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→Derivation: opeator -> operator |
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\end{aligned}</math>
The factor 1/2 in the molecular Hamiltonian drops out before the double integrals due to symmetry and the product rule. We may define [[Fock matrix|Fock
: <math>\hat{F}(\mathbf{x}_k)\phi_k(\mathbf{x}_k) \equiv \left[ \hat{h}(\mathbf{x}_k) + \hat{J}(\mathbf{x}_k) - \hat{K}(\mathbf{x}_k) \right]\phi_k(\mathbf{x}_k) = \epsilon_k \phi_k(\mathbf{x}_k),</math>
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The solution <math>\phi_k</math> and <math>\epsilon_k</math> are called molecular orbital and orbital energy respectively.
Although Hartree-Fock equation appears in the form of a eigenvalue problem, the Fock operator itself depends on <math>\phi</math> and must be solved by different technique.
===Total energy===
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