Path integral molecular dynamics

<h2 id="combination-with-other-simulation-techniques">Combination with other simulation techniques</h2>

The simulations done my PIMD can broadly characterize the biomolecular systems, covering the entire structure and organization of the membrane, including the permeability, protein-lipid interactions, along with "lipid-drug interactions, protein–ligand interactions, and protein structure and dynamics."

<h2 id="applications">Applications</h2>

PIMD is "widely used to describe nuclear quantum effects in chemistry and physics".<a class="footnote-ref" id="fnref:17" href="#fn:17">17</a>
Path Integral Molecular Dynamics can be applied to polymer physics, both field theories, quantum and not, string theory, stochastic dynamics, quantum mechanics, and quantum gravity. PIMD can also be used to calculate time correlation functions<a class="footnote-ref" id="fnref:18" href="#fn:18">18</a>

<h2 id="further-reading">Further reading</h2>
<ul><li>Feynman, R. P. (1972). "Chapter 3". Statistical Mechanics. Reading, Massachusetts: Benjamin. <a href="/facts/ISBN_(identifier)/15AdSPa9">ISBN</a> 0-201-36076-4.</li>
<li>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. <a href="/facts/Bibcode_(identifier)/9HtdQSGB">Bibcode</a>:<a href="https://ui.adsabs.harvard.edu/abs/1973JPSJ...35..980M">1973JPSJ...35..980M</a>. <a href="/facts/Doi_(identifier)/muM9Etpq">doi</a>:<a href="https://doi.org/10.1143%2FJPSJ.35.980">10.1143/JPSJ.35.980</a>.</li>
<li>Wiegel, F. W. (1975). "Path integral methods in statistical mechanics". Physics Reports. 16 (2): 57–114. <a href="/facts/Bibcode_(identifier)/9HtdQSGB">Bibcode</a>:<a href="https://ui.adsabs.harvard.edu/abs/1975PhR....16...57W">1975PhR....16...57W</a>. <a href="/facts/Doi_(identifier)/muM9Etpq">doi</a>:<a href="https://doi.org/10.1016%2F0370-1573%2875%2990030-7">10.1016/0370-1573(75)90030-7</a>.</li>
<li>Barker, J. A. (1979). "A quantum-statistical Monte Carlo method; path integrals with boundary conditions". The Journal of Chemical Physics. 70 (6): 2914–2918. <a href="/facts/Bibcode_(identifier)/9HtdQSGB">Bibcode</a>:<a href="https://ui.adsabs.harvard.edu/abs/1979JChPh..70.2914B">1979JChPh..70.2914B</a>. <a href="/facts/Doi_(identifier)/muM9Etpq">doi</a>:<a href="https://doi.org/10.1063%2F1.437829">10.1063/1.437829</a>.</li>
<li>Ceperley, D. M. (1995). "Path integrals in the theory of condensed helium". Reviews of Modern Physics. 67 (2): 279–355. <a href="/facts/Bibcode_(identifier)/9HtdQSGB">Bibcode</a>:<a href="https://ui.adsabs.harvard.edu/abs/1995RvMP...67..279C">1995RvMP...67..279C</a>. <a href="/facts/Doi_(identifier)/muM9Etpq">doi</a>:<a href="https://doi.org/10.1103%2FRevModPhys.67.279">10.1103/RevModPhys.67.279</a>.</li>
<li>Chakravarty, C. (1997). "Path integral simulations of atomic and molecular systems". International Reviews in Physical Chemistry. 16 (4): 421–444. <a href="/facts/Bibcode_(identifier)/9HtdQSGB">Bibcode</a>:<a href="https://ui.adsabs.harvard.edu/abs/1997IRPC...16..421C">1997IRPC...16..421C</a>. <a href="/facts/Doi_(identifier)/muM9Etpq">doi</a>:<a href="https://doi.org/10.1080%2F014423597230190">10.1080/014423597230190</a>.</li></ul>
<h2 id="external-links">External links</h2>
<ul><li><a href="https://web.archive.org/web/20160501213838/http://www.smac.lps.ens.fr/index.php/Programs_Chapter_3:_Density_matrices_and_path_integrals">"Density matrices and path integrals"</a>. SMAC-wiki. Archived from <a href="http://www.smac.lps.ens.fr/index.php/Programs_Chapter_3:_Density_matrices_and_path_integrals">the original</a> (computer code) on May 1, 2016. Retrieved May 12, 2012.</li>
<li>John Shumway; Matthew Gilbert (2008). <a href="http://nanohub.org/resources/pimc">"Path Integral Monte Carlo Simulation"</a>. <a href="/facts/Doi_(identifier)/muM9Etpq">doi</a>:<a href="https://doi.org/10.4231%2FD3T43J39D">10.4231/D3T43J39D</a>. {{cite journal}}: Cite journal requires |journal= (help)CS1 maint: multiple names: authors list (link)</li></ul>

<h2 id="references">References</h2>

<ol>
<li id="fn:1">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. <a href="https://apps.dtic.mil/sti/pdfs/ADA272809.pdf" target="_blank">https://apps.dtic.mil/sti/pdfs/ADA272809.pdf</a> <a href="#fnref:1" class="footnote-back-ref">↩</a></li>
<li id="fn:2">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. <a href="/wiki/Bibcode_(identifier)" target="_blank">/wiki/Bibcode_(identifier)</a> <a href="#fnref:2" class="footnote-back-ref">↩</a></li>
<li id="fn:3">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. <a href="/wiki/Bibcode_(identifier)" target="_blank">/wiki/Bibcode_(identifier)</a> <a href="#fnref:3" class="footnote-back-ref">↩</a></li>
<li id="fn:4">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. <a href="/wiki/ArXiv_(identifier)" target="_blank">/wiki/ArXiv_(identifier)</a> <a href="#fnref:4" class="footnote-back-ref">↩</a></li>
<li id="fn:5">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. <a href="/wiki/Bibcode_(identifier)" target="_blank">/wiki/Bibcode_(identifier)</a> <a href="#fnref:5" class="footnote-back-ref">↩</a></li>
<li id="fn:6">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. <a href="/wiki/Bibcode_(identifier)" target="_blank">/wiki/Bibcode_(identifier)</a> <a href="#fnref:6" class="footnote-back-ref">↩</a></li>
<li id="fn:7">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. <a href="/wiki/Bibcode_(identifier)" target="_blank">/wiki/Bibcode_(identifier)</a> <a href="#fnref:7" class="footnote-back-ref">↩</a></li>
<li id="fn:8">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. <a href="/wiki/Bibcode_(identifier)" target="_blank">/wiki/Bibcode_(identifier)</a> <a href="#fnref:8" class="footnote-back-ref">↩</a></li>
<li id="fn:9">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. <a href="/wiki/Bibcode_(identifier)" target="_blank">/wiki/Bibcode_(identifier)</a> <a href="#fnref:9" class="footnote-back-ref">↩</a></li>
<li id="fn:10">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. <a href="/wiki/Bibcode_(identifier)" target="_blank">/wiki/Bibcode_(identifier)</a> <a href="#fnref:10" class="footnote-back-ref">↩</a></li>
<li id="fn:11">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. <a href="978-0-7923-0549-1" target="_blank">978-0-7923-0549-1</a> <a href="#fnref:11" class="footnote-back-ref">↩</a></li>
<li id="fn:12">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. <a href="https://doi.org/10.1090%2FS0002-9939-1959-0108732-6" target="_blank">https://doi.org/10.1090%2FS0002-9939-1959-0108732-6</a> <a href="#fnref:12" class="footnote-back-ref">↩</a></li>
<li id="fn:13">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. <a href="/wiki/Bibcode_(identifier)" target="_blank">/wiki/Bibcode_(identifier)</a> <a href="#fnref:13" class="footnote-back-ref">↩</a></li>
<li id="fn:14">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. <a href="/wiki/Bibcode_(identifier)" target="_blank">/wiki/Bibcode_(identifier)</a> <a href="#fnref:14" class="footnote-back-ref">↩</a></li>
<li id="fn:15">"Non-Hamilton Theory". <a href="https://pubs.aip.org/aip/jcp/article-abstract/115/4/1678/451151/Non-Hamiltonian-molecular-dynamics-Generalizing" target="_blank">https://pubs.aip.org/aip/jcp/article-abstract/115/4/1678/451151/Non-Hamiltonian-molecular-dynamics-Generalizing</a> <a href="#fnref:15" class="footnote-back-ref">↩</a></li>
<li id="fn:16">"Nose-Hoover Chains" (PDF). 1992. <a href="https://www2.stat.duke.edu/~scs/Projects/REMD/NoseHooverChains1992.pdf" target="_blank">https://www2.stat.duke.edu/~scs/Projects/REMD/NoseHooverChains1992.pdf</a> <a href="#fnref:16" class="footnote-back-ref">↩</a></li>
<li id="fn:17">Hirshberg, Barak (2019). "PIMD for bosoms - PNAS". Proceedings of the National Academy of Sciences of the United States of America. 116 (43): 21445–21449. doi:10.1073/pnas.1913365116. PMC 6815177. PMID 31591226. <a href="https://www.ncbi.nlm.nih.gov/pmc/articles/PMC6815177" target="_blank">https://www.ncbi.nlm.nih.gov/pmc/articles/PMC6815177</a> <a href="#fnref:17" class="footnote-back-ref">↩</a></li>
<li id="fn:18">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. <a href="/wiki/Bibcode_(identifier)" target="_blank">/wiki/Bibcode_(identifier)</a> <a href="#fnref:18" class="footnote-back-ref">↩</a></li>
</ol>

Path integral molecular dynamics open-in-new

Path integral molecular dynamics