H and 13C NMR Scaling Factors for the Calculation of Chemical Shifts in Commonly Used Solvents Using Density Functional Theory Gregory K. Pierens* Calculation of NMR chemical shifts and coupling constants using quantum mechanical calculations [density functional theory (DFT)], has become a very popular tool for the determination of conformation and the assignment of stereochemistry within a molecule. We present the scaling factors (linear regression parameters) from 10 DFT methods for 10 commonly used NMR solvents using the same set of reference com-

pounds. The results were compared with the corresponding gas-phase calculations to assess the inclusion of the polarizC 2014 Wiley Periodable continuum model for solvent effects. V icals, Inc.


overcoming the “gauge problem,”[13] other methods were developed which include gauge including atomic orbital (GIAO)[14–16] and individual gauges for localized orbitals.[17,18] GIAO has become the method of choice for most NMR calculations. The conversion of calculated NMR isotropic shielding tensors to a chemical shift can be achieved in two ways. The first is to use a reference compound, for example, tetramethylsilane (TMS). The compound of interest and reference compound are calculated using the same method, and the reference compound is used to obtain the conversion factor shown in the following equation;

Quantum mechanical calculations of nuclear magnetic resonance (NMR) parameters, such as chemical shifts and coupling constants, have become a very popular tool for synthetic and natural product chemistry for the assignment of stereochemistry within a molecule. Calculations of NMR chemical shifts have been reviewed extensively.[1–9] These calculations have also been used for the reassignment of incorrectly assigned natural products,[10–12] as the validation of the proposed structure through gold standard methods like X-ray crystallography or total synthesis might not be achievable. Chemical shift databases are widely used for the prediction of NMR chemical shifts. This prediction requires a compound to have a good structure correlation to those represented within the database. However, if the compound is structurally different, large deviations could result compared to the experimentally measured chemical shifts. For example, natural products have a wide diversity of substructures, which might not be represented in the database. Another potential problem with using databases occurs for large compounds as the three-dimensional arrangement of the substructures within a large compound has an effect on the magnetic properties of nearby protons and carbons. Frequently, calculations of NMR chemical shifts are calculated from a single conformation although it is known that the NMR chemical shifts represent an average of several conformations. Therefore, each chemical shift should be Boltzmann averaged with respect to their energy for all conformations. To calculate chemical shifts for a compound, the NMR isotropic shielding tensor (r) must be first calculated. These calculations are almost always conducted with quantum mechanical modeling methods, most commonly with density functional theory (DFT), perturbation theory, or higher-level post-HartreeFlock (HF) methods. DFT methods have become very popular as there is a good compromise between accuracy and efficiency and there are numerous DFT functionals available. After

DOI: 10.1002/jcc.23638

di 5rref 2ri 1dref where di is the chemical shift of interest, dref is the chemical shift of reference compound, and rref and ri are the calculated isotropic magnetic shielding tensor for the reference and compound of interest, respectively.[19–22] The second and more accepted method is by linear regression. In this method several reference compounds are examined and their calculated NMR isotropic shielding tensors are plotted against their experimental chemical shifts. The slope and intercept of line of best fit are used to convert the calculated NMR isotropic shielding tensor into a chemical shift. The major benefit of this method is that the slope can be used to correct the chemical shift for any systematic error and the yintercept can provide an alternative to a single reference value, as mentioned above. The slope and y-intercept can be used to convert the isotropic magnetic shielding tensor into a chemical shift using the equation below; Gregory K. Pierens Centre for Advanced Imaging, The University of Queensland, St Lucia, Queensland 4072, Australia E-mail: [email protected] Contract/grant sponsor: Centre for Advanced Imaging, The University of Queensland C 2014 Wiley Periodicals, Inc. V

Journal of Computational Chemistry 2014, DOI: 10.1002/jcc.23638





intercept2r 2slope

It has been reported that a slope within 21.00 6 0.05 and a R2 of not less than 0.995 indicates a well-performing method.[7] When acquiring experimental NMR data, the compound of interest is usually dissolved in a suitable deuterated solvent. Chemical shifts can vary in different solvents, hence consideration of these differences are essential when predicting NMR chemical shifts. The availability of sufficient experimental data in a variety of solvents is one of the biggest limitations of the linear regression method. The majority of the DFT calculated chemical shifts that have been reported in the literature use chloroform as solvent. In this article, we present the calculated linear regression parameters (scaling factors) using 10 different DFT methods in 10 different solvents, calculated from a single set of reference compounds. The results obtained will be compared to the predicted chemical shifts calculated in gas phase and recommendations will be presented.

Methods Linear regression procedure for obtaining scaling factors Calculations were performed using Gaussian 09[23] software package on a linux platform. All compounds were initially optimized in gas phase using the B3LYP functional[24,25] and 6311G(d,p) basis set. This combination has been previously shown to provide accurate geometries for organic molecules at a reasonable low computational cost. For all optimizations, the vibrational frequencies were checked for imaginary frequencies to assure all final geometries corresponded to a true minimum on the electronic potential energy surface. The NMR isotropic shielding tensors were calculated from a single point calculation using the preoptimized structures, using the method above, with 10 different DFT functionals and basis sets combinations recommended in the literature (see Table 1).[7,26–28] The isotropic magnetic shielding tensors were computed using the gauge-independent atomic orbital (GIAO) methodology and the isotropic magnetic shielding tensors were averaged over all symmetry related carbons and hydrogens where applicable. Different solvent models have been investigated to improve the accuracy of chemical shift calculations to account for the solvent effects. The two main solvent models are the explicit cluster[29] and implicit solvent methods.[7,30–32] The first model is very computer intensive and will not be discussed further, whereas the latter method handles the effect of solvent using a continuum approach and yields the isotropic magnetic shielding tensor using the single point calculations, in a reasonable time frame.[7] Therefore, the isotropic magnetic shielding tensors were calculated in gas phase, as well as investigating effect of solvent via the inclusion of the polarizable continuum model (IEF-PCM),[33] which is the default solvent option in Gaussian 09 (scrf 5 (solvent 5 “XXXXX”), e.g., “XXXXX” 5 DMSO). The log files were processed using a shell script on the linux machine to extract the isotropic magnetic shielding tensors 2

Journal of Computational Chemistry 2014, DOI: 10.1002/jcc.23638

Table 1. DFT functionals and basis sets used in the single point NMR chemical shift calculations. Method

Density functional

Basis set



6-31G(d) 6-3111G(2d,p) cc-pVDZ aug-cc-pVDZ 6-31G(d) 6-311G(d) 6-3111G(2d,p) 6-3111G(2d,p) 6-31G(d) aug-cc-pVDZ

[a] PBE0  pbe1pbe. [b] WC04: blyp iop (3/76 5 1000007400, 3/77 5 0999900001, 3/78 5 0000109999).[28] [c] WP04: blyp iop (3/76 5 1000001189, 3/77 5 0961409999, 3/78 5 0000109999).[28]

and then, the linear regression was performed using MATLAB script for each solvent automatically. Examples of the file formats, shell scripts and MATLAB mat files are included in Supporting Information and can be used to create other scaling factors for DFT functional and basis sets (FBS) not included in the manuscript. Mexicanin 1 Monte Carlo Conformational searching was performed using €dinger Inc)[34] for Mexicanin 1. TorMacromodel v9.9 (Schro sional sampling [Monte Carlo Multiple Minimum (MCMM)] was performed with 1000 steps per rotatable bond. Each step was minimized with the OPLS-2005 force field using TNCG method with maximum iterations of 50,000 and energy convergence threshold of 0.02. All other parameters were left as the default values. The low energy conformations (

1H and 13C NMR scaling factors for the calculation of chemical shifts in commonly used solvents using density functional theory.

Calculation of NMR chemical shifts and coupling constants using quantum mechanical calculations [density functional theory (DFT)], has become a very p...
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