Towards density functional approximations from coupled cluster correlation energy densities

Exact Mo̷ller-Plesset Adiabatic Connection Correlation Energy Densities

The Mo̷ller-Plesset adiabatic connection (MPAC) provides a powerful tool for developing density functional theory (DFT)-like approximations that map Hartree-Fock densities to the wave function-based correlation energy, thereby leveraging both wave function and DFT concepts for electronic structure approximations. A key object in this context is the correlation energy density, which represents the local (pointwise) contribution to the total correlation energy. While well-studied in DFT, it remains largely unexplored in the wave function framework. Here, we introduce a rigorous formulation of the wave function-based correlation energy density within MPAC, implement it via full configuration interaction calculations, and analyze its behavior and physically meaningful contributions for representative small (di)atomic systems. We define this quantity by employing a general gauge strategy, from which the conventional DFT correlation energy density gauge also arises. We then discuss the resulting commonalities and differences between correlation energy densities in the DFT and wave function frameworks and derive the small-interaction (MP2) limit of the latter in terms of Hartree-Fock orbitals. Finally, we show how these newly introduced energy densities can serve as new approximation targets in both machine-learning-assisted and traditional electronic structure methods for mapping HF-density-based features to correlation energy within the wave function framework.

Balancing the Contributions to the Gradient Expansion: Accurate Binding and Band Gaps with a Nonempirical Meta-GGA

The gradient expansion has been a long-standing guide rail in density-functional theory. We here demonstrate that for exchange-correlation approximations that depend on the gradient of the density and the kinetic energy density, i.e., for meta-generalized gradient approximations (meta-GGAs), there is a so far unexploited degree of freedom in the gradient expansion that allows to shift the relative weight of gradient and kinetic energy contributions. As the dependence on the kinetic energy density determines the derivative discontinuity, this allows to construct meta-GGAs that adhere to the known exact constraints, yet have new properties. We demonstrate this with the construction of a meta-GGA that describes both electronic bonds and band gaps with remarkable accuracy.

Fast Estimation of Møller-Plesset Correlation Energies Based on Atomic Contributions

Dynamic correlation plays an important role in the accurate calculation of chemical compounds such as the description of equilibrium structures in chemical systems. A model for the fast estimation of dynamic correlation energy is introduced in this work. This model is based on the idea of decomposition of the contribution of dynamic correlation energy calculated by nth order Møller-Plesset perturbation (MPn) theory with respect to atomic regions. Multiple levels of theory, including MP2, MP2.5, and MP4, are used as the reference, and the corresponding correlation energy densities are calculated. The proposed model is concise, fast, and promising for practical use, such as the prediction of reaction energies. It can also work as a baseline model or pretrained model for follow-up studies of machine learning.

Pure non-local machine-learned density functional theory for electron correlation

Density-functional theory (DFT) is a rigorous and (in principle) exact framework for the description of the ground state properties of atoms, molecules and solids based on their electron density. While computationally efficient density-functional approximations (DFAs) have become essential tools in computational chemistry, their (semi-)local treatment of electron correlation has a number of well-known pathologies, e.g. related to electron self-interaction. Here, we present a type of machine-learning (ML) based DFA (termed Kernel Density Functional Approximation, KDFA) that is pure, non-local and transferable, and can be efficiently trained with fully quantitative reference methods. The functionals retain the mean-field computational cost of common DFAs and are shown to be applicable to non-covalent, ionic and covalent interactions, as well as across different system sizes. We demonstrate their remarkable possibilities by computing the free energy surface for the protonated water dimer at hitherto unfeasible gold-standard coupled cluster quality on a single commodity workstation.

Semilocal density functionals, while computationally efficient, do not account for non-local correlation. Here, the authors propose a machine-learning approach to DFT that leads to non-local and transferable functionals applicable to non-covalent, ionic and covalent interactions across system of different sizes.

Psi4 1.4: Open-source software for high-throughput quantum chemistry

PSI4 is a free and open-source ab initio electronic structure program providing implementations of Hartree-Fock, density functional theory, many-body perturbation theory, configuration interaction, density cumulant theory, symmetry-adapted perturbation theory, and coupled-cluster theory. Most of the methods are quite efficient, thanks to density fitting and multi-core parallelism. The program is a hybrid of C++ and Python, and calculations may be run with very simple text files or using the Python API, facilitating post-processing and complex workflows; method developers also have access to most of PSI4's core functionalities via Python. Job specification may be passed using The Molecular Sciences Software Institute (MolSSI) QCSCHEMA data format, facilitating interoperability. A rewrite of our top-level computation driver, and concomitant adoption of the MolSSI QCARCHIVE INFRASTRUCTURE project, makes the latest version of PSI4 well suited to distributed computation of large numbers of independent tasks. The project has fostered the development of independent software components that may be reused in other quantum chemistry programs.