bluuebunny/crossref_metadata_2025_split huggingface dataset:
Photochemische Umwandlungen, 41 [1] 3ω → 3 π‐Isomerisierungen von Monohetero‐trishomobenzol‐derivaten. Vorläufige mitteilung
Authors: Prinzbach H. , Stusche D. 
Published: December 2004

AbstractThe 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

AbstractThe 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

AbstractA 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

AbstractThe 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

AbstractAfter 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

AbstractFranck–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

AbstractThe 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

AbstractAnalytical 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

AbstractThe 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

AbstractMoleculer 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

AbstractA 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

AbstractWe 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

AbstractIn 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

AbstractThe 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.
The symmetry of molecular polarization tensors
Authors: Boyle L. L. 
Published: December 2004

AbstractPolarization 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

AbstractThe 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

AbstractThe 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

AbstractA 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

AbstractSelf‐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

AbstractIn 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

AbstractIt 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

AbstractSCGF 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

AbstractA 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

AbstractThe 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.