Calculating nuclear magnetic resonance chemical shifts in solvated systems

The nuclear magnetic resonance (NMR) chemical shift is extremely sensitive to molecular geometry, hydrogen bonding, solvent, temperature, pH, and concentration. Calculated magnetic shielding constants, converted to chemical shifts, can be valuable aids in NMR peak assignment and can also give detailed information about molecular geometry and intermolecular effects. Calculating chemical shifts in solution is complicated by the need to include solvent effects and conformational averaging. Here, we review the current state of NMR chemical shift calculations in solution, beginning with an introduction to the theory of calculating magnetic shielding in general, then covering methods for inclusion of solvent effects and conformational averaging, and finally discussing examples of applications using calculated chemical shifts to gain detailed structural information.     

Predicting 195Pt NMR Chemical Shifts in Water-Soluble Inorganic/Organometallic Complexes with a Fast and Simple Protocol Combining Semiempirical Modeling and Machine Learning

Water-soluble Pt complexes are the key components in medicinal chemistry and catalysis. The well-known cisplatin family of anticancer drugs and industrial hydrosylilation catalysts are two leading examples. On the molecular level, the activity mechanisms of such complexes mostly involve changes in the Pt coordination sphere. Using ¹⁹⁵Pt NMR spectroscopy for operando monitoring would be a valuable tool for uncovering the activity mechanisms; however, reliable approaches for the rapid correlation of Pt complex structure with ¹⁹⁵Pt chemical shifts are very challenging and not available for everyday research practice. While NMR shielding is a response property, molecular 3D structure determines NMR spectra, as widely known, which allows us to build up 3D structure to ¹⁹⁵Pt chemical shift correlations. Accordingly, we present a new workflow for the determination of lowest-energy configurational/conformational isomers based on the GFN2-xTB semiempirical method and prediction of corresponding chemical shifts with a Machine Learning (ML) model tuned for Pt complexes. The workflow was designed for the prediction of ¹⁹⁵Pt chemical shifts of water-soluble Pt(II) and Pt(IV) anionic, neutral, and cationic complexes with halide, NO₂⁻, (di)amino, and (di)carboxylate ligands with chemical shift values ranging from −6293 to 7090 ppm. The model offered an accuracy (normalized root-mean-square deviation/RMSD) of 1.08 %/145.02 ppm on the held-out test set.     

Toward an accurate determination of 195Pt chemical shifts by density functional computations: the importance of unspecific solvent effects and the dependence of Pt magnetic shielding constants on structural parameters

Density functional theory using the zero-order regular approximate two-component relativistic Hamiltonian has been applied to calculate the 195Pt chemical shifts for the complexes [PtCl6]2-, [PtCl4]2-, and [Pt2(NH3)2Cl2((CH3)3CCONH)2(CH2COCH3)]Cl. It is demonstrated that, in contrast to recent findings by other authors, platinum chemical shift calculations require not only a basis set beyond polarized triple-zeta quality for the metal atom but also, in principle, the consideration of explicit solvent molecules in addition to a continuum model for the first two complexes. We find that the inclusion of direct solvent-solute interactions at the quantum mechanical level is important for obtaining reasonable results despite that fact that these solvent effects are rather nonspecific. The importance of solvent effects has also implications on how experimental data should be interpreted. Further, in contrast to several previous studies of heavy-metal NMR parameters, functionals beyond the local density approximation were required both in the geometry optimization and the NMR calculations to obtain reasonable agreement between the computed and experimental NMR data. This comes with the disadvantage, however, of increased Pt-ligand bond distances leading to less good agreement with experiment for structural data. A detailed analysis of the results for the two chloroplatinate complexes is presented. The same computational procedure has then been applied to the dinuclear Pt(III) complex. Chemical shifts have been calculated with respect to both [PtCl6]2- and [PtCl4]2- chosen as the NMR reference, yielding good agreement with experiment. The determination of preferred solvent locations around the complexes studied turned out to be important for reproducing experimental data.     

Solvent effects on 195Pt and 205Tl NMR chemical shifts of the complexes [(NC)5Pt--Tl(CN)n]n- (n=0-3), and [(NC)5Pt--Tl--Pt(CN)5]3- studied by relativistic density functional theory

The 295Pt and 205Tl NMR chemical shifts of the complexes [(NC)5Pt-Tl(CN)n]n- n=0-3, and of the related system [(NC)5Pt--Tl--Pt(CN)5]3- have been computationally investigated. It is demonstrated that based on relativistically optimized geometries, by applying an explicit first solvation shell, an additional implicit solvation model to represent the bulk solvent effects (COSMO model), and a DFT exchange-correlation potential that was specifically designed for the treatment of response properties, that the experimentally observed metal chemical shifts can be calculated with satisfactory accuracy. The metal chemical shifts have been computed by means of a two-component relativistic density functional approach. The effects of electronic spin-orbit coupling were included in all NMR computations. The impact of the choice of the reference, which ideally should not affect the accuracy of the computed chemical shifts, is also demonstrated. Together with recent calculations by us of the Pt and Tl spin-spin coupling constants, all measured metal NMR parameters of these complexes are now computationally determined with sufficient accuracy in order to allow a detailed analysis of the experimental results. In particular, we show that interaction of the complexes with the solvent (water) must be an integral part of such an analysis.     

Solvent effects on NMR isotropic shielding constants. a comparison between explicit polarizable discrete and continuum approaches

The gas-to-aqueous solution shifts of the 17O and 13C NMR isotropic shielding constants for the carbonyl chromophore in formaldehyde and acetone are investigated. For the condensed-phase problem, we use the hybrid density functional theory/molecular mechanics approach in combination with a statistical averaging over an appropriate number of solute-solvent configurations extracted from classical molecular dynamics simulations. The PBE0 exchange-correlation functional and the 6-311++G(2d,2p) basis set are used for the calculation of the shielding constants. London atomic orbitals are employed to ensure gauge-origin independent results. The effects of the bulk solvent molecules are found to be crucial in order to calculate accurate solvation shifts of the shielding constants. Very good agreement between the computed and experimental solvation shifts is obtained for the shielding constants of acetone when a polarizable water potential is used. Supermolecular results based on geometry-optimized molecular structures are presented. We also compare the results obtained with the polarizable continuum model to the results obtained using explicit MM molecules to model the bulk solvent effect.     

Computing the 7Li NMR chemical shielding of hydrated Li+ using cluster calculations and time-averaged configurations from ab initio molecular dynamics simulations

Ab initio molecular dynamics (AIMD) simulations have been used to predict the time-averaged Li NMR chemical shielding for a Li(+) solution. These results are compared to NMR shielding calculations on smaller Li(+)(H(2)O)(n) clusters optimized in either the gas phase or with a polarizable continuum model (PCM) solvent. The trends introduced by the PCM solvent are described and compared to the time-averaged chemical shielding observed in the AIMD simulations where large explicit water clusters hydrating the Li(+) are employed. Different inner- and outer-coordination sphere contributions to the Li NMR shielding are evaluated and discussed. It is demonstrated an implicit PCM solvent is not sufficient to correctly model the Li shielding, and that explicit inner hydration sphere waters are required during the NMR calculations. It is also shown that for hydrated Li(+), the time averaged chemical shielding cannot be simply described by the population-weighted average of coordination environments containing different number of waters.     

Effects of Quantum Nuclear Delocalisation on NMR Parameters from Path Integral Molecular Dynamics

The influence of nuclear delocalisation on NMR chemical shifts in molecular organic solids is explored using path integral molecular dynamics (PIMD) and density functional theory calculations of shielding tensors. Nuclear quantum effects are shown to explain previously observed systematic deviations in correlations between calculated and experimental chemical shifts, with particularly large PIMD‐induced changes (up to 23 ppm) observed for carbon atoms in methyl groups. The PIMD approach also enables isotope substitution effects on chemical shifts and J couplings to be predicted in excellent agreement with experiment for both isolated molecules and molecular crystals. An approach based on convoluting calculated shielding or coupling surfaces with probability distributions of selected bond distances and valence angles obtained from PIMD simulations is used to calculate isotope effects.     

Analyzing Pt chemical shifts calculated from relativistic density functional theory using localized orbitals: the role of Pt 5d lone pairs

Pt chemical shifts were calculated from two-component relativistic density functional theory (DFT). The shielding tensors were analyzed by using a recently developed method to decompose the spin-orbit DFT results into contributions from spin-free localized orbitals (here: natural localized molecular orbitals (NLMOs) and natural bond orbitals (NBOs)). Seven chemical shifts in six Pt complexes with Pt oxidation states II, III, and IV; and halide, amino, and amidate ligands were analyzed, with particular focus on the role of nonbonding Pt 5d orbitals. A simple d-orbital 'rotation' model has been used to rationalize some of the observed trends such as the main difference between Pt(II) and Pt(IV) chemical shifts. The localized orbital analysis data showed that most of this difference as well as trends among different Pt complexes with similar coordination can be rationalized by comparing properties of the nonbonding Pt 5d orbitals. We have also analyzed the spin-orbit effects on the chemical shifts of [PtCl4](2-) compared to [PtBr4](2-).     

Prediction of the 1H and 13C NMR spectra of alpha-D-glucose in water by DFT methods and MD simulations

We have applied computational protocols based on DFT and molecular dynamics simulations to the prediction of the alkyl 1H and 13C chemical shifts of alpha-d-glucose in water. Computed data have been compared with accurate experimental chemical shifts obtained in our laboratory. 13C chemical shifts do not show a marked solvent effect. In contrast, the results for 1H chemical shifts provided by structures optimized in the gas phase are only fair and point out that it is necessary to take into account both the flexibility of the glucose structure and the strong effect exerted by solvent water thereupon. Thus, molecular dynamics simulations were carried out to model both the internal geometry as well as the influence of solvent molecules on the conformational distribution of the solute. Snapshots from the simulation were used as input to DFT NMR calculations with varying degrees of sophistication. The most important factor that affects the accuracy of computed 1H chemical shifts is the solute geometry; the effect of the solvent on the shielding constants can be reasonably accounted for by self-consistent reaction field models without the need of explicitly including solvent molecules in the NMR property calculation.     

DFT calculations of 1H and 13C NMR chemical shifts in transition metal hydrides

Transition metal hydrides are of great interest in chemistry because of their reactivity and their potential use as catalysts for hydrogenation. Among other available techniques, structural properties in transition metal (TM) complexes are often probed by NMR spectroscopy. In this paper we will show that it is possible to establish a viable methodological strategy in the context of density functional theory, that allows the determination of 1H NMR chemical shifts of hydride ligands attached to transition metal atoms in mononuclear systems and clusters with good accuracy with respect to experiment. 13C chemical shifts have also been considered in some cases. We have studied mononuclear ruthenium complexes such as Ru(L)(H)(dppm)2 with L = H or Cl, cationic complex [Ru(H)(H2O)(dppm)2]+ and Ru(H)2(dppm)(PPh3)2, in which hydride ligands are characterized by a negative 1H NMR chemical shift. For these complexes all calculations are in relatively good agreement compared to experimental data with errors not exceeding 20% except for the hydrogen atom in Ru(H)2(dppm)(PPh3)2. For this last complex, the relative error increases to 30%, probably owing to the necessity to take into account dynamical effects of phenyl groups. Carbonyl ligands are often encountered in coordination chemistry. Specific issues arise when calculating 1H or 13C NMR chemical shifts in TM carbonyl complexes. Indeed, while errors of 10 to 20% with respect to experiment are often considered good in the framework of density functional theory, this difference in the case of mononuclear carbonyl complexes culminates to 80%: results obtained with all-electron calculations are overall in very satisfactory agreement with experiment, the error in this case does not exceed 11% contrary to effective core potentials (ECPs) calculations which yield errors always larger than 20%. We conclude that for carbonyl groups the use of ECPs is not recommended, although their use could save time for very large systems, for instance in cluster chemistry. The reliance of NMR chemical shielding on dynamical effects, such as intramolecular rearrangements or trigonal twists, is also examined for H2Fe(CO)4, K+[HFe(CO)](-), HMn(CO)5 and HRe(CO)5. The accuracy of the theory is also examined for complexes with two dihydrogen ligands (Tp*RuH(H2)2 and [FeH(H2)(DMPE)2]+) and a ruthenium cluster, [H3Ru4(C6H6)4(CO)]+. It is shown that for all complexes studied in this work, the effect of the ligands on the chemical shielding of hydrogen coordinated to metal is suitably calculated, thus yielding a very good correlation between experimental chemical shifts and theoretical chemical shielding.     

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.     

Molecular dynamics averaging of Xe chemical shifts in liquids

The Xe nuclear magnetic resonance chemical shift differences that afford the discrimination between various biological environments are of current interest for biosensor applications and medical diagnostic purposes. In many such environments the Xe signal appears close to that in water. We calculate average Xe chemical shifts (relative to the free Xe atom) in solution in eleven liquids: water, isobutane, perfluoro-isobutane, n-butane, n-pentane, neopentane, perfluoroneopentane, n-hexane, n-octane, n-perfluorooctane, and perfluorooctyl bromide. The latter is a liquid used for intravenous Xe delivery. We calculate quantum mechanically the Xe shielding response in Xe-molecule van der Waals complexes, from which calculations we develop Xe (atomic site) interpolating functions that reproduce the ab initio Xe shielding response in the complex. By assuming additivity, these Xe-site shielding functions can be used to calculate the shielding for any configuration of such molecules around Xe. The averaging over configurations is done via molecular dynamics (MD). The simulations were carried out using a MD technique that one of us had developed previously for the simulation of Henry's constants of gases dissolved in liquids. It is based on separating a gaseous compartment in the MD system from the solvent using a semipermeable membrane that is permeable only to the gas molecules. We reproduce the experimental trends in the Xe chemical shifts in n-alkanes with increasing number of carbons and the large chemical shift difference between Xe in water and in perfluorooctyl bromide. We also reproduce the trend for a given solvent of decreasing Xe chemical shift with increasing temperature. We predict chemical shift differences between Xe in alkanes vs their perfluoro counterparts.     

Calculation of <Superscript>15</Superscript>N NMR chemical shifts of amines in the framework of the density functional theory

The ¹⁵N NMR magnetic shielding constants (followed by recalculation into chemical shifts) in a representative series of amines were calculated in the framework of the density functional theory. The results were compared with experiment. The accuracy factors of this calculation (functional, basis set, solvent effects, and multistandard) were studied. Taking into account all the above factors leads to a noticeable decrease in the average absolute error in the calculation of the ¹⁵N NMR chemical shifts (from 13 to 4 ppm) in a range of their changing in the studies series of compounds of ～60 ppm (which is 6—7% in relative units).     

Platinum-modified adenines: unprecedented protonation behavior revealed by NMR spectroscopy and relativistic density-functional theory calculations

Two novel Pt(IV) complexes of aromatic cytokinins with possible antitumor properties were prepared by reaction of selected aminopurines with K(2)PtCl(6). The structures of both complexes, 9-[6-(benzylamino)purine] pentachloroplatinate (IV) and 9-[6-(furfurylamino)purine] pentachloroplatinate (IV), were characterized in detail by using two-dimensional NMR spectroscopy ((1)H, (13)C, (15)N, and (195)Pt) in solution and CP/MAS NMR techniques in the solid state. We report for the first time the X-ray structure of a nucleobase adenine derivative coordinated to Pt(IV) via the N9 atom. The protonation equilibria for the complexes in solution were characterized by using NMR spectroscopy (isotropic chemical shifts and indirect nuclear spin-spin coupling constants) and the structural conclusions drawn from the NMR analysis are supported by relativistic density-functional theory (DFT) calculations. Because of the presence of the Pt atom, hybrid GGA functionals and scalar-relativistic and spin-orbit corrections were employed for both the DFT calculations of the molecular structure and particularly for the NMR chemical shifts. In particular, the populations of the N7-protonated and neutral forms of the complexes in solution were characterized by correlating the experimental and the DFT-calculated NMR chemical shifts. In contrast to the chemical exchange process involving the N7-H group, the hydrogen atom at N3 was determined to be unexpectedly rigid, probably because of the presence of the stabilizing intramolecular interaction N3-H···Cl. The described methodology combining the NMR spectroscopy and relativistic DFT calculations can be employed for characterizing the tautomeric and protonation equilibria in a large family of transition-metal-modified purine bases.     

MP2 calculation of 77Se NMR chemical shifts taking into account relativistic corrections

The main factors affecting the accuracy and computational cost of the Second‐order Möller‐Plesset perturbation theory (MP2) calculation of ⁷⁷Se NMR chemical shifts (methods and basis sets, relativistic corrections, and solvent effects) are addressed with a special emphasis on relativistic effects. For the latter, paramagnetic contribution (390–466 ppm) dominates over diamagnetic term (192–198 ppm) resulting in a total shielding relativistic correction of about 230–260 ppm (some 15% of the total values of selenium absolute shielding constants). Diamagnetic term is practically constant, while paramagnetic contribution spans over 70–80 ppm. In the ⁷⁷Se NMR chemical shifts scale, relativistic corrections are about 20–30 ppm (some 5% of the total values of selenium chemical shifts). Solvent effects evaluated within the polarizable continuum solvation model are of the same order of magnitude as relativistic corrections (about 5%). For the practical calculations of ⁷⁷Se NMR chemical shifts of the medium‐sized organoselenium compounds, the most efficient computational protocols employing relativistic Dyall's basis sets and taking into account relativistic and solvent corrections are suggested. The best result is characterized by a mean absolute error of 17 ppm for the span of ⁷⁷Se NMR chemical shifts reaching 2500 ppm resulting in a mean absolute percentage error of 0.7%. Copyright © 2015 John Wiley & Sons, Ltd.     

Thermal and solvent effects on the NMR and UV parameters of some bioreductive drugs

15N NMR chemical shifts and n-->pi* electronic transition energy for metronidazole (1) has been calculated and compared with experimental data. A detailed computational study of 1 is presented, with special attention to the performance of various theoretical methods for reproducing spectroscopic parameters in solution. The most sophisticated approach involves density functional based on the Car-Parrinello molecular dynamics simulations of 1 in aqueous solution (BP86 level) and averaging chemical shifts and deltaE(n-->pi*) over snapshots from the trajectory. In the NMR and UV calculations for these snapshots (performed at the B3LYP level), a small number of discrete water molecules are retained, and the remaining bulk solution effects are included via a polarizable continuum model (PCM). A good agreement with experiment is also obtained using static geometry optimization and NMR computation of pristine 1 employing a PCM approach. Further theoretical predictions are also reported for 17O NMR and deltaE(n-->pi*) of three hydroxycinnamic acid derivatives, which suggest that it is essential to incorporate the dynamics and solvent effects for NMR and UV calculations in the condensed phase.     

Computational studies of 13C NMR chemical shifts of saccharides

The (13)C NMR chemical shifts for alpha-D-lyxofuranose, alpha-D-lyxopyranose (1)C(4), alpha-D-lyxopyranose (4)C(1), alpha-D-glucopyranose (4)C(1), and alpha-D-glucofuranose have been studied at ab initio and density-functional theory levels using TZVP quality basis set. The methods were tested by calculating the nuclear magnetic shieldings for tetramethylsilane (TMS) at different levels of theory using large basis sets. Test calculations on the monosaccharides showed B3LYP(TZVP) and BP86(TZVP) to be cost-efficient levels of theory for calculation of NMR chemical shifts of carbohydrates. The accuracy of the molecular structures and chemical shifts calculated at the B3LYP(TZVP) level is comparable to those obtained at the MP2(TZVP) level. Solvent effects were considered by surrounding the saccharides by water molecules and also by employing a continuum solvent model. None of the applied methods to consider solvent effects was successful. The B3LYP(TZVP) and MP2(TZVP)(13)C NMR chemical shift calculations yielded without solvent and rovibrational corrections an average deviation of 5.4 ppm and 5.0 ppm between calculated and measured shifts. A closer agreement between calculated and measured chemical shifts can be obtained by using a reference compound that is structurally reminiscent of saccharides such as neat methanol. An accurate shielding reference for carbohydrates can be constructed by adding an empirical constant shift to the calculated chemical shifts, deduced from comparisons of B3LYP(TZVP) or BP86(TZVP) and measured chemical shifts of monosaccharides. The systematic deviation of about 3 ppm for O(1)H chemical shifts can be designed to hydrogen bonding, whereas solvent effects on the (1)H NMR chemical shifts of C(1)H were found to be small. At the B3LYP(TZVP) level, the barrier for the torsional motion of the hydroxyl group at C(6) in alpha-D-glucofuranose was calculated to 7.5 kcal mol(-1). The torsional displacement was found to introduce large changes of up to 10 ppm to the (13)C NMR chemical shifts yielding uncertainties of about +/-2 ppm in the chemical shifts.