Improving MP2 bandgaps with low-scaling approximations to EOM-CCSD.

Despite its reasonable accuracy for ground-state properties of semiconductors and insulators, second-order Møller-Plesset perturbation theory (MP2) significantly underestimates bandgaps. In this work, we evaluate the bandgap predictions of partitioned equation-of-motion MP2 (P-EOM-MP2), which is a second-order approximation to EOM coupled-cluster theory with single and double excitations. On a test set of elemental and binary semiconductors and insulators, we find that P-EOM-MP2 overestimates bandgaps by 0.3 eV on average, which can be compared to the underestimation by 0.6 eV on average exhibited by the G0W0 approximation with a Perdew-Burke-Ernzerhof reference. We show that P-EOM-MP2, when interpreted as a Green's function-based theory, has a self-energy that includes all first- and second-order diagrams and a few third-order diagrams. We find that the GW approximation performs better for materials with small gaps and P-EOM-MP2 performs better for materials with large gaps, which we attribute to their superior treatment of screening and exchange, respectively.

Dynamical correlation energy of metals in large basis sets from downfolding and composite approaches.

Coupled-cluster theory with single and double excitations (CCSD) is a promising ab initio method for the electronic structure of three-dimensional metals, for which second-order perturbation theory (MP2) diverges in the thermodynamic limit. However, due to the high cost and poor convergence of CCSD with respect to basis size, applying CCSD to periodic systems often leads to large basis set errors. In a common "composite" method, MP2 is used to recover the missing dynamical correlation energy through a focal-point correction, but the inadequacy of finite-order perturbation theory for metals raises questions about this approach. Here, we describe how high-energy excitations treated by MP2 can be "downfolded" into a low-energy active space to be treated by CCSD. Comparing how the composite and downfolding approaches perform for the uniform electron gas, we find that the latter converges more quickly with respect to the basis set size. Nonetheless, the composite approach is surprisingly accurate because it removes the problematic MP2 treatment of double excitations near the Fermi surface. Using this method to estimate the CCSD correlation energy in the combined complete basis set and thermodynamic limits, we find that CCSD recovers 85%-90% of the exact correlation energy at rs = 4. We also test the composite approach with the direct random-phase approximation used in place of MP2, yielding a method that is typically (but not always) more cost effective due to the smaller number of orbitals that need to be included in the more expensive CCSD calculation.

Integrative Approaches for the Identification and Localization of Specialized Metabolites in Tripterygium Roots.

Members of the genus Tripterygium are known to contain an astonishing diversity of specialized metabolites. The lack of authentic standards has been an impediment to the rapid identification of such metabolites in extracts. We employed an approach that involves the searching of multiple, complementary chromatographic and spectroscopic data sets against the Spektraris database to speed up the metabolite identification process. Mass spectrometry-based imaging indicated a differential localization of triterpenoids to the periderm and sesquiterpene alkaloids to the cortex layer of Tripterygium roots. We further provide evidence that triterpenoids are accumulated to high levels in cells that contain suberized cell walls, which might indicate a mechanism for storage. To our knowledge, our data provide first insights into the cell type specificity of metabolite accumulation in Tripterygium and set the stage for furthering our understanding of the biological implications of specialized metabolites in this genus.

Active space approaches combining coupled-cluster and perturbation theory for ground states and excited states.

We evaluate the performance of approaches that combine coupled-cluster and perturbation theory based on a predefined active space of orbitals. Coupled-cluster theory is used to treat excitations that are internal to the active space and perturbation theory is used for all other excitations, which are at least partially external to the active space. We consider a variety of schemes that differ in how the internal and external excitations are coupled. Such approaches are presented for ground states and excited states within the equation-of-motion formalism. Results are given for the ionization potentials and electron affinities of a test set of small molecules and for the correlation energy and band gap of a few periodic solids.

On the Relation between Equation-of-Motion Coupled-Cluster Theory and the GW Approximation.

We discuss the analytic and diagrammatic structure of ionization potential (IP) and electron affinity (EA) equation-of-motion coupled-cluster (EOM-CC) theory, in order to put it on equal footing with the prevalent GW approximation. The comparison is most straightforward for the time-ordered one-particle Green's function, and we show that the Green's function calculated by EOM-CC with single and double excitations (EOM-CCSD) includes fewer ring diagrams at higher order than does the GW approximation, due to the former's unbalanced treatment of time-ordering. However, the EOM-CCSD Green's function contains a large number of vertex corrections, including ladder diagrams, mixed ring-ladder diagrams, and exchange diagrams. By including triple excitations, the EOM-CCSDT Green's function includes all diagrams contained in the GW approximation, along with many high-order vertex corrections. In the same language, we discuss a number of common approximations to the EOM-CCSD equations, many of which can be classified as elimination of diagrams. Finally, we present numerical results by calculating the principal charged excitations energies of the molecules contained in the so-called GW100 test set [ J. Chem. Theory Comput. 2015 , 11 , 5665 - 5687 ]. We argue that (in molecules) exchange is as important as screening, advocating for a Hartree-Fock reference and second-order exchange in the self-energy.