2 Isotope 13 2H S1V Momentum 1 2 1 1 2 Here is the same program run when no arguments are supplied on the command line lgammal gt a out Spin system filename test sys System CDV Spin 0 1 2 Isotope 13C 2H 51V Momentum 1 2 1 7 2 Scott Smith Copyright S A Smith May 22 1998 GAMMA Classes 17 Users Manual Spin Operators 2 4 See the difference Now your GAMMA program can be run repeatedly with any number of input spin system files Yep the current program doesn t do much but wait until you use spin systems to do simulations later This is the means by which you will soon learn how one can just make a general COSY simulator for any spin system containing any isotopes The above was run on my SPARC20 a machine with the prompt
70. programs just as you freely manipulated double precision numbers in the last example Variables of type matrix row_vector and col_vector have the following data type properties 1 Matrices and vectors may be declared anywhere in a program 2 An array of matrices and or vectors can be readily declared and accessed with 3 Matrices and Vectors come with their own functions exp lt lt 4 Matrices and Vectors have a defined algebra 2 2 1 Basic GAMMA Program Using Matrices amp Vectors Have a look at the following code include lt gamma h gt main double x This is an empty double matrix mx This is an empty matrix row_vector rv This is an empty row vector col_vector cvs 10 These are 10 empty column vectors matrix mx1 2 3 7 A 2x3 matrix filled with 7 s complex z 2 1 3 A complex number 2 1 31 matrix mx2 3 5 z 11 A3x5 matrix filled with z mx2 put complex 2 2 0 1 Set lt 1lmxI2 gt to be 2 21 rv row_vector 3 1 Now rv s a row vector of length 3 with 1 s matrix mx3 exp x rv mx2 complexi What the heck just playing around cout lt lt mx3 Let s have a look at mx3 isn t it 1x5 In GAMMA programs you can build up any vectors and matrices you need and then you may ma nipulate them as readily as you would a double precision number Make arrays of matrices take their exponentials do whatever you like within reason they are objects for you
71. s contributes the most to spectral linewidths We shall NOT cover all of these aspects in these documents See one of the GAMMA Examples DOCUMENTATION Books Instead we will do just a couple of such simulations and try and cov er the fundamental aspects of these calculations Tilo Levante Scott Smith May 22 1998 GAMMA NMR Simulations 50 NMR Examples Ideal 90 Pulse 4 8 N Homonuclear Spin Systems 5 4 I most often use FrameMaker output of the simulated spectra so that they may be incorpo rated directly into this document You don t have to Just go back to the Plotting chapter find the appropriate command s to relace the FM output function that will output the spectra in the format you can deal with On occasion UU add in a couple of output formats 5 4 Ideal 90 Pulse 4 8 N Homonuclear Spin Systems Since you ve gone through this user manual and are now a seasoned GAMMA programmer well work on a general level in our programs even if we use simple mathematical models The figure below is the pulse sequence we want to simulation the sigmas are density operators that define the state of the spin system trough the pulse sequence Acquire dh Wun On OG Git To keep the program general and simplify the code we ll read in our spin system that which de fines the sample in the spectrometer from an external ASCII file You ll see this treatment time and time again because reading in the s
72. s into the same graph by using the function FM_1Dm Instead of providing a single vector to the function the user just provides an array of vectors Dipolar Longitudinal Relaxation Times versus Correlation Time 8 A N y N S E log T Figure 19 3 Dipolar longitudinal relaxation times for several spin pairs versus correlation time The Scott Smith Copyright S A Smith May 22 1998 GAMMA Plotting 36 Users Manual Plotting Figures 4 2 distance between the spins was kept at 2A and the field strength set to 500 MHz The above plot was made with a simple GAMMA program using the FM_1Dm program see GAMMA DIPOLAR RELAXATION DOCUMENTATION 4 5 4 xy Plane Plots Plots in the xy plane can be produced with the FrameMaker function FM_xyPlot Unlike the func tion FM_1D this function need not have the horizontal coordinate always increasing The plot be low is a typical example It has been annoted and resized in FrameMaker after creatation with GAMMA rf Field Offset Effects Increasing Offset Have your GAMMA program fill up a row vector with the simulated data points you wish to plot Then make a function call to FM_xyPlot with the row vector and an output file name given as ar guments The output file can be read by FrameMaker Please note that GAMMA takes no time to make pretty output you can do the cosmetic work within FrameMaker Here is a simple example include lt gamma h gt main row_v
73. section However here is a small modification that uses a function The function precedes the main part of the program but is included in the same file include lt gamma h gt String evenworse int 1 1 1 lt 0 return String Cruel else if i 1 return String Very Cruel return String Extremely Cruel main cout lt lt n tJust How Cruel 0 1 2 int i 0 cin gt gt 1 cout lt lt n tHello lt lt evenworse 1 lt lt World Assuming that this file is named hello2 cc we shall compile and name the output executable onemore noesy gt gamma hello2 cc o onemore GAMMA Other Messages Scott Smith Copyright S A Smith May 22 1998 GAMMA Introduction Users Manual Basics of C Programs 1 1 noesy gt To run the program noesy gt onemore Just How Cruel 0 1 2 2 Hello Extremely Cruel World noesy gt We could have added more functions that take different arguments and we could have put the func tion codes in external files You ll have to learn as you go This covers the very basics of C pro gramming If you wish to become versed in C buy a nice book on that subject and look at other programs The reset of this document will teach you some C as we make GAMMA programs and you can look at the GAMMA sources for other ways to do things Scott Smith Copyright S A Smith May 22 1998 GAMMA Classes 10 Users Manual Double Precision
74. spin system and let the system itself tell us what these values are That is almost exactly what GAMMA does However it does NOT use the basic spin system class spin_sys to do so It uses an isotropic spin system class spin_system to do that job Vari ables of class spin_system contain all of the information that variables of class spin_sys do but in addition they contain isotropic shift values for each spin and isotropic scalar couplings for each spin pair Now lets have a look at building our isotropic Hamiltonian again spin_system sys An isotropic system not spin_sys sys read ABX sys Read in the system from file int i j ns sys spins Needed integers number of spins Scott Smith Copyright S A Smith May 22 1998 GAMMA Classes 20 Users Manual Isotropic Spin Systems 2 5 for i 0 i lt ns i Loop over the spins HO sys shift 1 Fz sys 1 Add shift contributions forg i 1 j lt ns j Loop spin pairs HO sys J i j Add coupling contributions Fz sys 1 Fz sys j Fx sys i Fx sys j Fy sys i Fy sys j This is NOT a complete GAMMA program I haven t defined HO yet However it does illustrate a key concept in C derived classes GAMMA s class spin_system is derived from the base spin system class spin_sys As such all functions that take variables of type spin_sys will also take vari ables of type spin_system So accessing the spin operators in the abo
75. step processes explicitly Here is another way to do the evolution in the last line of the previous code gen_op U exp complexi 2 0 PI H t gen_op sigmal U sigma adjoint U Here s another way to do it gen_op U exp complexi 2 0 PI H t gen_op sigmal evolve sigma U Here s yet another way to do it gen_op U prop H t gen_op sigmal evolve sigma U We could make a few dozen more too As you get used to using GAMMA and become convinced that functions such as Ho are every bit as good as you writing out the sums over spin operators yov ll switch to the simpler more cryptic not really Ho is Ho and evolve is just that code But if you don t like to write out the steps Sometimes one needs a specialized Hamiltonian or opera tors and the best way to get it is to just add up various spin components Scott Smith Copyright S A Smith May 22 1998 GAMMA Magnetic Resoance Library 25 Users Manual Hamiltonians 3 1 3 Magnetic Resoance Library At this point you have learned how to build C and GAMMA programs You ve also experienced the use of GAMMA provided data types spin systems operators superoperators tensors Along with these data types GAMMA also provides a number of functions which perform manipulations on them which are common to magnetic resonance simulations For example rather than building the isotropic NMR Hamiltonian stepwise there is a simple func tion which returns that Hamiltonian as
76. t gamma h gt main int argc char argv Spin_sys sys System sys Scott Smith Copyright S A Smith May 22 1998 GAMMA Magnetic Resoance Library 27 Users Manual Ideal Pulses 3 2 sys read test sys System reads itself from file test sys gen op sigma0 sigma_eq sys Equilibrium density operator gen op sigmal Iypuls sys sigma0 90 0 Apply 90y ideal pulse direct gen_op U90y Iypuls_U sys 90 0 Pulse propagator for 90y sigmal evolve sigma0 U90y Again the 90y pulse with prop sigmal Fx sys About the same thing gen_op sigma2 Ixpuls sys sigmal 33 3 Now pulse about x angle 33 3 deg sigmal Iypuls sys sigma0 2 18 9 Apply 18 9 deg y pulse to 3rd spin gen op U90x1H Ixpuls_U sys 1H 90 0 Propagator for 90x on protons gen op U90 Ixypuls_U sys 51V 45 0 90 0 90 pulse phase 45 on vanadiums Enough There s more Note that I used spin_sys in the above program That s because these pulse functions don t care about things like chemical shifts and coupling constants that doesn t af fect them at all What would happen if you used spin_system instead in this program NO EF FECT AT ALL If you just want to see that a 90y pulse on FZ produces FX just use class spin_sys If you want to generate a 1D NMR spectrum the use class spin_system because you ll need those shift and J values in other parts of your program Class spin_system
77. to coincide with the pro gram code Acquire A ITTV Oo O O ty The spin system will be read in from a disk file From this the equilibrium density matrix Og can be generated This density matrix is then treated by a 90 degree pulse along the y axis and prop agated in time including in an unscaled fashion the effects of dipole dipole relaxation while the FID is computed The detection operator necessary for determining the FID will be set to F_ for the entire spin system The is equivalent to a operator which samples xy magnetization F_ in combination with a pulse along the y axis produces a properly phased spectrum In this simulation the FID does decay somewhat as shown in the pulse sequence diagram on its own via relaxation processes Thus no apodization is utilized during the spectral workup 5 8 One Pulse Finite Length This example is another implementation of the one pulse experiment simulation on a two spin sys tem The pulse sequence is shown below with density matrices labeled to coincide with the pro gram code 1 2 Acquire Oo OG O t gt The spin system will be read in from a disk file From this the equilibrium density matrix Og can be generated This density matrix is then treated by a 90 degree pulse along the y axis and prop Tilo Levante Scott Smith May 22 1998 GAMMA NMR Simulations 75 NMR Examples One Pulse Finite Length 5 8 agated in time including in an unscaled fashion the ef
78. to wield to your hearts content much in the same way you can do in MATLAB Pll no longer bother with the compilation step just look to the previous examples Here is the result of running the above program Scott Smith Copyright S A Smith May 22 1998 GAMMA Classes 13 Users Manual Basic Spin Systems 2 3 GAMMA 1 x 5 Full Matrix 3 90 6 00 0 60 6 00 3 90 6 00 3 90 6 00 3 90 6 00 Note that the strength of GAMMA in NOT in it matrix and vector manipulations That is a power ful feature but it is shared by other types of programs to some extent Yes GAMMA can read and write matrices to and from MATLAB The wonderful thing about GAMMA for those working in magnetic resonance will be demonstrated through use of the MR tailored classes 2 3 Basic Spin Systems At this point we will depart from the mathematical classes and switch our focus to a GAMMA provided class spin_sys This is a data type which embodies a fundamental entity in magnetic res onance namely a collection of spins and associated spin quantum numbers I will not continue em phasizing the flexibility one has when working with data types Yes you can make an array of spin systems if you wish 2 3 1 GAMMA Base Spin System Primitive Construction Standard Output Heres a simple program which is very much like the original Hello World program include lt gamma h gt main spin_sys sys 3 System sys 3 spins cout lt
79. ve code looks identical to the previous programs which used base systems except now we are putting in an isotropic spin system when calling the functions 2 5 1 GAMMA Isotropic Spin System Interactive NMR Hamiltonian To illustrate this lets now make the isotropic NMR Hamiltonian We ll read in a spin system from an external file and then build and output the isotropic Hamiltonian to the screen Here goes include lt gamma h gt main int argc char argv spin_system sys System sys sys ask_read argc argv 1 Ask for and or Read system cout lt lt Ho sys Have a look at Ho Well Not too hard was it Hopefully you haven t forgotten about the ask_read function dis cussed in the spin_sys section nor the arguments in the main call Sure I could have left in the looping over spins and spin pairs but the isotropic Hamiltonian is simply used too often in NMR simulations Thus it is just a function in GAMMA that we will learn all about shortly If you looked at the code for the Ho function you would find that it is just that a loop over the spins and spin pairs and the summing up of components Lets try out the program Pll use the following ASCII file sosi sys as my input system SysName 2 C D Name of the Spin System NSpins 0 2 Number of Spins in the System Iso 0 2 13C Spin Isotope Type Iso 1 2 2H Spin Isotope Type Scott Smith Copyright S A Smith May 22
80. would work for watching FZ gt FZ but class spin_sys won t make it easy for you to make a 1D spectrum Get it If by some odd circumstance you need to pulse with a different spin selectivity than what I ve shown above there is indeed a way to do it Say you want to pulse only spins 2 3 amp 6 what you do is set their spin flags in the spin system just on off switches that don t affect anything in partic ular and call a special ideal pulse function that is active only on the spins who have their flags set Have a look in the ideal pulse documentation for specifics it s not a big stretch Remember we are dealing exclusively with ideal pulses in this section Other sections will cover square pulses shaped pulses pulse trains and how to include relaxation effects during the pulses If all of this is stuff about density operators confuses you get away from the quantum mechanics and look at the GAMMA treatment of the Bloch equations and magnetization vectors You can do pulses and delays in that context too Scott Smith Copyright S A Smith May 22 1998 GAMMA Plotting 28 Users Manual Plotting Sections 4 1 4 Plotting This chapter discusses methods of visualizing output from GAMMA simulations Since each sim ulation in GAMMA is produced by a C program the user always has the freedom to produce output to screen or file with the standard I O functions available in C and C as well as the ability to link his her program s
81. y 22 1998 GAMMA NMR Simulations 59 NMR Examples One Ideal Pulse Homonuclear Spin System 5 5 5 5 2 Discussion Read in Parameters Following the output of the program description an arbitrary spin sys tem is read in from an external file specified Afterwards the number of points in the FID is inter actively set Because it is useful to examine the weak coupling case the user is then allowed to specify weak or strong coupling Determine the Isotope Detected A check is made to see if the input spin system is homo nuclear or heteronuclear If heteronuclear the user must choose the isotope type to be detected Set Up Spectral Parameters Here all chemical shifts for spins of the isotope type being detected may be altered so as to be referenced to an optimal rotating frame Following this a Nyquist frequency is chosen and both the dwell time and spectral width set Set Variables A 1D data block is declared to hold the simulated FID A general operator is declared and set to the equilibrium density matrix Another general operator is declared and set to be either the strong or weak coupling isotropic Hamiltonian Finally a general operator is declared and set to hold the detection operator Pulse Sequence The pulse sequence is very short a two step sequence is performed with two program lines The first step makes use of the function Iypuls which takes on the equilibrium den sity matrix and applies a 90 pulse along the y axis t
82. ystem is highly desirable when working with large spin sys tems with using the same system repeatedly in different programs or when running the same pro gram with differing spin systems At the same time the code presented will be set to run interactively taking parameters the spin system filename dwell time number of acquisition points either from the command line or interactively by query to the user For this example if the spin system filename is not given as input the program will ask for it then wait for the filename to be supplied We will test the program on two different test systems both forms of parameter input will be demonstrated 5 4 1 Program include lt gamma h gt main int argc char argv Read in Parameters String filename Name of spin system file double dt Dwell time for acquisition Tilo Levante Scott Smith May 22 1998 GAMMA NMR Simulations 51 NMR Examples Ideal 90 Pulse 4 8 N Homonuclear Spin Systems 5 4 int t2pts Number of points in FID query_parameter argc argv Get or ask for filename 1 1 AnSpin system filename filename query_parameter argc argv Get or ask for dwell time 2 2 nDwell time dt query_parameter argc argv Get or ask for block size 3 3 nNumber of points t2pts spin_system sys Declare spin system sys sys read filename Read system from filename Set Variables block_1D data t2pts Storage for the

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