Finite-size corrections in numerical simulation of liquid water

Monte Carlo (MC) simulations of the SPC/E liquid water model are performed at two numbers of molecules N = 100 and 512 and in canonical NVT, isobaric NPT, and grand canonical μVT ensembles. The molecular non-spherically symmetric pair distribution function g(r, Ω) (pdf) is accumulated in terms of projections $$ onto rotational invariants. The precisely measured differences between N values and between ensembles are in very good agreement with the theoretical predictions for the expected finite-size corrections of different origins: (1) the canonical simulation is affected by explicit corrections due to the absence of density fluctuations. Beyond the well-known shift in the long-range asymptote, all projections exhibit rich short-range contributions. These corrections vanish exactly in the isobaric ensemble provided that the pdf is constructed using the rigorous definition. (2) In the presence of dielectric discontinuity with the external medium surrounding the central box and its replica within the Ewald treatment of the Coulombic interactions, the disagreement with the prediction of the literature, already noticed recently for dipolar fluids, is confirmed in the present site-site model. (3) The implicit corrections originate from the coupling between the environment around a given particle and that around its periodic images in the neighboring cells. The recent, powerful MC/HNC mixed integral equation, which offers a complete and exact description of the molecular correlations in the whole real and Fourier spaces, enables us to quantify the observed N-dependence in the pdf projections down to the sub 10^-3 levels.