Hamiltonian minimality

Renner-Teller Effect in Nonlinear Molecules Choice of Hamiltonian Minimal Models Pragmatic Models Benchmark Handling Effective Hamiltonians Beyond the Two-State Renner-Teller Effect... 

A Moeller-Plesset Cl correction to v / is based on perturbation theory, by which the Hamiltonian is expressed as a Hartree-Fock Hamiltonian perturbed by a small perturbation operator P through a minimization constant X... 

Semiempirical calculations are set up with the same general structure as a HF calculation in that they have a Hamiltonian and a wave function. Within this framework, certain pieces of information are approximated or completely omitted. Usually, the core electrons are not included in the calculation and only a minimal basis set is used. Also, some of the two-electron integrals are omitted. In order to correct for the errors introduced by omitting part of the calculation, the method is parameterized. Parameters to estimate the omitted values are obtained by fitting the results to experimental data or ah initio calculations. Often, these parameters replace some of the integrals that are excluded. 

The use of QM-MD as opposed to QM-MM minimization techniques is computationally intensive and thus precluded the use of an ab initio or density functional method for the quantum region. This study was performed with an AMi Hamiltonian, and the first step of the dephosphorylation reaction was studied (see Fig. 4). Because of the important role that phosphorus has in biological systems [62], phosphatase reactions have been studied extensively [63]. From experimental data it is believed that Cys-i2 and Asp-i29 residues are involved in the first step of the dephosphorylation reaction of BPTP [64,65]. Alaliambra et al. [30] included the side chains of the phosphorylated tyrosine, Cys-i2, and Asp-i 29 in the quantum region, with link atoms used at the quantum/classical boundaries. In this study the protein was not truncated and was surrounded with a 24 A radius sphere of water molecules. Stochastic boundary methods were applied [66]. 

For the calculation of the LDA ground-state one can proceed either via the direct" methods, i.e. via the glocal minimization of the total free energy with respect to the electronic degrees of freedom, or via the the diagonalization (for large PW basis-sets necessarily iterative diagonalization) of the KS Hamiltonian in combination with an iterative update of chai ge-density and potential. 

For matrices of modest dimensions 1024 matrix diagonalizations may not be a serious CPU problem for a PC, but if we include (as we will in the next chapter) distributions in the spin Hamiltonian parameters the required CPU time goes up by, say, two orders of magnitude, and if we want to implement automatic minimization, we must pay with another two or three orders of magnitude in CPU-time. 

Hamiltonian equations, 627-628 II electronic states, 632-633 triatomic molecules, 587-598 minimal models, 615-618 Hartree-Fock calculations ... 

Hamiltonian equations, 610—615 minimal models, 615-618 multi-state effects, 624 pragmatic models, 618—621 spectroscopic properties, 598-610 linear molecules ... 

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