Nonorthogonal orbital basedN-body reduced density matrices and their applications to valence bond theory. I. Hamiltonian matrix elements between internally contracted excited valence bond wave functions

The spin-coupled valence bond theory of molecular electronic structure is developed, according to which the single configuration spin-coupled theory is reformulated so as to yield both ground and excited orbitals. These orbitals are subsequently used to generate v.b. structures, the Hamiltonian matrix of which is diagonalized as in the conventional v.b. method. The fundamental feature of the excited spin-coupled orbitals is that, except those with the highest energy, they retain the characteristic distorted atomic form of the ground state orbitals, and correspondingly possess negative orbital energies. This leads to compact and rapidly convergent wavefunctions for the ground and lower-lying excited states, thus overcoming one of the basic drawbacks of the original v.b. theory. The theory is applied to the 2 ∑ + states of BeH by using 53, 71 and 80 structures of this kind. Very good convergence is found for the lowest six states, and the total energy of the ground state is below that given by a very large m.o.c.i. calculation. The present theory is thus a powerful and flexible alternative to m.o.c.i. calculations but using about an order of magnitude fewer functions.

Download Full-text

ELECTRONIC DELOCALIZATION: A QUANTITATIVE STUDY FROM MODERN AB INITIO VALENCE BOND THEORY

Journal of Theoretical and Computational Chemistry ◽

10.1142/s0219633602000099 ◽

2002 ◽

Vol 01 (01) ◽

pp. 137-151 ◽

Cited By ~ 11

Author(s):

YIRONG MO ◽

LINGCHUN SONG ◽

WEI WU ◽

ZEXING CAO ◽

QIANER ZHANG

Keyword(s):

Ab Initio ◽

Valence Bond ◽

Free Valence ◽

Matrix Elements ◽

Resonance Theory ◽

Valence Bond Theory ◽

Quantitative Level ◽

Electronic Delocalization ◽

Bond Theory ◽

Overlap Matrix

An ab initio spin-free valence bond code called Xiamen-99 has been developed based on an efficient algorithm called paired-permanent-determinant approach, where Hamiltonian and overlap matrix elements are expressed in terms of paired-permanent-determinants. With this tool, we probed the electronic delocalization phenomenon in a few typical examples including benzene, formamide and ethane. Our computations revealed that ab initio valence bond methods are able to estimate the energetic contribution from the delocalization effect to the stabilization of molecules, thus pave the way to illuminate the resonance theory at the quantitative level. In particular, we analyzed the cyclic electronic delocalization in benzene and showed that different understandings on the resonance may originate from the different usage of one-electron orbitals in the valence bond theory. Our investigation into the hyperconjugative interaction in ethane demonstrated that the hyperconjugation effect is not the dominating factor in the preference of the staggered conformer of ethane.

Download Full-text

Comment on ‘‘Valence-bond theory and the evaluation of electronic energy matrix elements between nonorthogonal Slater determinants’’

Physical Review A ◽

10.1103/physreva.34.671 ◽

1986 ◽

Vol 34 (1) ◽

pp. 671-671 ◽

Cited By ~ 2

Author(s):

G. A. Gallup

Keyword(s):

Valence Bond ◽

Electronic Energy ◽

Matrix Elements ◽

Energy Matrix ◽

Valence Bond Theory ◽

Bond Theory

Download Full-text

Polar structures in the theory of conjugated molecules. II. Symmetry properties and matrix elements for polar structures

Proceedings of the Royal Society of London Series A - Mathematical and Physical Sciences ◽

10.1098/rspa.1950.0024 ◽

1950 ◽

Vol 200 (1062) ◽

pp. 390-401 ◽

Cited By ~ 18

Keyword(s):

Valence Bond ◽

Matrix Elements ◽

Conjugated Molecules ◽

Energy Calculations ◽

Valence Bond Theory ◽

Energy Parameters ◽

Symmetry Properties ◽

The Matrix ◽

Bond Theory ◽

Usual Formalism

The inclusion of polar structures in the valence-bond theory of π-electrons entails some additions to the usual formalism, and these are given in this part. The symmetry properties of sets of structures, both non-polar and polar, and the matrix elements that come into energy calculations, are dealt with. Using the work of part I, and the conclusions of this part, the energy parameters for work with polar structures are evaluated.

Download Full-text

Electronic levels in simple conjugated systems, I. Configuration interaction in cyclobutadiene

Proceedings of the Royal Society of London Series A - Mathematical and Physical Sciences ◽

10.1098/rspa.1950.0115 ◽

1950 ◽

Vol 202 (1071) ◽

pp. 498-506 ◽

Cited By ~ 28

Keyword(s):

Molecular Orbital ◽

Configuration Interaction ◽

Energy Levels ◽

Valence Bond ◽

Wave Functions ◽

The Other ◽

Orbital Theory ◽

Valence Bond Theory ◽

Symmetry Properties ◽

Bond Theory

In the simplest cyclic system of π-electrons, cyclobutadiene, a non-empirical calculation has been made of the effects of configuration interaction within a complete basis of antisymmetric molecular orbital configurations. The molecular orbitals are made up from atomic wave functions and all the interelectron repulsion integrals which arise are included, although those of them which are three- and four-centre integrals are only known approximately. In this system configuration interaction is a large effect with a strongly differential action between states of different symmetry properties. Thus the 1 A 1g state is several electron-volts lower than the lowest configuration of that symmetry, whereas for 1 B 1g the comparable figure is about one-tenth of an electron-volt. The other two states examined, 1 B 2g and 3 A 2g are affected by intermediate amounts. The result is a drastic change in the energy-level scheme compared with that based on configuration wave functions. Neither the valence-bond theory nor the molecular orbital theory (in which the four states have the same energy) gives a satisfactory account of the energy levels according to these results. One conclusion from the valence-bond theory which is, however, confirmed, is the somewhat unexpected one that the non-totally symmetrical 1 B 2g state is more stable than the totally symmetrical 1 A 1g . On the other hand, it is clear that the valence-bond theory, with the usual value for its exchange integral, grossly exaggerates the resonance splitting of the states, giving separations between them several times too great. Thus the valence-bond theory leads to large values of the resonance energy (larger, per π-electron, than in benzene) and so associates with the molecule a considerable π-electron stabilization. This expectation has no support in the present more detailed and non-empirical calculations.

Download Full-text