Assessment of Empirical Models versus High-Accuracy Ab Initio Methods for Nucleobase Stacking: Evaluating the Importance of Charge Penetration

Quantum Mechanics Characterization of Non-Covalent Interaction in Nucleotide Fragments

Accurate calculation of non-covalent interaction energies in nucleotides is crucial for understanding the driving forces governing nucleic acid structure and function, as well as developing advanced molecular mechanics forcefields or machine learning potentials tailored to nucleic acids. Here, we dissect the nucleotides' structure into three main constituents: nucleobases (A, G, C, T, and U), sugar moieties (ribose and deoxyribose), and phosphate group. The interactions among these fragments and between fragments and water were analyzed. Different quantum mechanical methods were compared for their accuracy in capturing the interaction energy. The non-covalent interaction energy was decomposed into electrostatics, exchange-repulsion, dispersion, and induction using two ab initio methods: Symmetry-Adapted Perturbation Theory (SAPT) and Absolutely Localized Molecular Orbitals (ALMO). These calculations provide a benchmark for different QM methods, in addition to providing a valuable understanding of the roles of various intermolecular forces in hydrogen bonding and aromatic stacking. With SAPT, a higher theory level and/or larger basis set did not necessarily give more accuracy. It is hard to know which combination would be best for a given system. In contrast, ALMO EDA2 did not show dependence on theory level or basis set; additionally, it is faster.

Hybrid classical/machine-learning force fields for the accurate description of molecular condensed-phase systems

Electronic structure methods offer in principle accurate predictions of molecular properties, however, their applicability is limited by computational costs. Empirical methods are cheaper, but come with inherent approximations and are dependent on the quality and quantity of training data. The rise of machine learning (ML) force fields (FFs) exacerbates limitations related to training data even further, especially for condensed-phase systems for which the generation of large and high-quality training datasets is difficult. Here, we propose a hybrid ML/classical FF model that is parametrized exclusively on high-quality ab initio data of dimers and monomers in vacuum but is transferable to condensed-phase systems. The proposed hybrid model combines our previous ML-parametrized classical model with ML corrections for situations where classical approximations break down, thus combining the robustness and efficiency of classical FFs with the flexibility of ML. Extensive validation on benchmarking datasets and experimental condensed-phase data, including organic liquids and small-molecule crystal structures, showcases how the proposed approach may promote FF development and unlock the full potential of classical FFs.

The Energetic Origins of Pi-Pi Contacts in Proteins

Accurate potential energy models of proteins must describe the many different types of noncovalent interactions that contribute to a protein's stability and structure. Pi-pi contacts are ubiquitous structural motifs in all proteins, occurring between aromatic and nonaromatic residues and play a nontrivial role in protein folding and in the formation of biomolecular condensates. Guided by a geometric criterion for isolating pi-pi contacts from classical molecular dynamics simulations of proteins, we use quantum mechanical energy decomposition analysis to determine the molecular interactions that stabilize different pi-pi contact motifs. We find that neutral pi-pi interactions in proteins are dominated by Pauli repulsion and London dispersion rather than repulsive quadrupole electrostatics, which is central to the textbook Hunter-Sanders model. This results in a notable lack of variability in the interaction profiles of neutral pi-pi contacts even with extreme changes in the dielectric medium, explaining the prevalence of pi-stacked arrangements in and between proteins. We also find interactions involving pi-containing anions and cations to be extremely malleable, interacting like neutral pi-pi contacts in polar media and like typical ion-pi interactions in nonpolar environments. Like-charged pairs such as arginine-arginine contacts are particularly sensitive to the polarity of their immediate surroundings and exhibit canonical pi-pi stacking behavior only if the interaction is mediated by environmental effects, such as aqueous solvation.

Understanding the Structure-Activity Relationship through Density Functional Theory: A Simple Method Predicts Relative Binding Free Energies of Metalloenzyme Fragment-like Inhibitors

Despite being involved in several human diseases, metalloenzymes are targeted by a small percentage of FDA-approved drugs. Development of novel and efficient inhibitors is required, as the chemical space of metal binding groups (MBGs) is currently limited to four main classes. The use of computational chemistry methods in drug discovery has gained momentum thanks to accurate estimates of binding modes and binding free energies of ligands to receptors. However, exact predictions of binding free energies in metalloenzymes are challenging due to the occurrence of nonclassical phenomena and interactions that common force field-based methods are unable to correctly describe. In this regard, we applied density functional theory (DFT) to predict the binding free energies and to understand the structure-activity relationship of metalloenzyme fragment-like inhibitors. We tested this method on a set of small-molecule inhibitors with different electronic properties and coordinating two Mn²⁺ ions in the binding site of the influenza RNA polymerase PA_N endonuclease. We modeled the binding site using only atoms from the first coordination shell, hence reducing the computational cost. Thanks to the explicit treatment of electrons by DFT, we highlighted the main contributions to the binding free energies and the electronic features differentiating strong and weak inhibitors, achieving good qualitative correlation with the experimentally determined affinities. By introducing automated docking, we explored alternative ways to coordinate the metal centers and we identified 70% of the highest affinity inhibitors. This methodology provides a fast and predictive tool for the identification of key features of metalloenzyme MBGs, which can be useful for the design of new and efficient drugs targeting these ubiquitous proteins.

An Imbalance in the Force: The Need for Standardized Benchmarks for Molecular Simulation

Force fields (FFs) for molecular simulation have been under development for more than half a century. As with any predictive model, rigorous testing and comparisons of models critically depends on the availability of standardized data sets and benchmarks. While such benchmarks are rather common in the fields of quantum chemistry, this is not the case for empirical FFs. That is, few benchmarks are reused to evaluate FFs, and development teams rather use their own training and test sets. Here we present an overview of currently available tests and benchmarks for computational chemistry, focusing on organic compounds, including halogens and common ions, as FFs for these are the most common ones. We argue that many of the benchmark data sets from quantum chemistry can in fact be reused for evaluating FFs, but new gas phase data is still needed for compounds containing phosphorus and sulfur in different valence states. In addition, more nonequilibrium interaction energies and forces, as well as molecular properties such as electrostatic potentials around compounds, would be beneficial. For the condensed phases there is a large body of experimental data available, and tools to utilize these data in an automated fashion are under development. If FF developers, as well as researchers in artificial intelligence, would adopt a number of these data sets, it would become easier to compare the relative strengths and weaknesses of different models and to, eventually, restore the balance in the force.

Regularized by Physics: Graph Neural Network Parametrized Potentials for the Description of Intermolecular Interactions

Simulations of molecular systems using electronic structure methods are still not feasible for many systems of biological importance. As a result, empirical methods such as force fields (FF) have become an established tool for the simulation of large and complex molecular systems. The parametrization of FF is, however, time-consuming and has traditionally been based on experimental data. Recent years have therefore seen increasing efforts to automatize FF parametrization or to replace FF with machine-learning (ML) based potentials. Here, we propose an alternative strategy to parametrize FF, which makes use of ML and gradient-descent based optimization while retaining a functional form founded in physics. Using a predefined functional form is shown to enable interpretability, robustness, and efficient simulations of large systems over long time scales. To demonstrate the strength of the proposed method, a fixed-charge and a polarizable model are trained on ab initio potential-energy surfaces. Given only information about the constituting elements, the molecular topology, and reference potential energies, the models successfully learn to assign atom types and corresponding FF parameters from scratch. The resulting models and parameters are validated on a wide range of experimentally and computationally derived properties of systems including dimers, pure liquids, and molecular crystals.

Polarizable Molecular Block Model: Toward the Development of an Induced Dipole Force Field for DNA

For flexible and highly ionized macromolecules such as DNA, it is important to correctly evaluate the intramolecular polarization in an induced dipole force field. In a proposed polarizable molecular block (PMB) model, a large molecule is divided into several molecular blocks. The atomic charges of the blocks are optimized by using the respective electrostatic potentials (ESPs) on the molecular surface. By using the capped hydrogen removal operation, the total charge of the blocks is controlled exactly to have an integer charge. The atomic polarizabilities of the blocks are optimized by using the respective polarized one-electron potentials that are the differences between ESPs with and without an external test charge. Induced dipole-charge interactions between the blocks are all included, but those interactions within the blocks are strictly excluded. All dipole-dipole interactions are included, but the damping functions are applied to the close dipole-dipole pairs. Several types of damping (simple scaling, exponential, linear, and Gaussian) are evaluated. The validity of the PMB model was verified by using trinucleotide duplexes which have A-, B-, and Z-DNA forms. The reference energies of trinucleotide duplexes including counterions (GGT3Na-ACC3Na, GAC3Na-GTC3Na, and GCG3Na-CGC3Na) are calculated using ωB97XD/aug-cc-pVDZ. All damping types reproduced well the reference interaction energies, dipole moments, and ESPs. Among them, the simple scaling with strong attenuation to 1-2 atomic pairs showed the highest stability against the polarization catastrophe. This study shows that it is possible to develop a high-quality polarizable force field by treating the intramolecular polarization on a block-by-block basis.

Minimal Basis Set Hartree-Fock Corrected with Atom-Centered Potentials for Molecular Crystal Modeling and Crystal Structure Prediction

Crystal structure prediction (CSP), determining the experimentally observable structure of a molecular crystal from the molecular diagram, is an important challenge with technologically relevant applications in materials manufacturing and drug design. For the purpose of screening the randomly generated candidate crystal structures, CSP protocols require energy ranking methods that are fast and can accurately capture the small energy differences between molecular crystals. In addition, a good ranking method should also produce accurate equilibrium geometries, both intramolecular and intermolecular. In this article, we explore the combination of minimal-basis-set Hartree-Fock (HF) with atom-centered potentials (ACPs) as a method for modeling the structure and energetics of molecular crystals. The ACPs are developed for the H, C, N, and O atoms and fitted to a set of reference data at the B86bPBE-XDM level in order to mitigate basis-set incompleteness and missing correlation. In particular, ACPs are developed in combination with two methods: HF-D3/MINIs and HF-3c. The application of ACPs greatly improves the performance of HF-D3/MINIs for lattice energies, crystal energy differences, energy-volume and energy-strain relations, and crystal geometries. In the case of HF-3c, the improvement in the crystal energy differences is much smaller than in HF-D3/MINIs, but lattice energies and particularly crystal geometries are considerably better when ACPs are used. The resulting methods may be useful for CSP but also for quick calculation of molecular crystal lattice energies and geometries.

Quantum mechanical study of interactions between sunscreen ingredients and nucleotide bases

Interactions between the popular sunscreen ingredients oxybenzone and homosalate and DNA bases have been studied using density functional theory and ab initio methods. Low-energy structures for each sunscreen ingredient interacting with each nucleotide base in either a pi-stacked or hydrogen-bonded fashion were found. The binding energies are comparable to those for the Watson-Crick-Franklin Ade-Thy and Cyt-Gua pairs. Pi-stacked and hydrogen-bonded structures are comparable in energy, with hydrogen-bonded structures having a more negative counterpoise-corrected binding energy, while the final pi-stacked structures are lower in energy. This is due to a geometrical rearrangement required to form the hydrogen bonds that raise the total energy of the complex. It was also found that when using the M06-2X density functional, the STO-3G basis set favors hydrogen bonding, but 6-31G(d) and 6-31 + G(s) basis sets predict similar binding geometries.

Affinity and Correlation in DNA

A statistical analysis of important DNA sequences and related proteins has been performed to study the relationships between monomers, and some general considerations about these macromolecules can be provided from the results. First, the most important relationship between sites in all the DNA sequences examined is that between two consecutive base pairs. This is an indication of an energetic stabilization due to the stacking interaction of these couples of base pairs. Secondly, the difference between human chromosome sequences and their coding parts is relevant both in the relationships between sites and in some specific compositional rules, such as the second Chargaff rule. Third, the evidence of the relationship in two successive triplets of DNA coding sequences generates a relationship between two successive amino acids in the proteins. This is obviously impossible if all the relationships between the sites are statistical evidence and do not involve causes; therefore, in this article, due to stacking interactions and this relationship in coding sequences, we will divide the concept of the relationship between sites into two concepts: affinity and correlation, the first with physical causes and the second without. Finally, from the statistical analyses carried out, it will emerge that the human genome is uniform, with the only significant exception being the Y chromosome.

Small-Basis Set Density-Functional Theory Methods Corrected with Atom-Centered Potentials

Density functional theory (DFT) is currently the most popular method for modeling noncovalent interactions and thermochemistry. The accurate calculation of noncovalent interaction energies, reaction energies, and barrier heights requires choosing an appropriate functional and, typically, a relatively large basis set. Deficiencies of the density-functional approximation and the use of a limited basis set are the leading sources of error in the calculation of noncovalent and thermochemical properties in molecular systems. In this article, we present three new DFT methods based on the BLYP, M06-2X, and CAM-B3LYP functionals in combination with the 6-31G* basis set and corrected with atom-centered potentials (ACPs). ACPs are one-electron potentials that have the same form as effective-core potentials, except they do not replace any electrons. The ACPs developed in this work are used to generate energy corrections to the underlying DFT/basis-set method such that the errors in predicted chemical properties are minimized while maintaining the low computational cost of the parent methods. ACPs were developed for the elements H, B, C, N, O, F, Si, P, S, and Cl. The ACP parameters were determined using an extensive training set of 118655 data points, mostly of complete basis set coupled-cluster level quality. The target molecular properties for the ACP-corrected methods include noncovalent interaction energies, molecular conformational energies, reaction energies, barrier heights, and bond separation energies. The ACPs were tested first on the training set and then on a validation set of 42567 additional data points. We show that the ACP-corrected methods can predict the target molecular properties with accuracy close to complete basis set wavefunction theory methods, but at a computational cost of double-ζ DFT methods. This makes the new BLYP/6-31G*-ACP, M06-2X/6-31G*-ACP, and CAM-B3LYP/6-31G*-ACP methods uniquely suited to the calculation of noncovalent, thermochemical, and kinetic properties in large molecular systems.

Fast and Accurate Quantum Mechanical Modeling of Large Molecular Systems Using Small Basis Set Hartree-Fock Methods Corrected with Atom-Centered Potentials

There has been significant interest in developing fast and accurate quantum mechanical methods for modeling large molecular systems. In this work, by utilizing a machine learning regression technique, we have developed new low-cost quantum mechanical approaches to model large molecular systems. The developed approaches rely on using one-electron Gaussian-type functions called atom-centered potentials (ACPs) to correct for the basis set incompleteness and the lack of correlation effects in the underlying minimal or small basis set Hartree-Fock (HF) methods. In particular, ACPs are proposed for ten elements common in organic and bioorganic chemistry (H, B, C, N, O, F, Si, P, S, and Cl) and four different base methods: two minimal basis sets (MINIs and MINIX) plus a double-ζ basis set (6-31G*) in combination with dispersion-corrected HF (HF-D3/MINIs, HF-D3/MINIX, HF-D3/6-31G*) and the HF-3c method. The new ACPs are trained on a very large set (73 832 data points) of noncovalent properties (interaction and conformational energies) and validated additionally on a set of 32 048 data points. All reference data are of complete basis set coupled-cluster quality, mostly CCSD(T)/CBS. The proposed ACP-corrected methods are shown to give errors in the tenths of a kcal/mol range for noncovalent interaction energies and up to 2 kcal/mol for molecular conformational energies. More importantly, the average errors are similar in the training and validation sets, confirming the robustness and applicability of these methods outside the boundaries of the training set. In addition, the performance of the new ACP-corrected methods is similar to complete basis set density functional theory (DFT) but at a cost that is orders of magnitude lower, and the proposed ACPs can be used in any computational chemistry program that supports effective-core potentials without modification. It is also shown that ACPs improve the description of covalent and noncovalent bond geometries of the underlying methods and that the improvement brought about by the application of the ACPs is directly related to the number of atoms to which they are applied, allowing the treatment of systems containing some atoms for which ACPs are not available. Overall, the ACP-corrected methods proposed in this work constitute an alternative accurate, economical, and reliable quantum mechanical approach to describe the geometries, interaction energies, and conformational energies of systems with hundreds to thousands of atoms.

Accurate Modeling of RNA Hairpins Through the Explicit Treatment of Electronic Polarizability with the Classical Drude Oscillator Force Field

Molecular dynamics (MD) simulations play a crucial role in modeling biomolecular systems in which the electrostatic interactions are critical in dictating the structural and dynamical properties. Thus, the treatment of the electrostatic interactions defined in the underlying force field (FF) strongly affects the simulation accuracy. Most FFs use fixed partial atomic charges to include electrostatic interactions, and therefore lack the electronic polarization response, representing an intrinsic limitation. To address this limitation, polarizable FFs have been developed that treat atomic polarizabilities explicitly. Here we present the application of the all-atom polarizable (Drude) and non-polarizable (CHARMM) nucleic acid FFs in RNA hairpin systems to investigate the impact of polarization on structural properties, dipole moment distributions, and cation interactions. Results show that the presence of polarizability in the FF significantly improves the stabilization of RNA hairpin structure. As expected, the distributions of dipole moments show more fluctuations when simulated using the polarizable FF, with the variation in dipoles contributing to the stabilization of the structures of the loop regions of the RNAs. Contact map analyses between the bases and cations show that the variation of the ion distribution around the entire hairpin is larger for the polarizable FF and the cations occupy the outer hydration shell to a greater extent. The presented results indicate the importance of the explicit treatment of electronic polarizability in molecular simulations of RNA, including in non-canonical regions.

Short-Range Imbalances in the AMBER Lennard-Jones Potential for (Deoxy)Ribose···Nucleobase Lone-Pair···π Contacts in Nucleic Acids

The lone-pair···π (lp···π) (deoxy)ribose···nucleobase stacking is a recurring interaction in Z-DNA and RNAs that is characterized by sub-van der Waals lp···π contacts (<3.0 Å). It is a part of the structural signature of CpG Z-step motifs in Z-DNA and r(UNCG) tetraloops that are known to behave poorly in molecular dynamics (MD) simulations. Although the exact origin of the MD simulation issues remains unclear, a significant part of the problem might be due to an imbalanced description of nonbonded interactions, including the characteristic lp···π stacking. To gain insights into the links between lp···π stacking and MD, we present an in-depth comparison between accurate large-basis-set double-hybrid Kohn-Sham density functional theory calculations DSD-BLYP-D3/ma-def2-QZVPP (DHDF-D3) and data obtained with the nonbonded potential of the AMBER force field (AFF) for NpN Z-steps (N = G, A, C, and U). Among other differences, we found that the AFF overestimates the DHDF-D3 lp···π distances by ∼0.1-0.2 Å, while the deviation between the DHDF-D3 and AFF descriptions sharply increases in the short-range region of the interaction. Based on atom-in-molecule polarizabilities and symmetry-adapted perturbation theory analysis, we inferred that the DHDF-D3 versus AFF differences partly originate in identical nucleobase carbon atom Lennard-Jones (LJ) parameters despite the presence/absence of connected electron-withdrawing groups that lead to different effective volumes or vdW radii. Thus, to precisely model the very short CpG lp···π contact distances, we recommend revision of the nucleobase atom LJ parameters. Additionally, we suggest that the large discrepancy between DHDF-D3 and AFF short-range repulsive part of the interaction energy potential may significantly contribute to the poor performances of MD simulations of nucleic acid systems containing Z-steps. Understanding where, and if possible why, the point-charge-type effective potentials reach their limits is vital for developing next-generation FFs and for addressing specific issues in contemporary MD simulations.

NENCI-2021. I. A large benchmark database of non-equilibrium non-covalent interactions emphasizing close intermolecular contacts

In this work, we present NENCI-2021, a benchmark database of ∼8000 Non-Equilibirum Non-Covalent Interaction energies for a large and diverse selection of intermolecular complexes of biological and chemical relevance. To meet the growing demand for large and high-quality quantum mechanical data in the chemical sciences, NENCI-2021 starts with the 101 molecular dimers in the widely used S66 and S101 databases and extends the scope of these works by (i) including 40 cation-π and anion-π complexes, a fundamentally important class of non-covalent interactions that are found throughout nature and pose a substantial challenge to theory, and (ii) systematically sampling all 141 intermolecular potential energy surfaces (PESs) by simultaneously varying the intermolecular distance and intermolecular angle in each dimer. Designed with an emphasis on close contacts, the complexes in NENCI-2021 were generated by sampling seven intermolecular distances along each PES (ranging from 0.7× to 1.1× the equilibrium separation) and nine intermolecular angles per distance (five for each ion-π complex), yielding an extensive database of 7763 benchmark intermolecular interaction energies (E_int) obtained at the coupled-cluster with singles, doubles, and perturbative triples/complete basis set [CCSD(T)/CBS] level of theory. The E_int values in NENCI-2021 span a total of 225.3 kcal/mol, ranging from -38.5 to +186.8 kcal/mol, with a mean (median) E_int value of -1.06 kcal/mol (-2.39 kcal/mol). In addition, a wide range of intermolecular atom-pair distances are also present in NENCI-2021, where close intermolecular contacts involving atoms that are located within the so-called van der Waals envelope are prevalent-these interactions, in particular, pose an enormous challenge for molecular modeling and are observed in many important chemical and biological systems. A detailed symmetry-adapted perturbation theory (SAPT)-based energy decomposition analysis also confirms the diverse and comprehensive nature of the intermolecular binding motifs present in NENCI-2021, which now includes a significant number of primarily induction-bound dimers (e.g., cation-π complexes). NENCI-2021 thus spans all regions of the SAPT ternary diagram, thereby warranting a new four-category classification scheme that includes complexes primarily bound by electrostatics (3499), induction (700), dispersion (1372), or mixtures thereof (2192). A critical error analysis performed on a representative set of intermolecular complexes in NENCI-2021 demonstrates that the E_int values provided herein have an average error of ±0.1 kcal/mol, even for complexes with strongly repulsive E_int values, and maximum errors of ±0.2-0.3 kcal/mol (i.e., ∼±1.0 kJ/mol) for the most challenging cases. For these reasons, we expect that NENCI-2021 will play an important role in the testing, training, and development of next-generation classical and polarizable force fields, density functional theory approximations, wavefunction theory methods, and machine learning based intra- and inter-molecular potentials.

Optimized damping parameters for empirical dispersion corrections to symmetry-adapted perturbation theory

Symmetry-adapted perturbation theory (SAPT) has become an invaluable tool for studying the fundamental nature of non-covalent interactions by directly computing the electrostatics, exchange (steric) repulsion, induction (polarization), and London dispersion contributions to the interaction energy using quantum mechanics. Further application of SAPT is primarily limited by its computational expense, where even its most affordable variant (SAPT0) scales as the fifth power of system size [O(N⁵)] due to the dispersion terms. The algorithmic scaling of SAPT0 is reduced from O(N⁵)→O(N⁴) by replacing these terms with the empirical D3 dispersion correction of Grimme and co-workers, forming a method that may be termed SAPT0-D3. Here, we optimize the damping parameters for the -D3 terms in SAPT0-D3 using a much larger training set than has previously been considered, namely, 8299 interaction energies computed at the complete-basis-set limit of coupled cluster through perturbative triples [CCSD(T)/CBS]. Perhaps surprisingly, with only three fitted parameters, SAPT0-D3 improves on the accuracy of SAPT0, reducing mean absolute errors from 0.61 to 0.49 kcal mol^-1 over the full set of complexes. Additionally, SAPT0-D3 exhibits a nearly 2.5× speedup over conventional SAPT0 for systems with ∼300 atoms and is applied here to systems with up to 459 atoms. Finally, we have also implemented a functional group partitioning of the approach (F-SAPT0-D3) and applied it to determine important contacts in the binding of salbutamol to G-protein coupled β₁-adrenergic receptor in both active and inactive forms. SAPT0-D3 capabilities have been added to the open-source Psi4 software.

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.

Improved Basis-Set Incompleteness Potentials for Accurate Density-Functional Theory Calculations in Large Systems

The accurate calculation of chemical properties using density-functional theory (DFT) requires the use of a nearly complete basis set. In chemical systems involving hundreds to thousands of atoms, the cost of the calculations place practical limitations on the number of basis functions that can be used. Therefore, in most practical applications of DFT to large systems, there exists a basis-set incompleteness error (BSIE). In this article, we present the next iteration of the basis-set incompleteness potentials (BSIPs), one-electron potentials designed to correct for basis-set incompleteness error. The ultimate goal associated with the development of BSIPs is to allow the calculation of molecular properties using DFT with near-complete-basis-set results at a computational cost that is similar to a small basis set calculation. In this work, we develop BSIPs for 10 atoms in the first and second rows (H, B-F, Si-Cl) and 15 common basis sets of the Pople, Dunning, Karlsruhe, and Huzinaga types. Our new BSIPs are constructed to minimize BSIE in the calculation of reaction energies, barrier heights, noncovalent binding energies, and intermolecular distances. The BSIPs were obtained using a training set of 15 944 data points. The fitting approach employed a regularized linear least-squares method with variable selection (the LASSO method), which results in a much better fit to the training data than our previous BSIPs while, at the same time, reducing the computational cost of BSIP development. The proposed BSIPs are tested on various benchmark sets and demonstrate excellent performance in practice. Our new BSIPs are also transferable; i.e., they can be used to correct BSIE in calculations that employ density functionals other than the one used in the BSIP development (B3LYP). Finally, BSIPs can be used in any quantum chemistry program that have implemented effective-core potentials without changes to the software.

How accurate are approximate quantum chemical methods at modelling solute-solvent interactions in solvated clusters?

In this paper, the performance of a wide range of DFT methods is assessed for the calculation of interaction energies of thermal clusters of a solute in water. Three different charge states (neutral, proton transfer transition state and zwitterion) of glycine were solvated by 1 to 40 water molecules as sampled from molecular dynamics simulations. While some ab initio composite methods that employ insufficiently large basis sets incurred significant errors even for a cluster containing only 5 water molecules relative to the W1X-2 benchmark, the DLPNO-CCSD(T)/CBS and DSD-PBEP86 (triple zeta basis set) levels of theory predicted very accurate interaction energies. These levels of theory were used to benchmark the performance of 16 density functionals from different rungs of Jacob's Ladder. Of the Rung 4 functionals examined, the ωB97M-V and ωB97X-V functionals stood out for predicting absolute interaction energies in 40-water clusters with mean absolute deviations (MAD) ∼4 kJ mol-1. The B3LYP-D3(BJ) functional performed exceptionally well with a MAD ∼1.7 kJ mol-1 and is the overall best performing method. Calculations of relative interaction energies allow for cancellation of systematic errors, including basis set truncation and superposition errors, and the ωB97M-V and B3LYP-D3(BJ) double zeta basis set calculations yielded relative interaction energies that are within ∼3 kJ mol-1 of the benchmark. The ONIOM approximation provides another strategy for accelerating the calculation of accurate absolute interaction energies provided that the calculations have converged with respect to the size of the "high-level-layer".

QM Implementation in Drug Design: Does It Really Help?

Computational chemistry allows one to characterize the structure, dynamics, and energetics of protein-ligand interactions, which makes it a valuable tool in drug discovery in both academic research and pharmaceutical industry. Molecular mechanics (MM)-based approaches are widely utilized to assist the discovery of new drug candidates. However, the complexity of protein-ligand interactions challenges the accuracy and efficiency of the commonly used empirical methods. Aiming to provide better accuracy in the description of protein-ligand interactions, quantum mechanics (QM)-based approaches are becoming increasingly explored. In principle, QM calculation includes all contributions to the energy, accounting for terms usually missing in empirical force fields, and provides a greater degree of transferability. The usefulness of QM in drug design cannot be overemphasized. In this chapter, we present recent developments and applications of fragment-based QM method in studying the protein-ligand and protein-protein interactions. We critically discuss the performance of the fragment-based QM method at different ab initio levels while trying to answer a critical question: do QM-based methods really help in drug design?

Revisiting the Potential Energy Surface of the Stacked Cytosine Dimer: FNO-CCSD(T) Interaction Energies, SAPT Decompositions, and Benchmarking

Nucleobase stacking interactions are crucial for the stability of nucleic acids. This study investigates base stacking energies of the cytosine homodimer in different configurations, including intermolecular separation plots, detailed twist dependence, and displaced structures. Highly accurate ab initio quantum chemical single point energies using an energy function based on MP2 complete basis set extrapolation ([6 → 7]ZaPa-NR) and a CCSD(T)/cc-pVTZ-F12 high-level correction are presented as new reference data, providing the most accurate stacking energies of nucleobase dimers currently available. Accurate SAPT2+(3)δMP2 energy decomposition is used to obtain detailed insights into the nature of base stacking interactions at varying vertical distances and twist values. The ab initio symmetry adapted perturbation theory (SAPT) energy decomposition suggests that the base stacking originates from an intricate interplay between dispersion attraction, short-range exchange-repulsion, and Coulomb interaction. The interpretation of the SAPT data is a complex issue as key energy terms vary substantially in the region of optimal (low energy) base stacking geometries. Thus, attempts to highlight one leading stabilizing SAPT base stacking term may be misleading and the outcome strongly depends on the used geometries within the range of geometries sampled in nucleic acids upon thermal fluctuations. Modern dispersion-corrected density functional theory (among them DSD-BLYP-D3, ωB97M-V, and ωB97M-D3BJ) is benchmarked and often reaches up to spectroscopic accuracy (below 1 kJ/mol). The classical AMBER force field is benchmarked with multiple different sets of point-charges (e.g. HF, DFT, and MP2-based) and is found to produce reasonable agreement with the benchmark data.

Read between the Molecules: Computational Insights into Organic Semiconductors

The performance and key electronic properties of molecular organic semiconductors are dictated by the interplay between the chemistry of the molecular core and the intermolecular factors of which manipulation has inspired both experimentalists and theorists. This Perspective presents major computational challenges and modern methodological strategies to advance the field. The discussion ranges from insights and design principles at the quantum chemical level, in-depth atomistic modeling based on multiscale protocols, morphological prediction and characterization as well as energy-property maps involving data-driven analysis. A personal overview of the past achievements and future direction is also provided.

A physically grounded damped dispersion model with particle mesh Ewald summation

Accurate modeling of dispersion is critical to the goal of predictive biomolecular simulations. To achieve this accuracy, a model must be able to correctly capture both the short-range and asymptotic behavior of dispersion interactions. We present here a damped dispersion model based on the overlap of charge densities that correctly captures both regimes. The overlap damped dispersion model represents a classical physical interpretation of dispersion: the interaction between the instantaneous induced dipoles of two distinct charge distributions. This model is shown to be an excellent fit with symmetry adapted perturbation theory dispersion energy calculations, yielding an RMS error on the S101x7 database of 0.5 kcal/mol. Moreover, the damping function used in this model is wholly derived and parameterized from the electrostatic dipole-dipole interaction, making it not only physically grounded but transferable as well.

AMOEBA Polarizable Atomic Multipole Force Field for Nucleic Acids

The AMOEBA polarizable atomic multipole force field for nucleic acids is presented. Valence and electrostatic parameters were determined from high-level quantum mechanical data, including structures, conformational energy, and electrostatic potentials, of nucleotide model compounds. Previously derived parameters for the phosphate group and nucleobases were incorporated. A total of over 35 μs of condensed-phase molecular dynamics simulations of DNA and RNA molecules in aqueous solution and crystal lattice were performed to validate and refine the force field. The solution and/or crystal structures of DNA B-form duplexes, RNA duplexes, and hairpins were captured with an average root-mean-squared deviation from NMR structures below or around 2.0 Å. Structural details, such as base pairing and stacking, sugar puckering, backbone and χ-torsion angles, groove geometries, and crystal packing interfaces, agreed well with NMR and/or X-ray. The interconversion between A- and B-form DNAs was observed in ethanol-water mixtures at 328 K. Crystal lattices of B- and Z-form DNA and A-form RNA were examined with simulations. For the RNA tetraloop, single strand tetramers, and HIV TAR with 29 residues, the simulated conformational states, 3 J-coupling, nuclear Overhauser effect, and residual dipolar coupling data were compared with NMR results. Starting from a totally unstacked/unfolding state, the rCAAU tetranucleotide was folded into A-form-like structures during ∼1 μs molecular dynamics simulations.

Physics-based all-atom modeling of RNA energetics and structure

The database of RNA sequences is exploding, but knowledge of energetics, structures, and dynamics lags behind. All-atom computational methods, such as molecular dynamics, hold promise for closing this gap. New algorithms and faster computers have accelerated progress in improving the reliability and accuracy of predictions. Currently, the methods can facilitate refinement of experimentally determined nuclear magnetic resonance and x-ray structures, but are 'unreliable' for predictions based only on sequence. Much remains to be discovered, however, about the many molecular interactions driving RNA folding and the best way to approximate them quantitatively. The large number of parameters required means that a wide variety of experimental results will be required to benchmark force fields and different approaches. As computational methods become more reliable and accessible, they will be used by an increasing number of biologists, much as x-ray crystallography has expanded. Thus, many fundamental physical principles underlying the computational methods are described. This review presents a summary of the current state of molecular dynamics as applied to RNA. It is designed to be helpful to students, postdoctoral fellows, and faculty who are considering or starting computational studies of RNA. WIREs RNA 2017, 8:e1422. doi: 10.1002/wrna.1422.

An optimized charge penetration model for use with the AMOEBA force field

The principal challenge of using classical physics to model biomolecular interactions is capturing the nature of short-range interactions that drive biological processes from nucleic acid base stacking to protein-ligand binding. In particular most classical force fields suffer from an error in their electrostatic models that arises from an ability to account for the overlap between charge distributions occurring when molecules get close to each other, known as charge penetration. In this work we present a simple, physically motivated model for including charge penetration in the AMOEBA (Atomic Multipole Optimized Energetics for Biomolecular Applications) force field. With a function derived from the charge distribution of a hydrogen-like atom and a limited number of parameters, our charge penetration model dramatically improves the description of electrostatics at short range. On a database of 101 biomolecular dimers, the charge penetration model brings the error in the electrostatic interaction energy relative to the ab initio SAPT electrostatic interaction energy from 13.4 kcal mol^-1 to 1.3 kcal mol^-1. The model is shown not only to be robust and transferable for the AMOEBA model, but also physically meaningful as it universally improves the description of the electrostatic potential around a given molecule.

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.

Polarizable Force Field for DNA Based on the Classical Drude Oscillator: II. Microsecond Molecular Dynamics Simulations of Duplex DNA

The structure and dynamics of DNA are governed by a sensitive balance between base stacking and pairing, hydration, and interactions with ions. Force-field models that include explicit representations of electronic polarization are capable of more accurately modeling the subtle details of these interactions versus commonly used additive force fields. In this work, we validate our recently refined polarizable force field for DNA based on the classical Drude oscillator model, in which electronic degrees of freedom are represented as negatively charged particles attached to their parent atoms via harmonic springs. The previous version of the force field, called Drude-2013, produced stable A- and B-DNA trajectories on the order of hundreds of nanoseconds, but deficiencies were identified that included weak base stacking ultimately leading to distortion of B-DNA duplexes and unstable Z-DNA. As a result of extensive refinement of base nonbonded terms and bonded parameters in the deoxyribofuranose sugar and phosphodiester backbone, we demonstrate that the new version of the Drude DNA force field is capable of simulating A- and B-forms of DNA on the microsecond time scale and the resulting conformational ensembles agree well with a broad set of experimental properties, including solution X-ray scattering profiles. In addition, simulations of Z-form duplex DNA in its crystal environment are stable on the order of 100 ns. The revised force field is to be called Drude-2017.

Polarizable Force Field for DNA Based on the Classical Drude Oscillator: I. Refinement Using Quantum Mechanical Base Stacking and Conformational Energetics

Empirical force fields seek to relate the configuration of a set of atoms to its energy, thus yielding the forces governing its dynamics, using classical physics rather than more expensive quantum mechanical calculations that are computationally intractable for large systems. Most force fields used to simulate biomolecular systems use fixed atomic partial charges, neglecting the influence of electronic polarization, instead making use of a mean-field approximation that may not be transferable across environments. Recent hardware and software developments make polarizable simulations feasible, and to this end, polarizable force fields represent the next generation of molecular dynamics simulation technology. In this work, we describe the refinement of a polarizable force field for DNA based on the classical Drude oscillator model by targeting quantum mechanical interaction energies and conformational energy profiles of model compounds necessary to build a complete DNA force field. The parametrization strategy employed in the present work seeks to correct weak base stacking in A- and B-DNA and the unwinding of Z-DNA observed in the previous version of the force field, called Drude-2013. Refinement of base nonbonded terms and reparametrization of dihedral terms in the glycosidic linkage, deoxyribofuranose rings, and important backbone torsions resulted in improved agreement with quantum mechanical potential energy surfaces. Notably, we expand on previous efforts by explicitly including Z-DNA conformational energetics in the refinement.

Density-fitted open-shell symmetry-adapted perturbation theory and application to π-stacking in benzene dimer cation and ionized DNA base pair steps

Symmetry-Adapted Perturbation Theory (SAPT) is one of the most popular approaches to energy component analysis of non-covalent interactions between closed-shell systems, yielding both accurate interaction energies and meaningful interaction energy components. In recent years, the full open-shell equations for SAPT up to second-order in the intermolecular interaction and zeroth-order in the intramolecular correlation (SAPT0) were published [P. S. Zuchowski et al., J. Chem. Phys. 129, 084101 (2008); M. Hapka et al., ibid. 137, 164104 (2012)]. Here, we utilize density-fitted electron repulsion integrals to produce an efficient computational implementation. This approach is used to examine the effect of ionization on π-π interactions. For the benzene dimer radical cation, comparison against reference values indicates a good performance for open-shell SAPT0, except in cases with substantial charge transfer. For π stacking between hydrogen-bonded pairs of nucleobases, dispersion interactions still dominate binding, in spite of the creation of a positive charge.

Polarizable Multipole-Based Force Field for Aromatic Molecules and Nucleobases

Aromatic molecules with π electrons are commonly involved in chemical and biological recognitions. For example, nucleobases play central roles in DNA/RNA structure and their interactions with proteins. The delocalization of the π electrons is responsible for the high polarizability of aromatic molecules. In this work, the AMOEBA force field has been developed and applied to 5 regular nucleobases and 12 aromatic molecules. The permanent electrostatic energy is expressed as atomic multipole interactions between atom pairs, and many-body polarization is accounted for by mutually induced atomic dipoles. We have systematically investigated aromatic ring stacking and aromatic-water interactions for nucleobases and aromatic molecules, as well as base–base hydrogen-bonding pair interactions, all at various distances and orientations. van der Waals parameters were determined by comparison to the quantum mechanical interaction energy of these dimers and fine-tuned using condensed phase simulation. By comparing to quantum mechanical calculations, we show that the resulting classical potential is able to accurately describe molecular polarizability, molecular vibrational frequency, and dimer interaction energy of these aromatic systems. Condensed phase properties, including hydration free energy, liquid density, and heat of vaporization, are also in good overall agreement with experimental values. The structures of benzene liquid phase and benzene-water solution were also investigated by simulation and compared with experimental and PDB structure derived statistical results.

Implications of Charge Penetration for Heteroatom-Containing Organic Semiconductors

The noncovalent interactions of neutral π-conjugated cores, pertinent to organic semiconductor materials, are intimately related to their charge transport properties and involve a subtle interplay of dispersion, Pauli repulsion, and electrostatic contributions. Realizing structural arrangements that are both energetically preferred and sufficiently conductive is a challenge. We tackle this problem by means of charge penetration contribution to the interaction energy, boosted in systems containing large heteroatoms (e.g., sulfur, selenium, phosphorus, silicon, and arsenic). We find that in both the model and "realistic" dimers of such heteroatom-containing cores dispersion is balanced out by the exchange and interaction energy is instead governed by substantial charge penetration. These systems also feature stronger electronic couplings compared to the dispersion-driven dimers of oligoacenes and/or the herringbone assemblies. Thus, charge penetration, enhanced in the π-conjugated cores comprising larger heteroatoms, arises as an attractive strategy toward potentially more stable and efficient organic electronic materials.

General van der Waals potential for common organic molecules

This work presents a systematic development of a new van der Waals potential (vdW2016) for common organic molecules based on symmetry-adapted perturbation theory (SAPT) energy decomposition. The Buf-14-7 function, as well as Cubic-mean and Waldman-Hagler mixing rules were chosen given their best performance among other popular potentials. A database containing 39 organic molecules and 108 dimers was utilized to derive a general set of vdW parameters, which were further validated on nucleobase stacking systems and testing organic dimers. The vdW2016 potential is anticipated to significantly improve the accuracy and transferability of new generations of force fields for organic molecules.

Beyond Born-Mayer: Improved Models for Short-Range Repulsion in ab Initio Force Fields

Short-range repulsion within intermolecular force fields is conventionally described by either Lennard-Jones (A/r(12)) or Born-Mayer (A exp(-Br)) forms. Despite their widespread use, these simple functional forms are often unable to describe the interaction energy accurately over a broad range of intermolecular distances, thus creating challenges in the development of ab initio force fields and potentially leading to decreased accuracy and transferability. Herein, we derive a novel short-range functional form based on a simple Slater-like model of overlapping atomic densities and an iterated stockholder atom (ISA) partitioning of the molecular electron density. We demonstrate that this Slater-ISA methodology yields a more accurate, transferable, and robust description of the short-range interactions at minimal additional computational cost compared to standard Lennard-Jones or Born-Mayer approaches. Finally, we show how this methodology can be adapted to yield the standard Born-Mayer functional form while still retaining many of the advantages of the Slater-ISA approach.

Revised Damping Parameters for the D3 Dispersion Correction to Density Functional Theory

Since the original fitting of Grimme's DFT-D3 damping parameters, the number and quality of benchmark interaction energies has increased significantly. Here, conventional benchmark sets, which focus on minimum-orientation radial curves at the expense of angular diversity, are augmented by new databases such as side chain-side chain interactions (SSI), which are composed of interactions gleaned from crystal data and contain no such minima-focused bias. Moreover, some existing databases such as S22×5 are extended to shorter intermolecular separations. This improved DFT-D3 training set provides a balanced description of distances, covers the entire range of interaction types, and at 1526 data points is far larger than the original training set of 130. The results are validated against a new collection of 6773 data points and demonstrate that the effect of refitting the damping parameters ranges from no change in accuracy (LC-ωPBE-D3) to an almost 2-fold decrease in average error (PBE-D3).

A Universal and Straightforward Approach to Include Penetration Effects in Electrostatic Interaction Energy Estimation

To compensate for the lack of the explicit treatment of charge penetration in classical force fields, we propose a new charge-distribution model based on a promolecule augmented with point charges (aug-PROmol). It relies on a superposition of spherical atomic electron densities obtained for each chemical element from SCF energy optimized atomic orbitals. Atomic densities are further rescaled by partial point charges computed from fits to the molecular electrostatic potential. Aug-PROmol was tested on the S66 benchmark dataset extended to nonequilibrium geometries (J. Chem. Theory Comput., 2011, 7, 3466). The model does not need any additional parametrization other than point charges. Despite its simplicity, aug-PROmol approximates the electrostatic energy with good agreement (RMSE=0.76 kcal mol(-1) to DFT-SAPT with B3LYP/aug-cc-pVTZ).