Molecular dynamics simulations augmented with quantum mechanics
Path integral molecular dynamics (PIMD) is a method of incorporating quantum mechanics into molecular dynamics simulations using Feynman path integrals. In PIMD, one uses the Born–Oppenheimer approximation to separate the wavefunction into a nuclear part and an electronic part. The nuclei are treated quantum mechanically by mapping each quantum nucleus onto a classical system of several fictitious particles connected by springs (harmonic potentials) governed by an effective Hamiltonian, which is derived from Feynman's path integral. The resulting classical system, although complex, can be solved relatively quickly. There are now a number of commonly used condensed matter computer simulation techniques that make use of the path integral formulation including Centroid Molecular Dynamics (CMD),[1][2][3][4][5]Ring Polymer Molecular Dynamics (RPMD),[6][7] and the Feynman-Kleinert Quasi-Classical Wigner (FK-QCW) method.[8][9] The same techniques are also used in path integral Monte Carlo (PIMC).[10][11][12][13][14]
^Cao, J.; Voth, G. A. (1994). "The formulation of quantum statistical mechanics based on the Feynman path centroid density. I. Equilibrium properties" (PDF). The Journal of Chemical Physics. 100 (7): 5093. Bibcode:1994JChPh.100.5093C. doi:10.1063/1.467175. Archived from the original on September 24, 2017. Retrieved April 29, 2018.
^Cao, J.; Voth, G. A. (1994). "The formulation of quantum statistical mechanics based on the Feynman path centroid density. II. Dynamical properties". The Journal of Chemical Physics. 100 (7): 5106. Bibcode:1994JChPh.100.5106C. doi:10.1063/1.467176.
^Jang, S.; Voth, G. A. (1999). "A derivation of centroid molecular dynamics and other approximate time evolution methods for path integral centroid variables". The Journal of Chemical Physics. 111 (6): 2371. Bibcode:1999JChPh.111.2371J. doi:10.1063/1.479515.
^RamíRez, R.; LóPez-Ciudad, T. (1999). "The Schrödinger formulation of the Feynman path centroid density". The Journal of Chemical Physics. 111 (8): 3339. arXiv:cond-mat/9906318. Bibcode:1999JChPh.111.3339R. doi:10.1063/1.479666. S2CID 15452314.
^Polyakov, E. A.; Lyubartsev, A. P.; Vorontsov-Velyaminov, P. N. (2010). "Centroid molecular dynamics: Comparison with exact results for model systems". The Journal of Chemical Physics. 133 (19): 194103. Bibcode:2010JChPh.133s4103P. doi:10.1063/1.3484490. PMID 21090850.
^Craig, I. R.; Manolopoulos, D. E. (2004). "Quantum statistics and classical mechanics: Real time correlation functions from ring polymer molecular dynamics". The Journal of Chemical Physics. 121 (8): 3368–3373. Bibcode:2004JChPh.121.3368C. doi:10.1063/1.1777575. PMID 15303899.
^Braams, B. J.; Manolopoulos, D. E. (2006). "On the short-time limit of ring polymer molecular dynamics". The Journal of Chemical Physics. 125 (12): 124105. Bibcode:2006JChPh.125l4105B. doi:10.1063/1.2357599. PMID 17014164.
^Smith, Kyle K. G.; Poulsen, Jens Aage; Nyman, Gunnar; Rossky, Peter J. (June 28, 2015). "A new class of ensemble conserving algorithms for approximate quantum dynamics: Theoretical formulation and model problems". The Journal of Chemical Physics. 142 (24): 244112. Bibcode:2015JChPh.142x4112S. doi:10.1063/1.4922887. hdl:1911/94772. ISSN 0021-9606. PMID 26133415.
^Smith, Kyle K. G.; Poulsen, Jens Aage; Nyman, Gunnar; Cunsolo, Alessandro; Rossky, Peter J. (June 28, 2015). "Application of a new ensemble conserving quantum dynamics simulation algorithm to liquid para-hydrogen and ortho-deuterium". The Journal of Chemical Physics. 142 (24): 244113. Bibcode:2015JChPh.142x4113S. doi:10.1063/1.4922888. hdl:1911/94773. ISSN 0021-9606. OSTI 1237171. PMID 26133416.
^Berne, B. J.; Thirumalai, D. (1986). "On the Simulation of Quantum Systems: Path Integral Methods". Annual Review of Physical Chemistry. 37: 401–424. Bibcode:1986ARPC...37..401B. doi:10.1146/annurev.pc.37.100186.002153.
^Gillan, M. J. (1990). "The path-integral simulation of quantum systems, Section 2.4". In C. R. A. Catlow; S. C. Parker; M. P. Allen (eds.). Computer Modelling of Fluids Polymers and Solids. NATO ASI Series C. Vol. 293. pp. 155–188. ISBN 978-0-7923-0549-1.
^Trotter, H. F. (1959). "On the Product of Semi-Groups of Operators". Proceedings of the American Mathematical Society. 10 (4): 545–551. doi:10.1090/S0002-9939-1959-0108732-6. JSTOR 2033649.
^Chandler, D. (1981). "Exploiting the isomorphism between quantum theory and classical statistical mechanics of polyatomic fluids". The Journal of Chemical Physics. 74 (7): 4078–4095. Bibcode:1981JChPh..74.4078C. doi:10.1063/1.441588.
^Marx, D.; Müser, M. H. (1999). "Path integral simulations of rotors: Theory and applications". Journal of Physics: Condensed Matter. 11 (11): R117. Bibcode:1999JPCM...11R.117M. doi:10.1088/0953-8984/11/11/003. S2CID 250913547.
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