Scaling factors for carbon NMR chemical shifts obtained from DFT B3LYP calculations

A linear scaling of the calculated chemical shifts is used in order to improve the accuracy of the DFT predicted ¹³C NMR chemical shifts. The widely applied method of GIAO B3LYP/6-311+G(2d,p) using the B3LYP/6-31G(d) optimized geometries is chosen, which allows cost-effective calculations of the ¹³C chemical shifts in the molecular systems with 100 and more atoms. A set of 27 ¹³C NMR chemical shifts determined experimentally for 22 simple molecules with various functional groups is used in order to determine scaling factors for reproducing experimentally measured values of ¹³C chemical shifts. The results show that the use of a simple relationship (δ_scalc = 0.95 δ_calc + 0.30, where δ_calc and δ_scalc are the calculated and the linearly scaled values of the ¹³C chemical shifts, respectively) allows to achieve a three-fold improvement in mean absolute deviations for 27 chemical shifts considered. To test the universal applicability of the scaling factors derived, we have used complex organic molecules such as taxol and a steroid to demonstrate the significantly improved accuracy of the DFT predicted chemical shifts. This approach also outperforms the recently recommended usage of the Hartree-Fock optimized geometries for the GIAO B3LYP/6-311+G(2d,p) calculations of the ¹³C chemical shifts.     

Theoretical investigation on multinuclear NMR chemical shifts of some tris(trifluoromethyl)boron complexes

Tris(trifluoromethyl)boron complexes have unusual properties and may find applications in many fields of chemistry, biology, and physics. To gain insight into their NMR properties, the isotropic ¹¹B, ¹³C, and ¹⁹F NMR chemical shifts of a series of tris(trifluoromethyl)boron complexes were systematically studied using the gauge‐included atomic orbitals (GIAO) method at the levels of B3LYP/6‐31 + G(d,p)//B3LYP/6‐31G* and B3LYP/6‐311 + G(d,p)//B3LYP/6‐311 + G(d,p). Solvent effects were taken into account by polarizable continuum models (PCM). The calculated results were compared with the experimental values. The reason that the structurally inequivalent fluorine atoms in a specific species give a same chemical shift in experimental measurements is attributed to the fast rotation of CF₃ group around the B? C(F₃) bond because of the low energy barrier. The calculated ¹¹B, ¹³C(F₃), and ¹⁹F chemical shifts are in good agreement with the experimental measurements, while the deviations of calculated ¹³C(X, X = O, N) chemical shifts are slightly large. For the latter, the average absolute deviations of the results from B3LYP/6‐311 + G(d,p)//B3LYP/6‐311 + G(d,p) are smaller than those from B3LYP/6‐31 + G(d,p)//B3LYP/6‐31G*, and the inclusion of PCM reduces the deviation values. The calculated ¹⁹F and ¹¹B chemical shieldings of (CF₃)₃BCO are greatly dependent on the optimized structures, while the influence of structural parameters on the calculated ¹³C chemical shieldings is minor. Copyright © 2009 John Wiley & Sons, Ltd.     

A theoretical study of inversion barriers and NMR chemical shifts of 3-pyrazolines (2,3-dihydro-1H-pyrazoles)

A rather neglected family of heterocyclic compounds, the 3-pyrazolines or 2,3-dihydro-1H-pyrazoles, has been studied theoretically at the B3LYP/6–311++G(d,p) level to obtain geometries and energies and at the GIAO/B3LYP/6–311++G(d,p) level for NMR chemical shifts. The calculated barriers of inversion of the N-substituents reproduce adequately the scarce experimental data. The calculated ¹H and ¹³C chemical shifts are consistent with those reported in the literature. A combination of both results, geometries, and ¹³C chemical shifts, shed light on the conformation of N-phenyl groups.     

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

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

Density functional theory study of 13C NMR chemical shift of chlorinated compounds

The use of the standard density functional theory (DFT) leads to an overestimation of the paramagnetic contribution and underestimation of the shielding constants, especially for chlorinated carbon nuclei. For that reason, the predictions of chlorinated compounds often yield too high chemical shift values. In this study, the WC04 functional is shown to be capable of reducing the overestimation of the chemical shift of Cl‐bonded carbons in standard DFT functionals and to show a good performance in the prediction of ¹³C NMR chemical shifts of chlorinated organic compounds. The capability is attributed to the minimization of the contributions that intensively increase the chemical shift in the WC04. Extensive computations and analyses were performed to search for the optimal procedure for WC04. The B3LYP and mPW1PW91 standard functionals were also used to evaluate the performance. Through detailed comparisons between the basis set effects and the solvent effects on the results, the gas‐phase GIAO/WC04/6‐311+G(2d,p)//B3LYP/6‐31+G(d,p) was found to be specifically suitable for the prediction of ¹³C NMR chemical shifts of chlorides in both chlorinated and non‐chlorinated carbons. Further tests with eight molecules in the probe set sufficiently confirmed that WC04 was undoubtedly effective for accurately predicting ¹³C NMR chemical shifts of chlorinated organic compounds. Copyright © 2012 John Wiley & Sons, Ltd.     

13C and 15N NMR spectra of high‐energy polyazidocyanopyridines

¹³C and ¹⁵N NMR spectra of high‐energy 2,4,6‐triazidopyridine‐3,5‐dicarbonitrile, 2,3,5,6‐tetraazidopyridine‐4‐carbonitrile and 3,4,5,6‐tetraazidopyridine‐2‐carbonitrile are reported. The assignment of signals in the spectra was performed on the basis of density functional theory calculations. The molecular geometries were optimized using the M06‐2X functional with the 6‐311+G(d,p) basis set. The magnetic shielding tensors were calculated by the gauge‐independent atomic orbital method with the Tao–Perdew–Staroverov–Scuseria hybrid functional known as TPSSh. In all the calculations, a polarizable continuum model was used to simulate solvent effects. This approach provided accurate predictions of the ¹³C and ¹⁵N chemical shifts for all the three compounds despite complications arising due to non‐coplanar arrangement of the azido groups in the molecules. It was found that the ¹⁵N chemical shifts of the N_α atoms in the azido groups of 2,4,6‐triazidopyridines correlate with the ¹³C chemical shifts of the carbon atoms attached to these azido groups. Copyright © 2016 John Wiley & Sons, Ltd.     

Quantum‐chemical analyses of aromaticity,UV spectra,and NMR chemical shifts in plumbacyclopentadienylidenes stabilized by Lewis bases

We carried out a series of zeroth‐order regular approximation (ZORA)‐density functional theory (DFT) and ZORA‐time‐dependent (TD)‐DFT calculations for molecular geometries, NMR chemical shifts, nucleus‐independent chemical shifts (NICS), and electronic transition energies of plumbacyclopentadienylidenes stabilized by several Lewis bases, (Ph)₂(^tBuMe₂Si)₂C₄PbL₁L₂ (L₁, L₂ = tetrahydrofuran, Pyridine, N‐heterocyclic carbene), and their model molecules. We mainly discussed the Lewis‐base effect on the aromaticity of these complexes. The NICS was used to examine the aromaticity. The NICS values showed that the aromaticity of these complexes increases when the donation from the Lewis bases to Pb becomes large. This trend seems to be reasonable when the 4n‐Huckel rule is applied to the fractional π‐electron number. The calculated ¹³C‐ and ²⁰⁷Pb‐NMR chemical shifts and the calculated UV transition energies reasonably reproduced the experimental trends. We found a specific relationship between the ¹³C‐NMR chemical shifts and the transition energies. As we expected, the relativistic effect was essential to reproduce a trend not only in the ²⁰⁷Pb‐NMR chemical shifts and J[Pb‐C] but also in the ¹³C‐NMR chemical shifts of carbons adjacent to the lead atom. © 2014 Wiley Periodicals, Inc.     

Ab initio molecular modeling of 13C NMR chemical shifts of polymers. 1. Ethylene–norbornene copolymers

Cycloolefin copolymers (COC) have recently raised much interest because of their excellent thermal and optical properties, largely determined by the chain composition and stereochemistry. Previous force‐field computations allowed us to define the main conformational characteristics of ethylene–norbornene (E–N) copolymers and to contribute to the elucidation of their microstructure on the basis of empirical relationships between conformation and ¹³C nuclear magnetic resonance (NMR) chemical shifts. A thorough test of ab initio ¹³C chemical shifts computations [gauge‐invariant atomic orbitals (GIAO)] on known cases shows that the agreement with experimental data is quite good, especially with the MPW1PW91 density functional theory (DFT), using the 6‐311+G(2d,p) basis set on properly energy‐minimized structures. We applied this method on proper model compounds to confirm the signal assignment of the spectra of E–N copolymers in the presence of norbornene microblocks, where strong effects arising from ring distortions are expected to occur. The results nicely confirm the latest assignment of norbornene signals belonging to ENNE sequences. This shows the great potentialities of GIAO/DFT computations with regard to complex spectra interpretation and polymer microstructural investigations. © 2002 Wiley Periodicals, Inc. Int J Quantum Chem, 2002     

Theoretical investigation on 1H and 13C NMR chemical shifts of small alkanes and chloroalkanes

Using density functional theory (DFT) with the B3LYP, PBE, and PBE0 exchange-correlation functionals as well as the Moller-Plesset second-order perturbation theory (MP2) combined with a series of rather extended basis sets, 1H and 13C chemical shifts of small alkanes and chloroalkanes (with different numbers of chlorine atoms on specific positions) have been simulated and compared to experimental data. For the 1H chemical shifts, theory tends to reproduce experiment within the limits of the experimental errors. In the case of 13C chemical shift, the differences between theory and experiment increase monotonically with the number of chlorine atoms and exhibit a deviation from additivity. This behavior is related to the saturation of the experimental 13C chemical shifts with the number of chlorine atoms, whereas the evolution is mostly linear at both DFT and MP2 levels of approximation. This difference has been traced back to the relativistic spin-orbit coupling effects, which are exalted as a result of the enhancement of the s character of the C atom when increasing the number of linked Cl atoms. Thus, it was demonstrated that not only electron correlation but also relativistic effects have to be considered for estimating the 13C chemical shifts when several Cl atoms are directly attached to the C atom. Linear (theory/experiment) regressions have then been performed for the different types of C atoms, i.e., bearing one, two, and three Cl atoms, with excellent correlation coefficients. The linear correlation relationships so obtained can then serve to predict and facilitate the interpretation of the nuclear magnetic resonance spectra of more complex compounds. Furthermore, by investigating the basis set effects, the correlation between the chemical shifts calculated using the 6-311 + G(2d,p) basis set and the more extended 6-311 + G(2df,p) and aug-cc-pvtz basis sets is excellent, demonstrating that the choice of the 6-311 + G(2d,p) basis set for calculating the 1H and 13C chemical shifts is relevant.     

The increment scheme for the prediction of13C NMR chemical shifts in polychlorinated dibenzo-p-dioxins

A topological method for the calculation of¹³C NMR chemical shifts was developed for polychlorinated dibenzo-p-dioxins (PCDD). Based on previous results for polychlorinated benzenes and polyhydroxybenzenes, the collective influence of the substituents on carbon chemical shifts is presented as the sum of two-particle increments. The increments only of two new monosubstituted graphs have to be added to those known for PCDD spectra: 1-Cl-DD and 2-Cl-DD. All structural situations in the¹³C NMR chemical shifts of the whole class of 75 PCDD can be covered with a few model compounds. The coefficients of the increment scheme are independent of the change of CDCl₃ for acetone-d₆, so it may be a new reliable criterion for recognizing PCDD by¹³C NMR, in spite of the close resemblance of NMR spectra of aromatic compounds.Translated fromIzvestiya Akademii Nauk. Seriya Khimicheskaya, No. 2, pp. 280–284, February, 1995.     

DFT-GIAO calculations of 19F NMR chemical shifts for perfluoro compounds

The (19)F NMR shieldings for 53 kinds of perfluoro compounds were calculated by the B3LYP-GIAO method using the 6-31G(d), 6-31+G(d), 6-31G(d,p), 6-31++G(d,p), 6-311G(d,p), 6-311++G(d,p), 6-311G(2d,2p), 6-311++G(2d,2p), 6-311++G(2df,2p), 6-311++G(3d,2p), and 6-311++G(3df,2p) basis sets. The diffuse functions markedly reduce the difference between the calculated and experimental chemical shifts. The calculations using the 6-31++G(d,p) basis set give the chemical shifts within 10 ppm deviations from experimental values except for the fluorine nuclei attached to an oxygen atom, a four- and a six-coordinated sulfur atom, and FC(CF(3))(2) attached to a sulfur atom.     

13C and 15N NMR spectra of aminobenzimidazoles in solution and in the solid state

The ¹³C [hexadeutero‐dimethylsulfoxide (DMSO‐d₆), hexamethyl‐phosphoramide (HMPA)‐d₁₈and solid‐state] and ¹⁵N (solid‐state) NMR spectra of six C‐aminobenzimidazoles have been recorded. The tautomerism of 4(7)‐aminobenzimidazoles and 5(6)‐aminobenzimidazoles has been determined and compared with B3LYP/6‐311 + + G(d,p) calculations confirming the clear predominance of the 4‐amino tautomer and the slight preference for the 6‐amino tautomer. GIAO‐calculated absolute shieldings compare well with experimental chemical shifts. Copyright © 2008 John Wiley & Sons, Ltd.     

Effects of different GIAO and CSGT models and basis sets on 2-aryl-1,3,4-oxadiazole derivatives

The direct molecular structure implementations of the gage-including atomic orbital (GIAO), individual gages for atoms in molecules (IGAIM) and continuous set of gage transformations (CSGT) methods for calculating nuclear magnetic shielding tensors at both the Hartree-Fock (HF) and density functional (B3LYP) levels of theory with 6-31G(d), 6-311G(d), 6-31++G(d,p), 6-311++G(d,p), and 6-311++G(df,pd) basis sets are presented. Dependence on the ¹H and ¹³C NMR chemical shifts on the choice of method and basis set have been investigated. Also, these chemical shifts of 2-aryl-1,3,4-oxadiazoles 5a–g have been performed related to dihedral angles (C4–C3–C2–O) of two conformers. The optimized molecular geometries and ¹H and ¹³C chemical shift values of 2-aryl-1,3,4-oxadiazoles 5a–g in the ground state have been obtained. The linear correlation coefficients of ¹³C NMR chemical shifts for these molecules were given. The new nuclear magnetic shielding tensors of tetramethylsilane (TMS) were calculated. The data of 2-aryl-1,3,4-oxadiazole derivatives display significant molecular structure and NMR analysis. Also, these provide the basis for future design of efficient materials having the 1,3,4-oxadiazole core.     

Regression formulas for density functional theory calculated 1H and 13C NMR chemical shifts in toluene-d8

This study aimed at investigating the performance of a series of basis sets, density functional theory (DFT) functionals, and the IEF-PCM solvation model in the accurate calculation of (1)H and (13)C NMR chemical shifts in toluene-d(8). We demonstrated that, on a test set of 37 organic species with various functional moieties, linear scaling significantly improved the calculated shifts and was necessary to obtain more accurate results. Inclusion of a solvation model produced larger deviations from the experimental data as compared to the gas-phase calculations. Moreover, we did not find any evidence that very large basis sets were necessary to reproduce the experimental NMR data. Ultimately, we recommend the use of the BMK functional. For the (1)H shifts the use of the 6-311G(d) basis set gave linearly scaled mean unsigned (MU) and root-mean-square (rms) errors of 0.15 ppm and 0.21 ppm, respectively. For the calculation of the (13)C chemical shifts the 6-31G(d) basis set produced MUE of 1.82 ppm and RMSE of 3.29 ppm.     

Evaluation of <Superscript>13</Superscript>C NMR spectra of cyclopropenyl and cyclopropyl acetylenes by theoretical calculations

A convenient methodology was developed for a very accurate calculation of ¹³C NMR chemical shifts of the title compounds. GIAO calculations with density functional methods (B3LYP, B3PW91, PBE1PBE) and 6-311+G(2d,p) basis set predict experimental chemical shifts of 3-ethynylcyclopropene (1), 1-ethynylcyclopropane (2) and 1,1-diethynylcyclopropane (3) with high accuracy of 1–2 ppm. The present article describes in detail the effect of geometry choice, density functional method, basis set and effect of solvent on the accuracy of GIAO calculations of ¹³C NMR chemical shifts. In addition, the particular dependencies of ¹³C chemical shifts on the geometry of cyclopropane ring were investigated.     

Calculations and assignments of endohedral helium-3 chemical shifts of open-cage fullerenes and higher fullerenes

The endohedral ³He NMR chemical shifts of open-cage fullerene compounds and higher fullerenes ³He@C _n (n = 82, 84, 86) have been calculated at the GIAO-B3LYP/3-21G//AM1 level. The predicted ³He NMR chemical shifts of open-cage fullerene compounds agree well with the experimental data. More importantly, the challenging peak assignments in the two ³He NMR spectra of higher fullerenes have been successfully achieved by our computed endohedral ³He chemical shifts in combination with experimental results.     

29Si and 13C NMR spectra of permethylpolysilanes

²⁹Si, ¹³C and ¹H NMR spectra are reported for the series of linear permethylpolysilanes Me(SiMe₂)_nMe where n = 1 to 6, for the cyclic permethylpolysilanes (Me₂Si)_n where n = 5 to 8, and for a few related compounds. For linear polysilanes the ²⁹Si and ¹³C chemical shifts can be accurately calculated from simple additivity relationships based on the number of silicon atoms in α, β, γ and δ positions. Adjacent (α) silicon atoms lead to upfield shifts in the ²⁹Si and ¹³C resonances, whereas more remote silicon atoms lead to downfield shifts. The ²⁹Si chemical shifts of the polysilane chains are linearly related to the ¹³C shifts of the carbon atoms attached to the silicon. The ²⁹Si and ¹³C resonances of the cyclic silanes deviate from this relationship. Ring current effects arising from σ delocalization are suggested as an explanation for the deviations. Proton-coupled ²⁹Si NMR spectra are reported for Me₃SiSiMe₃ and for (Me₂Si)_n, n = 5 to 7.     

Quantum-chemical calculations of NMR chemical shifts of organic molecules: XIV. Solvation effects in calculations of chemical shifts in 13C NMR spectra of chlorine-containing compounds

Analysis of precision factors in calculations of ¹³C NMR chemical shifts in the series of saturated and unsaturated organochlorine compounds was performed in the framework of the method of electron density functional theory GIAO-DFT-KT3/pcS-2 in the gas phase and with accounting for solvent effect by the polarized continuum model IEF-PCM. The accounting for solvation effects in calculations of ¹³C NMR chemical shifts within the framework of the IEF-PCM model is not fundamental for organochlorine compounds, yet it considerably improves the precision of calculations up to 2.5 ppm.     

Synthesis of new cyano-substituted analogues of Tröger's bases from bromo-derivatives. A stereochemical dependence of long-range (nJHH,n = 4, 5, and 6) proton–proton and proton–carbon (nJCH,n = 1, 2, 3, 4, and 5) coupling constants of these compounds

A free-catalyst microwave-assisted cyanation of brominated Tröger's base derivatives ( 2a - f ) is reported. The procedure is simple, efficient, and clean affording the nitrile compounds ( 3a - e, I ) in very good yields. Complete assignment of ¹H and ¹³C chemical shifts of 2a - f, I and 3a - d, I was achieved using gradient selected 1D nuclear magnetic resonance (NMR) techniques (1D zTOCSY, PSYCHE, DPFGSE NOE, and DEPT), homonuclear 2D NMR techniques (gCOSY and zTOCSY), and heteronuclear 2D NMR techniques (gHSQCAD/or pure-shift gHSQCAD, gHMBCAD, bsHSQCNOESY, and gHSQCAD-TOCSY) with adiabatic pulses. Determination of the long-range proton–proton coupling constants ⁿJ_HH (n = 4, 5, 6) was accomplished by simultaneous irradiation of two protons at appropriate power levels. In turn, determined coupling constants were tested by an iterative simulation program by calculating the ¹H NMR spectrum and comparing it to the experimental spectrum. The excitation-sculptured indirect-detection experiment (EXSIDE) and ¹H-¹⁵N CIGARAD-HMBC (constant time inverse-detection gradient accordion rescaled heteronuclear multiple bond correlation) were applied for determination of long-range carbon–proton coupling constants ⁿJ_CH (n = 2, 3, and 4) and for assignment of ¹⁵N chemical shift at natural abundance, respectively. DFT/B3LYP optimization studies were performed in order to determine the geometry of 2c using 6-31G(d,p), 6-311G(d,p), and 6–311 + G(d,p) basis sets. For calculation of ¹H and ¹³C chemical shifts, ⁿJ_HH (n = 2, 3, 4, 5, and 6), and ⁿJ_CH (n = 1, 2, 3, and 4) coupling constants, the GIAO method was employed at the B3LYP/6-31G(d,p), B3LYP/6-31+G(d,p), B3LYP/6-311+G(d,p), B3LYP/6-311++G(2d,2p), B3LYP/cc-pVTZ), and B3LYP/aug-cc-pVTZ) levels of theory. For the first time, a stereochemical dependence magnitude of the long-range ⁿJ_HH (n = 4, 5, and 6) and ⁿJ_CH (n = 1, 2, 3, 4, and 5) have been found in bromo-substituted analogues of Tröger's bases.     

Investigation of 1H NMR chemical shifts of organic dye with hydrogen bonds and ring currents

The (1)H NMR chemical shifts were theoretically computed for the organic dyes 2-(2,6-dimethyl-4H-pyran-4-ylidene)-malononitrile (1), cyano-(2,6-dimethyl-4H-pyran-4-ylidene)-acetic acid methyl ester (2), 2-(2,6-bis(4-(dimethylamino)styryl)-4H-pyran-4-ylidene)-malononitrile (3), and methyl 2-(2,6-bis(4-(dimethylamino)styryl)-4H-pyran-4-ylidene)-2-cyanoacetate (4) at the GIAO/B3LYP/6-311++G(d,p)//B3LYP/6-311++G(d,p) level of theory. Moreover, the intramolecular rotational barriers of the molecules were calculated to evaluate the internal flexibility with respect to the torsional degrees of freedom, and the nuclear-independent chemical shifts (NICS) were employed to analyze the ring currents. The difference was explained in terms of intramolecular hydrogen bonds and ring currents of the molecules. The (1)H NMR spectra were reproduced by experiments for the comparison with computationally constructed data. Our results suggest a good guideline in interpreting (1)H NMR chemical shifts using computational methods and furthermore a reliable perspective for designing molecular structures.