Signature properties of water: Their molecular electronic origins Vlad P. Sokhana,1, Andrew P. Jonesb, Flaviu S. Cipciganb, Jason Craina,b, and Glenn J. Martynab,c aNational Physical Laboratory, Teddington, Middlesex TW11 0LW, United Kingdom; bSchool of Physics and Astronomy, The University of Edinburgh, Edinburgh EH9 3JZ, United Kingdom; and cIBM Thomas J. Watson Research Center, Yorktown Heights, NY 10598 Edited by Paul Madden, University of Oxford, Oxford, United Kingdom, and accepted by the Editorial Board March 31, 2015 (received for review October 1, 2014) Water challenges our fundamental understanding of emergent combination of multiscale descriptions and statistical sampling have materials properties from a molecular perspective. It exhibits a led to insights into physical phenomena across biology, chemistry, uniquely rich phenomenology including dramatic variations in physics, materials science, and engineering (14). Significant progress behavior over the wide temperature range of the liquid into water’s now requires novel predictive models with reduced empirical input crystalline phases and amorphous states. We show that many-body that are rich enough to embody the essential physics of emergent responses arising from water’s electronic structure are essential mech- systems and yet simple enough to retain intuitive features (14). anisms harnessed by the molecule to encode for the distinguishing Typically, atomistic models of materials are derived from a features of its condensed states. We treat the complete set of these common strategy. Interactions are described via a fixed functional many-body responses nonperturbatively within a coarse-grained elec- form with long-range terms taken from low orders of perturbation tronic structure derived exclusively from single-molecule properties. theory and are parameterized to fit the results of ab initio com- Such a “strong coupling” approach generates interaction terms of all putations on test systems (both condensed and gas phase) and/or symmetries to all orders, thereby enabling unique transferability to physical properties of systems of interest (15, 16). This approach diverse local environments such as those encountered along the co- presumes that the physics incorporated by the functional form is existence curve. The symmetries of local motifs that can potentially transferable outside the parameterization regime. In addition, first emerge are not known a priori. Consequently, electronic responses principles methods efficient enough to treat the condensed phase PHYSICS unfiltered by artificial truncation are then required to embody the will also miss diagrams leading to truncation (e.g., local density terms that tip the balance to the correct set of structures. Therefore, functional theory neglects dispersion). If the truncation scheme is our fully responsive molecular model produces, a simple, accurate, inappropriate for the problem of interest, predictions can go sig- and intuitive picture of water’s complexity and its molecular origin, nificantly awry (17, 18). Clearly, this is likely to be true for water predicting water’s signature physical properties from ice, through with the directional, locally polarizing, H-bonded network of its liquid–vapor coexistence, to the critical point. liquid being disrupted in the less-associated gas phase. Conse- quently, the key physics underpinning a fully predictive model subcritical water | intermolecular interactions | many-body dispersion | of water has yet to be identified. coarse-grained model | electronic responses The strategy adopted here captures water’s properties from an atomistic perspective by incorporating individual water molecules, ater is a ubiquitous yet unusual substance exhibiting anom- designed to respond with full many-body character, which can A–C Walous physical properties for a liquid and forming many assemble to form condensed phases, as depicted in Fig. 1 . crystalline ices and (at least) two distinct amorphous states of dif- This is a radical departure from standard approaches given above – ferent density (1). As the biological solvent, it is critical that water (11, 12). It is enabled by recent work (19 21) which has shown that molecules form a liquid over a very wide range of temperatures (2) it is possible to represent the complete hierarchy of long-range and pressures (3, 4) to support life under a wide variety of condi- responses within a many-body system using a coarse-grained tions. Indeed, water’s simple molecular structure, a three-atom, two- projection of the electronic structure onto an interacting set of species moiety, yields a surprisingly rich phenomenology in its condensed phases. Significance It is well-known that many signature properties of water have their molecular origin in the hydrogen-bonding interactions be- Water is one of the most common substances yet it exhibits tween molecules (5, 6). These directional networks are also the anomalous properties important for sustaining life. It has been source of enhanced molecular polarization in the liquid state rela- an enduring challenge to understand how a molecule of such tive to the gas (7). In addition, there is speculation that dispersion apparent simplicity can encode for complex and unusual be- interactions which arise from quantum-mechanical fluctuations of havior across a wide range of pressures and temperatures. We the charge density are also an important factor in the equilibrium reveal that embedding a complete hierarchy of electronic re- properties of the ambient liquid (8, 9). The question of the ranges of sponses within the molecule allows water’s phase behavior temperature and density where these interactions influence and signature properties to emerge naturally even within a observable properties is important for the construction of a con- simple model. The key result is a simple and accurate, pre- – ceptually simple but broadly transferable physical model linking diction of liquid gas phase equilibria from freezing to the critical molecular and condensed phase properties with the minimum of point thus establishing a direct link between molecular and additional assumptions. Liquid water exhibits anomalies at both condensed phase properties and a sound physical basis for a extremes of temperature––including a point of maximum density conceptually simple but broadly transferable model for water. near freezing, an unusually high critical temperature relative to Author contributions: V.P.S., J.C., and G.J.M. designed research; V.P.S. and F.S.C. performed other hydrides, and significant changes in physical properties along research; V.P.S., A.P.J., F.S.C., J.C., and G.J.M. analyzed data; V.P.S., A.P.J., F.S.C., J.C., and G.J.M. the coexistence curve––thereby presenting a unique challenge for wrote the paper. predictive simulation and modeling (10–13). The authors declare no conflict of interest. Today, simulation and modeling are considered the third pillar This article is a PNAS Direct Submission. P.M. is a guest editor invited by the Editorial of the scientific method, together with analytical theory and ex- Board. periment. Studies of condensed phase molecular systems via the 1To whom correspondence should be addressed. Email: [email protected]. www.pnas.org/cgi/doi/10.1073/pnas.1418982112 PNAS Early Edition | 1of6 Downloaded by guest on September 28, 2021 quantum oscillators, one per single molecule––an approach that Table 1. QDO model for water principal parameters can be handled nonperturbatively and parameterized to the di- Parameter Value lute gas limit using monomer molecular properties only. Thus, within Gaussian statistics, many-body responses arising from dis- ROH 1.8088 a0 tortions of the electronic charge distribution (many-body polariza- ∠HOH 104.52° tion) and correlated quantum-mechanical charge density fluctuations qH 0.605 jej (many-body dispersion) are included to all orders in the condensed ROM 0.504 a0 phase, along with nontrivial cross-interactions––a novel strong mD 0.3656 me ω =Z coupling approach that has yet to be explored in molecular D 0.6287 Eh ± ± simulation. A description of the monomer electrostatics is added qD 1.1973 jej κ to capture lower-order molecular moments via point charges 1 613.3 Eh λ −1 embedded in a rigid molecule frame, an approach borrowed from 1 2.3244 a0 κ seminal early work (5, 10). A short-range pair potential determined 2 10.5693 Eh λ 1.5145 a−1 from a single-dimer energy surface completes the quantum Drude 2 0 σ = σ = σ oscillator (QDO) picture of water. All parameters used to simulate D H M 0.1 a0 σ the model are given in Table 1––the parameters were not fit ex- c 1.2 a0 haustively through, for example, a machine-learning procedure which adds interest to the results presented below. Reasons for successes (or failure) and region of validity of the model are as given in Fig. 2A. We emphasize that the liquid–vapor density given following the presentation of the data. differences are very large near ambient conditions inducing ex- treme molecular-scale alterations, both in local spatial order Results (hydrogen bonding) and electronic structure. We determine the T ρ Properties Along the Liquid–Gas Coexistence Curve. Water’s liquid– critical constants of the QDO model, f c, cg, by fitting the vapor coexistence curve in Fig. 2A has several unique features: Wegner expansion (22) to our data, which express the difference The curve is wide and the critical point remarkably high for a between liquid and vapor densities (ρl and ρv, respectively), as β β+Δ molecular liquid; there is also a temperature of maximum density ρl − ρv = A0τ + A1τ , where τ = 1 − T=Tc, β ≈ 0.325 for the Ising (TMD)showninFig.2A, Inset, a characteristic anomaly of water. In universality class, and Δ = 0.5. The results, {Tc = 649ð2Þ K, ρ = 3 Fig. 3 A–C, the local structure is given in terms of the partial c 0.317ð5Þ g/cm }, agree well with experimental values, T = ρ = 3 radial distribution functions which indicate strong tetrahedral { c 647.096 K, c 0.322 g/cm }(23).