bluuebunny/crossref_metadata_2025 huggingface dataset:
The application of the graph‐theoretical method in the QSAR scheme: Possibilities and limits
Authors: Romanowska Krystyna
Published: January 2005

The correlation between topological features of molecular structure and physicochemical as well as biological properties of molecules were examined for some sets of compounds, using graph–theoretical desciptions. It was found that the topological similarity plays a role in the determination of molecular properties for almost all compound sets studied. As a conclusion, one can presume that the less elaborated and complicated similarity measure based on the graphtheoretical description is sufficient in the case of distinct structure–property dependence.
Complex scaling for subsets of coordinates and associated virial‐type relations
Authors: Garcia‐Sucre M.
Published: January 2005

We generalize the usual complex virial theorem using a procedure of complex scaling for only some of the coordinates of the system. This result can also be considered as an extension of the virial theorem obtained in a previous work using real scaling for a subset of coordinates.
Molecular structure and polarity of the C3NH carbene
Authors: Da Silva João Bosco P. , Ramos Mozart N.
Published: January 2005

Ab initio MP2/4‐31G** calculations indicate that the most stable form of C3NH is bent and singlet and that the linear structure corresponds to a maximum. The effect of changing the CNH angle on the total energy is slight, but it is quite pronounced on the molecular polarity. The wider angle tends to increase the polarity of C3NH. MP2/4‐31G** calculations predict a difference of polarity between linear and bent structures of 0.8 D.
Formulation of the coupled cluster theory with localized orbitals in correlation calculations on polymers
Authors: Förner Wolfgang
Published: January 2005

It is shown that in the framework of coupled cluster theory both the correlation energy per unit cell and quasi‐particle band structures of polymers can be computed directly from matrix elements of the excitation operator and the two‐electron integrals calculated in localized orbital basis. Further, it is described how to thake advantage of the localized nature of the orbitals applied. Ab initio test calculations on a finite model system similar to the Pariser–Parr–Pople Hamiltonian are presented.
Computation of two‐, three‐, and four‐center exchange integrals over Slater basis by means of optimized Gaussian expansions
Authors: Montagnani Raffaele , Salvetti Oriano
Published: January 2005

A new way of computing two‐electron integrals over Slater functions by means of optimized Gaussian expansions is proposed. Expansions up to five terms have been optimized for 1s, 2s, and 2p STOs and applied to the computation of many‐center two‐electron integrals. All these integrals can be quickly evaluated and the SCF energy computed from them is very accurate.
Linear dependence in basis‐set calculations for extended systems
Authors: Aissing Gerrard , Monkhorst Hendrik J.
Published: January 2005

The problem of linear dependence in basis‐set calculations for extended systems is discussed. We show that the problem is intrinsic in three‐dimensionally extended systems, but is not as serious in systems with extension in fewer dimensions. The possibility of choosing suitable basis sets that avoid linear dependence is discussed. It is shown that for systems extended in three dimensions in which the orbitals near the Fermi‐level are well described by plane waves a mixed atomicorbital/plane‐wave (AO–PW) basis set with tight orbitals to describe the cores avoids the problem in the most efficient way. Numerical experiments with 1s Slater‐type orbitals and plane waves on a simple cubic lattice are presented for illustration. © 1992 John Wiley & Sons, Inc.
Improving an algebraic approach to calculate approximate Franck–Condon factors of diatomic molecules
Authors: Rivas‐Silva J. F. , Campoy G. , Palma A.
Published: January 2005

Using the BCH theorem, we express the Hamiltonian of a Morse oscillator as a complete series of powers of the creation and annihilation operators for the harmonic oscillator. In this way, we improve the results of a previous work that uses a Bogoliubov–Tyablikov tranformation to calculate the Franck–Condon factors by means of equivalent harmonic oscillators potentials. © 1992 John Wiley & Sons, Inc.
On coordinate transformations in steepest descent path and stationary point locations
Authors: Banerjee Ajit , Adams Noah P.
Published: January 2005

Two aspects of the problems of calculating steepest descent paths and locating stationary points on surfaces E(X), which are sources of some confusion in the literature, are addressed. These include writing proper expressions for the gradient and Hessian, and their transformation properties relative to coordinate transformations, based on the invariance of the surface E(X). The appropriate transformation is derived, based on a constrained energy minimization condition, to achieve what we call the Hessian eigenvalue representation. This not only allows decoupling of the variables, but also points to the minimization direction and preserves the eigenvalues of the Hessian. These results allow one to use the steepest descent path and stationary point location algorithms in any coordinate system and obtain invariant results. The validity of these considerations are also confirmed through numerical examples. The stationary condition with constrained kinematic path length is also shown to yield a Hessian eigenvalue representation for the normal modes for small vibrations. Lastly, we have constructed a mathematically consistent definition of mass‐weighted Cartesians where the intrinsic reaction path of Fukui is a steepest descent path. © 1992 John Wiley & Sons, Inc.
Products of class‐sums of the symmetric group: Generalizing the recurrence relations
Authors: Katriel Jacob
Published: January 2005

The formulation of a combinatorial theory of the structure of the class‐algebra of the symmetric group is pursued. Recurrence relations for reduced class‐coefficients involving imbedded cycles are presented. It is pointed out that for bridging cycles one can obtain elimination rules that involve symmetrization over sets of reduced class‐coefficients with common cycle‐structures but inequivalent index distributions. Consequently, some of these reduced class‐coefficients remain individually inaccessible. © 1993 John Wiley & Sons, Inc.
MAPLE symbolic computation of the long‐range many‐body intermolecular potentials: Three‐body induction forces between two atoms and a linear molecule
Authors: Piecuch Piotr
Published: January 2005

General theory of the long‐range intermolecular potentials, resulting from the use of the Rayleigh–Schrödinger perturbation theory at the multipole approximation level and the irreducible tensor formalism, is applied to describe the three‐body induction effects in a system composed of two atoms and a linear molecule. Explicit expressions for the leading van der Waals coefficients are derived by employing the symbolic computation language MAPLE. Both the general geometry and the special case of the isosceles triangular configuration are considered. Final equations are presented using the interface between MAPLE and the typesetting language LATEX. Some technical aspects associated with the use of MAPLE in theory of long‐range intermolecular potentials are briefly discussed. Explicit expressions obtained in this article should be useful in determination of the nonadditive induction effects in van der Waals clusters composed of two atoms and a diatomic molecule. In particular, they may be helpful in explaining the discrepancies between experiment and theory that are observed in high‐resolution microwave studies of the complex Ar ⃛Ar ⃛HCl. © 1993 John Wiley & Sons, Inc.
Intrinsic reaction coordinate of perturbed potential energy surfaces: Construction of perturbed energy profiles
Authors: Mestres Jordi , Duran Miquel
Published: January 2005

This contribution analyzes the changes in the intrinsic reaction coordinate (IRC) and in the potential energy profiles (PEP) caused by application of a uniform electric field evaluated using standard ab initio MO methods. Two typical organic processes have been studied, namely, the Friedel–Crafts and the Walden inversion reactions, which are modeled by suitable simple systems. The results for the Walden inversion reaction show that the IRC for the field‐free and that for perturbed processes are almost coincident; in this case, using the field‐free IRC to compute the perturbed energy profile is a very good approximation. On the contrary, for the Friedel–Crafts model reaction, the two IRCs differ slightly, so the energy profiles using the perturbed and the unperturbed IRCs are somewhat different. © 1993 John Wiley & Sons, Inc.
Accurate computation of eigenfunctions for Schrödinger operators in one dimension
Authors: Núñez Marco A. , Izquierdo B. Gustavo
Published: January 2005

A numerical method is developed to obtain sequences of functions converging to the eigenfunctions of a Schrödinger operator in the Hilbert space L2(−∞, ∞), whose norm is used to introduce the criterion of convergence in the norm and we show that it guarantees the accurate computation of expected values of a symmetric operator. The method consists in solving the Dirichlet problem associated to the eigenvalue problem in the interval [−n, n] by the Ritz method, whose convergence to both eigenvalues and eigenfunctions is guaranteed by the compactness criterion. Using the asymptotic perturbation theory in L2(−∞, ∞), we prove the convergence of both eigenvalues and eigenfunctions of the Dirichlet problem to those of the unbounded system when the interval [−n, n] is expanded. The method is applied to the harmonic oscillator, the Mitra potential, as well as to the potential V(r) = r and the Coulomb and Yukawa potentials; in each case, the convergence of eigenvalues and eigenfunctions is shown. © 1993 John Wiley & Sons, Inc.
Rayleigh–Schrödinger perturbation theory for nonlinear Schrödinger equations with linear perturbation
Authors: Ángyán János G.
Published: January 2005

Rayleigh–Schrödinger‐type perturbation theory is developed for the nonlinear Schrödinger equation, which contains a linear perturbation operator. Typical applications involve the self‐consistent reaction‐field model of solvent effects. Consideration of external perturbations, like electric fields, allows. Calculation of the response properties of solvated species. The general formulae allow development of a consistent Møller‐Plesset perturbation theory of solvated molecules. © 1993 John Wiley & Sons, Inc.
A first‐principles approach to high‐Tc superconductivity. II. The superconducting ground state
Authors: Fritsche L.
Published: January 2005

We show that a consistent N‐electron theory of a solid can within the Born–Oppenheimer (BO) approximation lead only to normal conductivity or to an insulating state. If one leaves the BO approximation by turning on electron–phonon interaction, one can establish a lower‐lying new ground state that has the characteristic properties of the Bardeen–Cooper–Schrieffer (BSC) ground state. We demonstrate that an (N + Nn)‐particle Schrödinger equation that describes the motion of N electrons and Nn nuclei of a solid can lead only to phonon‐induced superconductivity. © 1993 John Wiley & Sons, Inc.
The low‐lying excitation energies of polyenes investigated with a chain‐length‐dependent screened potential
Authors: Siregar R. E. , Tjia M. O.
Published: January 2005

The chain‐length dependencies of 2Ag and 1Bu excitation energies as well as their unexpected inversion observed experimentally in trans‐polyenes have so far been explained satisfactorily only in terms of configuration interactions within the standard Pariser–Parr–Pople (PPP) parametrization scheme with at least double excitations involving prohibitively large computational labor for long polyenes. A simpler calculation allowing nonzero differential overlap and employing restricted (first‐order) single‐excitation configuration interaction with chain‐length‐dependent screened potential is shown to provide an adequate alternative for the studies of those basic spectroscopic features of polyene excited states. The screening factor is parametrized in accordance with the chain‐length‐dependent behavior of the electrical polarizabilities of polyenes derived within the standard PPP approximation scheme. © 1993 John Wiley & Sons, Inc.
Valence electronic states of NH2+ and PH2+ dications
Authors: Park Jong Keun , Sun Hosung
Published: January 2005

The ab initio second‐order effective valence‐shell Hamiltonian that is based on the multireference many‐body perturbation theory has been applied to determine adiabatic potential energy curves for the valence states of NH2+ and PH2+ dications. For PH2+, three low‐lying quasi‐bound states (X1∑+, a3 Π, A1Π) are found and their spectroscopic constants are characterized. In NH2+, no quasi‐bound states are found. The potential energy curves for NH2+ are compared with those for PH2+ to understand the difference between these two valence isoelectronic cations. © 1993 John Wiley & Sons, Inc.
Self‐consistent approximate solution of the second‐order contracted Schröudinger equation
Authors: Colmenero F. , Valdemoro C.
Published: January 2005

The general theoretical background for solving approximately the contracted Schrödinger equation (CSchE) in a self‐consistent (SC) way has recently been proposed [F. Colmenero and C. Valdemoro, Phys. Rev. A 47, 979 (1993)]. Here, a spin‐free procedure is developed and the convergence of the SC iterative process is analyzed using as test cases the beryllium atom and four isoelectronic ions in their ground states. Damping and extrapolation procedures are employed to improve and accelerate the convergence. The results obtained are in very close agreement with those obtained by means of the full configuration‐interaction (FCI) method. © 1994 John Wiley & Sons, Inc.
Improvement of methods for molecular dynamics integration
Authors: Janežič Dušanka , Orel Bojan
Published: January 2005

An application of symplectic implicit Runge–Kutta (RK) integration schemes, the s‐stage Gauss–Legendre Runge–Kutta (GLRK) methods of order 2s, for the numerical solution of molecular dynamics (MD) equation is described. The two‐stage fourth‐order GLRK method, the implicit midpoint rule, and the three‐stage diagonally implicit RK method of order four are studied. The fixed‐point iteraction was used for solving the resulting nonlinear system of equations. The algorithms were applied to a complex system of N particles interacting through a Lennard‐Jones potential. The proposed symplectic methods for MD integration permit a wide range of time steps, are highly accurate and stable, and are thus suitable for the MD integration. © 1994 John Wiley & Sons, Inc.
Thermal reaction rates with a two‐point flux–flux correlation function
Authors: Lefebvre R. , Moiseyev N. , Ryaboy V.
Published: January 2005

The thermal rate constant of a bimolecular reaction is shown to be expressible as the time limit of the time integral of a correlation function involving the reactive flux at two different points along the path leading from reactants to products. This extension provides some additional flexibility in the finite basis‐set representation of the rate given by Miller–Schwartz–Tromp [J. Chem. Phys. 79, 4889 (1983)]. Some of the features of this expression are examined in the case of one‐dimensional Eckart barrier. © 1994 John Wiley & Sons, Inc.
Some current problems in theoretical chemical physics to be solved
Authors: Löwdin Per‐Olov
Published: January 2005

Quantum Chemistry can today boast the fact that ordinary chemists—by means of personal computers and programs available—can study many theoretical properties of molecules by solving the Schrödinger equation and get an advance idea of how to properly arrange their experiments to find new features. For small molecules, they can use ab initio programs of the Hartree–Fock type, and for large molecules, they can use semiempirical programs available. To achieve higher accuracy and to include electron correlation properly, however, one has in the ab initio approach to use configurational interaction methods and giant computers, whereas in the semiempirical methods, the effect of correlating is often taken into account in the adjustable parameters forming the basis for this approach. In connection with the ab initio methods, it is further emphasized that the resolvent methods combined with the partitioning technique provide an excellent conceptual and mathematical framework for getting solutions of any accuracy desired, but that most of the programming of this approach remains to be done. Ordinary wave mechanics is valid at absolute zero of temperature, and—in order to include such important chemical concepts as temperature, entropy, free energy, etc.—one has to go over to general quantum theory and the Liouvillian formalism. One can stil start from the Coulombic Hamiltonian, but it becomes of importance to include the nuclear motion properly and preferably on the same level as that of the electronic motion. It is further emphasized that the irreversibility problem is not yet fully solved, that the theory of the interaction between matter and electromagnetic fields still needs some improvements, and that the question of the proper introduction of relativistic corrections in the quantum theoretical treatment of molecular systems involving heavier atoms still has a great deal to desire. © 1994 John Wiley & Sons, Inc.
Statistical properties of spin‐adapted reduced Hamiltonians
Authors: Mas V. , Planelles J. , Karwowski J. , Rajadell F.
Published: January 2005

The first two moments of the spectral density distributions of the second‐ and the third‐order spin‐adapted reduced Hamiltonian (SRH) matrices have been calculated and compared with the corresponding quantities describing the full configuration interaction (FCI) Hamiltonian matrix. It has been demonstrated that the differences between the SRH and FCI spectral density distributions sharply increase with increasing difference between the number of electrons and the order of SRH. © 1994 John Wiley & Sons, Inc.
Temporal rearrangement of electronic densities in slow atomic collisions
Authors: Micha David A.
Published: January 2005

Electronic rearrangement is a common occurrence in interactions of an atom with other atoms or with solid surfaces and in molecular photodissociation by visible and UV light. In this contribution, the emphasis is on the way properties change over time, as a system progresses from its initial to its final state in a collision. An overview is presented of our recent work describing electronic rearrangement in terms of coupled differential equations for electronic orbitals and nuclear degrees of freedom. An eikonal/(time‐dependent Hartree–Fock) approximation is described and a new compact formulation is given in terms of operators in Liouville space, for both small and extended molecular systems. A method is described for treating the coupling of degrees of freedom with very different time scales. The method is illustrated with selected results for temporal atomic population changes in ion–atom and ion–solid surface interactions. © 1994 John Wiley & Sons, Inc.
A microscopic theory for solution chemical reactions: Introduction of reactant and medium structures into generalized langevin equation formalism
Authors: Nagaoka Masataka , Okuno Yoshishige , Yoshida Naoto , Yamabe Tokio
Published: January 2005

A microscopic formulation of solution chemical reactions, taking reactants and medium structures into consideration, is presented on the basis of microscopic understandings obtained by recent quantum chemical methods (i.e., ab initio molecular orbital theory, etc.). Assuming thermal equilibrium of the medium bath, an effective internal Hamiltonian is derived, and, further, its derivative with respect to internal normal coordinates is proved explicitly to give the same force field as is provided by the free‐energy surface or potential of mean force. The free‐energy surface can be expressed in the composite normal coordinate system (CNCS) consisting of some normal coordinate systems of isolated reactants and surrounding solvent molecules (i.e., medium solvent molecules). In CNCS, in use of diagonal elements obtained in the Hessian matrix of the free‐energy surface, effective normal‐mode frequencies, which reflect the equilibrium solvent effect, are estimated. Furthermore, on the generalized Langevin equation (GLE) treatment, a closed expression of the time‐dependent frictional coefficient is derived on a microscopic basis, reflecting the reactant and solvent structures. The nonequilibrium effect is estimated by an analytical expression similar to that in the Grote–Hynes theory. The rate constant is evaluated for a typical model system and it is shown that the equilibrium rate constants should be reduced by a factor 0.997. Finally, it is concluded that the present microscopic theory is reasonably applicable to the estimation of chemical reaction rate constants in solution. © 1994 John Wiley & Sons, Inc.
Many‐Electron, many‐photon theory of nonstationary states
Authors: Nicolaides C. A. , Mercouris T. H. , Komninos Y. , Petsalakis I. D.
Published: January 2005

A number of physical processes, such as autoionization, predissociation, ac– or dc‐field‐induced ionization, multiphoton dissociation, or chemical transformations, can be formulated as problems involving a nonstationary state satisfying a time‐independent complex eigenvalue Schrödinger equation (CESE). The CESE gives rise to all the conceptual and practical difficulties associated with the polyelectronic structures of excited states, as well as novel ones due to the presence of external fields and to the physical significance of the continuous spectrum. In a series of articles from this institute, it has been shown how advanced electronic structure theory and methods suitable for excited states can be integrated in a practical way into selected elements of the rigorous theory of discrete states interacting with the continous spectrum in order to solve the CESE nonperturbatively and efficiently and compute properties such as positions and widths of inner hole or multiply excited states, multiphoton ionization rates, multichannel predissociation lifetimes, nonlinear static and frequency‐dependent polarizabilities, and tunneling rates. The present article constitutes a review of the basic features of this theory and its computational methods. © 1994 John Wiley & Sons, Inc.
Mathematical characterization and shape analysis of localized, fractal, and complex distributions in extended systems
Authors: Pipek János , Varga Imre
Published: January 2005

The availability of recent supercomputers and massively parallel computing facilities makes possible the calculation of the electronic structure of highly extended (mesoscopic) molecular networks. Disorder, which is practically always present in these systems, causes an extreme complexity of the wave function that typically shows multifractal behavior in the intermediate length scale. Multifractal analysis, however, is possible only on systems that cover several orders of length scales. Though such calculation can be carried out on model systems, it is beyond the bounds of present ab initio or semiempirical treatments. In this contribution, a shape‐analysis method of the wave function is given that is applicable both for localized and multifractal one‐particle states even in moderately large networks without a regular geometrical structure. No boxing of the distributions is necessary through several orders of magnitude of scaling distances. Multifractal behavior and different regularly decaying localization shape functions can be distinguished. Finite‐size multifractal distributions are also discussed. The described method is intended to serve as an easily applicable and efficient tool for bridging over the gap between the wave‐function analysis of systems containing macroscopic and moderately large number of particles. © 1994 John Wiley & Sons, Inc.
Analysis of chemical phenomena by solving constrained hartree‐fock equation. I. Method and application to resonance energy in linear polyenes
Authors: Ichikawa Hiroshi , Kagawa Hirotaka
Published: January 2005

The authors proposed a general method to analyze chemical phenomena in such static states as resonance and aromaticity, without changing the variational space of the trial wave function. Solution of the Hartree–Fock–Roothaan (HFR) equation for a molecular system gives the ground‐state electronic structure and its energy. One can impose constraint conditions, which have chemical meanings, on the HFR equation (the constrained HF equation). The presented method is to analyze the energy differences between usual and constrained HF solutions. This method has an advantage over conventional methods in that it neither varies the trial wave function nor the geometry. The method was applied to interpretation of resonance energy in unsaturated linear hydrocarbons to show that both vertical and adiabatic resonance energies are produced proportionally to the number of ethylene units and that they originate by the lowering of the kinetic energy of π electrons, namely, resonance releases the kinetic‐energy pressure of π electrons. This is consistent with the previous investigations © 1994 John Wiley & Sons, Inc.
Semiempirical quantum chemical treatment of the standard reduction potentials of quinone and plastoquinone in water
Authors: Mallik Buddhadeb , Datta Sambhu N.
Published: January 2005

The standard electrode potential for the quinone (Q)‐hydroquinone (QH2) couple in aqueous acidic media has been explicitly calculated. Molecular geometries of Q and QH2 have been optimized. Protonation of Q, i.e., the formation of QH+ and QH, have been considered. Molecular geometries of these species have been thoroughly optimized. The energy of complexation of these molecules with water have been calculated by optimizing the structures of the hydrated complexes Q · 6H2O, QH2 · 6H2O, QH+ · 6H2O. and QH · 6H2O. The ion–solvent interaction energy of QH+ · 6H2O, in turn, has been calculated by considering the complex QH+ · 6H2O…︁ 2H2O, where the two extra water molecules approach the charge center of the complex QH+ · 6H2O vertically from top and bottom of the quinonoid ring. The standard reduction potential calculated by the CNDO method, 0.8548 V, is somewhat larger than the experimental potential, 0.6998 V, at 25°C. But the INDO value, 0.7085 V, is in excellent agreement with the observed potential. The electrode potential for the plastoquinone (PQ)‐plastohydroquinone (PQH2) couple present in the aqueous pool in chloroplast has been calculated by the INDO method. The basic geometries of PQ, PQH+, and PQH2/sb have been synthesized by adopting the optimized geometries of Q, QH+, and QH2 and considering methyl substituents as well as an isoprenoid side chain containing up to 3 isoprene units with possible geometrical isomerism. The hydrated species PQ · 6H2O, PQH+ · 6H2O, and PQH2 · 6H2O are unstable compared to the isolated species PQ, PQH+, and PQH2, respectively. In fact, we have found that the hydration of PQH+ and PQH2 is much less extensive, and stability arises only when the hydroxyl groups in these two molecules are hydrogen‐bonded to water molecules. But PQH+ is also stabilized through the association of two more water molecules in the vertical direction. For this reason, we have calculated the reduction potential of the PQ/PQH2 system from the energies of the isolated molecules PQH2 and the hydrated species PQH+ · 2H2O. The computed standard reduction potential is 0.2785 V and it yields a potential of 0.07V at pH 7 at 25°C, which is in good agreement with the reduction potential 0.11 V observed for plastoquinone in the aqueous pool in chloroplast. © 1994 John Wiley & Sons, Inc.
Calculations on the spectra and nonlinear third‐order optical susceptibility of c70
Authors: Li Jun , Feng Jikang , Sun Chiachung
Published: January 2005

The equilibrium geometry and UV‐visible spectra of C70 were examined using semiempirical INDO/2 and INDO/CI methods. The results obtained are in good accord with experimental results. On the basis of correct electronic spectra, calculations of the nonlinear third‐order optical susceptibility (γijkl) of C70 were performed using the INDO/SDCI method combined with a sum‐over‐states expression. The calculated value for <γ> (‐2 ω, ω, ω, O) is 0.882 × 10−33 esu (ω = 1.91 μm), which is in good agreement with observation. © 1994 John Wiley & Sons, Inc.
Transition states and energy barriers from density functional studies: Representative isomerization reactions
Authors: Abashkin Yury , Russo Nino , Toscano Marirosa
Published: January 2005

Three representative isomerization reactions (HNC → HCN, CH3NC → CH3CN, and N2H2 trans → cis and sin) have been studied using both the LCGTO–LSD and LCGTO–NLSD density functional methods and employing a new algorithm for the search and the refinement of the transition‐state structures. The inclusion of the nonlocal corrections and the use of large basis sets improve the reliability of the energetic parameters. Results are in good agreement with previous accurate first‐principle computations and available experimental data. © John Wiley & Sons, Inc.
An analysis of the integrand occurring in correlation energy functionals
Authors: Fortunelli Alessandro , Salvetti Oriano
Published: January 2005

An analysis of the integrand occurring in current density functional calculations is presented, concentrating attention on correlation energy functionals and the atomic regions, i.e., the regions of space surrounding atomic centers. The analysis follows the structure of a previously proposed numerical integration scheme for three‐dimensional integrals occurring in electronic structure calculations. The scheme is based on the choice of density‐based weight functions that naturally partition the space into «atomic» volumes (in which the integration is performed in terms of spherical coordinates) and «diatomic» volumes (in which the integration is performed in terms of confocal elliptical coordinates). From this analysis, a simplified procedure for the atomic «internal» integrations is developed, whereas preliminary results are discussed for the atomic and diatomic «external» integrations. The numerical tests are performed on the C60 molecule in the symmetrical configuration. © John Wiley & Sons, Inc.
The determination of intrinsic reaction coordinates by density functional theory
Authors: Deng Liqun , Ziegler Tom
Published: January 2005

The first implementation of the intrinsic reaction coordinate (IRC) method within the density functional theory (DFT) framework is presented. The implementation has been applied to four different types of chemical reactions represented by the isomerization process, HCN  HNC (A); the SN2 process, H− + CH4  CH4 + H− (B); the exchange process, H˙ + HX  HX + H˙ (X  F,Cl) (C); and the elimination process, C2H5Cl  C2H4 + HCl (D). The present study presents for each process optimized structures and calculated harmonic vibrational frequencies for the reactant(s), the transition state, and the product(s) along with the IRC path connecting the stationary points. The calculations were carried out within the local density approximation (LDA) as well as the LDA/NL scheme where the LDA energy expression is augmented by Perdew's and Becke's nonlocal (NL) corrections. The LDA and LDA/NL results are compared with each other as well as the best available ab initio calculations and experimental data. For reaction (D), ab initio calculations based on MP2 geometries and MP4SDTQ energies have been added due to the lack of accurate published post‐HF calculations on this process. A detailed discussion is provided on the efficiency of the IRC algorithms, the relative accuracy of the DFT and ab initio schemes, as well as the reaction mechanisms of the four reactions. It is concluded that the LDA/NL scheme affords the same accuracy as does the MP4 method. The post‐HF methods seem to overestimate activation energies, whereas the corresponding LDA/NL estimates are too low. The LDA activation energies are even lower than the LDA/NL counterparts. The incorporation of the IRC method into the DFT framework provides a promising and reliable tool for probing the chemical reaction path on the potential energy surfaces, even for large‐size systems. IRC calculations by ab initio methods of an accuracy similar to the LDA/NL scheme, such as the MP4 scheme, are not feasible. © John Wiley & Sons, Inc.
Numerical grids for density functional calculations of molecular properties
Authors: Goursot A. , Pápai I. , Daul C. A.
Published: January 2005

There is an increasing number of applications using methods based on density functional theory (DFT) describing a large variety of systems of chemical interest. All these calculations are performed through evaluations of integrals of exchange and correlation contributions to the energy and the potential, which depend on the density and also on its first and second derivatives (nonlocal functionals). Within our DF program, the integrand is decomposed into single‐center components, through the introduction of weight functions, and its radial and angular dependence can be chosen. In this article, we give a brief description of these features, with compared performances of different grids for the evaluation of different integrals, such as the total number of electrons and the exchange and correlation energies. More complex properties, such as total energies and equilibrium geometries, are also studied with respect to the choice of the grid of points, in order to determine the most favorable radial and angular quadrature schemes. The incidence of this choice is analyzed in the case of the metal–metal bond of the Ru2, Rh2, and Pd2 dimers. Finally, the use of an extended grid of points is shown necessary for systems involving weak interactions, such as the Ar2 molecule. © John Wiley & Sons, Inc.
Coulomb‐Hole–Hartree–Fock functional
Authors: Clementi E. , Hofmann D. W. M.
Published: January 2005

We have extended to molecules a density functional previously parametrized for atomic computations. The Coulomb‐hole–Hartree–Fock functional, introduced by Clementi in 1963, estimates the dynamical correlation energy by the computations of a Hartree–Fock‐type single‐determinant wave function, where the Hartree–Fock potential was augmented with an effective potential term, related to a hard Coulomb hole enclosing each electron. The method was later revisited by S. Chakravorty and E. Clementi [Phys. Rev. A 39, 2290 (1989)], where a Yukawa‐type soft Coulomb hole replaced the previous hard hole; atomic correlation energies, computed for atoms with Z = 2 to Z = 54 as well as for a number of excited states, validated the method. In this article, we parametrized a function, which controls the width of the soft Coulomb hole, by fitting the first and second atomic ionization potentials of the atoms with 1 ⩽ Z ⩽ 18. The parametrization has been preliminarily validated by computing the dissociation energy for a number of molecules. A few‐determinant version of the Coulomb‐hole–Hartree–Fock method, necessary to account for the nondynamic correlation corrections, is briefly discussed. © 1994 John Wiley & Sons, Inc.
Ground‐state properties of CdxSn1–xTe: The role of d‐electrons
Authors: Grosch G. H. , Freytag B. , Range K.‐J. , Rössler U.
Published: January 2005

Within the framework of density functional theory (DFT), we calculate the ground‐state electronic properties of CdxSn1–x Te using norm‐conserving pseudopotentials in connection with the local density (LDA) and virtual crystal approximation (VCA). Our particular interest is in the influence of the Cd‐4d and the Sn‐4d electrons by comparing results obtained with pseudopotentials, which either consider the d‐electrons explicitly or in the frozen core.
In the mixed crystal system CdxSn1–x Te, the transition from a ten‐ (x = 0) to an eight‐electron (x = 1) system is realized, which is accompanied by a change of the crystal structure from rock salt (SnTe) to zinc blende (CdTe). By calculating the ground‐state energies, we find the equilibrium lattice constant as the function of x and the bulk modulus, as well as the crossover value of x for the transition from rock‐salt to zinc blende. The calculated lattice constants and bulk moduli are in much closer agreement with experimental data if the d‐electrons are taken into account explicitly, whereas the crossover is rather insensitive with respect to the d‐electrons. In view of the electronic charge density, we demonstrate the decrease of ionicity for increasing x. © 1994 John Wiley & Sons, Inc.
Application of second‐order density functional methods to the calculation of the LiFH potential energy surface
Authors: Suárez Cristina , Aguado Alfredo , Tablero César , Paniagua Miguel
Published: January 2005

Second‐order density functional methods are used to introduce the electron correlation in Hartree‐Fock (HF) ab initio electronic energy calculations of three‐dimensional potential energy surfaces (PES). We analyze the behavior of these methods in PES calculations by applying them to the Li + FH reaction, which has been considered a prototype of the elementary atom–diatom reactions. This system has been studied also by the usual techniques, allowing a point‐by‐point (for a total of 317 grid points) comparison for the lowest 2A' adiabatic state. In particular, we compare the results obtained using the HF, Møller–Plesset (MP3 level), and configuration interaction (CISD and MRDCI levels) methods with the corresponding results obtained using the Colle–Salvetti (CS) and Moscardó‐San Fabián (MSF) procedures using the HF results as the starting point. We found that the CS and MSF procedures support the prediction of a shallow well in the entrance channel that deepens slightly away from collinearity and disappears for a bond angle Θ < 74°. We also found that the constrained saddle‐point positions remain essentially constant from Θ = 180°–90° and are clearly in the exit channel as for the MRDCI approach (corresponding to the best results). In conclusion, there is a good overall agreement, but there is a question in which this agreement is less pronounced: the heights of the saddle points including the transition state. In particular, the transition‐state height is about 3 kcal/mol higher than the more accurate value obtained with the MRDCI approach. However, the second‐order density functional methods have been capable of reducing the HF barrier from 18 to 9 kcal/mol (all of these values obtained by spline interpolation), the latter value being very similar to the CISD result. © 1994
John Wiley & Sons, Inc.
Ionization potentials of atoms calculated with a nonlocal exchange and a local correlation functional
Authors: Cordero N. A. , Gritsenko O. V. , Rubio A. , BalbáS L. C. , Alonso J. A.
Published: January 2005

We calculate the first ionization potential of atoms (3 ⩽ Z ⩽ 54) by means of a nonlocal density functional approach and the results are compared with those obtained using other recent density functional approaches based on density gradients. In these calculations, we use a nonlocal weighted spin‐density approximation of exchange effects and a local spin‐density approximation of Coulomb correlation, both based on novel forms of the pair‐correlation functions. We also calculate the total energies of the He, Be, and Ne isoelectronic series. © 1994 John Wiley & Sons, Inc.
Density functional treatment of water–carbon dioxide van der waals complex
Authors: Abashkin Yuri , Mele Franca , Russo Nino , Toscano Marirosa
Published: January 2005

LCGTO–LSD and LCGTO–NLSD methods have been tested for the study of water–carbon dioxide weakly bound binary complex. Different local and nonlocal exchange‐correlation energy functionals and many grid radial points have been used. Results show that both nonlocal corrections and a large number of radial points in the grid are mandatory for well reproducing the experimental data. © 1994 John Wiley & Sons, Inc.
Quantum mechanical valence study of a bond‐breaking–bond‐forming process in triatomic systems
Authors: Nalewajski Roman F. , Formosinho Sebastiãto J. , Varandas AntÓnio J.C. , Mrozek Janusz
Published: January 2005

The recently introduced set of the quadratic, two‐electron covalent and ionic valence indices is used to investigate the bond‐breaking–bond‐forming (BB‐BF) process in an atom exchange reaction between H2 and X (X = H, F—I) as well as in the O2—H system. Valence changes accompanying selected charge reorganizations are examined within the three‐orbital model and valence diagrams for symmetric transition states (TSs) are given. The UHF valence data for Li2O and CO2 and the H—H—X, O—O—H, and O—H—O (ABC) TSs (collinear and angular) are reported and compared to valence data in the separated fragments limits (SFL), AB and BC. The overall valence, ν(ABC), and the total (ionic plus covalent) diatomic valences, νAB and νBC, are used as measures of the overall bond‐order in a concerted BB–BF reaction, to test the postulate of the bond‐energy–bond‐order (BEBO) model. In collinear TSs of H2X, ν ≊ −1, i.e., one bonding electron pari, is found to be roughly preserved, whereas in the angular H2X and in collinear O—H—O TSs, the effect of increased valence at the saddle‐point is observed, relative to that of diatomic fragments (reactiants or products). For the angular O—O—H TS, a similar increase in | ν (ABC)| relative to both O2 and OH SFLs is detected; smaller changes relative to the O2 data are found in the collinear TS. This observation is in agreement with earlier predictions from the intersecting‐state model. The relative diatomic valences, ν/ν and ν/ν, are shown to conserve the overall relative bond multiplicity around 1 in both collinear and angular TSs of the H2—X systems. © 1994 John Wiley & Sons, Inc.
Improved tight‐binding method
Authors: Telezhkin V. A. , Rafalovich A. A.
Published: January 2005

An improved tight‐binding method, taking into exact account the kinetic energy oerator, is proposed. The potential part of the Hamiltonian is represented by its matrix elements on some set of localized functions (like the LCAO method). The spectrum and the density matrix are determined by means of solving the nonlinear eigenvalue problem. © 1994 John Wiley & Sons, Inc.
Two types of Kramers rate equations for reactions in condensed media
Authors: Christov S. G.
Published: January 2005

Two cases of bilinear coupling of a particle to a medium are compared. They differ in that one of the mediums does not modify the particle potential, whereas the other does. Two corresponding kramers‐type rate equations for adiabatic reactions are derived directly from a dynamic rate theory and interpreted from the view of the stochastic theory. Both equations become identical in the weak coupling limit. Their relations to transition‐state theory are also discussed. Corresponding results for nonadiabatic reactions are considered. © 1994 John Wiley & Sons, Inc.
The coordination chemistry of the catalytic zinc ion in alcohol dehydrogenase studied by ab initio quantum chemical calculations
Authors: Ryde Ulf
Published: January 2005

The coordination chemistry of the zinc ion in the active site of alcohol dehydrogenase has been studied by the ab initio Hartree–Fock method. Geometry optimizations were performed using analytical gradients and basis sets of double‐zeta quality. Correlation effects were included at the MP2 level. The active site was modeled by Zn(HS)2XL(H2O)0–2, where X denotes ammonia or imidazole and L denotes water, methanol, ethanol, or the corresponding aldehydes or anions. It is shown that with uncharged L‐ligands the four‐coordinate complexes are about 20, 17, and 40kJ/mol more stable than are the corresponding three‐, five‐, and six‐coordinate complexes, respectively. If the L‐ligand is negatively charged, only the four‐coordinate complexes are stable. These results suggest that the active‐site zinc ion in alcohol dehydrogenase prefers a coordination number of four during the catalytic reaction, especially when the nonprotein ligand is negatively charged. Ligand exchange at the zinc ion is likely to proceed by an associative mechanism with intermittent formation of a five‐coordinate complex. The results lend no support to mechanistic proposals attributing an important catalytic role to a negatively charged five‐coordinate hydroxide or alkoxide ligand. © 1994 John Wiley & Sons, Inc.
Self‐consistent methods for the treatment of low‐lying molecular vibrations
Authors: Schmidt P. P.
Published: January 2005

The subject of this article is the self‐consistent‐field (SCF) treatment of low‐lying molecular vibrations in molecules subject to solvent effects and light atom migration. The analyses use a Cartesian Gaussian basis and Gaussian functional expansions of potential energy operators. The objective of the work was to establish approximate and practical methods of analysis of vibrational degrees of freedom in molecules that build on and compare well with the highly accurate treatments of vibrations in small molecular systems of the past decade. An application to a system in which hydrogen bonding contributes the major anharmonic effect illustrates the method. © 1995 John Wiley & Sons, Inc.
The evaluation of matrix elements in the analysis of anharmonic molecular vibrations: Functional taylor series expansions
Authors: Schmidt P. P.
Published: January 2005

This article presents methods for computing Cartesian Gaussian matrix elements using a Taylor series for general potential energy operators that admit well‐behaved radial derivatives. These operators arise in the analyses of anharmonic vibrations in molecules. Application to the evaluation of matrix elements for hydrogen associated two wells illustrates the method. © 1995 John Wiley & Sons, Inc.
Unified treatment of two‐center Coulomb, hybrid, and exchange integrals over Slater‐type orbitals
Authors: Guseinov I. I. , Yassen R. F.
Published: January 2005

Using Neumann expansion for 1/r12 in elliptical coordinates a combined formula has been obtained for two‐center Coulomb, hybrid, and exchange integrals with Slater‐type orbitals. © 1995 John Wiley & Sons, Inc.
Ensemble representable densities for atoms and molecules. I. General theory
Authors: Cassam‐Chenaí P.
Published: January 2005

A method to obtain ensemble representable densities from experimental diffraction data is proposed. The method uses ab initio molecular densities instead of the commonly employed one‐electron orbital densities, and as a result, few parameters need to be optimized in the fitting procedure to the experimental structure factors. The optimized coefficients can provide information about intra‐ and intermolecular electronic correlations, spin‐orbit coupling, etc. This work also provides new explicit formulas to determine the rank of a fermionic wave function, i.e., the rank of the one‐fermion density matrix. © 1995 John Wiley & Sons, Inc.
A method of calculation of the matrix elements between the spin‐projected nonorthogonal Slater determinants
Authors: Igawa Akira
Published: January 2005

In the resonating Hartree–Fock calculation, we have to calculate the matrix element between spin‐projected nonorthogonal Slater determinants (S dets). The matrix element between coherently spin‐rotated S dets are given by a linear transformation of the spin‐projected ones. Using the inverse transformation, we get the projected matrix elements from the coherently spin‐rotated ones. By appropriately choosing the angles of the spin rotation, the required computational time is considerably reduced. © 1995 John Wiley & Sons, Inc.