Systematic studies on the computation of nuclear magnetic resonance shielding constants and chemical shifts: the density functional models

We present a systematic density functional investigation on the prediction of the 13C, 15N, 17O, and 19F NMR properties of 23 molecules with 21 density functionals. Extensive comparisons are made for both 13C magnetic shieldings and chemical shifts with respect to the gas phase experimental data and the best CCSD(T) results. We find that the OPBE and OPW91 exchange-correlation functionals perform significantly better than some popular functionals such as B3LYP and PBE1PBE, even surpassing, in many cases, the standard wavefunction-based method MP2. Further analysis has been performed to explore the individual role played by various exchange and correlation functionals. We find that the B88 and PBE exchange functionals have a too strong tendency of deshielding, leading to too deshielded magnetic shielding constants; whereas the OPTX exchange functional performs remarkably well. We claim that the main source of error arises from the exchange functional, but correlation functional also makes important contribution. We find that the correlation functionals may be grouped into two classes. class A, such as LYP and B98, leads to deshielded NMR values, deteriorating the overall performance; whereas class B, such as PW91 and PBE, generally increases the absolute shieldings, which complements the exchange functionals, leading to improved results in the calculation of NMR data.     

Remarks on GIAO-DFT predictions of 13C chemical shifts

Predicting (13)C chemical shifts by GIAO-DFT calculations appears to be more accurate than frequently expected provided that: (a) the comparison between experimental and theoretical data is performed using the linear regression method, (b) a sufficiently high level of theory [e.g. B3LYP/6-311 + + G(2d,p)//B3LYP/6-311 + + G(2d,p) or PBE1PBE/6-311 + G(2df,p)//B3LYP/6-311 + + G(2d,p)] is used, (c) the experimental data originate from the measurements performed in one solvent whose influence is taken into account at the molecular geometry optimization step and, first of all, during the shielding calculation, (d) the experimental data are free of heavy atom effects or such effects are appropriately treated in calculations, and finally (e) the conformational compositions of the investigated objects are known.     

A simple graphical approach to predict local residue conformation using NMR chemical shifts and density functional theory

The dependency of amino acid chemical shifts on φ and ψ torsion angle is, independently, studied using a five‐residue fragment of ubiquitin and ONIOM(DFT:HF) approach. The variation of absolute deviation of ¹³C^α chemical shifts relative to φ dihedral angle is specifically dependent on secondary structure of protein not on amino acid type and fragment sequence. This dependency is observed neither on any of ¹³C^β, and ¹H^α chemical shifts nor on the variation of absolute deviation of ¹³C^α chemical shifts relative to ψ dihedral angle. The ¹³C^α absolute deviation chemical shifts (ADCC) plots are found as a suitable and simple tool to predict secondary structure of protein with no requirement of highly accurate calculations, priori knowledge of protein structure and structural refinement. Comparison of Full‐DFT and ONIOM(DFT:HF) approaches illustrates that the trend of ¹³C^α ADCC plots are independent of computational method but not of basis set valence shell type. © 2016 Wiley Periodicals, Inc.     

1H and 13C NMR scaling factors for the calculation of chemical shifts in commonly used solvents using density functional theory

Calculation of NMR chemical shifts and coupling constants using quantum mechanical calculations [density functional theory (DFT)], has become a very popular tool for the determination of conformation and the assignment of stereochemistry within a molecule. We present the scaling factors (linear regression parameters) from 10 DFT methods for 10 commonly used NMR solvents using the same set of reference compounds. The results were compared with the corresponding gas‐phase calculations to assess the inclusion of the polarizable continuum model for solvent effects. © 2014 Wiley Periodicals, Inc.     

Density functional computations of 99Ru chemical shifts: relativistic effects, influence of the density functional, and study of solvent effects on fac-[Ru(CO)3I3]-

Solvent effects on the 99Ru NMR chemical shift of the complex fac-[Ru(CO)3I3]- are investigated computationally using density functional theory. Further, benchmark calculations of the 99Ru shift for a set of ten Ru complexes have been performed in order to calibrate the computational model and to determine the importance of relativistic effects on the 99Ru nuclear magnetic shielding and on the chemical shift. A computational model for fac-[Ru(CO)3I3]- that includes both explicit solvent molecules and a continuum model is shown to yield the best agreement with experiment. Relativistic corrections are shown to be of minor importance for determining 99Ru chemical shifts. On the other hand, the nature of the density functional is of importance. In agreement with literature data for ligand trends of 99Ru chemical shifts, the chemical shift range for different solvents is also best reproduced by a hybrid functional.     

Performance of density functional theory methods to describe intramolecular hydrogen shifts

The performance of three exchange and correlation density functionals, LDA, BLYP and B3LYP, with four basis sets is tested in three intramolecular hydrogen shift reactions. The best reaction and activation energies come from the hybrid functional B3LYP with triple-ζ basis sets, when they are compared with high-level post-Hartree-Fock results from the literature. For a fixed molecular geometry, the electrophilic Fukui function is computed from a finite difference approximation. Fukui function shows a small dependence with both the exchange and correlation functional and the basis set. Evolution of the Fukui function along the reaction path describes important changes in the basic sites of the corresponding molecules. These results are in agreement with the chemical behavior of those species.     

The observed and calculated 1H and 13C chemical shifts of tertiary amines and their N-oxides

A series of model tertiary amines were oxidized in situ in an NMR tube to amine N-oxides and their (1)H and (13)C NMR spectra were recorded. Next, the chemical shifts induced by oxidation (Δδ) were calculated using different GIAO methods investigating the influence of the method [Hartree-Fock (HF), Moeller-Plesset perturbation, density functional theory (DFT)], the functional applied in the DFT (B3LYP, BPW, OPBE, OPW91) and the basis set used [6-31G*, 6-311G**, 6-311 + + G** and 6-311 + + G(3df,3pd)]. The best results were obtained with the HF/6-311 + + G** and OPBE/6-311 + + G** methods. The computation/experiment comparison approach was used for the configuration prediction of chiral amine N-oxides-(R) and (S)-agroclavine-6-N-oxide.     

Computational modeling of polyoxotungstates by relativistic DFT calculations of (183)W NMR chemical shifts

The (183)W nuclear shielding in a variety of tungsten polyoxometalates (POM) (Lindqvist, Anderson, decatungstates, Keggin) of different shapes and charges has been modeled by DFT calculations that take into account relativistic effects, by means of the zero-order regular approximation (ZORA), and solvent effects, by the conductor-like screening model (COSMO) continuum method. The charge/surface area ratio (q/A) is proposed as an indicator of the charge density to which the solvation energies of all POMs are correlated in a satisfactory way. Among the various theoretical levels tested (ZORA scalar or spin-orbit, frozen-core or all-electron basis set, geometry optimization in the gas phase or in the continuum solvent, etc.), the best results are obtained when both geometry optimization in solvent and spin-orbit shielding are included (mean absolute error of delta=35 ppm). The quality of the computed chemical shifts depends systematically on the charge density as expressed by q/A; thus, POMs with low q/A ratios display the best agreement with experimental data. The performance of the method is such that computed values can aid the assignment of the (183)W NMR spectra of polyoxotungstates, as shown by the case of alpha-[PW(11)TiO(40)](5-), whose six signals are ranked computationally so as to almost reproduce the experimental ordering even though the signals are spaced by as little as 5 ppm.     

Accurate density functional theory description of binding constants and NMR chemical shifts of weakly interacting complexes of C60 with corannulene‐based molecular bowls

Density functional calculations on “catch and release” complexes of C₆₀ with corannulene derived molecular bowls show that computationally obtained ¹H nuclear magnetic resonance (NMR) chemical shifts can be used as a reliable predictor of binding constants. A wide range of functionals was benchmarked against accurate ab initio calculations to ensure a credible representation of the weak forces that dominate the interactions in these systems. The most reliable density functional theory (DFT) results were then calibrated using experimentally observed NMR data. Careful analysis and comparison of a wide range of commonly used density functionals shows that the explicit inclusion of dispersion corrections is currently the only reliable way to accurately describe the systems investigated in our study. Moreover, we are able to show that the B97‐D and ωB97X‐D functionals are not only able to reproduce ab initio benchmark calculations, but they do so accurately with a moderately sized basis sets and without the problems of numerical integration we encountered with other functionals in this study. © 2013 Wiley Periodicals, Inc.     

Hybrid density functional theory investigation of a series of alloxan-based thiosemicarbazones and semicarbazones

Recently, the synthesis and the NMR characterization of a series of eight alloxan-based thiosemicarbazones and semicarbazones were reported. These compounds exhibit a strongly hydrogenbonded hydrazinic proton that is a part of a characteristic six-membered ring. This proton is highly deshielded and resonates far downfield in the proton NMR spectra. In this report, mPW1PW91/6-31+G(d,p) calculations have been used to investigate the structure and other molecular properties of this series of eight compounds. The relationship between the ¹H and ¹³C NMR chemical shifts and various geometric parameters was investigated, and linear relationships for proton peaks that are involved in hydrogen-bond interactions were found.     

Studies of chemical hardness and Fukui function using the exact solution of the density functional theory

Neal's procedure has been applied to determine the electron density ρ(x) for the H₂ molecule. The chemical hardness has been calculated employing the ab initio and density functional theory methods and the values are found to be reasonably good. The principle of maximum hardness (PMH) was tested. Fukui functions and the distribution of electron density around the internuclear distance were studied employing the electron density of the H₂ molecule. © 2001 John Wiley & Sons, Inc. Int J Quant Chem 81: 4–10, 2001     

Accurate prediction of proton chemical shifts. II. Peptide analogues

Proton chemical shifts of eight cyclic amide molecules were measured in DMSO and D2O solutions. The magnetic shieldings of the corresponding aliphatic, aromatic, and amide protons were calculated by Hartree-Fock and DFT, using the 6-311G**, 6-311++G**, and TZVP basis sets. For aliphatic protons, all of these methods reproduce the experimental values in DMSO solutions excellently after linear regression. The Hartree-Fock method tends to give slightly better agreement than DFT. The best performance is given by the HF/6-311G** method, with an rms deviation of 0.068 ppm. The deviations from experimental chemical shifts in D2O solutions are only slightly larger than those in DMSO solutions. This suggests that we can use the calculated gas phase proton chemical shifts directly to predict experimental data in various solvents, including water. For amide protons, which exchange with water and form hydrogen bonds with DMSO, only modest agreement is obtained, as expected. The present studies confirm that the GIAO approach can reach high accuracy for the relative chemical shifts of aliphatic and aromatic protons at a low cost. Such calculations may provide constraints for the conformational analysis of proteins and other macromolecules.     

Intramolecular hydrogen bonding of novel o-hydroxythioacetophenones and related compounds evaluated by deuterium isotope effects on 13C chemical shifts

A new class of compounds, the 2-hydroxythioacetophenones, and related compounds have recently been synthesized. The hydrogen-bond system has been characterized by NMR chemical shifts and deuterium isotope effects on these as well as by DFT calculations. Use of solid-state (13)C NMR has enabled measurements of the intrinsic deuterium isotope effects of the most abundant tautomer of beta-thioxoketones. The compounds show very interesting long-range deuterium isotope effects on the thiocarbonyl carbon. The intramolecular hydrogen bonds of o-hydroxythioacetophenones are found to be slightly stronger than those of the corresponding acetophenones. The reactivity and stability of the compounds can be related to hydrogen bonding and to the presence of electron donating substituents.     

Density functional calculations of NMR chemical shifts and ESR g-tensors

An overview is given on recent advances of density functional theory (DFT) as applied to the calculation of nuclear magnetic resonance (NMR) chemical shifts and electron spin resonance (ESR) g-tensors. This is a new research area that has seen tremendous progress and success recently; we try to present some of these developments. DFT accounts for correlation effects efficiently. Therefore, it is the only first-principle method that can handle NMR calculations on large systems like transition-metal complexes. Relativistic effects become important for heavier element compounds; here we show how they can be accounted for. The ESR g-tensor is related conceptually to the NMR shielding, and results of g-tensor calculations are presented. DFT has been very successful in its application to magnetic properties, for metal complexes in particular. However, there are still certain shortcomings and limitations, e.g., in the exchange-correlation functional, that are discussed as well. Received: 24 October 1997 / Accepted: 19 December 1997     

Substituent effects on 13C chemical shifts of ketenimines: a GIAO/HF and DFT study

GIAO/HF and DFT methods were utilized to predict the ¹³C chemical shifts of substituted ketenimines. GIAO HF/6–311+G(2d,p) and B3LYP/6–311+G(2d,p) methods were applied on the optimized B3LYP/6–31G(d) geometries and ¹³C chemical shifts of C_α and C_β of substituted ketenimines were correlated with group electronegativities. HF and DFT calculations indicated that increasing substituent group electronegativity leads to increasing chemical shift of C_β of substituted ketenimines, whereas the C_α values decrease. Copyright © 2003 John Wiley & Sons, Ltd.     

The devil in the details: A tutorial review on some undervalued aspects of density functional theory calculations

Density functional theory (DFT) has become ubiquitous for chemical applications in research and in education. The exact functional at the foundation of DFT is unfortunately unknown, and issues arise when choosing an approximation for a specific application. With this tutorial review, we tackle the selection problem and many related ones, such as the choices of a basis set and of an integration grid, that are often overlooked by occasional practitioners and by more experienced users as well. We offer a practical approach in the form of a commented notebook containing 12 experiences that can be run on a simple computer in just a few hours. We propose this review as a primary source for those who are willing to include DFT in their everyday research or teaching activities in a way that reflects the research advances of the field in the last couple of decades.     

Benchmarking of density functionals for a soft but accurate prediction and assignment of 1H and 13C NMR chemical shifts in organic and biological molecules

A number of programs and tools that simulate ¹H and ¹³C nuclear magnetic resonance (NMR) chemical shifts using empirical approaches are available. These tools are user‐friendly, but they provide a very rough (and sometimes misleading) estimation of the NMR properties, especially for complex systems. Rigorous and reliable ways to predict and interpret NMR properties of simple and complex systems are available in many popular computational program packages. Nevertheless, experimentalists keep relying on these “unreliable” tools in their daily work because, to have a sufficiently high accuracy, these rigorous quantum mechanical methods need high levels of theory. An alternative, efficient, semi‐empirical approach has been proposed by Bally, Rablen, Tantillo, and coworkers. This idea consists of creating linear calibrations models, on the basis of the application of different combinations of functionals and basis sets. Following this approach, the predictive capability of a wider range of popular functionals was systematically investigated and tested. The NMR chemical shifts were computed in solvated phase at density functional theory level, using 30 different functionals coupled with three different triple–ζ basis sets. © 2016 Wiley Periodicals, Inc.     

Evaluating electronic structure methods for accurate calculation of 19F chemical shifts in fluorinated amino acids

The ability of electronic structure methods (11 density functionals, HF, and MP2 calculations; two basis sets and two solvation models) to accurately calculate the ¹⁹F chemical shifts of 31 structures of fluorinated amino acids and analogues with known experimental ¹⁹F NMR spectra has been evaluated. For this task, BHandHLYP, ωB97X, and Hartree–Fock with scaling factors (provided within) are most accurate. Additionally, the accuracy of methods to calculate relative changes in fluorine shielding across 23 sets of structural variants, such as zwitterionic amino acids versus side chains only, was also determined. This latter criterion may be a better indicator of reliable methods for the ultimate goal of assigning and interpreting chemical shifts of fluorinated amino acids in proteins. It was found that MP2 and M062X calculations most accurately assess changes in shielding among analogues. These results serve as a guide for computational developments to calculate ¹⁹F chemical shifts in biomolecular environments. © 2017 Wiley Periodicals, Inc.     

GIAO/DFT evaluation of 13C NMR chemical shifts of selected acetals based on DFT optimized geometries

DFT/B3LYP calculations of the ground-state conformation of eight cyclic and acyclic acetals are presented and compared with experimental data. Results of single-point GIAO/DFT calculations at five different levels of theory show that isotropic shieldings need to be empirically scaled to achieve agreement with experimental chemical shifts. Statistical evaluation of data indicates that the most accurate prediction of 13C chemical shifts is achieved at the MPW1PW91/6-311G** level of theory. An empirical equation describing the relationship between delta values and shielding constants is postulated. This equation has been applied to the non-chair ground-state conformation of the six-membered acetonide and to the conformationally flexible benzodioxonine derivative. The agreement observed between the experimental and predicted chemical shifts shows that calculations at the MPW1PW91/6-311G** level of theory are adequate for addressing questions of conformation.     

Performance of density functional theory in computing nonresonant vibrational (hyper)polarizabilities

A set of exchange‐correlation functionals, including BLYP, PBE0, B3LYP, BHandHLYP, CAM‐B3LYP, LC‐BLYP, and HSE, has been used to determine static and dynamic nonresonant (nuclear relaxation) vibrational (hyper)polarizabilities for a series of all‐trans polymethineimine (PMI) oligomers containing up to eight monomer units. These functionals are assessed against reference values obtained using the Møller–Plesset second‐order perturbation theory (MP2) and CCSD methods. For the smallest oligomer, CCSD(T) calculations confirm the choice of MP2 and CCSD as appropriate for assessing the density functionals. By and large, CAM‐B3LYP is the most successful, because it is best for the nuclear relaxation contribution to the static linear polarizability, intensity‐dependent refractive index second hyperpolarizability, static second hyperpolarizability, and is close to the best for the electro‐optical Pockels effect first hyperpolarizability. However, none of the functionals perform satisfactorily for all the vibrational (hyper)polarizabilities studied. In fact, in the case of electric field‐induced second harmonic generation all of them, as well as the Hartree–Fock approximation, yield the wrong sign. We have also found that the Pople 6–31+G(d) basis set is unreliable for computing nuclear relaxation (hyper)polarizabilities of PMI oligomers due to the spurious prediction of a nonplanar equilibrium geometry. © 2013 Wiley Periodicals, Inc.