Alternant Molecular Orbital Method Research Articles

Alternant Molecular Orbital Method

THE alternant molecular orbital method as formulated by Lowdin1 for a molecular system of alternant character, is based on the fact that by using a parameter θ, a bonding orbital ψj and a corresponding anti-bonding orbitalψj′ may be linearly combined to form the basic orbitals:

Alternant Molecular Orbital Method

THE alternant molecular orbital method as formulated by Lowdin1 for a molecular system of alternant character, is based on the fact that by using a parameter θ, a bonding orbital ψj and a corresponding anti-bonding orbitalψj′ may be linearly combined to form the basic orbitals:

Many-Parameter Alternant Molecular Orbital Calculations for Large Cyclic Systems with Closed-Shell Structure

Computer calculations of the energies for various ring systems with closed-shell structure have been carried out within the framework of the many-parameter alternant molecular orbital method. A significant improvement is obtained over the corresponding single-parameter results. Since the explicit energy minimizations are rather time consuming, some semiempirical relations between the relevant parameters are also discussed.

Studies on the Alternant Molecular Orbital Method. V. A Many-Parameter Energy Expression for States with Different Multiplicities; Application to Benzene

Within the framework of the refined alternant molecular orbital method, a general energy expression is derived for the lowest state of any desired multiplicity of an arbitrary system with closed-shell structure. A numerical analysis of the lowest singlet, triplet, and quintet state of the pi-electron sextet in benzene reveals that the many-parameter alternant molecular orbital wavefunction does, in each case, account for better than 90% of the energy improvement obtained in a full configuration interaction treatment. A detailed comparison of the AMO and CI wavefunctions for both triplet and quintet state is presented. Both methods yield a singlet—triplet separation that is too low, which suggests a basic deficiency in the customary approach to the quantum chemistry of conjugated hydrocarbons.

The application of the alternant molecular orbital method to aromatic compounds

The alternant molecular orbital method is a device for taking into account the horizontal correlation among electrons posessing different spins. A comparison with the configuration interaction treatment suggests that in the case of aromatic hydrocarbons the method can yield reliable results only if the molecular orbitals which are used in the construction of the alternant molecular orbitals are SCF MO's.

Studies on the Alternant Molecular Orbital Method. IV. Generalization of the Method to States with Different Multiplicities

A general formulation of the alternant molecular orbital method, applicable to states of different multiplicities in systems with an even number of atoms, is presented. The treatment is formulated in such a way that the same integral sums appear in the energy expression for the states belonging to different multiplicities. The resultant energy expressions show a simple dependence on the mixing parameter λ. Application to cyclic systems shows that the best λ values decrease slowly with increasing multiplicity. Comparison with the configuration interaction treatment reveals that the AMO method corresponds to a restricted CI treatment, but it is capable of yielding a considerable part of the energy improvement obtained by the latter method.

Studies on the Alternant Molecular Orbital Method. III. A Many-Parameter Energy Expression for Systems with Closed-Shell Structure

A refined alternant molecular orbital (AMO) method is described in which we allow for different variable parameters for each MO pair which is coupled. A corresponding many-parameter energy expression for the ground state of an arbitrary system with closed-shell structure is derived. Results of a numerical analysis involving the pi-electron sextet in benzene are briefly reviewed. Possible future applications of this scheme are suggested.

Studies on the Alternant Molecular Orbital Method. II. Application to Cyclic Systems

Using the general energy expression for an alternant system with closed-shell structure, obtained in our previous paper on the alternant molecular orbital (AMO) method, a numerical analysis is presented of cyclic systems consisting of 2n=4v+2 electrons moving in the field of 2n[Complex chemical formula]centers. Special attention is paid to the case of large n, when we are essentially dealing with a linear chain with Born-von Karman periodicity condition. The most important result obtained is that the energy depression per electron (a measure for the effectiveness of the method to take into account electron correlation) decreases only slowly with increasing n and approaches a limit in the neighborhood of 0.4 ev. Hence the AMO method is useful even in the case of large systems and may provide a powerful tool for tackling certain problems in solid-state theory. A detailed discussion is given of the various approximations incorporated in our analysis and a critical comparison is made with some related results recently obtained by other investigators.

Studies on the Alternant Molecular Orbital Method. I. General Energy Expression for an Alternant System with Closed-Shell Structure

The alternant molecular orbital method is used to derive a general energy expression for an arbitrary alternant system with closed-shell structure. This expression exhibits a simple dependence on a single mixing parameter, minimization with respect to which yields the optimum energy. An analysis reveals the effectiveness of the method to depend on the relative magnitude of two quantities, one involving the one-electron operator energies and the other related to electron interaction integrals which connect the bonding with the antibonding orbitals from the simple ASMO scheme. Some comments on the method, in the light of the results obtained, are added.

Spin Densities in Odd Alternant Hydrocarbon Radicals

The spin densities at the starred and unstarred carbon atoms of odd alternant hydrocarbon radicals have been calculated using the method of alternant molecular orbitals introduced by Löwdin. The spin densities at unstarred positions are shown to be negative in sign and to depend upon the electron correlation parameter θ. Observed spin densities on one carbon atom can be used to estimate θ and to calculate spin densities on other carbon atoms. Illustrative calculations for the cases of triphenylmethyl and perinaphthenyl are described.

Applications of the Alternant Molecular Orbital Method to Six- and Four-Electron Systems

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