School of Chemistry, University of Southampton, Highfield, Southampton SO17 1BJ, United Kingdom.
J Chem Phys. 2013 Dec 7;139(21):214103. doi: 10.1063/1.4832338.
We present a method for the calculation of four-centre two-electron repulsion integrals in terms of localised non-orthogonal generalised Wannier functions (NGWFs). Our method has been implemented in the ONETEP program and is used to compute the Hartree-Fock exchange energy component of Hartree-Fock and Density Functional Theory (DFT) calculations with hybrid exchange-correlation functionals. As the NGWFs are optimised in situ in terms of a systematically improvable basis set which is equivalent to plane waves, it is possible to achieve large basis set accuracy in routine calculations. The spatial localisation of the NGWFs allows us to exploit the exponential decay of the density matrix in systems with a band gap in order to compute the exchange energy with a computational effort that increases linearly with the number of atoms. We describe the implementation of this approach in the ONETEP program for linear-scaling first principles quantum mechanical calculations. We present extensive numerical validation of all the steps in our method. Furthermore, we find excellent agreement in energies and structures for a wide variety of molecules when comparing with other codes. We use our method to perform calculations with the B3LYP exchange-correlation functional for models of myoglobin systems bound with O2 and CO ligands and confirm that the same qualitative behaviour is obtained as when the same myoglobin models are studied with the DFT+U approach which is also available in ONETEP. Finally, we confirm the linear-scaling capability of our method by performing calculations on polyethylene and polyacetylene chains of increasing length.
我们提出了一种基于局域非正交广义 Wannier 函数（NGWFs）计算四中心双电子排斥积分的方法。我们的方法已经在 ONETEP 程序中实现，并用于计算具有混合交换相关泛函的 Hartree-Fock 和密度泛函理论（DFT）计算的 Hartree-Fock 交换能分量。由于 NGWFs 是根据等效于平面波的系统地可改进基组就地优化的，因此可以在常规计算中实现大基组精度。NGWFs 的空间局域化允许我们利用具有带隙的系统中密度矩阵的指数衰减来计算交换能，而计算工作量随原子数线性增加。我们描述了在 ONETEP 程序中实现这种方法的情况，以进行线性标度第一性原理量子力学计算。我们对我们方法的所有步骤进行了广泛的数值验证。此外，当与其他代码进行比较时，我们发现对于各种分子，在能量和结构方面都非常吻合。我们使用我们的方法对与 O2 和 CO 配体结合的肌红蛋白系统的 B3LYP 交换相关泛函进行计算，并确认当使用同样的肌红蛋白模型与 ONETEP 中也可用的 DFT+U 方法进行研究时，得到了相同的定性行为。最后，我们通过对越来越长的聚乙烯和聚乙炔链进行计算，确认了我们方法的线性标度能力。
