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  • Atomic, Molecular and Optical Physics  (172)
  • Wiley-Blackwell  (172)
  • American Chemical Society (ACS)
  • Reidel
  • 1970-1974  (172)
  • 1973  (108)
  • 1970  (64)
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  • Wiley-Blackwell  (172)
  • American Chemical Society (ACS)
  • Reidel
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  • 1970-1974  (172)
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  • 1
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    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 4 (1970), S. 97-107 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
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  • 2
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    International Journal of Quantum Chemistry 4 (1970), S. 431-450 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: A one-centre CI wave function for HeH+ reported by Stuart and Matsen for 0.1 ≤ R ≤ 5.0 has been analysed in detail from the viewpoint of molecular formation. Further, by means of a natural orbital analysis, it was possible to obtain some measure of the electron correlation contained within such wave functions for various R values. These effects were illustrated by means of a series of difference maps for the electron density. One- and two-particle expectation values were obtained as a function of R. Thus, it was possible to study several aspects of the influence of the proton on the electron charge cloud as we pass from He through to the united atom Li+. The occupation numbers within the natural expansions were compared with those which arise from a similar analysis of a two-centre wave function for HeH+. The “character” of such wave functions for HeH+, and also for He and Li+, were analysed and compared.
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  • 3
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    International Journal of Quantum Chemistry 4 (1970), S. 465-486 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The quadrupolar and octupolar distortion of the ions in the He-sequence caused by an external electro-magnetic field has been studied by a variation-perturbation method in the Hartree-Fock scheme. For certain frequencies singularities appear in the response of the system to the perturbation. Approximate representations for the excited d and f states have been obtained from a study of these resonances. Such a perturbation calculation has the advantage that representations of the different excited states are obtained independently. The orthogonality to all the lower lying levels of the same symmetry is not required. The only source of inaccuracy implicit in the procedure lies in the improper consideration of the inter-electronic interaction. This is corrected for by an independent calculation, which is again formulated in terms of a perturbation treatment. The resulting wave functions for the excited states are accurate in the Hartree-Fock model. Expectation values of several operators have been calculated with these corrected wave functions.
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  • 4
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    International Journal of Quantum Chemistry 4 (1970), S. 365-387 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The utility of the separated electron pair (SEP) model (strongly orthogonal geminals) is examined quantitatively, for pyramidal and planar nuclear configurations of the NH3 molecule. The best SEP wave function computed for each species is capable of recovering about half of the correlation energy obtained by a fairly accurate configuration interaction (CI) calculation, (corresponding to roughly 25% of the total molecular correlation energy). It is illustrated that the model can be systematically extended with only a modest effort to yield more accurate results (about 40% of the total correlation energy). The fact that the corrections to the SEP model have a simple physical interpretation suggests that this model may be a useful starting point for “brute force” CI calculations on larger chemical systems.
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  • 5
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    International Journal of Quantum Chemistry 4 (1970) 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
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  • 6
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    International Journal of Quantum Chemistry 4 (1970), S. 451-452 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
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  • 7
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    International Journal of Quantum Chemistry 4 (1970), S. 503-518 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Ab initio calculations using a small Gaussian basis set, including 3d orbitals on the sulphur atom, have been performed on the fluorosulphate radical and the related ions SO3F+ and SO3F-. A new SCF procedure is described and applied to the open shell cases discussed here. The results are compared with recent CNDO calculations and with the experimental transition energies of the radical.
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  • 8
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    International Journal of Quantum Chemistry 4 (1970), S. 519-527 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Polikanov's perturbation method for the solution of the radial Schrödinger equation is shown to be equivalent to the usual Rayleigh-Schrödinger method but with full normalization instead of intermediate noralization. The energy corrections are shown to be the same to all orders. The computational advantages of Polikanov's method are discussed. The method is illustrated by considering the two-electron ions in the Hartree-Fock approximation.
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  • 9
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    International Journal of Quantum Chemistry 4 (1970), S. 533-539 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: A mathematical model of a molecule is proposed. The electronic structure is described using a molecular orbital wave function constructed from a small number of spherical Gaussians with optimized parameters. The models exhibit the desirable properties of numerical stability, objectivity and transferability. Results are given for CH4, C2H6, cyclo-propane, H2O, CH2O and C2H4. They can be given a chemical interpretation in terms of chemical bonds, lone pairs and atomic cusps.
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  • 10
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: A method proposed recently for the generation of modified Hartree-Fock virtual orbitals has been tested by performing a simple configuration-interaction calculation for the ground state of the He atom. A very compact truncated basis set was constructed by using an a priori criterion based on the probability density within the region of the occupied orbital. The best results were obtained by making the virtual orbital energies more positive.
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  • 11
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    International Journal of Quantum Chemistry 7 (1973), S. 459-473 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: In this paper we obtain formulae useful in methods for the direct minimization of the energy functional in the LCAO-MO-MC-SCF approach. The formulae are appropriate for dealing with variations in both the linear and nonlinear parameters. We include formulae for the usual closed- and open-shell problems as special cases.
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  • 12
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    International Journal of Quantum Chemistry 7 (1973), S. 1-13 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The treatment of electrostatic interactions between molecular groups is based on quantum mechanical electron density distributions. A general method is suggested using tesseral harmonic multipole expansions and representing each set of point multipoles by a cluster of discrete charges small with respect to atomic dimensions. The procedure is carried out for the amino group with an electron density derived from the wave function of ammonia. We evaluate the optical rotation of two aminopyrrolidones as a test case. Expansions are compared for several approximate wave functions for ammonia.
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  • 13
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    International Journal of Quantum Chemistry 7 (1973), S. 51-62 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The energy terms arising in the water calculation by the FSGO method are analyzed as a function of the bond angle in order to gain insight into the reasons for the particular equilibrium configuration. The analysis is made in terms of symmetrically orthogonalized orbitals so as to exclude three- and four-orbital electron repulsion terms.
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  • 14
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    International Journal of Quantum Chemistry 7 (1973), S. 87-108 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The instabilities of the solutions to the Hartree-Fock equations for the nonalternants in the pentalene, heptalene, etc., series and in the azulene, etc., series are examined. The systems are found to have symmetry-adapted solutions which are unstable for values of the core integral β close to the standard (spectroscopic) value; for example, the pentalene solution is unstable with β equal to 75% of its standard value. The “broken” symmetry solutions although exhibiting only a very slightly lower energy (0.01 eV) may exhibit dramatically different values for other properties, e.g., 30% changes in bond orders. The off-diagonal charge-density wave (CDW) appearing in the “broken” symmetry solutions at the onset of instability is amplified as the cooperative phenomena dominate, until in the “fully correlated” limit, the linked-ethylenic (bond alternating) structure is obtained.
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  • 15
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    International Journal of Quantum Chemistry 7 (1973), S. 133-134 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
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  • 16
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    International Journal of Quantum Chemistry 7 (1973) 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
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  • 17
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    International Journal of Quantum Chemistry 7 (1973), S. 759-777 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The electron spin dipole-dipole interaction in CH2 has been calculated as a function of bond angle with configuration-interaction wave functions built from contracted gaussianlobe basis functions. The values D = 0.781 cm-1 and E = 0.050 cm-1 were obtained for the spin dipole-dipole contribution to these parameters for the best CI wave function at the equilibrium geometry. The angular dependence of D shows that the assumption of perfect orbital following is not valid. Based on previous estimates of the spin-orbit contribution to D, the total D is estimated to be 0.9 ± 0.1 cm-1 which is higher than the current experimental value 0.76 ± 0.02 cm-1.
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  • 18
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    International Journal of Quantum Chemistry 7 (1973) 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
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  • 19
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Expressions are derived for the n-dependent, hydrogen-like relativistic corrections to the magnetic dipole and electric quadrupole radial hyperfine integrals of an arbitrary atomic state.Good agreement has been obtained earlier between these corrections and the relativistic Hartree-Fock results for s1/2 states. The agreement remains good for the p1/2 states. For the p3/2 states in heavier atoms the hydrogenic corrections still reproduce the Hartree-Fock trend. For the higher l values the agreement is poor. Numerical tables are given for 1 ≤ Z ≤ 100 for the s1/2, p1/2, and p3/2 magnetic dipole cases and the p3/2 quadrupole case.
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  • 20
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    International Journal of Quantum Chemistry 7 (1973), S. 27-34 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: SCF-LCAO-MO-CI calculations made on 2- and 4-amino-, and 2,4-diaminopteridines indicate that the most favorable site where the protonation can take place is N-1.
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  • 21
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    International Journal of Quantum Chemistry 7 (1973), S. 15-25 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: It is shown that gauge terms can be introduced into the Gaussian functions used as the basis functions for an ab initio calculation of the energy of a molecule in the presence of a uniform magnetic field so that all the integrals become independent of the origin of the vector potential. The perturbation treatment of the diamagnetic susceptibility is considered in the molecular orbital approximation. The results show that the susceptibility can be calculated using only the unperturbed orbitals and their first-order corrections. All the integrals that arise can be expressed in terms of known functions.
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  • 22
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    International Journal of Quantum Chemistry 7 (1973), S. 285-300 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Formulae are presented for the evaluation of some definite integrals in which the Laguerre orthogonal functions are contained. In some cases mechanical quadratures are to be preferred, and a scheme is presented for generating such a quadrature as it is needed.
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  • 23
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    International Journal of Quantum Chemistry 7 (1973), S. 345-355 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Upper and lower bounds for the second-order energy in both coupled and uncoupled Hartree-Fock perturbation theories are derived. Using these bounds inequalities are derived for the error in the geometric approximation.
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  • 24
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    International Journal of Quantum Chemistry 4 (1970), S. 1-3 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: A perturbation variation treatment of two-electron atoms using exp (-αr〈 - βr〉) as the zeroth order wave function is presented. The parameters α and β are variationally determined and the results are compared with the “physical” choice α = Z, β = Z - 1, and with Z-1 theory. The energy is given through fifth order in the perturbation.
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  • 25
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    International Journal of Quantum Chemistry 4 (1970), S. 529-532 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The systems C2H4F+ and C2H4CH3+ have been investigated by the SCF-MO-P (LCGO) method. It will be shown that the results agree with the empirical rule of Markownikoff. An explanation of the rule of Markownikoff is given by means of the computed results.
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  • 26
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    International Journal of Quantum Chemistry 4 (1970) 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
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  • 27
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    International Journal of Quantum Chemistry 4 (1970), S. 579-586 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: A detailed study of the performance of the Morse, the Hulburt--Hirschfelder and the Lippincott potential energy functions has been carried out by comparing them with the Rydberg-Klein-Rees potential energy curves for a number of electronic states of various diatomic molecules. Further, by employing the above potential energy functions, the radial Schrödinger equation has been solved for the vibrational energy levels, G(v), and the vibrational wave functions, ψv. The latter have been employed to determine the rotational constants, Bv, for the individual vibrational energy levels. Then the molecular constants, we, wexe, weye, Be, αe and γe for the various electronic states, have been computed by using the values of G(v) and Bv. A comparison of the molecular constants derived in this manner with the experimental ones reveals better agreement, in most cases, than that reported by previous workers.
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  • 28
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    International Journal of Quantum Chemistry 7 (1973), S. 521-536 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Alternant molecular orbitals for the lithium metal are constructed in different ways. The corresponding first-order density matrix is calculated for different shapes of the Fermi surface. Numerical methods to calculate the first-order density matrix are described.
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  • 29
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    International Journal of Quantum Chemistry 7 (1973), S. 547-560 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The all-valence electron band structures of the periodic DNA models polyC, polyT, and polyA have been calculated with the aid of the CNDO/2 and MINDO/2 crystal orbital (CO) method.According to the obtained results the valence and conduction bands are always of π type. The widths of the bands are usually larger in the CNDO case, than those obtained for the same systems in the PPP CO approximation. On the other hand the MINDO results show similar widths as the PPP ones. The forbidden bandwidths are by 3-4 eV larger in the CNDO/2 case, than in the PPP one, while the MINDO/2 CO method has resulted in similar gaps like the PPP calculation.
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  • 30
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    International Journal of Quantum Chemistry 4 (1970) 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
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  • 31
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: 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.
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  • 32
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    International Journal of Quantum Chemistry 4 (1970), S. 149-172 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: 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.
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  • 33
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    International Journal of Quantum Chemistry 4 (1970), S. 219-221 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
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  • 34
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    International Journal of Quantum Chemistry 7 (1973), S. 187-193 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: A theorem is proved which demonstrates the relationship between a product of group functions describing the correlated motion of a particular group of electrons in an N-electron system and a wave function obtained from the exact wave function which describes the correlation of the same group of electrons. By considering such products of group functions as elements in a variational wave function, an expansion for correlated wave functions is suggested, which emphasizes the correlated motion of groups of electrons in the whole system.
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  • 35
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    International Journal of Quantum Chemistry 7 (1973), S. 223-232 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Approximate and ab initio molecular wave functions are obtained using Gaussian expansions of different length for the Slater orbitals. The expectation values of several one-electron operators are obtained and the accuracy of different wave functions discussed.
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  • 36
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    International Journal of Quantum Chemistry 7 (1973), S. 333-344 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Consideration is given to the problem of interactions between molecular systems (magnetic couplings being neglected) by highlighting the fact that the main difficulty of a perturbation theory that takes into account the exchange effects, resides in the differentiated symmetry of the unperturbed state and of the state of interaction (at an overlap other than zero). This difficulty has been overcome by choosing for the Schrödinger equation of the interacting systems a particular representation on the set of unperturbed functions and by reversing the symmetry properties onto the operators. This will lead to a new equation no longer presenting any difficulties for the symmetry interconnection. This equation is used for a double perturbational expansion both in Coulomb and in exchange terms, thus obtaining general perturbation equations. Explicit solutions are provided (up to the second total order) which are briefly discussed.
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    International Journal of Quantum Chemistry 7 (1973), S. 383-404 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: After a discussion of different concepts of anisotropy with reference to the icosahedron, the unusual problems surrounding the construction of icosahedral irreducible tensors are discussed. Tables of these tensors are then presented and applied to orbital problems, molecular polarization phenomena and to the construction of projection operators.
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    Notes: A proof of the convergence of the double infinite series form of the radial factor in the bipolar expansion of r12-1 is given. It consists of demonstrating the validity of the required term-by-term integrations.
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  • 39
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    International Journal of Quantum Chemistry 7 (1973), S. 853-867 
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    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
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    Topics: Chemistry and Pharmacology
    Notes: A class of reference full density matrices and their reduced density matrices is presented. These density matrices are designed to be of value as references from which to describe and measure the effects of electron correlation in atoms, molecules, and solids. A given reference full density matrix is constructed to contain the least possible information consistent with having the (recognized) symmetry properties of - and reducing to the 1-matrix of - a given “true” full density matrix (which in a typical application is constructed from a correlated variational wave function). Therefore, the reduced density matrices derived from are representable and depend only upon the 1-matrix of and the (recognized) symmetry properties of for their construction. Furthermore, the property of containing the least possible information consistent with the given constraints makes these reference density matrices ideally suitable as references from which to describe the electron correlation contained in the “true” full density matrix .
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  • 40
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    International Journal of Quantum Chemistry 7 (1973), S. 869-876 
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    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The method of functional iteration applied to orbital optimization is proposed. The main problem, i.e., the most economical parametrization of the rotations of the molecular orbitals, is resolved. First and second derivatives of rotations with respect to the parameters are given. The fact that the orbital space can be decomposed in subspaces such that energy is invariant against transformations of these subspaces into themselves is explicitly taken into consideration.
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    International Journal of Quantum Chemistry 7 (1973), S. 893-903 
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    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
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    Topics: Chemistry and Pharmacology
    Notes: An ab initio valence bond (VB) method for calculating energies and wave functions for simple electronic systems is described and the results of its application to methylene are given together with extensive comparisons with previous theoretical results.
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  • 42
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    International Journal of Quantum Chemistry 7 (1973), S. 951-958 
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    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
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    Topics: Chemistry and Pharmacology
    Notes: Various optimization criteria are compared for the hydrogen atom to find orbitals which improve lower bounds computed from the Weinstein, Temple, and Stevenson-Crawford formulas. Minimization of squared energy deviation, “variance,” is recommended because the resulting lower bound orbitals give excellent lower bounds, converge to the exact wave function, are relatively easy to optimize, and are insensitive to the estimated energy eigenvalue. New linear combinations of Gaussian orbitals which minimize the variance are presented for the 1s, 2s, 2p, 3s, 3p, and 3d orbitals. These orbitals are compared with previous linear combinations with regard to their expectation values and local properties.
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  • 43
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    International Journal of Quantum Chemistry 7 (1973), S. 991-998 
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    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
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    Topics: Chemistry and Pharmacology
    Notes: The third-order interaction between two nonpolar molecules due to the instantaneous induced dipole effect of an infinitely long linear molecule is assessed following arguments similar to earlier research on three-body effects. It is found that an attractive force favors small polar angles in approach to the linear molecule; such behavior could be of interest to processes such as those involved in replication of DNA.
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    International Journal of Quantum Chemistry 7 (1973), S. 131-132 
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    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
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  • 45
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    International Journal of Quantum Chemistry 7 (1973), S. 139-153 
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    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
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    Topics: Chemistry and Pharmacology
    Notes: A theoretical study of the spin-optimized self-consistent field methods is given in a second quantization formalism using the occupation-branching number representation and a biorthogonal basis treatment given by Moshinsky and Seligman. A diagrammatic presentation can then be introduced. Further investigation will be thus facilitated.
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  • 46
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    International Journal of Quantum Chemistry 7 (1973), S. 195-213 
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    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
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    Topics: Chemistry and Pharmacology
    Notes: The Green functions and Kubo linear-response theory are used to calculate the absorption coefficient of a collection of diatomic molecules embedded in a one-dimensional lattice. The effect of the environment is restricted to the coupling between the molecular internal vibration and lattice vibrations. For the molecular oscillators, both harmonic and anharmonic models are considered. The absorption line shape is expressed in closed form whether the molecular frequency falls outside or within the allowed phonon frequency range. In both cases a frequency shift is found. In the anharmonic case there is a broadening of the absorption lines. Expressions for the shift and line width are given.
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    Notes: 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.
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    International Journal of Quantum Chemistry 4 (1970), S. 389-395 
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    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
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    Topics: Chemistry and Pharmacology
    Notes: A group-theoretical method is presented whereby the number and identity of the non-zero components of a property tensor in a (molecular or crystalline) environment of low symmetry may be determined.
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    International Journal of Quantum Chemistry 4 (1970), S. 427-429 
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    Notes: The analytical conditions are obtained and discussed under which the vibronic equations for dimers can be decoupled.
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    Notes: An upper bound for E0, which has been derived from the conjugate eigenvalue problem by Hall, is discussed. It is emphasized that the bound is only guaranteed when V is negative-definite. An alternative bound is presented which is free from this restriction, and the underlying iterative procedure is given. Hall's result is generalized to admit internuclear distances, and the theory is illustrated by a one-dimensional system with delta-function potentials. Some disadvantages of the approach are mentioned.
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    International Journal of Quantum Chemistry 4 (1970), S. 625-630 
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    Notes: Extended Gaussian orbital basis set calculations have been carried out on an assumed staggered and eclipsed classical geometrical configuration of C2H5+. 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.
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    International Journal of Quantum Chemistry 4 (1970), S. 631-631 
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    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
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    International Journal of Quantum Chemistry 7 (1973), S. 623-634 
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    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
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    Notes: A modified Gaussian function g(u, v, w, a, R) = const s(a, R) is considered where l = u + v + w, s (a, R) is a 1s-type Gaussian function centered at R, a is the coefficient in the exponent of the 1 s Gaussian function and X, Y, Z are components of R. General formulae are derived for overlap integrals, kinetic energy integrals, nuclear attraction integrals, and electron repulsion integrals, valid for any l. The formulae are much simpler than those derived by Huzinaga for Cartesian Gaussian functions.
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    International Journal of Quantum Chemistry 7 (1973), S. 667-674 
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    Notes: A simple, “nearly free electron” model for the dihydrides of Be, Mg, Ca, Sr and Ba is investigated. To zeroth order the valence electrons are assumed to form a free gas. Effects of band structure are included in second-order pseudopotential perturbation theory. The stability of three probable crystal structures is investigated, and lattice parameters are calculated for two different choices of the pseudopotential.
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    International Journal of Quantum Chemistry 7 (1973), S. 647-665 
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    Notes: A computational approach for general Heisenberg spin Hamiltonians for a finite number of interacting doublet species is described. Maximum use of permutation and point group symmetry is incorporated in factorizing the secular equation. Associated problems in the computation of symmetric group characters, related frequencies, and selection of linearly independent kets from a large linearly dependent set are also solved.
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    International Journal of Quantum Chemistry 7 (1973), S. 725-737 
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    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
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    Topics: Chemistry and Pharmacology
    Notes: An ab initio self-consistent computation has been performed on the permanganate ion (MnO4-) in a large basis set of contracted gaussian functions. The ground state description as well as those of the first two excited states are discussed and compared with those obtained experimentally from photoelectron spectroscopy, ESCA, optical spectroscopy and magnetic circular dichroism.
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    International Journal of Quantum Chemistry 4 (1970), S. 57-72 
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    Topics: Chemistry and Pharmacology
    Notes: 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.
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    International Journal of Quantum Chemistry 4 (1970), S. 73-87 
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    Notes: The electronic structure of the benzyl radical in its ground state has been computed using a model Hamiltonian due to Pariser-Parr with full configuration interaction as well as with different truncated configurational sets built on SCF open-shell orbitals. The correlation energy corresponding to this model was found to be equal to -0.929722 eV. With the singly excited configurations only 18% of this energy is taken into account. By extending the basis to include the doubly excited configurations one can account for 94% of the correlation energy. An analysis of the accuracy of the proton hyperfine splitting calculation caused by inaccurate computation of the wave function is given. If only singly and even doubly excited configurations are taken into account one cannot hope to obtain splittings with an accuracy of more than 0.5 g. Inclusion of triply excited configurations lowers this error by one order. In addition, the use of the simple McConnell relation may lead to an error in splitting calculations of no less than 1.5 g.
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    International Journal of Quantum Chemistry 4 (1970), S. 89-95 
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    Topics: Chemistry and Pharmacology
    Notes: Self-consistent perturbation theory is introduced to facilitate making small, simultaneous variations in orbital exponents. This is accomplished by interpreting these variations as perturbations on the quantum mechanical system. The minimum-energy condition yields a set of linear equations for the desired exponential corrections.
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    International Journal of Quantum Chemistry 4 (1970), S. 121-121 
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    International Journal of Quantum Chemistry 4 (1970), S. 173-189 
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    Notes: Further energies for types of N2O4 valence structures (or valence formulae) are reported. The results indicate that two sets of formulae might give satisfactory distributions of the mobile σ-electrons. These are (i)Resonance between covalent and ionic formulae ((B) and (D) of Part II[8]);(ii)A non-paired spatial orbital formula ((F) of Part II [8]).One estimate of the σ-bond order for the NN bond is 0.4-0.5. For this, (i) is to be preferred, because it involves a much lower energy than (ii). But should the order be about 0.7, the energies of (i) and (ii) are similar, and both descriptions are satisfactory.The ionic formula of (i) involves non-localized bonding for the NO2+ moiety. It may be replaced by a formula with localized bonds, and an almost identical energy.
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    International Journal of Quantum Chemistry 4 (1970), S. 257-270 
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    Notes: The problem of upper and lower bounds to the first few eigenvalues of a very large or infinite tridiagonal matrix H is studied. Those eigenvalues of a comparison-matrix Mn which are lower than a characteristic limit, together with the corresponding eigenvalues of the variational matrix Hn are shown to bracket exact eigenvalues of H. Mn differs from Hn only in the last off-diagonal element and is easily obtained from H. Sufficient conditions for lower bounds are based on a low estimate of the characteristic limit. For increasing dimensions n, the lower bounds approach the exact eigenvalues from below. As a numerical illustration, brackets to the known eigenvalues of the harmonic oscillator with a linear perturbation are calculated.
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    International Journal of Quantum Chemistry 4 (1970), S. 271-287 
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    Notes: Using the criterion for maximizing the projection of localized bond orbitals onto the space spanned by the occupied MO's, a method for constructing hybrid orbitals of a molecule is described. For illustration purposes the method is applied to single-determinant closed shell wave functions, calculated by means of ab initio and semiempirical procedures, for the molecules of methane, acetylene, ethylene, ethane, propylene, butadiene, ammonia and hydrogen cyanide. The predictions of hybridization are briefly discussed.
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    International Journal of Quantum Chemistry 4 (1970), S. 347-353 
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    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
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    Topics: Chemistry and Pharmacology
    Notes: The charge on each atom of some ethers and chloro-substituted ethers, their dipole moments and the quadrupole coupling constants of the chloroethers have been calculated with the method suggested by Del Re. There appears to be an intimate connection between the charge density on the oxygen atoms and the capacity of forming hydrogen bond.
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    International Journal of Quantum Chemistry 4 (1970), S. 5-20 
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    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
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    Notes: In this paper the minimum principle proposed for atomic systems by Hall, Hyslop and Rees [1] is generalized to molecules. It is shown that this generalization retains the advantage of admitting the use of a larger class of trial wave functions, for example those with discontinuities, than is possible in the usual minimum energy principle. The further advantage that the upper bounds obtained by this treatment are always at least as good as those of the Rayleigh-Ritz method is also preserved.The theory is applied to the H2+ ion, potential energy curves are obtained for various “cut-off” wave functions, and the equilibrium internuclear distance is calculated. The optimization of the “cut-off” region so that the upper bound is minimized is also discussed.
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    International Journal of Quantum Chemistry 4 (1970), S. 413-425 
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    Topics: Chemistry and Pharmacology
    Notes: Fifth-rank molecular polarization tensors are discussed in terms of their tensor group which includes both the spatial symmetry and the permutation symmetry of the suffixes. This latter may be described by certain four-dimensional point groups, which in the nontotally symmetric cases may be projected into three-dimensional space. The study leads to a determination of the number of independent components of these tensors and a discussion of the types of phenomena which they may be expected to produce.
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    International Journal of Quantum Chemistry 4 (1970), S. 541-543 
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    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
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    Notes: The Z-expansion of two-electron systems is analyzed with the Padé technique with emphasis on establishing analytical properties of the function E(Z) formally associated with the power series expansion. The concept of critical point in this connection is stressed. For this sequence it occurs at Zc = 0.911246 with E(Zc) = -0.415184. The structure of E(Z) for Z 〈 Zc is investigated.The use of Padé approximants to extrapolate values of electron affinities is emphasized.
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    International Journal of Quantum Chemistry 4 (1970), S. 613-623 
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    Notes: The Schrödinger equation for helium is written as a generalized eigenvalue equation and this is solved perturbatively for the ground state. The zero order equation is taken to be that of a “six-dimensional hydrogen atom” since, in generalized eigenvalue form, this has a discrete spectrum. Although the zero-order wave function is very poor and gives only 86% of the energy the perturbation procedure is able to improve this to 99% through third-order.
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    International Journal of Quantum Chemistry 4 (1970), S. 289-295 
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    Notes: The Hartree-Fock equations are derived in the MO-LCAO approximation for the case when the integrals (except overlap integrals) over the atomic orbitals are charge-dependent. It is shown that inclusion of the overlap matrix in the iterative procedure gives equations which are too complicated for the simple model under consideration. The approach is applied to the VESCF method in the PPP scheme.
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    International Journal of Quantum Chemistry 4 (1970), S. 337-339 
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    International Journal of Quantum Chemistry 7 (1973), S. i 
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    International Journal of Quantum Chemistry 7 (1973), S. 63-73 
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    Topics: Chemistry and Pharmacology
    Notes: The exchange polarization energy and higher-order exchange corrections arising in the second order of the Murrell-Shaw and Musher-Amos (MS-MA) theory are evaluated analytically for the hydrogen molecule ion. At large internuclear distances the second-order exchange energy predicted by MS-MA theory behaves like \documentclass{article}\pagestyle{empty}\begin{document}$- \frac{1}{{18}}Re^{ - R}$\end{document}. It represents only 80% of the difference between the exact result of Holstein and the asymptotic value of the first-order exchange energy. The same result holds for the case of Hirschfelder-van der Avoird (HAV) and Hirschfelder-Silbey (HS) theories.
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    International Journal of Quantum Chemistry 7 (1973), S. 127-130 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
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  • 77
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    International Journal of Quantum Chemistry 7 (1973), S. 569-581 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Applying an extended form of the Mulliken approximation and a monopole approximation for the Coulomb integrals the Hartree-Fock nonorthogonal energy expression is decoupled. Thus, the total energy splits into a sum of one-electron increments. The increments are minimized directly with respect to the linear coefficients and orbital exponents. Further, the ZDO approximation is used in the decoupled energy expression to avoid difficulties arising in connection with the evaluation of multicenter integrals. “Rigid core” calculations were carried out for the valence electrons of first-row diatomics. In case of nonpolar molecules good results are obtained for equilibrium distances and force constants. The method fails for molecules with atoms having very different nuclear charges.
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  • 78
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    International Journal of Quantum Chemistry 7 (1973), S. 609-622 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Various molecular properties have been calculated for pyridine and pyrazine from Gaussian lobe ab initio SCF molecular wave functions. Values are compared with available experimental data. In general, agreement is satisfactory with the exception of the rather sensitive asymmetry parameter of the quadrupole coupling tensor. The distributions of total electronic charge, and of selected molecular orbitals have been displayed as plots of the charge density contours in two dimensions.
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  • 79
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    International Journal of Quantum Chemistry 7 (1973), S. 641-646 
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    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: For an estimation of the pair correlation the interelectronic distance r12 in geminal ψk(12) is introduced. The calculations are carried out by the local energy method [1, 2]. The influence of other electrons are taken into consideration with the help of the one- and two-electron integrals depending upon r1 and r2 as parameters. If the strong orthogonality condition is satisfied all two-electron integrals and most of the one-electron integrals vanish. All atomic orbitals are expressed in terms of Gaussian functions. A trial calculation is made for the beryllium atom.POUR tenir compte de la corrélation, on introduit la distance interélectronique r12 dans la géminale ψk(12). Le calcul est réalisé par une méthode des énergies locales [1, 2]. L'influence des autres électrons est décrite par des intégrales à un et deux electrons, dépendantes de r1 et r2 comme paramètres. Dans les conditions de l'orthogonalité forte, toutes les intégrales à un électron et la plupart des intégrales à deux électrons disparaissent. Pour simplifier l'algorithme du problème, toutes les orbitales sont exprimées par les fonctions de Gauss. Le calcul est réalisé sur le modèle de l'atome Be.Für Berechnung der Korrelation wird der Interelektronenabstand r12 in Geminal ψk(12) eingeführt. Die Berechnung wird mit der Lokalenenergiemethode durchgeführt [1, 2]. Die Einwirkung der anderen Elektronen wird durch 1- und 2-Elektronenintegrale berücksichtigt, die von Parametern r1 und r2 abhängen. Bei Erfüllung der starken Orthogonalitätsbedingung verschwinden alle 2-Elektronen- und die Mehrzahl der 1-Elektronenintegrale. Alle Orbitale werden durch Gaussfunktionen ausgedrückt. Eine Berechnung für das Atom Be wird durchgeführt.
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  • 80
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    International Journal of Quantum Chemistry 7 (1973), S. 675-686 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: As until now proposed in the literature, in the local energy calculations we can distinguish “few-points” procedures, in which the number M of configurational points is strictly related to the number N of trial functions used, and statistical “many-points” procedures, in which the number M of points can be arbitrarily increased. In this paper we demonstrate that the energy errors resulting from a “many-points” calculation M points/N functions (M 〉 N) can be connected in a simple way with the errors of the (MN) partial calculations N points/N functions.This suggests a possible approach for the problem of the choice of the configurational points to be introduced in the calculation, and leads to a simple interpretation of the numerical meaning of the error associated with the ordinary Ritz energy. Numerical examples on the hydrogen atom are reported.
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  • 81
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    International Journal of Quantum Chemistry 7 (1973), S. 717-723 
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    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: It is shown how to obtain pseudonatural orbitals directly from the equations of motion. A sample calculation on the ground state of the Be atom is given.
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  • 82
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    International Journal of Quantum Chemistry 7 (1973), S. 155-171 
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    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Exchange perturbation theory of the Rayleigh-Schrödinger type is applied, in first and second orders, to the problem of bonding in rare-gas halides. The basic model is that of a four-electron, three-center system with one effective electron replacing the unpaired electrons of a halogen atom, and two spin-paired electrons representing the closed shells of the rare-gas atom. On the basis of exchange perturbation theory, the model verifies a direct parallelism between bonding in rare-gas compounds and the phenomenon of super-exchange in ionic solids with paramagnetic cations. It is found that the observed stability and specific geometric configuration of the xenon and krypton fluorides are readily reproduced by the model. In addition, the model explains why other dihalides cannot exist. The two principal components of the interaction energy are found to be indirect exchange between halogen atoms via the rare-gas atoms (attractive in the stable configurations) and, in compounds with coordination higher than two, simultaneous interactions between three halogen atoms (always repulsive). The observed approximate constancy of the binding energy per bond in xenon fluorides with increasing coordination is accounted for.
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  • 83
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    Topics: Chemistry and Pharmacology
    Notes: Slater orbital r12-1 integrals are calculated with a numerical Fourier-transform method based on a formulation first given by Bonham, Peacher and Cox. Spherical wave expansions are introduced that decouple the Feynman integrations for the charge distribution Fourier transforms. The Feynman integrals are evaluated semianalytically, and their properties are analyzed in detail. The final computational step involves a numerical integration over charge distribution quantities. Results for (coplanar) multicenter exchange integrals over 1s orbitals are given. As long as the charge distributions are overlapping considerably, the method gives good results, even when these distributions are highly asymmetric. The method as presently implemented fails when highly disconnected charge distributions are involved.
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  • 84
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    International Journal of Quantum Chemistry 7 (1973), S. 253-284 
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    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Tensorial sets adapted to sequences of finite subgroups are applied to the crystal field problem, and a general method for generating sequence-adapted molecular tensors using finite group algebra is formulated. All subgroup sequences of the abstract finite group G(24), isomorphic to the octahedral, O, tetrahedral, Td, and symmetric, S(4), groups are tabulated with explicit isomorphisms provided. The sequences fall into eight equivalence classes. A catalog of irreducible representations of G(24) adapted to a member of each of the eight sequence classes is given together with the transformations which generate representations adapted to all other sequences. With this data it is possible to systematically generate tensorial sets adapted to any sequence of a realization of G(24). Unitary transformations which adapt conventional forms of first- and second-rank irreducible tensorial sets of the rotation group to the eight sequences of the octahedral group are provided. Forms suitable for use with magnetic fields are included. The problem of a d1 ion in a trigonal crystal field is treated with sequence-adapted molecular tensors, and the utility of different sequences for descent in symmetry is discussed.
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    International Journal of Quantum Chemistry 7 (1973), S. 1051-1061 
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    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The coarse structure magnetic theory presented here is a reformulation of conventional magnetic theory which emphasizes the spin-free (i.e., the coulombic) nature of the electron-electron interaction. We show that the magnetic properties of a system for which fine and hyperfine structure can be neglected depend only on the energy spectrum of a spin-free Hamiltonian. As an example, we treat the Heisenberg linear chain.
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    International Journal of Quantum Chemistry 7 (1973), S. 1077-1090 
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    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The infinite interaction range model (IIRM) for ferromagnetic systems is presented in its spin-free formulation. In this formulation the states are labelled by partitions which provide a natural variable for thermodynamic computation. We have extended the calculations of Kittel and Shore by computing to a practical thermodynamic limit (N ∼ 100,000). The heat capacity, magnetic susceptibility and the magnetization of the first two functions exhibit a critical temperature while the magnetization is zero at zero field for all temperatures. Spontaneous magnetization is obtained by linear extrapolation from high field or equivalently by a polarized partition function. Relationships are explored among IIRM, the Heisenberg model and the mean field model. Application to IIRM of the Yang-Lee condition for a phase transition yields a critical temperature identical to that obtained by the direct calculation.
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    International Journal of Quantum Chemistry 7 (1973), S. 1175-1182 
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    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Theoretical electronic wave functions, potential curves, and expectation values of some one-electron properties are given for the c3IIu state of the hydrogen molecule. The calculations are carried out by the matrix Hartree-Fock method and use a 2-center basis of Slater-type orbitals. A total energy of -0.7292 a.u. is obtained in the best calculation. Our potential curve is reasonably consistent with that calculated by Browne, but we have examined the region of small internuclear distances (those at and below Re for the ground state) more extensively than any previous calculation. At R ≦ 1.6 a.u. our calculated potential curve is in excellent agreement with experiment.
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    International Journal of Quantum Chemistry 7 (1973), S. 1203-1220 
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    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The expressions for matrix elements of spin-independent operators F and G with the use of Young operators are obtained in the case of arbitrary nonorthogonalized orbital configuration, including both singly and doubly filled orbitals and corresponding to the definite value of total spin. The formulas obtained do not require a preliminary construction of linear combinations of determinants and turn into known Löwdin formulas in the particular case of fully antisymmetric spatial states.
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    International Journal of Quantum Chemistry 7 (1973), S. 1227-1228 
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    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
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    International Journal of Quantum Chemistry 7 (1973), S. 637-637 
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    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
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    Topics: Chemistry and Pharmacology
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    International Journal of Quantum Chemistry 7 (1973), S. 699-705 
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    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: A discussion of Hartree damping in closed-shell Hartree-Fock theory is given indicating when the method might force convergence of intrinsically divergent cases. An alternative, but closely related principle, “level shifting” is described, and the advantages of the latter procedure discussed.
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    International Journal of Quantum Chemistry 7 (1973), S. 687-698 
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    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The half-projected Hartree-Fock function (HPHF) for singlet states is defined as a linear combination of two Slater determinants, which contains only spin eigenfunctions with even quantum number. Using a self-consistent procedure based on the generalized Brillouin's theorem, the RHF, HPHF and PHF functions are deduced for the ground states of the Li-, Be, B+, and C2+ systems, in a limited basis set. It is found that the HPHF function yields better energy values than the RHF function, very close to that of the PHF one. The HPHF scheme seems thus to be useful as a substitute for the PHF model, specially in the case of large electronic systems in which the latter method becomes unmanageable.
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    Topics: Chemistry and Pharmacology
    Notes: A procedure for the use of the plethysm operation for classification of the permitted electronic terms of impurity complexes in a crystal is presented. The cases of polyatomic symmetrical complexes are discussed as examples.
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    International Journal of Quantum Chemistry 7 (1973) 
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  • 95
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    International Journal of Quantum Chemistry 7 (1973), S. 561-568 
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    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: A quadratically convergent process using a continued fraction method for finding the square root of the overlap matrix used in Löwdin orthogonalization is presented. The continued fraction method is compared to several other methods for finding the square root of a matrix. The method is found to be more efficient than the other methods when high accuracy is desired.
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    International Journal of Quantum Chemistry 7 (1973), S. 635-636 
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    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
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  • 97
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    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
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    International Journal of Quantum Chemistry 7 (1973), S. 707-715 
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    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: A core model approach to the calculation of deuteron quadrupole coupling constants is investigated using NH3 as an example. First the deuteron quadrupole coupling constant is calculated from a CNDO wave function. This result is subsequently improved by recomputing the N - D bond orbital by means of a variational calculation using the CNDO function to construct a core potential for the bond Hamiltonian. In order to simplify integrations a single-center basis is chosen to represent the variational wave function. A projection operator formalism is used as a computational scheme to maintain orthogonality of the bond orbital to core orbitals. Excellent agreement with experiment is obtained. The procedure is applicable to more complicated molecules.
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    International Journal of Quantum Chemistry 7 (1973), S. 779-783 
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    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The time-dependent variational principle due to Frenkel is derived from Hamilton's principle using a suitable general expression for the variational wave function. The connections with a recent comment of P. O. Löwdin and P. K. Mukherjee on the same subject are discussed.
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    International Journal of Quantum Chemistry 7 (1973), S. 807-817 
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    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: 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.
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