bluuebunny/crossref_metadata_2025 huggingface dataset:
Van der Waals molecules: Quantum chemistry, physical properties, and reactivity
Authors: Hobza P. , Zahradník R.
Published: December 2004

Interaction energies ΔE accompanying the formation of van der Waals (VDW) systems may be estimated by means of the formula ΔE = ΔESCF + BSSE + ED(r−6, r−8, r−10), where BSSE is the basis set superposition error and ED is the dispersion energy in the expanded form. Twenty one stationary points were located on the potential energy surfaces of hydrogen‐bonded complexes; of those, 18 were local minima and 3 were saddle points. Thermodynamic characteristics calculated on the basis of molecular constants, quantum chemically generated, were obtained for 12 hydrogen‐bonded complexes and for competition equilibria between VDW molecules. The role of the VDW forces in some rate processes and in a prototype of enzyme–substrate interactions is outlined. In connection with enzymic catalysis, the intramolecular discrimination in 1,2‐difluorohydrazine, and the stability of hydrogen‐bonded complexes in a cation field is discussed.
Contracted CI calculations of models for catalytic reactions involving transition metals
Authors: Blomberg M. , Brandemark U. , Pettersson L. , Siegbahn P.
Published: December 2004

Theoretical models for reductive elimination from transition metal containing molecules have been studied using large scale contracted CI calculations. Four different models were treated, namely, NiH2, PdH2, Ni(CH3)2, and Pd(H2O)2H2, in order to study the effects of adding ligands, exchanging hydrogens with methyl groups, and comparing nickel and palladium. The most interesting result already appeared for the simplest system NiH2. A closed‐shell‐type 1A1 state with a small bond angle of only 57° is bound compared to Ni and H2 with only a very small barrier for formation. The bond distance is short, shorter than in NiH, and the d orbitals are strongly involved in the binding. The hydrogen atoms bind both to nickel and to each other. With methyl groups rather than hydrogens, this double sided bonding situation is destroyed and Ni(CH3)2 has a negative binding energy with the carbon bonds pointing towards nickel. For PdH2 only a weakly bound complex between an essentially unchanged H2 and Pd was found. The bond distance is very long. Adding H2O ligands to Pd shortens the bond distance and significantly opens up the bond angle. The methods used in the investigation and the chemical implications of the results are discussed.
Scattering in view of the Titchmarsh–Weyl theory
Authors: Rittby Magnus , Elander Nils , Brändas Erkki
Published: December 2004

The Titchmarsh–Weyl theory for a singular second‐order differential equation is presented. The equations, however, are arranged such that the theory is immediately applicable to the multichannel formulation. The mathematical basis of the Titchmarsh–Weyl theory (TWT) is outlined and the Titchmarsh–Weyl m function is presented. Relations to the associated Green's function and the spectral function are given. It is shown how some quantities common in scattering theory can be expressed in terms of the TWT. The method of complex rotation is then applied to the TWT to create a complex rotated analog of the Titchmarsh–Weyl theory. This is then extended as exterior complex scaling is introduced. An outline of a proof for the method of exterior complex scaling is presented and some numerical results of the complete theory are given.
Ordinary field‐theoretic methods for self‐consistent wave functions which describe bond formation and dissociation. II. Commutative coupling case
Authors: England Walter B.
Published: December 2004

Hartree–Bogoliubov–Valatin (HBV) theory may be implemented with Lipkin Hamiltonians to obtain self‐consistent BCS wave functions which describe bond formation and dissociation. These wave functions are in turn vacuua for Nambu's representation of Feynman–Dyson–Goldstone diagrammatic perturbation theory, and hence provide suitable references for the many‐body treatment of correlation. Exact SCF solutions of the HBV equations are equivalent to special even‐replacement MC–SCF solutions. The latter are similar to generalized valence bond theory, and require one Fock operator for each one‐particle shell. The commutative coupling case of HBV theory is realized when the number‐conserving renormalized one‐body and number‐nonconserving pairing operators commute. In this case, a set of orbital equations which involves a single Fock operator may be solved. Since this could prove to be a significant simplification for large systems, the commutative coupling and exact solutions are compared here for the fragmentation of H2 and F2. Results suggest that commutative coupling orbitals will be useful for the aforementioned many‐body theory.
Application of the many‐body perturbation theory by using localized orbitals
Authors: Kapuy Ede , Csépes Zoltán , Kozmutza Cornelia
Published: December 2004

Diagrammatic formulation of the many‐body perturbation theory is investigated when both the occupied orbitals and the virtual ones are localized, i.e., they are unitary transforms of the canonical Hartree–Fock orbitals. All diagrams representing ground state correlation energy can be generated through fifth order. For cyclic polyenes C6H6 and C10H10 as model systems, the energy corrections are calculated in the Pariser–Parr–Pople approximation for a wide range of the coupling constant β−1, through fourth order including some fifth order terms. The results are compared to those obtained by other methods: perturbation theory by using canonical orbitals and full CI. The effect of neglecting contributions from orbitals localized into neighboring sites is also studied.
Scaling in pseudopotential theory
Authors: Gáspár R.
Published: December 2004

Simple Gaussian nonlocal pseudopotentials are determined for K shells. Extrapolation formulas are derived for the parameters as functions of the reduced atomic number. Small hydrids are used for the basis function analysis. Comparison is made with the set of molecules in the book by Snyder and Basch, and detailed results are presented for the molecules BH3, CH4, NH3, H2O, HF, N2, CO, BF, CH3F, C2H2, HCN, CHONH2, and CHOOH. Results on energy levels, total energy, total valence energy and dipolmoment and in a few cases some geometry predictions are made.
Exchange, correlation, and band gaps in conjugated linear chains
Authors: André J. M. , Brédas J. L. , Thémans B. , Piela L.
Published: December 2004

In the case of conjugated polyenic chains (polyacetylene), the relationships between the long‐ (or short‐) range nature of the restricted Hartree–Fock exchange interaction, the role of correlation effects, and the size of energy gaps are illustrated.
Survey of structural regularities in molecular properties. I. Carbon‐13 chemical shifts in alkanes
Authors: Randić Milan
Published: December 2004

Many regularities in properties among structurally related compounds are known but a systematic approach to investigate all such cases is rare. A plan is outlined for a systematic study of structural regularities that is based on use of selected graph invariants as prime auxiliary quantities. In this paper carbon‐13 chemical shifts in alkanes are examined. Since NMR spectra of paraffins are well understood, the example provides a useful illustration of the approach, introduces basic concepts, and illustrates the kind of the results that the graph‐theoretical scheme generates. Differences and similarities between graph‐theoretical viewing of the problem of structural regularities and customary direct use of additivities are discussed in some detail.
Coordinate rotation studies of H−, He−, Be−, Mg− resonances: Basis set and configuration list dependence
Authors: Chuljian David T. , Simons Jack
Published: December 2004

We have performed coordinate rotated configuration interaction calculations on well‐studied Feshbach resonances of H− and He− and on 2P shape resonances of Be− and Mg−. The focus of our efforts was the dependence of computed resonance energies on both the quality of the atomicorbital basis and the level of treatment of electron correlation. Our results indicate that great care must be taken to guarantee that a basis is adequate; commonly used quantum‐chemistry bases are probably far from satisfactory. Our findings also indicate that a proper treatment of inner‐shell orbitals within coordinate rotation calculations is a formidable task. We are therefore encouraged to look carefully for modified coordinate rotation techniques that focus on the active valence‐level orbitals and may avoid spurious complex energies arising from improper treatment of inner shells.
Theoretical study of degree of covalency in some CoF6(n‐) complexes (n = 4, 3, and 2)
Authors: Miyoshi Eisaku , Obara Shigeru , Takada Toshikazu , Kashiwagi Hiroshi , Ohno Kimio
Published: December 2004

On the basis of a high‐quality LCAO MO SCF calculation, covalency versus ionicity of a Co–F bond in the CoF6(n‐) complexes, where n = 4, 3, and 2, is discussed. The overlap and gross atomic populations, delocalization of certain MOS, and the charge densities in the bond region as well as around F's all indicate that the covalency increases as n decreases or the valency of Co increases in these complexes.
Applicability of non‐degenerate many‐body perturbation theory to quasidegenerate electronic states: A model study
Authors: Wilson S. , Janmkowski K. , Paldus J.
Published: December 2004

The nondegenerate finite‐order many‐body perturbation theory is applied to simple model systems in which the degree of quasidegeneracy can be continuously varied over a wide range. Three ab initio minimum basis set models involving four hydrogen atoms in various spatial arrangements are considered. The results are compared with the exact full configuration‐interaction approach, double‐excitation configuration‐interaction and the coupled‐pair many‐electron theory.
Usage de l'Algèbre de Lie su (n) dans l'Etude des Systèmes Quantiques à n Etats. II. Transformation de l'Espace des Observables, Problèmes d'Evolution
Authors: Tillieu Jacques , Van Groenendael Augugstin
Published: December 2004

In the previous paper we examined, for a quantum system, the relation between its n‐dimensional state space and the su (n) Lie algebra. The present paper is devoted to relations between unitary transformations in the state space and orthogonal transformations in Lie's algebra. Two cases can happen. First, the transformations are independently chosen in the two spaces; this amounts to changing the former relation. On the other hand, the relation is maintained and the unitary operators are then related to some of the orthogonal operators. This second case is used to study the evolution operators.
The externally contracted CI method applied to N2
Authors: Siegbahn Per E. M.
Published: December 2004

An approximate multireference CI method is presented. By grouping together configurations with the same internal parts and freezing their relative weights by the use of perturbation theory, the number of variational parameters is drastically reduced. The loss of correlation energy is shown to be usually less than 2%, and the timing is less than one ordinary CI iteration. Examples from calculations on some states of the nitrogen atom and nitrogen molecule are given. The basis set convergence for the lowest excitation energy in the atom is very slow. Less than 50% of the correlation effect is obtained at the s, p, d limit. After the inclusion of ƒ functions this value is improved to 83%. The dissociation energies of the molecule also show slow basis set convergence with errors of 0.5 eV even after addition of ƒ functions. The bond distances are, howeever, accurately reproduced with errors of less than 0.005 Å for all the states. A qualitative discussion of predissociation in the a 1Πg and B 3Πgstates caused by spin–orbit interaction with the 5Σg+ state, is finally presented. Rapidly oscillating lifetimes between the different vibrational states are predicted.
Hartree–Fock exchange energy of an inhomogeneous electron gas
Authors: Becke A. D.
Published: December 2004

We examine the short‐range behavior of the spherically averaged Hartree–Fock exchange charge density by performing a simple Taylor expansion. On the basis of this expansion, a theoretical model is constructed that generates gradient correction terms to the local density approximation for the exchange energy of an inhomogeneous electron gas. In particular, we derive the Xαβ exchange energy functional and a theoretical value for the parameter β. Our value for β agrees well with previous empirical estimates, and with empirical calculations in the present work.
Avoided crossing and intermediate states in certain photochemical reactions
Authors: Lee Tieh‐Sheng , Chu San‐Yan
Published: December 2004

An attempt to classify various types of avoided surface crossings originally discussed by Salem and co‐workers is presented. From the present scheme, an order‐of‐forbiddenness criterion regarding reactivity is established from a consideration of electron and orbital counting. Since the new classification is qualitatively related to the energy gap created in the avoided crossing, the classification appears to be more systematic and informative. Energy transfer processes involved in electronically excited states may also be rationalized by such an application. Three major mechanistic types are distinguished: concerted two‐electron process, concerted one‐electron process, and stepwise one‐electron process involving an ionic‐pair intermediate.
Quantum model of coherent X‐ray diffraction: Extension to Bloch orbitals
Authors: Goldberg M. J. , Massa L. J.
Published: December 2004

The description of electron density in solids by quantum theory and by x‐ray diffraction experiments should closely coincide. A formalism for describing the electronic structure of single crystals in terms of a density matrix is presented. Iterative equations for calculating the density matrix in a basis of Bloch orbitals using measured crystallographic intensity data are derived. Numerical results are presented. The Bloch orbital formalism explicitly accounts for the mutual interaction of atoms in different unit cells, and is useful for insulators, semiconductors, and metals.
Discussion of several analytical approximate expressions for the eigenvalues of the bounded harmonic oscillator and hydrogen atom
Authors: Arteca Gustavo A. , Maluendes Sergio A. , Fernández Francisco M. , Castro Eduardo A.
Published: December 2004

Several approximate analytical formulas for the multidimensional isotropic bounded oscillators and the bounded hydrogen atom are compared. Numerical results show that the coth z method is in both cases better than the Padé approximants method. Perturbational polynomials, necessary in order to build the approximate eigenvalues, are obtained through the hypervirial perturbative method.
Violations of the noncrossing rule due to special symmetry and alternance
Authors: Zhixing Chen , Ruiyu Hong , Yala Zhang
Published: December 2004

This paper reports a study on which behavior of the Hamiltonian gives rise to violation of the noncrossing rule. In principle, the noncrossing rule may be violated when a special symmetry other than spatial and spin symmetries is present or there exists the so‐called alternance, which corresponds to a Hamiltonian in a real vector space anticommuting with a Hermitian operator. In the HMO models for pericyclic reactions, violations due to special symmetry or alternance have been found. The [m,n] supra–antara cycloadditions have no symmetry in the traditional sense, but have special symmetry leading to the existence of crossings in the correlation diagram. Alternance results in one crossing in the middle of the correlation diagram of a forbidden pericyclic reaction with intermediate states in the form of even alternant hydrocarbon. For the reactions with intermediate states in the form of odd alternant hydrocarbon such as [2,4]‐cycloaddition of an allyl cation or an allyl anion to butadiene, there should be no crossing in the correlation diagrams, and both the supra–supra and the supra–antara processes are predicted to be allowed. Such a prediction is beyond the Woodward–Hoffmann rule.
Analytical MO study of the singlet–triplet coupling in xylylenes
Authors: Karafiloglou Padeleimon
Published: December 2004

The singlet–triplet energy difference in para‐, meta‐, and ortho‐xylylenes is studied as the interaction of two radical centers through the benzene ring. An SCF perturbative procedure adapted to open‐shell systems leads to two benzyl‐like nonbonding molecular orbitals (NBMOS) and to benzene‐like occupied and vacant MOS whatever the xylylene isomer. The superposition of these NBMOS in para‐, meta‐, and ortho‐positions and their interaction with the benzene‐like MOS lead, at the configuration interaction level, to the following results: The exchange energy (which favors the triplet state) and the charge transfer energy (which favors the singlet state) are important only in the meta‐xylylene; the dynamic (or double) spin polarization favors the triplet in meta and the singlet in para and ortho‐isomers; the super‐exchange energy (which favors the singlet) is important only in para‐ and ortho‐isomers. The above results are independent of the chosen geometry.
Gap equations for molecular systems
Authors: Sykja Besnik , Calais Jean‐Louis
Published: December 2004

The gap equations for different Fukutome classes are derived in the formalism of second quantization. Compact orbital forms are given for the gap and related to energy difference of the new LUMO and HOMO, ϵLU–ϵHO, obtained from the old RHF molecular orbitals. Approximate expressions are obtained by maximizing the average electron–electron repulsion energy. The simplifications obtained and possible applications to molecular systems are discussed and compared with the instability analysis of an RHF state.
A theoretical study of medium effects on the transmission mechanisms of the fermi contact term of spin–spin coupling constants in the acetamide molecule
Authors: Facelli J. C. , Giribet C. G. , Contreras R. H.
Published: December 2004

Solvent effects on different transmission mechanisms of spin–spin coupling constants are analyzed from a theoretical viewpoint. Medium effects are introduced using the solvaton model, and the decomposition of coupling constants in σ‐ and π‐electron transmitted components is accomplished with the PRMO method. Trends thus obtained are in fairly good agreement with experimental findings reported in the literature. In all types of couplings studied in this work, σ and π components show opposite behavior when increasing the polarity of the solvent.
Molecular theory of critical phenomena in aliphatic carboxylic acid monolayers
Authors: Dunne Lawrence J. , Bell George M. , Combs Leon L.
Published: December 2004

A statistical mechanical theory is presented for the behavior of monolayers of aliphatic carboxylic acids at the air/water interface. A lattice fluid model is introduced with monomer states to represent molecules in the all‐trans conformation directed perpendicular to the interface, dimer states to represent rotational isomers, and vacant sites or “holes.” Using a Flory–Huggins‐type approximation, the temperature and chain length dependences of the monolayer behavior are satisfactorily reproduced for a certain range of parameters. These parameters are compared with those intermolecular energies calculated using the methods of computational quantum chemistry. The agreement thus obtained is fairly satisfactory indicating that the higher‐order nature of fatty acid monolayer transitions is due to the onset of the rotational ordering of pairs of chains about their longitudinal axes, while the sensitive temperature dependence is attributed to the flexible nature of fatty acid molecules. Some possible effects due to the presence of the substrate are discussed.
The band structure of porphyrinatonickel(II). A semiempirical crystal orbital study based on the tight‐binding formalism
Authors: Böhm Michael C.
Published: December 2004

The band structure of porphyrinatonickel(II) (2) has been studied by means of crystal orbital calculations that are based on the tight‐binding approximation; the computational framework is a recently developed INDO model for transition metal compounds of the 3d series. The porphyrinato polymer has been studied in an eclipsed arrangement (2a) and in a staggered conformation (2b) where neighboring layers are rotated by 41°. The total energy of the metallomacrocycle has been decomposed into one‐ and two‐center contributions; the latter interaction parameters have been fragmented into physically feasible resonance, exchange, and classical electrostatic (electron–electron, electron–core, core–core) interactions. It is shown that individual two‐center potentials between atoms in neighboring layers are prevailingly determined by the electrostatic interaction energy. The NiNi coupling in the chain is highly repulsive; important stabilizing interactions are predicted between the 3d center of one cell and the electronegative N atoms in the neighboring layers. Stabilizing and destabilizing electrostatic interaction potentials largely compensate each other; the net stabilization in the polymer comes from the accumulation of resonance and exchange increments. The unoxidized Ni(II) porphyrinato polymer is an insulator. Several ligand bands (π, σ, and lone‐pair) are predicted on top of bands with significant Ni 3d admixtures; the conduction band of the unoxidized strand is of ligand π* character. The dense manifold of ligand states in the vicinity of the Ni 3d states (3d, 3d, 3dxz/3dyz) prevents the formation of bands in the polymer that are strongly localized at the 3d center. Ni 3d and 3d interact strongly with ligand lone‐pair and σ states. Avoided crossings between ϵ(k) curves in k space lead to compositions in the various bands that differ significantly at the bottom and the top. The INDO crystal orbital formalism predicts a partial oxidation of ligand bands in derivatives of 2 that contain oxidants (e.g., halides). The theoretical findings derived for 2 are compared with available experimental data on highly conducting porphyrinatonicke(II) polymers (tetrabenzo and octamethyltetrabenzo derivatives of 2).
Bond length alternation in cyclic polyenes. V. Local finite‐order perturbation theory approach
Authors: Takahashi M. , Paldus J.
Published: December 2004

The finite‐order many‐body perturbation theory using the localized Wannier orbital basis is applied to the problem of bond length alternation in the Pariser–Parr–Pople model of cyclic polyenes CN HN, N = 4v + 2, which may be regarded as a simplified model of polyacetylene. Both the Møller–Plesset and the Epstein–Nesbet‐type partitionings of the model Hamiltonian are employed. The localized orbital basis enables an efficient truncation of the perturbation theory summations over the intermediate states as well as an elimination of energetically unimportant diagrams, thus enabling one to obtain the fourth‐order Møller–Plesset‐perturbation energies with a relatively small computational effort even for large polyenes. The results obtained with the second‐, third‐, and fourth‐order Møller–Plesset and with the third‐order Epstein–Nesbet perturbation theories yield very similar bond length distortions (about 0.05 Å) and stabilization energies per site (about 0.04 eV) as obtained earlier with the RHF, one‐parameter AMO, and delocalized orbital perturbation theories. The effects of truncation and diagram elimination in the fourth‐order Møller–Plesset perturbation theory and the abnormal behavior of the second‐order Epstein–Nesbet perturbation theory results in the localized Wannier basis near the instability threshold of the RHF solutions are discussed.
Effective basis sets for calculations of exchange‐repulsion energy
Authors: Gutowski Maciej , Chałasiǹski Grzegorz , Van Duijneveldt‐Van De Rijdt Jeanne
Published: December 2004

Usefulness of different Gaussian basis sets for reproducing the “tail” region of the SCF wavefunctions employed in calculations of the exchange‐repulsion effect is investigated for the model He‐He interaction. It has been shown that extension of the monomer‐centered basis set in the scheme of regularized even‐tempered basis sets [M. W. Schmidt and K. Ruedenberg, J. Chem. Phys. 71, 3951 (1979)] can be more efficient than augmentation of the fully energy‐optimized basis set with diffuse basis functions. It has been also found that Landshoff term vanishes and the “tail” region is well reproduced if monomer wavefunctions are calculated with the basis set of the dimer.
Solution of a correlation function's defining integral equation for complex domains
Authors: Oriade Joseph
Published: December 2004

We discuss the solution of the integral equation

over complex domains of integration, such as the constant energy volume in solids and numerically tabulated functions, in the biquadratic limit. This will come in handy in the consistent inclusion of correlation effects in solid‐state computations.
Many‐electron theory of autoionizing states using complex coordinates: The position and the partial and total widths of the Ne+ 1s hole state
Authors: Nicolaides C. A. , Mercouris Th. , Komninos Y.
Published: December 2004

This article presents the first results of the application of quantum mechanics with complex coordinates to the calculation of partial widths for the radiationless decay of an inner‐hole excited autoionizing state, the Ne+1s2s22p6 2S. This is succeeded by the reduction of the multi‐electron, multichannel problem in the complex energy plane to five, symmetry adapted, two‐electron problems, in accordance with a published theory of many‐electron resonances. These two‐electron problems are solved independently by using rotated analytic Hartree‐Fock orbitals (expressed in terms of Slater orbitals) for the localized components, and Slater plus Gamow orbitals for the rotated, asymptotic square‐integrable functions carrying the width information. A recently proposed variational principle is employed for the optimization of nonlinear parameters. Within this independent asymptotic pair approximation (IAPA), our results for the partial widths to the five Ne2+ channels are (in 10−2 a.u.): 1s‐2p2 1D: 0.560, 1S: 0.048; 1s‐2s2p, 3P0: 0.029, 1P0: 0.154; 1s‐2s2, 1S: 0.044. The total width is 0.835. These numbers agree reasonably well with those obtained by Kelly [Phys. Rev. A 11, 556 (1975)] from a many‐body perturbation theory (MBPT) calculation, and by Howat et al. [J. Phys. B 11, 1575 (1978)] from a configuration‐interaction in the continuum calculation. The most recent experimental results yield 0.604, 0.089, 0.063, 0.174, and 0.060, respectively, with a total width of 0.99. Previous real‐coordinate many‐electron calculations by Beck and Nicolaides–including relativistic and radiative effects–have predicted the position of the Ne+ 1s hole state at E0 = 870.4 eV above the Ne ground state. It has already been shown that the real energy corresponding to the localized component of the autoionizing state is stable under rotations of the function space describing it. Therefore, the earlier E0 can be incorporated into the present calculation in the complex plane. The shift due to the additive contribution of the IAPA is found to be − 0.09 eV. When this is added to E0, the final E = 870.3 eV is in excellent agreement with experiment [870.3 eV; T. D. Thomas and R. W. Shaw, Jr., J. Electron. Spectrosc. Relat. Phenom. 8, 45 (1976)].
Electronic structure of the peptide linkage. II. A molecular orbital treatment of the electronic spectra of benzohydroxamic acids
Authors: Abu‐Eittah Rafie , Hilal Rifaat , Moustafa Hussein
Published: December 2004

The electronic absorption spectra of some benzohydroxamic acids have been analyzed and interpreted using the results of molecular‐orbital calculations. Charge density distributions, dipole moments, and the extent of delocalization of the MOS were used to interpret the observed solvent effects. Comparison between the spectra of benzohydroxamic acids and that of simple amides led to conclusions regarding the structural differences between the two classes of compounds.
What do local energy maps tell about local error?
Authors: Casida Mark
Published: December 2004

The usefulness of the notion that a one‐particle reduced local energy map can measure local errors in a trial wave function is investigated. Examination of the literature suggests that this notion rests on the assumption that a map of the relative error in the one‐particle density behaves like the one‐particle reduced local energy map. This is tested for several spinless one‐dimensional one‐particle systems. The assumption is discovered to be ill founded when applied to a certain contrived situation, and not to be quantitative when applied to familiar situations. The possibility remains, however, that the assumption may sometimes be useful for obtaining the correct ordering of trial wave functions with respect to the accuracy of certain types of expectation values.
A note on the convergence of multiconfigurational many‐body perturbation theory
Authors: Iijima Naoto , Saika A.
Published: December 2004

The convergence of multiconfigurational many‐body perturbation theory (MC MBPT) is discussed in connection with the intruder state. Its convergence properties are first examined with a fictitious three‐level system employing a Hermitian version of MC MBPT, which permits a general model space. It is then applied to the H2—H2 and N2 systems. The results suggest that a more extensive model space is likely to embrace new intruder states and the space extension be executed with due caution.
Controlled orthogonalization of localized orbitals
Authors: Pipek J.
Published: December 2004

The electron correlation theories for extended systems require an orthogonal and at the same time well‐localized virtual orbital system. An iterative method is suggested, by which extremely nonorthogonal basis sets can be orthogonalized without destroying the localization, in contrast to other well‐known procedures. With the help of a general formulation of the problem not only the localization but other properties can be achieved as well. The method is compared to Löwdin's orthogonalization. Calculations for model and real systems were carried out and the convergence properties and the stability of the fixed points of the iterative procedure were investigated.
Local exchange‐correlation approximations and first‐row molecular dissociation energies
Authors: Becke A. D.
Published: December 2004

Recent Xα calculations of bond energies and other related properties of first‐row diatomic molecules show very encouraging agreement with experiment. In the worst cases, however, the Xα dissociation energies overestimate the experimental values by almost 2 eV. Therefore, we have examined several refinements of the Xα theory and their effects on molecular bond lengths, bond energies, and vibrational frequencies. Among them, gradient corrections to the Xα exchange energy and also some variations of the local spin‐density correlation energy approximation are considered. We find that a local exchange‐correlation functional with gradient corrections gives dissociation energies in significantly better agreement with experiment than the Xα approximation.
An extension of the pairing theorem
Authors: Karadakov Peter
Published: December 2004

An extended pairing scheme is presented which ensures the fulfillment of pairing conditions not only between the sets of occupied orbitals for spin α and for spin β, but also between their orthogonal complements, i.e., the sets of virtual orbitals for spin α and spin β, as well as between occupied orbitals for spin α and virtual orbitals for spin β and between virtual orbitals for spin α and occupied orbitals for spin β. It is shown that the extended pairing properties are suggested by some aspects of the construction of alternant molecular orbitals. The algorithm for singular value decomposition of rectangular matrices is proposed for use in practical implementations of the (extended) pairing scheme.
Molecular properties from perturbation theory: A Unified treatment of energy derivatives
Authors: Almlöf Jan , Taylor Peter R.
Published: December 2004

The definition of a molecular property as a derivative of the electronic energy with respect to one or more applied perturbations is reviewed. The explicit enumeration of terms entering the derivative formulas is performed by considering in turn the various parameter spaces on which the energy and wave function depend. After deriving general expressions for first, second, and third derivatives for different types of perturbation, the parameter spaces involved in MCSCF and CI cases are identified and used to obtain expressions for the first and second derivatives. An example of an MCSCF third derivative is also given. In addition, the various equation systems defining the perturbed wave functions in each order are derived. Some attention is given to the efficient computer implementation of derivative calculations, and the present work is compared with that of other authors.
Molecular orbital study of the ring nitrogen basicity of various dihydrofolate reductase inhibitors
Authors: Ghose Arup K. , Crippen Gordon M.
Published: December 2004

We present molecular orbital (CNDO/2) calculations on the key fragments of different dihydrofolate reductase inhibitors. Distance geometry analysis, physicochemical parameter dependent QSAR, and molecular shape analysis raised some questions regarding the basicity of the ring nitrogen (N1) in these inhibitors and the effect of the various substituents on the basicity. We show that the ring nitrogen N1 of methotrexate has a considerably higher tendency to be protonated compared to that of folic acid. However, not all 2,4‐diamino inhibitors are equally basic. Even 2‐amino‐4‐hydroxyquinazoline is sufficiently basic to be protonated, but not the 2,4‐diamino‐5‐sulfonyl derivatives. The pyrimidinium ion seems to be highly solvated, since in spite of its high protonation energy it is strongly basic. Triazines were found to be the most basic of all the classes studied.
A comparison of two group theoretical models of reaction mechanisms on potential surfaces
Authors: Mezey Paul G.
Published: December 2004

The collection of families of equivalent reaction paths within the low lying regions of potential energy hypersurfaces can be characterized in terms of a group, the fundamental group of reaction mechanisms. This group is compared to the family of all general reaction mechanisms on a complete potential energy hypersurface (considering all nuclear configurations of a fixed set of nuclei). This latter family also has an algebraic structure (a groupoid) that contains a group for every reactant. This groupoid and its subgroups are defined in terms of sequences of open neighborhoods of critical points (representing chemical structures) on the hypersurface, and provide a complete algebraic description of all general reaction mechanisms. This approach simplifies the intractable problem of all possible reaction paths on a surface to a well defined algebraic problem of a discrete set of reaction mechanisms. The relevance of the approach to computer based quantum chemical synthesis planning is pointed out.
Applicability of nondegenerate many‐body perturbation theory to quasi‐degenerate electronic states. II. A two‐state model
Authors: Wilson S. , Jankowski K. , Paldus J.
Published: December 2004

In reply to Kaldor's [Int. J. Quantum Chem. XX, XXX (1985)] criticism of our study of simple four‐electron models, in which the degree of quasi‐degeneracy can be continuously varied, by the finite‐order nondegenerate many‐body perturbation theory, we examine in more detail a simple two‐state model that the used to substantiate his claim that “the low order sum of the perturbation series is not very meaningful” in view of its divergence. It is shown that in contrast to Kaldor's claim, the partitioning used increases the radius of convergence of the considered perturbation series and is in principle capable to make it convergent. It is also shown that the convergence of the series is not very essential and that even divergent series can provide useful estimate of the exact result, particularly when the resummation techniques, such as Padè approximants or continued fractions, are employed. Finally, the shortcomings of the existing multi‐reference perturbation approaches, which Kaldor advocates, are pointed out.
On the evaluation of the integral 〈pu|∂/∂ν|s〉 occurring in covalency reduction factor
Authors: Jaiswal P. S. , Lahiry S.
Published: December 2004

Explicit expressions for integrals of the form 〈pu|∂/∂ν|s〉 occurring in expression of covalence reduction factors, introduced by Stevens and Tinkham, have been derived for various types of atomic functions. Numerical values of the integral for some common ligands are given. Misconceptions regarding the sign and the magnitude of this integral existing in the literature have been clarified.
Molecular‐orbital treatment of some heterocycles with three hetero‐atoms and their benzo‐derivatives
Authors: Abu‐Eittah Rafie H. , Hamed Maher M. , Nigm Abdullah , El‐Azhary Adel
Published: December 2004

Molecular‐orbital calculations, using the INDO procedures, were carried out on the tautomers of 1, 2, 4‐triazole and its benzo‐derivative as well as on 1, 2, 5‐oxadiazole and its benzo‐derivative. Calculations of the transition energy as well as the dipole moment helped to predict the predominant tautomer in an equilibrium mixture. The correspondence between the calculated and observed data is satisfactory. The results of calculations indicated some differences in the electronic structures of the tautomers of a compound.
Quasirelativistic methods
Authors: Karwowski J. , Kobus J.
Published: December 2004

A comparative study of quasirelativistic equations used in atomic structure calculations has been performed. A uniform derivation of all the equations is presented, and some of their specific features are discussed in detail. Electron density distributions, orbital energies, and expectation values of rn obtained with different methods are compared with the ones resulting from the Schrödinger and Dirac equations. The most accurate are found to be the equations of Wood and Boring and of Barthelat, Pelissier, and Durand. (They reproduce almost exactly the Dirac electron densities and expectation values.) The simplest, though least accurate, equation is proposed by us. It gives the relativistic energy corrections with about 6% accuracy and retains exactly the form of the nonrelativistic Schródinger equation. Consequently, its application in analytical SCF‐CI calculations does not require any additional integral calculation.
The difluoroethylenes: A reconsideration of the “Cis effect”
Authors: Heaton M. M. , El‐Talbi M. R.
Published: December 2004

Ab initio molecular orbital calculations have been carried out on all three isomers of difluoroethylene with geometry optimization. The calculations were done with a “double‐zeta” basis set. After correction of the SCF energies for the effect of electron correlation, the 1,1‐isomer is shown to be 8 kcal/mole lower in energy than the cis, which is 1 kcal/mole more stable than the trans. As the stabilization of the isomers increases, the distance between the fluorine atoms decreases: trans, 3.57 Å; cis, 2.77 Å; 1,1‐isomer 2.20 Å. A simple explanation for these trends is based upon electrostatics and the small size and high electronegativity of the fluorine atom. As the fluorine atoms come closer together, the destabilization due to nuclear repulsions and electron repulsions is offset by the increased stabilizing electrons‐nuclei attractions.
On bond orders and valences in the Ab initio quantum chemical theory
Authors: Mayer I.
Published: December 2004

The concept of bond order and valence indices calculated at the ab initio level is discussed in connection with their close relationship to the nonclassical exchange effects in bonding. An improved definition of bond order and free valence indices is given for the open‐shell SCF (UHF) case, and the generalization of the bond order and valence indices to correlated wave functions is also introduced.
New global constraints on electronic energy hypersurfaces
Authors: Mezey Paul G.
Published: December 2004

Improved global energy bounds — valid for the entire electronic energy hypersurfaces of a variety of polyatomic molecular systems — are proposed. The new constraints are applicable to a larger class of molecules and are tighter than the constraints proposed earlier. The new global bounds are easily applicable using readily available energy values of atoms and atom‐ions. The actual evaluation of these constraints typically involves only “back‐of‐the‐envelope” calculations, providing both upper and lower bounds for a complete energy hypersurface, even for very large molecules. Such global energy bounds are of some importance in theoretical studies of chemical reactions and conformational changes. The proposed bounds are likely to find some practical applications in computer‐based quantum‐chemical synthesis planning, using multidimensional potential surfaces.
Computer‐generated formulas for four‐center integrals over slater‐type orbitals
Authors: Jones Herbert W.
Published: December 2004

A triple infinite sum of formulas is generated by a computer algebra implementation of the Löwdin α function method (supplemented by a C matrix with integer elements that characterize an orbital) for a fourcenter two‐electron repulsion integral over 1s Slater‐type orbitals, with screening constants of 1. In this example, one orbital is placed at the origin and the others at equal distances along the x, y, and z axes. Surprisingly few terms are needed for five figure accuracy. There should be no problem in generalizing these methods to all cases of four‐center integrals.
Reality and complexity in asymptotic expansions for eigenvalues and eigenfunctions, with application to the JWKB connection‐formula problem
Authors: Silverstone Harris J.
Published: December 2004

Asymptotic expansions occur widely in quantum physics. The Rayleigh‐Schrödinger perturbation theory for hydrogen in an electrostatic field (the LoSurdo—Stark effect) is one example. The 1/R expansion for the hydrogen molecule ion H is a second. The quantum defect theory and the JWKB method are two more. It is not so widely known that the sum of such real asymptotic expansions may be complex, while the sum of complex asymptotic expansions may be real. The key to this nonintuitive behavior is Borel summation. By examining a simple example related to the exponential integral, the nature of this real‐iscomplex, complex‐is‐real phenomenon is made simple. Then special application is made to derive and clarify the connection formulas (to all orders) in the JWKB method.
On the irreducible tensor operators and the unitarily invariant decomposition of hermitian operators
Authors: Zeng Zonghao , Sun Chia‐Chung
Published: December 2004

In this paper, the unitarily invariant decomposition of Hermitian operators is performed by means of irreducible tensor operators to give the explicit expression of the coupling coefficients for [1m] X [r‐n] → [2s, 1t] with respect to the group structure

with the Gel'fand chain of subgroups

.
Double coset for symmetry orbitals
Authors: Qianer Zhang , Xiangzhu Li
Published: December 2004

In this paper it is shown that, by use of the double coset decompositions of the point symmetry group and permutation group, the related symmetry coefficients and Clebsch–Gordan coefficients can be given in close formulas.
Open‐Shell coupled‐cluster method: Variational and nonvariational calculation of ionization potentials
Authors: Haque Azizul , Kaldor Uzi
Published: December 2004

A hermitian, variational open‐shell coupled‐cluster method is described and applied to the calculation of H2O and N2 ionization potentials in the T ≈ T2 approximation. A nonvariational calculation is also carried out, with the inclusion of T1 and T3 in addition to T2. Both methods give fair agreement with experiment when only T2 is taken into account. T3, which is included at present in the nonvariational scheme only, has a considerable effect on the results and gives good agreement with experiment.
Neutral organic lewis acids of π type
Authors: Cammi Roberto , Ghio Caterina , Tomasi Jacopo
Published: December 2004

The interaction of some neutral acids of π type, bearing appropriate unsymmetrical substitutions at the CC group with some selected bases (H2O, NH3, OH−), is compared with that of the parent compound of a new set of neutral π acids, bearing symmetrical substitutions at the CC group with the same bases. The analyses of the interaction energy, performed according to two decomposition schemes, with and without the counterpoise corrections, make clear the similarity of symmetrically and unsymmetrically substituted neutral organic acids.
A structural rule of polyhedral boranes and heteroboranes
Authors: Tang Au‐Chin , Li Qian‐Shu
Published: December 2004

In this paper we propose a topological rule to account for both the simple and conjuctopolyhedral boranes and heteroboranes. The calculated results are in good agreement with the real molecular formulas. Furthermore, we have also made some quantum chemistry calculations to verify and discuss the rule.
Quantum mechanical treatment of biopolymers as solids: Possible implications for carcinogenesis
Authors: Ladik J. , Otto P. , Bakhshi A. K. , Seel M.
Published: December 2004

After briefly reviewing the results of ab initio band structure calculations on periodic polynucleotides, it is shown how these band structures can be corrected for correlation (quasi particle band structures). Some new results on the electronic structure of aperiodic polypeptides (having up to four different amino acids as components) obtained with the help of the matrix block negative factor counting technique are then presented. They are supplemented by similar results calculated for nonperiodic nucleotide base stacks. Some plausible long‐range effects for the activation of oncogenes through carcinogens are then reviewed. Finally, the preparation of much better defined samples of biopolymers (on which reliable physical measurements could be performed) is discussed.
High‐resolution photoelectron spectrum of ozone
Authors: Cvitaš T. , Klasinc L. , Kovač B.
Published: December 2004

The photoelectron spectra of ozone have been recorded and the first three electronic band systems reassigned on the basis of observed vibrational structure and calculations reported in the literature. The systems X̃,Ã, and B̃ at 12.75, 13.03, and 13.57 eV are assigned as 2A1, 2A2, and 2B2, respectively.
Weak intermolecular interactions: Statics and dynamics
Authors: Zahradník Rudolf , Hobza Pavel
Published: December 2004

This contribution consists of four parts: energy calculations, physical (mainly spectroscopic) characteristics, and static and dynamic aspects of interactions leading to the formation of van der Waals species.

The main, first, part includes specific comments on computational procedures for systems of different size ([number of atoms, number of electrons]: small [4, 10], medium [dozens, hundreds], large [103, 104]) and colloid systems (considering also supermolecular structures). Rigorous and simplified methods of molecular quantum mechanics can be used with the first and second groups, respectively; for larger systems, only empirical potentials and the methods of the physics of a continuum are available. The transferability of empirical potential parameters is critically examined. The role of temperature, Gibbs energy, and entropy is mentioned together with the ensemble theory. The search for stationary points on potential energy surfaces (PES) and analytical fits to PES are reviewed briefly.

The second part is an outline of what is expected from computational chemistry to meet the needs of spectroscopists. The third section deals with selection rules, equilibria and the rates of processes involving van der Waals species, and the role of these species in common chemical reactivity. The crucial role of entropy is mentioned in connection with hydrophobic phenomena, entropy‐driven processes, and partitioning of substances between water and a nonpolar phase.

In the final section, the role of computer experiments (molecular dynamics, Monte Carlo) is pointed out. Some shortcomings and promising features of these techniques are summarized.