Journal•ISSN: 0065-3276

# Advances in Quantum Chemistry

Elsevier BV

About: Advances in Quantum Chemistry is an academic journal published by Elsevier BV. The journal publishes majorly in the area(s): Density functional theory & Molecular orbital. It has an ISSN identifier of 0065-3276. Over the lifetime, 897 publications have been published receiving 26567 citations.

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TL;DR: In this paper, a model that relies on the knowledge of the molecular electrostatic potential, which is derived from a molecular wave function by using the usual methods for calculating the mean expectation value of an operator, is discussed.

Abstract: Publisher Summary This chapter discusses a model that relies on the knowledge of the molecular electrostatic potential, which is derived from a molecular wavefunction by using the usual methods for calculating the mean expectation value of an operator. In its basic premises the model employs quantum mechanics, with only the approximations necessary in molecular quantal calculations. The model is also discussed regarding its relationships with the Hellmann–Feynman theorem. The electrostatic potential V itself is examined in order to show how the electrostatic potential reflects the characteristics of the electronic distribution of a molecule and then the reliability of V is discussed as a reactivity index. The shape of the electrostatic potential and its relationship to the electronic molecular structure is discussed with the aid of various examples. One of them includes the glycine tautomers and the corresponding anion example. The chapter also discusses the electrostatic molecular potential in terms of local group contributions.

1,116 citations

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TL;DR: The main point of the method of Gaspar, Kohn, and Sham is that they derived the approximate exchange correction from an approximate Hamiltonian for the system by varying the spin-orbitals to minimize the average value of this Hamiltonians for the ground state as discussed by the authors.

Abstract: Publisher Summary This chapter discusses statistical exchange-correlation in the self-consistent field. There are two sides to a self-consistent field calculation: the determination of the potential and the solution of Schrodinger's equation for the one-electron problem. The solution of Schrodinger's equation has fortunately advanced far enough through the application of the electronic digital computer so that it can be regarded for most purposes as being a standardized technique. The main point of the method of Gaspar, Kohn, and Sham is that they derive the approximate exchange correction from an approximate Hamiltonian for the system by varying the spin-orbitals to minimize the average value of this Hamiltonian for the ground state. The approximate Hamiltonian has many important and valuable features that are described in the chapter.

874 citations

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TL;DR: In this paper, the linear-response limit of time-dependent density functional theory along with applications to the photo-response of atoms, molecules and metallic surfaces is described, and a simplified version of the time dependent Kohn and Sham (KS) scheme is implemented in this context.

Abstract: Publisher Summary
Density functional theory for stationary states or ensembles is a formulation of many-body theory in terms of the particle density Time-dependent density functional theory as a complete formalism is of more recent origin, although a time-dependent version This chapter describes the linear-response limit of time-dependent density functional theory along with applications to the photo-response of atoms, molecules and metallic surfaces Beyond the regime of linear response, the description of atomic and nuclear collision processes appears to be a promising field of application where the time-dependent Kohn and Sham (KS) scheme could serve as an economical alternative to time-dependent configuration-interaction calculation So far, only a simplified version of the time-dependent KS scheme has been implemented in this context Another possible application beyond the regime of linear response is the calculation of atomic multiphoton ionization which, in the case of hydrogen, has recently been found 54i55 to exhibit chaotic behavior A full-scale numerical solution of the time-dependent Schriidinger equation for a hydrogen atom placed in strong time-dependent electric fields has recently been reported A time-dependent Hartree–Fock calculation has been achieved for the multiphoton ionization of helium For heavier atoms an analogous solution of the time dependent Kohn-Sham equations offers itself as a promising application of time-dependent density functional theory

868 citations

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TL;DR: In the self-consistent field (SCF)-Xα scattered-wave model that is also a first-principle technique, there is no basis set problem because Schrodinger's equation for an Xα potential is numerically integrated as discussed by the authors.

Abstract: Publisher Summary The limitations of applying an ab initio linear combination of atomic orbitals (LCAO) methods to complex molecules and solids are the size of the basis sets and the number of multicenter integrals or equivalent Hartree-Fock matrix elements In the self-consistent field (SCF)-Xα scattered-wave model that is also a first-principle technique, there is no basis-set problem because Schrodinger's equation for an Xα potential is numerically integrated There are no multicenter integrals and the model is practicable in both spin-restricted and spin-unrestricted forms for polyatomic systems of considerable stereochemical complexity The SCF-Xα scattered-wave technique uses only a small fraction of the computer time required by an ab initio Hartree–Fock LCAO method The applications of the scattered-wave method to polyatomic molecules and crystals are concerned with the generation of one-electron energy and wave functions While an SCF-Xα one-electron analysis leads to an accurate quantitative description of many chemical and physical properties, it is also very important to determine the total many-electron energy As the present method leads to a rapidly convergent numerical representation of the orbital wave functions, the accuracy of the theoretical model can easily be improved via perturbation theory, when necessary Finally, the original theoretical formalism can be extended to more general forms of superposed-atom Xα potentials by means of the generalized scattered-wave theory

755 citations

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TL;DR: In this paper, the problem of reducing molecular orbital calculations to expressions involving one-and two-electron integrals over the spatial coordinates, with coefficients determined by the group theoretical properties of the spin functions and the electronic permutations, is addressed.

Abstract: Publisher Summary This chapter deals with the formal problem of reducing molecular orbital calculations to expressions involving one- and two-electron integrals over the spatial coordinates, with coefficients determined by the group theoretical properties of the spin functions and the electronic permutations. This problem is encountered, for example, when one undertakes to write the expectation value of the Hamiltonian for a given anti-symmetrized spin-orbital product, and in that particular case, the answer is well-known. The focus is on wave functions, which are constructed to be eigenfunctions of the spin, and shall consider the reduction of expressions not only for the energy and other spin-free one- and two-electron operators, but also for general one- and two-electron spin-dependent operators, such as the spin density or the Fermi contact interaction. It has been shown as how a spin-projected single-determinantal wave function based on different spatial orbitals for different spins can be related to the matrix representation method, and it is shown, how to calculate expectation values of both spin-free and spin-dependent operators.

696 citations