bluuebunny/crossref_metadata_2025 huggingface dataset:
Two‐parameter ω‐technique for MO calculations
Authors: Mathur S. C. , Singh D. C. , Kumar B. , Mitra S.
Published: December 2004

A two‐parameter ω‐technique for MO calculations is proposed. The parameters ω and ω′ are chosen empirically to obtain a good agreement between calculated and observed bond lengths. The method amounts to an inclusion of the effect of nearest‐neighbour electronic repulsion integrals into the conventional ω‐technique.
The pairwise correlated generalized valence bond model of electronic structure. II. A simple physical model for electron correlation
Authors: Petersson G. A.
Published: December 2004

When electron pair correlations are incorporated into generalized valence bond wave functions, the necessary and sufficient wave functions for the quantitative description of chemical reactions are achieved. The resulting electron pair correlation functions are shown to be invariant; hence the generalized valence bond orbitals contain all the information in the correlated wave functions. In the case of pair correlation energies, this information is expressed through a simple function of the orbital overlaps. The resulting overlap approximation is applied to ground states, excited states, and transition states for chemical reactions. In all cases the exact energy is reproduced to within 0.5 kcal/mol (0.001 hartree). The pairwise correlated generalized valence bond method provides an opportunity to accurately predict reaction pathways for system of chemical interest.
Application of graphical methods of spin algebras to limited CI approaches. I. Closed shell case
Authors: Paldus J. , Adams B. G. , Čížek J.
Published: December 2004

The time independent diagrammatic technique based on the mathematical methods of quantum electrodynamics (second quantization, Wick's theorem, Feynman‐like diagrams) is combined with graphical techniques of spin algebras to derive general expressions for the matrix elements of spin independent one‐ and two‐particle operators between spin symmetry adapted ground, mono‐ and bi‐excited configurations of a closed shell system. Two coupling schemes are considered for bi‐excited states and their relative merits are discussed. Finally, the results are used to derive compact expressions for the coupling coefficients of the direct configuration interaction from molecular integrals (CIMI) method.
Application of graphical methods of spin algebras to limited CI approaches. II. A simple open shell case
Authors: Adams B. G. , Paldus J. , Čížek J.
Published: December 2004

A time independent diagrammatic technique based on the Wick theorem and graphical methods of spin algebras, as outlined in Part I, is applied to a simple open shell case having one unpaired electron in addition to the pure singlet closed shell. Compact explicit expressions for the matrix elements of a spin independent Hamiltonian between conveniently chosen spin symmetry adapted states are given for the ground, mono‐ and bi‐excited configurations.
Electronic computation of first‐order wave functions using green's functions
Authors: Laurenzi Bernard J. , Flamberg Alan
Published: December 2004

Green's functions and the symbol manipulative computer language LISP have been used to obtain exact, closed form, first‐order functions and second‐order energies for the first fourteen states of the hydrogen atom in electric and magnetic fields.
Lower bound molecular orbitals for H, HeH++, and H
Authors: Johnson J. W. , Poshusta R. D.
Published: December 2004

Gaussian orbitals are used to calculate Temple lower bounds for H, HeH++, and H. Molecular orbitals are constructed from individual Gaussian‐type orbitals (GTO) and from GTO contractions adapted for either upper or lower bounds of the hydrogen atoms. The MOS are optimized by minimizing either the upper bound, 〈H〉, or the variance, 〈(H – E)2〉. The best Temple lower bounds achieved by these methods are −0.60336 a.u. for , − 1.06224 a.u. for HeH++, and −0.13003 a.u. for H. Comparison is made with other types of molecular orbitals and with the exact wave functions for , HeH++. Analysis of the nuclear cusps is given. A prescription for constructing lower bound molecular orbitals is offered.
Coupled Hartree‐Fock calculation of static dipole polarizations of open‐shell ions
Authors: Roy H. P. , Gupta A. , Mukherjee P. K.
Published: December 2004

In this paper static dipole polarizabilities and shielding factors of 3p open‐shell atomic systems from A1 to C1 are presented using coupled Hartree‐Fock theory in the Roothaan scheme. The calculation was made for the ground as well as for some valence excited states of the ions. A variational approach was adopted to obtain the polarizability values and the results are compared with the existing data wherever possible. The shielding factor values are in good agreement with the theoretical N/Z ratio.
Formulas for evaluation of expectation values of monoelectric operators with modified gaussian functions
Authors: Biondi Franco , Salvetti Oriano , Gołebiewski A.
Published: December 2004

Formulas are presented for the evaluation of the expectation values of various monoelectronic operators. The integrals are based on „Hermite‐Gausian”︁ or „Modified Gaussian Functions”︁ and are expressed in suitable form for a computer programming. It is pointed out that the final expresions are simpler than the analogou omes obtained from the usual Gausian functions and can be written as linear combinations of a few baic integrals.
Correlation energy contributions to reaction heats
Authors: George Philip , Trachtman Mendel , Brett Alistair M. , Bock Charles W.
Published: December 2004

New, more accurate, Hartree‐Fock limit energies (EHF) for ethane and ethylene are obtained from SCF total molecular energie using Ermler and Kern's procedure. These results, together with EHF values for other small closed shell molecules, are employed to calculate correlation energy (Ec) contributions to reaction heats. Cancellation to within 98% of the total Ec involved, and often to more than 99%, is found for a wide variety of chemical reactions, which strongly suggests that there are systematic regularities in the contribution to Ec from the different kinds of electron pairs in the valence shell. Assuming trictly localized pairs occupying orbitals having strongly directional character, Ec for the valence shell is evaluated in terms of Ec per lone pair, Ec per XH bond, and Ec per X/X shared pair for Ne and for molecules containing first row atoms, where X is C, N, O, and F.
Correlation effects to the expectation values of atomic systems
Authors: Brown Richard E. , Larsson S.
Published: December 2004

The Hartree‐Fock and first natural spin determinants were compared as reference determinants for calculating various one‐electron properties such as ρ(0), 〈½∇〉, 〈r−2〉,…, 〈r3〉, and r−112〉. Calculations were made on various small atoms and their positive and negative ions. For nearly all the expectation values studied, the first natural spin orbital determinant gave consistently superior results. In particular, the Hartree‐Fock functions gave markedly inferior results for some long range properties such as the magnentic susceptibilities of negative ions. The major correlation error in the expectation values is primarily an orbital effect which may be accounted for by including correlation terms in the one‐particle Hamiltonian. Such approximate Brueckner or best overlap orbitals should reproduce most one‐electron expectation values accurately.
Simplified methods for ab initio calculations. The valence states of CH2 and CH
Authors: Gervy D. , Verhaegen G.
Published: December 2004

Three simplifying methodds are discussed and applied to the four lowest valence states of CH2(3B1, 1A1, 1B1 and 1Σ(1A)) and to the two lowest of CH(2A1 and 2∏u(2B1)). These methods concern: (1) the development of polarization functions for Gaussian‐lobe basis sets by least‐square fitting of numebrical multiconfigurational atomic fuinctions (this approach is tested also on (C2H2, (2) the use of intermediate Hamiltonians to calculate avoided crossings between potential hypersurfaces, and (3) thecalculation of correlation energies using an atoms‐in‐molecule approach.

The calculated equilibrium geometries of the CH2 States are within 0.02 Å and 5° of available experimental data. The calculated term values and ionization potentials, Te(1A1 = 0.35 eV, Te (1B1) = 1.22 eV, Te (1Σ(1A)) 2.48 eV, I.P. (2A1) = 10.39 eV and I. P. (2∏u(2B1)) = 10.58 eV, are in agreement with some recent theoretical studies, and are very close to existing experimental information.
State vectors and propagators in many‐electron theory. A unified approach
Authors: Linderberg Jan , Öhrn Yngve
Published: December 2004

A unitary group formulation of the many‐electron problem is employed to give explicit representations of state vectors which are convenient for the discussion of progerties derived from propagatorcalculations. New results are obtained concerning the nature of various random‐phase‐like approximations and ground state representatives are generated from consistency requirements for the spectral resolution of the polarization propagator. The explicit solution admits the calculation of ground state average values for arbitrary operators and a variational upper bound to the ground state energy.
A note on the importance of d orbitals in the calculation of effective interactions and the excitation spectra of atoms and molecules
Authors: Cherng Sharon , Westhaus Paul
Published: December 2004

The focal point of our discussion is the examination of truncated basis sets used in obtaining an accurate first principles clculation of the effective valence shell Hamiltonian by the canonical transformation‐cluster expansion approasch. Subsequent diagonalization of this effecitve valence shell hamiltonian yields the valence shell transition energies. A detailed analysis of numerical results obtained using a number of different basis sets of hydrogen‐like orbitals together with rigorous symmetry arguments celarly demonstrates the special role played by d orbitals in computing the 3P → 1D transition energy in carbon. The failure of early attempts to calculate the effective Hamiltonian for ethylene from first principles is examined in the light of recent ab initio calculations on ethylene involving d orbitals and the computations reported in this paper. We conclude that accurate calculations of the effective valence shell Hamiltonian for molecules must consider d orbitals in the excited orbital basis set.
SCF scheme for excited states and analysis of the orbital relaxation effect for H2O and FNO
Authors: Mrozek J. , Gołȩbiewski A.
Published: December 2004

An SCF scheme for excited states of closed‐shell systems based on the direct minimization technique is discussed. The utility of the scheme is tested for several excited states of H2O. The contribution of various tyeps of optimization of orbitals occupied in the excited state is discussed using the example of H2 O and FNO. It was found that relaxation of doubly occupied orbitals always gives a significnat contribution to the lowering of the excited state energy in the SCF process. Unexpectedly, on the other hand, optimization of the excited orbital in many cases gave negligible results.
Localized states in a simple cubic crystal via the next‐nearest neighbor approximation
Authors: Stȩślicka Maria , Stankiewicz B.
Published: December 2004

The energy spectrum of localized states in a simple cubic crystal is analysed, using the next‐nearest neighbor approximation. The main distinguishing feature between the nearest and next‐nearest neighbor approximation is the energy distribution of the localized states. Contrary to the tight‐binding approximation, a non‐symmetric distribution is found for clean surfaces, and split energy bands are found for surfaces completely covered by adsorbed atoms.
Test of an integral approximation scheme based on semiorthogonalized orbitals in LCAO SCF MO CI calculations of naphthalene
Authors: Kashiwagi Hiroshi , Takada Toshikazu
Published: December 2004

Ab initio LCAO SCF MO CI calculations of naphthalene are carried out with a minimal basis set to test an integral approximation scheme proposed in a previous paper. When 71.3 and 53.0% of the two‐electron integrals are neglected, the errors in the SCF total energy are only −0.0534 and −0.0006 a.u., respectively. In the latter case, the maximum absolute errors of the orbital energy and the gross AO population are 0.007 a.u. and 0.001, respectively. Even in the former case the errors of the excitation energies are less than 0.0004 a.u. Errors of oscillator strengths are also examined and are found to be tolerably small.
Ab initio valence bond calculations. VII. HF, HF+, and H2F+
Authors: Tantardini G. F. , Simonetta M.
Published: December 2004

Ab initio valence bond calculations for the ground and excited states of HF and HF+ are presented. Total energies, equilibrium geometries, dissociation energies, dipole moments, and spectroscopic constants for HF and HF+ have been calculated. The photoelectron spectrum of HF has been examined and interpreted by means of the valence bond formalism. The ground state of the protonated species H2F+ has been investigated.
A semi‐empirical MO theory for ionization potentials and electron affinities. II. Vertical and adiabatic values, benzenoid and nonbenzenoid aromatic hydrocarbons, and conjugated molecules with heteroatoms
Authors: Selsby R. G. , Grimison Alec
Published: December 2004

Further developments of a recent semiempirical, variable effective charge MO theory for calculation of ionization potentials (IP) and electron affinities (EA) as energy differences between separately minimized ground and ionized states are reported. The method is extended to adiabatic as well as vertical IPS and EAS by including core repulsion and σ bond compression energies in the total energy. The method is generalized to heteroatomic systems and is simplified by neglecting penetration integrals. As before, only two molecular parameters, the vertical IPS of benzene and naphthalene, are required to set the magnitude of the σ changes associated with the polarization of the core during loss or gain of a π charge. Twenty‐seven aromatic molecules are studied, including polyacenes, condensed ring compounds, nonbenzenoids with five and seven member rings, nonplanar molecules, and heteroatomics with N+, as in pyridine, N+2, as in pyrrole, and O+2, as in furan. The results are within 0.2 eV of the photoelectron spectroscopic vertical IPS and the predicted vertical‐adiabatic separation is consistent with the shape of the first band. The calculated EAS are within 0.2 eV of the observed values.

The calculation is used to predict the IP and EA of the ionic photosensitizing cyanine dye, pinacyanol. The values obtained are consistent with the latest measured IP and EA of the adsorbed dye, corrected for surface and aggregation polarization effects.
Perturbation corrections to Koopmans' theorem. IV. Energy‐shifted perturbation theory
Authors: Chong Delano P. , Takahata Yuuzi
Published: December 2004

Energy‐shifted perturbation theory is studied in connection with corrections to Koopmans' theorem. The first three vertical Ionization potentials of N2, C2H2, and HCN are computed with basis sets of double‐zeta Gaussian‐type orbitals and double‐zeta GTO plus polarization functions. The average absolute deviation of calculation ionization potentials from the observed values is found to be 0.4 eV, whether one uses Brillouin‐Wigner or Rayleigh‐Schrödinger perturbation theory.
Removal of singularities in the numerical integrals for an STO basis set
Authors: Careless P. N. , Hyatt D. , Stanton L.
Published: December 2004

Advantages and difficulties of numerical integration in relation to a transcorrelated solution of the molecular Schrödinger equation are discussed. Because singularities in the two‐electron integrals can be completely removed in a transcorrelated calculation, the major difficulty remaining to be resolved is that of singularities in the one‐electron integrals. A general method of treating this problem is given which involves the derivation of some new polycentric expansion functions which are everywhere finite under the one‐electron part of the Hailtonian. The important improvements obtained are illustrated by some calculations on LiH.
The relationship between the unrestricted and projected Hartree–Fock methods in a simple three‐electron model system
Authors: Paldus J. , Čížk J. , Laforgue A.
Published: December 2004

Various forms of the unrestricted Hartree–Fock (UHF) scheme are studied for a simple three‐electron model system, represented by the PPP (Pariser–Parr–Pople) π‐electron model of the allyl radical. Both spin and space symmetry are violated in the UHF trial wave function, either individually or simultaneously. A comparison with the projected Hartree–Fock (PHF) schemes studied earlier is made and the effect of the order in which various symmetries are broken in both UHF and PHF schemes is studied. The effectiveness of various schemes follows from a comparison of the correlation energy and the wave function is obtained by various UHF (or projected UHF) and PHF schemes, in the whole range of the coupling constant, with the corresponding quantities given by the exact solution of the model. Finally, the implications of the stability of the restricted HF solutions for the behavior of various single‐ and multiparameter UHF and PHF schemes are briefly outlined and exemplified on the studied model.
Ab initioLCAO‐MO‐SCF calculation of the electrostatic molecular potential of chlorpromazine and promazine
Authors: Petrongolo Carlo , Preston Harry J. T. , Kaufman Joyce J.
Published: December 2004

The electrostatic potential V(r) arising from the ab initio LCAO‐MO‐SCF wave functions of chlorpromazine (CPZ) and promazine (PZ) has been calculated and discussed. In this approximation, the most probable sites of attack and reaction paths of electrophilic reagents are pointed out and compared. The analysis of V(r) shows that the phenothiazine group has strong nucleophilic properties which are influenced by the phenothiazine substituent and that the electrostatic reactivity of CPZ and PZ is decidedly different near the phenothiazine substituent and similar near the side chain N atom. The dependence of V(r) on the accuracy of the wave function has also been discussed by comparing some ab initio results on pyrrole, pyrazole, and imidazole obtained with a large basis set with an ab initio minimum basis set and with CNDO calculations.
Dynamics of molecules in contact with an external medium at equilibrium
Authors: Simons Jack
Published: December 2004

When considering the dynamical properties of a molecule in contact with an external medium whose degrees of freedom are at equilibrium, one can adopt either of two approaches to the problem. The equations of motion which govern the coupled molecule‐medium system can be solved (or approximately solved), after which the initial values of the medium's coordinates are averaged over (with an equilibrium distribution function as weighting factor) to obtain the desired property of the molecule. In the second approach, which is the subject of the present work, the effects of the medium on the molecule of interest are incorporated into a time‐dependent effective potential which contains the equilibrium average molecule‐medium interaction as well as terms arising from fluctuations in the medium's coordinates about their equilibrium values. By introducing such an effective potential via the cumulant expansion technique, the problem of studying dynamical properties of the molecule is reduced to the study of a molecule which is in the presence of a time varying external field which no longer depends explicitly upon the coordinates of the medium. In addition to developing the basic method for treating such problems, applications of the method to interesting problems are briefly discussed.
Bond length alternation in cyclic polyenes. I. Restricted Hartree–Fock method
Authors: Paldus J. , Chin E.
Published: December 2004

The problem of bond length alternation in cyclic polyene models as described by the Pariser–Parr–Pople π‐electron Hamiltonian and its relationship to the singlet stability problem for symmetry adapted Hartree–Fock solutions for these systems is investigated using the restricted Hartree–Fock method. The σ‐energy contribution is approximated by a quasiharmonic empirical potential. It is shown that the restricted Hartree–Fock energies favor the cyclic polyene distortion and an estimate of the distortion and of the stabilization energy for infinite linear polyenes is obtained.
SCF and CI Studies of Hund's rules for the effects of electronic correlation and delocalization. I
Authors: Brown Richard E. , Colpa Johannes Pieter
Published: December 2004

In connection with the reinterpretation of Hund's multiplicity rules for molecules, a detailed study has been made of the energy differences in the total energy and its components for the triplet and singlet Πu states of the hydrogen molecule and the analogous states of the four‐ and six‐membered hydrogen atom rings. For the hydrogen molecule, both SCF and CI studies indicated that the outer electron is considerably more contracted in the triplet than in the singlet state. In both approximations, the energy difference is dominated for all bond distances of chemical and physical significance by the electron‐nuclear attraction component and not by the electron repulsion component as predicted by simple first‐order perturbation theory. Although the correlation energy for each of the states is of the same magnitude as the energy differences considered here, the difference of the correlation energies is much smaller. It had little effect on the qualitative differences between these states of the hydrogen molecule. For the four‐ and six‐membered rings, SCF studies were made on the lowest singlet and triplet states where one electron was promoted from the σg to a Πu orbital. Even though the coupled electrons were more delocalized in these cases, the electron repulsion became relatively more important. However in all cases, the lower state had the highest electron repulsion energy and lower electron‐nuclear attraction. The triplet state continued to have the more contracted outer open‐shell orbital.
Ab initio calculation of the heptamer (NH3)7 as a reasonable starting point for a description of the ammonia crystal
Authors: Bridet Jacques , Fliszár Sándor , Odiot Simone , Pick Robert
Published: December 2004

Quasi‐Wannier functions for the ammonia crystal have been determined from optimized ab initio calculations of the heptamer (NH3)7, thus accounting for all the first neighbor interactions. The calculated geometry and binding energy are in good agreement with their experimental counterparts.
On the Sanibel coefficients in the expansion of spin‐projected slater determinants
Authors: Löwdin Per‐Olov
Published: December 2004

Every Slater determinant D may be uniquely analyzed in terms of spin components Dl = OlD which are pure spin eigenfunctions, so that S2Dl = l(l+1)D. Every component Dl = OlD may in turn be written as a sum of symmetric combinations of Slater determinants, Tk = [αμ−kβk‖αkβν−k], and the coefficients c in the expansion OlD = ∑k c Tk are known as the “Sanibel coefficients.” By using the relation S2Dl = l(l+1)D, a recursion formula for the coefficients c is derived, which is then explicitly solved in the special case when Sz has the pure quantum number m = 0.
Ab initio molecular fragment calculations with pseudopotentials: Model peptide studies
Authors: Gáspár R. , Gáspár R.
Published: December 2004

The energetics of rotation about the NC′(ω); NCα(φ), and CαC′(ϕ) bonds of the peptide unit have been investigated in the pseudo‐FSGO fragment scheme on model compounds formamide and N‐methylacetamide. The results indicated that the position of the minimum in ω is in the near vicinity of 0°, i.e., the planar arrangement of the peptide unit. The minimum in φ (C′NCαH) has been found to be 180° and in ψ(HCαC′N) to be 60°, in good agreement with PCILO and Gaussian‐70 results.
Lie algebra and unitarily invariant decomposition of Hermitian operators
Authors: Sun Chia‐Chung , Li Xue‐Qui , Tang Au‐Chin
Published: December 2004

The unitarily invariant decomposition of Hermitian operators is performed by means of Lie algebra.
Vibrational–rotational levels of diatomic RKR potentials
Authors: Requena A. , Zuñiga J. , Peña R.
Published: December 2004

The vibration–rotation levels for the diatomic RKR potential curve are solved using both perturbational and variational approaches. To obtain any‐order correction of the energy from unperturbed parameters, an iterative scheme is formulated in the hypervirial framework. Variational calculations are carried out upon a rotationless Morse oscillator basis set and using a transformation technique to treat the effective potential energy function. Numerical results for the RbH X 1Σ+ state are obtained. The accuracy of the energy levels is tested by solving the Schrödinger equation by a numerical procedure.
Vibronic coupling of electronic states. IV. Harmonic CBO potentials with equal minima positions—the influence of different vibronic coupling strengths on the electronic absorption and emission spectra containing a longest‐wavelength electronically forbidden transition
Authors: Gustav Klaus , Colditz Roland
Published: December 2004

The influence of vibronic coupling between two harmonic CBO potentials with equal minima positions on the electronic absorption and emission spectra is investigated in the framework of our model using the variational procedure. The numerical results, being identical with those obtained through the vibronic coupling model of Fulton, Gouterman, and Brickmann, are discussed with regard to the longest‐wavelength electronically forbidden transition, its vibrational structure, and the Stokes loss.
Quantum‐chemical study of electrophilic addition reaction of iodine to ethylene
Authors: Suqian (S. Q. Jin) Jin , Ruozhuang (R. Z. Liu) Liu
Published: December 2004

The relative stability of and barrier to interconversion of the two possible intermediates in the electrophilic addition of iodine to ethylene have been studied by means of ab initio molecular calculations with pseudopotential approximations. The geometries of the 2‐iodoethyl and ethylene iodonium cations have been optimized by the energy gradient technique with pseudopotential approximations. From the results of the calculations, it is found that the only possible intermediate is the cyclic ethylene iodonium ion, as shown by experiments.
New derivation of the Waller–Hartree–Fock spatial wave function
Authors: Pauncz Ruben
Published: December 2004

A new derivation is given for the Waller–Hartree–Fock double‐determinantal spatial wave function. One starts from the single‐determinant wave function in which a orbitals are doubly occupied, and decomposes it into a sum of products of spatial and spin functions. The spatial product of the first genealogical spin eigenfunction is a double‐determinantal function. The derivation is based on the simple form of U1ƒ(P) when the representation matrix is obtained from the genealogical spin eigenfunction.
Chemical shifts calculation in a CNDO framework. I. Formulation and analysis of the model
Authors: Riera Josep M. , Mariné Josep
Published: December 2004

Expressions for the second‐row nuclei chemical shifts calculation using a CNDO‐SCF wave function are outlined. In collating it with the Pugmire and Grant's equations, a term with a changed sign appears. Both sets of equations are applied to a study of carbon‐13 chemical shifts in alkanes down to C7; results are interpreted with aid of the Lindeman–Adams' empirical equation. Expressions proposed are confirmed for an excellent agreement with experimental data.
Study of potential curves by UHF‐type methods. VI. Spin‐extended Hartree–Fock method
Authors: Klimo Villiam , Tiňo Josef
Published: December 2004

An improved computational procedure of the spin‐extended Hartree–Fock method is presented. The main features of the EHF potential curves for the dissociation of the LiH, BeH, and Li2 molecules are discussed. The results are compared with curves calculated by the perturbation or CI methods using the same basis set.
Singularities of magnetic‐field induced electron current density: A study of the ethylene molecule
Authors: Lazzeretti P. , Rossi E. , Zanasi R.
Published: December 2004

The singularities of the quantum‐mechanical electron current density induced in a molecule by an external magnetic field are analyzed via the theory of the real autonomous systems of differential equations. Group‐theoretical techniques, based on the idea of color symmetry, are developed, which predict the occurrence of singularities about molecular symmetry elements. Plots of induced electron current density have been obtained for the ethylene molecule through accurate coupled SCF calculations. The theoretical magnetic properties of ethylene obtained through this investigation are the most accurate reported so far.
Fourier transforms of atomic orbitals. I. Reduction to four‐dimensional harmonics and quadratic transformations
Authors: Niukkanen A. W.
Published: December 2004

A general expression for the Fourier transform of the basis functions of exponential class has been derived. Particular cases of Slater functions, hydrogen‐like functions, Shull and Löwdin functions, Shavitt, Filter, and Steinborn functions have been considered. In many particular cases the Fourier transforms have been shown to reveal some important special properties (reduction to four‐dimensional harmonics, quadratic transformations, etc.) which considerably simplify the mathematical treatment of these functions and lead to new possibilities in the development of calculation methods for multicenter integrals.
The nodal structure of the momentum distributions of molecules
Authors: Simas Alfredo M. , Smith Vedene H. , Kaijser Per
Published: December 2004

The nodal structure of molecular momentum distributions is studied by considering the simplest case of the ground state of the hydrogen molecular ion. By examining the exact expansion of the H2+ momentum distribution, it is shown that an infinite sequence of nodes does exist along the pz axis (z axis parallel to the bond axis) but not nodal planes perpendicular to the pz axis (as is found for the simplest LCAO function). The nodes are those points where nonplanar nodal surfaces cross the pz axis. It is also shown that molecular systems with more than one electron cannot, in the ground state, have nodal surfaces in their momentum distributions. Implications for the directional Compton profiles J(q) are discussed.
Anisotropic electronic intracule densities for diatomics
Authors: Thakkar Ajit J. , Tripathi A. N. , Smith Vedene H.
Published: December 2004

The electronic intracule density, a three‐dimensional contraction of the spinless electron pair density, is the probability density function for an interelectronic vector. A computationally efficient algorithm for the evaluation of the basic two‐electron intracule integral for GTOs is presented. In order to provide an initial understanding of the topography of intracule distributions, anisotropic intracule densities for the X1Σ ground states of the H2 and N2 molecules are reported and analyzed.
Ab initio Hartree–Fock approach to the study of polymers: Application to polyacetylenes
Authors: Dovesi Roberto
Published: December 2004

An ab initio Hartree–Fock method devoted to the study of polymers is presented, truncation criteria for the exchange and the Coulomb series are discussed, and it is shown that the error in the total energy evaluation can be reduced to below 0.0001 a.u./cell with little computational effort. Results for six polyacetylene isomers are presented and compared with previous ab initio data obtained using the same basis set. In agreement with the experimental findings, the alternating all‐trans structure is the most stable.
New efficient numerical method for solving pair correlation equations for diatomic molecules
Authors: Adamowicz Ludwik , Bartlett Rodney J.
Published: December 2004

A new method for solving correlation pair equations for diatomics is presented and followed by numerical results for the H2 and LiH molecules. The essential feature of the new approach is a numerical representation of both basis two‐electron functions and Coulomb and exchange potentials in pair equations. It is shown that this significantly simplifies the pair function optimization procedure.
Ab initio studies of negative ion‐molecule(s) clusters present in the atmosphere. III. OH−(CO2)n for n = 1, 2
Authors: Sapse Anne‐Marie , Osorio Louis , Snyder Grace
Published: December 2004

Clusters formed by the OH− ion and carbon dioxide are investigated using ab initio Hartree–Fock calculations, with 6–31 G and 6–31 G* basis sets. Geometries and binding energies are determined.
Configuration interaction matrix elements for atoms using permutation group algebra
Authors: Dinesha K. V. , Hinze Juergen
Published: December 2004

A procedure is described for the efficient evaluation of the energy matrix elements necessary for atomic configuration‐interaction calculations. With the orbital configurations of an N electron system in spin state S written as the irreducible representations [21/2N−S, 12S] of the permutation group S( N ), it is possible to evaluate readily the energy matrix elements of a spin‐free Hamiltonian expressed in terms of the generators of the unitary group. We show how the use of angular momentum ladder operators permits the effective generation of a basis of eigenstates of ℒ︁2, ℒ︁z as well as 𝒮2 and 𝒮z, for which the energy matrix elements may be evaluated with ease.
Molecular integrals arising in the linear response theory of van der waals forces
Authors: Ishida Kazuhiro
Published: December 2004

General formulas are derived for molecular integrals which arise in the linear‐response theory when it is applied to the van der Waals interactions between molecules. These integrals are essentially the matrix elements of the Fourier transformed double Coulomb operator between any Cartesian Gaussians. The computational aspects of these formulas are also discussed.
On a semiclassical interpretation of inter‐ and intramolecular interactions
Authors: Bonaccorsi Rosanna , Ghio Caterina , Tomasi Jacopo
Published: December 2004

The semiclassical models considered here are composed by charge distributions coming from ab initio quantum‐mechanical calculations on actual molecular systems. These charge distributions interact with one another according to the laws of classical electrostatics. This article describes some results of a systematic examination of the performances of this model in a variety of cases, with the aim of putting in evidence the usefulness and the limits of this inherently approximate representation of chemical interactions. Intermolecular interactions are examined first; the test cases are interactions of neutral molecules with H+, Li+, and C1−, and the formation of H‐bonded complexes. Attention is paid mainly to the energetics of the processes; each interacting molecule is considered as a unique entity and classical molecular reactivity indexes (electrostatic potential V, polarization term P) are introduced to compute the interaction energy, to interpret the details of the interaction process, and then to elaborate on less expensive computational procedures. Intramolecular interactions are considered. Attention is paid to the question of defining chemical groups starting from SCF molecular wavefunctions. The transferability and conservation degree of groups derived from localized orbitals of actual molecules is examined in detail, taking as tests their ability to reproduce charge distribution, one‐electron observables, and energy. The effect of classical fields on these groups is then examined, taking into consideration external fields originated either by a point charge or by a solvent, and internal fields deriving from substitution of chemical groups. The intergroup analysis is then extended to the case of bimolecular reaction acts by considering the whole system as a supermolecule. Approximate computational procedures able to reproduce the main features of these interactions are proposed and tested. All through the article the performances of the classical models are compared with ab initio SCF calculations (mainly of low or intermediate quality).
Remarks on the concept of an atom in a molecule and on charge transfer between atoms on molecule formation
Authors: Parr Robert G.
Published: December 2004

Density functional theory provides a natural and rigorous definition of an atom in a molecule in its ground state: The molecular electron density is the sum of atomic densities, the atoms have the same chemical potential as does the molecule, and the atoms are minimally promoted from their ground states. These atoms in general are not spherical, and in general they bear nonintegral charges. Charge transfer on molecule formation is thereby uniquely defined. Calculations by Palke and by Guse are reviewed, in which the hydrogen atom is identified in the hydrogen molecule.
The concept of the chemical bond
Authors: Julg A.
Published: December 2004

The concept of the chemical bond is very old. Many interpretations have been proposed. Nevertheless, the problem is far from being solved. At the present time, the chemist has the choice between two models: the Lewis model (electron pairs) and the quantum model. In spite of a current opinion, both models are not logically equivalent. The localization of molecular orbitals is only a mathematical operation which does not involve any physic localization of the electrons. The loge theory is not more satisfying owing to the fact that loges with minimal fluctuation do not exist in all molecules. The theory of orbital domains seems to bring a solution. Nevertheless, its interpretation can be obtained only outside the strict framework of quantum mechanics.
Convergence of LCAO density matrices in Hartree—Fock calculations on extended model chains
Authors: Delhalle J.
Published: December 2004

Some mathematical implications of the extended nature of model chains are reviewed to call attention to their importance in electronic structure calculations at the restricted Hartree‐Fock Roothaan level.
Structure and function of protamines: An investigation of clupeine properties by nuclear magnetic resonance
Authors: Paolillo L. , Andini S. , Ferrara L. , Wurzburger S.
Published: December 2004

In this paper a detailed study of the structural properties of the three main fractions YI, YII, and Z of clupeine (protamines) has been performed with the aid of nuclear magnetic resonance methods. The investigation includes chemical shift data of protons and C‐13 nuclei and measurement of the T1 relaxation times of the C‐13 nuclei. These data demonstrate that the flexibility of the three fractions is different and that in the presence of inorganic phosphate fraction YI exhibits structural changes more relevant than the other two fractions. The measurement of the relaxation times, under the assumption of a rigid ellipsoid model, gives an estimate of the rough molecular size of the clupeine fractions. Different side chain mobilities that complement the previous observations based on chemical shift data are determined. A further extension of this work concerns the interaction of the clupeines with natural mononucleotides. An appreciable interaction takes place between fraction YI and purinic nucleotides while a simple electrostatic interaction seems to exist with the other two fractions. A possible explanation of this different behavior seems to involve the formation of large aggregates solely in the case of fraction YI.
Soft agonist receptor interactions: Theoretical and experimental simulation of the active site of the receptor of sweet molecules
Authors: Temussi P. A. , Lelj F. , Tancredi T. , Morelli M. A. Castiglione , Pastore A.
Published: December 2004

The structure‐activity relationship of sweet molecules is chosen as an example to illustrate a mechanistic approach of soft agonist‐receptor interactions. It is shown that an essentially geometric model of the receptor site can explain the activity of most sweet molecules, both rigid and flexible. The relevant conformations of flexible molecules in solution are extracted from a combination of NMR data and of energy calculations. A possible experimental simulation of the receptor environment in solution is illustrated by the complex of a dipeptide sweetener with a crown‐ether.
Hartree‐Fock cluster study of interstitial transition metals in silicon
Authors: Broer R. , Aissing G. , Nieuwpoort W. C. , Feiner L. F.
Published: December 2004

Results are presented of a Hartree‐Fock cluster study of interstitial Ti, V, Cr, and Mn impurities in silicon. A Si10 cluster models the nearest Si atoms around a tetrahedral interstitial site in crystalline Si. The dangling bonds of the Si atoms are saturated by hydrogens. The effect of the Si core electrons is represented by an effective potential. Characteristic for the electronic structure of the low‐lying states of the neutral, singly positive, and doubly positive ions in silicon is the presence of fairly delocalized but still predominantly transition‐metal (3d)‐like orbitals of t2 and e symmetry. For all ions the energy of the weighted average of the terms belonging to a configuration is lowest for the configuration with maximum occupation of the t2 orbitals. Ground states with maximum spin multiplicity are found for all ions, except Ti0.
Analytical fitting of potential energy surfaces for the Hxy systems
Authors: Last I. , Baer M.
Published: December 2004

Use of the London‐Eyring‐Polanyi + 3‐Center + power‐series (LEP‐3C‐PS) analytical potential as a fit to potential energy surfaces (PES) which are known numerically only are suggested. This analytical fit was performed for the diatomics‐in‐molecules + 3 Center (DIM‐3C) PES of HCl2 and HI2 systems. The HCl2 analytical LEP‐3C‐PS potential was used for classical trajectory calculations of the Cl' + HCl → HCl' + Cl reaction. The rate constant obtained from these calculations for T = 358° K is 1.95 X 109 cm3/mol sec which is close to the experimental value of 2.5 109 cm3/mol sec.
Studies of unoccupied orbitals of BF3 and BCL3 by electron transmission spectroscopy and multiple scattering Xα calculations
Authors: Tossell J. A. , Moore J. H. , Olthoff J. K.
Published: December 2004

Electron transmission spectroscopy (ETS) and bound‐state and continuum multiple‐scattering Xα (MS‐Xα) calculations are employed to characterize the unoccupied a′2, a′1 and e′ orbitals of BF3 and BCl3. The a′2 orbital of BF3, which produces a peak about 7 eV below threshold in the x‐ray absorption spectrum (XAS), generates a scattering resonance at 3.5 eV in ETS. Similarly, the e′ orbital that lies about 2 eV above threshold in XAS occurs about 13‒16 eV above threshold in ETS. Dissociation of F− from BF3 due to electron attachment is attributed to a core‐excited shape resonance involving an e″ → a″2 excitation and electron capture into the a′2 orbital. In BCl3 all the unoccupied orbitals lie at lower energy than in BF3 and are closely spaced, making definitive spectral assignments difficult. Both Hartree‐Fock (HF) and MS‐Xα methods apparently underestimate the stability of the unoccupied e′ orbital of BCl3. Vibronic coupling due to out‐of‐plane bending may significantly affect the spectral intensities. Feshbach resonances are observed for BCl3 at energies close to those observed in the vacum‐UV absorption spectrum. The lower energies of the unoccupied orbitals of BCl3 are consistent with their stronger bonding to nucleophiles.
The effect of correlation energy (MP2) on computed vibrational frequencies
Authors: Michalska D. , Andes Jr. B. Hess, , Schaad L. J.
Published: December 2004

The IR frequencies of cyclopropene and methylenecyclopropene were computed with inclusion of correlation (MP2/6‐31G*). These along with those of ethylene obtained earlier by Pople were compared with SCF results (DZ + P). It was found that the MP2 frequencies agreed better with experiment, but that the order of the bands remained the same as those computed without correlation.
Some new aspects of bonding in cyclopropane
Authors: Pan Dao‐Kai , Gao Jian‐Nan , Lin Hai‐Lun , Huang Ming‐Bao , Eugen Schwarz W. H.
Published: December 2004

The peculiar properties of the three‐membered ring in cyclopropane are partially due to characteristic relaxation effects of the carbon orbitals in the molecule. AO contraction in the two strongly CC bonding MO's of A type is essential for the stability of the C3 ring, whereas AO expansion in the E'‐type HOMO contributes to the π character of the peripheral CC bonds.
Atomic partitioning of two‐center potentials for slater basis
Authors: Rico Jaime Fernáandez , Lóapez Rafael , Paniagua Miguel , Fernáandez‐Alonso Jose Ignacio
Published: December 2004

In a previous paper we have shown that the long‐range potential generated by the two‐center distributions can be written as a sum of two multipolar expansions centered at the terminal atoms and defined so that the two series of multipoles be minimal. In this paper we show that both charge distributions and short‐range potentials can also be separated in atomic contributions in a way consistent with the above mentioned partition of the long‐range potentials.
Calculation of the minimum energy conformation of biomolecules by using a global optimization technique. V. Preferred conformations of the thyrotropin‐releasing hormone
Authors: Rao Gita Subba , Tyagi R. S. , Mishra R. K.
Published: December 2004

The preferred conformations of the thyrotropin‐releasing hormone (TRH) have been calculated by the global optimization method proposed earlier by us. [G. Subba Rao, R. S. Tyagi, and R. K. Mishra, J. Theor. Biol. 90, 377 (1981)]. The potential function used comprises the electrostatic, nonbonded, torsional and hydrogen‐bonding terms. The results are in good agreement with the crystal structures of TRH. No intramolecular hydrogen bonding is found to occur.
Some theoretical studies on hydrogen molecule capture by platinum atoms
Authors: Poulain E. , Garcia‐Prieto J. , Ruiz M. E. , Novaro O.
Published: December 2004

Pseudopotential SCF‐LCAO‐MO and variational and perturbative Cl calculations were carried out for H2 molecule capture by a single Pt atom with C2v symmetry. A pseudopotential for the platinum atom including relativistic effects was used. Singlet and triplet states of the Pt‐H2 interaction having different representations of the mentioned C2v symmetry were studied. The triplet ground state of Pt leads to two A1 and B2 states in which the metal atom cannot capture H2; i.e., both have repulsive interaction energies. The electronic state responsible for the capture of H2 is the closed‐shell, singlet A1 excited state. The equilibrium geometry of the system is reached with a broken HH bond at a HPtH angle of about 100°. Additionally another shallower minimum for a singlet A1 linear structure is observed. Specific predictions for the thermal and photochemical Pt + H2 reactions that can be carried out under matrix isolation conditions are made.
An ab initio study of intermolecular hydrogen bonding between small peptide fragments
Authors: Sapse A. M. , Fugler L. M. , Cowburn D.
Published: December 2004

Several small peptide fragments are investigated with ab initio (Hartree‐Fock) calculations, using Gaussian basis sets. Complexation energies, net atomic charges, and optimum geometries are obtained. The geometries predicted by the STO‐6G, and 6–31G* basis sets are quite similar, whereas the binding energies obtaiend by the 6–31G calculations are higher than those obtained with STO‐6G and 6–31G* basis sets.