bluuebunny/crossref_metadata_2025 huggingface dataset:
Recherches en vue de la synthèse de barbiturates organostanniques
Authors: Maire Jean‐Claude , Van Rietschoten Jurphaas
Published: December 2004

Triphenyl and tributyltin hydrides have been found to add to the terminal double bond of unsaturated ethyl malonates to give organotin substituted ethyl malonates. Attempted cyclisation of the latter into barbituric compounds failed.
Photochemische Umwandlungen, 41 [1] 3ω → 3 π‐Isomerisierungen von Monohetero‐trishomobenzol‐derivaten. Vorläufige mitteilung
Authors: Prinzbach H. , Stusche D.
Published: December 2004

The all‐cis‐oxa‐ and azatrishomobenzene diesters 4a and 4b resp. undergo thermally a very clean 3ω → 3π isomerization reaction yielding the heterocyclonona‐2, 5, 8‐triene derivatives 6a and 6b resp. (Ea = 27.4 and 26.5 kcal/mole). In contrast, the cis, cis, trans‐oxatrishomobenzene diester 9 is stable up to 170°. Some applications and limitations of this 3ω → 3π‐route to iso‐ and heterocyclononatriene derivatives are discussed.
Quantum‐mechanical treatment of molecules. I. Calculations of the potential energy curves and molecular constants of the ground and ionized states of N2
Authors: Sahni R. C. , Sawhney B. C.
Published: December 2004

The self‐consistent‐field molecular‐orbital method in LCAO (linear combination of atomic orbitals) approximation is applied to the ground and three ionized states of N2 at a number of internuclear distances for the computation of the potential energy curves. In these calculations both the linear coefficients and the screening constants of the atomic orbitals have been optimized. The molecular constants ωe, ωexe, Be, αe, and Re have also been calculated for the above states from the computed potential energy curves. The computed spectral results are compared with the experimental data as well as with the results reported by others from ab initio calculations.
Energy eigenvalue spectroscopy
Authors: Blinder S. M.
Published: December 2004

A wave function which is other than an exact eigenfunction, if it obeys appropriate analytical conditions, can be considered to represent the initial configuration of a nonstationary state. In the course of its subsequent time development the quantum system exhibits implicitly its entire eigenvalue spectrum. A method based, in principle, on Fourier analysis of the evolving quantum system is applied to the direct calculation of the energy eigenvalue spectrum. The spectral function is expressed as a moment expansion, in terms of expectation values of powers of the Hamiltonian. When the expansion is truncated, as it must be in any practical application, the corresponding spectral function represents a smeared‐out eigenvalue spectrum. An alternative approximation leads to the quantum‐mechanical method of moments. As the number of terms is increased, the computed spectrum becomes sharper and more accurate. In certain cases the moment expansion can be circumvented, if the action of the evolution operator can be evaluated in closed form. This is equivalent to finding some solution of the time‐dependent Schrödinger equation. The various methods of eigenvalue spectroscopy are applied to the harmonic oscillator.
Spectral analysis of the Green's function
Authors: Blinder S. M.
Published: December 2004

The energy eigenvalue spectrum for a conservative dynamical system is contained implicitly in its Green's function. It becomes explicit in the Fourier transform of either the Green's function or its trace. The trace exists only when the spectrum is entirely discrete. Applications are made to the free particle, the linear harmonic oscillator, and the hydrogen atom. In the latter two cases determination of the Green's function can be considerably simplified by similarity transformations on the Hamiltonian operator.
On the choice and definition of atomic‐orbital bases. I. General considerations; promotion and hybridization; electric dipole moments
Authors: Del Re Giuseppe
Published: December 2004

After a brief discussion of the physical significance of the choice of the basis in molecular calculations, the nature and definition of an atomic‐orbital basis for use in limited calculations is discussed, in view of the possibility of replacing, say, ordinary 2s and 2p Slater orbitals by appropriate hybridized‐promoted atomic orbitals. It is indicated that, if the orbitals must be defined in connection with a given interpretation scheme for the behavior of molecules, hybridization and promotion may be necessary.

The two kinds of conditions one may wish to impose on a restricted atomic‐orbital set are explicitly considered. The first is that the atomic orbitals should be hybrids directed along the bonds and at the same time satisfy the maximum overlap criterion; the other is the requirement that the atomic orbitals should be such that the electric dipole moment of a polyatomic molecule described in terms of a semiempirical bond‐orbital scheme should be expressed as the dipole moment of the system of bond charges located at the nuclei.

The latter condition is treated in detail, showing that it implies a cancellation of atomic and overlap moments. The equations defining the atomic orbitals satisfying the condition in question are given.

In the course of the mathematical treatment some general results concerning the expression of the dipole moment of a molecule and the definition of net atomic charges are given, showing that, for systems where overlap integrals are low, the atomic populations can be taken as sums of the squares of the coefficients of orthogonalized atomic orbitals.

Applications of the results will be presented in part II.
Transition probabilities for the ionization of N2, O2, NO and CO molecules
Authors: Jain D. C. , Sahni R. C.
Published: December 2004

Franck–Condon factors are presented for the normal and stable isotope‐labelled N2, O2, NO and CO molecules for transitions to the observed ionized states by using the Rydberg–Klein–Rees (RKR) potential energy curves of the various electronic states involved. It has been observed that for some transitions, the Franck–Condon factors based on the RKR potential energy curves differ appreciably from those based on the Morse potential function. The effect of isotopic substitution on the transition probabilities is also quite significant in a number of cases.
On the total number of atomic assocations of an N‐atomic molecule
Authors: Schnupp Peter
Published: December 2004

The total number of different possible atomic associations of an N‐atomic molecule lies between a value PN (all N atoms identical) and AN (all atoms different). PN may be obtained reducing the problem to a classical problem in number theory. AN may be given as an operator expression which can be evaluated using the non‐numerical programming language FORMAC. The relation PN ≦ 2N–1 ≦ AN gives a rough estimate for the orders of magnitude to be expected. The number Z of all atomic associations of grade (number of “partial unions”) G for N atoms can be computed using a recursive formula.
X‐ray and electron scattering factors for many‐electron atomic system
Authors: Benesch Robert , Malli Gulzari
Published: December 2004

Analytical expressions are developed for the x‐ray and electron scattering factors for a many‐electron atomic system when the single configuration wave function of the system is written as a sum of Slater determinants of spin orbitals. The radial part of the orbital is expanded in terms of Slater‐type orbitals (STO's). The expressions so developed have been used to calculate the coherent and incoherent x‐ray and electron scattering factors and intensities for all the neutral atoms up to krypton (Z = 36) and for some positive and negative ions of chemical interest. The results obtained are used to test the value of Hartree–Fock wave functions for the evaluation of “one‐electron properties” of many‐electron atomic systems.
Physical nature of the chemical bond II. Valence atomic orbital and energy partitioning studies of linear nitriles
Authors: Moffat J. B. , Popkie H. E.
Published: December 2004

The valence atomic orbitals (VAO's) of several linear nitriles are determined using non‐empirical SCF–LCAO–MO wave functions expanded in a minimal (CN−, HCN, FCN, C2N2), double‐zeta (CN−, HCN), or double‐zeta + polarization (HCN) basis of Slater atomic orbitals (AO's). The molecular energy of each system (except the double‐zeta + polarization HCN system) is partitioned according to the procedure of Ruedenberg to obtain numerical values of nitrile C and N atomic and CN bond components of the energy. In addition, the nitrile results are compared with minimal AO basis results obtained previously by other authors for homonuclear diatomics, diatomic hydrides and H2O. The numerical data are used to test the internal self‐consistency of the various definitions entering the partitioning method, i.e. whether or not analogous quantities assume similar values in chemically similar situations.

The analysis of nitrile SCF–MO wave functions in terms of the set of VAO's characteristic of the system under consideration is shown to be a promising approach to the problem of extracting useful information from the wave functions. In general, numerical results for the nitrile systems studied are fairly consistent with the concepts on which the partitioning method is based: promotion, quasi‐classical interaction, sharing penetration, sharing interference and charge transfer. However, the VAO expansions for several energy components need to be investigated further and possibly revised.
Effects of complex‐valued electronic wave functions on nuclear motions
Authors: Coulson C. A. , Gerber R. B.
Published: December 2004

Moleculer species and colliding groups of atoms are considered for which the electronic wave functions are complex‐valued, having arguments that depend parametrically on the nuclear coordinates.

The effective Hamiltonian for nuclear motions in the adiabatic approximation that arises in the present case differs from the ordinary Born–Oppeneheimer Hamiltonian, the latter being obtained when restriction to real‐valued electronic functions is made.

The asymptotic boundary conditions imposed in collision theory lead to in‐ and out‐ states [8], and hence to complex‐valued wave functions in the coordinate representation. The study of the influence of electron–molecule scattering on nuclear motions therefore necessitates the use of the new effective Hamiltonian, which leads to results differing from those predicted on the basis of the Born–Oppenheimer operator. It is shown that momentum‐dependent potentials occurring in the new Hamiltonian might cause “distortions” to the vibrational patterns of some electron–molecule metastable states. Also, these terms can give rise to non‐Born–Oppenheimer resonances when motions in an internuclear coordinate become unbounded. We derive expressions for the relevant level widths and line shapes, showing them to be subject to an isotope effect.

Even when real‐valued electronic functions may be used, the selections of complex‐valued functions in their linear span is still optional. Although exact treatments lead to the same results in both real and complex cases we show how the choice of the argument of the electronic function to be non‐zero and dependent on nuclear coordinates may be useful for the application of certain approximation schemes. It is demonstrated that for certain systems a suitable choice of the argument assures convergence when the related Lippmann–Schwinger Equation is iterated. It is also shown that in this way an nth order term in the series expansion of the T matrix [8] for moleculer systems can be made negligibly small.
A configuration interaction study of the four lowest 1∑+ states of the LiH molecule
Authors: Brown Richard E. , Shull Harrison
Published: December 2004

A configuration interaction study was completed on the 1∑+ states of the LiH molecule using a nonorthogonal one‐electron basis in elliptical coordinates. A few wave functions with highly optimized parameters were obtained for the X1∑+ and A1∑+ states and combined to construct a larger wave function which gave improved results for both states over a wide range of R values. The third and fourth roots are also reported since the wave function is extensive enough to give good upper bounds for the two states. Calculations were completed for 34 values R in the range 1 ≤ R ≤ 10 bohr (b).

The calculated X1∑+ curve has a minimum at Re = 3.060b (3.015b), with E(Re) = −8.0556 Hartree (H) (−8.0704), μ(Re) = −5.89 debye (d) (−5.88d) and μ/(R dμ/dR)|Re = 1.75 (1.80 ± 0.3). For the A1∑+ state, Re = 4.928b (4.906b), E(Re) = −7.9372H(−7.9496H), μ(Re) = +3.96d and μ/(R dμ/dR)|Re = −‐0.471. The values in parentheses are experimental results for comparison. The numerical vibrational and rotational analysis agreed well with experiment for both states. The A1∑+ state exhibited a pronounced negative anharmonicity. Both states show strong interaction of three zeroth‐order configurations, the nature of which changes considerably with R.

The thus far unobserved second excited state has two minima, a metastable one at R = 3.70b and another at R ≈ 10.00b. The third excited state also appears to have a minimum at R ≈ 7.00b.
On the least squares procedure for atomic calculations
Authors: Lloyd M. H. , Delves L. M.
Published: December 2004

We discuss the properties of one version of the least squares (LS) method for the solution of the Schrödinger equation. These properties are exemplified by a number of calculations on the n1S and n3S states of helium, up to principal quantum number three, which are very much more accurate than previous LS calculations on helium. Particular attention is paid to the convergence properties of the LS procedure and we compare it with the simpler Rayleigh–Ritz (RR) procedure in the case when the RR matrix elements are evaluated numerically over the same quadrature mesh as used in the LS procedure. We conclude that although the LS procedure is capable of high accuracy it has no advantages which would justify its sole use in place of the RR procedure. However, it does have some advantages when used in conjunction with RR, in that it gives an estimate of the numerical accuracy of the RR energies.
A minimum principle for atomic systems allowing the use of discontinuous wave functions
Authors: Hall G. G. , Hyslop J. , Rees D.
Published: December 2004

In this paper a variational principle proposed by Hall [1] is shown to be a minimum principle for coulombic systems. Into this principle it is possible to admit a larger class of trial wave functions than is possible in the conventional variational treatment, including wave functions with discontinuities. It is further shown that the upper bounds given by this treatment are always at least as good as that given by the Rayleigh–Ritz method.

The theory is then applied to the hydrogen atom and upper bounds to the energy are calculated for various “cutoff” wave functions. It is usually possible to define an optimum “cut off” distance which minimizes the upper bound.
Theory of biorbitals. Study of conjugated systems in their ground and excited electronic states
Authors: Bessis G. , Espagnet P. , Bratož S.
Published: December 2004

The biorbital theory called also “identical geminals theory” is applied to the study of a number of conjugated molecules. All basic integrals are determined by means of the Pariser–Parr–Pople procedure. The biorbital theory reproduces about 40 per cent of the correlation energy of the ground state of the molecule; this number is raised to about 70 per cent for the lowest triplet state. The low lying excited states are well represented from the point of view of transition energy as well as from the point of view of symmetry. The occupation number matrix and the charge‐bond order matrix are defined and discussed. The overall chemical description of conjugated molecules produced by the biorbital theory is similar to that produced by other theories of electronic structure of molecules. It is concluded that the biorbital theory provides a description the quality of which is, roughly speaking, about half way between those provided by the SCF‐MO and complete CI theories, respectively.
Some calculations on the hydrogen bond: The system LiH ⃛ Li+
Authors: Shaw G.
Published: December 2004

Some calculations are presented on the hydrogen bond using a perturbation theory approach. Results confirm indications of earlier work that perturbation theory is capable of giving a reasonable description of hydrogen bonded systems.
The symmetry of molecular polarization tensors
Authors: Boyle L. L.
Published: December 2004

Polarization tensors are discussed in terms of their intrinsic symmetry group which is a direct product of the point group and the subgroup of the permutation group relevant to the experiment. The study of these latter groups is simplified by use of the isomorphism with certain point groups and permutations of suffixes can be visualized by rotations and reflections of the vertices of various objects in space. The approach unites the previous treatments and provides a means of constructing the bases for the irreducible tensor components. The difficulties introduced by Laplace's equation are explained and the information obtainable from induced birefringence experiments (Kerr and Cotton–Mouton effects) discussed for various systems.
A multi‐configuration LCAO–MO study for complex unsaturated molecules. II. Application to the benzene cation
Authors: Nakayama M. , I'Haya Y. J.
Published: December 2004

The method of the MC–LCAO–MO approach, described in the preceding paper, is further applied to the benzene cation. Through the iteration process the π‐electron energies and the molecular shapes are computed for the ground and two lowest excited states of the cation in both D6h and D2h geometries. A remarkable fact obtained is that a comparatively small variation of the geometrical structure (c. 0.010 – 0.013 Å bond length difference) brings about a considerable change of the energy value (c. 0.85 – 1.25 eV).

The π‐electronic excitation energies obtained from the iteration process are compared with the transition energies calculated from the usual method in which the structures of the excited states are assumed to be the same as the corresponding ground state structures. The difference in the excitation energy between the cation and the anion, and the CI effect on the excited states, are discussed. It is found that the doubly excited configurations play an important role in CI, which is somewhat different from that of the singly excited configurations. The stabilization energy due to the Jahn–Teller distortion is estimated for the ground state of the cation.
Study of the electronic structure of alternant radicals by the DODS method
Authors: Kruglyak Yuri A. , Ukrainsky I. I.
Published: December 2004

The polarization of closed shells in an alternant radical due to the field of its unpaired electron is discussed. It is shown that the Hartree–Fock solution is unstable relative to a small perturbation caused by polarization of closed shells in a long polyene radical. Its ground state is found to be antiferromagnetic with a forbidden zone in the spectra of one‐particle excitations.
Group‐theoretical method for determining permitted terms of the electronic states of polyatomic molecules taking account of spin‐orbit interaction
Authors: Men A. N. , Cherepanov V. I. , Farberov D. S. , Mitrofanov V. Ja. , Chufarov Gr. I.
Published: December 2004

A group‐theoretical method for determining the permitted states of polyatomic molecules, proceeding from given atomic states in which the spin‐orbit interaction has been taken into account, is proposed.
Self‐consistent pseudo‐eigenvalue equations in parametric charge‐dependent MO methods
Authors: Karlsson Göran
Published: December 2004

Self‐consistent pseudo‐eigenvalue equations are explicitly derived for the iterative extended Hückel method with use of the minimum‐energy criterion. It is shown that inclusion of the overlap matrix in the iterative procedure gives equations that are too complicated for the simple model under consideration. An expression for the total energy is derived, and it is shown that if the eigenvalues of the pseudo‐eigenvalue equations are interpreted as ionization potentials and electron affinities, then the empirical parameters of the Hamiltonian matrix must be reinterpreted. The connection with the Hartree–Fock equations is mentioned. It is proposed that minimizing the energy in the VESCF method should be done in a manner similar to the one used in the iterative Hückel methods. Numerical applications to benzene and pyridine have been made.
Self‐consistent calculation of excited 1P state wave functions of atoms
Authors: Mukherjee P. K. , Sengupta S. , Mukherji A.
Published: December 2004

In an earlier paper (Bibliography [1]) it has been shown that approximate representations of excited states of atoms can be obtained from the study of the singularities in the dynamic polarizability. Starting with these wave functions a more accurate calculation of the excited states in the Hartree–Fock scheme can be made by a perturbation treatment. The resulting wave functions yield significantly improved energy values. The 21P, 31P and 41P states of the He sequence up to C4+ are studied. The expectation values of a number of operators are calculated. The results obtained by the present method compare favourably with other elaborate calculations.
Die Konvergenz der Brillouin–Wigner Störungsrechnung
Authors: Ahlrichs Reinhart
Published: December 2004

It is the aim of the present paper to give a mathematically oriented foundation of BW‐perturbation theory, which is along the lines of Kato's previous work for RS‐perturbation theory. For this purpose we firstly derive the expressions of BW‐perturbation theory by the use of the contour integral method (Kap. I). In Kap. II sufficient criteria for the convergence of BW‐perturbation theory are derived and applied to the 1/Z‐expansion of the isoelectronic series of the He atom. The characteristic differences of the derivation and convergence properties of the two different kinds of perturbation theory are discussed in detail.
Self‐consistent group calculations on polyatomic molecules V. Molecules with a double or triple bond
Authors: Klessinger Martin
Published: December 2004

SCGF calculations are reported for the ground state of ethylene, formaldehyde, acetylene and hydrogen cyanide. A minimum basis of contracted Gaussians was used and optimum hybridization was determined for each of the molecules by systematic variation of the hybridization parameters until the total electronic energy was a minimum. Properties of CH bonds as well as CC, CO and CN σ and π bonds are discussed in some detail. The results show that the assumption of transferable framework integrals β, basic to all semiempirical methods of calculating molecular wave functions, is strictly justified within the SCGF method.
Solution of the Hartree–Fock problem by expansion onto nested bases
Authors: Marron M. T. , Handy N. C. , Parr R. G. , Silverstone H. J.
Published: December 2004

A method for solving the Hartree–Fock problem in a finite basis set is derived, which permits each orbital to be expanded in a different basis. If the basis set for each orbital ϕi contains the basis functions for the preceding orbitals, ϕi−1, ϕi−2,… ϕ1, then the ϕi form an orthonormal set. One advantage over the standard Hartree–Fock method is that a different long range behavior for each orbital, as for example is required in the Hartree–Fock‐Slater method, can be forced. A calculation on the ground state of beryllium is performed using the nested procedure. Very little energy is lost because of nesting, and the node in the 1s orbital disappears.
The theoretical treatment of the Li2‐molecule
Authors: Gombás P. , Szondy T.
Published: December 2004

The Li2 molecule is treated both with the method of moments and with the method of energy variation for the following distances of the nuclei R = 2aH, 4aH, 6aH, 8aH and 10aH. The calculations have been performed with the Hartree–Fock method (HF) and with the method of pseudo‐potentials (PSP). The results show that the HF method and PSP method lead practically to the same result. This may be important in the treatment of more complicated molecules.
Gaussian molecular orbital calculations of the barrier to internal rotation in the ethyl cation
Authors: Massa L. J. , Ehrenson S. , Wolfsberg M.
Published: December 2004

Extended Gaussian orbital basis set calculations have been carried out on an assumed staggered and eclipsed classical geometrical configuration of C2H. The best total energies obtained for these geometries were −78.170692 a.u. and −78.170674 a.u. respectively, corresponding to a barrier to internal rotation of 1.8 × 10−5 a.u. or 11 kcal/mole. An analysis of the charge density matrix indicates that charge is distributed in these molecules in a manner consistent with the concept of hyperconjugation.
Gaussian expansion method for molecular integrals of molecular properties
Authors: Matsuoka Osamu
Published: December 2004

The finite Gaussian Expansion method for molecular integrals proposed by Taketa, O‐ohata and Huzinaga has been extended to the integrals of molecular properties. The integral formulas of so‐called moment, field and field gradient integrals have been derived. It has been numerically shown that in order to evaluate the field and the field gradient integrals based on Slater type orbitals, eight‐ or ten‐term Gaussian expansions are sufficient but this method fails to attain sufficient effective numbers for the moment integrals.
Configuration interaction study of X‐ray and fast electron scattering factors for light atomic systems
Authors: Tanaka Kiyoshi , Sasaki Fukashi
Published: December 2004

A study of X‐ray and fast electron scattering by light atoms and ions has been carried out in the first Born approximation. Coherent and incoherent scattering factors calculated with configuration interaction wave functions are compared with those obtained with Hartree–Fock wave functions. These configuration interaction wave functions involve only L‐shell correlation. It is shown that the changes in the coherent scattering factors due to configuration interaction are not negligible and that the electron correlation effects on the incoherent scattering factors are important. Tables of coherent and incoherent scattering factors for light atomic systems are given.
Analysis of reduced density matrices in the coordinate representation. I. Definitions and basic formulas
Authors: Sperber Gunnar
Published: December 2004

The probability interpretation of density matrics is reviewed and certain quantities suggested for study by means of diagrams. The case of a “spin‐symmetric ensemble” is further discussed.
Irreducible tensor operator methods in strong‐field coupling
Authors: König E. , Kremer S.
Published: December 2004

The algebra of irreducible tensor operators is developed in the strong‐field coupling case. The method is of general applicability to any symmetry group G including nonsimply reducible groups and mixed configurations. The Wigner–Eckart theorem is given for irreducible tensor operators as well as for their Kronecker and scalar products. The expressions required for the calculation of ligand field splitting, Coulomb repulsion, spin–orbit interaction, and Zeeman effect are given in detail. Applications to problems in the spectroscopy and magnetism of transition metal compounds are referred to.
About the relationship between some necessary conditions for N‐representability
Authors: Kummer H.
Published: December 2004

The relationship between well known necessary conditions for N‐representability of the reduced two‐density matrix is investigated. It is shown that the G‐condition implies two conditions of the operator endomorphism type: the C‐ and the B‐condition.
A comparison of geometric methods with other methods for the characterization of density matrices
Authors: Harriman John E.
Published: December 2004

Some recently developed geometric methods for characterizing the subset of density matrices within the space of Hermitian matrices are compared with methods commonly used for the approximate characterization of reduced density matrices. The decomposition of a density matrix into components in terms of the reducing basis set is compared with decomposition in terms of representations of U(r).
Transition moment closure tests for ethylene
Authors: Martin Richard L. , McMurchie Larry E. , Davidson Ernest R.
Published: December 2004

The completeness of a basis set for ethylene is examined relative to its ability to describe transition moments. The double zeta (Dunning contraction) plus polarization plus Rydberg Cartesian Gaussian set does much better for length than for velocity moments. An attempt is made to interpret the transition moment sums for the occupied orbitals.
Electronic structure of excimer molecular lasers
Authors: Michels H. H. , Hobbs R. H. , Wright L. A. , Connolly J. W. D.
Published: December 2004

The electronic structure, potential energy curves, and radiative transition probabilities of excimer systems have been examined using quantum mechanical methods. These molecules are characterized by repulsive or weakly bound ground state potential curves and by bound, strongly ionic, or Rydberg, excited states. They constitute a very interesting class of molecules which offer the possibility for high power, high efficiency UV laser operation. Calculations have been carried out using the density functional SCF‐Xα method, modified extensively to correct for well known errors arising from approximations to the potential and exchange terms. A limited number of ab initio calculations were also carried out for comparison purposes. For the ArF system we find that the lowest excited ionic state has symmetry 2∑, and that the dominant laser transition observed at 1933 Å should be assigned to B 2∑ → X 2∑. The C 2Π3/2 → X 2∑ transition is calculated to be two orders of magnitude smaller in emission intensity than the dominant transition, thus ruling out this assignment for the observed laser line in ArF. Preliminary calculations carried out for Ar2F indicate that the bound upper ionic state has 2B2 symmetry and that the most probable ground state also has 2B2 symmetry. This polyatomic system is predicted to exhibit a broadband emission spectrum with a relatively long radiative lifetime.
Hartree‐like methods in electronic structure theory
Authors: Harris Frank E.
Published: December 2004

We consider the “Hartree Problem,” here defined as the problem of finding the orthogonal one‐electron states which in a single determinant minimize the electronic energy, excluding exchange contributions. These states may provide a useful basis for correlation‐energy studies. It is shown how the “Hartree Problem,” although superficially not of pseudoeigenvalue form, can nevertheless be cast in such a form and solved by an iterative diagonalization process.
Automatic geometry optimization for molecules with d orbitals. I. General analytic formulas for derivatives of slater orbitals
Authors: Beran S. , Slanina Z. , Zidarov D. C.
Published: December 2004

General analytic formulas for derivatives of real Slater orbitals with respect to the Cartesian coordinates x and y have been derived. The application of this result to molecular geometry optimization or to the construction of a force constant matrix is briefly discussed.
Notes on density matrix model for coherent x‐ray diffraction
Authors: Frishberg C. A. , Massa L. J.
Published: December 2004

It is shown how an idempotent density matrix provides a proper model for interpretation of the x‐ray coherent diffraction experiment.
Study of correlation holes. I. Number–sum rules and infinite system
Authors: Resta Raffaele
Published: December 2004

The correlation holes in a finite system of any size are known to satisfy integral number–sum rules directly related to the N‐representability of the reduced density matrices. In regard to infinite systems, the same rules are known to be satisfied in the electron gas. It is shown that the number–sum rules are not generally satisfied in any infinite system, and that this happens independently of the kind of boundary conditions assumed in the N → ∞ limit. A violation is explicitly found within the alternant molecular orbital formalism. The apparent paradox is explained in terms of surface effects (end effects in a linear system), which are present in a large, but finite system. In other words the N‐representability does not imply the number–sum rules. In the N → ∞ limit the rules are satisfied only in physical systems having short‐range correlation.
Biorthonormal basis sets and the interaction between one‐electron atoms
Authors: Dahl Jens Peder
Published: December 2004

The properties of biorthonormal sets and their use in quantum chemistry are discussed. A theoretical description of the interaction between one‐electron atoms is presented. The description is based on a single orbital per electron but is otherwise complete. Structurally simple relations are derived for the energy of interaction, and theoretical justifications for the London equation and the diatomics‐in‐molecules method are presented. Some comments on the stability of spin‐coupling‐optimized methods are made.
Ab initio Hartree–Fock and configuration‐interaction treatment of the interaction between two nickel atoms
Authors: Shim Irene , Dahl Jens Peder , Johansen Helge
Published: December 2004

The interaction between two nickel atoms in the configurations (3d)8(4s)2 and (3d)9 (4s)1 has been calculated using ab initio methods (Hartree–Fock and configuration interaction). The results of the calculations compare favorably with the optical spectrum. The discrepancy between the calculated and the experimental dissociation energy is discussed, and a new estimate of the dissociation energy is given. The configuration‐interaction calculations show that the interaction between the two nickel atoms is of a very complex nature. In spite of this the binding can be interpreted in a simple way. The bond is minly due to the 4sσg molecular orbital while the 3d orbitals of the two nuclei are exchange coupled.
A dynamical theory describing superconductant DNA
Authors: Paine Douglas A. , Pensinger William L.
Published: December 2004

A dynamical model describing DNA as superconductant is proposed. The status of superconductivity is described as being represented by a radiation‐induced harmonic oscillation of a parcel of π electrons between the reference level and critical temperatures. A set of field equations is used to describe the information exchange process mediated by a coherent wave phenomenon.
Characteristics of the consistent ground state of the random phase approximation
Authors: Öhrn Yngve , Linderberg Jan
Published: December 2004

Detailed considerations of the ground‐state vector derived for the random phase approximation obtained earlier in a generator coordinate representation employing the unitary group parameter space reveal a particular correlated pair structure. The results of explicit calculations of ground‐state averages are discussed.
Correlation problems in atomic and molecular systems. VII. Application of the open‐shell coupled‐cluster approach to simple π‐electron model systems
Authors: Saute M. , Paldus J. , C̆íz̆ek J.
Published: December 2004

The coupled‐cluster variational‐like direct approach to the calculation of ionization and electron attachment energies and of excitation energies is applied to several π‐electron model systems, using the PPP Hamiltonian with various parametrizations. A simple approximation, which represents the triexcited clusters in terms of disconnected W1T2 terms, is employed. All the necessary diagrams for both excitation energy and ionization potential (electron affinity) calculations are given in the compact Hugenholtz nonoriented form. The results of the calculations for benzene, trans‐butadiene, all‐trans‐hexatriene, and fulvene are compared with the corresponding full CI results, and the conclusions about the validity and efficiency of this approach are drawn.
Role of Ca+2 ion in the abortifacient action of prostaglandins. I. Molecular‐orbital and conformation‐energy calculations of PGF2α
Authors: Kothekar V. , Dutta S.
Published: December 2004

The paper reports the study of a possible mechanism of Ca+2 activation of prostaglandin PGF2α on the basis of molecular‐orbital and conformation‐energy calculations. The electronic charges on various atoms of the molecule have been evaluated from the available crystallographic data by the extended Hückel theory (EHT). Conformation energies were calculated for intrinsic torsional rotations around the C11C12, C7C8, and C14C15 bonds. The minimum energy conformation was found to differ from the crystallographic conformation by 9.3 kcal/mol. Some additional local energy minima are also reported within this range. The calculation of the long‐range interchain interaction energy between the α and ω chains shows variation with conformation. The binding site for the Ca+2 ion has been estimated on the basis of the molecular electrostatic potentials. Such a binding site was found near the carboxyl group, which agrees with the current chemical thinking. Changes in the electronic charge distribution due to Ca+2 complexation were studied by EHT method using the supramolecular approach. Calcium complexation decreases the conformation energy by 2–3 kcal/mol and has a small effect on the interchain interaction energy.
Nonbonded interactions in membrane‐active cyclic biopolymers. III. Analogs of valinomycin
Authors: Sundaram K. , Tyagi R. S.
Published: December 2004

Several analogs of valinomycin have been simulated. These are analogs obtained by changing the configuration of the amino acid and hydroxy acid residues one at a time. Nonbonded interactions have been calculated for three conformations of each analog. The electrostatic and polarization contributions to the energy are conformation selective, whereas the Pauli repulsion is the only component which is isomer selective. For the ring chirality considered here the analog of valinomycin having all the three L‐valyl residues replaced by D‐valyl residues is predicted to be frozen in a “top open” conformation.
Note on the Fermi–Amaldi correction for the Thomas–Fermi theory of atoms
Authors: Csavinszky P.
Published: December 2004

The aim of this note is to ascertain the importance of the Fermi–Amaldi (FA) correction for the Thomas–Fermi (TF) theory of atoms. For this purpose, an analytic trial electron density has been chosen and the Thomas–Fermi–Amaldi (TFA) energy expression has been minimized by the Ritz method for the closed‐shell atoms Ne, Ar, Kr, Xe, and Rn. The variationally obtained electron densities have then been used for calculating the diamagnetic susceptibilities of these atoms. The calculated values show only a very small improvement over values calculated by Jensen by an analogous procedure from the TF energy expression.
Configuration‐Interaction study of lower excited states of O2: Valence and rydberg characters of the two lowest 3Σu− states
Authors: Tatewaki Hiroshi , Tanaka Kiyoshi , Sasaki Fukashi , Obara Shigeru , Ohno Kimio , Yoshimine Megumu
Published: December 2004

Configuration‐interaction calculations, with an extended basis, are carried out on the ground and lower excited states of O2 and O2+ at and near the equilibrium internuclear distance (R = 2.3 a.u.) of the ground state of O2. Particular attention has been paid to the two lowest 3Σu− states, and the mixing of the valence and Rydberg characters in these states are studied. The lowest 3Σu− state is a Rydberg‐type state for R < 2.3 a.u., but becomes valence‐type for R ≳ 2.3 a.u. The second 3Σu− state, which is 1.6 eV above the lowest 3Σu− at R = 2.3 a.u., changes its character from Rydberg to valence, valence to Rydberg, and then to valence again when R increases from 1.9 to 3.1 a.u. Satisfactory agreement between the calculated and experimental vertical excitation energies is obtained.
Density functionals for coulomb systems
Authors: Lieb Elliott H.
Published: December 2004

This paper has three aims: (i) To discuss some of the mathematical connections between N‐particle wave functions ψ and their single‐particle densities ρ (x). (ii) To establish some of the mathematical underpinnings of “universal density functional” theory for the ground state energy as begun by Hohenberg and Kohn. We show that the HK functional is not defined for all ρ and we present several ways around this difficulty. Several less obvious problems remain, however. (iii) Since the functional mentioned above is not computable, we review examples of explicit functionals that have the virtue of yielding rigorous bounds to the energy.
Vibronic coupling of electronic states. III. The definitive breakdown of the CBO potential picture within the framework of our model
Authors: Gustav Klaus , Colditz Roland
Published: December 2004

The definitive breakdown of the CBO potential picture in consequence of the vibronic coupling of two electronic states is discussed on the basis of our model. The present treatment differs from that given in the literature.
Ab initio quantum‐mechanical characterization of the electronic states of anthraquinone, quinizarin, and 1,4‐diamino anthraquinone
Authors: Petke J. D. , Butler Paul , Maggiora Gerald M.
Published: December 2004

The ground and excited singlet and triplet states of 9,10‐anthraquinone and its 1,4‐dihydroxy and 1,4‐diamino derivatives are investigated by ab initio configuration interaction calculations, using a floating Gaussian basis. For anthraquinone the calculated electronic absorption spectrum is consistent with previous experimental and theoretical results. The possible mechanisms of intersystem crossing and intensity borrowing in phosphorescence are discussed in terms of first‐ and second‐order spin‐orbit and vibronic perturbations of the computed singlet and triplet states. The calculated spectra of the 1,4‐disubstituted derivatives are more complex than previously suggested from low‐resolution polarized absorption studies. The principal effect of 1,4‐substitution by electron donating groups is shown to be a powerful conjugative effect which significantly modifies selected molecular orbitals of anthraquinone; the resultant effect on the absorption spectra is the creation of two new substituent‐induced π → π* transitions, one of which corresponds to the intense visible absorption band of these systems.
Electronic structure of DNA dimer units, d(AA) · d(TT), d(TA)2, and d(AT)2, in A and B conformations by DV‐Xα cluster calculations
Authors: Shinoda Takako , Shima Nobuyuki , Tsukada Masaru
Published: December 2004

The electronic structure of d(AA) · d(TT), d(TA)2 and d(AT)2, which are stacked base pairs in the DNA double helix, is elucidated for both A and B conformations in detail by DV–Xα cluster calculations. The results are compared with those of a previous study on the electronic structure of d(GG) · d(CC), d(CG)2, and d(GC)2. A hexanucleotide −10 sequence of the promoters in DNA transcription initiation, TATAAT, can be interpreted as the best sequence for the strong promoters by using the S̃r values of the O2 of each phosphate. The reactivity of polymerization at neighboring thymines in the AA/TT unit is discussed from the electronic structure. © 1993 John Wiley & Sons, Inc.
Electron correlation effects in the Rydberg‐like 33D and 31D states of helium‐like ions
Authors: Cann Natalie Mary , Boyd Russell J. , Thakkar Ajit J.
Published: December 2004

The small and subtle effects of electron correlation in the Rydberg‐like 31D and 33D states of the helium‐like ions are studied using very accurate explicitly correlated wave functions. In particular, the effects of electron correlation on one‐electron densities, probability distributions for the interelectronic distance, and their moments are examined with the help of density and Coulomb holes. Statistical electron correlation is examined with radial and angular correlation coefficients. The different methods of analysis provide complementary insight. © 1993 John Wiley & Sons, Inc.
Eigenvalues of single‐cycle class‐sums in the symmetric group. II
Authors: Katriel Jacob , Pauncz Ruben
Published: December 2004

Explicit expressions for the eigenvalues of the single‐cycle class‐sums [(p)(1)n–p]n of the symmetric group (Sn), with p ≤ 20, are constructed. A new algorithm is used that makes no use of representation‐theoretic data. The expressions obtained consist of polynomials in the symmetric power‐sums over the “contents” of the Young diagram specifying the irreducible representation, with coefficients that are polynomials in n. On the basis of the results obtained for p ≤ 20, a conjecture is proposed concerning the general form of the four leading terms in these polynomials. © 1993 John Wiley & Sons, Inc.
Stable electronic energy levels in the presence of off‐diagonal disorder
Authors: László István
Published: December 2004

It is demonstrated that the topological arrangement of atoms can guarantee the existence of stable electronic eigenvalues. These levels are stable in the presence of off‐diagonal disorder. Graph theory is used to describe the topological structure of the Hamiltonian. The actual applications are presented in tight‐binding approximation. It was found that graph theory can be used even if the atoms have more than one atomic orbital. Also, the localization properties of the topologically determined eigenvalues are studied. © 1993 John Wiley & Sons, Inc.
Antiaromaticity in relation to 1,3,5,7‐cyclooctatetraene structures
Authors: Politzer Peter , Murray Jane S. , Seminario Jorge M.
Published: December 2004

An isodesmic energy analysis has been carried out at the MP2/6–31G*//HF/3–21G level for the nonplanar ground state (1) of 1,3,5,7‐cyclooctateraene and for two planar forms, one having complete π delocalization (2) and the other having alternating single and double bonds (3). 1 is found to have a considerable degree of stabilization, which is attributed to limited π delocalization. The polyene 3 is the more stable of the two planar forms; it is a transition state in the inversion between two possible nonplanar structures. 2 is found to be a triplet at the Hartree–Fock level and is a critical point on an alternate pathway between the two possible arrangements of alternating single and double bonds in 3. Both 2 and 3 have negative isodesmic energies, indicating the presence of stabilizing factors. Our results for 3 show that an “antiaromatic” system need not necessarily show a net destabilization. © 1994 John Wiley & Sons, Inc.
Search for stationary points of arbitrary index by augmented Hessian method
Authors: Khait Yu. G. , Panin A. I. , Averyanov A. S.
Published: December 2004

Convergence properties of the augmented Hessian (AH) method when searching for stationary points of an arbitrary fixed index are investigated. It is shown that the displacement vector of this method is proportional to one of the Hessian eigenvectors if the current point is far from a stationary one of the required index. A simple and reliable criterion for nearness of the current point to a stationary one of the desired index is proposed. The efficiency of a new one‐dimensional optimization scheme that uses this criterion is studied. The case of coincidence of Hessian eigenvalues, which is a bottleneck of the standard AH method, is analyzed. A relation of the AH method to those by Poppinger and Wales is outlined. The correctness of the results obtained is illustrated on an example of a model surface. © 1995 John Wiley & Sons, Inc.
Matrix elements for Ĵ2 and Ĵz operators over explicitly correlated Cartesian Gaussian functions
Authors: Kozlowski Pawel M. , Adamowicz Ludwik
Published: December 2004

General formalism for evaluation of multiparticle integrals involving J̌2 and J̌z operators over explicitly correlated Cartesian Gaussian functions is presented. The integrals are expressed in terms of the general overlap integrals. An explicitly correlated Cartesian Gaussian function is a product of spherical orbital Gaussian functions, powers of the Cartesian coordinates of the particle, and exponential Gaussian factors, which depend on interparticular distances. This development is relevant to both adiabatic and nonadiabatic calculations of energy and properties of multiparticle systems. © 1995 John Wiley & Sons, Inc.