Feynman-Hibbs effective potential

Obtain the QFH correction from the Feynman-Hibbs effective potential by Taylor expansion of the potential. 

Sese, L. M. 1994, Study of the Feynman-Hibbs effective potential against the path-integral formalism for Monte Carlo simulations of quantum many-body Lennard-Joncs systems . Mol. Phy.s. 81, 1297 1312. 

In their simulations, L6vesque et used a standard Leimard-Jones interaction potential between hydrogen molecules, and included the effect of quadrupolar interactions by adding a Coulomb interaction term in which each hydrogen molecule is represented by three effective charges q (q = 0.4829e at the position of the protons and q = -e at the centre of mass of the molecule). The adsorbate-adsorbent interaction was modeled with a standard Lennard-Jones potential. In order to partially account for quantum effects at 77 K, a semi-classical approach based on the Feynman-Hibbs effective potential was used ... 

J. D. Doll, J. Chem. Phys. 81, 3536 (1984). In Appendix A of this paper, it was speculated that the quantum-activated rate constant might be computed from classical dynamics on the Feynman-Hibbs effective potential energy surface. 

Because the path integral techniques can account for quantum effect directly in the simulations, the methodology has been used mostly in studies of the behavior of quantum solutes, including tunneling, charge transfer between solutes, and hydrated electrons. Simulations of pure water ° investigated quantum corrections to effective potentials. The Feynman-Hibbs effective potential is a computationally simple method for estimating quantum effects and has been used to examine the differences in the properties of H2O and 02 . ... 

Voth, G. A. (1991). Calculation of equihbrium averages with Feynman-Hibbs effective classical potentials and similar variational approximations. Phys. Rev. A 44, 5302-... 

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 ... 

Sese, L. M., Feynman-Hibbs quantum effective potentials for Monte Carlo simulations of liquid neon, Mol. Phys. 1993, 78, 1167-1177... 

Here U N) is the interaction potential energy for the complete system at a specific configuration, uniformly the same quantity that has been discussed above. U(TV) is an ejfective potential designed to be used in classical-limit partition function calculations, e.g. Eq. (3.17), p. 40, in order to include quantum mechanical effects approximately. We will call this /(TV) the quadratic Feynman-Hibbs (QFH) model. In Eq. (3.67), Mj is the mass of atom j, and V is the Laplacian of the... 

We have resorted to an approximate technique which attempts to include the above mentioned main quantum effects via the construction of effective potentials V. Basically, each pmticle is represented by a single particle wavefunction tmd the Ehrenfest theorem is applied. Similar ideas have been used with good success ev( n for quantum solids like hydrogmi [38]. Effective quantum potentials ajx also among the results of the Feynman-Hibbs treatment [12] which have been apjjlied to pure neon clusters in the past [34]. 

Empirical potentials, which are usually functions that are fit to experimental data, tend to predict the net effect of a variety of phenomena over a range of conditions, and are consequently less accurate than ah initio PES for describing N-body interactions. The virial coefiicients that are calculated Irom an input interaction potential (empirical or ab initio PES) without modification are known as classical virial coefficients because they do not include nuclear quantum effects explicitly. Virial coefficients computed using an effective potential such as the Quadratic Feynman-Hibbs (QFH) [1] that includes a quantum correction are known as semi-classical virial coefficients. 

Other more powerful semiclassical schemes based on the PI formalism, and hence different from WK, are also amenable to this sort of general formulation. They extend the seminal work by Feynman and Hibbs [12] and produce reliable quantum effective pair potentials vJiR p,h,m) [34, 124, 125]. These Pl-based semiclassical schemes avoid asymptotic problems and present a much wider range of applicability than WK, as they stem from a variational principle for the free energy of the quantum system. All of them are built using the centroid concept for continuous closed paths, which generalizes the discretized version given in Eq. (36). At this point it is worth recalling that the centroid concept plays a key role in many PI applications. A number of them are specifically... 

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