Wavefunction-like Correlation Model for Use in Hybrid Density Functionals

Abstract

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.

Towards density functional approximations from coupled cluster correlation energy densities

“…Such 'higher-rung' functionals are typically based on the random-phase approximation (RPA) or second-order perturbation theory (double-hybrid functionals). [25][26][27][28][29][30] This strongly improves their thermochemical accuracy, and allows for the description of van-der-Waals interactions. The virtual orbital dependence of these methods translates to a quite unfavourable formal scaling with the basis-set size (typically O(N 5 ) or worse, compared to O(N 3 ) for GGAs), which is further aggravated by the fact that they additionally require larger (correlation consistent) basis sets.…”

Accurate Hybrid Density Functionals with UW12 Correlation

“…To evaluate the UW12 integrals, we expand the geminal function as a series of Gaussians and optimize the coefficients for a given set of exponents using the procedure outlined in Ref. 23. In order to optimize the functional, we calculate the unscaled contribution of each component of the geminal expansion separately for each system.…”

“…Of these test sets, both BH76 and BHPERI are in the training set, while the remaining four are new for GMTKN55. These sets cover a range of different barrier heights.The BH76 barrier height test set covers hydrogen transfer and non-hydrogen transfer barrier heights and is a superset of the earlier HTBH38 and NHTBH38 test sets,93,94 from which the DBH24 subset we had previously used to test barrier heights was taken 23,101. BHPERI is made up of barrier heights from pericyclic reactions, PX13 and WCPT18 consist of protontransfer barriers, and BHROT27 includes barriers of rotation.For these sets, results for B-LYP-osUW12 are positive, errors for BHPERI and BHDIV10 are the lowest of the non-dispersion corrected functionals.…”

Towards Density Functional Approximations from Coupled Cluster Correlation Energy Densities

“…Such 'higher-rung' functionals are typically based on the random-phase approximation (RPA) or second-order perturbation theory (double-hybrid functionals). [25][26][27][28][29][30] This strongly improves their thermochemical accuracy, and allows for the description of van-der-Waals interactions. The virtual orbital dependence of these methods translates to a quite unfavourable formal scaling with the basis-set size (typically O(N 5 ) or worse, compared to O(N 3 ) for GGAs).…”