Incremental CCSD(T)(F12*)|MP2: A Black Box Method To Obtain Highly Accurate Reaction Energies

Third-Order Incremental Dual-Basis Set Zero-Buffer Approach for Large High-Spin Open-Shell Systems

The third-order incremental dual-basis set zero-buffer approach (inc3-db-B0) is an efficient, accurate, and black-box quantum chemical method for obtaining correlation energies of large systems, and it has been successfully applied to many real chemical problems. In this work, we extend this approach to high-spin open-shell systems. In the open-shell approach, we will first decompose the occupied orbitals of a system into several domains by a K-means clustering algorithm. The essential part is that we preserve the active (singly occupied) orbitals in all the calculations of the domain correlation energies. The duplicated contributions of the active orbitals to the correlation energy are subtracted from the incremental expansion. All techniques of truncating the virtual space such as the B0 approximation can be applied. This open-shell inc3-db-B0 approach is combined with the CCSD and CCSD(T) methods and applied to the computations of a singlet-triplet gap and an electron detachment process. Our approach exhibits an accuracy better than 0.6 kcal/mol or 0.3 eV compared with the standard implementation, while it saves a large amount of the computational time and can be efficiently parallelized.

Exploring the Accuracy Limits of Local Pair Natural Orbital Coupled-Cluster Theory

The domain based local pair natural orbital coupled cluster method with single-, double-, and perturbative triple excitations (DLPNO–CCSD(T)) is an efficient quantum chemical method that allows for coupled cluster calculations on molecules with hundreds of atoms. Because coupled-cluster theory is the method of choice if high-accuracy is needed, DLPNO–CCSD(T) is very promising for large-scale chemical application. However, the various approximations that have to be introduced in order to reach near linear scaling also introduce limited deviations from the canonical results. In the present work, we investigate how far the accuracy of the DLPNO–CCSD(T) method can be pushed for chemical applications. We also address the question at which additional computational cost improvements, relative to the previously established default scheme, come. To answer these questions, a series of benchmark sets covering a broad range of quantum chemical applications including reaction energies, hydrogen bonds, and other noncovalent interactions, conformer energies, and a prototype organometallic problem were selected. An accuracy of 1 kcal/mol or better can readily be obtained for all data sets using the default truncation scheme, which corresponds to the stated goal of the original implementation. Tightening of the three thresholds that control DLPNO leads to mean absolute errors and standard deviations from the canonical results of less than 0.25 kcal/mol (<1 kJ/mol). The price one has then to pay is an increased computational time by a factor close to 3. The applicability of the method is shown to be independent of the nature of the reaction. On the basis of the careful analysis of the results, three different sets of truncation thresholds (termed “LoosePNO”, “NormalPNO”, and “TightPNO”) have been chosen for “black box” use of DLPNO–CCSD(T). This will allow users of the method to optimally balance performance and accuracy.

First UHF Implementation of the Incremental Scheme for Open-Shell Systems

The incremental scheme makes it possible to compute CCSD(T) correlation energies to high accuracy for large systems. We present the first extension of this fully automated black-box approach to open-shell systems using an Unrestricted Hartree-Fock (UHF) wave function, extending the efficient domain-specific basis set approach to handle open-shell references. We test our approach on a set of organic and metal organic structures and molecular clusters and demonstrate standard deviations from canonical CCSD(T) values of only 1.35 kJ/mol using a triple ζ basis set. We find that the incremental scheme is significantly more cost-effective than the canonical implementation even for relatively small systems and that the ease of parallelization makes it possible to perform high-level calculations on large systems in a few hours on inexpensive computers. We show that the approximations that make our approach widely applicable are significantly smaller than both the basis set incompleteness error and the intrinsic error of the CCSD(T) method, and we further demonstrate that incremental energies can be reliably used in extrapolation schemes to obtain near complete basis set limit CCSD(T) reaction energies for large systems.

Incremental evaluation of coupled cluster dipole polarizabilities

In this work we present the first implementation of the incremental scheme for coupled cluster linear-response frequency-dependent dipole polarizabilities.

Computational electrochemistry: prediction of liquid-phase reduction potentials

This article reviews recent developments and applications in the area of computational electrochemistry. Our focus is on predicting the reduction potentials of electron transfer and other electrochemical reactions and half-reactions in both aqueous and nonaqueous solutions. Topics covered include various computational protocols that combine quantum mechanical electronic structure methods (such as density functional theory) with implicit-solvent models, explicit-solvent protocols that employ Monte Carlo or molecular dynamics simulations (for example, Car-Parrinello molecular dynamics using the grand canonical ensemble formalism), and the Marcus theory of electronic charge transfer. We also review computational approaches based on empirical relationships between molecular and electronic structure and electron transfer reactivity. The scope of the implicit-solvent protocols is emphasized, and the present status of the theory and future directions are outlined.

Water 26-mers Drawn from Bulk Simulations: Benchmark Binding Energies for Unprecedentedly Large Water Clusters and Assessment of the Electrostatically Embedded Three-Body and Pairwise Additive Approximations

It is important to test methods for simulating water, but small water clusters for which benchmarks are available are not very representative of the bulk. Here we present benchmark calculations, in particular CCSD(T) calculations at the complete basis set limit, for water 26-mers drawn from Monte Carlo simulations of bulk water. These clusters are large enough that each water molecule participates in 2.5 hydrogen bonds on average. The electrostatically embedded three-body approximation with CCSD(T) embedded dimers and trimers reproduces the relative binding energies of eight clusters with a mean unsigned error (MUE, kcal per mole of water molecules) of only 0.009 and 0.015 kcal for relative and absolute binding energies, respectively. Using only embedded dimers (electrostatically embedded pairwise approximation) raises these MUEs to 0.038 and 0.070 kcal, and computing the energies with the M11 exchange-correlation functional, which is very economical, yields errors of only 0.029 and 0.042 kcal.

New accurate benchmark energies for large water clusters: DFT is better than expected

In this work, we use MP2 and coupled-cluster with single, double, and perturbative triple excitations [CCSD(T)] as well as their corresponding explicitly correlated (F12) counterparts to compute the interaction energies of water icosamers. The incremental scheme is used to compute benchmark energies at the CCSD(T)/CBS(45) and CCSD(T)(F12*)/cc-pVQZ-F12 level of theory. The four structures, dodecahedron, edge sharing, face sharing, and fused cubes, are part of the WATER27 test set and therefore, highly accurate interaction energies are required. All methods applied in this work lead to new benchmark energies for these four systems. To obtain these values, we carefully analyze the convergence of the interaction energies with respect to the basis set. Furthermore, we investigate the influence of the basis set superposition error and the core-valence correlation. The interaction energies are: dodecahedron -198.6 kcal/mol, edge sharing -209.7 kcal/mol, face sharing -208.0 kcal/mol, and fused cubes -208.0 kcal/mol. For water clusters, we recommend to use the PW6B95 density functional of Truhlar in combination with Grimme's dispersion correction (D3), as the mean absolute error is 0.9 and the root mean-squared deviation is only 1.4 kcal/mol.

Chemical applications carried out by local pair natural orbital based coupled-cluster methods

Local pair natural orbital coupled-cluster methods are suitable for accurate assessment of the energies of large molecular and supramolecular systems.