|Molecule Types Linear Molecules||<Prev Next>|
|Nucleus||Index, starting from 1, of the nuclear spin involved in perturbation; 0 (the default) for those not involving a nuclear spin.|
|SymSelect||Possible values are all
(normal use), e_only
(only affect e
levels) and f_only
(only affect f
levels). Was ParitySelect in previous versions.
|ScalePrev||Scale factor with respect to preceding perturbation|
|Op||Perturbation type. See below for possible values. If only
Npower and/or Srank, Scomp are
needed, use Op = Luncouple with n = 0.
|n||Power of operator in perturbation.|
|Npower||Power of N (for centrifugal distortion of
perturbation). Perturbation operator is ½[N2,Op]+.
is set, N is replaced by R.
|OmegaSelect||Set to all (the default) for normal use; set to a specific value to restrict the perturbation to a specific value of Ω. Note that the current implementation applies the constraint to both connected wavefunctions, so is only useful for ΔΩ = 0 matrix elements.|
|Srank||If Srank <= 0: adds a
term S±Scomp and changes the
power of J or N. See the Op
If Srank > 0: spherical tensor operator for S with overall rank Srank and component Scomp.
Note that both of these are only implemented for Op = Luncouple, Suncouple and LNuncouple. Versions before 10.033 require Srank < 0 for S±Scomp.
|Value||Size of perturbation; the expressions and operators given
below should be understood to be multiplied by this.
||Spin orbit coupling, with the
Ω dependence from the Wigner-Eckart theorem; see for
example Lefebvre-Brion and Field, 2nd Edition Equation
The perturbation parameter is the reduced matrix element arranged so that Λ' > Λ and Λ' > 0 (or S' > S if Λ' = Λ). It is perhaps more normal to quote the value including the 3j symbol, but this is ambiguous when the spin-orbit operator connects more than one component of a pair of states. Some common non-zero values of the 3j symbol are tabulated below.
||L uncoupling; Using the
default n = 1 this can be used to model the term omitted from the
rotational operator. The perturbation parameter is the value
of the matrix element:
for Λ > 0 with the matrix element of L- derived by symmetry
If Srank <= 0 the operator becomes: J+n+ScompS+-ScompL-n+J-n+ScompS--ScompL+n
||J+nS-n+J-nS+n||S uncoupling. (Note that this
term with n = 1 is present in the normal Hamiltonian
within a single vibronic state; it only makes sense to add
it as a perturbation between states.) It checks for
ΔΛ = 0 and |ΔΣ| = n, but
does not check for ΔS
= 0. S is taken from the Ket. (Note this form is not
useful with Srank <= 0).
electrostatic or vibrational perturbation with a
ΔΩ = 0 selection rule with no Ω or J
||N.S (n is ignored)
||R.S (n is ignored)
||N+nL-n+N-nL+n||Similar to Luncouple, but with J
replaced by N.
If Srank <= 0 the operator becomes: N+n+ScompS+-ScompL-n+N-n+ScompS--ScompL+n
||Nuclear Spin Orbit
||Nuclear magnetic dipole
|eQq1||Nuclear electric quadrupole perturbation|
||(Luncouple)||0||2||0||0||1||N2 is replaced by R2 if RSquaredH is set|
|D||N4||(Luncouple)||0||4||0||0||-1||N4 is replaced by R4 if RSquaredH is set|
|H||N6||(Luncouple)||0||6||0||0||1||N6 is replaced by R6 if RSquaredH is set|
|L||N8||(Luncouple)||0||8||0||0||1||N8 is replaced by R8 if RSquaredH is set|
|M||N10||(Luncouple)||0||10||0||0||1||N10 is replaced by R10 if RSquaredH is set|
|PP||N12||(Luncouple)||0||12||0||0||1||N12 is replaced by R12 if RSquaredH is set|
which gives the LzSz operator form
||LS||1||2||0||0||Scale factor as for A above which gives the ½[N2,LzSz]+ operator form|
||0||0||Scale factor as for A above which gives the ½[N4,LzSz]+ operator form|
||0||0||Scale factor as for A above which gives the ½[N6,LzSz]+ operator form|
||0||0||Scale factor as for A above which gives the ½[N8,LzSz]+ operator form|
|gammaD||½[N2,N.S]+||NS||1||2||0||0||1||N2 (only) is replaced by R2 if RSquaredH is set|
|gammaH||½[N4,N.S]+||NS||1||4||0||0||1||N4 (only) is replaced by R4 if RSquaredH is set|
|gammaL||½[N6,N.S]+||NS||1||6||0||0||1||N6 (only) is replaced by R6 if RSquaredH is set|
||0||(8/3)½||N2 (only) is replaced by R2 if RSquaredH is set|
||0||(8/3)½||N4 (only) is replaced by R4 if RSquaredH is set|
For all of these operators, the N is replaced by R
is set; the N+ and N-
operators are not changed.
A few lambda doubling operators for Δ
states are built into PGOPHER, though note that these
use the form involving J rather than N, and the
name is not standard for some of them. The form involving N
can be obtained by replacing Luncouple with LNuncouple
and lambda operators for higher values of Λ can be obtained
by setting n = 2Λ. Centrifugal distortion can be
added using NPower, as for Π states above.
|o||S+4L-4+S-4L+4||Luncouple||4||0||-1||-4||½||The conventional name would be m
|oD||J+S+3L-4+J-S-3L+4||Luncouple||4||0||-1||-3||-½||The conventional name would be n|
|oH||J+2S+2L-4+J-2S-2L+4||Luncouple||4||0||-1||-2||½||The conventional name would be o|