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.

中文翻译：

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复合和低成本的分子晶体结构预测方法

分子晶体结构预测（CSP）需要准确而有效地评估候选晶体结构之间晶格能量的差异。在这项工作中，我们在平面波/伪势近似中探索和比较了几种低成本的色散校正密度泛函理论（DFT）替代方法，这是目前用于CSP的最准确和通用的方法。考虑了三种类型的低成本方法：具有有限支持数字轨道的小基础集的DFT（SIESTA方法），经色散校正的高斯小或最小基集的Hartree-Fock和具有附加经验校正的DFT（HF） -3c和PBEh-3c），以及自恒定电荷分散校正的密度功能紧密结合（SCC-DFTB3-D3）。此外，我们研究了复合方法的性能，这些方法包括使用低成本方法进行几何优化，然后使用精确但相对昂贵的B86bPBE-XDM功能进行单点计算。测试了所有方法产生绝对晶格能量，相对晶格能量和晶体几何形状的能力。我们表明，根据各种方法产生绝对晶格能量的能力来评估各种方法可能会产生误导，并且相对晶格能量是CSP性能的更好指标。提出了EE14的同手性和异手性手性晶体的相对溶解度集，用于相对晶格能量基准。我们的结果表明，PBE-D2加上数字轨道的DZP基础集，再加上最终的B86bPBE-XDM单点计算，尽管具有对B86bPBE-XDM完整计算的成本，但其性能却是其成本的一小部分。计算协议的特定细节。B86bPBE-XDM // PBE-D2 / DZP方法随后在我们实际的CSP应用中得到了测试，该方法来自于我们最近对手性有机半导体1-氮杂[6]螺旋烯的对映体和外消旋体形式的晶体结构的研究。我们的结果表明，这种多级方法能够正确再现两种晶型的能级。B86bPBE-XDM // PBE-D2 / DZP方法随后在我们实际的CSP应用中得到了测试，该方法来自于我们最近对手性有机半导体1-氮杂[6]螺旋烯的对映体和外消旋体形式的晶体结构的研究。我们的结果表明，这种多级方法能够正确再现两种晶型的能级。B86bPBE-XDM // PBE-D2 / DZP方法随后在我们实际的CSP应用中得到了测试，该方法来自于我们最近对手性有机半导体1-氮杂[6]螺旋烯的对映体和外消旋体形式的晶体结构的研究。我们的结果表明，这种多级方法能够正确再现两种晶型的能级。