Towards the versatile DFT and MP2 computational schemes for 31P NMR chemical shifts taking into account relativistic corrections

The Scope of the Applicability of Non-relativistic DFT Calculations of NMR Chemical Shifts in Pyridine-Metal Complexes for Applied Applications

Heavy metals are toxic, but it is impossible to stop using them. Considering the variety of molecular systems in which they can be present, the multicomponent nature and disorder of the structure of such systems, one of the most effective methods for studying them is NMR spectroscopy. This determines the need to calculate NMR chemical shifts for expected model systems. For elements beyond the third row of the periodic table, corrections for relativistic effects are necessary when calculating NMR parameters. Such corrections may be necessary even for light atoms due to the shielding effect of a neighboring heavy atom. This work examines the extent to which non-relativistic DFT calculations are able to reproduce experimental 15N and 113Cd NMR chemical shift tensors in pyridine-metal coordination complexes. It is shown that while for the calculation of 15N NMR chemical shift tensors there is no real need to consider relativistic corrections, for 113Cd, on the contrary, none of the tested calculation methods could reproduce the experimentally obtained tensor to any extent correctly.

Systematic QM/MM Study for Predicting 31P NMR Chemical Shifts of Adenosine Nucleotides in Solution and Stages of ATP Hydrolysis in a Protein Environment

NMR (nuclear magnetic resonance) spectroscopy allows for important atomistic insights into the structure and dynamics of biological macromolecules; however, reliable assignments of experimental spectra are often difficult. Herein, quantum mechanical/molecular mechanical (QM/MM) calculations can provide crucial support. A major problem for the simulations is that experimental NMR signals are time-averaged over much longer time scales, and since computed chemical shifts are highly sensitive to local changes in the electronic and structural environment, sufficiently large averages over representative structural ensembles are essential. This entails high computational demands for reliable simulations. For NMR measurements in biological systems, a nucleus of major interest is 31P since it is both highly present (e.g., in nucleic acids) and easily observable. The focus of our present study is to develop a robust and computationally cost-efficient framework for simulating 31P NMR chemical shifts of nucleotides. We apply this scheme to study the different stages of the ATP hydrolysis reaction catalyzed by p97. Our methodology is based on MM molecular dynamics (MM-MD) sampling, followed by QM/MM structure optimizations and NMR calculations. Overall, our study is one of the most comprehensive QM-based 31P studies in a protein environment and the first to provide computed NMR chemical shifts for multiple nucleotide states in a protein environment. This study sheds light on a process that is challenging to probe experimentally and aims to bridge the gap between measured and calculated NMR spectroscopic properties.

New efficient pecS-n (n = 1, 2) basis sets for quantum chemical calculations of 31P NMR chemical shifts

The basis sets that are used in the quantum chemical calculations of ³¹P NMR chemical shifts have always been one of the most important factors of accuracy. Regardless of what high-quality approach is employed, using basis sets of insufficient flexibility in the important angular regions may give poor results and lead to misassignments of the signals in the ³¹P NMR spectra. In this work, it was found that the existing nonrelativistic basis sets for phosphorus atom of double- and triple-ζ quality, specialized for the ³¹P NMR chemical shifts calculations, are essentially undersaturated in the d-angular space that occurred to play a significant role in the overall accuracy of these calculations. This problem has been thoroughly investigated, and new pecS-n (n = 1, 2) basis sets for phosphorus chemical shifts calculations were proposed. The exponents and contraction coefficients for the pecS-n basis sets were generated with the property-energy consistent method that has been introduced in our earlier paper, and has been proven useful in the creation of efficient property-oriented basis sets. New basis sets were optimized using the GIAO-DFT method with the B97-2 functional. Extensive benchmark calculations showed that the pecS-1 and pecS-2 basis sets provide very good accuracy, characterized by the corrected mean absolute percentage errors against the experiment of about 7.03 and 4.42 ppm, respectively. In particular, the accuracy of ³¹P NMR chemical shifts calculations achieved with the pecS-2 basis set is one of the most favorable accuracies for today. We believe that our new pecS-n (n = 1, 2) basis sets for phosphorus atom will prove useful in modern large-scale quantum chemical calculations of ³¹P NMR chemical shifts.

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

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

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.

The Ad-MD method to calculate NMR shift including effects due to conformational dynamics: The 31 P NMR shift in DNA

A method for averaging of NMR parameters by molecular dynamics (MD) has been derived from the method of statistical averaging in MD snapshots, benchmarked and applied to structurally dynamic interpretation of the ³¹ P NMR shift (δ_31P ) in DNA phosphates. The method employs adiabatic dependence of an NMR parameter on selected geometric parameter(s) that is weighted by MD-calculated probability distribution(s) for the geometric parameter(s) (Ad-MD method). The usage of Ad-MD for polymers is computationally convenient when one pre-calculated structural dependence of an NMR parameter is employed for all chemically equivalent units differing only in dynamic behavior. The Ad-MD method is benchmarked against the statistical averaging method for δ_31P in the model phosphates featuring distinctively different structures and dynamic behavior. The applicability of Ad-MD is illustrated by calculating ³¹ P NMR spectra in the Dickerson-Drew DNA dodecamer. δ_31P was calculated with the B3LYP/IGLO-III/PCM(water) and the probability distributions for the torsion angles adjacent to the phosphorus atoms in the DNA phosphates were calculated using the OL15 force field.

Defect-Assisted Loading and Docking Conformations of Pharmaceuticals in Metal-Organic Frameworks

Understanding of drug-carrier interactions is essential for the design and application of metal-organic framework (MOF)-based drug-delivery systems, and such drug-carrier interactions can be fundamentally different for MOFs with or without defects. Herein, we reveal that the defects in MOFs play a key role in the loading of many pharmaceuticals with phosphate or phosphonate groups. The host-guest interaction is dominated by the Coulombic attraction between phosphate/phosphonate groups and defect sites, and it strongly enhances the loading capacity. For similar molecules without a phosphate/phosphonate group or for MOFs without defects, the loading capacity is greatly reduced. We employed solid-state NMR spectroscopy and molecular simulations to elucidate the drug-carrier interaction mechanisms. Through a synergistic combination of experimental and theoretical analyses, the docking conformations of pharmaceuticals at the defects were revealed.

Theoretical prediction of 13C NMR spectrum of mixed triglycerides by mean of GIAO calculations to improve vegetable oils analysis

This pioneering study based on GIAO-DFT methods is aimed to the best prediction of ¹³C Nuclear Magnetic Resonances (NMR) arising from triglycerides (and also glycerols), known to be the main component of vegetable oils. Provided that fatty esters bound to the glycerol moiety are not affected by the other esterification chains, and slightly affected by their own esterification position (2- internal, or 1/3- external), eight natural molecules are first optimized despite the challenging presence of many non-hydrogen atoms and the large conformational freedom. This preliminary study sheds light on the total chemical shift prediction concerning five fatty esters (Oleic, Palmitic, Linoleic, Stearic and Linolenic) either present in internal or external positions (ten fragments in total); these results display a very good matching to the experimental profile recorded for several vegetable oils chosen as natural mixtures of glycerides. In order to further improve the theoretical to experimental matching, ten simplified triglycerides with the mentioned fatty esters in the two different esterification positions, and flanked by acetyl esters, were studied and optimized. Beyond the best matching reached so far, we notice that the theoretical rationalisation of the overcrowding in the 28.7-29 ppm spectral region in unable to decode the necessary resolution, nonetheless the same theoretical prediction can still drive the appropriate assignments (as for the fifth and sixth carbon attribution of every chain) even against actual misleading reports.

Recent advances in computational 31 P NMR: Part 1. Chemical shifts

This is the first part of two closely related reviews dealing with the computation of phosphorus-31 nuclear magnetic resonance chemical shifts in a wide series of organophosphorus compounds including complexes, clusters, and bioorganic phosphorus compounds. In particular, the analysis of the accuracy factors, such as substitution effects, solvent effects, vibrational corrections, and relativistic effects, is presented. This review is dedicated to the Full Member of the Russian Academy of Sciences Professor Boris A. Trofimov in view of his invaluable contribution to the field of synthesis, nuclear magnetic resonance, and computation studies of organophosphorus compounds.

A Simple Coulombic Model for 31P NMR Spectra of Cluster-Encapsulated Phosphorus Atoms

While sophisticated computational methods can predict ³¹P NMR spectra of phosphorus atoms encapsulated within Keggin-derived heteropoly tungstate and molybdate cluster anions, calculated and experimental chemical shift values typically deviate considerably from one another. Motivated by the observation that experimentally determined ³¹P chemical shift values within a series of water-soluble plenary and metal-cation substituted lacunary Keggin anions, [PM ⁿW₁₁O₃₉]^{(7- n)-} (M ⁿ = Ag⁺, Zn²⁺, Nb⁵⁺, W⁶⁺) and [(PW₁₁O₃₉)₂M ⁿ]^{(14- n)-} (M ⁿ = Y³⁺, Zr⁴⁺), varied as a linear function of the oxidation states, n, of the complexed M ⁿ cations, a linear correlation was sought between observed chemical shift values and the net Coulombic forces experienced by the encapsulated phosphorus atoms. The Coulombic model based on Shannon radii, published electronegativity values, and bond angles from X-ray crystallographic data remarkably accounted for the relative ³¹P chemical shift values of phosphorus atoms in over 50 metal-oxide cluster anions, including large structures comprised of up to four Keggin-derived fragments with an overall R² value of 0.974. With the model being applied here to three cluster anions whose ³¹P chemical shift values are reported here for the first time, predicted and experimental values differed by only ±0.4 ppm.

Toward the comprehensive calculations on the relationship between 1 H, 13 C, 31 P chemical shifts, 2 JPH , and the bonding structure of different phosphoryl benzamides

A comprehensive investigation was performed on ¹ H, ¹³ C, and ³¹ P nuclear magnetic resonance (NMR) chemical shifts (CSs) of phosphoryl benzamide derivatives (C₆ H₅ C(O)NHP(O)R₁ R₂ ), (R₁ , R₂  = aziridine [L₁ ], azetidine [L₂ ], pyrrolidine [L₃ ], piperidine [L₄ ], azepane [L₅ ], 4-methylpiperidine [L₆ ], propane-2-amine [L₇ ], and 2-methylpropane-2-amine [L₈ ]) by the gauge-independent atomic orbital method (GIAO) to find the most accordant level of theory with the experimental values. To achieve this goal, all the structures were optimized using the B3LYP, BP86, PBE1PBE, M06-2X, MPWB1K, and MP2 methods with 6-31+G* basis set. Computed structural parameters demonstrate that BP86 has the best agreement to the experimental values between the other methods. The def2-TZVP and aug-cc-pVDZ basis sets were also employed to inspect the effect of different types of basis sets with higher polarization and diffuse functions. The correlation between the empirical and computational values attests that 6-31+G* basis set is the optimum case regarding minimization of the costs and results. The comparison between calculated and experimental CSs at all mentioned combinations illustrated that in accordance with structural results, the best level of theory in CSs is also BP86/6-31+G*. Besides, ² J_PH values were computed with an acceptable agreement to experimental data at the optimum level of theory. The dependency between ² J_PH and the bonding structure of studied ligands was also scrutinized by the Natural Bond Orbital (NBO) analysis that interprets the relationship between the electronic properties and ² J_PH values.

Structural interpretation of the 31P NMR chemical shifts in thiophosphate and phosphate: key effects due to spin–orbit and explicit solvent

Structural interpretation of the ³¹P NMR shifts measured in different molecules including thiophosphate or phosphate group was obtained by means of theoretical calculations including the effects of geometry, molecular dynamics, solvent, relativistic effects and the effect of NMR reference.

Relativistic heavy atom effect on the 31 P NMR parameters of phosphine chalcogenides. Part 1. Chemical shifts

Four-component density functional theory calculations of ³¹ P NMR chemical shifts have been performed for the representative series of 56 phosphine chalcogenides in order to investigate an influence of different functional groups on the heavy atom relativistic effect on the NMR chemical shifts of light phosphorous atoms (Heavy Atom on Light Atom effect). The validity of the 4-component density functional theory approach used for the wide-scale calculations of the phosphorous chemical shifts in a wide series of phosphine chalcogenides has been confirmed on a small series of 5 representative compounds with the aid of high-quality coupled cluster singles and doubles calculations taking into account solvent, vibrational, and the relativistic corrections in comparison with the experiment.

Relativistic heavy atom effect on 13 C NMR chemical shifts initiated by adjacent multiple chalcogens

In this paper, we have investigated the cumulative peculiarity of the "heavy atom on light atom" effect on the ¹³ C NMR chemical shifts, initiated by the adjacent chalcogens. For this purpose, the most accurate hybrid computational scheme for the calculation of chemical shifts of carbon nuclei, directly bonded with several heavy chalcogens, is introduced and attested on the representative series of molecules. The best hybrid scheme combines the nonrelativistic coupled cluster-based approach with the different types of corrections, including vibrational, solvent, and relativistic. The dependences of the total relativistic corrections to carbon shielding constants in 2 series of model compounds, namely, X═¹³ C═Y (X, Y = O, S, Se, Te) and C(XH)_m (YH)_n (ZH)_p (QH)_s H_1-m H_1-n H_1-p H_1-s (X, Y, Z, Q = S, Se, Te and m, n, p, s = 0, 1), on the total atomic number of the adjacent chalcogens have been obtained.

Evaluation of the Factors Impacting the Accuracy of 13C NMR Chemical Shift Predictions using Density Functional Theory-The Advantage of Long-Range Corrected Functionals

The various factors influencing the accuracy of ¹³C NMR calculations using density functional theory (DFT), including the basis set, exchange-correlation (XC) functional, and isotropic shielding calculation method, are evaluated. A wide selection of XC functionals (over 70) were considered, and it was found that long-range corrected functionals offer a significant improvement over the other classes of functionals. Based on a thorough study, it is recommended that for calculating NMR chemical shifts (δ) one should use the CSGT method, the COSMO solvation model, and the LC-TPSSTPSS exchange-correlation functional in conjunction with the cc-pVTZ basis set. A selection of problems in natural product identification are considered in light of the newly recommended level of theory.

The benchmark of 31P NMR parameters in phosphate: a case study on structurally constrained and flexible phosphate

A benchmark for structural interpretation of the ³¹P NMR shift and the ²J_P,C spin–spin coupling in the phosphate group was obtained by means of theoretical calculations and measurements in diethylphosphate and 5,5-dimethyl-2-hydroxy-1,3,2-dioxaphosphinane 2-oxide.

Normal halogen dependence of 13 C NMR chemical shifts of halogenomethanes revisited at the four-component relativistic level

The 'Normal Halogen Dependence' of ¹³ C NMR chemical shifts in the series of halogenomethanes is revisited at the four-component relativistic level. Calculations of ¹³ C NMR chemical shifts of 70 halogenomethanes have been carried out at the density functional theory (DFT) and MP2 levels with taking into account relativistic effects using the four-component relativistic theory of Dirac-Coulomb within the different computational methods (4RPA, 4OPW91) and hybrid computational schemes (MP2 + 4RPA, MP2 + 4OPW91). The most efficient computational protocols are derived for practical purposes. Relativistic shielding effect reaches as much as several hundreds of ppm for heavy halogenomethanes, and to account for this effect in comparison with experiment at the qualitative level, relativistic Dyall's basis sets of triple-zeta quality or higher are to be used within the framework of the four-component relativistic theory taking into account solvent effects. Relativistic geometrical optimization (as compared with the non-relativistic level) is essential for the molecules containing at least two iodines at one carbon atom. Copyright © 2016 John Wiley & Sons, Ltd.

Four-component relativistic DFT calculations of (77) Se NMR chemical shifts: A gateway to a reliable computational scheme for the medium-sized organoselenium molecules

A versatile high-accuracy computational scheme for the (77) Se nuclear magnetic resonance (NMR) chemical shifts of the medium-sized organoselenium compounds is suggested within a framework of a full four-component relativistic density functional theory (DFT). The main accuracy factors (DFT functionals, relativistic geometry, vibrational corrections, and solvent effects) are addressed. The best result is achieved with NMR-oriented KT2 functional of Keal-Tozer characterized by a fairly small error of only 30 ppm for the span of about 1700 ppm (<2%).

Quantum chemical calculations of31P NMR chemical shifts: scopes and limitations

High level of theory is not necessarily needed to obtain rather accurate predictions of³¹P chemical shifts by GIAO method. For example, the PBE1PBE/6-311G(2d,2p)//PBE1PBE/6-31+G(d) combination allowed to obtain good results for variety of middle-size organophosphorus compounds (M= 200–700 Da).

Accurate calculation of31P NMR chemical shifts in polyoxometalates

We search for an optimal DFT/basis set combination for computationally reproducing³¹P NMR chemical shifts in polyoxometalates.