Ernest R. Davidson

Comment on “Comment on Dunning's correlation-consistent basis sets”

Abstract By using a general linear transformation of Dunnings contracted basis set, the contraction length can be reduced even more than noted in the Comment by Hashimoto et al. With GAUSSIAN 94, this results in a considerable savings in computer time. If one is willing to neglect small coefficients, even greater savings are possible.

One‐electron properties of several small molecules using near Hartree–Fock limit basis sets

Selected one‐electron properties for eight small molecules (H2O, CO, N2, H2S, NH3, PH3, HCl, and HF) have been computed using extended Gaussian basis sets at the SCF and CI levels. The basis sets and CI methodologies were capable of recovering approximately 86% of the estimated total correlation energy (88% of the valence) and, to the best of our knowledge, yielded the lowest variational energies and closest overall agreement with experimentally determined properties to date. Compared to numerical Hartree–Fock properties the current values are generally within 1%, with the largest deviation being 2.6% for δ at the nucleus. The sensitivity of the computed properties to the basis set composition and type of CI are discussed.

A test of the Hirshfeld definition of atomic charges and moments

SummaryThe Hirshfeld population analysis scheme which carves the molecular density into atomic density contributions is tested. This method does not require a reference to basis sets or their respective locations, but is based on a different physical and mathematical footing. The advantage of this method is that, when the molecular deformation density converges to the true solution, the computed net charges will necessarily converge. This method also allows a straightforward definition for “local” moments. About 36 molecules have been used to compute the conventional Mulliken and Löwdin population analyses with STO3G, 6311G** and Dunning-Hay split valence basis sets. These results have been compared to the estimates provided by the Hirshfeld model. The charges found in the Hirshfeld method are smaller than those from the other methods.

Considerations in constructing a multireference second‐order perturbation theory

Several possible definitions for a multireference second‐order perturbation theory are suggested. These are tested against some standard test problems from the literature.

An analysis of the hydrogen bond in ice

In this study, the total self‐consistent field binding energy of a small ice cluster is estimated as the sum of two‐ and three‐body interaction terms. The energy of each term is analyzed using the Morokuma method. Counterpoise calculations were performed to estimate the basis set superposition errors. Additional calculations were done to determine the correlation energy contribution to the total binding energy. Results show that the nearest‐neighbor two‐body components contribute most to the total binding energy, but also that the contiguous three‐body terms must be included to reproduce the total binding energy of the system.

Electron momentum spectroscopy of the valence orbitals of H2O and D2O: Quantitative comparisons using Hartree—Fock limit and correlated wavefunctions

Abstract The large discrepancies found earlier between experimental measurements and calculations based on near Hartree—Fock wavefunctions for the valence orbital electron momentum distributions of H 2 O are reinvestigated. New and improved electron momentum spectroscopy measurements for the valence orbitals of H 2 O and D 2 O, together with existing experimental data, have been placed on a common intensity scale using the binding energy spectra. Investigation of possible vibrational effects by means of new measurements of the momentum distributions of D 2 O indicates no detectable differences with the H 2 O results, within experimental error. A quantitative comparison of these experimental results with both the shapes and magnitudes of momentum distributions calculated in the PWIA and THFA approximations using new, very precise Hartree—Fock (single-configuration) wavefunctions is made. These wavefunctions, which include considerable polarization and which are effectively converged at the HF limit for total energy, dipole moment and momentum distribution permit establishment of basis set independence. The significant discrepancies between theory and experiment which still remain for the momentum distributions of the 1b 1 , 3a 1 and 2a 1 orbitals at the THFA level are largely removed by CI calculations of the full ion—neutral overlap amplitude. These CI wavefunctions for the final ion and neutral ground states, generated from the accurate HF limit basis sets, recover up to 88% of the correlation energy. The present work clearly shows the need for adequate consideration of electron correlation effects in describing the low-momentum parts of the 1b 1 , 3a 1 and 2a 1 electron distributions, a region which is of crucial importance in problems related to chemical bonding and reactivity. The high level of quantitative agreement obtained between experiment and calculations using sufficiently sophisticated wavefunctions provides support for the essential validity of the plane wave impulse approximation as used in the interpretation of EMS experiments on small molecules.

Perturbation theory for open shell systems

Abstract Two new forms of perturbation theory are presented that are applicable to open shell systems. They are based entirely on the restricted open shell Hartree-Fock formalism and can be used on the lowest energy of a given symmetry at that geometry. The methods are compared with other approaches and some test cases are presented.

Super-matrix methods

Abstract Iterative methods for finding a few eigenvalues of very large matrices are reviewed. Some suggestions are given for strategies which should be tried.

Improved algorithms for the lowest few eigenvalues and associated eigenvectors of large matrices

Abstract Some modifications of Davidsons eigenvalue algorithm are discussed and their performances on a number of test cases are assessed. They are found to offer improvements over the original algorithm. A method for solving the equations stemming from the quasi degenerate variational perturbation theory is presented. Solutions can be obtained as simply as with the eigenvalue algorithm for both ground and excited states.

Zero kinetic energy photoelectron spectra of jet‐cooled aniline

Zero kinetic energy electron spectra of aniline are recorded and a number of ion vibrational frequencies accurately measured. The adiabatic ionization potential of aniline is found to be 62 271±2 cm−1. Ab initio calculations provide insights into the bonding changes that take place in aniline upon ionization. Reasonable agreement between calculated and measured frequencies in the ground states of aniline neutral and ion is obtained.