Ryan M. Richard

Time-Dependent Density-Functional Description of the 1La State in Polycyclic Aromatic Hydrocarbons: Charge-Transfer Character in Disguise?

The electronic spectrum of alternant polycyclic aromatic hydrocarbons (PAHs) includes two singlet excited states that are often denoted (1)La and (1)Lb. Time-dependent density functional theory (TD-DFT) affords reasonable excitation energies for the (1)Lb state in such molecules, but often severely underestimates (1)La excitation energies and fails to reproduce observed trends in the (1)La excitation energy as a function of molecular size. Here, we examine the performance of long-range-corrected (LRC) density functionals for the (1)La and (1)Lb states of various PAHs. With an appropriate choice for the Coulomb attenuation parameter, we find that LRC functionals avoid the severe underestimation of the (1)La excitation energies that afflicts other TD-DFT approaches, while errors in the (1)Lb excitation energies are less sensitive to this parameter. This suggests that the (1)La states of certain PAHs exhibit some sort of charge-separated character, consistent with the description of this state within valence-bond theory, but such character proves difficult to identify a priori. We conclude that TD-DFT calculations in medium-size, conjugated organic molecules may involve significant but hard-to-detect errors. Comparison of LRC and non-LRC results is recommended as a qualitative diagnostic.

Accurate Ionization Potentials and Electron Affinities of Acceptor Molecules I. Reference Data at the CCSD(T) Complete Basis Set Limit

In designing organic materials for electronics applications, particularly for organic photovoltaics (OPV), the ionization potential (IP) of the donor and the electron affinity (EA) of the acceptor play key roles. This makes OPV design an appealing application for computational chemistry since IPs and EAs are readily calculable from most electronic structure methods. Unfortunately reliable, high-accuracy wave function methods, such as coupled cluster theory with single, double, and perturbative triples [CCSD(T)] in the complete basis set (CBS) limit are too expensive for routine applications to this problem for any but the smallest of systems. One solution is to calibrate approximate, less computationally expensive methods against a database of high-accuracy IP/EA values; however, to our knowledge, no such database exists for systems related to OPV design. The present work is the first of a multipart study whose overarching goal is to determine which computational methods can be used to reliably compute IPs and EAs of electron acceptors. This part introduces a database of 24 known organic electron acceptors and provides high-accuracy vertical IP and EA values expected to be within ±0.03 eV of the true non-relativistic, vertical CCSD(T)/CBS limit. Convergence of IP and EA values toward the CBS limit is studied systematically for the Hartree-Fock, MP2 correlation, and beyond-MP2 coupled cluster contributions to the focal point estimates.

Accurate Ionization Potentials and Electron Affinities of Acceptor Molecules IV: Electron-Propagator Methods

Comparison of ab initio electron-propagator predictions of vertical ionization potentials and electron affinities of organic, acceptor molecules with benchmark calculations based on the basis set-extrapolated, coupled cluster single, double, and perturbative triple substitution method has enabled identification of self-energy approximations with mean, unsigned errors between 0.1 and 0.2 eV. Among the self-energy approximations that neglect off-diagonal elements in the canonical, Hartree-Fock orbital basis, the P3 method for electron affinities, and the P3+ method for ionization potentials provide the best combination of accuracy and computational efficiency. For approximations that consider the full self-energy matrix, the NR2 methods offer the best performance. The P3+ and NR2 methods successfully identify the correct symmetry label of the lowest cationic state in two cases, naphthalenedione and benzoquinone, where some other methods fail.

Achieving the CCSD(T) Basis-Set Limit in Sizable Molecular Clusters: Counterpoise Corrections for the Many-Body Expansion.

An efficient procedure is introduced to obtain the basis-set limit in electronic structure calculations of large molecular and ionic clusters. This approach is based on a Boys-Bernardi-style counterpoise correction for clusters containing arbitrarily many monomer units, which is rendered computationally feasible by means of a truncated many-body expansion. This affords a tractable way to apply the sequence of correlation-consistent basis sets (aug-cc-pVXZ) to large systems and thereby obtain energies extrapolated to the complete basis set (CBS) limit. A three-body expansion with three-body counterpoise corrections is shown to afford errors of ≲0.1-0.2 kcal/mol with respect to traditional MP2/CBS results, even for challenging systems such as fluoride-water clusters. A triples correction, δCCSD(T) = ECCSD(T) - EMP2, can be estimated accurately and efficiently as well. Because the procedure is embarrassingly parallelizable and requires no electronic structure calculations in systems larger than trimers, it is extendible to very large clusters. As compared to traditional CBS extrapolations, computational time is dramatically reduced even without parallelization.

Approaching the complete-basis limit with a truncated many-body expansion

High-accuracy electronic structure calculations with correlated wave functions demand the use of large basis sets and complete-basis extrapolation, but the accuracy of fragment-based quantum chemistry methods has most often been evaluated using double-ζ basis sets, with errors evaluated relative to a supersystem calculation using the same basis set. Here, we examine the convergence towards the basis-set limit of two- and three-body expansions of the energy, for water clusters and ion-water clusters, focusing on calculations at the level of second-order Møller-Plesset perturbation theory (MP2). Several different corrections for basis-set superposition error (BSSE), each consistent with a truncated many-body expansion, are examined as well. We present a careful analysis of how the interplay of errors (from all sources) influences the accuracy of the results. We conclude that fragment-based methods often benefit from error cancellation wherein BSSE offsets both incompleteness of the basis set as well as higher-order many-body effects that are neglected in a truncated many-body expansion. An n-body counterpoise correction facilitates smooth extrapolation to the MP2 basis-set limit, and at n = 3 affords accurate results while requiring calculations in subsystems no larger than trimers.

Correction to Accurate Ionization Potentials and Electron Affinities of Acceptor Molecules IV: Electron-Propagator Methods

C of a program error that erroneously substituted the ionization potential self-energy for its electron affinity (EA) counterpart in the renormalized partial third order (P3+) approximation leads to an average error (μ) of−0.02 eV, a mean unsigned error (MUE) of 0.09 eV, and a standard deviation (σ) of 0.11 eV for a test set of electron acceptor molecules. (See revised Figure 4 parts m, n, and o and the Supporting Information.) The P3+ method therefore exhibits the best performance of all tested electron propagator methods for EAs (see revised Figure 6) and provides the best compromise of accuracy and efficiency of all methods that employ the diagonal self-energy approximation. Also, an omitted funding source has been added here in the acknowledgment.