Abstract
We introduce the two-particle probability density X(x) of x= r 12· p 12=( r 1 − r 2)·( p 1 − p 2). The fundamental equations involved in the derivation of this new intracule X(x), which we call the Posmom intracule, are derived and we show how to derive X(x) from the many-particle wave-function. We contrast it with the Dot intracule [Y.A. Bernard, D.L. Crittenden, and P.M.W. Gill, Phys. Chem. Chem. Phys. 10, 3447 (2008)] which can be derived from the Wigner distribution and show the relationships between the Posmom intracule and the one-particle Posmom density [Y.A. Bernard, D.L. Crittenden, and P.M.W. Gill, J. Phys. Chem. A 114, 11984 (2010)]. To illustrate the information provided by the Posmom intracule, we apply this new formalism to various two-electron systems: the three-dimensional parabolic quantum dot, the helium-like ions and the ground and excited states of the helium atom.
Acknowledgements
We thank Joshua Hollett for helpful comments. YAB thanks the ANU Research School of Chemistry for a PhD scholarship. PMWG thanks the Australian Research Council (Grants DP0984806, DP1094170, and DP120104740) for funding. PFL thanks the Australian Research Council for a Discovery Early Career Researcher Award (Grant DE130101441). PFL and PMWG thank the NCI National Facility for a generous grant of supercomputer time.
Notes
a Reference [Citation14]: 7 basis functions.
bReference [Citation46]: 11 basis functions.