Convergence of Nuclear Magnetic Shieldings in the Kohn-Sham Limit for Several Small Molecules

Implementation and First Evaluation of Strong-Correlation-Corrected Local Hybrid Functionals for the Calculation of NMR Shieldings and Shifts

Local hybrid functionals containing strong-correlation factors (scLHs) and range-separated local hybrids (RSLHs) have been integrated into an efficient coupled-perturbed Kohn-Sham implementation for the calculation of nuclear shielding constants. Several scLHs and the ωLH22t RSLH have then been evaluated for the first time for the extended NS372 benchmark set of main-group shieldings and shifts and the TM70 benchmark of 3d transition-metal shifts. The effects of the strong-correlation corrections have been analyzed with respect to the spatial distribution of the sc-factors, which locally diminish exact-exchange admixture at certain regions in a molecule. The scLH22t, scLH23t-mBR, and scLH23t-mBR-P functionals, which contain a "damped" strong-correlation factor to retain the excellent performance of the underlying LH20t functional for weakly correlated situations, tend to make smaller corrections to shieldings and shifts than the "undamped" scLH22ta functional. While the latter functional can also deteriorate agreement with the reference data in certain weakly correlated cases, it provides overall better performance, in particular for systems where static correlation is appreciable. This pertains only to a minority of systems in the NS372 main-group test set but to many more systems in the TM70 transition-metal test set, in particular for high-oxidation-state complexes, e.g., Cr(+VI) complexes and other systems with stretched bonds. Another undamped scLH, the simpler LDA-based scLH21ct-SVWN-m, also tends to provide significant improvements in many cases. The differences between the functionals and species can be rationalized on the basis of one-dimensional plots of the strong-correlation factors, augmented by isosurface plots of the fractional orbital density (FOD). Position-dependent exact-exchange admixture is thus shown to provide substantial flexibility in treating response properties like NMR shifts for both weakly and strongly correlated systems.

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

NMR spectroscopy undoubtedly plays a central role in determining molecular structures across different chemical disciplines, and the accurate computational prediction of NMR parameters is highly desirable. In this work, a new Δ-machine learning approach is presented to correct DFT-computed NMR chemical shifts using input features from the calculation and in addition highly accurate reference data at the CCSD(T)/pcSseg-2 level of theory with a basis set extrapolation scheme. The model is trained on a data set containing 1000 optimized and geometrically distorted structures of small organic molecules comprising most elements of the first three periods and containing data for 7090 ¹H and 4230 ¹³C NMR chemical shifts. Applied to the PBE0/pcSseg-2 method, the mean absolute deviation (MAD) on the internal NMR shift test set is reduced by 81% for ¹H and 92% for ¹³C at virtually no additional computational cost. For 12 different DFT functional and basis set combinations, the MAD of the ML-corrected NMR shifts ranges from 0.021 to 0.039 ppm (¹H) and from 0.38 to 1.07 ppm (¹³C). Importantly, the new method consistently outperforms the simple and widely used linear regression correction technique. This behavior is reproduced on three different external benchmark sets, confirming the generality and robustness of the correction scheme, which can easily be applied in DFT-based spectral simulations.

Probing a Hydrogen-π Interaction Involving a Trapped Water Molecule in the Solid State

The detection and characterization of trapped water molecules in chemical entities and biomacromolecules remains a challenging task for solid materials. We herein present proton-detected solid-state Nuclear Magnetic Resonance (NMR) experiments at 100 kHz magic-angle spinning and at high static magnetic-field strengths (28.2 T) enabling the detection of a single water molecule fixed in the calix[4]arene cavity of a lanthanide complex by a combination of three types of non-covalent interactions. The water proton resonances are detected at a chemical-shift value close to zero ppm, which we further confirm by quantum-chemical calculations. Density Functional Theory calculations pinpoint to the sensitivity of the proton chemical-shift value for hydrogen-π interactions. Our study highlights how proton-detected solid-state NMR is turning into the method-of-choice in probing weak non-covalent interactions driving a whole branch of molecular-recognition events in chemistry and biology.

Basis Set Extrapolation of Vibrational Frequencies

We investigate three different approaches for extrapolating harmonic vibrational frequencies to the complete basis set limit, by direct extrapolation of the frequencies, by calculation of frequencies based on extrapolated Hessians, or based on the Hessian from optimization of the extrapolated energy surface. For regular molecules, the three extrapolation procedures yield essentially identical results, but for loosely bound complexes, the frequencies derived from extrapolated Hessians yield unpredictable behavior. None of the basis set extrapolations, however, provide any significant improvement over the results upon which the extrapolation is based.

Electron Correlation or Basis Set Quality: How to Obtain Converged and Accurate NMR Shieldings for the Third-Row Elements?

The quality of theoretical NMR shieldings calculated at the quantum-chemical level depends on various theoretical aspects, of which the basis set type and size are among the most important factors. Nevertheless, not much information is available on the basis set effect on theoretical shieldings of the NMR-active nuclei of the third row. Here, we report on the importance of proper basis set selection to obtain accurate and reliable NMR shielding parameters for nuclei from the third row of the periodic table. All calculations were performed on a set of eleven compounds containing the elements Na, Mg, Al, Si, P, S, or Cl. NMR shielding tensors were calculated using the SCF-HF, DFT-B3LYP, and CCSD(T) methods, combined with the Dunning valence aug-cc-pVXZ, core-valence aug-cc-pCVXZ, Jensen polarized-convergent aug-pcSseg-n and Karlsruhe x2c-Def2 basis set families. We also estimated the complete basis set limit (CBS) values of the NMR parameters. Widely scattered nuclear shieldings were observed for the Dunning polarized-valence basis set, which provides irregular convergence. We show that the use of Dunning core-valence or Jensen basis sets effectively reduces the scatter of theoretical NMR results and leads to their exponential-like convergence to CBS. We also assessed the effect of vibrational, temperature, and relativistic corrections on the predicted shieldings. For systems with single bonds, all corrections are relatively small, amounting to less than 4% of the CCSD(T)/CBS value. Vibrational and temperature corrections were less reliable for H₃PO and HSiCH due to the high anharmonicity of the molecules. An abnormally high relativistic correction was observed for phosphorus in PN, reaching ~20% of the CCSD(T)/CBS value, while the correction was less than 7% for other tested molecules.

Experimental and theoretical characterization of chelidonic acid structure

Chelidonic acid (4-oxo-4H-pyran-2,6-dicarboxylic acid) is present in plants of Papaveraceae family, especially in Chelidonium majus. Due to its anticancer, antibacterial, hepatoprotective, and antioxidant properties, it has been used in medical treatments. In this work, the X-ray structure of methanol solvate of chelidonic acid was determined. Layers of chelidonic acid are held by hydrogen bonds via COOH and C = O fragments and additionally bridged by methanol. The formed H-bond network between two acid units is different from typical –COOH dimers observed, e.g., in crystals of isophtalic acid. The molecular structure of 2,6-dimethyl-γ-pyrone (2Me4PN) and chelidonic acid, a 2,6-dicarboxylic derivate of γ-pyrone (4PN), was verified in silico using density functional theory (DFT-B3LYP) combined with large correlation-consistent basis sets. The impact of –CH3 and –COOH substituents on 4PN ring structure, dipole moments, geometric/magnetic indexes of aromaticity, and NBO charges was assessed following unconstrained geometry optimization in the gas phase, chloroform, methanol, DMSO, and water with solvent effect introduced using the polarized continuous model (PCM). H-bond network formed in chelidonic acid–methanol complex was analyzed and their interaction energy estimated. Theoretical modeling enabled prediction of accurate structural parameters, dipole moments, and geometric/magnetic indexes of aromaticity of the studied 4PN, 2Me4PN, and chelidonic acid molecules.

Computational 1 H and 13 C NMR in structural and stereochemical studies

Present review outlines the advances and perspectives of computational ¹ H and ¹³ C NMR applied to the stereochemical studies of inorganic, organic, and bioorganic compounds, involving in particular natural products, carbohydrates, and carbonium ions. The first part of the review briefly outlines theoretical background of the modern computational methods applied to the calculation of chemical shifts and spin-spin coupling constants at the DFT and the non-empirical levels. The second part of the review deals with the achievements of the computational ¹ H and ¹³ C NMR in the stereochemical investigation of a variety of inorganic, organic, and bioorganic compounds, providing in an abridged form the material partly discussed by the author in a series of parent reviews. Major attention is focused herewith on the publications of the recent years, which were not reviewed elsewhere.

Electron correlation and vibrational effects in predictions of paramagnetic NMR shifts

Electronic structure calculations are fundamentally important for the interpretation of nuclear magnetic resonance (NMR) spectra from paramagnetic systems that include organometallic and inorganic compounds, catalysts, or metal-binding sites in proteins. Prediction of induced paramagnetic NMR shifts requires knowledge of electron paramagnetic resonance (EPR) parameters: the electronic g tensor, zero-field splitting D tensor, and hyperfine A tensor. The isotropic part of A, called the hyperfine coupling constant (HFCC), is one of the most troublesome properties for quantum chemistry calculations. Yet, even relatively small errors in calculations of HFCC tend to propagate into large errors in the predicted NMR shifts. The poor quality of A tensors that are currently calculated using density functional theory (DFT) constitutes a bottleneck in improving the reliability of interpretation of the NMR spectra from paramagnetic systems. In this work, electron correlation effects in calculations of HFCCs with a hierarchy of ab initio methods were assessed, and the applicability of different levels of DFT approximations and the coupled cluster singles and doubles (CCSD) method was tested. These assessments were performed for the set of selected test systems comprising an organic radical, and complexes with transition metal and rare-earth ions, for which experimental data are available. Severe deficiencies of DFT were revealed but the CCSD method was able to deliver good agreement with experimental data for all systems considered, however, at substantial computational costs. We proposed a more computationally tractable alternative, where the A was computed with the coupled cluster theory exploiting locality of electron correlation. This alternative is based on the domain-based local pair natural orbital coupled cluster singles and doubles (DLPNO-CCSD) method. In this way the robustness and reliability of the coupled cluster theory were incorporated into the modern formalism for the prediction of induced paramagnetic NMR shifts, and became applicable to systems of chemical interest. This approach was verified for the bis(cyclopentadienyl)vanadium(II) complex (Cp₂V; vanadocene), and the metal-binding site of the Zn²⁺ → Co²⁺ substituted superoxide dismutase (SOD) metalloprotein. Excellent agreement with experimental NMR shifts was achieved, which represented a substantial improvement over previous theoretical attempts. The effects of vibrational corrections to orbital shielding and hyperfine tensor were evaluated and discussed within the second-order vibrational perturbation theory (VPT2) framework.

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.

Efficiently Computing NMR 1H and 13C Chemical Shifts of Saccharides in Aqueous Environment

Determining the structure of saccharides in their native environment is crucial to understanding their function and more accurately targeting their utilization. Nuclear magnetic resonance observables such as the nuclear Overhauser effect or spin-spin coupling constants are routinely utilized to study saccharides in their native water environment. However, while highly sensitive to the local environment, chemical shifts are mostly overlooked, despite being commonly measured for compounds identification. Although chemical shifts carry considerable structural information, their direct association with structure is notoriously difficult. This is mostly due to the similarity in the chemical nature of most saccharides causing similar physicochemical environments close to sugar C and H atoms, resulting in comparable chemical shifts. The rise of computational power allows one to compute reliable chemical shifts and use them to determine atomistic details of these sugars in solution. However, any prediction is severely limited by the computational protocol used and its accuracy. In this work, we studied a set of 31 saccharides on which we evaluated various computational protocols to calculate the total number of 375 ¹H and 327 ¹³C chemical shifts of sugars in an aqueous environment. Our study proposes two cost-effective protocols for simulating ¹H and ¹³C chemical shifts that we recommend for further use. These protocols can help with the interpretation of experimental spectra, but we also show that they are also capable of structure prediction independently. This is possible because of the low mean absolute deviations of calculated shifts from the experiment (0.06 ppm for ¹H and 1.09 ppm for ¹³C). We explore different solvation methods, basis sets, and optimization schemes to reach such accuracy. A correct sampling of the conformation phase space of flexible sugar molecules is also key to obtaining accurately converged theoretical chemical shifts. The linear regression method was applied to convert the calculated isotropic nuclear magnetic shielding constants to simulated chemical shifts comparable with the experiment. The achieved level of accuracy can help in utilizing chemical shifts for elucidating the 3D atomistic structure of saccharides in aqueous solutions. All linear regression parameters obtained on our extensive set of sugars for all the tested protocols can be reutilized in future works.

Towards Elucidating Structure–Spectra Relationships in Rhamnogalacturonan II: Computational Protocols for Accurate 13C and 1H Shifts for Apiose and Its Borate Esters

Apiose is a naturally occurring, uncommon branched-chain pentose found in plant cell walls as part of the complex polysaccharide Rhamnogalacturonan II (RG-II). The structural elucidation of the three-dimensional structure of RG-II by nuclear magnetic resonance (NMR) spectroscopy is significantly complicated by the ability of apiose to cross-link via borate ester linkages to form RG-II dimers. Here, we developed a computational approach to gain insight into the structure–spectra relationships of apio–borate complexes in an effort to complement experimental assignments of NMR signals in RG-II. Our protocol involved structure optimizations using density functional theory (DFT) followed by isotropic magnetic shielding constant calculations using the gauge-invariant atomic orbital (GIAO) approach to predict chemical shifts. We evaluated the accuracy of 23 different functional–basis set (FBS) combinations with and without implicit solvation for predicting the experimental 1H and 13C shifts of a methyl apioside and its three borate derivatives. The computed NMR predictions were evaluated on the basis of the overall shift accuracy, relative shift ordering, and the ability to distinguish between dimers and monomers. We demonstrate that the consideration of implicit solvation during geometry optimizations in addition to the magnetic shielding constant calculations greatly increases the accuracy of NMR chemical shift predictions and can correctly reproduce the ordering of the 13C shifts and yield predictions that are, on average, within 1.50 ppm for 13C and 0.12 ppm for 1H shifts for apio–borate compounds.

A new double-reference correction scheme for accurate and efficient computation of NMR chemical shieldings

Our novel correction procedure yields high-accuracy DFT predictions of absolute NMR shieldings and enables outliers due to relativistic effects or manifestly inadequate modelling of electron correlation to be easily and unambiguously identified.

Extended Benchmark Set of Main-Group Nuclear Shielding Constants and NMR Chemical Shifts and Its Use to Evaluate Modern DFT Methods

An extended theoretical benchmark set, NS372, for light main-group nuclear shieldings and NMR shifts has been constructed based on high-level GIAO-CCSD(T)/pcSseg-3//CCSD(T)/cc-pVQZ reference data. After removal of the large static-correlation cases O₃, F₃^-, and BH from the statistical evaluations for the ¹⁷O, ¹⁹F, and ¹¹B subsets, the benchmark comprises overall 372 shielding values in 117 molecules with a wide range of electronic-structure situations, containing 124 ¹H, 14 ¹¹B, 93 ¹³C, 43 ¹⁵N, 31 ¹⁷O, 47 ¹⁹F, 14 ³¹P, and 6 ³³S shielding constants. The CCSD(T)/pcSseg-3 data are shown to be close to the basis-set and method limit and thus provide an excellent benchmark to evaluate more approximate methods, such as density functional approaches. This dataset has been used to evaluate Hartree-Fock (HF) and MP2, and a wide range of exchange-correlation functionals from local density approximation (LDA) to generalized gradient approximations (GGAs) and meta-GGAs (focusing on their current-density functional implementations), as well as global hybrid, range-separated hybrid, local hybrid, and double-hybrid functionals. Starting with absolute shielding constants, the DSD-PBEP86 double hybrid is confirmed to provide the highest accuracy, with an aggregate relative mean absolute error (rel. MAE) of only 0.9%, followed by MP2 (1.1%). MP2 and double hybrids only show larger errors for a few systems with the largest static-correlation effects. The double-hybrid B2GP-PLYP, the two local hybrids cLH12ct-SsirPW92 and cLH12ct-SsifPW92, and the current-density functional meta-GGA cB97M-V follow closely behind (all 1.5%), as do some further functionals, cLH20t and cMN15-L (both 1.6%), as well as B2PLYP and KT3 (both 2.0%). Functionals on the lower rungs of the usual ladder offer the advantage of lower computational cost and access to larger molecules. Closer examination also reveals the best-performing methods for individual nuclei in the test set. Different ways of treating τ-dependent functionals are evaluated. When moving from absolute shielding constants to chemical shifts, some of the methods can benefit from systematic error compensation, and the overall error range somewhat narrows. Further methods now achieve the 2% threshold of relative MAEs, including functionals based on TPSS (TPSSh, cmPSTS).

1H/13C chemical shift calculations for biaryls: DFT approaches to geometry optimization

Twelve common density functional methods and seven basis sets for geometry optimization were evaluated on the accuracy of 1H/13C NMR chemical shift calculations for biaryls. For these functionals, 1H shifts calculations for gas phase optimized geometries were significantly less accurate than those for in-solution optimized structures, while 13C results were not strongly influenced by geometry optimization methods and solvent effects. B3LYP, B3PW91, mPW1PW91 and ωB97XD were the best-performing functionals with lowest errors; among seven basis sets, DGDZVP2 and 6-31G(d,p) outperformed the others. The combination of these functionals and basis sets resulted in high accuracy with CMAEmin = 0.0327 ppm (0.76%) and 0.888 ppm (0.58%) for 1H and 13C, respectively. The selected functionals and basis set were validated when consistently producing optimized structures with high accuracy results for 1H and 13C chemical shift calculations of two other biaryls. This study highly recommends the IEFPCM/B3LYP, B3PW91, mPW1PW91 or ωB97XD/DGDZVP2 or 6-31G(d,p) level of theory for the geometry optimization step, especially the solvent incorporation, which would lead to high accuracy 1H/13C calculation. This work would assist in the fully structural assignments of biaryls and provide insights into in-solution biaryl conformations.

DFT Calculations of 1H NMR Chemical Shifts of Geometric Isomers of Conjugated Linolenic Acids, Hexadecatrienyl Pheromones, and Model Triene-Containing Compounds: Structures in Solution and Revision of NMR Assignments

A DFT study of the ¹H NMR chemical shifts, δ(¹H), of geometric isomers of 18:3 conjugated linolenic acids (CLnAs), hexadecatrienyl pheromones, and model triene-containing compounds is presented, using standard functionals (B3LYP and PBE0) as well as corrections for dispersion interactions (B3LYP-D3, APFD, M06–2X and ωB97XD). The results are compared with literature experimental δ(¹H) data in solution. The closely spaced “inside” olefinic protons are significantly more deshielded due to short-range through-space H^…H steric interactions and appear close to or even beyond δ-values of aromatic systems. Several regularities of the computational δ(¹H) of the olefinic protons of the conjugated double bonds are reproduced very accurately for the lowest-energy DFT-optimized single conformer for all functionals used and are in very good agreement with experimental δ(¹H) in solution. Examples are provided of literature studies in which experimental resonance assignments deviate significantly from DFT predictions and, thus, should be revised. We conclude that DFT calculations of ¹H chemical shifts of trienyl compounds are powerful tools (i) for the accurate prediction of δ(¹H) even with less demanding functionals and basis sets; (ii) for the unequivocal identification of geometric isomerism of conjugated trienyl systems that occur in nature; (iii) for tackling complex problems of experimental resonance assignments due to extensive signal overlap; and (iv) for structure elucidation in solution.

Updating atomic charge parameters of aliphatic amino acids: a quest to improve the performance of molecular modeling via sequential molecular dynamics and DFT-GIAO-NMR calculations

In this work, we observe the behavior of the dipole moment, atomic charges, solute-solvent interactions and NMR spectroscopy of aliphatic amino acids in a water solution via the computational simulations of classical molecular dynamics and DFT quantum calculations. Our results indicate that the convergence of the atomic charge of the solute, from an iterative process, together with the dipole moment of the amino acid, alters the lifetime of hydrogen bonds present in the first solvation shell, resulting in the modification of its structure and dynamics. Using GIAO-DFT-NMR calculations, we assessed the impact of these structural solute-solvent modifications on the magnetic shielding constants of the solute carbon atoms. In this sense, we evaluate the importance of an update in parameters that describe atomic charges present in the CHARMM36 force field.

Finding the direct energy-structure correlations in intramolecular aromaticity assisted hydrogen bonding (AAHB)

A predictive model for intramolecular hydrogen bond energy (E_HB) calculation of polyaromatic ortho-hydroxyaldehydes based on a set of small, functionalized hydrocarbons is developed. The complete data set of 18 compounds was used for this study. The model is based on one of four optional categories of molecular descriptors: geometric, spectroscopic, bond order and topological indices. The model of Wiberg bond indices (WBIs) as descriptors of the CC involved bond based on stepwise regression has acceptable prediction abilities for 14 structures of ortho-hydroxyformylobenzo[a]pyrene derivatives already at the semiempirical level. The presented correlation enables a significantly more rapid and quantitative description of the hydrogen bonding strength than the much more time-consuming MTA method. Thus, WBIs are shown to provide a reliable means for fast prescreening of the energy of chelate hydrogen bonds potentially for any polyaromatic derivatives.

One-bond 1 J(15 N,H) coupling constants at sp2 -hybridized nitrogen of Schiff bases, enaminones and similar compounds: A theoretical study

¹ J(¹⁵ N,H) coupling constants for enaminones and NH-forms of intramolecularly hydrogen-bonded Schiff bases as model compounds for sp² -hybridized nitrogen atoms are evaluated using density functional theory (DFT) to find the optimal functionals and basis sets. Ammonia is used as a test molecule and its one-bond coupling constant is compared with experiment. A methylamine Schiff base of a truncated molecule of gossypol is used for checking the performance of selected B3LYP, O3LYP, PBE, BHandH, and APFD density functionals and standard, modified, and dedicated basis sets for coupling constants. Both in vacuum and in chloroform, modeled by the simple continuum model of solvent, the modified basis sets predict significantly better the ¹ J(¹⁵ N,H) value in ammonia and in the methylamine Schiff base of a truncated molecule of gossypol than the standard basis sets. This procure is then used on a broad set of intramolecularly hydrogen-bonded molecules, and a good correlation between calculated and experimental one-bond NH coupling constants is obtained. The ¹ J(¹⁵ N,H) couplings are slightly overestimated. The calculated data show for hydrogen-bonded NH interatomic distances that the calculated values depend on the NH bond lengths. The shorter the bond lengths, the larger the ¹ J(¹⁵ N,H). A useful correlation between ¹ J(¹⁵ N,H) and NH bond length is derived that enables realistic predictions of one-bond NH coupling constants. The calculations reproduce experimentally observed trends for the studied molecules.

What is the form of muscimol from fly agaric mushroom (Amanita muscaria) in water? An insight from NMR experiment supported by molecular modeling

The biologically active alkaloid muscimol is present in fly agaric mushroom (Amanita muscaria), and its structure and action is related to human neurotransmitter _γ -aminobutyric acid (GABA). The current study reports on determination of muscimol form present in water solution using multinuclear ¹ H and ¹³ C nuclear magnetic resonance (NMR) experiments supported by density functional theory molecular modeling. The structures of three forms of free muscimol molecule both in the gas phase and in the presence of water solvent, modeled by polarized continuous model, and nuclear magnetic isotropic shieldings, the corresponding chemical shifts, and indirect spin-spin coupling constants were calculated. Several J-couplings observed in proton and carbon NMR spectra, not available before, are reported. The obtained experimental spectra, supported by theoretical calculations, favor the zwitterion form of muscimol in water. This structure differs from NH isomer, previously determined in dimethyl sulfoxide (DMSO) solution. In addition, positions of signals C3 and C5 are reversed in both solvents.

Computational 1 H NMR: Part 2. Chemical applications

This is the second one of three closely interrelated reviews dealing with computation of ¹ H NMR chemical shifts and ¹ H-¹ H spin-spin coupling constants prepared for Magnetic Resonance in Chemistry. Presented in this review are some basic notes and illustrative examples of how modern computational ¹ H NMR could be used for structural elucidation and stereoelectronic studies of the medium-sized organic molecules involving saturated, unsaturated, aromatic, and heteroaromatic compounds together with their functional derivatives and coordination complexes to get deeper insight into their stereochemical structure and stereodynamic behavior.

Computational 1 H NMR: Part 1. Theoretical background

This is the first one of the three closely interrelated reviews to be published in Magnetic Resonance in Chemistry dealing with accordingly theoretical background, chemical applications, and biochemical studies of and by means of computational ¹ H NMR. Presented in the first part of the review is a general outline of the modern theoretical methods and accuracy factors of computational ¹ H NMR involving locally dense basis set schemes, solvent effects, vibrational corrections, and relativistic effects performed at the density functional theory and/or nonempirical levels. This review is dedicated to Prof. Stephan Sauer in view of his invaluable contribution to the field of computational nuclear magnetic resonance.

Performance of polarization-consistent vs. correlation-consistent basis sets for CCSD(T) prediction of water dimer interaction energy

Detailed study of Jensen’s polarization-consistent vs. Dunning’s correlation-consistent basis set families performance on the extrapolation of raw and counterpoise-corrected interaction energies of water dimer using coupled cluster with single, double, and perturbative correction for connected triple excitations (CCSD(T)) in the complete basis set (CBS) limit are reported. Both 3-parameter exponential and 2-parameter inverse-power fits vs. the cardinal number of basis set, as well as the number of basis functions were analyzed and compared with one of the most extensive CCSD(T) results reported recently. The obtained results for both Jensen- and Dunning-type basis sets underestimate raw interaction energy by less than 0.136 kcal/mol with respect to the reference value of − 4.98065 kcal/mol. The use of counterpoise correction further improves (closer to the reference value) interaction energy. Asymptotic convergence of 3-parameter fitted interaction energy with respect to both cardinal number of basis set and the number of basis functions are closer to the reference value at the CBS limit than other fitting approaches considered here. Separate fits of Hartree-Fock and correlation interaction energy with 3-parameter formula additionally improved the results, and the smallest CBS deviation from the reference value is about 0.001 kcal/mol (underestimated) for CCSD(T)/aug-cc-pVXZ calculations. However, Jensen’s basis set underestimates such value to 0.012 kcal/mol. No improvement was observed for using the number of basis functions instead of cardinal number for fitting.

Performance of revised STO(1M)-3G basis set for prediction of 5-fluorocytosine chemical shifts

Nuclear shieldings and chemical shifts of 5-fluorocytosine (5FC) were predicted in the gas phase and DMSO solution modeled by polarizable continuum model using B3LYP density functional and revised STO(1M)-3G basis set. For comparison, eight arbitrary selected basis sets including STO-3G and medium-size Pople-type and larger dedicated Jensen-type ones were applied. The former basis sets were significantly smaller, but the calculated structural parameters, harmonic vibrational frequencies, were very accurate and close to those obtained with larger, polarization-consistent ones. The predicted ¹³ C and ¹ H chemical shieldings of 5FC and cytosine, selected as parent molecule, were acceptable (root mean square for ¹³ C chemical shifts in DMSO of about 5 ppm and less) though less accurate than those calculated with large basis sets, dedicated for prediction of nuclear magnetic resonance parameters.

Local aromaticity mapping in the vicinity of planar and nonplanar molecules

We report on nucleus-independent magnetic shielding (NICS) scans over the centers of six- and five-membered rings in selected metal phthalocyanines (MPc) and fullerene C60 for more accurate characterization of local aromaticity in these compounds. Detailed tests were conducted on model aromatic molecules including benzene, pyrrole, indole, isoindole, and carbazole and subsequently applied to H₂ Pc, ZnPc, Al(OH)Pc, and CuPc. Similar behavior of three selected magnetic probes, Bq, ³ He, and ⁷ Li⁺ , approaching perpendicularly the ring centers, was observed. For better visualization of shielding zone over the centers of aromatic rings, we introduced a simple mathematical procedure: the first and second derivatives of scan curves with respect to magnetic probe position enabled their additional examination. It allowed an easier localization of curve minimum and discrimination between areas in space varying by the magnetic field magnitude and to illustrate local aromaticity of two different kinds of rings in MPc with better resolution. Our results supported earlier reports on very low aromaticity indexes of pyrrole ring incorporated into MPc and significant aromaticity of the central macrocycle. No direct dependence between harmonic oscillator model of aromaticity and NICS was observed. Instead, a correlation between position of scan curve minimum and its magnitude were observed. In addition, the NICS values and ³ He chemical shifts in the middle of neutral C60 and C60^6- anion agreed well with the reported experimental NMR values for He@C60 and He@C60^6- .

Computational protocols for calculating 13C NMR chemical shifts

The most recent results dealing with the computation of ¹³C NMR chemical shifts in chemistry (small molecules, saturated, unsaturated and aromatic compounds, heterocycles, functional derivatives, coordination complexes, carbocations, and natural products) are reviewed, paying special attention to theoretical background and accuracy, the latter involving solvent effects, vibrational corrections, and relativistic effects.

Computational Prediction of 1 H and 13 C NMR Chemical Shifts for Protonated Alkylpyrroles: Electron Correlation and Not Solvation is the Salvation

Prediction of chemical shifts in organic cations is known to be a challenge. In this article we meet this challenge for α-protonated alkylpyrroles, a class of compounds not yet studied in this context, and present a combined experimental and theoretical study of the ¹³ C and ¹ H chemical shifts in three selected pyrroles. We have investigated the importance of the solvation model, basis set, and quantum chemical method with the goal of developing a simple computational protocol, which allows prediction of ¹³ C and ¹ H chemical shifts with sufficient accuracy for identifying such compounds in mixtures. We find that density functional theory with the B3LYP functional is not sufficient for reproducing all ¹³ C chemical shifts, whereas already the simplest correlated wave function model, Møller-Plesset perturbation theory (MP2), leads to almost perfect agreement with the experimental data. Treatment of solvent effects generally improves the agreement with experiment to some extent and can in most cases be accomplished by a simple polarizable continuum model. The only exception is the NH proton, which requires inclusion of explicit solvent molecules in the calculation.

Method Calibration or Data Fitting?

We investigate by explicit parameter optimization to what extent basis sets of polarized double-ζ quality can introduce compensating errors in five different density functional methods. It is shown that minor changes in the contraction coefficients of the valence functions in the basis sets can have a significant impact and allow different density functional methods to achieve very similar performances. This holds for nuclear magnetic shielding constants and for isomerization energies, barrier heights, and noncovalent interactions. It is furthermore shown that errors due to neglect of vibrational and solvent effects can be absorbed in the combined method and basis set errors. These findings hold for data sets consisting of 50-150 data points. This raises the question of whether the common practice of identifying combinations of density functional methods and basis sets that have a good performance against a selected set of reference data should be considered as data fitting in the combined parameter space spanned by the method and basis set.

Understanding the Molecular Structure of the Sialic Acid-Phenylboronic Acid Complex by using a Combined NMR Spectroscopy and DFT Study: Toward Sialic Acid Detection at Cell Membranes

The origin of the unusually high stability of the sialic acid (SA) and phenylboronic acid (PBA) complex was investigated by a combined nuclear magnetic resonance (NMR) spectroscopy and density functional theory (DFT) study. SA is a glycan-terminating monosaccharide, and its importance as a clinical target has long been recognized. Inspired by the fact that the binding properties of SA-PBA complexation are anomalously high relative to those of typical monosaccharides, great effort has been made to build a clinical platform with the use of PBA as a SA-selective receptor. Although a number of applications have been reported in recent years, the ability of PBA to recognize SA-terminating surface glycans selectively is still unclear, because high-affinity SA-PBA complexation might not occur in a physiological environment. In particular, different forms of SA (α- and β-pyranose) were not considered in detail. To answer this question, the combined NMR spectroscopy/DFT study revealed that the advantageous binding properties of the SA-PBA complex arise from ester bonding involving the α-carboxylate moieties (C1 and C2) of β-SA but not α-SA. Moreover, the facts that the C2 atom is blocked by a glycoside bond in a physiological environment and that α-SA basically exists on membrane-bound glycans in a physiological environment lead to the conclusion that PBA cannot selectively recognize the SA unit to discriminate specific types of cells. Our results have a significant impact on the field of SA-based cell recognition.

Convergence of nuclear magnetic shieldings and one-bond 1 J(11 B1 H) indirect spin-spin coupling constants in small boron molecules

Self-consistent field Hartree-Fock, density functional theory, and coupled-cluster calculations of the nuclear magnetic shielding constants of BH and BH₃ molecules have been conducted to characterize the convergence of individual results obtained with correlation-consistent and polarization-consistent basis sets. The individual ¹¹ B and ¹ H NMR parameters were estimated in the complete basis set limit and compared with benchmark results. Only the KT3 density functional accurately reproduced ¹¹ B shielding in BH molecule.

Influence of Solvent Representation on Nuclear Shielding Calculations of Protonation States of Small Biological Molecules

In this study, we assess the influence of solvation on the accuracy and reliability of isotropic nuclear magnetic shielding calculations for amino acids in comparison to experimental data. We focus particularly on the performance of solvation methods for different protonation states, as biological molecules occur almost exclusively in aqueous solution and are subject to protonation with pH. We identify significant shortcomings of current implicit solvent models and present a hybrid solvation approach that improves agreement with experimental data by taking into account the presence of direct interactions between amino acid protonation state and water molecules.

Method and basis set dependence of the NICS indexes of aromaticity for benzene

The role of theory level in prediction of benzene magnetic indexes of aromaticity is analysed and compared with calculated nuclear magnetic shieldings of ³ He used as NMR probe. Three closely related nucleus-independent chemical shift (NICS) based indexes were calculated for benzene at SCF-HF, MP2, and DFT levels of theory and the impact of basis set on these quantities was studied. The changes of benzene NICS(0), NICS(1), and NICS(1)zz parameters calculated using SCF-HF, MP2 and several density functionals were within 1 to 3 ppm. Similar deviations between magnetic indexes of aromaticity were observed for values calculated with selected basis sets. Only very small effect of polar solvent on benzene aromaticity was predicted. The ³ He nuclear magnetic isotropic shielding (σ) and its zz-components (σ_zz ) of helium atom approaching the centre of benzene ring from above produced similar curves versus benzene-He distance to NICS parameters calculated for similarly moving Bq ghost atom. We also propose an experimental verification of NICS calculations by designing the ³ He NMR measurement for benzene saturated with helium gas or in low temperature matrices.

Magnetic properties with multiwavelets and DFT: the complete basis set limit achieved

Multiwavelets are emerging as an attractive alternative to traditional basis sets such as Gaussian-type orbitals and plane waves. One of their distinctive properties is the ability to reach the basis set limit (often a chimera for traditional approaches) reliably and consistently by fixing the desired precision ε. We present our multiwavelet implementation of the linear response formalism, applied to static magnetic properties, at the self-consistent field level of theory (both for Hartree-Fock and density functional theories). We demonstrate that the multiwavelets consistently improve the accuracy of the results when increasing the desired precision, yielding results that have four to five digits precision, thus providing a very useful benchmark which could otherwise only be estimated by extrapolation methods. Our results show that magnetizabilities obtained with the augmented quadruple-ζ basis (aug-cc-pCVQZ) are practically at the basis set limit, whereas absolute nuclear magnetic resonance shielding tensors are more challenging: even by making use of a standard extrapolation method, the accuracy is not substantially improved. In contrast, our results provide a benchmark that: (1) confirms the validity of the extrapolation ansatz; (2) can be used as a reference to achieve a property-specific extrapolation scheme, thus providing a means to obtain much better extrapolated results; (3) allows us to separate functional-specific errors from basis-set ones and thus to assess the level of cancellation between basis set and functional errors often exploited in density functional theory.

Calculation of 15N NMR chemical shifts: Recent advances and perspectives

Recent advances in computation of ¹⁵N NMR chemical shifts are reviewed, concentrating mainly on practical aspects of computational protocols and accuracy factors. The review includes the discussion of the level of theory, the choice of density functionals and basis sets together with taking into account solvent effects, rovibrational corrections and relativistic effects. Computational aspects of ¹⁵N NMR are illustrated for the series of neutral and protonated open-chain nitrogen-containing compounds and nitrogen heterocycles, coordination and intermolecular complexes.

Systematic investigation of DFT-GIAO 15N NMR chemical shift prediction using B3LYP/cc-pVDZ: application to studies of regioisomers, tautomers, protonation states and N-oxides

The calculation of ¹⁵N NMR chemical shifts has been systematically investigated using density functional theory-gauge including/invariant atomic orbitals (DFT-GIAO) approximation at the B3LYP/cc-pVDZ level of theory. General linear regression terms for ¹⁵N chemical shift predictions were calculated for nitromethane and liquid ammonia references in DMSO. Both aliphatic and aromatic nitrogens were studied using a diverse set of molecular scaffolds. Statistical error analysis between experiment and prediction revealed that, with the exception of primary amines, 95% of linear scaled N-15 chemical shifts are within a ±9.56 ppm range. Comparison of the ¹⁵N calculated isotropic chemical shifts with the experimentally determined chemical shifts provided accurate assignment of the correct structure in cases where experimental data was ambiguous or inconclusive. Application of ¹⁵N prediction proved to be highly effective in identifying the correct regio-isomer, oxidation state, protonation state and preferred tautomer in solution.

Toward engineering efficient peptidomimetics. Screening conformational landscape of two modified dehydroaminoacids

Effective peptidomimetics should posses structural rigidity and appropriate interaction pattern leading to potential spatial and electronic matching to the target receptor site. Rational design of such small bioactive molecules could push chemical synthesis and molecular modeling toward faster progress in medicinal chemistry. Conformational properties of N-t-butoxycarbonyl-glycine-(E/Z)-dehydrophenylalanine N',N'-dimethylamides (Boc-Gly-(E/Z)-ΔPhe-NMe2 ) in chloroform were studied by NMR and IR spectroscopy. The experimental findings were supported by extensive calculations at DFT(B3LYP, M06-2X) and MP2 levels of theory and the β-turn tendency for both isomers of the studied dipeptide were determined in vacuum and in solution. The theoretical data and experimental IR results were used as an additional information for the NMR-based determination of the detailed solution conformations of the peptides. The obtained results reveal that N-methylation of C-terminal amide group changes dramatically the conformational properties of studied dehydropeptides. Theoretical conformational analysis reveals that the tendency to adopt β-turn conformations is much weaker for the N-methylated Z isomer (Boc-Gly-(Z)-ΔPhe-NMe2 ), both in vacuum and in polar environment. On the contrary, N-methylated E isomer (Boc-Gly-(E)-ΔPhe-NMe2 ) can easily adopt β-turn conformation, but the backbone torsion angles (φ1, ψ1, φ2, ψ2) are off the limits for common β-turn types.

Rovibrational and Temperature Effects in Theoretical Studies of NMR Parameters

The demand for high precision calculations of NMR shieldings (or their related values, chemical shifts δ) and spin–spin coupling constants facilitating and supporting detailed interpretations of NMR spectra increases hand in hand with the development of computational techniques and hardware resources. Highly sophisticated calculations including even relativistic effects are nowadays possible for these properties. However, NMR parameters depend not only on molecular structure and environment but also on molecular flexibility and temperature and the apparent success of theoretical predictions for molecular equilibrium geometries creates a demand for zero-point vibrational and temperature corrections. In this chapter we describe briefly the theory behind rovibrational corrections and review then some important contributions to this field.

Predicting the structure and vibrational frequencies of ethylene using harmonic and anharmonic approaches at the Kohn-Sham complete basis set limit

In this work, regular convergence patterns of the structural, harmonic, and VPT2-calculated anharmonic vibrational parameters of ethylene towards the Kohn–Sham complete basis set (KS CBS) limit are demonstrated for the first time. The performance of the VPT2 scheme implemented using density functional theory (DFT-BLYP and DFT-B3LYP) in combination with two Pople basis sets (6-311++G** and 6-311++G(3df,2pd)), the polarization-consistent basis sets pc-n, aug-pc-n, and pcseg-n (n = 0, 1, 2, 3, 4), and the correlation-consistent basis sets cc-pVXZ and aug-cc-pVXZ (X = D, T, Q, 5, 6) was tested.

The BLYP-calculated harmonic frequencies were found to be markedly closer than the B3LYP-calculated harmonic frequencies to the experimentally derived values, while the calculated anharmonic frequencies consistently underestimated the observed wavenumbers. The different basis set families gave very similar estimated values for the CBS parameters. The anharmonic frequencies calculated with B3LYP/aug-pc-3 were consistently significantly higher than those obtained with the pc-3 basis set; applying the aug-pcseg-n basis set family alleviated this problem. Utilization of B3LYP/aug-pcseg-n basis sets instead of B3LYP/aug-cc-pVXZ, which is computationally less expensive, is suggested for medium-sized molecules. Harmonic BLYP/pc-2 calculations produced fairly accurate ethylene frequencies.

Graphical Abstract

Theoretical and experimental NMR studies on muscimol from fly agaric mushroom (Amanita muscaria)

In this article we report results of combined theoretical and experimental NMR studies on muscimol, the bioactive alkaloid from fly agaric mushroom (Amanita muscaria). The assignment of (1)H and (13)C NMR spectra of muscimol in DMSO-d6 was supported by additional two-dimensional heteronuclear correlated spectra (2D NMR) and gauge independent atomic orbital (GIAO) NMR calculations using density functional theory (DFT). The effect of solvent in theoretical calculations was included via polarized continuum model (PCM) and the hybrid three-parameter B3LYP density functional in combination with 6-311++G(3df,2pd) basis set enabled calculation of reliable structures of non-ionized (neutral) molecule and its NH and zwitterionic forms in the gas phase, chloroform, DMSO and water. GIAO NMR calculations, using equilibrium and rovibrationally averaged geometry, at B3LYP/6-31G* and B3LYP/aug-cc-pVTZ-J levels of theory provided muscimol nuclear magnetic shieldings. The theoretical proton and carbon chemical shifts were critically compared with experimental NMR spectra measured in DMSO. Our results provide useful information on its structure in solution. We believe that such data could improve the understanding of basic features of muscimol at atomistic level and provide another tool in studies related to GABA analogs.