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  • 1
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 83 (1985), S. 3500-3506 
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: Using the translational and rotational invariance of the energy, we show that for an N-body system there exists a subset of 3N−6 Cartesian coordinates such that the derivatives of the energy of a given order with respect to the members of this subset form an independent and complete set. That is, all other derivatives can be calculated knowing these independent derivatives. We further show that this subset of coordinates can be chosen to be a bonafide set of internal coordinates. Since these coordinates are a subset of the 3N Cartesian coordinates, they are orthonormal and uniform. Applications have been made of such internal coordinates in algorithms which search for stationary points on potential energy surfaces. It is shown that the surface walking algorithms are exactly separable for these coordinates. Thus the problem can be reexpressed in terms of (3N−6) Cartesian variables without the annoying zero eigenvalues of the Hessian (of the energy) matrix corresponding to the translational and rotational eigenvalues.
    Type of Medium: Electronic Resource
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  • 2
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 82 (1985), S. 4566-4576 
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: Based upon the invariance under translations and rotations of quantum chemical one- and two-electron integrals, a method for obtaining a complete set of independent relations among integral derivatives is presented. Due to the unitary form of the operators corresponding to finite translations and rotations, this analysis is generally applicable to all orders of integral derivatives. It is shown that the number of dependent integral derivatives is equal to the number of such independent relations. These dependent integral derivatives can thus be straightforwardly determined in terms of the remaining derivatives which must be explicitly calculated. For example, out of a total of 21, 45, and 78 second-derivative integrals for the two- , three- , and four-center cases, respectively, only 1, 6, and 21 such integral derivatives need be explicitly calculated. The set of such independent and dependent integral derivatives can be chosen in a manner which imposes no restrictions on the allowable geometries of the nuclear positions. The special case of colinear nuclear centers is also separately analyzed.
    Type of Medium: Electronic Resource
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  • 3
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 84 (1986), S. 3581-3581 
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Type of Medium: Electronic Resource
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  • 4
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 95 (1991), S. 395-402 
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: A new method for correlated electronic structure calculations that makes explicit reference to valence electrons only is presented for atomic and molecular processes in which the core electrons remain inert. The method is based on constructing a valence Hamiltonian that includes a one-electron effective potential for the core–valence interactions. It exactly reproduces all properties (wave functions, energies, etc.) of an all electron calculation with frozen core wave functions with same bases. It has no adjustable parameters, and no restrictions on the choice of basis sets. It yields considerable savings of computer time and space over the corresponding all electron calculations. Self-consistent field (SCF) and complete active space multiconfiguration self-consistent field (CAS-MCSCF) test calculations on ground states of F, F−, and S are presented.
    Type of Medium: Electronic Resource
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  • 5
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 91 (1989), S. 5444-5450 
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: We show that an invariance of a system of N particles simplifies the solution of the classical equations of motion.A transformation can be constructed in a straightforward manner to yield a set of active and redundant coordinates in which Hamilton's equations are separable. That is, the redundant coordinates are cyclic and the kinetic energy is block diagonal between the two sets. Furthermore, the active coordinates have properties very similar to the parent Cartesian coordinates; e.g., the derivatives of the Hamiltonian remain unchanged. The numerical application of the procedure is very straightforward; we have performed trajectories of symmetric motions of an A2B-type molecule within the subspace of the C2v configurations.
    Type of Medium: Electronic Resource
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  • 6
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 96 (1992), S. 1150-1157 
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: We have performed a series of calculations on small models (number of atoms ranging from 10 to 34) of graphite and lithium intercalated graphite (LIG) at the UHF level with a minimal basis set for the valence electrons and an effective core potential for the core electrons (CEP-4G), where the basis and the CEP is optimal for free atoms. We have shown that small model hosts, such as C10 (Bernal i.e., AB) and C12 (primitive hexagonal, i.e., AA), enable us to make several predictions regarding LIG. Firstly, lithium looses its valence electron upon entering either type of host lattice and eventually falls into a body-centered position in an AA host lattice. Secondly, lithium strongly destabilizes the AB lattice, while it strongly stabilizes the AA lattice. Thirdly, the barrier for site hopping in the limit of infinite dilution (Ea) can be estimated along with a related quantity which we call the hilltop energy (see text). Further, we have shown that by building up to host models no larger than C32 (AA) we can make a better estimate of Ea (0.72 eV), determine that the dynamics of Li (within any two-dimensional solvated sheet) is largely determined by ionic interactions with screening from adjacent carbon layers effecting an approximately 20% reduction of naked two-dimensional Li Coulombic forces, and give a reasonable indication of how much energy is liberated as Li is moved from infinity to a vacant site in unsaturated LIG (1.1±0.7 eV).
    Type of Medium: Electronic Resource
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  • 7
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 92 (1990), S. 7330-7339 
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: Dynamics of classical systems often involve finding a path of evolution of the system between chosen initial and final configurations such as reactant and product states. We develop a method for calculating the dynamics of such classical systems posed as boundary value (configurations) problems. This method is based on recasting the principle of stationary action into a computationally tractable form which can be applied to a wide variety of boundary problems. We demonstrate that a path of minimum action does not always exist except for a short enough path. However, saddle points of the action can reveal interesting dynamical pathways. We give examples from particle mechanics and applications to reaction mechanisms for the H+H2→H2+H reaction.
    Type of Medium: Electronic Resource
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  • 8
    Electronic Resource
    Electronic Resource
    s.l. : American Chemical Society
    Journal of the American Chemical Society 101 (1979), S. 6174-6178 
    ISSN: 1520-5126
    Source: ACS Legacy Archives
    Topics: Chemistry and Pharmacology
    Type of Medium: Electronic Resource
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  • 9
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 100 (1994), S. 3695-3705 
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: A new ab initio method for fully relativistic (four-component Dirac many-body formalism) correlated electronic structure calculations, which makes explicit reference to valence electrons only, is presented for atomic and molecular processes in which the core electrons remain inert. The method exactly reproduces all properties (wave functions, energies, etc.) of an all electron calculation with frozen core wave functions and thus provides a great computational advantage. The method is based on constructing a valence Hamiltonian which includes a one-electron effective potential for the core–valence interactions. This interaction potential, which needs to be calculated once and for all, is exact for a chosen basis since it is constructed (all constituent local and nonlocal interactions) in matrix form in the current basis. This potential is used subsequently in valence-electron-only calculations, based on a novel algorithm, by constructing explicitly valence orbitals orthogonal to the core orbitals as linear combinations only among themselves. It has no adjustable parameters and no restrictions on the choice of basis sets. It yields considerable savings of computer time and space over the corresponding frozen core all-electron calculations. Dirac-Fock SCF calculations are presented for the ground states of closed- and open-shell atoms Li, Be, B, C, N, O, F, F−, Ne, Na+, Na, Al, and S for demonstration.
    Type of Medium: Electronic Resource
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  • 10
    Electronic Resource
    Electronic Resource
    s.l. : American Chemical Society
    The @journal of physical chemistry 〈Washington, DC〉 89 (1985), S. 52-57 
    Source: ACS Legacy Archives
    Topics: Chemistry and Pharmacology , Physics
    Type of Medium: Electronic Resource
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