Diffusion Monte Carlo Study of Para-Diiodobenzene Polymorphism Revisited.

Kenta Hongo,Alán Aspuru-Guzik,Mark A Watson,Ryo Maezono,Toshiaki Iitaka

doi:10.1021/ct500401p

Abstract

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.

Highlights

In our previous study,[73,74] we investigated for the first time using FN-diffusion Monte Carlo (DMC) the polymorphism of the para-diiodobenzene (p-DIB) organic molecular crystal, a strongly anisotropic system
It was found that the model periodic Coulomb (MPC) and kinetic energy corrections to the energy difference between the polymorphs were larger than the original difference itself
We show that a calculation with the largest simulation cell, 2×6×6, is unfeasible, even with hundreds of thousands of cores and the large memory capacities provided by massively-parallel conventional supercomputers

Summary

Introduction

The prediction of molecular crystal polymorphism[1,2] is one of the most challenging issues for current ab initio electronic structure calculations in both a theoretical and computational sense.[3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,23,24,25,26,27,28,29,30,31,32] The polymorphism is governed by very subtle interactions, such as weak noncovalent bonds. More sophisticated DFT simulations were performed based on DFT-∆12 12 and DFT-D,10 both of which agreed with our FN-DMC results This does not imply, that the KZK scheme adopted in our previous study appropriately describes the FSEs in our FNDMC simulations because there is no a priori reason that the FSEs in isotropic systems should be similar to those in anisotropic systems. The following two points should be carefully investigated in the FN-DMC simulations of the p-DIB molecular crystal polymorphism: (1) FSE effects for anisotropic molecular crystals, i.e., choice of simulation cell size, their aspect ratios and the performance of finite-size correction schemes; (2) the nodal surface dependence for an accurate description of noncovalent interactions. Section “Discussions” gives a detailed analysis of several finite-size corrections as well as computational aspects in our DMC simulations

Computational Methods

Methods

Findings

Concluding Remarks