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Applications of Resolutions of the Coulomb Operator in Quantum
Applications of Resolutions of the Coulomb Operator in Quantum

... scientists including Boltzmann [16], Planck [17], Einstein [18], de Broglie [19] and Heisenberg [20] involved in the conception of this new field of physics. As the unique feature of this new theory is the discretization or quantization of energy levels, it later became known as “quantum mechanics”. ...
PDF file - Comp Chem - University of Minnesota
PDF file - Comp Chem - University of Minnesota

... the space spanned by the strongly coupled electronic state vectors, then the electronic configuration space should be transformed to one that in some sense minimizes the nuclear momentum coupling, at least in regions where the nonadiabatic coupling is large. The fourfold way is designed to accomplish ...
Ab initio embedded cluster study of optical second harmonic
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Version 1.6 - Clark Science Center
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Lower Diamondoids and Their Derivatives as Molecular Building

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Electron-hole correlations in semiconductor quantum dots with tight-binding wave functions

... require a selection of specific atomic orbitals that cannot be explicitly related to the tight-binding parameters. Hence, a key question that we address in this work is how sensitive the calculated electron-hole properties are to specific choices of orbitals used to calculate the Coulomb matrix elem ...
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... heavy-atom molecules is solution of the eigenvalue problem using the DiracCoulomb (DC) or Dirac-Coulomb-Breit (DCB) Hamiltonians [46–48] when some approximation for the four-component wave function is chosen. However, even applying the four-component single configuration (SCF) approximation, Dirac-F ...
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Hartree–Fock method

In computational physics and chemistry, the Hartree–Fock (HF) method is a method of approximation for the determination of the wave function and the energy of a quantum many-body system in a stationary state.The Hartree–Fock method often assumes that the exact, N-body wave function of the system can be approximated by a single Slater determinant (in the case where the particles are fermions) or by a single permanent (in the case of bosons) of N spin-orbitals. By invoking the variational method, one can derive a set of N-coupled equations for the N spin orbitals. A solution of these equations yields the Hartree–Fock wave function and energy of the system.Especially in the older literature, the Hartree–Fock method is also called the self-consistent field method (SCF). In deriving what is now called the Hartree equation as an approximate solution of the Schrödinger equation, Hartree required the final field as computed from the charge distribution to be ""self-consistent"" with the assumed initial field. Thus, self-consistency was a requirement of the solution. The solutions to the non-linear Hartree–Fock equations also behave as if each particle is subjected to the mean field created by all other particles (see the Fock operator below) and hence the terminology continued. The equations are almost universally solved by means of an iterative method, although the fixed-point iteration algorithm does not always converge.This solution scheme is not the only one possible and is not an essential feature of the Hartree–Fock method.The Hartree–Fock method finds its typical application in the solution of the Schrödinger equation for atoms, molecules, nanostructures and solids but it has also found widespread use in nuclear physics. (See Hartree–Fock–Bogoliubov method for a discussion of its application in nuclear structure theory). In atomic structure theory, calculations may be for a spectrum with many excited energy levels and consequently the Hartree–Fock method for atoms assumes the wave function is a single configuration state function with well-defined quantum numbers and that the energy level is not necessarily the ground state.For both atoms and molecules, the Hartree–Fock solution is the central starting point for most methods that describe the many-electron system more accurately.The rest of this article will focus on applications in electronic structure theory suitable for molecules with the atom as a special case.The discussion here is only for the Restricted Hartree–Fock method, where the atom or molecule is a closed-shell system with all orbitals (atomic or molecular) doubly occupied. Open-shell systems, where some of the electrons are not paired, can be dealt with by one of two Hartree–Fock methods: Restricted open-shell Hartree–Fock (ROHF) Unrestricted Hartree–Fock (UHF)↑ ↑
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