Dispersion-Weighted Explicitly Correlated Coupled-Cluster Theory [DW-CCSD(T**)-F12]

Anisotropy, segmental dynamics and polymorphism of crystalline biogenic carboxylic acids

Carboxylic acids of the Krebs cycle possess invaluable biochemical significance. Still, there are severe gaps in the availability of thermodynamic and crystallographic data, as well as ambiguities prevailing in the literature on the thermodynamic characterization and polymorph ranking. Providing an unambiguous description of the structure, thermodynamics and polymorphism of their neat crystalline phases requires a complex multidisciplinary approach. This work presents results of an extensive investigation of the structural anisotropy of the thermal expansion and local dynamics within these crystals, obtained from a beneficial cooperation of NMR crystallography and ab initio calculations of non-covalent interactions. The observed structural anisotropy and spin-lattice relaxation times are traced to large spatial variations in the strength of molecular interactions in the crystal lattice, especially in the orientation of the hydrogen bonds. A completely resolved crystal structure for oxaloacetic acid is reported for the first time. Thanks to multi-instrumental calorimetric effort, this work clarifies phase behavior, determines third-law entropies of the crystals, and states definitive polymorph ranking for succinic and fumaric acids. These thermodynamic observations are then interpreted in terms of first-principles quasi-harmonic calculations of cohesive properties. A sophisticated model capturing electronic, thermal, and configurational-entropic effects on the crystal structure approaches captures the subtle Gibbs energy differences governing polymorph ranking for succinic and fumaric acids, representing another success story of computational chemistry.

CLIFF: A component-based, machine-learned, intermolecular force field

Computation of intermolecular interactions is a challenge in drug discovery because accurate ab initio techniques are too computationally expensive to be routinely applied to drug-protein models. Classical force fields are more computationally feasible, and force fields designed to match symmetry adapted perturbation theory (SAPT) interaction energies can remain accurate in this context. Unfortunately, the application of such force fields is complicated by the laborious parameterization required for computations on new molecules. Here, we introduce the component-based machine-learned intermolecular force field (CLIFF), which combines accurate, physics-based equations for intermolecular interaction energies with machine-learning models to enable automatic parameterization. The CLIFF uses functional forms corresponding to electrostatic, exchange-repulsion, induction/polarization, and London dispersion components in SAPT. Molecule-independent parameters are fit with respect to SAPT2+(3)δMP2/aug-cc-pVTZ, and molecule-dependent atomic parameters (atomic widths, atomic multipoles, and Hirshfeld ratios) are obtained from machine learning models developed for C, N, O, H, S, F, Cl, and Br. The CLIFF achieves mean absolute errors (MAEs) no worse than 0.70 kcal mol^-1 in both total and component energies across a diverse dimer test set. For the side chain-side chain interaction database derived from protein fragments, the CLIFF produces total interaction energies with an MAE of 0.27 kcal mol^-1 with respect to reference data, outperforming similar and even more expensive methods. In applications to a set of model drug-protein interactions, the CLIFF is able to accurately rank-order ligand binding strengths and achieves less than 10% error with respect to SAPT reference values for most complexes.

Canonical and explicitly-correlated coupled cluster correlation energies of sub-kJ mol-1 accuracy via cost-effective hybrid-post-CBS extrapolation

Cost-effectiveness and accuracy are two basic pillars in electronic structure calculations. While cost-effectiveness enhances applicability, high accuracy is sustained when employing advanced computational tools. With the gold standard method of ab initio quantum chemistry at the focal point, canonical CCSD(T) and modern explicitly correlated CCSD(T)-F12 calculations are employed hand in hand to develop accurate hybrid post-CBS extrapolation schemes, which are validated using popular training sets involving a total of 130 molecules. By using raw valence-only calculations at CCSD(T)/VDZ and CCSD(T)/VQZ-F12 levels of theory, the novel scheme leads to the prediction of absolute energies that differ on average (-0.170 ± 0.224) kcal mol-1 from the highest affordable CCSD(T)-F12b/V(Q,5)Z-F12 extrapolations, but only (-0.048 ± 0.228) kcal mol-1 from the post-CBS extrapolated values based on CBS(D,T), CBS(D,Q) and CBS(T,Q) energies. From the cost-effectiveness standpoint, the approach is a kind of pseudo one-point extrapolation scheme since its cost is basically that of the highest-rung raw energy where it is based. Variants that imply no additional cost are also discussed, emerging h-pCBS(dt,dq)ab as the most effective. The approach can also be used with PNO-based local correlation methods that gained popularity due to allowing coupled-cluster calculations even for large molecules at reduced computational cost, namely local PNO-CCSD(T) and PNO-CCSD(T)-F12b. To gauge the approach performance, both the hydrogen molecule and the O-C2H5 torsion path of ethyl-methyl-ether, an extra molecule here considered with presupposed existence in astrophysical objects, are also studied. Additionally, the nonbonding interactions in the A24 test set are revisited per se. The results show that the title approach may be useful in high-accuracy quantum chemistry, with further improvements requiring the inclusion of contributions beyond the theory here employed such as the ones due to relativistic and nonadiabatic effects.

Towards reliable ab initio sublimation pressures for organic molecular crystals - are we there yet?

Knowledge of molecular crystal sublimation equilibrium data is vital in many industrial processes, but this data can be difficult to measure experimentally for low-volatility species. Theoretical prediction of sublimation pressures could provide a useful supplement to experiment, but the exponential temperature dependence of sublimation (or any saturated vapor) pressure curve makes this challenging. An uncertainty of only a few percent in the sublimation enthalpy or entropy can propagate to an error in the sublimation pressure exceeding several orders of magnitude for a given temperature interval. Despite this fundamental difficulty, this paper performs some of the first ab initio predictions of sublimation pressure curves. Four simple molecular crystals (ethane, methanol, benzene, and imidazole) have been selected for a case study showing the currently achievable accuracy of quantum chemistry calculations. Fragment-based ab initio techniques and the quasi-harmonic approximation are used for calculations of cohesive and phonon properties of the crystals, while the vapor phase is treated by the ideal gas model. Ab initio sublimation pressure curves for model compounds are compared against their experimental counterparts. The computational uncertainties are estimated, weak points of the computational methodology are identified, and further improvements are proposed.

Dynamics of benzene excimer formation from the parallel-displaced dimer

Excimers play a key role in a variety of excited-state processes, such as exciton trapping, fluorescence quenching, and singlet-fission. The dynamics of benzene excimer formation in the first 2 ps after S₁ excitation from the parallel-displaced geometry of the benzene dimer is reported here. It was simulated via nonadiabatic surface-hopping dynamics using the second-order algebraic diagrammatic construction (ADC(2)). After excitation, the benzene rings take ∼0.5-1.0 ps to approach each other in a parallel-stacked structure of the S₁ minimum and stay in the excimer region for ∼0.1-0.4 ps before leaving due to excess vibrational energy. The S₁-S₂ gap widens considerably while the rings visit the excimer region in the potential energy surface. Our work provides detailed insight into correlations between nuclear and electronic structure in the excimer and shows that decreased ring distance goes along with enhanced charge transfer and that fast exciton transfer happens between the rings, leading to the equal probability of finding the exciton in each ring after around 1.0 ps.

Alchemical and structural distribution based representation for universal quantum machine learning

We introduce a representation of any atom in any chemical environment for the automatized generation of universal kernel ridge regression-based quantum machine learning (QML) models of electronic properties, trained throughout chemical compound space. The representation is based on Gaussian distribution functions, scaled by power laws and explicitly accounting for structural as well as elemental degrees of freedom. The elemental components help us to lower the QML model's learning curve, and, through interpolation across the periodic table, even enable "alchemical extrapolation" to covalent bonding between elements not part of training. This point is demonstrated for the prediction of covalent binding in single, double, and triple bonds among main-group elements as well as for atomization energies in organic molecules. We present numerical evidence that resulting QML energy models, after training on a few thousand random training instances, reach chemical accuracy for out-of-sample compounds. Compound datasets studied include thousands of structurally and compositionally diverse organic molecules, non-covalently bonded protein side-chains, (H₂O)₄₀-clusters, and crystalline solids. Learning curves for QML models also indicate competitive predictive power for various other electronic ground state properties of organic molecules, calculated with hybrid density functional theory, including polarizability, heat-capacity, HOMO-LUMO eigenvalues and gap, zero point vibrational energy, dipole moment, and highest vibrational fundamental frequency.

The BioFragment Database (BFDb): An open-data platform for computational chemistry analysis of noncovalent interactions

Accurate potential energy models are necessary for reliable atomistic simulations of chemical phenomena. In the realm of biomolecular modeling, large systems like proteins comprise very many noncovalent interactions (NCIs) that can contribute to the protein's stability and structure. This work presents two high-quality chemical databases of common fragment interactions in biomolecular systems as extracted from high-resolution Protein DataBank crystal structures: 3380 sidechain-sidechain interactions and 100 backbone-backbone interactions that inaugurate the BioFragment Database (BFDb). Absolute interaction energies are generated with a computationally tractable explicitly correlated coupled cluster with perturbative triples [CCSD(T)-F12] "silver standard" (0.05 kcal/mol average error) for NCI that demands only a fraction of the cost of the conventional "gold standard," CCSD(T) at the complete basis set limit. By sampling extensively from biological environments, BFDb spans the natural diversity of protein NCI motifs and orientations. In addition to supplying a thorough assessment for lower scaling force-field (2), semi-empirical (3), density functional (244), and wavefunction (45) methods (comprising >1M interaction energies), BFDb provides interactive tools for running and manipulating the resulting large datasets and offers a valuable resource for potential energy model development and validation.

π–π stacking between polyaromatic hydrocarbon sheets beyond dispersion interactions

A slipped parallel structure of a stacked graphene flake showing a biconcave curvature.

Appointing silver and bronze standards for noncovalent interactions: a comparison of spin-component-scaled (SCS), explicitly correlated (F12), and specialized wavefunction approaches

A systematic examination of noncovalent interactions as modeled by wavefunction theory is presented in comparison to gold-standard quality benchmarks available for 345 interaction energies of 49 bimolecular complexes. Quantum chemical techniques examined include spin-component-scaling (SCS) variations on second-order perturbation theory (MP2) [SCS, SCS(N), SCS(MI)] and coupled cluster singles and doubles (CCSD) [SCS, SCS(MI)]; also, method combinations designed to improve dispersion contacts [DW-MP2, MP2C, MP2.5, DW-CCSD(T)-F12]; where available, explicitly correlated (F12) counterparts are also considered. Dunning basis sets augmented by diffuse functions are employed for all accessible ζ-levels; truncations of the diffuse space are also considered. After examination of both accuracy and performance for 394 model chemistries, SCS(MI)-MP2/cc-pVQZ can be recommended for general use, having good accuracy at low cost and no ill-effects such as imbalance between hydrogen-bonding and dispersion-dominated systems or non-parallelity across dissociation curves. Moreover, when benchmarking accuracy is desirable but gold-standard computations are unaffordable, this work recommends silver-standard [DW-CCSD(T**)-F12/aug-cc-pVDZ] and bronze-standard [MP2C-F12/aug-cc-pVDZ] model chemistries, which support accuracies of 0.05 and 0.16 kcal/mol and efficiencies of 97.3 and 5.5 h for adenine·thymine, respectively. Choice comparisons of wavefunction results with the best symmetry-adapted perturbation theory [T. M. Parker, L. A. Burns, R. M. Parrish, A. G. Ryno, and C. D. Sherrill, J. Chem. Phys. 140, 094106 (2014)] and density functional theory [L. A. Burns, Á. Vázquez-Mayagoitia, B. G. Sumpter, and C. D. Sherrill, J. Chem. Phys. 134, 084107 (2011)] methods previously studied for these databases are provided for readers' guidance.

A Parametrized Coupled-Pair Functional for Molecular Interactions: PCPF-MI

We present a parametrized coupled-pair functional, optimized to describe molecular interactions (PCPF-MI). The method has the same computational cost as singles and doubles configuration interaction, is size extensive, and yields energies that are stationary with respect to variations in all of its excitation coefficients. This last property facilitates the construction of density matrices and the evaluation of one- and two-electron properties. For the S22, HSG, S66, and A24 databases of van der Waals dimers, PCPF-MI computations yield interaction energies with mean unsigned errors of 0.326, 0.149, 0.214, and 0.044 kcal mol(-1), respectively, relative to benchmark computations. PCPF-MI interaction energies consistently improve upon those obtained from several other coupled-pair methods, including the averaged coupled-pair functional (ACPF), the coupled electron-pair approximation [CEPA(n), n = 0,1,3], and averaged quadratic coupled cluster (AQCC). Optimal parameters for spin-component-scaled (SCS) variants of each of these methods are also presented. SCS-CEPA(0), SCS-CEPA(1), SCS-ACPF, and SCS-PCPF-MI all perform similarly, with average errors for the four databases of roughly 0.1 kcal mol(-1). The PCPF-MI method, without additional SCS parametrization, has an average error of 0.192 kcal mol(-1) over the four databases and, when compared to the SCS-parametrized coupled-pair methods, has the added benefit that the energy is stationary with respect to variations in all its excitation coefficients.

Accelerating MP2C dispersion corrections for dimers and molecular crystals

The MP2C dispersion correction of Pitonak and Hesselmann [J. Chem. Theory Comput. 6, 168 (2010)] substantially improves the performance of second-order Møller-Plesset perturbation theory for non-covalent interactions, albeit with non-trivial computational cost. Here, the MP2C correction is computed in a monomer-centered basis instead of a dimer-centered one. When applied to a single dimer MP2 calculation, this change accelerates the MP2C dispersion correction several-fold while introducing only trivial new errors. More significantly, in the context of fragment-based molecular crystal studies, combination of the new monomer basis algorithm and the periodic symmetry of the crystal reduces the cost of computing the dispersion correction by two orders of magnitude. This speed-up reduces the MP2C dispersion correction calculation from a significant computational expense to a negligible one in crystals like aspirin or oxalyl dihydrazide, without compromising accuracy.

Noncovalent Interactions of DNA Bases with Naphthalene and Graphene

The complexes of a DNA base bound to graphitic systems are studied. Considering naphthalene as the simplest graphitic system, DNA base-naphthalene complexes are scrutinized at high levels of ab initio theory including coupled cluster theory with singles, doubles, and perturbative triples excitations [CCSD(T)] at the complete basis set (CBS) limit. The stacked configurations are the most stable, where the CCSD(T)/CBS binding energies of guanine, adenine, thymine, and cytosine are 9.31, 8.48, 8.53, 7.30 kcal/mol, respectively. The energy components are investigated using symmetry-adapted perturbation theory based on density functional theory including the dispersion energy. We compared the CCSD(T)/CBS results with several density functional methods applicable to periodic systems. Considering accuracy and availability, the optB86b nonlocal functional and the Tkatchenko-Scheffler functional are used to study the binding energies of nucleobases on graphene. The predicted values are 18-24 kcal/mol, though many-body effects on screening and energy need to be further considered.

Accurate Noncovalent Interaction Energies Using Truncated Basis Sets Based on Frozen Natural Orbitals

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(-1) versus canonical CCSD(T) values. The same method exhibits a mean absolute error of 0.020 kcal mol(-1) for the S11 data set in the aug-cc-pVTZ basis set versus canonical CCSD(T) values.