{VERSION 1 0 "X11/Motif" "1.0"}{GLOBALS 1 1}{FONT 0 "-adobe-helve
tica-bold-r-normal--14-*" "helvetica" "Helvetica-Bold" 8 12 0 "He
lvetica-Bold" 12}{FONT 1 "-adobe-times-medium-r-normal--14-*" "ti
mes" "Times-Roman" 4 12 64 "Times-Roman" 12}{FONT 2 "-adobe-couri
er-medium-r-normal--14-*" "courier" "Courier" 4 12 192 "Courier" 
12}{FONT 3 "-adobe-new century schoolbook-bold-r-normal--*-180-*-
*-*-*-*-*" "new century schoolbook" "Times-Bold" 8 18 64 "Times-B
old" 18}{FONT 4 "-adobe-new century schoolbook-bold-r-normal--*-1
80-*-*-*-*-*-*" "new century schoolbook" "Times-Bold" 8 18 64 "Ti
mes-Bold" 18}{SCP_R 1 0 37{COM_R 2 0{TEXT 4 51 "Homonuclear A2MX \+
J-resolved spectrum, with hetero X"}}{COM_R 3 0{TEXT 1 60 "\015Co
pyright (1994) Rene P.F. Kanters\012KANTERS@urvax.urich.edu\012"}
}{INP_R 4 0 "> "{TEXT 0 53 "with(share): readshare(pof, science);
 # read `pof.m`;"}}{OUT_R 5 0 4{TEXT 2 71 "See ?share and ?share,
contents for information about the share library\012"}}{OUT_R 6 0
 4{DAG n3\`pof`}}{COM_R 7 0{TEXT 1 350 "We are going to calculate
 the J-resolved spectrum for an A2MX spinsystem, in which X is a \+
heteronucleus, and is only coupled to spin M, not A2.\012\012The \+
pulse sequence for a J-resolved spectrum is\012        (Pi/2)x - \+
tau/2 - (Pi)y - tau/2 - t2\012\012In order to make life a little \+
easier we'll define the set H to contain the spins that we pulse \+
on and observe:"}}{INP_R 8 0 "> "{TEXT 0 12 "H:=\{A,A2,M\}:"}}
{COM_R 9 0{TEXT 1 160 "\015To define that  J[A,X] is zero, we fir
st need to initialize the spinsystem, since that will define the \+
J table to contain all possible couplings in the system."}}{INP_R
 10 0 "> "{TEXT 0 25 "spinsystem([[A,A2],M,X]):"}}{INP_R 11 0 "> \+
"{TEXT 0 10 "J[A,X]:=0:"}}{COM_R 12 0{TEXT 1 170 "\015Since we ar
e not interested in the evolution of spin X (it is not being puls
ed on or observer) we might as well start out with an xpulse on o
nly Iz terms of A, A2 and M."}}{INP_R 13 0 "> "{TEXT 0 34 "xpulse
(Iz[A]+Iz[A2]+Iz[M],H,Pi/2):"}}{COM_R 14 0{TEXT 1 157 "\015Now le
t's look at the product operator expression that we obtain after \+
an evolution time of tau seconds with in the middle of that a ref
ocussing (Pi) pulse:"}}{INP_R 15 0 "> "{TEXT 0 55 "evolve(\",\{\}
,tau/2): ypulse(\",H,Pi): evolve(\",\{\},tau/2);"}}{OUT_R 16 0 15
{DAG +15*7b3n3\`Ix`,2n3\`A`j2x0001b3n3\`Iz`,2n3\`M`p8(3n3\`Sin`,2
*7n3\`Pi`p8b3n3\`J`,3p6pEp8n3\`tau`p8p8j2x0002*7b3pBp5p8b3p3pDp8(
3p12,2+3p15p24p8p8b3n3\`Iy`pD/3i2x0001p24*7b3p3,2n3\`A2`p8pAp8p11
p8p24*5b3p38p42p8(3n3\`Cos`p14p8p3C*5b3p38p5p8p50p8p3C*5p37p8(3p5
1p31p8p3B*7p27p8b3pBp42p8p37p8p24*7p69p8p2Bp8p2Fp8p8*9p27p8p69p8p
37p8p61p8i2x0002}}{COM_R 17 0{TEXT 1 714 "We immediately notice t
hat the expression is not dependant on any chemical shift informa
tion, since chemical shifts refocus. Also only J[A,M] is present,
 and not J[M,X] since the heteronuclear, but not homonuclear, cou
plings refocus also.\012This means that in the tau domain only th
e homonuclear couplings will be present.\012\012In the observatio
n domain, both homonuclear and heteronuclear couplings will evolv
e, in addition to the shifts.\012We will observe the magnetizatio
n long the -y axis. We could have just observed it along the x-ax
is, but then we would have to perform a phase correction in the F
ourier transform of the observation time domain. We will assign t
he result to a variable so we can use it again later."}}{INP_R 18
 0 "> "{TEXT 0 26 "obs:=observe(\",H,t,-Pi/2);"}}{OUT_R 19 0 18
{DAG :3n3\`obs`+15*Bn3\`I`j2x0001(3n3\`Cos`,2+3*7n3\`Pi`p7b3n3\`J
`,3n3\`A`n3\`M`p7n3\`tau`p7j2x0002p7(3n3\`Sin`,2+3*7pFp7b3n3\`W`,
2p18p7n3\`t`p7p1Ep7(3pA,2*7pFp7b3p13,3n3\`X`p18p7p2Fp7p7(3pA,2+3*
7pFp7p12p7p2Fp7p1Ep7/3p7j2x0004*7(3pA,2pEp7(3pA,2+3*7pFp7b3p2A,2p
16p7p2Fp7p1Ep7(3pA,2p48p7p7*9p5p7p56p7(3p22p5Dp7p6Bp7p7*7p5p7p21p
7p34p7p51*9p5p7(3p22p58p7p76p7(3p22p6Dp7i2x0001*9p9p7(3pAp24p7p34
p7p44p7p51*5p97p7p34p7p51*7p88p7p5Bp7p8Ep7p92*Bp5p7(3p22pCp7p21p7
p34p7(3p22p46p7/3p92p53*9pB1p7p97p7p34p7pB9p7pBD}}{COM_R 20 0
{TEXT 1 298 "\015We will first look at the modulation that is pre
sent in the peaks due to the length of tau. In order to do that w
e will make sure that we only obtain absorption peaks from the Fo
urier transformation of the observation time domain, v2. We are a
lso only interested in the real part of that spectrum."}}{INP_R 
21 0 "> "{TEXT 0 17 "Di:=proc() 0 end:"}}{INP_R 22 0 "> "{TEXT 0 
31 "spc1:=evalc(Re(FT(obs,0,t,v)));"}}{OUT_R 23 0 22{DAG :3n4\`sp
c1`+11(3n3\`Ab`,3+5b3n3\`W`,2n3\`M`j2x0001b3n3\`J`,3n3\`X`pE/3i2x
0001j2x0002n3\`v`/3p10j2x0008(3p6,3+5pAp10p12/3p10p1Cp1Ep20*5(3n3
\`Cos`,2+3*7n3\`Pi`p10b3p13,3n3\`A`pEp10n3\`tau`p10p1Cp10(3p6,3+7
pAp10p12p2Bp3Ap10p1Ep10/3p10j2x0016*5p31p10(3p6,3+7pAp10p12p2Bp3A
p1Ap1Ep10p52*5p31p10(3p6,3+7pAp10p12p19p3Ap10p1Ep10p52*5p31p10(3p
6,3+7pAp10p12p19p3Ap1Ap1Ep10p52*5(3p32,2p36p10(3p6,3+5b3pB,2p3Dp1
0p3Ap19p1Ep10p2B*5p87p10(3p6,3+5p90p10p3Ap2Bp1Ep10p2B}}{COM_R 24 
0{TEXT 1 142 "\015We see that we need to define the T2 for A and \+
B, coupling values for A,M and M,X and the chemical shifts of A a
nd M before we can plot this."}}{INP_R 25 0 "> "{TEXT 0 86 "T2:=t
able([A=.5,M=.5]):Jv:=table(symmetric,[(A,M)=4,(M,X)=10]): Wv:=ta
ble([A=5,M=15]):"}}{INP_R 26 0 "> "{TEXT 0 92 "nmrplot2d(spc1,v=0
..30,tau=0..0.5,shading=Z,axes=FRAME,numpoints=900, orientation=[
120,60]);"}}{COM_R 27 0{TEXT 1 310 "This worked on my Mac IIfx ru
nning Maple V version 5.0.1, but on the SUN running Maple V versi
on 2 it stopped the engine quitted Maple and caused a core dump\0
15\015Now, to get the real spectrum that we would have obtained, \+
we need to make sure that dispersion peaks can be generated, by u
ndefining the Di procedure."}}{INP_R 28 0 "> "{TEXT 0 9 "Di:='Di'
:"}}{INP_R 29 0 "> "{TEXT 0 42 "sp2:=evalc(Re(FT(FT(obs,0,t,v),0,
tau,j)));"}}{OUT_R 30 0 29{DAG :3n3\`sp2`+1D*5(3n3\`Di`,3+7b3n3\`
W`,2n3\`M`j2x0001b3n3\`J`,3n3\`X`pE/3i2x0001j2x0002b3p13,3n3\`A`p
Ep1An3\`v`p10(3p6,3+3p1Ep1An3\`j`p10/3p1Aj2x0016*5(3n3\`Ab`,3+5pA
p10p12/3p10p1Cp25p10(3p37,3j2x0000p2Ep10/3p10j2x0008*5(3p6,3+5b3p
B,2p21p10p1Ep3Ep25p10(3p6,3+3p1Ep3Ep2Ep10p19*5(3p6,3+7pAp10p12p19
p1Ep10p25p10(3p6,3p1Ep2Ep10p31*5(3p6,3+5p53p10p1Ep19p25p10(3p6,3+
3p1Ep19p2Ep10p19*5(3p37,3+7pAp10p12p3Ep1Ep10p25p10(3p37p74p10/3p1
0p33*5(3p37,3+7pAp10p12p3Ep1Ep1Ap25p10(3p37p2Ap10p9E*5(3p37,3+5pA
p10p12p19p25p10p43p10p4A*5(3p37p51p10(3p37p5Ep10p3E*5(3p37p8p10pA
Ep10p9E*5(3p37p68p10p9Ap10p9E*5(3p6pA4p10p28p10p31*5(3p37p7Cp10(3
p37p86p10p3E*5(3p6p90p10p72p10p31}}{COM_R 31 0{TEXT 1 231 "\015We
 see that the peaks long the j-axis do not have any chemical shif
t information in them, so in order to give them a linewidth we ne
ed to define the T2 from spin '0', before we can make a two-dimen
sional stack plot of the spectrum"}}{INP_R 32 0 "> "{TEXT 0 11 "T
2[0]:=0.5:"}}{INP_R 33 0 "> "{TEXT 0 136 "nmrplot2d(sp2,v=0..30,j
=-7.5..7.5,shading=Z,axes=FRAME,numpoints=900, orientation=[120,6
0],labels=[`v`,`J`,``],title=`A2MX J-resolved`);"}}{COM_R 34 0
{TEXT 1 339 "Again this cause the Maple engine to stop running, e
xiting Maple and dumping the core.\015\015This took a quite some \+
time, but it is clear that the peaks are not pure absorption peak
s.\012\012In order to make a superposition spectrum of this, we n
eed to get rid of the dispersion contributions to see what the pu
re absorption spectrum would look like:"}}{INP_R 35 0 "> "{TEXT 0
 17 "Di:=proc() 0 end:"}}{INP_R 36 0 "> "{TEXT 0 118 "super2d(sp2
,v,j,shading=Z,axes=FRAME,numpoints=8*8, orientation=[100,60],lab
els=[`v`,`J`,``],title=`A2MX J-resolved`);"}}{COM_R 37 0{TEXT 1 0
 ""}}{COM_R 38 0{TEXT 1 378 "From this it is easy to see that hom
onuclear couplings give rise to peaks along lines with an angle o
f 45 degrees with the frequency axis. In order for these to becom
e parallel to the coupling axis, we need to tilt the spectrum ano
ther 45 degrees.\012\012If we tilt the spectrum in that manner an
d project the peaks onto the v-axis we would obtain a homonuclear
 decoupled 1D spectrum."}}}{END}
