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Probe Type II Band Alignment in One-Dimensional Van Der Waals Heterostructures Using First-Principles Calculations

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Physical understanding through variational reasoning: electron sharing and covalent bonding.

Klaus Ruedenberg¹, Michael W Schmidt

¹Department of Chemistry and Ames Laboratory, United States Department of Energy, Iowa State University, Ames, Iowa 50011, USA.

The Journal of Physical Chemistry. A

|February 21, 2009

Summary

This study explains molecular bonding using variational principles. It shows how electron orbitals in molecules lower energy by balancing nuclear attraction and kinetic pressure, unlike in atoms.

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Area of Science:

Quantum Chemistry
Theoretical Chemistry
Computational Chemistry

Background:

Energy changes in stationary states are governed by the Hamiltonian.
Ground states represent an optimal balance between nuclear attraction and electron kinetic energy.
Understanding these forces is key to explaining chemical bond formation.

Purpose of the Study:

To analyze the variational competition between kinetic and potential energy functionals in the hydrogen molecule ion.
To elucidate the electronic structure and bonding in H2+ using ab initio methods.
To detail the contributions of polarization, sharing, and contraction to binding energy.

Main Methods:

Variational reasoning applied to kinetic and potential energy functionals.
Analysis of the exact ab initio ground-state wave function of the hydrogen molecule ion (H2+).
Examination of electronic wave function differences between H2+ and atomic hydrogen.

Main Results:

Molecular orbitals in H2+ lower potential energy by simultaneous contraction toward two nuclei while maintaining delocalization.
The kinetic energy functional is lower for molecular orbitals compared to atomic orbitals.
This weaker kinetic energy pressure allows tighter orbital attachment to nuclei in molecules.

Conclusions:

The formation of the chemical bond in H2+ is a result of a favorable compromise between potential and kinetic energy functionals.
Differences in electronic wave functions (polarization, sharing, contraction) drive molecular stability.
The findings clarify the role of the virial theorem and generalize to other molecules.