Diffusion Monte Carlo Study of Para-Diiodobenzene Polymorphism Revisited

We revisit our investigation of the diffusion Monte Carlo (DMC) simulation of para-diiodobenzene (p-DIB) molecular crystal polymorphism. [See J. Phys. Chem. Lett. 2010, 1, 1789-1794.] We perform, for the first time, a rigorous study of finite-size effects and choice of nodal surface on the prediction of polymorph stability in molecular crystals using fixed-node DMC. Our calculations are the largest that are currently feasible using the resources of the K-computer and provide insights into the formidable challenge of predicting such properties from first principles. In particular, we show that finite-size effects can influence the trial nodal surface of a small (1 × 1 × 1) simulation cell considerably. Therefore, we repeated our DMC simulations with a 1 × 3 × 3 simulation cell, which is the largest such calculation to date. We used a density functional theory (DFT) nodal surface generated with the PBE functional, and we accumulated statistical samples with ∼6.4 × 10(5) core hours for each polymorph. Our final results predict a polymorph stability that is consistent with experiment, but they also indicate that the results in our previous paper were somewhat fortuitous. We analyze the finite-size errors using model periodic Coulomb (MPC) interactions and kinetic energy corrections, according to the CCMH scheme of Chiesa, Ceperley, Martin, and Holzmann. We investigate the dependence of the finite-size errors on different aspect ratios of the simulation cell (k-mesh convergence) in order to understand how to choose an appropriate ratio for the DMC calculations. Even in the most expensive simulations currently possible, we show that the finite size errors in the DMC total energies are much larger than the energy difference between the two polymorphs, although error cancellation means that the polymorph prediction is accurate. Finally, we found that the T-move scheme is essential for these massive DMC simulations in order to circumvent population explosions and large time-step biases.