Slater's Exchange Parameters α for Analytic and Variational Xα Calculations

Area of Science:

• Computational Chemistry
• Quantum Chemistry
• Materials Science

Background:

• Density Functional Theory (DFT) is a powerful quantum mechanical modeling method.
• Accurate calculation of molecular properties requires precise effective potentials.
• Slater's Xα method offers a simplified approach but lacks flexibility for complex systems.

Purpose of the Study:

• To introduce a fully analytical and variational implementation of a subset of DFT, the Slater-Roothaan (SR) method.
• To determine optimal Slater exchange parameters (α) for atoms H through Cl.
• To evaluate the SR method's accuracy in predicting molecular atomization energies.

Main Methods:

• Developed the Slater-Roothaan (SR) method, extending Slater's Xα approach with adjustable atomic exchange parameters (α).
• Determined α values by matching computed physical quantities (atomic energies, ionization potentials) to exact values.
• Employed Gaussian basis sets for orbitals and the one-body effective potential.

Main Results:

• Derived sets of α values for atoms H-Cl, reproducing exact atomic energies and ionization potentials.
• Calculated atomization energies for the G2 set of molecules using the SR method.
• Achieved a mean absolute error of 17 kcal/mol for atomization energies, outperforming Hartree-Fock and LDA but less accurate than GGAs.

Conclusions:

• The SR method provides a flexible and accurate approach for electronic structure calculations.
• Determined atomic and molecular α values offer insights into chemical bonding and properties.
• The SR method shows potential for extrapolating elemental properties to complex heteroatomic molecules.