The molecular orbital theory of chemical valency XIV. Paired electrons in the presence of two unlike attracting centres

1953 ◽  
Vol 218 (1134) ◽  
pp. 327-333 ◽  
Keyword(s):  
Perturbation Method ◽  
Molecular Orbital ◽  
Essential Feature ◽  
Formal Solution ◽  
Wave Functions ◽  
The Other ◽  
Molecular Orbital Theory ◽  
Chemical Bonds ◽  
Orbital Theory ◽  
Antisymmetric Part

As a step towards an understanding of chemical bonds in diatomic molecules which contain unlike atoms, a theory of paired electrons in the presence of two unlike attractive centres has been worked out. The essential feature of the method is that the field of these centres is expressed as a sum of two fields, one of which is symmetrical and the other antisymmetrical in the plane midway between the two centres. A formal solution having been provided in earlier papers for the wave functions and energies of two electrons in the symmetrical part of the field, this is used as a basis for a perturbation method to calculate the effect of the antisymmetric part of the field.

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

1950 ◽  
Vol 202 (1071) ◽  
pp. 498-506 ◽  
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.

The molecular orbital theory of chemical valency XIII. Orbital wave functions for excited states of a homonuclear diatomic molecule

1953 ◽  
Vol 216 (1126) ◽  
pp. 424-433 ◽  
Keyword(s):  
Molecular Orbital ◽  
Excited States ◽  
Valence Bond ◽  
Present Theory ◽  
Wave Functions ◽  
Molecular Orbital Theory ◽  
Orbital Theory ◽  
Bond Theory ◽  
Homonuclear Diatomic Molecules ◽  
Approximate Wave

The expansions for the exact wave functions for excited states of homonuclear diatomic molecules derived in part XII are used as the basis for discussing various approximate wave functions of the orbital type. The states considered in detail are the lowest states of symmetries 1 Σ u + , 3 Σ u + . The calculus of variations is used to determine the optimum forms for the component orbital functions. A transformation to equivalent orbitals is used to bring out the physical significance of the various wave functions, and to relate the present theory to earlier theories, in particular the molecular orbital theory, the valence-bond theory and their generalizations.

The molecular orbital theory of chemical valency XVII. Higher approximations

1954 ◽  
Vol 225 (1160) ◽  
pp. 136-146 ◽  
Keyword(s):  
General Theory ◽  
Finite Number ◽  
Linear Combination ◽  
Molecular Orbital ◽  
Unitary Transformation ◽  
Natural Extension ◽  
Wave Functions ◽  
Molecular Orbital Theory ◽  
Orbital Theory ◽  
Electronic Wave Functions

The equations determining the best electronic wave functions for a molecule expressed as a linear combination of determinants constructed from a finite number of one-electron orbitals are discussed. It is shown that these orbitals are determined only to within a unitary transformation. As a result the general theory is a natural extension of the singledeterminant theory given in the early parts of this series. The group-symmetric properties of the orbitals are discussed.

The molecular orbital theory of chemical valency. III. Properties of molecular orbitals

1950 ◽  
Vol 202 (1069) ◽  
pp. 155-165 ◽  
Keyword(s):  
Perturbation Theory ◽  
Molecular Orbital ◽  
Molecular Orbitals ◽  
Molecular Properties ◽  
The Other ◽  
Molecular Orbital Theory ◽  
Special Significance ◽  
Orbital Theory ◽  
Molecular Systems ◽  
Normal States

The discussion of molecular orbitals and equivalent orbitals, given in previous papers, is carried a stage further. It is shown that certain molecular properties can be evaluated using either equivalent or molecular orbitals. On the other hand, a study of the changes produced by ionization demonstrates that molecular orbitals have a special significance and that certain energy parameters associated with them are closely related to ionization potentials. For the purpose of this discussion a perturbation theory is developed to deal with the changes produced in molecular systems when disturbed from their normal states.

Bonding in Transition Metal Silyl Dimers. Molecular Orbital Theory

1989 ◽  
Author(s):  
Alfred B. Anderson ◽  
Paul Shiller ◽  
Eugene A. Zarate ◽  
Claire A. Tessier-Youngs ◽  
Wiley J. Youngs
Keyword(s):  
Transition Metal ◽  
Molecular Orbital ◽  
Molecular Orbital Theory ◽  
Orbital Theory
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