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  • 1
    Electronic Resource
    Electronic Resource
    A density-functional calculation of dynamic dipole polarizabilities of noble gas atoms (1983)
    Springer
    Theoretical chemistry accounts 62 (1983), S. 209-217 
    Details
    ISSN: 1432-2234
    Keywords: Density-functional theory ; Dynamic polarizability ; Noble gas atoms ; Variation-perturbation method ; Direct density calculation
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology
    Notes: Abstract Using a very simple trial function and unperturbed electron densities calculated by a new procedure, the frequency-dependent dipole polarizability α (ω) of Ne, Ar, Kr and Xe has been calculated in the range 0 ≤ ω ≤ 0.45 a.u., by a Karplus-Kolker-type variation-perturbation method. Results progressively worsen for larger systems so that, for Xe, α(0) is only 75% of the experimental value. Probable reasons for this are discussed.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00548835
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  • 2
    Electronic Resource
    Electronic Resource
    On the theoretical foundation of Walsh's rules of molecular geometry in terms of the Hellmann-Feynman theoremAbstracted from part of a D.Phil. thesis submitted by B. M. Deb to the University of Oxford, 1969. (1971)
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 5 (1971), S. 411-434 
    Details
    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 new interpretation of the ordinate in a Walsh diagram for a polyatomic molecule is suggested in terms of the Hellmann-Feynman theorem. This makes use of the fact that in a single-configurational MO wave function the total one-electron density is the sum of individual densities in the occupied orbitals. Walsh-type diagrams have been constructed for three different molecules, water, ammonia and hydrogen peroxide.In H2O and NH3 calculation of the force, and thus of the energy, in terms of the valence angle, is made on the assumption that the central (heavy) atom is kept fixed while each of the lighter atoms moves in a plane containing the principal symmetry axis and the relevant bond, in a totally symmetric fashion; for H2O2 the two oxygen atoms are kept fixed.The angular correlation diagrams obtained reproduce the general features of those obtained by plotting Hartree-Fock MO energies as functions of the valence angles. The conclusion emerges that the force formulation provides a satisfactory pictorial basis for understanding molecular geometry in terms of the balance between the electron-nucleus attractive forces resulting from the charge densities in the occupied MO'S, and the nuclear repulsive forces. However, in the absence of highly accurate charge distributions such an approach is unsuitable for the quantitative prediction of molecular quantities such as valence angles, force constants or energy barriers.
    Additional Material: 8 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/qua.560050406
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  • 3
    Electronic Resource
    Electronic Resource
    Quantum fluid dynamics of many-electron systems in three-dimensional space (1982)
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 22 (1982), S. 871-888 
    Details
    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 presence of external electric and magnetic fields, the Schrödinger equation for many-electron systems is transformed into a continuity equation and an Euler-type equation of motion in configuration space. Then, using the natural-orbital Hamiltonian, as defined by Adams, the two fluid-dynamical equations are derived in the three-dimensional space. This generates a “classical” view of such quantum systems, corresponding to an MCSCF wave function: The many-electron Schrödinger fluid consists of individual fluid components, each corresponding to a natural orbital and having its own charge density and current density. The local observables, viz., the net charge density and net current density, are obtained by merely summing over the natural orbitals, with the occupation numbers as weight factors; but, the net velocity field cannot be so obtained. Further, although each fluid component moves irrotationally in the absence of a magnetic field, the net velocity field is not irrotaional. The irrotational character of each velocity component is destroyed by rotation of the nuclear framework of the system while electron spin introduces an additional term, the spin magnetization moment, into each component current density. The physical significance of the fluid-dynamical equations as well as their advantages and disadvantages are discussed.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/qua.560220503
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  • 4
    Electronic Resource
    Electronic Resource
    Internal stresses and chemical binding in the H2+ molecule (1981)
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 20 (1981), S. 1315-1329 
    Details
    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: Following an interpretive formalism presented earlier, chemical binding in the H2+ molecule has been studied in terms of the variations, with respect to R, of electrostatic field and stress components at five selected points on the interuclear axis. At three points phenomena analogous to those recorded earlier for H2 have been observed. In particular, the existence of extremal relationships for the difference density field and the total field, as well as for the corresponding stresses, at R ≃ Req for certain specific points on the internuclear axis has been confirmed. As in the case of H2, chemical binding in H2+ occurs due to local variations of electrostatic pressure from point to point in such a manner as to cause the vanishing of either the total electrostatic force density or the difference force density at certain points on the internuclear axis.
    Additional Material: 9 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/qua.560200614
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  • 5
    Electronic Resource
    Electronic Resource
    New method for the direct calculation of electron density in many-electron systems. I. Application to closed-shell atoms (1983)
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 23 (1983), S. 1-26 
    Details
    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 new density-functional equation is suggested for the direct calculation of electron density ρ(r) in many-electron systems. This employs a kinetic energy functional T2 + f(r)T0, where T2 is the original Weizsäcker correction, T0 is the Thomas-Fermi term, and f(r) is a correction factor that depends on both r and the number of electrons N. Using the Hartree-Fock relation between the kinetic and the exchange energy density, and a nonlocal approximation to the latter, the kinetic energy-density functional is written (in a.u.) \documentclass{article}\pagestyle{empty}\begin{document}$$ t[\rho] = {\raise0.7ex\hbox{$1$} \!\mathord{\left/ {\vphantom {1 4}}\right.\kern-\nulldelimiterspace}\!\lower0.7ex\hbox{$4$}}\nabla ^2 \rho + {\raise0.7ex\hbox{$1$} \!\mathord{\left/ {\vphantom {1 8}}\right.\kern-\nulldelimiterspace}\!\lower0.7ex\hbox{$8$}}(\nabla \rho \cdot \nabla \rho)/\rho + C_k f({\bf r})\rho ^{5/3}, $$\end{document} where \documentclass{article}\pagestyle{empty}\begin{document}$ C_k = {\raise0.7ex\hbox{$2$} \!\mathord{\left/ {\vphantom {2 {10}}}\right.\kern-\nulldelimiterspace}\!\lower0.7ex\hbox{${10}$}}(3\pi ^2)^{2/3} $\end{document}. Incorporating the above expression in the total energy density functional and minimizing the latter subject to N representability conditions for ρ(r) result in an Euler-Lagrange nonlinear second-order differential equation \documentclass{article}\pagestyle{empty}\begin{document}$$ \left[{ - {\raise0.7ex\hbox{$1$} \!\mathord{\left/ {\vphantom {1 2}}\right.\kern-\nulldelimiterspace}\!\lower0.7ex\hbox{$2$}}\nabla ^2 + v_{{\rm nuc}} ({\bf r}) + v_{{\rm cou}} ({\bf r}) + v_{XC} ({\bf r}) + {\raise0.7ex\hbox{$5$} \!\mathord{\left/ {\vphantom {5 3}}\right.\kern-\nulldelimiterspace}\!\lower0.7ex\hbox{$3$}}C_k g({\bf r})\rho ^{2/3}} \right]\phi ({\bf r}) = \mu \phi ({\bf r}) $$\end{document} where μ is the chemical potential, we have ρ(r) = |φ(r)|2, and g(r) is related to f(r). Numerical solutions of the above equation for Ne, Ar, Kr, and Xe, by modeling f(r) and g(r) as simple sums over Gaussians, show excellent agreement with the corresponding Hartree-Fock ground-state densities and energies, indicating that this is likely to be a promising method for calculating fairly accurate electron densities in atoms and molecules.
    Additional Material: 12 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/qua.560230104
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  • 6
    Electronic Resource
    Electronic Resource
    Phase associated with the single-particle density of many-electron systems (1991)
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 40 (1991), S. 501-510 
    Details
    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 excited states of atoms and molecules, as well as in time-dependent situations, the one-electron density no longer suffices to completely characterize the electronic state; in addition, one now requires information about the electronic phase or the current density. We show that, for a stationary electronic state, the continuity equation of quantum fluid dynamics represents a differential equation for the electronic phase, which must be solved subject to certain periodicity conditions. These periodicity conditions arise from the nodal topology of the wave function and give rise to quantized vortices of current. The consequences of writing an electronic “wave function” for a many-electron system directly in terms of the single-particle density and phase have been investigated. We have shown that such a procedure leads to the appearance of an “internal magnetic vector potential.” We also establish the connection between the electronic phase and the geometrical (“Berry”) phase accompanying the adiabatic transport of a quantal system around a closed loop in parameter space. This leads to a generalization of the current density concept and allows us to discuss the geometrical phase in terms of the circulation of this current in parameter space.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/qua.560400406
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  • 7
    Electronic Resource
    Electronic Resource
    Femtosecond quantum fluid dynamics of helium atom under an intense laser field (1998)
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 70 (1998), S. 441-474 
    Details
    ISSN: 0020-7608
    Keywords: quantum fluid dynamics ; atom-laser interaction ; femtosecond dynamics ; density functional theory ; high harmonic generation ; Chemistry ; Theoretical, Physical and Computational Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: A comprehensive, nonperturbative, time-dependent quantum mechanical (TDQM) approach is proposed for studying the dynamics of a helium atom under an intense, ultrashort (femtoseconds) laser pulse. The method combines quantum fluid dynamics (QFD) and density functional theory. It solves a single generalized nonlinear Schrödinger equation of motion (EOM), involving time and three space variables, which is obtained from two QFD equations, namely, a continuity equation and an Euler-type equation. A highly accurate finite difference scheme along with a stability analysis is presented for numerically solving the EOM. Starting from the ground-state Hartree-Fock density for He at t=0, the EOM yields the time-dependent (TD) electron density, effective potential surface, difference density, difference effective potential, ground-state probability, 〈r〉, magnetic susceptibility, polarizability, flux, etc. By a Fourier transformation of the TD dipole moment along the linearly polarized-field direction, the power and rate spectra for photoemission are calculated. Eleven mechanistic routes for photoemission are identified, which include high harmonic generation as well as many other spectral transitions involving ionized, singly excited, doubly excited (autoionizing), and continuum He states, based on the evolution of the system up to a particular time. Intimate connections between photoionization and photoemission are clearly observed through computer visualizations. Apart from being consistent with current experimental and theoretical results, the present results offer certain predictions on spectral transitions which are open to experimental verification.   © 1998 John Wiley & Sons, Inc. Int J Quant Chem 70: 441-474, 1998
    Additional Material: 14 Ill.
    Type of Medium: Electronic Resource
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  • 8
    Electronic Resource
    Electronic Resource
    “Atom” as a complex system: One- and two-dimensional cellular automata simulations (1996)
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 60 (1996), S. 21-28 
    Details
    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: One- and two-dimensional cellular automata (CA) simulations of neutral “atoms,” viewed as “complex” distributions of electron density around a central nucleus, are performed in order to explore CA-based discretized and connectionist approaches to the synthesis and structure-dynamics problems of many-electron systems. A link between CA and the quantum mechanics of atoms is made by taking the Thomas-Fermi theory as an illustrative example. Starting from a nonstationary distribution, the stationary distribution of electron density around a nucleus arises out of a natural stability criterion described through CA rules. © 1996 John Wiley & Sons, Inc.
    Additional Material: 5 Ill.
    Type of Medium: Electronic Resource
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  • 9
    Electronic Resource
    Electronic Resource
    Improved local density functional approach for atomic systems (1994)
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 51 (1994), S. 79-85 
    Details
    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: Through a new local density approximation to the kinetic energy density functional introduced by us recently, a simple Thomas-Fermi-like scheme for the direct calculation of electron density in atoms is proposed. The calculated density is nonsingular at the nucleus and the energy values are in very good agreement with the corresponding Hartree-Fock results for atoms. © 1994 John Wiley & Sons, Inc.
    Additional Material: 1 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/qua.560510203
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  • 10
    Electronic Resource
    Electronic Resource
    Time-dependent quantum fluid dynamics of the photoionization of the He atom under an intense laser field (1995)
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 56 (1995), S. 707-732 
    Details
    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 time-dependent (TD), nonperturbative quantum fluid density functional equation of motion, developed in our laboratory, is numerically solved for studying the photoionization dynamics of the He atom under an intense, ultrasharp, ultrashort laser pulse. The generalized nonlinear Schrödinger equation is obtained through a hydrodynamical continuity equation and an Euler-type equation of motion. It yields the electron density, effective potential surface, and other density-based quantities from start to finish. Starting from the ground-state Hartree-Fock density for He at t = 0, various singlet and triplet states of singly and doubly excited (autoionizing) He as well as several states of He+ have been identified in the time-evolved electron density, by a Fourier transformation of the time variable of the complex autocorrelation function. Computer visualizations of the TD difference density and difference potential show distinctly nonlinear and extremely interesting geometrical features of the oscillating atom. Detailed mechanistic routes for multiphoton, sequential, and above-threshold ionization have been obtained, each route involving many states. The present, comprehensive method reveals the important physical features of the atom-laser interaction and the calculated results are consistent with current experimental and theoretical results. This emphasizes the validity of the hydrodynamical approach for studying TD quantum mechanical phenomena. © 1995 John Wiley & Sons, Inc.
    Additional Material: 7 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/qua.560560608
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