AmericanChemicalSociety.com

Introduction

In the second year of the funding period we have extended the reach of the methods developed in the first year to cover bond-breaking processes which are ubiquitous in petroleum and atmospheric chemistry. First, we have developed ways to incorporate high-rank clusters into the the explicitly-correlated coupled-cluster methods, in rigorous and perturbative fashions. Secondly, we have developed an explicitly-correlated R12 approach that can be combined with any electronic structure method, including any multireference wave functions. We also have started the benchmarking of the CCSD(T)_R12 method developed in the first year of the project for computing activation barriers included in Truhlar's DBH24 database.

High-rank explicitly-correlated coupled-cluster methods

With the help of the automated derivation and implementation machinery developed in the first year of the funding period, we have demonstrated for the first time a computer implementation of nontruncated formulation of high-rank CC-R12 approaches, up to CCSDTQ-R12. In collaboration with Prof. Hirata of the University of Florida we used these methods for benchmark applications to small polyatomics. For example, the electronic ground-state energy of the water molecule was computed with error estimated at 0.004 % (2 kcal/mol)! This marked the first time that near-chemical-accuracy has been attained for a polyatomic molecule with a non-empirical approach.

We have also developed simpler perturbative approaches that include high-rank clusters into the coupled-cluster R12 approaches. The objective of this work was to develop more practical approaches to apply the accurate high-rank coupled-cluster methods to larger molecular systems. We have proposed a family of methods which included rank-3 and rank-4 clusters by perturbation theory and R12 terms iteratively with and without approximations. For example, one of the

methods, CCSD(R12)(2)_T, has a cost comparable to that of the standard CCSD(T) method, but it can break single bond in hydrogen fluoride without the artifactual activation barrier that plagues the latter. This methods thus seems to be a practical explicitly-correlated alternative to the CCSD(T) method.

Universal explicitly-correlated methods

We have also developed a universal approach to include the explicit correlation into an arbitrary electronic wave state, single- or multi-reference, ground or excited. The new approach incorporates the explicitly correlated terms by a perturbative correction with zero optimized parameters. The current formulation of such correction requires only one- and two-particle density matrices, and up to two-electron integrals. Preliminary results are encouraging. For the classic problem of a dissociation of the triple bond in N₂, we found that only a double-zeta basis is necessary with the R12 variant of a multireference CI method to match the accuracy of a much more expensive standard quadruple-zeta computation across an entire potential energy surface! The first communication announcing these results is currently in press in the Journal of Chemical Physics.

Application of the explicitly-correlated coupled-cluster methods to first-principles kinetics

The novel CCSD(T)_R12 method that we developed in year 1 of the project is being tested for computing activation barriers of diverse chemical reactions included in the DBH24 database compiled by the Truhlar group. The preliminary findings indicate that only a double-zeta basis set is required with the R12 methods to match of exceed the accuracy of the standard triple-zeta result, all at a lower cost. Some calculations involved in this project were rather large in scope and thus required implementation of the density fitting in our R12 code in the open-source MPQC package

Future objectives

We will continue investigation of the highly-promising universal R12 method, including chemical application to excited states of conjugated hydrocarbons and polyradicals. We will also complete and publish the project that the ongoing investigation of the performance of the CCSD(T)_R12 method for computing reaction barriers.