The Hartree–Fock (HF) method is a method of approximation for the determination of the wave function and the energy of a quantum many-body system in a stationary state. Why does the Hartree-Fock require the Molecular Orbitals to be orthogonal to each other?
The term "orthogonal" has nothing to do with a geometric orientation, it is an orthogonality of functions in the function space, that means the integral of their product is zero. If you look into the derivation of HF, the ansatz for the wavefunction is a Slater determinant which is chosen because a determinant automatically matches the Pauli exclusion principle.
Strictly spoken, the functions in the determinant do not need to be orthogonal functions, but if you look at the defining properties of determinants you find that non-orthogonal contributions just add 0 to the final scalar value of the determinant - and if one component has only non-orthogonal contributions, i.e. it is a linear combination of other components, the whole determinant is 0. Therefore it makes sense to work with orthogonal functions since the rest just is 0, anyway.
You don't need to start with an all-orthogonal set, however, actually the Roothan-Hall approach (https://en.wikipedia.org/wiki/Roothaan_equations) to the Hartree-Fock equation starts with a non-orthonormal set, but the orthonormality is then in usual implementations created in the next step of the program.
furthermore, Hartree-Fock theory is one idea to approximate the many-body wave function with a single Slater determinant.The molecular orbital is eigenfunctions of Fock operator in the conventional Hartree-Fock (HF) theory.The determinant, any non-orthogonal component of the orbitals is irrelevant and only the orthogonal part survives. The complete set of orthogonal basis functions and corresponding set of eigenvalues of this operator (orbital energies) are also real.
The orbital transition energies are detailed in this paper.
The precise role of UV exposure time in controlling the orbital transition energies, optical and electrical parameters of thermally vacuum evaporated Se 50 Te 50 thin film
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