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Hartree-Fock method notations

This chapter introduces the basic concepts, techniques, and notations of quantum chemistry. We consider the structure of many-electron operators (e.g., the Hamiltonian) and discuss the form of many-electron wave functions (Slater determinants and linear combinations of these determinants). We describe the procedure for evaluating matrix elements of operators between Slater determinants. We introduce the basic ideas of the Hartree-Fock approximation. This allows us to develop the material of this chapter in a form most useful for subsequent chapters where the Hartree-Fock approximation and a variety of more sophisticated approaches, which use the Hartree-Fock method as a starting point, are considered in detail. [Pg.39]

The calculation of Mitroy started by calculating the Hartree—Fock approximation to the ground state 3s where we denote the states by the orbitals of the two active electrons in the configuration with the largest coefficient, in addition to the symmetry notation. The calculation used the analytic method with the basis set of Clementi and Roetti (1974) augmented by further Slater-type orbitals in order to give flexibility for the description of unoccupied orbitals. The total energy calculated by this method was —199.614 61, which should be compared with the result of a numerical Hartree—Fock calculation, —199.614 64. [Pg.136]

In principle, the correspondence between the two theories is not complete, because scattering theory is the more general formulation. For our purposes, however, the fact that the applications to atomic physics obtained by both methods are quite consistent with each other is an important and useful conclusion. The same result and connections have been obtained independently by Komninos and Nicolaides [378]. Both [373] and [378] noted that the derivation of MQDT from Wigner s scattering theory establishes its basic structure and theorems without special assumptions about the asymptotic forms of wavefunctions. The approach of Komninos and Nicolaides [378] is designed for applications involving Hartree-Fock and multiconfigurational Hartree-Fock bases. In the present exposition, we follow the approach and notation of Lane [379] and others [380, 381], who exploit the analytic K-matrix formalism and include photon widths explicitly when interferences occur. [Pg.248]

To describe a quantum-mechanical calculation, one specifies the method and the basis set. The letters HF (for Hartree-Fock) denote any ab initio SCF MO calculation, whether or not the basis set is large enough to come close to the Hartree-Fock limit. Thus the notation HF/3-21G denotes an ab initio SCF MO calculation that uses the 3-21G basis set. [Pg.494]

In the notation CI-SD/DZP, the method used precedes the slash and the basis-set designation follows the slash. For the SCF MO method, the abbreviation HF (for Hartree-Fock) is often used, without implying that the Hartree-Fock limiting energy has been reached. Thus, HF/3-21G signifies an SCF MO calculation with the 3-21G basis set... [Pg.559]

In reality, elearons avoid each other better than can be described by a Hartree-Fock (HF) wavefunction. The ab initio total energy of an HF wavefunction is in error with respect to the true nonrelativistic energy by an amount called the correlation energy. A wavefunction that accounts for more of the elearon correlation gives a lower (better) total energy. There are two popular methods to account for electron correlation. To properly explain these requires a fuller development than is possible here. However, we wish to mention them in order to at least give a flavor of what is involved. The interested reader is direaed to excellent texts that describe details of the notation. [Pg.334]

Four different Fock/Kohn-Sham operators have been applied to obtain the orbitals, which are subsequently localized by the standard Foster-Boys procedure. In addition to the local/semi-local functionals LDA and PBE, the range-separated hybrid RSHLDA [37, 56] with a range-separation parameter of /r = 0.5 a.u. as well as the standard restricted Hartree-Fock (RHF) method were used. The notations LDA[M] and LDA[0] refer to the procedure applied to obtain the matrix elanents either by the matrix algebra [M] or by the operator algebra [O] method. All calculations were done with the aug-cc-pVTZ basis set, using the MOLPRO quantum chemical program package [57]. The matrix elements were obtained by the MATROP facility of MOLPRO [57] the Cg coefficients were calculated by Mathematica. [Pg.106]


See other pages where Hartree-Fock method notations is mentioned: [Pg.318]    [Pg.300]    [Pg.107]    [Pg.181]    [Pg.121]    [Pg.83]    [Pg.110]    [Pg.126]    [Pg.14]    [Pg.298]    [Pg.118]    [Pg.527]    [Pg.315]   
See also in sourсe #XX -- [ Pg.84 ]




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Hartree-Fock method

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