Molecule Types Symmetric Tops  <Prev Next> 
Nucleus  Index, starting from 1, of nuclear spin involved in perturbation; 0 (default) for those not involving a nuclear spin. 
SymSelect  Symmetry select 
ScalePrev  Scale factor with respect to preceding perturbation 
JPower  Twice power of N^{2} = N(N+1) (= J(J+1)
for closed shell systems with S = 0). 
zPower  Power of N_{z}; If both zPower and pPower are non zero
then the effective operator is either: N^{JPower/2}[N_{z}^{zPower}, N_{+}^{pPower}+N_{}^{pPower}]_{+}
or N^{JPower/2}[N_{z}^{zPower1},[N_{z}, N_{+}^{pPower}+N_{}^{pPower}]_{+}]_{+} if zPower is odd and < 2 
pPower  Power of N_{±} 
lPower  Select l
dependence; valid values are 0 (l independent), 1 or 1. If lChange is 0, the
matrix element is multiplied by l*lPower,
otherwise the matrix element is multiplied by sign(l'l)*lPower. 
lChange  Power of l_{+} or l_{}; < 0 implies opposite sign to change in K; valid values are 2..2 
KSelect  K the perturbation applies to 
SPower  Twice power of S^{2} = S(S+1) 
SzPower  Power of S_{z}.
If this is combined with a rotational operator, the overall
operator is:[N^{JPower/2}[N_{z}^{zPower}, N_{+}^{pPower}+N_{}^{pPower}]_{+},S_{z}^{SzPower}]+ 
SpPower  Power of S_{±}.
If this is combined with a rotational operator, the overall
operator is (if pPower and SpPower have
the same sign):[N^{JPower/2}[N_{z}^{zPower},N_{+}^{pPower}]_{+}, S_{+}^{SpPower}]_{+} + [N^{JPower/2}[N_{z}^{zPower},N_{}^{pPower}]_{+}, S_{}^{SpPower}]_{+ }If pPower and SpPower have opposite signs: [N^{JPower/2}[N_{z}^{zPower},N_{+}^{pPower}]_{+}, S_{}^{SpPower}]_{+} + [N^{JPower/2}[N_{z}^{zPower},N_{}^{pPower}]_{+}, S_{+}^{SpPower}]_{+} 
NSPower  Power of N.S. 
Value  Size of perturbation. 
Operator 
JPower 
zPower 
pPower 
lPower 
lChange 
Scale Factor 
Notes 

B  N^{2}  2 
0  0 
0  0  1 
Both terms required to replicate B[J(J+1)  K^{2}] 
N_{z}^{2}  0 
2 
0 
0 
0 
1 

C  N_{z}^{2}  0  2  0  0 
0  1 

DJ  N^{4} ≡ N^{2}(N+1)^{2}  4  0  0  0  0  1  
DJK  N^{2}N_{z}^{2} ≡ N(N+1)K^{2}  2  2 
0  0  0  1  
DK  N_{z}^{4}≡ K^{4}  0  4 
0  0  0  1  
zeta 
N_{z}l_{z}  0 
1 
0 
1 
0 
2C 
In this form, parameter must be 2Cζ, not 2ζ 
etaJ 
^{ }N^{2}N_{z}l_{z}  2 
1 
0 
1 
0 
1 

etaK 
^{}N_{z}^{3}l_{z}  0 
3 
0 
1 
0 
1 

qplus 
N_{+}^{2}l_{+}^{2}+N_{}^{2}l_{}^{2}  0 
0 
2 
0 
2 
½ 

qminus 
N_{+}^{2}l_{}^{2}+N_{}^{2}l_{+}^{2}  0 
0 
2 
0 
2 
½  
r 
[N_{+}l_{}^{2}+N_{}l_{+}^{2},N_{z}]_{+}  0 
1 
1 
0 
2 
1 

DqJ 
N^{2}(N_{+}^{2}l_{+}^{2}+N_{}^{2}l_{}^{2})  2 
0 
2 
0 
2 
½  
DqK 
[N_{+}^{2}l_{+}^{2}+N_{}^{2}l_{}^{2},N_{z}^{2}]_{+}  0 
2 
2 
0 
2 
½  
DrJ 
N^{2}[N_{+}l_{}^{2}+N_{}l_{+}^{2},N_{z}]_{+}  0 
1 
1 
0 
2 
1 

DrK 
[[N_{+}l_{}^{2}+N_{}l_{+}^{2},N_{z}]_{+},N_{z}^{2}]_{+}  0 
3 
1 
0 
2 
1 
zPower <= 3 flags use of two
anticommutators 
HJ  N^{6}  6  0  0  0  0  1 

HJK  N^{4}N_{z}^{2}  4  2 
0  0  0  1 

HKJ  N^{2}N_{z}^{4}  2  4 
0  0  0  1 

HK  N_{z}^{6}  0  6 
0  0  0  1 

LJ  N^{8}  8  0  0  0  0  1 

LJJK  N^{6}N_{z}^{2}  6  0  0  0  0  1 

LJK  N^{4}N_{z}^{4}  4  0  0  0  0  1 

LKKJ  N^{2}N_{z}^{6}  2  0  0  0  0  1 

LK  N_{z}^{8}  0  0  0  0  0  1 
Operator 
JPower 
zPower 
pPower 
lPower 
lChange  SzPower 
SpPower 
SPower 
NSPower 
Scale Factor 

ebb  N_{+}S_{} + S_{+}N_{}+
N_{}S_{+} + S_{}N_{+} = 2(N_{+}S_{} + N_{}S_{+}) = 8(N_{x}S_{x}+N_{y}S_{y}) 
0 
0 
1 
0 
0 
0 
1 
0 
0 
1/4 
ecc 
N_{z}S_{z} + S_{z}N_{z}
=2N_{z}S_{z} 
0 
1 
0 
0 
0 
1 
0 
0 
0 
½ 
DsN  N^{2}N.S  2 
0 
0 
0 
0 
0 
0 
0 
1 
1 
DsNK 
[N^{2}, N_{z}S_{z}]_{+}  2 
1 
0 
0 
0 
1 
0 
0 
0 
½ 
DsKN 
N.S N_{z}^{2}  0 
2 
0 
0 
0 
1 
0 
0 
1 
1 
DsK 
[N_{z}^{3}, S_{z}]_{+}
= 2N_{z}^{3}S_{z} 
0 
3 
0 
0 
0 
1 
0 
0 
0 
½ 
alpha 
S_{z}^{2}  0 
0 
0 
0 
0 
2 
0 
0 
0 
3 
S^{2}  0 
0 
0 
0 
0 
0 
0 
2 
0 
1 

beta 
S_{+}^{2}S_{}^{2}  0 
0 
0 
0 
0 
0 
2 
0 
0 
½ 
aeff 
l_{z}S_{z}  0 
0 
0 
1 
0 
1 
0 
0 
0 
1 