Potential truncation

Figure 4. Potential energy of the 7.5 A cutoff potentials (truncate, shift, switch) and the no cutoff potential on the heating portion of the trajectories of (a) the no cutoff simulation and (b) the 7.5 A shift simulation. Continued on next page.

The product J Eg)coQ is equal to Eg for a harmonic oscillator potential truncated at = Eg, and to 2Eg for a Morse potential with dissociation energy equal to Eg. Equation (2.41) is the low-friction limit result of Kramers. There are other methods to derive the results obtained in the previous section. One is to look for the eigenvalue with smallest positive real part of the ojjerator L defined so that dP/dt = — LP is the relevant Fokker-Planck or Smoluchowski equation. Under the usual condition of time scale separation this smallest real part is the escapie rate for a single well potential. Another way uses the concept of mean passage time. For the one-dimensional Fokker-Planck equation of the form... 

The matrix K relates the changes in the Coulomb and the exchange-correlation parts of the Kohn-Sham effective potential (truncated to the linear terms) and the... 

Fig. 3. Values of A" (r) for dipolar hard spheres at p = 0.8 and /i —2.57 dashed curve, LHNC for an infinite system with the potential truncated at /i —3.4rf crosses, MC results for Af—256, Rc= iAd-, triangles, MC results for 864, /J. =3.4d solid curve, LHNC for an infinite system with the potential truncated at = 5.1d big dots, MC results for Af—864, = dotted curve, LHNC for an infinite system with an untruncated potential. (Results from Ref. 52.)...

As already mentioned above, the extent of tail correetions strongly depends on the property under study. In the case of pressure, this correction can be very large for example, in the case of a Lennard-Jones potential truncated at rc=2.5a, at conditions close to the triple point, E/Ne=-6.12, to which the tail correction contributes -0.48, but pP/p=0.22, of which -1.24 comes to the tail. The neglecting of the tail correction would lead to a strongly positive value for pressure. ... 

Asymptotic Properties of Radiae Distribution Functions and Potential Truncations... 

One clever approach to obtaining better convergence is to include asymptotic properties of the pair correlation functions (Lebowitz and Percus 1963). In particular, exact asymptotic expressions have been obtained by Attard and coworkers (Attard 1990 Attard et al. 1991), such as for dipolar fluids. Other work has extended simulation results for a system with a truncated potential to give those for the full potential (Lado 1964). The effects on pair distribution functions of potential truncations are important. 

Figure 6.4 shows the values of continuous curve drawn through all the points. (The results of Rao and Levesque and of Rao and Beme are for a potential truncated at r=2-Sd, and have been increased by O-SO and 0-40 respectively to make them comparable with... 

The electron-ion and electron-ammonia interactions were treated using pseudopotentials. For Li we used a bare coulomb potential truncated at a radius (Rq) that yields essentially the correct spectroscopic term value for the 2s electron. The electron-solvent molecule potential consisted of electron-charge site contributions but with Rq = 1.0 A for the protons. No allowance was made for polarization or exchange contributions. Our crude potential is justified a posteriori since it yields a reasonable description of an electron in liquid ammonia. ... 

The model parameters used for the non-bonded interaction are given in Table 2. In the standard form of this potential, the exp-6 potential is non-monotonic in the repulsive regime and has a maximum at a separation r. In the MD simulations, separations r < r are never accessed, and this cutoff plays no role since V r )/kBT > 40. However in the PRISM calculations, single-chain Monte Carlo simulations using the pivot algorithm are employed, and it is necessary to modify the standard potential at short distance in Eq. (14) so that V r) = V r ) for r < r [64], Some of the MD calculations and all of the PRISM calculations were done for a purely repulsive cut and shifted version of Eq. (14). Additional MD simulations were also carried out for the interaction potential truncated at either 6 or 12 A [64]. 

In molecular dynamics with only pair interactions, the speed of program execution is limited by evaluation of the force on each particle, eq. (9). Since simulations usually utilize pair potentials truncated at some pair separation r L/2, a significant increase in program execution speed can be obtained by... 

---