bluuebunny/crossref_metadata_2025 huggingface dataset:
Ab initio calculations including electron correlation for the minimum energy path of the (1A1) CH2+(1Σ)H2→ (1A1) CH4 insertion reaction
Authors: Jeziorek Danuta , Żurawski Bronisław
Published: December 2004

Ab initio calculations on the SCF level and with the inclusion of valence shell electron correlation in the IEPA–PNO (independent electron pair approximation with pair natural orbitals), the PNO–CI (pair‐natural‐orbital configuration interaction) and the CEPA–PNO (coupled electron pair approximation with pair natural orbitals) schemes with Gaussian lobe functions of “double zeta quality” have been performed for the minimum energy path of the insertion of singlet (1A1) methylene to the (1Σ)H2 molecule to yield methane. The energy was minimized on the SCF level to all geometrical parameters for various values of the “approximate” reaction coordinate. The energy along the reaction path decreases monotonically without a barrier and the curves representing the total energy of the system as a function of approximate reaction coordinates obtained at different levels of approximations have the same shape. From the physical point of view three phases of the reaction can be distinguished (chemically two steps) with different geometrical arrangements and different internal geometries of the partners.
Electronic structural properties and photosynthesis
Authors: Christoffersen Ralph E.
Published: December 2004

A review of recent theoretical studies of molecules of interest to photosynthesis is given, in which the results of ab initio self‐consistent‐field plus configuration‐interaction studies are discussed. Ground‐state and low‐lying excited singlet and triplet state descriptions are presented for six molecules, including Mg‐porphine, Mg‐chlorin, ethyl chlorophyllide a, and their corresponding magnesium‐free analogs. The data are then used to rationalize a variety of observed properties, including molecular orbital structure, ionization potentials, chemical reactivity, Franck‐Condon transition energies, oscillator strengths, transition polarizations, and other properties. As a result, relatively comprehensive and complete descriptions of the electronic structural features of chlorophyll a and related molecules are obtained, which are in general in good agreement with available experimental data, but which also provide new concepts and reinterpretation of existing data in several instances.
Model studies on the active site of carbonic anhydrase: Ligand properties and CO2 binding
Authors: Pullman A. , Demoulin D.
Published: December 2004

In view of building a workable molecular model of tetraliganded zinc at the active site of carbonic anhydrase, an ab initio SCF study using pseudopotentials is performed on Zn2+(OH2)n from n = 2 to 6, Zn2+(NH3)n−1 (OH2) for n = 2 and 4, Zn2+(NH3)2 (imidazole) (OH2), and their ionized species involving OH− or imidazolate, considering in particular the evolution of the properties of the ligands and of the bound cation upon increasing n and upon replacement of one ligand by another. (Comparison of NH3 and imidazole binding was made in a full SCF calculation.) The results obtained in the tetraliganded complex confirm that zinc binding facilitates water deprotonation more than imidazole deprotonation, so as to reverse the order of their intrinsic ease of ionization. A study of the approach of CO2 toward the active site is made in an electrostatic approximation using as models the most representative of the computed four‐ligand complexes.
Interaction of water with DNA single and double helix in the B conformation
Authors: Clementi E. , Corongiu G.
Published: December 2004

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.
On the validity range of the qualitative theory of chemical reactivity
Authors: Basilevsky M. V. , Weinberg N. N.
Published: December 2004

An attempt is made to refine the physical background underlying qualitative quantum‐chemical concepts that are an essential component of the modern theory of chemical reactivity. The energy of electron delocalization in a transition state (stabilization energy, SE) is used as a measure of chemical reactivity. Using Coulson's integral representation for bond order matrix enables one to present the Woodward–Hoffmann rules and the effects of conjugated substitutents as theorems for a Hückel SE in alternant systems. A part of the results are extended to heteroatomic systems. The validity of the present treatment is discussed in terms of the SCF PPP theory.
Fock coordinate function method for separation of spin variables in transition density matrices
Authors: Klimko G. T. , Mestechkin M. M. , Whyman G. E.
Published: December 2004

The Fock generating function method is employed for the separation of spin variables into two‐particle transition density matrices. Their spatial components introduced by McWeeny are expressed through Schrödinger's coordinate wave functions. Some nontrivial integral relations between these components and the charge and transition spin density matrices are obtained. The interrelation between the mentioned spatial components and the Matsen–Poshusta symmetrized density matrices of an arbitrary spatial function is found.
Asymptotic forms of atomic scattering factors and momentum densities
Authors: Yusaf M. S. , Lawes G. P. , March N. H.
Published: December 2004

Within the framework of the nonrelativistic Schrödinger equation, the Coulomb field case is used to assess the range of validity of the Thomas–Fermi statistical theory of atoms. In particular, attention is focused on (a) the x‐ray scattering factor, which is the Fourier transform of the electron density; and (b) the momentum density. In each case the predictions of the statistical theory are compared with the exact results for the Coulomb potential. These can conveniently be calculated using earlier work of Fock. Some assessment is also made of the accuracy of the statistical approximation for the kinetic energy density; this is of interest in connection with the density functional approach. Finally, some brief comments are made on the relation between the self‐consistent Thomas–Fermi method and the Hartree theory for atoms.
Energy levels for perturbed Morse oscillators
Authors: Requena A. , Peña R. , Serna A.
Published: December 2004

The energy levels and perturbation expansions for the expectation values of arbitrary powers of position for a perturbed Morse oscillator are obtained by application of the hypervirial and Hellmann–Feynman theorems, solely in terms of the unperturbed energy. We obtain expressions for the first‐order corrections for (1 − e−aq )m for 4 ⩽ m ⩽ 8 and the expressions to second and third order for the quartic perturbation. A numerical application to the CO molecule is made.
Behavior of molecular potential energy curves for large nuclear separations
Authors: Morgan John D. , Simon Barry
Published: December 2004

We prove by elementary geometric methods and within the Born–Oppenheimer approximation that as the nuclei of a molecule are dissociated into spatially separated clusters, the discrete molecular energies approach sums of the energies of isolated subsystems. Our methods also show that the spectral projections associated with the discrete molecular spectrum asymptotically approach direct sums of suitable spectral projections for the isolated subsystems. These results apply to any system of particles interacting by asymptotically vanishing pair potentials. We prove that the 1/R expansion for discrete molecular potential curves is asymptotic as R → ∞, and we discuss the behavior of the coefficients of the 1/R expansion for the ground state of H2+.
Effect of substituents on electron energy redistribution in uracil derivatives and their ionization in polar solvents
Authors: Blagoy Y. U. P. , Sheina G. G. , Luzanov A. V. , Silina L. K. , Pedash V. F. , Rubin Y. U. V. , Leibina E. A.
Published: December 2004

It is assumed that the chemical reactivity may be described in terms of the appropriate energy density calculated for each atom. Indices of energy density for deprotonization of uracil, 5‐nitro‐ and 5‐aminouracil are presented. The results of a quantum chemical calculation of the deprotonization energy are in qualitative agreement with experimental pK and ΔH values.
Permutational–symmetry‐adapted powers of representations of the point groups deduced from the unitary group
Authors: Flurry R. L. , Siddall T. H.
Published: December 2004

The construction of symmetrized powers of representations of the point groups can be deduced by decomposing the appropriate representation of the unitary group into the representations of the group of the sphere, and then mapping these representations onto the point group. The method is generally simpler than the traditional method based on the character tables of the symmetric group. As an example, the symmetry‐adapted powers (N) of the representations of the icosahedral group are presented for 2≤N≤5.
One‐center expansion method with model potentials. I. Formulation and test calculations
Authors: Tindimubona Alex R.
Published: December 2004

The one‐center expansion (OCE) method is extended to evaluate molecular wave functions for molecules with heavy off‐center nuclei. This extension is achieved through the use of model potentials (MP) to approximate the highly bound core orbitals. The remaining diffuse valence charge distribution is then rather easy to simulate using OCE. The formulation of the method is described. New molecular integrals are solved to a high degree of accuracy. Successful results are reported for H2O, H2S, and N2. The valence electron distributions and orbital energies are in good agreement with those obtained from more complete calculations. The method combines the computational economy of both OCE and MP procedures, resulting in a potentially useful package for further chemical applications.
Orbital contributions to some two‐electron properties
Authors: Largo‐Cabrerizo J. , Calvo F. M. Duque
Published: December 2004

Analytical formulas are given for the orbital contributions to two‐electron properties such as 〈r〉, with n = −2, −1, 1, 2, 3, and 4, for atomic systems in which orbitals are expanded as linear combinations of Gaussian functions. Numerical values for all possible contributions in the atoms Li to Ne have been calculated at the Hartree–Fock level. These quantities are compared and discussed to show what kind of information can be obtained from such quantities. The influence of the basis set size has also been considered.
Semiempirical molecular‐orbital studies on the problem of nonclassical resonance in the homoallylic cation
Authors: Murthy A. S. N. , Ranganathan Shoba
Published: December 2004

The quantum‐mechanical methods (EHT and CNDO/2) have been applied to the homoallylic cation. Both methods successfully predict that the ion need not be represented as a nonclassical structure.
Many‐body calculation of the electric field gradient in the hydrogen molecule
Authors: Itagaki T. , Saika A.
Published: December 2004

The electric field gradient in the hydrogen molecule has been calculated by diagrammatic many‐body perturbation theory (MBPT) in Gaussian basis sets. The procedure through third order in electron correlation gives a value for the field gradient of 0.34041 a.u., which is 0.8% greater than the accurate value. The result is discussed in terms of the completeness of the basis sets and the convergence of the perturbation expansion.
Study of correlation holes. II. CI calculations on model polyatomic systems
Authors: Cimiraglia Renzo , Resta Raffaele
Published: December 2004

The shape of correlation holes in many‐electron systems is at present scarcely known, even where correlated wave functions are available. We investigate here the kind of electron correlation brought about by configuration interaction (CI), within a given basis set, in the wavefunction of a polyatomic system. The model ring system H6 (in two different bonding circumstances) and H14 have been chosen for a detailed study, because of their paradigmatic importance. We set out the equal‐spin and different‐spin correlation holes as obtained from complete CI calculations in H6 and partial ct in H14, both within a minimal basis set. We basically find the spinless correlation as being short range, while the spin‐dependent correlation holes show long‐range oscillations of antiferromagnetic character. We also present a natural spin‐geminal analysis of the two‐body reduced density matrices in these systems; we find a peculiarity possibly related to the long‐range correlation discussed above. Finally, we compare the electron correlation as given from our CI wavefunction to other pictures of electron correlation, as obtained essentially from alternant molecular orbital wave functions and from the electron–gas literature.
Antisymmetric product of geminals in the context of the method of moments
Authors: Røeggen I.
Published: December 2004

A scheme for obtaining approximate solutions of the electronic Schrödinger equation is formulated within the context of the method of moments. The flexibility of the method of moments is utilized in the construction of a model based on an antisymmetric product of geminals (APG). This APG model is compared with a model based on an antisymmetric product of strongly orthogonal geminals (APSG). As a test example the advocated APG model is applied to the ground state of ammonia. Our best APG function recovers 37% of the total molecular correlation energy to be compared with an estimated 31% for the best APSG function.
Electronic structure of the metabolites of cyclophosphamide
Authors: Ulmer W.
Published: December 2004

Some physical and chemical properties of the metabolites of the cancerostat cyclophosphamide (trade name: ENDOXAN) have been calculated with an appropriately prepared CNDO/S‐CI method. The ground state properties (e.g., charge densities and free valences) do not indicate a significant change, compared with the results of cyclophosphamide, and the same fact is also true for the energy levels of the two lowest excited singlet and triplet states. With respect to the dipole transition moments only the metabolite N‐mustard‐diamido‐phosphoric acid (Friedman acid) differs drastically from cyclophosphamide and the other metabolites. The chemical reactivity has been considered under the aspect of singlet–triplet transitions between quasidegenerate singlet and triplet states. Again Friedman acid behaves quite differently from the other compounds, and only this metabolite exhibits the remarkable ability to act as an alkylating agent via splitting off chloride ions.
Direct energy minimization of self‐consistent electron pair by an orthogonal transformation of the basis
Authors: Fantucci Piercarlo , Polezzo Stefano , Trombetta Laura
Published: December 2004

In the frame of direct minimization of MC–SCF energy by an orthogonal transformation of the basis, a new procedure for iteratively solving the orbital equations is presented, in which the orthogonal matrix is calculated by the singular value and vector decomposition of a nonsymmetric matrix. The procedure is applied to the self‐consistent electron pair theory and tested on LiH molecule. Convergence rate and numerical stability are found to be satisfactory.
Three‐body potential energy terms for methane trimers
Authors: Novaro O. , Castillo S. , Kołos W. , Leś A.
Published: December 2004

An SCF LCAO MO calculation on the methane–methane–methane system is presented, in order to analyze the deviation from pairwise additivity of the interaction energy. Three‐body terms are shown to be remarkably similar to those of noble gas trimers both in magnitude and in their dependence on the geometrical arrangements of the three molecules.
Uniform quality gaussian basis sets for molecular calculations. IV. Gradient and charged optimized basis sets for CH4
Authors: Poirier Raymond A. , Daudel Raymond , Csizmadia Imre G.
Published: December 2004

Comparison of the molecular Q‐optimized and molecular gradient optimized carbon basis sets for CH4 showed that molecular Q optimization is an excellent substitute to the more expensive molecular gradient optimization. The parameter Q of the Q optimization is related to the population (i.e., net charge) on the atom.
Dna‐Dependent rna polymerase from E. coli: Structure investigation
Authors: Marchenko T. V. , Lipkin V. M. , Yu. Chertov O. , Sverdlov E. D. , Ovchinnikov Yu. A.
Published: December 2004

E. Coli RNA polymerase holoenzyme consists of two large subunits—β and β' (molecular weights 155,000 and 165,000), of two identical α subunits (molecular weight 36,500), and of the initiation factor α (molecular weight 86,000). The complete amino acid sequence of the RNA polymerase α subunit was determined. According to the primary structure the polypeptide chain of the α subunit has a molecular weight of 36,512 and consists of 329 amino acid residues. In order to determine the primary structure of large β and β' subunits of E. coli RNA polymerase, the protein fragmentation and sequencing procedure was combined with sequencing of the corresponding structural genes, which facilitated the ordering of the peptide fragments obtained during sequencing of the polypeptide chains. In all, 4714 base pairs of the rpoBC operon were sequenced including the entire structural gene of the β subunit and an initial segment (528 base pairs) of the β' structural gene. The β subunit appeared to consist of 1342 amino acid residues from which molecular mass was calculated to be 150618.6 daltons. The spatial organization of DNA‐dependent RNA polymerase was studied with the aid of chemical modification and limited proteolysis. Photochemical affinity modifications were used to find out subunits of the enzyme responsible for binding of the DNA template and the RNA product.
Molecular orbital studies on nucleoside antibiotics. IV. conformation of 3'‐deoxyadenosine (cordycepin) and 3'‐amino‐3'‐deoxyadenosine
Authors: Saran Anil , Patnaik Lalit N.
Published: December 2004

PCILO computations have been carried out on the conformation of 3'‐deoxyadenosine (cordycepin) and 3'‐amino‐3'‐deoxyadenosine. These nucleoside antibiotics results as a consequence of modification in the sugar part of adenosine. Both C(2')‐endo and C(3')‐endo sugar puckerings have been considered in the computations and the results obtained indicate that these nucleoside antibiotics have very similar conformational preferences as compared to those of the parent nucleoside adenosine. This similarity which is quite marked in aqueous solution has important biological significance.
Significance of the electron trap parameters of glow curves of photosynthetic membranes
Authors: Tatake V. G.
Published: December 2004

Several methods are available to determine the electron trap parameters such as activation energy E, preexponential frequency factor s, and the lifetime τ of the electrons in the trap states in photosynthesis. These parameters are also related by the Arrhenius expression which helps in calculating the E values without any assumptions regarding the particular order of kinetics applicable or the values of preexponential factors. Subsequent calculation then yields the values for s and τ in a straightforward manner. However, application of these methods (as well as the Arrhenius expression) to some of the experimental data has recently yielded such values that give rise to some questions regarding the meaning attributable to these parameters. The significance of these findings are discussed in view of the correlation of thermoluminescence and delayed light emission studies in photosynthetic membranes.
Active transport in the light of thermodynamics of open systems
Authors: Panda B. C.
Published: December 2004

A brief thermodynamic analysis of transport processes in open systems is presented. It is shown that the concept of an active transport in the usual sense of the existence of a flow against the direction of its conjugate force is operationally unrealistic. The so‐called metabolically coupled active transport has been shown to be mathematically falacious. The experimental establishment in favor of the active transport process by the use of metabolic inhibitors has been logically disproven. From this analysis it is naturally concluded that all transport processes in the living organisms can be reduced to passive ones if one recognizes all the possible potential gradients existing in the system. Assuming the existence of active transport process is as erroneous as taking for granted a vital force explaining the life phenomena. It simply indicates our lack of knowledge about the pattern of superposition of a complete set of driving forces or about the nature of a yet unknown physical driving force and the generating mechanism of such a force.
Relationship of correlation energy and size
Authors: Ang M. H. , Yates K. , Csizmadia I. G. , Daudel R.
Published: December 2004

Analysis of available data on atoms has led to a relatively simple empirical relationship between the correlation energy and second moment , a measure of the size of the electron density. With the aid of this simple relationship it is possible to predict correlation energies with fair accuracy given the SCF or Hartree–Fock limit values for the size of the electron density. Preliminary extensions of this work to two‐ and ten‐electron molecules indicate that it may be possible to predict molecular correlation energies to semiquantitative accuracy from SCF data on the electronic distribution.
Inclusion of hydrogen p orbitals in the semiempirical calculation of NMR parameters. III: INDO CHF calculations of orbital and dipolar contributions to spin–spin coupling constants involving protons
Authors: Facelli J. C. , Contreras R. H.
Published: December 2004

The self‐consistent perturbation theory is used to calculate noncontract contributions to spin–spin coupling constants involving protons. Molecular wave functions were obtained with a modified version of the INDO method which includes hydrogen 2p orbitals in its basis set. It is found that in many cases the orbital and dipolar terms are by no means negligible, being particularly important in geminal HH couplings. Results reported in this paper for this type of coupling, reproduce experimental trends in the series CH4, NH3, and OH2. In general, noncontact terms are found to decrease as the number of bonds separating the interacting nuclei increases.
Studies in Löwdin's partitioning technique in quantum theory. I. Invertibility of the operator K
Authors: Wilson R. G. , Sharma C. S.
Published: December 2004

In this paper we establish the necessary and sufficient conditions for the invertibility of the operator K in Löwdin's treatment of the partitioning technique for the solving problems in quantum mechanics.
Self‐Consistent APW–k · p method. II. Application to NaCl
Authors: Da Cunha Lima I. C. , Da Silva A. Ferreira , Parada N. J.
Published: December 2004

The self‐consistent APW–k · p method is utilized to obtain the band structure of NaCl in the “muffin‐tin” approximation. Qe have investigated the convergence of many intermediate results, e.g., crystalline potential, matrix elements of the momentum operator, and energy eigenvalues at the Γ point. The summation in reciprocal space, included in the definition of the matrix D of the theory, is performed by direct sum and also by a special points technique. For the convergence criteria used, the results converged after five iterations.
Calculation of one‐electron properties using limited configuration interaction techniques
Authors: Raghavachari Krishnan , Pople John A.
Published: December 2004

One‐electron properties may be evaluated by configuration interaction methods using analytical differentiation of the total energy with respect to an external perturbation parameter. Dipole moments are reported using such a method for CO and H2CO. Inclusion of single substitutions does not change calculated dipole moments appreciably with this method. The differences between this method and the direct evaluation of an expectation value are discussed.
Computer‐generated formulas for two‐center coulomb integrals over slater‒ type orbitals
Authors: Jones Herbert W.
Published: December 2004

Formulas can be automatically generated for all two‐center Coulomb integrals over Slater‐type orbitals by means of the “C‐matrix” single‐center expansion method with use of “computer algebra.” The formula coefficients may be stored in two‐dimensional arrays.
Perturbation theory in large order for some elementary systems
Authors: Bender Carl M.
Published: December 2004

Reasons for understanding the general problem of perturbation theory in large order are discussed. It is shown that the behavior of perturbation theory in larger order is generally very simple because it reflects just the semiclassical content of the theory. Many simple examples are given, including some graph‐counting problems. The behavior of mass‐renormalized perturbation series for some very simple field‐theory models is examined. It is shown that mass renormalization hardly affects the large‐order behavior of a weak‐coupling perturbation series. However, in a strong‐coupling perturbation series mass renormalization has a dramatic effect.
Unified derivation of the perturbation series for the real and imaginary parts of the energy of hydrogen in the stark effect and of the negatively anharmonic oscillator
Authors: Silverstone Harris J.
Published: December 2004

The wave function for hydrogen in the Stark effect (or for the negatively anharmonic oscillator) with an outgoing‐wave boundary condition, constructed in Langer‐Cherry fJWKB form, is continued back to the origin. The asymptotic expansions for ReE and ImE are determined by the requirement that the wave function be regular at the origin to zeroth and first order in the exponentially small parameter that characterizes ImE. One fJWKB function turns out to be the Rayleigh‐Schrödinger perturbation theory wave function.
Numerical estimates of the convergence of the Rayleigh‐Schrödinger perturbation expansions for the energy levels of various models of the benzene molecule
Authors: Pellegatti Alain , Čížek Jiří , Paldus Josef
Published: December 2004

We estimate radii of convergence of the Rayleigh‐Schrödinger perturbation expansions for various energy levels of the π‐electron model of the benzene molecule, described by the Hubbard Hamiltonian in both weakly and strongly correlated limits. They are determined using a “generalized” Cauchy criterion applied to the numerically determined coefficients of the pertinent expansions.
Superoperator approach to propagator approximations
Authors: Weiner Brian , Goscinski Osvaldo
Published: December 2004

The superoperator formalism for matrix propagators is reviewed, with special attention to the validity of superoperator resolution of the identity. The equation of motion for the particle‐hole propagator is discussed. Decoupling procedures based on inner projections and partitioning are examined showing the desirability of self‐consistent approximations. The conditions under which a state can be a vacuum for a given linear manifold of operators are analyzed.
Coupling of internal rotations in propanelike molecules
Authors: Wesenberg G. , Weinhold F.
Published: December 2004

A linear‐combination‐of‐bond‐orbitals (LCBO) formulation of INDO–SCF–MO theory is employed to investigate the origin of rotation barrier coupling in propane and related molecules. The dominant contributions to rotor coupling in propane are identified to be (i) a direct steric (bond–bond) interaction, involving the close approach of two methyl CH bonds in the eclipsed–eclipsed geometry, and (ii) a nonvicinal bond–antibond effect, which arises when the side of a σCH bond orbital in an eclipsed methyl group comes into favorable overlap with the “backside” lobe of the coplanar σ antibond in the staggered–eclipsed geometry. A smaller nonadditive interaction of each methyl rotor with the central group is noted to be of importance when the central atom contains lone pairs. Aspects of this qualitative picture, and its dependence on geometry changes, are tested in applications to (CH3)2CHF, (CH3)2NH, (CH3)2O, (CH3)2CCH2, (CH3)2CO, and C(CH3)4.
Ab initio Hartree–Fock–Slater calculation of Tetrathiafulvalene (TTF) and the TTF1+ and TTF2+ ions
Authors: Trsic M. , Laidlaw W. G.
Published: December 2004

The electronic structures of TTF, TTF1+, and TTF2+ are described by means of an ab initio Hartree–Fock–Slater procedure with a double‐zeta STO basis. Electronic and photoemission spectra, bonding, and charge distributions are discussed and compared to experiments and previous calculations.
Connections between perturbation theory and the Van Vleck transformation: Illustrative calculations on the perturbed harmonic oscillator
Authors: Westhaus Paul
Published: December 2004

We continue to examine the connection between perturbation theory and the Van Vleck unitary transformation. Here we illustrate the formalism derived earlier by applying it to compute the stationary states of the perturbed harmonic oscillator. We find that each solution of the traditional Brillouin‐Wigner perturbation theory equations gives rise to a different unitary transformation which, when operating on the unperturbed ground state, produces one or the other of the perturbed eigenstates. With any of the perturbed states able to be reached by a unitary transformation on the unperturbed ground state, we advise caution in using approximate solutions of the perturbation equations in general cases, lest an unexpected stationary state be obtained.
Construction of an effective hamiltonian for open‐shell molecular systems
Authors: Biskupič Stanislav , Kvasnička Vladimír
Published: December 2004

An effective Hamiltonian for open‐shell molecular systems is constructed. The unrestricted Hartree–Fock orbitals are applied as a basis set of one‐particle functions. This effective Hamiltonian is determined as a simple product of the original total Hamiltonian and the spin annihilator. The second‐quantization formalism and the Feynman–Goldstone diagrammatic technique are used. The resulting effective hamiltonian is composed of zero‐ to four‐particle terms. A possibility of applying the nondegenerate diagrammatic perturbation theory constructed over this effective Hamiltonian is discussed.
Charge and spin correlation structures of conjugated π systems: Analysis of full CI wave functions of the PPP hamiltonian
Authors: Hashimoto Katsufumi
Published: December 2004

An analysis of the electronic correlation structures by means of the charge and spin correlation functions is carried out for full CI wave functions of four, five, and six membered conjugated π systems described by the Pariser–Parr–Pople Hamiltonian. The low‐lying states of these systems are classified as covalent (CV) and ionic (IN) states depending on whether the probability of finding two electrons simultaneously at the same position is small or large. It is found that many of excited CV states, the typical ones of which are the 21Ag state of linear π systems, have stronger CV character than the ground CV state, and their spin coupling structures are different from each other as well as from that of the ground CV state. The spin coupling structure in the ground CV state has an “antiferromagnetic” spin arrangement in favor of antiparallel coupling between nearest neighbor spins while in excited CV states the extent of the antiparallel spin coupling between nearest neighbor sites is decreased. IN states, which are less common for low‐lying states than CV ones, are also found to have characteristic modulations in the charge correlation. In particular, the charge correlations in the lowest singlet IN states, 11Bu of linear π systems, 11B2g of cyclobutadiene and 11B1U of benzene, are alternating.
Reduced local energy as a criterion for the accuracy of approximate Hartree–Fock wave functions. Application to H2O and CH4
Authors: Grelland Hans H. , Almlöf Jan
Published: December 2004

The reduced local energy EL of Rothstein and co‐workers is discussed as a criterion for the local accuracy of approximate wave functions. The behavior of EL for different approximation levels is discussed. It is shown that, for particular classes of wave functions, fluctuations of EL reflect local inaccuracies of the wave function as compared to certain convergence limits. The applicability of this criterion is illustrated with approximate Hartree–Fock wave functions for water and methane.
Transformation of spin projected slater determinants under orbital permutation
Authors: Gallup G. A.
Published: December 2004

This paper gives a proof that spin projected Slater determinants provide a basis for Young's natural representation of the symmetric groups under permutation of the orbitals. The general reduction of sums of spin projected Slater determinants to give functions of pure spatial symmetry type requires this transformation.
Evaluation of two‐center overlap and coulomb integrals derived from slater‐type orbitals
Authors: Jones Herbert W.
Published: December 2004

The strategy for the evaluation of two‐center overlap and Coulomb integrals is illustrated by using computer‐generated formulas produced from 1s orbitals. There is no loss in generality as these formulas have the same structure for higher quantum numbers. For small parameter values, singularities may be removed from the formulas by expanding exponential functions and collecting coefficients of like powers by machine. Suitable terminated expansions, along with exact formulas, permit high accuracy throughout the entire possible range of parameter values.
Potential adaption: Use of polynomials as anharmonic oscillator potentials
Authors: Gustav Klaus , Colditz Roland
Published: December 2004

A potential adaption procedure by means of polynomials is described for diatomic molecules. The conditions of the adaption and numerical results obtained on the basis of the model are presented.
Quantitative structure activity relationships for some antitumor platinum(II) complexes
Authors: Abdul‐Ahad P. G. , Webb G. A.
Published: December 2004

The INDO–SCF method is used to provide electronic indices which are used as independent variables. These attempt to account for the variation in the antitumor activity and toxicity observed within a series of analogs of cis‐diamino dichloro platinum(II).
Two‐body operator matrix elements for pure and mixed orbital configurations in the unitary group approach
Authors: Kent R. D. , Schlesinger M.
Published: December 2004

A complete list of expressions is given covering all possible types of nontrivial two‐body operator matrix elements in the unitary group approach. The matrix elements are expressed in terms of factors which depend on the unique spin coupling chain indicated by each Weyl tableau. The method applies equally to pure and mixed orbital configurations. The results extend and clarify previous general treatments of Drake and Schlesinger and Paldus and Boyle. We worked out two examples of 3(ƒ4) matrix elements of V4. V4 interaction and of 4(ƒ5)→4([2(ƒ3)]d2) matrix elements of V1 · V1 interaction.
Remarks on the use of the average occupation numbers in the SCF process for open shell systems
Authors: Colle Renato , Salvetti Oriano
Published: December 2004

It is shown that the utilization of an average occupation number for open shell orbitals, having different occupation numbers in a degenerate wave function, tantamounts to disregard first order contributions in a CI‐type expansion of the wave function. These contributions are taken into account in a SCF process that derives the differently occupied open shell orbitals as eigenfunctions of different Fock‐type operators and accounts for the total symmetry.
Generalized Euler transformation in extracting useful information from divergent (asymptotic) perturbation series and the construction of Padé approximants
Authors: Bhattacharyya Kamal
Published: December 2004

Euler transformation for accelerating convergence of a series is considered in the context of handling divergent (asymptotically convergent) perturbation series. A generalized (parametrized) version of this transformation is developed, based on the conjecture of Dalgarno and Stewart, which works better. Viewed from this standpoint, the Padé approximants follow as a special case of the parametrized Euler transformation (PET), as is the case with the μ transformation procedure of Feenberg in a perturbative context. The PET is shown to serve as a more general method of handling a divergent series and is able to appreciate the construction and convergence behavior of specific sequences of Padé approximants. The role of parametrization in the context of the Z−1 perturbation theory of atoms is also noted and the workability of the adopted strategy is demonstrated by choosing some specific test cases.
Unrestricted‐Hartree–Fock wave functions approximating low‐lying covalent states of ring π systems
Authors: Hashimoto Katsufumi
Published: December 2004

We show that spin projected unrestricted‐Hartree–Fock (PUHF) wave functions are able to well approximate some low‐lying covalent states of ring π systems. The UHF wave functions belong to either the axial or torsional spin density wave class. Their spin structures are found to be approximations for the spin correlation structures of the corresponding exact wave functions. The PUHF wave functions become close to exact eigenstates with homopolar valence bond characters in the strong correlation limit.
Dilated Weyl theory applied to a set of N‐coupled singular second‐order differential equations
Authors: Elander Nils , Rittby Magnus , Brändas Erkki
Published: December 2004

Weyl's theory for a set of N‐coupled singular second‐order differential equations is analyzed in relation to S‐matrix theory and a dilated version is presented. Applications of this theory to two single channel scattering model problems and a two‐channel model problem are given. Some implications of the present theory are discussed.
Kinetic theory of bridge processes
Authors: Christophorov L. N. , Gorbach V. V. , Kharkyanen V. N.
Published: December 2004

The detailed consideration of the kinetic aspect of the bridge process has allowed us to correctly write a kinetic equation beginning with knowledge of system microparameters. The solution of the equations makes it possible to elucidate the character of the relaxation process and to determine its typical constants as functions of those microparameters. Particular attention was given to kinetics in the presence of polaron effects. In this case the standard perturbation theory applied to derive the kinetic equations is not valid. The solutions obtained for this case are different both in the form of correlation functions and in the character of the interaction taken into account.
Localized bond model for molecular energy to fourth order in perturbation theory
Authors: Cullen John M. , Zerner Michael C.
Published: December 2004

The localized bond model of Malrieu, Diner, and Claverie is extended to fourth order in perturbation theory. Single, double, triple, and quadruple replacements from the doubly occupied bonding reference function are included utilizing a symmetric form of diagrammatic perturbation theory. The fourth order theory derived executes on a computer as quickly as does the third order theory. Results are examined utilizing the Pariser–Parr–Pople and CNDO/2 model Hamiltonians, and are compared with third order results and with either exact results where they are known, or with a configuration interaction of all singles and doubles. The influence of the initial hybridization, localization, and bond polarization is discussed. In general, the fourth order corrections are of comparable size to third order. Improvement in results appears to be marginal in the Nesbet–Epstein scheme in passing to fourth order because of the oscillating nature of the series; for Moller–Plesset theory errors are approximately halved. The relative energies as a function of modest geometry change about minima is about the same at third order as it is at fourth for most cases examined.
Further calculations on the internal rotation spectrum of phenol
Authors: Smeyers Y. G. , Hernández‐Laguna A.
Published: December 2004

The influence of a small deformation of CĈO angle in phenol (tilt), into the rotational far‐infrared (FIR) spectrum is analyzed using several approaches. In all of them, the CNDO/2 method is used to determine the potential energy functions. In a first step, the CO bond and the rotation axis are both supposed to coincide with the C2 symmetry axis of the phenyl group. With this assumption the torsional frequencies are calculated in both the symmetric and asymmetric rotor approximations. In a second step, the tilt of the COH bond is determined theoretically and found to be −3°, measured from the C2 symmetry axis, the COH bond crossing this axis, Using this second geometry, and taking as the rotation axis the C2 axis, the torsional frequencies are again determined in both approximations. An improvement of the calculated transition energies is encountered at each stage of the calculation, when compared with experimental data. Finally the importance of the introduction of a tilt into the FIR torsional frequency calculations is discussed.
Electrostatic potential around halogenated anesthetics. Acidic hydrogen; chlorine vs. fluorine
Authors: Ruelle P. , Sandorfy C.
Published: December 2004

Maps of electrostatic potential around a number of halocarbon anethetics have been obtained through Gaussian ab initio calculations. Information is obtained on the mode of association of these compounds with possible receptors. The positive potential found along the extension of the CH bonds substantiates the role of the “acidic hydrogen.” The presence of fluorines on the carbon atom to which it is bound restricts the access to this positive site through the repulsive action of the fluorine lone pairs, an observation that explains the very different behavior of chloroform and fluoroform, for example, with respect to their anesthetic potencies and hydrogen bonding abilities. In the absence of an acidic hydrogen the chlorine atoms can serve as associative sites.
Obtaining self–consistent wave functions which satisfy the virial theorem
Authors: Magnoli Douglas E. , Murdoch Joseph R.
Published: December 2004

The virial theorem has played an important role in applying quantum mechanics to chemical problems. It has served as one criterion of a satisfactory wave function and its consequences on chemical bonding, molecular structure, and substituent effects have been analyzed extensively. A common method of gaining compliance with the virial theorem is to introduce a “scale” factor which adjusts all distances by a factor η. Optimizing the scale factor through the variational principle produces a wave function satisfying the virial theorem. In the present paper it is shown that when this “scaling” procedure is applied to self‐consistent wave functions, the virial theorem can be satisfied, but self‐consistency is lost. Scaling generally has a small effect on the total energy, but the effects on the energy components (T, Vne, Vee, Vnn) can be two to three orders of magnitude larger and in the range of tens to hundreds of kcal. Consequently, for applications where the energy components are useful, it is highly desirable to obtain wave functions which satisfy the virial theorem and are self‐consistent. In the present paper, a simple, inexpensive extrapolation technique is reported which requires one integral evaluation and two SCF cycles to achieve convergence. Applications to atoms and small molecules are reported.
Cluster analysis of the full configuration interaction wave functions of cyclic polyene models
Authors: Paldus J. , Boyle M. J.
Published: December 2004

The first two members of the cyclic polyene homologous series are studied over a wide range of the coupling constant using the Hubbard and Pariser–Parr–Pople model Hamiltonians. The full and various limited configuration interaction (CI) correlation energies and wave functions are calculated exploiting the unitary group approach. The formalism for the cluster analysis of the exact wave function expressed through the unitary group formalism electronic Gelfand states is developed and applied to the full CI wave functions of the cyclic polyene models studied. It is shown that the connected tetraexcited clusters become essential in the fully correlated limit and that their contribution also significantly increases with electron number even for the coupling constant corresponding to the spectroscopic parametrization of the model Hamiltonians used.
Thomas–Fermi term as the simplest correction to the Weizsacker term
Authors: Ludeñta Eduardo V.
Published: December 2004

The nature of the correlation function G(1,2) appearing in the definition of the reduced first order density operator γ′(1,2) = ρ(1)1/2ρ(2)1/2G(1,2) is analyzed. It is shown that when G(1,2) is expanded in terms of plane waves in the context of a single‐determinant approximation to the wave function, the correction to the Weizsacker term in the kinetic energy density expression is the Thomas–Fermi term.
Löwdin partitioning in a Lanczos basis: Applications to scattering states
Authors: Hermann M. R. , Langhoff P. W.
Published: December 2004

Methods are reported for construction of closed‐form optical potentials that provide useful L2‐basis‐set approximations to the discrete and continuum Schrödinger states of self‐adjoint Hamiltonian operators. The potentials are obtained employing information from a finite (Lanczos) reference space only, but nevertheless correspond to explicit summation over an infinite‐dimensional remainder space. Connections are indicated between the Stieltjes–Tchebycheff orbital solutions of the resulting optical‐potential Schrödinger problem and previously described corresponding moment‐theory approximations to spectral densities and distributions. Use of a Lanczos basis insures that the orbital eigenvalues are generalized Gaussian or Radau quadrature points of the spectral density, and that their (reciprocal) norms provide the associated quadrature weights. Convergence of the orbitals in the limit of high order is obtained to Schrödinger eigenstates of finite norm in the discrete spectral region, and to scattering states of improper (infinite) norm in the essential portion of the spectrum. In finite orders the spatial characteristics of the Stieltjes–Tchebycheff orbitals correspond to spectral averages in the neighborhoods of the quadrature points over the correct Schrödinger states. Explicit closed‐form expressions are obtained for the spectral content of individual orbitals in terms of orthogonal polynomials without reference to the correct Schrödinger states. A computational application to regular Coulomb l waves illustrates the nature and convergence of the development.
Concept of the “stability” of the quantum mechanical state
Authors: Tachibana Akitomo
Published: December 2004

A new concept of the “stability” of the quantum mechanical state is presented. This concept is closely related to the hydrodynamical theory of quantum mechanics. For charged particles, the “stability” against the application of the external electromagnetic field is examined. Under a nonlinear interaction, a new type of the solitonlike phenomenon is shown as a novel, illustrative example of the “stable” state. An extension for the relativistic treatment is also examined.