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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.

The pseudorotation of tetrahydrofuran (THF) (C4H8O) has been studied using density functional theory, with respect to the valence orbital responses to the ionization potentials and to orbital electron and momentum distributions. Three conformations of THF, the global minimumstructure Cs, local minimum structure C2, and a transition state structure C1, which arecharacteristic configurations on the potential energy surface, are examined using the SAOP∕et-pVQZ//B3LYP∕6-311++G** models with the aforementioned dual space analysis. It is noted in the ionization energy spectra that the minimum structures Cs and C2 are not directly connected by pseudorotation, but through the transition state structure C1. As a result, some orbitals of the Cs conformer are able to “correlate” to orbitals of the C2 conformer without a strict symmetry constraint, i.e., orbital 7a′ of the Cs conformer is correlated to orbital 5b of the C2 conformer. It is also noted that although the valence orbital ionization potentials are not significantly altered by the pseudorotation of THF, their spectra (mainly due to excitation) are quite different indeed. Detailed orbital analysis based on dual space analysis is given. The valence orbital behavior of the conformations is orbital dependent. It can be approximately divided into three groups: the “signature group” is associated with orbitals experiencing significant changes. The frontier orbitals are in this group. The “nearly identical group” includes orbitals without apparent changes across the conformations. Most of the orbitals showing a certain degree of distortion during the pseudorotation process belong to the third group. The present study demonstrates that a comprehensive understanding of the pseudorotation of THF and its dynamics requires multidimensional information and that the information gained from momentum space is complementary to that from the more familiar coordinate space.

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