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(June 30, 2021)

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 10.14.1 (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)]

Operator Label | Description | Integral |
---|---|---|

dipole or diplen | dipole (length gauge) | $\u27e8{\chi}_{\mu}|{\mathbf{r}}_{O}|{\chi}_{\nu}\u27e9$ |

quadrupole | second moment (length gauge) | $\u27e8{\chi}_{\mu}|{\mathrm{\mathbf{r}\mathbf{r}}}^{T}|{\chi}_{\nu}\u27e9$ |

multipole | arbitrary-order Cartesian moment (length gauge) | $\u27e8{\chi}_{\mu}|{x}^{i}{y}^{j}{z}^{k}|{\chi}_{\nu}\u27e9$ |

fermi or fc | Fermi contact | $\frac{4\pi {g}_{e}}{3}\u27e8{\chi}_{\mu}|\delta ({\mathbf{r}}_{K})|{\chi}_{\nu}\u27e9$ |

spindip or sd | spin dipole | $\frac{{g}_{e}}{2}\u27e8{\chi}_{\mu}|\frac{3{\mathbf{r}}_{K}{\mathbf{r}}_{K}^{T}-{r}_{K}^{2}}{{r}_{K}^{5}}|{\chi}_{\nu}\u27e9$ |

angmom or dipmag | angular momentum | $\u27e8{\chi}_{\mu}|{\mathbf{L}}_{O}|{\chi}_{\nu}\u27e9$ |

dipvel | dipole (velocity gauge) | $\u27e8{\chi}_{\mu}|\nabla |{\chi}_{\nu}\u27e9$ |

Origin Label | Description |
---|---|

zero | Cartesian origin, same as (0.0, 0.0, 0.0) |

(x, y, z) | arbitrary point (double precision, units are bohrs) |