Improved density functional theory results for frequency-dependent polarizabilities, by the use of an exchange-correlation potential with correct asymptotic behavior.

The exchange‐correlation potentials vxc which are currently fashionable in density functional theory (DFT), such as those obtained from the local density approximation (LDA) or generalized gradient approximations (GGAs), all suffer from incorrect asymptotic behavior. In atomic calculations, this leads to substantial overestimations of both the static polarizability and the frequency dependence of this property. In the present paper, it is shown that the errors in atomic static dipole and quadrupole polarizabilities are reduced by almost an order of magnitude, if a recently proposed model potential with correct Coulombic long‐range behavior is used. The frequency dependence is improved similarly. The model potential also removes the overestimation in molecular polarizabilities, leading to slight improvements for average molecular polarizabilities and their frequency dependence. For the polarizability anisotropy we find that the model potential results do not improve over the LDA and GGA results. Our method for calculating frequency‐dependent molecular response properties within time‐dependent DFT, which we described in more detail elsewhere, is summarized

Erratum: “Calculating frequency-dependent hyperpolarizabilities using time-dependent density functional theory” [J. Chem. Phys. 109, 10644 (1998)]

An accurate determination of frequency-dependent molecular hyperpolarizabilities is at the same time of possible technological importance and theoretically challenging. For large molecules, Hartree–Fock theory was until recently the only available ab initio approach. However, correlation effects are usually very important for this property, which makes it desirable to have a computationally efficient approach in which those effects are (approximately) taken into account. We have recently shown that frequency-dependent hyperpolarizabilities can be efficiently obtained using time-dependent density functional theory. Here, we shall present the necessary theoretical framework and the details of our implementation in the Amsterdam Density Functional program. Special attention will be paid to the use of fit functions for the density and to numerical integration, which are typical of density functional codes. Numerical examples for He, CO, and para-nitroaniline are presented, as evidence for the correctness of the equations and the implementation.<br/

Response calculations based on an independent particle system with the exact one-particle density matrix: Excitation energies

Adiabatic response time-dependent density functional theory (TDDFT) suffers from the restriction to basically an occupied → virtual single excitation formulation. Adiabatic time-dependent density matrix functional theory allows to break away from this restriction. Problematic excitations for TDDFT, viz. bonding-antibonding, double, charge transfer, and higher excitations, are calculated along the bond-dissociation coordinate of the prototype molecules

Accurate density functional calculations on frequency-dependent hyperpolarizabilities of small molecules

In this paper we present time-dependent density functional calculations on frequency-dependent first (β) and second (γ) hyperpolarizabilities for the set of small molecules,

Construction of the Foldy-Wouthuysen transformation and solution of the Dirac equation using large components only

It is shown that it is possible to construct, within the framework of a basis set expansion method, the full Foldy–Wouthuysen transformation (i.e., to all orders in the inverse velocity of light) for an arbitrary potential once the Dirac equation has been solved. On this basis an iterative procedure to solve the Dirac equation is suggested that involves only the large component, obviating the time‐consuming (at least in molecular calculations) introduction of large basis sets for a proper description of just the small components. The methods are used to compare the expectation value of the radial distance operator in the Dirac picture and in the Schrödinger picture for the orbitals of the Uranium atom