Institute of Computational Chemistry and Catalysis and Department of Chemistry, University of Girona, 17071 Girona, Spain.
J Chem Phys. 2013 Jun 7;138(21):214107. doi: 10.1063/1.4807775.
The effective atomic orbitals have been realized in the framework of Bader's atoms in molecules theory for a general wavefunction. This formalism can be used to retrieve from any type of calculation a proper set of orthonormalized numerical atomic orbitals, with occupation numbers that sum up to the respective Quantum Theory of Atoms in Molecules (QTAIM) atomic populations. Experience shows that only a limited number of effective atomic orbitals exhibit significant occupation numbers. These correspond to atomic hybrids that closely resemble the core and valence shells of the atom. The occupation numbers of the remaining effective orbitals are almost negligible, except for atoms with hypervalent character. In addition, the molecular orbitals of a calculation can be exactly expressed as a linear combination of this orthonormalized set of numerical atomic orbitals, and the Mulliken population analysis carried out on this basis set exactly reproduces the original QTAIM atomic populations of the atoms. Approximate expansion of the molecular orbitals over a much reduced set of orthogonal atomic basis functions can also be accomplished to a very good accuracy with a singular value decomposition procedure.
在 Bader 分子中的原子理论框架下，已经实现了有效原子轨道，用于一般波函数。这种形式主义可以用来从任何类型的计算中检索一组合适的、归一化的数值原子轨道，其占据数加起来等于相应的分子中的原子量子理论（QTAIM）原子数。经验表明，只有少数有效原子轨道具有显著的占据数。这些对应于与原子的核心和价壳非常相似的原子杂化。其余有效轨道的占据数几乎可以忽略不计，除了具有超价特征的原子。此外，可以将计算的分子轨道精确地表示为这组归一化数值原子轨道的线性组合，并且在此基础集上进行的 Mulliken 布居分析精确地再现了原子的原始 QTAIM 原子数。也可以通过奇异值分解过程，以非常高的精度，将分子轨道近似展开到更小的一组正交原子基函数上。
