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Analytical Correlation in the H$_{2}$ Molecule from the Independent Atom Ansatz
- Publication Year :
- 2024
-
Abstract
- The independent atom ansatz of density functional theory yields an accurate analytical expression for dynamic correlation energy in the H$_{2}$ molecule: $E_{c} = 0.5(1 - \sqrt{2})(ab|ba)$ for the atom-additive self-consistent density $\rho = |a|^{2} + |b|^{2}$. Combined with exact atomic self-exchange, it recovers more than 99.5 % of nearly exact SCAN exchange-correlation energy at R > 0.5 $\r{A}$, differing by less than 0.12 eV. The total energy functional correctly dissociates the H-H bond and yields absolute errors of 0.002 $\r{A}$, 0.19 eV, and 13 cm$^{-1}$ relative to experiment at the tight binding computational cost. The chemical bond formation is attributed to the asymptotic Heitler-London resonance of quasi-orthogonal atomic states ($- (ab|ba)$) with no contributions from kinetic energy or charge accumulation in the bond.<br />Comment: 7 pages, 4 figures
- Subjects :
- Physics - Chemical Physics
Quantum Physics
Subjects
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.2405.15809
- Document Type :
- Working Paper