Fokke Dijkstra

Software news and updates

A parallel version of the valence bond program TURTLE has been developed. In this version the calculation of matrix elements is distributed over the processors. The implementation has been done using the message‐passing interface (MPI), and is, therefore, portable. The parallel version of the program is shown to be quite efficient with a speed‐up of 55 at 64 processors.

Gradients in valence bond theory

A gradient method for general valence bond wave functions is presented. The electronic energy is used as a Lagrange multiplier. The derivatives of the normalization and of the first- and second-order cofactors present in the energy expression have to be evaluated, giving rise to first-, second-, and third-order cofactors. This evaluation is done using an extension of methods described previously. The use of gradients is illustrated with some calculations on organic molecules, viz. ethene, 1, 4-butadiene, and benzene.

Aromaticity of bent benzene rings: A VBSCF study

The effect of ring deformation on aromaticity has been studied for bent benzene molecules in which two carbon atoms have been bent out of plane, resulting in . a boat conformation. Valence-bond self-consistent field VBSCF calculations have been performed on these molecules to obtain insight into the aromaticity of bent benzenes. Results for total energy, structure energies, weights, and orbital overlaps show that the molecule keeps its aromatic nature up to 558. After 558 a transition to Dewar benzene occurs. The valence-bond model, by showing the weights of both Dewar and Kekule ´ structures, is an excellent tool to study deformed benzene. Q 1999 John Wiley & Sons, Inc. Int J Quant Chem 74: 213)221, 1999 .

TURTLE - A gradient VBSCF Program. Theory and Studies of Aromaticity

The Ab Initio Valence Bond program TURTLE has been under development for about 12 years and is now becoming useful for the non-specialist computational chemist as is exemplified by its incorporation in the GAMESSUK program. We describe here the principles of the matrix evaluation and orbital optimisation algorithms and the extensions required to use the Valence Bond wavefunctions in analytical (nuclear) gradient calculations. For the applications, the emphasis is on the selective use of restrictions on the orbitals in the Valence Bond wavefunctions, to investigate chemical concepts, in particular resonance in aromatic systems.

1,3,5-Cyclohexatriene captured in computro; the importance of resonance

The geometry and energy of 1,3,5-cyclohexatriene, the reference molecule for the determination of the extra stabilization of benzene, have been calculated using an Ab Initio Valence Bond method. The theoretical resonance energy, according to Dewar, calculated as the energy difference between two-structure benzene and single-structure 1,3,5-cyclohexatriene, both with completely optimized geometries and orbitals, is only )12.05 kcal/mol. Resonance energies of )25.37 (local orbitals), )19.82 (delocal orbitals) and )44.13 (breathing orbitals) kcal/mol are found using the Pauling definition. The concept of the vertical resonance energy, however, is proven to be not tenable beyond a minimal basis. 2002 Elsevier Science B.V. All rights reserved.

On the Rapid Evaluation of Cofactors in the Calculation of Nonorthogonal Matrix Elements

The calculation of matrix elements involving nonorthogonal orbitals is speeded up by recognizing the orthogonalities between orbitals, leading to generalized Slater rules. The block structure present in the overlap matrix makes an efficient evaluation of its cofactors possible. These cofactors are calculated per subblock, each with its own parity sign. An adjustment parity sign has to be evaluated, which is added to the combined local signs, to give the correct total sign for the matrix element. An algorithm for the evaluation of this adjustment sign has been developed, making an easy and correct evaluation possible. The current scheme is shown to be very efficient, but possibilities for further improvement remain. Q 1998 John Wiley & Sons, Inc. Int J Quant Chem 67: 77)83, 1998

THE INTERACTING CORRELATED FRAGMENTS METHOD WITH NON-ORTHOGONAL ORBITALS

The interacting correlated fragments (ICF) method proposed by Liu and McLean is employed using non-orthogonal orbital spaces for the interacting fragments. This way orthogonalization schemes may be avoided and the orbitals may be optimized separately at each internuclear distance. This approach is illustrated using a calculation on the He dimer, which is one of the ® rst systems to which ICF was applied. It is found that the use of non-orthogonal orbitals gives a more attractive potential. Although the orbital basis inconsistency is avoided completely, the con® guration basis inconsistency still gives rise to a considerable basis set superposition error.