Department of Chemistry, Duke University, Durham, North Carolina 27708, USA.
J Phys Chem A. 2010 Aug 26;114(33):8878-83. doi: 10.1021/jp1027838.
Localized molecular orbitals (LMOs) are much more compact representations of electronic degrees of freedom than canonical molecular orbitals (CMOs). The most compact representation is provided by nonorthogonal localized molecular orbitals (NOLMOs), which are linearly independent but are not orthogonal. Both LMOs and NOLMOs are thus useful for linear-scaling calculations of electronic structures for large systems. Recently, NOLMOs have been successfully applied to linear-scaling calculations with density functional theory (DFT) and to reformulating time-dependent density functional theory (TDDFT) for calculations of excited states and spectroscopy. However, a challenge remains as NOLMO construction from CMOs is still inefficient for large systems. In this work, we develop an efficient method to accelerate the NOLMO construction by using predefined centroids of the NOLMO and thereby removing the nonlinear equality constraints in the original method ( J. Chem. Phys. 2004 , 120 , 9458 and J. Chem. Phys. 2000 , 112 , 4 ). Thus, NOLMO construction becomes an unconstrained optimization. Its efficiency is demonstrated for the selected saturated and conjugated molecules. Our method for fast NOLMO construction should lead to efficient DFT and NOLMO-TDDFT applications to large systems.
局域分子轨道（LMO）是比典型分子轨道（CMO）更紧凑的电子自由度表示。最紧凑的表示是由非正交局域分子轨道（NOLMO）提供的，它们是线性无关的，但不是正交的。LMO 和 NOLMO 都可用于大体系电子结构的线性标度计算。最近，NOLMO 已成功应用于密度泛函理论（DFT）的线性标度计算和重制定量密度泛函理论（TDDFT）以计算激发态和光谱。然而，由于从 CMO 构建 NOLMO 对于大型系统仍然效率低下，因此仍然存在挑战。在这项工作中，我们开发了一种有效的方法，通过使用 NOLMO 的预定义质心来加速 NOLMO 的构建，从而消除原始方法中的非线性等式约束（J. Chem. Phys. 2004, 120, 9458 和 J. Chem. Phys. 2000, 112, 4 ）。因此，NOLMO 的构建成为无约束优化。我们选择了饱和和共轭分子来证明其效率。我们用于快速 NOLMO 构建的方法应该会导致 DFT 和 NOLMO-TDDFT 在大型系统中的有效应用。
