Physics Department - Recent Progress in Path Integral Molecular Dynamics: Efficient Isobaric–Isothermal Sampling and the Geometric Phase
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Abstract
Path integral molecular dynamics (PIMD) provides a rigorous framework for simulating nuclear quantum effects in complex molecular systems, yet practical challenges remain in efficient sampling and the inclusion of nonadiabatic topological effects. This seminar will highlight two latest advancements addressing these critical frontiers.
First, to accurately model real-world chemical and biological experiments typically performed under controlled pressure and temperature, a unified "middle" scheme for the isobaric–isothermal ensemble will be presented. This scheme accurately samples the coordinate and volume distributions for either classical or quantum processes. The formulation applies to various barostats and thermostats with or without holonomic constraints. Benchmark tests across standard molecular simulation packages demonstrate that this "middle" scheme enables a 5~10-fold increase in the simulation time step without sacrificing the accuracy of converged thermodynamic properties (density, heat capacity, isothermal compressibility, thermal expansion coefficient, free energy, and so on).
Second, the discussion will pivot to the profound consequences of the geometric phase (GP) induced by conical intersections. While standard Born–Oppenheimer PIMD approaches neglect these topological features—often leading to significant errors in low-temperature thermodynamics—the multi-electronic-state path integral (MES-PI) formulation provides a complete resolution. The presentation will demonstrate how MES-PIMD naturally captures the GP through the electronic trace of the product of statistically weighted overlap matrices between successive imaginary-time slices. By introducing a geometric signature matrix and winding-number-induced phase factor to construct an ad hoc GP-excluded baseline, the unambiguous impact of the GP is quantified. Together, these methodological developments establish a highly efficient, general, and accurate approach applicable to realistic complex molecular systems, even when the location and underlying topology of conical intersection seams are not known a priori.
References
[1] J. Liu, D. Li, X. Liu, J. Chem. Phys. 145, 024103 (2016)
[2] Z. Zhang, X. Liu, Z. Chen, H. Zheng, K. Yan, J. Liu, J. Chem. Phys. 147, 034109 (2017)
[3] X. Liu, J. Liu, J. Chem. Phys. 148, 102319 (2018)
[4] W. Liang, S. Wang, C. Wang, W. Wang, X. She, C. Wang, J. Shao, J. Liu, J. Chem. Theory Comput. 21(13), 6394–6409 (2025)
[5] Y. Zhai, Y. Shang, J. Liu, J. Phys. Chem. Lett. 17(15), 4274-4291 (2026)
Jian Liu is a Boya Distinguished Professor at Peking University. He received his BS from the University of Science & Technology of China and his PhD from the University of Illinois at Urbana-Champaign. He then did postdoctoral work at the University of California, Berkeley, and was a research associate at Stanford University before joining Peking University. He was the recipient of the 2019 Pople Medal of the Asia-Pacific Association of Theoretical and Computational Chemists and was elected a member of the International Academy of Quantum Molecular Science (IAQMS) in 2025. Since 2026, he has served as the Member at Large of the IAQMS board and a Senior Editor of The Journal of Physical Chemistry (ACS Publications). His research interests have focused on the development of generalized phase-space formulations of quantum mechanics and trajectory-based methods for studying dynamics and statistical mechanics of real complex (large) molecular systems.