Comparison of four methods to compute the dielectric permittivity of liquids from molecular dynamics simulations

Four methods to compute the dielectric permittivity epsilon of a liquid from molecular simulations are compared in the context of the simple point charge (SPC) water model. In the first method (unrestrained method), epsilon is evaluated from the fluctuations of the box dipole moment M, monitored during a single equilibrium simulation. In the three other methods, epsilon is evaluated from the probability distribution p(M) of the dipole moment norm. This distribution is itself evaluated in three different ways: (i) from multiple simulations involving a M-dependent biasing potential (umbrella-sampling method), (ii) from multiple simulations involving a constrained dipole moment norm (M-constraint method), or (iii) from fitting of incomplete p(M) estimates to a Maxwell distribution (fitting method). The four methods are shown to converge to an identical estimate of epsilon =61 +/-1 for SPC water (256 molecules, reaction-field electrostatics). The convergence properties, advantages, and drawbacks of the different methods are analyzed in detail. (C) 2001 American Institute of Physics.