HF-3c Method Research Articles

Low-cost quantum mechanical descriptors for data efficient skin sensitization QSAR models

Quantitative Structure Activity Relationship modelling methodologies need to incorporate relevant mechanistic information to have high predictive performance and validity. Electrophilic reactivity is a common mechanistic feature of skin sensitization endpoints which could be concisely characterized with electronic descriptors which is key to enabling the modelling of small datasets in this domain. However, quantum mechanical methodologies have previously featured high computational costs which would exclude the use of large datasets. Consequently, we investigate the use of electronic descriptors calculated using the Hartree Fock with 3 corrections (Hf-3c) method, a low-cost ab initio methodology that has higher chemical accuracy than previous semiempirical methodologies for modelling in vitro skin sensitization assay outcomes. We also model the Ames assay as a surrogate for determining skin sensitization outcomes. The quantum chemical descriptors calculated using the Hf-3c method with conductor-like polarizable continuum model (CPCM) implicit solvation found improved QSAR model performance for the in vitro Ames (n = 6049, 0.770 AUC), KeratinoSens (n = 164, 0.763 AUC), and Direct Peptide Reactivity Assay (n = 122, 0.750 AUC) datasets, with their combination producing high predictive performance for unseen in vivo Local Lymph Node Assay (n = 86, 0.789 AUC) and Human Repeated Insult Patch Test (n = 86, 0.791 AUC) assay toxicant outcomes.

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.

Efficient and Accurate Potential Energy Surfaces of Puckering in Sugar-Modified Nucleosides.

Puckering of the sugar unit in nucleosides and nucleotides is an important structural aspect that directly influences the helical structure of nucleic acids. The preference for specific puckering modes in nucleic acids can be analyzed via in silico conformational analysis, but the large amount of conformations and the accuracy of the analysis leads to an extensive amount of computational time. In this paper, we show that the combination of geometry optimizations with the HF-3c method with single point energies at the RI-MP2 level results in accurate results for the puckering potential energy surface (PES) of DNA and RNA nucleosides while significantly reducing the necessary computational time. Applying this method to a series of known xeno nucleic acids (XNAs) allowed us to rapidly explore the puckering PES of each of the respective nucleosides and to explore the puckering PES of six-membered modified XNA (HNA and β-homo-DNA) for the first time.

Balancing Cost and Accuracy in Quantum Mechanical Simulations on Collagen Protein Models.

Collagen proteins are spread in almost every vertebrate's tissue with mechanical function. The defining feature of this fundamental family of proteins is its well-known collagen triple-helical domain. This helical domain can have different geometries, varying in helical elongation and interstrands contact, as a function of the amino acidic composition. The helical geometrical features play an important role in the interaction of the collagen protein with cell receptors, but for the vast majority of collagen compositions, these geometrical features are unknown. Quantum mechanical (QM) simulations based on the density functional theory (DFT) provide a robust approach to characterize the scenario on the collagen composition-structure relationships. In this work, we analyze the role of the adopted computational method in predicting the collagen structure for two purposes. First, we look for a cost-effective computational approach to apply to a large-scale composition-structure analysis. Second, we attempt to assess the robustness of the predictions by varying the QM methods. Therefore, we have run geometry optimization on periodic models of the collagen protein using a variety of approaches based on the most commonly used DFT functionals (PBE, HSE06, and B3LYP) with and without dispersion correction (D3ABC). We have coupled these methods with several different basis sets, looking for the highest accuracy/cost ratio. Furthermore, we have studied the performance of the composite HF-3c method and the semiempirical GFN1-xTB method. Our results identify a computational recipe that is potentially capable of predicting collagen structural features in line with DFT simulations, with orders of magnitude reduced computational cost, encouraging further investigations on the topic.

Rationalization of Lattice Thermal Expansion for Beta-Blocker Organic Crystals

Anisotropic lattice expansion could be a source of misunderstanding in powder pattern recognitions, especially in the case of organic crystals where for the interpretation of room temperature patterns single crystal data at low temperature are usually used. Trying to rationalize the thermal lattice expansion, we studied two close related β-blocker molecules with similar packing in the solid state but with different thermal behavior. Solid state calculations, using the fast and accurate HF-3c method and the quasi harmonic approximation for the simulation of the lattice expansion, were able to reproduce the experimental trends with good accuracy. The complete analysis of the calculated thermal expansion of the two structures, as well as of other structures with similar packing found in a database survey, revealed the primary role of the hydrogen bonds. Secondary non-covalent interactions in the plane perpendicular to the hydrogen bond system could also play a role.

Importance of model size in quantum mechanical studies of DNA intercalation.

The convergence of DFT-computed interaction energies with increasing binding site model size was assessed. The data show that while accurate intercalator interaction energies can be derived from binding site models featuring only the flanking nucleotides for uncharged intercalators that bind parallel to the DNA base pairs, errors remain significant even when including distant nucleotides for intercalators that are charged, exhibit groove-binding tails that engage in noncovalent interactions with distant nucleotides, or that bind perpendicular to the DNA base pairs. Consequently, binding site models that include at least three adjacent nucleotides are required to consistently predict converged binding energies. The computationally inexpensive HF-3c method is shown to provide reliable interaction energies and can be routinely applied to such large models.

Cost-Effective Quantum Mechanical Approach for Predicting Thermodynamic and Mechanical Stability of Pure-Silica Zeolites.

Several computational techniques for solid-state applications have recently been proposed to enlarge the scope of computer simulations of large molecular systems. In this contribution, we focused on two of these, namely, HF-3c and PBEh-3c. They were recently proposed by the Grimme’s group, as “low-cost” ab initio-based techniques for electronic structure calculation of large systems and were proved to be effective essentially for organic molecules. HF-3c is based on a Hartree–Fock Hamiltonian with a minimal Gaussian quality basis set, whereas PBEh-3c is a density functional theory (DFT) based method with a hybrid functional and a medium-quality basis set. Both HF-3c and PBEh-3c account for dispersion (London) interactions and are free from the basis set superposition error due to limited basis set size, through several pairwise semiempirical corrections. To the best of our knowledge, despite the promising results on the cost-accuracy side of molecular simulations of organic molecules, these methods have been used only in few cases for solid-state applications. In this contribution, we studied the performance of HF-3c and PBEh-3c for predicting the properties of inorganic crystals to enlarge the applicability of these cheap and fast methodologies. As a testing ground, we have chosen a well-known class of material, e.g., microporous all-silica zeolites. We benchmarked geometries, formation energies, vibrational features, and mechanical properties by comparing the results with literature data from both experiment and computer simulation. For structures, HF-3c is extremely accurate in predicting the zeolites cell volume, albeit we do not include any vibrational contribution, neither zero point nor thermal, on the computed volumes, which may introduce small variations in the predicted values. For the energetic, the relative stability of the zeolites using the DFT//HF-3c approach allows predictions within the experimental error for most of the cases taken into consideration when the experimental enthalpies were corrected back to electronic energies by using the HF-3c thermodynamic contributions computed in the harmonic approximation. This strategy is particularly convenient, as the slow step (geometry optimization) is carried out with the cheapest HF-3c method, whereas the fast step (single point energy evaluation) is carried out with costly DFT methods. In this sense, the use of the DFT//HF-3c approach results to be a promising one to predict the stability and structure of microporous materials. Finally, the HF-3c method predicts the mechanical properties of the zeolite set in reasonable agreement with respect to those computed with the state-of-the-art DFT simulations, indicating the HF-3c method as a possible technique for the mechanical stability screenings of microporous materials.

On the hydrogen activation by frustrated Lewis pairs in the solid state: benchmark studies and theoretical insights.

Recently, the concept of small molecule activation by frustrated Lewis pairs (FLPs) has been expanded to the solid state showing a variety of interesting reactivities. Therefore, there is a need to establish a computational protocol to investigate such systems theoretically. In the present study, we selected several FLPs and applied multiple levels of theory, ranging from a semi-empirical tight-binding Hamiltonian to dispersion corrected hybrid density functionals. Their performance is benchmarked for the computation of crystal geometries, thermostatistical contributions, and reaction energies. We show that the computationally efficient HF-3c method gives accurate crystal structures and is numerically stable and sufficiently fast for routine applications. This method also gives reliable values for the thermostatistical contributions to Gibbs free energies. The meta-generalized gradient approximated TPSS-D3 evaluated in a projector augmented plane wave basis set is able to produce sufficiently accurate reaction electronic energies. The established protocol is intended to support experimental studies and to predict new reactions in the emerging field of solid-state FLPs.This article is part of the themed issue 'Frustrated Lewis pair chemistry'.

Intermolecular interactions in the condensed phase: Evaluation of semi-empirical quantum mechanical methods.

To facilitate further development of approximate quantum mechanical methods for condensed phase applications, we present a new benchmark dataset of intermolecular interaction energies in the solution phase for a set of 15 dimers, each containing one charged monomer. The reference interaction energy in solution is computed via a thermodynamic cycle that integrates dimer binding energy in the gas phase at the coupled cluster level and solute-solvent interaction with density functional theory; the estimated uncertainty of such calculated interaction energy is ±1.5 kcal/mol. The dataset is used to benchmark the performance of a set of semi-empirical quantum mechanical (SQM) methods that include DFTB3-D3, DFTB3/CPE-D3, OM2-D3, PM6-D3, PM6-D3H+, and PM7 as well as the HF-3c method. We find that while all tested SQM methods tend to underestimate binding energies in the gas phase with a root-mean-squared error (RMSE) of 2-5 kcal/mol, they overestimate binding energies in the solution phase with an RMSE of 3-4 kcal/mol, with the exception of DFTB3/CPE-D3 and OM2-D3, for which the systematic deviation is less pronounced. In addition, we find that HF-3c systematically overestimates binding energies in both gas and solution phases. As most approximate QM methods are parametrized and evaluated using data measured or calculated in the gas phase, the dataset represents an important first step toward calibrating QM based methods for application in the condensed phase where polarization and exchange repulsion need to be treated in a balanced fashion.

Method Dependence of Proline Ring Flexibility in the Poly-l-Proline Type II Polymer.

We studied the sensitivity of the energetic and geometrical features of the proline ring (pyrrolidine) to the quantum mechanical computational approach by adopting the proline monomer, trimer, and polymer, as simplified collagen protein models. Within the Density Functional Theory (DFT) approach, we tested the ability of different functionals (GGA PBE and the hybrid B3LYP), added with a posteriori empirical dispersion corrections (D), to predict the conformational potential energy surface of the five-membered heterocycle pyrrolidine ring for the above models, dictating the collagen main features. We also compared the DFT-D results with those from the recently proposed cost-effective HF-3c method and our variant HF-3c-027, both based on Hartree-Fock Hamiltonian and Gaussian minimal basis set properly corrected for basis set superposition error, structure deficiencies, and dispersion interactions. We found that dispersion interactions are essential to destabilize specific conformers. While the HF-3c and its HF-3c-027 variant are unreliable to predict accurately the energy of the ring conformers, structures are accurate. Indeed, the cost-effective DFT-D//HF-3c-027 approach in which the energetic is from the accurate DFT-D method on HF-3c-027 structures provides energetic in line with that derived by the costly DFT-D//DFT-D approach, paving the way to simulate more realistic collagen models of much larger size. The adoption of either PBE or B3LYP functional for the electronic part of the DFT-D method gives very similar results, recommending the first as the most cost-effective method for simulating large collagen models. The predicted most stable conformation computed for the periodic poly proline (type II) model allows for a higher flexibility, in agreement with experimental studies on collagen protein. The present results open the way to large-scale calculations of the collagen/hydroxyapatite system, crucial for understanding the atomistic details in bones and teeth.

Assessment of Different Quantum Mechanical Methods for the Prediction of Structure and Cohesive Energy of Molecular Crystals.

A comparative assessment of the accuracy of different quantum mechanical methods for evaluating the structure and the cohesive energy of molecular crystals is presented. In particular, we evaluate the performance of the semiempirical HF-3c method in comparison with the B3LYP-D* and the Local MP2 (LMP2) methods by means of a fully periodic approach. Three benchmark sets have been investigated: X23, G60, and the new K7; for a total of 82 molecular crystals. The original HF-3c method performs well but shows a tendency at overbinding molecular crystals, in particular for weakly bounded systems. For the X23 set, the mean absolute error for the cohesive energies computed with the HF-3c method is comparable to the LMP2 one. A refinement of the HF-3c has been attempted by tuning the dispersion term in the HF-3c energy. While the performance on cohesive energy prediction slightly worsens, optimized unit cell volumes are in excellent agreement with experiment. Overall, the B3LYP-D* method combined with a TZP basis set gives the best results. For cost-effective calculations on molecular crystals, we propose to compute cohesive energies at the B3LYP-D*/TZP level of theory on the dispersion-scaled HF-3c optimized geometries (i.e., B3LYP-D*/TZP//HF-3c(0.27) also dubbed as SP-B3LYP-D*). Besides, for further benchmarking on molecular crystals, we propose to combine the three test sets in a new one denoted as MC82.