Enthalpy of Formation of Selected Carbonyl Radicals

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Enthalpy of formation of selected carbonyl radicals from theory and

comparison with experiment

Viskolcza and TiborBe la Be rces*b

a Department of Chemistry, J. Gy. T eacherÏs T raining College, H-6701 Szeged, P.O. Box 396,

Hungaryb Chemical Research Center, Institute for Chemistry, Hungarian Academy of Sciences,

H-1525 Budapest, P.O. Box 17, Hungary

Recei ved 7th June 2000, Accepted 10th October 2000

First published as an Ad vance Article on the web 7th 2000No¿ember

Enthalpies of formation and entropies are calculated for 13 carbonyl radicals. Radicals of atmospheric

importance are selected for study. The CBS-4 (Complete Basis Set 4) and G2(MP2,SVP) ab initio molecular

orbital methods are used to obtain the thermodynamic properties of the radicals. In addition to the enthalpy

of formation determinations based on atomization energy computations, enthalpies of formation are derived

for and by studying the isodesmic reactionsCH3CO, CF3CO CCl3CO CH3 ] CH3CHO \ CH4 ] CH3CO,and Good agreement is foundCH

3] CF

3CHO \ CH

4] CF

3CO CH

3] CCl

3CHO \ CH

4] CCl

3CO.

between the results obtained by these two approaches. For comparison, carbonyl radical enthalpies of

formation are estimated by using recent experimental room temperature rate coefficients for reactions of a

bromine atom with a series of aliphatic aldehydes. Systematic comparison is made of the theoretical results

with these experimentally based data and recommendations for the enthalpies of formation of carbonyl

radicals and the formyl C ÈH bond dissociation energies in the appropriate aldehydes are presented. Finally,

theoretical results are used to obtain reaction heats for carbonyl radical decomposition by CO elimination,

and the atmospheric implications of the results are discussed.

1. Introduction

Accurate values for bond dissociation energies of moleculesand free radicals are essential in the modelling of atmosphericand combustion processes. In such studies, the enthalpy of formation of the appropriate free radical is used (i) in the cal-culation of the rate coefficient using kinetic data for thereverse reaction and (ii) in the estimation of the branchingratio for competitive processes.

Carbonyl free radicals (R ÈC2O) are important short-livedintermediates in the atmospheric degradation of volatileorganic compounds. Carbonyl radicals are formed mainly byhydrogen abstraction from aldehydes and, to a smaller extent,by halogen extrusion from acyl halides. The troposphericremoval of these radicals can occur in a number of waysincluding photolysis, hydrolysis or thermal reactions. Littlequantitative knowledge is available on the atmospheric fate of

the carbonyl free radicals. The major chemical reaction of these radicals is either decomposition by loss of a CO mol-ecule or combination with giving a peroxy radical. TheseO

2two reaction paths have di†erent impact on atmosphericozone formation and on the degradation product distribu-tion.1,2 Recently the thermal decomposition of acyl radicalswas investigated by direct Ñash photolysis1 and the com-petition between thermal decomposition and addition hasO

2been studied2 in a photochemical reaction chamber.

In this work, the thermochemistry of the decomposition of carbonyl radicals by CO elimination is investigated using abinitio molecular orbital methods. In order to test the consis-tency and reliability of the computed geometries and energies,two di†erent methods were used, which are described in the

next section. Computations were carried out for carbonyl rad-icals of atmospheric importance. Thus, Ðrst we dealt with rad-icals andCF

3CO, CCl

3CO, CH

22CHCO, HOCH

2CO

for which no data or reliable thermodynamicCH3

OCOproperties are known. is a degradation product of theCF

3CO

alternative halocarbons of the type such as HFC-CF3CX2H,143a HFC-134a HCFC-141b(CF3

CH3

), (CF3

CFH2

),and HCFC-123 while is a(CF

3CClH

2) (CF

3CCl

2H), CCl

3CO

degradation product of chloroethane In order to(CCl3

CH3

).test the reliability of the computational results obtained forthese radicals, our study was extended to simple RCO freeradicals (where R is an alkyl group) for which experimentalheats of formation are available.

2. Computational methods

Two type of calculations were used : (i) CBS-4,3 CBS-Q3 andin a few cases CBS-APNO;4 (ii) G2(MP2, SVP)5,6 andG3MP27 for the simpler free radicals. All closed and open shellspecies were calculated using restricted and unrestricted wave-

functions, respectively.Petersson and co-workers have developed a series of theo-

retical models,3,4 based on complete basis set extrapolation,with the aim of determining the projected second-order (MP2)energy in the limit of a complete basis set. Among thesemethods CBS-APNO4 is the most accurate, while CBS-4 isthe most widely applicable treatment. The geometries wereobtained at the UHF level of theory using the 3-21G* basisset. The harmonic vibrational frequencies were calculated atthe same level of theory. Thermodynamic functions wereobtained by standard thermodynamic methods8 using fre-quencies scaled by 0.9167.3 Internal rotations were treated asvibrational motions which may introduce errors in the calcu-lated entropies, heat capacities, thermal corrections and zero-

point energies.The G2(MP2,SVP) method5 is a variant of the G2(MP2)

theory in which the size of the basis set used in the QCISD(T)

5430 Phys. Chem. Chem. Phys., 2000, 2, 5430 È5436 DOI : 10.1039/b004548i

This journal is The Owner Societies 2000(



energy calculations is reduced from 6-311G(d,p) to 6-31G(d).The geometries and harmonic vibrational frequencies werecalculated at the MP2(full)/6-31G(d) level of theory. The fre-quency scaling factor of 0.9427, recommended by Scott andRadom,9 was used. Thermodynamic functions were obtainedin the same way as for the CBS computations. In the energycalculation, a higher-level empirical correction (HLC) of 4.94

per electron pair (as suggested by Curtiss et al.10) wasmEh

used in order to accommodate remaining deÐciencies. In addi-tion, a spin Èorbit correction to the total energy was applied10

for species containing halogen atoms (i.e. [0.61 per Ñuo-mEhrine atom and [1.34 per chlorine atom). The G3(MP2)mEh

energies were obtained as in case of G2(MP2,SVP) except thatthe MP2(fc)/6-311&G(3df,2p) basis set was replaced by theG3MP2 basis.7

The assessment, on a total 148 molecules in the G2 neutraltest set, gave average absolute deviations between computedand experimental enthalpies of formation for the CBS-4,11G2(MP2,SVP)10 and G3(MP2)7 methods of 3.06, 1.93 and1.18 kcal mol~1, respectively. In this paper we use CBS-4 forall studied species, G2(MP2,SVP) for all RCO radicals, as wellas G3(MP2) and CBS-Q for some selected carbonyl radicals.

All ab initio calculations were performed with the GAUSS-IAN 94 molecular orbital packages.12

The enthalpies of formation of the free radicals wereobtained in two di†erent ways which are designated as““Version AÏÏ and ““Version BÏÏ.

In Version A, the enthalpy of formation for a carbonylradical, with the formula is obtained from theC

nX

2n`1CO,

theoretical reaction enthalpy of the hypothetical reaction

(n ] 1)C ]2n ] 1

2X

2]

1

2O

2]C

nX

2n`1CO (1)

according to the equation

*fH

298¡ (C

nX

2n`1CO) \ H

298¡ (C

nH

2n`1CO, g) [ (n ] 1)

] [H298¡ (C

graphite, s) [*

fH

298¡ (C, g)]

[2n ] 1

2H

298¡ (X

2, g) [

1

2H

298¡ (O

2, g) (2)

where the designations represent the computed totalH298¡

energies including zero-point energies and thermal correc-tions, and g) \ 171.29 ^ 0.1 kcal mol~1 is the ele-*

fH

298¡ (C,

mental correction for the C atom taken from the JANAFtables.13

Version B is based on the atomization reaction

CnX

2n`1CO] (n ] 1)C ] (2n ] 1)X ] O. (3)

The enthalpy of atomization for radical at 0 K isCnX

2n`1CO

obtained from the computed total energies including zero-point energies :

*rH

0¡ \ (n ] 1)H

0¡(C) ] (2n ] 1)H

0¡(X)

] H0¡(O) [ H0¡(CnX2n`1CO) (4)

With this theoretical enthalpy of atomization and the experi-mental enthalpies of formation for the appropriate atoms(taken from the JANAF tables13), the 0 K enthalpy of forma-tion of the radical is calculated:

*fH

0¡(C

nX

2n`1CO) \ (n ] 1)*

fH

0¡(C) ] (2n ] 1)

]*fH

0¡(X) ]*

fH

0¡(O) [*

rH

0¡ . (5)

Finally, the enthalpy of formation at 298.15 K is obtainedfrom the 0 K value using the heat capacity correction (given insquare brackets) :

*fH

298¡ (C

nX

2n`1CO) \*

fH

0¡(C

nX

2n`1CO)

] [H

298¡ [ H

0¡]

CnX2n`1CO[; [H

298¡ [ H

0¡]

atoms(6)

The heat capacity correction for is calculated byCnX

2n`1CO

using the scaled vibrational frequencies in the harmonic

approximation, the classical approximation for the trans-lational (3/2 RT ) and rotational (3/2 RT and RT for the non-linear and linear species, respectively) contributions and thePV term. The heat capacity corrections for the atoms weretaken from the JANAF tables.13

Version A and version B calculations were carried out inorder to see how the results agree. Which of them gives moreaccurate results depends on the accuracy of the calculated andexperimental atomization energies of the appropriate diatomicmolecules used in Version A and Version B, respectively.

Version A was recently used to obtain enthalpies of formationof acyl radicals and in this study we test it for the calculationof the enthalpies of formation for hetero-atom-containingradicals.

3. Results and discussion

3.1 Geometries and vibrational frequencies

At the HF/3-21G* level of theory, two stable conformers werefound for all RCO radicals where R is a saturated group: acis- and a trans-conformer with C ÈC ÈC ÈO ( o r X ÈC ÈC ÈO)dihedral angles of 0¡ and 180¡, respectively. However, with theMP2(full)/6-31G* method, only the cis-conformers proved tobe stable species. For the optimized trans-conformers one of

the frequencies was negative, thus the trans-conformers maybe identiÐed most probably as rotational transition states.

Similar observations were made for in theCF3

COBAC-MP4 calculations14 where the cis-conformer (withF ÈC ÈC ÈO dihedral angle equal to 0¡) proved to be the stablespecies, while the trans-conformer (with F ÈC ÈC ÈO dihedralangle equal to 180 degree) had an imaginary vibrational fre-quency.

The geometries published by Francisco and Abersold15 forand correspond to the trans-conformers (X ÈCH

3CO CF

3CO

C ÈC ÈO dihedral angle equals 180¡). However, the CF3

COgeometry optimized at the UMP2/6-31G* level of theory byDibble and Francisco16 is the geometry of the stable cis-conformer (with 0¡ for the F ÈC ÈC ÈO angle).

Geometries of the carbonyl radicals were computed in thiswork at the HF/3-21G* and the MP2(full)/6-31G* level of theory. The results of the two calculations are similar, with afew percent shorter MP2 bond lengths.

Selected bond lengths and bond angles of the cis-conformers, optimized at the MP2(full)/6-31G* level, are givenin Table 1. Since no experimental bond lengths and angles are

Table 1 Selected bond lengths in and bond angles in degrees of A the RCO radicals optimized at the MP2(full)/6-31G* level

Radicals r1

r2

a1

a2

a3

b(X1

CCO)

CH3

CO 1.196 1.513 127.5 111.1 108.6 0.0C

2H

5CO 1.198 1.517 126.9 113.5 106.6 0.0

n-C3

H7

CO 1.198 1 .517 126.9 1 13.7 106.8 0 .0i-C

3H

7CO 1.197 1 .525 127.5 1 08.7 107.4 0 .0

tert-C4

H9

CO 1.198 1.531 127.5 110.9 107.0 0.0CH

22CHCO 1.197 1.485 129.4 118.9 117.8 23.1

CH22C(CH

3)CO 1.205 1.485 127.9 116.6 116.8 24.1

CF3

CO 1.186 1.551 123.2 112.7 108.6 0.0CCl

3CO 1.183 1.554 127.3 112.1 106.0 0.0

HOCH2

CO 1.191 1.538 126.4 113.3 106.2 169.9aCH

3OCO 1.201 1.324c 130.2 114.6 È 0.0b

HC(O)CO 1.195 1 .557 122.6 1 13.6 121.8 8 1.3a

CH3C(O)CO 1.196 1.552 124.6 114.2 119.2 83.7a

a OCCO angle. b COCO angle. c C ÈO bond length.

Phys. Chem. Chem. Phys., 2000, 2, 5430 È5436 5431



Table 2 Harmonic vibrational frequencies in cm~1 and rotational constants (in square brackets) obtained at the MP2(full)/6-31G* level, as wellas ZPE in kcal mol~1 and heat capacities in cal mol~1 K~1 for carbonyl radicals(C

v)

Radicals Frequencies and rotational constants ZPE Cv

CH3

CO 81, 469, 899, 991, 1093, 1421, 1525, 1525, 1979, 3110, 3217, 3220 26.3 10.7[2.744, 0.331. 0.313]

C2

H5

CO 103, 252, 253, 633, 761, 852, 1023, 1082, 1132, 1312, 1374, 1471, 44.0 15.11518, 1560, 1562, 1954, 3121, 3122, 3168, 3212, 3220[0.609, 0.197, 0.158]

n-C3

H7

CO 72, 160, 194, 254, 348, 656, 735, 870, 874, 961, 1094, 1108, 1160, 61.4 19.81290, 1328, 1362, 1426, 1475, 1514, 1555, 1565, 1569, 1949, 3105,

3109, 3123, 3153, 3173, 3196, 3197 [0.541, 0.086, 0078]i-C3

H7

CO 44, 231, 248, 278, 361, 446, 618, 797, 937, 965, 1005, 1110, 1184, 61.3 18.51233, 1343, 1382, 1457, 1476, 1549, 1553, 1565, 1569, 1949, 3109,3110, 3112, 3199, 3203, 3210, 3211 [0.261, 0.138, 0.102]

tert-C4

H9

CO 21, 231, 253, 281, 288, 351, 355, 400, 458, 576, 750, 878, 983, 990, 78.2 26.1999, 1067, 1087, 1282, 1286, 1307, 1452, 1454, 1482, 1540, 1546,1550, 1561, 1564, 1578, 1940, 3100, 3101, 3104, 3190, 3191, 3195,3200, 3202, 3204 [0.153, 0.093, 0.093]

CH22CHCO 270, 323, 592, 691, 970, 1013, 1031, 1107, 1343, 1483, 1705, 1965, 31.6 12.9

3220, 3274, 3320 [0.892, 0.205, 0.168]CH

22C(CH

3)CO 157, 199, 276, 382, 469, 590, 717, 912, 950, 1040, 1053, 1104, 47.1 18.4

1325, 1463, 1493, 1540, 1556, 1730, 1975, 3108, 3190, 3209, 3212,3309 [0.330, 0.135, 0.098]

CF3

CO 43, 241, 405, 417, 541, 545, 673, 813, 1233, 1267, 1285, 2230 13.1 16.9[0.186, 0.100, 0.100]

CCl3

CO 38, 195, 273, 277, 331, 403, 456, 601, 837, 871, 890, 2116 9.8 20.3[0.062, 0.056, 0.052]

HOCH2CO 132, 253, 363, 521, 857, 908, 1128, 1213, 1366, 1430, 1525, 1939, 29.2 14.23066, 3180, 3774 [1.505, 0.143, 0.135]

CH3

OCO 139, 287, 389, 763, 949, 1192, 1195, 1231, 1509, 1550, 1554, 1867, 30.0 13.03137, 3239, 3275 [0.746, 0.228, 0.181]

HC(O)CO 91, 346, 559, 818, 1010, 1399, 1903, 2637, 3079 [1.295, 0.179, 16.0 11.70.167]

CH3

C(O)CO 74, 118, 118, 373, 502, 502, 744, 983, 983, 1212, 1439, 1439, 1527, 32.4 17.21899, 1899, 3111, 3197, 3197 [0.313, 0.141, 0.104]

CH3

CHO 147, 515, 799, 926, 1168, 1170, 1439, 1467, 1527, 1535, 1801, 33.7 11.02993, 3107, 3187, 3237 [1.886, 0.337, 0.302]

CF3

CHO 68, 259, 314, 434, 528, 530, 708, 868, 992, 1244, 1259, 1374, 1437, 20.1 17.41806, 3074 [0.181, 0.099, 0.098]

CCl3

CHO 77, 212, 260, 284, 332, 339, 461, 652, 792, 902, 1035, 1082, 1424, 17.1 20.61805, 3065 [0.062, 0.055, 0.051]

available for the carbonyl radicals, the calculated data arecompared with the results of previous theoretical studies.Dibble and Francisco16 published UMP2/6-31G* optimizedgeometries for while Bauschlicher17 reported geo-CF

3CO,

metrical parameters for which were computed at theCH3

COMP2/6-311&G(3df,2p) level of theory. As expected, theUMP2(fc)/6-31G(d) results reported by Dibble and Franciscoagree reasonably with the similar (MP2(full)/6-31G(d) resultsobtained in this work. The MP2 geometry of CH

3CO

obtained with the larger, 6-311&G(3df,2p) basis set di†ers fromthat calculated with the smaller basis set by about 0.01 inA bond length and 1¡ in bond angle.

The geometry of the RCO type carbonyl radicals dependson the nature of the R moiety. If R is an alkyl group, the

distance is roughly constant at around 1.197 for allr1(C2O) A studied carbonyl radicals, while the distancer

2(C ÈCO)

increases from 1.513 to 1.531 as the C-atom number (andA simultaneously the size) of the R group increases from toC

1This increase of the C ÈCO bond length parallels theC

4.

decrease of the C ÈCO bond energy (see later). The a1

(OCC)angle is around 127¡, while the and anglesa

2(CCH) a

3(CCH)

are 112¡ and 107¡, respectively. The bond angles do notchange signiÐcantly with the nature of R.

Introduction of halogen or oxygen atoms in the alkyl Rgroup, shortens the and lengthens the dis-r

1(C2O) r

2(C ÈCO)

tances. An angle, signiÐcantly lower than thea1

(OCC)average, is obtained for CF

3CO.

If the R group is an unsaturated hydrocarbon group (as in

and a considerably shorterCH22CHCO CH22C(CH3)CO),interatomic distance is obtained compared to thatr

2(C ÈCO)

in the radicals with saturated R groups. This is obviously the

result of conjugation in the former case. For these radicals, thegeometries obtained in the HF/3-21G* and in the MP2(full)/6-31G* geometry optimizations are signiÐcantly di†erent: allheavy atoms lie in a plane in the geometry derived at the HF/ 3-21G* level, while at the MP2(full)/6-31G* level, the carbon-yl oxygen atom is outside the plane determined by the rest of the heavy atoms.

A large di†erence was found between the MP2/6-31G* andthe HF/3-21G* geometries in the case of the HC(O)COradical. Geometry optimizations for the HC(O)CO radicalcarried out at the HF/6-311G(d,p) and QCISD/6-311G(d,p)level gave similar results to those of the MP2(full)/6-31G(d)calculations, i.e. non-planar geometry. (The OCCO dihedralangle was about 90¡.) In addition, the total energy of the non-

planar HC(O)CO radical obtained in the CBS-4//HF/6-311G(d,p) computations was found to be lower by about 5kcal mol~1 than that of the planar species obtained with theCBS-4//HF/3-21G* method. Moreover, the energy of the non-planar HC(O)CO radical derived with the CBS-APNOmethod was in excellent agreement with that obtained in theG2(MP2,SVP) computations.

On the basis of these experiences we prefer to use, in thecase of the carbonyl radicals with unsaturated R groups ( i.e.

HC(O)CO andCH22CHCO, CH

22C(CH

3)CO, CH

3C(O)CO),

the non-planar geometry derived at the MP2(full)/6-31G(d) orHF/6-311(d,p) level of theory.

Although and HC(O)CO, as well asCH22CHCO

and are isoelectronic free rad-CH22C(CH)

3CO CH

3C(O)CO

icals, with unsaturated R groups, there are considerable di†er-ences in the structures of these RCO radicals depending uponwhether R contains an oxygen atom or not: Compared to the

5432 Phys. Chem. Chem. Phys., 2000, 2, 5430 È5436



distance in RCO radicals with saturated alkyl Rr2

(C ÈCO)groups, the interatomic distance is considerablyr

2(C ÈCO)

shorter if R is an unsaturated hydrocarbon group, while thisbond is longer if R is an oxygen-containing unsaturatedgroup.

The spin contamination in the equilibrium structures, calcu-lated at the UHF/6-311&G(3df,2p) level of theory, was foundto be low and the expectation value SS**T was 0.75 È0.80, i.e.close to the correct value of 0.75. In addition, the occupationnumbers of the UHF natural orbitals did not di†er signiÐ-

cantly from 2 or 0 below and above the Fermi level, respec-tively, indicating that the single-conÐguration UHFwavefunctions provide an acceptable description.

Unscaled harmonic vibrational frequencies and rotationalconstants, calculated at the MP2(full)/6-31G* level, are givenin Table 2. The frequencies, scaled with a factor of 0.9669,were used to obtain the zero-point energies (ZPE) and heatcapacities as well as heat capacity corrections (HCC). The(C

v),

MP2(full)/6-31G* zero-point energies are higher, by 0.4 kcalmol~1 on average than those obtained at the HF/3-21G* levelof theory.

Our MP2(full)/6-31G* frequencies calculated for CH3

COand are in good agreement with those obtained byCF

3CO

Bauschlicher17 with the MP2/6-311]G(3df,2p) method andthe frequencies computed by Melius14 using the BAC-MP4technique, respectively.

3.2 Enthalpies of formation for carbonyl radicals and formyl

C –H bond dissociation energies for aldehydes

The computed total energies, together with the ZPE and HCCvalues, were used to obtain the enthalpy of formation for thecarbonyl free radicals. The calculated standard enthalpies of formation, derived according to Version A and Version B, aresummarized in Table 3. This Table also lists the enthalpies of formation for three selected aldehydes. Among these, no ther-modynamic properties can be found in the literature for

and while may serve as a testCF3

CHO CCl3

CHO, CH3

CHOcompound for which the thermodynamic properties are well

established.In addition to the enthalpies of formation, standard

entropies are also given in Table 3 for the carbonyl radicals.In the calculation of these values, internal rotations weretreated as harmonic oscillators. Since these low frequencymotions make signiÐcant contributions to the entropies, thegiven entropy values may be considered only as roughapproximations. If accurate entropies are required, more

sophisticated treatments have to be used for the low frequencymotions (for such treatments see for instance ref. 18 and 19).

Comparing the enthalpies of formation obtained by VersionA and Version B, one Ðnds good agreement for most species.However, signiÐcant deviations occur for the CBS-4 results of the Ñuorine-containing species and as wellCF

3CO CF

3CHO,

as for the G2(MP2,SVP) results of the RCO radicals where Ris an oxygen-containing group (i.e. HOCH

2CO, CH

3OCO,

HC(O)CO and In all these cases lower enth-CH3

C(O)CO).alpies of formation are obtained with Version A than with

Version B. Since Version A is based on the computation of theenthalpy of formation of RCO from diatomic molecules (andC), we have checked both with the CBS and the G2 methodsthe accuracy of the enthalpies of formation calculation of thediatomic molecules. The calculated enthalpies of formation at298 K are given, in kcal mol~1, below in brackets. CBS-4method : G2(MP2,H

2([0.37), O

2(1.18), F

2(4.57), Cl

2(0.87).

SVP) method : AsH2

([0.61), O2

(3.03), F2

(0.26), Cl2

([1.03).can be seen, the enthalpies of formation of and areF

2O

2signiÐcantly overestimated by the CBS-4 and G2(MP2,SVP)methods which explains most of the di†erence between theVersion A and Version B results. Therefore, in our further dis-cussions only Version B results will be considered.

For comparison of the CBS-4 enthalpies of formation withthe G2(MP2,SVP) results (all Version B calculations), theRCO radicals and RCHO molecules may be divided into fourgroups:

(i) For species where R is an alkyl group, the G2(MP2,SVP)results are systematically higher than the CBS-4 enthalpies of formation. As a check, higher level computations were carriedout. Thus, CBS-Q (Version B) calculations gave [2.5 kcalmol~1 for the enthalpy of formation of while G3MP2CH

3CO

(Version B) computations resulted in [22.1 kcal mol~1 forthe enthalpy of formation of the radical.tert-C

4H

9CO

Although with these results the deviation decreased some-what, however, the basic problem remained.

Examining the series of RCO radicals with alkyl R group,one Ðnds that the di†erence between the G2(MP2,SVP) andCBS-4 results increases with increasing size of the R group. It

has been found recently,20 in a theoretical study of alkyl rad-icals, that the CBS-4 method underestimates the enthalpy of formation of these radicals. In order to compensate for this,an empirical correction has been suggested. Such an under-estimation of the enthalpies of formation by the CBS-4method may explain (at least partly) the di†erence betweenthe CBS-4 and G2 results.

The consistency of the results obtained by the two methods

Table 3 Standard entropies (in cal mol~1 K~1) and heats of formation (in kcal mol ~1) for carbonyl radicals and selected aldehydes, calculatedby di†erent theoretical models

CBS-4//HF/3-21G* G2(MP2,SVP)//MP2(full)/6-31G(d)

*

f

H

298

¡ *

f

H¡

298Radicals S¡ Version A Version B S¡ Version A Version B

CH3

CO 64.0 [3.5 [3.6 64.8 [3.2 [3.0C

2H

5CO 72.2 [9.6 [10.1 71.3 [7.3 [8.0

n-C3

H7

CO 79.8 [15.5 [16.4 78.8 [11.6 [13.0i-C

3H

7CO 79.2 [16.6 [17.6 79.0 [12.8 [14.3

tert-C4

H9

CO 83.0 [25.8 [27.3 85.9 [20.6 [22.9CH

22CHCO 67.1 25.2 23.7 66.8 23.7 23.8

CH22C(CH

3)CO 75.3 8.7 8.1 74.8 14.0 13.3

CF3

CO 77.6 [152.9 [145.6 77.8 [153.5 [151.9CCl

3CO 83.7 [16.9 [15.1 85.9 [13.9 [14.1

HOCH2

CO 69.4 [36.3 [35.8 69.8 [39.2 [37.5CH

3OCO 70.1 [38.4 [37.9 68.8 [42.5 [40.8

HC(O)CO 66.5 [11.7 [10.9 68.3 [17.5 [15.1CH

3C(O)CO 74.9 [29.7 [29.3 76.8 [31.5 [30.4

CH

3

CHO 62.4 [40.9 [41.2 62.7 [41.0 [41.2

CF3CHO 75.3 [192.9 [185.8 75.9 [195.0 [193.7CCl

3CHO 81.8 [58.1 [56.6 82.8 [55.8 [56.4




has been tested by means of BensonÏs group additivity rule.21With a reasonable assumption for the group value of thegroup adjacent to the radical center and with published groupcontributions,20,22 the unknown group additivity value (GAV)of could be derived. Using the enthalpies of forma-[C 0 O-C]tion of carbonyl radicals obtained by the G2(MP2,SVP)method (Version B), a GAV of 7.2 ^ 0.1 kcal mol~1 wasdetermined. However, when testing the CBS-4 results, strongdependence of the GAVs on size of the R group was observed;i.e. in the series from to the GAVsCH

3CO tert-C

4H

9CO,

varied as 6.5, 4.9, 4.0 and 2.8 kcal mol~1, respectively.Among the species belonging to this group, the experimen-tal enthalpy of formation for is known23 to beCH

3CHO

[39.73 kcal mol~1, and the recommended value for theradical, derived in a recent critical evaluation,24 isCH

3CO

[2.9 ^ 0.7 kcal mol~1. Both of these are somewhat closer tothe G2(MP2,SVP) results. However, the reported enthalpy of formation for (i.e. [10.2 ^ 1 kcal mol~1) agreesC

2H

5CO25

better with the CBS-4 calculations.(ii) In the case of the RCO radicals with unsaturated hydro-

carbon R group, again the G2(MP2,SVP) results are higherthan the CBS-4 enthalpies of formation. Considering the

enthalpy of formation of 23.7 kcal mol~1CH22CHCO

obtained in our CBS-Q calculation, a value around 24 kcalmol~1 appears to be well established by theory. This is higherby almost 7 kcal mol~1 than the experimental value.25 Alarger di†erence is found between the G2(MP2,SVP) andCBS-4 results for The comparison of theCH

22C(CH

3)CO.

data obtained for the two unsaturated radicals is in favor of the former one.

(iii) In the third set of radicals with oxygen-containing Rgroup (i.e. HC(O)CO andHOCH

2CO, CH

3OCO,

relatively small di†erences are found betweenCH3

C(O)CO),the CBS-4 and G2(MP2,SVP) results. However, in contrast tothe results obtained for radicals belonging to the Ðrst andsecond set, the enthalpies of formation computed by theCBS-4 method for radicals with oxygen-containing R groupare systematically higher than those obtained by the G2(MP2,SVP) procedure. Calculations were carried out with higher

level CBS methods. Thus, CBS-Q computations forand gave enthalpies of formation of HOCH

2CO CH

3OCO

[36.1 and [39.8 kcal mol~1, respectively. CBS-APNO com-putations resulted in the value of [15.4 kcal mol~1 forHC(O)CO. These values are higher than the CBS-4 resultsand bring the CBS enthalpies of formation close to theG2(MP2,SVP) results. No experimental enthalpies of forma-tion are available in the literature for this group of radicals.

(iv) The Ðnal set consists of free radicals and aldehydes with

halogen atoms in the R group. The greatest di†erence betweenthe CBS-4 and G2(MP2,SVP) results are found in this set,especially for the Ñuorinated species and ItCF

3CO CF

3CHO.

was found6,10 in G2 calculations that spin Èorbit correction([0.61 per Ñuorine atom and [1.34 per chlorinemE

hmE

hatom) is required for molecules containing two or morehalogen atoms. This correction, which decreases the di†erencein the calculated results, is still far from explaining the signiÐ-cant discrepancies. Although no reliable experimental enth-alpies of formation are available, however, BAC-MP4

computations were carried out for these species.14 The calcu-lated enthalpies of formation at 298 K are [145.8 and[185.1 kcal mol~1 for and respectively,CF

3CO CF

3CHO,

which are in excellent agreement with the CBS-4 data butdi†er considerably from the G2(MP2,SVP) results. Computa-tions with the G3MP2 method (Version B calculations) yield[150.3 and [12.5 kcal mol~1 for andCF

3CO CCl

3CO,

respectively, i.e. the discrepancy still exists with the CBS-4results.

In order to obtain further information on the enthalpies of formation of the halogenated carbonyl radicals andCF

3CO

calculations were carried out for three isodesmicCCl3

CO,reactions, i.e. for reactions

CH3

] CH3

CHO \ CH4

] CH2

CO (7)

CH3 ] CF

3CHO \ CH

4 ] CF3

CO (8)

CH3

] CCl3

CHO \ CH4

] CCl3

CO (9)

The reaction enthalpies at 298 K, computed by the CBS-4method, are : kcal mol~1,*

rH

7¡ \ [15.18 *

rH

8¡ \ [11.57

kcal mol~1 and kcal mol~1. Using the enth-*rH

9¡ \ [11.14

alpy of formation for as well asCH3

,24 CH4

,23 CH3

CHO,23those for and (this work, CBS-4 results),CF

3CHO CCl

3CHO

the following enthalpies of formation are obtained:kcal mol~1,*

fH

298¡ (CH

3CO) \ [1.9 *

fH

298¡ (CF

3CO) \

kcal mol~1 and kcal[143.7 *fH

298¡ (CCl

3CO) \ [14.8

mol~1. These values also support the computed CBS-4 enth-alpies of formation for andCF

3CO CCl

3CO.

Summarizing the above considerations, we conclude that

the theoretical enthalpies of formation of RCO radicals andRCHO molecules are best represented by the G2(MP2,SVP)results if R is a saturated or unsaturated hydrocarbon group.The enthalpies of formation of radicals with oxygen-containing R groups are equally well represented by the CBSand G2 results. Finally, the enthalpies of formation of specieswith halogen-containing R groups are best characterized bythe CBS-4 values. The data given in Table 4, under theheading ““TheoryÏÏ, are selected in accordance with this con-

Table 4 Enthalpies of formation for carbonyl radicals, and formyl C ÈH bond dissociation energies of aldehydes,a D*fH

298¡ (RCO),

in kcal mol~1H298¡ (RC(O) ÈH),

Experiment Theory RecommendationSpecies *

fH

298¡ D H

298¡ *

fH

298¡ D H

298¡ *

fH

298¡ D H

298¡

CH3

CO [3.5 88.3 [3.0 88.8 [3.2 ^ 0.2 88.6C

2H

5CO [9.7 87.9 [8.0 89.6 [8.7 ^ 0.7 88.9

n-C3

H7

CO [13.0 88.0 [13 ^ 1 88i-C

3H

7CO [16.7 87.7 [14.3 90.1 [15.3 ^ 00.9 89.1

tert-C4

H9

CO [27.1 84.0b [22.9 88.2b [24.6 ^ 1.5 86.5bCH

22CHCO 23.8 90.5b 24 ^ 3 91b

CH22C(CH

3)CO 13.3 88.4b 14 ^ 4 89b

CF3

CO [144.5 93.4 [144.7c 93.2 [144.6 ^ 0.4 93.3CCl

3CO [7.0 101.7 [15.0c 93.7

HOCH2

CO [37.5 90.0bCH

3OCO [40.8 96.5b

HC(O)CO [15.1 87.7CH

3C(O)CO [30.4 86.5

a The enthalpies of formation of the aldehydes were taken from ref. 23, or estimated b by the additivity method. c Average of CBS-4 values givenin Table 3 and derived from calculations for isodesmic reactions.




clusion: i.e. CBS-4 results are preferred for the halogen-containing species and G2MP2 computations for the rest of the radicals. (Naturally, due attention was paid in the evalu-ation to the results derived from the higher level computationsand from the study of isodesmic reactions. This explains thesmall di†erence in the case of a few theoretical values given inTable 4 and Table 3.)

3.3 Comparison of theoretical and experimental results

In the absence of reliable experimental enthalpies of formationfor the great majority of the studied carbonyl radicals, estima-tions were made using recently determined room temperaturerate coefficients for reactions of a bromine atom with a seriesof aliphatic aldehydes : 26

Br ] RCHO]HBr ] RCO (10)

Activation energies for the bromine atom reactions with alde-hydes, were estimated from the room temperature rateE

10,

coefficients by assuming cm3 mol~1 s~1k10

A10

\ 7.8] 1012(the recommended A-factor27 for reaction toBr ] CH

3CHO)

be valid for the whole reaction series studied. Finally, second-law values for the RCO enthalpies of formation were obtainedwith the estimated values and assumed activationE

10E

~10energies for the RCO ] HBr reactions. The assumptionsmade were : kcal mol~1 andE

~10 \ 0.0 ^ 2.0 E~10 \ 2.0

kcal mol~1 for reactions of RCO radicals without and^ 2.0with halogen (F or Cl) substituents, respectively. (A higheractivation energy appears reasonable for the attack of theelectrophilic and radicals on the hydrogenCF

3CO CCl

3CO

atom of HBr carrying a partial positive charge.) The results of estimations are given in Table 4 under the heading““ExperimentÏÏ.

In addition to the enthalpies of formation of carbonyl freeradicals, the formyl C ÈH bond dissociation energies for theappropriate aldehydes are also given in Table 4. In the calcu-lation of the bond dissociation energy, the enthalpy of forma-tion of the aldehyde is taken from ref. 23 or is estimated bythe group additivity method.22 (For andCF

3

CHO CCl

3

CHO,

the values obtained in this work were used.)The theoretical enthalpies of formation of carbonyl radicals,

where R is an alkyl group, are systematically higher than theexperiment-based estimations. Considering the formyl C ÈHbond dissociation energies, the experimental values show thedecreasing trend expected by intuition, while the theoreticalvalues are practically constant within the group. This resultsin an increased di†erence between theory and experiment asthe complexity of the R group increases.

Among the halogenated carbonyl radicals, the theoreticaland experimental enthalpy of formation for are inCF

3CO

good agreement and the corresponding formyl C ÈH bond dis-sociation energies in are close to the 91.1 ^ 1.9 kcalCF

3CHO

mol~1 value derived by Amphlett and Whittle28 from the

study of thermal bromination of triÑuoroacetaldehyde. Thus,the enthalpy of formation of appears to be well estab-CF

3CO

lished. However, signiÐcant di†erence occurs between thetheoretical and experimental heat of formation of the CCl

3CO

radical. Since only a rough value could be determined26 byexperiment for the rate coefficient of the reaction of Br

we prefer the theoretical value, although an] CCl3

CHO,underestimation in the computations can not be excluded.

In the last two columns, recommended values for the car-bonyl radical enthalpies of formation and the formyl C ÈHbond dissociation energies of the appropriate aldehydes aregiven. These are selected by taking into account both theexperimental and theoretical values, with somewhat moreweight given to the latter ones (i.e. the weighting factors of 1

and 1.5 were used for the experimental and theoretical values,respectively). In the case of the radical, no recom-CCl

3CO

mended value is given in Table 4 due to the signiÐcant devi-

ation of the theoretical and experimental based enthalpies of formation.

3.4 Carbonyl radical decomposition by CO elimination andatmospheric implications

Carbonyl radical decomposition products, formed by COelimination, have also been studied by ab initio computations.Calculated CBS-4 results obtained in this work, together withresults of similar calculations taken from the literature, arelisted in the second column of Table 5. The comparison of

these computational results with experimental data showsexcellent agreement. The only exception is the trichloromethylradical where the theoretical value is considerably lower thanthe experimental one. Similar disagreement was observed alsofor the trichloroacetyl radical (see Table 4). It appears that thetheoretical methods used in this study underestimate the enth-alpies of formation of the chlorinated species. It is to be men-tioned, however, that the experimental enthalpy of formationof indicated in Table 5 (just like the experimental valueCCl

3of given in Table 4) is rather uncertain. Therefore,CCl

3CO

new theoretical and especially experimental investigations of the thermochemistry of these chlorinated radicals are highlydesirable.

The recommended enthalpies of formation of the carbonyl

radicals (from Table 4) and the experimental values of thedecomposition products (from Table 5) were used to estimatethe reaction enthalpies for the CO elimination reactions of thecarbonyl radicals. The results are given in Table 6. Thedecomposition enthalpies are seen to depend strongly on thestructure of the R group of the RCO radical. Among the RCOradicals with alkyl R group, the calculated stability stronglydecreases with increasing branching at the C atom adjacent tothe carbonyl group. This observation is in full agreement withthe result of a very recent experimental study2 and is related

Table 5 Enthalpies of formation for carbonyl radical decompositionproducts in kcal mol~1

Species Theory (CBS-4) Experiment

CH3

34.720 35.124C

2H

528.820 28.424

n-C3

H7

24.120 23.924i-C

3H

721.020 21.024

tert-C4

H9

12.320 11.524CH

22CH 70.7 71.524

CH22C(CH

3) 58.4

CF3

[112.4 [112.413CCl

39.3 17.027

HOCH2

[3.4 [4.029CH

3O 6.6 4.930

HCO 10.2 10.413CO [26.2 [26.413

Table 6 Reaction enthalpy (in kcal mol~1) at 298 K of carbonylradical decomposition by CO elimination

Decomposition *rH

298¡ (RCO2R ] CO)

CH3

CO]CH3

] CO 11.9C

2H

5CO]C

2H

5] CO 10.7

n-C3

H7

CO]n-C3

H7

] CO 10.5i-C

3H

7CO] i-C

3H

7] CO 9.9

tert-C4

H9

CO] tert-C4

H9

] CO 9.7CH

22CHCO]CH

22CH ] CO 21.1

CH22C(CH

3)CO]CH

22C(CH

3) ] CO 18.0

CF3

CO]CF3

] CO 5.8CCl

3CO]CCl

3] CO 5.6

HOCH2

CO]HOCH2

] CO 7.1CH

3

OCO]CH

3

O ] CO 19.3

HC(O)CO]CHO ] CO [1.0CH

3C(O)CO]CH

3CO ] CO 0.8




Fig. 1 Correlation between the reaction enthalpies of CO elimi-nation, and the length of the ruptured bond,*

rH

298¡ , r

2(C ÈCO).

to the decrease of the elimination barrier in the reactionseries.1

Comparing the reaction enthalpy of CO elimination withthe length of the splitting bond in RCO, an inverse relation-ship is found between and as shown in Fig.

*rH

298¡ , r

2(C ÈCO)

1. This empirical correlation indicates the inverse trend in thereaction series between the change of the decompositionbarrier and the length of the bond to be ruptured.

On the basis of the reaction enthalpies of CO elimination,the studied carbonyl radicals may be divided into threegroups:

(i) Free radicals andCH22CHCO, CH

22C(CH

3)CO

are stable with respect to CO elimination. TheCH3

OCOatmospheric fate of the Ðrst two species is association reactionwith oxygen forming RC(O)OO type acyl-peroxy radicals. Forthe radical, another decomposition pathCH

3OCO (CO

2elimination) exists, which is exothermic by 18.2 kcal mol~1.Thus, the radical will preferably decompose byCH

3OCO

elimination in the atmosphere.CO

2(ii) Free radicals HC(O)CO, CH3C(O)CO, HOCH2CO,and are relatively unstable and are expectedCF

3CO CCl

3CO

mainly to decompose in the atmosphere. Following CO elimi-nation, the R product radical will enter into an associationreaction with and participate as an ROO radical in theO

2atmospheric processes.

(iii) Finally, the RCO radicals where R is an alkyl group,are of intermediate stability. The stability decreases withincreasing branching of the alkyl group. For these radicals,the competition between decomposition and association withoxygen has to be considered:

RCO ] M ]R ] CO ] M (11)

RCO ] O2

] M]RC(O)O2

] M (12)

On the basis of the reaction thermochemistry, the k11

/ k12

[O2

]ratio is expected to increase with increasing branching at theC atom next to the CO group. However, using kinetic data forreactions (11) and (12) it can be shown1,2 that decompositionis negligible in the atmosphere (at 298 K in 1 atm air) com-pared to reaction with O

2.

Acknowledgements

This work was supported by the European Commissionproject entitled AFCAR (contract no. IC20-CT97-0037) and

by the Hungarian Science Foundation (OTKA, contract No.:T029722 and F030436). B. V. is grateful for the award of aMagyary Postdoctoral Fellowship (AMFK 535/2).Zolta n

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Enthalpy of Formation of Selected Carbonyl Radicals

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