NEST is an open-source framework for developing methods based on noncollinear electronic structure theory. It is built on top of the PySCF electronic structure package.

                                 PySCF
                                   │
                                   ▼
                                 NEST
                    (Multicollinear Framework)
                                   │
        ┌──────────────────────────┼──────────────────────────┐
        │                          │                          │
        ▼                          ▼                          ▼
       GKS                        UKS                        ROKS
        │                          │                          │
        ▼                          ▼                          ▼
Noncollinear TDDFT         Noncollinear SF-TDDFT      Noncollinear Tensor TDA
                                   ├── Gradients            ├── Gradients (in progress)
                                   ├── Oscillator strengths └── SOC (in progress)
                                   ├── NADC
                                   └── SOC

• Noncollinear DFT

  A general framework for extending collinear density functionals to noncollinear systems using the multicollinear approach.

• Noncollinear TDDFT

  A general TDDFT framework applicable to both two-component and four-component noncollinear theories.

• Noncollinear Spin-Flip TDDFT (SF-TDDFT)

  Within the noncollinear TDDFT formalism, SF-TDDFT and conventional spin-conserving TDDFT naturally emerge as two decoupled sectors for collinear reference states.

  • Analytic gradients
  • Oscillator strengths
  • Analytic nonadiabatic derivative couplings (NADC)
  • Spin–orbit coupling (SOC)

• Noncollinear Tensor TDA (NT-TDA)

  NT-TDA is a spin-consistent extension of noncollinear TDDFT that provides a unified treatment of spin-conserving and spin-flip excitations. For an open-shell reference state with total spin S, it can describe target states with total spins S−1 (except for S = 1/2), S, and S+1. All resulting states are free from spin contamination.

  • Analytic gradients (in progress)
  • SOC (in progress)

Yunlong Xiao
Associate Professor, Peking University
Theory and project direction.
Email: xiaoyl@pku.edu.cn

Tai Wang
Ph.D. Student, Peking University
Software development and maintenance.
Email: wtpeter@pku.edu.cn

Hao Yang
Undergraduate Student, Peking University
Benchmark calculations and validation.

From the repository root, install NEST and its runtime dependencies in editable mode:

python -m pip install -e .

Install the test and lint tools for development:

python -m pip install -e ".[dev]"

Importing a feature module registers its methods on the corresponding PySCF mean-field objects:

from pyscf import gto
from nest import nttda, sftda

mol = gto.M(atom="H 0 0 0; H 0 0 1", spin=2)
uks = mol.UKS(xc="HF")
roks = mol.ROKS(xc="HF")
sf = uks.SFTDA()
nt = roks.NTTDA()

See examples for complete calculations.

NEST is released under the Apache License 2.0.

If you use NEST in your research, please cite the relevant publication(s) listed below.

• Multicollinear approach (PRR, 2023) https://doi.org/10.1103/PhysRevResearch.5.013036
• Matrix representation (WIREs, 2026) https://doi.org/10.1002/wcms.70063
• Nonlocal functionals (JCP, 2025) https://doi.org/10.1063/5.0260762

• Noncollinear TDDFT and noncollinear SF-TDDFT (JCTC, 2023) https://doi.org/10.1021/acs.jctc.3c00059
• Real-time noncollinear TDDFT (JCTC, 2024) https://doi.org/10.1021/acs.jctc.4c01218

• Analytic gradients (JCTC, 2025) https://doi.org/10.1021/acs.jctc.5c00115
• Zero-excitation-energy theorem (JCTC, 2025) https://doi.org/10.1021/acs.jctc.5c00714
• Conical intersections and spin crossings (JCTC, 2025) https://doi.org/10.1021/acs.jctc.5c01272
• Analytic nonadiabatic derivative couplings (JCTC, 2026) https://doi.org/10.1021/acs.jctc.6c00556

• NT-TDA (https://arxiv.org/abs/2607.19933, 2026)