StereoFitter: How to use J-couplings

Introduction:

StereoFitter offers a versatile way to use scalar (J) couplings as restraints for conformational analysis, using either Karplus type empirical equations¹ or DFT predictions.² We will present here a rapid glimpse into the most frequent uses of J-coupling restraints inside StereoFitter.

The J-coupling restraints add a quadratic χ²J term to the global StereoFitter χ penalty function of the form:       Where Jexp are the experimentally measured scalar couplings, and Jcalc the conformationally averaged predicted values; Jcalc  values can be calculated using either Karplus-type empirical equations or DFT computations; Finally, σ is the (standard) error associated to each J-coupling restraint. This error controls the relative weight among the different J-couplings and other restraints.

The jcoupling_data block

J-coupling restraints are introduced in StereoFitter via the jcoupling_data block. This block has the following general syntax:

jcoupling_data {

idx1 idx2 j σ equation

}

Where idx1 and idx2 are the index numbers of the coupled nuclei (from 1 to N), j is the J-coupling value in Hz and σ the uncertainty (standard error in Hz) associated to this particular restraint. Finally, equation is either the name of the empirical Karplus-type equation used to predict this coupling or even to indicate that a DFT computation was done instead

Proton-proton vicinal couplings

The most frequently used empirical equation for prediction of vicinal proton-proton ¹JHH couplings is no doubt the Altona equation, which extends the Karplus relationship to account for the electronegativity and relative orientation of the substituents. This is the default equation in StereoFitter for prediction of ³JHH couplings and will be the equation to be used if any equation name is provided. Alternatively, the altona keyword can be used.

The default uncertainty σJ for scalar couplings in StereoFitter is 0.8 Hz, which corresponds to a previously calibrated uncertainty for the Altona equation. For instance, an input file for the a-santonin couplings between C-H vicinal protons would look like:

Go to page 1 of the Mnova document webtutorial_jcoupling_1.mnova and follow the instructions to run the above example. Two different stereoisomers are selected. (lowest AIC score number).

Use of other Karplus relationships

StereoFitter offers many Karplus-type relationships for the prediction of diverse types of heteronuclear couplings. These relationships can be used by just specifying the equation name in the corresponding line of the jcoupling_data block. All available equations are listed in the manual.

³JCH Common heteronuclear couplings employed in structural analysis are H-Csp^³-Csp^³-Csp^³  ³JCH couplings. For empirical prediction of ³JCH couplings in  systems  StereoFitter relies on Bifulco’s adaptation of the Altona equation.^³ In the following example⁴ the Bifulco equation is applied to the prediction of ³JCH couplings, which are also combined with Altona predicted ³JHH couplings:

Follow the instructions in this document jcoupling_webtutorial_2.mnova to run the above example.

Using DFT computations

In many cases Karplus-type equations do not hold for the type of J-couplings being used, as for instance ¹JCH couplings,⁵ or they exist but do not present enough versatility or accuracy. In those cases, a DFT prediction may be necessary. To use DFT predicted J-couplings as restraints a quantum mechanical prediction must be done for every conformation in the ensemble using a quantum chemistry program package. The folder containing the ouputs, for each conformation, must then be loaded into StereoFitter using the “Load from Folder” option in the ribbon menu. The computed J-couplings are automatically retrieved and conformationally-averaged values can then be computed by StereoFitter.

The use of DFT based J-coupling restraints the equation parameter must take the dft value instead of the name of a Karplus relationship.

jcoupling_data {

#a one bond j-coupling using DFT predictions

10 11 136.7 2.0 dft

}

Note that Karplus-type and DFT restraints can be mixed inside the same jcoupling_data block.

Prochiral protons

In many cases the stereochemical assignment of a prochiral methylene group is not known beforehand. How to use the J-couplings from a vicinal proton to a pair of unassigned protons.

In order to do that, the jcoupling_group_data block must be used,  which for the particular case of a H-C-C(Ha)Hb moiety takes the form

Run the above example using the following tutorial webtutorial_jcoupling_3.mnova:

When using this type of restraint StereoFitter will generate a pair of conformationally averaged predicted values and will compare them with the experimental values by ordering both pairs from higher to lower value. In this way a previous prochiral assignment it is not needed

Averaging J-coupling values. Long range coupling to methyl groups

A long-range coupling may contain important conformational information as the observation of a large ^⁴J or even ^⁵J coupling may involve the presence of a conformationally rigid M or W-type patterns. When one of the coupled partners is a methyl group StereoFitter can handle this situation, which gives a rich stereochemical information, by using an averaged value of the J-coupling.

Using custom Karplus equations

Sometimes a Karplus equation for a specific type of coupling is not available in the literature, or not implemented inside StereoFitter. It is possible to just input the coefficients of the desired series. Custom Karplus equations can be easily derived by least-squares fitting of  DFT computations of the Karplus curve.^⁶ For instance, a coupling between two nuclei governed by the Karplus equation ³J = 4.3cos2Φ + 2.4cosΦ -0.8 can be included in StereoFitter adding the following line to your jcoupling_data

jcoupling_data {

#there will be n+1 cosineterms in the expansion

10 11 6.0 fourierseries:(2,4.0,2.0,-0.8)

}

Further knowledge

Read the StereoFitter manual for a detailed description of all possibilities for the use of J-coupling restraints in configurational and conformational analysis. Judicious use of J-couplings can solve many stereochemical problems using simple NMR experiments!

References

(1) Navarro‐Vázquez, A.; Santamaría‐Fernández, R.; Sardina, F. J. MSpin-JCoupling. A Modular Program for Prediction of Scalar Couplings and Fast Implementation of Karplus Relationships. Magn. Reson. Chem. 2018, 56 (6), 505–512. https://doi.org/10.1002/mrc.4667.

(2) Bifulco, G.; Dambruoso, P.; Gomez-Paloma, L.; Riccio, R. Determination of Relative Configuration in Organic Compounds by NMR Spectroscopy and Computational Methods. Chem. Rev. 2007, 107 (9), 3744–3779. https://doi.org/10.1021/cr030733c.

(3) Palermo, G.; Riccio, R.; Bifulco, G. Effect of Electronegative Substituents and Angular Dependence on the Heteronuclear Spin−Spin Coupling Constant 3JC−H: An Empirical Prediction Equation Derived by Density Functional Theory Calculations. J. Org. Chem. 2010, 75 (6), 1982–1991. https://doi.org/10.1021/jo902704u.

(4) Trigo-Mouriño, P.; Navarro-Vázquez, A.; Ying, J.; Gil, R. R.; Bax, A. Structural Discrimination in Small Molecules by Accurate Measurement of Long-Range Proton–Carbon NMR Residual Dipolar Couplings. Angew. Chem. 2011, 123 (33), 7718–7722. https://doi.org/10.1002/ange.201101739.

(5) Buevich, A. V.; Saurí, J.; Parella, T.; Tommasi, N. D.; Bifulco, G.; Williamson, R. T.; Martin, G. E. Enhancing the Utility of 1JCH Coupling Constants in Structural Studies through Optimized DFT Analysis. Chem. Commun. 2019, 55 (41), 5781–5784. https://doi.org/10.1039/C9CC02469G.

(6) Navarro‐Vázquez, A.; Pennestri, M. Karplus Relationships of the 2JHNα and 3JΗΝβ Couplings in Organic Azides. Magn. Reson. Chem. 2021, 59 (2), 187–194. https://doi.org/10.1002/mrc.5101.