Analytic derivatives of quartic-scaling doubly hybrid XYGJ-OS functional: Theory, implementation, and benchmark comparison with M06-2X and MP2 geometries for nonbonded complexes

Analytic first derivative expression of opposite-spin (OS) ansatz-adapted quartic scaling doubly hybrid XYGJ-OS functional is derived and implemented into Q-Chem. The resulting algorithm scales quartically with system size as in OS-MP2 gradient, by utilizing the combination of Laplace transformation and density fitting technique. The performance of XYGJ-OS geometry optimization is assessed by comparing the bond lengths and the intermolecular properties in reference coupled cluster methods. For the selected nonbonded complexes in the S22 and S66 data sets used in the present benchmark test, it is shown that XYGJ-OS geometries are more accurate than M06-2X and RI-MP2, the two quantum chemical methods widely used to obtain accurate geometries for practical systems, and comparable to CCSD(T) geometries.