Computer simulation plays a central role in modern-day materials science. The utility of a given computational approach depends largely on the balance it provides between accuracy and computational cost. Molecular crystals are a class of materials of great technological importance which are challenging for even the most sophisticated ab initio electronic structure theories to accurately describe. This is partly because they are held together by a balance of weak intermolecular forces but also because the primitive cells of molecular crystals are often substantially larger than those of atomic solids. Here, we demonstrate that diffusion quantum Monte Carlo (DMC) delivers subchemical accuracy for a diverse set of molecular crystals at a surprisingly moderate computational cost. As such, we anticipate that DMC can play an important role in understanding and predicting the properties of a large number of molecular crystals, including those built from relatively large molecules which are far beyond reach of other high-accuracy methods.

Department of Chemical Physics and Optics Faculty of Mathematics and Physics Charles University CZ 12116 Prague 2 Czech Republic

Department of Earth Sciences University College London London WC1E 6BT United Kingdom

Department of Physics and Astronomy University College London London WC1E 6BT United Kingdom

Department of Physics and Astronomy University College London London WC1E 6BT United Kingdom;

J Heyrovský Institute of Physical Chemistry Academy of Sciences of the Czech Republic CZ 18223 Prague 8 Czech Republic

London Centre for Nanotechnology University College London London WC1H 0AH United Kingdom

Physics and Materials Science Research Unit University of Luxembourg L 1511 Luxembourg Luxembourg

Thomas Young Centre University College London London WC1E 6BT United Kingdom

Zobrazit více v PubMed

Burke K. Perspective on density functional theory. J Chem Phys. 2012;136:150901. PubMed

Curtarolo S, et al. The high-throughput highway to computational materials design. Nat Mat. 2013;12:191–201. PubMed

Marzari N. The frontiers and the challenges. Nat Mater. 2016;15:381–382. PubMed

Sun J, et al. Accurate first-principles structures and energies of diversely bonded systems from an efficient density functional. Nat Chem. 2016;8:831–836. PubMed

Cohen AJ, Mori-Sanchez P, Yang W. Insights into current limitations of density functional theory. Science. 2008;321:792–794. PubMed

Peverati R, Truhlar DG. Quest for a universal density functional: The accuracy of density functionals across a broad spectrum of databases in chemistry and physics. Phil Trans R Soc A. 2014;372:20120476. PubMed

Medvedev MG, Bushmarinov IS, Sun J, Perdew JP, Lyssenko KA. Density functional theory is straying from the path toward the exact functional. Science. 2017;355:49–52. PubMed

Hammes-Schiffer S. A conundrum for density functional theory. Science. 2017;355:28–29. PubMed

Grimme S, Hansen A, Brandenburg JG, Bannwarth C. Dispersion-corrected mean-field electronic structure methods. Chem Rev. 2016;116:5105–5154. PubMed

Klimeš J, Michaelides A. Perspective: Advances and challenges in treating van der Waals dispersion forces in density functional theory. J Chem Phys. 2012;137:120901. PubMed

Beran GJO. Modeling polymorphic molecular crystals with electronic structure theory. Chem Rev. 2016;116:5567–5613. PubMed

Hermann J, DiStasio RA, Jr, Tkatchenko A. First-principles models for van der Waals interactions in molecules and materials: Concepts, theory, and applications. Chem Rev. 2017;117:4714–4758. PubMed

Sun J, Ruzsinszky A, Perdew JP. Strongly constrained and appropriately normed semilocal density functional. Phys Rev Lett. 2015;115:036402. PubMed

Mardirossian N, Head-Gordon M. PubMed

Wang Y, Jin X, Yu HS, Truhlar DG, He X. Revised M06-L functional for improved accuracy on chemical reaction barrier heights, noncovalent interactions, and solid-state physics. Proc Natl Acad Sci USA. 2017;114:8487–8492. PubMed PMC

Cruz-Cabeza AJ, Reutzel-Edens SM, Bernstein J. Facts and fictions about polymorphism. Chem Soc Rev. 2015;44:8619–8635. PubMed

Reilly AM, et al. Report on the sixth blind test of organic crystal structure prediction methods. Acta Cryst B. 2016;72:439–459. PubMed PMC

Booth GH, Grüneis A, Kresse G, Alavi A. Towards an exact description of electronic wavefunctions in real solids. Nature. 2013;493:365–370. PubMed

Wen S, Nanda K, Huang Y, Beran GJO. Practical quantum mechanics-based fragment methods for predicting molecular crystal properties. Phys Chem Chem Phys. 2012;14:7578–7590. PubMed

Bygrave PJ, Allan NL, Manby FR. The embedded many-body expansion for energetics of molecular crystals. J Chem Phys. 2012;137:164102. PubMed

Yang J, et al. Ab initio determination of the crystalline benzene lattice energy to sub-kilojoule/mole accuracy. Science. 2014;345:640–643. PubMed

Werner HJ, Schütz M. An efficient local coupled cluster method for accurate thermochemistry of large systems. J Chem Phys. 2011;135:144116. PubMed

Schimka L, et al. Accurate surface and adsorption energies from many-body perturbation theory. Nat Mater. 2010;9:741–744. PubMed

Ren X, Tkatchenko A, Rinke P, Scheffler M. Beyond the random-phase approximation for the electron correlation energy: The importance of single excitations. Phys Rev Lett. 2011;106:153003. PubMed

Klimeš J. Lattice energies of molecular solids from the random phase approximation with singles corrections. J Chem Phys. 2016;145:094506. PubMed

Foulkes WMC, Mitas L, Needs RJ, Rajagopal G. Quantum Monte Carlo simulations of solids. Rev Mod Phys. 2001;73:33–83.

Dubecký M, Mitas L, Jurečka P. Noncovalent interactions by quantum Monte Carlo. Chem Rev. 2016;116:5188–5215. PubMed

Zen A, Sorella S, Gillan MJ, Michaelides A, Alfè D. Boosting the accuracy and speed of quantum Monte Carlo: Size-consistency and time-step. Phys Rev B. 2016;93:241118(R).

Fraser LM, et al. Finite-size effects and coulomb interactions in quantum Monte Carlo calculations for homogeneous systems with periodic boundary conditions. Phys Rev B. 1996;53:1814–1832. PubMed

Beran GJO, Hartman JD, Heit YN. Predicting molecular crystal properties from first principles: Finite-temperature thermochemistry to NMR crystallography. Acc Chem Res. 2016;49:2501–2508. PubMed

Reilly AM, Tkatchenko A. Understanding the role of vibrations, exact exchange, and many-body van der Waals interactions in the cohesive properties of molecular crystals. J Chem Phys. 2013;139:024705. PubMed

Otero-de-la Roza A, Johnson ER. A benchmark for non-covalent interactions in solids. J Chem Phys. 2012;137:054103. PubMed

Price SL, Reutzel-Edens SM. The potential of computed crystal energy landscapes to aid solid-form development. Drug Discov Today. 2016;21:912–923. PubMed

Pulido A, et al. Functional materials discovery using energy–structure–function maps. Nature. 2017;543:657–664. PubMed PMC

Santra B, et al. Hydrogen bonds and van der Waals forces in ice at ambient and high pressures. Phys Rev Lett. 2011;107:185701. PubMed

Gillan MJ, Alfè D, Bygrave PJ, Taylor CR, Manby FR. Energy benchmarks for water clusters and ice structures from an embedded many-body expansion. J Chem Phys. 2013;139:114101. PubMed

Cutini M, et al. Assessment of different quantum mechanical methods for the prediction of structure and cohesive energy of molecular crystals. J Chem Theor Comput. 2016;12:3340–3352. PubMed

Wen S, Beran GJO. Accurate molecular crystal lattice energies from a fragment QM/MM approach with on-the-fly ab initio force field parametrization. J Chem Theor Comput. 2011;7:3733–3742. PubMed

Podeszwa R, Rice BM, Szalewicz K. Predicting structure of molecular crystals from first principles. Phys Rev Lett. 2008;101:115503. PubMed

Bludský O, Rubeš M, Soldán P. Ab initio investigation of intermolecular interactions in solid benzene. Phys Rev B. 2008;77:092103.

Ringer AL, Sherrill CD. First principles computation of lattice energies of organic solids: The benzene crystal. Chem Eur J. 2008;14:2542–2547. PubMed

Klimeš J, Bowler DR, Michaelides A. Chemical accuracy for the van der Waals density functional. J Phys Cond Mat. 2010;22:022201. PubMed

Needs RJ, Towler MD, Drummond ND, Rios PL. Continuum variational and diffusion quantum Monte Carlo calculations. J Phys: Condens Matter. 2010;22:023201. PubMed

Trail JR, Needs RJ. Norm-conserving Hartree-Fock pseudopotentials and their asymptotic behavior. J Chem Phys. 2005;122:014112. PubMed

Trail JR, Needs RJ. Smooth relativistic Hartree-Fock pseudopotentials for H to Ba and Lu to Hg. J Chem Phys. 2005;122:174109. PubMed

Mitas L, Shirley EL, Ceperley DM. Nonlocal pseudopotentials and diffusion Monte Carlo. J Chem Phys. 1991;95:3467–3475.

Alfè D, Gillan MJ. Efficient localized basis set for quantum Monte Carlo calculations on condensed matter. Phys Rev B. 2004;70:161101.

Trail JR, Needs RJ. Pseudopotentials for correlated electron systems. J Chem Phys. 2013;139:014101. PubMed

Lin C, Zong FH, Ceperley DM. Twist-averaged boundary conditions in continuum quantum Monte Carlo algorithms. Phys Rev E. 2001;64:016702. PubMed

Williamson AJ, et al. Elimination of coulomb finite-size effects in quantum many-body simulations. Phys Rev B. 1997;55:R4851–R4854.

Kent PRC, et al. Finite-size errors in quantum many-body simulations of extended systems. Phys Rev B. 1999;59:1917–1929.

Chiesa S, Ceperley DM, Martin RM, Holzmann M. Finite-size error in many-body simulations with long-range interactions. Phys Rev Lett. 2006;97:076404. PubMed

Kwee H, Zhang S, Krakauer H. Finite-size correction in many-body electronic structure calculations. Phys Rev Lett. 2008;100:126404. PubMed

Umrigar CJ, Nightingale MP, Runge KJ. A diffusion Monte Carlo algorithm with very small time-step errors. J Chem Phys. 1993;99:2865–2890.