Comparison of local-density and Hartree–Fock calculations of molecular polarizabilities and hyperpolarizabilities

Abstract

This paper presents a comparison between density functional theory local density approximation (LDA) and Hartree–Fock approximation (HFA) calculations of dipole moments, polarizabilities, and first hyperpolarizabilities, using ‘‘comparable’’ basis sets, in order to assess the relative quality of the LDA and the HFA for calculating these properties. Specifically, calculations were done using basis sets of roughly double or triple zeta plus polarization quality, with and without added field-induced polarization (FIP) functions, for the seven small molecules H2, N2, CO, CH4, NH3, H2O, and HF, using the HFA option in the program HONDO8 and the LDA options in the programs DMol and deMon. For the calculations without FIP functions, the results from HONDO8 HFA and deMon LDA, both of which use Gaussian basis sets, are very similar, while DMol, which uses a LDA numerical atomic orbital basis set, gives substantially better results. Adding FIP functions does much to alleviate these observed basis set artifacts and improves agreement with experiment. With FIP functions, the results from the two sets of LDA calculations (deMon and DMol) are very similar to each other, but differ markedly from the HFA results, and the LDA results are in significantly better agreement with experiment. This is particularly true for the hyperpolarizabilities. This appears to be the first detailed study of DFT calculations of molecular first hyperpolarizabilities. We note that closer attention to numerical details of the finite field calculation of β⇊ is necessary than would usually be the case with traditional ab initio methods. A proof that the Hellmann–Feynman theorem holds for Kohn–Sham calculations is included in the Appendix.

A density functional theory study of frequency-dependent polarizabilities and Van der Waals dispersion coefficients for polyatomic molecules

“…These results can be used to estimate the reliability of the dispersion coefficients which will be presented in the remainder of the article. In agreement with previous work, [1][2][3][4] we note that the average polarizability ␣ 0 is generally satisfactory, but somewhat too high. The anisotropies 0 do not show clear systematic deviation.…”

“…For the correct description of such sensitive properties as polarizabilities, it is mandatory to add diffuse functions to the basis. Our first extension of the 3Z2P basis, which we will denote by 3Z2P*, adds the diffuse s, p and d functions with exponents recommended by Zeiss et al 38,4 in the case of the H, F, N, O and C atoms. For the rare gas atoms we follow Colwell et al, 5 by adding diffuse s, p and d functions with exponents which were one third of the smallest exponents used in the standard 3Z2P basis.…”

“…These are either finite field calculations [1][2][3][4] or an implementation of the coupled KohnSham equations. 5,6 To the best of our knowledge, all the calculations of frequency-dependent ͑hyper-͒polarizabilities in DFT until now, have made use of time-dependent DFT in which the Adiabatic Local Density Approximation ͑ALDA͒ is used.…”

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

“…Its time-dependent extension, time-dependent DFT [3][4][5] is not yet that well explored. It was given a firm theoretical basis in 1984, by Runge and Gross 6 and offers the possibility to calculate frequency-dependent response properties, whereas finite-field calculations [7][8][9][10][11] only give access to static properties. Most calculations with time-dependent DFT have been restricted to atoms.…”

Mapping the frontier electronic structures of triphenylamine based organic dyes at TiO2interfaces

“…The time-dependent DFT (TDDFT) calculations of the valence excitations which were performed with the Gaussian 03 program 24 employing the B3LYP hybrid functional 21,25 and triple-zeta valence basis sets including polarization functions 26 to link the information from experiments to the photo-excitation occurring in the solar-cell. To ensure a localization of the core-hole in the case of core-excitations, all other atoms of the same element, as the target of the core-excitation, were described by effective corepotentials.…”