Local Coupled-cluster Research Articles

Automatic Orbital Pair Selection for Multilevel Local Coupled-Cluster Based on Orbital Maps.

We present an automatic, orbital-map based orbital-pair selection scheme for multilevel local coupled-cluster approaches that exploits the locality of chemical reactions by focusing on the part of the molecule directly involved in the reaction. The previously introduced pair-selected multilevel extension to domain-based local pair natural orbital coupled-cluster with singles, doubles, and semicanonical perturbative triples [DLPNO-CCSD(T0)] partitions the orbital pairs according to relative changes in pair correlation energies [Bensberg, M.; Neugebauer, J. Orbital pair selection for relative energies in the domain-based local pair natural orbital coupled-cluster method. J. Chem. Phys. 2022, 157, 064102. 10.1063/5.0100010]. To this end, maps between localized orbitals are required which in turn require maps between the atoms of structures along reaction paths. So far, these atom maps have been manually determined, which can be a (human) time-consuming procedure. Here, we present an automatic atom mapping algorithm based on the principle of minimum chemical distance that incorporates orientation dependence through dihedral angles. A similar strategy is then introduced to obtain orbital maps, which proves advantageous over the previously used direct orbital selection. Along with a modified orbital pair prescreening, this results in an improved variant of the pair-selected multilevel DLPNO-CCSD(T0) method. The performance of this approach is demonstrated for various reaction types showing a significant efficiency gain and accurate results due to beneficial, systematic error cancellation. The presented method operates in a black-box manner due to its fully automatized algorithms with only the need to specify a single target-accuracy parameter. Additionally, we demonstrate that basis set extrapolation techniques can be applied. In this context, the approach shows deficiencies for the use of large basis sets, especially with diffuse basis functions, which can be traced back to the semicanonical triples correction.

New Mechanistic Insights into the Primary Thermolysis Reactions of 1,3,4,6-Tetranitrooctahydroimidazo-[4,5-d]imidazole (BCHMX) from Predictive Local Coupled Cluster Calculations.

Theoretical studies of the decomposition mechanism of energetic materials quite often scrutinize only the primary thermolysis reactions. However, the secondary reactions are crucial, inter alia, for proper building of the combustion models and understanding the autocatalytic processes. In the present study, we applied predictive DLPNO-CCSD(T) calculations to elucidate the kinetics and decomposition mechanism of a novel promising energetic material, 1,3,4,6-tetranitrooctahydroimidazo [4,5-d] imidazole (BCHMX). We identified eight previously unknown BCHMX conformers, both cis and trans in accordance to the spatial position of the H atoms bonded to a carbon bridge. Among them, the relative enthalpies of cis isomers lie in the narrow range ∼10 kJ mol-1 rendering them thermally accessible in the course of decomposition. The radical N-NO2 bond cleavage via one of the novel conformers is the dominant primary decomposition channel of BCHMX with the kinetic parameters Ea = 168.4 kJ mol-1 and log(A, s-1) = 18.5. We also resolved several contradictory assumptions on the mechanism and key intermediates of BCHMX thermolysis. To get a deeper understanding of the decomposition mechanism, we examined a series of unimolecular and bimolecular secondary channels of BCHMX. Among the former reactions, the C-C bond unzipping followed by another radical elimination of a nitro group is the most energetically favorable pathway with an activation barrier ∼113 kJ mol-1. However, contrary to the literature assumptions, the bimolecular H atom abstraction from a pristine BCHMX molecule by a primary nitramine radical product, not the nitro one, followed by another NO2 radical elimination, is the most important bimolecular secondary thermolysis reaction of BCHMX at lower temperatures. The isokinetic temperature of the bimolecular and unimolecular secondary reactions is ∼620 K. Unimolecular reactions might be important in dilute solutions, where bimolecular reactions are suppressed. The secondary reactions considered in the present work might be pertinent in the case of related energetic nitramines (e.g., RDX, HMX, and CL-20).

Accurate Calculation of Isomerization and Conformational Energies of Larger Molecules Using Explicitly Correlated Local Coupled Cluster Methods in Molpro and ORCA.

An overview of the approximations in the explicitly correlated local coupled cluster methods PNO-LCCSD(T)-F12 in Molpro and DLPNO-CCSD(T)F12 in ORCA is given. Options to select the domains of projected atomic orbitals (PAOs), pair natural orbitals (PNOs), and triples natural orbitals (TNOs) in both programs are described and compared in detail. The two programs are applied to compute isomerization and conformational energies of the ISOL24 and ACONFL test sets, where the former is part of the GMTKN55 benchmark suite. Thorough studies of basis set effects are presented for selected systems. These revealed large intramolecular basis set superposition effects that make it practically impossible to reliably determine the complete basis set (CBS) limits without including explicitly correlated terms. The latter strongly reduce the basis set dependence and at the same time also errors caused by the local domain approximations. On the basis of these studies, the PNO-LCCSD(T)-F12 method is applied to determine new reference energies for the above-mentioned benchmark sets. We are confident that our results should agree within a few tenths of a kcal mol-1 with the (unknown) CCSD(T)/CBS values, which therefore allowed us to define computational settings for accurate explicitly correlated local coupled cluster methods with moderate computational effort. With these protocols, especially PNO-LCCSD(T)-F12b/AVTZ', reliable reference values for comprehensive benchmark sets can be generated efficiently. This can significantly advance the development and evaluation of the performance of approximate electronic structure methods, especially improved density functional approximations or machine learning approaches.

Exploring the Accuracy Limits of PNO-Based Local Coupled-Cluster Calculations for Transition-Metal Complexes.

While the domain-based local pair natural orbital coupled-cluster method with singles, doubles, and perturbative triples (DLPNO-CCSD(T)) has proven instrumental for computing energies and properties of large and complex systems accurately, calculations on first-row transition metals with a complex electronic structure remain challenging. In this work, we identify and address the two main error sources that influence the DLPNO-CCSD(T) accuracy in this context, namely, (i) correlation effects from the 3s and 3p semicore orbitals and (ii) dynamic correlation-induced orbital relaxation (DCIOR) effects that are not described by the local MP2 guess. We present a computational strategy that allows us to completely eliminate the DLPNO error associated with semicore correlation effects, while increasing, at the same time, the efficiency of the method. As regards the DCIOR effects, we introduce a diagnostic for estimating the deviation between DLPNO-CCSD(T) and canonical CCSD(T) for systems with significant orbital relaxation.

Reconciling Local Coupled Cluster with Multireference Approaches for Transition Metal Spin-State Energetics

Spin-state energetics of transition metal complexes remain one of the most challenging targets for electronic structure methods. Among single-reference wave function approaches, local correlation approximations to coupled cluster theory, most notably the domain-based local pair natural orbital (DLPNO) approach, hold the promise of bringing the accuracy of coupled cluster theory with single, double, and perturbative triple excitations, CCSD(T), to molecular systems of realistic size with acceptable computational cost. However, recent studies on spin-state energetics of iron-containing systems raised doubts about the ability of the DLPNO approach to adequately and systematically approximate energetics obtained by the reference-quality complete active space second-order perturbation theory with coupled-cluster semicore correlation, CASPT2/CC. Here, we revisit this problem using a diverse set of iron complexes and examine several aspects of the application of the DLPNO approach. We show that DLPNO-CCSD(T) can accurately reproduce both CASPT2/CC and canonical CCSD(T) results if two basic principles are followed. These include the consistent use of the improved iterative (T1) versus the semicanonical perturbative triple corrections and, most importantly, a simple two-point extrapolation to the PNO space limit. The latter practically eliminates errors arising from the default truncation of electron-pair correlation spaces and should be viewed as standard practice in applications of the method to transition metal spin-state energetics. Our results show that reference-quality results can be readily achieved with DLPNO-CCSD(T) if these principles are followed. This is important also in view of the applicability of the method to larger single-reference systems and multinuclear clusters, whose treatment of dynamic correlation would be challenging for multireference-based approaches.

Fragment-Based Local Coupled Cluster Embedding Approach for the Quantification and Analysis of Noncovalent Interactions: Exploring the Many-Body Expansion of the Local Coupled Cluster Energy.

Herein, we introduce a fragment-based local coupled cluster embedding approach for the accurate quantification and analysis of noncovalent interactions in molecular aggregates. Our scheme combines two different expansions of the domain-based local pair natural orbital coupled cluster (DLPNO-CCSD(T)) energy: the many-body expansion (MBE) and the local energy decomposition (LED). The low-order terms in the MBE are initially computed in the presence of an environment that is treated at a low level of theory. Then, LED is used to decompose the energy of each term in the embedded MBE into additive fragment and fragment-pairwise contributions. This information is used to quantify the total energy of the system while providing at the same time in-depth insights into the nature and cooperativity of noncovalent interactions. Two different approaches are introduced and tested, in which the environment is treated at different levels of theory: the local coupled cluster in the Hartree–Fock (LCC-in-HF) method, in which the environment is treated at the HF level; and the electrostatically embedded local coupled cluster method (LCC-in-EE), in which the environment is replaced by point charges. Both schemes are designed to preserve as much as possible the accuracy of the parent local coupled cluster method for total energies, while being embarrassingly parallel and less memory intensive. These schemes appear to be particularly promising for the study of large and complex molecular aggregates at the coupled cluster level, such as condensed phase systems and protein–ligand interactions.

Accurate Thermochemistry of Novel Energetic Fused Tricyclic 1,2,3,4-Tetrazine Nitro Derivatives from Local Coupled Cluster Methods.

Highly accurate theoretical values of formation enthalpies and bond energies are crucial for reliable predictions of performance and detonation-related phenomena of energetic materials (EM). However, high-level ab initio calculations even for medium-sized important EMs still remain a demanding challenge. In the present work, we studied in detail the gas-phase thermochemistry of novel high-energy polynitro derivatives of 5/6/5 structural frameworks comprised of fused 1,2,3,4,-tetrazine and two 1,2,4-triazole or pyrazole rings. To this end, we proposed and benchmarked a "bottom-up" approach. First, highly accurate multilevel procedures W2-F12 and/or W1-F12 in conjunction with the atomization energy approach were utilized for smaller species. In turn, for medium-sized species (up to 24 non-H atoms), these values were complemented with the enthalpies of isodesmic reactions calculated using the recently proposed domain-based local pair natural orbital (DLPNO) modifications of coupled cluster techniques. The benchmarks on a number of atomization energies and enthalpies of isodesmic reactions reveal that the DLPNO-CCSD(T)/aVQZ approach does not deteriorate the quality of the W1-F12 and W2-F12 procedures and exhibits overall accuracy close to "chemical" (∼1 kcal mol-1). We obtained a set of accurate and mutually consistent gas-phase formation enthalpies for 12 energetic heterocyclic species. Among them, the gas-phase formation enthalpy of 1,2,9,10-tetranitrodipyrazolo[1,5-d:5',1'-f][1,2,3,4]tetrazine, a novel promising EM, turned out to be ΔfHgas0 = 214.5 kcal mol-1, which is ∼12 kcal mol-1 higher than the best theoretical estimates available in the literature. The formation enthalpy of another novel EM, a fused tricyclic 1,2,3,4-tetrazine with two nitro-1,2,4-triazole moieties, was predicted to be ΔfHgas0 = 213.5 kcal mol-1, which is also ∼4 kcal mol-1 higher than the reported value. Apart from this, we considered the thermodynamics of radical reactions (viz., C-NO2 bond scission) and the thermochemistry of the corresponding radicals. The difference between DLPNO-CCSD(T)/aVQZ and CCSD(T)-F12/VTZ-F12 benchmark values did not exceed 1 kcal mol-1. In a more general sense, the use of DLPNO-CCSD(T) in conjunction with the bottom-up approach is promising for quantitative thermochemical calculations of energetic materials composed of species up to several dozens of CHNO atoms.

Multilayer Divide-Expand-Consolidate Coupled-Cluster Method: Demonstrative Calculations of the Adsorption Energy of Carbon Dioxide in the Mg-MOF-74 Metal-Organic Framework.

The implementation and evaluation of a multilayer extension of the divide-expand-consolidate (DEC) scheme within the LSDalton program is presented. The DEC scheme is a linear-scaling, fragmentation-based local coupled-cluster (CC) method that provides a means of overcoming the scaling wall associated with canonical CC electronic structure calculations on large molecular systems. Taking advantage of the local nature of correlation effects, the correlation energy for the full molecule is calculated from a set of independent fragments using localized molecular orbitals. However, when only a small subsystem of a larger system is of interest, for example, adsorption sites or catalytically active sites, the majority of the computational time may be spent evaluating the correlation energy of fragments which have little effect on the properties in the area of interest (AOI). The multilayer DEC (ML-DEC) scheme addresses this by taking advantage of the independent nature of the fragments in order to evaluate the correlation energy of various regions of the system at different levels of theory. Regions far from the AOI are evaluated at lower (cheaper) levels of theory such as Hartree-Fock (HF) or Møller-Plesset second-order perturbation theory (MP2), while the area immediately surrounding the AOI is treated with a higher level CC model. Through the ML-DEC scheme, the computational cost of CC calculations on these types of systems can be significantly reduced while maintaining the accuracy of higher-level calculations. Results from HF/RI-MP2 and RI-MP2/CCSD ML-DEC calculations of the binding energy of a fatty acid dimer are presented. We find that the ML-DEC scheme is capable of reproducing DEC energy differences at a target level of theory, provided that the region treated at the target level of theory is chosen to be sufficiently large. Time-to-solution is found to be significantly reduced, particularly in the RI-MP2/CCSD calculations. Finally, the ML-DEC scheme is applied to the calculation of CO2 adsorption in a Mg-MOF-74 channel.

Accurate Intermolecular Interaction Energies Using Explicitly Correlated Local Coupled Cluster Methods [PNO-LCCSD(T)-F12

We present benchmark results for the A24, S66, and X40 sets of intermolecular interaction energies obtained with our recently developed PNO-LCCSD(T)-F12 method. Using the aug-cc-pVQZ-F12 basis set and tight domain options, the root-mean-square (RMSD) and maximum (MAXD) deviations from the currently best CCSD(T)/CBS estimates for the S66 set amount to only 0.02 and 0.06 kcal mol-1, respectively. The corresponding triple-ζ (aug-cc-pVTZ-F12) results are similarly accurate, and even with double-ζ (aug-cc-pVDZ-F12) basis sets the RMSD and MAXD deviations amount to only 0.05 and 0.11 kcal mol-1, respectively. Preliminary PNO-LCCSD(T)-F12 calculations on the X40 set of intermolecular interactions of halogenated molecules yield interaction energies in reasonable agreement with the original CCSD(T)/CBS estimates. The PNO-LCCSD(T)-F12 method does not rely on error cancellations as the popular ΔCCSD(T) approach and can yield comparable or better accuracy at a fraction of the cost. This accuracy is of importance for studying reactions involving large molecules, in which intramolecular noncovalent interactions are important and no counterpoise corrections are possible.

Correction to Scalable Electron Correlation Methods. 4. Parallel Explicitly Correlated Local Coupled Cluster with Pair Natural Orbitals (PNO-LCCSD-F12).

Correction to Scalable Electron Correlation Methods. 4. Parallel Explicitly Correlated Local Coupled Cluster with Pair Natural Orbitals (PNO-LCCSD-F12).

Efficient Estimation of Formation Enthalpies for Closed-Shell Organic Compounds with Local Coupled-Cluster Methods.

Efficient estimation of the enthalpies of formation for closed-shell organic compounds via atom-equivalent-type computational schemes and with the use of different local coupled-cluster with single, double, and perturbative triple excitation (CCSD(T)) approximations was investigated. Detailed analysis of established sources of uncertainty, inclusive of contributions beyond frozen-core CCSD(T) and errors due to local CCSD(T) approximations and zero-point energy anharmonicity, suggests the lower limit of about 2 kJ·mol-1 for the expanded uncertainty of the proposed estimation framework. Among the tested computational schemes, the best-performing cases demonstrate expanded uncertainty of about 2.5 kJ·mol-1, based on the analysis against 44 critically evaluated experimental values. Computational efficiency, accuracy commensurable with that of a typical experiment, and absence of the need for auxiliary reactions and additional experimental data offer unprecedented advantages for practical use, such as prompt validation of existing measurements and estimation of missing values, as well as resolution of experimental conflicts. The utility of the proposed methodology was demonstrated using a representative sample of the most recent experimental measurements.

Scalable Electron Correlation Methods. 5. Parallel Perturbative Triples Correction for Explicitly Correlated Local Coupled Cluster with Pair Natural Orbitals.

A well-parallelized perturbative triples correction implementation for the pair natural orbital based coupled cluster method PNO-LCCSD(T)-F12 is presented. A composite approach is adopted in addressing the coupling due to off-diagonal Fock matrix elements, in which the local triples amplitudes are iteratively solved using small domains of triples natural orbitals, and a semicanonical (T0) domain correction with larger domains is applied to reduce the domain errors. This treatment adds only about 20% to the computational cost of (T0) calculations with large domains, and the errors due to the use of small domains in the iterations are very small. In addition, a two-step triple list selection method is applied: First, an initial triple list is generated using LCCSD-F12 pair energy criteria, and the (T0) triples energies are computed using small domains. Second, this list is reduced by neglecting triples with small energy contributions, and the final calculation with large domains is only carried out for the reduced list. The cost of the (T) calculation scales asymptotically linear with the molecular size and shows excellent parallelization efficiency up to hundreds of CPU cores. The convergence of the (T) contribution to the relative energies of large molecular systems is carefully tested, and for most of the cases the results obtained with our default thresholds agree within ∼0.5 kcal mol-1 with those computed with very tight thresholds. For all tested molecular systems where canonical calculations are still feasible, the PNO-LCCSD(T)-F12 relative energies also agree within 0.5 kcal mol-1 with the canonical CCSD(T)-F12 results using the same F12 treatment. The (T) calculation generally takes 3-5 times the cost of the preceding PNO-LCCSD-F12 calculation, primarily due to the large number of triples required in obtaining accurate relative energies. We find that for large molecular systems the triple selection criteria used in previous local triples methods are insufficient, and a much larger number of triples are required than it was assumed so far. Still, using a commodity computer cluster, the PNO-LCCSD(T)-F12 calculation of molecules with ∼100 atoms using augmented triple-ζ basis sets can be carried out in a few hours of elapsed time.

Scalable Electron Correlation Methods. 4. Parallel Explicitly Correlated Local Coupled Cluster with Pair Natural Orbitals (PNO-LCCSD-F12).

We present an efficient explicitly correlated pair natural orbital local coupled cluster (PNO-LCCSD-F12) method. The method is an extension of our previously reported PNO-LCCSD approach ( Schwilk et al., J. Chem. Theory Comput. 2017 , 13 , 3650 - 3675 ). Near linear scaling with the molecular size is achieved by using pair, domain, and projection approximations, local density fitting and local resolution of the identity, and by exploiting the sparsity of the local molecular orbitals as well as of the projected atomic orbitals. The effect of the various domain approximations is tested for a wide range of chemical reactions and intermolecular interactions. In accordance with previous findings, it is demonstrated that the F12 terms significantly reduce the domain errors. The convergence of the reaction and interaction energies with respect to the parameters that determine the domain sizes and pair approximations is extensively tested. The results obtained with our default thresholds agree within a few tenths of a kcal mol-1 with the ones computed with very tight options. For cases where canonical calculations are still feasible, the relative energies of local and canonical calculations agree within similar error bounds. The PNO-LCCSD-F12 method needs only 25-40% more computer time than a corresponding PNO-LCCSD calculation while greatly improving the accuracy. Our program is well parallelized and capable of computing accurate correlation energies for molecules with more than 150 atoms using augmented triple-ζ basis sets and more than 5000 basis functions. Using several nodes of a small computer cluster, such calculations can be carried out within a few hours.

Scalable Electron Correlation Methods. 3. Efficient and Accurate Parallel Local Coupled Cluster with Pair Natural Orbitals (PNO-LCCSD).

A well-parallelized local singles and doubles coupled-cluster (LCCSD) method using pair natural virtual orbitals (PNOs) is presented. The PNOs are constructed using large domains of projected atomic orbitals (PAOs) and orbital specific virtual orbitals (OSVs). We introduce a hierarchy of close, weak, and distant pairs, based on pair energies evaluated by local Møller-Plesset perturbation theory (LMP2). In contrast to most previous implementations of LCCSD methods, the close and weak pairs are not approximated by LMP2 but treated by higher-order methods. This leads to greatly improved accuracy for large systems, in particular when long-range dispersion interactions are important. Close pair amplitudes are optimized using approximate LCCSD equations, in which slowly decaying terms that mutually cancel at long-range are neglected. For weak pairs, the same approximations are used, but in addition, the nonlinear terms are neglected (coupled electron pair approximation). Distant pairs are treated by spin-component scaled (SCS)-LMP2 using multipole approximations. For efficiency reasons, various projection approximations are also introduced. The impact of these approximations on absolute and relative energies depends on the PNO domain sizes. The errors are found to be negligible, provided that sufficiently large PNO domains are used for close and weak pairs. For the selection of these domains the usual natural orbital occupation number criterion is found to be insufficient, and an additional energy criterion is used. For extended one-dimensional systems, the computational effort of the method scales nearly linearly with the number of correlated electrons, but the linear scaling regime is usually not reached in real-life applications for three-dimensional systems. Nevertheless, due to the parallelization that is efficient up to about 100-200 CPU cores (dependent on the molecular size), accurate calculations for three-dimensional molecules with about 100 atoms and augmented triple-ζ basis sets (e.g., cc-pVTZ-F12) can be carried out in 1-3 h of elapsed time (depending on the molecular structure and the number of CPU cores, excluding the time for Hartree-Fock). The convergence of the results with respect to the thresholds and options that control the domain, pair, and projection approximations is extensively tested. Benchmark examples for several difficult and large cases are presented, which demonstrate that the errors of relative energies (e.g., reaction energies, barrier heights) caused by the pair and projection approximations can be reduced to below 1 kJ mol-1. The remaining errors are mainly caused by the finite PAO domains. The larger these are made, the more intramolecular or intermolecular basis set superposition errors are introduced, and the canonical results are approached only very slowly. This problem is eliminated in the explicitly correlated variant of our method (PNO-LCCSD-F12), which will be described in a separate paper, along with a larger set of benchmark calculations.

Communication: Multipole approximations of distant pair energies in local correlation methods with pair natural orbitals.

The accuracy of multipole approximations for distant pair energies in local second-order Møller-Plesset perturbation theory (LMP2) as introduced by Hetzer et al. [Chem. Phys. Lett. 290, 143 (1998)] is investigated for three chemical reactions involving molecules with up to 92 atoms. Various iterative and non-iterative approaches are compared, using different energy thresholds for distant pair selection. It is demonstrated that the simple non-iterative dipole-dipole approximation, which has been used in several recent pair natural orbitals (PNO)-LMP2 and PNO-LCCSD (local coupled-cluster with singles and doubles) methods, may underestimate the distant pair energies by up to 50% and can lead to significant errors in relative energies, unless very tight thresholds are used. The accuracy can be much improved by including higher multipole orders and by optimizing the distant pair amplitudes iteratively along with all other amplitudes. A new approach is presented in which very small special PNO domains for distant pairs are used in the iterative approach. This reduces the number of distant pair amplitudes by 3 orders of magnitude and keeps the additional computational effort for the iterative optimization of distant pair amplitudes minimal.

Decomposition of Intermolecular Interaction Energies within the Local Pair Natural Orbital Coupled Cluster Framework.

The local coupled cluster method DLPNO-CCSD(T) allows calculations on systems containing hundreds of atoms to be performed while typically reproducing canonical CCSD(T) energies with chemical accuracy. In this work, we present a scheme for decomposing the DLPNO-CCSD(T) interaction energy between two molecules into physical meaningful contributions, providing a quantification of the most important components of the chemical interaction. The method, called Local Energy Decomposition (LED), is straightforward and requires negligible additional computing time. Both the Hartree-Fock and the correlation energy are decomposed into contributions from localized or pairs of localized occupied orbitals. Assigning these localized orbitals to fragments allows one to differentiate between intra- and intermolecular contributions to the interaction energy. Accordingly, the interaction energy can be decomposed into electronic promotion, electrostatic, exchange, dynamic charge polarization, and dispersion contributions. The LED scheme is applied to a number of test cases ranging from weakly, dispersively bound complexes to systems with strong ionic interactions. The dependence of the results on the one-particle basis set and various technical aspects, such as the localization scheme, are carefully studied in order to ensure that the results do not suffer from technical artifacts. A numerical comparison between the DLPNO-CCSD(T)/LED and the popular symmetry adapted perturbation theory (DFT-SAPT) is made, and the limitations of the proposed scheme are discussed.

Coupled-cluster interaction energies for 200-atom host-guest systems.

We have developed a method to calculate interaction energies of large systems (such as host-guest or even protein-ligand systems) at the local coupled-cluster with singles, doubles, and perturbative triples level, and with extrapolation to the limit of a complete basis set. The method is based on the polarizable multipole interactions with supermolecular pairs molecular fractionation approach, which combines a pairwise quantum-mechanical evaluation of the short-range interactions with a polarizable multipole treatment of many-body effects. The method is tested for nine guest molecules binding to an octa-acid host (in total 198-207 atoms), as part of the SAMPL4 blind challenge. From the test calculations, the accuracy of the approach is found to be 10 kJ mol(-1) or better. Comparison with dispersion-corrected density functional theory reveals that the latter underestimates the dispersion contribution for this type of system, which leads to a difference in the ranking of the ligands.

An efficient linear-scaling CCSD(T) method based on local natural orbitals

An improved version of our general-order local coupled-cluster (CC) approach [Z. Rolik and M. Kállay, J. Chem. Phys. 135, 104111 (2011)] and its efficient implementation at the CC singles and doubles with perturbative triples [CCSD(T)] level is presented. The method combines the cluster-in-molecule approach of Li and co-workers [J. Chem. Phys. 131, 114109 (2009)] with frozen natural orbital (NO) techniques. To break down the unfavorable fifth-power scaling of our original approach a two-level domain construction algorithm has been developed. First, an extended domain of localized molecular orbitals (LMOs) is assembled based on the spatial distance of the orbitals. The necessary integrals are evaluated and transformed in these domains invoking the density fitting approximation. In the second step, for each occupied LMO of the extended domain a local subspace of occupied and virtual orbitals is constructed including approximate second-order Mo̸ller-Plesset NOs. The CC equations are solved and the perturbative corrections are calculated in the local subspace for each occupied LMO using a highly-efficient CCSD(T) code, which was optimized for the typical sizes of the local subspaces. The total correlation energy is evaluated as the sum of the individual contributions. The computation time of our approach scales linearly with the system size, while its memory and disk space requirements are independent thereof. Test calculations demonstrate that currently our method is one of the most efficient local CCSD(T) approaches and can be routinely applied to molecules of up to 100 atoms with reasonable basis sets.

How Accurate Can a Local Coupled Cluster Approach Be in Computing the Activation Energies of Late-Transition-Metal-Catalyzed Reactions with Au, Pt, and Ir?

To improve the accuracy of local coupled cluster (LCC) methods in computing activation energies, we propose herein a new computational scheme. Its applications to various types of late-transition-metal-catalyzed reactions involving Au, Pt, and Ir indicate that the new corrective approach for LCC methods can downsize the mean unsigned deviation and maximum deviation, from the CCSD(T)/CBS reference, to about 0.3 and 0.9 kcal/mol. Using this method, we also calibrated the performance of popular density functionals, with respect to the same test set of reactions. It is concluded that the best functional is the general-purpose double hybrid functional B2GP-PLYP. Other well-performing functionals include the "kinetic" functionals M06-2X and BMK, which have a large percentage of HF exchange, and general-purpose functionals like PBE0 and wB97X. Comparatively, general-purpose functionals like PBE0 and TPSSh perform much better than the tested "kinetic" functionals for Pt-/Ir-catalyzed reactions, while the opposite is true for Au-catalyzed reactions. In contrast, wB97X performs more uniformly in these two classes of reactions. These findings hint that even within the scope of late transition metals, different types of reactions may require different types of optimal DFT methods. Empirical dispersion correction of DFT was found to have a small or no effect on the studied reactions barriers.

Comparison of explicitly correlated local coupled-cluster methods with various choices of virtual orbitals

Explicitly correlated local coupled-cluster (LCCSD-F12) methods with pair natural orbitals (PNOs), orbital specific virtual orbitals (OSVs), and projected atomic orbitals (PAOs) are compared. In all cases pair-specific virtual subspaces (domains) are used, and the convergence of the correlation energy as a function of the domain sizes is studied. Furthermore, the performance of the methods for reaction energies of 52 reactions involving 58 small and medium sized molecules is investigated. It is demonstrated that for all choices of virtual orbitals much smaller domains are needed in the explicitly correlated methods than without the explicitly correlated terms, since the latter correct a large part of the domain error, as found previously. For PNO-LCCSD-F12 with VTZ-F12 basis sets on the average only 20 PNOs per pair are needed to obtain reaction energies with a root mean square deviation of less than 1 kJ mol(-1) from complete basis set estimates. With OSVs or PAOs at least 4 times larger domains are needed for the same accuracy. A new hybrid method that combines the advantages of the OSV and PNO methods is proposed and tested. While in the current work the different local methods are only simulated using a conventional CCSD program, the implications for low-order scaling local implementations of the various methods are discussed.