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8 18 64 "Times-Bold" 18}{SCP_R 1 0 45{COM_R 2 0{TEXT 6 42 "Homonu
clear A2MX one-dimensional spectrum."}}{COM_R 3 0{TEXT 1 60 "\015
Copyright (1994) Rene P.F. Kanters\012KANTERS@urvax.urich.edu\012
"}}{COM_R 4 0{TEXT 1 183 "We are going to calculate the 1D spectr
um of a homonuclear A2MX system.\012The pulse sequence for a 1D s
pectrum is:\012                (Pi/2)y - observe\015\012First we \+
read in the pof procedures"}}{INP_R 5 0 "> "{TEXT 0 53 "with(shar
e): readshare(pof, science); # read `pof.m`;"}}{OUT_R 6 0 5{TEXT 
2 71 "See ?share and ?share,contents for information about the sh
are library\012"}}{OUT_R 7 0 5{DAG n3\`pof`}}{COM_R 8 0{TEXT 1 33
 "\015Now we can define our spinsystem"}}{INP_R 9 0 "> "{TEXT 0 
25 "spinsystem([[A,A2],M,X]):"}}{COM_R 10 0{TEXT 1 0 ""}}{COM_R 
11 0{TEXT 1 76 "In order to give a ypulse on all spins present, w
e can use the global list T"}}{INP_R 12 0 "> "{TEXT 0 17 "ypulse(
\",T,Pi/2):"}}{COM_R 13 0{TEXT 1 203 "\015Observation with quadra
ture detection yields the FID.\015We will observe all spins, so w
e can use an empty set as the argument for the spins that we want
 the chemical shift evolution for during observation"}}{INP_R 14 
0 "> "{TEXT 0 18 "observe(\",\{\},t,0);"}}{OUT_R 15 0 14{DAG +15*
7(3n3\`Cos`,2+3*7n3\`Pi`j2x0001b3n3\`W`,2n3\`A`pAn3\`t`pAj2x0002p
A(3p3,2*7p8pAb3n3\`J`,3p10n3\`M`pAp13pApA(3p3,2*7p8pAb3p20,3p10n3
\`X`pAp13pApApA*7n3\`I`pA(3n3\`Sin`,2+3*7p8pAb3pD,2p24pAp13pAp16p
A(3p3,2*7p8pAb3p20,3p24p34pAp13pApA/3pAj2x0004*5(3p3,2+3*7p8pAb3p
D,2p34pAp13pAp16pAp50pAp5F*5(3p3p42pAp50pAp5F*9p3CpA(3p40p66pAp50
pA(3p3,2+3p2Dp16pAp5F*9p3CpA(3p40p5pAp19pAp2ApApA*9p3CpAp3FpAp50p
A(3p3,2+3p1Cp16pAp5F*7p78pAp50pApA3pAp5F*7p64pAp50pAp88pAp5F*7p3C
pAp82pAp50pAp5F}}{COM_R 16 0{TEXT 1 168 "\015The complex FID expr
ession needs to be Fourier transformed in order to obtain the spe
ctrum that would be obtained, but we are only interested in the r
eal part of that:"}}{INP_R 17 0 "> "{TEXT 0 30 " spec:=evalc(Re(F
T(\",0,t,v)));"}}{OUT_R 18 0 17{DAG :3n4\`spec`+21(3n3\`Ab`,3+5b3
n3\`W`,2n3\`M`j2x0001b3n3\`J`,3pEn3\`X`/3p10j2x0002n3\`v`/3p10j2x
0008(3p6,3+7b3pB,2n3\`A`p10b3p13,3p2ApE/3i2x0001p1Bb3p13,3p2Ap17p
32p1D/3p10j2x0004(3p6,3+7pAp10p12p32p2Dp33p1D/3p10j2x0016(3p6,3+7
p27p10p2Dp19p36p19p1Dp3D(3p6,3+7pAp10p12p19p2Dp33p1Dp4C(3p6,3+7pA
p10p12p19p2Dp10p1Dp4C(3p6,3+7b3pB,2p17p10p12p32p36p10p1Dp4C(3p6,3
+7p78p10p12p19p36p33p1Dp4C(3p6,3+7p78p10p12p32p36p33p1Dp4C(3p6,3+
7pAp10p12p32p2Dp10p1Dp4C(3p6,3+7p78p10p12p19p36p10p1Dp4C(3p6,3+5p
Ap10p12p32p1Dp1F(3p6,3+5p78p10p12p19p1Dp1F(3p6,3+5p78p10p12p32p1D
p1F(3p6,3+7p27p10p2Dp32p36p19p1Dp3D(3p6,3+7p27p10p2Dp19p36p32p1Dp
3D}}{COM_R 19 0{TEXT 1 373 "In order to be able to plot the spect
rum ,we will have to define the global variables required for nmr
plot, i.e., Jv, Wv, and T2. Notice that Jv is a symmetric table s
o that by defining the value for Jv[M,X] automatically the value \+
of Jv[X,M] is known. The latter one will be used for the plot pro
cedure since the J is going to be replaced with its numerical cou
nterpart Jv"}}{INP_R 20 0 "> "{TEXT 0 104 "T2:=table([A=1,M=1,X=1
]): Wv:=table([A=10,M=25,X=40]):\012Jv:=table(symmetric,[(A,X)=2,
(M,X)=5,(A,M)=0.7]):"}}{COM_R 21 0{TEXT 1 165 "\015Now we are rea
dy to plot the spectrum. We will use a large number of points bec
ause the lines are reasonably sharp and we want to get well defin
ed peaks in the plot"}}{INP_R 22 0 "> "{TEXT 0 49 "nmrplot(spec,v
=5..50,numpoints=500,title=`A2MX`);"}}{COM_R 23 0{TEXT 1 0 ""}}
{COM_R 24 0{TEXT 1 380 "We observe that the A site (around 10 Hz)
 consists of a doublet (J[M,X]) of doublets (J[ A,M]) site M (aro
und 25 Hz) is a doublet (J[M,X]) of triplets (J[A,M]) and finally
 site X (around 40Hz) is also a doublet (J[M,X]) of triplets (J[A
,M]).\012\012What would happen if we accidentally had the same si
ze of coupling between A and X and M and X?\015The first order sp
ectrum would look like:"}}{INP_R 25 0 "> "{TEXT 0 67 "Jv[M,X]:=Jv
[A,X]: nmrplot(spec,v=5..50,numpoints=500,title=`A2MX`);"}}{COM_R
 26 0{TEXT 1 1 "\015"}}{COM_R 27 0{TEXT 1 130 "It looks like our \+
X site becomes a quartet.\012\012In order to see what the spectru
m expression is we can substitute J[M,X] with J[A,X]:"}}{INP_R 28
 0 "> "{TEXT 0 25 "subs(J[M,X]=J[A,X],spec);"}}{OUT_R 29 0 28{DAG
 +1D(3n3\`Ab`,3+5b3n3\`W`,2n3\`M`j2x0001b3n3\`J`,3n3\`A`n3\`X`/3p
Cj2x0002n3\`v`/3pCj2x0008(3p2,3+7b3p7,2p12pCb3pF,3p12pA/3i2x0001p
18pEp2Ep1A/3pCj2x0004(3p2,3+7p6pCpEp2Ep29p2Fp1A/3pCj2x0016(3p2,3+
7p24pCp29p16pEp16p1Ap35(3p2,3+7p6pCpEp16p29p2Fp1Ap44(3p2,3+7p6pCp
Ep16p29pCp1Ap44(3p2,3+5b3p7,2p14pCpEp16p1A/3j2x0003p46(3p2,3+5p70
pCpEp2Ep1Ap78(3p2,3+5p70pCpE/3i2x0003p18p1Ap44(3p2,3+7p6pCpEp2Ep2
9pCp1Ap44(3p2,3+5p70pCpE/3p79p18p1Ap44(3p2,3+5p6pCpEp2Ep1Ap1C(3p2
,3+7p24pCp29p2EpEp16p1Ap35(3p2,3+7p24pCp29p16pEp2Ep1Ap35}}{COM_R 
30 0{TEXT 1 107 "\015We can write a small procedure to obtain onl
y the peaks that contribute to the multiplet for X by issuing:"}}
{INP_R 31 0 "> "{TEXT 0 86 "map(proc(s) if(member(W[X],map(op,map
(indets,indets(s))))) then s else 0 fi end,spec);"}}{OUT_R 32 0 
31{DAG +D(3n3\`Ab`,3+7b3n3\`W`,2n3\`X`j2x0001b3n3\`J`,3n3\`M`pA/3
i2x0001j2x0002b3pF,3n3\`A`pApCn3\`v`/3pCj2x0016(3p2,3+7p6pCpE/3pC
p18p1Ap16p21p23(3p2,3+7p6pCpEp15p1Ap16p21p23(3p2,3+7p6pCpEp2Ep1Ap
Cp21p23(3p2,3+5p6pCpEp2Ep21/3pCj2x0008(3p2,3+5p6pCpEp15p21p56}}
{COM_R 33 0{TEXT 1 128 "\015That looked a little hard, so we will
 write a procedure oneD(spinsystem,pulsset,evolutionset) to calcu
late a whole 1D spectrum:"}}{COM_R 34 0{TEXT 1 0 ""}}{INP_R 35 0 
"> "{TEXT 0 101 "oneD:=proc(s,p,e)\012  spinsystem(s): ypulse(\",
p,Pi/2): observe(\",e,t,0):\012  evalc(Re(FT(\",0,t,v))):\012end:
"}}{COM_R 36 0{TEXT 1 69 "\015and now calculate our spectrum with
 observation of only the X spins:"}}{INP_R 37 0 "> "{TEXT 0 34 "o
neD([[A,A2],M,X],\{A,A2,M,X\},\{X\});"}}{OUT_R 38 0 37{DAG +D(3n3
\`Ab`,3+7b3n3\`W`,2n3\`X`j2x0001b3n3\`J`,3n3\`M`pA/3i2x0001j2x000
2b3pF,3n3\`A`pApCn3\`v`/3pCj2x0016(3p2,3+7p6pCpE/3pCp18p1Ap16p21p
23(3p2,3+7p6pCpEp15p1Ap16p21p23(3p2,3+7p6pCpEp2Ep1ApCp21p23(3p2,3
+5p6pCpEp2Ep21/3pCj2x0008(3p2,3+5p6pCpEp15p21p56}}{COM_R 39 0
{TEXT 1 46 "\015When we substitute that J[M,X]=J[A,X] we get:"}}
{INP_R 40 0 "> "{TEXT 0 22 "subs(J[M,X]=J[A,X],\");"}}{OUT_R 41 0
 40{DAG +9(3n3\`Ab`,3+5b3n3\`W`,2n3\`X`j2x0001b3n3\`J`,3n3\`A`pA/
3pCj2x0002n3\`v`/3j2x0003j2x0016(3p2,3+5p6pCpE/3i2x0001p17p19p1B(
3p2,3+5p6pCpE/3i2x0003p17p19/3pCp1E(3p2,3+5p6pCpE/3p1Cp17p19p39}}
{COM_R 42 0{TEXT 1 406 "and we see that the intensities going fro
m -3/2J[X,A] up are 1:3:3:1.\012\012This is indeed the intensity \+
relationship expected for a real quartet, but a real quartet also
 has that all the chemical shifts of the 3 spins are the same, wh
ich we don't have here. So even though this multiplet looks like \+
a quartet, it is not a real one.\012\012Just to check the intensi
ties in a real quartet (A3X system for the X spins):"}}{INP_R 43 
0 "> "{TEXT 0 36 "oneD([[A,A2,A3],X],\{A,A2,A3,X\},\{X\});"}}
{OUT_R 44 0 43{DAG +9(3n3\`Ab`,3+5b3n3\`W`,2n3\`X`j2x0001b3n3\`J`
,3n3\`A`pA/3pCj2x0002n3\`v`/3j2x0003j2x0016(3p2,3+5p6pCpE/3i2x000
1p17p19p1B(3p2,3+5p6pCpE/3i2x0003p17p19/3pCp1E(3p2,3+5p6pCpE/3p1C
p17p19p39}}{INP_R 45 0 "> "{TEXT 0 0 ""}}{INP_R 46 0 "> "{TEXT 0 
0 ""}}}{END}
