Mulliken Population when using double zeta basis

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SUMMARY

The discussion centers on the interpretation of Mulliken Population Analysis, particularly regarding negative occupation values in atomic orbitals, such as the 5p orbital. The total charge is noted as 6.00, with specific occupation values provided for various orbitals. Participants highlight the challenges of interpreting density matrix (D) and overlap matrix (S) products, which can yield problematic results, including negative occupations and values exceeding 2 for orbitals. A reference to a relevant paper by Gordon et al. (1999) is provided for further reading.

PREREQUISITES
  • Understanding of Mulliken Population Analysis
  • Familiarity with density matrices and overlap matrices in quantum chemistry
  • Knowledge of atomic orbital theory
  • Basic concepts of charge distribution in molecular systems
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  • Research the implications of negative occupation values in Mulliken Population Analysis
  • Study the density matrix and overlap matrix calculations in quantum chemistry
  • Explore alternative population analysis methods, such as Natural Population Analysis
  • Read the paper by Gordon M. S. et al. (1999) for deeper insights into Mulliken Analysis
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Chemists, quantum chemists, and researchers involved in computational chemistry who are analyzing molecular electronic structures and interpreting population analysis results.

Teng YANG
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Is there anyone who can help me?


I was bothered by the negative occupation in atomic orbital like 5p here.
I don't understand what it means. By the way, 6.00 here is the total number of charges.

# 5s 5s 5py 5pz 5px 5py 5pz 5px 4dxy 4dyz 4dz2 4dxz 4dx2-y2 4dxy 4dyz 4dz2 4dxz 4dx2-y2
------------------------------------------------------------------------
6.000 0.206 0.751 -0.784 -0.784 -0.784 0.788 0.788 0.788 0.981 0.981 1.011 0.981 1.011 0.087 0.087 -0.098 0.087 -0.098


Thank you!
 
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I know very little about Mulliken Pop Analysis, but I do remember that interpreting the DS (I'm not sure if this is the standard convention, but I'm talking about the product of the density matrix, D, and the overlap matrix, S) matrix elements as atomic orbital occupation values is "problematic". One of the reasons is what you've pointed out (negative occupations), and the other is that sometimes you get occupation numbers greater than 2 for an orbital.

I have no clue what one does about this.

You may find something here : Gordon M. S., Schmidt, M. W., Chaban, G. M., Glaesemann, K. R., Stevens, W. J. & Gonzalez, C. (1999) J. Chem. Phys. 110, 4199-4207.
 

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