Fock 運算子可以很完整的描述分子對環境的所有作用力。因此，分子軌域的性質可以使用“採用原子軌域的分子軌域”和來自那些原子軌域的Fock矩陣來描述。在無關粒子近似法中只有Fock 運算子的本徵值和本徵函數是有意義的。企圖在原子軌域線性組合成的分子軌域（LCAO-MO） ＝ ＋ )中的係數 中的可能意義通常導致模糊的結果。因為在LCAO-MO中的原子軌域 和 不是Fock 運算子的本徵態。因此，並未被假設為 原子軌域。取代重疊的電荷轉移到鍵結區域的圖像，新的分析方法認為是電子α（或β）自旋電子的電子密度產生了自旋密度流的流動。因此，對於單電子分子軌域的共價鍵可以根據Fock矩陣分析的觀點來定義。

The Fock operator can take all interaction within the molecular environment into account, therefore the character of the molecular orbitals can be better accounted for in terms of molecular adapted atomic orbitals and the Fock matrix expanded in these atomic orbital set. Within the independent particle approximation only the eigenvalues and the eigenstates of the Fock operator are meaningful.Attempt to associate the coefficients in the LCAO-MO ＝ ＋ )with the meaning of probability often leads to ambiguous results because the AOs and in the LCAO-MO are not the eigenstates of the Fock operator and thus they are not the assumed atomic orbitals. Instead of the picture that overlap charge migrates into the bonding region, the new analysis display another picture that the charge densities for the electron with α(orβ) spin gives rise to spin density flow. Thus a criterion for the covalent bond in the one-electron MO level can be defined according to the Fock matrix analysis.

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