X-ray molecular orbital analysis. I. Quantum mechanical and crystallographic framework.

Area of Science:

• Crystallography
• Quantum Chemistry
• Materials Science

Background:

• Accurate molecular orbital (MO) determination is crucial for understanding chemical bonding and electronic properties.
• Traditional methods often require complex calculations or are limited by experimental data.
• X-ray diffraction provides valuable structural information but direct MO derivation is challenging.

Purpose of the Study:

• To develop and validate the X-ray molecular orbital (XMO) analysis method for deriving MOs directly from X-ray diffraction data.
• To refine the XMO method by addressing issues of correlated MO coefficients in least-squares refinement.
• To demonstrate the capability of XMO analysis in accurately representing electron density distributions.

Main Methods:

• Utilized ab initio self-consistent field (SCF) MO method for initial MO calculations.
• Employed well-tempered basis functions to avoid cusps in residual density maps.
• Developed a variable selection strategy to mitigate severe correlations among MO coefficients during least-squares refinement.
• Applied the refined XMO method to diformohydrazide, refining MOs alongside crystallographic parameters.

Main Results:

• The XMO method successfully determined molecular orbitals averaged by atomic thermal vibrations.
• Electron-density distributions, including maxima on covalent bonds, were accurately represented for diformohydrazide.
• The refinement strategy effectively handled correlated MO coefficients, improving accuracy.
• Demonstrated the potential for obtaining MOs and atomic orbitals (AOs) without phase factors.

Conclusions:

• XMO analysis is a viable technique for obtaining accurate molecular orbitals from X-ray diffraction data.
• The method successfully visualizes electron density, providing detailed insights into chemical bonding.
• Combined XMO and X-ray AO analysis offers a powerful approach for electronic structure determination across various compound types.