%0 Journal Article %1 lesiuk:134102 %A Lesiuk, Michał %A Jeziorski, Bogumił %A Moszynski, Robert %D 2013 %I AIP %J The Journal of Chemical Physics %K chemistry correlation mechanics physics quantum unread %N 13 %P 134102 %R 10.1063/1.4822045 %T On the large interelectronic distance behavior of the correlation factor for explicitly correlated wave functions %U http://link.aip.org/link/?JCP/139/134102/1 %V 139 %X In currently most popular explicitly correlated electronic structure theories, the dependence of the wave function on the interelectronic distance rij is built via the correlation factor f (rij). While the short-distance behavior of this factor is well understood, little is known about the form of f (rij) at large rij. In this work, we investigate the optimal form of f (r12) on the example of the helium atom and helium-like ions and several well-motivated models of the wave function. Using the Rayleigh-Ritz variational principle, we derive a differential equation for f (r12) and solve it using numerical propagation or analytic asymptotic expansion techniques. We found that for every model under consideration, f (r12) behaves at large rij as r12ρ eBr12 and obtained simple analytic expressions for the system dependent values of ρ and B. For the ground state of the helium-like ions, the value of B is positive, so that f (r12) diverges as r12 tends to infinity. The numerical propagation confirms this result. When the Hartree-Fock orbitals, multiplied by the correlation factor, are expanded in terms of Slater functions rne−βr, n = 0,…,N, the numerical propagation reveals a minimum in f (r12) with depth increasing with N. For the lowest triplet state, B is negative. Employing our analytical findings, we propose a new “range-separated” form of the correlation factor with the short- and long-range r12 regimes approximated by appropriate asymptotic formulas connected by a switching function. Exemplary calculations show that this new form of f (r12) performs somewhat better than the correlation factors used thus far in the standard R12 or F12 theories.

@article{lesiuk:134102, abstract = {In currently most popular explicitly correlated electronic structure theories, the dependence of the wave function on the interelectronic distance rij is built via the correlation factor f (rij). While the short-distance behavior of this factor is well understood, little is known about the form of f (rij) at large rij. In this work, we investigate the optimal form of f (r12) on the example of the helium atom and helium-like ions and several well-motivated models of the wave function. Using the Rayleigh-Ritz variational principle, we derive a differential equation for f (r12) and solve it using numerical propagation or analytic asymptotic expansion techniques. We found that for every model under consideration, f (r12) behaves at large rij as r12ρ eBr12 and obtained simple analytic expressions for the system dependent values of ρ and B. For the ground state of the helium-like ions, the value of B is positive, so that f (r12) diverges as r12 tends to infinity. The numerical propagation confirms this result. When the Hartree-Fock orbitals, multiplied by the correlation factor, are expanded in terms of Slater functions rne−βr, n = 0,…,N, the numerical propagation reveals a minimum in f (r12) with depth increasing with N. For the lowest triplet state, B is negative. Employing our analytical findings, we propose a new “range-separated” form of the correlation factor with the short- and long-range r12 regimes approximated by appropriate asymptotic formulas connected by a switching function. Exemplary calculations show that this new form of f (r12) performs somewhat better than the correlation factors used thus far in the standard R12 or F12 theories.}, added-at = {2013-10-08T15:29:41.000+0200}, author = {Lesiuk, Micha\l and Jeziorski, Bogumi\l and Moszynski, Robert}, biburl = {https://www.bibsonomy.org/bibtex/218ce2855a5afbcf68b15e3e3594da4c6/drmatusek}, doi = {10.1063/1.4822045}, eid = {134102}, interhash = {a8f756c54fdcef00b6cc67912a371941}, intrahash = {18ce2855a5afbcf68b15e3e3594da4c6}, journal = {The Journal of Chemical Physics}, keywords = {chemistry correlation mechanics physics quantum unread}, month = oct, number = 13, numpages = {16}, pages = 134102, publisher = {AIP}, timestamp = {2013-10-08T15:29:41.000+0200}, title = {On the large interelectronic distance behavior of the correlation factor for explicitly correlated wave functions}, url = {http://link.aip.org/link/?JCP/139/134102/1}, volume = 139, year = 2013 }