Self-consistent equations for nonempirical tight-binding theory.

Area of Science:

• Computational Chemistry
• Quantum Chemistry
• Materials Science

Background:

• Density Functional Theory (DFT) is a cornerstone of modern computational chemistry.
• Accurate electronic structure calculations are crucial for understanding chemical bonding and reactivity.
• Existing DFT methods face challenges in describing bond dissociation and require significant computational resources.

Purpose of the Study:

• Introduce a new reference state for DFT, the independent atom ansatz.
• Develop self-consistent equations for this ansatz.
• Demonstrate its accuracy and efficiency for molecular systems.

Main Methods:

• Derivation of general and asymptotic forms of self-consistent equations for the independent atom ansatz.
• Formulation of a total energy functional resembling tight-binding theory.
• Analytical derivation of tight-binding Hamiltonian matrix elements in a weak interaction limit.

Main Results:

• The independent atom ansatz allows for exact electron density representation using atom-localized orbitals.
• The method accurately reproduces potential energy curves for diatomic molecules (He2 to Ne2).
• It achieves CCSD(T)-level accuracy for bond lengths and dissociation energies of N2, O2, and F2 with a minimal basis set.
• Outperforms CCSD(T) and some DFT functionals in describing bond dissociation away from equilibrium.

Conclusions:

• The independent atom ansatz provides a computationally efficient and accurate approach for electronic structure calculations.
• It offers insights into energy decomposition, charge analysis, and links to tight-binding and electronegativity concepts.
• This formalism shows significant promise for describing chemical bonding and reaction pathways.