Feature Description
The particle-particle Random Phase Approximation (ppRPA), which was originally used to describe the nuclear many-body correlation, has been developed to predict ground-state and excited-state properties of molecular and bulk systems. The ppRPA correlation energy is exact up to the second order electron-electron interaction and is equivalent to ladder CCD. For calculations of excitation energies in ppRPA, the excitation energies of the N-electron system can be calculated as the differences between the two-electron addition energies of the (N-2)-electron system from the particle-particle channel. Similarly, the excitation energies can also be obtained from the differences between the two-electron removal energies of the (N+2)-electron system from the hole-hole channel. The choice of the particle-particle or the hole-hole channels enhances the flexibility of the ppRPA method.
The formal scaling of ppRPA for computing excitation energies is $N^4$ with the Davidson algorithm. The computational cost can be further significantly reduced by using active-space approach, which directly truncates ppRPA matrix in the molecular orbital space without loss of accuracy.
Publications for theoretical background and implementations:
Publications for applications:
- energy barrier: J. Chem. Phys. 139, 174110
- double excitation energy: J. Chem. Phys. 162, 094101 J. Chem. Phys. 139, 224105
- defect excitation energy: J. Phys. Chem. Lett. 2024, 15, 10, 2757–2764 J. Chem. Theory Comput. 2024, 20, 18, 7979–7989
- diradical singlet-triplet gap: J. Phys. Chem. A 2015, 119, 20, 4923–4932 Proc. Natl. Acad. Sci. U. S. A. 2016, 113, E5098– E5107
- charge-transfer excitation: J. Chem. Phys. 146, 124104
- valence excitation: J. Chem. Phys. 141, 124104
Relevant Modules and Files
- examples/pprpa/01-pprpa_total_energy.py
- examples/pprpa/02-pprpa_excitation_energy.py
- examples/pprpa/03-hhrpa_excitation_energy..py
- examples/pprpa/04-gamma_pprpa_excitation_energy.py
- examples/pprpa/05-gamma_hhrpa_excitation_energy.py
- pyscf/pprpa/tests/test_rpprpa.py
- pyscf/pprpa/rpprpa_davidson.py
- pyscf/pprpa/rpprpa_direct.py
- pyscf/pprpa/upprpa_direct.py
Documentation
pyscf.github.io #173
Long-term Maintenance Plan
Jiachen Li (@lijiachen417) and Jincheng Yu (@pi246) will maintain the main functionalities in ppRPA. Chaoqun Zhang (@Warlocat) is expected to implement ppRPA gradient in 2025-2026 and maintain it.
Authorship
Jincheng Yu (University of Maryland, College Park/Duke University)
Jiachen Li (Yale University/Duke University)
Feature Description
The particle-particle Random Phase Approximation (ppRPA), which was originally used to describe the nuclear many-body correlation, has been developed to predict ground-state and excited-state properties of molecular and bulk systems. The ppRPA correlation energy is exact up to the second order electron-electron interaction and is equivalent to ladder CCD. For calculations of excitation energies in ppRPA, the excitation energies of the N-electron system can be calculated as the differences between the two-electron addition energies of the (N-2)-electron system from the particle-particle channel. Similarly, the excitation energies can also be obtained from the differences between the two-electron removal energies of the (N+2)-electron system from the hole-hole channel. The choice of the particle-particle or the hole-hole channels enhances the flexibility of the ppRPA method.
The formal scaling of ppRPA for computing excitation energies is$N^4$ with the Davidson algorithm. The computational cost can be further significantly reduced by using active-space approach, which directly truncates ppRPA matrix in the molecular orbital space without loss of accuracy.
Publications for theoretical background and implementations:
Publications for applications:
Relevant Modules and Files
Documentation
pyscf.github.io #173
Long-term Maintenance Plan
Jiachen Li (@lijiachen417) and Jincheng Yu (@pi246) will maintain the main functionalities in ppRPA. Chaoqun Zhang (@Warlocat) is expected to implement ppRPA gradient in 2025-2026 and maintain it.
Authorship
Jincheng Yu (University of Maryland, College Park/Duke University)
Jiachen Li (Yale University/Duke University)