Accuracy of DLPNO–CCSD(T) Method for Noncovalent Bond Dissociation Enthalpies from Coinage Metal Cation Complexes

Assessing the domain-based local pair natural orbital (DLPNO) approximation for non-covalent interactions in sizable supramolecular complexes

The titular domain-based local pair natural orbital (DLPNO) approximation is the most widely used method for extending correlated wave function models to large molecular systems, yet its fidelity for intermolecular interaction energies in large supramolecular complexes has not been thoroughly vetted. Non-covalent interactions are sensitive to tails of the electron density and involve nonlocal dispersion that is discarded or approximated if the screening of pair natural orbitals (PNOs) is too aggressive. Meanwhile, the accuracy of the DLPNO approximation is known to deteriorate as molecular size increases. Here, we test the DLPNO approximation at the level of second-order Møller-Plesset perturbation theory (MP2) and coupled-cluster theory with singles, doubles, and perturbative triples [CCSD(T)] for a variety of large supramolecular complexes. DLPNO-MP2 interaction energies are within 3% of canonical values for small dimers with ≲10 heavy atoms, but for larger systems, the DLPNO approximation is often quite poor unless the results are extrapolated to the canonical limit where the threshold for discarding PNOs is taken to zero. Counterpoise correction proves to be essential in reducing errors with respect to canonical results. For a sequence of nanoscale graphene dimers up to (C96H24)2, extrapolated DLPNO-MP2 interaction energies agree with canonical values to within 1%, independent of system size, provided that the basis set does not contain diffuse functions; these cause the DLPNO approximation to behave erratically, such that results cannot be extrapolated in a meaningful way. DLPNO-CCSD(T) calculations are typically performed using looser PNO thresholds as compared to DLPNO-MP2, but this significantly impacts accuracy for large supramolecular complexes. Standard DLPNO-CCSD(T) settings afford errors of 2-6 kcal/mol for dimers involving coronene (C24H12) and circumcoronene (C54H18), even at the DLPNO-CCSD(T1) level.

Tunable molecular editing of indoles with fluoroalkyl carbenes

Building molecular complexity from simple feedstocks through precise peripheral and skeletal modifications is central to modern organic synthesis. Nevertheless, a controllable strategy through which both the core skeleton and the periphery of an aromatic heterocycle can be modified with a common substrate remains elusive, despite its potential to maximize structural diversity and applications. Here we report a carbene-initiated chemodivergent molecular editing of indoles that allows both skeletal and peripheral editing by trapping an electrophilic fluoroalkyl carbene generated in situ from fluoroalkyl N-triftosylhydrazones. A variety of fluorine-containing N-heterocyclic scaffolds have been efficiently achieved through tunable chemoselective editing reactions at the skeleton or periphery of indoles, including one-carbon insertion, C3 gem-difluoroolefination, tandem cyclopropanation and N1 gem-difluoroolefination, and cyclopropanation. The power of this chemodivergent molecular editing strategy has been highlighted through the modification of the skeleton or periphery of natural products in a controllable and chemoselective manner. The reaction mechanism and origins of the chemo- and regioselectivity have been probed by both experimental and theoretical methods.

Structure prediction of physiological bis(amino acidato)copper(II) species in aqueous solution: The copper(II) compounds with l-glutamine and l-histidine

Neutral (l-histidinato)(l-glutaminato)copper(II) [Cu(His)(Gln)] has been established as the most abundant ternary copper(II) amino acid compound of the exchangeable copper(II) pool in blood plasma. The experimental studies of Cu(His)(Gln) and bis(glutaminato)copper(II) [Cu(Gln)2] in solutions did not specify their complete geometries. To determine the geometries, this paper investigates the conformers, energy landscapes, and a structure-magnetic parameters relation of Cu(Gln)2 and Cu(His)(Gln) by the density functional theory (DFT) calculations. We assume a glycine-like coordination of Gln (other coordination patterns are dismissed because of steric reasons), and three His in-plane copper(II) binding modes. The conformational analyses are performed in the gas phase and implicitly modeled aqueous solution. The reliability of the DFT relative electronic and Gibbs free energies of the Cu(His)(Gln) conformers is confirmed by benchmarking against the corresponding energies obtained by the domain-based local pair natural orbital coupled-cluster method with singles, doubles, and perturbative triples [DLPNO-CCSD(T)]. Several cis- and trans-Cu(His)(Gln) conformers with His in the histaminate-like and glycine-like modes have low Gibbs free energies, and the greatest estimated metal-binding affinities. The DFT-calculated magnetic parameters of the low-energy conformers reproduce best the experimental electron paramagnetic resonance parameters measured in aqueous solutions for trans- and cis-Cu(Gln)2 conformers having two oxygen atoms (either from Gln or water molecules) at the apical positions, and Cu(His)(Gln) conformers having His in the histaminate-like mode with an apically placed carboxylato oxygen atom. The predicted conformational flexibility of His‑copper(II)-amino acid compounds may be connected with their physiological abundance, and the role in copper(II) exchange reactions in blood plasma.

Benchmarking Density Functional Theory Methods for Metalloenzyme Reactions: The Introduction of the MME55 Set

We present a new benchmark set of metalloenzyme model reaction energies and barrier heights that we call MME55. The set contains 10 different enzymes, representing eight transition metals, both open and closed shell systems, and system sizes of up to 116 atoms. We use four DLPNO-CCSD(T)-based approaches to calculate reference values against which we then benchmark the performance of a range of density functional approximations with and without dispersion corrections. Dispersion corrections improve the results across the board, and triple-ζ basis sets provide the best balance of efficiency and accuracy. Jacob's ladder is reproduced for the whole set based on averaged mean absolute (percent) deviations, with the double hybrids SOS0-PBE0-2-D3(BJ) and revDOD-PBEP86-D4 standing out as the most accurate methods for the MME55 set. The range-separated hybrids ωB97M-V and ωB97X-V also perform well here and can be recommended as a reliable compromise between accuracy and efficiency; they have already been shown to be robust across many other types of chemical problems, as well. Despite the popularity of B3LYP in computational enzymology, it is not a strong performer on our benchmark set, and we discourage its use for enzyme energetics.

Supramolecular Diversity, Theoretical Investigation and Antibacterial Activity of Cu, Co and Cd Complexes Based on the Tridentate N,N,O-Schiff Base Ligand Formed In Situ

The four new complexes, [Cu(HL¹)(L²)Cl] (1), [Cu(HL¹)(L¹)]∙Cl∙2H₂O (2), [Co(L¹)₂]∙Cl (3) and [Cd(HL¹)I₂]∙dmso (4), have been prepared by one-pot reactions of the respective chloride or iodide metal salt with a non-aqueous solution of the polydentate Schiff base, HL¹, resulted from in situ condensation of benzhydrazide and 2-pyridinecarboxaldehyde, while a ligand HL², in case of 1, has been formed due to the oxidation of 2-pyridinecarboxaldehyde under reaction conditions. The crystallographic analysis revealed that the molecular building units in 1-4 are linked together into complex structures by hydrogen bonding, resulting in 1D, 2D and 3D supramolecular architectures for 1, 2 and 4, respectively, and the supramolecular trimer for 3. The electronic structures of 1-4 were investigated by the DFT theoretical calculations. The non-covalent interactions in the crystal structures of 1-4 were studied by means of the Hirshfeld surface analysis and the QTAIM theory with a special focus on the C-H⋯Cl bonding. From the DFT/DLPNO-CCSD(T) calculations, using a series of charged model {R₃C-H}⁰⋯Cl^- assemblies, we propose linear regressions for assessment of the interaction enthalpy (ΔH, kcal mol^-1) and the binding energy (BE, kcal mol^-1) between {R₃C-H}⁰ and Cl^- sites starting from the electron density at the bond critical point (ρ(r_BCP), a.u.): ΔH = -678 × ρ(r) + 3 and BE = -726 × ρ(r) + 4. It was also has been found that compounds 1, 3 and 4 during in vitro screening showed an antibacterial activity toward the nine bacteria species, comprising both Gram-positive and Gram-negative, with MIC values ranging from 156.2 to 625 mg/L. The best results have been obtained against Acinetobacter baumannii MβL.

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.

A DLPNO-CCSD(T) benchmarking study of intermolecular interactions of ionic liquids

The accuracy of correlation energy recovered by coupled cluster single-, double-, and perturbative triple-excitations, CCSD(T), has led to the method being considered the gold standard of computational chemistry. The application of CCSD(T) has been limited to medium-sized molecular systems due to its steep scaling with molecular size. The recent development of alternative domain-based local pair natural orbital coupled-cluster method, DLPNO-CCSD(T), has significantly broadened the range of chemical systems to which CCSD(T) level calculations can be applied. Condensed systems such as ionic liquids (ILs) have a large contribution from London dispersion forces of up to 150 kJ mol^-1 in large-scale clusters. Ionic liquids show appreciable charge transfer effects that result in the increased valence orbital delocalization over the entire ionic network, raising the question whether the application of methods based on localized orbitals is reliable for these semi-Coulombic materials. Here the performance of DLPNO-CCSD(T) is validated for the prediction of correlation interaction energies of two data sets incorporating single-ion pairs of protic and aprotic ILs. DLPNO-CCSD(T) produced results within chemical accuracy with tight parameter settings and a non-iterative treatment of triple excitations. To achieve spectroscopic accuracy of 1 kJ mol^-1 , especially for hydrogen-bonded ILs and those containing halides, the DLPNO settings had to be increased by two orders of magnitude and include the iterative treatment of triple excitations, resulting in a 2.5-fold increase in computational cost. Two new sets of parameters are put forward to produce the performance of DLPNO-CCSD(T) within chemical and spectroscopic accuracy.

Theoretical investigation of the olefin cycle in H-SSZ-13 for the ethanol-to-olefins process using ab initio calculations and kinetic modeling

The formation of the hydrocarbon pool (HCP) in the ethanol-to-olefins (ETO) process catalyzed by H-SSZ-13 is studied in a kinetic model with ab initio computed reaction barriers.

Computational Protocol to Calculate the Phosphorescence Energy of Pt(II) Complexes: Is the Lowest Triplet Excited State Always Involved in Emission? A Comprehensive Benchmark Study

The reliable calculation of phosphorescence energies of phosphor materials is at the core of designing efficient phosphorescent organic light-emitting diodes (PhOLEDs). Therefore, it is of paramount importance to have a robust computational protocol to perform those calculations in a black-box manner. In this work, we use Domain-Based Local Pair Natural Orbital Coupled Cluster theory with single, double, and perturbative triple excitation (DLPNO-CCSD(T)) calculations to attain the phosphorescence energies of a large pool of Pt(II) complexes. Several approaches to incorporate relativistic effects in our calculations were tested. In addition, we have used the DLPNO-CCSD(T) values (i.e., our best theoretical values) to assess the performance of different flavors of density functional theory including pure, hybrid, meta-hybrid, and range-separated functionals. Among the tested functionals, the M06HF functional provides the best values compared with the DLPNO-CCSD(T) ones, with a mean absolute deviation (MAD) value of 0.14 eV. In its turn, and thanks to the increased accuracy achieved in the calculation of phosphorescence energies, we also demonstrate that not all of the investigated complexes emit from their lowest-lying triplet state (T₁). The outlier complexes include different complex photophysical scenarios and both Kasha and anti-Kasha types of complexes. Finally, we provide a general computational protocol to pre-screen whether T₁ is actually the emissive state and to accurately calculate the phosphorescence energies of Pt(II) complexes.

Assessing Density Functional Theory for Chemically Relevant Open-Shell Transition Metal Reactions

Due to the principle lack of systematic improvement possibilities of density functional theory, careful assessment of the performance of density functional approximations (DFAs) on well-designed benchmark sets, for example, for reaction energies and barrier heights, is crucial. While main-group chemistry is well covered by several available sets, benchmark data for transition metal chemistry is sparse. This is especially the case for larger, chemically relevant molecules. Addressing this issue, we recently introduced the MOR41 benchmark which covers chemically relevant reactions of closed-shell complexes. In this work, we extend these efforts to single-reference open-shell systems and introduce the "reactions of open-shell single-reference transition metal complexes" (ROST61) benchmark set. ROST61 includes accurate coupled-cluster reference values for 61 reaction energies with a mean reaction energy of -42.8 kcal mol^-1. Complexes with 13-93 atoms covering 20 d-block elements are included, but due to the restriction to single-reference open-shell systems, important elements such as iron or platinum could not be taken into account, or only to a small extent. We assess the performance of 31 DFAs in combination with three London dispersion (LD) correction schemes. Further, DFT-based composite methods, MP2, and a few semiempirical quantum chemical methods are evaluated. Consistent with the results for the MOR41 closed-shell benchmark, we find that the ordering of DFAs according to Jacob's ladder is preserved and that adding an LD correction is crucial, clearly improving almost all tested methods. The recently introduced r²SCAN-3c composite method stands out with a remarkable mean absolute deviation (MAD) of only 2.9 kcal mol^-1, which is surpassed only by hybrid DFAs with low amounts of Fock exchange (e.g., 2.3 kcal mol^-1 for TPSS0-D4/def2-QZVPP) and double-hybrid (DH) DFAs but at a significantly higher computational cost. The lowest MAD of only 1.6 kcal mol^-1 is obtained with the DH DFA PWPB95-D4 in the def2-QZVPP basis set approaching the estimated accuracy of the reference method. Overall, the ROST61 set adds important reference data to a sparsely sampled but practically relevant area of chemistry. At this point, it provides valuable orientation for the application and development of new DFAs and electronic structure methods in general.

DFT Functionals for Modeling of Polyethylene Chains Cross-Linked by Metal Atoms. DLPNO-CCSD(T) Benchmark Calculations

Density functional theory (DFT) functionals for calculations of binding energies (BEs) of the polyethylene (PE) chains cross-linked by selected metal atoms (M) are benchmarked against DLPNO-CCSD(T) and DLPNO-CCSD(T1) data. PEX-M-PEX complexes as compared with plain parallel PEX···PEX chains with X = 3-9 carbon atoms are model species characterized by a cooperative effect of covalent C-M-C bonds and interchain dispersion interactions. The accuracy of DLPNO-CC methods was assessed by a comparison of BEs with the canonical CCSD(T) results for small PE3-M-PE3 complexes. Functionals for PEX···PEX and closed-shell PEX-M-PEX complexes (M = Be, Mg, Zn) were benchmarked against DLPNO-CCSD(T) BEs; open-shell complexes (M = Li, Ag, Au) were benchmarked against the DLPNO-CCSD(T1) method with iterative triples. Three dispersion corrections were combined with 25 DFT functionals for calculations of BEs with respect to PEX-M and PEX fragments employing def2-TZVPP and def2-QZVPP basis sets. Accuracy to within 5% for the closed-shell PEX-M-PEX complexes was achieved with five functionals. Less accurate are functionals for the open-shell PEX-M-PEX complexes; only two functionals deviate by less than 15% from DLPNO-CCSD(T1). Particularly problematic were PEX-Li-PEX complexes. A reasonable overall performance across all complexes in terms of the mean absolute percentage error is found for the range-separated hybrid functionals ωB97X-D3 and CAM-B3LYP/D3(BJ)-ABC.

Revisiting stacking interactions in tetrathiafulvalene and selected derivatives using tight-binding quantum chemical calculations and local coupled-cluster method

The engineering of supramolecular architectures needs accurate descriptions of the intermolecular interactions in crystal structures. Tetrathiafulvalene (TTF) is an effective building block used in the construction of promising functional materials. The parallel packing of the neutral TTF-TTF system was studied previously using the high-level quantum chemical method, advancing it as a valuable model system. The recently developed tight-binding quantum chemical method GFN2-xTB and local coupled-cluster method DLPNO-CCSD(T) were used to investigate the stacking interactions of TTF and selected derivatives deposited in the Cambridge Structural Database. Using the interaction energy of the TTF-TTF dimer calculated at the CCSD(T)/CBS level as the reference, the accuracies of the two methods are investigated. The energy decomposition analysis within the DLPNO-CCSD(T) framework reveals the importance of dispersion interaction in the TTF-related stacking systems. The dispersion interaction density plot vividly shows the magnitude and distribution of the dispersion interaction, providing a revealing insight into the stacking interactions in crystal structures. The results show that the GFN2-xTB and DLPNO-CCSD(T) methods could achieve accuracy at an affordable computational cost, which would be valuable in understanding the nature of parallel stacking in supramolecular systems.

Mechanism for the Reaction of White Phosphorus with Cp2Cr2(CO)6 Leading Ultimately to the Triple-Decker Sandwich Cp2Cr2(μ-η5,η5-P5): A Theoretical Study

The experimentally known reaction of Cp₂Cr₂(CO)₆ with white phosphorus (P₄) to give CpCr(CO)₂(η³-P₃), Cp₂Cr₂(CO)₄(μ-η,²η²-P₂), and the triple-decker sandwich Cp₂Cr₂(μ-η,⁵η⁵-P₅) is of interest since the P₄ reactant having a tetrahedral cluster of four phosphorus atoms is converted to products having P₂, P₃, and P₅ ligands. The mechanism of this obviously complicated reaction can be dissected into three stages using a coupled cluster theoretical method that has been benchmarked with the P₂, Mn(CO)₅, and CpCr(CO)₃ dimerization processes. The first stage of the Cp₂Cr₂(CO)₆/P₄ reaction mechanism generates the unsaturated singlet intermediate Cp₂Cr₂(CO)₅ that combines with the P₄ reactant. Decarbonylation of the resulting Cp₂Cr₂(CO)₅(P₄) complex provides a singlet tetracarbonyl readily fragmenting into the stable triphosphacyclopropenyl complex CpCr(CO)₂(η³-P₃) and the chromium phosphide CpCr(CO)₂(P). The isomeric triplet tetracarbonyl Cp₂Cr₂(CO)₄(P₄), readily fragments into CpCr(CO)₂(η²-P₂), which can generate the stable diphosphaacetylene complex Cp₂Cr₂(CO)₄(η,²η²-P₂) as well as the pentamer [CpCr(CO)₂]₅(P₁₀). Combination of the coordinately unsaturated CpCr(CO)(η³-P₃) with CpCr(CO)₂(η²-P₂) can lead to a ring expansion. This generates the P₅ pentagonal ligand in a Cp₂Cr₂(CO)₃(P₅) precursor to the experimentally observed carbonyl-free triple-decker sandwich Cp₂Cr₂(μ-η,⁵η⁵-P₅) after three successive decarbonylations.

Selective Oxidation of 5-Hydroxymethylfurfural to 2,5-Diformylfuran by Visible Light-Driven Photocatalysis over In Situ Substrate-Sensitized Titania

Solar energy-driven processes for biomass valorization are priority for the growing industrialized society. To address this challenge, efficient visible light-active photocatalyst for the selective oxidation of biomass-derived platform chemical is highly desirable. Herein, selective oxidation of 5-hydroxymethylfurfural (HMF) to 2,5-diformylfuran (DFF) was achieved by visible light-driven photocatalysis over titania. Pristine titania is photocatalytically inactive under visible light, so an unconventional approach was employed for the visible light (λ=515 nm) sensitization of titania via a formation of a visible light-absorbing complex of HMF (substrate) on the titania surface. Surface-complexation of HMF on titania mediated ligand-to-metal charge transfer (LMCT) under visible light, which efficiently catalyzed the oxidation of HMF to DFF. A high DFF selectivity of 87 % was achieved with 59 % HMF conversion after 4 h of illumination. The apparent quantum yield obtained for DFF production was calculated to be 6.3 %. It was proposed that the dissociative interaction of hydroxyl groups of HMF and the titania surface is responsible for the surface-complex formation. When the hydroxyl groups of titania were modified via surface-fluorination or calcination the oxidation of HMF was inhibited under visible light, signifying that hydroxyl groups are decisive for photocatalytic activity.

Theoretical study on conformational energies of transition metal complexes

Conformational energies are an important chemical property for which a performance assessment of theoretical methods is mandatory. Existing benchmark sets are often limited to biochemical or main group element containing molecules, while organometallic systems are generally less studied. A key problem herein is to routinely generate conformers for these molecules due to their complexity and manifold of possible coordination patterns. In this study we used our recently published CREST protocol [Pracht et al., Phys. Chem. Chem. Phys., 2020, 22, 7169-7192] to generate conformer ensembles for a variety of 40 challenging transition metal containing molecules, which were then used to form a comprehensive conformational energy benchmark set termed TMCONF40. Several low-cost semiempirical, density functional theory (DFT) and force-field methods were compared to high level DLPNO-CCSD(T1) and double-hybrid DFT reference values. Close attention was paid to the energetic ordering of the conformers in the statistical evaluation. With respect to the double-hybrid references, both tested low-cost composite DFT methods produce high Pearson correlation coefficients of rp,mean,B97-3c//B97-3c = 0.922 and rp,mean,PBEh-3c//B97-3c = 0.890, with mean absolute deviations close to or below 1 kcal mol-1. This good performance also holds for a comparison to DLPNO-CCSD(T1) reference energies for a smaller subset termed TMCONF5. Based on DFT geometries, the GFNn-xTB methods yield reasonable Pearson correlation coefficients of rp,mean,GFN1-xTB//B97-3c = 0.617 (MADmean = 2.15 kcal mol-1) and rp,mean,GFN2-xTB//B97-3c = 0.567 (MADmean = 2.68 kcal mol-1), outperforming the widely used PMx methods on the TMCONF40 test set. Employing the low-cost composite DFT method B97-3c on GFN2-xTB geometries yields an slightly improved correlation of rp,mean,B97-3c//GFN2-xTB = 0.632. Furthermore, for 68% of the investigated complexes at least one low-energy conformer was found that is more stable than the respective crystal structure conformation, which signals the importance of conformational studies. General recommendations for the application of the CREST protocol and DFT methods for transition metal conformational energies are given.

Theoretical investigation of the side-chain mechanism of the MTO process over H-SSZ-13 using DFT and ab initio calculations

The side-chain mechanism of the methanol-to-olefins process over the H-SSZ-13 acidic zeolite was investigated using periodic density functional theory with corrections from highly accurate ab intio calculations on large cluster models.

Ambiguities in solvation free energies from cluster-continuum quasichemical theory: lithium cation in protic and aprotic solvents

Gibbs free energies for Li+ solvation in water, methanol, acetonitrile, DMSO, dimethylacetamide, dimethoxyethane, dimethylformamide, gamma-butyrolactone, pyridine, and sulfolane have been calculated using the cluster-continuum quasichemical theory. With n independent solvent molecules S initial state forming the "monomer" thermodynamic cycle, Li+ solvation free energies are found to be on average 14 kcal mol-1 more positive compared to those from the "cluster" thermodynamic cycle where the initial state is the cluster Sn. We ascribe the inconsistency between the "monomer" and "cluster" cycles mainly to the incorrectly predicted solvation free energies of solvent clusters Sn from the SMD and CPCM continuum solvation models, which is in line with the earlier study of Bryantsev et al., J. Phys. Chem. B, 2008, 112, 9709-9719. When experimental-based solvation free energies of individual solvent molecules and solvent clusters are employed, the "monomer" and "cluster" cycles result in identical numbers. The best overall agreement with experimental-based "bulk" scale lithium cation solvation free energies was obtained for the "monomer" scale, and we recommend this set of values. We expect that further progress in the field is possible if (i) consensus on the accuracy of experimental reference values is achieved; (ii) the most recent continuum solvation models are properly parameterized for all solute-solvent combinations and become widely accessible for testing.

Basis set extrapolation in pair natural orbital theories

We present the results of a benchmark study of the effect of Pair Natural Orbital (PNO) truncation errors on the performance of basis set extrapolation. We find that reliable conclusions from the application of Helgaker's extrapolation method are only obtained when using tight PNO thresholds of at least 10^-7. The use of looser thresholds introduces a significant risk of observing a false basis set convergence and underestimating the residual basis set errors. We propose an alternative extrapolation approach based on the PNO truncation level that only requires a single basis set and show that it is a viable alternative to hierarchical basis set extrapolation methods.

Bootstrap Embedding For Large Molecular Systems

Recent developments in quantum embedding theories have provided attractive approaches to correlated calculations for large systems. In this work, we extend our previous work [J. Chem. Theory Comput. 2019, 15, 4497-4506; J. Phys. Chem. Lett. 2019, 10, 6368-6374] on bootstrap embedding (BE) to enable correlated ab initio calculations at the coupled cluster with singles and doubles (CCSD) level for large molecules. We introduce several new algorithmic developments that significantly reduce the computational cost of BE, while maintaining its accuracy. The resulting implementation scales as O(N³) for the integral transform and O(N) for the CCSD calculation. Numerical results on a series of conjugated molecules suggest that BE with reasonably sized fragments can recover more than 99.5% of the total correlation energy of a full CCSD calculation, while the required computational resources (time and storage) compare favorably to one popular local correlation scheme: domain localized pair natural orbital (DLPNO). The largest BE calculation in this work involves ∼2900 basis functions and can be performed on a single node with 16 CPU cores and 64 GB of memory in a few days. We anticipate that these developments represent an important step toward the application of BE to solve practical problems.

Toward Simple, Predictive Understanding of Protein-Ligand Interactions: Electronic Structure Calculations on Torpedo Californica Acetylcholinesterase Join Forces with the Chemist's Intuition

Contemporary efforts for empirically-unbiased modeling of protein-ligand interactions entail a painful tradeoff - as reliable information on both noncovalent binding factors and the dynamic behavior of a protein-ligand complex is often beyond practical limits. We demonstrate that information drawn exclusively from static molecular structures can be used for reproducing and predicting experimentally-measured binding affinities for protein-ligand complexes. In particular, inhibition constants (Ki) were calculated for seven different competitive inhibitors of Torpedo californica acetylcholinesterase using a multiple-linear-regression-based model. The latter, incorporating five independent variables - drawn from QM cluster, DLPNO-CCSD(T) calculations and LED analyses on the seven complexes, each containing active amino-acid residues found within interacting distance (3.5 Å) from the corresponding ligand - is shown to recover 99.9% of the sum of squares for measured Ki values, while having no statistically-significant residual errors. Despite being fitted to a small number of data points, leave-one-out cross-validation statistics suggest that it possesses surprising predictive value (Q2LOO=0.78, or 0.91 upon removal of a single outlier). This thus challenges ligand-invariant definitions of active sites, such as implied in the lock-key binding theory, as well as in alternatives highlighting shape-complementarity without taking electronic effects into account. Broader implications of the current work are discussed in dedicated appendices.

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.

Toward a less costly but accurate calculation of the CCSD(T)/CBS noncovalent interaction energy

The popular method of calculating the noncovalent interaction energies at the coupled-cluster single-, double-, and perturbative triple-excitations [CCSD(T)] theory level in the complete basis set (CBS) limit was to add a CCSD(T) correction term to the CBS second-order Møller-Plesset perturbation theory (MP2). The CCSD(T) correction term is the difference between the CCSD(T) and MP2 interaction energies evaluated in a medium basis set. However, the CCSD(T) calculations with the medium basis sets are still very expensive for systems with more than 30 atoms. Comparatively, the domain-based local pair natural orbital coupled-cluster method [DLPNO-CCSD(T)] can be applied to large systems with over 1,000 atoms. Considering both the computational accuracy and efficiency, in this work, we propose a new scheme to calculate the CCSD(T)/CBS interaction energies. In this scheme, the MP2/CBS term keeps intact and the CCSD(T) correction term is replaced by a DLPNO-CCSD(T) correction term which is the difference between the DLPNO-CCSD(T) and DLPNO-MP2 interaction energies evaluated in a medium basis set. The interaction energies of the noncovalent systems in the S22, HSG, HBC6, NBC10, and S66 databases were recalculated employing this new scheme. The consistent and tight settings of the truncation parameters for DLPNO-CCSD(T) and DLPNO-MP2 in this noncanonical CCSD(T)/CBS calculations lead to the maximum absolute deviation and root-mean-square deviation from the canonical CCSD(T)/CBS interaction energies of less than or equal to 0.28 kcal/mol and 0.09 kcal/mol, respectively. The high accuracy and low cost of this new computational scheme make it an excellent candidate for the study of large noncovalent systems.

Homolytic Versus Heterolytic Bond Breaking in Functionalized [R-C20 H10 ]+ Systems

The comprehensive theoretical investigation of stability of functionalized corannulene cations [R-C₂₀ H₁₀ ]⁺ with respect to two alternative bond-breaking mechanisms, namely, homolytic or radical ([R-C₂₀ H₁₀ ]⁺  → R^•  + C₂₀ H₁₀ ^+• ) and heterolytic or cationic ([R-C₂₀ H₁₀ ]⁺  → R⁺  + C₂₀ H₁₀ ), was accomplished. The special focus was on the influence of the nature of R-group on the energetics of the bond cleavage. Detailed study of energetics of both mechanisms has revealed that the systems with small alkyl groups such as methyl tend to undergo bond breaking in accordance with homolytic mechanism. Subsequent elongation of the chain of the R-group resulted in shifting the paradigm, making heterolytic path more energetically favorable. Subsequent analysis of different components of the bonding between R-group and corannulene polyaromatic core helped to shed light on trends observed. In both mechanisms, the covalent contribution was found to be dominating, whereas ionic part contributes ~25-27%. Two leading components of ΔE_orb , C₂₀ H₁₀ → R and R → C₂₀ H₁₀ , were identified with NOCV-EDA approach. While the homolytic pathway is best described as R → C₂₀ H₁₀ process, the heterolytic mechanism shows domination of the C₂₀ H₁₀ → R term. Surprisingly, the preparation energy (ΔE_prep ) was identified as a key player in stability tendencies found. In other words, the relative stability of corresponding molecular fragments (here R-groups as the corannulene fragment remains the same for all systems) in their cationic or radical forms determine the preference given to a specific bond breaking path and, as consequence, the total stability of target functionalized cations. These conclusions were further confirmed by extending a set of R-groups to conjugated (allyl, phenyl), bulky (iPr, tBu), β-silyl (CH₂ SiH₃ , CH₂ SiMe₃ ), and benzyl (CH₂ Ph) groups. © 2019 Wiley Periodicals, Inc.

Principal Domains in Local Correlation Theory

The computational efficiency of local correlation methods is strongly dependent on the size of the domain of functions used to expand local correlating orbitals such as orbital specific or pair natural orbitals. Here, we define a principal domain of order m as the subset of m one-particle functions that provides the best support for a given n-electron wave function by maximizing the partial trace of the one-body reduced density matrix. Principal domains maximize the overlap between the wave function and its approximant for two-electron systems and are the domain selection equivalent of Löwdin's natural orbitals. We present an efficient linear scaling greedy algorithm for obtaining principal domains of projected atomic orbitals and demonstrate its utility in the context of the pair natural orbital local correlation theory. We numerically determine thresholds such that the projected atomic orbital domain error is an order of magnitude smaller than the pair natural orbital truncation error.

Superhalogen and Superacid

A superhalogen F@C₂₀ (CN)₂₀ and a corresponding Brønsted superacid were designed and investigated on DFT and DLPNO-CCSD(T) levels of theory. Calculated compounds have outstanding electron affinity and deprotonation energy, respectively. We consider superacid H[F@C₂₀ (CN)₂₀ ] to be able to protonate molecular nitrogen. The stability of these structures is discussed, while some of the previous predictions concerning neutral Brønsted superacids of record strength are doubted. © 2019 Wiley Periodicals, Inc.

Modulation of Gas-Phase Lithium Cation Basicities by Microsolvation

In contrast to the extensive knowledge of lithium cation affinities and basicities, the thermochemistry of microsolvated lithium cations is much less explored. Here, we determine the relative stabilities of Li(A,B)_n⁺ complexes, n = 2 and 3, by monitoring their gas-phase reactions with A and B substrate molecules, A/B = Me₂O, Et₂O, tetrahydrofuran, and MeCN, in a three-dimensional quadrupole-ion trap mass spectrometer. Kinetic analysis of the observed ligand displacement reactions affords equilibrium constants, which are then converted into Gibbs reaction energies. In addition, we use high-level quantum chemical calculations to predict the structures and sequential ligand dissociation energies of the homoleptic Li(A)_n⁺ complexes, n = 1-3. As expected, the ligands dissociate more easily from complexes in higher coordination states. However, the very nature of the ligand also matters. Ligands with different steric demands can, thus, invert their relative Li⁺ affinities depending on the coordination state of the metal center. This finding shows that microsolvation of Li⁺ can result in specific effects, which are not recognized if the analysis takes into account only simple lithium cation affinities and basicities.

Catalytic synthesis of 9-cis-retinoids: mechanistic insights

The regioselective Z-isomerization of thermodynamically stable all-trans retinoids remains challenging, and ultimately limits the availability of much needed therapeutics for the treatment of human diseases. We present here a novel, straightforward approach for the catalytic Z-isomerization of retinoids using conventional heat treatment or microwave irradiation. A screen of 20 transition metal-based catalysts identified an optimal approach for the regioselective production of Z-retinoids. The most effective catalytic system was comprised of a palladium complex with labile ligands. Several mechanistic studies, including isotopic H/D exchange and state-of-the-art quantum chemical calculations using coupled cluster methods indicate that the isomerization is initiated by catalyst dimerization followed by the formation of a cyclic, six-membered chloropalladate catalyst-substrate adduct, which eventually opens to produce the desired Z-isomer. The synthetic development described here, combined with thorough mechanistic analysis of the underlying chemistry, highlights the use of readily available transition metal-based catalysts in straightforward formats for gram-scale drug synthesis.

Perturbative triples correction to domain-based local pair natural orbital variants of Mukherjee's state specific coupled cluster method

In this article we report an implementation of the perturbative triples correction to Mukherjee's state-specific multireference coupled cluster method based on the domain-based pair natural orbital approach (DLPNO-MkCC). We tested the performance of DLPNO-MkCCSD(T) in calculations involving tetramethyleneethane and isomers of naphthynes. These tests show that more than 97% of triples energy was recovered with respect to the canonical MkCCSD(T) method, which together with the DLPNO-MkCCSD part accounts for about 99.70-99.85% of the total correlation energy. The applicability of the method was demonstrated on calculations of singlet-triplet gaps for several large systems: triangulene, dynemicin A, and a beryllium complex.

Computational Approach to Molecular Catalysis by 3d Transition Metals: Challenges and Opportunities

Computational chemistry provides a versatile toolbox for studying mechanistic details of catalytic reactions and holds promise to deliver practical strategies to enable the rational in silico catalyst design. The versatile reactivity and nontrivial electronic structure effects, common for systems based on 3d transition metals, introduce additional complexity that may represent a particular challenge to the standard computational strategies. In this review, we discuss the challenges and capabilities of modern electronic structure methods for studying the reaction mechanisms promoted by 3d transition metal molecular catalysts. Particular focus will be placed on the ways of addressing the multiconfigurational problem in electronic structure calculations and the role of expert bias in the practical utilization of the available methods. The development of density functionals designed to address transition metals is also discussed. Special emphasis is placed on the methods that account for solvation effects and the multicomponent nature of practical catalytic systems. This is followed by an overview of recent computational studies addressing the mechanistic complexity of catalytic processes by molecular catalysts based on 3d metals. Cases that involve noninnocent ligands, multicomponent reaction systems, metal-ligand and metal-metal cooperativity, as well as modeling complex catalytic systems such as metal-organic frameworks are presented. Conventionally, computational studies on catalytic mechanisms are heavily dependent on the chemical intuition and expert input of the researcher. Recent developments in advanced automated methods for reaction path analysis hold promise for eliminating such human-bias from computational catalysis studies. A brief overview of these approaches is presented in the final section of the review. The paper is closed with general concluding remarks.

A noncovalent interaction insight onto the concerted metallation deprotonation mechanism

The CMD/AMLA mechanisms of cyclopalladation and the parent fictitious cyclonickelation of N,N-dimethylbenzylamine have been investigated by joint DFT-D and DLPNO-CCSD(T) methods assisted by QTAIM.

Bond dissociation energies of carbonyl gold complexes: a new descriptor of ligand effects in gold(i) complexes?

Ligand electronic effects in gold(i) chemistry have been evaluated by means of the experimental determination of M-CO bond dissociation energies for 16 [L-Au-CO]⁺ complexes, bearing L ligands widely used in gold catalysis. Energy-resolved analyses have been made using tandem mass spectrometry with collision-induced dissociation. Coupled with DFT calculations, this approach enables the quantification of ligand effects based on the LAu-CO bond strength. A further energy decomposition analysis gives access to detailed insights into this bond's characteristics. Whereas small differences are observed between phosphine- and phosphite-containing gold complexes, carbene ligands are shown to stabilize the gold-carbonyl bond much more efficiently.