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.

[1]  V. Barone,et al.  Quantum Calculation of Molecular Energies and Energy Gradients in Solution by a Conductor Solvent Model , 1998 .

[2]  Jacopo Tomasi,et al.  A new definition of cavities for the computation of solvation free energies by the polarizable continuum model , 1997 .

[3]  J. Gauss.  Effects of electron correlation in the calculation of nuclear magnetic resonance chemical shifts , 1993 .

[4]  Parr,et al.  Development of the Colle-Salvetti correlation-energy formula into a functional of the electron density. , 1988, Physical review. B, Condensed matter.

[5]  Giuseppe Bifulco,et al.  Comparison of different theory models and basis sets in the calculation of 13C NMR chemical shifts of natural products , 2004, Magnetic resonance in chemistry : MRC.

[6]  A. D. McLean,et al.  Contracted Gaussian basis sets for molecular calculations. I. Second row atoms, Z=11–18 , 1980 .

[7]  Michael J. Frisch,et al.  Self‐consistent molecular orbital methods 25. Supplementary functions for Gaussian basis sets , 1984 .

[8]  Giuseppe Bifulco,et al.  Determination of the relative stereochemistry of flexible organic compounds by Ab initio methods: conformational analysis and Boltzmann-averaged GIAO 13C NMR chemical shifts. , 2002, Chemistry.

[9]  P. C. Hariharan,et al.  Accuracy of AH n equilibrium geometries by single determinant molecular orbital theory , 1974 .

[10]  Kirk A. Peterson,et al.  Benchmark calculations with correlated molecular wave functions. IV. The classical barrier height of the H+H2→H2+H reaction , 1994 .

[11]  Jacopo Tomasi,et al.  Geometry optimization of molecular structures in solution by the polarizable continuum model , 1998 .

[12]  T. Dunning,et al.  Electron affinities of the first‐row atoms revisited. Systematic basis sets and wave functions , 1992 .

[13]  J. Tomasi,et al.  The IEF version of the PCM solvation method: an overview of a new method addressed to study molecular solutes at the QM ab initio level , 1999 .

[14]  K C Nicolaou,et al.  Chasing molecules that were never there: misassigned natural products and the role of chemical synthesis in modern structure elucidation. , 2005, Angewandte Chemie.

[15]  N. Handy,et al.  Left-right correlation energy , 2001 .

[16]  Nicholas C. Handy,et al.  Assessment of a new local exchange functional OPTX , 2001 .

[17]  K. Burke,et al.  Generalized Gradient Approximation Made Simple [Phys. Rev. Lett. 77, 3865 (1996)] , 1997 .

[18]  Jacopo Tomasi,et al.  Approximate evaluations of the electrostatic free energy and internal energy changes in solution processes , 1982 .

[19]  J. Goodman,et al.  Assigning the stereochemistry of pairs of diastereoisomers using GIAO NMR shift calculation. , 2009, The Journal of organic chemistry.

[20]  A. Bagno.  Complete prediction of the 1H NMR spectrum of organic molecules by DFT calculations of chemical shifts and spin-spin coupling constants. , 2001, Chemistry.

[21]  Dennis R. Salahub,et al.  Calculations of NMR shielding constants by uncoupled density functional theory , 1993 .

[22]  Jonathan M Goodman,et al.  Assigning stereochemistry to single diastereoisomers by GIAO NMR calculation: the DP4 probability. , 2010, Journal of the American Chemical Society.

[23]  D. Colombo,et al.  Stereochemical analysis of the 3α‐ and 3β‐hydroxy metabolites of tibolone through NMR and quantum‐chemical investigations. An experimental test of GIAO calculations , 2002 .

[24]  Gil Valdo José da Silva,et al.  Chemical shifts calculations on aromatic systems: a comparison of models and basis sets , 2004 .

[25]  R. Ditchfield,et al.  Self-consistent perturbation theory of diamagnetism , 1974 .

[26]  K. Pihlaja,et al.  Modeling NMR parameters by DFT methods as an aid to the conformational analysis of cis-fused 7a(8a)-methyl octa(hexa)hydrocyclopenta[d][1,3]oxazines and [3,1]benzoxazines. , 2003, Journal of the American Chemical Society.

[27]  D. Giesen,et al.  A hybrid quantum mechanical and empirical model for the prediction of isotropic 13C shielding constants of organic molecules , 2002 .

[28]  Jacopo Tomasi,et al.  Evaluation of Solvent Effects in Isotropic and Anisotropic Dielectrics and in Ionic Solutions with a Unified Integral Equation Method: Theoretical Bases, Computational Implementation, and Numerical Applications , 1997 .

[29]  Ying Zhang,et al.  Systematic studies on the computation of nuclear magnetic resonance shielding constants and chemical shifts: The density functional models , 2007, J. Comput. Chem..

[30]  Giovanni Vignale,et al.  Magnetic Fields and Density Functional Theory , 1990 .

[31]  T. Keith,et al.  A comparison of models for calculating nuclear magnetic resonance shielding tensors , 1996 .

[32]  A. Becke.  Density-functional thermochemistry. III. The role of exact exchange , 1993 .

[33]  Kim K. Baldridge,et al.  Correlation of Empirical δ(TMS) and Absolute NMR Chemical Shifts Predicted by ab Initio Computations , 1999 .

[34]  Todd A. Keith,et al.  Calculation of magnetic response properties using atoms in molecules , 1992 .

[35]  J. Pople,et al.  Self‐consistent molecular orbital methods. XX. A basis set for correlated wave functions , 1980 .

[36]  P. C. Hariharan,et al.  The influence of polarization functions on molecular orbital hydrogenation energies , 1973 .

[37]  F. London,et al.  Théorie quantique des courants interatomiques dans les combinaisons aromatiques , 1937 .

[38]  Shoshannah A. Pearlman,et al.  A Comparison Of Density Functional Methods For The Estimation Of Proton Chemical Shifts With Chemical Accuracy , 1999 .

[39]  T. H. Dunning.  Gaussian basis sets for use in correlated molecular calculations. I. The atoms boron through neon and hydrogen , 1989 .

[40]  Jacopo Tomasi,et al.  Second-Order Møller-Plesset Analytical Derivatives for the Polarizable Continuum Model Using the Relaxed Density Approach , 1999 .

[41]  Alessandro Bagno,et al.  Toward the complete prediction of the 1H and 13C NMR spectra of complex organic molecules by DFT methods: application to natural substances. , 2006, Chemistry.

[42]  J. Tomasi,et al.  Electrostatic interaction of a solute with a continuum. A direct utilizaion of AB initio molecular potentials for the prevision of solvent effects , 1981 .

[43]  D. Truhlar,et al.  Improved description of nuclear magnetic resonance chemical shielding constants using the M06-L meta-generalized-gradient-approximation density functional. , 2008, The journal of physical chemistry. A.

[44]  Peter Pulay,et al.  Efficient implementation of the gauge-independent atomic orbital method for NMR chemical shift calculations , 1990 .

[45]  John E. Bercaw,et al.  NMR Chemical Shifts of Trace Impurities: Common Laboratory Solvents, Organics, and Gases in Deuterated Solvents Relevant to the Organometallic Chemist , 2010 .

[46]  J. Pople,et al.  Self‐Consistent Molecular‐Orbital Methods. IX. An Extended Gaussian‐Type Basis for Molecular‐Orbital Studies of Organic Molecules , 1971 .

[47]  Giuseppe Bifulco,et al.  Structure validation of natural products by quantum-mechanical GIAO calculations of 13C NMR chemical shifts. , 2002, Chemistry.

[48]  R. Mcweeny.  Perturbation Theory for the Fock-Dirac Density Matrix , 1962 .

[49]  Trygve Helgaker,et al.  Ab Initio Methods for the Calculation of NMR Shielding and Indirect Spin-Spin Coupling Constants , 1999 .

[50]  A. Albuquerque,et al.  GIAO-HDFT scaling factor for 13C NMR chemical shifts calculation† , 2010 .

[51]  Rupal Jain,et al.  Calculating accurate proton chemical shifts of organic molecules with density functional methods and modest basis sets. , 2009, The Journal of organic chemistry.

[52]  T. Clark,et al.  Regression formulae for ab initio and density functional calculated chemical shifts , 2005, Journal of molecular modeling.

[53]  David Forsyth,et al.  Computed 13C NMR Chemical Shifts via Empirically Scaled GIAO Shieldings and Molecular Mechanics Geometries. Conformation and Configuration from 13C Shifts , 1997 .

[54]  Burke,et al.  Generalized Gradient Approximation Made Simple. , 1996, Physical review letters.

[55]  Jan M. L. Martin,et al.  Development of density functionals for thermochemical kinetics. , 2004, The Journal of chemical physics.

[56]  Gustavo E. Scuseria,et al.  A novel form for the exchange-correlation energy functional , 1998 .

[57]  O. Malkina,et al.  Chemical Shifts and Spin−Spin Coupling Constants in Me α-d-Xylopyranoside: A DFT Approach , 2001 .

[58]  John F. Stanton,et al.  Coupled-cluster calculations of nuclear magnetic resonance chemical shifts , 1967 .

[59]  Christopher J Cramer,et al.  Hybrid Density Functional Methods Empirically Optimized for the Computation of (13)C and (1)H Chemical Shifts in Chloroform Solution. , 2006, Journal of chemical theory and computation.

[60]  Giovanni Scalmani,et al.  New developments in the polarizable continuum model for quantum mechanical and classical calculations on molecules in solution , 2002 .

[61]  Todd A. Keith,et al.  Calculation of magnetic response properties using a continuous set of gauge transformations , 1993 .

[62]  Mark S. Gordon,et al.  The isomers of silacyclopropane , 1980 .

[63]  Alessandro Bagno,et al.  Predicting 13C NMR Spectra by DFT Calculations , 2003 .

[64]  Giovanni Scalmani,et al.  Polarizable dielectric model of solvation with inclusion of charge penetration effects , 2001 .

[65]  Alessandro Bagno,et al.  Can two molecules have the same NMR spectrum? Hexacyclinol revisited. , 2009, Organic letters.

[66]  Giuseppe Bifulco,et al.  Determination of relative configuration in organic compounds by NMR spectroscopy and computational methods. , 2007, Chemical reviews.

[67]  Jonathan M Goodman,et al.  Stereostructure assignment of flexible five-membered rings by GIAO 13C NMR calculations: prediction of the stereochemistry of elatenyne. , 2008, The Journal of organic chemistry.

[68]  T. Kupka,et al.  Convergence of Nuclear Magnetic Shieldings in the Kohn-Sham Limit for Several Small Molecules. , 2010, Journal of chemical theory and computation.

[69]  J. Tomasi,et al.  Ab initio study of ionic solutions by a polarizable continuum dielectric model , 1998 .

[70]  Jacopo Tomasi,et al.  A new integral equation formalism for the polarizable continuum model: Theoretical background and applications to isotropic and anisotropic dielectrics , 1997 .

[71]  D. Truhlar,et al.  The M06 suite of density functionals for main group thermochemistry, thermochemical kinetics, noncovalent interactions, excited states, and transition elements: two new functionals and systematic testing of four M06-class functionals and 12 other functionals , 2008 .

[72]  Ariel M. Sarotti,et al.  A multi-standard approach for GIAO (13)C NMR calculations. , 2009, The Journal of organic chemistry.

[73]  Jacopo Tomasi,et al.  Continuum solvation models: A new approach to the problem of solute’s charge distribution and cavity boundaries , 1997 .

[74]  J. Tomasi,et al.  Ab initio study of solvated molecules: A new implementation of the polarizable continuum model , 1996 .

[75]  Reko Leino,et al.  Conformation of the galactose ring adopted in solution and in crystalline form as determined by experimental and DFT 1H NMR and single-crystal X-ray analysis. , 2004, The Journal of organic chemistry.

[76]  Iñaki Tuñón,et al.  GEPOL: An improved description of molecular surfaces. III. A new algorithm for the computation of a solvent‐excluding surface , 1994, J. Comput. Chem..

[77]  E. Fattorusso,et al.  Isolation and Structure Determination of Aplidinones A‐C from the Mediterranean Ascidian Aplidium conicum: A Successful Regiochemistry Assignment by Quantum Mechanical 13C NMR Chemical Shift Calculations. , 2005 .

[78]  W. Kutzelnigg.  Theory of Magnetic Susceptibilities and NMR Chemical Shifts in Terms of Localized Quantities , 1982 .

[79]  Jörg Kussmann,et al.  Ab initio NMR spectra for molecular systems with a thousand and more atoms: a linear-scaling method. , 2004, Angewandte Chemie.

[80]  Mark S. Gordon,et al.  Self‐consistent molecular orbital methods. XXIII. A polarization‐type basis set for second‐row elements , 1982 .

[81]  Giovanni Scalmani,et al.  Continuous surface charge polarizable continuum models of solvation. I. General formalism. , 2010, The Journal of chemical physics.

[82]  J. Pople,et al.  Self—Consistent Molecular Orbital Methods. XII. Further Extensions of Gaussian—Type Basis Sets for Use in Molecular Orbital Studies of Organic Molecules , 1972 .