Computational chemistry electronic textbooks

With the advent of the electronic computers in the early 1950s it was finally possible to reexamine the two main approaches, and to take a closer look at the error implicit in these formulations. Thus we witness a three-way effort first, to establish a solid theoretical method, second, to develop all the needed mathematical algorithms for its implementation and third to be able to effectively use the new tool, the electronic computer, to obtain routinely numerical solutions. Incidentally, at the time there were relatively few quantum chemical textbooks computationally relevant , computers were still extremely expensive and rare in short computational chemistry hardly existed for lack of teachers, students, hardware and software. 

Although computational chemistry has developed into a classroom subject, there is no major change with regard to introductory-level textbooks commonly used. In computational quantum chemistry, textbooks such as Ab initio Molecular Orbital Theory of Hehre, Radom, Pople, and Schleyer or Modem Quantum Chemistry of Szabo and Ostlund are still among the most frequently used. With regard to advanced-level textbooks, the situation is quite different. Several new publications, mainly in the form of monographs, have appeared and help to disseminate the state-of-the-art methods. Examples are Modern Electronic Structure Theory edited by D. R. Yarkony, or the Lecture Notes in Quantum... 

Although all his research applications are in the realm of ab initio electronic structure theory and computations, Rauk has taught the theory of structure and bonding from a frontier orbital point of view. He is the author of a graduate-level textbook on the orbital interaction theory of organic chemistry.208... 

The molecular volume descriptor, V, can be recognized as an important descriptor once one realizes that the free energy of solution is related in part to the size of the cavity that must be carved out of the solvent bath by the solute molecule during the solvation process. The surface area, A, of a molecule or a fragment of a molecule may be construed as a measure of the region available for interaction with another molecule. For computing V and A, one could use a particular electron density contour or a non-QM-derived measure of atomic size such as the van der Waals radii available from standard tables in physical chemistry textbooks. 

The rise of density functional theory (DPT) to the prominence and popularity it enjoys today was hardly anticipated by computational chemists 40 or even 30 years ago. As recently as 1983, when DPT was but a footnote in quantum chemistry textbooks, Robert Parr was writing a review to alert the physical chemistry community to the promise and the charm of the density functional theory of electronic structure of atoms and molecules [1]. Two decades later, DPT is a household tool for computing everything from atoms to biopolymers. How did this extraordinary reversal of fortunes come about ... 

The field of relativistic electronic structure theory is generally not part of theoretical chemistry education, and is therefore not covered in most quantum chemistry textbooks. This is due to the fact that only in the last two decades have we learned about the importance of relativistic effects in the chemistry of heavy and super-heavy elements. Developments in computer hardware together with sophisticated computer algorithms make it now possible to perform four-component relativistic calculations for larger molecules. Two-component and scalar all-electron relativistic schemes are also becoming part of standard ab-initio and density functional program packages for molecules and the solid state. The second volume of this two-part book series is therefore devoted to applications in this area of quantum chemistry and physics of atoms, molecules and the solid state. Part 1 was devoted to fundamental aspects of relativistic electronic structure theory. Both books are in honour of Pekka Pyykko on his 60 birthday - one of the pioneers in the area of relativistic quantum chemistry. 

Our aim in this chapter will be to establish the basic elements of those quantum mechanical methods that are most widely used in molecular modelling. We shall assume some familiarity with the elementary concepts of quantum mechanics as found in most general physical chemistry textbooks, but little else other than some basic mathematics (see Section 1.10). There are also many excellent introductory texts to quantum mechanics. In Chapter 3 we then build upon this chapter and consider more advanced concepts. Quantum mechanics does, of course, predate the first computers by many years, and it is a tribute to the pioneers in the field that so many of the methods in common use today are based upon their efforts. The early applications were restricted to atomic, diatomic or highly symmetrical systems which could be solved by hand. The development of quantum mechanical techniques that are more generally applicable and that can be implemented on a computer (thereby eliminating the need for much laborious hand calculation) means that quantum mechanics can now be used to perform calculations on molecular systems of real, practical interest. Quantum mechanics explicitly represents the electrons in a calculation, and so it is possible to derive properties that depend upon the electronic distribution and, in particular, to investigate chemical reactions in which bonds are broken and formed. These qualities, which differentiate quantum mechanics from the empirical force field methods described in Qiapter 4, will be emphasised in our discussion of typical applications. 

Eq.(2.14) is called the Roothaan equation and widely used as the basic equation in many computational program codes in quantum chemistry. Improvement of the approximation beyond the Hartree-Fock method introduced here, say taking account of the electron correlation effect, are discussed in many textbooks. 

The theorem that forces acting on nuclei result from classical interactions with electron density (computed by a quantum mechanical method) was first proved ty Hans Gustav Adolf Hellmann in the world s first textbook of quantum chemistry Einflihning... 

In most cases, however, the relativistic effects are rather weak and may be separated into spin-orbit coupling effects and scalar effects. The latter lead to compression and/or expansion of electron shells and can rather accurately be treated by modifying the one-electron part of the non-relativistic many-electron Hamiltonian. With this scalar-relativistic Hamiltonian the (modified) energies and wave functions are computed and subsequently an effective spin-orbit part is added to the Hamiltonian. The effects of the spin-orbit term on the energies and wave functions are commonly estimated using second-order perturbation theory. More information for the interested reader can be found in excellent textbooks on relativistic quantum chemistry [2, 3]. 

Energy is an extensive property. This fundamental thermodynamic principle is introduced early in most general chemistry textbooks, and it provides the foundation for the supermolecule description of intermolecular interactions. Unfortunately, not all electronic structure techniques are size con-sistent (or more generally size extensive ). That is, the energy computed by some methods does not scale properly with the number of noninteracting fragments. Readers interested in more detail may be interested in the sections discussing size consistency and extensivity in the review of coupled-cluster theory by Crawford and Schaefer. ... 

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