Skip to main content
SpringerLink
Log in

A valence bond perspective of the reaction force formalism

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

Abstract

The reaction force formalism represents a convenient approach to analyze the course of a reaction step. From this analysis, the reaction path can be separated in a number of regions that are associated to either structural changes or electronic reorganization. This empirical observation is rationalized in this work on the basis of a simple two-state valence bond correlation diagram. We demonstrate that the ratio between the integrated reaction force and the region of interest (\(w_{\text{ii}}/w_{\text{i}}\) for the forward reaction and \(w_{\text{iii}}/w_{\text{iv}}\) for the backward reaction) increases with the ratio between the quantum mechanical resonance energy and the energy required to reach the crossing point at the transition state, we call to this ratio the strength of the resonance. This observation means that the size of the transition region (region ii and iii), that includes the transition state, depends on the strength of the resonance, and the structural zones (region i and iv), that are regions associated with the pure valence bond state curves (no resonance). We propose a simple analytical relationship for \(w_{\text{ii}}/w_{\text{i}}\) and \(w_{\text{iii}}/w_{\text{iv}}\) based on three parameters: (i) the quantum mechanical resonance energy, (ii) the energy of the reaction and (iii) the overlap between the VB structures at the transition state. The previous conclusions were supported by a reaction force analysis of a \({\text{S}}_{N}2\) reactions, \({\text{X}}^{-} + {\text{CH}}_{3}{-}{\text{Y}} \rightarrow {{\text{X}}{-}{\text{CH}}}_{3} + {\text{Y}}^{-} ({\text{X}} = {\text{F}}, {\text{Cl}}, {\text{Br}})\). The valence bond parameters for these reactions are estimated from empirical considerations. A very good agreement is found between the computed reaction force ratios and the predicted one.

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

Similar content being viewed by others

References

  1. Fukui K (1970) Formulation of the reaction coordinate. J Phys Chem 74(23):4161–4163. https://doi.org/10.1021/j100717a029

    Article  CAS  Google Scholar 

  2. Fukui K (1981) The path of chemical reactions-the irc approach. Acc Chem Res 14(12):363–368. https://doi.org/10.1021/ar00072a001

    Article  CAS  Google Scholar 

  3. Toro-Labbe A (1999) Characterization of chemical reactions from the profiles of energy, chemical potential, and hardness. J Phys Chem A 103(22):4398–4403. https://doi.org/10.1021/jp984187g

    Article  CAS  Google Scholar 

  4. Politzer P, Toro-Labbe A, Gutierrez-Oliva S, Herrera B, Jaque P, Concha M, Murray J (2005) The reaction force: three key points along the intrinsic reaction coordinate. J Chem Sci 117(5):467–472. https://doi.org/10.1007/BF02708350

    Article  CAS  Google Scholar 

  5. Toro-Labbe A, Gutierrez-Oliva S, Murray J, Politzer P (2007) A new perspective on chemical and physical processes: the reaction force. Mol Phys 105(19–22):2619–2625. https://doi.org/10.1080/00268970701604663

    Article  CAS  Google Scholar 

  6. Toro-Labbe A, Gutierrez-Oliva S, Murray J, Politzer P (2009) The reaction force and the transition region of a reaction. J Mol Model 15(6):707–710. https://doi.org/10.1007/s00894-008-0431-8

    Article  CAS  PubMed  Google Scholar 

  7. Murray J, Toro-Labbe A, Clark T, Politzer P (2009) Analysis of diatomic bond dissociation and formation in terms of the reaction force and the position-dependent reaction force constant. J Mol Model 15(6):701–706. https://doi.org/10.1007/s00894-008-0400-2

    Article  CAS  PubMed  Google Scholar 

  8. Politzer P, Reimers J, Murray J, Toro-Labbe A (2010) Reaction force and its link to diabatic analysis: a unifying approach to analyzing chemical reactions. J Chem Phys Lett 1(19):2858–2862. https://doi.org/10.1021/jz101135y

    Article  CAS  Google Scholar 

  9. Politzer P, Toro-Labbe A, Gutierrez-Oliva S, Murray J (2012) Perspectives on the reaction force. Adv Quantum Chem 64:189–209. https://doi.org/10.1016/B978-0-12-396498-4.00006-5

    Article  CAS  Google Scholar 

  10. Jaque P, Toro-Labbe A, Politzer P, Geerling P (2008) Reaction force constant and projected force constants of vibrational modes along the path of an intermolecular proton transfer reaction. Chem Phys Lett 456:135–140. https://doi.org/10.1016/cplett.2008.03.054

    Article  CAS  Google Scholar 

  11. Yepez D, Murray J, Politzer P, Jaque P (2012) The reaction force constant: an indicator of the synchronicity in double proton transfer reactions. Phys Chem Chem Phys 14(31):11125–11134. https://doi.org/10.1039/C2CP41064H

    Article  Google Scholar 

  12. Politzer P, Murray J, Jaque P (2013) Perspectives on the reaction force constant. J Mol Model 19(10):4111–4118. https://doi.org/10.1007/s00894-012-1713-8

    Article  CAS  PubMed  Google Scholar 

  13. Yepez D, Donoso-Tauda O, Perez P, Murray J, Politzer P, Jaque P (2013) The reaction force constant as an indicator of synchronicity/nonsynchronicity in \([4+2]\) cycloaddition processes. Phys Chem Chem Phys 15(19):7311–7320. https://doi.org/10.1039/C3CP44197K

    Article  Google Scholar 

  14. Cortes-Arriaga D, Toro-Labbe A, Mora J, Rincon L, Mereau R, Torres F (2017) Theoretical analysis of c-f bond cleavage mediated by cob[i]alamin-based structures. J Mol Model 23:264. https://doi.org/10.1007/s00894-017-3431-8

    Article  CAS  Google Scholar 

  15. Politzer P, Burda J, Concha M, Lane P, Murray J (2006) Analysis of the reaction force for a gas phase \({\text{S}}_{N}2\) process. J Phys Chem A 110:756–761. https://doi.org/10.1021/jp0582080

    Article  CAS  PubMed  Google Scholar 

  16. Burda J, Toro-Labbe A, Gutierrez-Oliva S, Murray J, Politzer P (2007) Reaction force decomposition of activation barriers to elucidate solvent effects. J Phys Chem A 111(13):2455–2457. https://doi.org/10.1021/jp0709353

    Article  CAS  PubMed  Google Scholar 

  17. Giri S, Echegaray E, Ayers P, Nuñez A, Lund F, Toro-Labbe A (2012) Insights into the mechanism of an S\(_{N}\)2 reaction from the reaction force and the reaction electronic flux. J Phys Chem A 116(40):10015–10026. https://doi.org/10.1021/jp3076707

    Article  CAS  PubMed  Google Scholar 

  18. Burda J, Morray J, Toro-Labbe A, Gutierrez-Oliva S, Politzer P (2009) Analysis of solvent effects in the addition of hcl to propene. J Phys Chem A 115:6500–6505. https://doi.org/10.1021/jp9025927

    Article  CAS  Google Scholar 

  19. Jaque P, Toro-Labbe A, Geerling P, De Proft F (2009) Theoretical study of the regioselectivity of [2+2] photocycloaddition reaction of acrolein with olefins. J Phys Chem A 113:332–344. https://doi.org/10.1021/jp807754f

    Article  CAS  PubMed  Google Scholar 

  20. Toro-Labbe A, Gutierrez-Oliva S, Concha M, Murray J, Politzer P (2004) Analysis of two intramolecular proton transfer processes in terms of the reaction force. J Chem Phys 121(10):4570–4576. https://doi.org/10.1064/1.1777216

    Article  CAS  PubMed  Google Scholar 

  21. Herrera B, Toro-Labbe A (2004) The role of the reaction force to characterize local specific interactions that activate the intramolecular proton transfer in dna bases. J Chem Phys 121:7096–7102. https://doi.org/10.1064/1.1792091

    Article  CAS  PubMed  Google Scholar 

  22. Rincon E, Jaque P, Toro-Labbe A (2006) A reaction force analysis of the effect of Mg(II) on the 1,3 intramolecular hydrogen transfer in thymmine. J Phys Chem A 120:9478–9485. https://doi.org/10.1021/jp062870u

    Article  CAS  Google Scholar 

  23. Yepez D, Murray J, Santos J, Toro-Labbe A, Politzer P, Jaque P (2013) Fine structure in the transition region: reaction force analyses of water-assisted proton transfer. J Mol Model 19(7):2689–2697. https://doi.org/10.1007/s00894-012-1475-3

    Article  CAS  Google Scholar 

  24. Inostrosa-Rivera R, Herrera B, Toro-Labbe A (2014) Using the reaction force and the reaction electronic flux on the proton transfer of formamide derived systems. Phys Chem Chem Phys 16:14489–14495. https://doi.org/10.1039/c3cp55159h

    Article  CAS  Google Scholar 

  25. Murray J, Lane P, Nieder A, Klapotke T, Politzer P (2009) Enhanced detonation sensitivities of silicon analogs of petn: Reaction force analysis and the role of \(\sigma\)-hole interactions. Theor Chem Acc 127(4):345–354. https://doi.org/10.1007/s00214-009-0723-9

    Article  CAS  Google Scholar 

  26. Murray J, Lane P, Gobel M, Klapotke T, Politzer P (2009) Reaction force analysis of nitro-aci tautomerizations of trinitromethane, the elusive trinitromethanol, picric acid and 2,4-dinitro-1h-imidazole. Theor Chem Acc 124:355–363. https://doi.org/10.1007/s00214-009-0630-2

    Article  CAS  Google Scholar 

  27. Labet V, Morrel A, Grand A, Toro-Labbe A (2008) Theoretical study of cytosine deamination from the perspective of the reaction force analysis. J Phys Chem A 112:11487–11494. https://doi.org/10.1021/jp8059097

    Article  CAS  PubMed  Google Scholar 

  28. Cortes-Arriagada D, Gutierrez-Oliva S, Herrera B, Soto K, Toro-Labbe A (2014) The mechanism of chemisorption of hydrogen atom on graphene: insights from the reaction force and the reaction electronic flux. J Chem Phys 141:134701. https://doi.org/10.1063/1.4896611

    Article  CAS  PubMed  Google Scholar 

  29. Villegas-Escobar N, Toro-Labbe A, Becera M, Real-Enriquez M, Mora J, Rincon L (2017) A dft study of hydrogen and methane activation by \(b(c_{6}f_{5})_{3}/p(t-bu)_{3}\) and \(al(c_{6}f_{5})_{3}/p(t-bu)_{3}\) frustrated lewis pairs. J Mol Model 23:234. https://doi.org/10.1007/s00894-017-3404-y

    Article  CAS  PubMed  Google Scholar 

  30. Polanyi J, Zewail A (1995) Direct observation of the transition state. Acc Chem Res 28:199–132. https://doi.org/10.1021/ar00051a005

    Article  Google Scholar 

  31. Shaik S (1981) What happens to molecules as they react? A valence bond approach to reactivity. J Am Chem Soc 103(13):3692–3701. https://doi.org/10.1021/ja00403a014

    Article  CAS  Google Scholar 

  32. Pross A, Shaik S (1983) A qualitative valence-bond approach to organic reactivity. Acc Chem Res 16(10):363–370. https://doi.org/10.1021/ar00094a001

    Article  CAS  Google Scholar 

  33. Shaik S (1985) The collage of \({\text{S}}_{N}2\) reactivity patterns: a state correlation diagram model. Prog Phys Org Chem 15:197. https://doi.org/10.1021/ja00403a014

    Article  CAS  Google Scholar 

  34. Shaik S, Schlegel H, Wolfe S (1992) Theoretical aspects of physical organic chemistry. The S\(_{N}\)2 mechanism. Wiley, New York

    Google Scholar 

  35. Shaik S, Hiberty P (1995) Valence bond mixing and curve crossing diagrams in chemical reactivity and bonding. Adv Quantum Chem 26:99–163. https://doi.org/10.1016/S0065-3276(08)60112-4

    Article  CAS  Google Scholar 

  36. Shaik S, Shurki A (1999) Vb diagrams and chemical reactivity. Angew Chem Int Ed 38(5):586–625 https://doi.org/10.1002/(SICI)1521-3773(19990301)38:5%3c586::AID-ANIE586%3e3.0.CO;2-T

    Article  Google Scholar 

  37. Shaik S, Hiberty P (2008) A chemist’s guide to valence bond theory. Wiley, New York

    Google Scholar 

  38. Martinez J, Toro-Labbe A (2004) Energy and chemical force profiles from the marcus equation. Chem Phys Lett 392(1–3):132–139. https://doi.org/10.1016/j.cplett2004.05.034

    Article  CAS  Google Scholar 

  39. Gutierrez-Oliva S, Herrera B, Toro-Labbe A (2017) An estension of the Marcus equation: the Marcus potential energy function. J Mol Model 24:104. https://doi.org/10.1007/s00894-018-3633-8

    Article  CAS  Google Scholar 

  40. Marcus RA (1964) Chemical and electrochemical electron-transfer theory. Annu Rev Phys Chem 15:155–196. https://doi.org/10.1146/annurev.pc.15.100164.001103

    Article  CAS  Google Scholar 

  41. Marcus RA (1992) Electron transfer reactions in chemistry. Theory and experiment. Rev Mod Phys 65:599–610. https://doi.org/10.1103/RevModPhys.65.599

    Article  Google Scholar 

  42. Zhao Y, Truhlar D (2008) Exploring the limit of accuracy of the global hybrid meta density functional for main-group thermochemistry, kinetics, and noncovalent interactions. J Chem Theory Comput 4:1849. https://doi.org/10.1021/ct800246v

    Article  CAS  PubMed  Google Scholar 

  43. Frisch MJ, Trucks GW, Schlegel HB, Scuseria GE, Robb MA, Cheeseman JR, Scalmani G, Barone V, Petersson GA, Nakatsuji H, Li X, Caricato M, Marenich AV, Bloino J, Janesko BG, Gomperts R, Mennucci B, Hratchian HP, Ortiz JV, Izmaylov AF, Sonnenberg JL, Williams-Young D, Ding F, Lipparini F, Egidi F, Goings J, Peng B, Petrone A, Henderson T, Ranasinghe D, Zakrzewski VG, Gao J, Rega N, Zheng G, Liang W, Hada M, Ehara M, Toyota K, Fukuda R, Hasegawa J, Ishida M, Nakajima T, Honda Y, Kitao O, Nakai H, Vreven T, Throssell K, Montgomery JA Jr, Peralta JE, Ogliaro F, Bearpark MJ, Heyd JJ, Brothers EN, Kudin KN, Staroverov VN, Keith TA, Kobayashi R, Normand J, Raghavachari K, Rendell AP, Burant JC, Iyengar SS, Tomasi J, Cossi M, Millam JM, Klene M, Adamo C, Cammi R, Ochterski JW, Martin RL, Morokuma K, Farkas O, Foresman JB, Fox DJ (2016) Gaussian\(^{\sim }\)16 Revision C.01. Gaussian Inc., Wallingford

    Google Scholar 

  44. Schlegel HB (1987) Optimization of equilibrium geometries and transition structures. Adv Chem Phys 67:249. https://doi.org/10.1002/9780470142936.ch4

    Article  CAS  Google Scholar 

  45. Hratchian HP, Schlegel HB (2004) Accurate reaction paths using a Hessian based predictor–corrector integrator. J Chem Phys 120:9918–9924. https://doi.org/10.1063/1.1724823

    Article  CAS  PubMed  Google Scholar 

  46. Jones E, Oliphant T, Peterson P et al (2001) Scipy: open source scientific tools for python. http://www.scipy.org/

  47. Wu W, Su P, Shaik S, Hiberty P (2011) Classical valence bond approach by modern methods. Chem Rev 111(11):7557–7593. https://doi.org/10.1021/cr100228r

    Article  CAS  PubMed  Google Scholar 

  48. Song L, Wu W, Hiberty PC, Shaik S (2006) Identity \({\text{S}}_{N}2\) reactions \(\text{x}^{-} + \text{ch}_{3}\text{x} \rightarrow \text{x-ch}_{3} + \text{x}^{-}\) (x = f, cl, br and i) in vacuum and in aqueos solution: a valence bond study. Chem Eur J 12:7458–7466. https://doi.org/10.1002/chem.200600372

    Article  CAS  PubMed  Google Scholar 

  49. Shaik SS, Duzy E, Bartuv A (1990) The quantum mechanical resonance energy of transition states. An indicator of transition state grometry and electronic structure. J Phys Chem 94:6574–6582. https://doi.org/10.1021/j100380a011

    Article  CAS  Google Scholar 

Download references

Acknowledgements

This work has been performed by employing the resources of the USFQ’s High Performance Computing system (HPC-USFQ). The authors would like to thank to the 2019 USFQ’s collaboration grants and Poli-grants program for financial support.

Author information

Authors and Affiliations

  1. Grupo de Química Computacional y Teórica, Departamento de Ingeniería Química, Universidad San Francisco de Quito, Diego de Robles y Via Interoceanica, 17-1200-841, Quito, Ecuador

    Luis Rincon, F. Javier Torres, Jose R. Mora & Cesar H. Zambrano

  2. Instituto de Simulación Computacional, Universidad San Francisco de Quito, Diego de Robles y Via Interoceanica, 17-1200-841, Quito, Ecuador

    Luis Rincon, F. Javier Torres, Jose R. Mora & Cesar H. Zambrano

  3. Departamento de Matemáticas, Universidad San Francisco de Quito, Diego de Robles y Via Interoceanica, 17-1200-841, Quito, Ecuador

    Vladimir Rodriguez

Authors
  1. Luis Rincon
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. F. Javier Torres
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Jose R. Mora
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Cesar H. Zambrano
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Vladimir Rodriguez
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Luis Rincon.

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 derived from the Chemical Concepts from Theory and Computation.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Rincon, L., Torres, F.J., Mora, J.R. et al. A valence bond perspective of the reaction force formalism. Theor Chem Acc 139, 13 (2020). https://doi.org/10.1007/s00214-019-2538-7

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s00214-019-2538-7

Keywords

Search

Navigation