bluuebunny/crossref_metadata_2025 huggingface dataset:
Wellenmechanische behandlung der protonisierung des äthylens unter berücksichtigung aller elektronen
Authors: Fratev F. , Janoschek R. , Preuss H.
Published: December 2004

The system C2H5+ has been investigated as ethyl cation and as protonated ethylene using the SCF–MO–LC(LCGO) method. Equilibrium distances and angles have been estimated by different potential curves. No difference in total energy was found between the π‐ and the σ‐complex.
Long‐range interactions in the ground and two excited states of the HeH+ molecule
Authors: Piela Lucjan
Published: December 2004

The long‐range interaction energies for different dissociation products of the HeH+ molecule have been calculated using the Rayleigh–Schrödinger perturbation theory up to the third order in the energy. The calculations were carried out for the ground state (He(ls2) + H+), the first excited state (H(ls) + He+(ls)) and the second excited state Π(H(2pπ) + He+(ls)). The unperturbed states correspond to the dissociation products denoted in parentheses. Assuming the overlap to be zero, expanding the interaction potential in the inverse powers of the internuclear distance R and using the familiarly known perturbation‐variational technique, the coefficients of various powers of R−1 in the energy expansion were evaluated. They correspond to different multipole‐multipole interactions. The potential energy curves of all three states under consideration were calculated for large values of R. Also calculated were the multipole polarizabilities of the hydrogen atom in the is and 2pπ states and of the helium atom in the ground state.
Bounds to second‐order perturbation energies (particularly dispersion) for excited states
Authors: Abdulnur Suheil F.
Published: December 2004

Upper and lower bound expressions are derived to the second‐order energy relating to an unperturbed degenerate excited state in those cases where both the first‐order energy and the off diagonal matrix elements in the secular equation vanish, making use of the partitioning technique, operator inequalities and inner projection approach. These expressions, which involve an arbitrary basis, are then developed to yield reasonably good bounds to van der Waals dispersion energies for systems of the type H (first excited state) — other atom b (ground state). The particular choice of basis used in the development yields the latter bounds easy to evaluate by expressing them in terms of the ground state sum rule values, S(k) of atom b. This same choice is also utilized in Lindner and Löwdin's expressions [1] to obtain bounds to systems of the type H (ground state) — other atom b (ground state) that are comparable to those found by other more elaborate semi‐empirical methods.
Gaussian wave functions for CH3 and NH
Authors: Kari R. E. , Csizmadia I. G.
Published: December 2004

Ground state single determinant LCAO‐MO‐SCF wave functions, using a large contracted Gaussian basis set (6s, 2p, 1d/3s, 1p), have been computed for the 9 electron molecular systems of CH3 and NH. The minimum energies obtained using Roothaan's open shell SCF procedure for the planar equilibrium geometries were −39.5703 Hartree for CH3 and −55.8945 Hartree for NH. Additional properties such as electron populations and multiple moments were calculated from the planar wave functions.
Molecular one‐electron integrals over slater‐type atomic orbitals and irregular solid spherical harmonics
Authors: Steinborn E. Otto , Ruedenberg Klaus
Published: December 2004

The one‐electron integral over Slater‐type atomic orbitals centered at A and B and irregular solid spherical harmonics as operator centered at C is evaluated analytically by using elliptical coordinates and translation of the solid spherical harmonics from center C to either focus A or B. A special case is the three‐center nuclear attraction integral which is also evaluated by means of the Neumann expansion and expressed without associate Legendre functions of the second kind. The strict observation of the charge distribution concept leads to compact expressions for the integral. It has the further advantage that the charge density distributions which have been developed for the two‐center cases and used in calculations for diatomic molecules can be utilized.
The use of explicitly correlated, partially antisymmetric wave functions in atomic and molecular calculations
Authors: Simons Jack
Published: December 2004

Trial wave functions, written as the sum of a configuration interaction expansion and an explicitly correlated term which is not antisymmetric, are proposed for use in calculating the electronic properties of atoms and molecules. A variational principle, modified to allow the use for such partially antisymmetric wave functions, is developed. It is shown that the consequences of partial antisymmetry on calculated expectation values can be estimated. The method avoids difficult three‐electron integrals which arise in other theories.
Electronic structure of long cumulene chains
Authors: Ukrainsky I. I.
Published: December 2004

The analysis of the equations of the unrestricted Hartree–Fock (UHF) method for polyenes CNHN+2 with even and odd N » 1 is carried out. The equations of the UHF method are shown to be the same in both cases. The comparison of the UHF method with the extended Hartree–Fock (EHF) method applied to large systems is performed. The ground state and π‐electron spectra of long cumulene chains CNH4 are treated by the EHF Method. The end effects are taken into consideration. It is shown that the EHF method gives a finite value of the first optical transition frequency and, at the same time, zero value of torsion barrier of end CH2–groups in long cumulene chains (N → ) in contrast to previous calculations of cumulenes by the Huckel method and the restricted Hartree–Fock method.
A comparative quantum chemical study of ethylcarbonium ion and hydroxymethylcarbonium ion
Authors: Tel Luis M. , Wolfe Saul , Csizmadia Imre G.
Published: December 2004

Nonempirical molecular orbital calculations of the energies of CH3CH (ethylcarbonium ion) and HOCH (hydroxymethylcarbonium ion) as a function of rotation about the CC or CO bonds and deviation from coplanarity at the carbonium ion center are reported. As expected, and in agreement with previous work, both carbonium centers are planar and there is no barrier to rotation in the planar ethylcarbonium ion. However, for the planar configuration at carbon, the conjugative interaction between oxygen and carbon produces a barrier to rotation about the CO bond of HOCH of 19.6 Kcal/mole.

When a pyramidal geometry is imposed upon the carbonium ion center of CH3CH, a typical three‐fold barrier results. As the deviation from coplanarity increases there is a regular increase in the barrier height (1.72 Kcal/mole at the tetrahedral geometry), but the energy minimum remains at the same position in each case (60°). For HOCH, imposition of a pyramidal geometry on the carbonium ion center causes a change in both rotational barriers. One decreases slightly (from 19.6 to 15.4 Kcal/mole) and the other increases to 30.5 Kcal/mole. There is an accompanying change in the position of the minimum of the rotational potential, from 90° towards the gauche structure.
CNDO/2 and MINDO/2 energy band structures of some homopolynucleotides
Authors: Suhai S. , Ladik J.
Published: December 2004

The all‐valence electron band structures of the periodic DNA models polyC, polyT, and polyA have been calculated with the aid of the CNDO/2 and MINDO/2 crystal orbital (CO) method.

According to the obtained results the valence and conduction bands are always of π type. The widths of the bands are usually larger in the CNDO case, than those obtained for the same systems in the PPP CO approximation. On the other hand the MINDO results show similar widths as the PPP ones. The forbidden bandwidths are by 3–4 eV larger in the CNDO/2 case, than in the PPP one, while the MINDO/2 CO method has resulted in similar gaps like the PPP calculation.
Spin projected extended Hartree‐Fock equations
Authors: Mayer I. , Ladik J. , Biczó G.
Published: December 2004

The (spin projected) extended Hartree‐Fock equations are derived and discussed in the general (“many λi”) case. The derivation is based on the corresponding generalized Brillouin theorem, substituting in its expression the spin projected DODS Slater determinant as a linear combination of determinants. The expressions obtained for the elements of the different matrices εcd (c = a or b, and d = a or b) occurring in the equations are analyzed. The transformation of the equations into the form of a pseudoeigenvalue problem and the LCAO form of the equations are given, too. Finally the relation to the Goddard's GF equations is discussed in detail.
Nondiagonal second order intermolecular forces for interactions involving molecules
Authors: Riera A. , Meath William J.
Published: December 2004

Very often only “diagonal” second order energies, varying as an even power of R−1, occur in the multipole expansion of the interaction energy. However for many molecular interactions important “nondiagonal” second order energies, varying as an odd or even power of R−1 can arise. This point is emphasized by a general discussion and by a detailed specific example, the interaction of an ionized dipolar molecule with a nondegenerate atom. Also some useful theorems, on the orientation average of various types of second order energies, are derived.
Effect of the exchange integral K2s2p on the 2p‐orbitals of the 1P and 3P states of the beryllium isoelectronic sequence arising from the configuration (1s)2(2s)(2p)
Authors: Tatewaki Hiroshi
Published: December 2004

The 1P and 3P states arising from the configuration (1s)2(2s)(2p) of the Be isoelectronic sequence are investigated. In the single configuration approximation, the energies of the two states are expressed as E0 + K2s2p and E0 ‐ K2s2p, respectively. K2s2p is the exchange integral between the 2s and 2p electrons and E0 is the energy of a model in which K2s2p is deleted. First we calculate the 2s‐ and 2p‐orbitals in this model. Second, by taking account of K2s2p in this model, effects of this term on the 2p‐orbitals in the 1,3P states are investigated. In this manner, an explanation is given for the following facts which are obtained from a minimal Slater‐type orbital set; (1) for Be and B+, the 2p‐orbital of the 1P state is broader than that of the 3P state; (2) for C2+, the extension of the 2p‐orbital in the two states is almost the same; (3) for O4+ and Ne6+, in contrast to Be and B+, the 2p‐orbital of the 1P state is tighter than that of the 3P state.
Symmetry in the Heitler‐London method. I. The connection of the molecular point group with its electron permutation group in the Heitler‐London method
Authors: Ledovskaya E. M. , Petrashen M. I.
Published: December 2004

The connection between the electron coordinates permutation group and the molecular point group is exhibited in the framework of the Heitler‐London method. It is shown that the initial wave function of a molecule in the Heitler‐London method can be written in such a form, that the effect of the point group operations upon this function corresponds to the permutation of the sets of electron coordinates of the ions and the subsequent multiplication of this function by some constants.
Molecular integrals over generalized gaussian basis sets
Authors: Van Duijnen P. Th.
Published: December 2004

A method is given for obtaining the common molecular integrals over generalized gaussian functions:

The present algorithms are expected to be more efficient than those given in earlier work by the same author.
Symmetry adaptation and the relation between the spin‐free and space‐spin formulations of electronic structure
Authors: Klein D. J. , Cantu A. A.
Published: December 2004

An information‐theoretic degree of symmetry adaptation of a ket with respect to a given group is introduced. Then the general equivalence between spin‐free electronic kets and antisymmetrized space‐spin kets is obtained so long as our attention is restricted to spin‐independent observables. It is noted that there are spin‐free kets for which there exists no single antisymmetrized space‐spin ket giving all the same expectation values; the converse is also noted.
The Coulomb hole in the 23S state of the helium isoelectronic sequence
Authors: Boyd R. J. , Katriel J.
Published: December 2004

The pair distribution functions evaluated for the 23S state of the helium isoelectronic sequence from the Hart and Herzberg correlated wave functions and those corresponding to the Hartree‐Fock approximation are used to determine the shape of the corresponding Coulomb holes. As a consequence of a discontinuity in the Hartree‐Fock solution between He and Li+, the Coulomb hole has a different shape for He than for Li+ and the other isoelectronic ions.
Generalized open shell SCF theory
Authors: Caballol Rosa , Gallifa Ramóan , Riera Josep M. , Carbóa Ramóan
Published: December 2004

A generalized form of the coupling operator technique in SCF theory has been developed. In the formalism presented here, the monoconfigurational problem may be treated as a particular case of the multiconfigurational framework. The matrix form of the operators has been analyzed; in the LCAO context a structure has been found which is very adequate for computational purposes.

Some examples are also presented which show the usefulness of the theory, emphasising the CNDO and INDO approximations. Within the application of the method to ab initio calculations, some He and second row atoms states have been studied. The He first excited singlet is also studied, the result of the analysis of such a problem being that the nonorthogonality between the singlet functions of the fundamental and of the first excited states play a primordial role in the efficiency of the method.

In no case have the calculation problems, appearing in the application of the theory, been of a more difficult nature than those normally found in the application of the formalism for closed shells.
Eigenspace manipulation in SCF theory: General formalism
Authors: Carbóa Ramóan
Published: December 2004

A general formalism in order to deal with SCF eigenspace manipulation is developed. It can be shown that the initial generalized secular equation splits into a set of secular equations, each of which in turn can modify independently any predetermined subset of the SCF manifold.
An improved Hellmann‐type pseudopotential for atoms and molecules
Authors: Pohl Herbert A. , Fowler Donald R.
Published: December 2004

The concept of pseudopotentials offers much attractiveness for the quantum mechanical evaluation of the physical properties of atoms and molecules. The ideas of Hellmann, in which the repulsive and fermion character of inner electrons can be mimicked by an experimentally fitted, exponentially damped potential term, are especially attractive. Unfortunately, it is found that such a simple expression can only be used in a very limited number of cases, such as for the alkali metals, and even then fails for the simple case of lithium.

The present study shows that the Hellmann idea can readily be extended by including a second “shielded potential” term evaluated from tabulated previous Hartree‐Fock calculations. The new expression for the model pseudopotential is both simple and effective. With it, the inner potential of any of the alkali metal atoms, including lithium, can be represented so that calculation of the molecular properties of the metal dimers can be accomplished. Calculations for Li2, Na2, and K2 show the binding energies and equilibrium interatomic distances to be quite well given, in agreement with both chemical experience and spectroscopic evidence.
Extended Hartree–Fock self‐consistent field with some results for berylliumlike atomic systems
Authors: Jucys A. P. , Lazauskas V. M.
Published: December 2004

The general methods of deriving the extended Hartree–Fock equations are described. The rules for going over from the energy expression in the ordinary method of calculation to that in an extended one are reformulated and illustrated. The extended Hartree—Fock equations for berylliumlike atomic systems based on the use of nonorthogonal radial orbitals are given and solved. The numerical values of overlap integrals and total energies are given and discussed.
Ab initio calculations on urea
Authors: Elbert Stephen T. , Davidson Ernest R.
Published: December 2004

Multiconfiguration wave functions constructed from contracted Gaussian‐lobe functions have been found for the ground and valence‐excited states of urea. ICSCF molecular orbitals of the excited states were used as the parent configurations for the CI calculations except for the 1A1(π → π*) state. The 1A1(π → π*) state used as its parent configuration an orthogonal linear combination of natural orbitals obtained from the second root of a three‐configuration SCF calculation. The lowest excited states are predicted to be the n π → π* and π → π* triplet states. The lowest singlet state is predicted to be the n π → π* state with an energy in good agreement with the one known UV band at 7.2 eV. The π → π* singlet state is predicted to be about 1.9 eV higher, contrary to several previous assignments which assumed the lowest band was a π → π* amide resonance band. The predicted ionization energy of 9.0 eV makes this and higher states autoionizing.
Basis dependence of wave functions of the ground state and low‐lying excited states of planar formaldehyde
Authors: Tanaka Kiyoshi
Published: December 2004

By the use of three bases containing 3p STO's possessing different diffuseness, the electronic structure of several excited states (valence‐ and Rydberg‐type) of planar formaldehyde is investigated by limited CI calculations. The spatial extension of the valence‐type state is independent of the bases, whereas a diffuse orbital is important in describing the Rydberg‐type state. The natural orbital analysis shows that the Rydberg‐type states can be described as an outer electron plus an electronic cloud representing the ionized state to which the Rydberg states converge.
Ab initio computations of spin‐orbit interactions in polyatomic molecules. Splitting of sulfur LII,III states and singlet–triplet transitions in SO2
Authors: Bendazzoli G. L. , Palmieri P.
Published: December 2004

Spin‐orbit interactions among the ground and the first few excited electronic states of SO2, are computed with ab initio molecular wave functions and Gaussian atomic orbitals. All spin‐other orbits contributions to the matrix elements are included.

The computed intensity of the first singlet–triplet transition is found to be in broad agreement with experiment and sensitive to an extension of the configuration interaction expansion of molecular wave functions. Also, the splitting of sulfur LII,III states in SO2 is derived as an example of large spin‐orbit interactions among electronic states.
On a new partitioning of the Hamiltonian in many‐body calculation of pair‐correlation energies in closed‐shell systems
Authors: Mukhopadhyay Atri , Moitra Raj Kumar , Mukherjee Debashis
Published: December 2004

We introduce here a new partitioning of the Hamiltonian in calculating pair‐correlation energies using many‐body perturbation theory, by which we are able to eliminate the off‐diagonal particle–hole (p–h) ladders exactly to all orders in the perturbation expansion. In this formulation, the particle states turn out to be different for each distinct pair of hole states in the correlation energy calculation. We have also included the contributions of the diagonal particle–particle (p–p) and hole–hole ladders exactly to all orders. The effect of the off‐diagonal p–p ladders has been estimated for each pair by computing the third‐, foruth‐ and fifth‐order energies. For highly symmetric systems the present partitioning yields in general symmetry‐broken orbitals. Here one may use an average kind of partitioning for all the partners of the degenerate sets, which restores the symmetry and at the same time ensures cancellation of the p–h ladders exactly at the lowest order and approximately at the higher orders. Results are presented for a selection of 6π‐electron conjugated systems. The correlation energy for each pair is in excellent agreement with that obtained from a partial CI calculation involving all double excitations from this pair. The advantages of implementing the present scheme in larger systems has been discussed.
Smooth interpolation, Fourier transformation, and two‐center overlap integrals for numerical atomic orbitals
Authors: Thulstrup Poul W.
Published: December 2004

A smooth interpolation method for the calculation of Fourier transforms of numerical atomic orbitals is presented and the method is used to calculate two‐center overlap integrals. Examples applying various definitions of smoothness are given.
Application of many‐body green's functions to the calculation of molecular ionization potentials
Authors: Nerbrant Per‐olof
Published: December 2004

We present a method for calculating the one‐particle Green's function for molecules. The scheme is essentially that proposed by Schneider and Taylor [1]. The Green's function is obtained through the Dyson equation. Closed expressions result by using the functional derivation technique to truncate an infinite set of coupled equations. A physical interpretation of the approximation is given and a connection with the equations‐of‐motion method is pointed out. In a numerical application the ionization potentials are obtained for the molecules N2, H2O, NH3 and CH4.
On the scattering of slow protons by diatomic targets
Authors: Gianturco F. A.
Published: December 2004

Inelastic collisions leading to rotationally excited molecular targets and involving protons as projectiles are theoretically examined from the point of view of both the scattering equations in the close coupling formalism and the interaction potentials between the partners.

A phenomenological approach is suggested for constructing such interactions and computational results are reported for simple diatomic targets. The inadequacy of more traditional ‘static’ approaches, when called for explaining dynamic couplings with open channels and centrifugal effects, is also discussed.
Asymptotic properties of inverses of cyclic overlap matrices in the large separation limit
Authors: Ra Øystein
Published: December 2004

This paper contains a discussion of asymptotic properties of inverses of cyclic overlap matrices relevant to LCAO theory based on localized orbitals. For inverse metric elements, Δ, and for large distances, R, between centres of localized orbital α in cell l and localized orbital β in cell l′, it is shown that:
one‐dimensional case:

two‐dimentional case:

three‐dimentional case:

These results are quite general and do not presuppose any restrictions as to symmetry (apart from the cyclic one), number of orbitals per unit cell, or vanishing of overlap integrals associated with neighbours beyond a fixed order. By way of illustration, explicit applications to one‐, two‐, and three‐dimensional, simple, mono‐orbitalic lattices with first‐neighbour overlap only are included.
Integral approximations on the basis of semiorthogonalized orbitals
Authors: Kashiwagi Hiroshi
Published: December 2004

Semiorthogonalized orbitals are introduced as a basis of approximate ab initio molecular calculations. The semiorthogonalized orbitals are obtained from the usual overlapping atomic orbitals by means of a generalized Löwdin transformation. The new orbitals are characterized by two features: many overlaps between them are zero, and they are close to their corresponding initial atomic orbitals. On the basis of the semiorthogonalized orbitals, a scheme of integral approximations is proposed which allows one to carry out approximate ab initio calculations with less computational efforts and thus offers a possibility to perform calculations on much bigger molecules with limited computational facilities. Results are presented for model calculations on the anthracene π‐electron system. Orbital energies and electron distribution are quite close to the rigorously calculated values.
Calculation of j and jm symbols for arbitrary compact groups. III. Application to SO3 ⊃ T ⊃ C3 ⊃ C1
Authors: Butler P. H. , Wybourne B. G.
Published: December 2004

The methodology developed in earlier papers is used to compute the 6j symbols and 3jm factors that arise in the group chain SO3 ⊃ T ⊃ C1. The relevant character theory is given and the 2j and 3j symbols calculated. Selection rules are used to predict which j symbols or jm factors are necessarily zero, and then a set of 6j fundamentals computed for T. The complete set of primitive 6j symbols are then computed by application of the orthogonality and Racah backcoupling relations. Primitive 3jm factors are calculated for SO3 ⊃ T and T ⊃ C3 and, from these, all the 3jm factors for T ⊃ C3 and some of those for SO3 ⊃ T computed. A complete table of non‐equivalent 6j symbols for T and 3jm factors for T ⊃ C3 is given, together with a table for SO3 ⊃ T of all 3jm factors with j ≤ 2.
Spin‐Orbit coupling in aromatic hydrocarbons: A semiempirical evaluation of the radiative lifetimes of naphtalene and anthracene
Authors: Bendazzoli G. L. , Orlandi G. , Palmieri P.
Published: December 2004

Singlet‐triplet spin‐orbit matrix elements, which govern the lowest 3B1u ← 1Ag transition in typical aromatic molecules like naphtalene and anthracene, are calculated with INDO molecular orbitals and the conventional spin‐orbit one‐electron hamiltonian. The correct order of magnitude of the triplet radiative lifetimes is obtained for the two molecules, when INDO MO coefficients are referred to a symmetrically orthogonalized basis. The possibility of using the semiempirical Hamiltonian is explored using ab initio wave‐functions for a few test cases. Reasonably accurate doublet‐doublet and singlet‐triplet matrix elements have been computed.
An interative scheme for electronic systems using one‐electron green's functions
Authors: Hyslop J. , Rees D.
Published: December 2004

In this paper an iterative generalization of the minimum principle proposed for electronic systems by Hall, Hyslop, and Rees is investigated. It is shown that this generalization still retains the advantage of using members of a larger class of trial wave‐functions, for example those with discontinuities, as initial approximations to the wave‐functions. This scheme has the advantage that, at each stage of iteration, an upper bound is obtained which is at least as good as that obtained previously.

The theory is first applied to the hydrogen atom. It is then adapted to estimate the Hartree–Fock energy of the helium atom, the Hartree–Fock limit being obtained after a relatively small number of iterations.
Magneto‐optical properties of a spinless particle moving in a harmonic potential
Authors: Datta Sambhu , Richardson F. S.
Published: December 2004

Exact solutions to the quantum mechanical problem of an anisotropic oscillator in a one‐dimensional magnetic field are obtained. These solutions (eigenenergies and wave functions) are then applied to the problem of calculating the magneto‐optical properties of a charged spinless particle constrained to move in a harmonic potential field. General expressions for the dipole strengths and rotational strengths associated with radiation induced transitions between the eigenstates of this model system are developed, and these quantities are further related to observables of magneto‐optical absorption spectroscopy and Faraday effect studies.
Calculation of molecular electronic spectra by projected‐unrestricted Hartree–Fock theory
Authors: Schug John C. , Lengsfield Byron H. , Brewer Dana A.
Published: December 2004

This paper is concerned with a new application of projected‐unrestricted Hartree–Fock theory, namely, the calculation of electronic spectra for symmetric molecules. The excited electronic state is represented by a single determinant whose unrestricted nature allows for orbital rearrangement relative to the self‐consistent ground state. The self‐consistent calculation must be followed by spin projection to obtain appropriate spin eigenstates. It was necessary to develop modified procedures for portions of the spin projection calculation because our method of constructing the wave functions produces degeneracies among the natural orbitals. Illustrative calculations using the all‐valence‐electron INDO approximations produced results which compared favorably with configuration‐interaction treatments. The method described here should be most useful, however, in conjunction with ab initio calculations using flexible basis sets.
Theory of lone pairs. II. A moment analysis of localized molecular orbitals in ten‐electron hydrides
Authors: Daudel R. , Stephens M. E. , Csizmadia I. G. , Kozmutza C. , Kapuy E. , Goddard J. D.
Published: December 2004

Ab initio double‐zeta quality molecular orbital calculations have been carried out on an extensive series of ten‐electron hydrides. The Edmiston–Ruedenberg energy‐localized molecular orbitals were calculated and the total molecular and localized orbital densities analyzed in terms of dipole moments, contour plots, and a simplified model for the orbital density involving analysis of the first and second moments. The simplified moment analysis model may be easily visualized in terms of threedimensional geometric objects, spheres, and ellipsoids. The model summarizes the information on the effective functional distribution inherent in the more detailed orbital contour plots in a clear and concise manner.
Relativistic molecular orbitals for the double group D3h
Authors: Toivonen H. T. , Pyykkö P.
Published: December 2004

Relativistic symmetry orbitals are given for the double group D3h. For atomic orbitals at the symmetry center a general expression is presented. The atomic orbitals of the s, p½, and p3/2 variety outside the center are also considered. The representation matrices are given in explicit form.
Ab‐initio and approximately rigorous calculations on small, medium, and large systems
Authors: Kaufman Joyce J. , Popkie Herbert E. , Preston Harry J. T.
Published: December 2004

We have explored two areas of approximately rigorous calculations for computing nonempirical wave functions for heavy and/or large molecules orders of magnitude faster than with conventional ab‐initio methods but with the same chemical accuracy.

First, we have developed and used a series of programs (starting from our new fast sets of ab‐initio Gaussian SCF and SCF‐CI programs) incorporating ab‐initio effective core model potentials (MOD‐POT) which allow one to treat only the valence electrons explicitly, plus a charge conserving integral prescreening, which cuts down significantly on the number of integrals that have to be calculated, stored, or processed for a large molecule. We have named this latter procedure VRDDO (variable retention of diatomic differential overlap). With these MODPOT and MODPOT/VRDDO methods we have explored a variety of small, medium, and large systems ranging from electron affinities of atoms through to molecules of biological interest and large boron hydrides. The results compared to ab‐initio SCF or SCF/CI calcuations are very good, usually within 0.001 to 0.002 a.u. for orbital energies and gross atomic populations (GAPS) and even better along potential energy curves.

Secondly, we have explored the use of the MS‐Xα method for less conventional molecules and properties than those for which it is customarily employed.
Variational localized‐site cluster expansions. VI. General theory revisited
Authors: Klein D. J.
Published: December 2004

A general and systematic localized‐site cluster expansion is described. It provides simple physically appealing and computationally feasible wave function ansätze, as well as, via extension of the cluster expansion, a unique expression for general, possibly exact, wave functions. We show that a variety of matrix element evaluation techniques are available and that they are sometimes exact though relatively simple. These techniques often proceed in terms of computational time proportional to the number of different types of sites, rather than their total number. Thus it seems we have a new and viable many‐body theory, which is expected to be most accurate and most readily implementable when a physical picture with slightly perturbed localized sites is relevant.
Total cross section of the SF6 molecule for elastic electron scattering
Authors: Benedict M. G. , Gyemant I.
Published: December 2004

A multiple scattering method is used for determining the total cross section of elastic electron scattering for the SF6 molecule in the energy range 10–60 eV.
An efficient procedure to evaluate long‐range coulombic interactions within the framework of the LCAO–CO method for infinite polymers
Authors: Piela Lucjan , Delhalle Joseph
Published: December 2004

A very efficient and exact method for calculating the long‐range effects in polymers is reported. The method is based on the multipole expansion within the Fock operator, and exact summation up to infinity is carried out. Only a small number of one‐electron integrals have to be considered, while in the traditional approach one has to compute a large number of two‐electron integrals. Results on LiH model polymer have been obtained with a remarkable accuracy within a negligible computing time.
Applicaition of the statistical method in the theory of intermolecular interactions
Authors: Kołos Włodzimierz , Radzio Elżbieta
Published: December 2004

The approximate way of calculating the supermolecular density applied in the Gordon and Kim method is examined. If the supermolecular density is approximated by a sum of the subsystem densities, the results for the individual contributions to the interaction energy (kinetic, potential) appear to be incorrect as compared with those obtained in the SCF approach and in first‐order perturbation theory. However, a considerable improvement of the statistical results is obtained if a more suitably calculated supermolecular density is used. All calculations have been carried out for the He2 system.
Orientation of the Eckart frame in a polyatomic molecule by symmetric orthonormalization
Authors: Jørgensen Flemming
Published: December 2004

The Eckart frame is a frame of orthonormal vectors ei, i = 1, 2, 3, which follow a vibrating molecule while it rotates. The frame is orientated by the so‐called Eckart condition, which Eckart found by requiring the Coriolis interaction to be minimal. In the present paper we shall see that Eckart's frame also can be characterized by a simple least squares property. Eckart showed how to construct the ei's by a certain orthonormalization of three vectors Fi, i = 1, 2, 3. We observe that this orthonormalization is in fact Löwdin's symmetric. Then we consider the least squares property in the light of the Carlson‐Keller theorem—which is given a slightly different form. It is shown that the complete solution to Eckart's condition can be generated from the one of interest by C2 rotations around axes in an orthonormal set which originates from the Fi's by Löwdin's canonical Orthonormalization.
Asymptotic behavior of the primitive function of different “symmetry‐adapted” perturbation schemes for the H ground state
Authors: Kutzelnigg Werner
Published: December 2004

The leading terms in the asymptotic 1/R expansion of the wave functions and energies of various “symmetry‐adapted” perturbation schemes for intermolecular forces, as well as for the “polarization approximation” (PA) are derived for the H ground state, both exactly (i.e., to infinite order in λ) and in the first two orders of the λ expansion. It is pointed out that only in the PA and the Hirschfelder–Silbey scheme is the formal primitive function Φ genuinely primitive, whereas Φ in the other schemes is asymmetric in a rather strange way. In this lack of genuine primitivity lies the reason why in these schemes the leading term of the 1/R expansion is only recovered to infinite order in λ and requires knowledge of the R−4 term of the wave function, provided that one uses the “internal” energy expression. Four different energy expressions are compared that behave differently in the different schemes. The results obtained here are basis independent, but the implications of the basis completeness problem are discussed as well.
On the defects of molecular symmetry‐lobe orbitals
Authors: Le Rouzo H.
Published: December 2004

It is proved that two molecular symmetry‐lobe orbitals, belonging to different irreducible representations, can have a non‐negligible overlap. Using a previously reported multipolar analysis of Gaussian‐lobe orbitals (GLOs), it is demonstrated that such defects occur when individual symmetry orbitals (SOs) are both contaminated in a given Y1m subspace, even if such contaminations are very small. A numerical application illustrates this result in the case of the NH3 molecule, and it is shown that axial‐GLOs allow for the exact cancellation of the symmetry defects.
Heuristic intermolecular potential function for the methane–water interaction based on ab initio quantum‐mechanical calculations
Authors: Harrison S. W. , Swaminathan S. , Beveridge David L. , Ditchfield Robert
Published: December 2004

An analytical potential function for the pairwise interaction of methane and water is reported. The function is representative of 225 ab initio quantum‐mechanical calculations of the intermolecular interaction using 6–31G self‐consistent‐field molecular‐orbital theory. The statistical parameters of the curve fitting are given and isoenergy contour maps of the interaction energy are presented and discussed.
Half‐projected Hartree–Fock model for computing potential‐energy surfaces
Authors: Smeyers Yves G. , BruceñNta Angel M.
Published: December 2004

The possible uses of the half‐projected Hartree–Fock (HPHF) scheme for computing potential‐energy surfaces for both singlet and triplet states are investigated. For that purpose, a new procedure based on the simultaneous solution of two eigenvalue equations is presented for calculating the HPHF function. Applications are given in the cases of the singlet ground state and lowest triplet state of the lithium molecule. In both cases, the HPHF scheme is found to yield the correct general shape of the curves. The features of these curves are discussed. Finally, it is concluded that the HPHF model seems to be useful as a tool for determining potential‐energy surfaces, especially in the cases of large molecules where more sophisticated methods are unmanageable.
Equations of change in configuration space
Authors: Hirschfelder Joseph O. , Yang Kuo‐Ho
Published: December 2004

This paper is a summary of a detailed treatment, given elsewhere, in which (gauge invariant), equations of change (at points in configuration space) of arbitrary dynamical properties of an N‐particle quantum‐mechanical system in the presence (or absence) of an arbitrary (time‐ and space‐varying) classical electromagnetic field are derived for an arbitrary Hamiltonian by making use of both the Maxwell and the Schrödinger time‐dependent equations. The properties at a point in configuration space are defined so as to be closely related to observables and the forces are related to their classical counterparts. The rates of change of linear momentum and angular momentum are closely related to the classical Lorentz force and the Lorentz torque, respectively. The rate of change of energy is the work done on the system by E(t), the time‐dependent part of the external electromagnetic field. The reason for E(t) and its definition of the energy for a system in a time‐varying electromagnetic field is explained. The Breit‐Pauli Hamiltonian is required to treat “state‐to‐state” molecular problems and the detailed equations of change using this Hamiltonian are used as examples.
Ab initio molecular‐orbital study of the binding of ZnII with SH2 and SH−
Authors: Kothekar V. , Pullman A. , Demoulin D.
Published: December 2004

This paper reports an ab initio molecular‐orbital (MO) study of binding of SH2 and SH− with ZnII. The mechanism of binding of ZnII with these ligands is investigated using a detailed analysis of the energy decomposition and of the electronic distribution. The dependence of the results on the choice of the basis set for sulfur (in particular the effect of incorporation of diffuses p and d orbitals) on the geometry of ligand binding, the binding energy, and the proton affinity of SH− are investigated. Comparison made with the corresponding results concerning the binding of OH2, OH−, and NH3 shows that sulfur binding is less favorable although more covalent. Both sulfur ligands show a marked preference for angular conformations for binding with the metal ion. The effect of ZnII binding on the ease of deprotonation of H2S is quite similar to the corresponding effect found earlier for H2O.
Molecular calculations with the nonempirical ab initioMODPOT, VRDDO, and MODPOT/VRDDO procedures. IX. Carcinogenic benzo(a)pyrene and its metabolites using a MERGE technique
Authors: Kaufman Joyce J. , Popkie Herbert E. , Palalikit Surat , Hariharan P. C.
Published: December 2004

Ab initio MODPOT/VRDDO calculations have been carried out on carcinogenic benzo(a)pyrene and its metabolites. The MODPOT/VRDDO method incorporates two very desirable options into our fast ab initio Gaussian programs: MODPOT—ab initio effective core model potentials—and a charge‐conserving integral prescreening approximation which we named VRDDO (variable retention of diatomic differential overlap). For orbital energies and population analyses the MODPOT/VRDDO results agree to essentially three decimal places with completely ab initio calculations using the same valence atomic basis set. For this series of very closely related congeners a new MERGE technique was implemented that allows reuse of integrals of a common skeletal fragment. Since our program computes integrals efficiently by blocks, reusing information common to the block, it was more difficult to implement a MERGE technique than for integral programs which calculate the integrals one‐byone. The MODPOT/VRDDO calculations were performed for benzo(a)pyrene (BP), BP oxides, BP dihydrodiols, and BP dihydrodiol epoxides. The metabolites investigated were BP‐7,8‐oxide, BP‐4,5‐oxide, BP‐7,8‐dihydrodiol [cis(e, a), cis(a, e), trans(e, e), and trans(a, a)], and BP‐7,8‐dihydrodiol‐9,10‐epoxide [β,β,β (the most stable), β,β,α; α,α,β, and α,α,α all derived from cis‐BP‐7,8‐dihydrodiol and β,α,β; α,β,β and α,β,β derived from trans‐BP‐7,8‐dihydrodiol]. Several different conformations were calculated for each of the BP dihydrodiols and BP dihydrodiol epoxides. Calculations were carried out for the opening of the C9—O—C10 epoxide ring both toward C9 and C10 for the, most stable β,β,β isomer of BP‐7,8‐dihydrodiol‐9,10‐epoxide. Opening the epoxide ring between C10 and O leads to a more stable intermediate than opening the epoxide ring between C9 and C10. However, there is no buildup of positive charge in C10 as has been postulated by some cancer researchers, but rather the C10 becomes slightly more negative. Nor is there a buildup of negative charge on the O atom. rather it becomes slightly less negative. As the epoxide ring is opened further than 90° for the O—C9—C10 or O—C10—C9 angles, there appears to be a possible mixing of configurations that is being investigated further.
Perturbation treatment of multiple site reactivity. II. Additivity in trimolecular interactions
Authors: Chang Shih Y. , Weinstein Harel
Published: December 2004

A multiple perturbation method for the study of molecular reactivity following multiple site interactions has been extended to trimolecular systems. The theory is reformulated by the many‐body diagrammatic method. While adding no new physical content to the previous theory, the present formulation allows for a systematic way of evaluating higher‐order energies. The additivity of perturbation contributions to the modification of molecular reactivity is tested on dihydrated adenine. The results compare favorably with supermolecule calculations.
Optimum geometries and relative energies for cytosine, thymine, uracil, the imino tautomer of cytosine, the enol tautomer of thymine, and the enol tautomer of uracil by the MINDO/2 SCF MO method
Authors: Zielinski Theresa Julia , Rein Robert
Published: December 2004

A MINDO/2 SCF MO geometry optimization of cytosine (C), thymine (T), uracil (U), the imino tautomer of cytosine (C*), the enol tautomer of thymine (T*), and the enol tautomer of uracil (U*)was made. The optimized geometries for cytosine, thymine, and uracil agree well with crystallographic data. The optimized geometries for the tautomers show the correct trends in bond lengthening and bond angle except for the C4—O4 length and C4—O4—H angle of T* and U*. The energies of tautomerization were found to be 10.3, −9.0, and −14.2 kcal/mol for C⇌C*, T⇌T*, and U⇌U*, respectively, when optimized geometries are used. The overestimation of the C4—O4—H angle is speculated to arise because of an inadequacy in the parametrization of the one‐center integrals in MINDO/2.
Variable basis sets in perturbation theory: Numerical finite perturbation versus analytic approach
Authors: Epstein Saul T. , Sadlej Andrzej J.
Published: December 2004

We consider the problem of determining variational, external‐field‐dependent corrections to nonoptimal zero‐field nonlinear parameters. Both a direct analytic perturbation analysis and finite perturbation methods are described in a general way and in detail for the SCF approximation. The abstract theory is illustrated by reference to the results of several explicit calculations. Also, the sensitivity of the results to the choice of zero‐field values is discussed.
Semiempirical MO study on the abnormal bond orders of large networks of highly branched polyenes
Authors: Kanazawa Tomoko , Hosoya Haruo , Iwata Suehiro
Published: December 2004

The π‐electronic structures of the ground state of linear and highly branched polyenes with up to 80 π‐electrons are calculated with particular reference to the alternation of the bond orders. The MO methods adopted are HMO, PPP, variable‐β, γ, and its improved version. The effect of the electron correlation through singly and doubly excited configurations is estimated with a second‐order perturbation calculation. The calculated bond orders systematically vary with the degree of approximation used. Most of the bond order values can be grouped into either a single or double bond region. In certain series of highly branched polyenes the bond orders of double and single bonds at the root of branching, respectively, get smaller and larger as the size of the molecule increases and sometimes their difference gets diminishingly small. The origin of these abnormal bond orders is discussed in terms of the π‐electron flow networks.
Conformational possibilities of double‐helical nucleic acids: Theory and experiment
Authors: Ivanov V. I. , Zhurkin V. B. , Zavriev S. K. , Lysov Yu. P. , Minchenkova L. E. , Minyat E. E. , Frank‐Kamenetskii M. D. , Schyolkina A. K.
Published: December 2004

This survey covers the following topics: (1) Theoretical calculation of the total multitude of the energetically permitted regular DNA helices. (2) Theoretical study of flexibility of the double helix with emphasis on nucleosome structure. (3) Experimental data on the properties of the B to A transition of DNA in solution: the degree of cooperativity and influence of sequence. (4) The B‐A transition and its possible role in genes activation.
Ab initiocalculations and absolute rate theory. Critical test for a series of elementary gas‐phase reactions
Authors: Čársky P. , Zahradník R.
Published: December 2004

Absolute rate theory (ART) was applied to a series of reactions of the type A+BC → AB+C containing H, F, HF, H2, and F2,trans–cisisomerization of dideuteroethylene, and processes H + CH4→ H2+ CH3and H′+CH4→ H′CH3+ H. Geometries and energies of activated complexes were taken from the bestab initiostudies reported in the literature in which at least a DZ + P basis set was used and a large portion of the correlation energy was included. Vibrational frequencies needed for the zero‐point energies and vibrational partition functions were estimated from the reported potential surfaces (HHF and HFF) or evaluated fromSCF4‐31G calculations (HFH, FHF, twisted C2H4, and CH5complexes). Compatability of calculated rate constants with the experimental data was examined.