bluuebunny/crossref_metadata_2025 huggingface dataset:
Quantitative approach to conformations of proteins
Authors: Popov E. M.
Published: December 2004

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.
Determination of the secondary structures of proteins by circular dichroism spectra. Calculation of the protein basic circular dichroism spectra for antiparallel and parallel β‐structures and β‐bends
Authors: Bolotina I. A. , Chekhov V. O. , Lugauskas V. Yu.
Published: December 2004

New “reference” circular dichroism spectra of α helix, β‐structure (both parallel and antiparallel), β‐bends, and the unordered form are obtained from circular dichroism spectra and x‐ray data for six proteins (myoglobin, lysozyme, lactate dehydrogenase, papain, ribonuclease, and subtilisin BPN′). Circular dichroism spectra for α‐helix and antiparallel β‐structure are similar to those for poly(Llysine). The circular dichroism spectrum of the parallel β‐structure is qualitatively similar to that theoretically calculated by Madison and Schellman. The circular dichroism spectrum of β‐bends is qualitatively similar to that theoretically calculated by Woody. The spectrum of the unordered form is close to that of the denaturated proteins. These “reference” circular dichroism spectra used for the analysis of the secondary structure of ten globular proteins (besides the six reference proteins D‐glyceraldehyde 3‐phosphate dehydrogenase, concanavalin A, cytochrome c, and insulin).
Polarization Green's function with multiconfiguration self‐consistent‐field reference states
Authors: Banerjee Ajit , Kenney John W. , Simons Jack
Published: December 2004

The polarization Green's‐function formalism in the superoperator notation of Goscinski and Lukman is re‐derived using a multiconfiguration self‐consistent‐field (MC‐SCF) reference state to establish the superoperator metric. The potential advantages of employing this more general reference state in Green's‐function theories and certain inherent weaknesses associated with the traditional Hartree–Fock or Rayleigh–Schrödinger perturbation theory reference state choices are briefly discussed. The Hermiticity of the superoperators is analyzed within the framework of the MC–SCF reference state. Using a concept of order appropriate for this reference state choice, explicit formulas and computational procedures for the implementation of this Green's‐function theory are presented and specialized to include terms consistent through second order.
Collinear collision of an atom with a homonuclear diatomic molecule
Authors: van Dijk W. , Razavy M.
Published: December 2004

The problem of collinear scattering of an atom from a homonuclear diatomic molecule is formulated in terms of a first‐order nonlinear matrix differential equation for the variable coefficient of reflection. For a homonuclear molecule when the target Hamiltonian is invariant under the parity transformation, only transitions between even states or odd states are possible. This selection rule reduces the number of open or closed channels that contribute to the reflection and transmission coefficients. But for numerical calculation, under the conditions of the problem, one can approximate the target Hamiltonian by the Hamiltonian of a displaced harmonic oscillator. In this approximation, the reflectional symmetry of the Hamiltonian is not preserved and transitions between any two levels of the target are possible. To simplify the problem further, the interaction between the projectile and the target is assumed to be a sum of two Gaussian terms. For this combination of the potentials the many‐channel interaction can be expressed analytically. By fitting the Lennard–Jones potential with a sum of two Gaussian potentials and solving the matrix differential equation, transition probabilities are obtained for the HeH2 collision. The numerical results are compared with the results found by Secrest and Johnson, and by Clark and Dickinson.
Exact‐exchange Hartree–Fock calculations for periodic systems. I. Illustration of the method
Authors: Pisani C. , Dovesi R.
Published: December 2004

A scheme is presented for performing linear‐combination‐of‐atomic‐orbitals (LCAO) self‐consistent‐field (SCF) ab initio Hartree–Fock calculations of the electronic structure of periodic systems. The main aspects which characterize the present method are (i) a thorough discussion of both translational and local symmetry properties and the derivation of general formulas for the transformation of all the relevant monoelectronic and bielectronic terms under symmetry operators. (ii) The use of general yet powerful criteria for the truncation of infinite sums; in particular, the Coulomb electron–electron interactions are subdivided into terms corresponding to intersecting or nonintersecting charge distributions; the latter are grouped into shell contributions and the interaction is evaluated by multipolar expansions; the exchange interaction may be evaluated with great precision by retaining a relatively small number of two‐electron integrals according to a truncation criterion which fully preserves its nonlocal character. (iii) The use of a procedure for performing integrals over k, as needed in the evaluation of the Fermi energy and in the reconstruction of the Fock matrix, which is particularly simple because it employs partially intersecting small spheres as integration subdomains where linear extrapolation is admitted. A comparison is finally made of our fundamental equations in the critical SCF stage with those obtainable by a recent proposal which uses Fourier transforms to express Coulomb and exchange integrals.
Approximate theoretical determination of molecular static polarizabilities
Authors: Seger G. , Kochanski E.
Published: December 2004

Molecular polarizabilities are computed using ab initio SCF wave functions and second‐order perturbation theory with special attention given to the use of a shifted denominator. Rather small basis sets are used, in order to obtain reasonable values at a reduced cost. Results are presented for H2, CO, H2O, C2H4, OCS, C6H6, Cl2, Br2, I2.
Gaussian expansions of hydrogenic functions involving few variational parameters
Authors: Hoor Marten J. Ten
Published: December 2004

Fully optimized lengthy Gaussian expansions of hydrogenic 1s and 2pz functions have been practically reproduced by generating the variational parameters by means of suitably chosen functions involving only few parameters. Hydrogenic 3dxy and 4fxyz functions have been approximated in a similar way. The usefulness of such generating functions is briefly discussed.
Optical oscillator strengths for lithium
Authors: Ganas P. S.
Published: December 2004

A simple two‐parameter analytic potential adjusted so as to reproduce the experimental energy levels is used to generate wave functions for the ground and excited states of the lithium atom. Using these wave functions in conjunction with the Born approximation and the Russell–Saunders LS‐coupling scheme, we calculate the optical oscillator strengths for various excitations from the 1s22s(2S1/2) ground state. The results are compared to experiment and other calculations.
How similar is a molecule to another? An electron density measure of similarity between two molecular structures
Authors: Carbó Ramon , Leyda Luis , Arnau Mariano
Published: December 2004

A matching measure between two molecular structures based on density functions is described. Some examples related with an alarm pheromone activity are given; the results encourage the possible use of similarity density concepts in molecular engineering.
Ab initio Hartree–Fock and multiple‐scattering Xα calculation of the g factors for CuF2
Authors: Larsson Sven , Hehenberger Michael , De Mello Paulo Corrêa
Published: December 2004

Ab initio Hartree–Fock and multiple‐scattering wave functions are calculated for linear CuF2. These wave functions are used to calculate the spin–orbit coupling in a new way where the neglect of two‐ and many‐center terms is avoided and where experimental or calculated spin–orbit coupling constants for the atomic ions are used. The calculated value of g is too small by the MSXα method and too large by the ab initio method, indicating too much 3d–L interaction in the MSXα case and too little in the ab initio case.
Modified PCILO method. II. Second‐order energy and geometry of transition‐metal halides
Authors: Boča R. , Pelikán P.
Published: December 2004

The modified PCILO method, for which the use of the Rayleigh–Schrödinger many‐body perturbation theory with the Møller–Plesset type of Hamiltonian partitioning is characteristic, has been extended to energy calculations of transition metal compounds. On the CNDO/2 level of the Hamiltonian approximation the energy and geometry of the ions CuX42−, MCl42− and the molecules CuX (X = F, Cl, Br; M = Mn, Fe, Co, Ni, Cu) have been calculated. The comparison with MOLCAOSCF calculations (CNDO/2–UHF) shows that the localized bonding model used here can be regarded as a good zeroth‐order approximation describing the bonding situation in complexes of this type. The perturbation theory also provides an improvement of the harmonic force constants of the CuX molecules with respect to the SCF level of approximation.
Absorption spectrum of manganian andalusite: Cluster calculation by an ab initio method
Authors: Hehenberger Michael , Hålenius Ulf , Larsson Sven
Published: December 2004

The ground state and the first few excited states of an MnO69− cluster are calculated in the unrestricted Hartree–Fock model. The state ordering is 5B1 g, 5A1 g, 5B2 g, and 5Eg as can be expected from simpler models. Consistent with the results by the same method for copper complexes, we obtain d–d transition energies about one half or less of the experimental energies. The charge transfer spectrum is subject to a large spin polarization in the sense that the lowest charge transfer state (5Eu) has five unpaired spins on Mn.
Classical nonlinear field theory of chemical bonding
Authors: Hartmann Hermann , Chung Kyu‐Myung
Published: December 2004

A certain type of classical nonlinear field theory of chemical bonding has been proposed. The interaction between two neighboring atoms is assumed to be nonlinear. The coupled field equations are decoupled applying the methods of parametrization. The field energy associated with the coupled field has been determined perturbation theoretically. The chemical bonding energy equivalent to the change of field energy due to the coupling has been expressed in a closed form. The bonding energies of the molecules Li2, Na2, and K2 are evaluated.
Theoretical model for the phase transition of a membrane as a multicomponent system
Authors: Hosokawa Masahiko
Published: December 2004

A theoretical model is given that describes the nature of a membrane that is made up of several species of lipids. The model will partially simulate the biomembrane through numerical analysis.
Hypervirial analysis of enclosed quantum mechanical systems. I. Dirichlet boundary conditions
Authors: Fernández Francisco M. , Castro Eduardo A.
Published: December 2004

Diagonal hypervirial relations are applied to enclosed one‐dimensional systems when wave functions obey Dirichlet boundary conditions. A general formula for the energy is derived and it shows a striking difference with the usual formulas through an “extra” term. It constitutes a generalization of previous ones for the virial theorem when there exist nonusual boundary conditions. The values obtained are compared with other approximate methods. Several extensions are proposed.
Hypervirial analysis of enclosed quantum mechanical systems. II. von Neumann boundary conditions and periodic potentials
Authors: Fernández Francisco M. , Castro Eduardo A.
Published: December 2004

Previous results on the hypervirial analysis of confined systems are extended. Periodic potentials are discussed and an efficient alternative way to solve the Mathieu equation is proposed.
Some recent developments in the quantum theory of hydrogen bonding and other effects in proteins
Authors: Peters David , Peters Jane
Published: December 2004

Standard ab initio quantum chemical computations are quite effective in throwing light on binding features of biomolecules, in particular, hydrogen bonds. This is illustrated by a brief survey of recent work, including some interesting preliminary results on dipeptides, tripeptides, and tetrapeptides. Differential‐energy maps for analyzing results are presented and discussed. Basic theoretical questions, such as the significance of minimal‐basis calculations and localization on a subsection of a macromolecule, are also discussed.
Potential energy surface of the system CO + O: An ab initio study on the OCO bond formation
Authors: Bonapasta A. Amore , Bossa M. , Lapiccirella A.
Published: December 2004

Quantum mechanical computations on the potential energy surface of the system CO + O at an SCF–MO ab initio level are presented and discussed. The calculations are performed on a minimal basis set of atomic functions. Comparison with results obtained with extended basis sets are also presented.
Bond model for semiconducting materials
Authors: Garbato L. , Manca P. , Mula G.
Published: December 2004

A bond model directly derived from an LCAO Hamiltonian is applied to the study of Group IV elemental semiconductors. The derivation has been made through suitable approximations of the interaction integrals. The average and the lowest energy gaps of C, Si, Ge, and α‐Sn are then computed with the use of just one parameter. The overall reliability of the model has been checked by computing the lattice dilatation contribution to the temperature coefficient of the lowest energy gap of Ge. The result is in excellent agreement with the experiment.
Structure and function of Buthus eupeus scorpion neurotoxins
Authors: Grishin E. V.
Published: December 2004

At present the investigation of the complex mechanism of the signal conductance between nerve cells and their target organ is closely connected with application of neurotoxins as a valuable tool for study of important sites involved in nerve transmission. Particular interest is attributed to neurotoxins from scorpion venoms which slow down the inactivation rate of fast sodium channels of the excitable membrane. Fifteen different toxins have been isolated from Buthus eupeus scorpion venom by means of the combination of gel and ion exchange chromatography. The homologous insectotoxins I1, I3, I4, and I5 belong to the new structural type of scorpion toxins. The essential features of these toxins are low molecular weight (ca. 4000) and the presence of two or three methionine residues in their amino acid compositions. The complete amino acid sequences of two insectotoxins and one mammalian toxin have been estimated. All mammalian neurotoxins in concentration from 10−9M to 10−7M slow down the inactivation rate of fast sodium channels. The direct covalent binding of photosensitive radioactive neurotoxin derivatives presents one of the most effective approaches to the localization of the functionally important components of the fast sodium channels. Thus far 2,4‐dinitro‐5‐fluorophenylazide has been used for chemical modification of the mammalian neurotoxin M10. The prepared monosubstituted photosensitive neurotoxin derivative possessed a high biological activity according to the voltage clamp data. The neurotoxin derivative has been iodinated by 125I, the resulted product being both radioactively and photoaffinity labeled. Both native neurotoxin M10 and sea anemone toxin competitively inhibit the reception of the scorpion toxin derivative by rat brain synaptosomes. It was shown that covalent toxin‐receptor complexes are composed of two protein components with molecular weights 76,000 and 51,000, being near equal for synaptosomes, neuroblastoma cells, and crab nerve plasma membranes.
Energy calculations on helical polypeptides: Structure of polyglycine II
Authors: Balaji V. N.
Published: December 2004

Single chain and packing energy calculations have been made on polyglycine (threefold and fourfold helical structures) with interchain NH…︁O hydrogen bonds. In conformation A of polyglycine, in which the NH groups point away from the helix axis and the CO groups are nearer to the helix axis, the conformational energy is nearly the same for threefold and fourfold structures. However, the minimum energy conformation corresponds to a threefold structure of polyglycine with peptide configurations in conformation B in which the CO groups point away from the helix axis and NH groups are nearer to the helix axis. This structure is consistent with the polyglycine II x‐ray diffraction data.
Van der Waals force between two localized clusters of bosons
Authors: Mishra R. K. , Bhaumik K. , Srivastava A. , Chaudhary S. S.
Published: December 2004

In traditional quantum electrodynamic derivation of a intermolecular van der Waals force, the molecules are assumed to be localized clusters of electrons. In this paper we have assumed the molecules to be localized clusters of bosons and have shown that the expression of the potential remains formally the same. This vindicates, through a microscopic derivation, the established concept that the van der Waals interaction is essentially a macroscopic phenomenon.
Structure factor calculations of various DNA duplexes
Authors: Bansal Manju , Gupta Goutam
Published: December 2004

Based upon a stereochemical guideline, both right‐ and left‐handed duplexes were generated for A, B, and D forms of DNA using a mononucleotide as the repeat. Structure factor amplitudes were computed following two methods: (i) one employed an infinite helix as the motif and (ii) the other had an exact crystallographic repeat (e.g., 10 b.p. for B‐DNA) as the motif. Both the procedures showed that DNA in either handedness for A, B, and D forms of DNA are consistent with the observed fiber data. This observation is attributed to the fact that fibre pattern (resolved only upto 3 Å) only gives the image of the gross structure of the molecule. Thus, when the gross structure is suitably fitted to match the observed pattern, it is immaterial as to what the precise stereochemistry of the repeating unit (fine structure) and handedness of a model are. Sequence specific helical conformations were obtained using dinucleotide as the repeating unit. Helices fell into two classes: (i) right‐handed uniform (RU) and (ii) left‐handed zig‐zag (LZ) structures. A few aspects concerning the scattering profile of these helices are discussed.
Ionophores and channels
Authors: Ovchinnikov Yu. A.
Published: December 2004

The present state in the chemistry of peptides and proteins capable of transporting ions across biological and model membranes have been reviewed. The mechanisms of action of peptide ionophores valinomycin and enniatin and also the channel‐forming peptide gramicidin‐A have been discussed on the basis of spatial structure and dynamic conformational properties of the compounds. Recent progress in the studies of bacteriorhodopsin, cholinergic receptor from postsynaptic membrane, and sodium channel from the excitable nerve membrane, the integral membrane proteins acting as proton or metal ion channel formers is also discussed.
Application of NMR of oriented systems in biochemistry and biophysics
Authors: Khetrapal C. L.
Published: December 2004

General principles of NMR spectroscopy of oriented molecules are described. The use of the technique to problems of biological importance is discussed with emphasis on theoretical and experimental difficulties involved. Application of the technique to study the structure and the hindered rotation in N‐methylimidazole and phenyl silane, to investigate interactions of small molecules with lyotropic liquid crystals, to determine covalent and van der Waals radii, and to estimate non‐planar distortions in amides are described.
Effect of change of water structure on the phase transition of liposomes of dipalmitoyl phosphatidylcholine
Authors: Das Sudipto , Singhal Gaurishanker
Published: December 2004

The role of water structure around model membrane systems (e.g., liposomes) on phase transition of the lipid dipalmitoyl phosphatidylcholine was investigated. Water structure was altered by changing pH and by addition of solutes which are known breakers and makers of water structure. The structure makers broadened the zone of transition and changed the overall phase transition profile, while the main effect of structure breakers was to cause a shift in the transition temperature. The observed variation of Chapman transition temperature and broadening of zone of transition with varying pH is discussed in terms of altered water structure around the membrane–aqueous interface. Binding studies with the dye 1‐anilino‐8‐napthalene sulfonate showed that structure makers or breakers did not bind to the liposome surface directly. Thus the structure makers and breakers act on the membranes perhaps by altering the water structure differentially. Possible associated mechanisms of action are discussed.
Positron band structures for beryllium
Authors: Oriade Joseph Oladipo
Published: December 2004

We report on the band structure and wave functions of positrons, annihilating with electrons, from the thermalized state k+ = 0. We find that the bottom of the band to which the positron thermalizes in this metal is definitely nonambiguous. It is also found that even though the first few Bloch terms in the wave function can give the gross shape of the positron annihilation curve for this metal, the higher momentum components of high orders are definitely important if one is to assay the fine details of the curve.
Symmetry simplifications of space types in configuration interaction induced by orbital degeneracy
Authors: Balasubramanian K.
Published: December 2004

Symmetry simplifications are introduced in configuration interaction (CI) by reducing the number of symmetry‐allowed space types if there is degeneracy in some of the molecular orbitals by constructing the unique space types. A new symmetry group which we call the configuration symmetry group is defined and is shown to be expressible as a generalized wreath product group. Generating functions are derived for enumerating the equivalence classes of space types. A double coset method is expounded which constructs the representatives of all equivalence classes of space types using the cycle index of generalized wreath product and the double cosets of label subgroup with generalized wreath product in the symmetric group Sn, if n is twice the number of occupied and virtual orbitals. Method is illustrated with CI using the localized orbitals of polyenes, CI in benzene, and atomic CI for several reference states.
Variational‐Perturbation theory in the LCAO‐MO method for closed‐shell molecules
Authors: Malykhanov Yu. B.
Published: December 2004

Using the variational principle, equations have been obtained for density matrix of molecules with the external perturbation of the common type present. The perturbed wave function was taken as a superposition of the ground and single‐excited configurations made of the Hartree‐Fock molecular spin orbitals. On the basis of these equations a series of variants of static perturbation theory have been worked out for the ground and excited states of closed‐shell molecules.
Molecular tight‐binding method. I. Many‐electron method for hole bands of molecular crystals
Authors: Stolarczyk Leszek Z.
Published: December 2004

A method for calculating ab initio electronic excitation energies of molecular crystals, based on a many‐electron tight‐binding approximation, is described. The method follows Frenkel's model for excitons and allows a many‐electron treatment of the band‐structure problem of molecular crystals. The case of hole bands is studied in detail and various versions of the method are considered. A computational scheme is proposed, in which approximate correlation corrections to the HFR matrix equations of the one‐electron LCMO method are calculated. The main effects contributing to these corrections are the effect of relaxation of a molecular ion, the effect of intramolecular electronic‐correlation change, and the effect of polarization of the remaining molecules in a crystal. The method developed in the present paper is applied to calculation of the hole bands of the HCP helium crystal.
Equation matricielle de Hartree‐Fock permettant de déterminer la nième harmonique
Authors: Smet F. , Van Groenendael A.
Published: December 2004

The system of time‐dependent Hartree‐Fock equations allowing the calculation the of nth harmonic generation is established by using the same method used in a former paper in the same conditions. These equations are still subjected to orthonormalization conditions. Then by using a recurrence method, we express these equations in matrix form, as well as the orthonormalization conditions; and, as in the former paper, we then replace the solution of the matrix equation subjected to a constraint by that of a free equation. Finally the elimination of the spin variables allows a further simplification. So we obtain an equation allowing the calculation of the nth harmonic generation.
Analysis of the covalent bond: One center floating functions for the hydrogen molecule ion
Authors: Hurley A. C.
Published: December 2004

The roles of kinetic and potential energy operators in the formation of a chemical bond are investigated using the virial and electrostatic theorems. It is shown that an integrated form of the virial theorem throws a new light on a paradox involving changes in the mean kinetic energy on bond formation. Detailed calculations on the ground state of H lead to a surprisingly simple electrostatic approximation to the bond. The entire potential curve is given to good accuracy (ca. 80% bond energy) by the electrostatic forces between the two protons and a single, nodeless, spherically symmetric charge cloud representing the electron, provided that, if the bond is stretched beyond about 3.6 a.u. the charge cloud switches suddenly from a central location to a position near one proton.
Coordinate rotated TDHF excitation energies Li− 1S → 1P
Authors: Nielsen Egon S. , Simons Jack
Published: December 2004

We present the first application of the coordinate rotation method, within the time‐dependent Hartree–Fock framework, to calculation of positions and widths of metastable excited states. The method is briefly outlined and results of its application to 1P excited states of Li− are given. Comparison of our results to those obtained using electron scattering methods by other workers is also made.
Structures, stabilities, and energies of isomerization of α‐cyano and α‐isocyano carbanions
Authors: Moffat J. B.
Published: December 2004

Ab initio STO‐3G calculations show that α‐cyano‐ and α‐isocyano‐substitution on carbanions produce a significant approximately equal stabilization of these charged species. Evidence is presented which suggests that the mechanism of such stabilization is qualitatively different for the cyano and isocyano substituents. The former appears to act through an electron delocalization process while the latter may operate by an inductive effect.
Instabilities of the symmetry‐adapted restricted‐hartree–fock ground state in infinite polyenes. I. Singlet instabilities
Authors: Karadakov P. , Castan̄o O.
Published: December 2004

The singlet instabilities of the RHF ground state in infinite polyenes have been studied in the framework of a semiempirical PPP Hamiltonian, accounting for long‐range Coulomb interactions until convergence of the ground‐state energy per electron value. The symmetry‐adapted RHF solution (SAS) has been shown to be unstable to the formation of bond‐order alternation waves (BAW's) and charge‐density waves (CDW's). The CDW solutions have been shown to be higher in energy than the corresponding BAW solutions and to represent saddle points of the energy hypersurface, unstable to the formation of BAW's for physically realistic range of variation of the semiempirical parameters. Analytical formulas for the SAS ground‐state energy per electron have been derived in case of a Coulomb law and a Mataga–Nishimoto formula for the two‐center Coulomb integrals.
New method for the direct calculation of electron density in many‐electron systems. I. Application to closed‐shell atoms
Authors: Deb B. M. , Ghosh S. K.
Published: December 2004

A new density‐functional equation is suggested for the direct calculation of electron density ρ(r) in many‐electron systems. This employs a kinetic energy functional T2 + f(r)T0, where T2 is the original Weizsäcker correction, T0 is the Thomas–Fermi term, and f(r) is a correction factor that depends on both r and the number of electrons N. Using the Hartree–Fock relation between the kinetic and the exchange energy density, and a nonlocal approximation to the latter, the kinetic energy–density functional is written (in a.u.)

where \documentclass{article}\pagestyle{empty}\begin{document}$ C_k = {\raise0.7ex\hbox{$2$} \!\mathord{\left/ {\vphantom {2 {10}}}\right.\kern-\nulldelimiterspace}\!\lower0.7ex\hbox{${10}$}}(3\pi ^2)^{2/3} $\end{document}. Incorporating the above expression in the total energy density functional and minimizing the latter subject to N representability conditions for ρ(r) result in an Euler–Lagrange nonlinear second‐order differential equation

where μ is the chemical potential, we have ρ(r) = |ϕ(r)|2, and g(r) is related to f(r). Numerical solutions of the above equation for Ne, Ar, Kr, and Xe, by modeling f(r) and g(r) as simple sums over Gaussians, show excellent agreement with the corresponding Hartree–Fock ground‐state densities and energies, indicating that this is likely to be a promising method for calculating fairly accurate electron densities in atoms and molecules.
Quantum dynamics of wave packets on phase space cells in nonlinearly coupled oscillators
Authors: Brickmann Jürgen , Schmidt Peter C.
Published: December 2004

The time evolution of harmonic oscillator coherent states (minimum uncertainty wave packet) | Ψμ located on regular and random von Neumann lattice points in phase space is analyzed for nonlinearly coupled anharmonic vibrational systems. The Henon–Heiles system is studied as an example. A quasiprobability measure \documentclass{article}\pagestyle{empty}\begin{document}$ \bar P_{\mu \mu '} $\end{document} is introduced to investigate the relative probabilities for the transition between phase space cells within a narrow energy range. The probability \documentclass{article}\pagestyle{empty}\begin{document}$ \bar P_{\mu \mu '} $\end{document}, as well as the information entropy Sμ, is studied as a function of energy. A smooth transition from regular to chaotic motion is found indicated by a change of the fluctuations of these quantities as a function of energy.
Structure of the electron
Authors: Datzeff A. B.
Published: December 2004

Generalized nonlinear complex Maxwell equations, based on the hypothesis of a material carrier of the field, are proposed here. They give a nondivergent solution for the fields E,H, in the case of a toroidal electron model.
Chemical potential for harmonically interacting particles in a harmonic potential
Authors: Phillips Philip , Davidson Ernest R.
Published: December 2004

The chemical potential μ, as it appears in density functional theory, is examined extensively for harmonically interacting spin‐½ fermions in three dimensions. For this system the energy and chemical potential are discontinuous functions of the particle number if the most straightforward equation is used to define the energy for a noninteger particle number.
Two‐Dimensional fully numerical solutions of molecular Schrödinger equations. II. Solution of the Poisson equation and results for singlet states of H2 and HeH+
Authors: Laaksonen Leif , Pyykkö Pekka , Sundholm Dage
Published: December 2004

Two‐dimensional fully numerical solutions of the Hartree–Fock problem are reported for the singlet ground states of H−, He, H2, and HeH+. The H2 energy at R = 1.4 a.u. is −1.13362957 a.u.
Structure of dislocation cores in the silicon crystal
Authors: Altmann S. L. , Lapiccirella A. , Lodge K. W.
Published: December 2004

We have recently produced a Lifson–Warshel force field for the silicon crystal. This field, that goes further than the harmonic approximation, is particularly adapted for the calculation of defect structures. It requires five free parameters, but one of them in the field already produced, the linear bending term, is significant for the perfect lattice structure only and should be eliminated in dealing with defect structures. Also, one of the fixed parameters can be adjusted to fit precisely the experimental value of the stacking fault energy. We show that an excellent fitting of the phonon dispersion curves, in the least squares sense, is obtained with the parameters thus changed. We illustrate the use of this field in discussing the problem of reconstruction of the 90° partial dislocation in silicon.
Nonlinear Schrödinger‐type field equation for the description of dissipative systems. II. Frictionally damped motion in a magnetic field
Authors: Schuch D. , Chung K.‐M. , Hartmann H.
Published: December 2004

With the aid of a method similar to the one we used in an earlier work (part I) a new Schrödinger‐type field equation with logarithmic nonlinearity can be derived from a Fokker–Planck equation for a distribution function. This nonlinear field equation describes the frictinally damped motion of a system under the influence of a magnetic field and can be interpreted in the same way as the nonlinear Schrödinger‐type equation (NLSE) derived in part I, where no magnetic fields were taken into account. The NLSE for the two‐dimensional motion of a charged material system in a homogeneous magnetic field is solved exactly. The solutions are compared with the quantum‐mechanical solutions of the corresponding undamped problem. The method is extended to include also anisotropic conditions; i.e., in the Fokker–Plank equation the diffusion constant has to be replaced by a diffusion matrix, as different diffusion constants may be possible for different space directions. We regard the three‐dimensional motion under the combined influence of magnetic and electric fields according to K = (q/c)(v × B) + qE − mγv with Ey = (m/q)ωy, Ez = −(m/q)ωz, B = (0, 0, B) as an example. This is an approximation of the conditions existing in an ion cyclotron resonance spectrometry cell, neglecting an additional drift motion in the x direction which could be taken into account by Galilean transformation and gauge transformation. The corresponding NLSE for the coupled three‐dimensional motion is specified and solved exactly.
Spherical tensor theory of long‐range interactions between two molecules
Authors: Piecuch Piotr
Published: December 2004

The Rayleigh–Schrödinger perturbation treatment can be applied in the quantum mechanical study of long‐range interactions between molecules, when we can assume that the molecular charge distributions do not overlap. In these cases the multipole expansion is a good approximation of real interaction potential and can be treated as a perturbation. In this paper we obtain closed expressions for the anisotropic long‐range interaction energy between two molecules in all orders of the perturbation, using spherical tensor formalism. Then we show how spherical multipoles and polarizabilities of the isolated molecules can be inserted into general formulas for interaction energy.
Frozen orbital effects in the computation of excitation energies of the iron atom
Authors: Pelissier Michel , Davidson Ernest R.
Published: December 2004

The limitations arising from the use of a frozen orbital approximation applied to 3s and 3p electrons of the iron atom are investigated at the CI level.
Unitary group approach to the many‐electron problem. II. Adjoint tensor operators for U(n)
Authors: Gould M. D. , Chandler G. S.
Published: December 2004

In this paper we present a derivation of the U(n) adjoint coupling coefficients for the representations appropriate to many‐electron systems. Since the states of a many‐fermion system are to comprise the totally antisymmetric Nth rank tensor representation of U(2n), the work of this paper enables the matrix elements of the U(2n) generators to be evaluated directly in the U(n) × U(2) (i.e., spin orbit) basis using their transformation properties as adjoint tensor operators. A connection between the adjoint coupling coefficients, as derived in this paper, and the matrix elements of certain (spin independent) two‐body operators is also presented. This indicates that in CI calculations, one may obtain the matrix elements of spin‐dependent operators from the known matrix elements of certain spin‐independent two‐body operators. In particular this implies a segment‐level formula for the matrix elements of the U(2n) generators in the spin‐orbit basis.
Localized molecular orbitals for multiple bonds in the ZDO approximation: The σ‐π vs. banana bonds dilemma
Authors: Paniagua Juan Carlos , Moyano Albert , Tel Luis María
Published: December 2004

The multiple bond description supplied by localized molecular orbitals obtained within the ZDO approximation is analyzed. In particular, conditions for the appearance of σ‐π separation and of continuous degeneracy of the localization sum against σ‐π mixing are given for two current ZDO energy‐ and density‐localization methods. Likewise, a convenient modification of the latter is presented together with some illustrative examples.
Motion of a particle in a ring‐shaped potential: An approach via a nonbijective canonical transformation
Authors: Kibler Maurice , Negadi Tidjani
Published: December 2004

The problem of a particle in the three‐dimensional ring‐shaped potential ησ2(2a0/r − ηa/r2 sin2 θ)ε0 introduced by Hartmann is transformed into the problem of a coupled pair two‐dimensional harmonic oscillators with inverse quadratic potentials by using a nonbijective canonical transformation, viz., the Kustaanheimo–Stiefel transformation. The energy E of the levels for the ring‐shaped potential is obtained in a straightforward way from the one for the two‐dimensional potential — (4Eρ2 + η2σ2a ε0/ρ2).
Multibody analysis of potential energy surfaces for first‐ and second‐row tetramers. I. The tetrahedral structures of P4 and N4
Authors: Novaro O. , Castillo S.
Published: December 2004

SCF calculations using a split‐valence basis set were carried out for N3, P3, N4, and P4 showing that there are substantial structural differences between the clusters of these elements, nitrogen and phosphorus. An analysis of the nonadditive three‐ and four‐body contributions to the binding energies of these systems is carried out and shown to be quite close to the values predicted from qualitative considerations by Murrell [Chem. Phys. Lett. 55, 1 (1978)].
Interaction between photons, “trapped electron” and vibronic excitation
Authors: Mishra R. K. , Dubey S. K. , Tyagi R. S.
Published: December 2004

The role of “trapped electron,” photon, and vibronic state coupling has been worked out in relation to an aspect of cancer, namely, to the activity of an anticancer drug. The main emphasis for such study comes from the fact that in cancerous systems the participation of usual electronic states of the molecule may not be sufficient. Because of disorder in the cancer tumour, additional states, viz. trapped electron states, could be formed in the manner of localised states in solids. The drug activity of mitomycin C obtained in this way agrees with the experimental values. An additional feature of the study is that it shows that it will be effective mainly in the initial phases of cancer.
A theoretical investigation of electron correlation and relaxation in organometallic polymers
Authors: Böuhm Michael C.
Published: December 2004

The importance of many‐body interactions beyond the mean‐field approximation of the Hartree–Fock (HF) self‐consistent‐field crystal orbital formalism is analyzed in one‐dimensional (lD) transition‐metal (3d) polymers with extended organic π ligands. The correlation energies are expressed in a quasiparticle picture. They are divided into long‐range contributions that are coordinated with the basis of spatially uncorrelated Bloch orbitals and into short‐range correlations derived for local rearrangement processes that are described in terms of a one‐electron basis which breaks the translational symmetry of the lD system. Both contributions (long‐range and short‐range correlations) are fragmented into elements of physical significance (hole and electron self‐energies for the former interactions; relaxation, pair‐relaxation and pairremoval terms for the local virtual excitations). The magnitude of these elements is analyzed as a function of the characters of the one‐electron states in the HF bands, the occupation patterns at the 3d centers, the available particle and hole channels in the elementary fluctuations and the energies and shapes of the various bands. The broad spectrum of possible amplifications and compensations leading to the quasiparticle shifts in metallomacrocycles is discussed. The different mechanisms to change the dispersions and to modify the width of the ϵ(k) curves are studied. It is shown that electron correlation and relaxation in transition‐metal polymers can lead even to a broadening of the energy bands. This behavior is in contrast to the influence of many‐body effects in simpler homogeneous materials where electron correlation is in any case accompanied by a narrowing of the dispersions (i.e., detraction of the group velocities of particles and holes). Possible modifications in the shapes of the one‐particle curves and the quasiparticle bands are also considered in the text [transition from a “normal ϵ(k) dispersion” to an energy band with a negative slope as a result of electron correlation]. Simplified formulas are derived that allow for a rough assessment of the various correction terms even in structurally complicated transition‐metal stacks with extended organic ligands. The approximate relations are used to correct the HF band structures of complex onedimensional metallomacrocycles as well as simpler crystalline materials by means of the quasiparticle approximation.
Structure of the electronic energy bands of molecular crystal NMP‐TCNQ
Authors: Qi‐Yuan (Q. Y. Zhang) Zhang , Ji‐Min (J. M. Yan) Yan
Published: December 2004

The electronic energy band of the molecular crystal NMP‐TCNQ is calculated by means of the EHMO/LCAO‐MO‐CO method. In the calculation, both NMP and TCNQ are treated as quasi‐one‐dimensional columns, respectively. The results demonstrate that (i) the positions of the electronic energy bands of a molecular crystal are determined by that of the corresponding molecular orbitals of the respective isolated molecules; (ii) the widths of energy bands are determined by the interaction between the molecular orbitals of adjacent molecules in the crystal. These facts support the conclusion which we have given in the previous articles. The relationship between the structure of energy bands of the crystal NMP‐TCNQ and its electrical conductivity at room temperature is discussed and compared with the crystal TTF‐TCNQ. The differences of electrical conductivities of both crystals can be explained by the formula given by Fröhlich and Sewell.
Potential‐Derived point‐charge model study of electrostatic interaction energies in some hydrogen‐bonded systems
Authors: Ray Naba K. , Shibata Masayuki , Bolis Giorgio , Rein Robert
Published: December 2004

Mulliken's atomic charges (MC) and potential derived (PD) point charges obtained from STO‐3G wave functions are used to study the electrostatic interaction energies for a series of representative hydrogenbonded complexes. The results of the above‐mentioned models are compared with the more accurate results of segmental multipole moment (SMM) expansion, and it is shown that the PD model is superior to the Mc model. The results of PD model are shown to be well correlated with the results of SMM expansion technique. Results of our calculations using 6‐31G and 6‐31G** PD charges are also reported here. Electrostatic interaction energies obtained using 6‐31G** PD charges are compared with the 6‐31G** SCF interaction energies available for the nine hydrogen‐bonded dimers of ammonia, water, and hydrogen fluoride and a good con‐elation between the two is shown. The interrelationship between the results of different basis sets are also examined for the PD point‐charge model. The electrostatic interaction energies obtained using STO‐3G PD model are shown to be well correlated to the results of 6‐31G and 6‐31G** PD models.
Angular aspects of exchange correlation and the fermi hole
Authors: Ugalde J. M. , Boyd Russell J.
Published: December 2004

The complete (nonreduced) αα probability density functions evaluated from the Hartree–Fock and simple Hartree product wavefunctions have been used to elucidate the angular features of spin correlation and the Fermi hole in the 23S state of helium and the ground state of beryllium. This approach shows that the local Fermi holes in these two cases are very similar and that the Fermi hole is essentially spherically symmetric when the reference electron is close to the nucleus. As the reference electron is removed to larger radial distances, appreciable polarization of the Fermi hole is observed. The polarization is greater in the direction of the nucleus than away from the nucleus, contrary to the situation in the Coulomb hole of the helium ground state where the polarization is greater away from the nucleus than toward the nucleus. Several other differences between the He 23S Fermi hole and the He 11S Coulomb hole are noted.
Electronic structures of the π‐π type charge‐transfer complexes of pyridine with boron trihalides
Authors: Ji‐Min(J. M. Yan) Yan , Jian‐Guo (J. G. Zhao) Zhao
Published: December 2004

The electronic structures of the π‐π type complexes of pyridine with boron trihalides have been studied by means of IEHMO calculation. The results indicate that BX3(X = F, Cl, Br, I) tends to react with C5H5N in a planar configurations against the plane of C5H5N. The most stable configurations of complexes are at 60° of orientation angle φ for X = Cl, Br, I, but at 0° for X = F. A linear relationship between In Eb, the logarithm of rotation potential barriers, and the radii of halogen atoms r0 has been observed, and has been deduced from Morse potential function. In the complex, the donating properties of BX3 have an increase from X = F to I, and BF3 functions as an acceptor, but the others as donors. It has been shown that every energy level of the complex is corresponding to that of the donor or the acceptor, which we have discussed by the perturbation theory. The bonds between D and A appear essentially as π‐π type but not pure.
Approximate calculation of lifetimes of resonance states in the continuum from real stabilization graphs
Authors: Löwdin Per‐Olov
Published: December 2004

Simons has previously derived a simple formula for the linewidth Γ of a resonance state in the continuum from real stabilization graphs under the assumption that the energy curves vary almost linearly near the points of avoided crossing. This formula is now rederived without this restricting assumption under the condition that Γ is still small.