Accurate prediction of proton chemical shifts. II. Peptide analogues

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

NMR shielding constants for hydrogen guest molecules in structure II clathrates

Proton NMR shielding constants and chemical shifts for hydrogen guests in small and large cages of structure II clathrates are calculated using density-functional theory and the gauge-invariant atomic-orbital method. Shielding constants are calculated at the B3LYP level with the 6-311++G(d,p) basis set. The calculated chemical shifts are corrected with a linear regression to reproduce the experimental chemical shifts of a set of standard molecules. The calculated chemical shifts of single hydrogen molecules in the small and large structure II cages are 4.94 and 4.84 ppm, respectively, which show that within the error range of the method the H2 guest molecules in the small and large cages cannot be distinguished. Chemical shifts are also calculated for double occupancy of the hydrogen guests in small cages, and double, triple, and quadruple occupancy in large cages. Multiple occupancy changes the chemical shift of the hydrogen guests by approximately 0.2 ppm. The relative effects of other guest molecules and the cage on the chemical shift are studied for the cages with multiple occupancies.     

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.     

Highly efficient implementation of pseudospectral time‐dependent density‐functional theory for the calculation of excitation energies of large molecules

We have developed and implemented pseudospectral time‐dependent density‐functional theory (TDDFT) in the quantum mechanics package Jaguar to calculate restricted singlet and restricted triplet, as well as unrestricted excitation energies with either full linear response (FLR) or the Tamm–Dancoff approximation (TDA) with the pseudospectral length scales, pseudospectral atomic corrections, and pseudospectral multigrid strategy included in the implementations to improve the chemical accuracy and to speed the pseudospectral calculations. The calculations based on pseudospectral time‐dependent density‐functional theory with full linear response (PS‐FLR‐TDDFT) and within the Tamm–Dancoff approximation (PS‐TDA‐TDDFT) for G2 set molecules using B3LYP/6‐31G*^* show mean and maximum absolute deviations of 0.0015 eV and 0.0081 eV, 0.0007 eV and 0.0064 eV, 0.0004 eV and 0.0022 eV for restricted singlet excitation energies, restricted triplet excitation energies, and unrestricted excitation energies, respectively; compared with the results calculated from the conventional spectral method. The application of PS‐FLR‐TDDFT to OLED molecules and organic dyes, as well as the comparisons for results calculated from PS‐FLR‐TDDFT and best estimations demonstrate that the accuracy of both PS‐FLR‐TDDFT and PS‐TDA‐TDDFT. Calculations for a set of medium‐sized molecules, including C_n fullerenes and nanotubes, using the B3LYP functional and 6‐31G^** basis set show PS‐TDA‐TDDFT provides 19‐ to 34‐fold speedups for C_n fullerenes with 450–1470 basis functions, 11‐ to 32‐fold speedups for nanotubes with 660–3180 basis functions, and 9‐ to 16‐fold speedups for organic molecules with 540–1340 basis functions compared to fully analytic calculations without sacrificing chemical accuracy. The calculations on a set of larger molecules, including the antibiotic drug Ramoplanin, the 46‐residue crambin protein, fullerenes up to C₅₄₀ and nanotubes up to 14×(6,6), using the B3LYP functional and 6‐31G^** basis set with up to 8100 basis functions show that PS‐FLR‐TDDFT CPU time scales as N^2.05 with the number of basis functions. © 2016 Wiley Periodicals, Inc.     

Quantum vs. classical models of the nitro group for proton chemical shift calculations and conformational analysis

A model based on classical concepts is derived to describe the effect of the nitro group on proton chemical shifts. The calculated chemical shifts are then compared to ab initio (GIAO) calculated chemical shifts. The accuracy of the two models is assessed using proton chemical shifts of a set of rigid organic nitro compounds that are fully assigned in CDCl3 at 700 MHz. The two methods are then used to evaluate the accuracy of different popular post-SCF methods (B3LYP and MP2) and molecular mechanics methods (MMX and MMFF94) in calculating the molecular structure of a set of sterically crowded nitro aromatic compounds. Both models perform well on the rigid molecules used as a test set, although when using the GIAO method a general overestimation of the deshielding of protons near the nitro group is observed. The analysis of the sterically crowded molecules shows that the very popular B3LYP/6-31G(d,p) method produces very poor twist angles for these, and that using a larger basis set [6-311++G(2d,p)] gives much more reasonable results. The MP2 calculations, on the other hand, overestimate the twist angles, which for these compounds compensates for the deshielding effect generally observed for protons near electronegative atoms when using the GIAO method at the B3LYP/6-311++G(2d,p) level. The most accurate results are found when the structures are calculated using B3LYP/6-311++G(2d,p) level of theory, and the chemical shifts are calculated using the CHARGE program based on classical models.     

Geometric dependence of the B3LYP-predicted magnetic shieldings and chemical shifts

We perform a systematic investigation of how the B3LYP/6-311+G(2d,p) calculated 13C nuclear magnetic shielding constants depend on the 6-31G(d)-optimized geometries for a set of 18 molecules with various chemical environments. For absolute shieldings, the Hartree-Fock (HF)-optimized geometries lead to a mean absolute deviation (MAD) of 5.65 ppm, while the BLYP- and B3LYP-optimized geometries give MADs of 13.07 and 10.14 ppm, respectively. For chemical shifts, the HF, BLYP and B3LYP geometries lead to MADs of 2.36, 5.80, and 4.43 ppm, respectively. We find that the deshielding tendency of B3LYP can be effectively compensated by using the HF-optimized geometries. When we apply the B3LYP//HF protocol to versicolorin A and 5alpha-androstan-3,17-dione, MADs of 1.86 and 1.41 ppm, respectively, are obtained for chemical shifts, in satisfactory agreement with the experiment.     

On the accuracy factors and computational cost of the GIAO–DFT calculation of 15N NMR chemical shifts of amides

The main factors affecting the accuracy and computational cost of Gauge‐independent Atomic Orbital–density functional theory (GIAO–DFT) calculation of ¹⁵N NMR chemical shifts in the benchmark series of 16 amides are considered. Among those are the choice of the DFT functional and basis set, solvent effects, internal reference conversion factor and applicability of the locally dense basis set (LDBS) scheme. Solvent effects are treated within the polarizable continuum model (PCM) scheme as well as at supermolecular level with solvent molecules considered in explicit way. The best result is found for Keal and Tozer's KT3 functional used in combination with Jensen's pcS‐3 basis set with taking into account solvent effects within the polarizable continuum model. The proposed LDBS scheme implies pcS‐3 on nitrogen and pc‐2 elsewhere in the molecule. The resulting mean average error for the calculated ¹⁵N NMR chemical shifts is about 6 ppm. The application of the LDBS approach tested in a series of 16 amides results in a dramatic decrease in computational cost (more than an order of magnitude in time scale) with insignificant loss of accuracy.     

Ring current effects in crystals. Evidence from 13C chemical shift tensors for intermolecular shielding in 4,7-di-t-butylacenaphthene versus 4,7-di-t-butylacenaphthylene

13C chemical shift tensor data from 2D FIREMAT spectra are reported for 4,7-di-t-butylacenaphthene and 4,7-di-t-butylacenaphthylene. In addition, calculations of the chemical shielding tensors were completed at the B3LYP/6-311G** level of theory. While the experimental tensor data on 4,7-di-t-butylacenaphthylene are in agreement with theory and with previous data on polycyclic aromatic hydrocarbons, the experimental and theoretical data on 4,7-di-t-butylacenaphthene lack agreement. Instead, larger than usual differences are observed between the experimental chemical shift components and the chemical shielding tensor components calculated on a single molecule of 4,7-di-t-butylacenaphthene, with a root mean square (rms) error of +/-7.0 ppm. The greatest deviation is concentrated in the component perpendicular to the aromatic plane, with the largest value being a 23 ppm difference between experiment and theory for the 13CH2 carbon delta11 component. These differences are attributed to an intermolecular chemical shift that arises from the graphitelike, stacked arrangement of molecules found in the crystal structure of 4,7-di-t-butylacenaphthene. This conclusion is supported by a calculation on a trimer of molecules, which improves the agreement between experiment and theory for this component by 14 ppm and reduces the overall rms error between experiment and theory to 4.0 ppm. This intermolecular effect may be modeled with the use of nuclei independent chemical shieldings (NICS) calculations and is also observed in the isotropic 1H chemical shift of the CH2 protons as a 4.2 ppm difference between the solution value and the solid-state chemical shift measured via a 13C-1H heteronuclear correlation experiment.     

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.     

Stereochemical analysis of the 3α‐ and 3β‐hydroxy metabolites of tibolone through NMR and quantum‐chemical investigations. An experimental test of GIAO calculations

The configuration at C‐3 of the 3α‐ and 3β‐hydroxy metabolites of tibolone was studied by extensive application of one‐ and two‐dimensional ¹H and ¹³C NMR spectroscopy combined with molecular modeling performed at the B3LYP/6–31G(d) level. Using HF and DFT GIAO methods, shielding tensors of the two molecules were computed; comparison of the calculated NMR chemical shifts with the experimental values revealed that the density functional methods produced the best results for assigning proton and carbon resonances. Although steroids are relatively large molecules, the present approach appears accurate enough to allow the determination of relative configurations by using calculated ¹³C resonances; the chemical shift of pairs of geminal α/β hydrogen atoms can also be established by using calculated ¹H resonances. Copyright © 2002 John Wiley & Sons, Ltd.     

Additive chemical shift parameters for methylene protons. Shoolery's constants reinvestigated

Methylene proton chemical shifts have been studied using multiple linear regression analysis, and additive chemical shift parameters have been determined. Using a data set of 1007 chemical shifts, involving 48 different substituents, a standard error of estimate of 0.15 ppm was found for protons spread between 2.0 and 5.9 ppm. Provision was made in the data matrix for substituent effects for directly attached groups (α) and for groups attached via one intervening saturated carbon (β-substituents). The influence of groups more remotely located was assumed to be negligible. Although the parameters were optimized for deshielded methylene proton shifts, they also serve satisfactorily for the estimation of shifts in more shielded methylene cases.     

The nuclear magnetic resonance of heterocyclic compounds related to anthracene

The NMR spectra of a series of heterocyclic compounds analogous to anthracene have been investigated at 220 and 60 MHz. Correlations have been made with molecular geometry and parameters calculated from semi-empirical MO theory. For planar molecules, the chemical shift of the proton ortho to the heteroatom is linear with respect to the electron density on the heteroatom, but otherwise chemical shifts are independent of electron density. Planarity of the molecules is also a factor in some of the coupling constants.     

Accurate predictions of crystal densities using quantum mechanical molecular volumes

A quantum mechanically based procedure for estimation of crystal densities of neutral and ionic crystals is presented. In this method, volumes within 0.001 electrons/bohr3 isosurfaces of electron density for the constituent isolated neutral and ionic molecules are calculated to define the molecular volume or formula unit volumes used in predicting the crystal density. The B3LYP density functional theory in conjunction with the 6-31G** basis set were employed to generate the electron densities. The suitability of this method of crystal density prediction was assessed by subjecting a large number (289) of molecular and ionic crystals to the procedure and comparing results with experimental information. The results indicate that, for neutral molecular crystals, the root-mean-square (rms) deviation from experiment is within 4%, whereas the rms deviation is somewhat larger for the 71 ionic crystals evaluated (within 5%).     

DFT calculation of structures and NMR chemical shifts of simple models of small diameter zigzag single wall carbon nanotubes (SWCNTs)

Linearly conjugated benzene rings (acenes), belt‐shape molecules (cyclic acenes) and model single wall carbon nanotubes (SWCNTs) were fully optimized at the unrestricted level of density functional theory (UB3LYP/6‐31G*). The models of SWCNTs were selected to get some insight into the potential changes of NMR chemical shift upon systematic increase of the molecular size. The theoretical NMR chemical shifts were calculated at the B3LYP/pcS‐2 level of theory using benzene as reference. In addition, the change of radial breathing mode (RBM), empirically correlated with SWCNT diameter, was directly related with the radius of cyclic acenes. Both geometrical and NMR parameters were extrapolated to infinity upon increase in the studied systems size using a simple two‐parameter mathematical formula. Very good agreement between calculated and available experimental CC bond lengths of acenes was observed (RMS of 0.0173 Å). The saturation of changes in CC bond lengths and ¹H and ¹³C NMR parameters for linear and cyclic acenes, starting from 7–8 conjugated benzene rings, was observed. The ¹³C NMR parameters of individual carbon atoms from the middle of ultra‐thin (4,0) SWCNT formed from 10 conjugated cyclic acenes differ by about 130 ppm from the corresponding open end carbon nuclei. Copyright © 2011 John Wiley & Sons, Ltd.     

A joined theoretical-experimental investigation on the 1H and 13C NMR signatures of defects in poly(vinyl chloride)

1H and 13C chemical shifts of PVC chains have been evaluated using quantum chemistry methods in order to evidence and interpret the NMR signatures of chains bearing unsaturated and branched defects. The geometrical structures of the stable conformers have been determined using molecular mechanics and the OPLS force field and then density functional theory with the B3LYP functional and the 6-311G(d) basis set. The nuclear shielding tensor has been calculated at the coupled-perturbed Kohn-Sham level (B3LYP exchange-correlation functional) using the 6-311+G(2d,p) basis set. The computational scheme accounts for the large number of stable conformers of the PVC chains, and average chemical shifts are evaluated using the Maxwell-Boltzmann distribution. Moreover, the chemical shifts are corrected for the inherent and rather systematic errors of the method of calculation by employing linear regression equations, which have been deduced from comparing experimental and theoretical results on small alkane model compounds containing Cl atoms and/or unsaturations. For each type of defect, PVC segments presenting different tacticities have been considered because it is known from linear PVC chains that the racemic (meso) dyads are characterized by larger (smaller) chemical shifts. NMR signatures of unsaturations in PVC chains have been highlighted for the internal -CH=CH- and -CH=CCl- units as well as for terminal unsaturations like the chloroallylic -CH=CH-CH2Cl group. In particular, the 13C chemical shifts of the two sp2 C atoms are very close for the chloroallylic end group. The CH2 and CHCl units surrounding an unsaturation present also specific 13C chemical shifts, which allow distinguishing them from the others. In the case of the proton, the CH2 unit of the -CHCl-CH2-CCl=CH- segment presents a larger chemical shift (2.6-2.7 ppm), while some CHCl units close to the -CH=CH- unsaturations appear at rather small chemical shifts (3.7 ppm). The -CH2Cl and -CHCl-CH2Cl branches also display specific signatures, which result in large part from modifications of the equilibrium conformations and their reduced number owing to the increased steric interactions. These branches lead to the appearance of 13C peaks at lower field associated either to the CH unit linking the -CH2Cl and -CHCl-CH2Cl branches (50 ppm) or to the CHCl unit of the ethyl branches (60 ppm). The corresponding protons resonate also at specific frequencies: 3.5-4.0 ppm for the -CH2Cl branch or 3.8-4.2 ppm for the terminal unit of the -CHCl-CH2Cl branch. Several of these signatures have been detected in the experimental 1H and 13C NMR spectra and are consistent with the reaction mechanisms.     

Ab initio study of 2,4-substituted azolidines. II. Amino-imino tautomerism of 2-aminothiazolidine-4-one and 4-aminothiazolidine-2-one in water solution

The relative stabilities of the tautomers of 2-aminothiazolidine-4-one and 4-aminothiazolidine-2-one were calculated at the MP2/6-31+G(d,p) level by considering their mono- and trihydrated complexes. Single-point calculations at the MP4/6-31+G(d,p)//MP2/6-31+G(d,p) level of theory were performed to obtain more accurate energies. The values of proton transfer barriers in the isolated, mono- and trihydrated tautomers of 2-aminothiazolidine-4-one (2AT) and 4-aminothiazolidine-2-one (4AT) were calculated for two different mechanisms of tautomerisation. In the absence of water, the process of proton transfer should not occur. Addition of water molecules decreases the barrier making the process faster, as the participation of two water molecules in a proton transfer reaction is more favorable than the participation of only one water molecule. To estimate the effect of the medium (water) on the relative stabilities of the tautomers of the studied compounds we applied the polarizable continuum model (PCM). (13)C NMR chemical shieldings were calculated using the GIAO approach at MP2/6-31+G(d,p) optimized geometries. HF and the DFT B3LYP functional with 6-31+G(d,p) basis set were employed. The quantum chemical results for the chemical shifts in gas phase and in polar solvents (water and DMSO) were compared with experimental data. TD DFT B3LYP/aug-cc-pVTZ calculations were performed to predict the absorption maxima of tautomers A and B of 2AT and 4AT.     

Spin‐orbit ZORA and four‐component Dirac–Coulomb estimation of relativistic corrections to isotropic nuclear shieldings and chemical shifts of noble gas dimers

Hartree–Fock and density functional theory with the hybrid B3LYP and general gradient KT2 exchange‐correlation functionals were used for nonrelativistic and relativistic nuclear magnetic shielding calculations of helium, neon, argon, krypton, and xenon dimers and free atoms. Relativistic corrections were calculated with the scalar and spin‐orbit zeroth‐order regular approximation Hamiltonian in combination with the large Slater‐type basis set QZ4P as well as with the four‐component Dirac–Coulomb Hamiltonian using Dyall's acv4z basis sets. The relativistic corrections to the nuclear magnetic shieldings and chemical shifts are combined with nonrelativistic coupled cluster singles and doubles with noniterative triple excitations [CCSD(T)] calculations using the very large polarization‐consistent basis sets aug‐pcSseg‐4 for He, Ne and Ar, aug‐pcSseg‐3 for Kr, and the AQZP basis set for Xe. For the dimers also, zero‐point vibrational (ZPV) corrections are obtained at the CCSD(T) level with the same basis sets were added. Best estimates of the dimer chemical shifts are generated from these nuclear magnetic shieldings and the relative importance of electron correlation, ZPV, and relativistic corrections for the shieldings and chemical shifts is analyzed. © 2015 Wiley Periodicals, Inc.     

Study of the temperature‐dependent conformational averaging of 1H NMR resonances in vinylcyclopropane through the use of ab initio methodology and Boltzmann statistics

The temperature dependence of the ¹ H NMR resonance of the C‐4 olefinic proton in vinylcyclopropane was investigated through a combination of ab initio calculations and Boltzmann statistics. A torsional energy profile as a function of the 〈?〉 dihedral angle was obtained using HF methodology with a 6–311G** basis set, while the corresponding ¹ H chemical shift profiles for the C‐4 proton were computed using the GIAO approach and either HF, DFT (B3LYP) or MP2 methods at the 6–311G** level of theory. Chemical shifts at different temperatures calculated as canonical ensemble averages in which the different ab initio ¹ H chemical shift profiles and a Boltzmann factor defined by the HF/ 6–311G** energy function are employed reproduce remarkably well the temperature dependence observed experimentally. Attempts to perform a similar study using only the GIAO‐MP2 ¹ H chemical shift profile and 〈?〉 dihedral angle trajectories obtained from molecular dynamics simulations at different temperatures failed to reproduce the experimental trends. This shortcoming was attributed to the inability of the force fields employed, Tripos 6.0 and MMFF94, to reproduce properly the three‐well torsional potential of vinylcyclopropane. The application of both methodologies to the calculation of population‐dependent chemical shifts in other systems is discussed. Copyright © 2002 John Wiley & Sons, Ltd.     

Crystallographic and Dynamic Aspects of Solid‐State NMR Calibration Compounds: Towards ab Initio NMR Crystallography

The excellent results of dispersion‐corrected density functional theory (DFT‐D) calculations for static systems have been well established over the past decade. The introduction of dynamics into DFT‐D calculations is a target, especially for the field of molecular NMR crystallography. Four ¹³C ss‐NMR calibration compounds are investigated by single‐crystal X‐ray diffraction, molecular dynamics and DFT‐D calculations. The crystal structure of 3‐methylglutaric acid is reported. The rotator phases of adamantane and hexamethylbenzene at room temperature are successfully reproduced in the molecular dynamics simulations. The calculated ¹³C chemical shifts of these compounds are in excellent agreement with experiment, with a root‐mean‐square deviation of 2.0 ppm. It is confirmed that a combination of classical molecular dynamics and DFT‐D chemical shift calculation improves the accuracy of calculated chemical shifts.