Instantaneous dipole moment and orbitals

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SUMMARY

The discussion centers on the relationship between instantaneous dipole moments and atomic orbitals, specifically in hydrogen. It highlights the inconsistency of the Bohr model in explaining dipole moments, as electrons do not have fixed positions within orbitals. The participant emphasizes that while dipole moments can be understood in molecules like HCl, they are not applicable to individual hydrogen atoms due to the symmetrical distribution of electron probability around the nucleus. The conversation also touches on the role of external electric fields in inducing dipole moments and the nature of London dispersion forces involving multiple atoms.

PREREQUISITES
  • Quantum mechanics principles, particularly atomic orbitals
  • Understanding of dipole moments and their calculations
  • Familiarity with London dispersion forces
  • Knowledge of the limitations of the Bohr model of the atom
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  • Study quantum mechanics and the concept of atomic orbitals in detail
  • Research the mathematical derivation of dipole moments in quantum systems
  • Explore the role of external electric fields in atomic physics
  • Investigate London dispersion forces and their implications in molecular interactions
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Students and researchers in quantum chemistry, physicists studying atomic interactions, and anyone interested in the nuances of dipole moments and their implications in atomic and molecular physics.

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TL;DR
How can idea of instantaneous dipole moment for atoms like, for example hydrogen be consistent with idea of orbitals.
Hi. I have got question as in title. How can idea of instantaneous dipole moment for atoms like, for example hydrogen be consistent with idea of orbitals? At my level of knowledge London dispersion forces are derived taking into account Bohr model of atom. But we know today that this model is not correct. If it would be correct I understand that at each time electron is at some point at radius at some angle and there is dipole moment at this time from nucleus to electron at orbit. But how is it possible to atom like hydrogen have instantanous dipole moment if around nucleus "is" orbital so electron doesn't have position and, what is the most important - probability of finding electron around nucleus at some radius in whole angles is the same, so vector sum of negative charge contributions from each angle goes to zero. For me it means that existence of dipole moment is impossible because there isn't any negative resultant negative charge. At the end. I understand dipole moment in, for example HCl molecule but in H atom no. So I would be grateful if someone explain me this or give link to some paper that explain this phenomena.
 
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In case there exists external E field, permanent or instantaneous by fluctuation, atomic dipole moment would appear to lower the system energy.
 
When talking about London forces, you always need at least two atoms. Their dipole dipole interaction involves the product of the dipole moment operators d1 and d2 of the two atoms. While the expectation value of each of these operator vanishes, that of their product is non-vanishing, given that <0 | d1 d2 | 0> can be expanded in a sum involving excited states i, <0| d1 | i> <i| d2| 0> .
 

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