Energy Lennard-Jones term

The empirical XI potential (3.1) [248] consisting of a Lennard-Jones term for the nonelectrostatic part and a three-point-charge model for the electrostatics is used [140] to describe the N2-N2 interactions. The substrate-mediated dispersion energy as formulated by McLachlan [49, 225] is included... 

In the TIP4P model there is a (12-6) Lennard-Jones term centered at the oxygen atom with the parameters cr= 3.1536 A and = 0.649 kJ/mol. This larger value for s compared with the ST2 and TIP5P models compensates for the reduction in Coulomb energy because of the fact that the opposite charges cannot approach as near as in a 5-point model. 

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 ... 

The potential parameters used in the present calculations are identical to those in [18]. The ion interacts via electrostatic and Lennard-Jones terms, Vjj= - 332Qjgi/rjj + AjAj/r f - BjBj/rfj, where the subscript / denotes the ion and j is another atom with which it interacts. In order to calibrate the calculated hydration energies for different ions versus the non-bonded parameters, we first carry out FEP/MD simulations of a solvated ion in water. In these calculations, the Lennard-Jones parameters of the ion were gradually changed from (X , B ) = (2340.0,25.0) to (/4, B ) = (5.0,1.0). The calibration calculations in water covered a total simulation time of 40 ps for both the forward and backward transformation direction. 

In this study, n-hexane, n-hexadecane and cyclohexane are assumed as lubricants. The 3-D models of lubricants are shown in Figure 2. The intramolecular and intermolecular interactions are calculated using the OPLS-AA, optimized potentials for liquid simulations -all atom, force field potential [10,11]. In this force field, the potential energy function consists of harmonic bondstretching and angle-bending terms, a Fourier series for torsional energetics, and Coulomb and Lennard-Jones terms for the nonbonded interactions, as defined in eqs. (l)to(4). 

Ligand-Protein Interactions The energy of formation of ligand-protein contacts can be computed as a sum of non-bonded (Lennard-Jones and electrostatic) terms similar to those used in a molecular dynamics simulation. 

The Lennard-Jones 12-6 potential contains just two adjustable parameters the collision diameter a (the separation for which the energy is zero) and the well depth s. These parameters are graphically illustrated in Figure 4.34. The Lennard-Jones equation may also be expressed in terms of the separation at which the energy passes through a minimum, (also written f ). At this separation, the first derivative of the energy with respect to the internuclear distance is zero (i.e. dvjdr = 0), from which it can easily be shown that v = 2 / cr. We can thus also write the Lennard-Jones 12-6 potential function as follows ... 

The Lennard-Jones potential is characterised by an attractive part that varies as r ° and a repulsive part that varies as These two components are drawn in Figure 4.35. The r ° variation is of course the same power-law relationship foimd for the leading term in theoretical treatments of the dispersion energy such as the Drude model. There are no... 

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