¹³C NMR Chemical Shift Prediction of sp² Carbon Atoms in Acyclic Alkenes Using Neural Networks

The 13C NMR chemical shift of sp2 carbon atoms in acyclic alkenes was estimated with multilayer feedforward artificial neural networks (ANNs) and multilinear regression (MLR), using as structural descriptors a vector made of 12 components encoding the environment of the resonating carbon atom. The neural network quantitative model provides better results than the MLR model calibrated with the same data. The predictive ability of both the ANN and MLR models was tested by the leave-20%-out (L20%O) cross-validation method, demonstrating the superior performance of the neural model. The number of neurons in the hidden layer was varied between 2 and 7, and three activation functions were tested in the neural model: the hyperbolic tangent or a bell-shaped function for the hidden layer and a linear or a hyperbolic tangent function for the output layer. All four combinations of activation functions give close results in the calibration of the ANN model, while for the prediction a linear output function performs better than a hyperbolic tangent one, but from a statistical point of view one could not choose a particular combination against the others. For the ANNs with four neurons in the hidden layer, the standard deviation for calibration ranges between 0.59 and 0.63 ppm, while for prediction it lies between 0.89 and 1.07 ppm. We propose a parallel use of the four ANNs for the prediction of unknown shifts, because the mean of the four predictions exhibit a smaller number of outliers with lower residuals. The present model is compared with three additive schemes for the calculation of the sp2 13C NMR chemical shifts, and the statistical analysis of the results demonstrates that the ANN model gives better predictions than the classical ones.