The Python Simulations of Chemistry Framework: 10 years of an open-source quantum chemistry project

I. INTRODUCTION

• PySCF has more than 500,000 lines of code, over 1,000 dependent GitHub projects, and more than 1,000,000 annual downloads.Version 2.12 marks ten years since the first stable public release in 2015.Source: §I · p. 7
• The project’s developments since the previous overview target demands for high-throughput calculations, larger systems, and emerging hardware and programming paradigms.The review also provides an outlook on the project’s future.Source: §I · p. 7

A. Code organization

• PySCF’s expanded codebase is organized into core, staging, and companion repositories, alongside community extensions that are not officially supported.The core repository focuses on modules expected to serve the widest range of applications; pyscf-forge stages experimental features.Source: A. Code organization · p. 8

B. Periodic electronic structure infrastructure

• Periodic calculations can use FFTDF with plane-wave auxiliary bases or GDF with atom-centered Gaussian bases, selected for their different performance characteristics.FFTDF improvements support a broad range of applications when pseudopotentials are acceptable; GDF supports all-electron bases and hybrid or exact-exchange mean-field calculations.Source: B. Periodic electronic structure… · pp. 8–9
• Multigrid FFTDF enables DFT iterations on systems with up to 20,000 basis functions in a few seconds on one GPU.The implementation achieves state-of-the-art performance on CPUs and GPUs, and its GPU parallelization can saturate modern NVIDIA A100 and H100 GPUs.Source: B. Periodic electronic structure… · pp. 8–9
• Range-separated GDF accelerates large-unit-cell hybrid DFT and post-HF calculations, while RSJK supports efficient hybrid DFT for modest cells with more than 10,000 k-points.RSGDF is suited to Γ-point and moderate k-point counts, typically up to about 100.Source: B. Periodic electronic structure… · p. 9
• PySCF adds pure plane-wave infrastructure for three-dimensional periodic systems, supporting HF, DFT, MP2, and restricted CCSD.This infrastructure is currently in pyscf-forge and includes space-group symmetry, occupation smearing, and utilities for converting virtual orbitals to Gaussian bases before post-HF calculations.Source: B. Periodic electronic structure… · pp. 9–10

C. Density functional theory and related methods

• PySCF derives VV10 nonlocal-correlation derivatives through second order, enabling analytic gradients, Hessians, and polarizabilities, and refactors DFT modules for DFT-D3 and DFT-D4.The reported derivatives also enable related properties.Source: C. Density functional theory and… · p. 10
• Multi-collinear DFT supports energy evaluation and higher-order derivatives, while TDDFT adds higher-order derivatives, spin-flip calculations, and derivative couplings.The framework supports non-collinear GKS with spin-orbit coupling and two- and four-component relativistic Dirac-Kohn-Sham calculations.Source: C. Density functional theory and… · p. 10
• Seminumerical exchange has been accelerated using efficient grids, modified Becke partitioning, and density-matrix screening with tunable energy and potential error tolerances.The screening algorithm reduces asymptotic scaling for large systems.Source: C. Density functional theory and… · pp. 10–11
• PySCF broadens molecular and materials property calculations to include IR and Raman spectra, energy decomposition analysis, and four-component parity-violating contributions.The supplied passages also report periodic dipole moments, polarizabilities, hyperpolarizabilities, and X2C relativistic corrections; gradients and stress tensors are available for DFT and DFT+U solids.Source: C. Density functional theory and… · pp. 11–12
• DFT+U supports molecules and solids, with Γ-point and k-point sampling for periodic calculations and linear-response methods to obtain system-specific Hubbard U parameters.The linear-response method is available in both molecular and periodic modules.Source: C. Density functional theory and… · p. 12

D. High-order and low-scaling correlated wavefunction quantum chemistry

• Compact implementations of CCSDT and CCSDTQ use t1-dressed equations, symmetry-aware amplitude storage, and parallelized C routines, with memory as the main limit.With 30 electrons and 1.5 TB of memory, calculations can reach about 400 orbitals for CCSDT and 80 for CCSDTQ.Source: D. High-order and low-scaling… · p. 13
• LNO-CCSD and LNO-CCSD(T) solve overlapping fragment problems using truncated local natural orbital spaces, with an eigenvalue threshold controlling accuracy and cost.These methods can handle systems with about 5,000 orbitals, and ISDF can push that limit further.Source: D. High-order and low-scaling… · p. 13
• LNO infrastructure has been reused for automatic differentiation, providing CCSD(T) gradients and response properties for large systems and supporting low-scaling auxiliary-field quantum Monte Carlo development.The local methods are available for molecules and periodic solids, with or without k-point sampling.Source: D. High-order and low-scaling… · p. 14
• The protonated water-cluster figure presents experimental IR spectra, including probes of transitions at 3159 cm−1 and 3715 cm−1.The spectra are for H+(H2O)6·H2.Source: D. High-order and low-scaling… · p. 15, Figure 3 · p. 15

E. Auxiliary field quantum Monte Carlo

• Embedding AFQMC in the correlated-wavefunction framework enables direct method comparisons and mixing, including correlated-wavefunction trial states.The latest version introduces AFQMC support.Source: E. Auxiliary field quantum Monte Carlo · pp. 15–16
• AFQMC stochastically propagates a trial state in imaginary time; the phaseless approximation addresses the sign problem but introduces bias dependent on trial-wavefunction quality.The passage marks the phaseless approximation with 55.Source: E. Auxiliary field quantum Monte Carlo · p. 16
• With fixed stochastic error, HF-trial AFQMC scales as O(N^5) and is typically between CCSD and CCSD(T) in accuracy, while CISD trials scale as O(N^6) and often exceed CCSD(T).The stated accuracy comparison for HF trials is marked 57; the CISD-trial algorithms are marked 58.Source: E. Auxiliary field quantum Monte Carlo · p. 16
• 1000 orbitals are supported, with memory for two-electron integrals in a 3-index tensor format the main bottleneck.The integrals are stored via density fitting or Cholesky decomposition.Source: E. Auxiliary field quantum Monte Carlo · p. 17
• CISD-trial AFQMC is exact for two-electron systems and highly accurate for organic molecules, transition states, and systems containing transition metals.Its deviations from exact size-extensivity are generally modest.Source: E. Auxiliary field quantum Monte Carlo · p. 17
• LNO AFQMC is intended to enable linear scaling, but an LNO version with a CISD trial is unavailable because its lack of strict size-extensivity complicates a local formulation.The framework parallels LNO-CCSD, and work to address the limitation is in progress.Source: E. Auxiliary field quantum Monte Carlo · p. 17

F. Excited state theories

• TDDFT supports linear-response and spin-flip methods, excited-state properties and gradients, periodic excitons, continuum solvation, and derivative couplings for non-adiabatic dynamics.TDDFT-ris uses a minimal auxiliary basis to approximate Coulomb and exchange-type integrals, with substantial speedups over conventional TDDFT.Source: F. Excited state theories · pp. 18–19
• ppRPA extends PySCF beyond particle–hole RPA, supporting neutral excitations in molecular and periodic systems without k-point sampling.Its capabilities include valence, double, charge-transfer, Rydberg, and spin-defect excitations, plus oscillator strengths, natural transition orbitals, analytic gradients, and relativistic corrections.Source: F. Excited state theories · p. 19
• ADC provides neutral excitation energies, ionization potentials, and electron affinities, with Dyson orbitals and other properties for characterizing states.It supports open-shell references and periodic charged excitations, enabling band structures and photoelectron spectra of crystalline materials.Source: F. Excited state theories · pp. 19–20
• PySCF's GW implementations span numerical and self-consistency strategies for quasiparticle energies, with complementary options for balancing accuracy and efficiency across core and valence regimes.The package also supports molecular GW+BSE neutral excitations and optical spectra, as well as one-particle spectral functions at several many-body theory levels.Source: F. Excited state theories · pp. 20–21
• EOM-CCSD covers neutral, spin-flip, ionization-potential, and electron-attachment excitations, and has been generalized to periodic systems for quasiparticle and excitonic excitations in solids.Improvements to solver stability, memory usage, and parallel scalability enhance reliability across molecular and extended systems.Source: F. Excited state theories · p. 21
• More efficient eigensolvers and density-fitting techniques reduce cost and improve robustness, while consistent transition-property handling simplifies workflows combining methods.GPU acceleration and improved parallelization are beginning to reach excited-state modules.Source: F. Excited state theories · p. 22

G. Multireference wavefunction methods and multireference density

• SA-MCSCF now supports analytical nuclear gradients and non-adiabatic couplings, while PySCF adds DSRG methods, DSRG-MRPT2, APC active-space selection, and NOCI-based methods.APC complements AVAS for automating active-space selection in high-throughput workflows.Source: G. Multireference wavefunction methods… · p. 22
• MC-PDFT adds dynamical-correlation treatment for highly multiconfigurational states, with accuracy comparable to second-order multireference perturbation theory at much lower computational cost.Its protocol evaluates density and pair density from an unmodified underlying MCSCF wave function and supports available state-averaging schemes.Source: G. Multireference wavefunction methods… · pp. 22–23
• MC-PDFT supports modified full-CI solvers and active-space approximations such as DMRG when the required reduced density matrices are available.Such modifications usually disable analytical energy-gradient support; naïve MC-PDFT can also be qualitatively inaccurate near conical intersections or locally avoided crossings, motivating multi-state methods including L-PDFT.Source: G. Multireference wavefunction methods… · p. 23
• MC-PDFT's on-top density-functional component uses translated or fully translated functionals, with compatibility depending on the functional family and translation scheme.Both schemes support LDA and GGA functionals; the original translation scheme also supports certain meta-GGA functionals using kinetic energy density.Source: G. Multireference wavefunction methods… · p. 23
• Analytical MC-PDFT energy gradients are available for CASSCF and SA-CASSCF references, with gradients and non-adiabatic coupling vectors for some multi-state calculations and functional types.Spin–orbit effects can be included through a two-step state-interaction approach, and analytical dipole moments are among the implemented properties.Source: G. Multireference wavefunction methods… · p. 23

H. Molecular dynamics

• The MD module supports NVE velocity-Verlet and NVT Berendsen-thermostat simulations, with thermal initial velocities sampled from a user-specified Maxwell–Boltzmann distribution.More sophisticated thermostats are being implemented.Source: H. Molecular dynamics · p. 24
• Any PySCF electronic-structure method providing analytic gradients can propagate nuclei on its potential energy surface for computing spectroscopic and thermodynamic properties or probing reaction dynamics.NVE dynamics also offers a practical way to check active-space stability for CASSCF and MC-PDFT simulations.Source: H. Molecular dynamics · p. 24
• The integrated MD module provides a platform for testing machine-learning approaches that use intermediate electronic-structure information and for generating training datasets for machine-learned potentials.The paper describes the module as supporting hybrid quantum-machine-learning approaches within one Python-based platform.Source: H. Molecular dynamics · pp. 24–25

I. Solvation models and QM/MM

• Since PySCF 2.6.0, implicit-solvent support includes four additional PCM-type models with analytical gradients and Hessians, alongside dd-COSMO, dd-PCM, and SMD.SMD includes non-electrostatic terms modeled with solvent-accessible surface area and atomic surface tension.Source: §I · p. 25
• The solvent implementations use a direct solver; IEF-PCM and SS(V)PE require several times more memory than C-PCM and COSMO, and are designed for molecules under 100 atoms.For larger molecules, dd-COSMO and dd-PCM are recommended, but their analytical Hessians are unavailable; solvent calculations also support HF, DFT, TDDFT, and post-HF methods.Source: §I · p. 25
• Periodic QM/MM embeds a QM subsystem in periodic classical point or Gaussian-distributed charges and treats long-range electrostatics with a controllable-error multipolar Ewald approach.Analytic gradients for QM and MM positions enable geometry optimization and molecular dynamics on the QM/MM potential-energy surface; GPU acceleration covers QM/MM computational bottlenecks.Source: §I · pp. 25–26

• GPU4PySCF focuses mainly on DFT and related methods; its listed post-HF support is limited to integral-in-core restricted MP2 and CCSD, and multi-GPU scaling efficiency is relatively low.Most features run on a single GPU; the stated post-HF scope is for version 1.4.2.Source: J. GPU4PySCF · p. 26
• GPU4PySCF achieves 2–3 orders of magnitude speedup over PySCF CPU code; for medium-sized molecules, some single-A100 DF-DFT calculations outperform 1,000 CPU cores.The reported medium-sized range is 50–100 atoms.Source: J. GPU4PySCF · pp. 26–27
• Figure 8 tracks QM/MM energy convergence for GTP hydrolysis as the cutoff for short-range multipolar components increases.Source: Figure 8 · p. 27, J. GPU4PySCF · p. 27
• Density fitting delivers substantial GPU speedups for DFT ground-state energies, nuclear gradients, nuclear Hessians, and TDDFT.The passage attributes this advantage to tensor-contraction operations on GPUs.Source: J. GPU4PySCF · p. 27
• For molecules with more than 5,000 basis functions, integral-direct calculations perform particularly well, and GPU4PySCF routinely handles 30,000-basis-function calculations on one 80 GB VRAM GPU.Source: J. GPU4PySCF · p. 28
• Compatible PySCF and GPU4PySCF classes provide conversion methods, and GPU4PySCF generally follows PySCF naming, module structure, and function signatures.The .to_gpu() method converts a PySCF instance and its attributes to corresponding GPU4PySCF objects.Source: J. GPU4PySCF · p. 28

• PySCFAD is a fully differentiable, in-core reimplementation of PySCF that uses automatic differentiation to support property calculations and response theory.Source: K. PySCFAD · p. 29
• PySCFAD supports NumPy and JAX backends, with JAX providing differentiability and hardware acceleration via JIT compilation; included methods allow up to fourth-order nuclear derivatives.The listed subset includes HF, DFT, MP2, RPA, coupled-cluster, and orbital localization methods.Source: K. PySCFAD · p. 29
• The GFN1-xTB implementation in PySCFAD surpasses dxtb in most cases and uses JAX automatic vectorization for efficient batched calculations.Source: K. PySCFAD · p. 30
• Electron-integral evaluation in PySCFAD is currently CPU-only, despite JAX hardware acceleration elsewhere in the program.The authors identify integrating efficient GPU4PySCF electron-integral kernels as a future direction.Source: K. PySCFAD · p. 30

• Integration with libmsym enables generation of symmetry-adapted real orbitals from spherical atomic orbitals for any point group.Source: L. Symmetry · p. 31
• FCI solvers can impose cylindrical symmetry on wavefunctions, and a configuration state function formulation supports spin-symmetry-adapted FCI calculations.Source: L. Symmetry · p. 31
• With periodic boundary conditions, native space-group symmetry supports adapted mean-field, MP2, and coupled-cluster calculations using k-point sampling.Source: L. Symmetry · p. 31

M. Interoperability

• PySCF connects with ASE for molecular energy and force calculations and periodic mean-field stress tensors, and supports TREXIO, QCSchema, community file formats, Basis Set Exchange basis sets, and COSMO-RS exports.Source: M. Interoperability · p. 31

III. CONCLUSIONS

• After ten years, PySCF is described as mature cyberinfrastructure for quantum chemistry, materials modeling, machine learning, and quantum information science.Source: §III · p. 31
• The authors anticipate further work on GPU support, low-precision computation, PySCFAD and JIT compilation, linear-scaling methods, electron correlation, and molecular dynamics on ab initio-quality potential energy surfaces.Source: §III · p. 32