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DoNOF 2.0: A modern Open-Source Electronic Structure Program for Natural Orbital Functionals

Juan Felipe Huan Lew-Yee, Ion Mitxelena, Jorge M. del Campo, and Mario Piris

TL;DR

DoNOF 2.0 advances natural orbital functional theory by delivering an open-source, multi-language electronic-structure platform that efficiently handles strong correlation and multireference character. The paper details the NOF framework, explicit ON and NO optimizations, and practical implementation choices, including EKT-based excited states, ERPA for neutral excitations, and finite-field Romberg-Richardson NLOP computations. New capabilities—excited-state analysis, nonlinear optical properties, and AIMD—are demonstrated alongside robust support for Python and Julia interfaces, expanding accessibility and interoperability. Collectively, these developments position DoNOF as a flexible, scalable tool for researchers pursuing NOF-based chemistry and functional development, with broad potential impact in challenging systems and reaction dynamics.

Abstract

In this work, we present the second version of the Donostia Natural Orbital Functional Software, an open-source program for natural orbital functional calculations. The new release incorporates improved optimization algorithms, capabilities for excited-state computations, support for ab initio molecular dynamics, and integration with the libcint library. DoNOF 2.0 also extends its property toolbox by enabling the evaluation of nonlinear optical responses, including static polarizabilities and higher-order hyperpolarizabilities via a finite-field Romberg-Richardson scheme. Program Summary [Title: DoNOF; Developer's repository link: http://github.com/DoNOF/; Program's Manual link: https://donof.readthedocs.io/; Licensing provisions: GPLv3; Programming language: Fortran; additional implementations available in Python (PyNOF) and Julia (DoNOF.jl); Multinode capability: Support for distributed execution through a hybrid OpenMPI and OpenMP implementation]

DoNOF 2.0: A modern Open-Source Electronic Structure Program for Natural Orbital Functionals

TL;DR

DoNOF 2.0 advances natural orbital functional theory by delivering an open-source, multi-language electronic-structure platform that efficiently handles strong correlation and multireference character. The paper details the NOF framework, explicit ON and NO optimizations, and practical implementation choices, including EKT-based excited states, ERPA for neutral excitations, and finite-field Romberg-Richardson NLOP computations. New capabilities—excited-state analysis, nonlinear optical properties, and AIMD—are demonstrated alongside robust support for Python and Julia interfaces, expanding accessibility and interoperability. Collectively, these developments position DoNOF as a flexible, scalable tool for researchers pursuing NOF-based chemistry and functional development, with broad potential impact in challenging systems and reaction dynamics.

Abstract

In this work, we present the second version of the Donostia Natural Orbital Functional Software, an open-source program for natural orbital functional calculations. The new release incorporates improved optimization algorithms, capabilities for excited-state computations, support for ab initio molecular dynamics, and integration with the libcint library. DoNOF 2.0 also extends its property toolbox by enabling the evaluation of nonlinear optical responses, including static polarizabilities and higher-order hyperpolarizabilities via a finite-field Romberg-Richardson scheme. Program Summary [Title: DoNOF; Developer's repository link: http://github.com/DoNOF/; Program's Manual link: https://donof.readthedocs.io/; Licensing provisions: GPLv3; Programming language: Fortran; additional implementations available in Python (PyNOF) and Julia (DoNOF.jl); Multinode capability: Support for distributed execution through a hybrid OpenMPI and OpenMP implementation]

Paper Structure

This paper contains 14 sections, 28 equations, 4 figures, 3 tables.

Table of Contents

  1. Introduction
  2. Theory
  3. Occupation Number Optimization
  4. Natural Orbital Optimization
  5. Computational Details
  6. Single Point Energy Calculations
  7. Excited States
  8. NLOPs: Polarizabilities and Hyperpolarizabilities
  9. Gradients, Hessian and Optimization
  10. NOF-based molecular dynamics
  11. PyNOF + DoNOF.jl
  12. Conclusions
  13. Acknowledgements
  14. References

Figures (4)

  • Figure 1: Representation of the orbital-pairing structure for a system with 8 electrons. In this example, $S = 1$ (triplet) and $\mathrm{N_{I}} = 2$, so two orbitals make up the subspace $\Omega_\text{I}$, whereas six electrons ($\mathrm{N_{II}} = 6$) make up the subspace $\Omega_\text{II}$. Note that $\mathrm{N}_{g} = 2$. The arrows depict the values of the ensemble ONs, $\alpha$ ($\uparrow$) or $\beta$ ($\downarrow$), in each orbital.
  • Figure 2: Energy of N2/cc-pVDZ computed using several NOFs, compared with HF and CCSD(T).
  • Figure 3: Potential energy curve of H2 with excited states computed using PNOF-ERPA2 and the cc-pVDZ basis set.
  • Figure 4: Selected snapshots from the F- + H2 -> FH + H- dynamics. The bottom row indicates the time stamps corresponding to each snapshot.