BASICS OF QUANTUM CHEMISTRY

The approximation techniques described in the earlier sections apply to any (non-relativistic) quantum system and can be universally used. On the other hand, the specific methods necessary for modeling molecular PES that refer explicitly to electronic wave function (or other possible tools mentioned above adjusted to describe electronic structure) are united under the name of quantum chemistry (QC).15 Quantum chemistry is different from other branches of theoretical physics in that it deals with systems of intermediate numbers of fermions - electrons, which preclude on the one hand the use of the infinite number limit - the number of electrons in a system is a sensitive parameter. This brings one to the position where it is necessary to consider wave functions dependent on spatial r and spin s variables of all N electrons entering the system. In other words, the wave functions sought by either version of the variational method or meant in the frame of either perturbational technique - the eigenfunctions of the electronic Hamiltonian in eq. (1.27) are the functions D(xi. xN) where. r, stands for the pair of the spatial radius vector of i-th electron and its spin projection s to a fixed axis. These latter, along with the 

15 Modern quantum chemistry is described in numerous books of which we mention [17,18,27,29,30]. They differ in detail and depth. 

16 The nature of these conditions is still under dispute. The fact that too small particles cannot be ordered derives from quantum mechanics [21]. But the question whether the Pauli principle is an independent axiom of quantum mechanics or not is still unclear [34]. 

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Nice introduction to the basics of quantum chemistry, then a focus on semiem-pirical calculations and perturbation methods. Although published more than 40 years ago, the fundamentals, like the Schrodinger equation and wavefunctions, remain true, and the engagingly assertive style of the doyen of modem semiempiri-cal methods makes this book worth reading. 

Some familiarity with the very basics of quantum chemistry is assumed on the part of tlie reader Tlie Schrddinger equation, various Hamiltonians, the significance of ab initio vs. semi-empirical methods and 1-electron methods, and common parametrizations such as modified neglect of differential overlap (MNDO). These are found today in bachelor s level courses in nearly all the physical sciences, and can be gleaned from any introductory quantum chemistry book. The terminology we will use is that of quantum chemistry rather than quantum physics. We attempt as far as possible to stay away from multitudinous equations, which can be cumbersome for the lay reader from another field, and difficult-to-understand representations, such as band structures illustrated in terms of wavevectors. We instead focus on a comparison of results of various methods in terms of which is most useful in interpreting experimental data and predicting CP properties. Equations and band structures are however cited in appendices at the end of the chapter for reference. 

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