Hartree-Fock calculation methodology

In actual practice, self-consistent Kohn-Sham DFT calculations are performed in an iterative manner that is analogous to an SCF computation. This simiBarity to the methodology of Hartree-Fock theory was pointed out by Kohn and Sham. 

The QM/MM and ab initio methodologies have just begun to be applied to challenging problems involving ion channels [73] and proton motion through them [74]. Reference [73] utilizes Hartree-Fock and DFT calculations on the KcsA channel to illustrate that classical force fields can fail to include polarization effects properly due to the interaction of ions with the protein, and protein residues with each other. Reference [74] employs a QM/MM technique developed in conjunction with Car-Parrinello ab initio simulations [75] to model proton and hydroxide ion motion in aquaporins. Due to the large system size, the time scale for these simulations was relatively short (lOps), but the influences of key residues and macrodipoles on the short time motions of the ions could be examined. 

The tautomeric forms of 5-chloro-l,2,4-triazole 4 were investigated using Hartree-Fock and Meller-Plesset methodology in the 6-31G(d) basis, and the 35C1 nuclear quadrupole resonance (NQR) frequencies were calculated subsequently. These calculations suggest that tautomer 4 is predominant <2001CHE95, 2001KGS99>. 

We have previously defined the one-electron spin-density matrix in the context of standard HF methodology (Eq. (6.9)), which includes semiempirical methods and both the UHF and ROHF implementations of Hartree-Fock for open-shell systems. In addition, it is well defined at the MP2, CISD, and DFT levels of theory, which permits straightforward computation of h.f.s. values at many levels of theory. Note that if the one-electron density matrix is not readily calculable, the finite-field methodology outlined in the last section allows evaluation of the Fermi contact integral by an appropriate perturbation of the quantum mechanical Hamiltonian. 

Finally we describe several methods that combine molecule-dependent empirical parameters with a moderate level ab initio molecular orbital method. The BAC-MP4 method of Melius and coworkers115-118 combines a computationally inexpensive molecular orbital method with a bond additivity correction. This procedure uses a set of accurate experimental data to obtain a correction for bonds of different types that is then used to adjust calculated thermochemical data such as enthalpies of formation. Quite accurate results can be obtained if suitable reference molecules are available and if the errors in the calculation are systematic. The computational methodology is based on an MP4/6-31G(d,p)//HF/6-/31G(d) calculation. A pairwise additive empirical bond correction is derived for different bonds from fitting to experimental enthalpies of formation or in some cases to high quality ab initio computations. In addition, for open-shell molecules an additional correction is needed to compensate for spin contamination of the wavefunction from higher spin states in the unrestricted Hartree-Fock (UHF) method. 

The accurate calculation of these molecular properties requires the use of ab initio methods, which have increased enormously in accuracy and efficiency in the last three decades. Ab initio methods have developed in two directions first, the level of approximation has become increasingly sophisticated and, hence, accurate. The earliest ab initio calculations used the Hartree-Fock/self-consistent field (HF/SCF) methodology, which is the simplest to implement. Subsequently, such methods as Mpller-Plesset perturbation theory, multi-configuration self-consistent field theory (MCSCF) and coupled-cluster (CC) theory have been developed and implemented. Relatively recently, density functional theory (DFT) has become the method of choice since it yields an accuracy much greater than that of HF/SCF while requiring relatively little additional computational effort. 

Outline This review concentrates on work which mainly treats ILs from theoretical considerations and not from an experimental point of view. If calculations play only a supportive role in them, articles may have been neglected on principle. We also refrain from an introduction to methodological aspects and rather refer the reader to good textbooks on the subjects. The review is organized as follows Static QC calculations are discussed in detail in the next section including Hartree-Fock, density functional theory (Sect. 2.2) and correlated (i.e., more sophisticated) methods (Sect. 2.4) as well as semiempirical methods (Sect. 2.1). We start with these kinds of small system calculations because they can be considered as a basis for the other calculations, i.e., an insight into the intermolecular forces is obtained. 

Recently, there have been several successful attempts at the calculation of spin-spin coupling constants at the density functional theory (DFT) level. " In view of the success of the DFT methodology, it would in particular be interesting to see how well DFT performs with respect to the calculation of spin-spin coupling constants. In particular, recent results demonstrated that DFT does not suffer from the triplet-instability problems that have plagued the application of Hartree-Fock theory to the calculation of spin-spin... 

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