How to calculate the basis function energy from DFT programs?

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To calculate the density of states from DFT outputs, it is important to understand that basis functions, like "6s" or "4d+2", do not have intrinsic energy values; they are mathematical constructs used to form energy eigenstates. The energies of these eigenstates can be derived by applying the Hamiltonian to the basis functions, yielding a weighted list of energy eigenstates. An average energy can be obtained by calculating the expectation value of the Hamiltonian for a given basis function. However, this method may not provide useful insights for the intended analysis. Understanding the distinction between basis functions and energy eigenstates is crucial for accurate calculations in DFT studies.
peter308
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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.



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Yen
 
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peter308 said:
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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