Quantum mechanical region

The algorithms of the mixed classical-quantum model used in HyperChem are different for semi-empirical and ab mi/io methods. The semi-empirical methods in HyperChem treat boundary atoms (atoms that are used to terminate a subset quantum mechanical region inside a single molecule) as specially parameterized pseudofluorine atoms. However, HyperChem will not carry on mixed model calculations, using ab initio quantum mechanical methods, if there are any boundary atoms in the molecular system. Thus, if you would like to compute a wavefunction for only a portion of a molecular system using ab initio methods, you must select single or multiple isolated molecules as your selected quantum mechanical region, without any boundary atoms. 

Semi-empirical methods could thus treat the receptor portion of a single protein molecule as a quantum mechanical region but ab mdio methods cannot. However, both semi-empirical and ab initio methods could treat solvents as a perturbation on a quantum mechanical solute. In the future, HyperChem may have an algorithm for correctly treating the boundary between a classical region and an ab mdio quantum mechanical region in the same molecule. For the time being it does not. 

The mixed models used in MNDO, AMI, and PM3, are identical, because all of these three methods are derived based on NDDO. The core Hamiltonian correction due to the interaction of the charges between the quantum mechanical region and the classical region is... 

In the combined QM-MM methodology the system being studies is partitioned into a quantum mechanical region and a molecular mechanical region (Fig. 1). The quantum... 

The term that allows the quantum-mechanical region to see the MM region js the first term of equation 15.27, where the summation is over the quantum-jnechanical electrons and the MM atoms. 

The evaluation of interactions between particles inside and outside the quantum mechanical region is usually achieved on the basis of molecular mechanics, i.e. by the application of parametrised potential functions. Thus, parameters for partial charges and non-Coulombic interactions are required for all QM particles although these species are treated by quantum mechanics. The constmction of these functions is a time-consuming and tedious task requiring the evaluation of thousands of solute-solvent interaction points, which afterwards have to be fitted to an analytical representation in agreement with all other MM functions like the solvent-solvent interactions. As mentioned earlier the accuracy of these functions is in many cases insufficient for the treatment of polarisable compounds such as solvated ions [4,5,6,7,8], Sometimes these insufficiencies can be partially compensated by the inclusion of correction potentials as discussed above, but the accuracy is still not always satisfactory. 

Due to the extended size of the quantum mechanical region required for an ab initio QMCF MD simulation the only presently feasible quantum mechanical treatment... 

In this simulation the ion formed the core region . The centre of mass of the Hg + ion served as the centre of the quantum mechanical region, hence all water molecules up to a radius of 6.4 A have been included in the layer region. Figure 10-7a shows a snapshot of the simulation showing the typical arrangement of the ligands bound... 

Hybrid potentials of the type discussed in this chapter have been in use for twenty five years or so. Some of the earliest examples were those designed to study conjugated organic molecules in which the -electrons of the system were treated with a semiempirical QM method and the cr-bonding framework was described with a MM force field [8, 9], The methods were used to study the structure and spectra of the molecules [10, 11] and photoisomerization processes [12, 13], The first true combined potential in which both a and w electrons were considered in the quantum mechanical region was also developed by Warshel, in collaboration with Levitt, which they used to study the mechanism of the enzyme, lysozyme [14], They combined a semiempirical QM method to describe a portion of the enzyme and the substrate, and a standard MM force field to describe the rest of the atoms. 

Quantum Mechanical region (Active region) Modelled links between QM and MM region... 

The subscript i in Equation (11.86) refers to a quantum mechanical electron and the subscript a to a quantum mechamcal nucleus. The subscript M indicates a molecular mechanical nucleus and is its partial atomic charge. There are thus electrostatic interactions between the electrons of the quantum mechanical region and the molecular mechanical nuclei, electrostatic interactions between quantum mechanical and molecular mechanical nuclei, and van der Waals interactions between the quantum mechamcal and molecular mechanical atoms. The second and third terms in Equation (11.86) do not involve electronic coordinates and so can be calculated in a straightforward way (i.e. they are constant for a given nuclear configuration). The first term must be incorporated into the quantum mechanical calculation via one-electron integrals added to the one-electron matrix, These one-electron... 

Figure 1 Partition of the lysozyme-substrate system into quantum mechanical and classical regions. The shaded area defines the quantum mechanical region, which is presented in greater detail on the right-hand side of the Figure. Only part of the enzyme is awn, although the whole enzyme is included in the calculation.

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