Because the one-electron basis set limit is difficult to reach in correlated post-Hartree–Fock ab initio calculations, the low-cost route of using methods that extrapolate to the estimated basis set limit attracts immediate interest. The situation is somewhat more satisfactory at the Hartree–Fock level because numerical calculation of the energy is often affordable at nearly converged basis set levels. Still, extrapolation schemes for the Hartree–Fock energy are addressed here, although the focus is on the more slowly convergent and computationally demanding correlation energy. Because they are frequently based on the gold-standard coupled-cluster theory with single, double, and perturbative triple excitations [CCSD(T)], correlated calculations are often affordable only with the smallest basis sets, and hence single-level extrapolations from one raw energy could attain maximum usefulness. This possibility is examined. Whenever possible, this review uses raw data from second-order Møller–Plesset perturbation theory, as well as CCSD, CCSD(T), and multireference configuration interaction methods. Inescapably, the emphasis is on work done by the author's research group. Certain issues in need of further research or review are pinpointed.


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Literature Cited

  1. Helgaker T, Jørgensen P, Olsen J. 1.  2000. Molecular Electronic-Structure Theory Chichester, UK: Wiley [Google Scholar]
  2. Hättig C, Klopper W, Köhn A, Tew DP. 2.  2012. Explicitly correlated electrons in molecules. Chem. Rev. 112:4–74 [Google Scholar]
  3. Feller D, Peterson KA, Crawford TD. 3.  2006. Sources of error in electronic structure calculations on small chemical systems. J. Chem. Phys. 124:054107 [Google Scholar]
  4. Murrell JN, Carter S, Farantos SC, Huxley P, Varandas AJC. 4.  1984. Molecular Potential Energy Functions Chichester, UK: Wiley [Google Scholar]
  5. Varandas AJC, Galvão BLR. 5.  2014. Exploring the utility of many-body expansions: a consistent set of accurate potentials for the lowest quartet and doublet states of the azide radical with revisited dynamics. J. Phys. Chem. A 118:10127–33 [Google Scholar]
  6. Varandas AJC. 6.  1988. Intermolecular and intramolecular potentials: topographical aspects, calculation, and functional representation via a DMBE expansion method. Adv. Chem. Phys. 74:255–338 [Google Scholar]
  7. Varandas AJC. 7.  2013. Putting together the pieces: a global description of valence and long-range forces via combined hyperbolic inverse power representation of the potential energy surface. Reaction Rate Constant Computations: Theories and Applications KL Han, TS Chu 408–45 London: R. Soc. Chem. [Google Scholar]
  8. Kato T. 8.  1957. On the eigenfunctions of many-particle systems in quantum mechanics. Commun. Pure Appl. Math. 10:151–77 [Google Scholar]
  9. Kutzelnigg W, Klopper W. 9.  1991. Wave functions with terms linear in the interelectronic coordinates to take care of the correlation cusp. I. General theory. J. Chem. Phys. 94:1985–2001 [Google Scholar]
  10. Pack RT, Brown WB. 10.  1966. Cusp conditions for molecular wavefunctions. J. Chem. Phys. 45:556–59 [Google Scholar]
  11. Kutzelnigg W, Morgan JD. 11.  1992. Rates of convergence of the partial-wave expansions of atomic correlation energies. J. Chem. Phys. 96:4484–508 [Google Scholar]
  12. Flores JR, Slupski R, Jankowski K. 12.  2006. Toward benchmark second-order correlation energies for large atoms. II. Angular extrapolation problems. J. Chem. Phys. 124:104107 [Google Scholar]
  13. Schwartz C. 13.  1962. Importance of angular correlations between atomic electrons. Phys. Rev. 126:1015–19 [Google Scholar]
  14. Schwenke DW. 14.  2012. On one-electron basis set extrapolation of atomic and molecular correlation energies. Mol. Phys. 110:2557–67 [Google Scholar]
  15. Dunning TH Jr. 15.  1989. Gaussian basis sets for use in correlated molecular calculations. The atoms boron through neon and hydrogen. J. Chem. Phys. 90:1007–23 [Google Scholar]
  16. Dunning TH Jr., Peterson KA, Woon DE. 16.  1998. Basis sets: correlation consistent sets. Encyclopedia of Computational Chemistry PvR Schleyer, NL Allinger, T Clark, J Gasteiger, PA Kolman, et al. 88–115 Chichester, UK: Wiley [Google Scholar]
  17. Weigend F, Ahlrichs R. 17.  2005. Balanced basis sets of split valence, triple zeta valence and quadruple zeta valence quality for H to Rn: design and assessment of accuracy. Phys. Chem. Chem. Phys. 7:3297–305 [Google Scholar]
  18. Neto AC, Muniz EP, Centoducatte R, Jorge FE. 18.  2005. Gaussian basis sets for correlated wave functions. Hydrogen, helium, first- and second-row atoms. J. Mol. Struct. 718:219–24 [Google Scholar]
  19. Zhong S, Barnes EC, Petersson GA. 19.  2008. Uniformly convergent n-tuple-ζ augmented polarized (nZaP) basis sets for complete basis set extrapolations. I. Self-consistent field energies. J. Chem. Phys. 129:184116 [Google Scholar]
  20. Ranasinghe DS, Petersson GA. 20.  2013. CCSD(T)/CBS atomic and molecular benchmarks for H through Ar. J. Chem. Phys. 138:144104 [Google Scholar]
  21. Jensen F. 21.  2012. Atomic orbital basis sets. WIREs Comput. Mol. Sci. 3:273–95 [Google Scholar]
  22. Dunning TH Jr. 22.  2000. A road map for the calculation of molecular binding energies. J. Phys. Chem. A 104:9062–80 [Google Scholar]
  23. Helgaker T, Klopper W, Koch H, Noga J. 23.  1997. Basis-set convergence of correlated calculations on water. J. Chem. Phys. 106:9639–46 [Google Scholar]
  24. Halkier A, Helgaker T, Jørgensen P, Klopper W, Koch H. 24.  et al. 1998. Basis-set convergence in correlated calculations on Ne, N2, and H2O. Chem. Phys. Lett. 286:243–52 [Google Scholar]
  25. Raghavachari K, Anderson JB. 25.  1996. Electron correlation effects in molecules. J. Phys. Chem. 100:12960–73 [Google Scholar]
  26. Varandas AJC. 26.  2000. Basis-set extrapolation of the correlation energy. J. Chem. Phys. 113:8880–87 [Google Scholar]
  27. Kutzelnigg W. 27.  1994. Theory of the expansion of wave functions in a Gaussian basis. Int. J. Quantum Chem. 51:447–63 [Google Scholar]
  28. Papajak E, Truhlar DG. 28.  2012. What are the most efficient basis set strategies for correlated wave function calculations of reaction energies and barrier heights?. J. Chem. Phys. 137:064110 [Google Scholar]
  29. Feller D. 29.  2013. Benchmarks of improved complete basis set extrapolation schemes designed for standard CCSD(T) atomization energies. J. Chem. Phys. 138:074103 [Google Scholar]
  30. Vasilyev V. 30.  2017. Online complete basis set limit extrapolation calculator. Comput. Theor. Chem. 1115:1–3 [Google Scholar]
  31. Varandas AJC, Piecuch P. 31.  2006. Extrapolating potential energy surfaces by scaling electron correlation at a single geometry. Chem. Phys. Lett. 430:448–53 [Google Scholar]
  32. Varandas AJC. 32.  2007. Accurate global ab initio potentials at low-cost by correlation scaling and extrapolation to the one-electron basis set limit. Chem. Phys. Lett. 443:398–407 [Google Scholar]
  33. Gordon MS, Nguyen KA, Truhlar DG. 33.  1989. Parameters for scaling the correlation-energy of the bonds Si–H, P–H, S–H, and Cl–H and application to the reaction of silyl radical with silane. J. Phys. Chem. 93:7356–58 [Google Scholar]
  34. Brown FB, Truhlar DG. 34.  1985. A new semi-empirical method of correcting large-scale configuration interaction calculations for incomplete dynamic correlation of electrons. Chem. Phys. Lett. 117:307–13 [Google Scholar]
  35. Varandas AJC. 35.  1989. A semiempirical method for correcting configuration interaction potential energy surfaces. J. Chem. Phys. 90:4379–91 [Google Scholar]
  36. Varandas AJC. 36.  2007. Accurate ab initio potentials at low cost via correlation scaling and extrapolation: application to CO(A1Π). J. Chem. Phys. 127:114316 [Google Scholar]
  37. Lutz JJ, Piecuch P. 37.  2008. Extrapolating potential energy surfaces by scaling electron correlation: isomerization of bicyclobutane to butadiene. J. Chem. Phys. 128:154116 [Google Scholar]
  38. Varandas AJC. 38.  2007. Accurate ab initio-based molecular potentials: from extrapolation methods to global modelling. Phys. Scr. 76:C28–35 [Google Scholar]
  39. Scheiner S. 39.  2012. Extrapolation to the complete basis set limit for binding energies of noncovalent interactions. Comput. Theor. Chem. 998:9–13 [Google Scholar]
  40. Šponer J, Jurečka P, Hobza P. 40.  2006. Base stacking and base pairing. Computational Studies of RNA and DNA J Šponer, F Lankaš 343–88 Dordrecht, Neth: Springer [Google Scholar]
  41. Haldar S, Gnanasekarana R, Hobza P. 41.  2015. A comparison of ab initio quantum-mechanical and experimental D0 binding energies of eleven H-bonded and eleven dispersion-bound complexes. Phys. Chem. Chem. Phys. 17:26645–52 [Google Scholar]
  42. Neves RPP, Fernandes PA, Varandas AJC, Ramos MJ. 42.  2014. Benchmarking of density functionals for the accurate description of thioldisulfide exchange. J. Chem. Theory Comput. 10:4842–56 [Google Scholar]
  43. Boys F, Bernardi F. 43.  1970. The calculation of small molecular interactions by the differences of separate total energy. Some procedures with reduced error. Mol. Phys. 19:553–66 [Google Scholar]
  44. Wells BH, Wilson S. 44.  1983. Van der Waals interaction potentials—many-body basis set supperposition errors. Chem. Phys. Lett. 101:429–34 [Google Scholar]
  45. White JC, Davidson ER. 45.  1990. An analysis of the hydrogen-bond in ice. J. Chem. Phys. 93:8029–35 [Google Scholar]
  46. Valiron P, Mayer I. 46.  1997. Hierarchy of counterpoise corrections for N-body clusters: generalization of the Boys–Bernardi scheme. Chem. Phys. Lett. 275:46–55 [Google Scholar]
  47. Varandas AJC. 47.  2008. Can extrapolation to the basis set limit be an alternative to the counterpoise correction? A study on the helium dimer. Theor. Chem. Acc. 119:511–21 [Google Scholar]
  48. Varandas AJC. 48.  2010. Extrapolation to the complete basis set limit without counterpoise. The pair potential of helium revisited. J. Phys. Chem. A 114:8505–16 [Google Scholar]
  49. Varandas AJC. 49.  2010. Spin-component-scaling second-order Møller–Plesset theory and its variants for economical correlation energies: unified theoretical interpretation and use for quartet N3. J. Chem. Phys. 133:064104 [Google Scholar]
  50. Varandas AJC. 50.  2010. Helium-fullerene pair interactions: an ab initio study by perturbation-theory and coupled-cluster methods. Int. J. Quantum Chem. 111:416–29 [Google Scholar]
  51. Song YZ, Varandas AJC. 51.  2011. Accurate double many-body expansion potential energy surface for ground-state HS2 based on ab initio data extrapolated to the complete basis set limit. J. Phys. Chem. A 115:5274–83 [Google Scholar]
  52. Varandas AJC. 52.  2012. Ab initio treatment of bond-breaking reactions: accurate course of HO3 dissociation and revisit to isomerization. J. Chem. Theory Comput. 8:428–41 [Google Scholar]
  53. Srivastava S, Sathyamurthy N, Varandas AJC. 53.  2012. An accurate ab initio potential energy curve and the vibrational bound states of X2Σ+u state of H2. Chem. Phys. 398:160–67 [Google Scholar]
  54. Galvão BRL, Varandas AJC. 54.  2013. Accurate study of the two lowest singlet states of HN3: stationary structures and energetics at the MRCI complete basis set limit. J. Phys. Chem. A 117:4044–50 [Google Scholar]
  55. Varandas AJC. 55.  2013. Accurate determination of the reaction course in : a detailed analysis of the covalent- to hydrogen-bonding transition. J. Phys. Chem. A 117:7393–407 [Google Scholar]
  56. Varandas AJC. 56.  2014. On carbon dioxide capture: an accurate ab initio study of the Li3N + CO2 insertion reaction. Comput. Theor. Chem. 1036:61–71 [Google Scholar]
  57. Varandas AJC. 57.  2014. Is HO3 multiple-minimum and floppy? Covalent to van der Waals isomerization and bond rupture of a peculiar anion. Phys. Chem. Chem. Phys. 16:16997–7007 [Google Scholar]
  58. Bytautas L, Ruedenberg K. 58.  2008. Correlation energy and dispersion interaction in the ab initio potential energy curve of the neon dimer. J. Chem. Phys. 128:214308 [Google Scholar]
  59. Alvarez-Idaboy JR, Galano A. 59.  2010. Counterpoise corrected interaction energies are not systematically better than uncorrected ones: comparison with CCSD(T) CBS extrapolated values. Theor. Chem. Acc. 126:75–85 [Google Scholar]
  60. Sheng XW, Mentel L, Gritsenko OV, Baerends EJ. 60.  2011. Counterpoise correction is not useful for short and van der Waals distances but may be useful at long range. J. Comput. Chem. 32:2896–901 [Google Scholar]
  61. Mentel LM, Baerends EJ. 61.  2014. Can the counterpoise correction for basis set superposition effect be justified?. J. Chem. Theory Comput. 10:252–67 [Google Scholar]
  62. Sheng X, Hu F, Qian S. 62.  2016. On the complete basis set extrapolation procedures for the interaction energies. Comput. Theor. Chem. 1102:1–4 [Google Scholar]
  63. Deb DK, Sarkar B. 63.  2017. Theoretical investigation of gas-phase molecular complex formation between 2-hydroxy thiophenol and a water molecule. Phys. Chem. Chem. Phys. 19:2466–78 [Google Scholar]
  64. Spackman PR, Karton A. 64.  2015. Estimating the CCSD basis-set limit energy from small basis sets: basis-set extrapolations versus additivity schemes. AIP Adv 5:057148 [Google Scholar]
  65. Boese AD, Oren M, Atasoylu O, Martin JML, Kállay M, Gauss J. 65.  2004. W3 theory: robust computational thermochemistry in the kJ/mol accuracy range. J. Chem. Phys. 120:4129–41 [Google Scholar]
  66. Karton A, Martin JML. 66.  2012. Explicitly correlated Wn theory: W1-F12 and W2-F12. J. Chem. Phys 136:124114 [Google Scholar]
  67. Tarczay GT, Császár AG, Klopper W, Szalay V, Allen WD, Schaefer HF III. 67.  1999. The barrier to linearity of H2O. J. Chem. Phys. 110:11971–81 [Google Scholar]
  68. Curtiss LA, Raghavachari K, Trucks GW, Pople JA. 68.  1991. Gaussian-2 theory for molecular energies of first- and second-row compounds. J. Chem. Phys. 94:7221–30 [Google Scholar]
  69. Klopper W, Kutzelnigg W. 69.  1986. Gaussian basis sets and the nuclear cusp problem. J. Mol. Struct. 135:339–56 [Google Scholar]
  70. Peterson KA, Woon DE, Dunning TH Jr. 70.  1994. Benchmark calculations with correlated molecular wave functions. IV. The classical barrier height of the H + H2 → H2 + H reaction. J. Chem. Phys. 100:7410–15 [Google Scholar]
  71. Truhlar DG. 71.  1998. Basis-set extrapolation. Chem. Phys. Lett. 294:45–48 [Google Scholar]
  72. Halkier A, Helgaker T, Jorgensen P, Klopper W, Olsen J. 72.  1999. Basis-set convergence of the energy in molecular Hartree–Fock calculations. Chem. Phys. Lett. 302:437–46 [Google Scholar]
  73. Fast PL, Sanchez ML, Truhlar DG. 73.  1999. Infinite basis limits in electronic structure theory. J. Chem. Phys. 111:2921–26 [Google Scholar]
  74. Halkier A, Klopper W, Helgaker T, Jørgensen P, Taylor PR. 74.  1999. Basis set convergence of the interaction energy of hydrogen-bonded complexes. J. Chem. Phys. 111:9157–67 [Google Scholar]
  75. Lee JS, Park SY. 75.  2000. Basis set convergence of correlated calculations on He, H2, and He2. J. Chem. Phys. 112:10746–53 [Google Scholar]
  76. Klopper W. 76.  2001. A critical note on extrapolating helium pair potentials. J. Chem. Phys. 115:761–65 [Google Scholar]
  77. Klopper W. 77.  2001. Highly accurate coupled-cluster singlet and triplet pair energies from explicitly correlated calculations in comparison with extrapolation techniques. Mol. Phys. 99:481–507 [Google Scholar]
  78. Huh SB, Lee JS. 78.  2003. Basis set and correlation dependent extrapolation of correlation energy. J. Chem. Phys. 118:3035–42 [Google Scholar]
  79. Schwenke DW. 79.  2005. The extrapolation of one-electron basis sets in electronic structure calculations: how it should work and how it can be made to work. J. Chem. Phys. 122:014107 [Google Scholar]
  80. Jensen F. 80.  2005. Estimating the Hartree–Fock limit from finite basis set calculations. Theor. Chem. Acc. 113:267–73 [Google Scholar]
  81. Karton A, Martin JML. 81.  2006. Comment on “Estimating the Hartree–Fock limit from finite basis set calculations”. Theor. Chem. Acc. 115:330–33 [Google Scholar]
  82. Varandas AJC. 82.  2007. Extrapolation to the one-electron basis-set in electronic structure calculations. J. Chem. Phys. 126:244105 [Google Scholar]
  83. Junqueira GMA, Varandas AJC. 83.  2008. Extrapolating to the one-electron basis set limit in polarizability calculations. J. Phys. Chem. A 112:10413–19 [Google Scholar]
  84. Bakowies D. 84.  2007. Extrapolation of electron correlation energies to finite and complete basis set targets. J. Chem. Phys. 127:084105 [Google Scholar]
  85. Bakowies D. 85.  2007. Accurate extrapolation of electron correlation energies from small basis sets. J. Chem. Phys. 127:164109 [Google Scholar]
  86. Varandas AJC. 86.  2008. Generalized uniform singlet- and triplet-pair extrapolation of the correlation energy to the one electron basis set limit. J. Phys. Chem. A 112:1841–50 [Google Scholar]
  87. Williams TG, DeYonker NJ, Wilson AK. 87.  2008. Hartree–Fock complete basis set limit properties for transition metal diatomics. J. Chem. Phys. 128:044101 [Google Scholar]
  88. Varandas AJC. 88.  2009. Møller–Plesset perturbation energies and distances for HeC20 extrapolated to the complete basis set limit. J. Comp. Chem. 30:379–88 [Google Scholar]
  89. Pansini FNN, Varandas AJC. 89.  2015. Toward a unified single-parameter extrapolation scheme for the correlation energy: systems formed by atoms of hydrogen through neon. Chem. Phys. Lett. 631–632:70–77 [Google Scholar]
  90. Pansini FNN, Neto AC, Varandas AJC. 90.  2015. On the performance of various hierarchized bases in extrapolating the correlation energy to the complete basis set limit. Chem. Phys. Lett. 641:90–96 [Google Scholar]
  91. Okoshi M, Atsumi T, Nakai H. 91.  2015. Revisiting the extrapolation of correlation energies to complete basis set limit. J. Comput. Chem. 36:1075–82 [Google Scholar]
  92. Pansini FNN, Neto AC, Varandas AJC. 92.  2016. Extrapolation of Hartree–Fock and multiconfiguration self-consistent-field energies to the complete basis set limit. Theor. Chem. Acc. 135:261 [Google Scholar]
  93. Seino J, Nakai H. 93.  2016. Informatics-based energy fitting scheme for correlation energy at complete basis set limit. J. Comput. Chem. 37:2304–15 [Google Scholar]
  94. Peterson KA. 94.  2007. Gaussian basis sets exhibiting systematic convergence to the complete basis set limit. Annual Reports in Computational Chemistry 3 DC Spellmeyer, R Wheeler 195–206 Amsterdam: Elsevier [Google Scholar]
  95. Hepburn J, Scoles G, Penco R. 95.  1975. A simple but reliable method for the prediction of intermolecular potentials. Chem. Phys. Lett. 36:451–56 [Google Scholar]
  96. Murrell JN, Varandas AJC. 96.  1975. Perturbation calculations of rare-gas potentials near the van der Waals minimum. Mol. Phys. 30:223–36 [Google Scholar]
  97. Feller D. 97.  1992. Application of systematic sequences of wave functions to the water dimer. J. Chem. Phys. 96:6104–14 [Google Scholar]
  98. Bunge CF. 98.  1970. Electronic wave functions for atoms. 2. Some aspects of the convergence of the configuration interaction expansion for ground states of He isoelectronic series. Theor. Chim. Acta 16:126–44 [Google Scholar]
  99. Hill RN. 99.  1985. Rates of convergence and error estimation formulas for the Rayleigh–Ritz variational method. J. Chem. Phys. 83:1173–96 [Google Scholar]
  100. Martin JML, Taylor PR. 100.  1997. Benchmark quality total atomization energies of small polyatomic molecules. J. Chem. Phys. 106:8620–23 [Google Scholar]
  101. Valeev EF, Allen WD, Hernandez R, Sherrill CD, Schaefer HF. 101.  2003. On the accuracy limits of orbital expansion methods: explicit effects of k-functions on atomic and molecular energies. J. Chem. Phys. 118:8594 [Google Scholar]
  102. Klopper W, Samson CCM. 102.  2002. Explicitly correlated second-order Møller–Plesset methods with auxiliary basis sets. J. Chem. Phys. 116:6397–410 [Google Scholar]
  103. Bytautas L, Ruedenberg K. 103.  2005. Correlation energy extrapolation by intrinsic scaling. IV. Accurate binding energies of the homonuclear diatomic molecules carbon, nitrogen, oxygen and fluorine. J. Chem. Phys. 122:154110 [Google Scholar]
  104. Bak KL, Halkier A, Jorgensen P, Olsen J, Helgaker T, Klopper W. 104.  2001. Chemical accuracy from ‘Coulomb hole’ extrapolated molecular quantum-mechanical calculations. J. Mol. Struct. 567:375–84 [Google Scholar]
  105. Parthiban S, Martin JML. 105.  2001. Fully ab initio atomization energy of benzene via Weizmann-2 theory. J. Chem. Phys. 114:2051–54 [Google Scholar]
  106. Klopper W, Noga J. 106.  2003. Accurate quantum-chemical prediction of enthalpies of formation of small molecules in the gas phase. ChemPhysChem 4:32–48 [Google Scholar]
  107. Helgaker T, Ruden TA, Jorgensen P, Olsen J, Klopper W. 107.  2004. A priori calculation of molecular properties to chemical accuracy. J. Phys. Org. Chem. 17:913–33 [Google Scholar]
  108. Varandas AJC, Pansini FNN. 108.  2014. Narrowing the error in electron correlation calculations by basis set re-hierarchization and use of the unified singlet and triplet electron-pair extrapolation scheme: application to a test set of 106 systems. J. Chem. Phys. 141:224113 [Google Scholar]
  109. Klopper W, Bak KL, Jørgensen P, Olsen J, Helgaker T. 109.  1999. Highly accurate calculations of molecular electronic structure. J. Phys. B 32:R103 [Google Scholar]
  110. Pansini FNN, Neto AC, Varandas AJC. 110.  2015. Application of the unified singlet and triplet electron-pair extrapolation scheme with basis set rehierarchization to tensorial properties. J. Phys. Chem. A 119:1208–17 [Google Scholar]
  111. Huh SB, Lee JS. 111.  2003. Basis set and correlation dependent extrapolation of correlation energy. J. Chem. Phys. 118:3035–42 [Google Scholar]
  112. Englert BG, Schwinger J. 112.  1985. Atomic binding-energy oscillations. Phys. Rev. A 32:47–63 [Google Scholar]
  113. Kais S, Sung S, Herschbach DR. 113.  1994. Large-Z and -N dependence of atomic energies from renormalization of the large-dimension limit. Int. J. Quant. Chem. 49:657–74 [Google Scholar]
  114. Werner HJ, Knowles PJ, Lindh R, Manby FR, Schütz M. 114.  et al. 2010. Molpro v2010.1 Comput. Softw. http://www.molpro.net [Google Scholar]
  115. Wood GPF, Radom L, Petersson GA, Barnes EC, Frisch MJ, Montgomery JA Jr. 115.  2006. A restricted-open-shell complete-basis-set model chemistry. J. Chem. Phys. 125:094106 [Google Scholar]
  116. Fabiano E, Della Sala F, Grabowski I. 116.  2015. Accurate non-covalent interaction energies via an efficient MP2 scaling procedure. Chem. Phys. Lett. 635:262–67 [Google Scholar]
  117. Klopper W, Rafal AB, Hättig C, Tew DP. 117.  2010. Accurate computational thermochemistry from explicitly correlated coupled-cluster theory. Theor. Chem. Acc. 126:289–304 [Google Scholar]
  118. Hill JG, Peterson KA, Knizia G, Werner HJ. 118.  2009. Assessment of basis sets for F12 explicitly-correlated molecular electronic-structure methods. J. Chem. Phys. 131:194105 [Google Scholar]
  119. Bischoff FA, Wolfsegger S, Tew DP, Klopper W. 119.  2009. Assessment of basis sets for F12 explicitly-correlated molecular electronic-structure methods. Mol. Phys. 107:963–75 [Google Scholar]
  120. Balabin RM. 120.  2010. Intramolecular basis set superposition error as a measure of basis set incompleteness: Can one reach the basis set limit without extrapolation?. J. Chem. Phys. 132:211103 [Google Scholar]
  121. Xantheas SS. 121.  1996. On the importance of the fragment relaxation energy terms in the estimation of the basis set superposition error correction to the intermolecular interaction energy. J. Chem. Phys. 104:8821–23 [Google Scholar]
  122. Kalescky R, Kraka E, Cremer D. 122.  2014. Accurate determination of the binding energy of the formic acid dimer: the importance of geometry relaxation. J. Chem. Phys. 140:084315 [Google Scholar]
  123. Miliordos E, Xantheas SS. 123.  2015. On the validity of the basis set superposition error and complete basis set limit extrapolations for the binding energy of the formic acid dimer. J. Chem. Phys. 142:094311 [Google Scholar]
  124. Buckingham AD. 124.  1967. Permanent and induced molecular moments and long-range intermolecular forces. Adv. Chem. Phys. 12:107–42 [Google Scholar]
  125. Kobus J, Moncrieff D, Wilson S. 125.  2007. Comparison of the polarizabilities and hyperpolarizabilities obtained from finite basis set and finite difference Hartree–Fock calculations for diatomic molecules: III. The ground states of N2, CO and BF. J. Phys. B 40:877–96 [Google Scholar]
  126. Ral F, Vallet V, Clavagura C, Dognon JP. 126.  2008. In silico prediction of atomic static electric-dipole polarizabilities of the early tetravalent actinide ions: Th4+ (5f0), Pa4+ (5f1), and U4+ (5f2). Phys. Rev. A 78:052502 [Google Scholar]
  127. Montena R, Hajgatóa B, Deleuze MS. 127.  2011. Many-body calculations of molecular electric polarizabilities in asymptotically complete basis sets. Mol. Phys. 109:2317–39 [Google Scholar]
  128. Ruscic B, Wagner AF, Harding LB, Asher RL, Feller D. 128.  et al. 2002. On the enthalpy of formation of hydroxyl radical and gas-phase bond dissociation energies of water and hydroxyl. J. Phys. Chem. A 106:2727–47 [Google Scholar]
  129. Peterson KA, Feller D, Dixon DA. 129.  2012. Chemical accuracy in ab initio thermochemistry and spectroscopy: current strategies and future challenges. Theor. Chem. Acc. 131:1079 [Google Scholar]
  130. Coriani S, Helgaker T, Jørgensen P, Klopper W. 130.  2004. A closed-shell coupled-cluster treatment of the Breit–Pauli first-order relativistic energy correction. J. Chem. Phys. 121:6591–98 [Google Scholar]
  131. Sansonetti JE, Martin WC. 131.  2005. Handbook of basic atomic spectroscopic data. J. Phys. Chem. Ref. Data 34:1559–2259 [Google Scholar]
  132. Klopper W, Ruscic B, Tew DP, Bischoff FA, Wolfsegger S. 132.  2009. Atomization energies from coupled-cluster calculations augmented with explicitly-correlated perturbation theory. Chem. Phys. 356:14–24 [Google Scholar]
  133. Ruscic B, Pinzon RE, Morton ML, Srinivasan NK, Su MC. 133.  et al. 2006. Active thermochemical tables: accurate enthalpy of formation of hydroperoxyl radical, HO2. J. Phys. Chem. A 110:6592–601 [Google Scholar]
  134. Pansini FNN, Varandas AJC. 134.  2015. Toward a unified single-parameter extrapolation scheme for the correlation energy: systems formed by first- and second-row atoms. Chem. Phys. Lett. 631–632:70–77 [Google Scholar]
  135. Okoshi M, Atsumi T, Nakai H. 135.  2015. Revisiting the extrapolation of correlation energies to complete basis set limit. J. Comput. Chem. 36:1075–82 [Google Scholar]
  136. Feller D, Peterson KA. 136.  1999. Re-examination of atomization energies for the Gaussian-2 set of molecules. J. Chem. Phys. 110:8384–96 [Google Scholar]
  137. Feller D, Sordo JA. 137.  2000. Performance of CCSDT for diatomic dissociation energies. J. Chem. Phys. 113:485–93 [Google Scholar]
  138. Paranjothy M, Sun R, Zhuang Y, Hase WL. 138.  2013. Direct chemical dynamics simulations: coupling of classical and quasiclassical trajectories with electronic structure theory. WIREs Comput. Mol. Sci. 3:296–316 [Google Scholar]
  139. Wang LP, Titov A, McGibbon R, Liu P, Panda VS, Martínez TJ. 139.  2014. Discovering chemistry with an ab initio nanoreactor. Nat. Chem. 6:1044–48 [Google Scholar]
  140. Medvedev MG, Bushmarinov IS, Sun J, Perdew JP, Lyssenko KA. 140.  2017. Density functional theory is straying from the path toward the exact functional. Science 355:49–52 [Google Scholar]
  141. Varandas AJC, González MM, Montero-Cabrera LA, de la Vega JMG. 141.  2017. Assessing how correlated molecular orbital calculations can perform versus Kohn–Sham DFT: barrier heights/isomerizations. Chem. Eur. J. 23:9122–9129 [Google Scholar]

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