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High-order quantum chemistry is applied to hydrogen-bonded natural DNA nucleobase pairs [adenine:thymine (A:T) and guanine:cytosine (G:C)] and non-natural Hachimoji nucleobase pairs [isoguanine:1-methylcytosine (B:S) and 2-aminoimidazo[1,2a][1,3,5]triazin-4(1H)-one:6-amino-5-nitropyridin-2-one (P:Z)] to see how the intermolecular interaction energies and their energetic components (electrostatics, exchange-repulsion, induction/polarization, and London dispersion interactions) vary among the base pairs. We examined the Hoogsteen (HG) geometries in addition to the traditional Watson–Crick (WC) geometries. Coupled-cluster theory through perturbative triples [CCSD(T)] extrapolated to the complete basis set (CBS) limit and high-order symmetry-adapted perturbation theory (SAPT) at the SAPT2+(3)(CCD)δMP2/aug-cc-pVTZ level are used to estimate highly accurate noncovalent interaction energies. Electrostatic interactions are the most attractive component of the interaction energies, but the sum of induction/polarization and London dispersion is nearly as large, for all base pairs and geometries considered. Interestingly, the non-natural Hachimoji base pairs interact more strongly than the corresponding natural base pairs, by −21.8 (B:S) and −0.3 (P:Z) kcal mol–1in the WC geometries, according to CCSD(T)/CBS. This is consistent with the H-bond distances being generally shorter in the non-natural base pairs. The natural base pairs are energetically more stabilized in their Hoogsteen geometries than in their WC geometries. The Hoogsteen geometry makes the A:T base pair slightly more stable, by −0.8 kcal mol–1, and it greatly stabilizes the G:C+base pair, by −15.3 kcal mol–1. The G:C+stabilization is mainly due to the fact that C has typically added a proton when found in Hoogsteen geometries. By contrast, Hoogsteen geometries are substantially less favorable than WC geometries for non-natural Hachimoji base pairs, by 17.3 (B:S) and 13.8 (P:Z) kcal mol–1.

Organic radicals are unstable and stable radicals usually display non-luminescent properties. Luminescent radicals possess the all-in-one properties of optoelectronics, electronics, and magnetics. To date, the reported structures of luminescent radicals are limited to triphenylmethyl radical derivatives and their analogues, which are stabilized with extended π-conjugation. Here, we demonstrate the first example of a nonconjugated luminescent radical. In spite of the lack of delocalized π-stabilization, the radical polymer readily emits red luminescence in the solid state. A traditional luminescent quencher, 2,2,6,6-tetramethylpiperidin-1-yl turned into a red chromophore when grafted onto a polymer backbone. Experimental data confirm that the emission is associated with the nitroxide radicals and is also affected by the packing of the polymer. This work discloses a novel class of luminescent radicals and a distinctive pathway for luminescence from open-shell materials.

Nucleobase mimicking small molecules able to reconfigure DNA are a recently discovered strategy that promises to extend the structural and functional diversity of nucleic acids. However, only simple, unfunctionalized molecules such as cyanuric acid and melamine have so far been used in this approach. In this work, we show that the addition of substituted cyanuric acid molecules can successfully program polyadenine strands to assemble into supramolecular fibers. Unlike conventional DNA nanostructure functionalization, which typically end-labels DNA strands, our approach incorporates functional groups into DNA with high density using small molecules and results in new DNA triple helices coated with alkylamine or alcohol units that grow into micrometer-long fibers. We find that small changes in the small molecule functional group can result in large structural and energetic variation in the overall assembly. A combination of circular dichroism, atomic force microscopy, molecular dynamics simulations, and a new thermodynamic method, transient equilibrium mapping, elucidated the molecular factors behind these large changes. In particular, we identify substantial DNA sugar and phosphate group deformations to accommodate a hydrogen bond between the phosphate and the small-molecule functional groups, as well as a critical chain length of the functional group which switches this interaction from intra- to interfiber. These parameters allow the controlled formation of hierarchical, hybrid DNA assemblies simply through the addition and variation of small, functionalized molecules.

Aqueous solutions of equimolar mixtures of 2,4,6-triaminopyrimidine (TAP) and carboxylic acid substituted cyanuric acid (CyCo6 or R-4MeCyCo6) monomers self-assemble into gel-forming supramolecular polymers. Macroscopic fibers drawn from these mixtures were analyzed by X-ray diffraction to determine their molecular structures. Computational methods were used to explore the intrinsic intermolecular interactions that contribute to the structure and stability of these assemblies. Both polymers are formed by the stacking of hexameric rosettes, (TAP/CyCo6)3or (TAP/R-4MeCyCo6)3, respectively, into long, stiff, twisted stacks of essentially planar rosettes. Chiral, left-handed supramolecular polymers with a helical twist angle of −26.7° per hexad are formed when the pure enantiomer R-4MeCyCo6 is used. These hexad stacks pack into bundles with a hexagonal crystalline lattice organization perpendicular to the axis of the macroscopic fiber. Polymers formed from TAP and CyCo6, both of which are achiral, assemble into macroscopic domains that are packed as a centered rectangular lattice. Within these domains, the individual polymers exist as either right-handed or left-handed helical stacks, with twist angles of +15° or −15° per hexad, respectively. The remarkable ability of TAP and cyanuric acid derivatives to self-assemble in water, and the structural features of their supramolecular polymers reported here, provide additional support for the proposal that these heterocycles could have served as recognition units for an early form of nucleic acids, before the emergence of RNA.

Atomic charges are critical quantities in molecular mechanics and molecular dynamics, but obtaining these quantities requires heuristic choices based on atom typing or relatively expensive quantum mechanical computations to generate a density to be partitioned. Most machine learning efforts in this domain ignore total molecular charges, relying on overfitting and arbitrary rescaling in order to match the total system charge. Here, we introduce the electron-passing neural network (EPNN), a fast, accurate neural network atomic charge partitioning model that conserves total molecular charge by construction. EPNNs predict atomic charges very similar to those obtained by partitioning quantum mechanical densities but at such a small fraction of the cost that they can be easily computed for large biomolecules. Charges from this method may be used directly for molecular mechanics, as features for cheminformatics, or as input to any neural network potential.

Noncovalent interactions play a significant role in determining the structures of DNA, RNA, and proteins. Among the most prevalent are π−π interactions, which occur as favorable forces between the aromatic subunits of biochemical molecules. The aromatic side chains of amino acids tryptophan and phenylalanine are commonly modeled with indole and benzene, respectively. We have utilized the MP2 and SCS-MP2 methods with the aug-cc-pVDZ basis set to compute several T-shaped interaction energies and parallel displaced (PD) three-dimensional potential energy surfaces (PESs) at 3.4, 3.6, and 3.8 Å vertical separations. At selected minima, CCSD(T) results extrapolated to the complete-basis-set (CBS) limit were obtained. The trend of the T-shaped interactions has been rationalized by considering electrostatic potential maps and symmetry-adapted perturbation theory (SAPT) results. The global minimum has been verified to be the N−H/π T-shaped configuration with a CCSD(T)/CBS interaction energy of −5.62 kcal mol−1. For the PD PESs, the MP2 and SCS-MP2 methods predict different minimum configurations. The CCSD(T) method favors the SCS-MP2 PD configuration over the MP2 PD configuration by 0.18 kcal mol−1. Among the approximate methods considered here, the SCS-CCSD method extrapolated to the CBS limit incurs only around 2% error compared to CCSD(T)/CBS results and is the most reliable for the interaction energies of the indole−benzene complex. Overall, the extension of aromaticity and the highly positive hydrogen of the N−H bond, both exhibited by indole, enhance the strength of nonbonded interactions with benzene compared to those in the benzene dimer or in the pyridine-benzene complex.

The protein–ligand binding free energy is a central quantity in structure-based computational drug discovery efforts. Although popular alchemical methods provide sound statistical means of computing the binding free energy of a large breadth of systems, they are generally too costly to be applied at the same frequency as end point or ligand-based methods. By contrast, these data-driven approaches are typically fast enough to address thousands of systems but with reduced transferability to unseen systems. We introduce DrΔG-Net (or simply Dragnet), an equivariant graph neural network that can blend ligand-based and protein–ligand data-driven approaches. It is based on a 3D fingerprint representation of the ligand alone and in complex with the protein target. Dragnet is a global scoring function to predict the binding affinity of arbitrary protein–ligand complexes, but can be easily tuned via transfer learning to specific systems or end points, performing similarly to common 2D ligand-based approaches in these tasks. Dragnet is evaluated on a total of 28 validation proteins with a set of congeneric ligands derived from the Binding DB and one custom set extracted from the ChEMBL Database. In general, a handful of experimental binding affinities are sufficient to optimize the scoring function for a particular protein and ligand scaffold. When not available, predictions from physics-based methods such as absolute free energy perturbation can be used for the transfer learning tuning of Dragnet. Furthermore, we use our data to illustrate the present limitations of data-driven modeling of binding free energy predictions.

The field of organic electronics aspires to enable the fabrication of low-cost, solution-processed optoelectronic devices with unique mechanical, electrical, optical, and chemical properties. Critical to the success of these aspirations is the ability to fabricate controlled doping profiles vertically or laterally (i.e., to a limited depth or area extension). However, the fabrication of stable doping profiles in polymer films has proven particularly challenging, as neither solution processing nor evaporation of dopants, such as 2,3,5,6-tetrafluoro-7,7,8,8-tetracyanoquinodimethane (F4TCNQ), leads to vertical doping profiles due to fast diffusion on the length scale of the typical film thickness (∼100 nm). This challenge was surmounted in 2017 with the first demonstration of a successful solution-based technique to fabricate doping profiles in semiconducting polymer films through immersion into a phosphomolybdic acid (PMA) solution (Kolesov et al., 2017). Still, to date, no clear picture that explains the doping phenomena has emerged. In an attempt to identify some of the key variables that govern the PMA doping process and shed light onto why this technique produces vertical doping profiles in organic films, we here report on a study of the morphology of PMA doped semiconducting polymer films, complemented theoretically with ab initio quantum chemistry calculations. We believe these results may foster the extension of the technique to other organic optoelectronic systems.

Proton transfer using water bridges has been observed in bulk water, acid-base reactions, and several proton-translocating biological systems. In the photosynthetic water-oxidizing enzyme, photosystem II (PSII), protons from substrate water are transferred 35 Å from the Mn4CaO5catalytic site to the chloroplast lumen. This process leads to acidification of the lumen and ATP synthesis. Water oxidation occurs in a flash-induced, five-step Snstate cycle; acetate is a chloride-dependent inhibitor of the S2to S3step of this cycle. Here, we study the effect of acetate on a previous step of the cycle, the S1to S2transition, using reaction-induced infrared spectroscopy. PSII was isolated from spinach, and experiments were conducted at pH 7.5, using 532 nm laser flashes to advance the cycle from the dark-adapted state S1to the S2state. Isotope-editing of acetate reveals direct contributions to the S2-minus-S1infrared spectrum consistent with protonation of bound acetate in PSII. In the acetate-derived S2-minus-S1PSII spectra, an accompanying decrease in the intensity of a 2830 cm–1band is observed when compared to the chloride control. The 2830 cm–1band has been assigned previously to a stretching vibration of an internal, hydrated hydronium ion, Wn+. Density functional studies of a catalytic site model predict the spontaneous transfer of a proton from this internal hydronium ion to acetate, when acetate is substituted at a chloride-binding site. Taken together, the results show that the mechanism of PSII proton transfer at pH 7.5 involves proton hopping through an internal, water-containing network.

A comprehensive experimental survey consisting of 36 molecular balances was conducted to compare 18 pairs of S-π versus O-π interactions over a wide range of structural, geometric, and solvent parameters. A strong linear correlation was observed between the folding energies of the sulfur and oxygen balances across the entire library of balance pairs. The more stable interaction systematically switched from the O-π to S-π interaction. Computational studies of bimolecular PhSCH3-arene and PhOCH3-arene complexes were able to replicate the experimental trends in the molecular balances. The change in preference for the O-π to S-π interaction was due to the interplay of stabilizing (dispersion and solvophobic) and destabilizing (exchange-repulsion) terms arising from the differences in size and polarizability of the oxygen and sulfur atoms.

Psi4NumPydemonstrates the use of efficient computational kernels from the open-source Psi4 program through the popular NumPylibrary for linear algebra in Python to facilitate the rapid development of clear, understandable Python computer code for new quantum chemical methods, while maintaining a relatively low execution time. Using these tools, reference implementations have been created for a number of methods, including self-consistent field (SCF), SCF response, many-body perturbation theory, coupled-cluster theory, configuration interaction, and symmetry-adapted perturbation theory. Furthermore, several reference codes have been integrated into Jupyter notebooks, allowing background, underlying theory, and formula information to be associated with the implementation. Psi4NumPytools and associated reference implementations can lower the barrier for future development of quantum chemistry methods. These implementations also demonstrate the power of the hybrid C++/Python programming approach employed by the Psi4 program.

We explore the suitability of three popular density functionals (B97-D3, B3LYP-D3, M05-2X) for producing accurate equilibrium geometries of van der Waals (vdW) complexes with diverse binding motifs. For these functionals, optimizations using Dunning’s aug-cc-pVDZ basis set best combine accuracy and a reasonable computational expense. Each DFT/aug-cc-pVDZ combination produces optimized equilibrium geometries for 21 small vdW complexes of organic molecules (up to four non-hydrogen atoms total) that agree with high-level CCSD(T)/CBS reference geometries to within ±0.1 Å for the averages of the center-of-mass displacement and the mean least root-mean-squared displacement. The DFT/aug-cc-pVDZ combinations are also able to reproduce the optimal center-of-mass displacements interpolated from CCSD(T)/CBS radial potential energy surfaces in both NBC7x and HBC6 test sets to within ±0.1 Å. We therefore conclude that each of these denisty functional methods, together with the aug-cc-pVDZ basis set, is suitable for producing equilibrium geometries of generic nonbonded complexes.

Fragment-based methods promise accurate energetics at a cost that scales linearly with the number of fragments. This promise is founded on the premise that the many-body expansion (or another similar energy decomposition) needs to only consider spatially local many-body interactions. Experience and chemical intuition suggest that typically at most four-body interactions are required for high accuracy. Bettens and co-workers [J. Chem. Theory Comput.20149, 3699—3707] published a detailed study showing that for moderately sized water clusters, basis set superposition error (BSSE) undermines this premise. Ultimately, they were able to overcome BSSE by performing all computations in the supersystem basis set, but such a solution destroys the reduced computational scaling of fragment-based methods. Their findings led them to suggest that there is “trouble with the many-body expansion”. Since then, a subsequent follow-up study from Bettens and co-workers [J. Chem. Theory. Comput. 2015, 11, 5132–5143] as well as a related study by Mayer and Bakó [J. Chem. Theory Comput. 2017, 13, 1883—1886] have proposed new frameworks for understanding BSSE in the many-body expansion. Although the two frameworks ultimately propose the same working set of equations to the BSSE problem, their interpretations are quite different, even disagreeing on whether or not the solution is an approximation. In this work we propose a more general BSSE framework. We then show that, somewhat paradoxically, the two interpretations are compatible and amount to two different “normalization” conditions. Finally, we consider applications of these BSSE frameworks to small water clusters, where we focus on replicating high-accuracy coupled cluster benchmarks. Ultimately, we show for water clusters, using the present framework, that one can obtain results that are within ±0.5 kcal mol–1of the coupled cluster complete basis set limit without considering anymore than a correlated three-body computation in a quadruple-ζ basis set and a four-body triple-ζ Hartree–Fock computation.

Distinguishing the functionality of C–H···O hydrogen bonds (HBs) remains challenging, because their properties are difficult to quantify reliably. Herein, we present a study of the model methane–formaldehyde complex (MFC). Six stationary points on the MFCpotential energy surface (PES) were obtained at the CCSD(T)/ANO2 level. The CCSDT(Q)/CBS interaction energies of the conformers range from only −1.12 kcal mol–1to −0.33 kcal mol–1, denoting a very flat PES. Notably, only the lowest energy stationary point (MFC1) corresponds to a genuine minimum, whereas all other stationary pointsincluding the previously studied ideal case of ae(C–H···O) = 180°exhibit some degree of freedom that leads to MFC1. Despite the flat PES, we clearly see that the HB properties of MFC1align with those of the prototypical water dimer O–H···O HB. Each HB property generally becomes less prominent in the higher-energy conformers. Only the MFC1conformer prominently exhibits (1) elongated C–H donor bonds, (2) attractive C–H···OC interactions, (3) n(O) → σ*(C–H) hyperconjugation, (4) critical points in the electron density from Bader’s method and from the noncovalent interactions method, (5) positively charged donor hydrogen, and (6) downfield NMR chemical shifts and nonzero 2J(CM–HM···OF) coupling constants. Based on this research, some issues merit further study. The flat PES hinders reliable determinations of the HB-induced shifts of the C–H stretches; a similarly difficult challenge is observed for the experiment. The role of charge transfer in HBs remains an intriguing open question, although our BLW and NBO computations suggest that it is relevant to the C–H···O HB geometries. These issues notwithstanding, the prominence of the HB properties in MFC1serves as clear evidence that the MFCis predominantly bound by a C–H···O HB.

Psi4is an ab initio electronic structure program providing methods such as Hartree–Fock, density functional theory, configuration interaction, and coupled-cluster theory. The 1.1 release represents a major update meant to automate complex tasks, such as geometry optimization using complete-basis-set extrapolation or focal-point methods. Conversion of the top-level code to a Python module means that Psi4can now be used in complex workflows alongside other Python tools. Several new features have been added with the aid of libraries providing easy access to techniques such as density fitting, Cholesky decomposition, and Laplace denominators. The build system has been completely rewritten to simplify interoperability with independent, reusable software components for quantum chemistry. Finally, a wide range of new theoretical methods and analyses have been added to the code base, including functional-group and open-shell symmetry adapted perturbation theory, density-fitted coupled cluster with frozen natural orbitals, orbital-optimized perturbation and coupled-cluster methods (e.g., OO-MP2 and OO-LCCD), density-fitted multiconfigurational self-consistent field, density cumulant functional theory, algebraic-diagrammatic construction excited states, improvements to the geometry optimizer, and the “X2C” approach to relativistic corrections, among many other improvements.

The reliability of explicitly correlated methods for providing benchmark-quality noncovalent interaction energies was tested at various levels of theory and compared to estimates of the complete basis set (CBS) limit. For all systems of the A24 test set, computations were performed using both aug-cc-pVXZ (aXZ; X = D, T, Q, 5) basis sets and specialized cc-pVXZ-F12 (XZ-F12; X = D, T, Q, 5) basis sets paired with explicitly correlated coupled cluster singles and doubles [CCSD-F12n (n = a, b, c)] with triple excitations treated by the canonical perturbative method and scaled to compensate for their lack of explicit correlation [(T**)]. Results show that aXZ basis sets produce smaller errors versus the CBS limit than XZ-F12 basis sets. The F12b ansatz results in the lowest average errors for aTZ and larger basis sets, while F12a is best for double-ζ basis sets. When using aXZ basis sets (X ≥ 3), convergence is achieved from above for F12b and F12c ansatzë and from below for F12a. The CCSD(T**)-F12b/aXZ approach converges quicker with respect to basis than any other combination, although the performance of CCSD(T**)-F12c/aXZ is very similar. Both CCSD(T**)-F12b/aTZ and focal point schemes employing density-fitted, frozen natural orbital [DF-FNO] CCSD(T)/aTZ exhibit similar accuracy and computational cost, and both are much more computationally efficient than large-basis conventional CCSD(T) computations of similar accuracy.

Comparison of ab initioelectron-propagator predictions of vertical ionization potentials and electron affinities of organic, acceptor molecules with benchmark calculations based on the basis set-extrapolated, coupled cluster single, double, and perturbative triple substitution method has enabled identification of self-energy approximations with mean, unsigned errors between 0.1 and 0.2 eV. Among the self-energy approximations that neglect off-diagonal elements in the canonical, Hartree–Fock orbital basis, the P3 method for electron affinities, and the P3+ method for ionization potentials provide the best combination of accuracy and computational efficiency. For approximations that consider the full self-energy matrix, the NR2 methods offer the best performance. The P3+ and NR2 methods successfully identify the correct symmetry label of the lowest cationic state in two cases, naphthalenedione and benzoquinone, where some other methods fail.

In designing organic materials for electronics applications, particularly for organic photovoltaics (OPV), the ionization potential (IP) of the donor and the electron affinity (EA) of the acceptor play key roles. This makes OPV design an appealing application for computational chemistry since IPs and EAs are readily calculable from most electronic structure methods. Unfortunately reliable, high-accuracy wave function methods, such as coupled cluster theory with single, double, and perturbative triples [CCSD(T)] in the complete basis set (CBS) limit are too expensive for routine applications to this problem for any but the smallest of systems. One solution is to calibrate approximate, less computationally expensive methods against a database of high-accuracy IP/EA values; however, to our knowledge, no such database exists for systems related to OPV design. The present work is the first of a multipart study whose overarching goal is to determine which computational methods can be used to reliably compute IPs and EAs of electron acceptors. This part introduces a database of 24 known organic electron acceptors and provides high-accuracy vertical IP and EA values expected to be within ±0.03 eV of the true non-relativistic, vertical CCSD(T)/CBS limit. Convergence of IP and EA values toward the CBS limit is studied systematically for the Hartree–Fock, MP2 correlation, and beyond-MP2 coupled cluster contributions to the focal point estimates.

Molecular mechanics (MM) force field models have been demonstrated to have difficulty reproducing certain potential energy surfaces of π-stacked complexes. Here, we examine the performance of the AMBER and CHARMM models relative to high-quality ab initio data across systematic helical parameter scans and typical B-DNA geometries for π-stacking energies of nucleobase dimers. These force fields perform best for typical B-DNA geometries (mean absolute error < 1 kcal mol–1), whereas errors typically approach ∼2 kcal mol–1for broader potential scans, with maximum errors > 10 kcal mol–1relative to high-quality ab initio reference interaction energies. The adequate performance of MM models near minimum energy structures is accomplished through cancellation of errors in various energy terms, whereas large errors at short intermolecular distances are caused by large MM electrostatics errors due to a lack of explicit terms modeling charge penetration effects.

High-quality benchmark computations are critical for the development and assessment of approximate methods to describe noncovalent interactions. Recent advances in the treatment of dispersion by density functional theory and also the development of more efficient wave function techniques to reliably address noncovalent interactions motivate new benchmark computations of increasing accuracy. This work considers focal point approximations to estimate the complete basis set limit of coupled-cluster theory through perturbative triples [CCSD(T)/CBS] and evaluates how this approach is affected by the use or absence of counterpoise (CP) correction or, as has recently gained traction, the average of those values. Current benchmark protocols for interaction energies are computed with all CP procedures and assessed against the A24 and S22B databases and also to highly converged results for formic acid, cyanogen, and benzene dimers. Whether CP correction, no correction, or the average is favored depends upon the theoretical method, basis set, and binding motif. In recent high-quality benchmark studies, interaction energies often use second-order perturbation theory with extrapolated aug-cc-pVTZ (aTZ) and aug-cc-pVQZ (aQZ) basis sets [MP2/aTQZ] combined with a “coupled-cluster correction,” δMP2CCSD(T), evaluated in an aug-cc-pVDZ basis. For such an approach, averaging CP-corrected and uncorrected values for the MP2 component and using CP-corrected δMP2CCSD(T)values offers errors more balanced among binding motifs and generally more favorable overall. Other combinations of counterpoise correction are not quite as accurate. When employing MP2/aQ5Z extrapolations and an aTZ basis for δMP2CCSD(T), using CP-corrected or averaged MP2 estimates are about equally effective (and slightly superior to uncorrected MP2 values), but the counterpoise treatment of δMP2CCSD(T)makes little difference. Focal point estimates at this level achieve benchmark quality results otherwise accessible only with CCSD(T)/aQZ or better.

We present an algorithm for coupled-cluster through perturbative triples [CCSD(T)] based on a t1-dressed Hamiltonian and the use of density fitting (DF) or Cholesky decomposition (CD) approximations for the construction and contraction of all electron repulsion integrals (ERIs). An efficient implementation of this algorithm is then used to explore whether preoptimized density fitting basis sets [specifically, the (aug-)cc-pVXZ-RI series designed for DF-MP2 computations] are suitable for DF-CCSD(T) computations and how they compare to the CD representation of the integrals. The code is also used to systematically explore the accuracy and efficiency of DF/CD combined with frozen natural orbitals (FNOs) to reduce computational costs. The mean absolute errors due to DF/CD in the CCSD(T)/aug-cc-pVDZ interaction energies of 11 van der Waals dimers are only 0.001 kcal mol–1for the preoptimized RI basis set and only 0.002 and 0.001 kcal mol–1for CD with cutoffs of 10–4and 10–5, respectively. The very similar performance of the aug-cc-pVDZ-RI auxiliary set is a bit surprising considering that the numbers of CD vectors using these thresholds are, on average, 28% and 73% larger than the dimension of the RI set. When FNOs are coupled with DF/CD, the DF/CD error is roughly an order of magnitude less than the FNO truncation error (at a conservative FNO occupation cutoff of 10–5). Utilizing t1-dressed three-index integrals, which remove the explicit dependence of the doubles residual equations on the t1-amplitudes, results in a moderate performance acceleration for the CCSD portion of the algorithm. Moreover, the t1-dressing results in a simpler code which will be more amenable to parallelization. Utilizing both CD and FNO techniques, we observe a speedup of four times for the evaluation of the three-body contribution to the interaction energy for the benzene trimer described by an aug-cc-pVDZ basis set; the error incurred by the CD and FNO approximations in the three-body contribution is only 0.002 kcal mol–1.

We assess the accuracy of basis set truncations based on natural orbitals determined by second-order perturbation theory for computing noncovalent interaction energies with coupled cluster through perturbative triples [CCSD(T)]. We consider two methods for truncation: (i) the usual frozen natural orbital approach (FNO) in which the basis set truncation occurs before the iterative CCSD computation [FNO CCSD(T)] and (ii) an approach in which the truncation occurs only for the perturbative triples contribution [CCSD+FNO(T)]. The errors incurred are comparable for both methods and are small enough for the methods to be used for benchmark-quality studies of noncovalent interactions. For the FNO CCSD(T) method with a modest natural orbital occupation tolerance of 10–5, the mean absolute error in the interaction energies for the S22 data set in an aug-cc-pVDZ basis set is only 0.012 kcal mol–1versus canonical CCSD(T) values. The same method exhibits a mean absolute error of 0.020 kcal mol–1for the S11 data set in the aug-cc-pVTZ basis set versus canonical CCSD(T) values.

Noncovalent interactions play an important role in the stabilization of biological molecules. The effective fragment potential (EFP) is a computationally inexpensive ab initio-based method for modeling intermolecular interactions in noncovalently bound systems. The accuracy of EFP is benchmarked against the S22 and S66 data sets for noncovalent interactions [Jurečka, P.; Šponer, J.; Černý, J.; Hobza, P. Phys. Chem. Chem. Phys.2006, 8, 1985; Řezáč, J.; Riley, K. E.; Hobza, P. J. Chem. Theory Comput.2011, 7, 2427]. The mean unsigned error (MUE) of EFP interaction energies with respect to coupled-cluster singles, doubles, and perturbative triples in the complete basis set limit [CCSD(T)/CBS] is 0.9 and 0.6 kcal/mol for S22 and S66, respectively, which is similar to the MUE of MP2 and SCS-MP2 for the same data sets, but with a greatly reduced computational expense. Moreover, EFP outperforms classical force fields and popular DFT functionals such as B3LYP and PBE, while newer dispersion-corrected functionals provide a more accurate description of noncovalent interactions. Comparison of EFP energy components with the symmetry-adapted perturbation theory (SAPT) energies for the S22 data set shows that the main source of errors in EFP comes from Coulomb and polarization terms and provides a valuable benchmark for further improvements in the accuracy of EFP and force fields in general.

We propose a procedure denoted dispersion-weighted explicitly correlated coupled-cluster [DW-CCSD(T**)-F12] which mixes CCSD(T**)-F12a and CCSD(T**)-F12b so as to correct the small errors exhibited by each of the approximations in a small basis set, allowing for a black-box method that can provide high-quality interaction energies for a variety of nonbonded interactions. Relative to CCSD(T**)-F12a and CCSD(T**)-F12b, DW-CCSD(T**)-F12 reduces the mean absolute deviation by a factor of 2 and the maximum error by a factor of 3 (formic acid dimer) and 4 (stacked adenine–thymine) for the aug-cc-pVDZ basis set.

All intermolecular interactions involve London dispersion forces. The accurate treatment of dispersion is essential for the computation of realistic interaction potentials. In general, the most reliable method for computing intermolecular interactions is coupled-cluster singles and doubles with perturbative triples [CCSD(T)] in conjunction with a sufficiently flexible Gaussian atomic orbital basis set, a combination which is not routinely applicable due to its excessive computational demands (CPU time, memory, storage). Recently, many theoretical methods have been developed that attempt to account for dispersion in a more efficient manner. It is well-known that dispersion interactions are more difficult to compute in some systems than others; for example, π–π dispersion is notoriously difficult, while alkane–alkane dispersion is relatively simple to compute. In this work, numerous theoretical methods are tested for their ability to compute reliable interaction energies in particularly challenging systems, namely, the P2, PCCP, and NCCN dimers. Symmetry-adapted perturbation theory (SAPT) is applied to these dimers to demonstrate their sensitivity to the treatment of dispersion. Due to the small size of these systems, highly accurate CCSD(T) potential energy curves could be estimated at the complete basis set limit. Numerous theoretical methods are tested against the reliable CCSD(T) benchmarks. Methods using a treatment of dispersion that relies on time-dependent density functional theory (TDDFT) response functions are found to be the most reliable.

A largely unsolved problem in computational biochemistry is the accurate prediction of binding affinities of small ligands to protein receptors. We present a detailed analysis of the systematic and random errors present in computational methods through the use of error probability density functions, specifically for computed interaction energies between chemical fragments comprising a protein−ligand complex. An HIV−II protease crystal structure with a bound ligand (indinavir) was chosen as a model protein−ligand complex. The complex was decomposed into 21 interacting fragment pairs, which were studied using a number of computational methods. The chemically accurate complete basis set coupled cluster theory (CCSD(T)/CBS) interaction energies were used as reference values to generate our error estimates. In our analysis, we observed significant systematic and random errors in most methods, which was surprising, especially for parametrized classical and semiempirical quantum mechanical calculations. After propagating these fragment-based error estimates over the entire protein−ligand complex, our total error estimates for many methods are large compared to the experimentally determined free energy of binding. Thus, we conclude that statistical error analysis is a necessary addition to any scoring function attempting to produce reliable binding affinity predictions.

Noncovalent interactions such as hydrogen bonds, van der Waals forces, and π−π interactions play important roles influencing the structure, stability, and dynamic properties of biomolecules including DNA and RNA base pairs. In an effort to better understand the fundamental physics of hydrogen bonding (H-bonding), we investigate the distance dependence of interaction energies in the prototype bimolecular complexes of formic acid, formamide, and formamidine. Potential energy curves along the H-bonding dissociation coordinate are examined both by establishing reference CCSD(T) interaction energies extrapolated to the complete basis set limit and by assessing the performance of the density functional methods B3LYP, PBE, PBE0, B970, PB86, M05-2X, and M06-2X and empirical dispersion corrected methods B3LYP-D3, PBE-D3, PBE0-D3, B970-D2, BP86-D3, and ωB97X-D, with basis sets 6-311++G(3df,3pd), aug-cc-pVDZ, and aug-cc-pVTZ. Although H-bonding interactions are dominated by electrostatics, it is necessary to properly account for dispersion interactions to obtain accurate energetics. In order to quantitatively probe the nature of hydrogen bonding interactions as a function of distance, we decompose the interaction energy curves into physically meaningful components with symmetry-adapted perturbation theory (SAPT). The SAPT results confirm that the contribution of dispersion and induction are significant at and near equilibrium, although electrostatics dominate. Among the DFT/DFT-D techniques, the best overall results are obtained utilizing counterpoise-corrected ωB97X-D with the aug-cc-pVDZ basis set.

We present a systematic study of the synergistic effects of popular approximations to Møller−Plesset perturbation theory through the second order (MP2). This work applies the density-fitting (DF) approximation for two-electron integrals, the dual-basis (DB) approximation for the Hartree−Fock reference, and the use of “heavy augmented” Dunning basis sets for basis set reduction, as well as combinations of these, to the S22 benchmark set of weakly bound dimers. For each approach, we report an error analysis as well as relative speedups for the 22 interaction energies in the set. Compared to the MP2/aug-cc-pVTZ level of theory, the DB-DF-MP2/heavy-aug-cc-pVTZ approach achieves an average speedup of 18 with a root-mean-square error of only 0.076 kcal mol−1(2%).

A recently proposed double-hybrid functional called XYG3 and a semilocal GGA functional (B97-D) with a semiempirical correction for van der Waals interactions have been applied to study the potential energy curves along the dissociation coordinates of weakly bound pairs of molecules governed by London dispersion and induced dipole forces. Molecules treated in this work were the parallel sandwich, T-shaped, and parallel-displaced benzene dimer, (C6H6)2; hydrogen sulfide and benzene, H2S·C6H6; methane and benzene, CH4·C6H6; the methane dimer, (CH4)2; and the pyridine dimer, (C5H5N)2. We compared the potential energy curves of these functionals with previously published benchmarks at the coupled cluster singles, doubles, and perturbative triplets [CCSD(T)] complete-basis-set limit. Both functionals, XYG3 and B97-D, exhibited very good performance, reproducing accurate energies for equilibrium distances and a smooth behavior along the dissociation coordinate. Overall, we found an agreement within a few tenths of one kcal mol−1with the CCSD(T) results across the potential energy curves.

Bisalen—very cooperative: A novel styryl‐substituted, unsymmetrical bisalen is shown to be a versatile precursor to both soluble and insoluble cooperative catalysts for the hydrolytic kinetic resolution of epoxides. The unique bisalen motif ensures all catalysts derived from it have the necessary molecular‐level ligand pairing needed for cooperative bimetallic catalytic reactions (see scheme).

AlCl–salen (salen=N,N′‐bis(salicylidene)ethylenediamine dianion) catalysts supported onto macrocyclic oligomeric cyclooctene through linkers of varying length and flexibility have been developed to demonstrate the importance of support architecture on catalyst activity. The role played by the support and the linkers in dictating catalyst activity was found to vary for reactions with contrasting mechanisms, such as the bimetallic cyanide and the monometallic indole addition reactions. While the flexible support significantly enhanced the cyanide addition reaction, most likely by improving salen–salen interactions in the transition state, it lowered the reaction rate for the monometallic indole reaction. For both reactions, significant increase in catalytic activity was observed for catalysts with the longest linkers. The effect of the flexible macrocyclic support on catalysis was further exemplified by the enhanced activity of the supported catalyst in comparison with its unsupported analogue for the conjugate addition of tetrazoles, which is known to be catalyzed by dimeric μ‐oxo–salen catalysts. Our studies with the cyclooctene supported AlCl–salen catalysts provides significant insights for rationally designing highly efficient AlCl–salen catalysts for a diverse set of reactions.