Benchmarking Hydrogen and Carbon NMR Chemical Shifts at HF, DFT, and MP2 Levels.

An extensive study of error distributions for calculating hydrogen and carbon NMR chemical shifts at Hartree-Fock (HF), density functional theory (DFT), and Møller-Plesset second-order perturbation theory (MP2) levels is presented. Our investigation employs accurate CCSD(T)/cc-pVQZ calculations for providing reference data for 48 hydrogen and 40 carbon nuclei within an extended set of chemical compounds covering a broad range of the NMR scale with high relevance to chemical applications, especially in organic chemistry. Besides the approximations of HF, a variety of DFT functionals, and conventional MP2, we also present results with respect to a spin component-scaled MP2 (GIAO-SCS-MP2) approach. For each method, the accuracy is analyzed in detail for various basis sets, allowing identification of efficient combinations of method and basis set approximations.

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

[2]  J. Pople,et al.  Self‐Consistent Molecular‐Orbital Methods. I. Use of Gaussian Expansions of Slater‐Type Atomic Orbitals , 1969 .

[3]  J. Pople,et al.  Self‐Consistent Molecular Orbital Methods. IV. Use of Gaussian Expansions of Slater‐Type Orbitals. Extension to Second‐Row Molecules , 1970 .

[4]  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 .

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

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

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

[8]  Mark S. Gordon,et al.  Self-consistent molecular-orbital methods. 22. Small split-valence basis sets for second-row elements , 1980 .

[9]  A. Jameson,et al.  Gas-phase 13C chemical shifts in the zero-pressure limit: refinements to the absolute shielding scale for 13C , 1987 .

[10]  A. Becke,et al.  Density-functional exchange-energy approximation with correct asymptotic behavior. , 1988, Physical review. A, General physics.

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

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

[13]  Hans W. Horn,et al.  Fully optimized contracted Gaussian basis sets for atoms Li to Kr , 1992 .

[14]  Hans W. Horn,et al.  Direct computation of second-order SCF properties of large molecules on workstation computers with an application to large carbon clusters , 1992 .

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

[16]  A. Becke A New Mixing of Hartree-Fock and Local Density-Functional Theories , 1993 .

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

[18]  M. Frisch,et al.  Ab Initio Calculation of Vibrational Absorption and Circular Dichroism Spectra Using Density Functional Force Fields , 1994 .

[19]  Dieter Cremer,et al.  Sum‐over‐states density functional perturbation theory: Prediction of reliable 13C, 15N, and 17O nuclear magnetic resonance chemical shifts , 1996 .

[20]  J. Gauss,et al.  A direct implementation of the GIAO-MBPT(2) method for calculating NMR chemical shifts. Application to the naphthalenium and anthracenium ions , 1996 .

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

[22]  David Feller The role of databases in support of computational chemistry calculations , 1996 .

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

[24]  Christian Ochsenfeld,et al.  A reformulation of the coupled perturbed self-consistent field equations entirely within a local atomic orbital density matrix-based scheme , 1997 .

[25]  J. Gauss,et al.  Analytic CCSD(T) second derivatives , 1997 .

[26]  Vincenzo Barone,et al.  TOWARD CHEMICAL ACCURACY IN THE COMPUTATION OF NMR SHIELDINGS : THE PBE0 MODEL , 1998 .

[27]  J. Gauss,et al.  NON-ABELIAN POINT GROUP SYMMETRY IN DIRECT SECOND-ORDER MANY-BODY PERTURBATION THEORY CALCULATIONS OF NMR CHEMICAL SHIFTS , 1998 .

[28]  Vincenzo Barone,et al.  Exchange functionals with improved long-range behavior and adiabatic connection methods without adjustable parameters: The mPW and mPW1PW models , 1998 .

[29]  Tom Ziegler,et al.  Calculation of DFT-GIAO NMR shifts with the inclusion of spin-orbit coupling , 1998 .

[30]  Vincenzo Barone,et al.  Accurate excitation energies from time-dependent density functional theory: Assessing the PBE0 model , 1999 .

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

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

[33]  J. Grotendorst,et al.  Modern methods and algorithms of quantum chemistry : winterschool 21. - 25. February 2000 Forschungszentrum Jülich : proceedings / org. by John von Neumann Institute for Computing , 2000 .

[34]  David J. Tozer,et al.  Hybrid exchange-correlation functional determined from thermochemical data and ab initio potentials , 2001 .

[35]  Trygve Helgaker,et al.  Geometrical derivatives and magnetic properties in atomic-orbital density-based Hartree-Fock theory , 2001 .

[36]  C. Ochsenfeld,et al.  A study of a moleculartweezer host-guest system by a combination of quantum-chemical calculations and solid-state NMR experiments. , 2002, Solid state nuclear magnetic resonance.

[37]  J. Pople,et al.  Self-consistent molecular orbital methods. 21. Small split-valence basis sets for first-row elements , 2002 .

[38]  Eric Oldfield,et al.  Carbon-13 NMR shielding in the twenty common amino acids: comparisons with experimental results in proteins. , 2002, Journal of the American Chemical Society.

[39]  David J. Tozer,et al.  The exchange-correlation potential in Kohn–Sham nuclear magnetic resonance shielding calculations , 2003 .

[40]  S. Grimme Improved second-order Møller–Plesset perturbation theory by separate scaling of parallel- and antiparallel-spin pair correlation energies , 2003 .

[41]  Matt Challacombe,et al.  Density matrix perturbation theory. , 2003, Physical review letters.

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

[43]  Martin Head-Gordon,et al.  Scaled opposite-spin second order Møller-Plesset correlation energy: an economical electronic structure method. , 2004, The Journal of chemical physics.

[44]  F. Weigend,et al.  Balanced basis sets of split valence, triple zeta valence and quadruple zeta valence quality for H to Rn: Design and assessment of accuracy. , 2005, Physical chemistry chemical physics : PCCP.

[45]  PEKKA MANNINEN,et al.  Systematic Gaussian basis‐set limit using completeness‐optimized primitive sets. A case for magnetic properties , 2006, J. Comput. Chem..

[46]  Jun Li,et al.  Basis Set Exchange: A Community Database for Computational Sciences , 2007, J. Chem. Inf. Model..

[47]  Jörg Kussmann,et al.  Linear-scaling method for calculating nuclear magnetic resonance chemical shifts using gauge-including atomic orbitals within Hartree-Fock and density-functional theory. , 2007, The Journal of chemical physics.

[48]  Juha Vaara,et al.  Theory and computation of nuclear magnetic resonance parameters. , 2007, Physical chemistry chemical physics : PCCP.

[49]  Christian Ochsenfeld,et al.  Efficient linear-scaling calculation of response properties: density matrix-based Laplace-transformed coupled-perturbed self-consistent field theory. , 2008, The Journal of chemical physics.

[50]  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.

[51]  Jacob Kongsted,et al.  On the Accuracy of Density Functional Theory to Predict Shifts in Nuclear Magnetic Resonance Shielding Constants due to Hydrogen Bonding. , 2008, Journal of chemical theory and computation.

[52]  Frank Jensen,et al.  Basis Set Convergence of Nuclear Magnetic Shielding Constants Calculated by Density Functional Methods. , 2008, Journal of chemical theory and computation.

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

[54]  J. Kussmann,et al.  Quantum-chemical simulation of solid-state NMR spectra: the example of a molecular tweezer host–guest complex , 2010 .

[55]  R. Bartlett,et al.  Accuracy of Computed 15 N Nuclear Magnetic Resonance Chemical Shifts , 2010 .

[56]  R. Fink Spin-component-scaled Møller-Plesset (SCS-MP) perturbation theory: a generalization of the MP approach with improved properties. , 2010, The Journal of chemical physics.

[57]  Frans A A Mulder,et al.  NMR chemical shift data and ab initio shielding calculations: emerging tools for protein structure determination. , 2010, Chemical Society reviews.

[58]  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.

[59]  Jörg Kussmann,et al.  Nuclei-selected NMR shielding calculations: a sublinear-scaling quantum-chemical method. , 2011, The Journal of chemical physics.

[60]  T. Kupka,et al.  From CCSD(T)/aug‐cc‐pVTZ‐J to CCSD(T) complete basis set limit isotropic nuclear magnetic shieldings via affordable DFT/CBS calculations , 2011, Magnetic resonance in chemistry : MRC.

[61]  Ariel M. Sarotti,et al.  Application of the multi-standard methodology for calculating 1H NMR chemical shifts. , 2012, The Journal of organic chemistry.

[62]  S. Grimme,et al.  Spin‐component‐scaled electron correlation methods , 2012 .

[63]  T. Kupka,et al.  Estimation of isotropic nuclear magnetic shieldings in the CCSD(T) and MP2 complete basis set limit using affordable correlation calculations , 2013, Magnetic resonance in chemistry : MRC.

[64]  C. Ochsenfeld,et al.  A linear- and sublinear-scaling method for calculating NMR shieldings in atomic orbital-based second-order Møller-Plesset perturbation theory. , 2013, The Journal of chemical physics.

[65]  Jörg Kussmann,et al.  Pre-selective screening for matrix elements in linear-scaling exact exchange calculations. , 2013, The Journal of chemical physics.

[66]  J. Kussmann,et al.  Efficient distance-including integral screening in linear-scaling Møller-Plesset perturbation theory. , 2013, The Journal of chemical physics.

[67]  Jürgen Gauss,et al.  Benchmarking density-functional theory calculations of NMR shielding constants and spin-rotation constants using accurate coupled-cluster calculations. , 2013, The Journal of chemical physics.

[68]  Jörg Kussmann,et al.  Linear‐scaling self‐consistent field methods for large molecules , 2013 .