Author Topic: How is a Mulliken population broken up into orbital contributions?  (Read 4758 times)

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Offline Quantamania

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Friends,
     I have recently examined the effects of basis sets on Mulliken populations and other information in graphene and hexagonal BN layers.  When I keep the verbosity level at 10 in the NanoLanguage Scripter then watch the SCF convergence process, I notice that the Mulliken populations are distributed among orbitals of various angular momentum.  Parts of the population are allocated to s-orbitals, p-orbitals, and in the polarized basis sets, d-orbitals.  In the bilayers of graphene and h-BN, I observe that there are minor changes in some orbital contributions to the Mulliken population when the interface is formed, while other orbital shells do not change at all.

     How is this done, and is there any references related to decomposition of Mulliken populations into individual orbital factors?  This has never been extensively described in the literature, and I had considered looking at orbital contributions to try identify the major orbitals responsible for the interface that forms between the two different monolayers via pi-pi orbital overlap and hence the cause of energy perturbations that open the band gap in the graphene layer.

Offline Nordland

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The mulliken population is calculating by multiplying the density matrix with the overlap matrix. The trace of this product is used for calculating the number of electrons. The decomposition is done by restricting the trace to only contain certain orbitals. The mulliken population is per atom is calculating restricting  the trace orbitals in question for a the single atom. A single shell occupation is by restricting the trace to only include orbitals located on the atom in question, and orbital with the right angular momentum.

Offline Quantamania

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Nordland, thanks for the explanation.

Is it possible for a particular trace of the Mulliken population matrix with selections of specific angular momentum orbital sets to be a negative value?  If so, how is it achieved given that we have an electron density matrix and an orbital overlap matrix that we take the product of to compute the Mulliken population?  In some of the Mulliken population results I am studying, a few of the numbers are negative, while most of the other numbers are positive.  This is apparent in large basis sets, with lots of factors in their total sums.  The total populations, which are the sums of all the traces in different angular momentum sets, however, are positive.

Offline Nordland

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The full trace is always positive and equal to the number of electrons. As there are more basis function to span the same shell, a linear combination of these orbitals is used to form the occupation of this shell, and weighting of the individual orbitals in these linear combination can be negative.