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
SN - 0009-2614
VL - 378
SP - 317
EP - 322
JO - Chemical Physics Letters
JF - Chemical Physics Letters
IS - 3-4
ER -