6.3 MD Simulation of Liquid Water
The MD simulation has been performed with the GPW module (see Sec. 2.3.1 and Sec. 7.2.1) of the program package CP2K [21]. The trajectory of the system consisting of 64 molecules of water was computed using Born-Oppenheimer MD, yielding a total simulated time of 35 ps. The BLYP functional has been employed with the norm-conserving pseudopotentials of Goedecker and co-workers (GTH) [18] and a density cutoff of 300 Ry. The Gaussian basis set was a triple-zeta va- lence basis set augmented with two sets of d-type or p-type polarization functions (TZV2P). This basis set has already been shown to give converged structural and dynamical properties for liquid water at constant volume [80]. A time step of
0.48 fs has been applied and Nos´e-Hoover thermostats have been attached to the
ions with a temperature of 360 K and a time constant of 2000 cm−1. Although
17O and 2H are the desired nuclei for quadrupole interactions,16O and 1H masses
have been used for the simulation. The reasons will be explained below. The
supercell was set to 12.42x12.42x12.42 ˚A, corresponding to a density of 1 g/cm3.
The initial coordinates have been taken from a previous MD simulation [81] at comparable conditions, but the first 4 ps have not been taken into account for the subsequent calculation of the EFG, allowing for an equilibration of the system. The temperature is higher than in other simulations of water, which are mostly carried out at 330 K. Furthermore, the standard element masses have been ap- plied instead of the isotope’s masses. This has been done for compensating the tendency of DFT to yield overstructured water. The reason is an overestimation of the strength of the hydrogen bonds, caused by the exchange-correlation func- tionals, leading to a structure that is to stiff and exhibits much less fluctuations. This is a well known issue and has been addressed in many publications [29]. A significant error in the relaxation time and an increased computational effort would be caused by this effect. Both consequences of the deficiency of the DFT description should be avoided by this choice for temperature and masses. Still, the structural properties of the system have to be monitored carefully in order to keep the influences of the mentioned parameters under control. In Fig. 6.3 the evolution of the total energy during the MD simulation is plotted. After 35 ps
104 6 Quadrupole Relaxation in Water 0 5 10 15 20 25 30 35 40 Simulation time [ps] -5e-06 0 5e-06 1e-05 1.5e-05 2e-05 2.5e-05 3e-05 3.5e-05 4e-05 (E - E 0 )/|E 0 |
Figure 6.3: Relative change of the conserved quantity during a NVT simulation of water (normalized to the value at t = 0).
This can be considered a very good conservation, showing that the computational parameters of the simulation have been chosen properly [24].
Now, the above mentioned structural properties will be investigated. A common gauge of the structural and dynamical parameters are radial distribution func- tions (RDF). These are measures for the probability of finding another nucleus at distance r from a given one. In the book of Allen and Tildesley an introduction to this topic can be found [27]. Recently, a detailed overview of RDFs in water simulations has been published by Lee and Tuckerman [82]. The most significant parameter is the maximum of the oxygen-oxygen RDF. Most calculations yield numbers between 2.9 and 3.7, which is much larger than the most up to date experimental values, namely, 2.75 from neutron diffraction [83, 84] and 2.8 from x-ray scattering measurements [85, 86]. The cited simulations have been carried out between 300 K and 350 K, using both deuteron and proton masses.
The RDFs computed from this simulation are displayed in Fig. 6.4 and Fig. 6.5 for oxygen-oxygen and oxygen-hydrogen, respectively. It can be seen, that the simulation presented in this work, with the slightly adjusted masses and temper- ature, yields a maximum of 2.82. This agrees very well with the experimental data at ambient conditions and therefore justifies the choice of parameters. The
6.3 MD Simulation of Liquid Water 105 2 3 4 5 6 7 r [Å] 0 0.5 1 1.5 2 2.5 3 gOO (r)
Figure 6.4: Oxygen-oxygen radial distribution function obtained from a molecular dynamics simulation of water. ρ = 1g/cm3, T = 360K.
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 6 6.5 7 r [Å] 0 0.5 1 1.5 2 2.5 3 gOD (r)
Figure 6.5: Oxygen-hydrogen radial distribution function obtained from a molecular dynamics simulation of water. ρ = 1g/cm3, T = 360K.
106 6 Quadrupole Relaxation in Water
oxygen-hydrogen RDF is comparable to those from other publications and does not exhibit any unexpected or unusual features. The height of the second peak is 2.42, which agrees well with the findings of Kuo et al. [29]. While the analysis of RDFs in water with respect to all kinds of parameters has been an important issue in the literature during the past years, a more detailed treatment is out of the scope of this work. Here, the RDFs are only used for assuring a reasonable structural behavior of the simulated ensembles. Thus, the MD simulations used in this work provide a good starting point for the evaluation of relaxation times. An adjustment was made to the MD parameters in an attempt to compensate for the known problems of the DFT description. Still, the RDFs only describe the average structure of the system and cannot guarantee that the microscopic dynamics are correct. This, in turn, will be revealed by the autocorrelation of the electric field gradient as needed for the computation of NMR relaxation.
It should be noted that there is another quantity that is often given as a measure for the quality of the description of a water simulation, namely the diffusion constant. Since this parameter can only be calculated with a large error due to statistical problems, it does not give much insight into the dynamical properties of the system. Therefore, the diffusion constant is not presented here, the relaxation time is expected to be a much more appropriate criterion.