59th Annual Report on Research 2014

Accomplished project: accurate theoretical H-bond structure prediction of ab initio molecular dynamics (AIMD) based on PBE0 hybrid functional including van der Waals (vdW) interaction

A large part of the inaccuracy of current AIMD originates from the DFT functional approximation of GGA. Several studies showed that GGA is not good enough for H-bond structure predictions. On one hand GGA inherits the self-interaction errors from (semi)local exchange correlation approximations, which results in the over-structured pair correlation function from excessive proton delocalization and artificial red shifts of the OH stretching frequency. The self-interaction error can be largely alleviated by the hybrid-XC, e.g. PBE0, which mixes a fraction of Hartree-Fock exact exchange. It was found that PBE0 improves greatly the vibrational spectrum of liquid water, which softs the H-bond strength and reduces the discrepancy between experiment and theory for the first peak of OO and OH pair correlation functions. On the other hand, both hybrid-XC and GGA miss the attractive vdW interactions originating from the dynamic correlations of the electron density. Under the vdW forces, the density of non H-bonded molecules will be increased in the first coordination shell giving a further correction of theoretical structure towards the experiment.

In year 2013-2014 partially supported by PRF grant, we have adopted the semi-empirical a fully self-consistent implementation of the charge density-dependent dispersion correction of Tkatchenko and Scheffler (TS) to account for vdW interactions ach in our AIMD code package, which uses pair interaction with C₆ coefficients and cutoff radii that are functionals of the density functional theory (DFT) electron density on the fly of liquid trajectories from AIMD simulations. The TS functional uses accurate free atom C₆ values as reference and proves to be remarkably accurate. In addition, we have adopted the linear scaling method in building the exact exchange energy based on the maximally localized Wannier functions developed by the PI, which greatly increases the efficiency in computing PBE0 functional based AIMD. From the above arguments, it is clear that the self-interaction correction by hybrid-XC (PBE0), inclusion of vdW interaction, are both crucial in predicting an accurate H-bond structure. To prove this idea, we have performed an equilibrated PBE0+TS-vdW-AIMD trajectory for cubic cell with 128 water molecules with volume fixed at the experimental density at room temperature. Since the nuclei was treated classically, an elevated temperature 330K was used; this is because it was found that the 30K temperature increase can roughly mimic, for the property, quantum nuclei at 300K for the pair correlation of g_oo(r).  

The results are presented in Fig. 1(a) and (b). From Fig. 1(a), it is clear that the theoretically determined structure factors S_OO(Q) is in nearly quantitative agreement with the experimental results across the entire Q region accessible to the X-ray scattering experiments, with only a slightly noticeable shift towards higher Q values. At the same time, the over-structuring in the OO pair correlation function g_oo(r) is almost eliminated compared with conventional GGA-AIMD simulations. Moreover, the collective effects of exact exchange and vdW, as resulting from a large-scale AIMD simulation of (H2O)128 at the PBE0+TS-vdW(SC) level of theory  yield an oxygen-oxygen structure factor, SOO(Q), and corresponding gOO(r) that are in quantitative agreement with the best available experimental data. This increasingly more accurate description of the underlying hydrogen bond network in liquid water obtained at the PBE0+TS vdW( SC) (330 K) level of theory also yields higher-order correlation functions, such as the oxygen-oxygen-oxygen tripletangular distribution, POOO(¦È), and therefore the degree of local tetrahedrality, as well as electrostatic properties, such as the effective molecular dipole moment, that are in much better agreement with experiment.