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--- /dev/null
+++ b/jose.00286/10.21105.jose.00286.crossref.xml
@@ -0,0 +1,238 @@
+
+
+
+ 20250904145200-65c7d80fc9d546a236aa1c875e628b945f4f96a5
+ 20250904145200
+
+ JOSS Admin
+ admin@theoj.org
+
+ The Open Journal
+
+
+
+
+ Journal of Open Source Education
+ JOSE
+ 2577-3569
+
+ 10.21105/jose
+ https://jose.theoj.org
+
+
+
+
+ 09
+ 2025
+
+
+ 8
+
+ 91
+
+
+
+ PyQInt: A Teaching-Oriented Hartree–Fock Implementation in Python
+
+
+
+ I. A. W.
+ Filot
+
+ Inorganic Materials and Catalysis, Department of Chemical Engineering and Chemistry, Eindhoven University of Technology
+
+ https://orcid.org/0000-0003-1403-8379
+
+
+
+ 09
+ 04
+ 2025
+
+
+ 286
+
+
+ 10.21105/jose.00286
+
+
+ http://creativecommons.org/licenses/by/4.0/
+ http://creativecommons.org/licenses/by/4.0/
+ http://creativecommons.org/licenses/by/4.0/
+
+
+
+ Software archive
+ 10.5281/zenodo.17055029
+
+
+ GitHub review issue
+ https://github.com/openjournals/jose-reviews/issues/286
+
+
+
+ 10.21105/jose.00286
+ https://jose.theoj.org/papers/10.21105/jose.00286
+
+
+ https://jose.theoj.org/papers/10.21105/jose.00286.pdf
+
+
+
+
+
+ New developments in molecular orbital theory
+ Roothaan
+ Reviews of Modern Physics
+ 23
+ 10.1103/RevModPhys.23.69
+ 1951
+ Roothaan, C. C. J. (1951). New developments in molecular orbital theory. Reviews of Modern Physics, 23, 69–89. https://doi.org/10.1103/RevModPhys.23.69
+
+
+ Spin-unrestricted character of kohn-sham orbitals for open-shell systems
+ Pople
+ International Journal of Quantum Chemistry
+ 4
+ 56
+ 10.1002/qua.560560414
+ 1995
+ Pople, J. A., Gill, P. M. W., & Handy, N. C. (1995). Spin-unrestricted character of kohn-sham orbitals for open-shell systems. International Journal of Quantum Chemistry, 56(4), 303–305. https://doi.org/10.1002/qua.560560414
+
+
+ Convergence acceleration of iterative sequences. The case of scf iteration
+ Pulay
+ Chemical Physics Letters
+ 2
+ 73
+ 10.1016/0009-2614(80)80396-4
+ 0009-2614
+ 1980
+ Pulay, P. (1980). Convergence acceleration of iterative sequences. The case of scf iteration. Chemical Physics Letters, 73(2), 393–398. https://doi.org/10.1016/0009-2614(80)80396-4
+
+
+ Gaussian-expansion methods for molecular integrals
+ Taketa
+ Journal of the Physical Society of Japan
+ 11
+ 21
+ 10.1143/JPSJ.21.2313
+ 1966
+ Taketa, H., Huzinaga, S., & O-ohata, K. (1966). Gaussian-expansion methods for molecular integrals. Journal of the Physical Society of Japan, 21(11), 2313–2324. https://doi.org/10.1143/JPSJ.21.2313
+
+
+ Crystal orbital hamilton populations (COHP): Energy-resolved visualization of chemical bonding in solids based on density-functional calculations
+ Dronskowski
+ The Journal of Physical Chemistry
+ 33
+ 97
+ 10.1021/j100135a014
+ 1993
+ Dronskowski, R., & Bloechl, P. E. (1993). Crystal orbital hamilton populations (COHP): Energy-resolved visualization of chemical bonding in solids based on density-functional calculations. The Journal of Physical Chemistry, 97(33), 8617–8624. https://doi.org/10.1021/j100135a014
+
+
+ Students’ levels of explanations, models, and misconceptions in basic quantum chemistry: A phenomenographic study
+ Stefani
+ Journal of Research in Science Teaching
+ 46
+ 10.1002/tea.20279
+ 2009
+ Stefani, C., & Tsaparlis, G. (2009). Students’ levels of explanations, models, and misconceptions in basic quantum chemistry: A phenomenographic study. Journal of Research in Science Teaching, 46, 520–536. https://doi.org/10.1002/tea.20279
+
+
+ Reducing student misconceptions through problem-based learning with a computational chemistry-assisted question map approach
+ Hulyadi
+ Jurnal Penelitian Pendidikan IPA
+ 09
+ 10.29303/jppipa.v9i12.5936
+ 2023
+ Hulyadi, H., Muhali, M., & Gargazi, G. (2023). Reducing student misconceptions through problem-based learning with a computational chemistry-assisted question map approach. Jurnal Penelitian Pendidikan IPA, 09, 11207–11217. https://doi.org/10.29303/jppipa.v9i12.5936
+
+
+ Density-functional thermochemistry. III. The role of exact exchange
+ Becke
+ The Journal of Chemical Physics
+ 7
+ 98
+ 10.1063/1.464913
+ 0021-9606
+ 1993
+ Becke, A. D. (1993). Density-functional thermochemistry. III. The role of exact exchange. The Journal of Chemical Physics, 98(7), 5648–5652. https://doi.org/10.1063/1.464913
+
+
+ Development of the colle-salvetti correlation-energy formula into a functional of the electron density
+ Lee
+ Physical Review B
+ 37
+ 10.1103/PhysRevB.37.785
+ 1988
+ Lee, C., Yang, W., & Parr, R. G. (1988). Development of the colle-salvetti correlation-energy formula into a functional of the electron density. Physical Review B, 37, 785–789. https://doi.org/10.1103/PhysRevB.37.785
+
+
+ General performance of density functionals
+ Sousa
+ The Journal of Physical Chemistry A
+ 42
+ 111
+ 10.1021/jp0734474
+ 2007
+ Sousa, S. F., Fernandes, P. A., & Ramos, M. J. (2007). General performance of density functionals. The Journal of Physical Chemistry A, 111(42), 10439–10452. https://doi.org/10.1021/jp0734474
+
+
+ Construction of some molecular orbitals to be approximately invariant for changes from one molecule to another
+ Boys
+ Reviews of Modern Physics
+ 32
+ 10.1103/RevModPhys.32.296
+ 1960
+ Boys, S. F. (1960). Construction of some molecular orbitals to be approximately invariant for changes from one molecule to another. Reviews of Modern Physics, 32, 296–299. https://doi.org/10.1103/RevModPhys.32.296
+
+
+ Editorial: Modern architectures and their impact on electronic structure theory
+ Gordon
+ Chemical Reviews
+ 17
+ 120
+ 10.1021/acs.chemrev.0c00700
+ 2020
+ Gordon, M. S., & Windus, T. L. (2020). Editorial: Modern architectures and their impact on electronic structure theory. Chemical Reviews, 120(17), 9015–9020. https://doi.org/10.1021/acs.chemrev.0c00700
+
+
+ Modern quantum chemistry: Introduction to advanced electronic structure theory
+ Szabo
+ 1996
+ Szabo, A., & Ostlund, N. S. (1996). Modern quantum chemistry: Introduction to advanced electronic structure theory. Dover.
+
+
+ Elements of electronic structure theory
+ Filot
+ 978-90-386-6477-4
+ 2025
+ Filot, I. A. W. (2025). Elements of electronic structure theory. Eindhoven University of Technology Library. ISBN: 978-90-386-6477-4
+
+
+ PyQInt documentation
+ Filot
+ 2025
+ Filot, I. A. W. (2025). PyQInt documentation. https://ifilot.github.io/pyqint/index.html
+
+
+ Matplotlib: A 2D graphics environment
+ Hunter
+ Computing in Science & Engineering
+ 3
+ 9
+ 10.1109/MCSE.2007.55
+ 2007
+ Hunter, J. D. (2007). Matplotlib: A 2D graphics environment. Computing in Science & Engineering, 9(3), 90–95. https://doi.org/10.1109/MCSE.2007.55
+
+
+
+
+
+
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+
+
+
+
+
+
+
+Journal of Open Source Education
+JOSE
+
+2577-3569
+
+Open Journals
+
+
+
+286
+10.21105/jose.00286
+
+PyQInt: A Teaching-Oriented Hartree–Fock Implementation
+in Python
+
+
+
+https://orcid.org/0000-0003-1403-8379
+
+Filot
+I. A. W.
+
+
+*
+
+
+
+Inorganic Materials and Catalysis, Department of Chemical
+Engineering and Chemistry, Eindhoven University of
+Technology
+
+
+
+
+* E-mail:
+
+
+3
+9
+2023
+
+8
+91
+286
+
+Authors of papers retain copyright and release the
+work under a Creative Commons Attribution 4.0 International License (CC
+BY 4.0)
+2025
+The article authors
+
+Authors of papers retain copyright and release the work under
+a Creative Commons Attribution 4.0 International License (CC BY
+4.0)
+
+
+
+Quantum chemistry
+Electronic structure theory
+Hartree-Fock
+Gaussian basis functions
+Molecular integrals
+SCF method
+
+
+
+
+
+ Summary
+
PyQInt is a modular Python package for
+ learning and prototyping quantum chemistry methods, with a particular
+ focus on the Hartree-Fock formalism
+ (Roothaan,
+ 1951) using Gaussian-type orbitals
+ (Pople
+ et al., 1995). Designed to prioritize educational transparency,
+ PyQInt exposes all computational building
+ blocks—integrals, matrices, Hamiltonians, SCF procedures, and
+ gradients—through a clean, inspectable API.
+
Users can evaluate molecular integrals
+ (Taketa
+ et al., 1966), perform self-consistent field calculations with
+ direct inversion of iterative subspace (DIIS)
+ (Pulay,
+ 1980), construct and localize orbitals, compute crystal orbital
+ Hamilton population (COHP) coefficients
+ (Dronskowski
+ & Bloechl, 1993), and optimize molecular geometries.
+ PyQInt is especially well suited for students
+ and researchers who want to interact with and understand the
+ underlying steps of electronic structure theory, offering full access
+ to intermediate data structures and algorithmic pathways.
+
While numerical efficiency is not the primary goal,
+ PyQInt connects to a C++ backend for integral
+ evaluation, enabling practical computations on small molecules. The
+ package is fully documented and tested, and is ideal for use in
+ courses, tutorials, or prototyping new electronic structure ideas.
+
+
+ Statement of need
+
Electronic structure theory plays a foundational role in modern
+ computational chemistry, with widespread applications in materials
+ discovery, catalyst design, drug development, and the prediction of
+ molecular properties. As simulation tools become increasingly powerful
+ and accessible, they are now integral to both academic research and
+ industrial workflows
+ (Gordon
+ & Windus, 2020).
+
However, many students and early-career researchers engage with
+ these tools as users—relying on established software packages—without
+ gaining a clear understanding of the underlying theoretical models,
+ numerical procedures, or methodological limitations. This lack of
+ transparency can lead to misinterpretation of results, inappropriate
+ method selection, and an underappreciation of the approximations
+ involved in electronic structure calculations
+ (Hulyadi
+ et al., 2023;
+ Stefani
+ & Tsaparlis, 2009).
+
Although the Hartree-Fock (HF) method is rarely used in isolation
+ for practical applications, it remains a critical pedagogical
+ foundation for understanding more advanced approaches such as Density
+ Functional Theory (DFT) and post-Hartree-Fock correlation methods
+ (Szabo
+ & Ostlund, 1996). In particular, the explicit evaluation of
+ the exchange energy in Hartree-Fock forms the conceptual and
+ mathematical basis for hybrid functionals like B3LYP
+ (Becke,
+ 1993;
+ Lee
+ et al., 1988), which are among the most widely used methods in
+ applied quantum chemistry
+ (Sousa
+ et al., 2007).
+
PyQInt is designed to support education and
+ exploration in electronic structure theory through a modular and
+ transparent implementation of Hartree–Fock methodology using
+ Gaussian-type orbitals. In contrast to software packages that abstract
+ away computational details, PyQInt provides access to individual steps
+ such as integral evaluation, matrix construction, SCF procedures, and
+ orbital manipulation. This structure makes the program suitable for
+ instructional use as well as for prototyping and method
+ development.
+
+
Visualization of the coefficient matrix from a
+ Hartree–Fock calculation of the CO molecule using an STO-3g basis
+ set, obtained using PyQInt. The numeric
+ values shown along the x-axis correspond to orbital energies.
+
+
+
+
+
+ Features
+
PyQInt is a Python-based software package
+ developed to support instruction and exploration in electronic
+ structure theory. It implements the Hartree–Fock method using
+ Gaussian-type orbitals, with a particular emphasis on clarity,
+ inspectability, and modularity. Designed as both a pedagogical tool
+ and a platform for method prototyping, PyQInt
+ exposes the underlying components of electronic structure calculations
+ in a form that facilitates learning and experimentation. In addition
+ to its modular structure, the source code is richly commented
+ throughout, with the explicit intention that students and early-stage
+ researchers can read and understand the implementation details. This
+ transparency allows users not only to use the code but also to study
+ it as an educational resource, reinforcing theoretical concepts
+ through hands-on engagement with working algorithms.
+
The package provides functionality for constructing and
+ manipulating Gaussian basis functions, along with the evaluation of
+ the corresponding one- and two-electron integrals. These integrals are
+ computed using a C++ backend with OpenMP parallelization, which
+ ensures efficient performance suitable for small to medium-sized
+ systems. This low-level access supports detailed exploration of
+ integral evaluation and basis set structure. In addition, PyQInt
+ includes higher-level capabilities such as self-consistent field (SCF)
+ Hartree–Fock calculations with DIIS acceleration, orbital localization
+ using the Foster–Boys method
+ (Boys,
+ 1960), Crystal Orbital Hamilton Population (COHP) analysis
+ (Dronskowski
+ & Bloechl, 1993), and geometry optimization based on
+ analytic energy gradients.
+
A key design feature is that all calculations return structured
+ Python dictionary objects, which expose the internal matrices and
+ multidimensional arrays used during computation. These include, for
+ example, the overlap, kinetic energy, Coulomb, coefficient (see
+ [fig:co-coefficient]),
+ and Fock matrices, as well as the four-dimensional array representing
+ the two-electron repulsion integrals. By providing this level of
+ access, the program allows users to inspect, manipulate, and recompute
+ quantities such as electronic energy and orbital-specific
+ contributions using standard tools such as NumPy. This design supports
+ a more detailed understanding of the theoretical framework and
+ computational procedures that underpin quantum chemical models.
+
PyQInt also supports molecular orbital
+ visualization through both two-dimensional contour plots
+ ([fig:co-contour])
+ via Matplotlib
+ (Hunter,
+ 2007) and three-dimensional isosurface rendering
+ ([fig:co-isosurface]).
+ These features aid in connecting computational results to chemical
+ concepts and spatial representations.
+
+
Two-dimensional contour plots of selected molecular
+ orbitals of the CO molecule, visualized using
+ PyQInt. The titles of the subplots indicate
+ the corresponding orbital
+ energies.
+
+
+
+
Three-dimensional isosurface representations of selected
+ molecular orbitals of the CO molecule, generated with PyQInt and
+ rendered using
+ Blender.
+
+
+
All features of PyQInt are accompanied by comprehensive
+ documentation, which includes numerous examples and explanatory
+ materials. The documentation is designed to guide users through both
+ basic and advanced functionality, with an emphasis on clarity and
+ reproducibility. Many of the examples are presented as richly
+ commented Python code snippets, illustrating typical use cases and
+ highlighting key computational steps. This approach allows users to
+ connect theoretical concepts with practical implementation and lowers
+ the barrier to entry for students and early-stage researchers engaging
+ with electronic structure theory through programming.
+
+
+ Use in Teaching and Curriculum
+
PyQInt is one of two computational tools
+ used throughout the open-access textbook Elements of
+ Electronic Structure Theory
+ (Filot,
+ 2025a), which is freely available online. The textbook combines
+ theoretical instruction with practical Python-based exercises, aiming
+ to provide students with both a conceptual foundation and a working
+ familiarity with electronic structure methods.
+ PyQInt is introduced as a lightweight and
+ readable implementation of Hartree–Fock theory, enabling learners to
+ explore the mathematical and computational framework of quantum
+ chemistry from first principles.
+
The software supports exercises focused on basis function
+ construction, integral evaluation, self-consistent field procedures,
+ and orbital analysis. These activities are intended to promote active
+ engagement with the subject matter by encouraging students to
+ investigate and manipulate the internal components of electronic
+ structure calculations, rather than relying exclusively on
+ preconfigured, black-box software. The modular architecture of
+ PyQInt is consistent with the pedagogical
+ progression adopted in the accompanying textbook, facilitating
+ incremental learning and conceptual reinforcement through hands-on,
+ code-based experimentation.
+
PyQInt has been used in four iterations of
+ the course Theoretical and Computational Chemistry at
+ Eindhoven University of Technology, where it was
+ integrated into lectures and assignments. Student feedback collected
+ through course evaluations indicates a high level of appreciation for
+ the tool, with many students identifying it as instrumental in
+ developing their understanding of electronic structure calculations.
+ The transparency of the code and the accessibility of key
+ computational elements have been noted as particularly valuable for
+ clarifying how abstract theoretical concepts are translated into
+ numerical procedures.
+
This integration highlights the effectiveness of
+ PyQInt as an educational resource, particularly
+ in settings where algorithmic transparency and practical skill
+ development are prioritized. By facilitating direct interaction with
+ core matrices, energy terms, and orbital visualizations, the software
+ supports deeper insight into both the theory and implementation of
+ electronic structure methods. It is well suited for use in
+ introductory courses, flipped classroom environments, and independent
+ study contexts.
+
+
+ Availability and Deployment
+
In addition to its educational utility,
+ PyQInt is distributed through widely used
+ package managers, including PyPI and Anaconda, which simplifies
+ installation and integration across a range of computing environments.
+ This accessibility ensures that students and instructors can easily
+ incorporate the software into classroom exercises, Jupyter Notebooks,
+ or larger Python-based projects without the need for complex setup
+ procedures. The ability to install PyQInt with
+ a single command facilitates its use in teaching environments where
+ consistency and ease of deployment are critical, while also making it
+ suitable for use in virtual labs, remote instruction, and open science
+ workflows. Detailed documentation, including the installation
+ procedure, are available online
+ (Filot,
+ 2025b).
+
+
+
+
+
+
+
+
+ RoothaanC. C. J.
+
+ New developments in molecular orbital theory
+ Reviews of Modern Physics
+ American Physical Society
+ 195104
+ 23
+ https://link.aps.org/doi/10.1103/RevModPhys.23.69
+ 10.1103/RevModPhys.23.69
+ 69
+ 89
+
+
+
+
+
+ PopleJohn A.
+ GillPeter M. W.
+ HandyNicholas C.
+
+ Spin-unrestricted character of kohn-sham orbitals for open-shell systems
+ International Journal of Quantum Chemistry
+ 1995
+ 56
+ 4
+ https://onlinelibrary.wiley.com/doi/abs/10.1002/qua.560560414
+ 10.1002/qua.560560414
+ 303
+ 305
+
+
+
+
+
+ PulayPéter
+
+ Convergence acceleration of iterative sequences. The case of scf iteration
+ Chemical Physics Letters
+ 1980
+ 73
+ 2
+ 0009-2614
+ https://www.sciencedirect.com/science/article/pii/0009261480803964
+ 10.1016/0009-2614(80)80396-4
+ 393
+ 398
+
+
+
+
+
+ TaketaHiroshi
+ HuzinagaSigeru
+ O-ohataKiyosi
+
+ Gaussian-expansion methods for molecular integrals
+ Journal of the Physical Society of Japan
+ 1966
+ 21
+ 11
+ https://doi.org/10.1143/JPSJ.21.2313
+ 10.1143/JPSJ.21.2313
+ 2313
+ 2324
+
+
+
+
+
+ DronskowskiRichard
+ BloechlPeter E.
+
+ Crystal orbital hamilton populations (COHP): Energy-resolved visualization of chemical bonding in solids based on density-functional calculations
+ The Journal of Physical Chemistry
+ 1993
+ 97
+ 33
+ 10.1021/j100135a014
+ 8617
+ 8624
+
+
+
+
+
+ StefaniChristina
+ TsaparlisGeorgios
+
+ Students’ levels of explanations, models, and misconceptions in basic quantum chemistry: A phenomenographic study
+ Journal of Research in Science Teaching
+ 200905
+ 46
+ 10.1002/tea.20279
+ 520
+ 536
+
+
+
+
+
+ HulyadiHulyadi
+ MuhaliMuhali
+ GargaziGargazi
+
+ Reducing student misconceptions through problem-based learning with a computational chemistry-assisted question map approach
+ Jurnal Penelitian Pendidikan IPA
+ 202312
+ 09
+ 10.29303/jppipa.v9i12.5936
+ 11207
+ 11217
+
+
+
+
+
+ BeckeAxel D.
+
+ Density-functional thermochemistry. III. The role of exact exchange
+ The Journal of Chemical Physics
+ 199304
+ 98
+ 7
+ 0021-9606
+ 10.1063/1.464913
+ 5648
+ 5652
+
+
+
+
+
+ LeeChengteh
+ YangWeitao
+ ParrRobert G.
+
+ Development of the colle-salvetti correlation-energy formula into a functional of the electron density
+ Physical Review B
+ American Physical Society
+ 198801
+ 37
+ https://link.aps.org/doi/10.1103/PhysRevB.37.785
+ 10.1103/PhysRevB.37.785
+ 785
+ 789
+
+
+
+
+
+ SousaSérgio Filipe
+ FernandesPedro Alexandrino
+ RamosMaria João
+
+ General performance of density functionals
+ The Journal of Physical Chemistry A
+ 2007
+ 111
+ 42
+ https://doi.org/10.1021/jp0734474
+ 10.1021/jp0734474
+ 10439
+ 10452
+
+
+
+
+
+ BoysS. F.
+
+ Construction of some molecular orbitals to be approximately invariant for changes from one molecule to another
+ Reviews of Modern Physics
+ American Physical Society
+ 196004
+ 32
+ https://link.aps.org/doi/10.1103/RevModPhys.32.296
+ 10.1103/RevModPhys.32.296
+ 296
+ 299
+
+
+
+
+
+ GordonMark S.
+ WindusTheresa L.
+
+ Editorial: Modern architectures and their impact on electronic structure theory
+ Chemical Reviews
+ 2020
+ 120
+ 17
+ https://doi.org/10.1021/acs.chemrev.0c00700
+ 10.1021/acs.chemrev.0c00700
+ 9015
+ 9020
+
+
+
+
+
+ SzaboAttila
+ OstlundNeil S.
+
+ Modern quantum chemistry: Introduction to advanced electronic structure theory
+ Dover
+ Mineola, New York
+ 1996
+
+
+
+
+
+ FilotIvo A. W.
+
+ Elements of electronic structure theory
+ Eindhoven University of Technology Library
+ Eindhoven, The Netherlands
+ 2025
+ 978-90-386-6477-4
+
+
+
+
+
+ FilotIvo A. W.
+
+ PyQInt documentation
+ 2025
+ 20250818
+ https://ifilot.github.io/pyqint/index.html
+
+
+
+
+
+ HunterJ. D.
+
+ Matplotlib: A 2D graphics environment
+ Computing in Science & Engineering
+ IEEE COMPUTER SOC
+ 2007
+ 9
+ 3
+ 10.1109/MCSE.2007.55
+ 90
+ 95
+
+
+
+
+
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