Alternant molecular orbital method

Yoshizumi, H., and Itoh, T., J. Chem. Phys. 23, 412, "Applications of the alternant molecular orbital method to six and four electron systems."... 

J.-L. Calais, Abstracts of Uppsala Dissertations in Science 52 ( 1965 ), R. Pauncz, Alternant Molecular Orbital Method ( W. B. Saunders, Philadelphia 1967 )... 

Ruben Pauncz, Studies in Physics and Chemistry, No. 4. Alternant Molecular Orbital Method, Saunders, Philadelphia, 1967. 

Pauncz, R. Alternant Molecular Orbital Method, Philadelphia Saunders 1967. 3°) Empedocles, D. D., Linnett, J. W. Theoret. Chim. Acta 4, 377 (1966) Proc. 

In conclusion we note that the method of alternant molecular orbitals leads to a correct behavior of the energy curve for separated atoms, which is of essential importance in considering correlation effects (see Section II.D(4c)) and in studying magnetic phenomena. 

Lowdin, P.-O., Symposium on Molecular Physics atNikko, Japan, Maruzen, Tokyo, 1953, p. 13. A method of alternant molecular orbitals."... 

Abstract A mixed molecular orbital and valence bond (MOVE) method has been developed and applied to chemical reactions. In the MOVE method, a diabatic or valence bond (VE) state is defined with a block-localized wave function (ELW). Consequently, the adiabatic state can be described by the superposition of a set of critical adiabatic states. Test cases indicate the method is a viable alternative to the empirical valence bond (EVE) approach for defining solvent reaction coordinate in the combined qnantum mechanical and molecnlar mechanical (QM/MM) simulations employing exphcit molecular orbital methods. 

Nevertheless, acknowledging or denying the existence of differences between resonance theory and classical structural theory was dependent on their different assessments of the role of alternative methods to study molecular structure. Wheland equated resonance theory to the valence bond method and viewed them as alternatives to the molecular orbital method. Pauling conceded that the valence bond method could be compared with the molecular orbital method, but not with... 

The scientifically orthodox resolution of this difficulty is spelled out in many places (e.g., McWeeny, 1979, ch. 5). MO and VB theories are shown to be alternative first steps in a pair of schemes designed to successively approximate to an accurate quantum mechanical solution for the structure of a molecule. One aspect of this process that makes it seem a little less convincing is that the later steps in the approximation schemes differ markedly from the first. For example, with MO theory, a series of MO-Uke steps of successive approximation leads not to an accurate solution of the equations that arise from quantum theory but to the Hartree Fock limit. It is only by taking a rather different type of step, quite out of tune with the basis of the molecular orbital method—configuration interaction or some alternative—that the quantum theory solution can be approximated. 

There is, however, a method which has not been fully exploited yet, in particular for extended systems, namely the single-determinant method without any restrictions on the spin orbitals. Thanks to very important work by Fukutome and collaborators we now have a clear picture of the various possible forms of such spin orbitals, which includes, in addition to the well-known doubly filled restricted Hartree-Fock (RHF) orbitals, alternant molecular orbitals and other forms of different orbitals for different spins, Overhauser s spin density waves, as well as others. It has been known for a long time that a sufficiently general single determinant can... 

Semiempirical molecular orbital methods offer another alternative but must be used with caution. They are known to incorrectly reproduce certain key... 

Several calculations have been performed, particularly in the case of alkaline and alkaline-earth metals, using various methods i.e., molecular orbital method alternant molecular orbitals... 

A comparative study between the classical molecular orbital method and the more improved method of alternant molecular orbitals performed for lithium, shows that both procedures are in fact equivalent for interatomic distances close to the equilibrium distances in the crystal. Nevertheless, the cohesive energy obtained is equal to zero 1 This result is very depressing. The cohesive energy is in fact less than 1/100 of the total energy. Therefore, it is very difficult to obtain a good value, even using sophisticated methods. 

An alternative approach to extend the molecular orbital method is offered by the work of Hubbard for the study of narrow energy bands in solids with the aim to study magnetism. The main idea of this work is to analyze the many-electron problem for the case of separated atoms, which means the limit of zero bandwidth. 

Most molecular orbital methods find a bond alternation pattern in the minimum-energy structure, but calculations that include electron correlation lead to a delocalized minimum-energy structure. Thus, while the tt system in 1 is not completely planar, it appears to be sufficiently close to provide a delocalized 10-electron tt system. A resonance energy of 17.2 kcal/mol has been calculated on the basis of an experimental heat of hydrogenation. ... 

An alternative strategy was to develop methods wherein the two-electron integrals are parameterized to reproduce experimental heats of formation. As such, these are semi-empirical molecular orbital methods—they make use of experimental data. Beginning first with modified INDO (MINDO/1, MlNDO/2, and MINDO/3, early methods that are now little used), the methodological development moved on to modified neglect of diatomic differential overlap (MNDO). A second MNDO parameterization was created by Dewar and termed Austin method 1 (AMI), and finally, an "optimized" parametrization termed PM3 (for MNDO, parametric method 3) was formulated. These methods include very efficient and fairly accurate geometry optimization. The results they produce are in many respects comparable to low-level ab initio calculations (such as HF and STO-3G), but the calculations are much less expensive. 

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