Many-Body Interactions in Ice - Journal of Chemical Theory and

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Many-Body Interactions in Ice C. Huy Pham, Sandeep Kumar Reddy, Karl Chen, Christopher Knight, and Francesco Paesani J. Chem. Theory Comput., Just Accepted Manuscript • DOI: 10.1021/acs.jctc.6b01248 • Publication Date (Web): 28 Feb 2017 Downloaded from http://pubs.acs.org on March 3, 2017

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Journal of Chemical Theory and Computation

Many-Body Interactions in Ice C. Huy Pham,†,¶ Sandeep K Reddy,†,¶ Karl Chen,† Chris Knight,‡ and Francesco Paesani∗,† †Department of Chemistry and Biochemistry, University of California, San Diego, La Jolla, California 92093, United States ‡Leadership Computing Facility, Argonne National Laboratory, 9700 South Cass Avenue, Argonne, Illinois 60439, United States ¶Contributed equally to this work E-mail: [email protected]

Abstract Many-body effects in ice are investigated through a systematic analysis of the lattice energies of several proton ordered and disordered phases which are calculated with different flexible water models, ranging from pairwise additive (q-TIP4P/F) to polarizable (TTM3-F and AMOEBA) and explicit many-body (MB-pol) potential energy functions. Comparisons with available experimental and diffusion Monte Carlo data emphasize the importance of an accurate description of the individual terms of the many-body expansion of the interaction energy between water molecules for the correct prediction of the energy ordering of the ice phases. Further analysis of the MB-pol results in terms of fundamental energy contributions demonstrates that the differences in lattice energies between different ice phases depend sensitively on the subtle balance between short-range two-body and three-body interactions, many-body induction, and dispersion energy. By correctly reproducing many-body effects at both short and long range, it is found that MB-pol accurately predicts the energetics of different ice phases,

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which provides further support for the accuracy of MB-pol in representing the properties of water from the gas to the condensed phase.

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Introduction

Ice, in both pure and doped forms as well as at the interface with other substances, is directly involved in several fundamental processes of relevance to atmospheric science, environmental chemistry, biology, and materials research. 1–3 Due to the unique ability of the water molecules to form extended three-dimensional hydrogen-bonded (HB) structures, ice can exist in both amorphous and crystalline phases, depending on temperature and pressure. To date, sixteen crystalline phases (from ice I to ice XVI) and, at least, three amorphous forms of ice have been identified within well-defined regions of the phase diagram. 4 The sixteen ice phases are classified in two groups according to whether the positions of the water hydrogen atoms within the crystal are ordered (proton-ordered phases) or disordered (proton-disordered phases). With the exception of ice X, the water molecules in all ice phases are arranged in tetrahedral HB networks in which each water molecule is coordinated to four nearest neighbors. The hydrogen atoms are distributed according to the BernalFowler rules, 5 with only one H atom between two adjacent O atoms, and only two H atoms covalently bonded to each O atom. With the discovery of ices XIII, XIV, 6 and XV, 7 which are the proton-ordered counterparts of ices V, XII, and VI, respectively, the emerging phase diagram of ice displays a nearly perfect one-to-one correspondence between proton-ordered and proton-disordered phases. Specifically, six pairs of proton-ordered/proton-disordered phases are identified: XI/Ih , IX/III, XIII/V, XV/VI, VIII/VII, and XIV/XII, with only the proton-ordered phase II and the two proton disordered phases Ic and IV currently missing their corresponding counterparts. 8 The proton-disordered ice Ih , with a hexagonal lattice, is the most stable phase at ambient conditions. It sequentially transforms to higher density phases (i.e., ices II, XV, and VIII) as the pressure increases.

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With the development of new theoretical models and computer algorithms, which has been accompanied by a continued increase of computer power, molecular simulations have become powerful tools to characterize the properties of different ice phases. The predictive power of a computer simulation directly depends on the accuracy with which the underlying potential energy surface (PES) is represented. Over the years, numerous water models have been proposed, 9–11 with the most popular ones being those that neglect intramolecular flexibility and assume pairwise additivity of the intermolecular interactions. Among these models, TIP4P/2005 12 and the specialized TIP4P/Ice 13 overall provide structural and thermodynamic properties of ice in reasonable agreement with experimental data. 14 However, the lack of both intramolecular flexibility and electronic polarization limits the transferability of these models, preventing them from achieving chemical and spectroscopic accuracy across different phases. On the other hand, if the exact functional were known, density functional theory (DFT) would provide a correct description of all ice phases, completely from “first principles”. Unfortunately, existing DFT models for water have been shown to be affected by intrinsic deficiencies that significantly limit their predictive power. 15 For example, several DFT functionals predicted ice XV to be ferroelectric with Cc symmetry 16–18 while subsequent experimental measurements determined that the crystal structure of ice XV is antiferroelectric with P 1 symmetry. To date, only studies using fragment-based 2nd-order MøllerPlesset (MP2) and coupled cluster with single, double, and perturbative triple excitations (CCSD(T)) approaches have been able to reproduce the experimental data. 19 More recently, it has been shown that fully periodic calculations carried at the MP2 level of theory and within the random-phase approximation (RPA) predict the ferroelectric Cc structure to be the lowest-energy configuration, 20 although the energy difference between the Cc and P 1 structures is on the order of 0.1 kcal/mol. Ref. 20 also pointed out that tinfoil (i.e., metallic) boundary conditions, which are commonly applied to represent long-range electrostatic interactions according to the Ewald method, may not be appropriate for molecular systems

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with dipole net polarization within a medium of small dielectric constant (e.g., ice XV, an ordered phase, nucleating within ice VI a disordered phase). The small energy differences between different ice phases highlight the importance of an accurate determination of the underlying PES for a quantitative assignment of the relative stability of the different ice phases. In this context, the treatment of van der Waals (vdW) interactions, either implicitly or explicitly, within different DFT models was found to be important for improving the agreement between calculated and experimental lattice energies. 21–23 A few DFT models were shown to reproduce the lattice energies of several ice phases with mean absolute errors on the order of 1 kcal/mol relative to the experimental data, although the energy ordering is not always correctly predicted. 23 In addition, the computational cost associated with DFT simulations limits their applicability to relatively small systems and short time scales. In this context, the advent of potential energy functions (PEFs) rigorously derived from the many-body expansion (MBE) of the interaction energy between water molecules (e.g., CC-pol, 24–26 WHBB, 27–31 HBB2-pol, 32,33 and MB-pol 34–37 ) has recently enabled computer simulations of water from the gas to the condensed phase, with unprecedented accuracy. The focus of this study is to determine the role played by many-body effects in determining the energetics of different ice phases. To this purpose, a systematic analysis of the lattice energies is presented considering water PEFs that treat the leading terms of the MBE through effective (e.g., q-TIP4P/F model 38 ), implicit (e.g., TTM3-F 39 and AMOEBA 40–42 models), and explicit (e.g., MB-pol 34–37 ) many-body representations. The article is organized as follows: The technical details about the simulations are presented in Section 2. The results obtained with the four PEFs are presented in Section 3 and discussed in the context of DFT and RPA calculations reported in the literature. A summary highlighting the main findings is given in Section 4.

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Methods

For a system containing N molecules, the total energy can be formally expressed in terms of the MBE as, 43

EN =

N X i=1

V1B (i) +

N X

V2B (i, j) +

i

Many-Body Interactions in Ice - Journal of Chemical Theory and

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