Canonical CCSD Research Articles

On the Potential Energy Surface of the Pyrene Dimer

Knowledge of reliable geometries and associated intermolecular interaction energy () values at key fragments of the potential energy surface (PES) in the gas phase is indispensable for the modeling of various properties of the pyrene dimer (PYD) and other important aggregate systems of a comparatively large size (ca. 50 atoms). The performance of the domain-based local pair natural orbital (DLPNO) variant of the coupled-cluster theory with singles, doubles and perturbative triples in the complete basis set limit [CCSD(T)/CBS] method for highly accurate predictions of the at a variety of regions of the PES was established for a representative set of pi-stacked dimers, which also includes the PYD. For geometries with the distance between stacked monomers close to a value of such a distance in the minimum structure, an excellent agreement between the canonical CCSD(T)/CBS results and their DLPNO counterparts was found. This finding enabled us to accurately characterize the lowest-lying configurations of the PYD, and the physical origin of their stabilization was thoroughly analyzed. The proposed DLPNO-CCSD(T)/CBS procedure should be applied with the aim of safely locating a global minimum of the PES and firmly establishing the pertaining of even larger dimers in studies of packing motifs of organic electronic devices and other novel materials.

Accurate and efficient open-source implementation of domain-based local pair natural orbital (DLPNO) coupled-cluster theory using a t1-transformed Hamiltonian.

We present an efficient, open-source formulation for coupled-cluster theory through perturbative triples with domain-based local pair natural orbitals [DLPNO-CCSD(T)]. Similar to the implementation of the DLPNO-CCSD(T) method found in the ORCA package, the most expensive integral generation and contraction steps associated with the CCSD(T) method are linear-scaling. In this work, we show that the t1-transformed Hamiltonian allows for a less complex algorithm when evaluating the local CCSD(T) energy without compromising efficiency or accuracy. Our algorithm yields sub-kJ mol-1 deviations for relative energies when compared with canonical CCSD(T), with typical errors being on the order of 0.1kcal mol-1, using our TightPNO parameters. We extensively tested and optimized our algorithm and parameters for non-covalent interactions, which have been the most difficult interaction to model for orbital (PNO)-based methods historically. To highlight the capabilities of our code, we tested it on large water clusters, as well as insulin (787 atoms).

Scalable Ab Initio Electronic Structure Methods with Near Chemical Accuracy for Main Group Chemistry.

This study evaluates the precision of widely recognized quantum chemical methodologies, CCSD(T), DLPNO-CCSD(T), and localized ph-AFQMC, for determining the thermochemistry of main group elements. DLPNO-CCSD(T) and localized ph-AFQMC, which offer greater scalability compared to canonical CCSD(T), have emerged over the past decade as pivotal in producing precise benchmark chemical data. Our investigation includes closed-shell, neutral molecules, focusing on their heat of formation and atomization energy sourced from four specific small molecule data sets. First, we selected molecules from the G2 and G3 data sets, noted for their reliable experimental heat of formation data. Additionally, we incorporate molecules from the W4-11 and W4-17 sets, which provide high-level theoretical reference values for atomization energy at 0 K. Our findings reveal that both DLPNO-CCSD(T) and ph-AFQMC methods are capable of achieving a root-mean-square deviation of less than 1 kcal/mol across the combined data set, aligning with the threshold for chemical accuracy. Moreover, we make efforts to confine the maximum deviations within 2 kcal/mol, a degree of precision that significantly broadens the applicability of these methods in fields such as biology and materials science.

Performant automatic differentiation of local coupled cluster theories: Response properties and ab initio molecular dynamics

In this work, we introduce a differentiable implementation of the local natural orbital coupled cluster (LNO-CC) method within the automatic differentiation framework of the PySCFAD package. The implementation is comprehensively tuned for enhanced performance, which enables the calculation of first-order static response properties on medium-sized molecular systems using coupled cluster theory with single, double, and perturbative triple excitations [CCSD(T)]. We evaluate the accuracy of our method by benchmarking it against the canonical CCSD(T) reference for nuclear gradients, dipole moments, and geometry optimizations. In addition, we demonstrate the possibility of property calculations for chemically interesting systems through the computation of bond orders and Mössbauer spectroscopy parameters for a [NiFe]-hydrogenase active site model, along with the simulation of infrared spectra via ab initio LNO-CC molecular dynamics for a protonated water hexamer.

Linear Scaling Incremental Scheme for Correlation Energies with Embedding Generated Virtuals.

A novel incremental scheme is presented including an incremental expansion of the virtual space for the calculation of electron correlation energies, which is compatible with any size-extensive correlation method and scales asymptotically linear for large molecules. The performance is studied for organic molecules, water clusters, and a La(III)-water complex, where the compatibility with pseudopotentials is also examined. The computational requirements are already reduced tremendously for medium-sized water clusters and hydrocarbons with respect to the canonical CCSD as well as the ordinary incremental scheme references. Correlation energies within chemical accuracy have been observed for all studied systems. The novelty of the method is that relatively small virtual spaces are used in combination with tuples of localized occupied spaces. The corresponding orthonormal occupied and virtual orbitals are obtained from QM/QM embedding calculations and can thus be used with standard quantum chemistry codes for correlation calculations. It is presented how relevant virtual spaces are selected and the correlation energies are linked in the new virtual space expansion.

Approaching the Complete Basis Set Limit for Spin-State Energetics of Mononuclear First-Row Transition Metal Complexes.

Convergence to the complete basis set (CBS) limit is analyzed for the problem of spin-state energetics in mononuclear first-row transition metal (TM) complexes by taking under scrutiny a benchmark set of 18 energy differences between spin states for 13 chemically diverse TM complexes. The performance of conventional CCSD(T) and explicitly correlated CCSD(T)-F12a/b calculations in approaching the CCSD(T)/CBS limits is systematically studied. An economic computational protocol is developed based on the CCSD-F12a approximation and (here proposed) modified scaling of the perturbative triples term (T#). This computational protocol recovers the relative spin-state energetics of the benchmark set in excellent agreement with the reference CCSD(T)/CBS limits (mean absolute deviation of 0.4, mean signed deviation of 0.2, and maximum deviation of 0.8 kcal/mol) and enables performing canonical CCSD(T) calculations for mononuclear TM complexes sized up to ca. 50 atoms, which is illustrated by application to heme-related metalloporphyrins. Furthermore, a good transferability of the basis set incompleteness error (BSIE) is demonstrated for spin-state energetics computed using CCSD(T) and other wave function methods (MP2, CASPT2, CASPT2/CC, NEVPT2, and MRCI + Q), which justifies efficient focal-point approximations and simplifies the construction of multimethod benchmark studies.

Scalar Relativistic All-Electron and Pseudopotential Ab Initio Study of a Minimal Nitrogenase [Fe(SH)4H]- Model Employing Coupled-Cluster and Auxiliary-Field Quantum Monte Carlo Many-Body Methods.

Nitrogenase is the only enzyme that can cleave the triple bond in N2, making nitrogen available to organisms. The detailed mechanism of this enzyme is currently not known, and computational studies are complicated by the fact that different density functional theory (DFT) methods give very different energetic results for calculations involving nitrogenase models. Recently, we designed a [Fe(SH)4H]- model with the fifth proton binding either to Fe or S to mimic different possible protonation states of the nitrogenase active site. We showed that the energy difference between these two isomers (ΔE) is hard to estimate with quantum-mechanical methods. Based on nonrelativistic single-reference coupled-cluster (CC) calculations, we estimated that the ΔE is 101 kJ/mol. In this study, we demonstrate that scalar relativistic effects play an important role and significantly affect ΔE. Our best revised single-reference CC estimates for ΔE are 85-91 kJ/mol, including energy corrections to account for contributions beyond triples, core-valence correlation, and basis-set incompleteness error. Among coupled-cluster approaches with approximate triples, the canonical CCSD(T) exhibits the largest error for this problem. Complementary to CC, we also used phaseless auxiliary-field quantum Monte Carlo calculations (ph-AFQMC). We show that with a Hartree-Fock (HF) trial wave function, ph-AFQMC reproduces the CC results within 5 ± 1 kJ/mol. With multi-Slater-determinant (MSD) trials, the results are 82-84 ± 2 kJ/mol, indicating that multireference effects may be rather modest. Among the DFT methods tested, τ-HCTH, r2SCAN with 10-13% HF exchange with and without dispersion, and O3LYP/O3LYP-D4, and B3LYP*/B3LYP*-D4 generally perform the best. The r2SCAN12 (with 12% HF exchange) functional mimics both the best reference MSD ph-AFQMC and CC ΔE results within 2 kJ/mol.

The fundamental vibrational frequencies and spectroscopic constants of the C2O2H2 isomers: molecules known in simulated interstellar ice analogues.

While trans-glyoxal may not be easily observable in astronomical sources through either IR or radioastronomy due to its C2h symmetry, its cis conformer along with the cyc-H2COCO epoxide isomer should be ready targets for astrochemical detection. The present quantum chemical study shows that not only are both molecular isomers strongly polar, they also have notable IR features and low isomerisation energies of 4.1 kcal mol-1 and 10.7 kcal mol-1, respectively. These three isomers along with two other C2O2H2 isomers have had their full set of fundamental vibrational frequencies and spectroscopic constants characterised herein. These isomers have previously been shown to occur in simulated astrophysical ices making them worthy targets of astronomical search. Furthermore, the hybrid quartic force field (QFF) approach utilized herein to produce the needed spectral data has a mean absolute percent error compared to the experimentally-available, gas phase fundamental vibrational frequencies of 0.6% and rotational constants to better than 0.1%. The hybrid QFF is defined from explicitly correlated coupled cluster theory at the singles, doubles, and perturbative triples level [CCSD(T)-F12b] including core electron correlation and a canonical CCSD(T) relativity correction for the harmonic (quadratic) terms in the QFF and simple CCSD(T)-F12b/cc-pVDZ energies for the cubic and quartic terms, the so-called "F12-TcCR+DZ QFF." This method is producing spectroscopically-accurate predictions for both fundamental vibrational frequencies and principal spectroscopic constants. Hence, the values computed in this work should be notably accurate and, hence, exceptionally useful to the spectroscopy and astrochemistry communities.

Comparing coupled cluster and composite quantum chemical methods for computing activation energies and reaction enthalpies of radical propagation reactions.

Accurate determination of activation energies and reaction enthalpies is essential for understanding the propagation step in free radical polymerization, as it significantly affects polymer chain length and structure. In this study, we compare DLPNO-CCSD(T) to canonical CCSD(T) for 17 radical addition activation energies and 18 reaction enthalpies from Radom and Fischer's test set. Additionally, we compare the computationally efficient composite methods G3(MP2)-RAD and CBS-RAD against CCSD(T)/aug-cc-pVTZ and DLPNO-CCSD(T)/CBS methods. Compared to the CCSD(T)/aug-cc-pVTZ reference, our results indicate that DLPNO-CCSD(T)/CBS with unrestricted Hartree-Fock (UHF) or UB3LYP reference orbitals and NormalPNO parameters consistently achieves chemical accuracy, with mean absolute deviations of 3.5 kJ mol-1 for activation energies and 1.5 kJ mol-1 for reaction enthalpies. Comparing the two composite methods shows that CBS-RAD agrees most closely with coupled cluster reaction enthalpies, while G3(MP2)-RAD tracks the activation energies most closely.

Exploring CPS-Extrapolated DLPNO-CCSD(T1) Reference Values for Benchmarking DFT Methods on Enzymatically Catalyzed Reactions.

Domain-based local pair natural orbital coupled-cluster singles doubles with perturbative triples [DLPNO-CCSD(T)] is regularly used to calculate reliable benchmark reference values at a computational cost significantly lower than that of canonical CCSD(T). Recent work has shown that even greater accuracy can be obtained at only a small additional cost through extrapolation to the complete PNO space (CPS) limit. Herein, we test two levels of CPS extrapolation, CPS(5,6), which approximates the accuracy of standard TightPNO, and CPS(6,7), which surpasses it, as benchmark values to test density functional approximations (DFAs) on a small set of organic and transition-metal-dependent enzyme active site models. Between the different reference levels of theory, there are changes in the magnitudes of the absolute deviations for all functionals, but these are small and there is minimal impact on the relative rankings of the tested DFAs. The differences are more significant for the metalloenzymes than the organic enzymes, so we repeat the tests on our entire ENZYMES22 set of organic enzyme active site models [Wappett, D. A.; Goerigk, L. J. Phys. Chem. A 2019, 123, 7057-7074] to confirm that using the CPS extrapolations for the reference values has negligible impact on the benchmarking outcomes. This means that we can particularly recommend CPS(5,6) as an alternative to standard TightPNO settings for calculating reference values, increasing the applicability of DLPNO-CCSD(T) in benchmarking reaction energies and barrier heights of larger models of organic enzymes. DLPNO-CCSD(T1)/CPS(6,7) energies for ENZYMES22 are finally presented as updated reference values for the set, reflecting the recent improvements in the method.

MP2-Based Correction Scheme to Approach the Limit of a Complete Pair Natural Orbitals Space in DLPNO-CCSD(T) Calculations.

The domain-based local pair natural orbital (PNO) coupled-cluster DLPNO-CCSD(T) method has been proven to provide accurate single-point energies at a fraction of the cost of canonical CCSD(T) calculations. However, the desired "chemical accuracy" can only be obtained with a large PNO space and extended basis set. We present a simple yet accurate and efficient correction scheme based on a perturbative approach. Here, in addition to DLPNO-CCSD(T) energy, one calculates DLPNO-MP2 correlation energy with the same settings as in the preceding coupled-cluster calculation. In the next step, the canonical MP2 correlation energy is obtained in the same orbital basis. This can be efficiently performed for essentially all molecule sizes accessible with the DLPNO-CCSD(T) method. By taking the difference between the canonical MP2 and DLPNO-MP2 energies, we obtain a correction term that can be added to the DLPNO-CCSD(T) correlation energy. This way, one can obtain the total correlation energy close to the limit of the complete PNO space (cPNO). The presented approach allows us to significantly increase the accuracy of the DLPNO-CCSD(T) method for both closed- and open-shell systems. The latter are known to be especially challenging for locally correlated methods. Unlike the previously developed PNO extrapolation procedure by Altun, Neese, and Bistoni ( J. Chem. Theory Comput. 2020, 16, 6142-6149), this strategy allows us to get the DLPNO-CCSD(T) correlation energy at the cPNO limit in a cost-efficient way, resulting in a minimal overall increase in calculation time as compared to the uncorrected method.

F12+EOM Quartic Force Fields for Rovibrational Predictions of Electronically Excited States.

Quartic force fields (QFFs) constructed using a sum of ground-state CCSD(T)-F12b energies with EOM-CCSD excitation energies are proposed for computation of spectroscopic properties of electronically excited states. This is dubbed the F12+EOM approach and is shown to provide similar accuracy to previous methodologies at lower computational cost. Using explicitly correlated F12 approaches instead of canonical CCSD(T), as in the corresponding (T)+EOM approach, allows for 70-fold improvement in computational time. The mean percent difference between the two methods for anharmonic vibrational frequencies is only 0.10%. A similar approach is also developed herein which accounts for core correlation and scalar relativistic effects, named F12cCR+EOM. The F12+EOM and F12cCR+EOM approaches both match to within 2.5% mean absolute error of experimental fundamental frequencies. These new methods should help in clarifying astronomical spectra by assigning features to vibronic and vibrational transitions of small astromolecules when such data are not available experimentally.

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.

A Cost Effective Scheme for the Highly Accurate Description of Intermolecular Binding in Large Complexes.

There has been a growing interest in quantitative predictions of the intermolecular binding energy of large complexes. One of the most important quantum chemical techniques capable of such predictions is the domain-based local pair natural orbital (DLPNO) scheme for the coupled cluster theory with singles, doubles, and iterative triples [CCSD(T)], whose results are extrapolated to the complete basis set (CBS) limit. Here, the DLPNO-based focal-point method is devised with the aim of obtaining CBS-extrapolated values that are very close to their canonical CCSD(T)/CBS counterparts, and thus may serve for routinely checking a performance of less expensive computational methods, for example, those based on the density-functional theory (DFT). The efficacy of this method is demonstrated for several sets of noncovalent complexes with varying amounts of the electrostatics, induction, and dispersion contributions to binding (as revealed by accurate DFT-based symmetry-adapted perturbation theory (SAPT) calculations). It is shown that when applied to dimeric models of poly(3-hydroxybutyrate) chains in its two polymorphic forms, the DLPNO-CCSD(T) and DFT-SAPT computational schemes agree to within about 2 kJ/mol of an absolute value of the interaction energy. These computational schemes thus should be useful for a reliable description of factors leading to the enthalpic stabilization of extended systems.

C-AlO[formula omitted], c-HAlO[formula omitted], and c-(HN)OAlH spectroscopic constants and anharmonic frequencies

Aluminum forms strong bonds to oxygen, nitrogen, and hydrogen, but these motifs are relatively rare in the interstellar medium (ISM). However, no chemical rationale accounts for this observation. The cyclic molecules AlO2, HAlO2, and (HN)OAlH are quintessential examples of the aforementioned phenomenon, and the latter two are isoelectronic with each other. Matrix-isolation spectroscopic data and prior theoretical computations exist for cyclic AlO2, although it has yet to be observed astronomically. However, high-level theoretical data provided herein generate useful predictions for and insights into spectral data for these three molecules. Anharmonic vibrational frequencies and rotational constants are determined in this work for these molecules via quartic force fields at the CCSD(T)-F12b/cc-pVTZ-F12 level of theory and with canonical CCSD(T) for consideration of basis set convergence, core electron correlation, and relativity (CcCR). The present work finds that these aluminum oxides are weak-to-moderate infrared emitters but are much stronger microwave emitters with dipole moments of 4.95 D, 4.55 D, and 3.76 D respective of cyclic AlO2 (c-AlO2), cyclic HAlO2 (c-HAlO2), and cyclic (HN)OAlH (c-(HN)OAlH). Correlation to argon-matrix experiments for c-AlO2 is within the expected matrix shift for the ν3 bend computed here to be 527.8 cm−1. Astrophysical detection of these molecules could imply their role in the creation or degradation of aluminum-containing nanocrystals and interstellar dust of importance for the formation of rocky bodies, and the spectral data computed in this work should be able to assist in such classification.

Coupled Cluster Benchmarking of Large Noncovalent Complexes in L7 and S12L as Well as the C60 Dimer, DNA-Ellipticine, and HIV-Indinavir.

In this work, we report the benchmark binding energies of the seven complexes within the L7 data set, six host-guest complexes from the S12L data set, a C60 dimer, the DNA-ellipticine intercalation complex, and the largest system of the study, the HIV-indinavir system, which contained 343 atoms or 139 heavy atoms. The high-quality values reported were obtained via a focal point method that relies on the canonical form of second-order Møller-Plesset theory and the domain-based local pair natural orbital scheme for the coupled cluster with single double and perturbative triple excitations [DLPNO-CCSD(T)] extrapolated to the complete basis set (CBS) limit. The results in this work not only corroborate but also improve upon some previous benchmark values for large noncovalent complexes albeit at a relatively steep cost. Although local CCSD(T) and the largely successful fixed-node diffusion Monte Carlo (FN-DMC) have been shown to generally agree for small- to medium-size systems, a discrepancy in their reported binding energy values arises for large complexes, where the magnitude of the disagreement is a definite cause for concern. For example, the largest deviation in the L7 data set was 2.8 kcal/mol (∼10%) on the low end in C3GC. Such a deviation only grows worse in the S12L set, which showed a difference of up to 10.4 kcal/mol (∼25%) by a conservative estimation in buckycatcher-C60. The DNA-ellipticine complex also generated a disagreement of 4.4 kcal/mol (∼10%) between both state-of-the-art methods. The disagreement between local CCSD(T) and FN-DMC in large noncovalent complexes shows that it is urgently needed to have the canonical CCSD(T), the Monte Carlo CCSD(T), or the full configuration interaction quantum Monte Carlo approaches available to large systems on the hundred-atom scale to solve this dilemma. In addition, the performances of cheaper popular computational methods were assessed for the studied complexes with respect to DLPNO-CCSD(T)/CBS. r2SCAN-3c, B97M-V, and PBE0+D4 work well in large noncovalent complexes in this work, and GFN2-xTB performs well in π-π stacking complexes. B97M-V is the most reliable computationally efficient approach to predicting noncovalent interactions for large complexes, being the only one to have binding errors within the so-called 1 kcal/mol "chemical accuracy". The benchmark interaction energies of these host-guest complexes, molecular materials, and biological systems with electronic and medicinal implications provide crucial reference data for the improvement of current and future lower-cost methods.

Assessment of DLPNO-CCSD(T)-F12 and its use for the formulation of the low-cost and reliable L-W1X composite method.

In the present study, we have investigated the performance of RIJCOSX DLPNO-CCSD(T)-F12 methods for a wide range of systems. Calculations with a high-accuracy option ["DefGrid3 RIJCOSX DLPNO-CCSD(T1 )-F12"] extrapolated to the complete-basis-set limit using the maug-cc-pV[D+d,T+d]Z basis sets provides fairly good agreements with the canonical CCSD(T)/CBS reference for a diverse set of thermochemical and kinetic properties [with mean absolute deviations (MADs) of ~1-2kJ mol-1 except for atomization energies]. On the other hand, the low-cost "RIJCOSX DLPNO-CCSD(T)-F12D" option leads to substantial deviations for certain properties, notably atomization energies (MADs of up to tens of kJ mol-1 ). With the high-accuracy CBS approach, we have formulated the L-W1X method, which further includes a low-cost core-valence plus scalar-relativistic term. It shows generally good accuracy. For improved accuracies in specific cases, we advise replacing maug-cc-pV(n+d)Z with jun-cc-pV(n+d)Z for the calculation of electron affinities, and using well-constructed isodesmic-type reactions to obtain atomization energies. For medium-sized systems, DefGrid3 RIJCOSX DLPNO-CCSD(T1 )-F12 calculations are several times faster than the corresponding canonical computation; the use of the local approximations (RIJCOSX and DLPNO) leads to a better scaling than that for the canonical calculation (from ~6-7 down to ~2-4 for our test systems). Thus, the DefGrid3 RIJCOSX DLPNO-CCSD(T1 )-F12 method, and the L-W1X protocol that based on it, represent a useful means for obtaining accurate thermochemical quantities for larger systems.

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.

The MOBH35 Metal-Organic Barrier Heights Reconsidered: Performance of Local-Orbital Coupled Cluster Approaches in Different Static Correlation Regimes.

We have revisited the MOBH35 (Metal–Organic Barrier Heights, 35 reactions) benchmark [Iron, Janes, J. Phys. Chem. A, 2019, 123 ( (17), ), 3761−378130973722; ibid. 2019, 123, 6379–6380] for realistic organometallic catalytic reactions, using both canonical CCSD(T) and localized orbital approximations to it. For low levels of static correlation, all of DLPNO-CCSD(T), PNO-LCCSD(T), and LNO-CCSD(T) perform well; for moderately strong levels of static correlation, DLPNO-CCSD(T) and (T1) may break down catastrophically, and PNO-LCCSD(T) is vulnerable as well. In contrast, LNO-CCSD(T) converges smoothly to the canonical CCSD(T) answer with increasingly tight convergence settings. The only two reactions for which our revised MOBH35 reference values differ substantially from the original ones are reaction 9 and to a lesser extent 8, both involving iron. For the purpose of evaluating density functional theory (DFT) methods for MOBH35, it would be best to remove reaction 9 entirely as its severe level of static correlation makes it just too demanding for a test. The magnitude of the difference between DLPNO-CCSD(T) and DLPNO-CCSD(T1) is a reasonably good predictor for errors in DLPNO-CCSD(T1) compared to canonical CCSD(T); otherwise, monitoring all of T1, D1, max|tiA|, and 1/(εLUMO – εHOMO) should provide adequate warning for potential problems. Our conclusions are not specific to the def2-SVP basis set but are largely conserved for the larger def2-TZVPP, as they are for the smaller def2-SV(P): the latter may be an economical choice for calibrating against canonical CCSD(T). Finally, diagnostics for static correlation are statistically clustered into groups corresponding to (1) importance of single excitations in the wavefunction; (2a) the small band gap, weakly separated from (2b) correlation entropy; and (3) thermochemical importance of correlation energy, as well as the slope of the DFT reaction energy with respect to the percentage of HF exchange. Finally, a variable reduction analysis reveals that much information on the multireference character is provided by T1, IND/Itot, and the exchange-based diagnostic A100[TPSS].

BH9, a New Comprehensive Benchmark Data Set for Barrier Heights and Reaction Energies: Assessment of Density Functional Approximations and Basis Set Incompleteness Potentials.

The calculation of accurate reaction energies and barrier heights is essential in computational studies of reaction mechanisms and thermochemistry. To assess methods regarding their ability to predict these two properties, high-quality benchmark sets are required that comprise a reasonably large and diverse set of organic reactions. Due to the time-consuming nature of both locating transition states and computing accurate reference energies for reactions involving large molecules, previous benchmark sets have been limited in scope, the number of reactions considered, and the size of the reactant and product molecules. Recent advances in coupled-cluster theory, in particular local correlation methods like DLPNO-CCSD(T), now allow the calculation of reaction energies and barrier heights for relatively large systems. In this work, we present a comprehensive and diverse benchmark set of barrier heights and reaction energies based on DLPNO-CCSD(T)/CBS called BH9. BH9 comprises 449 chemical reactions belonging to nine types common in organic chemistry and biochemistry. We examine the accuracy of DLPNO-CCSD(T) vis-a-vis canonical CCSD(T) for a subset of BH9 and conclude that, although there is a penalty in using the DLPNO approximation, the reference data are accurate enough to serve as a benchmark for density functional theory (DFT) methods. We then present two applications of the BH9 set. First, we examine the performance of several density functional approximations commonly used in thermochemical and mechanistic studies. Second, we assess our basis set incompleteness potentials regarding their ability to mitigate basis set incompleteness errors. The number of data points, the diversity of the reactions considered, and the relatively large size of the reactant molecules make BH9 the most comprehensive thermochemical benchmark set to date and a useful tool for the development and assessment of computational methods.