Quadratic Feynman-Hibbs potentials

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... 

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. 

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