We present Unsöld-W12 (UW12), an approximation to the correlation energy of molecules that is an explicit functional of the single-particle reduced-density matrix. The approximation resembles one part of modern explicitly correlated second-order Møller-Plesset (MP2) theory and is intended as an alternative to MP2 in double-hybrid exchange-correlation functionals. Orbital optimization with UW12 is straightforward, and the UW12 energy is evaluated without a double summation over unoccupied orbitals, leading to a faster basis-set convergence than is seen in double-hybrid functionals. We suggest a one-parameter hybrid exchange-correlation functional XCH-BLYP-UW12. XCH-BLYP-UW12 is similar to double-hybrid functionals, but contains UW12 correlation instead of MP2 correlation. We find that XCH-BLYP-UW12 is more accurate than the existing double-hybrid functional B2-PLYP for small-molecule main-group reaction barrier heights and has roughly the same accuracy as the existing hybrid functional B3LYP for atomization energies.

In previous work, we suggested a single-parameter hybrid functional containing a novel correlation contribution based on the Unsöld approximation, UW12. This model resembles the explicitly correlated part of MP2-F12 theory and can be written as an explicit formula in terms of the single-particle reduced density matrix. Here we further investigate hybrid functionals containing UW12 correlation, and in particular look at functionals with a large fractions of exact exchange to reduce the self-interaction error. We suggest two new hybrid functionals B-LYP-osUW12 and fB-LYP-osUW12. On the test sets we use, our best hybrid functional overall (B-LYP-osUW12) is of similar accuracy to the best double hybrids considered, while eliminating the need for virtual orbitals.

We describe the a new molecular simulation package that is designed for ab initio molecular dynamics simulations of molecular and condensed-phase chemical reactions and other<br>processes, with particular focus on mean-field and quantum embedding methods for electronic structure.<br>