Combining first-principles and data modeling for the accurate prediction of the refractive index of organic polymers

Abstract

Organic materials with a high index of refraction (RI) are attracting considerable interest due to their potential application in optic and optoelectronic devices. However, most of these applications require an RI value of 1.7 or larger, while typical carbon-based polymers only exhibit values in the range of 1.3-1.5. This paper introduces an efficient computational protocol for the accurate prediction of RI values in polymers to facilitate in silico studies that can guide the discovery and design of next-generation high-RI materials. Our protocol is based on the Lorentz-Lorenz equation and is parametrized by the polarizability and number density values of a given candidate compound. In the proposed scheme, we compute the former using first-principles electronic structure theory and the latter using an approximation based on van der Waals volumes. The critical parameter in the number density approximation is the packing fraction of the bulk polymer, for which we have devised a machine learning model. We demonstrate the performance of the proposed RI protocol by testing its predictions against the experimentally known RI values of 112 optical polymers. Our approach to combine first-principles and data modeling emerges as both a successful and a highly economical path to determining the RI values for a wide range of organic polymers.

Advances of machine learning in molecular modeling and simulation

“…We thus retain as much of the physical foundations and robustness of traditional modeling as possible, while being pragmatic about the parts of a problem, where that is not possible (see, e.g., Refs. [29][30][31]).…”

Guest Editorial: Special Topic on Data-Enabled Theoretical Chemistry

“…Jørgensen et al 69 perform first-principles calculations on about 4 000 monomers and show that a grammar variational autoencoder using a simple string representation makes quite accurate predictions, reducing the cost of a search by up to a factor of 5. Afzal et al 70 model the refraction index of organic polymers by combining first-principles calculations with ML to predict packing fractions of the bulk polymers.…”

Extension and Evaluation of the D4 London Dispersion Model for Periodic Systems

“…Overall 73 monomer units of polymer structures have been extracted from Ref. 44 and re-optimized at the PBEh-3c 46 level of theory after searching for minimum conformers using the conformer-rotamer ensemble sampling tool 47 for each monomer unit. We calculate RI values as follows…”

“…where V m values are taken from Ref. 44 assuming a constant packing fraction of the bulk polymer. Figure 4 shows the relative deviation of RIs from experimental values 44 (the MAD of TD-DFT RIs from experimental RIs is 2.3% its RMSD 3.0%).…”

“…44 assuming a constant packing fraction of the bulk polymer. Figure 4 shows the relative deviation of RIs from experimental values 44 (the MAD of TD-DFT RIs from experimental RIs is 2.3% its RMSD 3.0%). As can be seen from the graph, all methods generally calculate too large RI values, which is partly due to the approximation of using molecular polarizabilities α in equation 4.…”