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Linear Molecule Perturbation

There will be one of these for each perturbation parameter in each state.

Settings

Nucleus Index, starting from 1, of the nuclear spin involved in perturbation; 0 (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
n Power of operator in perturbation.
Npower Power of N (for centrifugal distortion of perturbation). Perturbation operator is ½[N2,Op]+
OmegaSelect Set to all for normal use; set to a specific value to restrict the perturbation to a specific value of Ω
Srank
Scomp

Parameters

Value Size of perturbation.
The matrix elements are described individually below, but a general comment on specifying the value of the parameter is appropriate. In a Hund’s case (a) basis there are four related matrix elements of any operator:

PGOPHER will essentially take the one in the top left as the parameter, ordering the matrix such that Λ' > Λ and Λ' > 0 (or Σ' > Σ and Σ' > 0 if Λ' = Λ or S' > S if all the other quantum numbers are equal). The two rows of the matrix can be related using the reflection operator σv:

The columns can be related by requiring the Hamiltonian to be symmetric.

Perturbation Types

LS
Spin orbit coupling, with the Ω dependence from the Wigner-Eckart theorem; see for example Lefebvre-Brion and Field, 2nd Edition Equation 3.4.36:

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.

S. Σ' S Σ
½ -½ ½ ½
½ ½ ½ ½
1 0 0 0
1 1 0 0
1 1 1 1
1 1 1 0


Luncouple
 J+nL-n+J-nL+n
 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.
Suncouple
 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.
Homog
Simple homogeneous perturbation with ΔΩ = 0; Use only if one of the other types is not appropriate.
aL
 aI.L
 Nuclear Spin Orbit perturbation
e
Nuclear magnetic dipole perturbation
eQq1
Nuclear electric quadrupole perturbation