# How to calculate the basis function energy from DFT programs?

#### peter308

Dear all:

I need to calculate the density of states of electrons from metallic clusters. I ran a DFT program and output the mulliken population analysis datas, such as the following:

(I show only part of the data)

ATOM # 1

ORBITAL ALPHA OCCUPATION
5s 0.0061
6s 0.3406
7s -.0419
4py 0.0827
4pz 0.0827
4px 0.0827
5py 0.7021
5pz 0.7021
5px 0.7021
6py 0.2155
6pz 0.2155
6px 0.2152
4d-2 0.7892
4d-1 0.7898
4d+0 0.7906
4d+1 0.7895
4d+2 0.7909
5d-2 0.1637
5d-1 0.1635
5d+0 0.1633
5d+1 0.1637
5d+2 0.1633
6d-2 0.0397
6d-1 0.0409
6d+0 0.0405
6d+1 0.0399
6d+2 0.0395

However, the program seems not provide any information on energy value of the basis function orbitals, such as "6s" or "4d+2". I wonder how one can obtain it from the program?By the way, i use a software named "deMon2k" for doing dft calculations.I am appreciated if you could provide me with any ideas, thanks.

Best
Yen

Last edited:
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#### TeethWhitener

Science Advisor
Gold Member
However, the program seems not provide any information on energy value of the basis function orbitals, such as "6s" or "4d+2". I wonder how one can obtain it from the program?
There is a fundamental misunderstanding here. Linear combinations of the basis functions are used to construct energy eigenstates ($\psi_j=\sum_i a_i\phi_i$). It is an odd question to talk about the energies of the basis functions; they are really only mathematical constructs.

That said, you can certainly take the full Hamiltonian for the system in question and operate it on a basis function (which will in turn be a linear combination of energy eigenstates $\phi_j=\sum_i b_i \psi_i$). This will return a weighted list of energy eigenstates. You could get an average energy of the system by taking the expectation value of the Hamiltonian for a basis function $\langle \phi_j|H|\phi_j\rangle$. But I'm not sure if that procedure would give you any useful information.

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