Composite and Low-Cost Approaches for Molecular Crystal Structure Prediction

Molecular crystal structure prediction (CSP) requires evaluating differences in lattice energy between candidate crystal structures accurately and efficiently. In this work, we explore and compare several low-cost alternatives to dispersion-corrected density-functional theory (DFT) in the plane-waves/pseudopotential approximation, the most accurate and general approach used for CSP at present. Three types of low-cost methods are considered: DFT with a small basis set of finite-support numerical orbitals (the SIESTA method), dispersion-corrected Gaussian small or minimal-basis-set Hartree-Fock and DFT with additional empirical corrections (HF-3c and PBEh-3c), and self-consistent-charge dispersion-corrected density-functional tight binding (SCC-DFTB3-D3). In addition, we study the performance of composite methods that comprise a geometry optimization using a low-cost approach followed by a single-point calculation using the accurate but comparatively expensive B86bPBE-XDM functional. All methods were tested for their abilities to produce absolute lattice energies, relative lattice energies, and crystal geometries. We show that assessing various methods by their ability to produce absolute lattice energies can be misleading and that relative lattice energies are a much better indicator of performance in CSP. The EE14 set of relative solubilities of homochiral and heterochiral chiral crystals is proposed for relative lattice-energy benchmarking. Our results show that PBE-D2 plus a DZP basis set of numerical orbitals coupled with a final B86bPBE-XDM single-point calculation gives excellent performance at a fraction of the cost of a full B86bPBE-XDM calculation, although the results are sensitive to the particular details of the computational protocol. The B86bPBE-XDM//PBE-D2/DZP method was subsequently tested in a practical CSP application from our recent work on the crystal structure of the enantiopure and racemate forms of 1-aza[6]helicene, a chiral organic semiconductor. Our results show that this multilevel method is able to correctly reproduce the energy ranking of both crystal forms.