bluuebunny/crossref_metadata_2025_split huggingface dataset:
Optimization of molecular electronic structure calculations. 2. Calculation of symmetry‐reduced matrix elements
Authors: Kovrikov A. B. 
Published: January 2005

AbstractA suggested formalism of the local symmetricized orbitals in conjunction with the selection technique for independent blocks of integrals in an original basis is used for a construction of multielectron Hamiltonian matrix elements in the symmetry orbital basis. The optimal molecular electronic structure calculation algorithm with the Hartree–Fock–Roothaan method in the symmetricized basis was obtained as a result. The minimal number of fundamentally distinguished (symmetry attributed) elements both in original and in symmetricized basis is used in the calculations.
Electron correlation described by extended geminal models: The EXGEM7 and EXRHF3 models
Authors: Røeggen I. 
Published: January 2005

AbstractWithin the framework of the general extended geminal model, two new approximate models, EXGEM7 and EXRHF3, are introduced. Compared with previous models, these new models imply a more sophisticated approximation of the four‐electron terms {ϵKL}. The models are tested by calculations on the beryllium atom and the HF molecule.
Methods for electron correlation on large molecules
Authors: Sæbø Svein 
Published: January 2005

AbstractHigh‐quality ab initio calculations, i.e., calculations including electron correlations with large atomic basis sets, have been restricted to relatively small systems due to their excessive demand on computer facilities. To extend these methods to large systems, one is faced with two problems: the steep (6 power) increase of the computational task with the molecular size, and the large number of electron repulsion integrals that must be stored and retrieved. We have recently introduced new computational methods where both these problems have been addressed. The local correlation method reduces the steep dependency of computational effort with molecular size without significant loss of accuracy by taking advantage of the localizability of the electronic structure. For electron correlation calculations integrals in the MO basis are needed in addition to the two electron integrals in the AO basis, and the only way electron correlation can be applicable to large systems is by a direct approach in the spirit of Almlof's direct SCF. We have recently extended the direct approach to post Hartree–Fock methods. Description of both these methods including their supercomputer implementations are discussed.
Localized orbitals for the description of molecular interaction
Authors: Kozmutza C. , Kapuy E. 
Published: January 2005

AbstractThe intermolecular interaction between the molecules CH2O and NH3 was investigated by the supermolecule method. The interaction energies were first calculated at the ab initio SCF level, and the electron correlation was included via second‐order Møller‐Plesset perturbation theory (MP2). The basis set superposition error (BSSE) was taken into account by the counter‐poise (CP) method. The occupied and the virtual canonical molecular orbitals (CMOS) of the supermolecule were separately localized by the Boys' procedure. The correlation correction was calculated by the many‐body perturbation theory (MBPT) in the localized representation. Contributions of the third‐ and fourth‐order localized diagrams were added to those of the second‐order canonical diagram. This procedure gives a correction nearly equivalent to that of MP2. The possibility to separate LMO contributions responsible for the dispersion interaction was investigated.
Topological analysis of eigenvalues of particle in one‐ and two‐dimensional simple quantal systems: Net sign approach
Authors: Lee Shyi‐Long , Li Feng‐Yin , Lin Friday 
Published: January 2005

AbstractSimple net sign analysis has been carried out for particle in one‐ and two‐dimensional boxes and harmonic oscillators. The conclusion that no simple rule for the ordering of eigenvalues of two‐dimensional systems can be drawn is conjectured. Cyclobutadiene, naphthalene, benz‐cyclobutadiene, biphenylene, biphenyl, and p‐terphenyl are found to behave topologically as particle in either type of potential. Benzene, anthracene, naphthacene, and pentacene are found to behave topologically as particle in a two‐dimensional harmonic oscillator. This analysis provides the physical basis for the net sign approach in the signed graph theory.
Transition properties from multiple scattering X‐Alpha Calculations: A study of NO2
Authors: Howard S. T. , Huke J. P. , Parsons I. W. , Till S. J. 
Published: January 2005

AbstractThe usefulness of the MS‐Xα method for calculating molecular transition properties is investigated in a study of NO2. Two‐dimensional potential surfaces are obtained in C2v symmetry for the X̃2A1/Ã2B2 system. Potential curves that approximately follow the asymmetric stretch coordinate are also presented: On investigation, no symmetry‐broken solutions were found. At all nuclear geometries investigated, the muffin‐tin sphere radii were chosen by an energy‐minimization technique. The inclusion of corrections to the muffin‐tin form of the Xα total energy is shown to be essential, if the computed surfaces are to be qualitatively correct. The transition dipole moment connecting the two states is evaluated as a function of nuclear coordinates, using the transition‐state approximation. Finally, the radiative decay of a single vibronic level in NO2 is modeled and the relevance to experiment is discussed.
The system of harmonically interacting particles: An exact solution of the quantum‐mechanical problem
Authors: Osadchii M. S. , Murakhtanov V. V. 
Published: January 2005

AbstractAn original procedure has been developed to determine the eigenvalues and the eigenfunctions of quantum‐mechanical many‐body systems with a harmonic oscillator interaction. Exact solutions in the explicit form have been obtained for the case of systems containing three groups of identical particles. For the system containing two groups of identical particles, a solution in the adiabatic approximation has been obtained and compared with the exact one.
A general treatment of vibration‐rotation coordinates for triatomic molecules
Authors: Sutcliffe Brian T. , Tennyson Jonathan 
Published: January 2005

AbstractAn exact, within the Born–Oppenheimer approximation, body‐fixed Hamiltonian for the nuclear motions of a triatomic system is presented. This Hamiltonian is expressed in terms of two arbitrarily defined internal distances and the angle between them. The body‐fixed axis system is related to these coordinates in a general fashion. Problems with singularities and the domain of the Hamiltonian are discussed using specific examples of axis embedding. A number of commonly used coordinate systems including Jacobi, bond‐length‐bond‐angle, and Radau coordinates are special cases of this Hamiltonian. Sample calculations on the H2S molecule are presented using all these and other coordinate systems. The possibility of using this Hamiltonian for reactive scattering calculations is also discussed.
A correction to effective core potentials for transition metals
Authors: Pacios L. Fernandez , Olcina V. Botella 
Published: January 2005

AbstractThe correct description of energetic separations between atomic states arising from s2dn, s1dn+1, and dn+2 electronic configurations is known to be essential to treat transition metals. Effective core potentials calculations for first‐row transition elements with an Ar core show important errors in these energies when compared with all‐electron values. A procedure to eliminate errors while maintaining the formalism unaltered and retaining the ar core is proposed.
Charge‐transfer intensity in complexes with symmetrically equivalent acceptors
Authors: Parker W. L. , Crosby G. A. 
Published: January 2005

AbstractMulliken's model for the intensity of charge‐transfer absorption bands in donor/acceptor complexes is extended to transition‐metal compounds. Attention is focused on the analysis of systems containing a central metal ion and symmetrically equivalent π‐acceptor ligands. The theory is illustrated for a one‐donor/two‐acceptor complex in D2d point symmetry. Results are stated for symmetries of commonly occurring transition‐metal compounds that display well‐documented metal‐to‐ligand charge‐transfer transitions.
Model study of the abrupt excess‐energy dependence of radiationless decay in benzene and azabenzenes
Authors: Sobolewski A. L. , Lim E. C. , Siebrand W. 
Published: January 2005

AbstractModel studies are reported aimed at accounting for the abrupt dependence of radiationless decay‐rate constants on excess energy (known as channel‐three decay in the case of S1 benzene) in singlet and triplet manifolds of benzene and azabenzenes. The favored model involves La(ππ*) state, strongly distorted along an out‐of‐plane coordinate, crossing the ground‐state potential at an energy close to the minimum of the lowest excited state. The results are compared with experimental observations on benzene and three azabenzenes. Implications for photochemical reactions are also discussed.
Approximate separation of the hyperradius in the many‐particle Schrödinger equation
Authors: Avery J. , Goodson D. Z. , Herschbach D. R. 
Published: January 2005

AbstractFor large values of d = 3N, the radial distribution function of an N‐particle system is sharply peaked near the hyperradius rm = (d − 2)/2k0, where k0≡(2/E/)1/2. This fact allows an approximate separation of the hyperradius, leading to many‐dimensional hydrogenlike radial solutions. Kindred applications to dimensional scaling are also discussed, where d = DN, with D the spatial dimension. For the large D regime, illustrative analytic formulas are obtained giving the energy and effective nuclear charge for the lowest few S states of the helium atom.
SC‐MEH‐MO calculations on high Tc superconductors. 1: The YBa2Cu8O cluster in YBa2Cu3O7
Authors: Boudreaux Edward A. , Baxter Eric 
Published: January 2005

AbstractSC‐MEH‐MO calculations have been carried out on select clusters of the YBa2Cu3O7 lattice structure. The results of an earlier computation on small CuO clusters are presented for comparison with the finding obtained on a YBa2Cu8O26+ extended cluster. In the latter, the antiferromagnetic coupling of singularly occupied Cu and O levels is analyzed.
Hydrogenlike atoms in uniformly charged sphere model of atomic nucleus. I. Reference calculations of energy levels
Authors: Hasegawa T. , Fujimura N. , Matsuoka O. 
Published: January 2005

AbstractWe have adopted the uniformly charged sphere model of atomic nucleus for one‐electron atoms H, Ar17+, Xe53+, Hg79+, and U91+ and calculated several energy levels by solving the matching equations of the inward and the outward radial wave functions for the Schrödinger as well as for the Dirac equations. The finite‐size effect (FSE) of the atomic nucleus on the energy levels of nonrelativistic atoms has been found one order of magnitude smaller than the effect on the relativistic atoms. The FSE works mainly on s states for nonrelativistic atoms, whereas for relativistic atoms, it works on s and p1/2 states. The energy levels of p states have been calculated lower than the energies of the corresponding s states when we have included the FSE.
On the connection between certain properties of the second‐order reduced density matrix and the occurrence of coherent‐dissipative structures in disordered condensed matter
Authors: Brändas E. J. , Chatzidimitriou‐Dreismann C. A. 
Published: January 2005

AbstractIt is demonstrated, from general physical principles, that a new kind of quantum correlations, associated with the appropriate reduced density matrix, Γ, exist in amorphous condensed matter. The treatment starts from general representation properties of the second‐order reduced density matrix. The derivations, using general statistical notions in a quantum mechanical framework, lead to a decomposition of the two‐matrix into the large‐, the small‐, and the unpaired components. Since this result can be identified with the extreme case of Coleman, the formulation is automatically ensemble‐representable. Introducing the complex scaling method (CSM) into the Bloch–Liouville equation for Γ it is shown how the temperature T in the aforementioned ensemble can be specified. This defines, in the present development, thermalization in a system far from equilibrium. It is further shown that this thermalization leads to the formation of certain irreducible (Jordan) blocks containing some (incomplete) phase information. The connection between these irreducible blocks and the concept of a coherent‐dissipative structure is made. The treatment reveals general features of the coherent‐dissipative structure and a certain universality of the coherence‐breaking mechanism. The main equations relate the relaxation time Trcl and the temperature T with the minimum degrees of freedom Smin and the associated spatial domain dmin of the structure. Relevant examples are, e.g., proton transfer and H+ conductivity in water, conductivity of molten alkali chlorides, quantum correlation effects in high‐Tc superconductors, and spin dynamics of Gd far above the Curie point.
On the prüfer transformation in the H2+ problem
Authors: Úlehla Ivan 
Published: January 2005

AbstractThe application of the Prüfer transformation to the Schrödinger equation leads to a nonlinear first‐order differential equation. The advantage of this transformation is demonstrated in the calculation of the energy spectrum of the H2+ ion. In the second section, the classical problem is recalled and the transition to Prüfer transformation prepared. The definition of this transformations is contained in the third section. In the final paragraphs, the numerical results concerning the eigenvalues of H2+ energy are presented.
A pair‐excitation MCSCF calculation based on CNDO/INDO approximation I
Authors: Kumakura Shigekazu , Shiraishi Satoshi , Izawa Masaru , Hanamura Mitsuyasu 
Published: January 2005

AbstractSecond‐order multiconfigurational self‐consistent field (MCSCF) calculation has been programmed on the basis of CNDO/INDO molecular orbital bases, in which the configuration space employed is restricted within pair‐excitations. Test calculations have been carried out for 17 small molecules. All the MCSCF ground states of these molecules have been successfully converged to their respective optimal states by employing a simple weighting scheme. This procedure provides a great savings in computer time. The MCSCF calculation on azetidine required only 27 min on a HITAC M‐680H. The MCSCF energies of HF, F2, and BH show improved behaviors up to large atomic distances (∼7au).
Ab initio calculations on 5α‐androstane
Authors: Paša‐Tolić Lj. , Klasinc L. , Spiegl H. , Knop J. V. , McGlynn S. P. 
Published: January 2005

AbstractThe electronic structure of 5α‐androstane, the parent hydrocarbon of the hormonal steroids, has been computed by ab initio SCF methods in an STO‐3G basis. The results are compared with existing MNDO computations and are used to discuss long‐range electronic interactions between distant substituents that might be appended to rings A and D of 5α‐androstane. It is thought that these interactions are mediated by the ribbonlike MO'S of the parent molecule.
On geometric concepts in sensitivity analysis of molecular charge distribution
Authors: Nalewajski Roman F. 
Published: January 2005

AbstractA geometric interpretation of molecular charge redistributions [polarization (P) and/or charge transfer (CT)] is proposed. It regards the atoms‐in‐a‐molecule (AIM) electron populations, N = (N1,…, Nm), as components of the global electron population vector, \documentclass{article}\pagestyle{empty}\begin{document}$\overrightarrow N \equiv N$\end{document}, in a system of orthogonal AIM electron population axes, \documentclass{article}\pagestyle{empty}\begin{document}$(\overrightarrow N _1 ,...,\overrightarrow N _m )$\end{document}. The normal (decoupled) representation corresponds to the rotated, principal axes coordinate system, \documentclass{article}\pagestyle{empty}\begin{document}$(\overrightarrow Q _1 ,...,\overrightarrow Q _m )$\end{document}, in which the canonical AIM hardness tensor becomes diagonal. Such transformation preserves 𝒩 while not preserving the global electron population, N = ∑miNi, the usual parameter of the sensitivity analysis. The chemical potential, hardness, softness, and related concepts associated with 𝒩 are defined and their properties examined. A simple geometric model of a chemical reaction is proposed within the \documentclass{article}\pagestyle{empty}\begin{document}$ \{ \overrightarrow Q _\alpha \}$\end{document} space. It consists of two intersecting effective states representing the charge activation of reactants and the charge relaxation of products, respectively. Only the normal modes of reactants, which include the CT component, can participate in the CT reaction coordinate, whereas the pure P modes contribute only to the entropy factor of the reaction rate constant. The implications of the model for the chemical reactivity are briefly explored. Finally, the linear vector space interpretation of charge sensitivities is given and applied to define the optimum hybrid charge displacement modes of reactants.
Calculations on model systems using quasi‐degenerate variational perturbation theory with an average pair correction
Authors: Murray Christopher , Racine Stephen C. , Davidson Ernest R. 
Published: January 2005

AbstractA correction to quasi‐degenerate variational perturbation theory is proposed that is similar to the average coupled pair functional method. The correction is shown to lack solid theoretical justification when applied to importance‐selected multireference calculations and to systems with irreducible interpair contributions to the correlation energy. The method is shown to give improved results when applied to small model systems.
The properties of n‐electron wave functions built up with two kinds of geminals
Authors: Liu Chengbu , Deng Conghao , Hu Haiquan , Jin Beiyan 
Published: January 2005

AbstractThe properties of the n‐electron wave functions
equation image
with symplectic symmetries have been discussed. These functions are built up with two kinds of geminals. The well‐known antisymmetrized geminal power (AGP) function is only a special case of them. The first‐ and second‐order reduced density matrices and the natural expansions of these functions have been given, and the uniform expressions for system energies in the states corresponding to these functions have been deduced. It has been shown that the special case
equation image
is probably another consistent ground state for the particle‐hole propegator or random‐phase approximation (RPA) besides the AGP function.
Vibrational self‐consistent‐field approximation for triatomic molecules using hyperspherical modes with application to H2O
Authors: Bastida Adolfo , Zúlñiga José , Molina Antonio M. , Requena Alberto 
Published: January 2005

AbstractThe vibrational self‐consistent‐field approximation is used to calculate excited vibrational energy levels of the water molecule in hyperspherical coordinates. The calculations are made for a global realistic Sorbie–Murrell‐type potential surface for which exactum quantum variational results are known for comparison. The coupled SCF equations are solved using the discrete variable representation (DVR) method, which allows computation of the coupled multidimensional integrals in a very simple and efficient way. The results are in good agreement with exactum quantum calculations and are more accurate than SCF energy eigenvalues obtained using normal mode coordinates.
Extended Gaussian‐type valence basis sets for calculations involving nonempirical core pseudopotentials. II. PS‐21 G Basis for Li to Ca and Ga to Kr atoms
Authors: Hannachi Y. , Barthelat J. C. , Jolly L.‐H. , Silvi B. , Bouteiller Y. 
Published: January 2005

AbstractSplit valence basis sets adapted to Durand and Barthelat core pseudopotentials have been optimized for the three first rows of the main group elements. The reliability of these PS‐21G basis functions has been checked by performing test calculations on about 30 small molecule and crystalline systems. These studies indicate a satisfactory overall agreement between the PS‐21G results and those of all‐electron calculations carried out with basis sets having similar valence‐shell contractions.
Semianalytical method for four‐center molecular integrals over Slater‐type orbitals
Authors: Jones Herbert W. 
Published: January 2005

AbstractA strategy for the evaluation of four‐center molecular integrals over Slater‐type orbitals is developed using the Löwdin α‐function approach in which displaced orbitals are expanded in spherical harmonics. The harmonic potentials are produced analytically and evaluated along a grid. The harmonic charge distributions are given an analytical formulation and are evaluated over the common grid, and numerical integrations are performed for each harmonic. Using an example with 1s orbitals, only nine harmonics are needed for good results. Computer algebra and integer arithmetic are used to generate C, E, and F matrices that are stored as part of the data base. One‐dimensional T and X matrices are introduced as an aid in computation. The employment of look‐up tables and vector and parallel processing promises to make this method, which can be generalized, practical.
A method of calculating eigenvectors of real symmetric tridiagonal matrices in a hyperspherical space
Authors: Novosadov Boris K. , Zhogina Vera V. 
Published: January 2005

AbstractA novel direct method of calculating eigenvectors for real symmetric tridiagonal matrices has been proposed. An eigenvector is represented as a unit vector in a hyperspherical space set by hyperpolar angle coordinates. An algorithm has been examined for a series of tridiagonal matrices. Numerical calculations as compared with a conventional Householder algorithm have shown a good agreement within 8‐byte double precision for most eigenvectors computed.
Mills–Nixon effect in heteroanalogs of cyclopropabenzene
Authors: Eckert‐Maksić M. , Maksić Z. B. , Hodošček M. , Poljanec K. 
Published: January 2005

AbstractStructural properties of cyclopropabenzene and its heteroanalogs are studied at the SCF 6‐31G level of theory. It is found that the Mills–Nixon (MN) type of localization within the benzene ring is present in these systems. The origin of the bond fixation lies in rehybridization at the carbon junction atoms. π‐electron bond orders usually follow changes within the sigma framework but can be misleading sometimes. It is shown that a judicious choice of heteroatoms can considerably enhance the MN effect. A refined and better definition of the MN effect is offered. Finally, present calculations and analysis of the results in terms of hybridization model and π‐bond orders strongly indicate that experimental 4J(HCCMe) proton–proton spin–spin couplings over four bonds can be used in identification of the MN effect only with extreme caution.
Nonadiabatic theory of triatomics: Formalism for 1Πu/1Φg interaction, for electronic spin, and for 2Λ Renner–Teller effect
Authors: Petrongolo Carlo 
Published: January 2005

AbstractA recent theory of nonadiabatic effects in triatomic molecules is specialized to the four‐state Renner–Teller and Jahn–Teller 1Πu/1Φg interactions and is then generalized by including the electronic spin and by considering the 2Λ Renner–Teller effect.