Benson group increment theory

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Benson group-increment theory (BGIT), group-increment theory, or Benson group additivity uses the experimentally calculated heat of formation for individual groups of atoms to calculate the entire heat of formation for a molecule under investigation. This can be a quick and convenient way to determine theoretical heats of formation without conducting tedious experiments. The technique was developed by professor Sidney William Benson [1] of the University of Southern California. It is further described in Heat of formation group additivity.

Contents

Heats of formations are intimately related to bond-dissociation energies and thus are important in understanding chemical structure and reactivity. [2] Furthermore, although the theory is old, it still is practically useful as one of the best group-contribution methods aside from computational methods such as molecular mechanics. However, the BGIT has its limitations, and thus cannot always predict the precise heat of formation.

Origin

Benson and Buss originated the BGIT in a 1958 article. [3] Within this manuscript, Benson and Buss proposed four approximations:

  1. A limiting law for additivity rules.
  2. Zero-order approximation. Additivity of atomic properties.
  3. First-order approximation. Additivity of bond properties.
  4. Second-order approximation. Additivity of group properties.

These approximations account for the atomic, bond, and group contributions to heat capacity (Cp), enthalpy (ΔH°), and entropy (ΔS°). The most important of these approximations to the group-increment theory is the second-order approximation, because this approximation "leads to the direct method of writing the properties of a compound as the sum of the properties of its group". [4]

The second-order approximation accounts for two molecular atoms or structural elements that are within relative proximity to one another (approximately 3–5  ångstroms as proposed in the article). By using a series of disproportionation reactions of symmetrical and asymmetrical framework, Benson and Buss concluded that neighboring atoms within the disproportionation reaction under study are not affected by the change.

Symmetrical
Asymmetrical

In the symmetrical reaction the cleavage between the CH2 in both reactants leads to one product formation. Though difficult to see, one can see[ clarify ] that the neighboring carbons are not changed as the rearrangement occurs. In the asymmetrical reaction the hydroxyl–methyl bond is cleaved and rearranged on the ethyl moiety of the methoxyethane. The methoxy and hydroxyl rearrangement display clear evidence that the neighboring groups are not affected in the disproportionation reaction.

The "disproportionation" reactions that Benson and Buss refer to are termed loosely as "radical disproportionation" reactions. [5] From this they termed a "group" as a polyvalent atom connected together with its ligands. However, they noted that under all approximations ringed systems and unsaturated centers do not follow additivity rules due to their preservation under disproportionation reactions. A ring must be broken at more than one site to actually undergo a disproportionation reaction. This holds true with double and triple bonds, as they must break multiple times to break their structure. They concluded that these atoms must be considered as distinct entities. Hence we see Cd and CB groups, which take into account these groups as being individual entities. Furthermore, this leaves error for ring strain, as we will see in its limitations.

Heats of formations for alkane chains Heats-formation-chain-alkanes1.gif
Heats of formations for alkane chains

From this Benson and Buss concluded that the ΔHf of any saturated hydrocarbon can be precisely calculated due to the only two groups being a methylene [C−(C)2(H)2] and the terminating methyl group [C−(C)(H)3]. [6] Benson later began to compile actual functional groups from the second-order approximation. [7] [8] Ansylyn and Dougherty explained in simple terms how the group increments, or Benson increments, are derived from experimental calculations. [9] By calculating the ΔΔHf between extended saturated alkyl chains (which is just the difference between two ΔHf values), as shown in the table, one can approximate the value of the C−(C)2(H)2 group by averaging the ΔΔHf values. Once this is determined, all one needs to do is take the total value of ΔHf, subtract the ΔHf caused by the C−(C)2(H)2 group(s), and then divide that number by two (due to two C−(C)(H)3 groups), obtaining the value of the C−(C)(H)3 group. From the knowledge of these two groups, Benson moved forward obtain and list functional groups derived from countless numbers of experimentation from many sources, some of which are displayed below.

Applications

Simple Benson model of isobutylbenzene Example1-BensonApps.svg
Simple Benson model of isobutylbenzene

As stated above, BGIT can be used to calculate heats of formation, which are important in understanding the strengths of bonds and entire molecules. Furthermore, the method can be used to quickly estimate whether a reaction is endothermic or exothermic. These values are for gas-phase thermodynamics and typically at 298 K. Benson and coworkers have continued collecting data since their 1958 publication and have since published even more group increments, including strained rings, radicals, halogens, and more. [8] [10] [11] [12] Even though BGIT was introduced in 1958 and would seem to be antiquated in the modern age of advanced computing, the theory still finds practical applications. In a 2006 article, Gronert states: "Aside from molecular mechanics computer packages, the best known additivity scheme is Benson's." [13] Fishtik and Datta also give credit to BGIT: "Despite their empirical character, GA methods continue to remain a powerful and relatively accurate technique for the estimation of thermodynamic properties of the chemical species, even in the era of supercomputers" [14]

When calculating the heat of formation, all the atoms in the molecule must be accounted for (hydrogen atoms are not included as specific groups). The figure above displays a simple application for predicting the standard enthalpy of isobutylbenzene. First, it is usually very helpful to start by numbering the atoms. It is much easier then to list the specific groups along with the corresponding number from the table. Each individual atom is accounted for, where CB−(H) accounts for one benzene carbon bound to a hydrogen atom. This would be multiplied by five, since there are five CB−(H) atoms. The CB−(C) molecule further accounts for the other benzene carbon attached to the butyl group. The C−(CB)(C)(H)2 accounts for the carbon linked to the benzene group on the butyl moiety. The 2' carbon of the butyl group would be C−(C)3(H) because it is a tertiary carbon (connecting to three other carbon atoms). The final calculation comes from the CH3 groups connected to the 2' carbon; C−(C)(H)3. The total calculations add to −5.15 kcal/mol (−21.6 kJ/mol), which is identical to the experimental value, which can be found in the National Institute of Standards and Technology Chemistry WebBook [15]

Diogo and Piedade used BGIT to confirm their results for the heat of formation of benzo[k]fluoranthene. Example2-BensonApps.svg
Diogo and Piedade used BGIT to confirm their results for the heat of formation of benzo[k]fluoranthene.

Another example from the literature is when the BGIT was used to corroborate experimental evidence of the enthalpy of formation of benzo[k]fluoranthene. [16] The experimental value was determined to be 296.6 kJ/mol with a standard deviation of 6.4 kJ/mol. This is within the error of the BGIT and is in good agreement with the calculated value. Notice that the carbons at the fused rings are treated differently than regular benzene carbons. [8] Not only can the BGIT be used to confirm experimental values, but can also to confirm theoretical values.

Scheme showing a simple application of BGIT to rationalize relative thermodynamics between an alkene (top) and a ketone (bottom). Example3 Benson Apps.svg
Scheme showing a simple application of BGIT to rationalize relative thermodynamics between an alkene (top) and a ketone (bottom).

BGIT also can be used for comparing the thermodynamics of simplified hydrogenation reactions for alkene (2-methyl-1-butene) and ketone(2-butanone). This is a thermodynamic argument, and kinetics are ignored. As determined by the enthalpies below the corresponding molecules, the enthalpy of reaction for 2-methyl-1-butene going to 2-methyl-butane is −29.07 kcal/mol, which is in great agreement with the value calculated from NIST, [15] −28.31 kcal/mol. For 2-butanone going to 2-butanol, enthalpy of reaction is −13.75 kcal/mol, which again is in excellent agreement with −14.02 kcal/mol. While both reactions are thermodynamically favored, the alkene will be far more exothermic than the corresponding ketone.

Limitations

As powerful as it is, BGIT does have several limitations that restrict its usage.

Inaccuracy

There is an overall 2–3 kcal/mol error using the Benson group-increment theory to calculate the ΔHf. The value of each group is estimated on the base of the average ΔΔHf0 shown above and there will be a dispersion around the average ΔΔHf0. Also, it can only be as accurate as the experimental accuracy. That's the derivation of the error, and there is nearly no way to make it more accurate.

Group availability

The BGIT is based on empirical data and heat of formation. Some groups are too hard to measure, so not all the existing groups are available in the table. Sometimes approximation should be made when those unavailable groups are encountered. For example, we need to approximate C as Ct and N as NI in C≡N, which clearly cause more inaccuracy, which is another drawback.

Ring strain, intermolecular and intramolecular interactions

In the BGIT, we assumed that a CH2 always makes a constant contribution to ΔHf0 for a molecule. However, a small ring such as cyclobutane leads to a substantial failure for the BGIT, because of its strain energy. A series of correction terms for common ring systems has been developed, with the goal of obtaining accurate ΔHf0 values for cyclic system. Note that these are not identically equal to the accepted strain energies for the parent ring system, although they are quite close. The group-increment correction for a cyclobutane is based on ΔHf0 values for a number of structures and represents an average value that gives the best agreement with the range of experimental data. In contrast, the strain energy of cyclobutane is specific to the parent compound, with their new corrections, it is now possible to predict ΔHf0 values for strained ring system by first adding up all the basic group increments and then adding appropriate ring-strain correction values.

The same as ring system, corrections have been made to other situations such as gauche alkane with a 0.8 kcal/mol correction and cis- alkene with a 1.0 kcal/mol correction.

Also, the BGIT fails when conjugation and interactions between functional groups exist, [17] [18] such as intermolecular and intramolecular hydrogen bonding, which limits its accuracy and usage in some cases.

Related Research Articles

Allenes

Allenes are organic compounds in which one carbon atom has double bonds with each of its two adjacent carbon centres. Allenes are classified as cumulated dienes. The parent compound of this class is propadiene, which is itself also called allene. Compounds with an allene-type structure but with more than three carbon atoms are members of a larger class of compounds called cumulenes with X=C=Y bonding.

Enthalpy of vaporization Energy to convert a liquid substance to a gas; a function of pressure

The enthalpy of vaporization, also known as the (latent) heat of vaporization or heat of evaporation, is the amount of energy (enthalpy) that must be added to a liquid substance to transform a quantity of that substance into a gas. The enthalpy of vaporization is a function of the pressure at which that transformation takes place.

The standard enthalpy of formation or standard heat of formation of a compound is the change of enthalpy during the formation of 1 mole of the substance from its constituent elements, with all substances in their standard states. The standard pressure value p⦵ = 105 Pa (= 100 kPa = 1 bar) is recommended by IUPAC, although prior to 1982 the value 1.00 atm (101.325 kPa) was used. There is no standard temperature. Its symbol is ΔfH⦵. The superscript Plimsoll on this symbol indicates that the process has occurred under standard conditions at the specified temperature (usually 25 °C or 298.15 K). Standard states are as follows:

  1. For a gas: the hypothetical state it would have assuming it obeyed the ideal gas equation at a pressure of 1 bar
  2. For a solute present in an ideal solution: a concentration of exactly one mole per liter (1 M) at a pressure of 1 bar
  3. For a pure substance or a solvent in a condensed state (a liquid or a solid): the standard state is the pure liquid or solid under a pressure of 1 bar
  4. For an element: the form in which the element is most stable under 1 bar of pressure. One exception is phosphorus, for which the most stable form at 1 bar is black phosphorus, but white phosphorus is chosen as the standard reference state for zero enthalpy of formation.
Hesss law

Hess' law of constant heat summation, also known as Hess' law, is a relationship in physical chemistry named after Germain Hess, a Switzerland-born Russian chemist and physician who published it in 1840. The law states that the total enthalpy change during the complete course of a chemical reaction is the same whether the reaction is made in one step or in several steps.

Cyclopropane

Cyclopropane is the cycloalkane with the molecular formula C3H6, consisting of three carbon atoms linked to each other to form a ring, with each carbon atom bearing two hydrogen atoms resulting in D3h molecular symmetry. The small size of the ring creates substantial ring strain in the structure.

A carbanion is an anion in which carbon is trivalent and bears a formal negative charge.

Exothermic reaction Chemical reaction that releases energy as light or heat

An exothermic reaction is a "reaction for which the overall standard enthalpy change ΔH⚬ is negative." Exothermic reactions usually release heat and entail the replacement of weak bonds with stronger ones. The term is often confused with exergonic reaction, which IUPAC defines as "... a reaction for which the overall standard Gibbs energy change ΔG⚬ is negative." A strongly exothermic reaction will usually also be exergonic because ΔH⚬ makes a major contribution to ΔG⚬. Most of the spectacular chemical reactions that are demonstrated in classrooms are exothermic and exergonic. The opposite is an endothermic reaction, which usually takes up heat and is driven by an entropy increase in the system.

The bond-dissociation energy (BDE, D0, or DH°) is one measure of the strength of a chemical bond A–B. It can be defined as the standard enthalpy change when A–B is cleaved by homolysis to give fragments A and B, which are usually radical species. The enthalpy change is temperature-dependent, and the bond-dissociation energy is often defined to be the enthalpy change of the homolysis at 0 K (absolute zero), although the enthalpy change at 298 K (standard conditions) is also a frequently encountered parameter. As a typical example, the bond-dissociation energy for one of the C−H bonds in ethane (C2H6) is defined as the standard enthalpy change of the process

Conformational isomerism Different molecular structures formed only by rotation about single bonds

In chemistry, conformational isomerism is a form of stereoisomerism in which the isomers can be interconverted just by rotations about formally single bonds. While any two arrangements of atoms in a molecule that differ by rotation about single bonds can be referred to as different conformations, conformations that correspond to local minima on the potential energy surface are specifically called conformational isomers or conformers. Conformations that correspond to local maxima on the energy surface are the transition states between the local-minimum conformational isomers. Rotations about single bonds involve overcoming a rotational energy barrier to interconvert one conformer to another. If the energy barrier is low, there is free rotation and a sample of the compound exists as a rapidly equilibrating mixture of multiple conformers; if the energy barrier is high enough then there is restricted rotation, a molecule may exist for a relatively long time period as a stable rotational isomer or rotamer. When the time scale for interconversion is long enough for isolation of individual rotamers, the isomers are termed atropisomers. The ring-flip of substituted cyclohexanes constitutes another common form of conformational isomerism.

In chemistry, a molecule experiences strain when its chemical structure undergoes some stress which raises its internal energy in comparison to a strain-free reference compound. The internal energy of a molecule consists of all the energy stored within it. A strained molecule has an additional amount of internal energy which an unstrained molecule does not. This extra internal energy, or strain energy, can be likened to a compressed spring. Much like a compressed spring must be held in place to prevent release of its potential energy, a molecule can be held in an energetically unfavorable conformation by the bonds within that molecule. Without the bonds holding the conformation in place, the strain energy would be released.

A non-covalent interaction differs from a covalent bond in that it does not involve the sharing of electrons, but rather involves more dispersed variations of electromagnetic interactions between molecules or within a molecule. The chemical energy released in the formation of non-covalent interactions is typically on the order of 1–5 kcal/mol (1000–5000 calories per 6.02 × 1023 molecules). Non-covalent interactions can be classified into different categories, such as electrostatic, π-effects, van der Waals forces, and hydrophobic effects.

Hyperconjugation

In organic chemistry, hyperconjugation refers to the delocalization of electrons with the participation of bonds of primarily σ-character. Usually, hyperconjugation involves the interaction of the electrons in a sigma (σ) orbital with an adjacent unpopulated non-bonding p or antibonding σ* or π* orbitals to give a pair of extended molecular orbitals. However, sometimes, low-lying antibonding σ* orbitals may also interact with filled orbitals of lone pair character (n) in what is termed 'negative hyperconjugation'. Increased electron delocalization associated with hyperconjugation increases the stability of the system. In particular, the new orbital with bonding character is stabilized, resulting in an overall stabilization of the molecule. Only electrons in bonds that are in the β position can have this sort of direct stabilizing effect — donating from a sigma bond on an atom to an orbital in another atom directly attached to it. However, extended versions of hyperconjugation can be important as well. The Baker–Nathan effect, sometimes used synonymously for hyperconjugation, is a specific application of it to certain chemical reactions or types of structures.

Boudouard reaction

The Boudouard reaction, named after Octave Leopold Boudouard, is the redox reaction of a chemical equilibrium mixture of carbon monoxide and carbon dioxide at a given temperature. It is the disproportionation of carbon monoxide into carbon dioxide and graphite or its reverse:

Heat of formation group additivity methods in thermochemistry enable the calculation and prediction of heat of formation of organic compounds based on additivity. This method was pioneered by S. W. Benson.

Thermodynamic databases for pure substances Thermodynamic properties list

Thermodynamic databases contain information about thermodynamic properties for substances, the most important being enthalpy, entropy, and Gibbs free energy. Numerical values of these thermodynamic properties are collected as tables or are calculated from thermodynamic datafiles. Data is expressed as temperature-dependent values for one mole of substance at the standard pressure of 101.325 kPa, or 100 kPa. Unfortunately, both of these definitions for the standard condition for pressure are in use.

Allylic strain

Allylic strain in organic chemistry is a type of strain energy resulting from the interaction between a substituent on one end of an olefin with an allylic substituent on the other end. If the substituents are large enough in size, they can sterically interfere with each other such that one conformer is greatly favored over the other. Allyic strain was first recognized in the literature in 1965 by Johnson and Malhotra. The authors were investigating cyclohexane conformations including endocyclic and exocylic double bonds when they noticed certain conformations were disfavored due to the geometry constraints caused by the double bond. Organic chemists capitalize on the rigidity resulting from allylic strain for use in asymmetric reactions.

A Bordwell thermodynamic cycle use experimentally determined and reasonable estimates of Gibbs free energy (ΔG˚) values to determine unknown and experimentally inaccessible values.

Radicals in chemistry are defined as reactive atoms or molecules that contain unpaired electrons in an open shell. The unpaired electrons cause radicals to be unstable and reactive. Reactions in radical chemistry can generate both radical and non-radical products. Radical disproportionation encompasses a group of reactions in organic chemistry in which two radicals react to form two different non-radical products. These reactions can occur with many radicals in solution and in the gas phase. Due to the unstable nature of radical molecules, disproportionation proceeds rapidly and requires little to no activation energy. The most thoroughly studied radical disproportionation reactions have been conducted with alkyl radicals, but there are many organic molecules that can exhibit more complex, multi-step disproportionation reactions.

In chemistry, the ECW model is a semi-quantitative model that describes and predicts the strength of Lewis acid–Lewis base interactions. Many chemical reactions can be described as acid–base reactions, so models for such interactions are of potentially broad interest. The model initially assigned E and C parameters to each and every acid and base. The model was later expanded to the ECW model to cover reactions that have a constant energy term, W, which describes processes that precede the acid–base reaction. This quantitative model is often discussed with the qualitative HSAB theory, which also seeks to rationalize the behavior of diverse acids and bases.

1,1-Dimethyldiborane

1,1-Dimethyldiborane is the organoboron compound with the formula (CH3)2B(μ-H)2BH2. A pair of related 1,2-dimethyldiboranes are also known. It is a colorless gas that ignites in air.

References

  1. ↑ https://articles.latimes.com/2012/jan/09/local/la-me-passings-20120109
  2. ↑ Benson, S. W. Journal of Chemical Education42, 502–518 (1965).
  3. ↑ Sidney W. Benson and Jerry H. Buss (September 1958). "Additivity Rules for the Estimation of Molecular Properties. Thermodynamic Properties". J. Chem. Phys. 29 (3): 546–572. Bibcode:1958JChPh..29..546B. doi:10.1063/1.1744539.
  4. ↑ Benson, S. W.; Buss, J. H. Journal of Chemical Physics, 29, 546–572 (1958).
  5. ↑ International Union of Pure and Applied Chemistry. "disproportionation". Compendium of Chemical Terminology (Accessed December 03, 2008).
  6. ↑ Souders, M.; Matthews, C. S.; Hurd C. O., Ind. & Eng. Chemistry, 41, 1037–1048 (1949).
  7. ↑ Benson, S. W.; Cruicksh, F. R.; Golden, D. M., et al. Chemical Reviews, 69, 279–324 (1969).
  8. 1 2 3 Benson, S. W.; Cohen, N. Chemical Reviews, 93, 2419–2438 (1993).
  9. ↑ Eric V. Anslyn and Dennis A. Dougherty, Modern Physical Organic Chemistry, University Science Books, 2006.
  10. ↑ S. W. Benson, Thermochemical Kinetics: Methods for the Estimation of Thermochemical Data and Rate Parameters 2d ed., John Wiley & Sons, New York, 1976.
  11. ↑ E. S. Domalski, E. D. Hearing, "Estimation of the Thermodynamic Properties of C–H–N–O–S–X Compounds at 298 K", J. Phys. Chem. Ref. Data, 22, 805–1159 (1993).
  12. ↑ N. Cohen, "Revised Group Additivity Values for Enthalpies of Formation (at 298 K) of C–H and C–H–O Compounds", J. Phys. Chem. Ref. Data, 25, 1411–1481 (1996).
  13. ↑ Gronert, S. J. Org. Chem., 71, 1209–1219 (2006).
  14. ↑ Fishtik, I.; Datta, R. J. Phys. Chem. A, 107, 6698–6707 (2003).
  15. 1 2 NIST Chemistry WebBook (accessed December 3, 2008).
  16. ↑ Diogo, H. P.; Piedade, M. E. M. J. Chem. Thermodynamics, 34, 173–184 (2002).
  17. ↑ Knoll, H. Schliebs, R.; Scherzer, H. Reaction Kinetics and Catalysis Letters, 8, 469–475 (1978).
  18. ↑ Sudlow, K.; Woolf, A. A. Journal of Fluorine Chemistry, 71, 31–37 (1995).
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