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References

This page collects the scientific references cited throughout the manual and tutorials. Use the OpenQP platform paper when citing the code itself, and add method-specific references when a paper uses MP2, spin-scaled MP2, MRSF-TDDFT, BaekA multistate MECI, SOC, scalar relativistic correction, PCM/ddX, or related workflows.

OpenQP

  • Mironov V, Komarov K, Li J, Gerasimov I, Nakata H, Mazaherifar M, Ishimura K, Park W, Lashkaripour A, Oh M, Huix-Rotllant M, Lee S, and Choi CH. "OpenQP: A Quantum Chemical Platform Featuring MRSF-TDDFT with an Emphasis on Open-Source Ecosystem." Journal of Chemical Theory and Computation 20, 9464-9477 (2024). doi:10.1021/acs.jctc.4c01117

MP2 and Spin-Scaled MP2

  • Moller C and Plesset MS. "Note on an Approximation Treatment for Many-Electron Systems." Physical Review 46, 618-622 (1934). doi:10.1103/PhysRev.46.618
  • Grimme S. "Improved Second-Order Moller-Plesset Perturbation Theory by Separate Scaling of Parallel- and Antiparallel-Spin Pair Correlation Energies." Journal of Chemical Physics 118, 9095-9102 (2003). doi:10.1063/1.1569242
  • Jung Y, Lochan RC, Dutoi AD, and Head-Gordon M. "Scaled Opposite-Spin Second Order Moller-Plesset Correlation Energy." Journal of Chemical Physics 121, 9793-9802 (2004). doi:10.1063/1.1809602
  • DiStasio RA Jr. and Head-Gordon M. "Optimized Spin-Component Scaled Second-Order Moller-Plesset Perturbation Theory for Intermolecular Interaction Energies." Molecular Physics 105, 1073-1083 (2007). doi:10.1080/00268970701283781

MRSF-TDDFT

  • Lee S, Filatov M, Lee S, and Choi CH. "Eliminating spin-contamination of spin-flip time dependent density functional theory within linear response formalism by the use of zeroth-order mixed-reference (MR) reduced density matrix." Journal of Chemical Physics 149, 104101 (2018). doi:10.1063/1.5044202
  • Lee S, Kim EE, Nakata H, Lee S, and Choi CH. "Efficient implementations of analytic energy gradient for mixed-reference spin-flip time-dependent density functional theory (MRSF-TDDFT)." Journal of Chemical Physics 150, 184111 (2019). doi:10.1063/1.5086895
  • Park W, Komarov K, Lee S, and Choi CH. "Mixed-Reference Spin-Flip Time-Dependent Density Functional Theory: Multireference Advantages with the Practicality of Linear Response Theory." Journal of Physical Chemistry Letters 14, 8896-8908 (2023). doi:10.1021/acs.jpclett.3c02296
  • Lee S, Park W, and Choi CH. "Expanding Horizons in Quantum Chemical Studies: The Versatile Power of MRSF-TDDFT." Accounts of Chemical Research 58, 208-217 (2025). doi:10.1021/acs.accounts.4c00640
  • Park W, Lee S, Komarov K, Mironov V, Nakata H, Zeng T, Huix-Rotllant M, and Choi CH. "MRSF-TDDFT: A new tool in quantum chemistry for better understanding molecules and materials." Bulletin of the Korean Chemical Society 46, 330-346 (2025). doi:10.1002/bkcs.70011

BaekA Multistate MECI

  • Baek YS, Lee S, Filatov M, and Choi CH. "Optimization of Three State Conical Intersections by Adaptive Penalty Function Algorithm in Connection with the Mixed-Reference Spin-Flip Time-Dependent Density Functional Theory Method (MRSF-TDDFT)." Journal of Physical Chemistry A 125, 1994-2006 (2021). doi:10.1021/acs.jpca.0c11294

Spin-Orbit Coupling

  • Komarov K, Park W, Lee S, Zeng T, and Choi CH. "Accurate Spin-Orbit Coupling by Relativistic Mixed-Reference Spin-Flip-TDDFT." Journal of Chemical Theory and Computation 19, 953-964 (2023). doi:10.1021/acs.jctc.2c01036
  • Hess BA, Marian CM, Wahlgren U, and Gropen O. "A mean-field spin-orbit method applicable to correlated wavefunctions." Chemical Physics Letters 251, 365-371 (1996). doi:10.1016/0009-2614(96)00119-4
  • Marian CM. "Spin-orbit coupling and intersystem crossing in molecules." WIREs Computational Molecular Science 2, 187-203 (2012). doi:10.1002/wcms.83

Scalar Relativistic Correction

  • Douglas M and Kroll NM. "Quantum electrodynamical corrections to the fine structure of helium." Annals of Physics 82, 89-155 (1974). doi:10.1016/0003-4916(74)90333-9
  • Hess BA. "Applicability of the no-pair equation with free-particle projection operators to atomic and molecular structure calculations." Physical Review A 33, 3742-3748 (1986). doi:10.1103/PhysRevA.33.3742

PCM and ddX

  • Tomasi J, Mennucci B, and Cammi R. "Quantum mechanical continuum solvation models." Chemical Reviews 105, 2999-3094 (2005). doi:10.1021/cr9904009
  • Herbert JM. "Dielectric continuum methods for quantum chemistry." WIREs Computational Molecular Science 11, e1519 (2021). doi:10.1002/wcms.1519
  • Cances E, Maday Y, and Stamm B. "Domain decomposition for implicit solvation models." Journal of Chemical Physics 139, 054111 (2013). doi:10.1063/1.4816767
  • Lipparini F, Stamm B, Cances E, Maday Y, and Mennucci B. "Fast Domain Decomposition Algorithm for Continuum Solvation Models: Energy and First Derivatives." Journal of Chemical Theory and Computation 9, 3637-3648 (2013). doi:10.1021/ct400280b
  • ddX continuum-solvation library. ddsolvation/ddX

Nonadiabatic Dynamics

  • Tully JC. "Molecular dynamics with electronic transitions." Journal of Chemical Physics 93, 1061-1071 (1990). doi:10.1063/1.459170
  • Richter M, Marquetand P, Gonzalez-Vazquez J, Sola I, and Gonzalez L. "SHARC: ab Initio Molecular Dynamics with Surface Hopping in the Adiabatic Representation Including Arbitrary Couplings." Journal of Chemical Theory and Computation 7, 1253-1258 (2011). doi:10.1021/ct1007394
  • Mai S, Marquetand P, and Gonzalez L. "Nonadiabatic dynamics: The SHARC approach." WIREs Computational Molecular Science 8, e1370 (2018). doi:10.1002/wcms.1370
  • Granucci G and Persico M. "Critical appraisal of the fewest switches algorithm for surface hopping." Journal of Chemical Physics 126, 134114 (2007). doi:10.1063/1.2715585 — the energy-based decoherence correction (EDC) used by the md.decoherence=edc default.
  • Granucci G, Persico M, and Zoccante A. "Including quantum decoherence in surface hopping." Journal of Chemical Physics 133, 134111 (2010). doi:10.1063/1.3489004
  • Baeck KK and An H. "Practical approximation of the non-adiabatic coupling terms for same-symmetry interstate crossings by using adiabatic potential energies only." Journal of Chemical Physics 146, 064107 (2017). doi:10.1063/1.4975323
  • do Casal MT, Toldo JMT, Pinheiro Jr M, and Barbatti M. "Fewest switches surface hopping with Baeck-An couplings." Open Research Europe 1, 49 (2022). doi:10.12688/openreseurope.13624.2

ACID (Anisotropy of the Induced Current Density)

  • Herges R and Geuenich D. "Delocalization of Electrons in Molecules." Journal of Physical Chemistry A 105, 3214-3220 (2001). doi:10.1021/jp0034426
  • Geuenich D, Hess K, Kohler F, and Herges R. "Anisotropy of the Induced Current Density (ACID), a General Method To Quantify and Visualize Electronic Delocalization." Chemical Reviews 105, 3758-3772 (2005). doi:10.1021/cr0300901

QM/MM (ESPF) Embedding

  • Ferre N and Angyan JG. "Approximate electrostatic interaction operator for QM/MM calculations." Chemical Physics Letters 356, 331-339 (2002). doi:10.1016/S0009-2614(02)00343-3
  • Huix-Rotllant M and Ferre N. "Analytic Energy, Gradient, and Hessian of Electrostatic Embedding QM/MM Based on Electrostatic Potential-Fitted Atomic Charges Scaling Linearly with the MM Subsystem Size." Journal of Chemical Theory and Computation 17, 538-548 (2021). doi:10.1021/acs.jctc.0c01075
  • Bonfrate S, Ferre N, and Huix-Rotllant M. "An efficient electrostatic embedding QM/MM method using periodic boundary conditions based on particle-mesh Ewald sums and electrostatic potential fitted charge operators." Journal of Chemical Physics 158, 021101 (2023). doi:10.1063/5.0133646
  • Bonfrate S, Ferre N, and Huix-Rotllant M. "Analytic Gradients for the Electrostatic Embedding QM/MM Model in Periodic Boundary Conditions Using Particle-Mesh Ewald Sums and Electrostatic Potential Fitted Charge Operators." Journal of Chemical Theory and Computation 20, 4338-4349 (2024). doi:10.1021/acs.jctc.4c00201
  • Lin H and Truhlar DG. "Redistributed Charge and Dipole Schemes for Combined Quantum Mechanical and Molecular Mechanical Calculations." Journal of Physical Chemistry A 109, 3991-4004 (2005) — the RC / RCD frontier-charge redistribution used by qmmm.frontier_scheme at a covalent boundary. doi:10.1021/jp0446332
  • Shen Z and Glover WJ. "Flexible boundary layer using exchange for embedding theories. I. Theory and implementation." Journal of Chemical Physics 155, 224112 (2021) — the FlexiBLE solvent boundary of flexible. doi:10.1063/5.0067855

Method reference directory

Follow the tutorials · Browse worked examples

Choose a method below, or follow the Scientific references links on individual method and example pages. Cite OpenQP and the specific theory, functional, basis/ECP, property and dynamics treatment actually used. A reference explains a method; it does not establish implementation availability or validation.

HF and density functional theory

Foundational and method-specific literature for the corresponding manual sections.

  • Roothaan CCJ. “New Developments in Molecular Orbital Theory.” Reviews of Modern Physics 23, 69-89 (1951). doi:10.1103/RevModPhys.23.69
  • Hohenberg P, Kohn W. “Inhomogeneous Electron Gas.” Physical Review 136, B864-B871 (1964). doi:10.1103/PhysRev.136.B864
  • Kohn W, Sham LJ. “Self-Consistent Equations Including Exchange and Correlation Effects.” Physical Review 140, A1133-A1138 (1965). doi:10.1103/PhysRev.140.A1133

Exchange-correlation functionals

Foundational and method-specific literature for the corresponding manual sections.

  • Perdew JP, Burke K, Ernzerhof M. “Generalized Gradient Approximation Made Simple.” Physical Review Letters 77, 3865-3868 (1996). doi:10.1103/PhysRevLett.77.3865
  • Adamo C, Barone V. “Toward reliable density functional methods without adjustable parameters: The PBE0 model.” The Journal of Chemical Physics 110, 6158-6170 (1999). doi:10.1063/1.478522
  • Becke AD. “Density-functional exchange-energy approximation with correct asymptotic behavior.” Physical Review A 38, 3098-3100 (1988). doi:10.1103/PhysRevA.38.3098
  • Lee C, Yang W, Parr RG. “Development of the Colle-Salvetti correlation-energy formula into a functional of the electron density.” Physical Review B 37, 785-789 (1988). doi:10.1103/PhysRevB.37.785
  • Becke AD. “Density-functional thermochemistry. III. The role of exact exchange.” The Journal of Chemical Physics 98, 5648-5652 (1993). doi:10.1063/1.464913
  • Yanai T, Tew DP, Handy NC. “A new hybrid exchange–correlation functional using the Coulomb-attenuating method (CAM-B3LYP).” Chemical Physics Letters 393, 51-57 (2004). doi:10.1016/j.cplett.2004.06.011
  • Tao J, Perdew JP, Staroverov VN, Scuseria GE. “Climbing the Density Functional Ladder: Nonempirical Meta–Generalized Gradient Approximation Designed for Molecules and Solids.” Physical Review Letters 91, 146401 (2003). doi:10.1103/PhysRevLett.91.146401
  • Grimme S. “Semiempirical hybrid density functional with perturbative second-order correlation.” The Journal of Chemical Physics 124, 034108 (2006). doi:10.1063/1.2148954

SCF convergence and response solvers

Foundational and method-specific literature for the corresponding manual sections.

  • Pulay P. “Improved SCF convergence acceleration.” Journal of Computational Chemistry 3, 556-560 (1982). doi:10.1002/jcc.540030413
  • Davidson ER. “The iterative calculation of a few of the lowest eigenvalues and corresponding eigenvectors of large real-symmetric matrices.” Journal of Computational Physics 17, 87-94 (1975). doi:10.1016/0021-9991(75)90065-0

Linear-response TDHF and TDDFT

These establish the time-dependent density-functional foundation and Tamm–Dancoff approximation; a citation does not enlarge the implemented response-model scope.

  • Runge E, Gross EKU. “Density-Functional Theory for Time-Dependent Systems.” Physical Review Letters 52, 997-1000 (1984). doi:10.1103/PhysRevLett.52.997
  • Hirata S, Head-Gordon M. “Time-dependent density functional theory within the Tamm–Dancoff approximation.” Chemical Physics Letters 314, 291-299 (1999). doi:10.1016/S0009-2614(99)01149-5

Spin-flip theory

This is the SF-TDDFT foundation. Mixed-reference MRSF and unrestricted/other extensions have different constructions; the ordinary two-SOMO MRSF citations are not validation of every extension.

  • Shao Y, Head-Gordon M, Krylov AI. “The spin–flip approach within time-dependent density functional theory: Theory and applications to diradicals.” The Journal of Chemical Physics 118, 4807-4818 (2003). doi:10.1063/1.1545679

Coupled cluster

Foundational and method-specific literature for the corresponding manual sections.

  • Purvis GD, Bartlett RJ. “A full coupled-cluster singles and doubles model: The inclusion of disconnected triples.” The Journal of Chemical Physics 76, 1910-1918 (1982). doi:10.1063/1.443164
  • Raghavachari K, Trucks GW, Pople JA, Head-Gordon M. “A fifth-order perturbation comparison of electron correlation theories.” Chemical Physics Letters 157, 479-483 (1989). doi:10.1016/S0009-2614(89)87395-6

Multiconfigurational methods

CASSCF, CASPT2, NEVPT2, extended multistate CASPT2 and quasidegenerate perturbation theory have distinct reference spaces and zeroth-order Hamiltonians. Cite the method actually selected. Analytic-gradient availability is a separate implementation question.

  • Roos BrO, Taylor PR, Siegbahn PEM. “A complete active space SCF method (CASSCF) using a density matrix formulated super-CI approach.” Chemical Physics 48, 157-173 (1980). doi:10.1016/0301-0104(80)80045-0
  • Andersson K, Malmqvist Pk, Roos BrO. “Second-order perturbation theory with a complete active space self-consistent field reference function.” The Journal of Chemical Physics 96, 1218-1226 (1992). doi:10.1063/1.462209
  • Angeli C, Cimiraglia R, Malrieu JP. “n -electron valence state perturbation theory: A spinless formulation and an efficient implementation of the strongly contracted and of the partially contracted variants.” The Journal of Chemical Physics 117, 9138-9153 (2002). doi:10.1063/1.1515317
  • Shiozaki T, Győrffy W, Celani P, Werner HJ. “Communication: Extended multi-state complete active space second-order perturbation theory: Energy and nuclear gradients.” The Journal of Chemical Physics 135, 081106 (2011). doi:10.1063/1.3633329
  • Nakano H. “Quasidegenerate perturbation theory with multiconfigurational self-consistent-field reference functions.” The Journal of Chemical Physics 99, 7983-7992 (1993). doi:10.1063/1.465674

Geometry optimization and reaction paths

Foundational and method-specific literature for the corresponding manual sections.

  • Wang LP, Song C. “Geometry optimization made simple with translation and rotation coordinates.” The Journal of Chemical Physics 144, 214108 (2016). doi:10.1063/1.4952956
  • Henkelman G, Uberuaga BP, Jónsson H. “A climbing image nudged elastic band method for finding saddle points and minimum energy paths.” The Journal of Chemical Physics 113, 9901-9904 (2000). doi:10.1063/1.1329672
  • Peng C, Bernhard Schlegel H. “Combining Synchronous Transit and Quasi‐Newton Methods to Find Transition States.” Israel Journal of Chemistry 33, 449-454 (1993). doi:10.1002/ijch.199300051
  • Heyden A, Bell AT, Keil FJ. “Efficient methods for finding transition states in chemical reactions: Comparison of improved dimer method and partitioned rational function optimization method.” The Journal of Chemical Physics 123, 224101 (2005). doi:10.1063/1.2104507
  • Mallikarjun Sharada S, Zimmerman PM, Bell AT, Head-Gordon M. “Automated Transition State Searches without Evaluating the Hessian.” Journal of Chemical Theory and Computation 8, 5166-5174 (2012). doi:10.1021/ct300659d
  • Zimmerman P. “Reliable Transition State Searches Integrated with the Growing String Method.” Journal of Chemical Theory and Computation 9, 3043-3050 (2013). doi:10.1021/ct400319w

Vibrational and magnetic properties

For harmonic vibrations and IR/Raman theory: Wilson EB, Decius JC and Cross PC, Molecular Vibrations: The Theory of Infrared and Raman Vibrational Spectra. Dover publisher record.

Foundational and method-specific literature for the corresponding manual sections.

  • Wolinski K, Hinton JF, Pulay P. “Efficient implementation of the gauge-independent atomic orbital method for NMR chemical shift calculations.” Journal of the American Chemical Society 112, 8251-8260 (1990). doi:10.1021/ja00179a005

Basis sets and effective core potentials

Weigend–Ahlrichs covers the def2 basis family; Dunning covers correlation-consistent Gaussian bases. The pseudopotential paper is foundational: cite the actual element-specific basis/ECP source used, which may differ from that example.

  • Weigend F, Ahlrichs R. “Balanced basis sets of split valence, triple zeta valence and quadruple zeta valence quality for H to Rn: Design and assessment of accuracy.” Physical Chemistry Chemical Physics 7, 3297 (2005). doi:10.1039/B508541A
  • Dunning TH. “Gaussian basis sets for use in correlated molecular calculations. I. The atoms boron through neon and hydrogen.” The Journal of Chemical Physics 90, 1007-1023 (1989). doi:10.1063/1.456153
  • Dolg M, Wedig U, Stoll H, Preuss H. “Energy-adjusted a b i n i t i o pseudopotentials for the first row transition elements.” The Journal of Chemical Physics 86, 866-872 (1987). doi:10.1063/1.452288

Dispersion correction

Foundational and method-specific literature for the corresponding manual sections.

  • Caldeweyher E, Ehlert S, Hansen A, Neugebauer H, Spicher S, Bannwarth C, Grimme S. “A generally applicable atomic-charge dependent London dispersion correction.” The Journal of Chemical Physics 150, 154122 (2019). doi:10.1063/1.5090222

Excited-state analysis and ionization

Martin describes natural transition orbitals; Morrell, Parr and Levy describe the extended Koopmans foundation. These do not by themselves validate every MRSF-specific analysis or EKT extension; also cite the OpenQP implementation and the applicable MRSF papers.

  • Martin RL. “Natural transition orbitals.” The Journal of Chemical Physics 118, 4775-4777 (2003). doi:10.1063/1.1558471
  • Morrell MM, Parr RG, Levy M. “Calculation of ionization potentials from density matrices and natural functions, and the long-range behavior of natural orbitals and electron density.” The Journal of Chemical Physics 62, 549-554 (1975). doi:10.1063/1.430509

Software libraries and data formats

Cite the original functional/basis/method paper as well as a library that supplies it. For functionals beyond those listed here use the individual references in the Libxc functional catalogue.

  • Lehtola S, Steigemann C, Oliveira MJT, Marques MAL. “Recent developments in libxc — A comprehensive library of functionals for density functional theory.” SoftwareX 7, 1-5 (2018). doi:10.1016/j.softx.2017.11.002
  • Schaftenaar G, Noordik JH. “Molden: a pre- and post-processing program for molecular and electronic structures*.” Journal of Computer-Aided Molecular Design 14, 123-134 (2000). doi:10.1023/A:1008193805436
  • Eastman P, Swails J, Chodera JD, McGibbon RT, Zhao Y, Beauchamp KA, Wang LP, Simmonett AC, Harrigan MP, Stern CD, Wiewiora RP, Brooks BR, Pande VS. “OpenMM 7: Rapid development of high performance algorithms for molecular dynamics.” PLOS Computational Biology 13, e1005659 (2017). doi:10.1371/journal.pcbi.1005659

Molecular symmetry

This is the group-theory foundation for symmetry labels and selection rules, not a claim that every reduction or root-selection algorithm is implemented.

Umbrella sampling and free energy

  • Kumar S, Rosenberg JM, Bouzida D, Swendsen RH and Kollman PA. “The weighted histogram analysis method for free-energy calculations on biomolecules. I. The method.” Journal of Computational Chemistry 13, 1011–1021 (1992). doi:10.1002/jcc.540130812.

WHAM is a free-energy estimator for appropriately sampled overlapping windows; it does not establish equilibration, sampling sufficiency or validity of a particular electronic-structure/dynamics approximation.