TY - JOUR

T1 - A 'path-by-path' monotone extrapolation sequence for Feynman path integral calculations of quantum mechanical free energies

AU - Mielke, Steven L.

AU - Truhlar, Donald G.

N1 - Funding Information:
This work was supported in part by the National Science Foundation.

PY - 2003/9/5

Y1 - 2003/9/5

N2 - Feynman path integral methods based on the Trotter approximation represent paths by a set of P discrete points. We prove that the M-point partition function is an upper bound of the P-point one if M is a divisor of P. Also for this case, we show that, during calculations using P-point paths, it is possible - at negligible additional cost - to obtain M-point estimators of the partition function that, for each individual path, converge monotonically. This permits accurate extrapolation to infinite P, which greatly improves the accuracy of calculations of thermodynamic quantities.

AB - Feynman path integral methods based on the Trotter approximation represent paths by a set of P discrete points. We prove that the M-point partition function is an upper bound of the P-point one if M is a divisor of P. Also for this case, we show that, during calculations using P-point paths, it is possible - at negligible additional cost - to obtain M-point estimators of the partition function that, for each individual path, converge monotonically. This permits accurate extrapolation to infinite P, which greatly improves the accuracy of calculations of thermodynamic quantities.

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U2 - 10.1016/j.cplett.2003.07.007

DO - 10.1016/j.cplett.2003.07.007

M3 - Article

AN - SCOPUS:0141563352

VL - 378

SP - 317

EP - 322

JO - Chemical Physics Letters

JF - Chemical Physics Letters

SN - 0009-2614

IS - 3-4

ER -