An explicitly correlated local coupled cluster method for calculations of large molecules close to the basis set limit

The p-block challenge: assessing quantum chemistry methods for inorganic heterocycle dimerizations

The elements of the p-block of the periodic table are of high interest in various chemical and technical applications like frustrated Lewis-pairs (FLP) or opto-electronics. However, high-quality benchmark data to assess approximate density functional theory (DFT) for their theoretical description are sparse. In this work, we present a benchmark set of 604 dimerization energies of 302 "inorganic benzenes" composed of all non-carbon p-block elements of main groups III to VI up to polonium. This so-called IHD302 test set comprises two classes of structures formed by covalent bonding and by weaker donor-acceptor (WDA) interactions, respectively. Generating reliable reference data with ab initio methods is challenging due to large electron correlation contributions, core-valence correlation effects, and especially the slow basis set convergence. To compute reference values for these dimerization reactions, after thorough testing, we applied a computational protocol using state-of-the-art explicitly correlated local coupled cluster theory termed PNO-LCCSD(T)-F12/cc-VTZ-PP-F12(corr.). It includes a basis set correction at the PNO-LMP2-F12/aug-cc-pwCVTZ level. Based on these reference data, we assess 26 DFT methods in combination with three different dispersion corrections and the def2-QZVPP basis set, five composite DFT approaches, and five semi-empirical quantum mechanical methods. For the covalent dimerizations, the r2SCAN-D4 meta-GGA, the r2SCAN0-D4 and ωB97M-V hybrids, and the revDSD-PBEP86-D4 double-hybrid functional are found to be the best-performing methods among the evaluated functionals of the respective class. However, since def2 basis sets for the 4th period are not associated to relativistic pseudo-potentials, we obtained significant errors in the covalent dimerization energies (up to 6 kcal mol-1) for molecules containing p-block elements of the 4th period. Significant improvements were achieved for systems containing 4th row elements by using ECP10MDF pseudopotentials along with re-contracted aug-cc-pVQZ-PP-KS basis sets introduced in this work with the contraction coefficients taken from atomic DFT (PBE0) calculations. Overall, the IHD302 set represents a challenge to contemporary quantum chemical methods. This is due to a large number of spatially close p-element bonds which are underrepresented in other benchmark sets, and the partial covalent bonding character for the WDA interactions. The IHD302 set may be helpful to develop more robust and transferable approximate quantum chemical methods in the future.

Simple Composite Approach to Efficiently Estimate Basis Set Limit CCSD(T) Harmonic Frequencies and Reaction Thermochemistry

We introduce a simple strategy that combines the G3(MP2) composite method and explicitly correlated coupled cluster CCSD(T)-F12 method to efficiently estimate complete basis set CCSD(T) molecular geometries and harmonic vibrational frequencies at the cost of a double-ζ basis set calculation. Based on a large test set of 61 neutral, ionic, and open-shell molecules, and additionally 31 molecules in the HFREQ2014 data set, we demonstrate that this composite strategy has an average accuracy of 2 cm-1 or better relative to complete basis set CCSD(T) values. Using this approach, we estimated 696 CCSD(T)/CBS reaction energies of small to medium-sized systems containing up to 6 heavy atoms and confirmed existing approximations that use small basis set density functional theory methods [e.g., M06-2X/6-31+G(d)] to calculate thermal contributions to reaction enthalpies and Gibbs free energies that are accurate to within 0.2 kcal mol-1 on average.

Basis Set Limit of CCSD(T) Energies: Explicit Correlation Versus Density-Based Basis-Set Correction

A thorough comparison is carried out for explicitly correlated and density-based basis-set correction approaches, which were primarily developed to mitigate the basis-set incompleteness error of wave function methods. An efficient implementation of the density-based scheme is also presented, utilizing the density-fitting approximation. The performance of these approaches is comprehensively tested for the second-order Møller-Plesset (MP2), coupled-cluster singles and doubles (CCSD), and CCSD with perturbative triples [CCSD(T)] methods with respect to the corresponding complete basis set references. It is demonstrated that the density-based correction together with complementary auxiliary basis set (CABS)-corrected Hartree-Fock energies is highly robust and effectively reduces the error of the standard approaches; however, it does not outperform the corresponding explicitly correlated methods. Nevertheless, what still makes the density-corrected CCSD and CCSD(T) methods competitive is that their computational costs are roughly half of those of the corresponding explicitly correlated variants. Additionally, an incremental approach for standard CCSD and CCSD(T) is introduced. In this simple scheme, the total energies are corrected with the CABS correction and explicitly correlated MP2 contributions. As demonstrated, the resulting methods yield surprisingly good results, below 1 kcal/mol for thermochemical properties even with a double-ζ basis, while their computational expenses are practically identical to those of the density-based basis-set correction approaches.

Cluster-in-Molecule Approach with Explicitly Correlated Methods for Large Molecules

In this article, we present a series of explicitly correlated local correlation methods developed under the cluster-in-molecule (CIM) framework, including explicitly correlated second-order Møller-Plesset perturbation (MP2), coupled-cluster singles and doubles (CCSD), domain-based local pair natural orbital CCSD (DLPNO-CCSD), and DLPNO-CCSD with perturbative triples (DLPNO-CCSD(T)). In these methods, F12 correction is decomposed into contributions from each occupied local molecular orbital and then evaluated independently in a given cluster, which consists of a subset of localized orbitals. These newly developed methods allow F12 calculations of large molecules (up to 145 atoms for quasi-one-dimensional systems) on a single node. We use these methods to investigate the relative stability between extended and folded alkane C30H62, the relative stability of four secondary structures of a polyglycine Ace(Gly)10NH2, and the binding energies of two host-guest complexes. The results demonstrate that the combination of CIM with F12 methods is a promising way to investigate large molecules with small basis set errors.

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.

Analytic gradients for local density fitting Hartree-Fock and Kohn-Sham methods

We present analytic gradients for local density fitting Hartree-Fock (HF) and hybrid Kohn-Sham (KS) density functional methods. Due to the non-variational nature of the local fitting algorithm, the method of Lagrange multipliers is used to avoid the solution of the coupled perturbed HF and KS equations. We propose efficient algorithms for the solution of the arising Z-vector equations and the gradient calculation that preserve the third-order scaling and low memory requirement of the original local fitting algorithm. In order to demonstrate the speed and accuracy of our implementation, gradient calculations and geometry optimizations are presented for various molecular systems. Our results show that significant speedups can be achieved compared to conventional density fitting calculations without sacrificing accuracy.

Basis Set Limit CCSD(T) Energies for Extended Molecules via a Reduced-Cost Explicitly Correlated Approach

Several approximations are introduced and tested to reduce the computational expenses of the explicitly correlated coupled-cluster singles and doubles with perturbative triples [CCSD(T)] method for both closed and open-shell species. First, the well-established frozen natural orbital (FNO) technique is adapted to explicitly correlated CC approaches. Second, our natural auxiliary function (NAF) scheme is employed to reduce the size of the auxiliary basis required for the density fitting approximation regularly used in explicitly correlated calculations. Third, a new approach, termed the natural auxiliary basis (NAB) approximation, is proposed to decrease the size of the auxiliary basis needed for the expansion of the explicitly correlated geminals. The performance of the above approximations and that of the combined FNO-NAF-NAB approach are tested for atomization and reaction energies. Our results show that overall speedups of 7-, 5-, and 3-times can be achieved with double-, triple-, and quadruple-ζ basis sets, respectively, without any loss in accuracy. The new method can provide, e.g., reaction energies and barrier heights well within chemical accuracy for molecules with more than 40 atoms within a few days using a few dozen processor cores, and calculations with 50+ atoms are still feasible. These routinely affordable computations considerably extend the reach of explicitly correlated CCSD(T).

Exploring the Photochemistry of Solid 1,1-Diamino-2,2-dinitroethylene (FOX-7) Spanning Simple Bond Ruptures, Nitro-to-Nitrite Isomerization, and Nonadiabatic Dynamics

The UV photolysis of solid FOX-7 at 5 K with 355 and 532 nm photons was investigated to unravel initial isomerization and decomposition pathways. Isomer-selective single photon ionization coupled with reflectron time-of-flight mass spectrometry (ReTOF-MS) documented the nitric oxide (NO) loss channel at 355 nm along with a nitro-to-nitrite isomerization, which was observed by using infrared spectroscopy, representing the initial reaction pathway followed by O─NO bond rupture of the nitrite moiety. A residual gas analyzer detected molecular oxygen for the 355 and 532 nm photolysis at a ratio of 4.3 ± 0.3:1, which signifies FOX-7 as an energetic material that provides its own oxidant once the decomposition starts. Overall branching ratios for molecular oxygen versus nitric oxide were derived to be 700 ± 100:1 at 355 nm. It is notable that this is the first time that molecular oxygen was detected as a decomposition product of FOX-7. Computations show that atomic oxygen, which later combines to form molecular oxygen, is likely released from a nitro group involving conical intersections. The condensed phase potential energy profile computed at the CCSD(T) and CASPT2 level correlates well with the experiments and highlights the critical roles of conical intersections, nonadiabatic dynamics, and the encapsulated environment that dictate the mechanism of the reaction through intermolecular hydrogen bonds.

The potential energy profile of the decomposition of 1,1-diamino-2,2-dinitroethylene (FOX-7) in the gas phase

The decomposition products of 1,1-diamino-2,2-dinitroethylene (FOX-7) in the gas phase.

On the Accuracy of QM/MM Models: A Systematic Study of Intramolecular Proton Transfer Reactions of Amino Acids in Water

This work presents a systematic assessment of QM/QM' and QM/MM models with respect to direct QM calculations for the tautomerization (neutral to zwitterion) reactions of amino acids (glycine, alanine, valine, aspartate, and neutral and protonated histidine) solvated in a 160 water cluster. The effect of varying QM region size and choice of embedding potentials, including fixed-charge and polarizable molecular mechanics force fields (TIP3P and EFP) and various semiempirical QM methods (PM7, GFN2-xTB, DFTBA, DFTB3, HF-3c, and PBEh-3c), on the accuracy of the models was examined. A surprising finding was that molecular mechanics force fields outperformed many of the semiempirical methods. Generally, the errors in the QM/QM' and QM/MM models converge slowly with respect to the QM region size, requiring 50 or more waters to be included in the QM region before the error in the model falls below 1 kcal mol^-1 of its pure QM result. Different QM region selection schemes were also compared, and it was found that selection based on Natural Population Analysis (NPA) atomic charges significantly reduced the error in the QM/QM' and QM/MM models particularly if a low-quality embedding potential was used. It is envisaged that these results will be useful for the development of future hybrid QM models.

Speeding up Hartree-Fock and Kohn-Sham calculations with first-order corrections

Several approaches are presented to improve the efficiency of Hartree-Fock and Kohn-Sham self-consistent field (SCF) calculations relying on a simple first-order energy correction reminiscent of the scheme used in dual-basis SCF methods. The basic idea is to perform an initial SCF calculation computing approximate Fock-matrices and, in the final iteration step, to use a more complete Fock-matrix builder together with the energy correction to diminish the error. The approximation is tested for conventional and local density fitting (DF) SCF approaches combining various auxiliary basis sets, fitting metrics, and Fock-matrix construction algorithms in the initial and final iterations as well as for seminumerical SCF methods combining integration grids of different qualities. We also report the implementation of the occupied orbital resolution of identity exchange construction algorithm with local DF approximations. Benchmark calculations are presented for total energies, reaction energies, and molecular geometries. Our results show that speedups of up to 80% can be expected utilizing the new approaches without significant loss of accuracy.

CHAL336 Benchmark Set: How Well Do Quantum-Chemical Methods Describe Chalcogen-Bonding Interactions?

We present the CHAL336 benchmark set-the most comprehensive database for the assessment of chalcogen-bonding (CB) interactions. After careful selection of suitable systems and identification of three high-level reference methods, the set comprises 336 dimers each consisting of up to 49 atoms and covers both σ- and π-hole interactions across four categories: chalcogen-chalcogen, chalcogen-π, chalcogen-halogen, and chalcogen-nitrogen interactions. In a subsequent study of DFT methods, we re-emphasize the need for using proper London dispersion corrections when treating noncovalent interactions. We also point out that the deterioration of results and systematic overestimation of interaction energies for some dispersion-corrected DFT methods does not hint at problems with the chosen dispersion correction but is a consequence of large density-driven errors. We conclude this work by performing the most detailed DFT benchmark study for CB interactions to date. We assess 109 variations of dispersion-corrected and dispersion-uncorrected DFT methods and carry out a detailed analysis of 80 of them. Double-hybrid functionals are the most reliable approaches for CB interactions, and they should be used whenever computationally feasible. The best three double hybrids are SOS0-PBE0-2-D3(BJ), revDSD-PBEP86-D3(BJ), and B2NCPLYP-D3(BJ). The best hybrids in this study are ωB97M-V, PW6B95-D3(0), and PW6B95-D3(BJ). We do not recommend using the popular B3LYP functional nor the MP2 approach, which have both been frequently used to describe CB interactions in the past. We hope to inspire a change in computational protocols surrounding CB interactions that leads away from the commonly used, popular methods to the more robust and accurate ones recommended herein. We would also like to encourage method developers to use our set for the investigation and reduction of density-driven errors in new density functional approximations.

Predicting OH stretching fundamental wavenumbers of alcohols for conformational assignment: different correction patterns for density functional and wave-function-based methods

A model is presented for the prediction of OH stretching fundamental wavenumbers of alcohol conformers in the gas phase by application of a small set of empirical anharmonicity corrections to calculations in the harmonic approximation. In contrast to the popular application of a uniform scaling factor, the local chemical structure of the alcohol is taken into account to greatly improve accuracy. Interestingly, different correction patterns emerge for results of hybrid density functional (B3LYP-D3 and PBE0-D3) and wave-function-based methods (SCS-LMP2, LCCSD(T*)-F12a and CCSD(T)-F12a 1D). This raises questions about electronic structure deficiencies in these methods and differences in anharmonicity between alcohols. After its initial construction on the basis of literature assignments the model is tested with Raman jet spectroscopy of propargyl alcohol, cyclohexanol, borneol, isopinocampheol and 2-methylbutan-2-ol. For propargyl alcohol a spectral splitting attributed to tunneling is resolved. PBE0-D3 is identified as a well performing and broadly affordable electronic structure method for this model. A mean absolute error of 1.3 cm-1 and a maximum absolute error of 3 cm-1 result for 46 conformers of 24 alcohols in a 60 cm-1 range, when a single parameter is adjusted separately for each alcohol substitution class (methanol, primary, secondary, tertiary).

Accurate Reduced-Cost CCSD(T) Energies: Parallel Implementation, Benchmarks, and Large-Scale Applications

The accurate and systematically improvable frozen natural orbital (FNO) and natural auxiliary function (NAF) cost-reducing approaches are combined with our recent coupled-cluster singles, doubles, and perturbative triples [CCSD(T)] implementations. Both of the closed- and open-shell FNO-CCSD(T) codes benefit from OpenMP parallelism, completely or partially integral-direct density-fitting algorithms, checkpointing, and hand-optimized, memory- and operation count effective implementations exploiting all permutational symmetries. The closed-shell CCSD(T) code requires negligible disk I/O and network bandwidth, is MPI/OpenMP parallel, and exhibits outstanding peak performance utilization of 50-70% up to hundreds of cores. Conservative FNO and NAF truncation thresholds benchmarked for challenging reaction, atomization, and ionization energies of both closed- and open-shell species are shown to maintain 1 kJ/mol accuracy against canonical CCSD(T) for systems of 31-43 atoms even with large basis sets. The cost reduction of up to an order of magnitude achieved extends the reach of FNO-CCSD(T) to systems of 50-75 atoms (up to 2124 atomic orbitals) with triple- and quadruple-ζ basis sets, which is unprecedented without local approximations. Consequently, a considerably larger portion of the chemical compound space can now be covered by the practically "gold standard" quality FNO-CCSD(T) method using affordable resources and about a week of wall time. Large-scale applications are presented for organocatalytic and transition-metal reactions as well as noncovalent interactions. Possible applications for benchmarking local CCSD(T) methods, as well as for the accuracy assessment or parametrization of less complete models, for example, density functional approximations or machine learning potentials, are also outlined.

Scalable Electron Correlation Methods. 8. Explicitly Correlated Open-Shell Coupled-Cluster with Pair Natural Orbitals PNO-RCCSD(T)-F12 and PNO-UCCSD(T)-F12

We present explicitly correlated open-shell pair natural orbital local coupled-cluster methods, PNO-RCCSD(T)-F12 and PNO-UCCSD(T)-F12. The methods are extensions of our previously reported PNO-R/UCCSD methods (J. Chem. Theory Comput., 2020, 16, 3135-3151, https://pubs.acs.org/doi/10.1021/acs.jctc.0c00192) with additions of explicit correlation and perturbative triples corrections. The explicit correlation treatment follows the spin-orbital CCSD-F12b theory using Ansatz 3*A, which is found to yield comparable or better basis set convergence than the more rigorous Ansatz 3C in computed ionization potentials and reaction energies using double- to quaduple-ζ basis sets. The perturbative triples correction is adapted from the spin-orbital (T) theory to use triples natural orbitals (TNOs). To address the coupling due to off-diagonal Fock matrix elements, the local triples amplitudes are iteratively solved using small domains of TNOs, and a semicanonical (T0) domain correction with larger domains is applied to reduce the domain errors. The performance of the methods is demonstrated through benchmark calculations on ionization potentials, radical stabilization energies, reaction energies of fragmentations and rearrangements in radical cations, and spin-state energy differences of iron complexes. For a few test sets where canonical calculations are feasible, PNO-RCCSD(T)-F12 results agree with the canonical ones to within 0.4 kcal mol^-1, and this maximum error is reduced to below 0.2 kcal mol^-1 when large local domains are used. For larger systems, results using different thresholds for the local approximations are compared to demonstrate that 1 kcal mol^-1 level of accuracy can be achieved using our default settings. For a couple of difficult cases, it is demonstrated that the errors from individual approximations are only a fraction of 1 kcal mol^-1, and the overall accuracy of the method does not rely on error compensations. In contrast to canonical calculations, the use of spin-orbitals does not lead to a significant increase of computational time and memory usage in the most expensive steps of PNO-R/UCCSD(T)-F12 calculations. The only exception is the iterative solution of the (T) amplitudes, which can be avoided without significant errors by using a perturbative treatment of the off-diagonal coupling, known as (T1) approximation. For most systems, even the semicanonical approximation (T0) leads only to small errors in relative energies. Our program is well parallelized and capable of computing accurate correlation energies for molecules with 100-200 atoms using augmented triple-ζ basis sets in less than a day of elapsed time on a small computer cluster.

Assessing the validity of DLPNO-CCSD(T) in the calculation of activation and reaction energies of ubiquitous enzymatic reactions

The domain-based local pair natural orbital coupled-cluster with single, double, and perturbative triples excitation (DLPNO-CCSD(T)) method was employed to portray the activation and reaction energies of four ubiquitous enzymatic reactions, and its performance was confronted to CCSD(T)/complete basis set (CBS) to assess its accuracy and robustness in this specific field. The DLPNO-CCSD(T) results were also confronted to those of a set of density functionals (DFs) to understand the benefit of implementing this technique in enzymatic quantum mechanics/molecular mechanics (QM/MM) calculations as a second QM component, which is often treated with DF theory (DFT). On average, the DLPNO-CCSD(T)/aug-cc-pVTZ results were 0.51 kcal·mol^-1 apart from the canonic CCSD(T)/CBS, without noticeable biases toward any of the reactions under study. All DFs fell short to the DLPNO-CCSD(T), both in terms of accuracy and robustness, which suggests that this method is advantageous to characterize enzymatic reactions and that its use in QM/MM calculations, either alone or in conjugation with DFT, in a two-region QM layer (DLPNO-CCSD(T):DFT), should enhance the quality and faithfulness of the results.

Sublimation Properties of α,ω-Diamines Revisited from First-Principles Calculations

Sublimation enthalpies of alkane-α,ω-diamines exhibit an odd-even pattern within their homologous series. First-principles calculations coupled with the quasi-harmonic approximation for crystals and with the conformation mixing model for the ideal gas are used to explain this phenomenon from the theoretical point of view. Crystals of the odd and even alkane-α,ω-diamines distinctly differ in their packing motifs. However, first-principles calculations indicate that it is a delicate interplay of the cohesive forces, phonons, molecular vibrations and conformational equilibrium which governs the odd-even pattern of the sublimation enthalpies within the homologous series. High molecular flexibility of the alkane-α,ω-diamines predetermines higher sensitivity of the computational model to the quality of the optimized geometries and relative conformational energies. Performance of high-throughput computational methods, such as the density functional tight binding (DFTB, GFN2-xTB) and the explicitly correlated dispersion-corrected Møller-Plesset perturbative method (MP2C-F12), are benchmarked against the consistent state-of-the-art calculations of conformational energies and interaction energies, respectively.

Near-Linear Scaling in DMRG-Based Tailored Coupled Clusters: An Implementation of DLPNO-TCCSD and DLPNO-TCCSD(T)

We present a new implementation of density matrix renormalization group based tailored coupled clusters method (TCCSD), which employs the domain-based local pair natural orbital approach (DLPNO). Compared to the previous local pair natural orbital (LPNO) version of the method, the new implementation is more accurate, offers more favorable scaling, and provides more consistent behavior across the variety of systems. On top of the singles and doubles, we include the perturbative triples correction (T), which is able to retrieve even more dynamic correlation. The methods were tested on three systems: tetramethyleneethane, oxo-Mn(Salen), and iron(II)-porphyrin model. The first two were revisited to assess the performance with respect to LPNO-TCCSD. For oxo-Mn(Salen), we retrieved between 99.8 and 99.9% of the total canonical correlation energy which is an improvement of 0.2% over the LPNO version in less than 63% of the total LPNO runtime. Similar results were obtained for iron(II)-porphyrin. When the perturbative triples correction was employed, irrespective of the active space size or system, the obtained energy differences between two spin states were within the chemical accuracy of 1 kcal/mol using the default DLPNO settings.

Scalable Electron Correlation Methods. 7. Local Open-Shell Coupled-Cluster Methods Using Pair Natural Orbitals: PNO-RCCSD and PNO-UCCSD

We present well-parallelized local implementations of high-spin open-shell coupled cluster methods with single and double excitations (CCSD) using pair natural orbitals (PNOs). The methods are based on the spin-orbital coupled cluster theory using restricted open-shell Hartree-Fock (ROHF) reference functions. Two variants, namely, PNO-UCCSD and PNO-RCCSD are implemented and compared. In PNO-UCCSD, the coupled cluster amplitudes are spin-unrestricted, while in PNO-RCCSD the linear terms are spin-adapted by a spin-projection approach as described in J. Chem. Phys. 1993, 99, 5219-5227. Near linear scaling of the computational cost with the number of correlated electrons is achieved by applying domain and pair approximations. The PNOs are spin-independent and obtained using a semicanonical spin-restricted MP2 approximation with large domains of projected atomic orbitals (PAOs). The pair approximations of our previously described closed-shell PNO-LCCSD method are carefully revised so that they are compatible to the UCCSD theory, and PNO-UCCSD or PNO-RCCSD calculations for closed-shell molecules yield exactly the same results as corresponding spin-free closed-shell PNO-LCCSD calculations. The convergence of the results with respect to the thresholds and options that control the domain and pair approximations is demonstrated. It is found that large domains are required for the single excitations in open-shell calculations in order to obtain converged results. In general, the errors of relative energies caused by the local approximations can be reduced to below 1 kcal mol^-1, even for difficult cases. Presently, PNO-RCCSD and PNO-UCCSD calculations for molecules with 100-200 atoms and augmented triple-ζ basis sets can be carried out in a few hours of elapsed time using ∼100 CPU cores. In addition, the program is also capable of performing distinguishable cluster (PNO-RDCSD and PNO-UDCSC) calculations. The present work is a critical step in developing fully local open-shell PNO-RCCSD(T)-F12 methods.

The Molpro quantum chemistry package

Molpro is a general purpose quantum chemistry software package with a long development history. It was originally focused on accurate wavefunction calculations for small molecules but now has many additional distinctive capabilities that include, inter alia, local correlation approximations combined with explicit correlation, highly efficient implementations of single-reference correlation methods, robust and efficient multireference methods for large molecules, projection embedding, and anharmonic vibrational spectra. In addition to conventional input-file specification of calculations, Molpro calculations can now be specified and analyzed via a new graphical user interface and through a Python framework.

Biological control of S-nitrosothiol reactivity: potential role of sigma-hole interactions

S-Nitrosothiols (RSNOs) are ubiquitous biomolecules whose chemistry is tightly controlled in vivo, although the specific molecular mechanisms behind this biological control remain unknown. In this work, we demonstrate, using high-level ab initio and DFT calculations, the ability of RSNOs to participate in intermolecular interactions with electron pair donors/Lewis bases (LBs) via a σ-hole, a region of positive electrostatic potential on the molecular surface at the extension of the N-S bond. Importantly, σ-hole binding is able to modulate the properties of RSNOs by changing the balance between two chemically opposite (antagonistic) resonance components, R-S⁺[double bond, length as m-dash]N-O^- (D) and R-S^-/NO⁺ (I), which are, in addition to the main resonance structure R-S-N[double bond, length as m-dash]O, necessary to describe the unusual electronic structure of RSNOs. σ-Hole binding at the sulfur atom of RSNO promotes the resonance structure D and reduces the resonance structure I, thereby stabilizing the weak N-S bond and making the sulfur atom more electrophilic. On the other hand, increasing the D-character of RSNO by other means (e.g. via N- or O-coordination of a Lewis acid) in turn enhances the σ-hole bonding. Our calculations suggest that in the protein environment a combination of σ-hole bonding of a negatively charged amino acid sidechain at the sulfur atom and N- or O-coordination of a positively charged amino acid sidechain is expected to have a profound effect on the RSNO electronic structure and reactivity.

A straightforward a posteriori method for reduction of density-fitting error in coupled-cluster calculations

We present a simple method for a posteriori removal of a significant fraction of the density-fitting error from the calculated total coupled-cluster energies. The method treats the difference between the exact and density-fitted integrals as a perturbation, and simplified response-like equations allow us to calculate improved amplitudes and the corresponding energy correction. The proposed method is tested at the coupled-cluster singles and doubles level of theory for a diverse set of moderately-sized molecules. On average, error reductions by a factor of approximately 10 and 20 are observed in double-zeta and triple-zeta basis sets, respectively. Similar reductions are observed in calculations of interaction energies of several model complexes. The computational cost of the procedure is small in comparison with the preceding coupled-cluster iterations. The applicability of this method is not limited to the density-fitting approximation; in principle, it can be used in conjunction with an arbitrary decomposition scheme of the electron repulsion integrals.

Comprehensive Benchmark Results for the Domain Based Local Pair Natural Orbital Coupled Cluster Method (DLPNO-CCSD(T)) for Closed- and Open-Shell Systems

In this study we examine the accuracy of domain-based local pair natural orbital coupled cluster theory with single, double, and perturbative triple excitations (DLPNO-CCSD(T)) on a large benchmark data set. To this end, we use the recently published GMTKN55 superset of molecules that contains 1505 relative energies and 2462 single-point calculations. To our knowledge this is the most comprehensive benchmark evaluation of any highly correlated wave function based ab initio method to date. In the first part of the study, canonical CCSD(T) reference calculations were carried out on the entire test set in order to guarantee that the reference data are of uniform quality. Second, DLPNO-CCSD(T) calculations were carried out under identical conditions. The main finding is that with the exception of two data sets, all data sets have a MAD of 0.4 kcal/mol or less and the majority of sets have a MAD of less than 0.2 kcal/mol. For open shells, the accuracy of the DLPNO calculations was significantly improved through an iterative version of the triples correction.

HCnN anions in the ISM: exploring their existence and new paths to anionic carbonitriles for n = 3, 5

We have selected two neutral C-rich linear molecules, HC₃N and HC₅N, which are very abundant in the interstellar medium (ISM) to computationally investigate the stability of their anions and their possible existence in outer space, for which thus far there is no available evidence. Our present, ab initio structural studies strongly indicate that the neutral cyanopolyynes can have two types of stable anions by either forming slightly distorted non-linear structures of anionic Valence Bound States (VBSs), or linear more weakly bound dipole-bound states (DBSs) produced directly from the initial neutral linear configurations. Our present calculations further show that the stability of these anions increases with the number of C atoms in the chains. We carefully analyze possible physical causes for their lack of observation thus far: from the increased complexity of their rotational spectra with respect to those already observed, to their possible losses due to them entering the formation network of the C₃N^- and C₅N^- carbonitrile anions, which have been observed in the circumstellar envelopes and in the Titan atmosphere. We specifically suggest that de-hydrogenation reactions of the initial anions could take place by following either of two possible, well-known mechanisms: the fragmentation path usually ascribed to Dissociative Electron Attachment (DEA) processes or chemical recombination active in exothermic reactions with the H, N and O atoms present in the circumstellar envelopes. The results from such processes would be the loss of the stable anions of cyanopolyynes and the additional formation of their anionic carbonitriles.

The 1-Naphthol Dimer and Its Surprising Preference for π-π Stacking over Hydrogen Bonding

Using chirped-pulse Fourier transform microwave spectroscopy, we have experimentally identified the most abundant dimer of an alcohol analogue of naphthalene, 1-naphthol. The 1-naphthol dimer features a V-shaped, partially overlapping π-π stacked structure with no canonical hydrogen bonds between the subunits. This structural assignment is in contradiction to an earlier study of the 1-naphthol dimer using UV-IR dip double resonance spectroscopy in the O-H stretch region, which assigns a π-stacked but also canonically hydrogen-bonded structure. We use an improved theoretical analysis to resolve this discrepancy and show that the new, V-shaped structure is also consistent with the previously measured UV-IR data. These new computational and spectroscopic results shed light on the complicated nature of evaluating energetics and structures for larger, dispersion-bound systems.

Scalable Electron Correlation Methods. 6. Local Spin-Restricted Open-Shell Second-Order Møller-Plesset Perturbation Theory Using Pair Natural Orbitals: PNO-RMP2

We present a (near) linear scaling implementation of high-spin open-shell Møller-Plesset perturbation theory using pair natural orbitals (PNO-RMP2). The theory is based on a new variant of open-shell MP2 which is fully spin-adapted and uses a single set of spin-free amplitudes, as in closed-shell MP2. This method, denoted SROMP2, is invariant to unitary orbital transformations within the closed, open, and virtual orbital subspaces. Accordingly, only a single set of PNOs per spatial orbital pair is needed, and the efficiency is similar to closed-shell calculations. The PNOs are obtained using a semicanonical approximation with large domains of projected atomic orbitals (PAOs). Linear scaling is achieved provided that the open-shell orbitals are local, and distant pairs are treated by multipole approximations. The method is efficiently parallelized. The convergence of ionization and reaction energies as a function of the PAO and PNO domain sizes is demonstrated and found to be very similar as for closed-shell calculations. The suitability of the PNOs for explicitly correlated PNO-RCCSD-F12 calculations is also tested. So far, this method is only simulated using a conventional program with appropriate projections to the PAO and PNO subspaces. It is demonstrated for radical stabilization energies as well as ionization potentials that the errors caused by the local domain approximations with our default thresholds are negligible.

An Extended Computational Study of Criegee Intermediate-Alcohol Reactions

High-level ab initio calculations (DF-LCCSD(T)-F12a//B3LYP/aug-cc-pVTZ) are performed on a range of stabilized Criegee intermediate (sCI)-alcohol reactions, computing reaction coordinate energies, leading to the formation of α-alkoxyalkyl hydroperoxides (AAAHs). These potential energy surfaces are used to model bimolecular reaction kinetics over a range of temperatures. The calculations performed in this work reproduce the complicated temperature-dependent reaction rates of CH₂OO and (CH₃)₂COO with methanol, which have previously been experimentally determined. This methodology is then extended to compute reaction rates of 22 different Criegee intermediates with methanol, including several intermediates derived from isoprene ozonolysis. In some cases, sCI-alcohol reaction rates approach those of sCI-(H₂O)₂. This suggests that in regions with elevated alcohol concentrations, such as urban Brazil, these reactions may generate significant quantities of AAAHs and may begin to compete with sCI reactions with other trace tropospheric pollutants such as SO₂. This work also demonstrates the ability of alcohols to catalyze the 1,4-H transfer unimolecular decomposition of α-methyl substituted sCIs.

High-resolution synchrotron terahertz investigation of the large-amplitude hydrogen bond librational band of (HCN)2

The high-resolution terahertz absorption spectrum of the large-amplitude intermolecular donor librational band ν of the homodimer (HCN)₂ has been recorded by means of long-path static gas-phase Fourier transform spectroscopy at 207 K employing a highly brilliant electron storage ring source. The rovibrational structure of the ν band has the typical appearance of a perpendicular type band of a Σ-Π transition for a linear polyatomic molecule. The generated terahertz spectrum is analyzed employing a standard semi-rigid linear molecule Hamiltonian, yielding a band origin ν₀ of 119.11526(60) cm^-1 together with values for the excited state rotational constant B', the excited state quartic centrifugal distortion constant D_J' and the l-type doubling constant q for the degenerate state associated with the ν mode. The until now missing donor librational band origin enables the determination of an accurate experimental value for the vibrational zero-point energy of 2.50 ± 0.05 kJ mol^-1 arising from the entire class of large-amplitude intermolecular modes. The spectroscopic findings are complemented by CCSD(T)-F12b/aug-cc-pV5Z (electronic energies) and CCSD(T)-F12b/aug-cc-pVQZ (force fields) electronic structure calculations, providing a (semi)-experimental value of 17.20 ± 0.20 kJ mol^-1 for the dissociation energy D₀ of this strictly linear weak intermolecular CHN hydrogen bond.

Homogeneously Catalyzed Electroreduction of Carbon Dioxide-Methods, Mechanisms, and Catalysts

The utilization of CO₂ via electrochemical reduction constitutes a promising approach toward production of value-added chemicals or fuels using intermittent renewable energy sources. For this purpose, molecular electrocatalysts are frequently studied and the recent progress both in tuning of the catalytic properties and in mechanistic understanding is truly remarkable. While in earlier years research efforts were focused on complexes with rare metal centers such as Re, Ru, and Pd, the focus has recently shifted toward earth-abundant transition metals such as Mn, Fe, Co, and Ni. By application of appropriate ligands, these metals have been rendered more than competitive for CO₂ reduction compared to the heavier homologues. In addition, the important roles of the second and outer coordination spheres in the catalytic processes have become apparent, and metal-ligand cooperativity has recently become a well-established tool for further tuning of the catalytic behavior. Surprising advances have also been made with very simple organocatalysts, although the mechanisms behind their reactivity are not yet entirely understood. Herein, the developments of the last three decades in electrocatalytic CO₂ reduction with homogeneous catalysts are reviewed. A discussion of the underlying mechanistic principles is included along with a treatment of the experimental and computational techniques for mechanistic studies and catalyst benchmarking. Important catalyst families are discussed in detail with regard to mechanistic aspects, and recent advances in the field are highlighted.

Rotational spectra and theoretical study of tetramers and trimers of 2-fluoroethanol: dramatic intermolecular compensation for intramolecular instability

Cooperativity and chirality dominate in stabilizing the 2-fluoroethanol tetramer, thanks to a fully bifurcated C–H⋯F H-bond network.

Combining Accuracy and Efficiency: An Incremental Focal-Point Method Based on Pair Natural Orbitals

In this work, we present a new pair natural orbitals (PNO)-based incremental scheme to calculate CCSD(T) and CCSD(T0) reaction, interaction, and binding energies. We perform an extensive analysis, which shows small incremental errors similar to previous non-PNO calculations. Furthermore, slight PNO errors are obtained by using T_PNO = T_TNO with appropriate values of 10^-7 to 10^-8 for reactions and 10^-8 for interaction or binding energies. The combination with the efficient MP2 focal-point approach yields chemical accuracy relative to the complete basis-set (CBS) limit. In this method, small basis sets (cc-pVDZ, def2-TZVP) for the CCSD(T) part are sufficient in case of reactions or interactions, while some larger ones (e.g., (aug)-cc-pVTZ) are necessary for molecular clusters. For these larger basis sets, we show the very high efficiency of our scheme. We obtain not only tremendous decreases of the wall times (i.e., factors >10²) due to the parallelization of the increment calculations as well as of the total times due to the application of PNOs (i.e., compared to the normal incremental scheme) but also smaller total times with respect to the standard PNO method. That way, our new method features a perfect applicability by combining an excellent accuracy with a very high efficiency as well as the accessibility to larger systems due to the separation of the full computation into several small increments.

A study of the Group 1 metal tetra-aza macrocyclic complexes [M(Me4cyclen)(L)]+ using electronic structure calculations

Metal-cyclen complexes have a number of important applications. However, the coordination chemistry between metal ions and cyclen-based macrocycles is much less well studied compared to their metal ion-crown ether analogues. This work, which makes a contribution to address this imbalance by studying complex ions of the type [M(Me₄cyclen)(L)]⁺, was initiated by results of an experimental study which prepared some Group 1 metal cyclen complexes, namely [Li(Me₄cyclen)(H₂O)][BAr^F] and [Na(Me₄cyclen)(THF)][BAr^F] and obtained their X-ray crystal structures [J. M. Dyke, W. Levason, M. E. Light, D. Pugh, G. Reid, H. Bhakhoa, P. Ramasami, and L. Rhyman, Dalton Trans., 2015, 44, 13853]. The lowest [M(Me₄cyclen)(L)]⁺ minimum energy structures (M = Li, Na, K, and L = H₂O, THF, DEE, MeOH, DCM) are studied using density functional theory (DFT) calculations. The geometry of each [M(Me₄cyclen)(L)]⁺ structure and, in particular, the conformation of L are found to be mainly governed by steric hindrance which decreases as the size of the ionic radius increases from Li⁺ → Na⁺ → K⁺. Good agreement of computed geometrical parameters of [Li(Me₄cyclen)(H₂O)]⁺ and [Na(Me₄cyclen)(THF)]⁺ with the corresponding geometrical parameters derived from the crystal structures [Li(Me₄cyclen)(H₂O)]⁺[BAr^F]^- and [Na(Me₄cyclen)(THF)]⁺[BAr^F]^- is obtained. Bonding analysis indicates that the stability of the [M(Me₄cyclen)(L)]⁺ structures originates mainly from ionic interaction between the Me₄cyclen/L ligands and the M⁺ centres. The experimental observation that [M(Me₄cyclen)(L)]⁺[BAr^F]^- complexes could be prepared in crystalline form for M⁺ = Li⁺ and Na⁺, but that experiments aimed at synthesising the corresponding K⁺, Rb⁺, and Cs⁺ complexes failed resulting in formation of [Me₄cyclenH][BAr^F] is investigated using DFT and explicitly correlated calculations, and explained by considering production of [Me₄cyclenH]⁺ by a hydrolysis reaction, involving traces of water, which competes with [M(Me₄cyclen)(L)]⁺ formation. [Me₄cyclenH]⁺ formation dominates for M⁺ = K⁺, Rb⁺, and Cs⁺ whereas formation of [M(Me₄cyclen)(L)]⁺ is energetically favoured for M⁺ = Li⁺ and Na⁺. The results indicate that the number and type of ligands, play a key role in stabilising the [M(Me₄cyclen)]⁺ complexes and it is hoped that this work will encourage experimentalists to prepare and characterise other [M(Me₄cyclen)(L)]⁺ complexes.

Optimization of the linear-scaling local natural orbital CCSD(T) method: Redundancy-free triples correction using Laplace transform

An improved algorithm is presented for the evaluation of the (T) correction as a part of our local natural orbital (LNO) coupled-cluster singles and doubles with perturbative triples [LNO-CCSD(T)] scheme [Z. Rolik et al., J. Chem. Phys. 139, 094105 (2013)]. The new algorithm is an order of magnitude faster than our previous one and removes the bottleneck related to the calculation of the (T) contribution. First, a numerical Laplace transformed expression for the (T) fragment energy is introduced, which requires on average 3 to 4 times fewer floating point operations with negligible compromise in accuracy eliminating the redundancy among the evaluated triples amplitudes. Second, an additional speedup factor of 3 is achieved by the optimization of our canonical (T) algorithm, which is also executed in the local case. These developments can also be integrated into canonical as well as alternative fragmentation-based local CCSD(T) approaches with minor modifications. As it is demonstrated by our benchmark calculations, the evaluation of the new Laplace transformed (T) correction can always be performed if the preceding CCSD iterations are feasible, and the new scheme enables the computation of LNO-CCSD(T) correlation energies with at least triple-zeta quality basis sets for realistic three-dimensional molecules with more than 600 atoms and 12 000 basis functions in a matter of days on a single processor.

Basis set convergence of the binding energies of strongly hydrogen-bonded atmospheric clusters

We present the first binding energy benchmark set at the CBS limit of strongly hydrogen bonded atmospheric molecular clusters.