Path integral simulations

Gillan M J 1990 Path integral simulations of quantum systems Computer Modeling of Fluids and Polymers ed C R A Catlow et al (Dordrecht Kluwer)... 

It is necessary to sum over these pemuitations in a path integral simulation. (The same sum is needed for bosons, without the sign factor.) For femiions, odd pemuitations contribute with negative weight. Near-cancelling positive and negative pemuitations constitute a major practical problem [196]. 

Gao J, Wong K-Y, Major DT (2008) Combined QM/MM and path integral simulations of kinetic isotope effects in the proton transfer reaction between nitroethane and acetate ion in water. J Comput... 

Wang, Q. Johnson, J. K. Broughton, J. Q., Thermodynamic properties and phase equilibrium of fluid hydrogen from path integral simulations, Mol. Phys. 1996, 89, 1105-1119... 

There is considerable interest in the use of discretized path-integral simulations to calculate free energy differences or potentials of mean force using quantum statistical mechanics for many-body systems [140], The reader has already become familiar with this approach to simulating with classical systems in Chap. 7. The theoretical basis of such methods is the Feynmann path-integral representation [141], from which is derived the isomorphism between the equilibrium canonical ensemble of a... 

The Feynman-Hibbs and QFH potentials have been used extensively in simulations examining quantum effects in atomic and molecular fluids [12,15,25]. We note here that the centroid molecular dynamics method [54, 55] is related and is intermediate between a full path integral simulation and the Feynman-Hibbs approximation ... 

In this section, we will discuss some examples from the literature, in which the approximation methods derived in this chapter have been used. In several cases, the approximations have been compared with more-accurate path integral simulations to assess their validity. This is not meant as a full review rather, several case studies have been chosen to illustrate the tools we have developed. We will first look at simpler examples and then discuss water models and applications in enzyme kinetics. 

Modified force field models based on path integral simulations yield excellent agreement with experiment for thermodynamic properties. 

Morales, J. J. Singer, K., Path integral simulation of the free energy of Lennard-Jones neon, Mol. Phys. 1991, 73, 873-880... 

Liu, A. Beck, T. L., Determination of excess Gibbs free energy of quantum mixtures by MC path integral simulations, Mol. Phys. 1995, 86, 225-233... 

Stern, H. A. Berne, B. J., Quantum effects in liquid water path-integral simulations of a flexible and polarizable ab initio model, J. Chem. Phys. 2001,115, 7622... 

Predescu, C. Doll, J. D., Optimal series representations for numerical path integral simulations, J. Chem. Phys. 2003,117, 7448-7463... 

The centroid distribution function and the effective potential for the CMD simulation can be obtained through the path integral simulation method, - but... 

Room temperature simulations at the classical level yielded values of all AX° and quantities. Quantal results for G were also obtained from path integral simulations (in conjunction with Eq. 41) or semiclassical results based on spectral densities from the classical simulations [36]. The calculated classical G and 7. values and the AG° value were found to conform well to Eq. 112, and Gi t]) and Gf t]) functions were close to parabolic in form. Due to systematic deficiencies in the aqueous solvent model (a nonpolarizable force field and finite Coulombic cut-off, ca. 10 A), corrections to / were made on the basis of reference dielectric continuum models, and then G was corrected accordingly on the basis of Eq. 112. 

Wang, Q. and Johnson, J.K. (1998). Hydrogen adsorption on graphite and in carbon slit pores from path integral simulations. Mol. Phys., 95, 299-309. 

The path integral simulations can be extended to higher pressures, including the effect of adsorbate—adsorbate interactions. The selectivity as a function of pressure can be computed by performing a grand canonical Monte Carlo simulation of a mixture. The selectivity for the D2/H2 mixture, with a bulk composition of 99.95% H2, is shown in Fig. 15.12. The gases are assumed to adsorb only in the ICs of a perfect (10, 10) SWNT bundle and the temperature... 

Figure 15.11 Zero pressure selectivity at 20K for T2—H2 mixtures as a function of tube diameter. The diamonds are computed from an approximate theory, given by Eqn (15.3). The circles are computed from path integral simulations. A few specific tubes are labeled on the graph with their (n, m) indices. Sq in the (10, 10) Interstice is shown as an asterisk (theory) and an open square (simulations). (Reprinted with permission from Ref. [129] Copyright 2001 by the American Physical Society.)...

Figure 15.12 Selectivity in the (10, 10) interstice at 20K for a Dj—Hj mixture with bulk composition of 99.95 mol% H2. The solid line is computed from the ideal adsorbed solution theory. The points are from path integral simulations. (Reprinted with permission from Ref. [130] Copyright 2002 by the American Institute of Physics.)...

Gu, C., Gao, G.H., and Gao, H. (2002). Path integral simulation of hydrogen adsorption in single-walled carbon nanotubes at low temperatures. Phys. Chem. Chem. Phys., 4, 4700-8. 

It is of considerable interest to use the electron bubble as a probe for elementary excitations in finite boson quantum systems—that is, ( He)jy clusters [99, 128, 208, 209, 243-245]. These clusters are definitely liquid down to 0 K [46 9] and, on the basis of quantum path integral simulations [65, 155], were theoretically predicted (see Chapter II) to undergo a rounded-off superfluid phase transition already at surprising small cluster sizes [i.e., Amin = 8-70 (Table VI)], where the threshold size for superfluidity and/or Bose-Einstein condensation can be property-dependent (Section II.D). The size of the ( He)jy clusters employed in the experiments of Toennies and co-workers [242-246] and of Northby and coworkers [208, 209] (i.e., N lO -lO ) are considerably larger than Amin- In this large cluster size domain the X point temperature depression is small [199], that is, (Tx — 2 X 10 — 2 X 10 for V = lO -lO. Thus for the current... 

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