A semiempirical method based on geminal functions

An attempt has been made to develop a semiempirical method which considers only the n- and π-electrons, with the eigenfunctions expressed as an antisymmetrized product of two-electron functions or geminals. These geminals are expressed as a linear combination of products of Hückel-type MO's and the matrix elements are evaluated assuming the strong orthogonality condition to hold among the geminals, with an average effective Hamiltonian where the interaction between paired electrons is explicitly included. A first application of the method to N₂, HCN, C₂H₂, and C₂H^? was carried out without the introduction of parameters adjustable to best fit. A parametric approximation was then used for studying the electronic structure of diazabarrelene, an unknown molecule containing three pairs of π-electrons and two pairs of n-electrons. It is concluded that the explicit introduction of (π,π) and (n-π)-electron interaction describes the ground state more realistically than the simplest Hückel method. The separation of the energy levels was also affected, but the calculated transitions compared rather poorly with the spectroscopic observations. Diazabarrelene is expected to be not less stable than barrelene and attempts to its synthesis should be considered worthy of being made.     

A semiempirical method for treating unsaturated molecules in terms of electron pair functions

It is proposed to use the treatment of Girardeau for the calculation of energies of unsaturated molecular systems. This involves a second quantized formalism with electron pair basis functions. No strong orthogonality is assumed, instead a subsidiary condition is imposed on the state vectors. However this does not involve any approximation. Information regarding the ground and excited states can be obtained from various propagators. In order to determine these propagators the Green function method of the many body problem can be used.

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Zusammenfassung Es wird vorgeschlagen, Moleküle mit konjugierten Systemen nach einem Verfahren von Girardeau zu behandeln, das mit Geminalen ohne starke OrthogonalitÄt arbeitet. Man kann dabei die Greensche Punktion in der üblichen Weise benützen.

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Résumé Une théorie du type N-corps est formulée pour l'étude des molécules non-saturées avec les effects de corrélation en utilisant un formalisme de Girardeau avec une base de fonctions de paires électroniques, ou on ne suppose pas l'orthogonalité forte, mais impose à la place une condition sur les vecteurs d'état. Cependant ceci ne comporte aucune approximation. L'information relative à l'état fondamental et aux états excités peut Être obtenue à partir des différents propagateurs. Ces propagateurs peuvent Être déterminés à l'aide de la méthode de la fonction de Green du problème à N corps.

     

Molecular integrals over Gaussian-type geminal basis functions

We present formulas for the evaluation of molecular integrals over basis functions with an explicit Gaussian dependence on interelectronic coordinates. These formulas use expansions in Hermite Gaussian functions and represent an extension to the work of McMurchie and Davidson to two-electron basis functions. Integrals that depend on the coordinates of up to four electrons are discussed explicitly. A key feature of this approach is that it allows full exploitation of the shell structure of the orbital part of the basis. Received: 24 February 1997 / Accepted: 4 March 1997     

Spin adaptation of antisymmetrized geminal product wave functions

A spin-free polynomial representation of antisymmetrized geminal products is presented for several cases. In particular, products of identical geminals, which possess different spin multiplicity, are considered. The cases of singlet geminals, singlet geminals with one or two triplet geminals coupled to the lowest possible spin multiplet, and triplet geminals coupled to an arbitrary multiplet are considered in detail, and explicit polynomial representation is given.     

New generation of semiempirical methods of molecular modeling based on the theory of group functions

The semiempirical methods of modeling the molecular systems using the group function approximation for electronic structure calculations have been used by the author for many years. The review discusses the general structure of the semiempirical method that uses the group functions and the results obtained by the particular methods, namely, the crystal field effective Hamiltonian method designed for systems containing transition metal ions and methods based on the strictly local geminal approximation designed for modeling the “organic” molecules.     

Green's function method for photoelectron spectroscopy calculations based on MNDO and AM1 semiempirical approximations

Irkutsk State University. Translated from Zhurnal Strukturnoi Khimii, Vol. 30, No. 3, 137–139, May–June, 1989.     

A fast method of large-scale serial semiempirical calculations of docking complexes

A brief survey of the state of the art in methods of calculations of protein—ligand interaction energies in docking complexes is presented. A new computational technique is proposed that allows one to fundamentally improve the performance of large-scale serial calculations of docking complexes using the AM1/PM3 semiempirical methods. The technique explicitly allows for a specific feature of docking problems, viz., the need for calculating numerous ligand complexes with a specified protein whose noninteracting part remains “frozen” during computations. The interaction energies calculated using the new method differ only slightly from the results of complete AM1 calculations and the performance attained is high enough to solve practical drug design problems. Published in Russian in Izvestiya Akademii Nauk. Seriya Khimicheskaya, No. 9, pp. 1759–1764, September, 2008.     

A multireference configuration interaction method based on the separated electron pair wave functions

A multireference configurational interaction method based on the separated electron pair (SEP) wave functions, SEP‐CI approach, has been developed as an approximation to the traditional CASSCF method. It differs from the CASSCF method in that active orbitals are obtained from the SEP wave function without further optimization in the subsequent CI calculations, and the active space is automatically constructed according to the occupation coefficients of SEP natural orbitals. These features make the present SEP‐CI method computationally much less demanding than the CASSCF method. The applicability of the SEP‐CI method is illustrated with sample calculations on the insertion reaction of BeH₂ and dissociation energies of LiH, BH, FH, H₂O, and N₂. © 2005 Wiley Periodicals, Inc. J Comput Chem 27: 39–47, 2006     

New semiempirical SCF-MO method for calculating organometallic compounds

Journal of Structural Chemistry -     

NDDO/MC: A new semiempirical SCFMO method for transition metal complexes

A new semiempirical SCF MO procedure available for prediction of the transition-metal complexes' binding energy and molecular geometry is developed. The features of the method are (i) an explicit account of the orthogonality of the basis set; (ii) use of a new formula for the resonance integral; and (iii) an effective account of the Coulomb correlation of electrons in the calculation of the two-electron integrals based on approach of a model Coulomb hole function. The parameterization for H, C, N, O, Co, and Ni atoms is presented. The results of NDDO /MC (NDDO for Metal Compounds) calculations of molecular geometries and binding energies for a number of organic compounds and more than 30 cobalt and nickel complexes are compared with the available experimental and ab initio data. The average absolute errors for the binding energies of organic molecules and metal complexes are 8.8 and 5.0 kcal/mol, respectively. © 1992 John Wiley & Sons, Inc.     

Study of the semiempirical HAM/3 MO method

The semiempirical HAM/3 molecular orbital method, recently proposed by Åsbrink and coworkers, is studied. The speed and accuracy are confirmed by computations of vertical ionization potentials of some small molecules, sixteen 22-electron molecules, and the carbazole molecule. The negative comments of de Bruijn are examined and found to be partly valid but generally overcritical. Other aspects of HAM/3 are also discussed.     

LocalSCF method for semiempirical quantum-chemical calculation of ultralarge biomolecules

A linear-scaling semiempirical method, LocalSCF, has been proposed for the quantum-chemical calculations of ultralarge molecular systems by treating the large-scale molecular task as a variational problem. The method resolves the self-consistent field task through the finite atomic expansion of weakly nonorthogonal localized molecular orbitals. The inverse overlap matrix arising from the nonorthogonality of the localized orbitals is approximated by preserving the first-order perturbation term and applying the second-order correction by means of a penalty function. This allows for the separation of the orbital expansion procedure from the self-consistent field optimization of linear coefficients, thereby maintaining the localized molecular orbital size unchanged during the refinement of linear coefficients. Orbital normalization is preserved analytically by the variation of virtual degrees of freedom, which are orthogonal to the initial orbitals. Optimization of linear coefficients of localized orbitals is performed by a gradient procedure. The computer program running on a commodity personal computer was applied to the GroEL-GroES chaperonin complex containing 119,273 atoms.     

A study by Raman spectroscopy and the semiempirical AM1 method on several 1,2-dihydroxybenzene solutions

The Raman spectra of 1,2-dihydroxybenzene (catechol) dissolved in six different compounds have been obtained and, on the basis of frequencies and depolarization ratios, the relevant structure of the solute has been inferred in every case. In addition, rotational barrier calculations using the AMI semiempirical method have been performed on several catechol—solvent systems. The theoretical results were in accord with experimental data and were related to structural properties of the solvents.