炼金几何弛豫
Alchemical geometry relaxation
AI总结：
本文提出基于炼金微扰密度泛函理论（APDFT）的几何弛豫方法，通过推导混合二阶能量导数解析公式并结合Morse势插值，在保持组合效率的同时实现了对小分子及等电子掺杂突变体高精度的平衡能量与键长预测。
摘要：
我们提出使用炼金微扰密度泛函理论（APDFT）来弛豫整个化学化合物空间（CCS）的几何结构。APDFT是指在薛定谔方程的近似解中涉及核电荷变化的微扰理论。我们给出了在限制性Hartree-Fock情况下，计算关于核电荷和核位置的混合二阶能量导数（称为“炼金力”）的解析公式。我们实现并研究了该公式在各种参考分子和目标分子的几何弛豫中的应用。我们还分析了炼金力微扰级数的收敛性以及基组效应。将炼金预测的能量、力和Hessian矩阵插值到Morse势中，比执行标准Newton Raphson步骤能产生更准确的几何结构和平衡能量。我们对包括BF、CO、N2、CH$_4$、NH$_3$、H$_2$O和HF在内的小分子的数值预测表明，对于4阶APDFT预测，平衡能量和键长的平均绝对误差分别小于10 mHa和0.01 Bohr。我们的炼金几何弛豫仍然保持了APDFT的组合效率：基于苯的单个耦合微扰Hartree Fock导数，我们提供了所有17个等电子电荷中性BN掺杂突变体的平衡能量和弛豫结构的数值预测，其平均绝对偏差分别约为27 mHa和0.12 Bohr。
英文摘要：
We propose to relax geometries throughout chemical compound space (CCS) using alchemical perturbation density functional theory (APDFT). APDFT refers to perturbation theory involving changes in nuclear charges within approximate solutions to Schrödinger's equation. We give an analytical formula to calculate the mixed second order energy derivatives with respect to both, nuclear charges and nuclear positions (named "alchemical force"), within the restricted Hartree-Fock case. We have implemented and studied the formula for its use in geometry relaxation of various reference and target molecules. We have also analysed the convergence of the alchemical force perturbation series, as well as basis set effects. Interpolating alchemically predicted energies, forces, and Hessian to a Morse potential yields more accurate geometries and equilibrium energies than when performing a standard Newton Raphson step. Our numerical predictions for small molecules including BF, CO, N2, CH$_4$, NH$_3$, H$_2$O, and HF yield mean absolute errors of of equilibrium energies and bond lengths smaller than 10 mHa and 0.01 Bohr for 4$^\text{th}$ order APDFT predictions, respectively. Our alchemical geometry relaxation still preserves the combinatorial efficiency of APDFT: Based on a single coupled perturbed Hartree Fock derivative for benzene we provide numerical predictions of equilibrium energies and relaxed structures of all the 17 iso-electronic charge-netural BN-doped mutants with averaged absolute deviations of $\sim$27 mHa and $\sim$0.12 Bohr, respectively.
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