Showing papers in "International Journal of Quantum Chemistry in 1979"

MCSCF optimization through combined use of natural orbitals and the brillouin–levy–berthier theorem

Abstract: A novel approach is developed for optimizing molecular orbitals within the context of a multiconfiguration self-consistent-field problem. The MCSCF wave function is determined through a sequence of eigenvalue problems in the multiconfiguration space and the single-excitation space. They are used iteratively to improve the natural orbitals, which in turn are related, by successively improved transformations, to the MCSCF orbitals. The mathematical problems arising out of this general concept are solved and the computational implementation is discussed. In many applications the method has proven itself as a powerful approach in forcing rapid convergence. Adaptation to spin and spatial symmetry is maintained throughout, and the procedure is applicable to excited states as well as to ground states. 3 figures, 2 tables.

Formal theory of effective π‐electron hamiltonians

Abstract: The goal of developing a satisfactory general formalism for the justification of effective ..pi..-electron Hamiltonians, as well as for ab initio calculation of their parameters (..cap alpha.., ..beta.., and ..gamma..), has now been achieved. The need for a fully linked many-body formalism is emphasized; this feature requires a Rayleigh-Schroedinger (RS) type of degenerate perturbation theory. A number of apparently different degenerate RS perturbation formalisms are reviewed. Most of these formalisms are actually identical term-by-term, when their RS expansions are worked out explicity; the formal relations that prove their complete equivalence are presented and discussed. One of these formalisms, a version developed by the author for related open-shell problems in nuclear physics, is shown to be most convenient for many-body applications. This is owing to the relatively simple and transparent nature of its general algerbraic structure, which facilitates partial summation to infinite order. A simple and concise derivation is presented for the algerbraic features of this prefered formalism, and its many-body (linked cluster) aspects are briefly discussed. The recent development of a nonperturbative (coupled-cluster) analog of this formalism is also described. Some practical issues are examined, including the choice of orbital basis. Illustrative numercial results are presented, based on the calculationsmore » of Iwata and Freed. Several remaining problems are described; these are both qualitative and quantitative in nature, and their resolution will require some detailed calculations.« less

Electronic rearrangements during chemical reactions. II. Planar dissociation of ethylene

Abstract: The direct dissociation of ethylene into two methylenes is studied along the least motion reaction path by means of an ab initio multiconfiguration self-consistent-field (MCSCF) calculation. All eight configurations arising from those valence orbitals that form the CC bonds, seven of them singlet coupled and one triplet coupled, are taken into account. The HCH bond angle is optimized along the entire reaction path. Separate MCSCF optimizations are carried through for the lowest two states of /sup 1/A/sub g/ symmetry. The (/sup 1/A/sub g/sigma/sup 2/..pi../sup 2/) ethylene ground state dissociates into two (/sup 3/B/sub 1/sigma..pi..) ground-state methylenes. The (/sup 1/A/sub g/sigma/sup 2/..pi..*/sup 2/) excited state of ethylene dissociates into two (/sup 1/A/sub 1/sigma/sup 2/) excited methylenes. It is established that both these dissociations proceed without any barrier in the energy curve. In the ground state, where orbital symmetry is conserved, the ..pi..-bond breaks before the sigma-bond, and the calculated heat of reaction agrees within 6 kcal/mol with the experimental value. In the excited state, where orbital symmetry is not conserved, the nonbonded repulsion between methylene sigma/sup 2/ lone pairs is found to blend into the antibonding character of the excited ethylene, yielding an energy curve that is everywhere repulsive. However, themore » variation of the HCH angle during the dissociation process is not simple, initially it expands and subsequently it contracts. Quantitative analytical approaches are developed which furnish conceptual interpretations of the orbital changes and configurational changes along the reaction path.« less

Electrostatic isopotential maps for large biomolecules

Abstract: A new method for the calculation of electrostatic isopotential maps, based on completely transferable bond orbitals, is proposed. According to the simple form of the potential term the amount of computational work is proportional to the first power of the number of valence electrons. Slater-type atomic orbitals are used to construct the bond orbitals, thus all integrals can be calculated explicitly. The subtilisin charge-relay system is studied as an example. It is found, in agreement with the results of Beppu and Yomosa, that the two protons transfer in a stepwise manner.

Expansion and completeness theorems for operator manifolds

Abstract: Some expansion and completeness theorems for operator manifolds, which are currently being employed in propagator theory, are derived. It is shown that excitation or ionization operators satisfying the conditions Q|0〉 = |Λ〉 and QΛ|0〉 = 0 for general excited states |Λ〉 and reference state |0〉 may be expanded uniquely in particular sets of basis operators. These results are then used to discuss rigorous expressions for fermion propagators.

Solitons, bioenergetics, and the mechanism of muscle contraction

Abstract: The properties of exciton and soliton excitations in one-dimensional molecular systems and in α-helical protein molecules are investigated. It is shown that collective excitations—solitons, corresponding to a combination of vibrational excitations in peptide groups and a local deformation of molecules—are possible in α-helical protein molecules. These excitations move along the molecule without energy losses and are perfect energy carriers. A qualitative description of the shortening in the length of muscular fibers is given using the concept of solitons occurring under the hydrolysis of ATP molecules at the ends of thick fibers contained in the sarcomeres of muscular fibers.

Correlation problems in atomic and molecular systems. VII. Application of the open‐shell coupled‐cluster approach to simple π‐electron model systems

Abstract: The coupled-cluster variational-like direct approach to the calculation of ionization and electron attachment energies and of excitation energies is applied to several π-electron model systems, using the PPP Hamiltonian with various parametrizations. A simple approximation, which represents the triexcited clusters in terms of disconnected W1T2 terms, is employed. All the necessary diagrams for both excitation energy and ionization potential (electron affinity) calculations are given in the compact Hugenholtz nonoriented form. The results of the calculations for benzene, trans-butadiene, all-trans-hexatriene, and fulvene are compared with the corresponding full CI results, and the conclusions about the validity and efficiency of this approach are drawn.

Regularities of the processes of radiationless conversion in polyatomic molecules

Abstract: The processes of radiationless conversion in aromatic and heteroaromatic molecules are investigated theoretically. The values of constant rates of internal conversion are calculated. The theoretical estimation of constant rates of S–T conversion aromatic hydrocarbon molecules and in their carbonyl-, thiocarbonyl-, and nitroderivatives and in azaheterocyclic molecules are given. The S-T conversion probability between the states of different orbital nature (nπ* and ππ*) is equal to ca. 1010–1011 sec−1 that is two to four orders higher than the conversion probability between the states of the same orbital nature. It is shown that the process of T-S conversion may be described in the second and in the highest orders of perturbation theory. The luminescent characteristics of molecules are connected with the relative position of electron states of different orbital nature and multiplicity and conversion characteristics.

Characteristics of the consistent ground state of the random phase approximation

Abstract: Detailed considerations of the ground-state vector derived for the random phase approximation obtained earlier in a generator coordinate representation employing the unitary group parameter space reveal a particular correlated pair structure. The results of explicit calculations of ground-state averages are discussed.

First-order properties and the Hellmann–Feynman theorem in the case of a limited CI wave function

Abstract: Two distinct approaches to the calculation of first-order properties with a limited CI wave function are discussed. One is based on the Hellmann–Feynman theorem and the other on the direct evaluation of the total energy derivative at zero perturbation. Corrections to the Hellmann–Feynman expectation value are given for the CI wave function consisting of a single determinant reference state and all single and double replacements of this. These corrections are the extended Brillouin matrix elements and involve interactions between the zeroth-order wave function and triply substituted configurations. The usefulness of these matrix elements for the generation of MC SCF orbitals and for the calculation of cluster corrections to the wave function is briefly discussed. The formulas for the Brillouin matrix elements expressed in terms of one- and two-electron integrals have been automatically generated using the syntax of the algebraic program SCHOONSCHIP.

Ab initio Hartree–Fock and configuration‐interaction treatment of the interaction between two nickel atoms

Abstract: The interaction between two nickel atoms in the configurations (3d)8(4s)2 and (3d)9 (4s)1 has been calculated using ab initio methods (Hartree–Fock and configuration interaction). The results of the calculations compare favorably with the optical spectrum. The discrepancy between the calculated and the experimental dissociation energy is discussed, and a new estimate of the dissociation energy is given. The configuration-interaction calculations show that the interaction between the two nickel atoms is of a very complex nature. In spite of this the binding can be interpreted in a simple way. The bond is minly due to the 4sσg molecular orbital while the 3d orbitals of the two nuclei are exchange coupled.

Electronic factors affecting receptor binding of dibenzo‐p‐dioxins and dibenzofurans

Abstract: The electronic structure of a series of 25 chlorinated dibenzo-p-dioxins and dibenzofurans has been characterized by means of the ab initio molecular fragment technique. This information has been employed to investigate some of the factors affecting the affinity of the molecules for the hepatic cytosol binding species described by Poland, Glover, and Kende. A quantitative structure–activity relationship involving electronic and steric parameters could be established from the data. It appears that the toxins act as electron acceptors in a charge-transfer complex with the receptor.

Use of the overlap multipole expansion for approximating molecular electrostatic potentials

Abstract: The molecular electrostatic potentials computed by the overlap-multipole-expansion procedure (OMTP) are compared to exact electrostatic potentials computed with the same Gaussian basis set, for different molecular species. It is shown that at distances of the molecule larger than 2.2 A, the OMTP values compared to those of the exact ones are within an error of 0.5 kcal/mol. This error decreases with increasing distance. For distances below this limit the OMTP potentials may be used as a first indication of the trends of the molecule, provided the values to compare are not too close.

Symmetry properties of graphs of interest in chemistry. II. Desargues–Levi graph

Abstract: The Desargues--Levi graph represents important chemical transformations: (1) isomerization routes for some carbonium ion rearrangements, (2) isomerization of trigonal bipyramidal structures, and (3) some pseudorotations of octahedral complexes. Using the concept of the smallest binary code, all permutations which form the symmetry operations in the graph are registered. The resulting symmetry group can be represented as the direct product of S/sub 5/ ( the full symmetric permutation group on five objects) and C/sub i/ (the inversion in the center). There are 14 classes belonging to the following partitionings: 1/sup 20/(1), 1/sup 8/2/sup 6/(1), 1/sup 4/2/sup 8/(1), 1/sup 2/3/sup 6/(1), 1/sup 2/3/sup 2/6/sup 2/(1), 2 6/sup 3/(2), 2/sup 2/4/sup 4/(2), 2/sup 10/(3),5/sup 4/(1), and 10/sup 2/(1). The total of 240 symmetry operations are distributed among the above 14 classes as follows: 1, 10, 15, 20, 20, 20, 20, 30, 30, 15, 10, 1, 24, and 24, respectively. Since partitioning cannot uniquely characterize a class, it is suggested that the distance between vertices in a cycle be introduced as an additional parameter to discriminate among classes having identical partioning. Also, a suggestion to a generalization of the Mulliken notation for irreducible representations of the point molecular groups valid for more versatile symmetrymore » groups of graphs is indicated.« less

Molecular electrostatic potential of the B-DNA helix. I. Region of the guanine–cytosine base pair

Abstract: The electrostatic molecular potential minima around the guanine–cytosine base pair within a B-DNA minihelix are computed, taking into account the contributions of the sugar-phosphate backbone and of the adjacent base-pairs. The calculations are based on ab initioSCF wave functions of the different constituents of the nucleic acid. The results point to significant differences in the potential between the isolated nucleic acid bases or base-pairs and those within the DNA. Altogether the minima in the G–C regions are strongly enhanced in the minihelix. They benefit from the field created by the neighboring phosphates. From the purely electrostatic viewpoint an ambiguity remains as concerns the relative affinity of N7 and N3 of guanine for electrophiles. On the other hand, guanine should altogether be more susceptible than cytosine to such reagents, this ordering concerning also its NH2 group compared to that of cytosine.

Molecular structure–biological activity relationships on the basis of quantum‐chemical calculations

Abstract: Detailed quantum-chemical calculations by means of semiempirical all-valence electrons methods and a generalized (multivariable) rank correlation analysis are the fundamentals of a novel strategy of search for QSAR within homologous series of compounds. The set of molecular parameters (describing the electronic and conformational properties as well as potential interactions of the drugs) is calculated theoretically. Owing to the rank correlation method, no linear model (like LFER) for the dependence of the biological activity upon the molecular parameters is presumed. The computed correlation coefficients are valued by carefully determined levels of statistical significance. Significant correlations are used to predict unknown activities in terms of ranks relative to the basic sample.

Configuration interaction matrix elements. I. Algebraic approach to the relationship between unitary group generators and permutations

Abstract: The explicit expressions for the matrix elements of unitary group generators between geminally antisymmetric spin-adapted N-electron configurations in terms of the orbital occupancies and spin factors, given as spin function matrix elements of appropriate orbital permutations, are derived by use of the many-body time-independent diagrammatic techniques. It is also shown how this approach can be conveniently combined with graphical methods of spin algebras to obtain explicit expressions for the spin factors, once a definite coupling scheme is chosen. This method yields explicit expressions for the orbital permutations defining the spin factors. However, if desired, the explicit determination of line-up permutations can be avoided in this approach, since they are implicitly contained in the orbital diagrams. It also clearly indicates why the geminally antisymmetric spin functions have to be used when a simple formalism is desired. 5 figures.

Fourth-order terms in the diagrammatic perturbation expansion for the electronic energy of atoms and molecules

Abstract: Third-order diagrammatic perturbation theory provides a simple and accurate description of the electronic structure of atoms and molecules beyond that afforded by independent electron models. The largest corrections to such treatments, the fourth-order terms, are presented and discussed. All of the diagrams, which arise when the closed-shell Hartree--Fock function is utilized as a reference function, are given through fourth order. 18 references.

Tautomerism of pyrimidine bases—uracil, cytosine, isocytosine: Theoretical study with complete optimization of geometry

Abstract: The semiempirical MINDO/3 method with complete optimization of geometry is employed to calculate the electronic ground-state properties (dipole moments and ionization potentials) and the energies of various tautomeric forms of uracil, uracil monoanion, cytosine, and isocytosine. The results are shown to be consistent with most of the experimental data. Accuracy of various quantum–mechanical methods is discussed. Particular attention is paid to the influence of the geometry optimization on energy differences between various tautomers. Some qualitative conclusions of biological importance are drawn from these calculations.

Quantum chemistry by random walk: H4 square

Abstract: The random-walk method of solving the Schrodinger equation is applied to the 1B1g and 1B2g states of the H4 square with side length 2.4 a.u. The results provide an independent check of the accuracy of prior variational calculations for these states. With node structures for the 1B1g state taken from a variational calculation with a single-zeta basis set and taken in the simplest form meeting symmetry requirements, the calculated energies are lower than the expectation value of the energy for the single-zeta basis set but not as low as the expectation value for an optimized-exponent double-zeta basis set with polarization terms. Comparisons of results give no suggestion of a barrier height lower than ∼120 kcal/mol for passage through the square configuration in the exchange reaction H2 + D2 2HD. For the 1B2g state with node structure in the simplest form meeting symmetry requirements the calculated energy is ∼65 kcal/mol lower than the expectation value of the energy for variational calculations with a double-zeta basis set.

Quantitative approach to conformations of proteins

Abstract: A quantitative conformational theory of proteins is developed that enables one to predict the native structure of a protein from its amino acid sequence. The theory is based on the following principles: (1) the spatial structure and conformational properties of a protein are predetermined by its amino acid sequence; (2) the native conformation of a protein corresponds to the free energy minimum; (3) all interactions within a protein molecule are specified as short-, mediumy-, and long-range types, interactions of different types being consistent with each other. The role of the short-, medium-, and long-range interactions in the spatial organization of a protein globule is discussed, and a step-by-step analysis of amino acid sequences with gradually increasing lengths is presented. The proposed theory is based on a semiempirical computational method that involves quantitative evaluation of all pairwise atomic interactions within a protein molecule in an aqueous medium. Examples illustrating the suggested approach are presented.

Back donation in Ni(CO)4: Comments on papers by K. H. Johnson and by K. H. Johnson and U. Wahlgren

Abstract: It is shown that multiple scattering Xα calculations on Ni(CO)4 predict a strong back-donation effect contrary to what is stated in previous papers on the subject.

Interaction of water with DNA single and double helix in the B conformation

Abstract: The interaction energy between water and B-DNA in the single and double helix is computed at a number of planar cross sections perpendicular to the helix long axis and for a few cylindrical surfaces enclosing the helix. In addition, Monte Carlo simulations are presented for a small cluster of water around regions of energy minima. On the base of these simulations the structure of water for B-DNA in solution, the quaternary structure of B-DNA, is proposed and discussed. The intermolecular interaction used in the Monte Carlo computation has been derived from ab initio computations of complexes between water and the DNA bases, diethylphosphate, a ribose derivative, and other model compounds.

Accurate and stable numerical Hartree–Fock calculations for atoms. I. The 1s2 ground state of H−, He, Li+, and Be++

Abstract: New techniques have been developed for atomic self-consistent-field calculations by numerical integration. For the origin and tail regions we present analytical expansions which can represent the solutions to high accuracy. For the numerical integration in the central region a five-point generalization of the Numerov formula is used; the error term is of the order h/sup 10/. While this formula is unstable if used in the customary way, stability is achieved by using a Gaussian elimination technique. The new procedures are tested on the ground state of the helium isoelectronic series; with 251 integration points all quantities are calculated with an inherent accuracy of better than 10/sup -11/.

Recent developments on the mechanism of chemical carcinogenesis by aromatic hydrocarbons

Abstract: This paper presents a critical discussion of recent discoveries on the metabolic transformations of polycyclic aromatic hydrocarbons and their interactions with nucleic acids in the light of quantum-mechanical theories of chemical carcinogenesis. 8 figures.

Geometry of density matrices. III. Spin components

Abstract: A definition is given for the spin-tensorial components of a p-electron density matrix for arbitrary p. Certain of these are defined to be standard components, and it is shown that all others can be obtained from them by linear combinations of permutations. When the density matrix is reduced, the standard components either map into standard components of the fewer-electron density matrix or into the origin. One- and two-electron density matrices are treated in greater detail. Reducing bases are given for the spaces in which the spatial coefficients of the spin components are elements. For spin eigenstates traces of all components are determined, and the π = 1 parts of all components are determined in terms of two independent components, which are themselves determined by the two-electron charge density matrix. Geometric consequences are investigated.

Multimolecular clusters: Their isomerism and effective characteristics evaluated by quantum chemistry†

Abstract: A method is described for processing the enthalpy, entropy, and Gibbs free energy terms of formation of the individual isomers of n-particle clusters obtained by means of quantum-chemical calculations, to enable a comparison of these partial theoretical characteristics with the overall experimental ones. The general scheme of weighting treatment is illustrated by examples based on recent quantum-chemical results of studies of isomeric forms of (NO)2, (H2O)5 and (D2O)5, and CH3OH · 3H2O and CH3OH · 6H2O clusters.

Geometric approximation to nuclear spin–spin coupling constants in the water molecule

Abstract: The geometric aproximation is used within the framework of triple perturbation theory to evaluate the contributions to nuclear spin–spin coupling constants in the water molecule provided by the Fermi contact, the spin–orbit, and the spin–dipolar interactions. The results, obtained with SCF wave functions expanded over Gaussian basis sets of increasing quality, are compared with corresponding coupled Hartree–Fock estimates. The limits of the geometric approximation to coupling constants are discussed.

Heme proteins and metalloporphyrins: Redox chemistry and oxygen binding

Abstract: Metalloporphyrins perform a variety of functions in nature from the storage and transport of electrons and molecular oxygen to the decomposition of hydrogen peroxide and the activation of oxygen. The chemistry of both the centrally coordinated metal and the porphyrin macrocyde play important roles in these reactions. The use of model systems and metalloporphyrins, other than iron porphyrins, is described for the elucidation of the mechanism of action of the natural systems. Iron protoporphyrin (1), the prosthetic group of heme proteins, and the closely related photosynthetic pigments chlorophyll (2) and bacteriochlorophyll (3) are widespread in nature. While these pigments, in concert with their apoproteins, play many varied biochemical roles, their chemistry can be generalized as that principally related to redox reactions and the transport storage and activation of molecular oxygen.