Department of Inorganic and Physical Chemistry, Ghent University, Krijgslaan 281 (S3), 9000 Gent, Belgium.
Phys Chem Chem Phys. 2012 Feb 21;14(7):2408-16. doi: 10.1039/c2cp22543c. Epub 2012 Jan 16.
The Fukui function is considered as the diagonal element of the Fukui matrix in position space, where the Fukui matrix is the derivative of the one particle density matrix (1DM) with respect to the number of electrons. Diagonalization of the Fukui matrix, expressed in an orthogonal orbital basis, explains why regions in space with negative Fukui functions exist. Using a test set of molecules, electron correlation is found to have a remarkable effect on the eigenvalues of the Fukui matrix. The Fukui matrices at the independent electron model level are mathematically proven to always have an eigenvalue equal to exactly unity while the rest of the eigenvalues possibly differ from zero but sum to zero. The loss of idempotency of the 1DM at correlated levels of theory causes the loss of these properties. The influence of electron correlation is examined in detail and the frontier molecular orbital concept is extended to correlated levels of theory by defining it as the eigenvector of the Fukui matrix with the largest eigenvalue. The effect of degeneracy on the Fukui matrix is examined in detail, revealing that this is another way by which the unity eigenvalue and perfect pairing of eigenvalues can disappear.
福井函数被认为是位置空间中福井矩阵的对角元素，福井矩阵是单粒子密度矩阵（1DM）对电子数的导数。福井矩阵的对角化，用正交轨道基表示，可以解释为什么空间中存在负福井函数的区域。使用分子测试集，发现电子相关对福井矩阵本征值有显著影响。福井矩阵在独立电子模型水平上被数学证明始终有一个本征值等于 1，而其余本征值可能不等于零，但总和为零。1DM 在相关理论水平上的幂等性的丧失导致了这些性质的丧失。详细研究了电子相关的影响，并通过将其定义为最大本征值的福井矩阵特征向量，将前线分子轨道概念扩展到相关理论水平。详细研究了简并对福井矩阵的影响，揭示了这是另一种使单位本征值和本征值完美配对消失的方法。
