Electron-structure calculations

B3.1.1.3 WHAT IS LEARNED FROM AN ELECTRONIC STRUCTURE CALCULATION ... 

F) EFFICIENT AND WIDELY DISTRIBUTED COMPUTER PROGRAMS EXIST FOR CARRYING OUT ELECTRONIC STRUCTURE CALCULATIONS... 

This tool, which they call pseudospectralmethods, promises to reduce the CPU, memory and disk storage requirements for many electronic structure calculations, thus pemiitting their application to much larger molecular systems. In addition to ongoing developments in the underlying theory and computer... 

Becke A D 1983 Numerical Hartree-Fock-Slater calculations on diatomic molecules J. Chem. Phys. 76 6037 5 Case D A 1982 Electronic structure calculation using the Xa method Ann. 

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... 

The general potential LAPW teclmiques are generally acknowledged to represent the state of the art with respect to accuracy in condensed matter electronic-structure calculations (see, for example, [62, 73]). These methods can provide the best possible answer within DFT with regard to energies and wavefiinctions. 

Gain G 2000 Large-scale electronic structure calculations using linear scaling methods Status Solidi B 217 231... 

Williams A R, Feibelman P J and Lang N D 1982 Green s-function methods for electronic-structure calculations Phys. Rev. B 26 5433... 

The conceptually simplest approach to solve for the -matrix elements is to require the wavefimction to have the fonn of equation (B3.4.4). supplemented by a bound function which vanishes in the asymptote [32, 33, 34 and 35] This approach is analogous to the fiill configuration-mteraction (Cl) expansion in electronic structure calculations, except that now one is expanding the nuclear wavefimction. While successfiti for intennediate size problems, the resulting matrices are not very sparse because of the use of multiple coordinate systems, so that this type of method is prohibitively expensive for diatom-diatom reactions at high energies. 

M. Peric, B, Engels, and S. D. Peyerimhoff, Quantum Mechanical Electronic Structure Calculations with Chemical Accuracy, S. R. Langhoff, ed., Kluwer, Dordrecht, 1995, p. 261. 

Once the least-squares fits to Slater functions with orbital exponents e = 1.0 are available, fits to Slater function s with oth er orbital expon cn ts can be obtained by siin ply m ii Itiplyin g th e cc s in th e above three equations by It remains to be determined what Slater orbital exponents to use in electronic structure calculation s. The two possibilities may be to use the "best atom" exponents (e = 1. f) for II. for exam pie) or to opiim i/e exponents in each calculation. The "best atom expon en ts m igh t be a rather poor ch oicc for mo lecular en viron men ts, and optirn i/.at ion of non linear exponents is not practical for large molecules, where the dimension of the space to be searched is very large.. 4 com prom isc is to use a set of standard exponents where the average values of expon en ts are optirn i/ed for a set of sin all rn olecules, fh e recom -mended STO-3G exponents are... 

In our hydrogen molecule calculation in Section 2.4.1 the molecular orbitals were provided as input, but in most electronic structure calculations we are usually trying to calculate the molecular orbitals. How do we go about this We must remember that for many-body problems there is no correct solution we therefore require some means to decide whether one proposed wavefunction is better than another. Fortunately, the variation theorem provides us with a mechanism for answering this question. The theorem states that the... 

The Seetion on More Quantitive Aspects of Electronic Structure Calculations introduees many of the eomputational ehemistry methods that are used to quantitatively evaluate moleeular orbital and eonfiguration mixing amplitudes. The Hartree-Foek self-eonsistent field (SCF), eonfiguration interaetion (Cl), multieonfigurational SCF (MCSCF), many-body and Moller-Plesset perturbation theories. 

Semiempirical Methods of Electronic Structure Calculation G. A. Segal, Ed., Plenum, New York (1977). 

W. J. Hehre, Practical Strategies for Electronic Structure Calculations Wavefunction, Ii-vine (1995). 

POLYRATE can be used for computing reaction rates from either the output of electronic structure calculations or using an analytic potential energy surface. If an analytic potential energy surface is used, the user must create subroutines to evaluate the potential energy and its derivatives then relink the program. POLYRATE can be used for unimolecular gas-phase reactions, bimolecular gas-phase reactions, or the reaction of a gas-phase molecule or adsorbed molecule on a solid surface. 

In principle, we could find the minimum-energy crystal lattice from electronic structure calculations, determine the appropriate A-body interaction potential in the presence of lattice defects, and use molecular dynamics methods to calculate ab initio dynamic macroscale material properties. Some of the problems associated with this approach are considered by Wallace [1]. Because of these problems it is useful to establish a bridge between the micro-... 

Computer simulations of electron transfer proteins often entail a variety of calculation techniques electronic structure calculations, molecular mechanics, and electrostatic calculations. In this section, general considerations for calculations of metalloproteins are outlined in subsequent sections, details for studying specific redox properties are given. Quantum chemistry electronic structure calculations of the redox site are important in the calculation of the energetics of the redox site and in obtaining parameters and are discussed in Sections III.A and III.B. Both molecular mechanics and electrostatic calculations of the protein are important in understanding the outer shell energetics and are discussed in Section III.C, with a focus on molecular mechanics. 

J Li, L Noodleman, DA Case. Electronic structure calculations Density functional methods with applications to transition metal complexes. In EIS Lever, ABP Lever, eds. Inorganic Electronic Structure and Spectroscopy, Vol. 1. Methodology. New York Wiley, 1999, pp 661-724. 

In the RISM-SCF theory, the statistical solvent distribution around the solute is determined by the electronic structure of the solute, whereas the electronic strucmre of the solute is influenced by the surrounding solvent distribution. Therefore, the ab initio MO calculation and the RISM equation must be solved in a self-consistent manner. It is noted that SCF (self-consistent field) applies not only to the electronic structure calculation but to the whole system, e.g., a self-consistent treatment of electronic structure and solvent distribution. The MO part of the method can be readily extended to the more sophisticated levels beyond Hartree-Fock (HF), such as configuration interaction (Cl) and coupled cluster (CC). 

Now, let us return to our discussion of carrying out an electronic structure calculation for a nanotube using helical symmetry. The one-electron wavefunc-tions can be constructed from a linear combination of Bloch functions linear combination of nuclear-centered functions Xj(r),... 

In this chapter, we will consider the other half of a model chemistry definition the theoretical method used to model the molecular system. This chapter will serve as an introductory survey of the major classes of electronic structure calculations. The examples and exercises will compare the strengths and weaknesses of various specific methods in more detail. The final section of the chapter considers the CPU, memory and disk resource requirements of the various methods. 

Experimental research chemists with little or no experience with computational chemistry may use this work as an introduction to electronic structure calculations. They will discover how electronic structure theory can be used as an adjunct to their experimental research to provide new insights into chemical problems. 

Part 1, Essential Concepts Techniques, introduces computational chemistry and the principal sorts of predictions which can be made using electronic structure theory. It presents both the underlying theoretical and philosophical approach to electronic structure calculations taken by this book and the fundamental procedures and techniques for performing them. 

Part 3, Applications, discusses electronic structure calculations in the context of real-life research situations, focusing on how it can be used to illuminate a variety of chemical problems. 

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