1-Matrix functional for long-range interaction energy of two hydrogen atoms

Area of Science:

• Quantum Chemistry
• Computational Physics
• Molecular Spectroscopy

Background:

• Accurate calculation of molecular ground-state energies is crucial in chemistry and physics.
• Understanding the behavior of molecules at large internuclear separations (R → ∞) provides insights into intermolecular forces and asymptotic properties.
• The one-electron reduced density matrix and its associated natural orbitals (NOs) are fundamental for describing electronic structure.

Purpose of the Study:

• To derive the leading terms in the large-R asymptotics of the functional for the ground-state energy of the H2 molecule.
• To resolve the phase dilemma in the context of R → ∞ limit.
• To obtain accurate approximations for p-type "half-space" orbitals and their occupation numbers.

Main Methods:

• Solution of the phase dilemma at the R → ∞ limit.
• Derivation of natural orbitals (NOs) as symmetric and antisymmetric combinations of "half-space" orbitals.
• Minimization of the explicit functional to determine large-R asymptotics for occupation numbers and the C6 dispersion coefficient.

Main Results:

• Leading terms in the large-R asymptotics for the H2 ground-state energy functional were derived.
• Natural orbitals and amplitudes were characterized at the R → ∞ limit.
• The C6 dispersion coefficient was calculated, along with novel, highly accurate approximations for p-type "half-space" orbitals and their occupation numbers, which exhibit unexpected properties and decay as R⁻⁶.

Conclusions:

• The study successfully derived key asymptotic properties of the H2 molecule's ground-state energy.
• The developed formalism provides unprecedented accuracy for specific orbital types and their occupation numbers at large internuclear separations.
• These findings advance the understanding of intermolecular interactions and electronic structure theory at asymptotic limits.