46811-G6
Explicitly Correlated Electronic Structure Methods for Predictive Energetics and Kinetics of Radical Reactions
Introduction
Over the first year of the funding period we have made significant progress towards all objectives of our proposal. First, we have successfully developed rigorous as well as less-elaborate practical versions of the explicitly-correlated coupled-cluster methods applicable to open-shell species. Secondly, we have demonstrated the significant reduction of the basis set error when computing atomization energies and heats of formation of closed and open-shell species. These accomplishments set the stage for extensive applications of the developed technology to prototypical hydrocarbon chemistries as well as further extension of our approaches to describe radical species in electronically-excited states as well as polyradicals.
Perturbative explicitly-correlated coupled-cluster methods
We have developed an exciting perturbative approach for inclusion of the explicitly-correlated terms into the coupled-cluster framework. Our approach allows us to formulate a simple basis-set correction to the standard CCSD wave function and energy in a manner strongly resembling the established MP2-R12 method. The resulting CCSD(2)R12 method has much smaller and faster converging basis set errors than the CCSD counterpart. The key advantage of our formulation is that the standard coupled-cluster equations are unmodified, which allows for a very straightforward implementation of the CCSD(2)R12 method from existing CCSD and MP2-R12 programs. Because the approach is reminiscent of the equation-of-motion route to the gold-standard of quantum chemistry, the CCSD(T) method, we were also able to develop an R12 extension of the CCSD(T) method, dubbed the CCSD(T)R12 method, using spin-restricted and spin-unrestricted references for closed and open-shell species. The extra cost of introducing the R12 terms into the CCSD(T) method is negligible compared to the cost of the (T) correction, therefore the method is very practical. The existing implementation uses the freely-available open-source MPQC and PSI3 program packages and will appear in their upcoming public releases.
Rigorous explicitly-correlated coupled-cluster methods
We have also developed the first nontruncated formulation of the arbitrary-rank CC-R12 approach. Until now such development has not been possible due to the extreme complexity of the CC-R12 equations. In collaboration with Prof. Hirata of the University of Florida, we developed an automated approach to derivation, transformation, and implementation of the CC-R12 equations. Thus we performed the first analysis of the formal computational cost of these approaches as well as computed the first benchmark CCSD-R12 data for small molecules. Our work confirmed that the perturbative CCSD(2)R12 approach is exceptionally robust yet computationally trivial compared to the full CCSD-R12 method. Initial benchmark application using the CCSDTQ-R12 method are also underway and indicate the unprecedented accuracy of this approach.
Application of the explicitly-correlated coupled-cluster methods to thermochemistry of radicals
The novel CCSD(T)R12 method has been tested as a drop-in replacement for the standard CCSD(T) method in the HEAT method for computing accurate thermochemical properties. We found that the basis set error of the CCSD(T) correlation energy is reduced significantly by the use of the R12 counterpart. For example, only a triple-zeta basis set is necessary with the R12 method to reach a 1 kcal/mol basis set error and match the quadruple-zeta-quality accuracy when computing heats of formation. The use of R12-optimized basis sets should improve the comparison further between the standard and R12 approaches.
Future objectives
Our perturbative CC R12 approach can be extended straightforwardly to describe the excited states of radicals. We are also seeking a way to apply the idea to multireference methods that are necessary to describe biradicals and other molecules with near-degenerate electronic structure. Finally, we will test the performance of the already developed CCSD(T)R12 approach for computing reaction enthalpies and activation energies for prototypical hydrocarbon chemistries.
