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A heuristic estimate of molecular correlation energies using pair correlation energies of localized molecular orbitals

  • Michael Böckers
  • Robert FrankeEmail author
  • Volker Staemmler
Regular Article
  • 20 Downloads

Abstract

The biggest problem for the application of wavefunction-based quantum chemical ab initio methods is the calculation of the electronic correlation energy. Advanced methods such as coupled-cluster theory using iterative single and double excitations as well as perturbative triple excitations [CCSD(T)] are able to achieve an accuracy of ± 5 kJ/mol (‘chemical accuracy’) for small molecular systems, but become too time-consuming for routine applications to larger systems containing twenty or more heavy atoms. We propose a heuristic approach for a rapid estimate of correlation energies for larger molecules, based on parametrized pair correlation energies (PCEs) for localized molecular orbitals. Such PCEs were calculated for a training set of 112 small- and medium-sized neutral molecules from the G2/97 data set, using an approximate coupled-cluster method with single and double excitations (CCSD) and a basis set of quadruple zeta quality (def2-QZVP). The PCEs were then fitted to appropriate functional forms, taking into account the properties of the localized orbitals: type (lone pair, single bond, multiple bond), bond length, hybridization of the atoms involved in the bond, spatial extent, and distance between two orbitals. The ab initio results for the total correlation energies of the molecules in the training set could be reproduced within 1%. For most of the molecules in an extended test set containing also molecular ions a slightly lower accuracy of about 1% to 3% could be obtained.

Keywords

Correlation energies Heuristic estimate Pair correlation energies Localized molecular orbitals 

Notes

Supplementary material

214_2019_2422_MOESM1_ESM.docx (39 kb)
Supplementary material 1 (DOCX 38 kb)

References

  1. 1.
    Karton A (2017) How reliable is DFT in predicting relative energies of polycyclic aromatic hydrocarbon isomers? Comparison of functionals from different rungs of Jacob’s ladder. J Comput Chem 38:370–382CrossRefGoogle Scholar
  2. 2.
    Tew DP, Klopper W, Helgaker T (2007) Electron correlation: the many-body problem at the heart of chemistry. J Comput Chem 28:1307–1320CrossRefGoogle Scholar
  3. 3.
    Sparta M, Neese F (2014) Chemical applications carried out by local pair natural orbital based coupled-cluster methods. Chem Soc Rev 43:5032–5041CrossRefGoogle Scholar
  4. 4.
    Deglmann P, Schäfer A, Lennartz C (2015) Application of quantum calculations in the chemical industry—an overview. Int J Quantum Chem 115:107–136CrossRefGoogle Scholar
  5. 5.
    Kemnitz CR, Mackey JL, Loewen MJ, Hargrove JL, Lewis JL, Hawkins WE, Nielsen AF (2010) Origin of stability in branched alkanes. Chem Eur J 16:6942–6949CrossRefGoogle Scholar
  6. 6.
    Claeyssens F, Harvey JN, Manby FR, Mata RA, Mulholland AJ, Ranaghan KE, Schütz M, Thiel S, Thiel W, Werner HJ (2006) High-accuracy computation of reaction barriers in enzymes. Angew Chem 118:7010–7013CrossRefGoogle Scholar
  7. 7.
    Piccini G, Alessio M, Sauer J (2016) Ab initio calculation of rate constants for molecule-surface reactions with chemical accuracy. Angew Chem Int Ed 55:5235–5237CrossRefGoogle Scholar
  8. 8.
    Hollister C, Sinanoğlu O (1966) Molecular binding energies. J Am Chem Soc 88:13–21CrossRefGoogle Scholar
  9. 9.
    Sinanoğlu O, Pamuk HÖ (1972) A semi-empirical MO-electron correlation method for molecules and the correlation energies of π-system linear and polycyclic hydrocarbons. Theoret Chim Acta 27:289–302CrossRefGoogle Scholar
  10. 10.
    Pamuk HÖ (1972) Semi-empirical effective pair correlation parameters and correlation energies of BH, CH, NH, OH, HF, N2, and CH4. Theoret Chim Acta 28:85–98CrossRefGoogle Scholar
  11. 11.
    Pamuk HÖ (1978) Estimation of molecular correlation energies from semi-transferable orbital correlation energies. J Chem Soc Faraday Trans 2 74:1088–1093CrossRefGoogle Scholar
  12. 12.
    Pamuk HÖ, Trindl C (1978) Semiempirical estimation of correlation energy corrections to ionization potentials and dissociation energies for open-shell systems. Int J Quantum Chem Symp 12:271–282Google Scholar
  13. 13.
    Kristyán S (1997) Immediate estimation of correlation energy for molecular systems from the partial charges on atoms in the molecule. Chem Phys 224:33–51CrossRefGoogle Scholar
  14. 14.
    Kristyán S, Csonka GI (1999) New development in RECEP (rapid estimation of correlation energy from partial charges) method. Chem Phys Lett 307:469–478CrossRefGoogle Scholar
  15. 15.
    Kristyán S, Csonka GI (2001) Fitting atomic correlation parameters for RECEP (Rapid estimation of correlation energy from partial charges) method to estimate molecular correlation energies within chemical accuracy. J Comput Chem 22:241–254CrossRefGoogle Scholar
  16. 16.
    Kristyan S (2006) Rapid estimation of basis set error and correlation energy based on Mulliken charges and Mulliken matrix with the small 6–31 g* basis set. Theor Chem Acc 115:298–307CrossRefGoogle Scholar
  17. 17.
    Oleś AM, Pfirsch F, Fulde P, Böhm MC (1986) A method of calculating electron correlations for large molecules involving C, N, and H atoms. J Chem Phys 85:5183–5193CrossRefGoogle Scholar
  18. 18.
    Rościszewski K, Chaumet M, Fulde P (1990) Simple rules for electronic correlation energies in hydrocarbon molecules. Chem Phys 143:47–55CrossRefGoogle Scholar
  19. 19.
    Rościszewski K, Chaumet M, Fulde P (1991) Estimation of electronic correlation energies and binding energies for molecules composed of first-row atoms. Chem Phys 151:159–167CrossRefGoogle Scholar
  20. 20.
    Li SH, Li W, Ma J (2003) A quick estimate of the correlation energy for alkanes. Chin J Chem 21:1422–1429CrossRefGoogle Scholar
  21. 21.
    Bytautas L, Ruedenberg K (2002) Electron pairs, localized orbitals and correlation energy. Mol Phys 100:757–781CrossRefGoogle Scholar
  22. 22.
    Löwdin PO (1959) Correlation problem in many-electron quantum mechanics. I. Review of different approaches and discussion of some current ideas. Adv Chem Phys 2:207–322Google Scholar
  23. 23.
    G2/97 Molecular Data Set (1997) http://www.cse.anl.gov/OldCHMwebsiteContent/compmat/g2-97.htm. Accessed 23 July 2018
  24. 24.
    Staemmler V (1977) Note on open shell restricted SCF calculations for rotation barriers about C–C double bonds: ethylene and allene. Theoret Chim Acta 45:89–94CrossRefGoogle Scholar
  25. 25.
    Fink R, Staemmler V (1993) A multi-configuration reference CEPA method based on pair natural orbitals. Theoret Chim Acta 87:129–145CrossRefGoogle Scholar
  26. 26.
    Weigend F, Furche F, Ahlrichs R (2003) Gaussian basis sets of quadruple zeta valence quality for atoms H-Kr. J Chem Phys 119:12753–12762CrossRefGoogle Scholar
  27. 27.
    Boys SF (1960) Construction of some molecular orbitals to be approximately invariant for changes from one molecule to another. Rev Mod Phys 32:296–299CrossRefGoogle Scholar
  28. 28.
    Foster JM, Boys SF (1960) Canonical configurational interaction procedure. Rev Mod Phys 32:300–302CrossRefGoogle Scholar
  29. 29.
    Pipek J, Mezey PG (1989) A fast intrinsic localization procedure applicable for ab initio and semiempirical linear combination of atomic orbital wave functions. J Chem Phys 90:4916–4926CrossRefGoogle Scholar
  30. 30.
    Edmiston C, Ruedenberg K (1963) Localized atomic and molecular orbitals. Rev Mod Phys 35:457–465CrossRefGoogle Scholar
  31. 31.
    Kleier DA, Halgren TA, Hall JH, Lipscomb WN (1974) Localized molecular orbitals for polyatomic molecules I A comparison of the Edmiston-Ruedenberg and Boys localization methods. J Chem Phys 61:3905–3919CrossRefGoogle Scholar
  32. 32.
    Robb MA, Haines WJ, Csizmadia IG (1973) A theoretical definition of the “size” of electron pairs and its stereochemical implications. J Am Chem Soc 95:42–48CrossRefGoogle Scholar
  33. 33.
    Warczinski L, Franke R, Staemmler V (2018) A novel approach for a fast estimation of dynamic correlation energies in large organic molecules. (Submitted for publication)Google Scholar
  34. 34.
    NIST CCCBDB data bankGoogle Scholar
  35. 35.
    Curtiss LA, Raghavachari K, Redfern PC, Pople JA (1997) Assessment of Gaussian-2 and density functional theories for the computation of enthalpies of formation. J Chem Phys 106:1063–1079CrossRefGoogle Scholar

Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Lehrstuhl für Theoretische ChemieRuhr-Universität BochumBochumGermany
  2. 2.Theoretische Organische Chemie, Organisch-Chemisches Institut and Center for Multiscale Theory and SimulationWestfälische Wilhelms-Universität MünsterMünsterGermany
  3. 3.Evonik Performance Materials GmbHMarlGermany

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