Nuclear Quantum Effect and H/D Isotope Effect on Hydrogen-Bonded Systems with Path Integral Simulation
In the past two decades, ab initio path integral (PI) simulation, in particular, ab initio path integral molecular dynamics simulation has reached its maturity and has been widely used to take account of nuclear quantum effects, such as zero-point vibra
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Nuclear Quantum Effect and H/D Isotope Effect on Hydrogen-Bonded Systems with Path Integral Simulation Kimichi Suzuki, Yukio Kawashima and Masanori Tachikawa
Abstract In the past two decades, ab initio path integral (PI) simulation, in particular, ab initio path integral molecular dynamics simulation has reached its maturity and has been widely used to take account of nuclear quantum effects, such as zero-point vibrational energy and tunneling, in complex many-body systems. In particular, this method has significantly contributed to provide important insights into structures and fluctuation of the hydrogen-bonded systems as well as their isotopomers at finite temperature. In this chapter, we will review the recent advances in ab initio PI simulation. The development of an efficient algorithm for ab initio PI simulation and some applications will be featured. The efficient algorithm for path integral hybrid Monte Carlo method based on the second- and fourth-order Trotter expansion, which realizes large reduction of computational effort without loss of accuracy, will be described in detail. The applications focusing on the hydrogen-bonded systems, protonated and deprotonated water dimers (H5O2+ and H3O2−), F−(H2O)n (n = 1–3) clusters, and hydrogen maleate anion demonstrate the ability and powerfulness of PI simulation.
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Keywords Ab initio path integral simulation Nuclear quantum effect Hydrogen-bonded structure Geometrical isotope effect
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K. Suzuki ⋅ M. Tachikawa (✉) Quantum Chemistry Division, Graduate School of Science, Yokohama City University, 22-2 Seto, Kanazawa-ku, Yokohama 236-0027, Japan e-mail: [email protected] Y. Kawashima RIKEN Advanced Institute for Computational Science, 7-1-26 Minatojima-Minami-Machi, Chuo-ku, Kobe 650-0047, Japan e-mail: [email protected] © Springer Nature Singapore Pte Ltd. 2018 M.J. Wójcik et al. (eds.), Frontiers of Quantum Chemistry, https://doi.org/10.1007/978-981-10-5651-2_16
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Introduction
Path integral (PI) simulation, which is a numerically exact method for quantum many-body systems, allows us to treat the nuclear quantum effect at finite temperature. Feynman’s PI formulation has been presented as mathematically equivalent to the non-relativistic quantum theory of Schrödinger’s or Heisenberg’s equations [1]. The pioneering success of Fosdick and Jordan, combining PI with Monte Carlo (MC) simulation, which applied PI to nuclear quantum effect, has opened a new field in molecular simulation [2–4]. Now, PI simulations are essential for the description of chemical phenomenon, where the nuclear quantum effect plays an important role, such as the isotope effect on hydrogen-bonded systems discussed later on. The reader who is interested in the quantum statistics for boson or fermion by the PI simulations will find detailed description in some reviews [5, 6]. We summarize some important breakthroughs for PI simulation methodology and its algorithms in this section. Sprik and co-workers have introduced the staging algorithm to relieve
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