Hartree-Fock theory, early work

Regarding TDDFT benchmark studies of chiroptical properties prior to 2005, the reader is referred to some of the initial reports of TDDFT implementations and early benchmark studies for OR [15,42,47,53,98-100], ECD [92,101-103], ROA [81-84], and (where applicable) older work mainly employing Hartree-Fock theory [52,55, 85,104-111], Often, implementations of a new quantum chemistry method are verified by comparing computations to experimental data for relatively small molecules, and papers reporting new implementations typically also feature comparisons between different functionals and basis sets. The papers on TDDFT methods for chiroptical properties cited above are no exception in this regard. In the following, we discuss some of the more recent benchmark studies. One of the central themes will be the performance of TDDFT computations when compared to wavefunction based correlated ab initio methods. Various acronyms will be used throughout this section and the remainder of this chapter. Some of the most frequently used acronyms are collected in Table 1. 

For a detailed discussion of Hartree-Fock theory, see, for instance, Szabo and Ostlund. Many parallel self-consistent field implementations have been presented in the literature for a review of some of the early work in this field, see Harrison and Shepard. Several massively parallel, distributed data self-consistent field algorithms have been implemented. For example, Colvin et al. ... 

Early work based on a statistical treatment of the core electrons was published by Hellmaim (1935) and Gombas (1935) for molecular and solid-state physics, respectively. Quantum-mechanical justifications in the framework of the Hartree and Hartree-Fock theories were given by Fenyes (1943) and Szepfalusy (1955, 1956), respectively. The first derivation of the pseudopotential approach within the Hartree-Fock formalism which came to general attention is due to Phillips and Kleinman (1959) and was later generalized by Hazi and Rice (1968). The accuracy and limitations of the pseudopotential approach... 

Historically, the field of electronic structure calculations has seen two largely independent lines of development on the one hand molecular quantum chemists have based most work on wavefunction techniques (the Hartree Fock [2, 3] and post-HF theories [4]) on the other, condensed-matter physicists had their reference method in Density Functional Theory (DFT) [5-7]. This formal division between molecular and solid-state communities has been due to the poor transferability of the standard computational methods between the two fields early DFT functionals underperform post-HF techniques in reproducing the known properties of small molecules... 

Early comparisons of this sort were based on work by Handy and coworkers [37], who developed an efficient direct FCI approach in terms of determinants. Using a double-zeta (DZ) basis set, they considered stretching the 0-H bond lengths in the H2O molecule to 1.5 and 2.0 times their equilibrium values. The FCI results showed that even the restricted Hartree-Fock (RHF) based fourth-order many-body perturbation theory (MBPT) approach [38], which includes the effect of single, double, triple and quadruple excitations, did not accurately describe the stretching of the bond the error increased from 0.6 kcal/mole at to 10.3 kcal/mole... 

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