# SEARCH

** Linear response function energy **

The linear response functions (LR) nowadays are amply used both in gas phase and in solution for the characterization of excited states and of molecular properties. The complete equivalence between SS and LR results for the excitation energies was universally accepted, but recently it was shown (Cammi et al. 2005 Corni et al. 2005 Kongsted et al. 2002) that this equivalence is valid only in vacuo, and that LR results can be seriously in error in solution. A computational strategy to reduce this error was proposed (Caricato et al. 2006 Improta et al. 2006), efficient enough to allow the exploitation of the less expensive LR scheme. [Pg.1047]

The poles of the quadratic response function are the same as those of the linear response functions, i.e. the excitation energies of the system. This is also the case for the cubic response function which, furthermore, has the same kind of residues as the quadratic response function. [Pg.210]

The damped linear response function computed from the real part of Eq. 5 JO with the indicated values of the broadening F (corresponding to 0,250, 500,1,000, and 2,000 cm ). Electric dipole transition moments and excitation energies were obtained using CCSD for the hydrogen molecule with the aug-cc-pVDZ basis set [Pg.144]

In the last section we have derived an expression for the linear response function or polarization propagator in the frequency domain, Eq. (3.110). However, application of this expression requires that one knows all unperturbed excited states of the system and their energies En or the excitation energies En — od corresponding [Pg.57]

There are several possible ways of deriving the equations for TDDFT. The most natural way departs from density-functional perturbation theory as outlined above. Initially it is assumed that an external perturbation is applied, which oscillates at a frequency co. The linear response of the system is then computed, which will be oscillating with the same imposed frequency co. In contrast with the standard static formulation of DFPT, there will be special frequencies cov for which the solutions of the perturbation theory equations will persist even when the external field vanishes. These particular solutions for orbitals and frequencies describe excited electronic states and energies with very good accuracy. [Pg.33]

Linear response function approaches were introduced into the chemistry literature about thirty years ago Ref. [1,2]. At that time they were referred to as Green functions or propagator approaches. Soon after the introduction it became apparent that they offered a viable and attractive alternative to the state specific approaches for obtaining molecular properties as excitation energies, transition moments and second order molecular properties. [Pg.112]

A comparative study has been performed on electronic spectra of tetrazine, using on one hand density functional linear response theory and on the other multifunctional second-order perturbation theory, in order to establish the accuracy that the density functional-based methods can give for excitation energies and energy surfaces for excited states <1999MP859>. [Pg.644]

We would like to stress the similarity between Eqs. (5) and (18). The main difference is that the poles of the linear response function are excitation energies rather than energy eigenvalues (c./. Eq. (11)) but in both cases, the residues correspond to transition moments between the ground state and excited states. The two-step procedure for evaluating the linear response function is now (c.f. Eqs. (6) and (7) ) solve [Pg.79]

** Linear response function energy **

© 2019 chempedia.info