Hamiltonians semiempirical

The types of algorithms described above can be used with any ah initio or semiempirical Hamiltonian. Generally, the ah initio methods give better results than semiempirical calculations. HE and DFT calculations using a single deter-... 

The ah initio methods available are RHF, UHF, ROHE, GVB, MCSCF along with MP2 and Cl corrections to those wave functions. The MNDO, AMI, and PM3 semiempirical Hamiltonians are also available. Several methods for creating localized orbitals are available. 

Ab initio molecular orbital methodology or density functional theory [158-160] would be suited for this combined QM/MM approach. However, in order to be able to compute the QM energies along the Monte Carlo simulation, nowadays a semiempirical Hamiltonian, like AMI [161], is a much more computationally efficient method. Before using AMI, the goodness of the semiempirical results in gas phase in comparison with the ab initio ones has to be tested. For systems in which the semiempirical results are poor, the relation... 

Therefore the scaling transformation of the quantum-mechanical force field is an empirical way to account for the electronic correlation effects. As far as the conditions listed above are not always satisfied (e.g. in the presence of delocalized 7r-electron wavefunctions) the real transformation is not exactly homogeneous but rather of Puley s type, involving n different scale constants. The need of inhomogeneous Puley s scaling also arises due to the fact that the quantum-mechanical calculations are never performed in the perfect Hartree-Fock level. The realistic calculations employ incomplete basis sets and often are based on different calculation schemes, e.g. semiempirical hamiltonians or methods which account for the electronic correlations like Cl and density-functional techniques. In this context we want to stress that the set of scale factors for the molecule under consideration is specific for a given set of internal coordinates and a given quantum-mechanical method. 

J Semiempirical Hamiltonian (eq. (2)) First-principles many-electron Hamiltonian (eq. (6)) ... 

The eigenvalues of the first-principles Hamiltonian (19) for all RE ions are overestimated with respect to the eigenvalues of the semiempirical Hamiltonian (1) by 20-30%, as we have seen in the case of Pr3"1" in the previous section. This enabled us to introduce the ion-dependent scaling (reduction) factor by the following equation ... 

This is the simplest possible mechanistic model of the PES, derived from an approximate treatment of energy according to eq. (3.69). The FA type of treatment implies that the geminal amplitude-related ES V eqs. (2.78) and (2.81) are fixed at their invariant values eq. (3.7). This corresponds clearly to a simplified situation where all bonds are single ones. Within such a picture, the dependence of the energy on the interatomic distance reduces to that of the matrix elements of the underlying QM (MINDO/3 or NDDO) semiempirical Hamiltonian. 

According to Eqs.(38) - (41) the non-vanishing matrix elements of the semiempirical Hamiltonian (36) are given by two kinds of equations ... 

Other semiempirical Hamiltonians have also been used within the BKO model. A Complete Neglect of Differential Overlap (CNDO/2) ° study of the effect of solvation on hydrogen bonds has appeared. o The Intermediate Neglect of Differential Overlap (INDO) °2 formalism has also been employed for this purpose.2011 Finally, the INDO/S model,which is specifically parameterized to reproduce excited state spectroscopic data, has been used within the SCRF model to explain solvation effects on electronic spectra.222,310-312 jhis last approach is a bit less intuitively straightforward, insofar as the INDO/S parameters themselves include solvation by virtue of being fit to many solution ultraviolet/visible spectroscopic data.29J... 

Benighaus, T., Thiel, W. Efficiency and accuracy of the generalized solvent boundary potential for hybrid QM/MM simulations Implementation for semiempirical Hamiltonians. J. Chem. Theor. Comp. 2008,4,1600-9. 

One of the methods most frequently used in calculations of electronic excited states is the configuration interaction technique (CI). When combined with semiempirical Hamiltonians the CI method becomes an attractive method for investigations of electronic structure of large organic systems. Undoubtedly, it is the most popular method for calculations of electronic contributions to NLO properties based on the SOS formalism. The discussion of the CI/SOS techniques is presented in Section 4. 

As mentioned in section 1, the combination of the CI method and semiempirical Hamiltonians is an attractive method for calculations of excited states of large organic systems. However, some of the variants of the CI ansatz are not in practical use for large molecules even at the semiempirical level. In particular, this holds for full configuration interaction method (FCI). The truncated CI expansions suffer from several problems like the lack of size-consistency, and violation of Hellmann-Feynman theorem. Additionally, the calculations of NLO properties bring the problem of minimal level of excitation in CI expansion neccessary for the coirect description of electrical response calculated within the SOS formalism. 

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