:Bond-dissociation energy

The term bond-dissociation energy is similar to the related notion of bond-dissociation enthalpy (or bond enthalpy), which is sometimes used interchangeably. However, some authors make the distinction that the bond-dissociation energy (D₀) refers to the enthalpy change at 0 K, while the term bond-dissociation enthalpy is used for the enthalpy change at 298 K (unambiguously denoted DH°₂₉₈). The former parameter tends to be favored in theoretical and computational work, while the latter is more convenient for thermochemical studies. For typical chemical systems, the numerical difference between the quantities is small, and the distinction can often be ignored. For a hydrocarbon RH, where R is significantly larger than H, for instance, the relationship D₀(R−H) ≈ DH°₂₉₈(R−H) − 1.5 kcal/mol is a good approximation.{{cite journal |vauthors=Blanksby SJ, Ellison GB | title = Bond dissociation energies of organic molecules | journal = Accounts of Chemical Research | volume = 36 | issue = 4 | pages = 255–63 | date = April 2003 | pmid = 12693923 | doi = 10.1021/ar020230d | citeseerx = 10.1.1.616.3043 }} Some textbooks ignore the temperature dependence,{{cite book | title=Modern physical organic chemistry | first1 = Eric V. | last1 = Anslyn | first2 = Dennis A. | last2 = Dougherty | date=2006 |publisher=University Science |isbn=978-1-891389-31-3 |location=Sausalito, CA |oclc=55600610}} while others have defined the bond-dissociation energy to be the reaction enthalpy of homolysis at 298 K.{{cite book | last = Darwent | first = B. deB. | date = January 1970 | title = Bond Dissociation Energies in Simple Molecules | place = Washington, DC | publisher = U.S. National Bureau of Standards | series = NSRDS-NBS 31 | lccn = 70602101 | url = http://nvlpubs.nist.gov/nistpubs/Legacy/NSRDS/nbsnsrds31.pdf }}{{Cite book |title=Introduction to Organic Chemistry |last1=Streitwieser |first1=Andrew |last2=Heathcock |first2=Clayton H. |last3=Kosower |first3=Edward M. |publisher=Medtech (Scientific International, reprint of 4th revised edition, 1998, Macmillan) |year=2017 |isbn=978-93-85998-89-8 |location=New Delhi |page=101}}{{Cite book |title=Perspectives on structure and mechanism in organic chemistry | first = Felix A. | last = Carroll |date=2010 |publisher=John Wiley |isbn=978-0-470-27610-5 |edition= 2nd |location=Hoboken, N.J. |oclc=286483846}}

The bond dissociation energy is related to but slightly different from the depth of the associated potential energy well of the bond, D_e, known as the electronic energy. This is due to the existence of a zero-point energy ε₀ for the vibrational ground state, which reduces the amount of energy needed to reach the dissociation limit. Thus, D₀ is slightly less than D_e, and the relationship D₀ = D_e − ε₀ holds.

The bond dissociation energy is an enthalpy change of a particular chemical process, namely homolytic bond cleavage, and "bond strength" as measured by the BDE should not be regarded as an intrinsic property of a particular bond type but rather as an energy change that depends on the chemical context. For instance, Blanksby and Ellison cites the example of ketene (H₂C=CO), which has a C=C bond dissociation energy of 79 kcal/mol, while ethylene (H₂C=CH₂) has a bond dissociation energy of 174 kcal/mol. This vast difference is accounted for by the thermodynamic stability of carbon monoxide (CO), formed upon the C=C bond cleavage of ketene. The difference in availability of spin states upon fragmentation further complicates the use of BDE as a measure of bond strength for head-to-head comparisons, and force constants have been suggested as an alternative.{{Cite journal |last1=Kalescky |first1=Robert |last2=Kraka |first2=Elfi |last3=Cremer |first3=Dieter |date=2013-08-30 |title=Identification of the Strongest Bonds in Chemistry |journal=The Journal of Physical Chemistry A |language=en |volume=117 |issue=36 |pages=8981–8995 |doi=10.1021/jp406200w |pmid=23927609 |bibcode=2013JPCA..117.8981K |s2cid=11884042 |issn=1089-5639}}

Historically, the vast majority of tabulated bond energy values are bond enthalpies. More recently, however, the free energy analogue of bond-dissociation enthalpy, known as the bond-dissociation free energy (BDFE), has become more prevalent in the chemical literature. The BDFE of a bond A–B can be defined in the same way as the BDE as the standard free energy change (ΔG°) accompanying homolytic dissociation of AB into A and B. However, it is often thought of and computed stepwise as the sum of the free-energy changes of heterolytic bond dissociation (A–B → A⁺ + :B⁻), followed by one-electron reduction of A (A⁺ + e⁻ → A•) and one-electron oxidation of B (:B⁻ → •B + e⁻).{{cite journal |vauthors=Miller DC, Tarantino KT, Knowles RR | title = Proton-Coupled Electron Transfer in Organic Synthesis: Fundamentals, Applications, and Opportunities | journal = Topics in Current Chemistry | volume = 374 | issue = 3 | page = 30 | date = June 2016 | pmid = 27573270 | pmc = 5107260 | doi = 10.1007/s41061-016-0030-6 }} In contrast to the BDE, which is usually defined and measured in the gas phase, the BDFE is often determined in the solution phase with respect to a solvent like DMSO, since the free-energy changes for the aforementioned thermochemical steps can be determined from parameters like acid dissociation constants (pK_a) and standard redox potentials (ε°) that are measured in solution.{{Cite journal |last1=Bordwell |first1=F. G. |last2=Cheng |first2=Jin Pei |last3=Harrelson |first3=John A. |date=February 1988 |title=Homolytic bond dissociation energies in solution from equilibrium acidity and electrochemical data |journal=Journal of the American Chemical Society |volume=110 |issue=4 |pages=1229–1231 |doi=10.1021/ja00212a035 |bibcode=1988JAChS.110.1229B }}

Except for diatomic molecules, the bond-dissociation energy differs from the bond energy. While the bond-dissociation energy is the energy of a single chemical bond, the bond energy is the average of all the bond-dissociation energies of the bonds of the same type for a given molecule.{{Cite book |title=Principles of organic synthesis | first1 = Richard O. C. | last1 = Norman | first2 = James M. | last2 = Coxon |date=2001 |publisher=Nelson Thornes |isbn=978-0-7487-6162-3 |edition= 3rd |location=London |page=7 |oclc=48595804}} For a homoleptic compound EX_n, the E–X bond energy is (1/n) multiplied by the enthalpy change of the reaction EX_n → E + nX. Average bond energies given in tables are the average values of the bond energies of a collection of species containing "typical" examples of the bond in question.

For example, dissociation of HO−H bond of a water molecule (H₂O) requires 118.8 kcal/mol (497.1 kJ/mol). The dissociation of the remaining hydroxyl radical requires 101.8 kcal/mol (425.9 kJ/mol). The bond energy of the covalent O−H bonds in water is said to be 110.3 kcal/mol (461.5 kJ/mol), the average of these values.{{cite book | last1 = Lehninger | first1 = Albert L. | author-link1 = Albert L. Lehninger | last2 = Nelson | first2 = David L. | last3 = Cox | first3 = Michael M. | title = Lehninger Principles of Biochemistry | url = https://archive.org/details/lehningerprincip0000lehn_04ed | url-access = registration | edition = 4th | date = 2005 | publisher = W. H. Freeman | isbn = 978-0-7167-4339-2 | page = [https://archive.org/details/lehningerprincip0000lehn_04ed/page/48 48] | access-date = May 20, 2016 }}

In the same way, for removing successive hydrogen atoms from methane the bond-dissociation energies are 105 kcal/mol (439 kJ/mol) for D(CH₃−H), 110 kcal/mol (460 kJ/mol) for D(CH₂−H), 101 kcal/mol (423 kJ/mol) for D(CH−H) and finally 81 kcal/mol (339 kJ/mol) for D(C−H). The bond energy is, thus, 99 kcal/mol, or 414 kJ/mol (the average of the bond-dissociation energies). None of the individual bond-dissociation energies equals the bond energy of 99 kcal/mol.{{Cite web|title=Table of Bond Dissociation Energies|url=https://archive.org/details/bergman-r.-g.-streitwieser-a.-table-of-organic-bond-dissociation-energies-2018|last1=Streitwieser A.|last2=Bergman R. G.|date=19 September 2018|publisher=University of California, Berkeley|access-date=13 March 2019}}

According to experimental BDE data, the strongest measured single bonds are Si−F bonds. The BDE for H₃Si−F is 152 kcal/mol, almost 50% stronger than the H₃C−F bond (110 kcal/mol). The BDE for F₃Si−F is even larger, at 166 kcal/mol. One consequence to these data are that many reactions generate silicon fluorides, such as glass etching, deprotection in organic synthesis, and volcanic emissions.{{RubberBible87th}} The strength of the bond is attributed to the substantial electronegativity difference between silicon and fluorine, which leads to a substantial contribution from both ionic and covalent bonding to the overall strength of the bond.{{Cite journal |last=Gillespie |first=Ronald J. |date=July 1998 |title=Covalent and Ionic Molecules: Why Are BeF₂ and AlF₃ High Melting Point Solids whereas BF₃ and SiF₄ Are Gases? |journal=Journal of Chemical Education |language=en |volume=75 |issue=7 |page=923 |doi=10.1021/ed075p923 |bibcode=1998JChEd..75..923G |issn=0021-9584}} For the same reason, B–F bonds are also very strong, possibly stronger than Si−F, with the BDE for F₂B−F computed to be 172 kcal/mol at the CCSD(T)/CBS level of theory.{{Cite journal |last1=O'Reilly |first1=Robert J. |last2=Karton |first2=Amir |date=2023-07-28 |title=A Systematic Exploration of B-F Bond Dissociation Enthalpies of Fluoroborane-Type Molecules at the CCSD(T)/CBS Level |journal=Molecules (Basel, Switzerland) |volume=28 |issue=15 |pages=5707 |doi=10.3390/molecules28155707 |doi-access=free |issn=1420-3049 |pmid=37570677|pmc=10420309 }} The C−C single bond of diacetylene (HC≡C−C≡CH) linking two sp-hybridized carbon atoms is also among the strongest, at 160 kcal/mol. The strongest bond for a neutral compound, including multiple bonds, is found in carbon monoxide at 257 kcal/mol. The protonated forms of CO, HCN and N₂ are said to have even stronger bonds, although another study argues that the use of BDE as a measure of bond strength in these cases is misleading.

On the other end of the scale, there is no clear boundary between a very weak covalent bond and an intermolecular interaction. Lewis acid–base complexes between transition metal fragments and noble gases are among the weakest of bonds with substantial covalent character, with (CO)₅W:Ar having a W–Ar bond dissociation energy of less than 3.0 kcal/mol.{{Citation |author=Grills D. C. |author2=George M. W. |title=Transition metal-noble gas complexes |date=2001 |work=Advances in Inorganic Chemistry |pages=113–150 |publisher=Elsevier |doi=10.1016/s0898-8838(05)52002-6 |isbn=978-0-12-023652-7}}. Held together entirely by the van der Waals force, helium dimer, He₂, has the lowest measured bond dissociation energy of only 0.022 kcal/mol.{{Cite journal |last1=Cerpa |first1=Erick |last2=Krapp |first2=Andreas |last3=Flores-Moreno |first3=Roberto |last4=Donald |first4=Kelling J. |last5=Merino |first5=Gabriel |date=2009-02-09 |title=Influence of Endohedral Confinement on the Electronic Interaction between He atoms: A He₂@C₂₀H₂₀ Case Study |journal=Chemistry – A European Journal |language=en |volume=15 |issue=8 |pages=1985–1990 |doi=10.1002/chem.200801399 |pmid=19021178 |issn=0947-6539}}{{Cite journal |last1=Giese |first1=Timothy J. |last2=York |first2=Darrin M. |date=2004 |title=High-level ab initio methods for calculation of potential energy surfaces of van der Waals complexes |url=https://onlinelibrary.wiley.com/doi/10.1002/qua.20074 |journal=International Journal of Quantum Chemistry |language=en |volume=98 |issue=4 |pages=388–408 |doi=10.1002/qua.20074 |issn=0020-7608|url-access=subscription }}

Bonds can be broken symmetrically or asymmetrically. The former is called homolysis and is the basis of the usual BDEs. Asymmetric scission of a bond is called heterolysis. For molecular hydrogen, the alternatives are:

:

In the gas phase, the enthalpy of heterolysis is larger than that of homolysis, due to the need to separate unlike charges. However, this value is lowered substantially in the presence of a solvent.

The data tabulated below shows how bond strengths vary over the periodic table.

There is great interest, especially in organic chemistry, concerning relative strengths of bonds within a given group of compounds, and representative bond dissociation energies for common organic compounds are shown below.

• Bond energy
• Electronegativity
• Ionization energy
• Electron affinity
• Lattice energy

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Dissociation energy

Category:Binding energy