Wave function-based quantum chemistry

We begin our discussion of wave function based quantum chemistry by introducing the concepts of -electron and one-electron expansions. First, in Sec. 2.1, we consider the expansion of the approximate wave function in Slater determinants of spin orbitals. Next, we introduce in Sec. 2.2 the one-electron Gaussian functions (basis functions) in terms of which the molecular spin orbitals are usually constructed the standard basis sets of Gaussian functions are finally briefly reviewed in Sec. 2.3. 

Although the most accurate calculations are usually not possible on systems of biological interest, a careful calibration of each level in the hierarchy ensures that even the results of the simpler calculations may be used with confidence. Indeed, the presence of such systematic, universally adopted hierarchies is probably the most distinctive feature of modern wave function-based quantum chemistry, setting it apart from other computational techniques of electronic structure. 

This book starts with seven chapters devoted to methods for the computation of molecular structure molecular mechanics, semiempirical methods, wave function-based quantum chemistry, density-functional theory methods, hybrid methods, an assessment of the accuracy and applicability of these methods, and finally 3D structure generation and conformational analysis. 

These problems can be solved if one starts from the (untruncated ) Foldy-Wouthuysen transformation for a free particle, the only case for which the transformation is known anal3d ically, and incorporates the effects of the external potential on top. Along these lines, the so-called Douglas-Kroll-HeB (DKH) method [61-64] is constructed which is probably the most successful quasi-relativistic method in wave function based quantum chemistry. No details will be given here since this topic has been extensively discussed in volume 1 [34] of this series. Meanwhile several density functional implementations exist based on the Douglas-Kroll-HeJ3 approach [39-45]. In recent years. 

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