Informing Empirically Fitted Density Functionals about the Physics of Interelectronic Interactions.

Area of Science:

• Computational Chemistry
• Quantum Chemistry
• Materials Science

Background:

• Constructing accurate density functionals is challenging due to the complexity of interelectron interactions.
• Current fitting techniques often lead to overfitting, resulting in unreliable functionals for untrained properties.
• A method is needed to ensure physical correctness during the training of density functionals, especially for advanced models like neural networks.

Purpose of the Study:

• To devise and apply a physics-informed approach for training density functionals.
• To reparameterize the M06-2X functional using this new method to improve its accuracy and reliability.
• To explore the potential of this approach for developing future neural network-based functionals.

Main Methods:

• Developed a novel physics-informed training approach to maintain correct physical behavior during functional development.
• Applied this approach to reparameterize the M06-2X functional on its original training dataset.
• Compared the performance of the new physics-informed functionals (piM06-2X, piM06-2X-DL) with existing functionals like M06-2X and PBE0.

Main Results:

• The physics-informed functionals piM06-2X and piM06-2X-DL achieved accuracy comparable to M06-2X for thermochemical tasks.
• These new functionals also reached the accuracy of PBE0 for electron density properties, combining strengths of both.
• Surprisingly, the PBE-2X functional demonstrated similar performance without any fitting, suggesting inherent physical grounding.

Conclusions:

• The physics-informed approach successfully creates more robust and accurate density functionals.
• This method offers a way to combine the benefits of heavily fitted and physically grounded functionals.
• The proposed technique is essential for the future development of sophisticated neural network-based quantum chemistry functionals.