Geerd H. F. Diercksen

Methods in computational molecular physics

Molecular Integrals for Gaussian Type Functions.- On the Evaluation of Exponential (Slater) Type Integrals.- Basis Sets.- Matrix Eigenvector Methods.- Group Theory Applied to CI Methods.- The Multiconfigurational (MC) SCF Method.- The Direct CI Method.- Pair Correlation Theories.- On a Greens Function Method for the Calculation of Ionization Spectra in the Outer and Inner Valence Region.- Introductory Polarization Propagator Theory.- Diagrammatic Many-Body Perturbation Theory.- Schrodinger Spectra.- Computers and Computation in Molecular Physics.- Participants.

Self‐Consistent Perturbation Theory. II. Extension to Open Shells

The self‐consistent perturbation theory developed in earlier papers is extended to the open‐shell case. Density matrices for both shells are calculated iteratively until first‐order self‐consistency is achieved. A numerical application indicates the importance of considering both shells separately when discussing the effects of polarization on the charge density and the spin density.

SCF-CI studies of correlation effects on hydrogen bonding and ion hydration

Previous single-determinant Hartree-Fock studies on the equilibrium structures and stabilities of H2 O, H3 O+ as well as of the monohydrated ionic systems Li+ · H2O, F− · H2O and the hydrogen bonded water dimer, H2 O · HOH, are extended by large scale configuration interaction calculations including all the possible single and double excitations arising from the canonical set of Hartree-Fock molecular orbitals. The correlation energy effects on the equilibrium geometrical parameters of the systems under consideration are found to be quite small. The contributions of the correlation energy to the total binding energies of the weakly interacting composed systems are obtained to be of the order of 1 kcal/mole, leading to a considerable increase of the hydrogen bond strength in F− · H2O and H2O · HOH and to a small decrease of the binding energy in Li+ · H2 O. The observed strengthening of the hydrogen bonding interaction due to correlation is shown to be partly compensated by the change in the vibrational zero-point energy of the composed systems compared to the non-interacting subsystems. Approximate force constants corresponding to the intersystem vibrations in Li+ · H2O, F− · H2 O, and H2O · HOH are deduced from the calculated potential curve data on the SCF and the CI level of accuracy.

Self‐Consistent Perturbation Theory. I. General Formulation and Some Applications

The self‐consistent perturbation theory developed in an earlier paper is formulated more explicitly and applied to various types of perturbation: (i) one‐element change of the one‐electron Hamiltonian matrix (i.e., of Coulomb or resonance integral), (ii) uniform electric field, (iii) point charge near the system. The applications are to π‐electron systems, where the results have considerable chemical interest.

Correlation effects in the ionization of hydrocarbons

The spectral intensity for ionization as a function of binding energy for the valence electrons of ethylene, allene, butatriene, trans‐butadiene, acetylene, benzene, methane, ethane, and cyclopropane is computed by a many‐body Green’s function method. The results are used to interpret unidentified structures in experimental ionization spectra. For the ionization out of the inner valence orbitals of the unsaturated molecules the spectral intensity is found to be distributed over several lines, in sharp contrast to the ionization out of the inner valence orbitals of the saturated molecules where the greater part of the intensity appears in one main line. The reasons for this behavior are discussed. It is also found that there is a correspondence between the behavior of the spectral intensity in the inner valence region and the satellite structure in the outer valence region. For C6H6, C4H4, and C4H6 interesting satellite lines of considerable intensity are predicted to be situated in the outer valence regio...

On the accuracy of ionization potentials calculated by Green’s functions

A many‐body Green’s function method is used to calculate vertical valence ionization potentials to high accuracy for the atoms and molecules Ne, N2, F2, CO2, P2, H2O, and H2S. Large basis sets including several sets of polarization functions are used in the calculations to reach the limit of the presently achievable accuracy for molecular systems. The maximum errors in the computed ionization potentials are 0.1 to 0.25 eV depending on the molecule and the basis set. The results are extremely stable, when large basis sets are used. Comparison with other methods is made.

Legitimate calculation of first-order molecular properties in the case of limited CI functions. Dipole moments

Abstract Two alternative definitions for the calculation of first-order properties from limited CI functions are discussed. It is argued that computing the first-order properties by the differentiation of the perturbed CI energy is more appropriate than using the Hellmann—Feynman theorem. The energy derivative definition of the first-order properties corrects the Hellmann—Feynman results for an incomplete variational treatment of the perturbation effects. The additional term which is referred to as the Brillouin correction is computed for the dipole moments of FH, H 2 O, NH 3 and CO using the CI functions involving single and double substitutions with respect to the HF determinant. It is shown that the Brillouin correction gives a substantial contribution to the dipole moment of the CO molecule. This indicates that it may be fortuitous that some data previously calculated from CI functions by using the Hellmann-Feynman theorem are close to the experimental value. The structure of the Brillouin correction is analysed in terms of the diagrammatic expansion of the correlation corrections to the first-order properties. Additionally, some rough estimates of the influence of the unlinked diagrams are obtained by computing the so-called corrections due to Davidson and Siegbahn.

Rotational excitation of CO by He impact

Abstract To study rotational excitations of CO by He impact, configuration-interaction potential energy surfaces have been computed with two different basis sets. The surfaces are compared to one another, to an electron-gas surface, and to an experimentally determined surface. In addition, converged close-coupling calculations of the collision cross sections have been done on these surfaces for energies up to 100 cm −1 and compared. On the most accurate CI surface, cross sections have been computed using the infinite-order sudden (IOS) and quasi-classical methods as well.

The electronic structure of molecules by a many-body approach: II. Ionization potentials one-electron properties of pyridine and phosphoridine

Abstract The valence ionization potential (IPs) of pyridine and phosphoridine are studied by an ab initio many-body approach which includes the effects of electron correlation and reorganization beyond the Hartree-Fock approximation. For pyridine the order of the first three IPs is a 2 (π), a 1 (n), b 1 (π), but the IPs of the a 2 and a 1 orbitals are so close together that they have to be regarded as identical in binding energy, which is also concluded from experiment. Whereas for pyridine the ordering of the IPs calculated in the HF approximation is incorrect, it is correct for phosphoridine. For this latter molecule the first three ionization potentials are due to ionization from the b 1 (π), a 2 (π), and a 1 (n) orbitals. Several one-electron properties are calculated and compared with experimental and other theoretical data. The localized molecular orbitals are discussed as well.

Perturbation theory of the electron correlation effects for atomic and molecular properties. Second‐ and third‐order correlation corrections to molecular dipole moments and polarizabilities

The many‐body perturbation theory is applied for the calculation of the second‐ and third‐order correlation corrections to the SCF HF dipole moments and polarizabilities of FH, H2O, NH3, and CH4. All calculations are performed by using the finite‐field perturbation approach. The pertinent correlation corrections follow from the numerical differentiation of the second‐ and third‐order field‐dependent correlation energies. This computational scheme corresponds to a completely self‐consistent treatment of the perturbation effects. The third‐order corrected dipole moments are in excellent agreement with the experimental data and the best results of other authors. A comparison of the present perturbation corrections for polarizabilities with the PNO–CI and CEPA results of Werner and Meyer reveals that some cancellation of the third‐ and fourth‐order correlation contributions can be expected. The second‐order corrected polarizabilities are as a rule better than the results of the third‐order perturbation approa...