Spartan (software)

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Spartan'14 Software
Spartan'14 Windows GUI

Spartan Graphical User Interface
Developer(s) Wavefunction & Q-Chem
Initial release 1991 (1991)
Stable release 1.0.0 / August 7, 2013 (2013-08-07)
Development status Active
Written in C, C++, Fortran, Qt
Platform Cross-platform
License Wavefunction, Inc.
Website Wavefunction

Spartan is a molecular modeling and computational chemistry application from Wavefunction.[3] It contains code for molecular mechanics, semi-empirical methods, ab initio models,[4] density functional models,[5] post-Hartree-Fock models,[6] and thermochemical recipes including G3(MP2)[7] and T1.[1]

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 molecular orbital calculations, but especially calculations that include electron 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 the Hammond Postulate,[8] 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 QSAR[9] analyses, and intermolecular potentials for molecular mechanics and molecular dynamics calculations.

Spartan applies computational chemistry methods (theoretical models) to a number of a 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 Capabilities

This software provides the Molecular mechanics, MMFF,[10] (for validation test suite), MMFF with extensions, and SYBYL,[11] force fields calculation, Semi-empirical calculations, MNDO/MNDO(D),[12] AM1,[13] PM3,[14][15][16][17] RM1[18] PM6.[19]

  • Hartree-Fock / SCF methods, available with implicit solvent (SM8).[20]
    • Restricted, Unrestricted, and Restricted Open-shell Hartree-Fock
  • Density Functional Theory (DFT) methods, available with implicit solvent(SM8).[20]
The calculated T1[1] heat of formation (y axis) compared to the experimental heat of formation (x axis) for a set of >1800 diverse organic molecules from the NIST thermochemical database[2] with mean absolute and RMS errors of 8.5 and 11.5 kJ/mol, respectively.

Tasks Performed

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

  • Energy[67] - For a given geometry, provides energy and associated properties of a molecule or system. If quantum chemical models are employed, the wavefunction is calculated.
  • Equilibrium Geometry[68] - Locates the nearest local minimum and provides energy and associated properties.
  • Transition State Geometry[68] - 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[68] - Locates lowest-energy conformation. Often performed prior to calculating structure using a quantum chemical model.
  • Conformer Distribution[67] - 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[67] - 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[67] - Steps a molecule or system through a user defined coordinate set, providing equilibrium geometries for each step (subject to user-specified constraints).
  • Similarity Analysis[67] - 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

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; ChemDraw 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.[67]

Graphical Models

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.[69][70][71][72][73]

  • Surfaces:
    • Molecular Orbitals (Highest Occupied, Lowest Unoccupied, and others.)
    • Electron Density - The electron 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 electron density may be portrayed in terms of an isosurface (an 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 spin 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.[68]
    • Van der Waals surface
    • Solvent Accessible surface
    • Electrostatic Potential - The electrostatic 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 electrostatic potential at locations on a particular surface, most commonly a surface of electron density corresponding to overall molecular size.[67]
    • 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

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 JCAMP[82] (.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

Spartan accesses a number of external databases.

  • Quantum Chemical Calculations Databases:
    • Spartan Spectra & Properties Database (SSPD) - a collection of approximately 252,000 molecules along with structures, energies, NMR and IR spectra, and wave functions calculated using the EDF2[26] density functional modelwith the 6-31G* basis set.[83]
    • Spartan Molecular Database (SMD) - a collection of approximately 100,000 molecules calculated from following models:
      • Hartree-Fock with 3-21G, 6-31G*, and 6-311+G** basis sets[83]
      • B3LYP[24] density functional with 6-31G* and 6-311+G** basis sets
      • EDF1[25] density functional with 6-31G* basis set
      • MP2[51] with 6-31G* and 6-311+G** basis sets
      • G3(MP2)[7]
      • T1[1]
  • Experimental Databases:
    • NMRShiftDB[84] - an open-source database of experimental 1H and 13C chemical shifts.
    • Cambridge Structural Database[85] (CSD) - a large repository of small molecule organic and inorganic experimental crystal structures of approximately 600,000 entries.
    • NIST database[2] of experimental IR and UV/vis spectra.

Major Release history

  • 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, Linux, Macintosh versions

  • 2004 Spartan'04
  • 2006 Spartan'06
  • 2008 Spartan'08
  • 2010 Spartan'10
  • 2013 Spartan'14

See also

References

  1. ↑ 1.0 1.1 1.2 1.3 Ohlinger, William S.; Philip E. Klunzinger, Bernard J. Deppmeier, and Warren J. Hehre (January 2009). "Efficient Calculation of Heats of Formation". The Journal of Physical Chemistry A (ACS Publications) 113 (10): 2165–2175. doi:10.1021/jp810144q. PMID 19222177. 
  2. ↑ 2.0 2.1 NIST Chemistry WebBook
  3. ↑ Computational Chemistry, David Young, Wiley-Interscience, 2001. Appendix A. A.1.6 pg 330, SPARTAN
  4. ↑ Hehre, Warren J.; Leo Radom, Paul v.R. Schleyer, and John A. Pople (1986). AB INITIO Molecular Orbital Theory. John Wiley & Sons. ISBN 0-471-81241-2. 
  5. ↑ Hohenberg, Pierre; Walter Kohn (1964). "Inhomogeneous electron gas". Physical Review 136 (3B): B864–B871. Bibcode:1964PhRv..136..864H. doi:10.1103/PhysRev.136.B864. 
  6. ↑ Cramer, Christopher J. (2002). Essentials of Computational Chemistry. John Wiley & Sons. ISBN 978-0-470-09182-1. 
  7. ↑ 7.0 7.1 7.2 Larry A. Curtiss, Paul C. Redfern, Krishnan Raghavachari, Vitaly Rassolov, and John A. Pople (November 23, 1998). "Gaussian-3 theory using reduced Møller-Plesset order". The Journal of Chemical Physics (The American Institute of Physics) 110 (10): 4703–4710. Bibcode:1999JChPh.110.4703C. doi:10.1063/1.478385. 
  8. ↑ Hammond, G. S. (1955). "A Correlation of Reaction Rates". The Journal of the American Chemical Society (ACS Publications) 77 (2): 334–338. doi:10.1021/ja01607a027. 
  9. ↑ Leach, Andrew R. (2001). Molecular modelling: principles and applications. Englewood Cliffs, N.J: Prentice Hall. ISBN 0-582-38210-6. 
  10. ↑ Thomas A. Halgren (1996). "Merck molecular force field. I. Basis, form, scope, parameterization, and performance of MMFF94". Journal of Computational Chemistry (Wiley InterScience). 17 (5-6) (5–6): 490–519. doi:10.1002/(SICI)1096-987X(199604)17:5/6<490::AID-JCC1>3.0.CO;2-P. 
  11. ↑ Matthew Clark, Richard D. Cramer III, and Nicole Van Opdenbosch (1989). "Validation of the general purpose tripos 5.2 force field". Journal of Computational Chemistry (Wiley InterScience) 10 (8): 982–1012. doi:10.1002/jcc.540100804. 
  12. ↑ Michael J. S. Dewar and Walter Thiel (1977). "Ground states of molecules. 38. The MNDO method. Approximations and parameters". The Journal of the American Chemical Society (ACS Publications) 99 (15): 4899–4907. doi:10.1021/ja00457a004. 
  13. ↑ Michael J. S. Dewar, Eve G. Zoebisch, Eamonn F. Healy, James J. P. Stewart (1985). "Development and use of quantum molecular models. 75. Comparative tests of theoretical procedures for studying chemical reactions". The Journal of the American Chemical Society (ACS Publications) 107 (13): 3902–3909. doi:10.1021/ja00299a024. 
  14. ↑ James J. P. Stewart (1989). "Optimization of parameters for semiempirical methods I. Method". The Journal of Computational Chemistry (Wiley InterScience) 10 (2): 209–220. doi:10.1002/jcc.540100208. 
  15. ↑ James J. P. Stewart (1989). "Optimization of parameters for semiempirical methods II. Applications". The Journal of Computational Chemistry (Wiley InterScience) 10 (2): 221–264. doi:10.1002/jcc.540100209. 
  16. ↑ 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 (Wiley InterScience) 12 (3): 320–341. doi:10.1002/jcc.540120306. 
  17. ↑ 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 (Springer Berlin / Heidelberg) 10 (2): 155–164. doi:10.1007/s00894-004-0183-z. PMID 14997367. 
  18. ↑ 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 (Wiley InterScience) 27 (10): 1101–1111. doi:10.1002/jcc.20425. PMID 16691568. 
  19. ↑ >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 (Springer) 13 (12): 1173–1213. doi:10.1007/s00894-007-0233-4. 
  20. ↑ 20.0 20.1 Aleksandr V. Marenich, Ryan M. Olson, Casey P. Kelly, Christopher J. Cramer, and Donald G. Truhlar (2007). "Self-Consistent Reaction Field Model for Aqueous and Nonaqueous Solutions Based on Accurate Polarized Partial Charges". The Journal of Chemical Theory and Computation (ACS Publications) 3 (6): 2011–2033. doi:10.1021/ct7001418. 
  21. ↑ 21.0 21.1 21.2 21.3 A. D. Becke (September 1988). "Density-functional exchange-energy approximation with correct asymptotic behavior". Physical Review A (American Physical Society) 38 (6): 3098–3100. Bibcode:1988PhRvA..38.3098B. doi:10.1103/PhysRevA.38.3098. PMID 9900728. 
  22. ↑ John P. Perdew (1986). "Density-functional approximation for the correlation energy of the inhomogeneous electron gas". Physical Review B (American Physical Society) 33 (12): 8822–8824. Bibcode:1986PhRvB..33.8822P. doi:10.1103/PhysRevB.33.8822. 
  23. ↑ 23.0 23.1 23.2 Lee, Chengeth; Weitao Yang, and Robert G. Parr (January 15, 1988). "Development of the Colle-Salvetti correlation-energy formula into a functional of the electron density". Physical Review B (American Physical Society) 37 (2): 785–789. Bibcode:1988PhRvB..37..785L. doi:10.1103/PhysRevB.37.785. 
  24. ↑ 24.0 24.1 24.2 P. J. Stephens, F. J. Devlin, C. F. Chabalowski, M. J. Frisch (1994). "Ab Initio Calculation of Vibrational Absorption and Circular Dichroism Spectra Using Density Functional Force Fields". The Journal of Physical Chemistry (ACS Publications) 98 (45): 11623–11627. doi:10.1021/j100096a001. 
  25. ↑ 25.0 25.1 25.2 Ross D. Adamsona, Peter M. W. Gill and John A. Pople (1998). "Empirical density functionals". Chemical Physics Letters (Elsevier). 284 (5-6): 6–11. Bibcode:1998CPL...284....6A. doi:10.1016/S0009-2614(97)01282-7. 
  26. ↑ 26.0 26.1 26.2 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 (Commonwealth Scientific and Industrial Research Organization) 57 (4): 365–370. doi:10.1071/CH03263. 
  27. ↑ 27.0 27.1 27.2 Yan Zhao and 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 (Springer Berlin / Heidelberg). 120 (1-3): 215–241. doi:10.1007/s00214-007-0310-x. 
  28. ↑ 28.0 28.1 J. D. Chai and Martin Head-Gordon (2008). "Long-range corrected hybrid density functionals with damped atom-atom dispersion corrections". Physical Chemistry Chemical Physics (RSC Publishing) 10 (44): 6615–66120. Bibcode:2008PCCP...10.6615C. doi:10.1039/b810189b. PMID 18989472. 
  29. ↑ P.A.M. Dirac (July 1930). "Note on Exchange Phenomena in the Thomas Atom". Mathematical Proceedings of the Cambridge Philosophical Society (Cambridge Journals) 26 (3): 376–385. Bibcode:1930PCPS...26..376D. doi:10.1017/S0305004100016108. 
  30. ↑ Peter M. W. Gill (October 1996). "A new gradient-corrected exchange functional". Molecular Physics (Taylor & Francis) 89 (2): 433–445. Bibcode:1996MolPh..89..433G. doi:10.1080/00268979609482484. 
  31. ↑ A.T.B. Gilbert and P.M.W. Gill (1999). "Decomposition of exchange-correlation energies". Chemical Physics Letters (Elsevier). 312 (5-6) (5–6): 511–521. Bibcode:1999CPL...312..511G. doi:10.1016/S0009-2614(99)00836-2. 
  32. ↑ John P. Perdew and Yue Wang (1992). "Accurate and simple analytic representation of the electron-gas correlation energy". Physical Review B (American Physical Society) 45 (23): 13244–13249. Bibcode:1992PhRvB..4513244P. doi:10.1103/PhysRevB.45.13244. 
  33. ↑ Vosko, S.H.; L. Wilk and M. Nusair (August 1, 1980). "Accurate spin-dependent electron liquid correlation energies for local spin density calculations: a critical analysis". Canadian Journal of Physics (NRC Research Press) 58 (8): 1200–1211. Bibcode:1980CaJPh..58.1200V. doi:10.1139/p80-159. 
  34. ↑ John P. Perdew and Yue Wang (June 1992). "Accurate and simple analytic representation of the electron-gas correlation energy". Physical Review B (The American Physical Society) 45 (23): 13244–13249. Bibcode:1992PhRvB..4513244P. doi:10.1103/PhysRevB.45.13244. 
  35. ↑ J. P. Perdew (1981). "Density-functional approximation for the correlation energy of the inhomogeneous electron gas". Physical Review B (The American Physical Society) 23 (10): 5048. Bibcode:1981PhRvB..23.5048P. doi:10.1103/PhysRevB.23.5048. 
  36. ↑ J. P. Perdew and A. Zunger (1986). "Self-interaction correction to density-functional approximations for many-electron systems". Physical Review B (The American Physical Society) 33 (12): 8822–8824. Bibcode:1986PhRvB..33.8822P. doi:10.1103/PhysRevB.33.8822. 
  37. ↑ John P. Perdew, Kieron Burke, and Matthias Ernzerhof (October 1996). "Generalized Gradient Approximation Made Simple". Physical Review Letters (American Physical Society) 77 (18): 3865–3868. Bibcode:1996PhRvL..77.3865P. doi:10.1103/PhysRevLett.77.3865. PMID 10062328. 
  38. ↑ A. D. Becke and M. R. Roussel (1989). "Exchange holes in inhomogeneous systems: A coordinate-space model". Physical Review A (The American Physical Society) 39 (8): 3761–3767. Bibcode:1989PhRvA..39.3761B. doi:10.1103/PhysRevA.39.3761. PMID 9901696. 
  39. ↑ A. Daniel Boese and Jan M. L. Martin (2004). "Development of density functionals for thermochemical kinetics". The Journal of Chemical Physics (American Institute of Physics) 121 (8): 3405–3417. arXiv:physics/0405158. Bibcode:2004JChPh.121.3405B. doi:10.1063/1.1774975. PMID 15303903. 
  40. ↑ 40.0 40.1 Yan Zhao, Nathan E. Schultz, and Donald G. Truhlar (2006). "Design of Density Functionals by Combining the Method of Constraint Satisfaction with Parameterization for Thermochemistry, Thermochemical Kinetics, and Noncovalent Interactions". The Journal of Chemical Theory and Computation (ACS Publications) 2 (2): 364–382. doi:10.1021/ct0502763. 
  41. ↑ Yan Zhao and 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 (American Institute of Physics). 125 (8) (19): 194101–194119. Bibcode:2006JChPh.125s4101Z. doi:10.1063/1.2370993. 
  42. ↑ Yan Zhao and 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 (ACS Publications) 110 (49): 13126–13130. doi:10.1021/jp066479k. 
  43. ↑ 43.0 43.1 Jeng-Da Chai and Martin Head-Gordon (2006). "Systematic optimization of long-range corrected hybrid density functionals". The Journal of Chemical Physics (American Institute of Physics) 128 (8): 084106–084121. Bibcode:2008JChPh.128h4106C. doi:10.1063/1.2834918. 
  44. ↑ George D. Purvis and Rodney J. Bartlett (1982). "A full coupled‐cluster singles and doubles model: The inclusion of disconnected triples". The Journal of Chemical Physics (The American Institute of Physics) 76 (4): 1910–1919. Bibcode:1982JChPh..76.1910P. doi:10.1063/1.443164. 
  45. ↑ Krishnan Raghavachari, Gary W. Trucks, John A. Pople and, Martin Head-Gordon (March 24, 1989). "A fifth-order perturbation comparison of electron correlation theories". Chemical Physics Letters (Elsevier Science) 157 (6): 479–483. Bibcode:1989CPL...157..479R. doi:10.1016/S0009-2614(89)87395-6. 
  46. ↑ Troy Van Voorhis and Martin Head-Gordon (June 19, 2001). "Two-body coupled cluster expansions". The Journal of Chemical Physics (The American Institute of Physics) 115 (11): 5033–5041. Bibcode:2001JChPh.115.5033V. doi:10.1063/1.1390516. 
  47. ↑ C. David Sherrill, Anna I. Krylov, Edward F. C. Byrd, and Martin Head-Gordon (June 11, 1998). "Energies and analytic gradients for a coupled-cluster doubles model using variational Brueckner orbitals: Application to symmetry breaking in O4+". The Journal of Chemical Physics (The American Institute of Physics) 109 (11): 4171–4182. Bibcode:1998JChPh.109.4171S. doi:10.1063/1.477023. 
  48. ↑ Steven R. Gwaltney and Martin Head-Gordon (June 9, 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 (Elsevier). 323 (1-2): 21–28. Bibcode:2000CPL...323...21G. doi:10.1016/S0009-2614(00)00423-1. 
  49. ↑ Troy Van Voorhis and Martin Head-Gordon (November 17, 2000). "The quadratic coupled cluster doubles model". Chemical Physics Letters (Elsevier). 330 (5-6) (5–6): 585–594. Bibcode:2000CPL...330..585V. doi:10.1016/S0009-2614(00)01137-4. 
  50. ↑ 50.0 50.1 50.2 Anna I. Krylov, C. David Sherrill, Edward F. C. Byrd, and Martin Head-Gordon (September 15, 1998). "Size-consistent wave functions for nondynamical correlation energy: The valence active space optimized orbital coupled-cluster doubles model". The Journal of Chemical Physics (The American Institute of Physics) 109 (24): 10669–10678. Bibcode:1998JChPh.10910669K. doi:10.1063/1.477764. 
  51. ↑ 51.0 51.1 Chr. Møller and M. S. Plesset (October 1934). "Note on an Approximation Treatment form Many-Electron Systems". Physical Review (The American Physical Society) 46 (7): 618–622. Bibcode:1934PhRv...46..618M. doi:10.1103/PhysRev.46.618. 
  52. ↑ 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. 
  53. ↑ Pople, J. A.; Seeger, R.; Krishnan, R. (1977). "Variational configuration interaction methods and comparison with perturbation theory" (abstract). International Journal of Quantum Chemistry 12 (S11): 149–163. doi:10.1002/qua.560120820. 
  54. ↑ Pople, John A.; Binkley, J. Stephen; Seeger, Rolf (1976). "Theoretical models incorporating electron correlation" (abstract). International Journal of Quantum Chemistry 10 (S10): 1–19. doi:10.1002/qua.560100802. 
  55. ↑ Krishnan Raghavachari and John A. Pople (February 22, 1978). "Approximate fourth-order perturbation theory of the electron correlation energy". International Journal of Quantum Chemistry (Wiley InterScience) 14 (1): 91–100. doi:10.1002/qua.560140109. 
  56. ↑ Martin Feyereisena, George Fitzgeralda and Andrew Komornickib (May 10, 1993). "Scaled Second-Order Perturbation Corrections to Configuration Interaction Singles: Efficient and Reliable Excitation Energy Methods". Chemical Physics Letters (Elsevier). 208 (5-6) (5–6): 359–363. Bibcode:1993CPL...208..359F. doi:10.1016/0009-2614(93)87156-W. 
  57. ↑ Florian Weigend and Marco Häser (October 13, 1997). "RI-MP2: first derivatives and global consistency". Theoretical Chemistry Accounts (Springer Berlin / Heidelberg). 97 (1-4): 331–340. doi:10.1007/s002140050269. 
  58. ↑ Robert A. Distasio JR., Ryan P. Steele, Young Min Rhee, Yihan Shao, and Martin Head-Gordon (April 15, 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 (Wiley InterScience) 28 (5): 839–856. doi:10.1002/jcc.20604. 
  59. ↑ 59.0 59.1 Erich Runge and E. K. U. Gross (October 1984). "Density-Functional Theory for Time-Dependent Systems". Physical Review Letters (American Physical Society) 52 (12): 997–1000. Bibcode:1984PhRvL..52..997R. doi:10.1103/PhysRevLett.52.997. 
  60. ↑ 60.0 60.1 So Hirata and 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 (Elsevier). 302 (5-6) (5–6): 375–382. Bibcode:1999CPL...302..375H. doi:10.1016/S0009-2614(99)00137-2. 
  61. ↑ 61.0 61.1 David Maurice and Martin Head-Gordon (May 10, 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 (Taylor & Francis) 96 (10): 1533–1541. Bibcode:1999MolPh..96.1533M. doi:10.1080/00268979909483096. 
  62. ↑ 62.0 62.1 Martin Head-Gordon, Rudolph J. Rico, Manabu Oumi, and Timothy J. Lee (1994). "A doubles correction to electronic excited states from configuration interaction in the space of single substitutions". Chemical Physics Letters (Elsevier) 219 ((1-2)): 21–29. Bibcode:1994CPL...219...21H. doi:10.1016/0009-2614(94)00070-0. 
  63. ↑ 63.0 63.1 John A. Pople, Martin Head‐Gordon, and Krishnan Raghavachari (1987). "Quadratic configuration interaction. A general technique for determining electron correlation energies". The Journal of Chemical Physics (American Institute of Physics) 87 (10): 5968–35975. Bibcode:1987JChPh..87.5968P. doi:10.1063/1.453520. 
  64. ↑ 64.0 64.1 Rhee, Young Min; Martin Head-Gordon (May 4, 2007). "Scaled Second-Order Perturbation Corrections to Configuration Interaction Singles: Efficient and Reliable Excitation Energy Methods". The Journal of Physical Chemistry A (ACS Publications) 111 (24): 5314–5326. doi:10.1021/jp068409j. PMID 17521172. 
  65. ↑ Larry A. Curtiss, Krishnan Raghavachari, Gary W. Trucks, and John A. Pople (February 15, 1991). "Gaussian‐2 theory for molecular energies of first‐ and second‐row compounds". The Journal of Chemical Physics (The American Institute of Physics) 94 (11): 7221–7231. Bibcode:1991JChPh..94.7221C. doi:10.1063/1.460205. 
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