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Spartan (chemistry software)

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This article is about chemistry software. For other software, see Spartan (disambiguation).
Spartan
Developer(s)Wavefunction, Inc.[1] & Q-Chem
Initial release1991; 33 years ago (1991)
Stable release
Spartan'20 v.1.1 / 2021; 3 years ago (2021)
Written inC, C++, Fortran, Qt
Operating systemWindows, Mac OS X, Linux
Platformx86-64
Available inEnglish
TypeMolecular modelling, computational chemistry
LicenseProprietary commercial software
Websitewww.wavefun.com

Spartan is a molecular modelling and computational chemistry application from Wavefunction.[2] It contains code for molecular mechanics, semi-empirical methods, ab initio models,[3] density functional models,[4] post-Hartree–Fock models,[5] and thermochemical recipes including G3(MP2)[6] and T1.[7] Quantum chemistry calculations in Spartan are powered by Q-Chem.[8]

Primary functions are to supply information about structures, relative stabilities and other properties of isolated molecules. Molecular mechanics calculations on complex molecules are common in the chemical community. Quantum chemical calculations, including Hartree–Fock method molecular orbital calculations, but especially calculations that include electronic correlation, are more time-consuming in comparison.

Quantum chemical calculations are also called upon to furnish information about mechanisms and product distributions of chemical reactions, either directly by calculations on transition states, or based on Hammond's postulate,[9] by modeling the steric and electronic demands of the reactants. Quantitative calculations, leading directly to information about the geometries of transition states, and about reaction mechanisms in general, are increasingly common, while qualitative models are still needed for systems that are too large to be subjected to more rigorous treatments. Quantum chemical calculations can supply information to complement existing experimental data or replace it altogether, for example, atomic charges for quantitative structure-activity relationship (QSAR)[10] analyses, and intermolecular potentials for molecular mechanics and molecular dynamics calculations.

Spartan applies computational chemistry methods (theoretical models) to many standard tasks that provide calculated data applicable to the determination of molecular shape conformation, structure (equilibrium and transition state geometry), NMR, IR, Raman, and UV-visible spectra, molecular (and atomic) properties, reactivity, and selectivity.

Computational abilities

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This software provides the molecular mechanics, Merck Molecular Force Field (MMFF),[11] (for validation test suite), MMFF with extensions, and SYBYL,[12] force fields calculation, Semi-empirical calculations, MNDO/MNDO(D),[13] Austin Model 1 (AM1),[14] PM3,[15][16][17][18] Recife Model 1 (RM1)[19] PM6.[20]

The calculated T1[7] heat of formation (y axis) relative to the experimental heat of formation (x axis) for a set of >1800 diverse organic molecules from the NIST thermochemical database[30] with mean absolute and RMS errors of 8.5 and 11.5 kJ/mol, respectively.

Tasks performed

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Available computational models provide molecular, thermodynamic, QSAR, atomic, graphical, and spectral properties. A calculation dialogue provides access to the following computational tasks:

  • Energy[71] – For a given geometry, provides energy and associated properties of a molecule or system. If quantum chemical models are employed, the wave function is calculated.
  • Equilibrium molecular geometry[72] - Locates the nearest local minimum and provides energy and associated properties.
  • Transition state geometry[72] - Locates the nearest first-order saddle point (a maximum in a single dimension and minima in all others) and provides energy and associated properties.
  • Equilibrium conformer[72] – Locates lowest-energy conformation. Often performed before calculating structure using a quantum chemical model.
  • Conformer distribution[71] – Obtains a selection of low-energy conformers. Commonly used to identify the shapes a specific molecule is likely to adopt and to determine a Boltzmann distribution for calculating average molecular properties.
  • Conformer library[71] – Locates lowest-energy conformer and associates this with a set of conformers spanning all shapes accessible to the molecule without regard to energy. Used to build libraries for similarity analysis.
  • Energy profile[71] – Steps a molecule or system through a user defined coordinate set, providing equilibrium geometries for each step (subject to user-specified constraints).
  • Similarity analysis[71] – quantifies the likeness of molecules (and optionally their conformers) based on either structure or chemical function (Hydrogen bond acceptors–donors, positive–negative ionizables, hydrophobes, aromatics). Quantifies likeness of a molecule (and optionally its conformers) to a pharmacophore.

Graphical user interface

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The software contains an integrated graphical user interface. Touch screen operations are supported for Windows 7 and 8 devices. Construction of molecules in 3D is facilitated with molecule builders (included are organic, inorganic, peptide, nucleotide, and substituent builders). 2D construction is supported for organic molecules with a 2D sketch palette. The Windows version interface can access ChemDraw; which versions 9.0 or later may also be used for molecule building in 2D. A calculations dialogue is used for specification of task and computational method. Data from calculations are displayed in dialogues, or as text output. Additional data analysis, including linear regression, is possible from an internal spreadsheet.[71]

Graphical models

[edit]
A cut-away view of the electrostatic potential map of fullerene (C60), the blue area inside the molecule is an area of positive charge (relative to the superstructure, providing a pictorial explanation for fullerene's ability to encapsulate negatively charged species).

Graphical models, especially molecular orbitals, electron density, and electrostatic potential maps, are a routine means of molecular visualization in chemistry education.[73][74][75][76][77]

  • Surfaces:
    • Molecular orbitals (highest occupied, lowest unoccupied, and others)
    • Electron density – The density, ρ(r), is a function of the coordinates r, defined such that ρ(r)dr is the number of electrons inside a small volume dr. This is what is measured in an X-ray diffraction experiment. The density may be portrayed in terms of an isosurface (isodensity surface) with the size and shape of the surface being given by the value (or percentage of enclosure) of the electron density.
    • Spin density – The density, ρspin(r), is defined as the difference in electron density formed by electrons of α spin, ρα(r), and the electron density formed by electrons of β spin, ρβ(r). For closed-shell molecules (in which all electrons are paired), the spin density is zero everywhere. For open-shell molecules (in which one or more electrons are unpaired), the spin density indicates the distribution of unpaired electrons. Spin density is an indicator of reactivity of radicals.[72]
    • Van der Waals radius (surface)
    • Solvent accessible surface area
    • Electrostatic potential – The potential, εp, is defined as the energy of interaction of a positive point charge located at p with the nuclei and electrons of a molecule. A surface for which the electrostatic potential is negative (a negative potential surface) delineates regions in a molecule which are subject to electrophilic attack.
  • Composite surfaces (maps):
    • Electrostatic potential map (electrophilic indicator) – The most commonly employed property map is the electrostatic potential map. This gives the potential at locations on a particular surface, most commonly a surface of electron density corresponding to overall molecular size.[71]
    • Local ionization potential map – Is defined as the sum over orbital electron densities, ρi(r) times absolute orbital energies, ∈i, and divided by the total electron density, ρ(r). The local ionization potential reflects the relative ease of electron removal ("ionization") at any location around a molecule. For example, a surface of "low" local ionization potential for sulfur tetrafluoride demarks the areas which are most easily ionized.
    • LUMO map (nucleophilic indicator) – Maps of molecular orbitals may also lead to graphical indicators. For example, the LUMO map, wherein the (absolute value) of the lowest-unoccupied molecular orbital (the LUMO) is mapped onto a size surface (again, most commonly the electron density), providing an indication of nucleophilic reactivity.

Spectral calculations

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The calculated (DFT/EDF2/6-31G*) IR spectra (red), scaled and optimized to the experimental FT-IR spectra (blue) of phenyl 9-acridinecarboxylate (below).
2D rendering
3D rendering
The molecule phenyl 9-acridinecarboxylate.

Available spectra data and plots for:

Experimental spectra may be imported for comparison with calculated spectra: IR and UV/vis spectra in Joint Committee on Atomic and Molecular Physical Data (JCAMP)[86] (.dx) format and NMR spectra in Chemical Markup Language (.cml) format. Access to public domain spectral databases is available for IR, NMR, and UV/vis spectra.

Databases

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Spartan accesses several external databases.

  • Quantum chemical calculations databases:
  • Experimental databases:
    • NMRShiftDB[88] – an open-source database of experimental 1H and 13C chemical shifts.
    • Cambridge Structural Database (CSD)[89] - a large repository of small molecule organic and inorganic experimental crystal structures of about 600,000 entries.
    • NIST database[30] of experimental IR and UV/vis spectra.

Major release history

[edit]
  • 1991 Spartan version 1 Unix
  • 1993 Spartan version 2 Unix
  • 1994 Mac Spartan Macintosh
  • 1995 Spartan version 3 Unix
  • 1995 PC Spartan Windows
  • 1996 Mac Spartan Plus Macintosh
  • 1997 Spartan version 4 Unix
  • 1997 PC Spartan Plus Windows
  • 1999 Spartan version 5 Unix
  • 1999 PC Spartan Pro Windows
  • 2000 Mac Spartan Pro Macintosh
  • 2002 Spartan'02 Unix, Linux, Windows, Mac

Windows, Macintosh, Linux versions

[edit]
  • 2004 Spartan'04
  • 2006 Spartan'06
  • 2008 Spartan'08
  • 2010 Spartan'10
  • 2013 Spartan'14
  • 2016 Spartan'16
  • 2018 Spartan'18
  • 2021 Spartan'20

See also

[edit]

References

[edit]
  1. ^ Wavefunction, Inc.
  2. ^ Computational Chemistry, David Young, Wiley-Interscience, 2001. Appendix A. A.1.6 pg 330, Spartan
  3. ^ Hehre, Warren J.; Leo Radom; Paul v.R. Schleyer; John A. Pople (1986). Ab initio molecular orbital theory. John Wiley & Sons. ISBN 0-471-81241-2.
  4. ^ Hohenberg, Pierre; Walter Kohn (1964). "Inhomogeneous electron gas". Physical Review. 136 (3B): B864–B871. Bibcode:1964PhRv..136..864H. doi:10.1103/PhysRev.136.B864.
  5. ^ Cramer, Christopher J. (2002). Essentials of Computational Chemistry. John Wiley & Sons. ISBN 978-0-470-09182-1.
  6. ^ a b c Larry A. Curtiss; Paul C. Redfern; Krishnan Raghavachari; Vitaly Rassolov & John A. Pople (1998). "Gaussian-3 theory using reduced Møller-Plesset order". The Journal of Chemical Physics. 110 (10). The American Institute of Physics: 4703–4710. Bibcode:1999JChPh.110.4703C. doi:10.1063/1.478385.
  7. ^ a b c d Ohlinger, William S.; Philip E. Klunzinger; Bernard J. Deppmeier; Warren J. Hehre (2009). "Efficient Calculation of Heats of Formation". The Journal of Physical Chemistry A. 113 (10). ACS Publications: 2165–2175. Bibcode:2009JPCA..113.2165O. doi:10.1021/jp810144q. PMID 19222177.
  8. ^ Krylov, Anna I.; Gill, Peter M.W. (2013). "Q-Chem: an engine for innovation". Wiley Interdisciplinary Reviews: Computational Molecular Science. 3 (3): 317–326. doi:10.1002/wcms.1122. S2CID 16713704.
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  10. ^ Leach, Andrew R. (2001). Molecular modelling: principles and applications. Englewood Cliffs, N.J: Prentice Hall. ISBN 0-582-38210-6.
  11. ^ Thomas A. Halgren (1996). "Merck molecular force field. I. Basis, form, scope, parameterization, and performance of MMFF94". Journal of Computational Chemistry. 17 (5–6): 490–519. doi:10.1002/(SICI)1096-987X(199604)17:5/6<490::AID-JCC1>3.0.CO;2-P.
  12. ^ Matthew Clark; Richard D. Cramer III & Nicole Van Opdenbosch (1989). "Validation of the general purpose tripos 5.2 force field". Journal of Computational Chemistry. 10 (8): 982–1012. doi:10.1002/jcc.540100804. S2CID 97743988.
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  16. ^ James J. P. Stewart (1989). "Optimization of parameters for semiempirical methods II. Applications". The Journal of Computational Chemistry. 10 (2): 221–264. doi:10.1002/jcc.540100209. S2CID 98850840.
  17. ^ James J. P. Stewart (1991). "Optimization of parameters for semiempirical methods. III Extension of PM3 to Be, Mg, Zn, Ga, Ge, As, Se, Cd, In, Sn, Sb, Te, Hg, Tl, Pb, and Bi". The Journal of Computational Chemistry. 12 (3): 320–341. doi:10.1002/jcc.540120306. S2CID 94913344.
  18. ^ James J. P. Stewart (2004). "Optimization of parameters for semiempirical methods IV: extension of MNDO, AM1, and PM3 to more main group elements". The Journal of Molecular Modeling. 10 (2). Springer Berlin-Heidelberg: 155–164. doi:10.1007/s00894-004-0183-z. PMID 14997367. S2CID 11617476.
  19. ^ Gerd B. Rocha; Ricardo O. Freire; Alfredo M. Simas; James J. P. Stewart (2006). "RM1: A reparameterization of AM1 for H, C, N, O, P, S, F, Cl, Br, and I". The Journal of Computational Chemistry. 27 (10): 1101–1111. doi:10.1002/jcc.20425. PMID 16691568. S2CID 9017673.
  20. ^ James J. P. Stewart (2007). "Optimization of Parameters for Semiempirical Methods V: Modification of NDDO Approximations and Application to 70 Elements". The Journal of Molecular Modeling. 13 (12). Springer: 1173–1213. doi:10.1007/s00894-007-0233-4. PMC 2039871. PMID 17828561.
  21. ^ a b Aleksandr V. Marenich; Ryan M. Olson; Casey P. Kelly; Christopher J. Cramer & Donald G. Truhlar (2007). "Self-Consistent Reaction Field Model for Aqueous and Nonaqueous Solutions Based on Accurate Polarized Partial Charges". Journal of Chemical Theory and Computation. 3 (6). ACS Publications: 2011–2033. doi:10.1021/ct7001418. PMID 26636198.
  22. ^ a b c d A. D. Becke (1988). "Density-functional exchange-energy approximation with correct asymptotic behavior". Physical Review A. 38 (6). American Physical Society: 3098–3100. Bibcode:1988PhRvA..38.3098B. doi:10.1103/PhysRevA.38.3098. PMID 9900728.
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  26. ^ a b c Ross D. Adamsona, Peter M. W. Gill and John A. Pople (1998). "Empirical density functionals". Chemical Physics Letters. 284 (5–6). Elsevier: 6–11. Bibcode:1998CPL...284....6A. doi:10.1016/S0009-2614(97)01282-7.
  27. ^ a b c Peter M. W. Gill, Yeh Lin Ching and Michael W. George (2004). "EDF2: A density functional for predicting molecular vibrational frequencies". Australian Journal of Chemistry. 57 (4). Commonwealth Scientific and Industrial Research Organization: 365–370. doi:10.1071/CH03263.
  28. ^ a b c Yan Zhao & Donald G. Truhlar (2008). "The M06 suite of density functionals for main group thermochemistry, thermochemical kinetics, noncovalent interactions, excited states, and transition elements: two new functionals and systematic testing of four M06-class functionals and 12 other functionals". Theoretical Chemistry Accounts. 120 (1–3). Springer Berlin / Heidelberg: 215–241. doi:10.1007/s00214-007-0310-x.
  29. ^ a b J. D. Chai & Martin Head-Gordon (2008). "Long-range corrected hybrid density functionals with damped atom-atom dispersion corrections". Physical Chemistry Chemical Physics. 10 (44). RSC Publishing: 6615–66120. Bibcode:2008PCCP...10.6615C. doi:10.1039/b810189b. PMID 18989472. S2CID 32301575.
  30. ^ a b NIST Chemistry WebBook. nist.gov
  31. ^ P.A.M. Dirac (1930). "Note on Exchange Phenomena in the Thomas Atom". Mathematical Proceedings of the Cambridge Philosophical Society. 26 (3). Cambridge Journals: 376–385. Bibcode:1930PCPS...26..376D. doi:10.1017/S0305004100016108.
  32. ^ Peter M. W. Gill (1996). "A new gradient-corrected exchange functional". Molecular Physics. 89 (2). Taylor & Francis: 433–445. Bibcode:1996MolPh..89..433G. doi:10.1080/00268979609482484.
  33. ^ A.T.B. Gilbert & P.M.W. Gill (1999). "Decomposition of exchange-correlation energies". Chemical Physics Letters. 312 (5–6). Elsevier: 511–521. Bibcode:1999CPL...312..511G. doi:10.1016/S0009-2614(99)00836-2.
  34. ^ John P. Perdew & Yue Wang (1992). "Accurate and simple analytic representation of the electron-gas correlation energy". Physical Review B. 45 (23). American Physical Society: 13244–13249. Bibcode:1992PhRvB..4513244P. doi:10.1103/PhysRevB.45.13244. PMID 10001404.
  35. ^ Vosko, S.H.; Wilk, L.; Nusair, M. (1980). "Accurate spin-dependent electron liquid correlation energies for local spin density calculations: a critical analysis" (PDF). Canadian Journal of Physics. 58 (8). NRC Research Press: 1200–1211. Bibcode:1980CaJPh..58.1200V. doi:10.1139/p80-159. S2CID 122287164.
  36. ^ John P. Perdew & Yue Wang (1992). "Accurate and simple analytic representation of the electron-gas correlation energy". Physical Review B. 45 (23). The American Physical Society: 13244–13249. Bibcode:1992PhRvB..4513244P. doi:10.1103/PhysRevB.45.13244. PMID 10001404.
  37. ^ J. P. Perdew (1981). "Density-functional approximation for the correlation energy of the inhomogeneous electron gas". Physical Review B. 23 (10). The American Physical Society: 5048–5079. Bibcode:1981PhRvB..23.5048P. doi:10.1103/PhysRevB.23.5048.
  38. ^ J. P. Perdew & A. Zunger (1986). "Self-interaction correction to density-functional approximations for many-electron systems". Physical Review B. 33 (12). The American Physical Society: 8822–8824. Bibcode:1986PhRvB..33.8822P. doi:10.1103/PhysRevB.33.8822. PMID 9938299.
  39. ^ John P. Perdew; Kieron Burke & Matthias Ernzerhof (1996). "Generalized Gradient Approximation Made Simple". Physical Review Letters. 77 (18). American Physical Society: 3865–3868. Bibcode:1996PhRvL..77.3865P. doi:10.1103/PhysRevLett.77.3865. PMID 10062328. S2CID 6425905.
  40. ^ A. D. Becke & M. R. Roussel (1989). "Exchange holes in inhomogeneous systems: A coordinate-space model". Physical Review A. 39 (8). The American Physical Society: 3761–3767. Bibcode:1989PhRvA..39.3761B. doi:10.1103/PhysRevA.39.3761. PMID 9901696.
  41. ^ A. Daniel Boese & Jan M. L. Martin (2004). "Development of density functionals for thermochemical kinetics". The Journal of Chemical Physics. 121 (8): 3405–3417. arXiv:physics/0405158. Bibcode:2004JChPh.121.3405B. doi:10.1063/1.1774975. PMID 15303903. S2CID 29764068.
  42. ^ Truhlar Group
  43. ^ a b Yan Zhao; Nathan E. Schultz & Donald G. Truhlar (2006). "Design of Density Functionals by Combining the Method of Constraint Satisfaction with Parameterization for Thermochemistry, Thermochemical Kinetics, and Noncovalent Interactions". Journal of Chemical Theory and Computation. 2 (2). ACS Publications: 364–382. doi:10.1021/ct0502763. PMID 26626525.
  44. ^ Yan Zhao & Donald G. Truhlar (2008). "A new local density functional for main-group thermochemistry, transition metal bonding, thermochemical kinetics, and noncovalent interactions". The Journal of Chemical Physics. 125 (19). American Institute of Physics: 194101–194119. Bibcode:2006JChPh.125s4101Z. doi:10.1063/1.2370993. PMID 17129083.
  45. ^ Yan Zhao & Donald G. Truhlar (2008). "Density Functional for Spectroscopy: No Long-Range Self-Interaction Error, Good Performance for Rydberg and Charge-Transfer States, and Better Performance on Average than B3LYP for Ground States". The Journal of Physical Chemistry A. 110 (49). ACS Publications: 13126–13130. Bibcode:2006JPCA..11013126Z. doi:10.1021/jp066479k. PMID 17149824.
  46. ^ Head-Gordon Group
  47. ^ a b Jeng-Da Chai & Martin Head-Gordon (2006). "Systematic optimization of long-range corrected hybrid density functionals" (PDF). The Journal of Chemical Physics. 128 (8). American Institute of Physics: 084106–084121. Bibcode:2008JChPh.128h4106C. doi:10.1063/1.2834918. PMID 18315032.
  48. ^ George D. Purvis & Rodney J. Bartlett (1982). "A full coupled-cluster singles and doubles model: The inclusion of disconnected triples". The Journal of Chemical Physics. 76 (4). The American Institute of Physics: 1910–1919. Bibcode:1982JChPh..76.1910P. doi:10.1063/1.443164.
  49. ^ Krishnan Raghavachari; Gary W. Trucks; John A. Pople and; Martin Head-Gordon (1989). "A fifth-order perturbation comparison of electron correlation theories". Chemical Physics Letters. 157 (6). Elsevier Science: 479–483. Bibcode:1989CPL...157..479R. doi:10.1016/S0009-2614(89)87395-6.
  50. ^ Troy Van Voorhis & Martin Head-Gordon (2001). "Two-body coupled cluster expansions". The Journal of Chemical Physics. 115 (11). The American Institute of Physics: 5033–5041. Bibcode:2001JChPh.115.5033V. doi:10.1063/1.1390516.
  51. ^ C. David Sherrill; Anna I. Krylov; Edward F. C. Byrd & Martin Head-Gordon (1998). "Energies and analytic gradients for a coupled-cluster doubles model using variational Brueckner orbitals: Application to symmetry breaking in O+
    4    ". The Journal of Chemical Physics. 109 (11). The American Institute of Physics: 4171–4182. Bibcode:1998JChPh.109.4171S. doi:10.1063/1.477023.
  52. ^ Steven R. Gwaltney & Martin Head-Gordon (2000). "A second-order correction to singles and doubles coupled-cluster methods based on a perturbative expansion of a similarity-transformed Hamiltonian". Chemical Physics Letters. 323 (1–2). Elsevier: 21–28. Bibcode:2000CPL...323...21G. doi:10.1016/S0009-2614(00)00423-1.
  53. ^ Troy Van Voorhis & Martin Head-Gordon (2000). "The quadratic coupled cluster doubles model". Chemical Physics Letters. 330 (5–6). Elsevier: 585–594. Bibcode:2000CPL...330..585V. doi:10.1016/S0009-2614(00)01137-4.
  54. ^ a b c Anna I. Krylov; C. David Sherrill; Edward F. C. Byrd & Martin Head-Gordon (1998). "Size-consistent wave functions for nondynamical correlation energy: The valence active space optimized orbital coupled-cluster doubles model". The Journal of Chemical Physics. 109 (24). The American Institute of Physics: 10669–10678. Bibcode:1998JChPh.10910669K. doi:10.1063/1.477764.
  55. ^ a b Chr. Møller & M. S. Plesset (1934). "Note on an Approximation Treatment form Many-Electron Systems" (PDF). Physical Review. 46 (7). The American Physical Society: 618–622. Bibcode:1934PhRv...46..618M. doi:10.1103/PhysRev.46.618.
  56. ^ Head-Gordon, Martin; Pople, John A.; Frisch, Michael J. (1988). "MP2 energy evaluation by direct methods". Chemical Physics Letters. 153 (6): 503–506. Bibcode:1988CPL...153..503H. doi:10.1016/0009-2614(88)85250-3.
  57. ^ Pople, J. A.; Seeger, R.; Krishnan, R. (1977). "Variational configuration interaction methods and comparison with perturbation theory". International Journal of Quantum Chemistry. 12 (S11): 149–163. doi:10.1002/qua.560120820.
  58. ^ Pople, John A.; Binkley, J. Stephen; Seeger, Rolf (1976). "Theoretical models incorporating electron correlation". International Journal of Quantum Chemistry. 10 (S10): 1–19. doi:10.1002/qua.560100802.
  59. ^ Krishnan Raghavachari & John A. Pople (1978). "Approximate fourth-order perturbation theory of the electron correlation energy". International Journal of Quantum Chemistry. 14 (1): 91–100. doi:10.1002/qua.560140109.
  60. ^ Martin Feyereisena, George Fitzgeralda & Andrew Komornickib (1993). "Scaled Second-Order Perturbation Corrections to Configuration Interaction Singles: Efficient and Reliable Excitation Energy Methods". Chemical Physics Letters. 208 (5–6). Elsevier: 359–363. Bibcode:1993CPL...208..359F. doi:10.1016/0009-2614(93)87156-W.
  61. ^ Florian Weigend & Marco Häser (1997). "RI-MP2: first derivatives and global consistency". Theoretical Chemistry Accounts. 97 (1–4). Springer Berlin / Heidelberg: 331–340. doi:10.1007/s002140050269. S2CID 97649855.
  62. ^ Robert A. Distasio J.R.; Ryan P. Steele; Young Min Rhee; Yihan Shao & Martin Head-Gordon (2007). "An improved algorithm for analytical gradient evaluation in resolution-of-the-identity second-order Møller-Plesset perturbation theory: Application to alanine tetrapeptide conformational analysis". Journal of Computational Chemistry. 28 (5): 839–856. doi:10.1002/jcc.20604. PMID 17219361. S2CID 8438511.
  63. ^ a b Erich Runge & E. K. U. Gross (1984). "Density-Functional Theory for Time-Dependent Systems". Physical Review Letters. 52 (12). American Physical Society: 997–1000. Bibcode:1984PhRvL..52..997R. doi:10.1103/PhysRevLett.52.997.
  64. ^ a b So Hirata & Martin Head-Gordon (1999). "Time-dependent density functional theory for radicals: An improved description of excited states with substantial double excitation character". Chemical Physics Letters. 302 (5–6). Elsevier: 375–382. Bibcode:1999CPL...302..375H. doi:10.1016/S0009-2614(99)00137-2.
  65. ^ a b David Maurice & Martin Head-Gordon (1999). "Analytical second derivatives for excited electronic states using the single excitation configuration interaction method: theory and application to benzo[a]pyrene and chalcone". Molecular Physics. 96 (10). Taylor & Francis: 1533–1541. Bibcode:1999MolPh..96.1533M. doi:10.1080/00268979909483096.
  66. ^ a b Martin Head-Gordon; Rudolph J. Rico; Manabu Oumi & Timothy J. Lee (1994). "A doubles correction to electronic excited states from configuration interaction in the space of single substitutions". Chemical Physics Letters. 219 (1–2). Elsevier: 21–29. Bibcode:1994CPL...219...21H. doi:10.1016/0009-2614(94)00070-0.
  67. ^ a b John A. Pople; Martin Head-Gordon & Krishnan Raghavachari (1987). "Quadratic configuration interaction. A general technique for determining electron correlation energies". The Journal of Chemical Physics. 87 (10). American Institute of Physics: 5968–35975. Bibcode:1987JChPh..87.5968P. doi:10.1063/1.453520.
  68. ^ a b Rhee, Young Min; Martin Head-Gordon (2007). "Scaled Second-Order Perturbation Corrections to Configuration Interaction Singles: Efficient and Reliable Excitation Energy Methods". The Journal of Physical Chemistry A. 111 (24). ACS Publications: 5314–5326. Bibcode:2007JPCA..111.5314R. doi:10.1021/jp068409j. PMID 17521172. S2CID 20103672.
  69. ^ Larry A. Curtiss; Krishnan Raghavachari; Gary W. Trucks & John A. Pople (1991). "Gaussian-2 theory for molecular energies of first- and second-row compounds". The Journal of Chemical Physics. 94 (11). The American Institute of Physics: 7221–7231. Bibcode:1991JChPh..94.7221C. doi:10.1063/1.460205.
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