Electronic structure self-consistent field methods

Roos B O 1987 The complete active space self-consistent field method and its applications in electronic structure calculations Adv. Chem. Phys. 69 399-445... 

K. P. Lawley, Ed., chapter 69,399. John Wiley Sons Ltd., Chichester, England, 1987. The Complete Active Space Self-Consistent Field Method and its Applications in Electronic Structure Calculations. 

B. O. Roos, The Complete Active Space Self-Consistent Field Method and Its Application in Electronic Structure Calculation, Volume 69 olAdvances in Chemical Physics, Wiley, Chichester, 1987, p. 399. 

B. O. Roos. The complete active space self-consistent field method and its apphca-tion in electronic structure calculations. In K. P. Lawley, editor, Ab Initio Methods in Quantum Chemistry. Part II, volume 69 of Adv. Chem. Phys., pages 399-446. John Wiley, Chichester, 1987. 

Recently, the effects of static and dynamic structural fluctuations on the electron hole mobility in DNA were studied using a time-dependent self-consistent field method [33]. The motion of holes was coupled to fluctuations of two step parameters of a duplex, rise and twist (Fig. 1), namely the distances and the dihedral angles between base pairs, respectively. The hole mobility in an ideally ordered poly(G)-poly(C) duplex was found to be decreased by two orders of magnitude due to twisting of base pairs and static energy disorder. A hole mobility of 0.1 cm V s was predicted for a homogeneous system the mobility of natural duplexes is expected to be much lower [33]. In this context, one can mention several theoretical studies, based on band structure approaches, to estimate the electrical conductivity of DNA [85-87]. 

B.O.Roos, The Complete Active Space Self-Consistent Field Method and its Application in Electronic Structure Calculations. 

The focus then shifts to the delocalized side of Fig. 1.1, first discussing Hartree-Fock band-structure studies, that is, calculations in which the full translational symmetry of a solid is exploited rather than the point-group symmetry of a molecule. A good general reference for such studies is Ashcroft and Mermin (1976). Density-functional theory is then discussed, based on a review by von Barth (1986), and including both the multiple-scattering self-consistent-field method (MS-SCF-ATa) and more accurate basis-function-density-functional approaches. We then describe the success of these methods in calculations on molecules and molecular clusters. Advances in density-functional band theory are then considered, with a presentation based on Srivastava and Weaire (1987). A discussion of the purely theoretical modified electron-gas ionic models is... 

One very prominent development in DFT has been the coupling of electronic structure calculations (which, when the ground state is concerned, apply to zero temperature) with finite-temperature molecular dynamics simulations. The founding paper in this field was published by Carr and Parrinello in 1985 [13]. Carr and Parrinello formulate effective equations of motion for the electrons to be solved simultaneously with the classical equations of motion for the ions. The forces on the ions are calculated from first principles by use of the Hellman-Feynman theorem. An alternative to the Carr-Parrinello method is to solve the electronic structure self-consistently at every ionic time step. Both methods are referred to as ab initio molecular dynamics (AIMD) [14]. 

THE COMPLETE ACTIVE SPACE SELF-CONSISTENT FIELD METHOD AND ITS APPLICATIONS IN ELECTRONIC STRUCTURE CALCULATIONS... 

Aspects of the relativistic theory of quantum electrodynamics are first reviewed in the context of the electronic structure theory of atoms and molecules. The finite basis set parametrization of this theory is then discussed, and the formulation of the Dirac-Hartree-Fock-Breit procedure presented with additional detail provided which is specific to the treatment of atoms or molecules. Issues concerned with the implementation of relativistic mean-field methods are outlined, including the computational strategies adopted in the BERTHA code. Extensions of the formalism are presented to include open-shell cases, and the accommodation of some electron correlation effects within the multi-configurational Dirac-Hartree-Fock approximation. We conclude with a survey of representative applications of the relativistic self-consistent field method to be found in the literature. 

There is, in principle, nothing which limits the self-consistent field method to any particular form of the exchange-correlation potential, and the procedure outlined above has been used in connection with several approximations for exchange and correlation. Most notable in this respect is SLATER S Xa method [1.4] which has been applied to all atoms in the periodic table, to some molecules, and in the majority of the existing electronic-structure calculations for crystalline solids. 

There are no analytical forms for the radial functions, / ni(r), as solutions of the radial wave equation. Hartree, in 1928, developed the standard solution procedure, the self-consistent field method for the helium atom by using the simple product forms of equation 1.10 to represent the two-electron wave function. Herman and Skillman (4) programmed a very useful approximate form of the Hartree method in the early 1960s for atomic structure calculations on all the atoms in the Periodic Table. An executable version of this program, based on their FORTRAN code, modified to output data for use on a spreadsheet is included with the material on the CDROM as hs.exe. 

The Englishman, Hartree (1,60) the Russian, Fock (2,3) and the American, Slater (5-7), in the early development of modern quantum mechanics, pioneered the calculation of atomic electronic structure. Hartree based his method on the variation principle and this led naturally to the development of the self-consistent field method, which is at the heart of the design of modem molecular orbital programs. 

The formal analysis of the mathematics required incorporating the linear combination of atomic orbitals molecular orbital approximation into the self-consistent field method was a major step in the development of modem Hartree-Fock-Slater theory. Independently, Hall (57) and Roothaan (58) worked out the appropriate equations in 1951. Then, Clement (8,9,63) applied the procedure to calculate the electronic structures of many of the atoms in the Periodic Table using linear combinations of Slater orbitals. Nowadays linear combinations of Gaussian functions are the standard approximations in modem LCAO-MO theory, but the Clement atomic calculations for helium are recognized to be very instructive examples to illustrate the fundamentals of this theory (67-69). 

A. C. Wahl and G. Das, The multiconfiguration self-consistent field method, in Methods of Electronic Structure Theory H. F. Schaefer III (Ed.), Plenum, New York, 1977, p. 51. In addition to a survey of the formalism, this article contains a selection of numerical results. 

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