[FEATURE TRANSFER] Transfer the ppRPA Module to PySCF-Core

[lijiachen417]

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:

• ppRPA formulation: Phys. Rev. A 88, 030501 J. Chem. Phys. 140, 18A511
• spin-adaption: J. Chem. Phys. 139, 174110
• Davidson algorithm: J. Chem. Phys. 141, 124104
• active-space ppRPA: J. Phys. Chem. A 2023, 127, 37, 7811–7822

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)

[tberkel]

Dear Jiachen, Thanks for your work on ppRPA. We'll discuss and get back to you.

…

On Wed, Dec 4, 2024 at 1:28 PM Jiachen Li ***@***.***> wrote: Dear PySCF Board of Directors, I am writing to formally request the transfer of the particle-particle random phase approximation (ppRPA) module from PySCF-forge to PySCF-core. Since the first introduction of the ppRPA formalism in quantum chemistry by Weitao Yang's group at Duke University, this methodology has gained significant traction in the community. It has been effectively utilized for studying ground-state and excited-state properties across a wide range of systems, including: 1. dissociation energies and thermochemistry properties: Phys. Rev. A 88, 030501(R), J. Chem. Phys. 140, 18A511 (2014) 2. valence excitation energies: J. Chem. Phys. 139, 174110 (2013), J. Chem. Phys. 141, 124104 (2014) 3. singlet-triplet gaps of diradicals: Proc. Natl. Acad. Sci. U.S. A. 113.35 (2016): E5098-E5107, J. Phys. Chem. A 2015, 119, 20, 4923–4932 4. charge-transfer excitation energies: J. Chem. Phys. 146, 124104 (2017) 5. double excitation energies: arxiv.org/abs/2411.16599v1 6. defect excitation energies: J. Phys. Chem. Lett. 2024, 15, 10, 2757–2764, J. Chem. Theory Comput. 2024, 20, 18, 7979–7989 We believe ppRPA can be a useful component in PySCF to study the electronic structure and be interesting for quantum chemistry community. Thank you for considering this request. Please let me know if there are any additional details or steps required to proceed with this transfer. Best Regard, Jiachen Li Postdoc of Tianyu Zhu's group at Yale University — Reply to this email directly, view it on GitHub <#87>, or unsubscribe <https://github.com/notifications/unsubscribe-auth/ADGAJC2OGKFQIGVWIPEP6HT2D5CVPAVCNFSM6AAAAABTAZHHBGVHI2DSMVQWIX3LMV43ASLTON2WKOZSG4YTQNJQGMYDAMI> . You are receiving this because you are subscribed to this thread.Message ID: ***@***.***>

[lijiachen417]

@tberkel Thank you so much!

[lijiachen417]

Hi @sunqm, I modified this issue based on the feature transfer template, could you check it?