{ "id": "ep2sgzhe9p", "slug": "full-configuration-interaction", "title": "Full configuration interaction", "updated": "2026-10-15", "topic_path": [ { "id": "physical", "label": "Physical world and mathematics", "api_url": "https://www.edgepedia.org/api/v1/topics/physical" }, { "id": "physical.chemistry", "label": "Chemistry", "api_url": "https://www.edgepedia.org/api/v1/topics/physical.chemistry" }, { "id": "physical.chemistry.methods", "label": "Chemical principles and methods", "api_url": "https://www.edgepedia.org/api/v1/topics/physical.chemistry.methods" } ], "geo": [ { "id": "geo.nongeo.t1946.physical.chemistry.methods", "label": "Non-geographic · 1946 to 2000: Chemical principles and methods", "api_url": "https://www.edgepedia.org/api/v1/geo/geo.nongeo.t1946.physical.chemistry.methods", "path": [ { "id": "geo.nongeo", "label": "Non-geographic", "api_url": "https://www.edgepedia.org/api/v1/geo/geo.nongeo" }, { "id": "geo.nongeo.t1946", "label": "Non-geographic · 1946 to 2000", "api_url": "https://www.edgepedia.org/api/v1/geo/geo.nongeo.t1946" }, { "id": "geo.nongeo.t1946.physical", "label": "Physical world and mathematics", "api_url": "https://www.edgepedia.org/api/v1/geo/geo.nongeo.t1946.physical" }, { "id": "geo.nongeo.t1946.physical.chemistry", "label": "Chemistry", "api_url": "https://www.edgepedia.org/api/v1/geo/geo.nongeo.t1946.physical.chemistry" }, { "id": "geo.nongeo.t1946.physical.chemistry.methods", "label": "Chemical principles and methods", "api_url": "https://www.edgepedia.org/api/v1/geo/geo.nongeo.t1946.physical.chemistry.methods" } ] } ], "excerpt": "Full configuration interaction (FCI) is a quantum chemistry method that solves the electronic Schrödinger equation exactly in a chosen basis, serving as the calibration reference for approximate methods.", "snippet": "Full configuration interaction (FCI) is a quantum chemistry method that solves the electronic Schrödinger equation exactly in a chosen basis, serving as the calibration reference for approximate methods.", "node": "physical.chemistry.methods", "markdown": "# Full configuration interaction\n\nFull configuration interaction (FCI) is a quantum chemistry method that solves the nonrelativistic electronic [Schrödinger equation](https://www.edgepedia.org/schrodinger-equation) exactly within a chosen one-electron basis by diagonalizing the electronic Hamiltonian in the space of all possible Slater determinants (antisymmetrized wavefunction for electrons in orbitals).[1](https://vergil.chemistry.gatech.edu/static/content/ci.pdf) Because no determinant is excluded, the lowest eigenvalue is the variational minimum of the energy in that basis and an upper bound to the exact nonrelativistic ground-state energy; FCI therefore serves as the calibration reference for approximate methods such as truncated CI, many-body perturbation theory, and coupled cluster.[1](https://vergil.chemistry.gatech.edu/static/content/ci.pdf) The price is a determinant count that grows factorially with system size, restricting exact FCI to small molecules and active spaces.[2](https://www.nature.com/articles/s41467-025-65967-7)\n\n| Key fact | Value |\n|---|---|\n| Defining property | Exact diagonalization of the electronic Hamiltonian over all determinants in a given basis; variational upper bound[1](https://vergil.chemistry.gatech.edu/static/content/ci.pdf) |\n| Correlation energy | \\( E_{\\mathrm{corr}} = E_{0}^{\\mathrm{exact}} - E_{0}^{\\mathrm{HF}} \\), with the FCI energy taken as \\( E_{0}^{\\mathrm{exact}} \\)[3](https://hj.hi.is/reikniefnfr/notes_6-ConfigInteract.pdf) |\n| Problem size | With \\( N \\) spatial orbitals and fixed spin populations \\( n_{\\alpha}, n_{\\beta} \\), \\( \\binom{N}{n_{\\alpha}}\\binom{N}{n_{\\beta}} \\) determinants; the special case of equal spins, \\( n_{\\alpha} = n_{\\beta} = n/2 \\), gives \\( \\left( N!/(n/2)!(N-n/2)! \\right)^{2} \\)[4](https://simons.hec.utah.edu/papers/138.pdf) |\n| Example cost | Propane/STO-3G FCI requires about \\( 1.31 \\times 10^{12} \\) determinants; selected CI matches its correlation energy with \\( 10^{5} \\)[3](https://hj.hi.is/reikniefnfr/notes_6-ConfigInteract.pdf) |\n| Benchmark accuracy | On FCI111, CCSD(T) errs by 0.414 \\( \\mathrm{mE}_{\\mathrm{h}} \\) and CCSDTQ by 2.451 \\( \\mu\\mathrm{E}_{\\mathrm{h}} \\) against FCI[5](https://arxiv.org/html/2402.13111) |\n| Largest calculations | 1.31 trillion determinants (2024, distributed FCI); one quadrillion determinants (2025, relativistic CI)[6](https://pubs.acs.org/doi/full/10.1021/acs.jctc.3c01190) • [2](https://www.nature.com/articles/s41467-025-65967-7) |\n\n## How it works\n\nIn [second quantization](https://www.edgepedia.org/second-quantization) the electronic Hamiltonian contains only one- and two-body operators. CI expands the \\( N \\)-electron wavefunction as \\( |\\Psi_{0}\\rangle = C_{0}|\\Phi_{0}\\rangle + \\sum C_{i}^{a}|\\Phi_{i}^{a}\\rangle + \\sum C_{ij}^{ab}|\\Phi_{ij}^{ab}\\rangle + \\cdots \\) over all determinants \\( |\\Phi\\rangle \\) that can be built from the basis orbitals, and solves the matrix eigenvalue problem \\( \\hat{H}|\\Psi\\rangle = E|\\Psi\\rangle \\).[1](https://vergil.chemistry.gatech.edu/static/content/ci.pdf) • [7](https://compphysics.github.io/ComputationalPhysics2/doc/LectureNotes/_build/html/fcitheory.html) When no truncation is made, the lowest eigenvalue is the exact nonrelativistic energy for that basis; diagonalization also yields excited states and their eigenvectors directly.[7](https://compphysics.github.io/ComputationalPhysics2/doc/LectureNotes/_build/html/fcitheory.html)\n\nTwo properties follow from the full expansion. First, the energy is variational: the linear variational ansatz guarantees the lowest eigenvalue lies above the exact ground-state energy.[1](https://vergil.chemistry.gatech.edu/static/content/ci.pdf) Second, FCI is size consistent, while truncated CI such as CISD is not: FCI, which includes excitations to every level, does not have this defect.[3](https://hj.hi.is/reikniefnfr/notes_6-ConfigInteract.pdf) The difference between the FCI energy and the Hartree-Fock energy defines the correlation energy.[3](https://hj.hi.is/reikniefnfr/notes_6-ConfigInteract.pdf)\n\n## How it is done\n\nThe analyst chooses a one-electron basis and a set of orbitals, then generates all determinants with a fixed spin projection, an \"M-scheme\" basis that is easy to construct and store as occupation-number bit strings.[7](https://compphysics.github.io/ComputationalPhysics2/doc/LectureNotes/_build/html/fcitheory.html)\n\nThe Hamiltonian matrix is almost never formed explicitly. Direct CI techniques apply the Hamiltonian to the CI vector without storing the matrix, which is what made long expansions accessible.[8](https://onlinelibrary.wiley.com/doi/10.1002/9781119019572.ch11) • [9](https://www.tandfonline.com/doi/abs/10.1080/002689798168303) For dimensions below about \\( 10^{5} \\) direct diagonalization is used; above that, iterative solvers such as the Lanczos method or the Davidson method are used, and the dominant cost is the Hamiltonian matrix-vector product.[7](https://compphysics.github.io/ComputationalPhysics2/doc/LectureNotes/_build/html/fcitheory.html) • [10](https://www.jstage.jst.go.jp/article/jccj1999/12/4/12_4_301/_pdf/-char/ja) The Davidson method, an iterative scheme for the few lowest eigenvalues of large real-symmetric matrices, remains the standard workhorse.[11](https://doi.org/10.1016/0021-9991%2875%2990065-0)\n\n## Origin\n\nCI dates back to the earliest days of quantum mechanics; the earliest applications used 2 to 10 expansion terms, while modern CI calculations employ many millions of configuration state functions.[9](https://www.tandfonline.com/doi/abs/10.1080/002689798168303) Samuel Francis Boys reported a configuration interaction calculation for the ground state of the beryllium atom in 1950 in Proceedings of the Royal Society A,[12](https://doi.org/10.1098/rspa.1950.0047) and B. Roos published a method for large-scale CI calculations in 1972 in Chemical Physics Letters.[13](https://doi.org/10.1016/0009-2614%2872%2980140-4) In 1980 N. C. Handy published multi-root configuration interaction calculations using determinant-based methods in Chemical Physics Letters,[14](https://doi.org/10.1016/0009-2614%2880%2985158-x) A determinant-based full CI method was published in Chemical Physics Letters whose vectorized algorithm enabled a series of benchmark studies.[15](https://www.sciencedirect.com/science/article/abs/pii/000926148485513X) Knowles and Handy's 1989 paper \"Unlimited full configuration interaction calculations\" in The Journal of Chemical Physics added an extrapolation scheme for intractably large problems.[16](https://doi.org/10.1063/1.456997) Jeppe Olsen and colleagues published determinant-based CI algorithms for complete and restricted spaces in 1988 in The Journal of Chemical Physics,[17](https://doi.org/10.1063/1.455063) and Olsen, Jørgensen, and [Jack Simons](https://www.edgepedia.org/jack-simons) passed the one-billion determinant barrier in 1990 in Chemical Physics Letters.[18](https://doi.org/10.1016/0009-2614%2890%2985633-n)\n\n## Variants\n\nSeveral families approximate or reorganize the full diagonalization. Selected CI methods grow the expansion by choosing the determinants that matter most; the CIPSI scheme is the oldest named member of this family, and heat-bath configuration interaction (HCI) is a selected CI plus perturbation theory method controlled by two parameters that trade speed against accuracy.[19](https://pubs.acs.org/doi/full/10.1021/acs.jctc.6b00407) Its semistochastic extension, SHCI, adds stochastic evaluation of the perturbative correction.[20](https://doi.org/10.1063/5.0018577) Other selected-CI approaches include adaptive sampling CI (ASCI) and Monte Carlo CI (MCCI).[21](https://pmc.ncbi.nlm.nih.gov/articles/PMC10753805/)\n\nFCIQMC samples the determinant [Hilbert space](https://www.edgepedia.org/hilbert-space) with signed walkers propagated by stochastic application of the second-quantized Hamiltonian; unlike diffusion [Monte Carlo](https://www.edgepedia.org/monte-carlo) it needs no fixed-node approximation, and the nodal structure emerges from the walker dynamics.[22](https://pubs.aip.org/aip/jcp/article-pdf/doi/10.1063/5.0005754/16756540/034107_1_online.pdf) [Density matrix renormalization group](https://www.edgepedia.org/density-matrix-renormalization-group) (DMRG) is another dominant paradigm for approximate FCI.[23](https://arxiv.org/html/2207.12587) The iterative configuration interaction (ICIGSD) method of Hiroshi Nakatsuji and Ernest R. Davidson approaches the exact wavefunction with \\( M_{\\mathrm{GSD}} \\) variables per iteration, \\( n \\cdot M_{\\mathrm{GSD}} \\) in total, with each step variational.[24](https://doi.org/10.1063/1.1383032)\n\n## Applications\n\nFCI energies calibrate the whole hierarchy of approximate methods: multireference CI, many-body perturbation theory, and coupled cluster.[9](https://www.tandfonline.com/doi/abs/10.1080/002689798168303) • [25](https://www.sciencedirect.com/science/article/abs/pii/S0065327608605328) On the FCI111 benchmark, CCSD errs by 1.355 \\( \\mathrm{mE}_{\\mathrm{h}} \\), CCSD(T) by 0.414 \\( \\mathrm{mE}_{\\mathrm{h}} \\), CCSDT by 0.181 \\( \\mathrm{mE}_{\\mathrm{h}} \\), and CCSDTQ by 2.451 \\( \\mu\\mathrm{E}_{\\mathrm{h}} \\).[5](https://arxiv.org/html/2402.13111) SHCI extrapolated complete-basis-set atomization energies for the 55-molecule Gaussian-2 set deviate from experiment with mean absolute deviations of 0.46 kcal/mol (0.51 kcal/mol with a DFT basis-set correction), and have been used to benchmark CCSD(T).[26](https://pubs.aip.org/aip/jcp/article/153/12/124117/1062754/Almost-exact-energies-for-the-Gaussian-2-set-with)\n\nConcrete milestones show the pace of the determinant-count growth. Harrison and Zarrabian performed \\( 7.7 \\times 10^{7} \\)-determinant calculations on oxygen and its anion in 1989.[10](https://www.jstage.jst.go.jp/article/jccj1999/12/4/12_4_301/_pdf/-char/ja) • [27](https://doi.org/10.1016/0009-2614%2889%2987358-0) The 1990 billion-determinant calculation handled 10 electrons in 30 orbitals.[4](https://simons.hec.utah.edu/papers/138.pdf) In 2024 a distributed implementation computed the exact ground-state energy of C3H8/STO-3G with 1.31 trillion determinants in 113.6 hours on 512 processes across 256 servers.[6](https://pubs.acs.org/doi/full/10.1021/acs.jctc.3c01190) In 2025 a relativistic CI calculation reached one quadrillion (\\( 10^{15} \\)) determinants for 100 orbitals and 88 electrons, a space that would require about 16 petabytes to store a single CI vector of complex double-precision coefficients.[2](https://www.nature.com/articles/s41467-025-65967-7) Empirically, only about 1% of determinants contribute to FCI-level accuracy, which is what selected-CI methods exploit.[28](https://dl.acm.org/doi/10.1145/3806645.3807583)\n\nFCIQMC has supplied reference many-electron energies for real solids, benchmarking the coupled-cluster hierarchy up to CCSD(T) with small errors in predicted cohesive energies.[29](https://www.nature.com/articles/nature11770) An FCIQMC treatment of the 54-electron homogeneous electron gas at \\( r_{s} = 0.5 \\) a.u. covered a Hilbert space of \\( 10^{108} \\) Slater determinants and yielded a variational finite-basis energy lower than any previously published work for that system.[30](https://journals.aps.org/prb/abstract/10.1103/PhysRevB.85.081103) Within conventional quantum chemistry, FCI is the limiting case of the active-space diagonalization in CASSCF, which optimizes orbitals and CI coefficients together over all excitations within a labeled active orbital set.[3](https://hj.hi.is/reikniefnfr/notes_6-ConfigInteract.pdf) [Quantum computing](https://www.edgepedia.org/quantum-computing) uses FCI energies as targets: quantum-selected configuration interaction (QSCI) classically diagonalizes Hamiltonians in subspaces sampled from quantum-computer states,[31](https://link.aps.org/doi/10.1103/dmn4-snfx) and [Hamiltonian simulation](https://www.edgepedia.org/hamiltonian-simulation)-based QSCI (HSB-QSCI) reached chemical precision in simulations, with hardware runs up to 36 qubits capturing more than 99.18% of correlation energy using about 1% of all determinants.[32](https://pubs.rsc.org/en/content/articlehtml/2025/cp/d5cp02202a)\n\n## Limitations and alternatives\n\nThe central limitation is the exponential wall: as the determinant count grows factorially with system size, even iterative methods become intractable beyond a threshold, so exact FCI is feasible only for small systems.[2](https://www.nature.com/articles/s41467-025-65967-7) • [5](https://arxiv.org/html/2402.13111) An FCI energy is exact only for the basis used; basis-set incompleteness error remains and is removed by extrapolation, as in the homogeneous-electron-gas study above.[30](https://journals.aps.org/prb/abstract/10.1103/PhysRevB.85.081103) Standard nonrelativistic FCI also omits relativistic effects, which require the relativistic formulations used in the largest recent calculations.[2](https://www.nature.com/articles/s41467-025-65967-7)\n\nAmong alternatives, truncated CI is cheaper but not size consistent, and approximate fixes such as the quadratic CI approach arose directly from this extensivity fault.[3](https://hj.hi.is/reikniefnfr/notes_6-ConfigInteract.pdf) • [33](https://wires.onlinelibrary.wiley.com/doi/10.1002/wcms.1131) [Coupled cluster](https://www.edgepedia.org/coupled-cluster) also fails for strongly correlated systems: CCSD(T) does not give even a qualitatively correct description of the chromium dimer potential energy curve, where SHCI has been applied as the reference.[26](https://pubs.aip.org/aip/jcp/article/153/12/124117/1062754/Almost-exact-energies-for-the-Gaussian-2-set-with)\n\nRecent developments attack the exponential wall directly. The STP-DAS (small-tensor product distributed active space) framework reached quadrillion-determinant scale in 2025 by reformulating the CI matrix-vector product into small tensor products computed on the fly, achieving a 1000-fold increase in CI space and a \\( 10^{6} \\)-fold increase in floating-point operations over previous state-of-the-art CI calculations.[2](https://www.nature.com/articles/s41467-025-65967-7) On the quantum side, QSCI and HSB-QSCI couple quantum-computer state preparation to classical subspace diagonalization, with hardware demonstrations through 36 qubits.[31](https://link.aps.org/doi/10.1103/dmn4-snfx) • [32](https://pubs.rsc.org/en/content/articlehtml/2025/cp/d5cp02202a) GPU-accelerated determinant selection driven by neural network quantum states appeared in 2025, targeting the roughly 1% of determinants that determine FCI-level accuracy.[28](https://dl.acm.org/doi/10.1145/3806645.3807583)\n\n## References\n\n1. [An Introduction to Configuration Interaction Theory (Crawford, Georgia Tech lecture notes)](https://vergil.chemistry.gatech.edu/static/content/ci.pdf)\n2. [Numerically exact configuration interaction at quadrillion-determinant scale (Nature Communications 2025)](https://www.nature.com/articles/s41467-025-65967-7)\n3. [Post Hartree-Fock: A. Configuration Interaction (lecture notes)](https://hj.hi.is/reikniefnfr/notes_6-ConfigInteract.pdf)\n4. [Passing the One-Billion Limit in Full Configuration-Interaction (FCI) Calculations (Olsen, Jørgensen, Simons, Chem. Phys. Lett. 1990)](https://simons.hec.utah.edu/papers/138.pdf)\n5. [How Useful Can Selected Configuration Interaction Be? (arXiv 2024)](https://arxiv.org/html/2402.13111)\n6. [Distributed Implementation of Full Configuration Interaction for One Trillion Determinants (J. Chem. Theory Comput. 2024)](https://pubs.acs.org/doi/full/10.1021/acs.jctc.3c01190)\n7. [Full configuration interaction theory, Advanced Topics in Computational Physics lecture notes](https://compphysics.github.io/ComputationalPhysics2/doc/LectureNotes/_build/html/fcitheory.html)\n8. [Configuration-Interaction Theory (Helgaker, Jørgensen, Olsen, Molecular Electronic-Structure Theory, 2000)](https://onlinelibrary.wiley.com/doi/10.1002/9781119019572.ch11)\n9. [The history and evolution of configuration interaction (Shavitt, Molecular Physics 1998)](https://www.tandfonline.com/doi/abs/10.1080/002689798168303)\n10. [A full configuration interaction calculation based on Slater determinants. Application to AlH spectroscopic constants (J. Comput. Chem. Jpn.)](https://www.jstage.jst.go.jp/article/jccj1999/12/4/12_4_301/_pdf/-char/ja)\n11. [The iterative calculation of a few of the lowest eigenvalues and corresponding eigenvectors of large real-symmetric matrices (Journal of Computational Physics, 1975)](https://doi.org/10.1016/0021-9991%2875%2990065-0)\n12. [Samuel Francis Boys (1950). Electronic wave functions II. A calculation for the ground state of the beryllium atom. Proceedings of the Royal Society of London A Mathematical and Physical Sciences.](https://doi.org/10.1098/rspa.1950.0047)\n13. [A new method for large-scale Cl calculations (Chemical Physics Letters, 1972)](https://doi.org/10.1016/0009-2614%2872%2980140-4)\n14. [Multi-root configuration interaction calculations (Chemical Physics Letters, 1980)](https://doi.org/10.1016/0009-2614%2880%2985158-x)\n15. [A new determinant-based full configuration interaction method (Knowles & Handy, Chem. Phys. Lett. 1984)](https://www.sciencedirect.com/science/article/abs/pii/000926148485513X)\n16. [Peter J. Knowles, Nicholas C. Handy (1989). Unlimited full configuration interaction calculations. The Journal of Chemical Physics.](https://doi.org/10.1063/1.456997)\n17. [Jeppe Olsen and colleagues (1988). Determinant based configuration interaction algorithms for complete and restricted configuration interaction spaces. The Journal of Chemical Physics.](https://doi.org/10.1063/1.455063)\n18. [Passing the one-billion limit in full configuration-interaction (FCI) calculations (Chemical Physics Letters, 1990)](https://doi.org/10.1016/0009-2614%2890%2985633-n)\n19. [Heat-Bath Configuration Interaction: An Efficient Selected Configuration Interaction Algorithm Inspired by Heat-Bath Sampling (J. Chem. Theory Comput. 2016)](https://pubs.acs.org/doi/full/10.1021/acs.jctc.6b00407)\n20. [Yuan Yao and colleagues (2020). Almost exact energies for the Gaussian-2 set with the semistochastic heat-bath configuration interaction method. The Journal of Chemical Physics.](https://doi.org/10.1063/5.0018577)\n21. [Modular Approach to Selected Configuration Interaction in an Arbitrary Spin Basis: Implementation and Comparison of Approaches](https://pmc.ncbi.nlm.nih.gov/articles/PMC10753805/)\n22. [NECI: N-Electron Configuration Interaction with an emphasis on state-of-the-art stochastic methods (J. Chem. Phys.)](https://pubs.aip.org/aip/jcp/article-pdf/doi/10.1063/5.0005754/16756540/034107_1_online.pdf)\n23. [A truncated Davidson method for the efficient 'chemically accurate' calculation of full configuration interaction wavefunctions without any large matrix diagonalization (arXiv 2022)](https://arxiv.org/html/2207.12587)\n24. [Hiroshi Nakatsuji, Ernest R. Davidson (2001). Structure of the exact wave function. II. Iterative configuration interaction method. The Journal of Chemical Physics.](https://doi.org/10.1063/1.1383032)\n25. [The Configuration Interaction Method: Advances in Highly Correlated Approaches (Sherrill & Schaefer)](https://www.sciencedirect.com/science/article/abs/pii/S0065327608605328)\n26. [Almost exact energies for the Gaussian-2 set with the semistochastic heat-bath configuration interaction method (J. Chem. Phys. 153, 124117, 2020)](https://pubs.aip.org/aip/jcp/article/153/12/124117/1062754/Almost-exact-energies-for-the-Gaussian-2-set-with)\n27. [An efficient implementation of the full-CI method using an (n–2)-electron projection space (Chemical Physics Letters, 1989)](https://doi.org/10.1016/0009-2614%2889%2987358-0)\n28. [A Fully GPU-Accelerated Framework for High-Performance Configuration Interaction Selection with Neural Network Quantum States (HPDC '25)](https://dl.acm.org/doi/10.1145/3806645.3807583)\n29. [Towards an exact description of electronic wavefunctions in real solids (Nature, 2013)](https://www.nature.com/articles/nature11770)\n30. [Full configuration interaction perspective on the homogeneous electron gas (Phys. Rev. B 85, 081103(R), 2012)](https://journals.aps.org/prb/abstract/10.1103/PhysRevB.85.081103)\n31. [Quantum-selected configuration interaction: Classical diagonalization of Hamiltonians in subspaces selected by quantum computers (Phys. Rev. Research)](https://link.aps.org/doi/10.1103/dmn4-snfx)\n32. [Hamiltonian simulation-based quantum-selected configuration interaction for large-scale electronic structure calculations with a quantum computer (PCCP, 2025)](https://pubs.rsc.org/en/content/articlehtml/2025/cp/d5cp02202a)\n33. [From configuration interaction to coupled cluster theory: The quadratic configuration interaction approach (Cremer, WIREs CMS 2013)](https://wires.onlinelibrary.wiley.com/doi/10.1002/wcms.1131)\n\n---\n*Topic: Encyclopedia › Physical world and mathematics › Chemistry › Chemical principles and methods*\n\n*Initially written Sep 29, 2026 · Edited: Oct 15, 2026*\n\n*Copyright 2026 EdgeChat AI, a subsidiary of Biostate AI.*\n\nLicense: Edgepedia Community License 1.0, https://www.edgepedia.org/edgepedia/license\n", "same_as": [], "url": "https://www.edgepedia.org/full-configuration-interaction", "markdown_url": "https://www.edgepedia.org/full-configuration-interaction.md", "license": { "name": "Edgepedia Community License 1.0", "url": "https://www.edgepedia.org/edgepedia/license", "summary": "Free with credit, commercial use included. AI training is open to everyone. 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