Skip to main content
SpringerLink
Log in

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

  • Regular Article
  • Published:
Theoretical Chemistry Accounts Aims and scope Submit manuscript

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.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2

Similar content being viewed by others

References

  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 38:370–382

    Article  CAS  Google Scholar 

  2. Tew DP, Klopper W, Helgaker T (2007) Electron correlation: the many-body problem at the heart of chemistry. J Comput Chem 28:1307–1320

    Article  CAS  Google Scholar 

  3. Sparta M, Neese F (2014) Chemical applications carried out by local pair natural orbital based coupled-cluster methods. Chem Soc Rev 43:5032–5041

    Article  CAS  Google Scholar 

  4. Deglmann P, Schäfer A, Lennartz C (2015) Application of quantum calculations in the chemical industry—an overview. Int J Quantum Chem 115:107–136

    Article  CAS  Google Scholar 

  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 16:6942–6949

    Article  CAS  Google Scholar 

  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 118:7010–7013

    Article  Google Scholar 

  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 55:5235–5237

    Article  CAS  Google Scholar 

  8. Hollister C, Sinanoğlu O (1966) Molecular binding energies. J Am Chem Soc 88:13–21

    Article  CAS  Google Scholar 

  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 27:289–302

    Article  Google Scholar 

  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 28:85–98

    Article  CAS  Google Scholar 

  11. Pamuk HÖ (1978) Estimation of molecular correlation energies from semi-transferable orbital correlation energies. J Chem Soc Faraday Trans 2 74:1088–1093

    Article  CAS  Google Scholar 

  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 12:271–282

    CAS  Google Scholar 

  13. Kristyán S (1997) Immediate estimation of correlation energy for molecular systems from the partial charges on atoms in the molecule. Chem Phys 224:33–51

    Article  Google Scholar 

  14. Kristyán S, Csonka GI (1999) New development in RECEP (rapid estimation of correlation energy from partial charges) method. Chem Phys Lett 307:469–478

    Article  Google Scholar 

  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 22:241–254

    Article  Google Scholar 

  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 115:298–307

    Article  CAS  Google Scholar 

  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 85:5183–5193

    Article  Google Scholar 

  18. Rościszewski K, Chaumet M, Fulde P (1990) Simple rules for electronic correlation energies in hydrocarbon molecules. Chem Phys 143:47–55

    Article  Google Scholar 

  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 151:159–167

    Article  Google Scholar 

  20. Li SH, Li W, Ma J (2003) A quick estimate of the correlation energy for alkanes. Chin J Chem 21:1422–1429

    Article  CAS  Google Scholar 

  21. Bytautas L, Ruedenberg K (2002) Electron pairs, localized orbitals and correlation energy. Mol Phys 100:757–781

    Article  CAS  Google Scholar 

  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 2:207–322

    Google Scholar 

  23. G2/97 Molecular Data Set (1997) http://www.cse.anl.gov/OldCHMwebsiteContent/compmat/g2-97.htm. Accessed 23 July 2018

  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 45:89–94

    Article  CAS  Google Scholar 

  25. Fink R, Staemmler V (1993) A multi-configuration reference CEPA method based on pair natural orbitals. Theoret Chim Acta 87:129–145

    Article  CAS  Google Scholar 

  26. Weigend F, Furche F, Ahlrichs R (2003) Gaussian basis sets of quadruple zeta valence quality for atoms H-Kr. J Chem Phys 119:12753–12762

    Article  CAS  Google Scholar 

  27. Boys SF (1960) Construction of some molecular orbitals to be approximately invariant for changes from one molecule to another. Rev Mod Phys 32:296–299

    Article  CAS  Google Scholar 

  28. Foster JM, Boys SF (1960) Canonical configurational interaction procedure. Rev Mod Phys 32:300–302

    Article  CAS  Google Scholar 

  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 90:4916–4926

    Article  CAS  Google Scholar 

  30. Edmiston C, Ruedenberg K (1963) Localized atomic and molecular orbitals. Rev Mod Phys 35:457–465

    Article  CAS  Google Scholar 

  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 61:3905–3919

    Article  CAS  Google Scholar 

  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 95:42–48

    Article  CAS  Google Scholar 

  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)

  34. NIST CCCBDB data bank

  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 106:1063–1079

    Article  CAS  Google Scholar 

Download references

Author information

Author notes

  1. Michael Böckers

    Present address: Theoretische Organische Chemie, Organisch-Chemisches Institut and Center for Multiscale Theory and Simulation, Westfälische Wilhelms-Universität Münster, Corrensstraße 40, 48149, Münster, Germany

Authors and Affiliations

  1. Lehrstuhl für Theoretische Chemie, Ruhr-Universität Bochum, Universitätsstraße 150, 44801, Bochum, Germany

    Michael Böckers, Robert Franke & Volker Staemmler

  2. Evonik Performance Materials GmbH, Paul-Baumann-Str. 1, 45772, Marl, Germany

    Robert Franke

Authors
  1. Michael Böckers
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Robert Franke
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Volker Staemmler
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Robert Franke.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Electronic supplementary material

Below is the link to the electronic supplementary material.

Supplementary material 1 (DOCX 38 kb)

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Böckers, M., Franke, R. & Staemmler, V. A heuristic estimate of molecular correlation energies using pair correlation energies of localized molecular orbitals. Theor Chem Acc 138, 42 (2019). https://doi.org/10.1007/s00214-019-2422-5

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s00214-019-2422-5

Keywords

Search

Navigation