用可转移性逼近高斯轨道周期计算中的基组极限：简单半导体纯密度泛函的性能
Approaching the Basis Set Limit in Gaussian-Orbital-Based Periodic Calculations with Transferability: Performance of Pure Density Functionals for Simple Semiconductors
摘要：
用量子化学方法和高斯型轨道（GTO）模拟固体已经越来越受欢迎。尽管如此，很少有系统的研究，评估基组不完整性错误（BSIE）在这些GTO为基础的模拟在各种固体。在这项工作中，我们报告了一个基于GTO的固体实现，并应用它来解决基集收敛问题。我们采用一个简单的策略来生成大的无收缩（unc）GTO基集，我们称之为unc-def 2-GTH集。这些基组表现出系统的基础上的限制，以及良好的可转移性的基础上应用到43个简单的半导体的改进。最值得注意的是，我们发现的BSIE的unc-def 2-QZVP-GTH是小于0.7 m $E_h$每原子的总能量和20毫电子伏的带隙在这里考虑的所有系统。使用unc-def 2-QZVP-GTH，我们报告了组合设计的Meta广义梯度泛函（mGGA）B 97 M-rV的带隙基准，并表明B 97 M-rV与其他现代mGGA泛函M06-L（1.26 eV），MN 15-L（1.29 eV）和SCAN（1.20 eV）表现相似（均方根偏差（RMSD）为1.18 eV）。这代表了较旧的纯泛函如LDA（1.71 eV）和PBE（1.49 eV）的明显改进，尽管所有这些mGGA仍然远远不能定量准确。我们还提供了几个警示说明使用我们的无合同基地和GTO固体基组发展的未来研究。
英文摘要：
Simulating solids with quantum chemistry methods and Gaussian-type orbitals (GTOs) has been gaining popularity. Nonetheless, there are few systematic studies that assess the basis set incompleteness error (BSIE) in these GTO-based simulations over a variety of solids. In this work, we report a GTO-based implementation for solids, and apply it to address the basis set convergence issue. We employ a simple strategy to generate large uncontracted (unc) GTO basis sets, that we call the unc-def2-GTH sets. These basis sets exhibit systematic improvement towards the basis set limit as well as good transferability based on application to a total of 43 simple semiconductors. Most notably, we found the BSIE of unc-def2-QZVP-GTH to be smaller than 0.7 m$E_h$ per atom in total energies and 20 meV in band gaps for all systems considered here. Using unc-def2-QZVP-GTH, we report band gap benchmarks of a combinatorially designed meta generalized gradient functional (mGGA), B97M-rV, and show that B97M-rV performs similarly (a root-mean-square-deviation (RMSD) of 1.18 eV) to other modern mGGA functionals, M06-L (1.26 eV), MN15-L (1.29 eV), and SCAN (1.20 eV). This represents a clear improvement over older pure functionals such as LDA (1.71 eV) and PBE (1.49 eV) though all these mGGAs are still far from being quantitatively accurate. We also provide several cautionary notes on the use of our uncontracted bases and on future research on GTO basis set development for solids.
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