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]
Combination with other simulation techniques[edit]
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^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.
^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. PMID21090850.
^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. PMID15303899.
^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. ISSN0021-9606. PMID26133415.
^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. ISSN0021-9606. OSTI1237171. PMID26133416.
^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. ISBN978-0-7923-0549-1.
^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.
^Cao, J.; Voth, G. A. (1996). "Semiclassical approximations to quantum dynamical time correlation functions". The Journal of Chemical Physics. 104 (1): 273–285. Bibcode:1996JChPh.104..273C. doi:10.1063/1.470898.
Feynman, R. P. (1972). "Chapter 3". Statistical Mechanics. Reading, Massachusetts: Benjamin. ISBN0-201-36076-4.
Morita, T. (1973). "Solution of the Bloch Equation for Many-Particle Systems in Terms of the Path Integral". Journal of the Physical Society of Japan. 35 (4): 980–984. Bibcode:1973JPSJ...35..980M. doi:10.1143/JPSJ.35.980.
Barker, J. A. (1979). "A quantum-statistical Monte Carlo method; path integrals with boundary conditions". The Journal of Chemical Physics. 70 (6): 2914–2918. Bibcode:1979JChPh..70.2914B. doi:10.1063/1.437829.
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