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10.13 General Response Theory

10.13.3 $response Section and Operator Specification

(May 7, 2024)

The specification of operators used in solving for response vectors is designed to be very flexible. The general form of the $response input section is given by

  keyword_1 setting_1
  keyword_2 setting_2
  [operator_1_label, operator_1_origin]
  [operator_2_label, operator_2_origin]
  [operator_3_label, operator_3_origin]

where the keywords are those found in section 10.13.2 (with the exception of RESPONSE).

The specification of an operator is given within a line contained by [], where the first element is a label from table 10.4, and the second element is a label from table 10.5. Operator specifications may appear in any order. Response values are calculated for all possible permutations of operators and their components.

For the Cartesian moment operator, a third field within [] may be specified for the order of the expansion, entered as (i,j,k). For example, the molecular response to the moment of order (2, 5, 4) with its origin at (0.2, 0.3, 0.4) a.u. can be found with the operator specification

[multipole, (0.2, 0.3, 0.4), (2, 5, 4)]
Table 10.4: Available operators
Operator Label Description Integral
dipole or diplen dipole (length gauge) χμ|𝐫O|χν
quadrupole second moment (length gauge) χμ|𝐫𝐫T|χν
multipole arbitrary-order Cartesian moment (length gauge) χμ|xiyjzk|χν
fermi or fc Fermi contact 4πge3χμ|δ(𝐫K)|χν
spindip or sd spin dipole ge2χμ|3𝐫K𝐫KT-rK2rK5|χν
angmom or dipmag angular momentum χμ|𝐋O|χν
dipvel dipole (velocity gauge) χμ||χν
Table 10.5: Available operator origins
Origin Label Description
zero Cartesian origin, same as (0.0, 0.0, 0.0)
(x, y, z) arbitrary point (double precision, units are bohrs)