The Lennard-Jones Term

The pj term in Eq. (1) is the well-known Lennard-Jones energy , and is computed as the sum of two terms  

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In the study of reactivity, Jorgensen and col. have normally used both, the OPLS model and potential functions derived from ab initio calculations. As we have already indicated, when intermolecular pair potentials are applied to the study of a chemical process, the evolution of charges, as well as the Lennard-Jones terms, along the reaction coordinate, has to be considered. For the SN2 reaction in water between chloride anion... 

Thus, die electrostatic interaction term of Eq. (13.2) has been separated into an operator acting on die QM electrons (the first tenn on the r.h.s. of Eq. (13.3)) and the classical term for the interacdon of the MM atoms widi the solute nuclei. The Lennard-Jones term is the same in Eqs. (13.2) and (13.3) (although the parameters may certainly be different from one model to another). 

The Lennard-Jones term describes the nonbonded interaction between the hydrogen atom of an N—H group and the oxygen atom of a C=0 group. The second term describes the electrostatic interaction between two point dipoles centered on the oxygen atom and the hydrogen atom and having the orientation of the C=0 and N—H bonds. 

In many force fields, truncation schemes are often used to reduce the number of non-bonded electrostatic and Lennard-Jones interactions that need to be calculated. Such schemes, are readily incorporated into the.inter-action Hamiltonian either by omitting all interactions that have a distance greater than some cutoff or by multiplying the appropriate interactions by a tapering function that reduces the interactions to zero beyond a certain distance. It is to be noted that in some hybrid force fields (see, for example, [35]) the electrostatic interaction terms are not included and the QM/MM interaction is due solely to the Lennard-Jones terms (and link-atoms if they are present). This could be a reasonable approximation in non-polar systems (such as the transition metal complexes for which some of these force fields were developed) but it will not be sufficiently accurate in the general case. 

The Lennard—Jones terms in Eq. [4] account for the average dispersion interactions between the QM and MM atoms, which are neglected in the... 

In addition, there are two parameters associated with the QM atoms which are treated entirely classically. They are the Lennard-Jones parameters, cr and , in the last term of the solute-solvent (QM/MM) interaction Hamiltonian. The Lennard-Jones terms are necessary in a combined QM/MM potential because some MM atoms possess no partial charges and so would be invisible to the QM particles. In cases such as chloride versus bromide ions, the only distinction between the two would be reflected in the van der Waals terms.3 However, the existence of these parameters provides the opportunity to further optimize the performance of the combined QM/MM model, whether ab initio, DFT, or semiempirical in the QM treatment. This will also overcome some of the well-known problems in the semiempirical methods, including hydrogen bonding interactions. Fortunately, the Lennard-Jones parameters depend entirely on the nature of the QM atom and sometimes its... 

In this procedure, the electronic terms of the QM/MM interaction Hamiltonian for A and B are first annihilated, leaving only the Lennard-Jones terms, which are gradually mutated from structure A into structure B. The latter mutation consists of empirical potentials, while standard methods are employed for the conversion.Absolute free energies of solvation can also be determined following a procedure developed by Cieplak and Koll-man, in which A is made to vanish in solution ... 

Hqu/mm is the Hamiltonian for the interaction between the QM and MM regions. It is the definition of this Hamiltonian which is crucial to the success of the hybrid potential method. Several forms for this term are possible but one of the simplest and probably the most widely used consists of a sum of electrostatic and Lennard-Jones terms. As in the MM potential, the electrostatic terms model the interactions between the charge distributions of different atoms whereas the Lennard-Jones terms model the short range repulsive and the longer range dispersion interactions which are not accounted for by the electrostatic interactions. For the case of mat initio QM method and an MM potential in which there are partial charges on the MM atoms, the interaction Hamiltonian will have the form ... 

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