bluuebunny/crossref_metadata_2025 huggingface dataset:
Scintillation mechanisms in Ce3+ doped halide scintillators
Authors: Dorenbos Pieter
Published: January 2005

Last couple of years witnessed the development of various new Ce3+ doped halide scintillators (LaCl3, LaBr3, LuI3, Cs2LiYCl6, Cs2LiYBr6) that possess excellent gamma ray or thermal neutron detection properties. The scintillation pulse in LaBr3:Ce3+ is 20 times faster than in the most commonly used scintillator NaI:Tl. This, combined with a more then two times better energy resolution and higher gamma ray stopping power, makes it ideally suited for many different applications. In this work the scintillation properties and mechanisms of Ce3+ doped inorganic halide (Cl, Br, I) compounds are reviewed; especially the role of Vk centers and self trapped excitons (STEs) in the energy transfer from the ionization track to Ce3+ is treated. Aspects of the lifetime and thermal stability of the self trapped exciton, the migration speed of Vk centers and STEs, spectral overlap between STE emission and Ce3+ absorption, and the influence of the type of anion (Cl, Br, I) are addressed. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Multifrequency spectroscopy of defects in complex oxides
Authors: Malovichko G. , Grachev V. , Schirmer O. F.
Published: January 2005

The typical output of the one‐frequency methods is an image with a space resolution of the order of the used wavelength. Such images contain direct evidence about the space structure of a lattice or macroscopic defects; however, they are not very helpful for the study of the internal structure of the atomic‐size defects. Measurements which use sweeping of electromagnetic wave frequency or sweeping of an external parameter furnish spectra or dependencies of measured characteristics on the swept quantity. The spectra contain indispensable information about energetic characteristics of interactions of intrinsic and extrinsic defects with the lattice ions. Different frequencies in very wide region have to be used for the study of these interactions (multifrequency spectroscopy). An application of this new approach to defects in lithium niobate allowed to determine characteristics of various interactions with magnitudes from 104 to 1016 Hz, and to correlate them with definite models of the defects. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Creation of groups of spatially correlated excitations in wide‐gap solids
Authors: Kirm Marco , Lushchik Aleksandr , Lushchik Cheslav
Published: January 2005

Processes of efficient creation of groups of electronic excitations (EEs) or defects have been considered for radiation‐sensitive (alkali halides) and radiation‐resistant (metal oxides) single crystals. In MgO, pure or doped with Be2+, Ca2+ and Al3+ ions, the 7.63 eV edge emission of anion excitons is efficiently excited at 10 K in a wide region of 30–90 eV. Multiplication process with the creation of secondary electron–hole pairs and the decay process of cation excitations are compared in crystals of two types: (i) KCl, KBr and LiF, where anion excitons and valence holes undergo self‐trapping and (ii) a MgO crystal, where no self‐trapping of excitations occurs. In alkali halides, a group of spatially correlated EEs, formed at photon absorption, is transformed into an F–I–VK triplet of defects at 5 K or into a temperature‐stable F centre and a trihalide molecule (e.g., Br3–) at 295 K. In BaMgAl10O17:Eu at 295 K, the 2.72 eV emission of Eu2+ centres with quantum yield of 1.1–3.5 at the excitation by photons of 13–30 eV has been obtained. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Dislocation induced absorption in silver halides
Authors: Kondo Y.
Published: January 2005

Infrared absorption spectra of shallow electron centres in plastically deformed silver halide crystals are measured. The spectra consist of a sharp peak due to the isolated centres and a broad peak which shows splitting that may be due to the symmetry lowering along the dislocation edge, indicating some of the shallow electron centres are trapped on the dislocation lines. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Simplification of point group projection operators and its application to symmetry adaptation of multishell electron configurations
Authors: Taijin Zhou
Published: January 2005

A practical method for generating irreducible matrix reps of point groups and a concise formula about projection operators are proposed. By using this formula as well as versatile classification schemes, the symmetry adaptation of a many‐electron system is simplified. A unified algorithm and program of symmetry adaptation of spin‐free space have been developed.
Application of the recursion method to the study of the end effects on the bond length alternation in polyacetylene
Authors: Suzuki Masato , Imamura Akira
Published: January 2005

We describe how the local equilibrium electronic structure in a large system can be determined by using the recursion method of Haydock. By applying this method to the polyacetylene molecule, the energies of each atomic site and the forces acting on each bond are estimated and the equilibrium structure near the end of polyacetylene is determined. It is found out that the degree of localization of π electrons and the bond length alternation become stronger near the end of the polyacetylene molecule.
Contraction operator over electronic fock space. II. Weak representability problem
Authors: Panin A. I.
Published: January 2005

Two approaches in treating the weak representability problem for density operators are studied. In the first approach this problem is reduced to the minimization of a certain distance function. The second approach is based on inductive generation of linear inequalities for diagonal elements of the second‐order density operators. Generalization of Kuhn–Yoseloff's results is also discussed.
Alkylation of DNA bases by carcinogenic N‐nitrosamine metabolites: A theoretical study
Authors: Duncan Richard H. , Davies G. S.
Published: January 2005

N‐Nitrosamines are believed to act as carcinogens by alkylating DNA in their ultimate carcinogenic forms which are produced by metabolic activation. Alkylation at certain oxygen sites in DNA, described as “promutagenic,” appears to be of particular significance for mutagenesis and cancer, as indicated by experimental findings. This theoretical study deals with two factors involved in the alkylation of these promutagenic oxygen sites by N‐nitrosamine ultimate carcinogens. The first is the competition between alkylation at the promutagenic O6‐guanine and O4‐thymine sites and that at the nonmutagenic N7‐guanine site, which is here related to the degree of participation of cationic ultimate carcinogens as compared with neutral ultimate carcinogens. Parent dialkylnitrosamines are classified structurally according to their degree of cationic ultimate carcinogen participation and preference for promutagenic alkylation. The second factor is the thermodynamic facileness of alkylation at the O6‐guanine and O4‐thymine sites. Heats of alkylation by candidate ultimate carcinogens are calculated here for numerous parent dialkylnitrosamines. Finally, these two factors are jointly considered in an attempt to correlate them with experimental carcinogenic potency of the parent nitrosamines. Out of the patterns of correlation observed, light is shed on mechanistic factors likely to be involved in the modulation of parent carcinogenic potency.
Algebraic methods in molecular structure
Authors: Iachello F.
Published: January 2005

The use of algebraic methods in molecular structure is briefly reviewed. The fundamental algebra, 𝒢 ≡ U(4), of rotation–vibration spectra is introduced and its implications on spectra of di‐, tri‐, and polyatomic molecules are discussed.
Graphical unitary group approach to spin–spin interaction
Authors: Kent R. D. , Schlesinger M. , Shavitt I.
Published: January 2005

A detailed exposition of spin–spin operator matrix elements is presented in the context of the graphical unitary group approach (GUGA) to atomic and molecular physics and quantum chemistry. A compendium of subgraph types and formulae is given. Aspects of computer implementation within the structure of the Columbus CI programs is discussed.
Eigenvector and eigenvalues of some special graphs. IV. Multilevel circulants
Authors: Lee Shyi‐Long , Luo Yeung‐Long , Sagan Bruce E. , Yeh Yeong‐Nan
Published: January 2005

A multilevel circulant is defined as a graph whose adjacency matrix has a certain block decomposition into circulant matrices. A general algebraic method for finding the eigenvectors and the eigenvalues of multilevel circulants is given. Several classes of graphs, including regular polyhedra, suns, and cylinders can be analyzed using this scheme.
Valence bond approach exploiting Clifford algebra realization of Rumer–Weyl basis
Authors: Li Xiangzhu , Paldus Josef
Published: January 2005

A detailed algorithm is described that enables an implementation of a general valence bond (VB) method using the Clifford algebra unitary group approach (CAUGA). In particular, a convenient scheme for the generation and labeling of classical Rumer–Weyl basis (up to a phase) is formulated, and simple rules are given for the evaluation of matrix elements of unitary group generators, and thus of any spin‐independent operator, in this basis. The case of both orthogonal and nonrothogonal atomic orbital bases is considered, so that the proposed algorithm can also be exploited in molecular orbital configuration interaction calculations, if desired, enabling a greater flexibility for N‐electron basis‐set truncation than is possible with the standard Gel'fand–Tsetlin basis. Finally, an exploitation of this formalism for the VB method, based on semiempirical Pariser–Parr–Pople (PPP)‐type Hamiltonian and nonorthogonal overlap‐enhanced atomic orbital basis, and its computer implementation, enabling us to carry out arbitrarily truncated or full VB calculations, is described in detail.
Eigenvalues of single‐cycle class‐sums in the symmetric group
Authors: Pauncz Ruben , Katriel Jacob
Published: January 2005

Explicit expressions for the eigenvalues of the class sums [(p)(1)n−p]n, p = 2, 3,…,14, of the symmetric group Sn are presented. Partial results are given for the eigenvalues corresponding to arbitrary p.
The measure cone: Irreversibility as a geometrical phenomenon
Authors: Busch Paul , Ruch Ernst
Published: January 2005

The statistical state space is discussed in terms of the geometry of normed real vector spaces with particular reference to the novel concept of direction distance. Specialization to the geometry of the measure cone and the correspondingly specialized concept of mixing distance suggest strong mutual relationship as is shown subsequently in physically required generality. Thereby, the phenomenon of irreversibility attains an interpretation that seems to be the canonical mathematical background for classical and nonclassical statistical physics.
Freeon tensor product states and the unitary group formulation of the many‐electron problem
Authors: Campbell Loudon L.
Published: January 2005

The freeon tensor product basis provides a rapid method for the evaluation of matrix elements in the unitary group formulation of quantum chemistry. The method employs fast transformations between the Gel'fand and freeon tensor product basis.
On rotations as special cases of unitary transformations with some applications to the theory of spin
Authors: Löwdin Per‐Olov
Published: January 2005

Some problems in elementary geometry are approached from the point of view of linear algebra and generalized to the theory of linear spaces of finite or infinite dimensions having a positive definite binary product. The angle ω between two elements of the linear space is defined from the concept of length by means of the cosine‐theorem. A rotation is then defined as a special case of a unitary transformation moving all elements the same angle ω, except that under certain circumstances, some elements may stay invariant. In the former case, one speaks of a rotation around an “external axis,” and in the latter case, of a rotation around an “internal axis” defined by the invariant elements. It is shown that the finite rotations U of both types may be expressed in the simple exponential form U = exp(iωm), where the “generator” m in the former case is an operator satisfying the relation m2 = 1, and in the latter case, m3 = m. The structure of the group of finite rotations in the former case is clarified in some detail. As an illustration of the theory, some applications to the three‐ and two‐dimensional spaces as well as to the theory of spin are given. The coupling between the ordinary three‐dimensional rotations and the spinor transformations is considered in somewhat greater detail.
The Fix–Heiberger procedure for solving the generalized Ill‐conditioned symmetric eigenvalue problem
Authors: Jungen Martin , Kaufmann Karl
Published: January 2005

We review a formalism introduced by Fix and Heiberger in 1972 for solving the generalized (or nonorthogonal) eigenvalue problem for ill‐conditioned symmetric matrices and we discuss its application in quantum chemistry. A few examples dealing with the calculation of high Rydberg orbitals are presented.
Quasi‐Relativistic MS‐Xα approach to the electronic structures of protactinium halide ions of [PaX8]4− type
Authors: Nour Safouh , Mehadji Cherifa , Chermette Henry , Krupa Jean‐Claude
Published: January 2005

The recently developed inclusion of the spin‐orbit interaction into the quasi‐relativistic version of the MSXα method has been applied to the ThX4:Pa4+ (X ≡ Cl, Br) doped system. A new interpretation of the optical spectrum is given.
An optimized orbital transformation able to reproduce partially prefixed overlaps
Authors: Gianinetti Ermanno , Vandoni Ida
Published: January 2005

Given a function space spanned by a basis {ƒi}, we are interested in finding another basis {gi} for which the overlaps (gi | gi) assume arbitrarily prefixed values in a subset ℬ︁ of the full set of the pairs of indices (i, j). The other overlaps are let free. We show how it is possible to perform this linear transformation ƒi → gi minimizing the “distortion” J = Σi(gi – ƒi | gi – ƒi).
An open‐shell coupled‐cluster response method for static properties
Authors: Pal Sourav
Published: January 2005

This paper deals with a multideterminantal model space‐based coupled‐cluster response approach suitable for the calculation of static properties of quasi‐degenerate systems. The firstorder static property of one‐valence‐hole/particle system using this approach has been specifically discussed.
Molecular dynamic structure and dimerization of polyacetylene
Authors: Lü Tianxiong , Tachibana Akitomo , Yamabe Tokio
Published: January 2005

The vibronic interaction in an (A)2N chain (e.g., polyacetylene) has been studied within the Hückel framework. A Hückel framework scheme for calculating the parameters of molecular dynamic structure, i.e., the linear and quadratic orbital vibronic constants (OVCs), has been presented. Selection rules for the OVCs in this scheme have been obtained and discussed by using graph theory and group theory, under various boundary conditions. A Hückel noncoupling rule has been concluded and discussed. The dimerization of polyacetylene has then been discussed based on the molecular dynamic structure. It has been shown that for a finite undoped (A)2N chain the occupied orbital energy εn at the unified configuration has a negative slope in direction of Q2n. As a result, there exists a net Hellmann–Feynman force leading to dimerization. When the chain length goes to infinity, the slopes and forces tend to zero. However, a significant negative curvature in potential surface may occur in the direction of Q2n, due to the two‐phonon coupling of the π‐electrons, which could also induce the dimerization. These can be interpreted as the results of the hidden C4N+2 symmetry and the imaginary degeneracy in an (A)2N chain, according to the graph theory for molecular orbitals. Thus, the dimerization of an (A)2N chain actually destroys its hidden symmetry of C4N+2 and reduces its imaginary degeneracy.
Density of states due to donor‐pair molecules in three‐ and two‐dimensional semiconductor systems
Authors: Costa E. A. Guimarães , De Brito Mota F. , Ferreira Da Silva A.
Published: January 2005

The density of states is calculated for a random distribution of donor‐pairs of hydrogenlike impurities in three‐ and two‐dimensional systems. Recent investigations of the hydrogen molecule in the alternant–molecular–orbital approximation are here extended. We found that the lowest excited state 1Σu (i.e., H+H−), which is optically connected to the ground state, plays a relevant role in the absorption spectra of semiconductor systems.
Broken symmetry in the electronic structure of the ferrocene molecule
Authors: Cook David B.
Published: January 2005

Attempts to calculate the metal–ring distance in the ferrocene molecule using a well‐tried minimal basis reveal serious deficiencies in the minimal‐basis SCF model of the electronic structure of organometallics. It is found that the lowest state of the molecule in this approximation is a triplet and that there is a whole manifold of “states” in the ground‐state region that have broken spatial symmetry and high‐spin multiplicity.
Variation–iteration method for one‐dimensional two‐electron systems
Authors: Katyurin Svyatoslav V. , Glinkin Oleg B.
Published: January 2005

The variation–iteration method of Svartholm has been applied to the momentum‐space Schrödinger equation for one‐dimensional two‐electron systems. The first and second iteration momentum‐space wave functions have been evaluated in analytical forms. The momentum representation of the exact Hartree–Fock ground‐state wave function is chosen as the initial function. The influence of electron correlation on the distribution of momentum‐space probability density has been studied. It is shown for the one‐dimensional McWeeny–Coulson problem that the numerical value of the ground‐state energy of the one‐dimensional two‐electron atom is between the minimum energy values ε1/2 and ε1.
Green's function calculations using non‐Hartree–Fock orbitals
Authors: Holleboom L. J. , Snijders J. G.
Published: January 2005

The single‐particle Green's function is used to generate a new zero‐order Hamiltonian. The idea to generate a new zero order from the previous zero order by incorporating perturbative corrections up to certain order is attractive since it allows an iterative procedure to repeatedly improve the results by decreasing the perturbation. In particular, in those cases where the Hartree–Fock Hamiltonian is not a good approximation to the full Hamiltonian and where perturbation theory usually does not produce sufficiently accurate results, one might hope that such a repetitive procedure ultimately yields an improved zero order and accurate perturbative corrections from this newly generated zero order. Two such approaches are investigated: first, one in which the ω‐independent part of the self‐energy is fully incorporated in the zero order and, second, one in which the correlation energy is incorporated in a one‐electron potential in an average way. Numerical calculations are reported.
Algebraic formulae of matrix elements between valence‐bond determinants for periodic systems: The one‐band linear case
Authors: Fortunelli Alessandro
Published: January 2005

A simple valence‐bond approach is considered for treating extended systems of equivalent atoms. In this approach, a limited nonorthogonal basis set of atomic orbitals is utilized and only nearest‐neighbor interactions are supposed. By exploiting then the translational invariance of the system, expressions for the matrix elements between antisymmetrized products of such nonorthogonal orbitals are derived in an algebraic form suitable for the numerical implementation on a computer. The one‐band linear case is explicitly considered. Some possible applications of the proposed approach and its connections with model Hamiltonians such as the Hubbard and the Heisemberg ones are also discussed.
Applications of n‐electron wave functions built up with two kinds of geminals
Authors: Liu Chengbu , Deng Conghao , Jin Beiyan , Hu Haiquan
Published: January 2005

The ground states of atoms and molecules Li−, Be, LiH, LiH, and Li2 have been calculated using the n‐electron wave functions built up with two kinds of geminals. As a comparison, the above systems have been calculated with the Hartree–Fock self‐consistent field and the multi‐configuration self‐consistent field method as well. The results show that the wave functions in this work are capable of describing the electron correlations, and both kinds of geminals can be taken as a starting point in building up n‐electron ground states.
Different forms of perturbation theory for the calculation of the correlation energy
Authors: Murray Christopher , Davidson Ernest R.
Published: January 2005

Different forms of perturbation theory for the calculation of correlation energy in both closed‐and open‐shell systems are discussed. For closed‐shell systems, Epstein–Nesbet perturbation theory is compared with Møller–Plesset (MP) perturbation theory based on canonical Hartree–Fock orbitals and with MP theory based on internally consistent SCF orbitals. The traditional MP theory gives superior results despite its use of an inferior zeroth‐order Hamiltonian. This behavior is rationalized in terms of the larger denominators present in the traditional MP theory. These conclusions are used to support the restricted open‐shell perturbation methods proposed recently by Murray and Davidson, and these new methods are compared with spin‐restricted Epstein–Nesbet theory and the unrestricted MP (UMP) approach. © 1992 John Wiley & Sons, Inc.
Formulation of N‐ and ν‐representable density functional theory. V. Exchange‐only self‐consistent field
Authors: Kryachko Eugene S. , Ludeña Eduardo V.
Published: January 2005

The concept of a self‐consistent field is developed within the version of density functional theory based on local‐scaling transformations. It is shown that in this context there arise two types of consistency: one relating to the charge‐consistency within an orbit and another to “orbit jumping.” The latter is analyzed in terms of one‐particle equations. The connection with other methods is discussed. © 1992 John Wiley & Sons, Inc.
Proton affinities of molecules containing nitrogen and oxygen: comparing ab initio and semiempirical results to experiments
Authors: Ozment Judy L. , Schmiedekamp Ann M.
Published: January 2005

We report a comparison of theoretical and experimental proton affinities at nitrogen and oxygen sites within a series of small molecules. The calculated proton affinities are determined using the semiempirical methods AM1, MNDO, and PM3; the ab initio Hartree–Fock method at the following basis levels: 3‐21G//3‐21G, 3‐21+G//3‐21G, 6‐31G*//6‐31G*, and 6‐31+G(d, p)//6‐31G*; and Møller–Plesset perturbation calculations: MP2/6‐31G*//6‐31G*, MP3/6‐31G*//6‐31G*, MP2/6‐31G+(d, p)//6‐31G*, MP3/6‐31G+(d, p)//6‐31G*, and MP4(SDTQ)/6‐31G+G(d, p)//6‐31G*. The semiempirical methods have more nonsystematic scatter from the experimental values, compared to even the minimal 3‐21G level ab initio calculations. The thermodynamically corrected 6‐31G*//6‐31G* proton affinities provide acceptable results compared to experiment, and we see no significant improvement over 6‐31G*//6‐31G* in the proton affinities with any of the higher‐level calculations. © 1992 John Wiley & Sons, Inc.
A BSSE‐free SCF algorithm for intermolecular interactions. II. Sample calculations on hydrogen‐bonded complexes
Authors: Vibók Á. , Mayer I.
Published: January 2005

The usefulness and reliability of the recent BSSE‐free SCF algorithm based on the “chemical Hamiltonian approach” (CHA/F) is demonstrated by calculating potential curves for several hydrogen‐bonded complexes with 4‐31G, 6‐31G, and 6‐31G** basis sets. It is concluded that the CHA/F scheme gives results that are numerically close to those of the Boys–Bernardi a posteriori correction scheme but are free from the “overcompensation” characteristic of the latter at smaller distances and given basis sets. © 1992 John Wiley & Sons, Inc.
Comparative semiempirical calculations of tetrazole derivatives
Authors: Ivashkevich O. A. , Gaponik P. N. , Koren A. O. , Bubel O. N. , Fronchek E. V.
Published: January 2005

Heats of formation, protonation energies, charge distributions, dipole moments, and geometrical structures of thirty‐two 1‐, 2‐, 1,5‐, and 2,5‐substituted tetrazoles have been investigated by different semiempirical SCF MO calculations. MNDO and, in some cases, AM1 methods are the most acceptable for tetrazole derivatives. A number of linear correlations between available experimental data and the calculated energies and charge characteristics have been established. © 1992 John Wiley & Sons, Inc.
CASSCF optimization problem for a group of excited states
Authors: Khait Yu. G. , Panin A. I.
Published: January 2005

A second‐order version of the CASSCF approach to the optimization problem for a single (ground or excited) state and a group of excited states (involving, if necessary, also the ground state) is proposed. In contrast to the already existing methods, in the frameworks of our approach, there arises no need in completing the set of states to be optimized to the full basis set of configuration function space. Generation of secondary orbitals in the course of orbital optimization is also not required. All necessary integral transformations are performed only with active orbitals. These certainly attractive features of our approach appear due to employing the Gauss parametrization of average electronic energy domain, which is nonstandard in quantum chemistry. © 1992 John Wiley & Sons, Inc.
A simple proof for the formula to get symmetrized powers of group representations
Authors: Planelles J. , Zicovich‐Wilson C. M.
Published: January 2005

A general formula to decompose the p‐power of irreducible representations of an arbitrary space group into sum of sets of irreducible representations of such a group, having identical permutational symmetry, is presented. Its proof is based upon a straightforward application of the properties of the generalized projection (shift) operators. © 1993 John Wiley & Sons, Inc.
Relativistic theory for indirect nuclear spin–spin couplings within the polarization propagator approach
Authors: Aucar Gustavo A. , Oddershede Jens
Published: January 2005

We present a relativistic theory for the nuclear spin–spin coupling tensor within the polarization propagator approach using the particle‐hole Dirac–Coulomb–Breit Hamiltonian and the full four‐component wave function. We give explicit expressions for the coupling tensor in the random‐phase approximation, neglecting the Breit interaction. A purely relativistic perturbative electron–nuclear Hamiltonian is used and it is shown how the single relativistic contribution to the coupling tensor reduces to Ramsey's three second‐order terms (Fermi contact, spin–dipole, and paramagnetic spin–orbit) in the nonrelativistic limit. The principal propagator becomes complex and the leading property integrals mix atomic orbitals of different parity. The well‐known propagator expressions for the coupling tensor in the nonrelativistic limit is obtained neglecting terms of the order c−n (n ⩾ 1). © 1993 John Wiley & Sons, Inc.
Temperature dependence of hydrogen transfer reactions via tunneling at low temperatures
Authors: Chandra A. K. , Sreedhara Rao V.
Published: January 2005

In this paper, we present a symmetrical and adiabatic reaction path for hydrogen transfer from methane by methyl by an ab initio method using the 6‐31G** basis set with the MP2 corrections for UHF/6–31G** optimized geometries. The theoretical barrier is fitted with the symmetric Eckart function. We, then, take thermal averages of the rate constant (k) considering the discrete nature of the C–H oscillators and the continuous character of the various low‐frequency modes of the composite system. Finally, we present a linear relation between log k and temperature. It is shown that this relation gives a good description of the kinetic results of both thermal and photochemical H‐transfer reactions in the region of low temperatures. © 1993 John Wiley & Sons, Inc.
Electronic structures around the local defects in all‐trans‐polyacetylene: An analysis by the cluster‐series model
Authors: Maekawa Koji , Imamura Akira
Published: January 2005

A new approach to analyze the electronic structure around the local defects in a polymer chain is developed based on the cluster‐series model. In this approach, by extending the cluster molecule to both sides of the defect, the size effect on electronic structure can be estimated systematically and efficiently. Moreover, through the extension process, the periodicity of electronic structure can be extracted in the form of the periodic pattern of stationary orbitals, which are molecular orbitals unaltered by the extension of the cluster. Such periodic orbitals characterize the bulk states of periodic polymer and the energy band structure can be reconstructed from them. Illustrative analyses of some kinds of local defects in all‐trans‐polyacetylene are presented at the ab initio STO‐3G level. The effects of local defects can be detected by the deviation from periodic bulk states. © 1993 John Wiley & Sons, Inc.
Nonlinear Roothaan's equations
Authors: Marañón Julio
Published: January 2005

In the regime of the molecular‐orbital theory, a new approach beyond of the Hartree–Fock approximations is proposed. By an appropriate introduction of the quantum fluctuation into the molecular electronic ground state, the Hartree–Fock equations plus Gaussian fluctuation are obtained. Basically, the procedure proposed consists of an adequate utilization of the Gaussian approximation of the Ising model on a lattice (K.G. Wilson et al., Phys. Rep. C 12, 76 (1974)). It leads to an effective nonlinear Hamiltonian for the molecule for studying nonlinear problems in the molecular electronic structure. © 1993 John Wiley & Sons, Inc.
Explicitly connected expansion for the average value of an observable in the coupled‐cluster theory
Authors: Jeziorski Bogumił , Moszynski Robert
Published: January 2005

An explicitly connected commutator expansion for the average value of an observable in the coupled‐cluster theory is derived. Specifically, it is shown that the expectation value of an operator for the state Ψ, related to the Fermi vacuum Φ by the exponential Ansatz ψ = eT Φ, is expressed as a finite commutator series containing the cluster operator T and an auxiliary operator S, defined by a linear equation involving again a finite commutator series in T. The above result is applied to derive the explicitly connected commutator form of the order‐by‐order many‐body perturbation theory (MBPT) expansion for the expectation values and density matrices. We also show how the commutator expansion derived by us can be used as a basis for size‐extensive infinite‐order summation techniques. An operator technique of eliminating the nonlocal, “off‐energy shell” denominators from MBPT expressions is proposed and applied to obtain compact commutator formulas for the expectation values of one‐ and two‐electron operators through the fourth and third order, respectively, and for the correlation energy through the fifth order of perturbation theory. © 1993 John Wiley & Sons, Inc.
A first‐principles approach to high‐Tc superconductivity. I. A consistent one‐electron theory of the N‐electron problem
Authors: Fritsche L.
Published: January 2005

We review and update a recently developed one‐particle theory of N‐electron systems that bears a certain resemblance to density functional (DF) theory and has been put forward by the present author. As distinct from DF theory, the new one‐particle scheme applies to any N‐electron eigenstate including the ground state. For the latter case, the key equations become identical to those familiar from the Kohn–Sham version of DF theory. The theory given here constitutes the basis for a consistent treatment of normal conductivity and superconductivity, which will be discussed in Part II of this article. © 1993 John Wiley & Sons, Inc.
Finding transition states when second‐order Jahn–Teller instability occurs
Authors: Simons Jack
Published: January 2005

When second‐order Jahn–Teller couplings become strong along “streambeds” on potential energy surfaces, instability reflected in negative curvature along a symmetry‐lowering distortion coordinate can take place. The point where such negative curvature sets in is usually not a transition state because the gradient of the potential is usually large there. In this paper, it is demonstrated how to use the local energy, local gradient, local Hessian, and knowledge of how quickly the curvature for the symmetry‐breaking mode evolves along the streambed (i.e., the derivative of this curvature) to predict how far to move in the symmetry‐breaking mode in search of the desired transition state. It is shown that the Hessian matrix evaluated at the symmetry‐broken geometry suggested by this analysis has only one negative eigenvalue. Because this analysis is based on a local approximation to the potential, its predictions are, of course, approximate. As such, they only “suggest” the proper direction and magnitude that one should “step” to move toward a transition state. © 1993 John Wiley & Sons, Inc.
Ground and first excited states of fractionally charged sodium atoms
Authors: Pavão A. C. , Craw John Simon , Nascimento Marco Antonio Chaer
Published: January 2005

The energy levels in sodium atoms with quarks attached to the nucleus are obtained using the configuration interaction method. It is found that the calculated 3p (2P) → 3s (2S) electronic transition in the Na−1/3 quark–atom system is in agreement with that predicted by extrapolation of experimental data. Also, ionization potentials of fractionally charged sodium atoms are discussed. © 1993 John Wiley & Sons, Inc.
Some remarks on the resemblance theorems associated with various orthonormalization procedures
Authors: Löwdin Per‐Olov
Published: January 2005

A survey is given of the resemblance theorems associated with various types of orthonormalization procedures having different kinds of symmetry properties appearing in the current literature. It is shown that the proofs for the minimum properties are closely connected with the fact that the Hilbert–Schmidt norm of an operator is always nonnegative and has the lowest value equal to zero. © 1993 John Wiley & Sons, Inc.
Electric‐field mapping of some anions and cations of adenine and guanine
Authors: Mohan C. G. , Kumar Anil , Mishra P. C.
Published: January 2005

Electric‐field maps of certain anions and cations of adenine and guanine have been studied. The results are compared with those of neutral adenine and guanine. In all cases, the geometries were fully optimized using the MNDO molecular orbital method and the fields were computed using Mulliken charges. Reactivities and hydrogen‐bonding pattern predicted by electric fields, including those of cations, are in satisfactory agreement with experiment. © 1993 John Wiley & Sons, Inc.
Multiplication theorems for orthogonal polynomials
Authors: Kleindienst H. , Lüchow A.
Published: January 2005

In this paper, a general method is presented that allows the derivation of the expansion coefficients of the product of two orthogonal functions provided the generating function is known. For the three classical orthogonal polynomials, the Laguerre, the Hermite, and the Legendre polynomials, the coefficients blmn with ϕmϕn = ∑lblmnϕl are derived. © 1993 John Wiley & Sons, Inc.
Perturbation theory to determine the stable isomer of triatomic linear molecules
Authors: Su Ming‐Der
Published: January 2005

The electronegativity perturbation theory up to the fourth order has been used to study the preferred isomer of linear triatomic molecules. Systems with 10–16 valence–electron systems are discussed and our results are in good agreement with the experiment. The only exception is the isomers of PNO. The usefulness of the perturbation theory is briefly discussed. © 1993 John Wiley & Sons, Inc.
Recurrence relations for the evaluation of electron repulsion integrals over spherical Gaussian functions
Authors: Fortunelli Alessandro , Salvetti Oriano
Published: January 2005

Recurrence relations are derived for the evaluation of two‐electron repulsion integrals (ERIs) over Hermite and spherical Gaussian functions. Through such relations, a generic ERI or ERI derivative may be reduced to “basic” integrals, i.e., true and auxiliary integrals involving only zero angular momentum functions. Extensive use is made of differential operators, in particular, of the spherical tensor gradient 𝒴(∇). Spherical Gaussians, being nonseparable in the x, y, and z coordinates, were not included in previous formulations. The advantages of using spherical Gaussians instead of Cartesian or Hermite Gaussians are briefly discussed. © 1993 John Wiley & Sons, Inc.
Semiempirical evaluation for proton affinities of phosphorus compounds
Authors: Pierini Adriana B. , Duca José S.
Published: January 2005

We here report the AM1 and PM3 evaluation of proton affinities for phosphorus compounds. The substituent effects, the preferred site of protonation, and the geometry changes produced upon protonation are discussed in terms of the present semiempirical calculations that are compared with experimental data and previous ab initio results. © 1993 John Wiley & Sons, Inc.
Molecular calculations using space‐restricted basis functions
Authors: Goodfriend P. L. , Tsonchev S. I.
Published: January 2005

Molecular calculations are presented using “space‐restricted basis functions,” i.e., basis functions that are nonzero only in selected regions of space. The nature of the calculations their justification, and their possible utility to quantum chemistry are described. © 1993 John Wiley & Sons, Inc.
Some comments on the counterpoise correction for the basis set superposition error at the correlated level
Authors: Cook D .B. , Sordo J. A. , Sordo T. L.
Published: January 2005

The use of the counterpoise method for the mitigation of basis set superposition error at the correlated level is discussed. Evidence is presented to show that the ghost basis plays a dual role in the counterpoise method: The orbitals of the system are improved by the ghost basis but at the expense of a nonphysical increase in the dimension of the virtual space. This second factor has no effect on application of the counterpoise method at the SCF level but it makes the use of the counterpoise method at the correlated level much less straightforward. © 1993 John Wiley & Sons, Inc.
Some convergence aspects of the one‐center expansion methods
Authors: Bouferguene A. , Fares M.
Published: January 2005

Among the methods that may be used to carry out multicenter integrals over STOS, the one‐center two‐range expansion is probably the oldest one. However, the convergence of the leading series is generally slow and, hence, time‐consuming. Therefore, it was the aim of the present work to show that the so‐called nonlinear sequence transformations may be of substantial help for improving the rate of convergence of such series. © 1994 John Wiley & Sons, Inc.
Numerical procedures in electrochemical simulation
Authors: Cecilia Joan , Galceran Josep , Salvador José , Puy Jaume , Mas Francesc
Published: January 2005

The use of both the Laplace transformation technique and the finite element method has been analyzed in an electrochemical system. The diffusion‐controlled adsorption process of a species onto an electrode surface is studied in detail. © 1994 John Wiley & Sons, Inc.
Self‐consistent second‐order screening in many‐body theory
Authors: Van doren V. E. , Van camp P. E. , Straub G.
Published: January 2005

Self‐consistent screening arises in all many‐body problems where one‐particle equations containing functionals of the solutions are considered. In the theory of simple metals, e.g., these one‐particle equations are usually solved to second‐order perturbation in the crystal pseudopotential and to first order in the screening. However, higher‐order screening terms have a sizable effect on the form factors, the electron charge density, and the screened pseudopotential. The effects of second order are presented for the bcc simple metals Na and Ba. A nonlocal exchange‐correlation potential has been used since local density approximations such as ρ1/3 cause difficulties in the electron–electron dielectric function. © 1994 John Wiley & Sons, Inc.
Orbitals expanded in slater functions with single‐exponent by shell and by subshell
Authors: Garcia De La Vega J. M. , Miguel B.
Published: January 2005

Slater‐type orbitals (STOs) with a single‐exponent by shell or by subshell have been constructed to reduce the number of integrals evaluated in the electronic calculations. The expansion of orbitals in these new basis sets has been carried out in detail for the ground state of the Ne atom. We have carried out a study of STO basis sets with a different size for this atom that could help to propose empirical rules for the selection of these basis sets for other atoms. The usefulness of STOs with single‐exponent by shell and subshell and the splitting of s and p functions are discussed. © 1994 John Wiley & Sons, Inc.
Developments in multicenter molecular integrals over STOs using expansions in spherical harmonics
Authors: Jones Herbert W.
Published: January 2005

The strategy of using expansions in spherical harmonics of displaced Slater‐type orbitals for the evaluation of multicenter molecular integrals is reviewed and projected. Our Löwdin α–function method is augmented by computer algebra and C, E, and F matrices with rational elements. This permits exact evaluations of each term in an infinite sum using a commercial computer algebra program to investigate the three‐center nuclear attraction integral. Each term (harmonic potential) is important for proposed use in numerical evaluations of multicenter integrals. © 1994 John Wiley & Sons, Inc.
Statistical theory of spectra
Authors: Karwowski Jacek
Published: January 2005

The rapidly developing field of statistical theory of spectra of many‐electron systems is briefly reviewed. In particular, new formal developments, their implementations in studying general properties of the model spaces, and links to the reduction problem are addressed. Applications in molecular and atomic spectroscopy are also discussed. © 1994 John Wiley & Sons, Inc.
A new model of a molecule based on the soft body
Authors: Konarski J.
Published: January 2005

The basic idea of the deformable or soft‐body model of a molecule, which starts from a new definition of the reference configuration, is presented. It is shown that this model introduces into the Hamiltonian a new part that describes deformation energy of a molecule brought about by its rotation. This part leads to nonlinear terms, whose numerical values were compared with the semiempirical approach. © 1994 John Wiley & Sons, Inc.
Theory of the expansion of wave functions in a gaussian basis
Authors: Kutzelnigg Werner
Published: January 2005

The convergence properties of the expansions of (a) the function 1/r and (b) the function exp(‐αr) in an even‐tempered basis of Gaussians are studied analytically. The starting points are the Gaussian integral representations of 1/r and exp(−αr). One arrives at an expansion in a finite number of Gaussians in three steps: (1) a restriction of the integration domain, (2) a variable transformation, and (3) discretization of the integral. The cutoff error goes in both cases essentially as exp(−ah), and the discretization error, as exp(−b/h). The minimum overall error is reached for the β‐parameter of an even‐tempered basis β ∽ exp(c/√n), where n is the dimension of the basis, and the error itself decreases as ϵ ∽ exp(−d√n). Different optimum basis parameters are obtained depending on which quantity one wants to minimize, e.g., the error of the energy expectation value, the distance in Hilbert space, the variance of the energy, or the density at the nucleus. © 1994 John Wiley & Sons, Inc.
Quantum phase‐space densities for a quartic oscillator
Authors: De Polavieja G. G. , Borondo F. , Benito R. M.
Published: January 2005

A quantum analog to the classical Poincaré surface of section, based on the Husimi function, is calculated for the quartic oscillator: H = 1/2(P + P) + x2y2/2 + α(x4 + y4). The corresponding quantum densities in phase space are analyzed, and they show certain localization properties for a large number of states. © 1994 John Wiley & Sons, Inc.
Functional derivative δE/δρ in calculation of chemical potential for the Kohn–Sham electronic system
Authors: Tkacz‐śsamiech Katarzyna , Ptak W. S. , Koleżyński A. , Mrugalski J.
Published: January 2005

A method for finding the chemical potential for an electronic system with density ρ = Σρi represented within the Kohn–Sham approximation is proposed. To find the chemical potential of the system under consideration, we propose to refer to the definition μ = δE/δρ and to apply the mathematical properties of functional derivatives. Particularly, in the case examined, the result μ = μ(r) ≠ const has been obtained, which may be explained in the framework of the calculus of variation. Taking the limit limr→∞ μ(r) as the best approximation to the proper equilibrium chemical potential of a free atom, one obtains μ = −I, where I denotes first ionization energy. A possibility of further applications of the proposed method in relation to crystalline systems is also discussed. © 1994 John Wiley & Sons, Inc.
Computation of algebraic formulas for wigner 3‐j, 6‐j, and 9‐j symbols by maple
Authors: Lai Shan‐Tao
Published: January 2005

Three programs capable of computing algebraic formulas for Wigner 3‐j, 6‐j, and 9‐j symbols have been written in the Maple* program language. These programs can also compute numerically exact values of 3‐j, 6‐j, and 9‐j symbols. © 1994 John Wiley & Sons, Inc.
Path integral's semiclassical quantification
Authors: Marañtón Julio
Published: January 2005

We discuss here a new formal way to evaluate the electronic correlation energy of a molecular system. We use the path integral formalism in the regime of the molecular orbitals. The semiclassical approximation in this procedure is an expansion of the effective action Seff around the classical closed orbits into generalized phase space keeping only the quadratic fluctuation. Thus, after some transformations, we apply to the final expression analogous conditions to the Bohr‐Sommerfeld quantification rules. © 1994 John Wiley & Sons, Inc.
Potential‐barrier model at metal surfaces: Thin films and its dependence on the film thickness
Authors: Mola E. E. , Paola C. A. , Vicente J. L.
Published: January 2005

We propose a model for the potential of thin metal films, in which (1) we reproduce self‐consistent effective potentials (i.e., Lang and Kohn), in fact, better than any approximation in the existing literature, (2) we parameterize the potential as a function of the film thickness, and (3) we approach the classical image potential for large separation from the surfaces. Our potential does not diverge as the electron approaches the surfaces and takes into account the effect of the two surfaces. It reproduces the first peak in the effective potential, which is a Friedel oscillation. We present a simple dependence of the potential with the film thickness that (1) allows a direct description of the quantum size effects and (2) shows how the bulk surface potential is reached. This makes our model useful in the interpretation of tunnel experiments, field emission, and scanning tunneling microscopy. © 1994 John Wiley & Sons, Inc.
Theoretical conformational study of the stabilities and geometries of [2,2] (2,7)naphthalenophane‐1,11‐diene and related compounds
Authors: Rioseras‐garcia Ma. J. , Hernando‐huelmo J. Ma.
Published: January 2005

This theoretical study was to determine the relative stability of the different species proposed experimentally and to establish which of the two pathways suggested is the most probable. A conformational study of the geometries of the stable compounds has been carried out using the semiempirical quantum mechanic method AM1. © 1994 John Wiley & Sons, Inc.