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  • 1
    Electronic Resource
    Electronic Resource
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 22 (1982), S. 1033-1036 
    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 simple and straightforward derivation of (in)stability conditions for projected Hartree-Fock solutions is carried out and compared to the existing approaches to the problem.
    Type of Medium: Electronic Resource
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  • 2
    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 in the framework of the π-electron approximation even polyenes can be unambiguously divided into 4L- and 4L +2- classes. The classification scheme is based upon the sign alternation of the bond-order between the first and the last atoms and upon the different information content of the bond-order distribution for 4L- and 4L +2- polyenes, respectively. The classification has been shown to hold for the four lowest-lying electronic states: the ground state 1Ag-, the spectroscopically permitted excited state 1Bu+, the spectroscopically forbidden state 1Ag-, and the lowest triplet state 3Bu+ at all levels of sophistication in the π-electron approximation, ranging from the simple Hückel Hamiltonian to the PPP-multi-CI approach. It is shown that the proposed classification is valid also for heteropolyenes and polyenelike/heteropolyenelike fragments from complex organic molecules. The classification has been shown to be useful for the theoretical interpretation of thermo- and photoelectrocyclic reactions. The sign of the bond order between the first and the last atoms (or the average information content) determines unambiguously the topology of the forming cyclic transition state and, thence, the course and the mechanism of these reactions. The results obtained indirectly support the hypothesis that the lowest excited states in butadiene and hexatriene are of the type 1Bu+.
    Additional Material: 4 Ill.
    Type of Medium: Electronic Resource
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  • 3
    Electronic Resource
    Electronic Resource
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 22 (1982), S. 351-365 
    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 singlet instabilities of the RHF ground state in infinite polyenes have been studied in the framework of a semiempirical PPP Hamiltonian, accounting for long-range Coulomb interactions until convergence of the ground-state energy per electron value. The symmetry-adapted RHF solution (SAS) has been shown to be unstable to the formation of bond-order alternation waves (BAW's) and charge-density waves (CDW's). The CDW solutions have been shown to be higher in energy than the corresponding BAW solutions and to represent saddle points of the energy hypersurface, unstable to the formation of BAW's for physically realistic range of variation of the semiempirical parameters. Analytical formulas for the SAS ground-state energy per electron have been derived in case of a Coulomb law and a Mataga-Nishimoto formula for the two-center Coulomb integrals.
    Additional Material: 3 Ill.
    Type of Medium: Electronic Resource
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  • 4
    Electronic Resource
    Electronic Resource
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 22 (1982), S. 367-383 
    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 stability of the possible ground states of an infinite linear equidistant polyene model has been discussed in the PPP approximation of the unrestricted-Hartree-Fock (UHF) method. The emphasis has been placed upon the investigation of nonsinglet (triplet) instabilities: the spin-density waves (SDW's) and the spin-bond-order alternation waves (SBAW's). For physically realistic parameter sets the SDW ground state of the infinite linear equidistant polyene has been shown to be lowest in energy. Whereas the symmetry-adapted restricted HF (RHF) solution (SAS) has been shown to be unstable to the formation of SDW's and SBAW's for all investigated parametrizations, the bond-order alternation wave (BAW) solution has been found to be unstable to the formation of SDW's, but stable to the formation of SBAW's; in fact, the BAW's and the SBAW's have been shown to yield identical gap widths and ground-state energies (at least in the PPP method). It has been shown that there exist such sets of semiempirical parameters for which the charge-density wave (CDW) ground state is nonsinglet stable irrespective of the existence of an energetically advantageous SDW solution for the same parameter set.
    Additional Material: 3 Ill.
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  • 5
    Electronic Resource
    Electronic Resource
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 24 (1983), S. 453-477 
    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: This paper contains a derivation of stability conditions for closed-shell restricted Hartree-Fock (RHF) solutions in the framework of the projected Hartree-Fock (PHF) method. It is shown that for any projection operator whose choice is consistent with the symmetry of the RHF solution, one obtains four stability subproblems (one “singlet” and three “nonsinglet”). The stability conditions are specialized to several particular choices of the projection operator, including Löwdin's spin projection operator for the singlet case (this choice corresponds to the celebrated spin-PHF method). The stability of closed-shell RHF solutions for alternat π-electronic systems in the framework of the alternant molecular orbital (AMO) method is also discussed. The theoretical considerations are illustrated by PPP calculations for several closed-shell π-electronic models. The results for even alternant conjugated hydrocarbons show that the AMO construction is suggested by the structure of the eigenvector pointing into the direction of steepest descent from the pertinent RHF solution in the framework of the spin-PHF method. The minimization of the spin-PHF energy expectation value in this direction in a number of cases allows that value to approach rather closely the energy values obtained in a fully variational spin-PHF treatment and thus provides either a one-parameter variational method which is shown to be superior to the one-parameter AMO method or a convenient initial approximation to the solution of the spin-PHF equations.
    Additional Material: 4 Tab.
    Type of Medium: Electronic Resource
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