CHEM 4502 Lecture Notes - Lecture 31: Molecular Orbital Theory, Neutron Capture, Orbital Overlap
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When the electron is close to nucleus a, leaving last term is constant. 1st 2 terms: close to nucleus a we should have an orbital that resembles a hydrogen atomic orbital. More formally, we write the molecular orbitals as linear combinations of atomic orbitals (lcao) While an infinite set of atomic orbitals would provide an exact wavefunction, in practice the basis set is finite. The optimum values of the c r coefficients are found using the variational principle, which means solving the secular equations. H terms are matrix elements of the hamiltonian. S terms are overlap matrix elements optimize cr --> these secular equations have nontrivial solutions if. For the case of 2 atomic orbitals, a and b, we can evaluate the matrix elements: H atoms contribute same amount to the orbital alpha, beta, and s are different integrals and they lead to energy of mo --> determines if bond is stable overlap, coulomb, and resonance integrals.