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The PCM (point charge method) in VAMP

The combined QM/MM method in VAMP - PCM



Theory behind the PCM

Detailed descriptions of the PCM theory are given in ref. [1] and [2]. Usually quantum mechanical calculation assume a single molecule in a state which can be considered as a very high vacuum since there are no interactions with other species present.
The influence of additional molecules especially large ones like zeolite frameworks or proteins is treated by the PCM option in the semiempirical program VAMP. While the smaller molecule (ligand or guest) is handled in the usual quantum mechanical fashion, the larger environment is treated by the means of molecular mechanics similar to force fields. If there is a strict separation of the considered two systems having no covalent bonds between the quantum mechanical and the molecular mechanical part the calculation of the interactions can be limited to the intermolecular ones.
The total energy of both systems together is:

Etot = EQM + EMM + EQM,MM

which is the sum of the energy of the QM and the MM-system plus the interaction energy arising from the MM-system towards the QM-system. This interaction energy can be divided in two terms:

EQM,MM = EvdW + Epolarize

The van der Waals energy which is similar to the expression used in various force-fields containing a Lennard-Jones(6-12) potential which parameters are similar to the UFF force-field.[3]
While the van der Waals interactions are subject to extensive parameterization the electronic interaction energy which leads to a polarization of the QM-part by the MM-part can be calculated more consequent. This Coulomb interaction can be divided into core and electronic terms using the Born-Oppenheimer approximation. This involves a perturbation of the original QM Hamiltonian as well as the Fock matrix. The influence of the point charges in the environment can be screened by a constant, distance dependent or sigmoidal dielectricum .epsilon..
Thus the total energy of the QM-molecule finally yields:

ESCF(QM) = EoSCF + Eelec + Ecore + EvdW

References
[1] A. Alex, B. Beck, P. Gedeck, H. Lanig, T. Clark
J. Mol. Model., 5 (1999) 1-7. [2] M. C. Hutter, J. M. Hughes, J. R. Reimers, N. S. Hush
J. Phys. Chem. B 103 (1999) 4906-4915 [3] a) A. K. Rappé, C. Casewit, K. S. Colwell, W. A. Goddard III., W. M. Skiff
J. Am. Chem. Soc., 114 (1992) 10024.
b) C. J. Casewit, K. S. Colwell, A. K. Rappé
J. Am. Chem. Soc., 114 (1992) 10046.

Examples

methotrexate in 4dfr methylbutane in zeolite X cofactors in the photosyntheic reaction centre of Rh. viridis
These examples from my Ph.D. thesis show how the PCM was applied to investigate the binding position of an inhibitor inside the active site of an enzyme and for the calculation of heats of adsorption within zeolites. For further applications to zeolites see ref. [1] above. Another example is the application to the cofactors in the photosynthetic reaction centre in purple bacteria (see ref. [2]). Input examples are shown in the next section.

PCM related Keywords

PCM, filename, epsilon file type = vmp , mol, mol2, hin under construction

HYPERCHEMTM interface and related keywords

Seeing is believing, but finding a small organic molecule inside a large protein can be difficult. Therefore I have created an interface which makes the result of a VAMP calculation visible using HYPERCHEM. HYPERCHEMTM is available from Hypercube, Inc. for PC and SGI workstations.

HINOUT

The keyword HINOUT will create a filename.hin file in our output directory which can be retrieved by the HYPERCHEM browser. This works as well for normal semiempirical calculation as for PCM. As result of a PCM calulation the semiempirical treated molecule is always the last molecule in the .hin file. If possible AMBER atom types are determined.

ACSL

To improve the visuability the ACSL keyword can be used together with both HINOUT and PCM. This causes a special alignment to the semiempirical molecule. Depending on your HYPERCHEM preferences concerning the "selection" you will see the molecule highlighted or in a different colour than the rest of the structure. The nearest atoms in the MM-part will also be selected facilitating visual inspection.
ACSL makes use of information about amino acid residues if the environment file is a HYPERCHEM .hin file. Instead of just single atoms all heavy atoms of the nearest residues will be selected. Hydrogen atoms involved in possible hydrogen bonds to the semiempirical molecule will also be selected.
M. Hutter 22. June 1999

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