Evaluation of the Factors Impacting the Accuracy of 13C NMR

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Article Cite This: J. Chem. Theory Comput. 2017, 13, 5798-5819

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Evaluation of the Factors Impacting the Accuracy of 13C NMR Chemical Shift Predictions using Density Functional TheoryThe Advantage of Long-Range Corrected Functionals Mark A. Iron* Computational Chemistry Unit, Department of Chemical Research Support, Weizmann Institute of Science, Rehovot 7610001, Israel S Supporting Information *

ABSTRACT: 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.

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INTRODUCTION Nuclear magnetic resonance (NMR) is an indispensable tool in organic, organometallic, and inorganic chemistry. Its use is key in determining the structure of compoundsincluding stereochemistryand in monitoring reactions. On occasion, however, it is not always definitive, and the actual structure may be debated. One recent example that generated some discussion in the literature is the structure of hexacyclinol.1 Despite a substantive NMR study, subsequent experimental2 and computational3 studies revealed a structure that differs from that originally proposed. This highlights how computational determination of chemical shifts can greatly assist in assigning structure.4 In another casevannusal Bthe authors noted that calculations would have greatly saved effort in the determination of its structure.5 In fact, Willoughby et al. have published a Nature Protocol for assigning 1H and 13C chemical shifts.6 Moreover, it is one of the few methods that can be used to identify reaction intermediates, such as in our recent study of the reaction of hypervalent iodine reagents with ketones and enolates; it was found that the reaction proceeds via the less stable enolonium intermediate rather than the more stable ketone form based on the comparison of the experimental lowtemperature 13C{1H} NMR spectrum and the calculated spectra of the different potential intermediates.7 In recent years, there has been a paradigm shift in the field of computational chemistry. Whereas until a few years ago the art of using calculations to understand and/or predict chemical properties was relegated to a select group of experts armed with specialized computational equipment, recent advances in method development and computers have allowed experimentalists to carry out their own computational studies who otherwise would never have considered such a daunting task. The computational tools needed to predict NMR spectra are © 2017 American Chemical Society

implemented in a number of commercial software packages, such as GAUSSIAN8 (which is used in this study), QCHEM9, and AMSTERDAM DENSITY FUNCTIONAL (ADF),10 as well as several free (at least for academic use) packages including ORCA,11 NWCHEM,12 GAMESS,13 and DALTON.14 While these are primarily intended to be run under Linux, many of these packages have Microsoft Windows and/or Apple Mac OS X versions, and calculations on small to medium molecules can even be run on desktop computers within a reasonable amount of time. These calculations, once a particular level of theory has been chosen, can almost be run in a “black box” style after careful consideration of the results presented herein. A number of evaluation studies of NMR chemical shift predictions have recently be reported. Toomsalu and Burk published a study where a select number of common exchangecorrelation functionals, basis sets, and NMR methods were considered.15 Pierens considered linear regression as a means of determining chemical shift but used a limited set of methods.16 There is an older study by Benzi et al. where a number of cases were examined.17 Teale et al. recently considered the performance of various methods, including coupled-cluster and DFT, for the prediction of absolute isotropic shifts and coupling constants of small molecules.18 Meanwhile, Krivdin and co-workers evaluated the performance of selected DFT functionals and basis sets in predicting chemical shifts for 15 1931 20 N, P, and a few other nuclides21 and also considered solvent effects in 15N22 and 29Si (and also relativistic effects)23 NMR. Likewise, Toukach and Ananikov recently reviewed the computational prediction of the NMR parameters of Received: July 18, 2017 Published: October 10, 2017 5798

DOI: 10.1021/acs.jctc.7b00772 J. Chem. Theory Comput. 2017, 13, 5798−5819

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Journal of Chemical Theory and Computation ́ et al. examined various factors in carbohydrates,24 while Vicha the prediction of the NMR spectra of square-planar transition metal (Pd, Pt, Au, Rh) complexes.25 Furthermore, fragmentation methods have been considered for the calculation of the NMR spectra of very large molecules (e.g., large peptides) with remarkable accuracy compared to direct calculations on the whole system.26 Based on some initial findings, we recently used calculated 13C chemical shifts to identify the key intermediate in the reaction of ketones or enolates with hypervalent iodine reagents.7 Herein is an in-depth evaluation of the different factors affecting the prediction of chemical shifts, including the exchange-correlation method, the basis set, the integration grids, the solvation model, and the NMR methodology. Over 70 functionals are considered, including many newer ones that have yet to be considered. Based on these results, four case studies are considered: the hitherto unknown structure of the benzoquinazoline alkaloid samoquasine A, the four stereoisomers of artaboral, glabramycins B and C and the use of a characteristic 3JHH coupling constant to help differentiate between stereoisomers, and the six stereocenters of elatenyne and the recommendation of using a second, complementary spectroscopic method such as vibrational circular dichroism (VCD) to aid in discriminating between the 32 diasteriomeric pairs. There are two parts to this paper. The first deals with the technical aspects of predicting NMR spectra using DFT. The second is comprised of the four case studies based on the results in the first section. The reader primarily interested in the applications to organic chemistry is invited to skip directly to the second section.

• Correlation functionals • The correlation component of the Lee−Yang− Parr (LYP) correlation44 • The Perdew-86 (P86) functionals45 • Perdew and Wang’s 1991 (PW91) gradientcorrected correlation functional32 • Becke’s 1995 τ-dependent (meta-GGA) correlation functional46 • The correlation component of the Perdew− Burke−Ernzerhof (PBE)36 • The τ-dependent correlation part of TPSS38 • The revised version of TPSS (revTPSS)39 • The Krieger−Chen−Iafrate−Savin correlation functional (KCIS)47 • Becke−Roussel (BRc) correlation functional40 • Exchange-correlation combinations • A variety combinations of the above exchange and correlation functionalsdenoted by combining their abbreviations • Becke’s 3-parameter hybrid functional48 using B exchange and LYP correlation (B3LYP)49 • Austin−Frisch−Petersson functional with dispersion (APFD)50 • Cohen and Handy’s 3-parameter hybrid functional using OPTX exchange (O3LYP)51 • Xu and Goddard’s XC functional (X3LYP)52 • Becke 1-paramter functionals46 using B exchange and B95 correlation (B1B95),46 B exchange and LYP correlation (B1LYP),53 and mPW exchange34 and PW91 correlation32 (mPW1PW91)34 • Handy and co-workers’ long-range corrected version of B3LYP using the Coulomb-attenuating method (CAM-B3LYP)54 • Adamo and Barone’s hybrid XC function using PBE exchange and correlation (PBE0)55 • Hamprecht−Cohen−Tozer−Handy GGA functional (HCTH, the 407 version)56 • The τ-dependent version of HCTH (τHCTH)57 • The hybrid version of τHCTH (τHCTHhyb)57 • Boese and Martin’s τ-dependent hybrid functional for kinetics (BMK)58 • The hybrid version of TPSSTPSS (TPSSh)38 • Grimme’s XC functional including dispersion (B97-D)59 based on the Becke97 functional form60 • The modification by Hamprecht et al. of the B97 functional (B97-1),56c including exact HF exchange • Wilson, Bradley, and Tozer’s modification to B97 (B97-2),61 including exact HF exchange • Becke’s 1998 modification of the B97 XC functional (B98)60,62 • Head-Gordon and co-workers’ dispersion corrected long-range corrected hybrid functional (ωB97X-D)63 • Cramer and co-workers’ parametrized functionals designed for 13C and 1H NMR chemical shifts (WC04 and WP04, respectively)64,65 • van Voorhis and Scuseria’s τ-dependent gradientcorrected correlation functional (VSXC)66 • Zhao and Truhlar’s hybrid meta-GGA functional designed for broad accuracy for thermochemistry (PW6B95)67 including PW91 exchange32 and B95 correlation46

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COMPUTATIONAL METHODS Most calculations were performed using GAUSSIAN09 REVISIONS D.0127 and E.01;28 calculations involving MN15, MN15-L, M08-HX, and PW6B95 (vide infra) were done using GAUSSIAN16 REVISION A.03.8 Some calculations were also done using NWCHEM 6.612 (vide infra). A large number of DFT exchange-correlation functionals we used are listed: • Local spin-density approximation (LSDA) • SVWN5: Slater ρ4/3 exchange (S)29 with Vosko− Wilk−Nusair correlation functional V (VWN5)30 • Exchange functionals • Becke88 (B) exchange31 • Perdew−Wang 1991 (PW91)32 • Adamo and Barone’s33 modified PW91 (mPW)34 • Gill-96 (G96)35 • The exchange component of the Perdew−Burke− Ernzerhof (PBE)36 • Handy’s OPTX modification of Becke88 (O)37 • The exchange component of the Tao−Perdew− Staroverov−Scuseria (TPSS)38 • The revised version of TPSS (revTPSS)39 • The 1989 exchange functional of Becke and Roussel (BRx)40 • The exchange component of the Perdew−Kurth− Zupan−Blaha (PKZB) functional41 • The exchange part of the screened Coulomb potential of Heyd, Scuseria, and Ernzerhof (alternatively knowns as ωPBEh or HSE)42 • The 1998 revision of PBE (PBEh)43 5799


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• The basis sets IGLO-II and IGLO-III from Kutzelnigg et al.’s individual gauge for localized orbital (IGLO) NMR method.97 Where required, basis sets were obtained from the Basis Set Exchange.98 Four methods for calculating chemical shifts were used: • Gauge-independent atomic orbitals (GIAO)99 • Continuous set of gauge transformations (CSGT)100 • Individual gauges for atoms in molecules (IGAIM)100a,b • Single origin (SO) Bulk solvent effects were approximated by single point energy calculations using various implicit models: • a polarizable continuum model (PCM),105 specifically the integral equation formalism model (IEFPCM)105a,b,106 • the CPCM polarizable conductor calculation model,107 • a PCM calculation using Klamt’s form of the conductor reaction field (COSMO)108 • Truhlar’s empirically parametrized version of IEF-PCM− Solvation Model Density (SMD)109 When NMR coupling constants (J) are calculated, for technical reasons the GIAO method was used using Deng et al.’s two-step method (“mixed” option in GAUSSIAN09).101 Truhlar’s minimally augmented (i.e., calendar) may-cc-pVTZ basis set was used89 in conjunction with the LC-TPSSTPSS long-range corrected exchange-correlation functional. This functional was chosen based on the results presented hereinafter for chemical shifts; finding the best conditions for calculating coupling constants is beyond the scope of this study, although it does merit a study in of itself. Relativistic effects, when considered, were included using a second-order Douglas−Kroll−Hess (DKH2) Hamiltonian102 run using NWCHEM with the TZP-DKH (triple-ζ plus polarization specifically recontracted for DKH2 calculations) basis set.103 Geometries were optimized with the PBE functional with the def2-SVP basis set. To improve efficiency of the calculations using pure XC functionals, density-fitting (DF) was used.104 This requires the use of a density fitting basis set, specifically def2-SV designed for use with def2-SVP.93e This combination is denoted as DF-PBE/def2-SVP/def2-SV. For technical reasons, density-fitting was not used during NMR chemical shift calculations. Accurate energies were calculated using a Kozuch and Martin’s dispersion corrected (D3BJ),110 spin component scaled (i.e., an SCS111-MP287-like correlation contribution), double hybrid (DSD) functional, specifically DSD-PBEP86:112 this functional incorporates the PBE exchange36 and the Perdew-86 (P86) correlation45 functionals. This class of DFT functionals has been shown to provide energies approaching that of the “Gold Standard” in computational chemistry, specifically CCSD(T). There are a number of reviews and benchmark studies of double-hybrid functionals, which clearly show that the use of this class of functionals is highly recommended.112,113 The def2-TZVPP basis set and SMD solvation model (vide supra) with the relevant solvent were used for these calculations. Conformational analyses were done using VEGA ZZ114,115 starting from DF-PBE/def2-SVP/def2SV optimized geometries; this allows for conformers whose bonds and bond angles should not be too far from ideal. The energies of the top 50

• Truhlar’s Minnesota-06 (M06) family of functions, including M06 and M06-2X with twice the exchange,68 M06-HF with 100% HF exchange,69 and the local (nonhybrid) version M06-L33 • Truhlar’s M0570 and M05-2X71 functionals, earlier versions of the Minnesota-06 functionals • Truhlar’s Minnesota-11 family of functionals including the M1172 and the local version M11-L73 • Truhlar’s 2011 second-order GGA functional (SOGGA11)74 and its hybrid variant (SOGGA11X)75 • Truhlar’s Minnesota-12 family of functionals, including the local nonseparable gradient approximation (NGA) N12,76 the τ-dependent MN12L,77 and the screened exchange hybrid versions (N12-SX and MN12-SX)78 • The Heyd−Scuseria−Ernzerhof range-separated hybrid functional (HSE06)79 • Henderson, Izmaylov, Scuseria, and Savin’s rangeseparated hybrid functional (HISS)80 • Swart−Solà−Bickelhaupt dispersion corrected function based on spin states and SN2 barriers (SSB-D)81 run with NWCHEM • The long-range corrected version of ωPBE (LCωPBE)82 • Hirao and co-workers’ long-range correction method (LC-) that can be applied to any pure (nonhybrid) functional83 • Truhlar’s Minnesota-15 (MN15) hybrid metaGGA functional84 and its local counterpart MN15-L85 • Truhlar’s Minnesota-08 functionals with “high exchange” (M08-HX)86 In addition to the above DFT methods, from wave function theory, the second-order Møller−Plesset perturbation theory87 and the Hartree−Fock reference were used. With the above computational methods, a number of families of basis sets were used: • Dunning’s cc-pVnZ (n = D, T, Q, 5) correlation consistent basis sets and the corresponding augmented (diffuse) versions (aug-cc-pVnZ)88 • Selected members of Truhlar’s “calendar” basis sets where only s and p diffuse functions are added to the heavy atoms (i.e., beyond He)89 • Dunning’s cc-pCVnZ (n = D, T, Q, 5) correlation consistent core−valence basis sets and the corresponding augmented (aug-cc-pCVnZ) versions (which by definition are cc-pVnZ and aug-cc-pVnZ for H and He)88a,90 • Pople’s 6-31G and 6-311G family of functionals without and with diffuse functions (identified by “++” before the “G”) and with various sets of polarization functions91 • The second revision (def2) of Ahlrichs and co-workers’ basis sets92 (def2-SVP, def2-SVPD, def2-TZVP, def2TZVPP, def2-TZVPD, def2-TZVPPD, def2-QZVP)93 • Jensen’s polarized-consistent basis sets (pc-n, n = 0−4) and the augmented versions (aug-pc-n)94 • Jensen’s pc-n basis sets for nuclear magnetic shielding (pcS-n) and their augmented versions95 • Jensen’s segment contracted pcS-n basis sets (pcSseg-n) and their augmented versions (aug-pcSseg-n)96 5800


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Pierens recently used this methodbut flipped the axis definitionsto evaluate a few DFT methods.16 For the set of calibration compounds, the reported experimental chemical shifts of common solvents in various NMR solvents was used.121 Specifically, the chosen compounds are acetic acid, acetone, acetonitrile, benzene, tert-butanol, carbon dioxide (13C shifts only), carbon disulfide (13C shifts only), carbon tetrachloride (13C shifts only), chloroform, cyclohexane, 1,2-dichloroethane, dichloromethane (DCM), diethyl ether, dimethylformamide (DMF), 1,4-dioxane, dimethoxyethane (DME), ethane, ethanol, ethyl acetate, ethylene, hexamethyldisiloxane (HDMSO), hexamethylphosphoramide (HMPA), hydrogen (1H shifts only), imidazole, methane, methanol, nitromethane, n-pentane, propane, 2-propanol, propylene, pyridine, pyrrole, pyrrolidine, tetrahydrofuran (THF), tetramethylsilane (TMS, standard 0.00 ppm reference for 13C and 1H NMR spectroscopy), toluene, triethylamine (TEA), and water (1H shifts only). There are several computational aspects that potentially could affect the accuracy of the chemical shift predictions: (i) the exchange-correlation (XC) functional, (ii) basis set, (iii) integration grids, (iv) solvation model, (v) NMR method, (vi) relativistic effects, (vii) zero-point vibrational contributions, and (viii) choice of starting geometry. Each factor will be considered in turn (but not necessarily in this order). It is assumed that the effects of each factor are (mostly) independent of changes of the other factors. There are another two issues that in general should be considered regardless of the underlying computational methodology: averaging chemically equivalent signals and Boltzmann weighting of conformers.6 The NMR calculations are done on a single, optimized geometry, and this results in separate signals for “chemically equivalent” protons or carbon atoms. For example, a methyl or tert-butyl group is expected to rotate quickly relative to the NMR measurement time scale. Thus, a single proton signal is observed for the methyl group, and a single 13C signal is observed for the tert-butyl methyl carbons (obviously the central quaternary carbon will have a separate signal). Therefore, when one has such a group in one’s molecule, the “calculated” isotropic shift of the group is the average of the individual isotropic shifts obtained from the NMR calculations. This is done for all such cases in this study. The second issue is more complicated and to a degree related to the first. A molecule may have multiple conformers that can rapidly interconvert on the NMR time scale. For example, for methylcyclohexane there are two chair configurationsone with the methyl in an axial position and another with the methyl in an equatorial position. This will give rise to two distinct sets of NMR signals, but since the two conformers can rapidly interchange, the observed spectrum will be a Boltzmann-weighted average of the two. In such a case, one needs to optimize the structures of all possible conformers, calculate their relative energies, and average the signals appropriately:

conformers provided were calculated at the DF-PBE/6-31G*/ auto level of theory (where “auto” indicates that the automatic density fitting basis set generation algorithm in GAUSSIAN09 was used). Of these, the lowest 10 structures were optimized at the final level of theory. As noted above, the DSD-PBEP86 doublehybrid functional was used to obtain accurate energies for the Boltzmann distribution. (In no case were all ten structures energetically relevant according to the Boltzmann distributiondefined as >5% probability.) NMR chemical shifts were then calculated for any conformers with >5% probability in the Boltzmann distribution; when weighting the chemical shifts to obtain the final average chemical shifts, the Boltzmann distributions were recalculated using the final set of structures. (After completion of this study, an alternate means of performing conformer searches was found using Grimme’s QMDFF force-field, which is determined based on the DFT energy surface of the molecule in question,116 or using a tightbinding method specifically parametrized by Grimme and coworkers for geometries, vibrations, and noncovalent interactionsGFN-xTB.117) Vibrational circular dichroism (VCD) spectra118 were calculated119 at the PBE/def2-SVP level of theory (i.e., the same level of theory as the geometry optimization but without density fitting, which is incompatible with the GIAO part of the VCD calculation). The mathematical derivation of the modified DP4 probabilities (P DP4 ͠ ) was assisted by WOLFRAM MATHEMATICA 10 version 10.4.0.0 for Mac OS X (Wolfram Research Inc.).

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RESULTS AND DISCUSSIONDFT AND NMR One needs to obtain chemical shifts, which can be compared to experimental measurements, from the isotropic shifts (IS) obtained from the calculations. There are two common methods. One could use either a reference compound (tetramethylsilane is the experimental calibration standard for 1 H and 13C NMR) or linear regression from a set of calibration molecules.16 In the former method, the IS of the reference compound is calculated, along with the ISs of the molecule of interest. The chemical shift is then equal to δi = σref − σi + δref where δi and δref are the chemical shifts of the molecule of interest and of the reference, respectively, while σi and σref are the corresponding ISs. This is the simpler and more commonly used method. One problem is that there is not a systematic method of evaluating the associated error in δi. One assumption of this method is that any errors associated with calculating σi would be cancelled by the errors associated with σref. However, the more δi and δref differ, the less ideal this error cancellation would be. One could try using a reference more similar to the molecule of interest, but what happens if one has a series of molecules to consider?120 The alternativelinear regressionis to use a series of reference compounds. The wider range would provide more error cancellation as well as a measure of the error in the calculation. Here, the ISs of a series of molecules are calculated, and the experimental δref (i.e., on y-axis) is plotted versus the calculated σref (i.e., on x-axis). From linear regression of this plot, one obtains the slope (m) and y-axis intercept (b), and the chemical shifts of the molecule of interest are

pi =

−ΔGi R ·T

( )

exp

−ΔGj

( )

∑j exp

R ·T

where pi is the probability of species i and ΔGi is the relative Gibbs free energy of species i (relative to the most stable conformer). From this it follows that the observed chemical

δi = m ·σi + b 5801


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∑ pi ·δi = i

Table 1. Evaluation (coefficient of determination R2 and standard error se(δ) in ppm) of the Impact of the Integration Grid on the Accuracy of the 1H and 13C NMR Chemical Shift Predictions Using the PBE0 Exchange-Correlation Functional, the def2-TZVPD Basis Set, and the SMD Solvation Model

−ΔGi R ·T

( )

∑i δi·exp

−ΔGj

( )

∑j exp

R ·T

δ(13C)

In the above case, the energy difference was calculated to be 2.00 kcal/mol in favor of the equatorial conformer, resulting in a 97:3 equatorial:axial ratio.6 The observed chemical shift would be the weighted average of the calculated shifts of each conformer. In the evaluation set used, only small molecules are chosen to avoid instances of multiple conformers that would need to be considered. In the second part of this study, where selected case studies are examined using our methodology, this conformer issue is crucial. In their Nature Protocol, Willoughby et al. use the M06-2X/6-31+G(d,p) level of theory for determining the energy differences. However, the Boltzmann weighting is sensitive to the accuracy of the energy calculation, and therefore it is recommended that the energies be calculated as accurately as possible. Double-hybrid functionals113a are a newer class of DFT exchange-correlation functionals that incorporate an MP2-like correlation term. Their accuracy has been shown to rival the ab initio CCSD(T) “Golden Standard.”112,113 Therefore, here the relative energies are calculated using the DSD-PBEP86 double hybrid functional112a with a much larger basis set (def2-TZVPPsee Computational Methods section for full details). Using various techniques such as the RIJCOSX approximation122 in ORCA11energy calculations can be run quite efficiently even for large molecules with large basis sets. For evaluation purposes, initially the PBE0 XC functional, the def2-TZVPD basis set, the SMD solvation model (in dichloromethane), and the GIAO NMR method were used. PBE0 is a popular functional that has been shown to be reasonable, def2-TZVPD is a reasonably large basis set, and GIAO is often used. Likewise, the linear regression method of calibrating the NMR chemical shifts will be used. The geometries of all species were optimized at the DF-PBE/ def2-SVP/def2-SV level of theory (see Computational Methods for full explanations of all methods described hereinafter). Integration Grids. Integration grids are essential to the calculation of the XC energy. Generally, a larger grid leads to more reliable results. The five built-in grids in GAUSSIAN09 were considered (Table 1). Clearly, at least with this combination of functional and basis set (e.g., the Minnesota-06 functionals have been shown to be sensitive to the integration grid for the calculations of energy and geometry123), the choice of integration grid does not have any significant impact on the accuracy of the chemical shift predictions. One could thus choose to use any grid, and the default fine grid was chosen for the rest of the evaluations hereinafter. Basis Set Effects. Five families of basis sets were evaluated: (i) Ahlrichs, specifically the def2 version, (ii) Jensen’s polarization consistent (pc) basis sets, including variants specially optimized for NMR shielding (pcS and pcSseg), (iii) Dunning’s correlation consistent (cc) basis sets, (iv) Pople’s 631G and 6-311G sets of basis sets with varying levels of diffuse and polarization functions, and (v) Kutzelnigg’s IGLO basis sets specifically designed for NMR calculations. With the exception of the single-ζ pcS-0 basis set, which was considered only for completeness, within a family of basis sets, there is little

grid coarse (cg) SG1 fine (fg) ultrafine (ufg) superfine (sfg)

a

R (35, 110) (50, 194) (75, 302) (99, 590) (150, 974)

2

0.977 0.977 0.977 0.977 0.977

δ(1H) 2

se(δ)

R

8.42 8.40 8.41 8.40 8.40

0.986 0.986 0.986 0.986 0.986

se(δ) 0.303 0.306 0.307 0.303 0.303

a

The names are those given to the grids in GAUSSIAN09. In parentheses are the numbers of radial and angular points in the integration grid.

variation (Table 2). Neither increasing ζ nor adding polarization and/or diffuse functions has a significant impact on the linear regression. Of the five families, the Dunning and IGLO basis sets are the best performers, but the differences are small. This is somewhat unexpected given that the pcS-n and pcSseg-n basis sets were designed for chemical shifts.95,96 Because the IGLO-III basis set is available only for a limited set of atoms, the Dunning basis set (specifically cc-pVTZ) is recommended. It should be noted that there were some serious convergence problems for some members of the calibration set for the augpc-n, aug-pcS-n, and aug-pcSseg-n basis sets for n ≥ 3. One thing that is clear is that using basis sets beyond triple-ζ quality does not meaningfully improve the results (and in some cases, the errors slightly increase for the larger basis sets). The use of augmented basis sets beyond double-ζ does not meaningfully improve the results, especially given the significant increase in computer time, but the use of Truhlar’s “calendar” basis sets, which add only s and p diffuse functions on the heavy atoms,89d actually leads to slightly worse results than either the fully augmented or unaugmented basis sets. Previous studies also found that larger basis sets were not beneficial.15 Moreover, the use of a core-valence (cc-pCVTZ) basis set, which would capture any influence of the core on the NMR calculation, was found to have a negligible impact on the accuracy of the NMR calculations. One method for improving energy or property predictions is to extrapolate to the basis set limit.124 Using the 13C isotropic shifts, the complete basis set (CBS) limits for the cc-pVnZ and aug-cc-pVnZ basis sets were determined using an A + B·L−α extrapolation (where L is the highest angular momentum in the larger basis set, which in practice is n); for these two basis set groups, exponents α of 2.07 and 1.77, respectively, were found. Thus, this property seems to converge relatively slowly with respect to basis set size. The basis set convergences for five selected carbon signals are shown in Figure 1. One could use a two-point extrapolation to find the CBS limit: E (L → ∞ ) = E L 2 +

E L2 − E L1 α

( ) L2 L1

−1

However, it is apparent from the data in Table 2 that this yields poorer results than simply using the larger basis set in the extrapolation. Therefore, despite its advantages for other properties (notably energies), likely because of its slow 5802


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Table 2. Evaluation (coefficient of determination R2 and standard error se(δ) in ppm) of Selected Basis Sets Using the PBE0 Exchange-Correlation Functional and the SMD Solvation Model for Predicting 1H and 13C NMR Chemical Shifts δ(13C) basis set

2

R

δ(1H) se(δ)

R

2

δ(1H)

δ(13C) se(δ)

basis set

Ahlrichs Basis Sets 0.962 10.83 0.976 0.396 0.963 10.60 0.983 0.335 0.966 10.24 0.979 0.367 0.966 10.24 0.979 0.367 0.966 10.22 0.982 0.346 0.966 10.20 0.980 0.359 0.966 10.19 0.982 0.339 0.966 9.80 0.979 0.326 Jensen’s Polarization Consistent Basis Sets pc-0 0.967 10.13 0.963 0.489 pc-1 0.954 11.94 0.979 0.375 pc-2 0.968 9.89 0.985 0.316 pc-3 0.969 9.81 0.984 0.320 pc-4 0.968 9.89 0.984 0.321 aug-pc-0 0.967 10.14 0.970 0.443 aug-pc-1 0.957 11.44 0.983 0.333 aug-pc-2 0.966 10.17 0.984 0.326 Jensen’s Polarization Consistent Basis Sets for NMR Shielding pcS-0 0.966 10.20 0.965 0.479 pcS-1 0.968 9.85 0.981 0.348 pcS-2 0.969 9.74 0.985 0.309 pcS-3 0.968 9.86 0.984 0.320 pcS-4 0.968 9.86 0.984 0.321 aug-pcS-0 0.968 9.88 0.971 0.434 aug-pcS-1 0.968 9.96 0.985 0.318 aug-pcS-2 0.969 9.77 0.984 0.320 pcSseg-0 0.965 10.38 0.955 0.540 pcSseg-1 0.967 10.03 0.981 0.349 pcSseg-2 0.968 9.91 0.985 0.313 pcSseg-3 0.968 9.86 0.984 0.319 pcSseg-4 0.968 9.86 0.984 0.321 aug-pcSseg-0 0.965 10.42 0.971 0.436 aug-pcSseg-1 0.968 9.93 0.985 0.314 aug-pcSseg-2 0.967 10.00 0.984 0.321 Dunning’s Correlation Consistent Basis Sets cc-pVDZ 0.971 9.40 0.978 0.377 cc-pVTZ 0.978 8.28 0.987 0.294 cc-pVQZ 0.978 8.17 0.988 0.283 cc-pV5Z 0.979 8.08 0.988 0.278 cc-pV{D,T}Za 0.966 10.23 cc-pV{T,Q}Za 0.972 9.31 aug-cc-pVDZ 0.975 8.85 0.986 0.300 aug-cc-pVTZ 0.977 8.33 0.988 0.285

R

2

se(δ)

R

2

Dunning’s Correlation Consistent Basis Sets aug-cc-pVQZ 0.978 8.13 0.988 aug-cc-pV5Z 0.979 8.04 0.988 aug-cc-pV{D,T}Za 0.969 9.79 aug-cc-pV{T,Q}Za 0.971 9.42 jun-cc-pVDZ 0.968 9.84 0.986 may-cc-pVTZ 0.972 9.22 0.988 apr-cc-pVQZ 0.973 9.13 0.988 mar-cc-pV5Z 0.973 9.04 0.988 cc-pCVDZ 0.965 10.38 0.979 cc-pCVTZ 0.978 8.16 0.987 cc-pCVQZ 0.973 9.03 0.986 cc-pCV5Z 0.973 9.03 0.988 aug-cc-pCVDZ 0.969 9.80 0.986 aug-cc-pCVTZ 0.973 9.09 0.988 aug-cc-pCVQZ 0.973 9.01 0.988 aug-cc-pCV5Z 0.974 9.00 0.988 Pople’s Basis Sets 6-31G(d,p) 0.973 9.09 0.983 6-31G(2d,p) 0.973 9.14 0.979 6-31G(2d,2p) 0.972 9.2 0.982 6-31G(2df,2pd) 0.974 8.90 0.985 6-31G(3df,3pd) 0.973 9.06 0.986 6-311G(d,p) 0.974 8.97 0.982 6-311G(2d,p) 0.971 9.37 0.982 6-311G(2d,2p) 0.971 9.34 0.986 6-311G(2df,2pd) 0.972 9.19 0.987 6-311G(3df,3pd) 0.974 8.92 0.987 6-31++G(d,p) 0.974 8.98 0.988 6-31++G(2d,p) 0.973 9.00 0.987 6-31++G(2d,2p) 0.973 9.04 0.988 6-31++G(2df,2pd) 0.976 8.65 0.988 6-31++G(3df,3pd) 0.974 8.89 0.988 6-311++G(d,p) 0.974 9.00 0.986 6-311++G(2d,p) 0.972 9.25 0.985 6-311++G(2d,2p) 0.972 9.24 0.987 6-311++G(2df,2pd) 0.973 9.11 0.988 6-311++G(3df,3pd) 0.975 8.75 0.988 Kutzelnigg’s IGLO Basis Sets IGLO-II 0.977 8.40 0.983 IGLO-III 0.979 8.05 0.987

SVP SVPD TZVP TZVP (ufg) TZVPP TZVPD TZVPPD QZVP

se(δ) 0.279 0.279

0.298 0.282 0.278 0.279 0.374 0.294 0.299 0.281 0.301 0.284 0.279 0.287 0.338 0.367 0.343 0.315 0.303 0.339 0.340 0.301 0.292 0.291 0.283 0.291 0.286 0.278 0.276 0.303 0.309 0.288 0.278 0.275 0.329 0.293

a

Two-point extrapolation to the complete basis set limit using the two n-tuple basis sets listed in the braces; see text.

In Table 3, the top six performers for each nucleus are highlighted. The top XC functional for 13C predictions is LCωPBE, while, for what it is worth, the best functional for 1H is MN12-SX. Two methods are on the top-six list for both nuclei: LC-BLYP and HISS. For carbon shifts, a number of functionals outperform MP2, a wave function method that is often used when a “benchmark standard” is needed; moreover, its higher costs make it unfeasible for larger systems. Given the performance of MP2, one might expect that double-hybrid functionals (fifth rung of Perdew’s Ladder of DFT functionals125) would perform well, but evaluation of this class of functionals was not possible for technical reasons.

convergence, its use here is not beneficial. (See SI for more details.) DFT Exchange-Correlation Functional. There is a virtual alphabet soup of XC functionals available. A large variety of functions was evaluated, and the results are listed in Table 3. In this table, the functionals are sorted by class (see Computational Methods for explanation) and then alphabetically by name. One thing that is readily apparent is that the range of the errors is fairly small (6.8−11.2 ppm for 13C and 0.27−0.44 ppm for 1H). While an error of ±7 ppm for 13C NMR chemical shifts would still allow for reasonable predictive ability, ±0.3 ppm for 1H does not allow for meaningful predictions, although trends should still be reliable. 5803


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accuracy of carbon shift predictions. Two exchange functionals lowered the errors on 13C chemical shifts: PKZB and BRx. These are parts of a designed pair of exchange-correlation functionals. Thus, along with a number of other functional XC pairs, these were also evaluated (Table 6). Not surprisingly, these two pairs performed well for 13C chemical shifts, as did LC-TPSSTPSS. Reviewing all of the many functional combinations considered here, clearly a range-separated functional is recommended. For predicting carbon shifts, the preferred combinations, in order of increasing errors, are LC-BRxPBE (±6.6 ppm), LC-PKZBPKZB (±6.7 ppm), LC-PKZBPBE (±6.7 ppm), LC-TPSSTPSS (±6.7 ppm), LC-revTPSSrevTPSS (±6.7 ppm), and LC-OPBE (±6.7 ppm); it should be noted that many of the XC combination with the LC correction have very similar performance. If the LC correction is unavailable, another range separated functional, such as HISS (±7.5 ppm), M11 (±7.1 ppm), CAM-B3LYP(±7.9 ppm), or ωB97X-D (±7.9 ppm), can be used. If these are not available, M05-2X (±7.4 ppm), SOGGA11X (±7.6 ppm), WC04 (±7.9 ppm)a reparameterization of B3LYPor M06-2X (±8.0 ppm) can be used. The question remains why the range-separated and longrange corrected functionals perform so well. To the best of our knowledge, they have not previously been evaluated for NMR chemical shift predictions. One hypothesis is that they perform well specifically because they correct the long-range behavior of the functional, and it is known that NMR spectra are influenced by long-range effects (e.g., long-range through-space and through-bond coupling constants). Cencek and Szalewicz examined the behavior of long-range corrected functionals and concluded that, in general, a single “universal” (i.e., system-independent) ω of 0.4 bohr−1 does not perform well and that ω should be tuned (based on the ionization potential) for each system;126 this is in agreement with the conclusions of this paper in that a LC-functional with a standard value of ω is recommended. Needless to say, this is too complicated for a general purpose methodology, especially if several candidate structures (vide infra) are being considered. Nonetheless, Alipour and Fallahzadeh did consider this and tuned ω when predicting 31P−1 H spin−spin coupling constants.127 NMR Method. There are four methods for calculating NMR shielding tensors, from which the chemical shifts are determined. In GAUSSIAN09, the default is to use the gaugeindependent atomic orbital (GIAO) method, and, therefore, this method was chosen for the evaluation of the various components of the chemical shift calculations. The other methods available are the continuous set of gauge transformations (CSGT), individual gauges for atoms in molecules (IGAIM, a variation on CSGT), and single origin (SO). The comparison of all four methods is listed in Table 7. SO was included for completeness and, as advertised in the GAUSSIAN09 users’ manual, does quite poorly. CSGT and IGAIM perform similarly, and both outperform GIAO; similar observations were made by Toomsalu and Burk.15 Solvation Model. The SMD model has been shown to be reliable in many applications109 and therefore was selected as the default method. However, as is evident from the data in Table 8, the COSMO method is more accurate for these purposes. It should be noted that when solute−solvent hydrogen bonds are present, inclusion of an explicit solvent

Figure 1. Basis set convergence for five selected 13C chemical isotopic shifts (ppm) for the cc-pVnZ (top) and aug-cc-pVnZ (bottom) basis sets as a function of L. Note that the CH3CN (red) and CH4 (green) shifts are on the right axis.

Two functionals from the Cramer groupWP04 and WC04were specifically designed to predict proton and carbon chemical shifts, respectively (hence, the “P” and “C” in their names).64 While not in the top-five list for their respective nuclei, they do perform well. They should, however, not be used for other nuclei. Of the top six functionals, four are range-separated. Furthermore, most of the range-separated functionals appear at the top of the list. They correct, using various schemes, the tendency of the non-Coulomb part of the exchange functional to die off too quickly. It would appear that this is a significant factor affecting the performance. The “LC” correction of Hirao and co-workers83 can be applied to any pure (i.e., nonhybrid) functional. Thus, it would be of interest to see if there is a pair of exchange and correlation functionals that, within this LCcorrection scheme, gives better chemical shift predictions. Due to the large number of available exchange and correlation functionals, this would lead to too many combinations to be easily managed. Thus, initially the Becke88 (B) exchange functional was chosen and used with a variety of correlation functionals (Table 4). For 13C chemical shifts, many of the correlation functionals have similar performance (±6.7 ppm) and are an improvement on LCBLYP. Of these correlation functionals, PBE was chosen for the screening of the exchange functionals. Twelve exchange functionals were next considered using the PBE correlation functional (Table 5). With one exception, the choice of the exchange functional had little impact on the 5804


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Table 3. Evaluation (coefficient of determination R2 and standard error se(δ) in ppm) of Selected DFT Exchange-Correlation Functionals Using the def2-TZVPD Basis Set and the SMD Solvation Model for Predicting 1H and 13C NMR Chemical Shiftsa δ(13C) 2

functional

R

SVWN5 (LSDA)

0.966

δ(13C)

δ(1H) 2

se(δ)

R

se(δ)

10.18

0.980

0.363

GGA B97-D BLYP HCTH N12b SOGGA11 M06-L M11-Lb MN12-Lb MN15-Lb τ-HCTH TPSS VSXC APFD B1LYP B3LYP B97-1 B97-2 B98 mPW1PW91 O3LYP PBE0 SOGGA11X WC04 WP04 X3LYP

0.963 10.71 0.962 10.82 0.964 10.46 0.963 10.65 0.962 10.86 Meta-GGA 0.963 10.65 0.960 11.15 0.972 9.21 0.968 9.83 0.964 10.49 0.967 10.03 0.961 10.98 Hybrid 0.977 8.46 0.975 8.84 0.973 9.13 0.974 8.96 0.975 8.70 0.974 9.07 0.977 8.36 0.971 9.46 0.966 10.20 0.981 7.61 0.979 7.95 0.964 10.55 0.974 9.01

0.982 0.981 0.982 0.983 0.980

0.339 0.352 0.342 0.336 0.365

0.983 0.984 0.896 0.986 0.983 0.983 0.981

0.335 0.323 0.302 0.303 0.334 0.331 0.356

0.986 0.987 0.986 0.986 0.986 0.986 0.986 0.985 0.980 0.985 0.982 0.987 0.986

0.306 0.294 0.302 0.306 0.302 0.300 0.301 0.316 0.359 0.310 0.345 0.290 0.299

B1B95 BMK M05 M05-2X M06 M06-2X M06-HF M08-HX MN15b PW6B95 τ-HCTHhyb TPSSh LC-BLYP CAM-B3LYP HISS HSE06 LC-ωPBE M11b MN12-SXb N12-SXb ωB97X-D HF (SCF) MP2

δ(13C) functional

R

LC-BLYP LC-BP86 LC-BB95 LC-BPW91 LC-BPBE LC-BTPSS LC-BrevTPSS LC-BKCIS LC-BBRc LC-BPKZB

0.984 0.985 0.985 0.985 0.985 0.985 0.985 0.985 0.984 0.985

se(δ)

R

Hybrid Meta-GGA 0.978 8.25 0.977 8.45 0.973 9.05 0.982 7.40 0.972 9.27 0.979 8.01 0.973 9.17 0.977 8.43 0.977 8.35 0.971 9.37 0.972 9.36 0.972 9.25 Range-Separated GGA 0.984 6.97 Range-Separated Hybrid 0.980 7.86 0.982 7.50 0.977 8.41 0.985 6.83 0.981 7.61 0.978 8.20 0.978 8.18 0.980 7.92 WFT 0.979 7.99 0.979 7.96

se(δ)

0.986 0.986 0.983 0.986 0.986 0.986 0.971 0.986 0.987 0.987 0.985 0.985

0.299 0.303 0.330 0.306 0.305 0.305 0.437 0.306 0.290 0.293 0.311 0.310

0.987

0.288

0.988 0.987 0.986 0.986 0.985 0.989 0.985 0.988

0.284 0.288 0.307 0.305 0.315 0.270 0.295 0.295

0.987 0.989

0.290 0.272

The six functionals for each nucleus with the lowest errors are in bold. bNGA-based rather than GGA-based.

Table 5. Evaluation (coefficient of determination R2 and standard error se(δ) in ppm) of LC-Based Functionals Using the PBE Correlation Functional and Various Exchange Functionals and Using the def2-TZVPD Basis Set and the SMD Solvation Model for Predicting 1H and 13C NMR Chemical Shifts

δ(1H) 2

δ(1H) 2

a

Table 4. Evaluation (coefficient of determination R2 and standard error se(δ) in ppm) of LC-Based Functionals Using the Becke88 (B) Exchange Functional and Various Correlation Functionals and Using the def2-TZVPD Basis Set and the SMD Solvation Model for Predicting 1H and 13C NMR Chemical Shifts 2

R

functional

2

δ(13C) 2

se(δ)

R

se(δ)

functional

R

6.97 6.75 6.84 6.75 6.73 6.72 6.74 6.71 6.94 6.73

0.987 0.986 0.985 0.986 0.986 0.985 0.985 0.985 0.986 0.986

0.288 0.303 0.310 0.306 0.307 0.312 0.310 0.316 0.304 0.306

LC-BPBE LC-PW91PBE LC-mPWPBE LC-G96PBE LC-PBEPBE LC-OPBE LC-TPSSPBE LC-revTPSSPBE LC-BRxPBE LC-PKZBPBE LC-ωPBEhPBE (HSEPBE) LC-PBEhPBE

0.985 0.985 0.985 0.985 0.985 0.985 0.985 0.985 0.986 0.986 0.981 0.985

molecule is beneficial;128 this is beyond the scope here, and the systems were chosen such that this issue is avoided. Relativistic Effects. Given that both carbon and hydrogen are at the top of the periodic table, one would expect that relativistic effects would be negligible. However, looking beyond simple organic chemistry, one may be interested in systems that include atomssuch as transition metals or the heavy main-group elementswhere one cannot ignore their

δ(1H) 2

se(δ)

R

6.73 6.74 6.74 6.75 6.72 6.71 6.75 6.72 6.61 6.67 7.56 6.72

0.986 0.986 0.986 0.986 0.985 0.986 0.987 0.987 0.986 0.986 0.984 0.985

se(δ) 0.307 0.307 0.307 0.306 0.308 0.306 0.295 0.294 0.302 0.306 0.326 0.309

contributions. The effects of using the Douglas−Kroll−Hess second order scalar relativistic Hamiltonian (DKH) was considered (Table 9). While the impact is minimal, one needs a heavy atom to properly consider the impact of relativistic effects and the model used to account for them. One common method of accounting for relativistic effects is to use a 5805


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Journal of Chemical Theory and Computation Table 6. Evaluation (coefficient of determination R2 and standard error se(δ) in ppm) of LC-Based Functionals Using Various Exchange and Correlation Functionals Using the def2-TZVPD Basis Set and the SMD Solvation Model for Predicting 1H and 13C NMR Chemical Shifts δ(13C) 2

functional

R

LC-TPSSTPSS LC-rev-TPSSrevTPSS LC-PKZBPKZB LC-BRxBRc LC-HCTH LC-τHCTH LC-M06-L LC-M11-L LC-N12

0.985 0.985 0.986 0.985 0.983 0.982 0.983 0.960 0.983

results.) For instance, Iché-Tarrat and Marsden found that the RECPs that they tried yielded poor 19F NMR predictions in UVI complexes,129 yet Bayse had success in using an RECP on atoms other than Se in the prediction of 77Se chemical shifts (at least similar errors were obtained with an RECP and in allelectron calculations).130 Cosentino et al. found that the choice of RECP core was significant in the prediction of 13C chemical shifts in lanthanide(III) complexes.131 In particular, a heavy atom situated next to light atoms has been shown to have a significant influence on the chemical shifts of the light atoms the so-called HALA effect.132 Rusakov et al. systematically considered the effects of 3p and heavier groups 13−17 atoms (i.e., the heavy atom or HA) on 13C (i.e., the light atom or LA) chemical shifts and found that these effects become increasingly more important (and hence less ignorable) as one descends the periodic table.132 To properly account for relativistic effects, more rigorous two- or four-component methods, with special basis sets, may be required. Because of the inherent complexity of considering relativistic effects and the need for specialized codes and basis sets, this is beyond the scope of this study, especially given the intended focus on organic molecules where heavy atoms are less common. Nonetheless, it should be noted ́ et al. have presented a recommended methodology that Vicha for calculating chemical shifts in platinum and iridium complexes;133 it is reasonable that this should be transferable to other transition metal and heavy main-group systems. Recommended Sets of Parameters. Based on the above results, a recommended methodology can be suggested. From Table 7 either CSGT or IGAIM is recommended over the more popular GIAO method. Of the DFT exchange-correlation functionals tested, LC-BRxPBE (±6.6 ppm), LC-PKZBPKZB (±6.7 ppm), LC-PKZBPBE (±6.7 ppm), LC-TPSSTPSS (±6.7 ppm), LC-revTPSSrevTPSS (±6.7 ppm), and LC-OPBE (±6.7 ppm) were the best performers. While the choice of grids did not seem to affect the accuracy of the results (Table 1), too small a grid is not recommended, and, thus, the default grids in GAUSSIAN09 can be used. Based on Table 2, one could use either a Dunning basis set (either cc-pVTZ or aug-cc-pVDZ) or the IGLO-III basis set. However, since the latter is available only for a limited set of elements, the former is recommended. Not only are they available for the first row transition metals, but if a heavier nucleus is present in the molecule, Peterson’s cc-pVnZPP RECP-basis set134 can be used in conjunction with the corresponding Dunning basis set (after first evaluating its performance as noted above). While the accuracy provided by DFT is sufficient for predicting 13C chemical shifts, even the smallest error (MN12SX and LC-τHCTH at 0.27 ppm) is far too large for accurate 1 H chemical shift predictions, although this might suffice if one were interested in trends rather than absolute values. In summary, the recommended method would be CSGTLC-TPSSTPSS/cc-pVTZ. While LC-BRxPBE and LCPKZBPKZB did have a slightly lower errors, LC-TPSSTPSS is recommended since this functional is more commonly available in the various DFT codes. Having determined a recommended level of theory, the effect of the choice of the level of theory of the geometry optimizations was considered. All geometries were reoptimized using the LC-TPSSTPSS and the related TPSSTPSS XC functionals (with density-fitting), and the NMR evaluations are given in Table 10. Clearly there is an advantage to using LC-TPSSTPSS/def2-SVP geometries. It has been noted that meta-GGA functionals tend to be more

δ(1H) 2

se(δ)

R

se(δ)

6.71 6.71 6.66 6.81 7.23 7.44 7.32 11.15 7.30

0.986 0.987 0.986 0.986 0.988 0.989 0.987 0.984 0.987

0.299 0.296 0.305 0.298 0.274 0.270 0.292 0.323 0.295

Table 7. Evaluation (coefficient of determination R2 and standard error se(δ) in ppm) of the Choice of NMR Method on the Accuracy of the 1H and 13C NMR Chemical Shift Predictions Using the SMD-PBE0/def2-TZVPD Level of Theory δ(13C)

δ(1H)

functional

R2

se(δ)

R2

se(δ)

GIAO CSGT IGAIM SO

0.966 0.980 0.980 0.926

10.20 7.88 7.88 15.07

0.980 0.986 0.986 0.158

0.359 0.302 0.302 2.35

Table 8. Evaluation (coefficient of determination R2 and standard error se(δ) in ppm) of the Solvation Model on the Accuracy of the 1H and 13C NMR Chemical Shift Predictions Using the GIAO NMR Method Using the PBE0 ExchangeCorrelation Functional and the def2-TZVPD Basis Set δ(13C)

a

δ(1H)

solvation modela

R2

se(δ)

R2

se(δ)

SMD IEF-PCM COSMO CPCM

0.966 0.978 0.978 0.978

10.20 8.29 8.22 8.28

0.980 0.985 0.988 0.985

0.359 0.314 0.283 0.310

See Computational Methods section for details on each method.

Table 9. Evaluation (coefficient of determination R2 and standard error se(δ) in ppm) of the Impact of Relativistic Effects (DKH model) on the Accuracy of the 1H and 13C NMR Chemical Shift Predictions Using the PBE0 ExchangeCorrelation Functional and the SMD Solvation Model and Run Using NWCHEM δ(13C) 2

functional

R

PBE0/def2-TZVP PBE0/TZP-DKH SSB-D/def2-TZVP SSB-D/TZP-DKS

0.977 0.976 0.967 0.966

δ(1H) 2

se(δ)

R

8.36 8.60 10.04 10.24

0.986 0.987 0.979 0.980

se(δ) 0.299 0.295 0.372 0.365

relativistic effective core potential (RECP) on heavy atoms. However, in some cases this has been shown to be insufficient. (This is particularly true when calculating coupling constants (J) where an RECP could lead to physically meaningless 5806


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Journal of Chemical Theory and Computation Table 10. Evaluation (coefficient of determination R2 and standard error se(δ) in ppm) of the Recommended Methodology (COSMO-CSGT-LC-TPSS/cc-pVTZ) for 1H and 13C NMR Chemical Shift Predictions Using Geometries Optimized at Different Levels of Theory δ(13C)

corrections becomes increasingly more computationally expensive as the size of the system increases. Auer et al. calculated ΔσZPV for a series of small molecules (acetone and smaller) at the HF and MP2 levels and found corrections in the range of −0.5 to −4.5 ppm.136b While not negligible when considering absolute shieldings, they are highly systematic and their impact will be lessened when calculating chemical shifts. Moreover, if one uses linear regression to determine chemical shifts from the isotropic shifts, any missing systematic error should, at least in part, be accounted for in the regression, thereby even further reducing their impact. In a different study, Teale et al. found that including vibrational corrections to the equilibrium geometry (i.e., adding ΔσZPV) actually worsened the results when using DFT, although they did help when using coupled cluster methods.18 The rotational corrections were found to be around 2 orders of magnitude or more smaller135 and thus will have even less impact on the chemical shifts. The zero-point vibrational corrections ΔσZPV were calculated using the suggested level of theory (COSMO(CH2Cl2)-LCTPSSTPSS/cc-pVTZ//DF-LC-TPSSTPSS/def2-SVP). For the most part, the corrections for 13C are between −1 and 0, and the average value is −0.15 ppm. However, this value is skewed by CCl4, where the correction is actually positive and large (13.44 ppm), possible because the carbon atom is surrounded by four heavier atoms. Other systems that have large magnitude corrections include TMS (average −2.25 ppm), CHCl3 (−2.36 ppm), and formic acid (0.49 ppm). For 1H, the corrections are between −0.5 and 0.4 ppm and therefore will have a larger impact. However, for both nuclei the improvement obtained by calculating the zero-point vibrational corrections (Table 11) is small, especially considering the need of the cubic force constants that are so costly to calculate and scale so rapidly with system size (see Table S2 for a selected timings); this is going to be especially true with the sizes of the systems considered in the Results and DiscussionCase Studies section. Given that the rotational−vibrational corrections were previously found to be at least 2 orders of magnitude smaller,135 they were not considered here. Modified DP4 Probability. Smith and Goodman recently proposed the DP4 probability to assign computed structures to a set of experimental data138 (which was subsequently improved upon by Grimblat et al.139). If the molecule has N NMR signals and M possible structures being considered, they defined the DP4 probability as

δ(1H)

level of theory for geometry optimization

R2

se(δ)

R2

se(δ)

DF-PBE/def2-SVP DF-TPSSTPSS/def2-SVP DF-LC-TPSSTPSS/def2-SVP

0.982 0.982 0.986

7.45 7.51 6.48

0.984 0.983 0.981

0.327 0.336 0.350

sensitive to grid issues,113f but this was not observed here (see SI, Table S1). Rotational−Vibrational Corrections. Molecular properties that do not depend on the nuclear momentumsuch as NMR isotropic shifts (σ)can be calculated within the Born− Oppenheimer approximation. Within this approximation, the value is not equal to the value for the equilibrium (i.e., corresponding to a minimum on the potential energy surface) geometry (i.e., σeq), as is customarily done, but rather as the expectation value of the property as a function of nuclear coordinates σ(q): ⟨σ ⟩ =

⟨Ψ σ(q) Ψ⟩ ⟨Ψ Ψ⟩

where Ψ is the nuclear wave function of the appropriate vibrational state. This difference Δσ = σ − σeq can be calculated in different ways, although a convenient derivation using perturbation theory to give the zero-point vibrational (ZPV) correction gives135 Δσ ZPV =

1 4

nfreq

∑ i=1

1 ∂ 2σ · ωi ∂qi2

− q=0

1 4

nfreq

∑ i=1

1 ∂σ · ωi ∂qi

nfreq

∑ q=0 j=1

ϕijj ωj

where nfreq is the number of vibrational frequencies (equal to the number of degrees of freedom), ωi is the harmonic frequency of the ith normal mode, ϕijk is the reduced cubic force constant with respect to these normal modes, and qi is the reduced normal coordinate.135,136 The corresponding rotational−vibrational correction, which adds temperature dependence, is Δσ

ro − vib

1 =− 2 −

+

nfreq

∑ i=1

kBT 2πc 1 4

nfreq

∑ i=1

1 ∂σ · ωi ∂qi

⎛ nfreq ϕ ⎛ hcωi ⎞ ijj ·⎜⎜∑ ·coth⎜ ⎟ ⎝ 2kBT ⎠ j = 1 ωj q=0 ⎝

1 hcωi

∑ α=x ,y,z

i ⎤ ⎛ |δcomp , k − δexp, k| − μ ⎞ N ⎡ ⎟⎥ ∏k = 1 ⎢1 − T ν⎜ σ ⎝ ⎠⎦ ⎣ PDP 4(i) = |Δδ| − μ ⎤⎤ M ⎡ N ⎡ ∑ j = 1 ⎣⎢ ∏k = 1 ⎣1 − T ν ⎦⎦⎥ σ

⎞ aiαα ⎟ e ⎟ Iαα ⎠

⎛ hcωi ⎞ ∂ 2σ 1 ·coth⎜ ⎟· ωi ⎝ 2kBT ⎠ ∂qi2

(

)

Table 11. Evaluation (coefficient of determination R2 and standard error se(δ) in ppm) of the Effects of the Zero-Point Vibrational (ZPV) Corrections on the Preferred Methodology (COSMO-CSGT-LC-TPSS/cc-pVTZ) for 1H and 13C NMR Chemical Shift

q=0

Ieαα

where is the effective moment of inertia with respect to the normal mode and aiαα is the linear expansion coefficient of Ieαα.137 Because one needs the cubic force constants and the derivatives of the isotropic shifts (which themselves are already a second-derivative property, once with respect to the external magnetic field and once with respect to the nuclear magnetic moments of the atomic nuclei), the calculation of these

δ(13C) R uncorrected ZPV-corrected 5807

2

0.982 0.984

δ(1H) 2

se(δ)

R

7.51 7.07

0.983 0.986

se(δ) 0.336 0.306



■

where Tν is the cumulative Student t-distribution function with ν degrees of freedom, μ is the mean of the t distribution, and σ is the standard deviation. Since the NMR chemical shifts are scaled against the empirical data, μ = 0. Smith and Goodman found σ = 2.306 ppm and ν = 11.38 by fitting calculated (gasphase GIAO-B3LYP/6-31G(d,p)) and experimental 13C NMR shifts. The DP4 parameters for the method of choice found here were determined using the approach used by Smith and Goodman.138 Starting from the geometries in their paper, the geometries were reoptimized at the DF-LC-TPSSTPSS/def2SVP/def2-SV level of theory and the NMR isotropic shifts were calculated at the COSMO(solvent)-CSGT-LC-TPSSTPSS/ccpVTZ level of theory (solvent = solvent used in the experimental studies).140 The original DP4 equation has terms involving the

( |Δδσ| − μ ). The intent

is to have terms involving the probability of the error being greater than |Δδ| (i.e., the [|Δδ|, ∞] tail of the t-distribution function), but the use of the cumulative distribution function x T ν(x) = ∫−∞ t ν(t ) dt (where tν(x) is the probability distribution function used in the fitting), which is the probability that the error is less than x, means that the [−∞, −|Δδ|] tail is not consideredthe Student t-distribution is after all an even function symmetric around zero. The t-distribution curve is fit using Δδ, which can be both positive or negative. Thus, what one really wants are terms involving one minus twice the probability the error is between 0 and |Δδ|, or, with the assistance of Wolfram Mathematica 10: ⎡1 ν⎤ 1 − 2(T ν(x) − T ν(0)) = 1 − Iz⎢ , ⎥ ⎣2 2⎦

where x2 x +ν

x=

|Δδ| − μ σ

2

Table 12. Evaluation (coefficient of determination R2 and standard error se(δ) in ppm) of the LC-TPSSTPSS DFT Functional with the cc-pVTZ Basis Set, COSMO Solvation Model, and the CSGT NMR Method for 1H and 13C NMR Chemical Shift Predictions in Various Solvents and the Associated Linear Regression Parameters

and Iz[a, b] is the regularized incomplete beta function (equivalent to the cumulative beta distribution function).141 (A more complete explanation and derivation is presented in the SI along with two alternate derivations.) Thus, the modified DP4 probabilities are

P DP͠ 4(i) =

1 ν N ∏k = 1 1 − I zki ⎡⎣ 2 , 2 ⎤⎦

(

(

(

δ(13C) solvent

)

M 1 ν N ∑ j = 1 ∏k = 1 1 − I zkj⎡⎣ 2 , 2 ⎤⎦

RESULTS AND DISCUSSIONCASE STUDIES

A number of previously reported studies using DFT to predict NMR spectra were reexamined here. Hitherto, all of the evaluations were done in DCM solution (unless noted otherwise), but the literature studies involved other solvents (chloroform, methanol, and benzene). The LC-TPSSTPSS/ccpVTZ calibrations were repeated in these solvents, and the results are shown in Table 12. Samoquasine A. Samoquasine A, a benzoquinazoline alkaloid isolated from the seeds of Annona squamosa (custard apple), was isolated in 2000 and assigned structure 1a (Scheme 1).142 Compounds isolated from this tree have been shown to have various medicinal properties, including antiulcer143 and cytotoxic144 activities. After preparing 1a and determining that this is not the structure of the isolated samoquasine A, Yang et al. proposed an alternate structure (1b).145 A DFT study by Timmons and Wipf later proposed this same alternate structure (1b) based on comparison of calculated and experimental 13C NMR spectra.146 Nonetheless, 1b (also known as perlolidine) had previously been ruled out.147 Two other isomers (1c and 1d) were prepared by Monsieurs et al., characterized by NMR and powder X-ray diffraction, and conclusively demonstrated not to be samoquasine A.148 Thus, to the best of our knowledge, the structure of samoquasine A remains uncertain. Here, starting from the geometries of the 48 isomers provided by Timmons and Wipf in the SI to their paper,146 we applied our recommended methodology. All the geometries were reoptimized so that all calculations are consistent. From these structures, the 1H and 13C NMR spectra were calculated. As Timmons and Wipf did, the experimental and calculated chemical shifts were sorted numerically (vide infra), and the absolute differences (|Δδ|) between the experimental and each calculated spectrum were determined. Plotting the experimental shifts versus the calculated isotropic shifts gives the regression parameters to determine the calculated chemical shifts. Whereas Timmons and Wipf only used max(|Δδ|) to determine

cumulative Student t-distribution 1 − T ν

z=

Article

CH2Cl2 CHCl3 C6H6a MeOHb

))

where zki =

xi , k =

xi2, k xi2, k + ν i i |δscaled , k − δexp, k| − μ

R

2

0.986 0.986 0.986 0.976 δ(13C)

δ(1H) 2

se(δ)

R

6.56 6.42 6.45 8.70

0.982 0.982 0.987 0.890

se(δ) 0.343 0.344 0.291 0.804 δ(1H)

solvent

m

b

m

b

CH2Cl2 CHCl3 C6H6 MeOH

−0.9109 −0.9112 −0.9156 −0.9064

181.28 180.99 181.47 180.90

−0.9661 −0.9766 −0.9692 −0.9046

30.254 30.585 30.103 28.653

a

σ

The CH3OH signal, observed in DCM-d2, was not observed experimentally in C6D6, while the tBuOH was observed in C6D6 but not in DCM-d2. bThe alcohol OH and the pyrrole NH signals were not observed in CD3OD but were (except tBuOH) in DCM-d3.

Here, the obtained parameters for 13C are μ = 0 ppm, σ = 2.88 ppm, and ν = 19.26. 5808


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epoxide with five chiral carbon centers (Scheme 2). It is a good example of a system with multiple stereocenters whose structure has been identified by comparing experimental and calculated structures; a published crystal structure has not been reported. Fattorusso et al. identified a likely structure based on experimental NMR spectroscopic methods and then suggested one of the diastereomers based on comparison with calculated spectra. The geometries of the four structures suggested by Fattorusso et al. were optimized (single, fully optimized structure, no conformational analysis), and the associated 13C chemical shifts were calculated following the methodology used for samoquasine A. Structure A has the lowest MAD (1.1 ppm, Table 14) and 100% modified DP4 probability. The structure with the next lowest MAD is B (2.5 ppm); Fattorusso et al. had ruled out B based on the small 3JHH coupling constant between H8 (on the same carbon as the OH group) and H9 (on the adjacent carbon fused with the cyclobutane ring). The small coupling constant measured (1.5 Hz) is consistent with the dihedral angle ϕ(H8−H9) = −73.1° in A, but not with B (ϕ = 169.1°). This is also supported by the calculated corresponding 3 JHH constants (1.8 and 11.7 Hz for A and B, respectively; Table S4). Glabramycins B and C. Glabramycins B and C (Scheme 3) were isolated by Jayasuriya et al. from the Neosartorya glabra fungus in an attempt to find new, clinically useful antibiotics.150 These compounds have four stereocenters. Li recently reported a DFT NMR study in order to determine their structures.151 Jayasuriya et al. initially assigned the structure as (10S,11R,15R,20?) (or its enantiomer, where the chirality of C20 was not assigned) based on comparison to the structure of glabramycin A, whose NMR spectra were assigned based on various 2D NMR techniques.150 Li later, based on DFT calculations of the NMR chemical shifts, revised the structure to (10S,11S,15R,20S) (or its enantiomer) where C11 was inverted and the chirality of C20 was determined. Jayasuriya et al. assigned a trans-ring fusion (i.e., 10S,11R,15R or its enantiomer) based on the triplet resonance of H10 with 3JHH = 9.6 Hz, indicative of two pairs of trans-oriented hydrogen atoms. Nonetheless, because the 10-membered ring is more flexible, a cis-ring fusion has to be considered. Barfield and Smith found an empirical relation between the θ(H−C−C) angles and the ϕ(H−C−C−H) dihedral and the vicinal 3JHH coupling constants;152 using the DFT-optimized structures of all eight candidate structures each for glabramycin B and C and Smith and Barfield’s relation, all 16 structures would have two vicinal coupling constants of ∼9.6−10.7 Hz (see Table S5). However, Li only considered two (and froze a third) of the stereocenters (C11 and C20) and thus neglected four candidate

Scheme 1. Selected Potential Structures of Samoquasine A

which is the most likely structure of samoquasine A, here the mean absolute deviation (MAD) is also used. Timmons and Wipf numerically sorted the experimental and calculated chemical shifts and aligned the resulting lists.146 This assumes that the order of primary (CH3), secondary (CH2), tertiary (CH), and quaternary (C) carbons is the same in both lists; experimentally, this information is readily available from various NMR experiments like 13C-DEPT or HMBC. Sorting numerically can lead to deceptively small errors (cf. the errors for 1a,b in Table 13 with the “unsorted” errors of 3.5 and 7.8 ppm for 1a and 2.2 and 5.1 ppm for 1b); moreover, 1i would be predicted as the most probable structure with MUE, max(|Δδ|) and P DP4 probability of 1.5 ppm, 4.5 ppm, and ͠ 70.5%, respectively. Therefore, here the signals are sorted by type before being sorted numerically. The results for selected structures are given in Table 13 while the full set is given in the SI (Table S3). Structures 1a−d, which have already been ruled out, have large errors. Based on MUE of the 13C spectra, the most likely structures for samoquasine A is 1e, with the lowest MUEs and max(|Δδ|) and highest P DP4 ͠ probability. One could also consider, in decreasing likelihood, 1f−h. Artarborol. Artarborol−isolated by Fattorusso et al. from tree wormwood (Artemisia arborescens)149 − is a tricyclic Table 13. Mean Unsigned (MUE) and Maximum Absolute (max(|Δδ|)) Errors (both in ppm) of Selected Potential Structures of Samoquasine A and Associated Modified DP4 Probabilitiesa

a

structure

MUE

max(|Δδ|)

P DP4 ͠ (%)

1a 1b 1c 1d 1e 1f 1g 1h 1i

4.9 3.9 7.0 6.5 2.1 2.5 2.7 2.6 5.7

21.0 11.1 19.8 19.3 4.4 6.1 5.8 8.3 20.1

0.0 0.0 0.0 0.0 90.5 4.6 2.8 1.9 0.0

Scheme 2. Structure of Artaborol and the Stereochemisty of the Four Structures Considereda

a

See Table S3 in the SI for the full set of data. 5809

Drawn is structure A. DOI: 10.1021/acs.jctc.7b00772 J. Chem. Theory Comput. 2017, 13, 5798−5819

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rather than sorting the experimental and computational shifts, one obtains the same preferred structures but with larger errors (see Table S6). Using assignments is reliable (and probably recommended) if one can be assured that the assignments are correct. However, just looking at the data presented in the original Jayasuriya paper,150 it is apparent that C19 of glabramycin C is misassigned: in glabramycin A this signal is at 33.9 ppmthe highest of the four CH2 units of the 10membered ring, but in glabramycin C the highest signal (32.4 ppm) is assigned to C18. Here the signals are sorted, rather than using Jayasuriya et al.’s assignments, and this swapping of C18/ C19 signals is apparent from these calculated spectra. In addition, one notes that in glabramycin C, the signals assigned to the CH units C11 and C20 may need to be swapped (this can depend on which conformer is considered), as do the CH2 units of the reduced double bond C12 and C13 in glabramycin B. The calculated spectra of the favored diastereomers, with the new spectral assignments, are given in Table S7. Given the very small differences between the two sets of candidate structures, one should try to consider another identifying factor. In this case, there is a characteristic H−H coupling: 3JHH of H10. In glabramycin B this is a triplet with 3 JHH = 9.6 Hz while in glabramycin C a doublet of doublets with 3JHH = 10 and 4.5 Hz. These vicinal coupling constants were calculated (Table S8). For glabramycin B, the SSSS conformer has 3 JH H = 10.4 Hz and 3 JH H = 10.2 Hz, while

Table 14. Mean Unsigned (MUE) and Maximum Absolute (max(|Δδ|)) Errors (both in ppm) of the Four Conformers of Artaborol and Associated Modified DP4 Probabilities structure

MUE

max(|Δδ|)

P DP4 ͠ (%)

A B C D

1.1 2.6 4.3 3.3

2.9 6.0 10.2 8.8

100.0 0.0 0.0 0.0

Scheme 3. Structures of Glabramycins B (left) and C (right) Showing the Labelling of the Four Stereocenters

structures. Here, all eight possible enantiomer pairs are considered. The errors and modified DP4 probabilities for all eight isomers of glabramycin B and C are given in Table 15. Here again experimental and calculated shifts are sorted for each CHn type. In each case a different structure is predicted, which also differ from the predictions of Li.151 It should be noted, however, that the errors obtained are significantly lower than in the benchmark study (Table 12) and on the order of the standard deviation (σ = 2.88 ppm, vide supra) obtained for the DP4 fit set; one thus has to question how meaningful are the small differences in MUE and max(|Δδ|), even within a probability analysis like the modified DP4. Jayasuriya et al. assigned the NMR spectra of glabramycins B and C from the assigned spectrum of glabramycin A, and Li used these same assignments. If one uses these assignments

10 11

10 11

SRRR SRRS SSRR SSRS SRSR SRSS SSSR SSSS SRRR SRRS SSRR SSRS SRSR SRSS SSSR SSSS

MUE

max(|Δδ|)

Glabramycin B 3.1 2.8 2.5 2.7 2.2 2.6 2.8 2.8 Glabramycin C 3.8 3.1 2.5 2.7 2.8 2.7 2.7 2.8

P DP4 ͠ (%)

7.9 9.0 8.6 7.6 7.2 9.5 9.2 7.9

0.0 0.0 0.0 0.0 100.0 0.0 0.0 0.0

10.4 10.1 7.0 6.1 10.0 6.4 9.7 7.0

0.0 0.0 100.0 0.0 0.0 0.0 0.0 0.0

10 15

while these values do not exactly agree with experiment, the trend is apparent, and they are in better agreement with experiment than the values of 11.1 and 13.8 Hz calculated for the SSRS isomer. Elatenyne. Elatenyne is a compound with six stereocenters isolated from the marine red alga Laurencia elata.153 Originally identified, based on NMR spectroscopy, as a [2,2′]bifuranyl,153 a subsequent computational study suggested that a pyranopyran structure would be more consistent with the measured 13C {1H} NMR spectra154 a premise supported by recent synthetic and crystallographic studies.155 With six stereocenters (Scheme 4), there are 32 pairs of diastereomers. Starting from the structures from the SI of the paper by Smith et al., the geometries of the 32 diastereomers, as well as the originally proposed structure, were optimized, and their 13C chemical shifts were calculated. Because there are several rotatable bonds, a conformer search was done to provide a series of conformers from which Boltzmann-weighted average spectra were obtained. As with Samoquasine A, the experimental and calculated shifts were sorted by CHn-type and compared to each other. One could either calibrate the chemical shifts against the small molecule set or use the regression analysis of the experimental versus calculated

Table 15. Mean Unsigned (MUE) and Maximum Absolute (max(|Δδ|)) Errors (both in ppm) of the Eight Diastereomeric Pairs of Glabramycin B and C and the Associated Modified DP4 Probabilities stereochemistrya

10 15

for the SSRS isomer suggested by Li, these coupling constants are 13.5 and 14.9 Hz, significantly higher. For glabramycin C, 3 JH H = 12.0 Hz and 3 JH H = 7.7 Hz for the SSSS isomer;

Scheme 4. Originally Proposed (left) and Revised (right) Structures of Elatenyne, the Latter Showing the Stereocenter Labelling

a

Stereochemistry given in the form (10S,11R,15R,20R) etc. where the stereocenters are labeled as in Scheme 3. 5810


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Journal of Chemical Theory and Computation isotropic shifts. The latter method was used, and the structures with the lowest MUEs and max(|Δδ|) are listed in Table 16. While the structure (actually the enantiomer) that had subsequently been indentified by X-ray crystallography by Urban et al.155b (12−22 using Smith’s notation, see Scheme 4) was found to be fifth-most probable, it should be noted that the differences in MUE are smaller than the expected method error (vide supra); in fact, 12 isomers have MUEs less than 3.5 ppm. It should be noted that the originally proposed structure (11) has the highest MUE of all structures considered. The sole use of calculated 13C NMR spectra may be suitable for samoquasine A, where major structural differences are considered, or artaborol, which only has a few stereocenters, but for systems like elatenyne this becomes questionable. This system has many stereocenters (six), and the differences between diastereomers is small, especially compared to the changes in samoquasine A where the ring backbone structure is changed. As a result, many structures with similar spectra and MUEs are obtained, and even the use of probability-based methods, like P DP4 ͠ , may be dubious. On the other hand, the calculated NMR spectra can be used in conjunction with other spectroscopic methods, many of which can be predicted computationally; this has already been suggested in recent reviews by Petrovic et al.156 and by Tantillo.157 For artaborol and Glabramycins B and C (vide supra) an identifying proton coupling constant was calculated. Another example is vibrational circular dichroism (VCD) spectra118 that have positive and negative features unique to each diastereomer. The Boltzmann-weighted VCD spectra of the top five elatenyne candidates are shown in Figure 2. For instance, 12.32, 12.25, and 12.7 have strong features in the 900−1200 cm−1 region, while the features of 12.22 and 12.27 in this region are not as prominent. In addition, at 2700−2800 cm−1, 12.22 has a positive feature (actually positive−negative “doublet”), whereas the other four have negative features. The most important feature is that at ∼3300 cm−1 all five have a negative peak, and this can be used to determine whether this or the opposite enantiomer is present. VCD is a simple spectrum to measure experimentally (although without calculated predictions it

Figure 2. Boltzmann-averaged vibrational circular dichroism (VCD) spectra of the five most probable conformers of elatenyne. Three ranges are shown: top, 500−1500 cm−1; middle, 2700−3100 cm−1; bottom, 3200−3400 cm−1. There are no signals outside of these ranges (red, 12.32; blue, 12.25; green, 12.7; magenta, 12.27; black, 12.22).

Table 16. Mean Unsigned (MUE) and Maximum Absolute (max(|Δδ|)) Errors (both in ppm) of Selected Potential Structures of Elatenyne and the Associated Modified DP4 Probabilitiesa structure

stereochemistryb

MUE

max(|Δδ|)

P DP4 ͠

12.32 12.25 12.7 12.27 12.22 12.26 12.30 12.10 12.14 12.4 12.16 12.20 11

RSSSSS RSSRRR RRRSSR RSSRSR RSRSRS RSSRRS RSSSRS RRSRRS RRSSRS RRRRSS RRSSSS RSRRSS

2.9 2.9 3.1 3.2 3.2 3.3 3.3 3.3 3.2 3.3 3.4 3.4 4.8

5.8 10.6 9.1 6.8 8.1 6.4 8.5 9.5 10.2 10.5 9.3 11.0 10.1

75.6 9.7 4.6 2.4 1.7 1.7 1.3 0.6 0.6 0.1 0.1 0.1 0.0

would be challenging to predict positive and negative features and thus assign an absolute configuration) and, in combination with the predicted NMRand perhaps otherspectra, provides a more reliable method to assign stereochemistry. Moreover, as opposite enantiomers have opposite VCD spectra, with VCD it would be possible to assign the absolute configuration, which would not be possible with NMR alone.

■

CONCLUSIONS A comprehensive study of the factors affecting the calculations of chemical shifts is presented. It was found that long-range corrected functionals, which to date have yet to be considered, outperform the other classes of functionals. Thus, based on the results of this study, it is recommended that one use the COSMO-CSGT-LC-TPSSTPSS/cc-pVTZ level of theory for one’s simulations of NMR chemical shifts. While this level of theory is computationally more expensive than some of the

a

See Table S9 for full set of data. bStereochemistry given in the form (6R,7R,9R,10R,12R,13R) etc. where the stereocenters are labeled as in Scheme 4. 5811


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Table 17. Amounts of cpu Time (hh:mm:ss) As Reported by GAUSSIAN09 Required To Calculate the Chemical Shifts for Selected Moleculesa gas phase GIAO-B3LYP/6-31G(d,p) PCM-GIAO-B3LYP/6-31G(d,p) PCM-GIAO-B3LYP/6-311+G(2d,p) PCM-GIAO-B3LYP/cc-pVTZ COSMO-CSGT-LC-TPSSTPSS/cc-pVTZ a

samoquasine A (1a)

artaboral (A)

elatenyne (12−1)

glabramycin B (SRRR)

glabramycin C (SRRR)

5:21 7:20 46:12 2:13:17 2:18:05

18:17 21:03 2:23:33 6:36:22 6:53:44

17:08 21:46 2:44:12 8:04:47 6:45:31

33:30 36:40 5:49:40 15:28:55 14:16:26

31:40 35:04 5:39:55 14:15:40 13:18:25

All calculations were run on 8 cores of a E5-2670, E5-2630, E5-2650-v2, or E5-2660-v2 processor.

■

levels used in studies cited herein (see Table 17), the cost is not prohibitive, and the improved accuracy obtained is well worth the additional cost. Some studies use mPW1PW91 instead of B3LYP, but given that both are hybrid functionals, both should require similar computational cost. The B3LYP/cc-pVTZ level of theory was added, even though it was not used in any cited study, as it uses a “conventional” functional in combination with the larger basis set. Being a hybrid functional, it is understandably more expensive than the GGA for the larger systems. Furthermore, a GGA functionalsuch as LCTPSSTPSSshould scale more favorably with size than a hybridsuch as B3LYP or mPW1PW91; this should allow one to study larger systems. While the proper choice of method and related parameters can significantly improve the accuracy of the prediction of NMR spectra, one should still remember the limitations of the method. When the differences between candidate structures are small, such as in the case of multiple stereocenters, the minute differences may be too small to be definitive in differentiating between structures. In such cases, and as a general rule, one should also consider other identifying properties, such as spin− spin coupling constants or vibrational circular dichroism (VCD). While only 13C chemical shifts were considered, the findings here are likely also transferable to other NMR-active nuclei, other than 1H where the errors are too large compared to the relatively narrow spectral window.

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(1) Schlegel, B.; Härtl, A.; Dahse, H.-M.; Gollmick, F. A.; Gräfe, U.; Dorfelt, H.; Kappes, B. Hexacyclinol, a New Antiproliferative Metabolite of Panus rudis HKI 0254. J. Antibiot. 2002, 55, 814−817. (2) (a) Porco, J. A., Jr.; Su, S.; Lei, X.; Bardhan, S.; Rychnovsky, S. D. Total Synthesis and Structure Assignment of (+)-Hexacyclinol. Angew. Chem., Int. Ed. 2006, 45, 5790−5792. (b) Mehta, G.; Roy, S. Enantioselective total synthesis of the novel antiproliferative metabolite (+)-hexacyclinol. Tetrahedron Lett. 2008, 49, 1458−1460. (c) Pinkerton, D. M.; Banwell, M. G.; Willis, A. C. (+)-Hexacyclinol. Acta Crystallogr., Sect. E: Struct. Rep. Online 2010, 66, o342−o343. (3) (a) Rychnovsky, S. D. Predicting NMR Spectra by Computational Methods: Structure Revision of Hexacyclinol. Org. Lett. 2006, 8, 2895−2898. (b) Williams, A. J.; Elyashberg, M. E.; Blinov, K. A.; Lankin, D. C.; Martin, G. E.; Reynolds, W. F.; Porco, J. A., Jr.; Singleton, C. A.; Su, S. Applying Computer-Assisted Structure Elucidation Algorithms for the Purpose of Structure Validation: Revisiting the NMR Assignments of Hexacyclinol. J. Nat. Prod. 2008, 71, 581−588. (c) Saielli, G.; Bagno, A. Can Two Molecules Have the Same NMR Spectrum? Hexacyclinol Revisited. Org. Lett. 2009, 11, 1409−1412. (4) (a) Bagno, A.; Saielli, G. Addressing the stereochemistry of complex organic molecules by density functional theory-NMR. WIREs Comput. Mol. Sci. 2015, 5, 228−240. (b) Grimblat, N.; Sarotti, A. M. Computational Chemistry to the Rescue: Modern Toolboxes for the Assignment of Complex Molecules by GIAO NMR Calculations. Chem. - Eur. J. 2016, 22, 12246−12261. (5) Saielli, G.; Nicolaou, K. C.; Ortiz, A.; Zhang, H.; Bagno, A. Addressing the Stereochemistry of Complex Organic Molecules by Density Functional Theory-NMR: Vannusal B in Retrospective. J. Am. Chem. Soc. 2011, 133, 6072−6077. (6) Willoughby, P. H.; Jansma, M. J.; Hoye, T. R. A guide to smallmolecule structure assignment through computation of (1H and 13C) NMR chemical shifts. Nat. Protoc. 2014, 9, 643−660. (7) Arava, S.; Kumar, J. N.; Maksymenko, S.; Iron, M. A.; Parida, K. N.; Fristrup, P.; Szpilman, A. M. Enolonium Species − Umpoled Enolates. Angew. Chem., Int. Ed. 2017, 56, 2599−2603. (8) Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Scuseria, G. E.; Robb, M. A.; Cheeseman, J. R.; Scalmani, G.; Barone, V.; Petersson, G. A.; Nakatsuji, H.; Li, X.; Caricato, M.; Marenich, A. V.; Bloino, J.; Janesko, B. G.; Gomperts, R.; Mennucci, B.; Hratchian, H. P.; Ortiz, J. V.; Izmaylov, A. F.; Sonnenberg, J. L.; Williams-Young, D.; Ding, F.; Lipparini, F.; Egidi, F.; Goings, J.; Peng, B.; Petrone, A.; Henderson, T.; Ranasinghe, D.; Zakrzewski, V. G.; Gao, J.; Rega, N.; Zheng, G.; Liang, W.; Hada, M.; Ehara, M.; Toyota, K.; Fukuda, R.; Hasegawa, J.; Ishida, M.; Nakajima, T.; Honda, Y.; Kitao, O.; Nakai, H.; Vreven, T.; Throssell, K.; Montgomery, J. A., Jr.; Peralta, J. E.; Ogliaro, F.; Bearpark, M. J.; Heyd, J. J.; Brothers, E. N.; Kudin, K. N.; Staroverov, V. N.; Keith, T. A.; Kobayashi, R.; Normand, J.; Raghavachari, K.; Rendell, A. P.; Burant, J. C.; Iyengar, S. S.; Tomasi, J.; Cossi, M.; Millam, J. M.; Klene, M.; Adamo, C.; Cammi, R.; Ochterski, J. W.; Martin, R. L.; Morokuma, K.; Farkas, O.; Foresman, J. B.; Fox, D. J. Gaussian 16, Revision A.03; Gaussian, Inc.: Wallingford, CT, 2016. (9) Shao, Y.; Gan, Z.; Epifanovsky, E.; Gilbert, A. T. B.; Wormit, M.; Kussmann, J.; Lange, A. W.; Behn, A.; Deng, J.; Feng, X.; Ghosh, D.; Goldey, M.; Horn, P. R.; Jacobson, L. D.; Kaliman, I.; Khaliullin, R. Z.; Kuś, T.; Landau, A.; Liu, J.; Proynov, E. I.; Rhee, Y. M.; Richard, R. M.;

ASSOCIATED CONTENT

* Supporting Information S

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jctc.7b00772. Additional tables and schemes and extended discussions on the modified DP4 probabilities and basis set extrapolation (PDF)

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REFERENCES

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. ORCID

Mark A. Iron: 0000-0001-9774-2358 Funding

Research was supported by a Staff Scientist Internal Grant from the Weizmann Institute of Science. Notes

The author declares no competing financial interest.

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ACKNOWLEDGMENTS The author would like to thank Prof. Alex Szpilman (Ariel University) for many fruitful discussions. 5812


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