# Mean-field density matrix decompositions.

@article{Eriksen2020MeanfieldDM, title={Mean-field density matrix decompositions.}, author={Janus Juul Eriksen}, journal={The Journal of chemical physics}, year={2020}, volume={153 21}, pages={ 214109 } }

We introduce new and robust decompositions of mean-field Hartree-Fock and Kohn-Sham density functional theory relying on the use of localized molecular orbitals and physically sound charge population protocols. The new lossless property decompositions, which allow for partitioning one-electron reduced density matrices into either bond-wise or atomic contributions, are compared to alternatives from the literature with regard to both molecular energies and dipole moments. Besides commenting on…

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### Erratum: "Mean-field density matrix decompositions" [J. Chem. Phys. 153, 214109 (2020)].

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## 272 References

### Generalization of Intrinsic Orbitals to Kramers-Paired Quaternion Spinors, Molecular Fragments, and Valence Virtual Spinors.

- ChemistryJournal of chemical theory and computation
- 2021

This paper generalizes the intrinsic atomic and bonding orbitals to relativistic applications using complex and quaternion spinors, as well as to molecular fragments instead of atomic fragments only, and shows how localized valence virtual orbitals can be expressed on this intrinsic minimal basis.

### Completing density functional theory by machine learning hidden messages from molecules

- Computer Sciencenpj Computational Materials
- 2020

This study demonstrates that the functional can be systematically constructed using accurate density distributions and energies in reference molecules via machine learning, and will help enrich the DFT framework by utilizing the rapidly advancing machine-learning technique.

### Generalized Many-Body Expanded Full Configuration Interaction Theory.

- PhysicsThe journal of physical chemistry letters
- 2019

It is argued that generalized MBE-FCI theory possesses an immense potential to yield near-exact correlation energies for molecular systems of unprecedented size, composition, and complexity in the years to come.

### Machine learning accurate exchange and correlation functionals of the electronic density

- Computer ScienceNature Communications
- 2020

This work proposes a framework to create density functionals using supervised machine learning, termed NeuralXC, designed to lift the accuracy of baseline functionals towards that provided by more accurate methods while maintaining their efficiency.

### Quantum chemical accuracy from density functional approximations via machine learning

- ChemistryNature communications
- 2020

Kohn-Sham density functional theory (DFT) is a standard tool in most branches of chemistry, but accuracies for many molecules are limited to 2-3 kcal ⋅ mol−1 with presently-available functionals. Ab…

### A density-functional theory-based neural network potential for water clusters including van der Waals corrections.

- ChemistryThe journal of physical chemistry. A
- 2013

This work presents a high-dimensional neural network (NN) potential for water clusters based on density-functional theory (DFT) calculations, which is constructed using clusters containing up to 10 monomers and is in principle able to meet all these requirements.

### Solving the electronic structure problem with machine learning

- Computer Sciencenpj Computational Materials
- 2019

A machine-learning-based scheme to efficiently assimilate the function of the KS equation, and by-pass it to directly, rapidly, and accurately predict the electronic structure of a material or a molecule, given just its atomic configuration is introduced.

### Regularised atomic body-ordered permutation-invariant polynomials for the construction of interatomic potentials

- MathematicsMach. Learn. Sci. Technol.
- 2020

It is shown that the low dimensionality combined with careful regularisation actually leads to better transferability than the high dimensional, kernel based Gaussian Approximation Potential.

### Hartree-Fock energy partitioning in terms of Hirshfeld atoms.

- Physics, ChemistryChemphyschem : a European journal of chemical physics and physical chemistry
- 2006

The atomic potential energies are found to mimic trends based on exact expressions as well as trends displayed by molecular quantities, thus lending credibility to the partitioning scheme used.

### Symmetry-Adapted Machine Learning for Tensorial Properties of Atomistic Systems.

- Computer SciencePhysical review letters
- 2018

This work introduces a formalism that extends existing schemes and makes it possible to perform machine learning of tensorial properties of arbitrary rank, and for general molecular geometries, and derives a tensor kernel adapted to rotational symmetry.