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  • 1
    Electronic Resource
    Electronic Resource
    Amsterdam : Elsevier
    Journal of Molecular Structure: THEOCHEM 288 (1993), S. 111-118 
    ISSN: 0166-1280
    Source: Elsevier Journal Backfiles on ScienceDirect 1907 - 2002
    Topics: Chemistry and Pharmacology , Physics
    Type of Medium: Electronic Resource
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  • 2
    Electronic Resource
    Electronic Resource
    Amsterdam : Elsevier
    Journal of Molecular Structure: THEOCHEM 201 (1989), S. 49-57 
    ISSN: 0166-1280
    Source: Elsevier Journal Backfiles on ScienceDirect 1907 - 2002
    Topics: Chemistry and Pharmacology , Physics
    Type of Medium: Electronic Resource
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  • 3
    Electronic Resource
    Electronic Resource
    Springer
    Chemistry of heterocyclic compounds 15 (1979), S. 961-965 
    ISSN: 1573-8353
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology
    Type of Medium: Electronic Resource
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  • 4
    Electronic Resource
    Electronic Resource
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 60 (1996), S. 743-752 
    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: Secular polynomials (SPs) have been constructed and studied for the adjacency matrices A(GaCh) and A(GbCh) corresponding to chemical graphs of alkanes in terms of atoms (GaCh) and in terms of bonds (GbCh). The three second-class Chebyshev polynomials Up(Q), Up - 1(Q), and Up - 2(Q), with respect to the variable Q proportional to the SP of an isolated CH2-like subgraph, have been shown to appear within both SPs P[A(GaCh)] and P[A(GbCh)] and to play the role of algebraic analogues of a (CH2)p-like subgraph. Common noncanonical algebraic expressions for both SPs reflecting the regular internal structure of alkanes have been constructed on this basis. Spectral properties of both graphs GaCh and GbCh have been shown to be determined by those of Up(Q), e.g., the band limits of spectra proved to be related to the orthogonality interval Q = [-1;1] for polynomials Up(Q). Since the adjacency matrices (AMs) A(GbCh), but not A(GaCh), are proportional to definite model Hamiltonian matrices, the obtained results serve to interpret the one-electron spectra of alkanes in terms of peculiarities of usual chemical structure. © 1996 John Wiley & Sons, Inc.
    Additional Material: 2 Ill.
    Type of Medium: Electronic Resource
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  • 5
    Electronic Resource
    Electronic Resource
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 60 (1996), S. 717-729 
    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: An alternative approach to secular problems for Hamiltonian matrices H of regular quasi-one-dimensional systems is suggested. The essence of this approach consists of the inverted order of operations against that of the traditional solid-state theory, viz., taking into account the local structure of the system is followed by regarding the translational symmetry of the whole chain. The first step is performed by reducing the initial system of secular equations into an effective N × N-dimensional secular problem, wherein a single equation corresponds to each of N elementary fragments of the initial chain. An implicit form of the dispersion relation and the level density function follow directly from the reduced problem without passing into the delocalized description of the system. The resulting eigenfunctions of the matrix H prove to be expressed as the Bloch sums of N nonorthogonal eigenvalue-dependent local-structure-determined orbitals of algebraic form, each of them corresponding to a definite elementary fragment of the chain. © 1996 John Wiley & Sons, Inc.
    Additional Material: 2 Ill.
    Type of Medium: Electronic Resource
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  • 6
    Electronic Resource
    Electronic Resource
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 39 (1991), S. 11-17 
    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 common quantum mechanical problem for the total class of saturated hydrocarbons has been stated and solved within the framework of the effective Hamiltonian method. A quantum mechanical substantiation of the transferability of the electronic structure characteristics (bond dipole moments, bond energies, and bond force constants) as well as the investigation of the origin of transferability have been considered for the stated class of chemical compounds.
    Additional Material: 1 Ill.
    Type of Medium: Electronic Resource
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  • 7
    Electronic Resource
    Electronic Resource
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 53 (1995), S. 245-253 
    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: Two generalized interpretations of the high-energy band (HEB) within the photoelectron spectras (PES) of alkanes, usually referred to as the C2s band, have been suggested. The quantum chemical one consists of attributing to the HEB of any alkane (CnH2n+2) the chain of n similiar orbitals ηk (k = 1…n), each of them containing mainly one 2sc AO and some contributions of another four orbitals from its nearest environment. The structure of each orbital ηk has been shown to be similar to that of the lowest totally symmetric MO of methane. The chemical interpretation of the same band involves relating it and the definite subspectrum of the full chemical graph of alkane, associated mainly with its C skeleton. The interrelation of these two complementary interpretations follows from the one-to-one correspondence between the orbitals ηk and the CH2(CH3) groups in alkane. © 1995 John Wiley & Sons, Inc.
    Additional Material: 3 Ill.
    Type of Medium: Electronic Resource
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  • 8
    Electronic Resource
    Electronic Resource
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 64 (1997), S. 481-494 
    ISSN: 0020-7608
    Keywords: Polyethylene ; energy bands ; dispersion relation ; Hamiltonian matrix eigenfunctions ; non-one-dimensionality ; Chemistry ; Theoretical, Physical and Computational Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The alternative way of solving secular problems for the Hamiltonian matrices of regular quasi-one-dimensional systems developed previously [V. Gineityte, Int. J. Quant. Chem. 60(3), 717 (1996)] has been applied to polyethylene. An implicit form of the dispersion relation has been obtained in terms of three local-structure-determined energy-dependent functions δ(ε), τ(ε), and η(ε), describing the effective interactions inside a separate CH2 group and those between first- and second-neighboring CH2 groups, respectively. The actual shapes of dispersion curves proved to be determined by relative mean values of the functions τ(ε) and η(ε) within the ε region under interest. The unusual minimum within the low-energy branch of dispersion curves situated at a low-symmetry point of the first Brillouin zone (k≈0.6π/a) has been established to appear owing to considerable values of effective interactions between the second-neighboring CH2 groups within the respective energy interval. Just the latter type of interactions has been concluded to be responsible also for non-one-dimensionality of the polyethylene chain. The Hamiltonian matrix eigenfunctions of this chain have been expressed as the Bloch sums of eigenvalue-dependent local-structure-determined basis orbitals.   © 1997 John Wiley & Sons, Inc. Int J Quant Chem 64: 481-494, 1997
    Additional Material: 5 Ill.
    Type of Medium: Electronic Resource
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  • 9
    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 dependence of the intramolecular charge transfer through the σ-electron systems of substituted hydrocarbons on the spatial arrangement of the X(SINGLE BOND)Cα and Cβ(SINGLE BOND)Cγ bonds has been studied using the perturbation theory for the one-electron density matrix (DM). Analytical expressions for the populations of the orbitals pertinent to the cis- and trans-bonds with respect to the X(SINGLE BOND)Cα bond have been obtained and analyzed. The Hamiltonian matrix elements determining the predominant direction of the above-defined charge transfer (cis or trans) have been revealed. The electron-accepting and electron-donating substituents (X) have been considered separately and the dependence of the resulting charge-transfer direction on the properties of substituent has been established. © 1996 John Wiley & Sons, Inc.
    Additional Material: 3 Ill.
    Type of Medium: Electronic Resource
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  • 10
    Electronic Resource
    Electronic Resource
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 68 (1998), S. 119-127 
    ISSN: 0020-7608
    Keywords: Brillouin theorem ; noncanonical MOs ; Rayleigh-Schrödinger perturbation theory ; saturated organic molecules ; Chemistry ; Theoretical, Physical and Computational Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The block diagonalization problem for a Fockian or a Huckel-type model Hamiltonian matrix (H) of molecule originating from the Brillouin theorem and determining the noncanonical molecular orbitals (NCMOs) has been studied. An alternative form of the problem, viz. the so-called eigenblock equation for the matrix H, has been suggested, which formally resembles the usual secular equation for certain two-dimensional matrix. The operator analog of the eigenblock equation also has been derived, and it acquired the form of the usual secular problem for an operator. However, the multidimensional eigenblocks of the matrix H, playing the role of eigenvalues in this new equation, do not commute with the respective multidimensional eigenfunctions. A noncommutative Rayleigh-Schrödinger perturbation theory (PT) has been developed for the solution of operator problems of the above-mentioned type. It has been shown that the PT used previously when obtaining the NCMOs of saturated organic molecules on the basis of the Brillouin theorem [V. Gineityte, J. Mol. Struct. (Theochem) 343, 183 (1995)] actually corresponds to the case of two eigenfunctions (eigenvalues) of the noncommutative Rayleigh-Schrödinger PT. On the whole, search for NCMOs of molecules is shown to be related to a nontrivial generalization of a two-level problem, where multidimensional (noncommutative) characteristics stand for the usual ones.   © 1998 John Wiley & Sons, Inc. Int J Quant Chem 68: 119-127, 1998
    Type of Medium: Electronic Resource
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