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- Title
Upper and lower bounds to atomic radial position moments.
- Authors
Marmorino, M. G.
- Abstract
A procedure is developed to generate rigorous rough upper bounds to radial moments [r2n] with integer n ≥ − 2 for the ground and excited states of atoms and molecules. These rough upper bounds to [r2n] enable the calculation of accurate upper and lower bounds to the lesser moment [rn] through existing and new formulas that utilize a lower bound to the square overlap of a trial function and true wave function (in this case through an energy lower bound via the Eckart formula). Error bars to [r−1], [r], [r2], and [r4] are calculated for the ground state of the non-relativistic infinite nuclear mass helium atom to yield expectation values within 0.037%, 0.018%, 0.039%, and 0.24% respectively, of the true values. As a byproduct of this investigation, a new formula for the error bar to observables is derived which is a slight improvement upon similar error bars. Also Lieb's limit on the number of electrons that an atom can bind is reproduced.
- Subjects
HELIUM atom; ATOMIC mass; WAVE functions; EXCITED states; HELIUM isotopes; ELECTRONS
- Publication
Journal of Mathematical Chemistry, 2020, Vol 58, Issue 1, p88
- ISSN
0259-9791
- Publication type
Article
- DOI
10.1007/s10910-019-01073-6