Nuclear orbital plus molecular orbital theory: Simultaneous determination of nuclear and electronic wave functions without Born–Oppenheimer approximation

2007 ◽  
Vol 107 (14) ◽  
pp. 2849-2869 ◽  
Author(s):  
Hiromi Nakai
Keyword(s):  
Simultaneous Determination ◽  
Molecular Orbital ◽  
Wave Functions ◽  
Molecular Orbital Theory ◽  
Orbital Theory ◽  
Electronic Wave ◽  
Oppenheimer Approximation ◽  
Electronic Wave Functions

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.

scholarly journals The determination of molecular orbitals

1949 ◽  
Vol 198 (1052) ◽  
pp. 1-13 ◽  
Keyword(s):  
Molecular Orbital ◽  
Molecular Orbitals ◽  
Molecular Orbital Theory ◽  
Orbital Theory ◽  
Energy States ◽  
Molecular Framework

In the molecular orbital theory of valency the electrons are assigned to the whole molecule rather than to atoms or to other localized parts. While the method has advantages in dealing with the properties of a molecule as a whole, such as its energy states, the extension of each orbital over the molecular framework is a disadvantage when dealing with localized properties such as directed bonds. This paper deals in a general way with the equations which molecular orbitals must satisfy, allowing for the exchange of electrons between orbitals. It is then shown that when molecules have properties of symmetry the equations can be transformed so as to be satisfied by orbitals which have the property of equivalence. These can be regarded under certain conditions as directed orbitals and the conditions for these are discussed. To illustrate the method molecules of the type XY 2 are considered.

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.

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.

Bond Phase Determination of HOMO/LUMO and ‘Ethylene’ in Benzenoid Hydrocarbons

2002 ◽  
Vol 57 (11) ◽  
pp. 854-856
Author(s):  
Tetsuo Morikawa ◽  
Susumu Narita ◽  
Tai-ichi Shibuyaa
Keyword(s):  
Molecular Orbital ◽  
Molecular Orbital Theory ◽  
Orbital Theory ◽  
Benzenoid Hydrocarbons ◽  
Phase Determination ◽  
Molecular Graphs ◽  
Homo And Lumo ◽  
Valence Theory ◽  
Homo Lumo

Classical valence theory suggests the existence of strongly localized bonds (double bonds), i.e., of ethylene-like molecules, in benzenoid hydrocarbons (molecular graphs Bs); such an ‘ethylene’ is an edge in a hexagon that contacts with three hexagon faces in B. The phase of a bond is defined as the sign either plus for bonding or minus for antibonding. By use of perturbation molecular orbital theory we conclude that the phase of each bond that meets at the ethylene has necessarily the minus sign in HOMOof B; the bond phase alters in HOMO and LUMO of B.

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