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We have ground-state and excited-state calculations of 22,000 molecules [RHTL2015]. The question is: Knowing ground-state data and",
" excitation energy for a subset of these molecules — the training set — how well can we predict the excitation energies for other molecules in the set from only their ground-state data?
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We here use the simple Kernel Ridge Regression algorithm [MW-KRR]. The algorithm relies on numerical descriptors that express the similarity of two molecules as a distance. The predicted value is calculated by weighting known reference values from the training set according to their similarity to the test molecule.
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Choose different sizes of training set and different descriptors. The sorted Coulomb matrix (determined by the geometric structure) or the HOMO–LUMO gap (energy difference between highest occupied molecular orbital and lowest unoccupied molecular orbital which correlates with the actual excitation energy). Different types of descriptor can be weighted differently when determining the distance; these weights (called sigma) will affect how well the quantities are taken into account and affect the quality of predictions.
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Some exact definitions: The distance between two molecules is the L1 norm of the difference between their descriptors. The descriptor of a molecule is the vector containing all values of the sorted Coulomb matrix of the molecule divided by the structural normalization factor, and the HOMO–LUMO gap of the molecule divided by the electronic normalization factor. The kernel is the matrix of all values [exp(-|d(i) - d(j)|)] for each pair of descriptors d(i) and d(j).
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References:
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" - [RHTL2015] The Journal of Chemical Physics 143, 084111 (2015)
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" - [MW-KRR] Kernel-Ridge.pdf
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