Closed-shell normalization constant

As with the closed-shell case, this matrix should be constructed from the derivative integrals in the atomic-orbital basis. Indeed, it is possible to solve the entire set of equations in the AO basis if desired. From these equations, it can be seen that properties such as dipole moment derivatives can be obtained at the SCF level as easily for open-shell systems as is the case for closed-shell systems. Analytic second derivatives are also quite straightforward for all types of SCF wavefunction, and consequently force constants, vibrational frequencies and normal coordinates can be obtained as well. It is also possible to use the full formulae for the second derivative of the energy to construct alternative expressions for the dipole derivative. 

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