bluuebunny/crossref_metadata_2025 huggingface dataset:
Application of the configuration‐interaction method and the random phase approximation to the Ab Initio calculation of electronic excitation energies of H2o
Authors: Truhlar Donald G.
Published: December 2004

By performing calculations on H2 O similar to the calculations of Dunning and McKoy on C2H4 and HCHO [1a], it is shown that the singlet excited states of the water molecule cannot be adequately represented by an ab initio calculation (no semiempirical elements) using a valence‐like basis set (either minimum basis or double zeta) of Slater‐type orbitals. The triplets which are the lowest states of their symmetry appear to be described more accurately than the other states, and the lowest four triplet excitation energies are calculated to be 8.1, 8.4, 9.5, and 10.3 eV. The implications for the applicability of simple molecular orbital theory of the type commonly applied are discussed.
Perturbative ab initio calculations of intermolecular energies. I. Method
Authors: Daudey J. P. , Claverie P. , Malrieu J. P.
Published: December 2004

Starting from a knowledge of approximate wave functions of the isolated molecules (or atoms) A and B, a method is proposed to build up a zeroth‐order ground state and excited configurations for the complex AB in which the molecular orbitals keep their local significance. The standard Rayleigh‐Schrödinger perturbation in this basis provides a decomposition of the zeroth‐order interaction energy as a sum of the electrostatic and repulsion energy. In the second order, it is possible to identify the classical dispersion and polarization forces (modified by a term of order S2) and two additional contributions which are linked to the exchange possibility. The intramolecular correlation component is taken into account and compared with the correlation on the isolated molecules. It is moreover suggested that since we work in a rather limited basis set, the perturbed energy of AB must be compared with the unperturbed energies of A and B calculated in a basis including the vacant orbitals on their respective partner. Finally a possibility for going beyond the second order is described.
Perturbative ab initio calculations of intermolecular energies. III. The water dimer
Authors: Daudey J. P.
Published: December 2004

The interaction energy between two water molecules A and B is calculated by the method described in Paper I [1], previously applied for the interaction between two helium atoms (Paper II) [2]. This interaction energy is obtained as the difference between the energies of the complex (A + B) and the monomers (A) and (B), obtained by a perturbation method. The results obtained with the perturbation developed up to the second order in a minimal atomic basis set are decomposed into classical contributions and contributions linked to the exchange possibility. Charge transfer contributions are important and the localized character of the hydrogen bond is examined. It is pointed out that the definition of the set of excited configurations for the calculation of the energies of the isolated monomers is important, especially when one tries to use a small atomic basis set. A similar effect in SCF‐type calculations is evaluated. The contribution of higher orders is evaluated by the CIPSI method.
Matrix formulation of the generalized Hartree‐Fock methods
Authors: Mestechkin M. M. , Whyman G. E.
Published: December 2004

Spin‐projected one‐particle density and spin density matrices are presented as polynomials of suitable unprojected quantities with generalized Sasaki‐Ohno coefficients. Thus an explicit form of Harriman's theorems is given. For the two‐particle spatial density matrix an expansion in direct products of powers of unprojected residual electron and spin density matrices is given. For these basic matrices of the scheme the variational spin‐extended equations are formulated.
Configuration interaction calculations on the nitrogen molecule
Authors: Langhoff Stephen R. , Davidson Ernest R.
Published: December 2004

A contracted Gaussian basis set capable of describing about 63% of the correlation energy of N2 has been used in a detailed configuration‐interaction calculation. Second‐order perturbation theory overestimated the correlation energy by 23–50% depending on how H0 was chosen. Pair‐pair interaction affects the correlation energy by about 20% while quadruple excitations have an 8% effect.
Accurate analytical self‐consistent field wave functions for Tm2+ and Tm3+
Authors: Damommio A. , Synek M.
Published: December 2004

The analytical expansion self‐consistent field method was employed to perform ab initio calculations for the ground states of the rare‐earth ions, Tm2+, 4f13, 2F, and Tm3+, 4f12, 3H, (Z = 69). In each case the total number of basis functions used in the analytical expansions was 29, distributed as follows: 10, 8, 5, and 6, for the symmetries s, p, d, and f, respectively. All of the orbital exponents of the basis functions were optimized repeatedly, to the extent of the single‐precision computer representation. Values of 〈rn〉 for the 4f orbital of both ions are also presented, for the convenience of experimentalists.
More on molecular electronic structure of metal phthalocyanines
Authors: Mathur S. C. , Singh Jai
Published: December 2004

Molecular orbitals of some of the 3d‐transition metal phthalocyanines have been calculated. π‐Electron charge densities over the atomic sites and the optical properties of the metal phthalocyanines have been calculated. The effect of the introduction of different metal atoms in the centre of the organic ring on the physical properties of the metal phthalocyanines has been discussed.
Variation of the polarizability of the hydrogen molecule ion and the hydrogen molecule with internuclear separation
Authors: Zeroka Daniel
Published: December 2004

The variation of the polarizability of H and H2 with internuclear separation R = 1.6 – R = 2.4 a.u. for H and R = 1.0 – R = 2.0 a.u. for H2 is determined using a variational method suggested by Das and Bersohn. From these data, values of 〈α〉0,J for which nuclear motion due to zero point vibration and centrifugal stretching is taken into account, are calculated at 300°K. The relative percent increases of the motion averaged values compared to the equilibrium values are as follows: 10.50% for H and 6.52% for H2.
Floating one‐center perturbation treatments for H‐like molecules based on screened hydrogen atom or molecular puff unperturbed problems
Authors: Ali M. K. , Meath William J.
Published: December 2004

Various floating one‐center perturbation schemes are developed for H‐like molecules. Previous work for the ‘1s’ hydrogen atom approach is extended through third order in the energy. In the molecular puff approach an exact ‘closed form’ solution is obtained for the zeroth‐order problem, which corresponds to a double layer molecular puff. Semianalytical results for the first‐order correction to the floating molecular puff wave function and for the energy through third order are developed which offer a convenient alternative to previous approaches. Explicit calculations for ground state H show that for R > 3aO the ‘1s’ and the more complicated ‘puff’ treatments are equivalent and that neither the ‘1s’nor the molecular puff function is an adequate zeroth‐order wave function for the important intermediate values of R. The usefulness of some of these methods in a variety of problems, where one‐center zeroth‐order wave functions do appear to be adequate, is discussed briefly.
Application of the distinguishable electron method
Authors: Chong Delano P. , Scott William R. , Yue Chee P. , Wang Pearl S. C. , Benston Margaret L. , Palke William E.
Published: December 2004

In order to make a better assessment of the distinguishable electron method developed by Kirtman and co‐workers, we have applied the method to some two‐electron atoms and to H2 and LiH. Our results lend support to the contention held by Kirtman and co‐workers that the distinguishable electron method is a practical way of calculating reasonably accurate physical properties.
Unified treatment of two‐electron integrals. II. One‐center, electron repulsion, spin‐spin and spin‐orbit integrals containing rij
Authors: Matcha Robert L. , Milleur Mac B.
Published: December 2004

General formulas are obtained for evaluating a basic type of one‐center two‐electron integral which arises in the computation of expectation values of spin‐spin and spin‐orbit operators over explicitly correlated wave functions. The correlation terms are assumed to be in the form of products of Slater functions and powers (not necessarily integer) of the interelectronic coordinate rij.
Hybridization by the maximum overlap method
Authors: Randić Milan
Published: December 2004

A brief survey of the maximum overlap method is presented and some computational aspects of the approach are discussed. The hybrid compositions and bond overlaps are reported for some thirty small ring compounds and a list of characteristic hybrids for various structural environments is given. The table of characteristic hybrids is extended to acyclic hydrocarbons and the transferability of the maximum overlap hybrids is demonstrated. Those aspects of the method which depend on geometrical properties of molecules have been considered in some details and the discussion is extended to some structural features of cyclic systems. In particular the asymmetry of bonds of spiro carbon atom is examined and rationalization of puckering of large macrocyclic systems is presented. In the summary it is pointed to the method and its potential to discuss structural aspects of molecules at the particular level of accuracy expected to be of great use in organic and physical organic chemistry. Further development and improvement of the method is mentioned, but already in the present form it can produce hybrids which may constitute a useful basis for other more ambitious semiempirical calculations.
The hammerstein integral equation: a general technique for constructing a rapidly convergent padé‐type approximation to the logarithmic derivative
Authors: Pulfer J. D. , Whitehead M. A.
Published: December 2004

The radial one‐electron Schrödinger equation can be written as a nonlinear first‐order differential equation by making a suitable logarithmic transformation. The resulting Riccati equation has the equivalent Hammerstein integral representation [1],

where the kernel, N(r, r′) is

and H(r, r′) is the Heaviside unit step function. This kernel is a more general one than that developed in ref. [1]. Both kernels apply in cases where the Riccati equation corresponds to a Sturm–Liouville problem.

It is shown that this integral equation can be integrated by parts so that, for any local potential, the integrand decreases as the cyclic folding procedure is applied. During this cyclic folding, the kernel generates an equation that contains only coefficients of β(r)0 and β(r)1. Consequently, after truncating at the end of the nth cycle, it is possible to write down a Padé‐type approximation to the logarithmic derivative as a known function of the independent variable. All coefficients in this approximation can be evaluated as simple algebraic formulations of P(r), R(r), and integrals over P(r).
Transformation properties of many‐electron wave functions with special attention to the relation between pair‐correlated DODS and configuration interaction
Authors: Wormer P. E. S. , Van der Avoird A.
Published: December 2004

A method is presented that leads to a simple derivation of the explicit relation between pair‐correlated DODS schemes (e.g., the alternant molecular orbital method and the extended valence bond method) and configuration interaction.

This result is based on a reduction formula for the representations of the general linear group, GL(m), carried by the N‐electron function space. Generally, this paper deals with the effect of “partitioned” orbital transformations on states with “local” permutation symmetry.
A general ab initio molecular multi‐configuration self‐consistent field algorithm
Authors: Hackmeyer M.
Published: December 2004

The ab initio multiconfiguration self‐consistent‐field (MC SCF) techniques and computer programs of Basch [1, 2] and the ab initio configuration interaction (CI) techniques and programs of Whitten and Hackmeyer [3] have been combined and generalized to form a general technique and program to yield optimized ab initio MC SCF wavefunctions for any set of Slater determinants. The Slater determinants are read in as input data to the program along with the spin parity that is being considered (optional) and the program successively does the CI calculation and one iteration of the SCF calculation, constructing the proper Fock–Hamiltonians by examining the set of Slater determinants and their CI coefficients. The Fock–Hamiltonian matrices are calculated and diagonalized in succession, a single two‐dimensional array being used to store these matrices. The basis function integrals are read from a tape only once during each MC SCF iteration (one MC SCF iteration = a CI calculation followed by one iteration of the SCF calculation).
Calculation of the magneto–optical activity of the hydrogen molecule
Authors: Svendsen E. Nørby , Hameka Hendrik F.
Published: December 2004

We calculated the Verdet constant of the hydrogen molecule. We found that the angle of rotation may be represented by ϕ0 = A0Hv2/(v − v2)2 where A0 is 3.23 × 10−33 microminutes sec2 per oersted‐cm‐atmosphere. This is in agreement with the experimental observations where ϕ0 is given by the same frequency dependence with the constant A0 × 2.72 = 10−33 in terms of the same units.
Method of complex molecular orbitals
Authors: Hendekoviá J.
Published: December 2004

In the spirit of Löwdin's extended HF scheme, an SCF method for the description of the molecular ground state, based on complex molecular orbitals, is developed. As a special case the method of parity mixing in orbitals is formulated. A calculational procedure for solving derived secular equations is described and numerical results, obtained in the minimal basis set, are reported for the N2 and CO molecule. Resulting ground state energies are close to the energies of the CI calculations with the same set of orbitals.
Coupled hartree–fock calculation of static and shielding factors for open shell atomic systems
Authors: Gupta A. , Roy H. P. , Mukherjee P. K.
Published: December 2004

In this paper a calculation of the static quadrupole polarizabilities and the shielding factors of the atoms and ions of the 2p open shell systems is presented. A fully coupled Hartree–Fock method using the Roothaan formalism is adopted. Calculations have been done for the ground as well as for some valence excited states. An antishielding effect is observed for all the atoms and ions under study.
All‐pair wave function and reduced variational equation for electronic systems
Authors: Náray‐Szabó G.
Published: December 2004

A new type of wave function is proposed for atomic and molecular systems. This all‐pair function is constructed of N(N – 1)/2 identical geminals for N electrons. For systems with the highest multiplicity this is the full space part of the wave function. For closed shell systems it has to be multiplied by a Slater determinant according to the antisymmetry condition. In the case of maximal multiplicity a reduced variational equation is derived for the geminal. This equation is independent of the dimensionality of the system and contains the particle number as a multiplicative factor only. The method is extended to the closed shell case where a restriction has to be fulfilled. The reduction of the variational equation can be done only approximately. The use of identical geminals can be treated as a first approximation. An extension of the method, called the pair interdependent configuration interaction (PICI), is proposed. The special features of the method are discussed briefly.
Some remarks on the semiempirical one‐center electron repulsion integrals
Authors: Anno Tosinobu , Teruya Hirohide
Published: December 2004

The identification of the stage of ionization for various kinds of one‐center electron repulsion integrals, occurring when nonbonding or lone‐pair electrons are considered explicitly as well as π‐electrons, is discussed for conjugated organic molecules containing heteroatoms N. It is concluded that the value for the negative ions should be used for (πCπC | πCπC) in all the states but for (πNπN | πNπN) only in the π‐π states. In the n‐π states, the appropriate value of (πNπN | πNπN) is that of the neutral atom if the molecule contains only one N atom. If more than one N atom is involved in the molecule, some weighted mean of the values for the negative ion and for the neutral atom should be used. The value for the neutral atom is most adequate for one‐center repulsion integrals other than the (ππ | ππ) type in both the π‐π and the n‐π states. The method of determining these integrals is also discussed. It is concluded that they are to be determined from the consideration of appropriate electron‐transfer reactions except for exchange integrals. The exchange integrals are shown to have to be determined from the Slater–Condon parameters derived from the analysis of the experimental atomic energy levels. Illustrative calculations are given for the lower singlet levels of the formaldehyde, pyrazine, pyridine, and the p‐benzoquinone molecule. It is found that the calculated energies of the n‐π transitions become much too low unless the (ππ | ππ) values of the heteroatoms in the molecule are chosen differently in the n‐π states and in the π‐π states as pointed out theoretically in this article.
Singlet–triplet splittings as obtained from the Xα‐scattered wave method: A theoretical analysis
Authors: Bagus P. S. , Bennett B. I.
Published: December 2004

The theoretical determination of singlet–triplet splittings of the excited states of closed‐shell molecules is discussed with emphasis on the use of the Xα–scattered wave method. With this method, splittings can be computed in two independent ways. Both will have corrections due to orbital relaxation effects. The singlet–triplet splittings obtained with the Xα–scattered wave method for several large organic molecules are reviewed. It is seen that the results using the two splitting formulas differ by a large amount; in fact, they differ by the magnitude of the computed splitting. We provide a criterion for choosing the results obtained with one method over the other by showing that they both give upper bounds to the best result obtainable within the framework of the model. However, because of the large differences between the two methods, the quantitative value of the splitting should be viewed with caution.
Spin‐free quantum chemistry. XV Spin‐only neutron diffraction
Authors: Matsen F. A. , Picone J. M. , Welsher T. L.
Published: December 2004

The cross section for elastic neutron diffraction is analyzed for the spin‐only case, in which the orbital contributions to the magnetic moment density are negligible. For systems specified by spin‐free Hamiltonians, we show that the magnetic moment density is calculated from the unpaired electron density, a spin‐free quantity, which is equivalent to the spin density. The computation of the unpaired electron density is outlined and examples are discussed. The scattering cross section for an infinite interaction range Heisenberg model exhibits a temperature dependence which parallels that of the spontaneous magnetization. With a knowledge of the unpaired electron density one may determine the magnetic space group symmetry.
Spin‐free quantum chemistry. XVI. Spin correlation
Authors: Matsen F. A. , Welsher T. L.
Published: December 2004

We discuss the calculation of quasielastic critical neutron scattering for systems defined by a spin‐free Hamiltonian. The system dependent property which determines the critical scattering is the thermal average of a spin‐free operator called the general unpaired electron correlation operator. For localized models, we obtain the scattering as the Fourier transform of an unpaired site correlation function. The algebraic relationship between this correlation function and the usual spin correlation function is discussed as are its relationships to thermodynamic properties. Correlations in the infinite interaction range model, linear spin wave model, and infinite chain Heisenberg model are given. In the last case, an estimate of the low temperature correlation length is made.
SC Cellular multiple scattering in molecular electronic structure calculations
Authors: Keller Jaime
Published: December 2004

Recent advances in the statistical exchange approximation to the one‐electron potential and in the use of general potentials in multiple scattering are studied numerically and combined in a cellular multiple scattering calculation of the electronic structure of molecules. The particular examples of these calculations are SF6, H, and H2, the results being compared with those of previous approximations and other techniques. It is first seen that the Xαβ approximation or a similar one based on the use of a universal parametrization of the statistical exchange (and some effects of correlation) part of the potential will provide the maximum of freedom in the partition of the real space of the molecules into cells. This avoids arbitrariness in the assumed value of the parameters to be used in every cell. The usefulness of the Xαβ approximation in a muffin‐tin and in a cellular calculation is discussed. It is also found that the usual limitation to muffin‐tin‐like potentials, while simpler as a first approximation, can be removed without unduly increasing the computing effort. However, an accurate evaluation of the real self‐consistent potential in each cell (or even in a muffin‐tin) will increase the length of the program, the storage necessities and the computing time by a factor estimated to be between three and ten according to the geometry considered. It is concluded that the cellular multiple scattering method offers the best possibilities for a systematic use of multiple scattering techniques in molecular calculations.
Electronic correlation studies. III. Self‐correlated field method. Application to 2S ground state and 2P excited state of three‐electron atomic systems
Authors: Lissillour R. , Guerillot C. R.
Published: December 2004

The self‐correlated field method is based on the insertion in the group product wave function of pair functions built upon a set of correlated “local” functions and of “nonlocal” functions. This work is an application to three‐electron systems. The effects of the outer electron on the inner pair are studied. The total electronic energy and some intermediary results such as pair energies, Coulomb and exchange “correlated” integrals, are given. The results are always better than those given by conventional SCF computations and reach the same level of accuracy as those given by more laborious methods used in correlation studies.
Perturbation theories and wave functions for calculation of electronic polarizabilities application to DNA bases
Authors: Adams Steven , Nir Shlomo , Rein Robert
Published: December 2004

Three different forms of perturbation theories, variational perturbation, finite perturbation and second‐order, are evaluated regarding their value for calculation of electronic polarizabilities of small and intermediate size molecules. It is concluded that with the practical constraint of a small basis set the variational perturbation method is the most promising alternative for calculation of polarizabilities. For several small molecules, our calculated polarizabilities indicate that both IEHT and ab initio wave functions give values in close agreement with each other. Variational perturbation calculations of polarizabilities with IEHT wave functions also include the DNA bases.
Perturbation theory for degenerate states of atomic and molecular systems
Authors: Ivanov L. N. , Safronova U. I.
Published: December 2004

The first few terms of the perturbation expansions for the function and the energy shift of a degenerate state of an arbitrary quantum mechanical system are obtained using the adiabatic formula. It is shown how the expansion for the secular operator may be obtained from the expansion for the function. The results are used to calculate energies of the ground and some excited states and multiplet splittings of some beryllium‐like ions.
Coherent states and asymptotic behavior of the symmetric top wave functions
Authors: Doktorov E. V. , Malkin I. A. , Man'ko V. I.
Published: December 2004

Wave packets which may be considered as an analogue of the coherent states of the top are constructed. New integral representations are obtained for the D‐function; making use of those, various types of the asymptotic behaviour of the D‐function are obtained in the region of large quantum numbers.
Correlation effects in the PPP model of alternant π‐electronic systems: two‐point Padé approximant approach
Authors: ČÍŽek J. , Pellégatti A. , Paldus J.
Published: December 2004

A general procedure, based on the two‐point Padé approximant technique, is formulated, enabling an interpolation of the low‐lying energy levels of the PPP (Pariser–Parr–Pople) Hamiltonian over the divergency gap separating the asymptotic perturbation expansions in both strongly and weakly correlated limits. The methods for the determination of the first few terms of the perturbation expansions in both limits are also briefly outlined. The procedure is applied to the five lowest singlet energy levels of the PPP model of the benzene molecule and the results are compared with the exact solutions for this model. The advantages as well as the shortcoming of this approach are pointed out and illustrated on the model calculation for benzene. The applicability of this technique to larger π‐electronic systems is discussed and a feasible procedure for its implementation is formulated.
Adiabatic perturbation theory for the degenerate case. I. Perturbation of isolated degenerate or quasidegenerate levels
Authors: Dmitriev Yuri
Published: December 2004

Adiabatic formulae for secular operators and contracted Hamiltonians in an arbirary combination of degenerate or quasidegenerate subspaces are derived. A detailed consideration of the adiabatic limit in the power series is given, and “stability” of proper linear combinations with respect to a transformation produced by the Sα‐matrix is proved.
Energy of interaction of two hydrogen atoms using contracted Gaussian type valence‐bond wavefunctions
Authors: Olson Mark L. , Konowalow Daniel D.
Published: December 2004

Valence‐bond type wavefunctions based on contracted Gaussian atomic orbitals afford an adequate description of the potential of the ground 1Σ state of H2 for a wide range of internuclear separations. Semiempirical techniques for scaling the potential curve are evaluated. An efficient method for optimizing non‐linear variables in the wavefunctions is explored.
Iterative introduction of integral approximations with error bounds in SCF calculations
Authors: Jafri J. A. , Whitten J. L.
Published: December 2004

Another possible application of a previously reported approximation theory for electron repulsion integrals using rigorous error bounds is considered by incorporating the electron density matrix in the approximation scheme. Error bounds are set on the contribution of a given integral to the total energy for a given molecular wave‐function; the wave‐function is then refined cyclically and additional integrals are computed exactly if necessary until convergence is achieved.
Relativistic molecular spinors by generalized multiple scattering theory
Authors: Cartling Bo G. , Whitmore Douglas M.
Published: December 2004

A molecular one‐electron Dirac equation is derived by variation of a total energy density functional, whereby the one‐electron energies are ascribed a physical meaning. The multiple scattering formalism for molecular systems is relativistically generalized for the determination of molecular four‐component spinors. Optimal spinors and one‐electron energies for a finite basis set are derived by variation of a functional. The form of the secular equation is very similar to the nonrelativistic form. Using scattering theory, the quantities appearing in the secular equation are interpreted.
Perturbation theory with an approximate perturbation: The effect of charge overlap on interatomic interactions
Authors: Deal Walter J. , Young Ralph H.
Published: December 2004

The evaluation of interatomic interactions at large separations (R) typically involves neglecting electron exchange, treating the Coulomb interaction between atoms as a perturbation, neglecting third‐ and higher‐order energy contributions, and approximating the Coulomb interaction by a short expansion in spherical harmonics and, usually, powers of R−1. This last approximation, using an approximate perturbing Hamiltonian to evaluate a second‐order perturbed energy, is examined here; error bounds and a simple correction are introduced. Three illustrative applications to the HH+ interaction are given: the error incurred by truncating the spherical‐harmonic expansion is bounded, the R−1 expansion is corrected for the overlap of the “atomic” charge distributions, and the R−1 expansion is analyzed to see why it works as well as it does.
Singlet and triplet excited state electric dipole polarizabilities of conjugated hydrocarbons
Authors: Trsic M. , Sanhueza J. E. , Espinoza Ll.
Published: December 2004

First excited singlet and triplet electric dipole polarizabilities are reported. The π polarizability is calculated by means of a modified Rayleigh–Schrödinger perturbation theory and an SCF‐LCAO basis. The σ contribution is included by an additive scheme. The polarization of the σ electrons is partially accounted for through an empirical correction. Results compare satisfactorily with a configuration interaction perturbation calculation.
Comparative study of unconventional 1s basis functions for the 1Σ ground state of H2 and He
Authors: Leclerc Jean‐Claude
Published: December 2004

We investigated various nonstandard 1s basis functions (generalized Slater‐Gaussian, ellipsoidal Gaussian, floating spherical and ellipsoidal Gaussian, rational function, Hulthén approximation, two‐Slater‐type orbital, generalized Guillemin–Zener function, and various noninteger‐n elliptical orbitals) for approximating the 1Σ ground state of H2 and He2++. A CI trial wave‐function including Σg‐type MO's is adopted and molecular integrals are evaluated numerically. The energy improvement on the 1s STO is small except for noninteger‐n orbitals which closely approach the “SCF limit”.
Analysis of the half‐projected Hartree–Fock function: Density matrix, natural orbitals, and configuration interaction equivalence
Authors: Smeyers Yves. G. , Delgado‐Barrio G.
Published: December 2004

The half‐projected Hartree–Fock function for singlet states (HPHF) is analysed in terms of natural electronic configurations. For this purpose the HPHF spinless density matrix and its natural orbitals are first deduced.

It is found that the HPHF function does not contain any contribution from odd‐times excited configurations. It is seen in addition, in the case of the singlet ground states, this function is approximately equivalent to two closed‐shell configurations, although the nature of the excited one depends on the nuclear geometry. An example is given in the case of the LiH ground state. Finally, the application of this model for studying systems of more that two atoms is criticized.
A density matrix variational calculation for atomic Be
Authors: Garrod Claude , Fusco Mario A.
Published: December 2004

The ground‐state energy of the beryllium atom is calculated using a variational procedure in which the elements of the two‐body reduced density matrix (particle–particle matrix) are the variational parameters. It is shown that, for this problem and with the limited number of spin‐orbitals used, the trace condition and the simultaneous nonnegativity conditions on the particle–particle, the particle–hole, and the hole–hole matrices form a complete solution to the N‐representability problem.

The energy obtained is – 14.61425 a.u., practically identical to the value given by a configuration interaction calculation which uses the same states. The effects of weakening the nonnegativity conditions on each of the matrices in turn were also explored.
Spin‐free quantum chemistry. XVII. The Hückel–Hubbard theory and the Woodward–Hoffmann rules
Authors: Matsen F. A.
Published: December 2004

We have developed a many‐body version of Woodward–Hoffmann theory which is capable of rapid computation of π‐electronic surfaces. This theory, called the Hückel–Hubbard theory, employs Hückel parameters as reaction coordinates and the Hubbard parameter for electron repulsion. We apply it to the cis‐trans isomerization of ethylene and to several pericyclic reactions.
Spin‐Free quantum chemistry. XVIII. The unitary group formulation of the many‐electron problem
Authors: Matsen F. A.
Published: December 2004

The representation of an N‐electron Schrödinger Hamiltonian on an orthonormal, spin‐free (freon) orbital product space is exactly modeled by a second‐degree polynomial in the infinitesimal generators of the unitary group. Symmetry adaptation of the orbital product space with respect to the symmetric group yields Gel'fand states which provide base for irreducible represntations of the unitary group. These exist in closed form as, in consequence, does the representation of the model Hamiltonian in this same basis. We retain as physical only those states characterized by tableaux with no more than two columns for which the spin labelling is one‐half the difference in the lengths of the two columns. The unitary group formulation is equivalent to standard, number‐conserving, second‐quantized, many‐body theory.
Radial moment analysis of isovalent hybridization in N2
Authors: Aldrich Haven S. , Aiken John , Cusachs L. Chopin
Published: December 2004

A radial moment analysis has been performed for the Hartree–Fock molecular orbitals of the nitrogen molecule. The objective of the analysis was to determine the extent of isovalent hybridization in even and odd sigma molecular orbitals. The radial moment analysis for the LC‐SCF‐AO fragments of the 2σg, 2σu, and 3σg molecular orbitals substantiates Mulliken's earlier conjecture concerning promotion into 3s atomic orbitals for the 3σg molecular orbital. The concept of free isovalent hybridization is discussed in terms of the atomic orbital shape defined by the extracted moments.
A comparison of different DODS methods when the number of electrons increases
Authors: Mayer I. , Kertész M.
Published: December 2004

We have performed RHF, UHF, UHF with subsequent spin projection, and EHF calculations for the π‐electrons of some polyene chains of different lengths in order to investigate the relations among these methods when the number of electrons increases. Special attention is paid to the importance of spin projection for different energetic quantities.
On the hypervirial theorem and the scaling problem
Authors: Gopinathan M. S.
Published: December 2004

It is shown that wave‐functions obtained by a limited number of off‐diagonal hypervirial relations are often out of scale. Optimum scaling of these functions so as to satisfy the virial theorem gives highly improved wave‐functions and expectation values. The harmonic oscillator problem is treated as an example.
Molecular orbital interpretation of isomer shifts and quadrupole splitting of the mössbauer γ‐line in the compounds of Antimony and Tin
Authors: Kothekar V.
Published: December 2004

The electronic parameters in the Mössbauer spectroscopy, electric field gradient (EFG), and change in the charge density at the nucleus site Δψ2(0) are evaluated on the basis of the CNDO/II method for various compounds of antimony and tin and compared with experimental data. The correlation between the isomer shift adn the quadrupole splitting with these electronic parameters is used to evaluate δR/R and Q and compared with the results of other workers. Different methods for the theoretical interpretation of the Mössbauer parameters are discussed. It was found that Molecular Orbital (MO) methods give quite reliable results for antimony and tin compounds and can be used for elucidating the bonding mechanism in these compounds.
On the symmetry of filled shells
Authors: Beebe Nelson H. F.
Published: December 2004

A simple proof of the theorem that completely filled shells of fermions do not contain any symmetry component other than the totally symmetric representation is given.
Stability, continuity, and symmetry of variational wave‐functions
Authors: Moiseyev N. , Katriel J.
Published: December 2004

Interrelations between the local and the global aspects of the stability, continuity, and symmetry properties of variational wave‐functions are discussed. The spherical limit of one‐electron diatomic molecules and the Hartree–Fock approximation of the ground state of the two‐electron atom are shown to exhibit the various concepts involved in an ab initio, yet sufficiently simple, manner.
Complex molecular orbital method: Open‐shell theory
Authors: Hendeković Josip
Published: December 2004

A single‐determinant open‐shell formalism for complex molecular orbitals is developed. An iterative algorithm for solving the resulting secular equations is constructed. It is based on a sequence of similarity transformations and matrix triangularizations.
Halogénures Alcalins: Un Modèle Incluant une Délocalisation à Courte Distance Application à la Stabilité Relative des Divers Arrangements Cristallins
Authors: Marinelli Andre Julg Et Francis
Published: December 2004

The introduction of symmetry‐adapted hybrid atomic orbitals on the metallic atoms allows us to divide the crystal into elementary cells which contain 8 valence electrons each. These cells are described by linear combinations of the halogen valence shell s and p orbitals and the hybrid orbitals of the nearest metallic atoms which point to the halogen. The electronic delocalization of the halogen ions is very weak (⩽0.02) for: LiF, NaF, KF, LiCl, NaCI, and KCI. The cell energy in the crystal is obtained by using a first‐order perturbative treatment. In agreement with experiment, the f.c.c. type is found more stable than the b.c.c. or the blende type.
A study of Löwdin's criterion for completeness of basis sets
Authors: Leopold J. G. , Cohen M. , Katriel J.
Published: December 2004

Löwdin has formulated a useful criterion for testing the completeness of an expansion basis set. From this criterion one may obtain an incompleteness coefficient for a truncated (finite) basis set. We have investigated the significance of this incompleteness coefficient for some of the basis sets we have used in our recent calculations of bounds to quantum mechanical properties. The similarity of the convergence properties between our bounds and the incompleteness coefficient suggests that Löwdin's criterion is likely to be useful in practice.
Errors in molecular integrals: An influence on RHF energy values
Authors: Stepanov Nikolaj F. , Pupyshev Vladimir I.
Published: December 2004

The influence of errors in molecular integrals on the calculated RHF energy values is considered for two models which correspond to round‐off and shift errors. The energy variations induced by errors in elements of one‐ and two‐electron matrices and the overlap matrix are represented in a quadratic approximation and the same degree of accuracy is maintained for mean values and standard deviations. The formulas given point out that mean values are less than zero when some of the errors are non‐shifted. Special care is required when Gaussian lobe functions are used.
Cubic harmonics in Cartesian coordinates
Authors: Kwiatkowski T. , Olszewski S. , Wierzbicki A.
Published: December 2004

A full set of harmonics which are at the basis of all irreducible representations of the cubic point group and having order l ⩽ 16 has been calculated in terms of Cartesian coordinates. Due to their complication, former calculations of harmonics in Cartesian coordinates for half of the irreducible representations did not exceed l = 6. The method presented in this paper is a modification of that originally given by Von der Lage and Bethe; it can be readily applied to the calculation of harmonics of arbitrary order for any irreducible representation of the cubic point group.
Reduced local energy as a criterion for the accuracy of approximate H2 wave‐functions
Authors: Javor Frank , Thomas Gerald F. , Rothstein Stuart M.
Published: December 2004

The goodness of the local fit of an approximate wave‐function, \documentclass{article}\pagestyle{empty}\begin{document}$ \tilde \psi $\end{document}, to the exact function, ψ0, is \documentclass{article}\pagestyle{empty}\begin{document}$ |\tilde \psi - \psi _0 | $\end{document}. From this quantity the global accuracy of \documentclass{article}\pagestyle{empty}\begin{document}$ \tilde \psi $\end{document} is defined and a “working supposition” is presented, which quantitatively relates the global accuracy to the accuracy of expectation values. Two criteria based on the accuracy of the reduced local energy and the density respectively, are presented as alternatives to \documentclass{article}\pagestyle{empty}\begin{document}$ |\tilde \psi - \psi _0 | $\end{document}. The relative global accuracies of eight wave‐functions for H2 are determined using the two criteria. The ‘working supposition’ is applied and predictions are made concerning the relative accuracies of the expectation values of the following operators: z2, r2, x2 + y2, 3z2 −; r2, ξ, r, r, and EL (the reduced local energy). The success rate is high (>90%) except for those operators which are sensitive to interelectron coordinates or derivatives of the wave‐function.
Discontinuous approximate molecular electronic wave‐functions
Authors: Stuebing Edward W. , Weare John H. , Parr Robert G.
Published: December 2004

Following Kohn (reference 4), Schlosser and Marcus (reference 3), and Weare and Parr (reference 2), an energy functional is defined for a molecular problem which is stationary in the neighborhood of the exact solution and permits the use of trial functions that are discontinuous. The functional differs from the functional of the standard Rayleigh–Ritz method in the replacement of the usual kinetic energy operators T̂(μ) with operators T̂′(μ) = T̂(μ) + Î(μ), where Î(μ) generates contributions from surfaces of nonsmooth behavior. If one uses the ∇Ψ · ∇Ψ way of writing the usual kinetic energy contributions, one must add surface integrals of the product of the average of ∇Ψ and the change of ∇Ψ across surfaces of discontinuity.
A relationship between the sizes and energies of localized molecular orbitals. I. A study of selected first‐row hydrides
Authors: Daudel R. , Goddard J. D. , Csizmadia I. G.
Published: December 2004

Ab initio calculations have been performed on selected first‐row hydrides with a large Gaussian basis set. Energy localized molecular orbitals (LMO'S) were computed and analysed in terms of their sizes and shapes. The total molecular electronic energy was partitioned into components which may be associated with an MO, and the relationship between the sizes and energies of such orbitals was examined. It was found that a simple energy–size relationship exists for core LMO'S but only approximately holds for bond LMO'S.
A semi‐empirical MO theory for ionization potentials and electron affinities
Authors: Selsby R. G. , Machin C. , Hernandez M. L.
Published: December 2004

A method for calculating the vertical ionization potentials and electron affinities according to their fundamental definition as differences between energies of the singlet ground and doublet ionized states is developed for cyclic hydrocarbons. The method adopts a new approach based on the central idea of a recent ab initio IP and EA calculation in which orbital exponents are optimized for both ground and ionized states. Hence, all the semi‐empirical parameters of the MO theory are written as functions of the effective nuclear charge which, in turn, is made self‐consistent with the molecular electronic charge distribution of the species. Although the MO theory is developed in the π electron approximation, the changes in the σ electron density, resulting from the loss or gain of a π electron, are explicitly considered in the calculation. The theory is compared to the earlier work of Hoyland and Goodman and tested against the first five polyacenes and on the condensed ring aromatics phenanthrene, pyrene, and perylene. Except for perylene, the results are in close agreement with the latest photoelectron spectroscopic measurements.
Accurate Thomas–Fermi–Dirac calculations for diatomic systems
Authors: Yonei K. , Goodisman J.
Published: December 2004

The Thomas–Fermi–Dirac equation for the electron density in a homonuclear diatomic system is solved numerically. The problems arising and methods of dealing with them are discussed and attention is given to the accuracy of the calculated energies. Comparisons are made to previously published work employing approximations, permitting a discussion of their utility.
Rotational invariance of INDO theories including d‐orbitals into the basis set
Authors: Figeys H. P. , Geerlings P. , Van Alsenoy C.
Published: December 2004

It is proved that in general the INDO approximation to the full Roothaan theory does not lead to expressions which are invariant under a rotation of local atomic axes. However, when only s‐ and p‐functions are used in the atomic basis set, the equations obtained are invariant due to the special properties of the p‐functions. When d‐orbitals are included into the basis set, rotational invariance is lost but can be restored if a supplementary approximation is introduced.
Atomic SCF loge localized wave functions
Authors: Ludeña Eduardo V.
Published: December 2004

We report in this work SCF atomic calculations for Li, Be, B, C, and Ne using a basis set of completely loge‐localized functions. For these second row atoms the total volume R3 was partitioned into a spherical loge of radius R and its volume complement. The loge‐localized basis functions were constructed as a product of Slater‐type orbitals and a cut‐off factor. The energy values obtained differ significantly from the Hartree–Fock ones indicating that the delocalization effects—not included in these calculations—are important.
Potential energy curves for NiH and NiH2
Authors: Guse M. P. , Blint R. J. , Kunz A. B.
Published: December 2004

The potential energy curves for the NiH and linear HNiH molecules resulting from the 3d84s2 and 3d94s configuration of nickel are calculated using the unrestricted Hartree–Fock and perfect pairing generalized valence bond methods. NiH bonding in the 3d84s2 configuration is by means of an sp hybrid orbital which comes from the 4s2 shell leaving a singly occupied nonbonding orbital free to bond to another hydrogen atom. The bond to the 3d94s configuration contains primarily the 4s orbital leaving an empty orbital in the nickel 3d shell which in turn bonds very weakly with another hydrogen. These results are compared to similar studies of the hydrogen atom on Sc, Mn and Cu and some implications for hydrocarbon catalysis are considered.
A study of the convergence in iterative natural orbital procedures
Authors: Thunemann K. H. , Römelt J. , Peyerimhoff S. D. , Buenker R. J.
Published: December 2004

A series of five different Iterative Natural Orbital (INO) procedures are tested for the ground state of water and are compared on the basis of their respective convergence properties. The choice of configuration space employed in these methods is shown to be a key factor in determining the results of such calculations. If the CI space is generated by taking all single excitations with respect to a series of dominant or reference configurations, it is concluded that the practice of varying such generating species at each iteration is highly desirable. In general the choice of the configuration space is found to be much more important than the attainment of strict NO convergence, whereby experience indicates that inclusion of all singly and doubly excited configurations (or at least a select subset thereof) relative to a series of dominant configurations provides the most efficient means of approximating the true NOS of a given system within the general INO framework.