PyBEST is a Pythonic Black-box Electronic Structure Tool, written primarily in the Python programming language with additional parts written in C++ (interfaced using nanobind).

PyBEST is a fully-fledged modern electronic-structure software package, developed at NCU in Torun, released under the GNU General Public License. The package provides an efficient and reliable platform for electronic structure calculations at the interface of chemistry and physics using unique electronic structure methods. PyBEST is easy to use and easy to code in.

For more information, see our official homepage. You will also find there various versions of PyBEST to download and install including the most recent version of this documentation.

NOTE: The wheels are shipped with an integrated libint2 library built for a maximum angular momemtum of 4 (g-type functions). For higher angular momentum functions, PyBEST needs to be compiled from source as described here.

Graphical User Interface

A graphical user interface (GUI) is available to simplify the creation of PyBEST input files. The GUI is designed for intuitive interaction and facilitates setting up calculations without requiring manual file editing.

The GUI is publicly available on Zenodo.

NOTE: This version of PyBEST is compatible with the PyBEST GUI v1.1.0 or newer.

Main Features

Compatibility

• Integrating the LibInt2 library.

• Adapting a modular structure to easily combine PyBEST with custom developments.

• GPU-accelerated computing using the CuPy and PyTorch libraries.

Electronic Structure Methods

• Hamiltonians (various one- and two-electron integrals)

  • The electronic Schrödinger Hamiltonian in atom-centered Gaussian basis sets

    • One- and two-electron integrals computed with LibInt2

      • overlap, kinetic energy, nuclear, multipole, electron repulsion integrals (ERI)

    • pVp integrals

    • Cholesky-decomposed ERI

    • Douglas-Kroll-Hess Hamiltonian (DKH2)

    • eXact 2-Component (X2C) scalar relativistic Hamiltonian

    • Point-charge integrals

    • Static embedding potential integrals

  • Model Hamiltonians

    • 1-dimensional Hubbard model Hamiltonian (with and without periodic boundary conditions)

    • 1-dimensional contact interactions in an arbitrary external potential

    • Huckel and TB Hamiltonian

    • PPP Hamiltonian

  • User-provided Hamiltonians

    • Molpro's FCIDUMP format

• Hartree-Fock theory:

  • Restricted and unrestricted orbitals

  • Various DIIS algorithms

• Configuration Interaction methods

  • Configuration Interaction Singles (CIS)

  • Configuration Interaction Doubles (CID)

  • Configuration Interaction Singles and Doubles (CISD)

• Coupled Cluster-type methods

  • pair-Coupled Cluster Doubles (pCCD), also known as the Antisymmetry Product of 1 reference-orbital Geminals (AP1roG)

  • Linearized Coupled Cluster Doubles (LCCD)

  • Linearized Coupled Cluster Singles and Doubles (LCCSD)

  • pCCD-LCCD (pCCD with an LCCD correction on top of it)

  • pCCD-LCCSD (pCCD with an LCCSD correction on top of it)

  • pCCD-CCS (pCCD with a Coupled Cluster Singles correction on top of it)

  • Coupled Cluster Doubles (CCD) in any restricted orbital basis

  • Coupled Cluster Singles and Doubles (CCSD) in any restricted orbital basis

  • Frozen-pair Coupled Cluster and Doubles (fpCCD)

  • Frozen-pair Coupled Cluster Singles and Doubles (fpCCSD)

  • Tailored Couples Cluster Singles Doubles (tCCSD)

• Perturbation theory

  • Moller-Plesset Perturbation Theory of second order (MP2)

  • Symmetry Adapted Perturbation Theory (SAPT)

    • the SAPT0 un-coupled flavour for spin-restricted HF orbitals

  • Various Perturbation Theory models of second order with an pCCD reference function

    • PT2SDd (diagonal zero-order Hamiltonian, single determinant as dual state) with Doubles and Singles and Doubles

    • PT2MDd (diagonal zero-order Hamiltonian, pCCD as dual state) with Doubles and Singles and Doubles

    • PT2SDo (off-diagonal zero-order Hamiltonian, single determinant as dual state) with Doubles and Singles and Doubles

    • PT2MDo (off-diagonal zero-order Hamiltonian, pCCD as dual state) with Doubles and Singles and Doubles

    • PT2b (off-diagonal zero-order Hamiltonian, pCCD as dual state, full Hamiltonian as perturbation operator) with Doubles and Singles and Doubles including/excluding electron pairs

• Equation of Motion Coupled Cluster methods

  • Equation of Motion CCS (EOM-CCS equivalent to CIS)

  • EOM-pCCD

  • EOM-pCCD+S (single excitation are included in the EOM ansatz only, while the CC ansatz is restricted to pCCD)

  • EOM-pCCD-CCS

  • EOM-LCCD

  • EOM-LCCSD

  • EOM-pCCD-LCCD

  • EOM-pCCD-LCCSD

  • EOM-CCD

  • EOM-CCSD

• Ionization Potential Equation of Motion Coupled Cluster methods

  • IP-pCCD with 1 hole and 2 hole 1 particle operators ($S_z = 0.5, 1.5$)

  • IP-CCD with 1 hole and 2 hole 1 particle operators ($S_z = 0.5, 1.5$)

  • IP-CCSD with 1 hole and 2 hole 1 particle operators ($S_z = 0.5, 1.5$)

  • IP-LCCD with 1 hole and 2 hole 1 particle operators ($S_z = 0.5, 1.5$)

  • IP-LCCSD with 1 hole and 2 hole 1 particle operators ($S_z = 0.5, 1.5$)

  • IP-fpCCD with 1 hole and 2 hole 1 particle operators ($S_z = 0.5, 1.5$)

  • IP-fpCCSD with 1 hole and 2 hole 1 particle operators ($S_z = 0.5, 1.5$)

  • IP-pCCD-LCCD with 1 hole and 2 hole 1 particle operators ($S_z = 0.5, 1.5$)

  • IP-pCCD-LCCSD with 1 hole and 2 hole 1 particle operators ($S_z = 0.5, 1.5$)

  • DIP-pCCD with 2 hole and 3 hole 1 particle operators ($S_z = 0.0, 1.0, 2.0$)

  • DIP-CCD with 2 hole and 3 hole 1 particle operators ($S_z = 0.0$)

  • DIP-CCSD with 2 hole and 3 hole 1 particle operators ($S_z = 0.0$)

  • DIP-LCCD with 2 hole and 3 hole 1 particle operators ($S_z = 0.0$)

  • DIP-LCCSD with 2 hole and 3 hole 1 particle operators ($S_z = 0.0$)

  • DIP-fpCCD with 2 hole and 3 hole 1 particle operators ($S_z = 0.0$)

  • DIP-fpCCSD with 2 hole and 3 hole 1 particle operators ($S_z = 0.0$)

  • DIP-fpLCCD with 2 hole and 3 hole 1 particle operators ($S_z = 0.0$)

  • DIP-fpLCCSD with 2 hole and 3 hole 1 particle operators ($S_z = 0.0$)

• Electron Attachment Equation of Motion Coupled Cluster methods

  • EA-pCCD with 1 particle and 2 particle 1 hole operators ($S_z = 0.5, 1.5$)

  • EA-CCD with 1 particle and 2 particle 1 hole operators ($S_z = 0.5$)

  • EA-CCSD with 1 particle and 2 particle 1 hole operators ($S_z = 0.5$)

  • EA-fpCCD with 1 particle and 2 particle 1 hole operators ($S_z = 0.5$)

  • EA-fpCCSD with 1 particle and 2 particle 1 hole operators ($S_z = 0.5$)

  • EA-LCCD with 1 particle and 2 particle 1 hole operators ($S_z = 0.5$)

  • EA-LCCSD with 1 particle and 2 particle 1 hole operators ($S_z = 0.5$)

  • EA-fpLCCD with 1 particle and 2 particle 1 hole operators ($S_z = 0.5$)

  • EA-fpLCCSD with 1 particle and 2 particle 1 hole operators ($S_z = 0.5$)

  • DEA-pCCD with 2 particle and 3 particle 1 hole operators ($S_z = 0.0, 1.0, 2.0$)

• Reversed Spin Flip Equation of Motion Coupled Cluster methods

  • RSF-CCD creating four unpaired electrons ($S_z = 2$)

  • RSF-CCSD creating four unpaired electrons ($S_z = 2$)

  • RSF-LCCD creating four unpaired electrons ($S_z = 2$)

  • RSF-LCCSD creating four unpaired electrons ($S_z = 2$)

  • RSF-fpCCD creating four unpaired electrons ($S_z = 2$)

  • RSF-fpCCSD creating four unpaired electrons ($S_z = 2$)

  • RSF-fpLCCD creating four unpaired electrons ($S_z = 2$)

  • RSF-fpLCCSD creating four unpaired electrons ($S_z = 2$)

• Linear Response Coupled Cluster methods

  • LR-pCCD: Transition density matrices, dipole strengths, and oscillator strengths

  • LR-pCCD+S: Transition density matrices, dipole strengths, and oscillator strengths

Post-Processing

• Orbital entanglement and correlation analysis

  • for a pCCD reference function

  • for a pCCD-LCC reference function

• Orbital localization

  • Pipek-Mezey orbital localization

• Property calculations

  • Multipole moments using response density matrcies: dipole, quadrupole, and octupole moments with HF, pCCD, pCCD-LCC wavefunctions

  • Multipole moments using expectation-value density matrcies: dipole, quadrupole, and octupole moments with HF, pCCD, and all supported CC wavefunctions

Citing PyBEST

Please, refer to PyBEST as follows:

Saman Behjou, Filip Brzęk, Rahul Chakraborty, Kacper Cieślak, Antonina Dobrowolska, Seyedehdelaram Jahani, Zahra Karimi, Michał Kopczyński, Aleksandra Leszczyk, Artur Nowak, Ram Dhari Pandey, Emil Sujkowski, Julia Szczuczko, Lena Szczuczko, Julian Świerczyński, Somayeh Ahmadkhani, Katharina Boguslawski, Iulia Brumboiu, Marta Gałyńska, Dariusz Kędziera, Maximilian H. Kriebel, Paweł Tecmer, Piotr Szymon Żuchowski, PyBEST 2.2.0, 2026

If you use PyBEST, please cite the following:

Katharina Boguslawski, Filip Brzęk, Rahul Chakraborty, Kacper Cieślak, Seyedehdelaram Jahani, Aleksandra Leszczyk, Artur Nowak, Emil Sujkowski, Julian Świerczyński, Somayeh Ahmadkhani, Dariusz Kędziera, Maximilian H. Kriebel, Piotr Szymon Żuchowski, Paweł Tecmer, "PyBEST: Improved functionality and enhanced performance", Computer Physics Communications, 297, 2024, https://doi.org/10.1016/j.cpc.2023.109049.

Katharina Boguslawski, Aleksandra Leszczyk, Artur Nowak, Filip Brzęk, Piotr Szymon Żuchowski, Dariusz Kędziera, Paweł Tecmer, "Pythonic Black-box Electronic Structure Tool (PyBEST). An open-source Python platform for electronic structure calculations at the interface between chemistry and physics", Computer Physics Communications, 264, 2021, https://doi.org/10.1016/j.cpc.2021.107933.

Contact Information

If you have questions, please send them to our developer e-mail address pybest@umk.pl

Alternatively, you may directly contact the authors of a specific part of PyBEST.