11 Molecular Properties and Analysis 11.14.2 Romberg Finite-Field Procedure 11.15.1 Job Control

11.15 General Response Theory

Many of the preceding sections of chapter 11 are concerned with properties that require the solution of underlying equations similar to those from TDDFT (see eq. (7.15)), but in the presence of a (time-dependent) perturbation:

\left[\begin{pmatrix}\mathbf{A}&\mathbf{B}\\ \mathbf{B}^{*}&\mathbf{A}^{*}\end{pmatrix}-\omega_{f}\begin{pmatrix}\mathbf{% \Sigma}&\mathbf{\Delta}\\ -\mathbf{\Delta}^{*}&-\mathbf{\Sigma}^{*}\end{pmatrix}\right]\begin{pmatrix}% \mathbf{X}\\ \mathbf{Y}\end{pmatrix}=\begin{pmatrix}\mathbf{V}\\ -\mathbf{V}^{*}\end{pmatrix},

(11.84)

where $\mathbf{\Sigma}\rightarrow\mathbf{0}$ and $\mathbf{\Delta}\rightarrow\mathbf{1}$ for canonical HF/DFT MOs. The functionality for solving these equations with a general choice of operators representing a perturbation $\mathbf{V}$ is now available in Q-Chem. Both singlet⁴⁴⁰ and triplet⁶⁹⁰ response are available for a variety of operators (see table 11.4).

An additional feature of the general response module is its ability to work with non-orthogonal MOs. In a formulation analogous to TDDFT(MI)⁵⁸¹, the linear response for molecular interactions⁸⁷, or LR(MI), method is available to solve the linear response equations on top of ALMOs.

The response solver can be used with any density functional available in Q-Chem, including range-separated functionals (e.g. CAM-B3LYP, $\omega$ B97X) and meta-GGAs (e.g. M06-2X).

There are a few limitations:

•

No post-HF/correlated methods are available yet.
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Currently, only linear response is implemented.
•

Only calculations on top of restricted and unrestricted (not restricted open-shell) references are implemented.
•

Density functionals including non-local dispersion (e.g. VV10, $\omega$ B97M-V) are not yet available.

11.15.1 Job Control

11.15.2 $response Section and Operator Specification

11.15.3 Examples Including $response Section

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11.15 General Response Theory