Douglas J. Fox

Gaussian‐1 theory: A general procedure for prediction of molecular energies

A general procedure is developed for the computation of the total energies of molecules at their equilibrium geometries. Ab initio molecular orbital theory is used to calculate electronic energies by a composite method, utilizing large basis sets (including diffuse‐sp, double‐d and f‐polarization functions) and treating electron correlation by Mo/ller–Plesset perturbation theory and by quadratic configuration interaction. The theory is also used to compute zero‐point vibrational energy corrections. Total atomization energies for a set of 31 molecules are found to agree with experimental thermochemical data to an accuracy greater than 2 kcal mol−1 in most cases. Similar agreement is achieved for ionization energies, electron and proton affinities. Residual errors are assessed for the total energies of neutral atoms.

The shape‐driven graphical unitary group approach to the electron correlation problem. Application to the ethylene molecule

A new method for the approximate solution of Schrodinger’s equation for many electron molecular systems is outlined. The new method is based on the unitary group approach (UGA) and exploits in particular the shape of loops appearing in Shavitt’s graphical representation for the UGA. The method is cast in the form of a direct CI, makes use of Siegbahn’s external space simplifications, and is suitable for very large configuration interaction (CI) wave functions. The ethylene molecule was chosen, as a prototype of unsaturated organic molecules, for the variational study of genuine many (i.e.,≳2) body correlation effects. With a double zeta plus polarization basis set, the largest CI included all valence electron single and double excitations with respect to a 703 configuration natural orbital reference function. This variational calculation, involving 1 046 758 spin‐ and space‐adapted 1Ag configurations, was carried out on a minicomputer. Triple excitations are found to contribute 2.3% of the correlation ene...

Analytic second derivative techniques for self-consistent-field wave functions. A new approach to the solution of the coupled perturbed hartree-fock equations

Abstract A new method for the solution of the coupled perturbed Hartree-Fock equations is outlined which avoids the four-index transformation of electron repulsion integrals. This allows the extension of analytic energy second derivative methods to large molecular systems. The new approach has been implemented for both closed- and open-shell molecules and a number of test cases considered, including as many as 96 contracted gaussian basis functions. The time required for the determination of all cartesian force constants varies from 8% to 65% of that required for analytic gradient techniques.

Analytic second derivatives for Renner–Teller potential energy surfaces. Examples of the five distinct cases

Force constants at Renner–Teller stationary points fall into five distinct categories, which are readily explored using recently developed analytic energy second derivative methods. The nature of the Renner–Teller effect has been derived using symmetry principles and many‐electron perturbation theory. By considering the BH2, CH2, NH2, and CuH2 molecules, examples of all five cases are illustrated via ab initio molecular electronic structure theory.

Analytic energy second derivatives for general MCSCF wave functions

Expressions for the determination of analytic energy second derivatives for general MCSCF wave functions are presented. Equations for two distinct approaches: (1) direct differentiation of the energy expression and associated Lagrangian condition; and (2) power series expansion of the Hamiltonian and exponential‐i‐lambda transformation of the wave function, are developed. The problem of the nonzero nullity of the Hessian, and the resultant existence of redundant variables in the coupled perturbed multiconfiguration Hartree Fock (CPMCHF) equations, is discussed and a straightforward solution proposed. The viability of the methods presented in this paper are illustrated by a sample calculation on formaldehyde, using a double zeta (DZ) basis set and including 325 MCSCF configurations in the state space.

Analytic energy second derivatives for general correlated wavefunctions, including a solution of the first-order coupled-perturbed configuration-interaction equations

Abstract The first theoretical method for the analytic determination of energy second derivatives for configuration-interaction wave-functions is presented. Several test cases are reported, the largest being an 8385 configuration formaldehyde wavefunction.

Computing molecular electrostatic potentials with the PRISM algorithm

Abstract The PRISM integral algorithm has been applied to the computation of the ab initio molecular electrostatic potential and its derivatives. Implementational details which are relevant to the additional efficiency of the algorithm in the electrostatic case are discussed. On a range of machines, CPU timings of the PRISM electrostatic properties program, which is included in the GAUSSIAN 92 quantum chemistry package, reveal a dramatic performance increase (in some cases more than two orders of magnitude) over other commonly used electrostatic programs (GAUSSIAN 90, GAMESS, MOPAC ESP, CHELPG). In addition, timings are reported for a particularly large electrostatic potential evaluation job on the six base-pair oligonucleotide CTCGAG (C 116 H 138 N 46 O 68 P 10 10− .

THE PROTOTYPE ALUMINUM - CARBON SINGLE, DOUBLE, AND TRIPLE BONDS: Al - CH3, Al = CH2, AND Al. = CH

U3L - 10871 Preprint Submitted to The Journal of Chemical Physics THE PROTOTYPE ALUMINUM - CARBON SINGLE, DOUBLE, AND TRIPLE BONDS: Aft - CH 3, Aft ::: CH 2 , and Aft :: CH Douglas . Fox, Douglas Ray, Philip C. Rubesin, and Henry F. Schaefer, III Prepared for the U.S. Department of Energy under Contract W-7405-ENG-48 t!.

Electronic symmetry breaking in polyatomic molecules. Multiconfiguration self‐consistent field study of the cyclopropenyl radical C3H3

For equilateral triangle geometries (point group D3h), the C3H3 radical has a degenerate 2E″ electronic ground state. Although the 2A2 and 2B1 components separate in energy for C2v geometries, these two components should have identical energies for equilateral triangle structures. In fact, when approximate wave functions are used and the orbitals not required to transform according to the D3h irreducible representations, an energy separation between the 2A2 and 2B1 components is observed. At the single configuration self‐consistent field (SCF) level of theory this separation is 2.8 kcal with a double‐zeta basis set and 2.4 kcal with double‐zeta plus polarization. It has been demonstrated that this spurious separation may be greatly reduced using multiconfiguration self‐consistent field (up to 7474 variationally optimum configurations) and configuration interaction (up to 60 685 space and spin adapted configurations) techniques. Configurations differing by three and four electrons from the Hartree–Fock ref...

An improved criterion for evaluating the efficiency of two-electron integral algorithms

Abstract We present a general criterion for theoretical performance assessment of algorithms for two-electron integral computation which is appropriate for most modern computers. The new prescription is to minimize the total number of memory references in the algorithm, as opposed to the traditional approach of minimizing the total number of floating-point operations. CPU timings on a range of machines demonstrate that memory operations are better correlated to machine cycles than are floating-point operations.