Graham S. Chandler

Contracted Gaussian basis sets for molecular calculations. I. Second row atoms, Z=11–18

Contracted Gaussian basis sets for molecular calculations are derived from uncontracted (12,8) and (12,9) sets for the neutral second row atoms, Z=11–18, and for the negative ions P−, S−, and Cl−. Calculations on Na...2p63p, 2P and Mg...2p63s3p, 3P are used to derive contracted Gaussian functions to describe the 3p orbital in these atoms, necessary in molecular applications. The derived basis sets range from minimal, through double‐zeta, to the largest set which has a triple‐zeta basis for the 3p orbital, double‐zeta for the remaining. Where necessary to avoid unacceptable energy losses in atomic wave functions expanded in the contracted Gaussians, a given uncontracted Gaussian function is used in two contracted functions. These tabulations provide a hierarchy of basis sets to be used in designing a convergent sequence of molecular computations, and to establish the reliability of the molecular properties under study.

Second row homopolar diatomic molecules. Potential curves, spectroscopic constants, and dissociation energies at the basis set limit for SCF and limited CI wave functions

Single configuration SCF calculations near the HF limit and CI calculations have been performed for the ground and selected excited states of the molecules Al+ 2 , Al2, Si+ 2 , Si2, P+ 2 , P2, S+ 2 , S2, Cl+ 2 , and Cl2. The CI calculation includes single and interacting double excitations from the valence orbitals of the single HF configuration. Potential energy curves from HF and CI wave functions, and with corrections for quadruple excitations, have been obtained for regions near the equilibrium bond lengths. Equilibrium bond lengths and vibrational separations for v=0–3 are calculated from these curves. Calculated ionization potentials are reported. Dissociation energies are calculated by determining the energies of the separated fragments in separate atomic calculations at the same level as the molecular calculations. The calculations are critically evaluated with emphasis on obtaining guide lines for more accurate work.

Computed self‐consistent field and singles and doubles configuration interaction spectroscopic data and dissociation energies for the diatomics B2, C2, N2, O2, F2, CN, CP, CS, PN, SiC, SiN, SiO, SiP, and their ions

Single configuration self‐consistent field (SCF) calculations near the Hartree–Fock limit, and singles and doubles configuration‐interaction (CI)(SDCI) calculations from this single SCF configuration have been performed for the ground and selected excited states of the molecules B2+, B2, C2+, C2, N2+, N2, O2+, O2, F2+, F2, CN, CN−, CP, CS, PN, SiC, SiC−, SiN, SiN−, SiO, and SiP. Potential energy curves, with Davidson corrections, have been obtained around equilibrium separations. Equilibrium bond lengths, vibrational energies, ionization potentials, and dissociation energies are reported.Single configuration self‐consistent field (SCF) calculations near the Hartree–Fock limit, and singles and doubles configuration‐interaction (CI)(SDCI) calculations from this single SCF configuration have been performed for the ground and selected excited states of the molecules B2+, B2, C2+, C2, N2+, N2, O2+, O2, F2+, F2, CN, CN−, CP, CS, PN, SiC, SiC−, SiN, SiN−, SiO, and SiP. Potential energy curves, with Davidson corrections, have been obtained around equilibrium separations. Equilibrium bond lengths, vibrational energies, ionization potentials, and dissociation energies are reported.

Wavefunctions derived from experiment. IV. Investigation of the crystal environment of ammonia

Constrained Hartree-Fock calculations have been performed to obtain wavefunctions that reproduce experimental X-ray structure-factor magnitudes for crystalline NH3 to within the limits of experimental error. Different model densities using both a single molecule and clusters of NH3 in the calculation of X-ray structure-factor magnitudes have been examined. The effects of the crystalline lattice on the experimental wavefunction of the NH3 unit can be reproducibly recovered. The construction of structure-factor magnitudes based on normally distributed random perturbations of the experimental values has also been used to gauge the accuracy of integrated atomic properties obtained from the wavefunctions, the point at which the constraint procedure should be terminated, and the approximate error in the experimental sigma(k) values.

Unitary group approach to reduced density matrices

A fully spin‐adapted approach to many‐electron density matrices is developed in the context of the unitary group approach to many‐electron systems. An explicit expression for the single‐electron spin‐density operator, as a polynomial of degree two in the orbital U(n) generators, is derived for the case of spin‐independent systems. Extensions to spin‐dependent systems are also considered, leading to the appearance of total‐spin transition densities, whose general properties are investigated. A corresponding formalism for the two‐electron density matrix, which is capable of further generalization, is also developed. The results of this paper, together with recent developments on the matrix elements of the U(2n) generators in the electronic Gel’fand basis, afford a versatile method for the direct calculation of one‐ and two‐body density matrices in the unitary group approach framework.

Can a multipole analysis faithfully reproduce topological descriptors of a total charge density

Total charge densities rho(r) of solid NH(3) have been derived using an ab initio crystalline molecular-orbital approach and also from multipole refinement of the structure factors obtained from the same charge density. Comparison of the topological features of these charge densities, as defined by the quantum theory of atoms in molecules, has been used to probe the ability of the multipole analysis to reproduce exactly known total charge-density distributions. For the most part, multipole refinement satisfactorily returns the features of the original density, although the fit to theoretical data is not as good as that to the experimental data. The one topological parameter that is poorly reproduced is the Laplacian nabla (2)rho(r(b)) at NH bond critical points.

Spin Density and Bonding in the CoCl

We report improvement in the precision of certain of the polarized neutron diffraction data for Cs3CoCl5. The improvement allows us to analyse the data using a chemically based model of the spin-density distribution that is equivalent to a conventional multipole treatment to fourth order on the cobalt, and to second order on the chlorine atoms of the CoCl2–4 ion. To test the completeness of the model and to understand the meaning of the parameters in terms of the wavefunction, we have used it to analyse a set of theoretical magnetic structure factors. These are obtained from the wave-function of a Hartree–Fock calculation on the CoCl2–4 ion. We obtain an excellent fit to the theoretical ‘data’ and a much improved fit to the experimental data when the new model is used. We confirm the main features of the spin- and charge-density distributions deduced in our previous study, and we are now also able to interpret the experimental parameters in terms of the wavefunction by analogy with the fit to the theoretical data. We find that there is ca. 3 % of the total spin delocalized onto each chlorine atom of the CoCl2–4 ion, dominantly via σ - rather than π-bonding. There is a well defined diffuse spin density on the cobalt atom of 4p symmetry, and strong evidence for 3d–4p mixing. The spin density, in this almost cubic ion, has distinct non-cubic symmetry, which may arise from longer-range effects due to the rest of the tetragonal crystal.

^{2-}_4

Abstract The measurement of X-ray diffraction from crystals of (ND 4 ) 2 Cu(SO 4 ) 2 ·6D 2 O at 9 K gives a set of Bragg intensities as the basic observable. It is shown that ab initio quantum-mechanical calculations on individual isolated ions, near the Hartree—Fock limit, based on nuclear positions from a neutron diffraction experiment, when assembled into the crystal unit cell, reproduce the data set for the complex at a level close to the experimental error limits. This is accomplished using only four adjustable parameters related to the experimental details. Our procedure avoids the biasing effects of multipole models, of which a typical one used one hundred and eighty four parameters.

Ion in Cs

Neglect of differential overlap methods are treated as approximations to calculations in a symmetrically orthogonalized basis. The accuracy of this approximation is investigated in terms of a power series expansion of the overlap matrix. TheS-matrix can be transformed into a matrix which will give a convergent series, and this series is used in the examination. The only approximation having any justification from this point of view is the NDDO method and even this neglects certain important three-electron integrals. Corrected expressions for the repulsion integral scaling factors introduced by Chandrasekharet al. are also derived.

_3

Spin–orbit interaction plays a significant role in determining the magnetic density in some transition metal complexes. We present a new ab initio technique, based on an extension of unrestricted Hartree–Fock theory, which includes nonperturbatively these spin–orbit effects, and simultaneously also the effects of a finite magnetic field. We also present a new and efficient method for calculating magnetic structure factors, based on the current density rather than magnetic dipole moment density, for a crystal composed of noninteracting molecular fragments. These structure factors are directly comparable to polarized neutron diffraction experiments. Results for the Cs3CoCl5 crystal are compared with experiment and previous studies. Without one‐electron spin–orbit coupling terms, the magnitudes of the predicted structure factors are on average 10–15 % too low, whereas, with the spin–orbit terms, the magnitudes are 25–30% too high. Using an effective nuclear charge for Co in the spin–orbit term brings the res...