The meaning (and validity) of fractional occupations in QM

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SUMMARY

The discussion centers on the validity of fractional occupations in quantum mechanics (QM), particularly in relation to the Schrödinger equation (SE) and Kohn-Sham (KS) equations. Participants highlight a divide between chemists and physicists regarding the acceptance of fractional occupations in molecular or KS orbitals. The conversation emphasizes that allowing probabilities to distribute across orbitals in quantities less than one can lead to lower energy solutions, challenging traditional views on integer occupancies in quantum systems.

PREREQUISITES
  • Understanding of the Schrödinger equation (SE) and Kohn-Sham (KS) equations.
  • Familiarity with quantum mechanics principles, particularly regarding orbital occupancy.
  • Knowledge of Hamiltonians in quantum systems.
  • Basic concepts of probability distribution in quantum chemistry.
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  • Research the implications of fractional occupations in quantum chemistry.
  • Explore the differences between chemists' and physicists' approaches to quantum mechanics.
  • Study the role of Hamiltonians in determining orbital occupancy.
  • Investigate the concept of energy minimization in quantum systems with fractional occupations.
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Quantum chemists, physicists, and researchers interested in the theoretical foundations of quantum mechanics and the implications of fractional orbital occupations.

Einstein Mcfly
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Hello all. As I understand it, there's somewhat of a divide in the scientific community (basically between chemists and physicist) around the topic of solutions to the SE (or KS eqn) that give fractional occupations of molecular or KS orbitals. I myself see no physical reason why probability can't be allowed to leak into a number of orbitals in quantities less than one, particularly if it gives a lower energy solution. Is there anything that I should understand in this regard (ie, that these solutions violate some key property of QM such as <S**2> not being a good quantum #)?

Thanks for your thoughts.
 
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I'm a quantum chemist, and this is the first I've ever heard of such a thing. (Or indeed any kind of fundamental disagreement between chemists and physicists.)

You'll have to elaborate on what you mean; I don't see the problem. On the contrary, I don't know why anyone would expect integer occupancies for an interacting Hamiltonian in a single-particle basis.
 

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