Sæther Sandra, Kjærgaard Thomas, Koch Henrik, Høyvik Ida-Marie
Department of Chemistry, The Norwegian University of Science and Technology , Høgskoleringen 5, 7491 Trondheim, Norway.
qLEAP Center for Theoretical Chemistry, Department of Chemistry, Aarhus University , Langelandsgade 140, 8000 Aarhus C, Denmark.
J Chem Theory Comput. 2017 Nov 14;13(11):5282-5290. doi: 10.1021/acs.jctc.7b00689. Epub 2017 Oct 10.
We introduce a density-based multilevel Hartree-Fock (HF) method where the electronic density is optimized in a given region of the molecule (the active region). Active molecular orbitals (MOs) are generated by a decomposition of a starting guess atomic orbital (AO) density, whereas the inactive MOs (which constitute the remainder of the density) are never generated or referenced. The MO formulation allows for a significant dimension reduction by transforming from the AO basis to the active MO basis. All interactions between the inactive and active regions of the molecule are retained, and an exponential parametrization of orbital rotations ensures that the active and inactive density matrices separately, and in sum, satisfy the symmetry, trace, and idempotency requirements. Thus, the orbital spaces stay orthogonal, and furthermore, the total density matrix represents a single Slater determinant. In each iteration, the (level-shifted) Newton equations in the active MO basis are solved to obtain the orbital transformation matrix. The approach is equivalent to variationally optimizing only a subset of the MOs of the total system. In this orbital space partitioning, no bonds are broken and no a priori orbital assignments are carried out. In the limit of including all orbitals in the active space, we obtain an MO density-based formulation of full HF.
我们介绍了一种基于密度的多级哈特里-福克（HF）方法，其中电子密度在分子的给定区域（活性区域）中进行优化。活性分子轨道（MOs）由起始猜测原子轨道（AO）密度的分解生成，而非活性MOs（构成密度的其余部分）则从未生成或被引用。MO公式通过从AO基转换到活性MO基实现了显著的维度降低。分子的非活性区域和活性区域之间的所有相互作用都得以保留，并且轨道旋转的指数参数化确保活性和非活性密度矩阵分别以及总体上满足对称性、迹和幂等性要求。因此，轨道空间保持正交，此外，总密度矩阵代表单个斯莱特行列式。在每次迭代中，求解活性MO基中的（能级移动）牛顿方程以获得轨道变换矩阵。该方法等同于仅对整个系统的一部分MOs进行变分优化。在这种轨道空间划分中，没有键被打破，也没有进行先验的轨道分配。在活性空间中包含所有轨道的极限情况下，我们得到了基于MO密度的全HF公式。
