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# 10.13.1 Introduction

(December 20, 2021)

Many of the preceding sections of chapter 10 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:

 $\left[\begin{pmatrix}\mathbf{A}&\mathbf{B}\\ \mathbf{B}^{*}&\mathbf{A}^{*}\end{pmatrix}-\omega_{f}\begin{pmatrix}\mathbf{% \Sigma}&\mathbf{\Delta}\\ -\mathbf{\Delta}^{*}&-\mathbf{\Sigma}^{*}\end{pmatrix}\right]\begin{pmatrix}% \mathbf{X}\\ \mathbf{Y}\end{pmatrix}=\begin{pmatrix}\mathbf{V}\\ -\mathbf{V}^{*}\end{pmatrix},$ (10.86)

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 singlet 536 Jørgensen P., Jensen H. J. A., Olsen J.
J. Chem. Phys.
(1988), 89, pp. 3654.
and triplet 839 Olsen J., Yeager D. L., Jørgensen P.
J. Chem. Phys.
(1989), 91, pp. 381.
response are available for a variety of operators (see table 10.4).

An additional feature of the general response module is its ability to work with non-orthogonal MOs. In a formulation analogous to TDDFT(MI) 700 Liu J., Herbert J. M.
J. Chem. Phys.
(2015), 143, pp. 034106.
, the linear response for molecular interactions , 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.

• 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.