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This CECAM Flagship School (alternative format) will take place on June 4-8, 2023 at the CECAM-ISR node, Tel Aviv University. It will focus on the most recent advances in molecular simulations that are based on the path integral formulation of quantum mechanics. It will include a one-day advanced tutorial on the state-of-the-art and three and a half days of focused workshop sessions discussing the frontiers of the field.


Relying on the isomorphism [1] between the partition function of a quantum system and a fictitious classical system of ring polymers, early pioneering work developed Path Integral Molecular Dynamics (MD) [2-3] and Monte Carlo (MC) [4] algorithms to obtain equilibrium thermal properties of quantum condensed phases. Important progress was made when it was also shown that the classical dynamics of the ring polymers can be used to approximate real-time quantum correlation functions using Centroid [5] or Ring Polymer MD [6-7], providing access to quantum response properties such as diffusion coefficients, reaction rates and vibrational spectra. Thanks to the development of highly efficient algorithms in recent years, these methods have been applied more widely to include important nuclear quantum effects, such as delocalization, zero-point energy and tunneling in molecular simulations [8]. Many of them have been implemented in the open-source software i-PI [9] and are used routinely by a global community of computational chemists, physicists and material scientists, which has grown substantially in the last decade. 


A series of schools on path integral quantum mechanics organized with the support of CECAM (2012, 2016, 2018, 2021) helped train a young generation of graduate students and ECR in this expanding field. Together with senior faculty, they have recently contributed to several important advances in the field, extending path integral methods to describing phenomena such as nonadiabatic dynamics [10-12], excitons and quasiparticles in condensed phases [13-14], real-time dynamics of molecular aggregates and extended systems [15] and nonlinear spectroscopy [16]. The field has also benefited from important work on combining machine learning algorithms to describe the interparticle interactions with path integral methods to significantly accelerate the simulations. This powerful combination has been used to improve the description of quantum dynamics in aqueous systems [17], and in a range of other exciting applications, including an accurate description of the thermodynamic stabilities of molecular crystals [18], predicting a supersolid phase of deuterium at high pressure [19-20], understanding the supercritical behavior of liquid hydrogen [21] and predicting a superionic phase of water at planetary conditions [22]. 

This school will expose students and postdocs to the state-of-the-art recent advancement in the area, as well as the current outstanding challenges.  The event will take on an innovative, alternative format that combines both the training aspect of an advanced school on the first day, by including a hands-on tutorial using i-PI, followed by 3.5 days of workshop-style presentations and in-depth discussions. Participants who have little experience with path integral methods and/or i-PI will be invited to prepare for the advanced school by following an online course (accessible after free registration at before the start of the school.

We encourage the participants to apply as soon as possible. The deadline for submitting the application and the abstract is April 30th (2023).

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[2] M. Parrinello, A. Rahman, J. Chem. Phys., 80, 860-867 (1984)
[3] M. Tuckerman, B. Berne, G. Martyna, M. Klein, J. Chem. Phys. 99, 2796-2808 (1993)
[4] E. Pollock, D. Ceperley, Phys. Rev. B, 30, 2555-2568 (1984)
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[6] I. Craig, D. Manolopoulos, J. Chem. Phys., 121, 3368-3373 (2004)
[7] S. Habershon, D. Manolopoulos, T. Markland, T. Miller, Annu. Rev. Phys. Chem., 64, 387-413 (2013)
[8] T. Markland, M. Ceriotti, Nat. Rev. Chem., 2, 0109 (2018)
[9] V. Kapil, M. Rossi, O. Marsalek, R. Petraglia, Y. Litman, T. Spura, B. Cheng, A. Cuzzocrea, R. Meißner, D. Wilkins, B. Helfrecht, P. Juda, S. Bienvenue, W. Fang, J. Kessler, I. Poltavsky, S. Vandenbrande, J. Wieme, C. Corminboeuf, T. Kühne, D. Manolopoulos, T. Markland, J. Richardson, A. Tkatchenko, G. Tribello, V. Van Speybroeck, M. Ceriotti, Computer Physics Communications, 236, 214-223 (2019)
[10] N. Ananth, Annu. Rev. Phys. Chem., 73, 299-322 (2022)
[11] Y. Litman, E. Pós, C. Box, R. Martinazzo, R. Maurer, M. Rossi, J. Chem. Phys., 156, 194107 (2022)
[12] Y. Litman, E. Pós, C. Box, R. Martinazzo, R. Maurer, M. Rossi, J. Chem. Phys., 156, 194106 (2022)
[13] R. Remsing, J. Bates, J. Chem. Phys., 153, 121104 (2020)
[14] Y. Park, A. Obliger, D. Limmer, Nano Lett., 22, 2398-2404 (2022)
[15] S. Kundu, N. Makri, Annu. Rev. Phys. Chem., 73, 349-375 (2022)
[16] J. Provazza, F. Segatta, M. Garavelli, D. Coker, J. Chem. Theory Comput., 14, 856-866 (2018)

[17] F. Musil, I. Zaporozhets, F. Noé, C. Clementi, V. Kapil, J. Chem. Phys. 157, 181102 (2022)
[18] V. Kapil, E. Engel, Proc. Natl. Acad. Sci. U.S.A., 119, (2022)
[19] C. Myung, B. Hirshberg, M. Parrinello, Phys. Rev. Lett., 128, 045301 (2022)

[20] B. Hirshberg, V. Rizzi, M. Parrinello, Proc. Natl. Acad. Sci. U.S.A, 116, 21445 (2019)
[21] B. Cheng, M. Bethkenhagen, C. Pickard, S. Hamel, Nat. Phys., 17, 1228-1232 (2021)
[22] B. Cheng, G. Mazzola, C. Pickard, M. Ceriotti, Nature, 585, 217-220 (2020)

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