# Mulliken Population when using double zeta basis

• Teng YANG
In summary, the conversation discusses the issue of negative occupation values in atomic orbitals and the potential problems with interpreting the DS matrix elements as occupation values. It is suggested to refer to a research article for more information on this topic.

#### Teng YANG

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.

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.

The Mulliken population is a method used in quantum chemistry to calculate the distribution of electron density within a molecule or atom. It is often used when using a double zeta basis set, which is a more advanced and accurate method for calculating electronic structure compared to a single zeta basis set.

In this particular case, the negative occupation in the atomic orbital 5p indicates that there is a deficiency of electrons in that orbital. This could be due to the presence of a neighboring atom or molecule that is causing a redistribution of electron density.

The total number of charges, 6.00, is the sum of the positive and negative charges in the system. This value can provide insight into the overall charge and stability of the system.

If you require further assistance with understanding the results of your calculation, I would suggest consulting with a colleague or a more experienced researcher in your field. They may be able to provide more specific insights and guidance.

## 1. What is Mulliken Population analysis?

Mulliken Population analysis is a technique used in computational chemistry to determine the distribution of electrons in a molecule. It calculates the population of each atomic orbital based on the overlap of orbitals and the electronegativity of the atoms.

## 2. Why is Mulliken Population analysis important?

Mulliken Population analysis provides valuable information about the electronic structure of a molecule, which is crucial in understanding its chemical and physical properties. It can also help in predicting reactivity and reaction mechanisms in chemical reactions.

## 3. How is Mulliken Population calculated using a double zeta basis set?

Mulliken Population is calculated by multiplying the square of the coefficient of each atomic orbital with its corresponding charge and summing up these values for all the orbitals in a given atom. In the case of a double zeta basis set, the calculations are performed using two sets of basis functions for each atomic orbital.

## 4. What are the limitations of Mulliken Population analysis using a double zeta basis set?

One limitation is that Mulliken Population analysis does not take into account the effects of electron correlation, which can lead to inaccurate results. Additionally, the use of a double zeta basis set may not be sufficient for complex molecules, and higher basis sets may be required for more accurate calculations.

## 5. How can Mulliken Population be used in practical applications?

Mulliken Population analysis is often used in the design and development of new drugs, materials, and catalysts. It can also be used in studying the electronic structure of molecules in fields such as organic chemistry, biochemistry, and materials science.