Computation of CCSD(T)-Quality NMR Chemical Shifts via Δ-Machine Learning from DFT

NMR Crystallography Structure Determinations with 1H Chemical Shifts. GIPAW DFT Calculation Quality Can Be Substantially Degraded, but Nearly Identical Outputs Relative to Benchmark Computations Are Obtained: Why and So What?

Nuclear magnetic resonance (NMR) crystallography may be used in various solid-state structural characterization tasks. For organic compounds in this context, proton isotropic chemical shifts [δiso(1H)] are routinely used. It is typical to pair experimentally measured proton δiso values with δiso values that were computationally generated from crystal structure models. This can yield a δiso(1H) root-mean-squared deviation (RMSD) value for each crystal structure model. In this study, we monitor the way in which gauge including projector augmented wave (GIPAW) density functional theory (DFT) computations of 1H δiso values can be influenced by the quality of the computational input parameters. We consider 126 computationally generated (using crystal structure prediction, CSP) crystal structures for three molecules: cocaine (30 structures), flutamide (21 structures), and ampicillin (75 structures). The quality parameters selected are the plane wave energy cutoff (Ecut), and the k-point grid used to sample reciprocal (i.e., momentum) space. We also probe the utility of performing one-parameter and two-parameter linear mappings for transforming computed hydrogen isotropic magnetic shielding values (σiso) into computed δiso(1H) values. We find that both Ecut and the k-point grid can be degraded substantially (e.g., Ecut ∼ 25 Ry) and yet still produce very similar computed δiso(1H) values. We consider the mechanisms under GIPAW DFT that contribute to computed hydrogen σiso values to help understand this robustness: many contributions are zero or cancel out when converting σiso values to δiso(1H) values via the linear mapping. The robust nature of computed δiso(1H) values leads to consistent estimates of δiso(1H) RMSD values. It is then demonstrated using cocaine and flutamide that when δiso(1H) RMSD values are used in NMR crystallography tasks such as structure selection/determination, the quality of the GIPAW DFT computation can be severely degraded and still produce identical outcomes to those that used a more computationally intensive protocol. Ampicillin is selected as a practical example to probe how our findings might reasonably be applied in the structure determination of a complex organic molecule. We propose that relatively modest quality GIPAW DFT computations (i.e., Ecut = 35 Ry and a 1 × 1 × 1 k-point grid) may be used to first filter out obviously poor structure candidates. Subsequently, slightly higher quality GIPAW DFT computations can be used for structure selection/determination. Our findings indicate that it should be possible to, on average, reduce the computational resources required in such NMR crystallography tasks by approximately a factor of 3-4 in terms of CPU time.

The interplay of density functional selection and crystal structure for accurate NMR chemical shift predictions

Ab initio chemical shift prediction plays a central role in nuclear magnetic resonance (NMR) crystallography, and the accuracy with which chemical shifts can be predicted relative to experiment impacts the confidence with which structures can be assigned. For organic crystals, periodic density functional theory calculations with the gauge-including projector augmented wave (GIPAW) approximation and the PBE functional are widely used at present. Many previous studies have examined how using more advanced density functionals can increase the accuracy of predicted chemical shifts relative to experiment, but nearly all of those studies employed crystal structures that were optimized with generalized-gradient approximation (GGA) functionals. Here, we investigate how the accuracy of the predicted chemical shifts in organic crystals is affected by replacing GGA-level PBE-D3(BJ) crystal geometries with more accurate hybrid functional PBE0-D3(BJ) ones. Based on benchmark data sets containing 132 13C and 35 15N chemical shifts, plus case studies on testosterone, acetaminophen, and phenobarbital, we find that switching from GGA-level geometries and chemical shifts to hybrid-functional ones reduces 13C and 15N chemical shift errors by ∼40-60% versus experiment. However, most of the improvement stems from the use of the hybrid functional for the chemical shift calculations, rather than from the refined geometries. In addition, even with the improved geometries, we find that double-hybrid functionals still do not systematically increase chemical shift agreement with experiment beyond what hybrid functionals provide. In the end, these results suggest that the combination of GGA-level crystal structures and hybrid-functional chemical shifts represents a particularly cost-effective combination for NMR crystallography in organic systems.

Machine Learning-Corrected Simplified Time-Dependent DFT for Systems With Inverted Single-t-o-Triplet Gaps of Interest for Photocatalytic Water Splitting

Hydrogen gas (H2) can be produced via entirely solar-driven photocatalytic water splitting (PWS). A promising set of organic materials for facilitating PWS are the so-called inverted singlet-triplet, INVEST, materials. Inversion of the singlet (S1) and triplet (T1) energies reduces the population of triplet states, which are otherwise destructive under photocatalytic conditions. Moreover, when INVEST materials possess dark S1 states, the excited state lifetimes are maximized, facilitating energy transfer to split water. In the context of solar-driven processes, it is also desirable that these INVEST materials absorb near the solar maximum. Many aza-triangulenes possess the desired INVEST property, making it beneficial to describe an approach for systematically and efficiently predicting the INVEST property as well as properties that make for efficient photocatalytic water splitting, while exploring the large chemical space of the aza-triangulenes. Here, we utilize machine learning to generate post hoc corrections to simplified Tamm-Dancoff approximation density functional theory (sTDA-DFT) for singlet and triplet excitation energies that are within 28-50 meV of second-order algebraic diagrammatic construction, ADC(2), as well as the singlet-to-triplet, ΔES1T1, gaps of PWS systems. Our Δ-ML model is able to recall 85% of the systems identified by ADC(2) as candidates for PWS. Further, with a modest database of ADC(2) excitation energies of 4025 aza-triangulenes, we identified 78 molecules suitable for entirely solar-driven PWS.

Bent naphthodithiophenes: synthesis and characterization of isomeric fluorophores

Thiophene-containing heteroarenes are one of the most well-known classes of π-conjugated building blocks for photoactive molecules. Isomeric naphthodithiophenes (NDTs) are at the forefront of this research area due to their straightforward synthesis and derivatization. Notably, NDT geometries that are bent - such as naphtho[2,1-b:3,4-b']dithiophene (α-NDT) and naphtho[1,2-b:4,3-b']dithiophene (β-NDT) - are seldom employed as photoactive small molecules. This report investigates how remote substituents impact the photophysical properties of isomeric α- and β-NDTs. The orientation of the thiophene units plays a critical role in the emission: in the α(OHex)R2 series conjugation from the end-caps to the NDT core is apparent, while in the β(Oi-Pent)R2 series minimal change is observed unless strong electron acceptors, such as β(Oi-Pent)(PhCF3)2, are employed. This push-pull acceptor-donor-acceptor (A-D-A) fluorophore exhibits positive fluorosolvatochromism that correlates with increasing solvent polarity parameter, E T(30). In total, these results highlight how remote substituents are able to modulate the emission of isomeric bent NDTs.

Quantum chemical package Jaguar: A survey of recent developments and unique features

This paper is dedicated to the quantum chemical package Jaguar, which is commercial software developed and distributed by Schrödinger, Inc. We discuss Jaguar's scientific features that are relevant to chemical research as well as describe those aspects of the program that are pertinent to the user interface, the organization of the computer code, and its maintenance and testing. Among the scientific topics that feature prominently in this paper are the quantum chemical methods grounded in the pseudospectral approach. A number of multistep workflows dependent on Jaguar are covered: prediction of protonation equilibria in aqueous solutions (particularly calculations of tautomeric stability and pKa), reactivity predictions based on automated transition state search, assembly of Boltzmann-averaged spectra such as vibrational and electronic circular dichroism, as well as nuclear magnetic resonance. Discussed also are quantum chemical calculations that are oriented toward materials science applications, in particular, prediction of properties of optoelectronic materials and organic semiconductors, and molecular catalyst design. The topic of treatment of conformations inevitably comes up in real world research projects and is considered as part of all the workflows mentioned above. In addition, we examine the role of machine learning methods in quantum chemical calculations performed by Jaguar, from auxiliary functions that return the approximate calculation runtime in a user interface, to prediction of actual molecular properties. The current work is second in a series of reviews of Jaguar, the first having been published more than ten years ago. Thus, this paper serves as a rare milestone on the path that is being traversed by Jaguar's development in more than thirty years of its existence.

Highly Accurate Prediction of NMR Chemical Shifts from Low-Level Quantum Mechanics Calculations Using Machine Learning

Theoretical predictions of NMR chemical shifts from first-principles can greatly facilitate experimental interpretation and structure identification of molecules in gas, solution, and solid-state phases. However, accurate prediction of chemical shifts using the gold-standard coupled cluster with singles, doubles, and perturbative triple excitations [CCSD(T)] method with a complete basis set (CBS) can be prohibitively expensive. By contrast, machine learning (ML) methods offer inexpensive alternatives for chemical shift predictions but are hampered by generalization to molecules outside the original training set. Here, we propose several new ideas in ML of the chemical shift prediction for H, C, N, and O that first introduce a novel feature representation, based on the atomic chemical shielding tensors within a molecular environment using an inexpensive quantum mechanics (QM) method, and train it to predict NMR chemical shieldings of a high-level composite theory that approaches the accuracy of CCSD(T)/CBS. In addition, we train the ML model through a new progressive active learning workflow that reduces the total number of expensive high-level composite calculations required while allowing the model to continuously improve on unseen data. Furthermore, the algorithm provides an error estimation, signaling potential unreliability in predictions if the error is large. Finally, we introduce a novel approach to keep the rotational invariance of the features using tensor environment vectors (TEVs) that yields a ML model with the highest accuracy compared to a similar model using data augmentation. We illustrate the predictive capacity of the resulting inexpensive shift machine learning (iShiftML) models across several benchmarks, including unseen molecules in the NS372 data set, gas-phase experimental chemical shifts for small organic molecules, and much larger and more complex natural products in which we can accurately differentiate between subtle diastereomers based on chemical shift assignments.

Carbon-13 chemical shift tensor measurements for nitrogen-dense compounds

This paper reports the principal values of the 13 C chemical shift tensors for five nitrogen-dense compounds (i.e., cytosine, uracil, imidazole, guanidine hydrochloride, and aminoguanidine hydrochloride). Although these are all fundamentally important compounds, the majority do not have 13 C chemical shift tensors reported in the literature. The chemical shift tensors are obtained from 1 H→13 C cross-polarization magic-angle spinning (CP/MAS) experiments that were conducted at a high field of 18.8 T to suppress the effects of 14 N-13 C residual dipolar coupling. Quantum chemical calculations using density functional theory are used to obtain the 13 C magnetic shielding tensors for these compounds. The best agreement with experiment arises from calculations using the hybrid functional PBE0 or the double-hybrid functional PBE0-DH, along with the triple-zeta basis sets TZ2P or pc-3, respectively, and intermolecular effects modeled using large clusters of molecules with electrostatic embedding through the COSMO approach. These measurements are part of an ongoing effort to expand the catalog of accurate 13 C chemical shift tensor measurements, with the aim of creating a database that may be useful for benchmarking the accuracy of quantum chemical calculations, developing nuclear magnetic resonance (NMR) crystallography protocols, or aiding in applications involving machine learning or data mining. This work was conducted at the National High Magnetic Field Laboratory as part of a 2-week school for introducing undergraduate students to practical laboratory experience that will prepare them for scientific careers or postgraduate studies.

Machine learning-based correction for spin-orbit coupling effects in NMR chemical shift calculations

As one of the most powerful analytical methods for molecular and solid-state structure elucidation, NMR spectroscopy is an integral part of chemical laboratories associated with a great research interest in its computational simulation. Particularly when heavy atoms are present, a relativistic treatment is essential in the calculations as these influence also the nearby light atoms. In this work, we present a Δ-machine learning method that approximates the contribution to 13C and 1H NMR chemical shifts that stems from spin-orbit (SO) coupling effects. It is built on computed reference data at the spin-orbit zeroth-order regular approximation (ZORA) DFT level for a set of 6388 structures with 38 740 13C and 64 436 1H NMR chemical shifts. The scope of the methods covers the 17 most important heavy p-block elements that exhibit heavy atom on the light atom (HALA) effects to covalently bound carbon or hydrogen atoms. Evaluated on the test data set, the approach is able to recover roughly 85% of the SO contribution for 13C and 70% for 1H from a scalar-relativistic PBE0/ZORA-def2-TZVP calculation at virtually no extra computational costs. Moreover, the method is transferable to other baseline DFT methods even without retraining the model and performs well for realistic organotin and -lead compounds. Finally, we show that using a combination of the new approach with our previous Δ-ML method for correlation contributions to NMR chemical shifts, the mean absolute NMR shift deviations from non-relativistic DFT calculations to experimental values can be halved.

QM assisted ML for 19F NMR chemical shift prediction

BACKGROUND

Ligand-observed 19F NMR detection is an efficient method for screening libraries of fluorinated molecules in fragment-based drug design campaigns. Screening fluorinated molecules in large mixtures makes 19F NMR a high-throughput method. Typically, these mixtures are generated from pools of well-characterized fragments. By predicting 19F NMR chemical shift, mixtures could be generated for arbitrary fluorinated molecules facilitating for example focused screens.

METHODS

In a previous publication, we introduced a method to predict 19F NMR chemical shift using rooted fluorine fingerprints and machine learning (ML) methods. Having observed that the quality of the prediction depends on similarity to the training set, we here propose to assist the prediction with quantum mechanics (QM) based methods in cases where compounds are not well covered by a training set.

RESULTS

Beyond similarity, the performance of ML methods could be associated with individual features in compounds. A combination of both could be used as a procedure to split input data sets into those that could be predicted by ML and those that required QM processing. We could show on a proprietary fluorinated fragment library, known as LEF (Local Environment of Fluorine), and a public Enamine data set of 19F NMR chemical shifts that ML and QM methods could synergize to outperform either method individually. Models built on Enamine data, as well as model building and QM workflow tools, can be found at https://github.com/PatrickPenner/lefshift and https://github.com/PatrickPenner/lefqm .

Frontiers of molecular crystal structure prediction for pharmaceuticals and functional organic materials

The reliability of organic molecular crystal structure prediction has improved tremendously in recent years. Crystal structure predictions for small, mostly rigid molecules are quickly becoming routine. Structure predictions for larger, highly flexible molecules are more challenging, but their crystal structures can also now be predicted with increasing rates of success. These advances are ushering in a new era where crystal structure prediction drives the experimental discovery of new solid forms. After briefly discussing the computational methods that enable successful crystal structure prediction, this perspective presents case studies from the literature that demonstrate how state-of-the-art crystal structure prediction can transform how scientists approach problems involving the organic solid state. Applications to pharmaceuticals, porous organic materials, photomechanical crystals, organic semi-conductors, and nuclear magnetic resonance crystallography are included. Finally, efforts to improve our understanding of which predicted crystal structures can actually be produced experimentally and other outstanding challenges are discussed.