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Today I received a message from a user, since other users may also have interesting in this problem, I copy his question and my reply here

Q:

I saw that your program Multiwfn has a function to calculate the extent of the spatial overlap between two molecular orbitals (3.100.11 in your manual). I am currently looking into some organic polyradicals in which the overlap between the SOMOs is very important to determine the ground state multiplicity, using Gaussian 09 program, and I was wondering if you could guide me on how to use your program. Also, from a more technical point of view, I wonder how you actually perform the integral and how the phase of the orbitals is taken into account. Do you expand the MO in the basis of the atomic orbitals (expressed as gaussian orbitals) and then take the sum of each of the individual overlap?

A:

Proper way of choice of input file format for Multiwfn is described in Section 2.5 of the manual. As mentioned in Section 3.100.11, the needed information is GTF and atom coordinate, therefore according to the Table in Section 2.5, you can immediately know that you can use .wfn, .wfx or .fch generated by Gaussian as input file. Of course, the easiest way is directly using .fch file. After loading this file, enter main function 100 and select option 11, then input indices of the two orbitals you want to study, the overlap will be immediately outputted.

Technically, the overlap of absolutes of two orbitals is calculated in terms of Becke's multi-center integration method, detail can be found in JCP, 88, 2547 (1988). This is a numerical integration method, at each integration point, the program calculates psi_i and psi_j, and then get |psi_i|*|psi_j|, where psi is orbital wavefunction value and can be easily evaluated according to definition of basis functions and LCAO coefficients.

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