Method Calibration or Data Fitting?

DELTA50: A Highly Accurate Database of Experimental 1H and 13C NMR Chemical Shifts Applied to DFT Benchmarking

Density functional theory (DFT) benchmark studies of ¹H and ¹³C NMR chemical shifts often yield differing conclusions, likely due to non-optimal test molecules and non-standardized data acquisition. To address this issue, we carefully selected and measured ¹H and ¹³C NMR chemical shifts for 50 structurally diverse small organic molecules containing atoms from only the first two rows of the periodic table. Our NMR dataset, DELTA50, was used to calculate linear scaling factors and to evaluate the accuracy of 73 density functionals, 40 basis sets, 3 solvent models, and 3 gauge-referencing schemes. The best performing DFT methodologies for ¹H and ¹³C NMR chemical shift predictions were WP04/6-311++G(2d,p) and ωB97X-D/def2-SVP, respectively, when combined with the polarizable continuum solvent model (PCM) and gauge-independent atomic orbital (GIAO) method. Geometries should be optimized at the B3LYP-D3/6-311G(d,p) level including the PCM solvent model for the best accuracy. Predictions of 20 organic compounds and natural products from a separate probe set had root-mean-square deviations (RMSD) of 0.07 to 0.19 for ¹H and 0.5 to 2.9 for ¹³C. Maximum deviations were less than 0.5 and 6.5 ppm for ¹H and ¹³C, respectively.

Slater transition methods for core-level electron binding energies

Methods for computing core-level ionization energies using self-consistent field (SCF) calculations are evaluated and benchmarked. These include a "full core hole" (or "ΔSCF") approach that fully accounts for orbital relaxation upon ionization, but also methods based on Slater's transition concept in which the binding energy is estimated from an orbital energy level that is obtained from a fractional-occupancy SCF calculation. A generalization that uses two different fractional-occupancy SCF calculations is also considered. The best of the Slater-type methods afford mean errors of 0.3-0.4 eV with respect to experiment for a dataset of K-shell ionization energies, a level of accuracy that is competitive with more expensive many-body techniques. An empirical shifting procedure with one adjustable parameter reduces the average error below 0.2 eV. This shifted Slater transition method is a simple and practical way to compute core-level binding energies using only initial-state Kohn-Sham eigenvalues. It requires no more computational effort than ΔSCF and may be especially useful for simulating transient x-ray experiments where core-level spectroscopy is used to probe an excited electronic state, for which the ΔSCF approach requires a tedious state-by-state calculation of the spectrum. As an example, we use Slater-type methods to model x-ray emission spectroscopy.

Improving the accuracy of 31P NMR chemical shift calculations by use of scaling methods

Calculation of ³¹P NMR chemical shifts for a series of tri- and tetracoordinate phosphorus compounds using several basis sets and density functional theory (DFT) functionals gave a modest fit to experimental chemical shifts, but an excellent linear fit when plotted against the experimental values. The resultant scaling methods were then applied to a variety of "large" compounds previously selected by Latypov et al. and a set of stereoisomeric and unusual compounds selected here. No one method was best for all structural types. For compounds that contain P-P bonds and P-C multiple bonds, the Latypov et al. method using the PBE0 functional was best (mean absolute deviation/root mean square deviation (MAD/RMSD) = 6.9/8.5 ppm and 6.6/8.2 ppm, respectively), but for the full set of compounds gave higher deviations (MAD/RMSD = 8.2/12.3 ppm), and failed by over 60 ppm for a three-membered phosphorus heterocycle. Use of the M06-2X functional for both the structural optimization and NMR chemical shift calculation was best overall for the compounds without P-C multiple bonds (MAD/RMSD = 5.4/7.1 ppm), but failed by 30-49 ppm for compounds having any P-C multiple-bond character. Failures of these magnitudes have not been reported previously for these widely used functionals. These failures were then used to screen a variety of recommended functionals, leading to better overall methods for calculation of these chemical shifts: optimization with the M06-2X functional and NMR calculation with the PBE0 or ωB97x-D functionals gave values for MAD/RMSD = 6.9/8.5 ppm and 6.8/9.1 ppm, respectively, over an experimental chemical shift range of -181 to 356 ppm. Due to the unexplained failures observed, we recommend use of more than one method when looking at novel structures.

Systematic Evaluation of Counterpoise Correction in Density Functional Theory

A widespread belief persists that the Boys-Bernardi function counterpoise (CP) procedure "overcorrects" supramolecular interaction energies for the effects of basis-set superposition error. To the extent that this is true for correlated wave function methods, it is usually an artifact of low-quality basis sets. The question has not been considered systematically in the context of density functional theory, however, where basis-set convergence is generally less problematic. We present a systematic assessment of the CP procedure for a representative set of functionals and basis sets, considering both benchmark data sets of small dimers and larger supramolecular complexes. The latter include layered composite polymers with ∼150 atoms and ligand-protein models with ∼300 atoms. Provided that CP correction is used, we find that intermolecular interaction energies of nearly complete-basis quality can be obtained using only double-ζ basis sets. This is less expensive as compared to triple-ζ basis sets without CP correction. CP-corrected interaction energies are less sensitive to the presence of diffuse basis functions as compared to uncorrected energies, which is important because diffuse functions are expensive and often numerically problematic for large systems. Our results upend the conventional wisdom that CP "overcorrects" for basis-set incompleteness. In small basis sets, CP correction is mandatory in order to demonstrate that the results do not rest on error cancellation.

New pecJ-n (n = 1, 2) Basis Sets for High-Quality Calculations of Indirect Nuclear Spin–Spin Coupling Constants Involving 31P and 29Si: The Advanced PEC Method

In this paper, we presented new J-oriented basis sets, pecJ-n (n = 1, 2), for phosphorus and silicon, purposed for the high-quality correlated calculations of the NMR spin–spin coupling constants involving these nuclei. The pecJ-n basis sets were generated using the modified version of the property-energy consistent (PEC) method, which was introduced in our earlier paper. The modifications applied to the original PEC procedure increased the overall accuracy and robustness of the generated basis sets in relation to the diversity of electronic systems. Our new basis sets were successfully tested on a great number of spin–spin coupling constants, involving phosphorus or/and silicon, calculated within the SOPPA(CCSD) method. In general, it was found that our new pecJ-1 and pecJ-2 basis sets are very efficient, providing the overall accuracy that can be characterized by MAEs of about 3.80 and 1.98 Hz, respectively, against the benchmark data obtained with a large dyall.aae4z⁺ basis set of quadruple-ζ quality.

New pecS-n (n = 1, 2) basis sets for quantum chemical calculations of the NMR chemical shifts of H, C, N, and O nuclei

This paper demonstrates the performance of our previously suggested property-energy consistent method on the example of the generation of effective basis sets, pecS-1 and pecS-2, suited for the calculation of hydrogen, carbon, nitrogen, and oxygen chemical shifts. The new basis sets were successfully approbated in the GIAO-DFT calculations of the chemical shifts of 35 molecules using six different functionals. The pecS-1 basis set demonstrated very good accuracy, which makes this small basis set an effective means for the large-scale computations. At the same time, the pecS-2 basis set also gave very accurate results, thus putting it on a par with the other commensurate basis sets suited for the chemical shifts calculations.

Interaction of Amyloid-β-(1-42) Peptide and Its Aggregates with Lipid/Water Interfaces Probed by Vibrational Sum-Frequency Generation Spectroscopy

In this study, we use surface-sensitive vibrational sum-frequency generation (VSFG) spectroscopy to investigate the interaction between model lipid monolayers and Aβ(1-42) in its monomeric and aggregated states. Combining VSFG with atomic force microscopy (AFM) and thioflavin T (ThT) fluorescence measurements, we found that only small aggregates with probably a β-hairpin-like structure adsorbed to the zwitterionic lipid monolayer (DOPC). In contrast, larger aggregates with an extended β-sheet structure adsorbed to a negatively charged lipid monolayer (DOPG). The adsorption of small, initially formed aggregates strongly destabilized both monolayers, but only the DOPC monolayer was completely disrupted. We showed that the intensity of the amide-II' band in achiral (SSP) and chiral (SPP) polarization combinations increased in time when Aβ(1-42) aggregates accumulated at the DOPG monolayer. Nevertheless, almost no adsorption of preformed mature fibrils to DOPG monolayers was detected. By performing spectral VSFG calculations, we revealed a clear correlation between the amide-II' signal and the degree of amyloid aggregates (e.g., oligomers or (proto)fibrils) of various Aβ(1-42) structures. The calculations showed that only structures with a significant amyloid β-sheet content have a strong amide-II' intensity, in line with previous Raman studies. The combination of the presented results substantiates the amide-II(') band as a legitimate amyloid marker.

Machine learning to tame divergent density functional approximations: a new path to consensus materials design principles

Virtual high-throughput screening (VHTS) with density functional theory (DFT) and machine-learning (ML)-acceleration is essential in rapid materials discovery. By necessity, efficient DFT-based workflows are carried out with a single density functional approximation (DFA). Nevertheless, properties evaluated with different DFAs can be expected to disagree for cases with challenging electronic structure (e.g., open-shell transition-metal complexes, TMCs) for which rapid screening is most needed and accurate benchmarks are often unavailable. To quantify the effect of DFA bias, we introduce an approach to rapidly obtain property predictions from 23 representative DFAs spanning multiple families, “rungs” (e.g., semi-local to double hybrid) and basis sets on over 2000 TMCs. Although computed property values (e.g., spin state splitting and frontier orbital gap) differ by DFA, high linear correlations persist across all DFAs. We train independent ML models for each DFA and observe convergent trends in feature importance, providing DFA-invariant, universal design rules. We devise a strategy to train artificial neural network (ANN) models informed by all 23 DFAs and use them to predict properties (e.g., spin-splitting energy) of over 187k TMCs. By requiring consensus of the ANN-predicted DFA properties, we improve correspondence of computational lead compounds with literature-mined, experimental compounds over the typically employed single-DFA approach.

Machine learning (ML)-based feature analysis reveals universal design rules regardless of density functional choices. Using the consensus among multiple functionals, we identify robust lead complexes in ML-accelerated chemical discovery.

Computational Discovery of Transition-metal Complexes: From High-throughput Screening to Machine Learning

Transition-metal complexes are attractive targets for the design of catalysts and functional materials. The behavior of the metal-organic bond, while very tunable for achieving target properties, is challenging to predict and necessitates searching a wide and complex space to identify needles in haystacks for target applications. This review will focus on the techniques that make high-throughput search of transition-metal chemical space feasible for the discovery of complexes with desirable properties. The review will cover the development, promise, and limitations of "traditional" computational chemistry (i.e., force field, semiempirical, and density functional theory methods) as it pertains to data generation for inorganic molecular discovery. The review will also discuss the opportunities and limitations in leveraging experimental data sources. We will focus on how advances in statistical modeling, artificial intelligence, multiobjective optimization, and automation accelerate discovery of lead compounds and design rules. The overall objective of this review is to showcase how bringing together advances from diverse areas of computational chemistry and computer science have enabled the rapid uncovering of structure-property relationships in transition-metal chemistry. We aim to highlight how unique considerations in motifs of metal-organic bonding (e.g., variable spin and oxidation state, and bonding strength/nature) set them and their discovery apart from more commonly considered organic molecules. We will also highlight how uncertainty and relative data scarcity in transition-metal chemistry motivate specific developments in machine learning representations, model training, and in computational chemistry. Finally, we will conclude with an outlook of areas of opportunity for the accelerated discovery of transition-metal complexes.

An efficient method for generating property-energy consistent basis sets. New pecJ-n (n = 1, 2) basis sets for high-quality calculations of indirect nuclear spin-spin coupling constants involving 1H, 13C, 15N, and 19F nuclei

This paper presents a new method of generating property-energy consistent (PEC) basis sets that can be applied to any arbitrary molecular property. The PEC method generates a basis set that is optimized for the molecular property under interest, providing the least possible total molecular energy. The main algorithm of the PEC approach involves Monte Carlo simulations to generate random exponents in the predetermined range. In this work, the PEC method is introduced in the example of generation of new pecJ-n (n = 1, 2) basis sets suited for high-quality correlated calculations of indirect nuclear spin-spin coupling constants involving the most popular NMR-active nuclei: 1H, 13C, 15N, and 19F.

Putting Density Functional Theory to the Test in Machine-Learning-Accelerated Materials Discovery

Accelerated discovery with machine learning (ML) has begun to provide the advances in efficiency needed to overcome the combinatorial challenge of computational materials design. Nevertheless, ML-accelerated discovery both inherits the biases of training data derived from density functional theory (DFT) and leads to many attempted calculations that are doomed to fail. Many compelling functional materials and catalytic processes involve strained chemical bonds, open-shell radicals and diradicals, or metal-organic bonds to open-shell transition-metal centers. Although promising targets, these materials present unique challenges for electronic structure methods and combinatorial challenges for their discovery. In this Perspective, we describe the advances needed in accuracy, efficiency, and approach beyond what is typical in conventional DFT-based ML workflows. These challenges have begun to be addressed through ML models trained to predict the results of multiple methods or the differences between them, enabling quantitative sensitivity analysis. For DFT to be trusted for a given data point in a high-throughput screen, it must pass a series of tests. ML models that predict the likelihood of calculation success and detect the presence of strong correlation will enable rapid diagnoses and adaptation strategies. These "decision engines" represent the first steps toward autonomous workflows that avoid the need for expert determination of the robustness of DFT-based materials discoveries.

Recent developments in the use of fluorine NMR in synthesis and characterisation

A review of developments in fluorine NMR of relevance to synthesis, characterisation and industrial applications of small organic molecules. Developments considered include those in spectrometer technology, computational methods and pulse sequences. The review of 80 references outlines applications in areas of identification, quantitation, mixture analysis, reaction monitoring, environmental studies and fragment-based drug design.

Calculation of VS,max and Its Use as a Descriptor for the Theoretical Calculation of pKa Values for Carboxylic Acids

The theoretical calculation of pKa values for Brønsted acids is a challenging task that involves sophisticated and time-consuming methods. Therefore, heuristic approaches are efficient and appealing methodologies to approximate these values. Herein, we used the maximum surface electrostatic potential (V_S,max) on the acidic hydrogen atoms of carboxylic acids to describe the H-bond interaction with water (the same descriptor that is used to characterize σ-bonded complexes) and correlate the results with experimental pKa values to obtain a predictive model for other carboxylic acids. We benchmarked six different methods, all including an implicit solvation model (water): Five density functionals and the Møller–Plesset second order perturbation theory in combination with six different basis sets for a total of thirty-six levels of theory. The ωB97X-D/cc-pVDZ level of theory stood out as the best one for consistently reproducing the reported pKa values, with a predictive power of 98% correlation in a test set of ten other carboxylic acids.