Artificial Neural Network-Based Density Functional Approach for Adiabatic Energy Differences in Transition Metal Complexes

Abstract

During the past decades, approximate Kohn−Sham density functional theory schemes have garnered many successes in computational chemistry and physics, yet the performance in the prediction of spin state energetics is often unsatisfactory. By means of a machine learning approach, an enhanced exchange and correlation functional is developed to describe adiabatic energy differences in transition metal complexes. The functional is based on the computationally efficient revision of the regularized, strongly constrained, and appropriately normed functional and improved by an artificial neural network correction trained over a small data set of electronic densities, atomization energies, and/or spin state energetics. The training process, performed using a bioinspired nongradient-based approach adapted for this work from the particle swarm optimization, is analyzed and discussed extensively. The resulting machine learned meta-generalized gradient approximation functional is shown to outperform most known density functionals in the prediction of adiabatic energy differences for a diverse set of transition metal complexes with varying local coordinations and metal choices.

Modeling Fe(II) Complexes Using Neural Networks

“…To rapidly identify Fe­(II) complexes with desirable properties, in this work we model the potential energy surface of Fe­(II) complexes in both HS and LS states with ML. Neural network potentials (NNPs) have been widely investigated for organic molecules, − while less work has been done for TMCs. − However, to our best knowledge, none of these works have considered in detail the effect of ligand conformations on the energetics of TMCs. To achieve this, we first compile a set that includes both configurationally and conformationally diverse Fe­(II) complexes and then use this data set to predict both the relative energy of conformers and the spin splitting energy accurately.…”

Approaching the Complete Basis Set Limit for Spin-State Energetics of Mononuclear First-Row Transition Metal Complexes

“…Spin states resulting from different distributions of electrons on the metal d orbitals in transition metal (TM) complexes are highly relevant in inorganic chemistry, biochemistry, catalysis, and materials science. − Nevertheless, reliable computation of spin-state energetics (i.e., the energy differences between alternative spin states; also termed spin-state splittings) poses a formidable challenge for computational chemistry methods. − During the past decade, there have been numerous attempts to compute the spin-state energetics accurately using density functional theory (DFT) − or wave function theory (WFT) methods. ,− Despite the progress made, it also has been realized that the problem is very challenging due to a complicated interplay of dynamic and nondynamic correlation effects in TM complexes, so that divergent results are often reported even at high theory levels . Partly for this reason, but also due to the scarcity of definite benchmarks, practical computational protocols for predicting TM spin-state energetics unarguably within the chemical accuracy (i.e., ±1 kcal/mol) from the experimental values are still to be sought.…”

“…1 − 4 Nevertheless, reliable computation of spin-state energetics (i.e., the energy differences between alternative spin states; also termed spin-state splittings) poses a formidable challenge for computational chemistry methods. 5 − 9 During the past decade, there have been numerous attempts to compute the spin-state energetics accurately using density functional theory (DFT) 10 − 15 or wave function theory (WFT) methods. 12 , 16 − 27 Despite the progress made, it also has been realized that the problem is very challenging due to a complicated interplay of dynamic and nondynamic correlation effects in TM complexes, so that divergent results are often reported even at high theory levels.…”