10.13 General Response Theory 10.13.2 Job Control 10.13.4 Examples Including $response Section

10.13.3 $response Section and Operator Specification

(September 1, 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

$response
  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]
  ...
$end

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)	$\langle\chi_{\mu}\|\mathbf{r}_{O}\|\chi_{\nu}\rangle$
quadrupole	second moment (length gauge)	$\langle\chi_{\mu}\|\mathbf{r}\mathbf{r}^{T}\|\chi_{\nu}\rangle$
multipole	arbitrary-order Cartesian moment (length gauge)	$\langle\chi_{\mu}\|x^{i}y^{j}z^{k}\|\chi_{\nu}\rangle$
fermi or fc	Fermi contact	$\frac{4\pi g_{e}}{3}\langle\chi_{\mu}\|\delta(\mathbf{r}_{K})\|\chi_{\nu}\rangle$
spindip or sd	spin dipole	$\frac{g_{e}}{2}\langle\chi_{\mu}\|\frac{3\mathbf{r}_{K}\mathbf{r}_{K}^{T}-r_{K}% ^{2}}{r_{K}^{5}}\|\chi_{\nu}\rangle$
angmom or dipmag	angular momentum	$\langle\chi_{\mu}\|\mathbf{L}_{O}\|\chi_{\nu}\rangle$
dipvel	dipole (velocity gauge)	$\langle\chi_{\mu}\|\mathbf{\nabla}\|\chi_{\nu}\rangle$

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)

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10.13.3 $response Section and Operator Specification