Luis R. Kahn

Ab initio effective core potentials: Reduction of all‐electron molecular structure calculations to calculations involving only valence electrons

A formalism is developed for obtaining ab initio effective core potentials from numerical Hartree–Fock wavefunctions and such potentials are presented for C, N, O, F, Cl, Fe, Br, and I. The effective core potentials enable one to eliminate the core electrons and the associated orthogonality constraints from electronic structure calculations on atoms and molecules. The effective core potentials are angular momentum dependent, basis set independent, and stable against variational collapse of their eigenfunctions to core functions. They are derived from neutral atom wavefunctions using a pseudo‐orbital transformation which is motivated by considerations of the expected accuracy of their use and of basis set economy in molecular calculations. Then the accuracy is demonstrated by multiconfiguration Hartree–Fock calculations of potential energy curves for HF, HCl, HBr, HI, F2, Cl2, Br2, and I2 and one‐electron properties for HF and HBr. The differences between valence‐electron calculations employing the present...

Ab initio studies of AuH, AuCl, HgH and HgCl2 using relativistic effective core potentials

Relativistic effective core potentials (ECP) are derived for Au and Hg atoms, where the ECP incorporates the Coulomb and exchange contributions of the core orbitals, the core‐orthogonality terms for the valence orthogonality terms for the valence orbitals, and the effect of the ’’mass–velocity’’ and ’’Darwin’’ relativistic effects on the valence orbitals. The results of atomic valence‐electron (VE) calculations with the ECP’s compare favorably with relativistic Hartree–Fock and Dirac–Hartree–Fock calculations and with experiment, when the effects of spin–orbit coupling are included in the VE calculations. Nonrelativistic calculations, by contrast, lead to erroneous predictions and to differences in excitation energies of 1.5–3.5 eV. The large relativistic effects in the atoms carry over into the AuH, AuCl, and HgCl2 molecules, as they are important in determining correct bond lengths and bond energies and in influencing the charge distributions. Similarly large relativistic effects are encountered in ioni...

Relativistic effects in ab initio effective core potentials for molecular calculations. Applications to the uranium atom

The procedure of deriving ab initio effective core potentials (ECP) to incorporate the Coulomb and exchange effects as well as orthogonality constraints from the inner core electrons is extended to include the dominant relativistic effects on the valence orbitals. An ab initio approach is then described which enables the valence electrons in heavy atoms to be treated in a standard nonrelativistic manner by including the effect of the relativistic core–valence interactions directly into the ECP. The starting point for this procedure is the Pauli Hartree–Fock relativistic treatment of Cowan and Griffin. The pseudo‐orbital transformation and derivation of the l‐dependent effective core potentials are analogous to the nonrelativistic case with certain modifications. Analytic forms for the pseudo‐orbitals and ECP’s are derived for the U atom, and results of valence electron calculations are presented.

Relationships among derivatives of the integrals in the calculation of the gradient of the electronic energy with respect to the nuclear coordinates

The use of the translational invariance property of molecular integrals is extended by its combination with the closely related transformation properties under infinitesimal rotations. This further reduces the number of truly linearly independent derivatives of the molecular integrals that require calculation in obtaining the gradient of the electronic energy. The detailed linear equations that yield the linearly dependent derivatives in terms of the ’’independent’’ derivatives are presented.

Structure of HIF

The triatomic, inorganic free radical of unknown structure, HIF, is characterized by ab initio correlated many‐body theory. The calculations show that HIF has a bond angle of 137.5±3°, bond lengths R(HI) = 1.64±0.5 A and R(IF) = 2.04±0.5 A, and a ground state of 2A′ symmetry. The computed dissociation energy for the process HIF→IF+H is 25 kcal/mole, while the experimental value is 30. The bonding in HIF is very similar to a noncollinear superposition of the two diatomic molecules HI and IF. Correlated calculations for IF, HI, HF, and the electron affinity of F are also reported. The accuracy of the dissociation energy in HIF directly parallels the accuracy of the F electron affinity.

The theoretical determination of the B 1Πu potential energy curve for Li2

The Li2 B 1Πu potential energy curve has been calculated with a multiconfiguration SCF (MCSCF) wavefunction. Several different types of wavefunctions and basis sets have been examined and their accuracy determined. The most accurate wavefunction used predicts a binding energy of 0.3015 eV (0.08 eV above the experimental value of 0.385 eV) and a potential barrier of 0.0724 eV with its maximum at 10.6 bohr. It is argued that the theoretical value of the barrier is an upper bound to the experimental value. The long range behavior of the potential energy is found to match smoothly onto the form predicted from dispersion forces.

Generalized valence‐bond investigation of the reaction H+Br2 →HBr+Br

Ab initio quantum mechanical calculations have been carried out to predict the H+Br2→HBr+Br potential energy surface. We used ab initio effective core potentials and an extended valence basis set including polarization functions on each center and carried out open‐shell self‐consistent‐field calculations in the generalized valence bond–perfect‐pairing (GVB–PP) approximation. The orbitals of this calculation were used as a starting point for eight‐configuration–configuration‐interaction (GVB–CI) calculations. The CI calculations not only bring in electron correlation effects but also make up to a large extent the inability of the GVB–PP calculation to adequately treat the recoupling of orbitals which occurs near the transition state. The classical barrier height is predicted to be about 12 kcal mole−1 by the GVB–PP calculations and about 3.0 kcal mole−1 by the GVB–CI calculations. The latter value is in reasonable agreement with the experimental Arrhenius activation energy. The saddle point is predicted fr...

The accuracy of first‐order density matrices obtained by electronic structure methods involving the valence electrons only

First‐order density matrices are obtained from all‐electron unrestricted‐Hartree–Fock (UHF) calculations and from effective‐core‐potential valence‐electron UHF calculations for the silicon and argon atoms, and for the Si2 molecule. The density matrices are compared by means of their derived X‐ray scattering factors, directional Compton profiles, and the charge density, at selected points in k and r space.

Spin‐dependent effective core potentials for Ni++

Ni ions assume a divalent charge state in crystalline NiO. To facilitate SCF calculations on NiO clusters, we have derived effective core potentials to represent the Ni++ ion core. Different potentials were obtained for a valence electron with spin parallel and for one with spin antiparallel to the core spin. The potentials were tested in calculations for Ni ions and for a NiO molecule embedded in a matrix of point charges. Comparison is made where possible with previous all‐electron calculations and with experiment. The present pseudopotentials afford some prospects for realistic calculations of anion–anion interionic forces in NiO.