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Compact expressions for spherically averaged position and momentum densities
Deborah L Crittenden1, Yves A Bernard
1Research School of Chemistry, Australian National University, Canberra ACT 0200, Australia. deborah@rsc.anu.edu.au
The Journal of Chemical Physics
|August 14, 2009
Summary
This study presents compact formulas for position and momentum density integrals using spherical Bessel functions. These findings simplify ab initio calculations for various atomic orbital types and molecular systems.
Area of Science:
- Quantum Chemistry
- Computational Physics
Background:
- Accurate calculation of electron densities is crucial for understanding molecular properties.
- Ab initio methods require efficient computation of various integrals.
Purpose of the Study:
- To derive compact expressions for spherically averaged position and momentum density integrals.
- To tabulate these integrals for Gaussian functions of s, p, d, and f types.
- To demonstrate the isomorphism between position and momentum space calculations.
Main Methods:
- Utilizing spherical Bessel functions (j(n)) and modified spherical Bessel functions (i(n)).
- Tabulating integrals essential for ab initio calculations.
- Applying derived formulae to specific molecular systems.
Main Results:
- Compact formulas for position and momentum density integrals were derived.
- Isomorphism between position and momentum space formulae was highlighted.
- Calculations were performed for ten-electron and eighteen-electron molecular series.
Conclusions:
- The derived expressions offer a computationally efficient approach for ab initio studies.
- The established isomorphism simplifies theoretical treatments.
- The results provide valuable data for quantum chemical calculations.
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