Density Constraints Overcome the Energy-Density Trade-Off in Exchange-Correlation Functionals
Yuhao Chen, Donald G. Truhlar, Xiao He
原文摘要
Exchange--correlation functionals are trained mainly on energies, and their densities often degrade as their energies improve. We present a supervised-learning algorithm that trains functionals on energies and accurate densities without self-consistent-field (SCF) solutions. From one Fock build at a fixed accurate density, it predicts the density that the functional would reach self-consistently and penalizes its deviation from the reference; for functionals linear in their parameters, training is convex. Refitting the MN15 form to 1,500 reaction energies under a constraint on 98 coupled-cluster densities gives the density-constrained hybrid DCH-D4. On 19 held-out energy sets its mean normalized error ratio is 0.96, against 1.76 for MN15, and on 145 densities outside the fit its mean density error is 22 times lower than that of MN15. Deep-learning neural GGA and meta-GGA functionals (NN-GGA and NN-mGGA) trained on only 6 energies and 11 densities lower the atomization-energy error on 103 molecules from 14.6 to 5.6~kcal/mol relative to PBE and from 3.7 to 3.3~kcal/mol relative to SCAN, while roughly halving the density error of each base functional. Accurate densities can thus enter functional training at the scale of modern energy databases.
physics.chem-ph · cs.AI