Krzysztof Wolinski

Self-consistent perturbation theory: Open-shell states in perturbation-dependent non-orthogonal basis sets This work was partly supported by the Institute of Low Temperatures and Structure Research of the Polish Academy of Sciences under contract No. MR-I.9.4.3/2.

The density matrix form of Hartree-Fock perturbation theory is developed for the case in which the basis functions themselves are perturbation-dependent. Energy expressions are derived, through second order, for both single and double perturbations. The theory is applied in the calculation of electric dipole polarizabilities and hyperpolarizabilities for atoms (He, Be) and molecules (H2, LiH), with excellent results. The high computational efficiency of the method is discussed and possibilities of further development are outlined.

Second-order Møller–Plesset calculations with dual basis sets

Following the pioneering work of Jurgens-Lutovsky and Almlof [Chem. Phys. Lett. 178, 451 (1991)], a second-order Moller–Plesset program was developed which allows the use of a large basis set for the pair correlation functions and a more modest one for the self-consistent field (SCF) orbitals. For several test systems, correlation energies closely approximate the results of a large basis set calculation, at substantial savings. The SCF energy of the large basis set calculation can also be estimated using perturbation theory.

Efficient calculation of canonical MP2 energies

Abstract An efficient canonical second-order Moller–Plesset theory (MP2) procedure, based on the Saebo–Almlof integral–direct transformation technique, coupled with efficient prescreening of the atomic orbital (AO) integrals, is described. For large molecules, a fraction of the AO integrals suffices to produce energies to microhartree accuracy. Calculations up to 1800 basis functions and 240 correlated electrons have been performed on a single processor computer for symmetrical molecules. Calculations with ∼1000 basis functions and ∼120 electrons can be performed routinely for molecules with no symmetry. However, scaling of the second half transformation is still steep. Several basis sets used in correlated calculations are compared for economy and performance.

Molecular quadrupole moments

The performance of recently developed medium-size polarized basis sets in calculations of molecular quadrupole moments is examined at the SCF and correlated levels of approximation. The results for a series of small molecules are in good agreement with the data from large basis set calculations and with the experimental values. The computational approach suggests in this paper for calculations of molecular quadrupole moments is used to obtain trustworthy data for CH3OH, HCOOH and HCONH2. The magnitude and origin of the electron correlation contribution to molecular quadrupole moments and their implications for interaction potentials are discussed.

Polarized basis sets and the calculation of infrared intensities from nuclear electric shielding tensors

The idea of the basis set polarization which follows from the known dependence of basis set functions on the perturbation strength is applied to the calculation of the dipole moment derivatives with respect to nuclear displacements. The differentiation of the dipole moment function is replaced by the straightforward evaluation of derivatives of the intramolecular electric field with respect to the external electric field strength. The method and its efficiency are illustrated by a series of calculations of the dipole moment derivatives for the water molecule. Already a polarized basis set of 26 CGTOs derived from the minimal CGTO basis set provides fairly reasonable results.

Electric-field-variant orbitals. EFV GTO basis set for quadrupole polarizability calculations

Abstract The concept of electric-field-variant (EFV) gaussian-type bases is extended to an external field-gradient perturbation. The corresponding EFV GTO set si obtained from the original GTOs by the appropriate perturbation-dependent modification of orbital exponents. The efficiency of this basis set is illustrated by the calculation of the quadrupole polarizabilities of H, He and Be. The results are nearly as accurate as the best CHF data. The possibility of molecular calculations using field-gradient dependent EFV GTO bases is also discussed.

An efficient atomic orbital based second-order Møller–Plesset gradient program

Based on the orbital-invariant atomic orbital formulation of the MP2 (Møller-Plesset second-order perturbation theory) energy and gradient [P. Pulay and S. Saebø, Theor. Chim. Acta 69, 357 (1986)], we have derived and programmed detailed working equations for closed-shell MP2 gradients. The orbital-invariant form avoids the difficulties of other formulations with frozen orbitals, and allows the use of arbitrary occupied orbitals, an important consideration for local correlation theories, although the present program uses canonical molecular orbitals. The atomic orbital formulation offers savings both in storage and computer time. Test calculations on systems containing up to approximately 100 atoms and approximately 1000 basis functions, performed on a single personal computer, are reported. Parallelization of the code is underway.

Theoretical determination of the 1H NMR spectrum of ethanol

GIAO calculations of the 1H NMR chemical shifts for ethanol at the SCF and DFT levels of theory are presented. The importance of molecular geometry and basis set is discussed. Vibrational correction to the hydroxyl proton chemical shift is also considered in calculations for the monomer of ethanol. The final theoretical results for the monomer obtained at the optimized DFT/B3LYP/6-311G(d,p) geometry with the 6-311G++ (d,p) basis set for NMR are in very good agreement with gas phase experimental data. For the liquid phase ethanol the hydrogen bonding effects are taken into account by performing calculations on various clusters of ethanol. It is shown that inaccuracy due to molecular geometry and basis set in the monomer of ethanol is magnified significantly in calculations for its clusters. In this context the structure of liquid ethanol as predicted recently by quantum cluster equilibrium (QCE) theory is discussed.

Evaluation of the multipole-induced-multipole model: incremental dipole polarizabilities in the CH4…He system

The validity of the multipole-induced-multipole (MIM) model as applied to the intensity of collision induced rotational Raman scattering is examined in terms of directly calculated incremental dipole polarizabilities for the CH4…He system. The results of HFSCF and MBPT calculations are compared with the MIM data determined by using the dipole and dipole-quadrupole polarizabilities computed in this study at the level of the fourth order MBPT approximation. It is concluded that the long range interaction model may be sufficient for the determination of molecular dipole-quadrupole polarizabilities from the Raman scattering data. However, the determination of the next term in the MIM expansion will considerably suffer from the neglect of the valence repulsion contribution.

On the reliability of the MINDO/3 dipole moment derivatives☆

Abstract The applicability of the MINDO/3 method for theoretical prediction of IR intensities is examined. Calculated MINDO/3 dipole moment derivatives with respect to internal symmetry coordinates are compared with CNDO/2 and experimental data. Usually the MINDO/3 method leads to dipole moment derivatives of the correct magnitudes but in some cases it also completely fails to predict the right result. The observed discrepancies for CH 3 F and C 2 H 4 are analysed by a comparison of the MINDO/3 and the CNDO/2 density matrices. It follows that the MINDO/3 method may not correctly describe the details of electron density distributions, though the calculated total dipole moments are quite reasonable. It is concluded that, in spite of relatively correct MINDO/3 molecular geometries and force fields, the application of this method for the prediction of IR intensities requires some care.