Study of a first principles potential for water – QUANTEAU

The quantum potential considered to describe water is expanded as a sum over one, two and three body (molecule) terms, augmented from an overall polarization term. A feature of this potential concerns the implicit inclusion of the distorsion of water molecules, required for a realistic description (stretching of the O-H bond involved in the hydrogen bonding). It has been shown for example that such an expansion accounts for the whole interactions taking place in the water hexamer (H2O)6. This potential is presently tested against known experimental properties (TeraHertz and Infrared spectra, second virial coefficient) of the first water clusters (H2O)N , N=2..6. It consists principally to compare equilibrium geometries by means of rotational constants, and the infrared shifts of the O-H stretch involved in the hydrogen bond, which constitute the spectroscopic signature of the hydrogen bonded networks. The results obtained by a traditional quantum approach will allow us to test the new quantum statistical methods under development. These methods relie on a path integral approach, for structural and thermodynamical properties as well as dynamical ones. Concerning these latter properties, their actual determination still constitutes a non solved problem, but different approaches have been proposed : those of type «Ring Polymer« and «Wigner distribution« will be first considered.

This project required the development of new codes, some of them still in the test process. Amongst the first results obtained, one can cite :
1) Development of distributed multipoles and polarizability models, explicitly taking into account the distorsion of the water molecule.
2) Development of a quantum formulation of the second virial coefficient, and ab initio computation of the infrared shifts in the water dimer.
3) Unraveling the advantages and disadvantages of the quantum dynamics « Quantum Thermal Bath » method with respect to the vibrational spectroscopy of highly anhormonic systems.
Amelioration of the of the « Phase Integration Quasi-Classical » method aimed at vibrational spectroscopy calculations. It appears that it allows one to reproduce very satisfactorily the A-H hydrogen bands in the 2000-4000 cm-1 band. This is in contrast to the standard « Ring Polymer Molecular Dynamics » méthod which, although considered as the reference method for large systems, displays severe intrinsic limitations in this frequency range.

The availability of an accurate quantum potential for water will allow one to greatly speed up the present ab initio Molecular Dynamics codes. Indeed, these codes systematically recalculate the interactions between the solvent water molecules. Secondly, the development, test and diffusion of new quantum molecular dynamics codes, which can be used as well for small clusters (H2O)N as for the bulk, will constitute an important contribution to this community, whose codes are presently confidential.

Five papers, explicitly acknowledging ANR for its financial support, have been published so far : three of them dealt with testing the two-body term for two quantum potentials (CCpol-8sf and MBpol), by comparison to spectroscopic results obtained for the water dimer. It was shown for both potentials that they achieve a very high accuracy, leading to results in close agreement with experiments.
dx.doi.org/10.1021/ct400863t
dx.doi.org/10.1016/j.jqsrt.2014.02.016
dx.doi.org/10.1063/1.4865339
The other two wera aimed at testing two quantum dynamics methods designed for vibrational spectroscopy : it appeared that the so-called « Phase Integration Quassi-Classical » method lead to better results and will be used for the second part of our project.
dx.doi.org/10.1039/c3cp5049j
dx.doi.org/10.1080/08927022.2013.843776

There exists no genuine "first principles" liquid water potential, that is without any input from experimental results, which is of current use in bulk Molecular Dynamics (MD) simulations and able to accurately reproduce its peculiar properties. Combining new theoretical investigations from three related fields -namely Quantum Chemistry, water clusters Spectroscopy and classical/quantum MD simulations - we propose in this project the definition, assessment and testing of such a first principles (quantum) liquid water potential.
To describe molecular interactions, we will rely on the usual multi-body expansion but limited to third order and augmented with the global induction contribution, as recent studies on water hexamer and higher clusters have shown that four- and higher-body terms are negligible. We will use the recent CCpol-8s 2-body and induction terms of K.Szalewicz and coworkers which have been shown to constitute the most accurate potential energy surface (PES) available for the dimer. The assessment will then primarly concern the 3-body contribution taken to be, as a starting point, the SAPT 3-body potential of the same group. Energetics and structure of the PES's critical points will be compared, for water clusters, to their ab initio (CCSD(T)) counterparts. For bulk simulation, the present 25-site expansion of the two-body and induction terms constitutes a true bottleneck as the potential and its derivatives have to be evaluated many times. Its efficient implementation in a MD simulation code will be required in order to make such calculations tractable. The definition of an accurate flexible model included detailed dipole moment and polarizability surfaces, required to compute vibrational properties (IR, Raman), will also be considered.
We will perform far infrared spectrum simulation for the water trimer at very low temperature in order to compare with the numerous experimental results obtained by R.Saykally (UC Berkeley) in molecular beams. This provides a unique way to test the three-body term in the potential expansion. The trimer will be described within a collisional formulation in order to explicitly consider the multiple (48) equivalent minima, between which tunneling motions occur and constitute a signature of the spectrum. The energy levels will be obtained by means of a symmetry (G48) adapted vibrational SCF approach in order to greatly reduce the computational cost of this twelve-dimensional problem. Concerning higher clusters, we will employ the Rigid Body Diffusion Quantum Monte Carlo method which can furnish vibrationally averaged ground state properties.
In simulation of bulk water, the first necessary step will be to implement the resulting force field in a "classical" code in order to perform energy minimizations at vanishing temperatures or classical dynamics at finite temperatures, and characterize the associated cluster and bulk properties. We will then have to implement various quantum (nuclear) dynamics methods for clusters as well as condensed phase (periodic) boundary conditions. In priority, imaginary-time Path Integral method will be considered, which provides exact static properties including structural quantities (cluster geometries and radial distribution functions,...) and thermodynamic properties. Concerning the dynamics , and more specifically the quantum time correlation functions, an exact computation for many-body systems is still an unsolved issue. Among the various approximate methods proposed in the literature, we plan to develop/implement three of them : the Ring Polymer Molecular Dynamics approach, the Phase-space Wigner distribution method and the coloured-noise stochastic method.