Can Graph Machines Accurately Estimate 13C NMR Chemical Shifts of Benzenic Compounds?

Abstract

In the organic laboratory, the ¹³C nuclear magnetic resonance (NMR) spectrum of a newly synthesized compound remains an essential step in elucidating its structure. For the chemist, the interpretation of such a spectrum, which is a set of chemical-shift values, is made easier if he/she has a tool capable of predicting with sufficient accuracy the carbon-shift values from the structure he/she intends to prepare. As there are few open-source methods for accurately estimating this property, we applied our graph-machine approach to build models capable of predicting the chemical shifts of carbons. For this study, we focused on benzene compounds, building an optimized model derived from training a database of 10,577 chemical shifts originating from 2026 structures that contain up to ten types of non-carbon atoms, namely H, O, N, S, P, Si, and halogens. It provides a training root-mean-squared relative error (RMSRE) of 0.5%, i.e., a root-mean-squared error (RMSE) of 0.6 ppm, and a mean absolute error (MAE) of 0.4 ppm for estimating the chemical shifts of the 10k carbons. The predictive capability of the graph-machine model is also compared with that of three commercial packages on a dataset of 171 original benzenic structures (1012 chemical shifts). The graph-machine model proves to be very efficient in predicting chemical shifts, with an RMSE of 0.9 ppm, and compares favorably with the RMSEs of 3.4, 1.8, and 1.9 ppm computed with the ChemDraw v. 23.1.1.3, ACD v. 11.01, and MestReNova v. 15.0.1-35756 packages respectively. Finally, a Docker-based tool is proposed to predict the carbon chemical shifts of benzenic compounds solely from their SMILES codes.

Keywords: Docker; chemical shift; graph machines (GM); machine learning; structured data.

Figure 1

Scatter plot of ¹³C chemical-shift estimations computed by graph machine from SMILES (node function with 26 hidden neurons) for the 1637 compounds of the training set (blue circles) and the 114 compounds of the test set (red filled circles) vs. measured values of the chemical shift. The black line is the bisector of the plot.

Figure 2

Scatter plot of ¹³C chemical-shift predictions computed by graph machines (red disks) and MestReNova software v. 15.0.1-35756 (blue circles) vs. measured shift values for the 171 molecules of the test set. The black line is the bisector of the plot, and the dashed red and blue lines are the regression lines for the GM and MestReNova plots.

Figure 3

Structure of training * or test ^† set molecules with at least one carbon whose shift estimation with the GM26 model shows a large deviation (experimental minus estimated, in ppm). Shifts for blue carbon are underestimated, while they are overestimated for red carbons.

Figure 4

Deviations encountered in the prediction of carbon shifts of three molecules outside the scope of the GM26 model (experimental minus estimated, in ppm). Shifts for blue carbon are underestimated, while they are overestimated for red carbons.

Figure 5

Graph-machine construction process for two carbons of 2-methoxytoluene: (ⓐ) conversion of the 2D structure of 2-methoxytoluene into a cyclic graph, (ⓑ) construction of the two directed acyclic graphs for the carbons marked in red, and (ⓒ) generation of the corresponding graph machines.

Figure 6

Distribution of functional carbons (as percentages) for the molecules of the training (blue bars) and test (bistre-colored bars) sets.