Roland Wiest

A program system for ab initio MO calculations on vector and parallel processing machines: III. Integral reordering and four-index transformation

This series of three papers presents a program system for ab initio molecular orbital calculations on vector and parallel computers. Part III is devoted to the four-index transformation on a molecular orbital basis of size NMO of the file of two-electron integrals (pq∥rs) generated by a contracted Gaussian set of size NATO (number of atomic orbitals). A fast Yoshimine algorithm first sorts the (pq∥rs) integrals with respect to index pq only. This file of half-sorted integrals labelled by their rs-index can be processed without further modification to generate either the transformed integrals or the supermatrix elements. The large memory available on the CRAY-2 has made possible to implement the transformation algorithm proposed by Bender in 1972, which requires a core-storage allocation varying as (NATO)3. Two versions of Benders algorithm are included in the present program. The first version is an in-core version, where the complete file of accumulated contributions to transformed integrals is stored and updated in central memory. This version has been parallelized by distributing over a limited number of logical tasks the NATO steps corresponding to the scanning of the most external loop. The second version is an out-of-core version, in which twin fires are alternatively used as input and output for the accumulated contributions to transformed integrals. This version is not parallel. The choice of one or another version and (for version 1) the determination of the number of tasks depends upon the balance between the available and the requested amounts of storage. The storage management and the choice of the proper version are carried out automatically using dynamic storage allocation. Both versions are vectorized and take advantage of the molecular symmetry.

A program system for ab initio MO calculations on vector and parallel processing machines: II. SCF closed-shell and open-shell iterations

Abstract This series of three papers presents a program system for ab initio molecular orbital calculations on vector and parallel computers. Part II is devoted to SCF iterations on closed-shell and open-shell configurations starting from a file of two-electron integrals on the basis of contracted Gaussians (CGTOs). In a preliminary step, the two-electron integrals ( pq ‖ rs ) are reordered according to increasing values of index pq = p ( p −1)/2+ q . Then, in the first SCF iteration step, a file of semi-ordered P supermatrix elements (or P and Q supermatrix elements in the open-shell case) is generated from the file of semi-ordered integrals. This file is processed at each iteration step in an efficient vector loop to generate the electron repulsion matrix. Convergence is automatically controlled through level-shifting techniques. The most time-consuming parts are the integral sorting and the generation of the P supermatrix, which are carried out only once. Subsequent SCF iteration steps respectively require 0.9 s and 1.7 s for the process of 10 7 supermatrix elements by the closed-shell and the open-shell programs on a CRAY-2 processor.

The metal-carbon triple bond in Cl(Co)4crCH: A CAS SCF study of neutral carbyne complexes

Abstract Calculated SCF and CAS SCF potential curves are reported for the ground state of the Cl(CO)4CrCH carbyne complex. The totality of the computed bond energy (115 kcal mole ) is recovered from near-degeneracy correlation effects mainly involving the metal-carbyne π bonds. The Cr-C π population is almost equally distributed between the two atoms, but the σ bond retains the character of a donation from the carbyne carbon to chromium.

The CrCr quadruple bond length: Ab initio study of ligand effects

Abstract Ab initio SCF + Cl potential enery curves have been derived for Cr 2 (O 2 CH) 4 , Cr 2 (O 2 CH) 4 (H 2 O) 2 and Cr 2 (NHCHO) 4 . Equilibrium positions were obtained at 2.53, 2.58 and 1.92 A respectively, suggesting that the inductive effect of bridging ligands has a crucial influence on the CrCr bond length. A detailed rationalization is given for the effect of axial coordination, accounting for most observed characteristics.

The ground state of MoCr(O2CH)4 at theab initio SCF and CI levels. A symmetry adapted RHF energy functional with an artificial double minimum

Ab initio restricted Hartree-Fock (RHF) calculations carried out on the ground state of MoCr(O2CH)4 lead to two distinct energy minima according to the initial guess made for the set of trial vectors. It is shown that these two symmetry-adapted wavefunctions can be correlated with a twofold degenerate broken-symmetry solution previously characterized for the related system of higher symmetry Cr2(O2CH)4. Complete CI expansions have been carried out from either RHF polarized wavefunction using as a basis the set of eight frontier MOs with high metal character. These expansions yield poorly resymmetrized wavefunctions. A similar CI expansion has finally been carried out from a wavefunction resymmetrized at the SCF level and corresponding to a saddle point of the RHF energy hypersurface. The total energy associated with this latter expansion is the lowest obtained in the present work. The natural orbital analysis corresponds to (σ)1.86(π)3.58(δ)1.54(δ)0.46(π)0.42 (δ*)0.14 and shows that this resymmetrized CI expansion is in many respects similar to the correlated wavefunctions obtained for the homobinuclear parent systems.

Single excitations on multideterminantal CI wavefunctions: A treatment of the left—right correlation in multiple metal—metal bonds. Application to Cr2H6

Abstract The triple CrCr bond between two trigonal planar CrH 3 moieties is studied by means of CAS SCF calculations. The potential energy curve appears dissociative at the CAS SCF level for both the eclipsed and the staggered conformations. The use of a CI expansion restricted to single excitations from a properly selected multireference basis reverses this picture and produces a shallow minimum for the staggered conformation.

Correlated and Non-Correlated Wave Functions for Organometallics

Electron correlation is the everlasting concern of people involved in ab initio Hartree-Fock calculations. If the investigation is restricted to the structure and properties of the ground state, the importance of correlation depends i) on the type of bonding in the molecule under scrutiny, and ii) on the level of accuracy requested for the calculation, that is, on the sensitivity of the investigated property. This sensitivity may be highly interrelated with the nature of the bonding: in the specific area of organometallic complexes, it has been recognized since more than a decade that no realistic description of multiple, direct metal-metal bonds can be obtained without an adequate treatment of the left-right correlation.1,2 Accidental near degeneracies connected for instance with the sd hybridization in complexes of Ni(0) should also be accounted for in a systematic way.3 Other cases where correlation is susceptible to qualitatively modify the description of the ground state can be detected from the occurrence of Hartree-Fock instability which makes the energy of the considered system symmetry-dependant.4,5 Introducing a systematic treatment of correlation for large systems in the frame of the Hartree-Fock methodology would lead to technical problems and to an intolerable computer cost. Our experience in the computation of the ground state electronic structure and properties of dimetallic complexes and of clusters with higher nuclearity argues for a flexible approach of the correlation problem.

The photoelectron spectrum of hexacarbonyl-µ-di-t-butylacetylene-di-iron: a joint experimental and theoretical study

The He I and He II photoelectron spectra of [Fe2(CO)6(ButC2But)] are reported and assigned on the basis of ab initio self-consistent field (SCF) and configuration interaction (Cl) calculations carried out on the model system [Fe2(CO)6(HC2H)] assuming a perfect Cs symmetry. The calculations at the SCF level lead to the possibility of a triplet ground state for the model system. However, But substitution and observed deviations from Cs symmetry, along with the pair correlation energy not accounted for in the present work, are expected to reverse this trend. The ionization energies have therefore been computed assuming a closed-shell ground state for the neutral molecule. The highest occupied molecular orbital can be described in terms of a backdonation interaction from both metal atoms to a carbonyl ligand displaying some semibridging character. The Cl calculations, carried out on the ionized states using the molecular orbital set of the neutral molecule were expected to account for both the correlation effects (through two-electron excitations) and the relaxation effects (through one-electron excitations). These relaxation effects were, however, not completely accounted for, especially for localized d orbitals. The origin of the five bands reported between 7 and 12 eV can, however, be assigned with good confidence from the joint interpretation of the experimental and theoretical results.