Skip to main content
SpringerLink
Log in

Analyzing cases of significant nondynamic correlation with DFT using the atomic populations of effectively localized electrons

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

Abstract

Quantum multireference effects are associated with degeneracies and near-degeneracies of the ground state and are critical to a variety of systems. Most approximate functionals of density functional theory (DFT) fail to properly describe such effects. A number of diagnostics have been proposed to estimate in advance the reliability of a given single-reference solution in this respect. Some of these diagnostics, however, lack size-consistency while remaining computationally expensive. In this work, we propose the DFT method of atomic populations of effectively localized electrons (APELE) as a novel diagnostic in this vein. It is compared with existing diagnostics of nondynamic correlation on select exemplary systems. The APELE method is on average in good agreement with the popular T1 index, while being size-consistent and less costly. It becomes particularly informative in cases involving bond stretching or bond breaking. The APELE method is applied next to organic diradicals like the bis-acridine dimer and the p-quinodimethane molecule which possess unusually high nonlinear optical response, and to the reaction of ethylene addition to Ni dithiolene. Our results for this reaction are consistent with the T1 diagnostics and in addition, shed some light on the degree of d-electron localization at the Ni center.

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
Fig. 3
Fig. 4
Fig. 5
Fig. 6

Similar content being viewed by others

References

  1. Baerends EJ (2001) Exact exchange-correlation treatment of dissociated H2 in density functional theory. Phys. Rev. Lett. 87:133004

    Article  CAS  PubMed  Google Scholar 

  2. Buijse MA, Baerends EJ (2002) An approximate exchange-correlation hole density as a functional of the natural orbitals. Mol Phys 100:401

    Article  CAS  Google Scholar 

  3. Becke AD (2003) A real-space model of nondynamical correlation. J Chem Phys 119:2972

    Article  CAS  Google Scholar 

  4. Becke AD (2013) Density functionals for static, dynamical, and strong correlation. J. Chem. Phys 138:074109

    Article  PubMed  Google Scholar 

  5. Kong J, Proynov E (2016) Density functional model for nondynamic and strong correlation. J Chem Theory Comput 12:133

    Article  CAS  PubMed  Google Scholar 

  6. Janesko BG, Proynov E, Kong J, Scalmani G, Frisch MJ (2017) Practical density functionals beyond the overdelocalization-underbinding zero-sum game. J Phys Chem Lett 8:4314

    Article  CAS  PubMed  Google Scholar 

  7. Li C, Zheng X, Cohen AJ, Sanchez PM-, Yang W (2015) Local scaling correction for reducing delocalization error in density functional approximations. Phys. Rev. Lett. 114:053001

    Article  CAS  PubMed  Google Scholar 

  8. Chen L, Zheng X, Su NQ, Yang W (2017) Localized orbital scaling correction for systematic elimination of delocalization error in density functional approximations. Nat Sci Review 5:203

    Google Scholar 

  9. Su NQ, Li C, Yang W (2018) Describing strong correlation with fractional-spin correction in density functional theory. PNAS 115:9678

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  10. Lee TJ, Taylor PR (1989) A diagnostic for determining the quality of single-reference electron correlation methods. Int J Quantum Chem Quantum Chem Symp 23:199

    CAS  Google Scholar 

  11. Janssen CL, Nielsen IMB (1998) New diagnostics for coupled-cluster and moller-plesset perturbation theory. Chem Phys Lett 290:423

    Article  CAS  Google Scholar 

  12. Karton A, Daon S, Martin JML (2011) W11: a high-confidence benchmark dataset. Chem Phys Lett 510:165

    Article  CAS  Google Scholar 

  13. Takatsuka K, Fueno T, Yamaguchi K (1978) Distribution of odd electrons in ground-state molecules. Theoret Chim Acta 48:175

    Article  CAS  Google Scholar 

  14. Lain L, Torre A, Bochicchio RC, Ponec R (2001) On the density matrix of effectively unpaired electrons. Chem Phys Lett 346:283

    Article  CAS  Google Scholar 

  15. Staroverov VN, Davidson ER (2000) Distribution of effectively unpaired electrons. Chem Phys Lett 330:161

    Article  CAS  Google Scholar 

  16. Head-Gordon M (2003) Characterizing unpaired electrons from the one-particle density matrix. Chem Phys Lett 372:508

    Article  CAS  Google Scholar 

  17. Ramos-Cordoba E, Salvador P, Matito E (2016) Separation of dynamic and nondynamic correlation. Phys Chem Chem Phys 18:24015

    Article  CAS  PubMed  Google Scholar 

  18. Liu F, Duan C, Kulik HJ (2020) Rapid detection of strong correlation with machine learning for transition-metal complex high-throughput screening. J Phys Chem Lett 11:8067

    Article  CAS  PubMed  Google Scholar 

  19. Chai J-D (2012) Density functional theory with fractional orbital occupations. J. Chem. Phys. 136:154104

    Article  PubMed  Google Scholar 

  20. Ramos-Cordoba E, Matito E (2017) Local descriptors of dynamic and nondynamic correlation. J Chem Theory Comput 13:2705

    Article  CAS  PubMed  Google Scholar 

  21. Grimme S, Hansen A (2015) A practicable real-space measure and visualization of static electron-correlation effects. Angew Chem Int Ed 54:12308

    Article  CAS  Google Scholar 

  22. Nakano M, Kishi R, Nitta T et al (2005) Second hyperpolarizability (γ) of singlet diradical system: dependence of γ on the diradical character. J Phys Chem A 109:885

    Article  CAS  PubMed  Google Scholar 

  23. Proynov E, Liu F, Kong J (2013) Analysing effects of strong electron correlation within Kohn-Sham Density-functional theory. Phys. Rev. A 88:032510

    Article  Google Scholar 

  24. Fukuda K, Nakano M (2014) Intramolecular charge transfer effects on the diradical character character and second Hyperpolarizabilities of open-shell singlet X-pi-X (X= Donor/Acceptor) systems. J Phys Chem A 118:3463

    Article  CAS  PubMed  Google Scholar 

  25. Kamada K, Fuku-en S-i, Minamide S et al (2013) Impact of diradical character on two-photon absorption: Bis(acridine) dimers synthesized from an allenic precursor. J Am Chem Soc 135:232

    Article  CAS  PubMed  Google Scholar 

  26. Nakano M, Kishi R, Ohta S et al (2007) Relationship between third-order nonlinear optical properties and magnetic interactions in open-shell systems: a new paradigm for nonlinear optics. Phys. Rev. Letters 99:033001

    Article  Google Scholar 

  27. Nakano M, Kishi R, Ohta S et al (2006) Origin of the enhancement of the second hyperpolarizability of singlet diradical systems wuth intermediate diradical character. J. Chem. Phys. 138:244306

    Google Scholar 

  28. Nakano M, Kubo T, Kamada K et al (2006) Second hyperpolarizabilities of polycyclic aromatic hydrocarbons invoolving phenalenyl radical units. Chem Phys Lett 418:142

    Article  CAS  Google Scholar 

  29. Nakano M, Nagai H, Fukui H et al (2008) Theoretical study of third-order nonlinear optical properties in square nanographenes with open-shell singlet ground states. Chem Phys Lett 467:120

    Article  CAS  Google Scholar 

  30. Nagai H, Nakano M, Yoneda K et al (2010) Signature of Multiradical character in second hyperpolarizabilities of rectangular graphene nanoflakes. Chem Phys Lett 489:212

    Article  CAS  Google Scholar 

  31. Staroverov VN, Davidson ER (2000) Electron distributions in radicals. Int J Quant Chem 77:316

    Article  CAS  Google Scholar 

  32. Becke AD, Roussel MR (1989) Exchange holes in inhomogeneous systems: a coordinate-space model. Phys Rev A 39:3761

    Article  CAS  Google Scholar 

  33. Becke AD (2005) Real-space post-Hartree-Fock correlation models. J Chem Phys 122:64101

    Article  Google Scholar 

  34. Becke AD (1988) A multicenter numerical integration scheme for polyatomic molecules. J Chem Phys 88:2547

    Article  CAS  Google Scholar 

  35. Turney JM, Simmonett AC, Parrish RM et al (2012) Psi4: an open-source ab initio electronic structure program. WIRES Comput Mol Sci 2:556

    Article  CAS  Google Scholar 

  36. Frisch MJ, Trucks GW, Schlegel HB et al (2016) Gaussian development version, Revision I. 11. Gaussian Inc, Wallingford CT

    Google Scholar 

  37. Curtiss LA, Raghvachari K, Redfern PC, Rassolov V, Pople JA (1998) Gaussian-3 (G3) theory for molecules containing first and second-row atoms. J Chem Phys 109:7764

    Article  CAS  Google Scholar 

  38. Liu F, Kong J (2017) An algorithm for efficient computation of exchange energy density with Gaussian basis functions. J Chem Theory Comput 13:2571

    Article  CAS  PubMed  Google Scholar 

  39. Liu F, Furlani T, Kong J (2016) Optimal path search for recurrence relation in cartesian Gaussian integrals. J Phys Chem A 120:10264

    Article  CAS  PubMed  Google Scholar 

  40. Liu F, Kong J (2018) An efficient implementation of semi-numerical computation of the Hartree-Fock exchange on the Intel Phi processor. Chem Phys Letters 703:106

    Article  CAS  Google Scholar 

  41. Jiang W, DeYonker NJ, Wilson AK (2012) Multireference character for 3d TM compounds. J Chem Theory Comput 8:460

    Article  CAS  PubMed  Google Scholar 

  42. Wang J, Manivasagam S, Wilson AK (2015) Multireference character for 4d transition metal-containing molecules. J Chem Theory Comput 11:5865

    Article  CAS  PubMed  Google Scholar 

  43. Fogueri UR, Kozuch S, Karton A, Martin JML (2013) A simple DFT-based diagnostic for nondynamical correlation. Theor Chem Acc 132:1291

    Article  Google Scholar 

  44. Schultz NE, Zhao Y, Truhlar DG (2005) Density functionals for inorganometallic and organometallic chemistry. J Phys Chem A 109:11127

    Article  CAS  PubMed  Google Scholar 

  45. Lee TJ (2003) Comparison of the T1 and D1 diagnostics for electronicstructure theory: a new definition for the open-shell D1 diagnostic. Chem Phys Lett 372:362

    Article  CAS  Google Scholar 

  46. Cousins KR (2005) ChemDraw Ultra 9.0. J. Am. Chem. Soc 127: 4115

  47. Jacquemin D, Femenias A, Chermette H et al (2006) Assessment of several hybrid DFT functionals for the evaluation of bond length alternation of increasingly long oligomers. J Phys Chem A 110:5952

    Article  CAS  PubMed  Google Scholar 

  48. Liang SD, Bai YH, Beng B (2006) Peierls instability and persistent current in mesoscopic conducting polymer rings. Phys. Rev. B 74:113304

    Article  Google Scholar 

  49. Sawyer DT, Srivatsa GS, Bodini ME, Schaefer WP, Wing RM (1986) Redox chemistry and spectroscopy of toluene-3,4-dithiol (TDTH2) and of its M(TDT)22-/- complexes with zinc(II), copper(II), nickel(II), cobalt(II), iron(II), and manganese(II). Formation of a stable dn-(.cntdot.SR) bond upon oxidation by one electron. J Am Chem Soc 108:936

    Article  CAS  Google Scholar 

  50. Zuleta JA, Burberry MS, Eisenberg R (1990) Platinum(II) diimine dithiolates New solution luminescent complexes. Coord. Chem. Rev. 97:47

    Article  CAS  Google Scholar 

  51. Cassoux P, Valade L, Kobayashi H et al (1991) Molecular metals and superconductors derived from metal complexes of 1,3-dithiol-2-thione-4,5-dithiolate (dmit). Coord Chem Rev 110:115

    Article  CAS  Google Scholar 

  52. Pilato RS, Stiefel EI (1999) Bioinorganic catalysis. In: Bioinorganic Catalysis. Marcel Dekker, New York, pp 81–152

    Google Scholar 

  53. Dang L, Yang X, Zhou J, Brothers EN, Hall MB (2012) Computational studies on ethylene addition to nickel bis(dithiolene). J Phys Chem A 116:476

    Article  CAS  PubMed  Google Scholar 

  54. Jiang W, DeYonker NJ, Determan JJ, Wilson AK (2011) Toward accurate theoretical thermochemistry of first row transition metal complexes. J Phys Chem A 116:870

    Article  PubMed  Google Scholar 

Download references

Acknowledgements

JK thanks Dr. Pachter for very helpful discussions on the topic of this paper. He also thanks Dr. Hall for discussions on the Ni dithiolene reactions. The authors thank Drs. Liu, Wang and John for assistance. EP thanks Dennis Salahub for the long years of mentorship, friendship and support. This work received support from Air Force Research Laboratory of US Department of Defense under the AFRL Minority Leaders—Research Collaboration Program, contract FA8650-13-C-5800 (Clearance Authority: 88ABW-2016-5818), and from the National Science Foundation (Grant No. 1665344).

Author information

Authors and Affiliations

  1. Department of Chemistry, Middle Tennessee State University, Murfreesboro, TN, 37132, USA

    Conrad Lewis, Emil Proynov, Jianguo Yu & Jing Kong

  2. Center for Computational Sciences, Middle Tennessee State University, Murfreesboro, TN, 37132, USA

    Emil Proynov & Jing Kong

Authors
  1. Conrad Lewis
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Emil Proynov
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Jianguo Yu
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Jing Kong
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Jing Kong.

Additional information

Publisher's Note

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

Published as part of the special collection of articles “20th deMon Developers Workshop.”

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Lewis, C., Proynov, E., Yu, J. et al. Analyzing cases of significant nondynamic correlation with DFT using the atomic populations of effectively localized electrons. Theor Chem Acc 141, 17 (2022). https://doi.org/10.1007/s00214-022-02871-z

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s00214-022-02871-z

Keywords

Search

Navigation