8240
J. Phys. Chem. 1996, 100, 8240-8249
Ab Initio Study of r-Chlorinated Ethyl Hydroperoxides CH3CH2OOH, CH3CHClOOH, and CH3CCl2OOH: Conformational Analysis, Internal Rotation Barriers, Vibrational Frequencies, and Thermodynamic Properties Tsan H. Lay, Lev N. Krasnoperov, Carol A. Venanzi, and Joseph W. Bozzelli*,† Departments of Chemical Engineering, Chemistry, and EnVironmental Science, New Jersey Institute of Technology, Newark, New Jersey 07102
Nikolai V. Shokhirev Department of Chemistry, UniVersity of Arizona, Tucson, Arizona 85721 ReceiVed: October 6, 1995; In Final Form: February 7, 1996X
Ab initio calculations were performed on CH3CH2OOH, CH3CHClOOH, and CH3CCl2OOH molecules using the Gaussian92 system of programs. Geometries of stable rotational conformers and transition states for internal rotation were optimized at the RHF/6-31G* and MP2/6-31G* levels of theory. Harmonic vibrational frequencies were computed at the RHF/6-31G* level of theory. Potential barriers for internal rotations were calculated at the MP2/6-31G**/HF/6-31G* level. Parameters of the Fourier expansion of the hindrance potentials have been tabulated. Standard entropies (S°298) and heat capacities (Cp(T)’s, 300 e T/K e 1500) were calculated using the rigid-rotor-harmonic-oscillator approximation based on the information obtained from the ab initio studies. Contributions from hindered rotors were calculated by summation over the energy levels obtained by direct diagonalization of the Hamiltonian matrix of hindered internal rotations. Enthalpies of formation for these three molecules were calculated using isodesmic reactions. Enthalpies of formation were calculated to be ∆Hf°298(CH3CH2OOH) ) -41.5 ( 1.5 kcal mol-1, ∆Hf°298(CH3CHClOOH) ) -50.9 ( 3.4 kcal mol-1, and ∆Hf°298(CH3CCl2OOH) ) -55.3 ( 2.2 kcal mol-1. Entropies (S°298) are calculated to be 76.1, 79.2 and 86.6 cal mol-1 K-1 for CH3CH2OOH, CH3CHClOOH, and CH3CCl2OOH, respectively.
Introduction Alkyl radicals are important intermediates in pyrolysis, oxidation, and photochemical reactions of hydrocarbons. Reactions of these radicals with molecular oxygen form alkylperoxy radicals, ROO. Alkyl hydroperoxide compounds are produced in the further reactions of alkylperoxy radicals, ROO, with the hydroperoxy radical, HOO:1-3
RH + OH (or R′) f R + H2O (or R′H) R + O2 T ROO ROO + HOO T ROOH + O2 Alkyl hydroperoxides are also formed Via H-atom abstraction by ROO from other hydrocarbon species with weakly bonded hydrogen atoms (e.g., R′′H, where the R′′ is an aldehydic or allylic group).4
ROO + R′′H f ROOH + R′′ Alkyl hydroperoxides are especially important intermediates in low-temperature oxidation (such as in the initial stages of combustion5,6 and in the atmospheric photochemical oxidation of hydrocarbons7,8). Organic hydroperoxides are also widely used in industry and are important in synthetic chemistry.9 Chlorinated hydrocarbons are present in the troposphere at levels somewhat lower than those of major hydrocarbon pollutants.10 The presence of a Cl atom on a carbon site, however, reduces the C-H bond energy by about 4.0 kcal/mol,11 † X
E-mail:
[email protected]. Abstract published in AdVance ACS Abstracts, April 1, 1996.
S0022-3654(95)02976-5 CCC: $12.00
leading to lower activation energies for abstraction of the hydrogen on the R-carbon. This may lead to a faster formation of chlorinated alkyl radicals and subsequently chlorinated alkyl hydroperoxides.12 There are relatively few experimental studies on the thermodynamic properties of alkyl hydroperoxides. One reason for this is the difficulty in accurate determination of structures because of the strong influence of intramolecular and intermolecular forces in the condensed phase (solvent effects, crystal packing effect, etc.). Rapid interconversion of conformers and the instability of alkyl hydroperoxides lead to complexities in the study of these species. Experimental studies on the heats of formation (∆Hf°298) of a few alkyl hydroperoxides have been reported. Experimental values of ∆Hf°298 are available for HOOH (-32.5 kcal/mol),13 C2H5OOH (-47.6 kcal/mol),14 i-C3H7OOH (-65.0 kca/mol),14 t-C4H9OOH (-58.8 kcal/mol),15 and several cycloalkyl hydroperoxides. Another experimental ∆Hf°298 value for ethyl hydroperoxide was reported with a high uncertainty, -45 ( 12 kcal/mol.16,17 Benson17 and Baldwin18 comment that the enthalpy data, -47.6 kcal/mol for C2H5OOH and -65.0 kca/ mol for i-C3H7OOH quoted by Cox and Pilcher,19 are inconsistent with data on other hydroperoxides. Benson17 estimated ∆Hf°298(C2H5OOH) ) -40.2 kcal/mol and ∆Hf°298(i-C3H7OOH) ) -49.3 kcal/mol based on the group additivity approach using 48.0 kcal/mol17 as O-O bond energies. Entropy (S°298) and heat capacity (Cp(T)) data for alkyl hydroperoxides frequently used by the thermodynamic and kinetic research communities were estimated using Benson’s group additivity (GA) scheme and group values,20 derived from data on dialkyl peroxides and H2O2.18 Benson’s GA approach has proven to be a useful method for © 1996 American Chemical Society
R-Chlorinated Ethyl Hydroperoxides the estimation of thermodynamic properties.21 The accuracy of the group additivity scheme for alkyl hydroperoxides, however, cannot be comprehensively assessed, since limited reliable thermodynamic property data are available. The thermodynamic properties of alkyl hydroperoxide compounds are actually not well studied and characterized. The objective of this work is to calculate the thermodynamic functions ∆Hf°298, S°298, and Cp(T), 300 e T/K e 1500) for CH3CH2OOH (a), CH3CHClOOH (b), and CH3CCl2OOH (c) using ab initio molecular orbital theory for the analysis of molecular conformations, barriers to internal rotations, and harmonic vibrational frequencies. To our knowledge, neither experimental nor ab initio MO studies have been published for the determination of molecular structures, rotational barriers, and vibrational frequencies of chlorinated alkyl hydroperoxides with more than two carbon atoms. A comparison of ab initio molecular orbital (MO) calculations with experimental data for peroxides concludes that there is no general computational procedure that yields accurate molecular geometries.22 Large basis sets including polarization functions predict correct skew conformations but give O-O bond lengths that are too short. Inclusion of electron correlation corrections can improve the O-O bond length.22,23a Although more advanced approaches (G1,24 G225) were suggested, no calculations have been done for alkyl hydroperoxide molecules at these levels of theory. The general performance of semiempirical MO calculations on alkyl hydroperoxides is also of interest, since these methods are often used when ab initio MO calculations are not accessible or economical. Calculation Methods All ab initio calculations were performed using the Gaussian92 system of programs26 on the Cray YMP at Pittsburgh Supercomputing Center and the DEC6430 at New Jersey Institute of Technology. Equilibrium and saddle-point geometries were completely optimized using the closed shell restricted Hartree-Fock (RHF) method and second-order Møller-Plesset (MP2) perturbation theory with analytical gradients27 with the 6-31G* (6-31G(d)) basis set (HF/6-31G* and MP2/6-31G*).28-30 Single-point energies for equilibrium structures and saddle-point structures between rotational conformers were also calculated at the MP2/6-31G**//HF/6-31G* level of theory.28-30 Vibrational frequencies were calculated for all rotational conformers and saddle-points using analytical second derivatives at the HF/ 6-31G* level. Zero-point vibrational energies (ZPVE) were scaled by the factor of 0.9 as recommended23b because of the systematic overestimation of the HF-SCF harmonic vibrational frequencies by about 10%. The bond lengths calculated at the HF/6-31G* level of theory of two electronegative first-row atoms, e.g., N-O, O-O, O-F, and F-F bonds, are found to be substantially smaller than the experimental values.23a Hehre et al.23a comment that these errors are due largely to the restriction of single-determinant wavefunctions, and even the simplest of correlation procedures, like MP2, leads to a significant bond lengthening and much better agreement with the experimental data.23a The optimization of the molecular geometries is therefore performed at the MP2/ 6-31G* level of theory as well as the HF/6-31G* level. Enthalpies of formation of the three title molecules were calculated using the “isodesmic reaction” approach.23c The more advanced procedures, G1 and G2, were not used to perform energy computations. The standard entropies (S°298) and heat capacities (Cp(T), 300 e T/K e 1500) were calculated using the rigid-rotor-harmonic-oscillator (RRHO) approximation.31
J. Phys. Chem., Vol. 100, No. 20, 1996 8241 The calculation of contributions from hindered internal rotation to thermodynamic properties is carried out using direct diagonalization of the Hamiltonian matrix (see below). Two sets of isodesmic reactions were used to determine the enthalpies of formation of the title species Via theoretical calculation of the reaction enthalpies. The first scheme is based on the reaction of CH3OOH with alkanes to form the desired alkyl hydroperoxides and CH4:
SCHEME 1 CH3OOH + C2H6 f CH3CH2OOH + CH4
(R1)
CH3OOH + C2H5Cl f CH3CHClOOH + CH4 (R2) CH3OOH + 1,1-C2H4Cl2 f CH3CCl2OOH + CH4
(R3)
The second scheme is based on the reaction of CH3OOH with the alcohols to form the desired alkyl hydroperoxides and CH3OH:
SCHEME 2 CH3OOH + CH3CH2OH f CH3CH2OOH + CH3OH (R4) CH3OOH + CH3CHClOH f CH3CHClOOH + CH3OH (R5) CH3OOH + CH3CCl2OH f CH3CCl2OOH + CH3OH (R6) The method of isodesmic reactions relies upon the similarity of bonding environments in the reactants and products that leads to cancellation of systematic errors in the ab initio MO calculation.23c The basic requirement of the isodesmic reaction is that the number of bonds of each formal chemical bond type is conserved in the reaction. For instance, there are nine C-H, one C-O, one O-O, one O-H, and one C-C bonds present in both reactants and products in reaction R1. The conservation of chemical bond types and numbers can be referred as the firstorder criterion for isodesmic reactions. An isodesmic reaction will lead to more accurate results if the correlations of next-nearest-neighbor atoms in reactants and products are also conserved besides the bonding types. A simple way to implement this consideration is to break down each molecule in the isodesmic reaction into groups (where a group is defined as a polyvalent atom (ligancy g2) in a molecule together with all of its ligands20) and verify whether the number of groups of each group type is equal in reactants and products. For example, ethanol, CH3CH2OH, is expressed as three groups: a C atom bound to a C atom and three H atoms (C/ C/H3), plus a C atom bound to a C atom, two H atoms, and an O atom (C/C/H2/O), plus an O atom bound to a C atom and a H atom (O/C/H). The number of groups is conserved in reactions R4, R5, and R6 in Scheme 2, while in reactions R1R3 in Scheme 1 it is not. For example, in reaction R4 the following groups are present in both reactants and products: C/H3/O, O/C/O, O/H/O, C/C/H3, C/C/H2/O, and O/C/H. In R1 the group C/H3/O is present in reactants and is not present in products. The conservation of the number of groups in the reaction can be referred to as the second-order criterion for isodesmic reactions. The enthalpies of reactions determined by ab initio MO calculations are therefore considered to be more reliable for the reactions in Scheme 2, since they conserve the correlations of next-nearest-neighbor atoms compared to the reactions in Scheme 1.
8242 J. Phys. Chem., Vol. 100, No. 20, 1996
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TABLE 1: Comparison of Geometry Parametersa and Rotational Barriersb of H2O2 Determined by Far-IR and Microwave Spectroscopy and Molecular Orbital Calculations authors c
Busing, Levy, 1965 Khachkuruzov, Przhevalski,d 1974 Cremer,e 1978 Hehre et al.,f 1985 Chung-Phillips et al.,g 1995 this study this study
method
R(OH)
R(OO)
θ(HOO)
θ(HOOH)
neutron diffraction IR or MW (re) ab initio (11s6p2d/6s2p) ab initio (HF/6-31G*) ab initio (MP2/6-311+G(3df,2p)) AM1 PM3
0.988
1.453
102.7
90.2
0.965
1.452
100
0.967
1.451
0.949
1.393
0.964 0.983 0.945
V(trans)
V(cis)
119.3
1.1
7.4
102.2
115.2
0.9
9.2
1.441
100.1
111.9
1.2
7.8
1.300 1.482
106.0 96.5
128.1 179.6
119.1
a Bond distances (R) on Å. Bond angles and dihedral angles (θ) in degrees. b Barriers (V) in kcal/mol. c Reference 42. d Reference 43. The authors calculate the re values from the spectroscopic data of following literature. Redington, R. L.; Olson, W. B.; Cross, P. C. J. Chem. Phys. 1962, 36, 1311. Hunt et al. (ref 46). Oelke et al. (ref 47). e Reference 44. f Reference 23d. g Reference 45.
The value of ∆Hf°298(CH3OOH) was estimated to be -32.1 kcal/mol32 or -31.3 kcal/mol.20 Benassi et al.9 reported a third value: ∆Hf°298(CH3OOH) ) -33.0 kcal/mol. We used the experimentally determined value of ∆Hf°298(CH3OO) ) 2.70 ( 0.80 kcal/mol33 with an average bond energy, 88.2 ( 0.4 kcal/mol for the O-H bond in ROOH compounds,34 to estimate ∆Hf°298(CH3OOH) to be -33.4 ( 1.2 kcal/mol. This ∆Hf°298, -33.4 ( 1.2 kcal/mol, is in agreement with the number reported by Benassi et al.9 and is used in isodesmic reactions in this work to calculate ∆Hf°298 of the title species. There is a lack of experimental data on the enthalpies of formation of CH3CHClOH and CH3CCl2OH, which are required in Scheme 2. We estimate these values using ∆Hf°298(CH3CH2OH) and the enthalpy increments resulting from one and two chlorine substitutions on the R-carbon. Three sets of compounds and their enthalpies (in kcal/mol) are used to derive enthalpy increments due to chlorine substitutions: (i) C3H8 (-24.8),35 2-C3H7Cl (-35.0),35 2,2-C3H6Cl2 (-42.0);35 (ii) CH3OH (-48.1),35 CH2ClOH (-55.5),36 CHCl2OH (-66.6)36; (iii) C‚H2CH2OH (-4.6),36 C‚H2CHClOH (-15.2),36 C‚H2CCl2OH (-22.8).36 The average enthalpy increment due to the mono-chlorine substitution is -9.4 ( 2.0 kcal/mol and that for di-chlorine substitution is -18.0 ( 0.8 kcal/mol. ∆Hf°298(CH3CHClOH) and ∆Hf°298(CH3CCl2OH) then are estimated to be -65.5 ( 2.1 kcal/mol and -74.1 ( 0.9 kcal/mol, respectively, based on ∆Hf°298(CH3CH2OH) being equal to -56.1 ( 0.2 kcal/ mol.35 The harmonic vibrational frequencies calculated at the HF/ 6-31G* level of theory and the moments of inertia of molecular structures optimized at MP2/6-31G* were used to calculate the entropies and heat capacities. The AM137,38 and PM339 methods in the MOPAC 6.040 package were used to perform the semiempirical MO calculations. The molecular geometries and vibrational frequencies of the three title molecules were calculated with AM1 and PM3 parameters and compared to those obtained from the ab initio studies at the MP2/6-31G* and HF/6-31G* levels of theory. Calculation of Hindered Rotation Contribution to Thermodynamic Parameters A technique for the calculation of thermodynamic functions from hindered rotations with arbitrary potentials has been developed.41 This technique employs expansion of the hindrance potential in the Fourier series, calculation of the Hamiltonian matrix in the basis of the wave functions of free internal rotation, and subsequent calculation of energy levels by direct diagonalization of the Hamiltonian matrix.
In this work the torsional potential calculated at discrete torsional angles is represented by a truncated Fourier series:
V(φ) ) a0 + a1 cos(φ) + a2 cos(2φ) + a3 cos(3φ) + b1 sin(φ) + b2 sin(2φ) (F1) where values of the coefficients ai were calculated to provide the true minima and maxima of the torsional potentials with allowance of a shift of the theoretical extrema angular positions. Evaluation of the matrix elements of individual sine and cosine terms in the basis of the free rotor wave functions is straightforward. The terms sin(mφ) and cos(mφ) induce transitions with ∆K ) (m, where K is the rotational quantum number. Moreover, the matrix element does not depend on K, which leads to a simple form of the Hamiltonian matrix. The matrix has a band structure and consists of diagonal terms that are equal to those of the free rotor and subdiagonals of constant values that correspond to a different terms in the potential expansion, F1. The Hamiltonian matrix is then truncated to the size of 2Kmax + 1, where Kmax is the maximum rotational quantum number considered. The choice of the size of the truncated matrix is made by checking the independence of the thermodynamic properties calculated on Kmax. The truncated matrix (in reduced dimensionless form) is diagonalized, and the eigenvalues are used to calculate the partition function, entropy, heat capacity, etc. using direct summation over the calculated energy levels according to standard expressions of statistical thermodynamics.31 Results and Discussion HOOH and CH3OOH. Hydroperoxide, the simplest peroxide molecule, has been studied extensively.42-48 The comparison of the experimental determination, ab initio, and semiempirical (AM1, PM3) MO calculations for the conformational parameters and rotational barriers for H2O2 is listed in Table 1. The O-O bond length in H2O2 was determined to be 1.453 Å by Busing et al.42 using neutron diffraction and to be 1.452 Å by Khachkuruzov and Przhevalskii43 using IR spectroscopy. It should be noted that the ab initio bond length re corresponds to the position at the minimum in a potential energy that differs from those obtained experimentally, such as rR (from X-ray diffraction), rg (from electron diffraction), rs (from microwave or IR spectroscopy), etc., which are averaged over vibrational motion.49-51 The bond length reported by Khacuruzov and Przhevalskii,43 however, is re, obtained by correction of rs determined from IR and microwave spectra.
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J. Phys. Chem., Vol. 100, No. 20, 1996 8243
Figure 1. Definitions of nomenclature used in this work (m ) a if X ) Y ) H; m ) b if X ) H and Y ) Cl; m ) c if X ) Y ) Cl. “S” in the first position of the three-letter combination stands for “staggered”; “S” in the third position stands for “skew”; “E” stands for “eclipsed”; “T” stands for “trans”; “G” stands for “gauche”).
Cremer’s ab initio O-O bond length, 1.451 Å,44 is in excellent agreement with the experimental data. The calculation at the HF/6-31G* level gives the O-O bond length of 1.393 Å,23d which is too short, and that at the MP2/6-311+G(3df,2p) level results in an improved value, 1.441 Å.45 The two semiempirical methods, AM1 and PM3, do not provide an accurate O-O bond length; they give 1.300 and 1.482 Å, respectively. The skew conformation of HOOH with a dihedral angle of about 110-120° is the most stable.43-45 The potential energy curve for the HOOH internal rotation is, however, rather flat in the region around the trans conformation (dihedral angle ∠HOOH ) 180°) with about 1 kcal/mol barrier height (see Table 1). The barrier at the cis conformation (∠HOOH ) 0°) was determined to be about 7.0 kcal/mol by Hunt et al.46 and Oelfke et al.47 using infrared spectroscopy, compared to 7.4 and 7.94 kcal/mol reported by Cremer 44 and Radom et al.48 using ab initio MO calculations at the (11s6p2d/6s2p) and HF/4-31G levels of theory, respectively. The calculation at the HF/6-31G* level gives 9.2 kcal/mol23d as the barrier height at the cis conformation, which is about 2 kcal/mol higher than the above data, and that at the MP2/6-311+G(3df,2p) level leads to an improved value, 7.8 kcal/mol.45 The equilibrium geometry for methyl hydroperoxide (CH3OOH) was determined from microwave spectra52 to be the COOH skew conformation with (rs values) rOO ) 1.443 Å, rCO ) 1.437 Å, and 114° as the COOH dihedral angle (∠COOH). We calculate the geometry parameters of CH3OOH to be rOO ) 1.471 Å, rCO ) 1.422 Å, and ∠COOH ) 104° at the MP2/
6-31G* level of theory, which are in good agreement with the experimental data. The results of calculations at the HF/4-21G(O*) level,53 rOO ) 1.412 Å, rCO ) 1.422 Å, and ∠COOH ) 111°, are also in reasonable agreement with experimental data. The O-O bond length calculated at the HF/6-31G* level of theory, 1.394 Å,9 is too small. The calculations using the AM1 and PM3 methods give an O-O bond length of 1.304 and 1.525 Å, respectively. The C-O bond length obtained by the HF/631G* method9 is 1.399 Å, by the AM1 method, 1.436 Å, and by the PM3 method, 1.388 Å. The COOH dihedral angle in the most stable conformation was calculated to be 119° at the HF/6-31G* level,9 and it appears to be 137° and 180° using the AM1 and PM3 methods, respectively. No experimental data for CH3OOH rotational barriers have been published. The rotational barrier at the COOH cis conformation was determined to be 7.80 kcal/mol at the HF/ 4-21G(O*) level,53 7.99 kcal/mol at the HF/4-31G level,48 and 7.74 kcal/mol at the HF/6-31G* level.9 The barrier of another internal rotation for CH3OOH about the C-O bond was determined to be 2.94 kcal/mol determined at the HF/4-21G(O*) level of theory.53 CH3CH2OOH, CH3CHClOOH, and CH3CCl2OOH. The definitions and nomenclature for all rotational conformers that are used in the following discussions are illustrated in Figure 1. Selected parameters of the optimized geometry for each conformer are listed in Table 2. Harmonic vibrational frequencies were calculated for all rotational conformers and transition states. All vibrational frequencies and zero-point vibrational
8244 J. Phys. Chem., Vol. 100, No. 20, 1996
Lay et al.
TABLE 2: Selected Bond Lengths of Conformers Optimized at Different Levels of Theorya
CH3CH2OOH level 1a level 2a level 1 level 2 level 1 level 2
CC CO OO
CH3CHClOOH CC C2Cl6 CO OO
level 1 level 2 level 1 level 2 level 1 level 2 level 1 level 2
CH3CCl2OOH CC C2Cl6 CO OO
level 1 level 2 level 1 level 2 level 1 level 2 level 1 level 2
aSTSb
aETS
aSGS
aSEHS
aSECS
aSTT
aSTC
1.5168 1.5161 1.4060 1.4285 1.3932 1.4707
1.5314 1.5297 1.4087 1.4317 1.3926 1.4696
1.5188 1.5157 1.4068 1.4300 1.3960 1.4724
1.5177 1.5157 1.4166 1.4419 1.3930 1.4685
1.5183 1.5158 1.4236 1.4511 1.3915 1.4654
1.5168 1.5159 1.4030 1.4244 1.4020 1.4800
1.5163 1.5154 1.4001 1.4228 1.3987 1.4758
bSTSc
bETS
bSGC-HS
bSGC-ClS
bSEHS
bSECS
bSEClS
bSTT
bSTC
1.5112 1.5098 1.8191 1.8132 1.3738 1.3981 1.3866 1.4616
1.5269 1.5244 1.8218 1.8163 1.3753 1.3997 1.3858 1.4607
1.5143 1.5084 1.8034 1.7779 1.3795 1.4293 1.3933 1.4744
1.5112 1.5116 1.7851 1.7986 1.4002 1.4035 1.3957 1.4720
1.5102 1.5079 1.8176 1.8120 1.3857 1.4133 1.3902 1.4654
1.5137 1.5098 1.8070 1.8017 1.3955 1.4243 1.3928 1.4698
1.5142 1.5112 1.7827 1.7724 1.4149 1.4536 1.3821 1.4512
1.5128 1.5117 1.8090 1.8045 1.3723 1.3943 1.3980 1.4778
1.5117 1.5102 1.8167 1.8132 1.3682 1.3912 1.3949 1.4724
cSTSd
cETS
cSGS
cSEClS
aSECS
cSTT
cSTC
1.5164 1.5132 1.7978 1.7796 1.3678 1.3929 1.3835 1.4570
1.5354 1.5305 1.8015 1.7828 1.3701 1.3956 1.3826 1.4563
1.5157 1.5094 1.7720 1.8002 1.3814 1.4105 1.3880 1.4640
1.5171 1.5104 1.7721 1.7662 1.3979 1.4315 1.3820 1.4483
1.5173 1.5108 1.7846 1.7977 1.3834 1.4140 1.3897 1.4646
1.5176 1.5150 1.7878 1.7884 1.3633 1.3855 1.3954 1.4746
1.5150 1.5114 1.7883 1.8011 1.3567 1.3787 1.3929 1.4686
a Level 1: the conformers were optimized at HF/6-31G*; Level 2: the conformers were optimized at MP2/6-31G*. b COOH dihedral angle of aSTS: 116.52° (HF/6-31G*) and 119.19° (MP2/6-31G*). c COOH dihedral angle of bSTS: 93.89° (HF/6-31G*) and 93.71° (MP2/6-31G*). d COOH dihedral angle of cSTS: 97.54° (HF/6-31G*) and 94.21° (MP2/6-31G*).
frequencies (ZPVE) are scaled by 0.9 for all thermodynamic calculations. The rotational barriers and unscaled ZPVE are listed in Table 3. The values of the coefficients of the components of the Fourier expansion, ai and bi in equation F1 are listed in Table 4. Molecular Geometries. Effects of Including Electron Correlation on Molecular Geometries. The geometries of aSTS geometry were optimized at the HF/6-31G* and MP2/6-31G* levels of theory (see Table 2 for a comparison of selected bond lengths). The O-O bond length at the MP2/6-31G* level, 1.471 Å, is in good agreement with the experimental values, 1.443 Å of CH3OOH (rs values)52 and 1.452 Å of HOOH,43 while it is underestimated to be 1.393 Å at the HF/6-31G* level. The calculations at the HF/6-31G* level usually result in a bond between two electronegative first-row atoms which is too short,23a and this is improved by using MP2/6-31G*.23a The C-O bond length of aSTS is also slightly underestimated at the HF/6-31G* level to be 1.406 Å compared to the experimental value, 1.437 Å of CH3OOH (rs values),52 and it is calculated to be 1.429 Å at the MP2/6-31G* level. Both the HF/6-31G* and MP2/6-31G* methods predict skew as the most stable conformation, with the corresponding COOH dihedral angle 116.5° and 119.2°, respectively. Effects of Chlorine R-Substitution on Molecular Geometries. The C-C bond lengths in the equilibrium conformations of the three title molecules, aSTS, bSTS, and cSTS, optimized at the MP2/6-31G* level are similar, while the C-O bond lengths decrease in order: 1.429 Å in a, 1.398 Å in b, and 1.393 Å in c. The O-O bond length also decreases in this series from 1.471 Å in a to 1.462 Å in b to 1.457 Å in c. These trends of
C-O and O-O bond lengths are also observed in the geometries optimized at the HF/6-31G* level of theory. The skew conformations are the most stable in all three molecules, with the COOH dihedral angles (optimized at MP2/6-31G*) being 119.2°, 93.7°, and 94.2° for a, b, and c, respectively. The trans conformation of (CH3)CHCl-O(OH) and (CH3)CCl2-O(OH) (dihedral angle CCOO ≈ 180°) is more stable than the gauche (dihedral angle COOO ≈ 60° or -60°). This indicates that the electronic repulsion between the hydroxyl group (OH) and the methyl (CH3) group is stronger than that between the OH group and the Cl atom. The electronic repulsion between the OH group and the CH3 group is similar to that between the OH group and the hydrogen atom on the R-carbon in CH3CH2OOH, since the two conformers aSTS (dihedral angle CCOO ≈ 180°) and aSGS (dihedral angle COOO ≈ 60°) have equal potential energies. Rotational Barriers. The barriers for internal rotations are calculated to be the difference between the total energy of each conformation and that of the global equilibrium plus the scaled ZPVE difference (see Table 3). The barriers calculated at the MP2/6-31G**//HF/6-31G* level are consistent with those calculated at the MP2/6-31G*//MP2/6-31G* level, although the geometries of these molecules optimized at the HF/6-31G* level are known to result in O-O bonds that are too short. The discussion about rotational barriers is based on the results obtained at the MP2/6-31G*//MP2/6-31G* level unless otherwise noted. Barriers for Internal Rotations about C-C Bonds. The barrier for the internal rotation of the methyl group increases from 3.27 kcal/mol in a to 4.26 kcal/mol in b and 4.58 kcal/
R-Chlorinated Ethyl Hydroperoxides
J. Phys. Chem., Vol. 100, No. 20, 1996 8245
TABLE 3: Barriers for Internal Rotations and Zero-Point Vibrational Energies (ZPVE) rotational barrier (kcal/mol)a HF/6-31G*// HF/6-31G*
MP2/6-31G**// HF/6-31G*
0 3.35 0.36 2.96 6.34 0.49 7.42
0 3.32 -0.13 2.93 6.17 0.46 6.67
0 5.29 4.21 4.27 4.44 9.47 12.43 2.87 9.51
0 4.39 4.94 3.69 4.78 9.46 12.66 2.73 8.43
0 4.87 1.07 9.85 6.55 2.16 6.41
0 4.65 1.01 9.96 6.97 2.08 5.35
MP2/6-31G*// MP2/6-31G*
c
Z1
ZPVE (kcal/mol)b Z2d
Z3e
56.46
56.35
CH3CH2OOH aSTSf aETS aSGS aSEHS aSECS aSTT aSTC
0 3.27 -0.08 3.05 6.36 0.35 6.94
56.29 56.41
0 4.26 4.82 3.71 4.87 9.56 12.50 2.63 8.72
50.06 50.73
0 4.58 0.77 8.50 7.01 1.96 5.48
43.95 43.98
56.51 56.46 56.65 56.40 56.36
CH3CHClOOH bSTS bETS bSGC-HS bSGC-ClS bSEHS bSECS bSEClS bSTT bSTC
50.18
50.02
50.55 50.62 50.62 50.59 50.53 50.39 50.65
CH3CCl2OOH cSTS cETS cSGS cSEClS cSECS cSTT cSTC
44.04
43.88
44.01 43.81 44.00 43.85 43.82
a Rotational barriers were calculated as the difference in total energies + scaled (0.9) zero-point vibrational energies, where the corresponding torsional frequencies were excluded in the calculation of ZPVE. b Unscaled zero-point vibrational energy, in kcal/mol. The total ZPVE of the three molecules are 56.66 kcal/mol for CH3CH2OOH 50.39 kcal/mol for CH3CHClOOH and 44.26 kcal/mol for CH3CCl2OOH. c ZPVE with the frequency of torsion motion about the C-C bond excluded. d ZPVE with the frequency of torsion motion about the C-O bond excluded. e ZPVE with the frequency of torsion motion about the O-O bond excluded. f The total energies (in hartree) of aSTS are -228.836 727 8 at the HF/6-31G*, -229.508 236 0 at the MP2/6-31G**//HF/6-31G*, and -229.460 918 8 at the MP2/6-31G*. g The total energies (in hartree) of bSTS are -687.744 773 9 at the HF/6-31G*, -688.539 071 7 at the MP2/6-31G**//HF/6-31G*, and -688.500 295 9 at the MP2/6-31G*. h The total energies (in hartree) of cSTS are -1146.633 329 4 at the HF/6-31G*, -1147.556 375 7 at the MP2/6-31G**//HF/6-31G*, and -1147.525 451 7 at the MP2/6-31G*.
TABLE 4: Coefficientsa (kcal/mol) of Truncated Fourier Series Representation Expansions for Internal Rotation Potentials rotors C-C bond CH3-CH2OOH CH3-CHClOOH CH3-CCl2OOH C-O bond CH3CH2-OOH CH3CHCl-OOH CH3CCl2-OOH O-O bond CH3CH2O-OH CH3CHClO-OH CH3CCl2O-OH
a0
a1
a2
1.635 2.13 2.29
a3
b1
b2
1.635 2.13 2.29
2.1513 1.1539 1.0686 1.9861 6.0274 1.5592 -0.8774 2.5332 2.0496 -2.8759 4.2641 -0.2223 -0.7591 3.7273 2.3441 3.0590 1.9707
3.2950 3.0450 1.7600
1.3009 2.6160 1.7493
a Values of rotational barriers computed at the MP2/6-31G*//MP2/ 6-31G* level of theory are used to calculate the coefficients. Equation F1 in text.
mol in c (see Figure 2). This reflects the increase of electronic repulsion with increasing chlorine substitution on the R-carbon. The eclipse of the methyl groups with groups of the R-carbon also makes the C-C bond slightly longer (by 0.014-0.017 Å) than that in the staggered conformation. Barriers for Internal Rotations about C-O Bonds. The pattern of barriers for internal rotations about the C-O bond is more complex than that for the C-C bond (Figure 3). The most stable conformation obtained at the HF/6-31G* level for a is aSTS, 0.38 kcal/mol lower than aSGS. However, the calculations at the MP2/6-31G* level result in the energy of aSTS being 0.08 kcal/mol higher than that of aSGS. The
Figure 2. Potential barriers for internal rotations about C-C bonds of three molecules. Points are calculated values at the MP2/6-31G*// MP2/6-31G* level of theory. Lines are results of Fourier expansions, F1, with the coefficients listed in Table 4. The solid line and circle are for CH3CH2OOH; the dash-dot line and triangle are for CH3CHClOOH; the dash line and square are for CH3CCl2OOH.
maximum rotational barrier about the C-O bond in a occurs at the eclipse of C and O atoms (aSECS), which is 3.31 kcal/ mol higher than the eclipse of H and O atoms (aSEHS). For b the potential energy curve for the CCOO dihedral angle between 60° and 120° is rather flat. Calculations of potential energy as a function of the CCOO dihedral angle at the HF/6-
8246 J. Phys. Chem., Vol. 100, No. 20, 1996
Figure 3. Potential barriers for internal rotations about the C-O bonds of the three molecules. Points are calculated values at the MP2/6-31G*/ /MP2/6-31G* level of theory. Lines are results of Fourier expansions, F1, with the coefficients listed in Table 4. The solid line and circle are for CH3CH2OOH, and there is no conformation of eclipse of the chlorine atom and oxygen atom for this molecule. The dash-dot line and triangle are for CH3CHClOOH. The dash line and square are for CH3CCl2OOH, and there is no conformation of eclipse of the R-hydrogen atom and oxygen atom for this molecule.
31G* level were performed by varying CCOO angle by 15° intervals and by keeping all other parameters fixed, to verify the location of the transition state. The barriers for internal rotations using these “rigid” geometries are higher than those calculated by allowing geometry optimization. However, this “rigid-geometry” scan further confirms that there is no obvious local maximum in the range of the CCOO dihedral angle from 60° to 180°. The maximum barrier for rotation about the C-O bond in b, which occurs at the eclipse of Cl and O atoms (bSEClS), is 12.50 kcal/mol. This is 2.94 kcal/mol higher than the barrier of the eclipse of C and O atoms (bSECS), 9.56 kcal/ mol. The barriers for rotation about C-O in c are 8.50 kcal/mol for the eclipse of the Cl and O atoms (cSEClS) and 7.01 kcal/ mol for eclipse of the C and O atoms (cSECS) (see Figure 3). Note that the barrier at the eclipse of Cl and O atoms in c (cSEClS) is about 3.0 kcal/mol lower than in b (bSEClS). The energy difference between bSTS and bSEClS being larger than that between cSTS and cSEClS is due to the fact that in the two staggered conformations the OH group is affected by the repulsion from one Cl atom in bSTS and from two Cl atoms in cSTS. Barriers for Internal Rotations about O-O Bonds. The COOH skew conformations are the most stable in all cases with the COOH dihedral angle ranging from 94.2° to 119.2° (Figure 4). This is consistent with the orthogonal conformation of X-O-O-Y allowing for greater delocalization of lone pair electrons on two oxygen atoms than do the coplanar conformations (cis and trans).44 The internal rotational barriers about the O-O bond in alkyl hydroperoxides depend on the number of chlorine atoms on the R-carbon. However, the heights of the rotational barriers for the cis and trans conformations do not increase with an increase in the number of substituent chlorine atoms on the R-carbon. The bSTC conformation has the highest barrier at 8.72 kcal/mol, while aSTC and cSTC have lower barriers of 6.94 and 5.48 kcal/mol, respectively. Enthalpies of Formation. The total energies, ZPVE (unscaled) and experimental data, or evaluated values of ∆Hf°298 for the species participating in the isodesmic reactions used are given in Table 5. For each species in the isodesmic reactions, the molecular geometry is optimized at the HF/6-31G* level of
Lay et al.
Figure 4. Potential barriers for internal rotations about the O-O bonds of the three molecules. Points are calculated values at the MP2/6-31G*/ /MP2/6-31G* level of theory. Lines are results of Fourier expansions, F1, with the coefficients listed in Table 4. The solid line and circle are for CH3CH2OOH; the dash-dot line and triangle are for CH3CHClOOH; the dash line and square are for CH3CCl2OOH.
theory, and the single-point energy is then calculated at the MP2/ 6-31G** level of theory. The reaction energies and the calculated ∆Hf°298 for CH3CH2OOH (a), CH3CHClOOH (b), and CH3CCl2OOH (c) are listed in Table 6. The discrepancy between reaction enthalpies obtained from the single-point energies calculated at the HF/6-31G* and MP2/6-31G** levels is significant in Scheme 1 (∆H°rxn(HF/6-31G*) - ∆H°rxn(MP2/ 6-31G**), in kcal/mol): -2.7 for R1, -6.5 for R2, and -9.5 for R3. This discrepancy is smaller in Scheme 2: -0.1 for R4, -1.0 for R5, and -1.9 for R5, and it indicates that inclusion of electron correlation in the calculation of energy is more important in the determination of reaction enthalpies for Scheme 1. The discussion below about the determination of enthalpies of formation using isodesmic reactions is based on values obtained at the MP2/6-31G**//HF/6-31G* level of theory. Enthalpies of formation of a, b, and c are calculated using the reaction enthalpies and reference enthalpies of formation on species participating in isodesmic reactions. For instance, the reaction enthalpy (∆H°rxn) of R1 is determined to be -6.02 kcal/mol at the MP2/6-31G**//HF/6-31G* level of theory, i.e.,
∆Hf°298(CH3CH2OOH) + ∆Hf°298(CH4) ∆Hf°298(CH3OOH) - ∆Hf°298(CH3CH3) ) -6.02 kcal/mol ∆Hf°298(CH3CH2OOH) ) -6.02 kcal/mol ∆Hf°298(CH4) + ∆Hf°298(CH3OOH) + ∆Hf°298(CH3CH3) ) -6.02 - (-17.89) + (-33.4) + (-20.24) ) 41.8 kcal/mol The uncertainties in enthalpies of formation are estimated as the sums of the uncertainties of ∆Hf°298 of all species in the reactions except the target compounds. ∆Hf°298(CH3CH2OOH) is calculated to be -41.8 ( 1.4 kcal/ mol using R1 and -41.5 ( 1.5 kcal/mol using R4. Both values are in agreement with the previous value, -40.2 kcal/mol,17 obtained from the group additivity method. They are also in good agreement with another value, -41.3 kcal/mol, evaluated using the experimentally determined ∆Hf°298(CH3CH2OO), -5.2 kcal/mol,54 and the average bond enthalpy DH°(ROO-H), 88.2 kcal/mol.34 There is a discrepancy of ca. 5 kcal/mol between the enthalpies of formation calculated using the two isodesmic
R-Chlorinated Ethyl Hydroperoxides
J. Phys. Chem., Vol. 100, No. 20, 1996 8247
TABLE 5: Total Energies and Enthalpies of Formation for Species in Isodesmic Reactions
CH4 C2H6 C2H5Cl CH3CHCl2 CH3OH CH3OOH CH3CH2OH CH3CHClOH CH3CCl2OH
HF/6-31G* (hartree)
MP2/6-31G**//HF /6-31G* (hartree)
ZPVEa (kcal/mol)
∆Hf°298 (kcal/mol)
-40.191 571 7 -79.228 755 0 -538.131 520 3 -997.025 486 9 -115.035 418 -189.796 719 1 -154.075 744 6 -612.977 360 7 -1071.882 016 9
-40.364 648 6 -79.543 348 9 -538.563 911 0 -997.581 781 7 -115.381 274 2 -190.321 323 0 -154.568 272 6 -613.587 582 3 -1072.623 244 0
29.97 50.05 44.90 38.92 34.72 37.55 53.98 48.57 41.72
-17.89 ( 0.07b -20.24 ( 0.12b -26.70 ( 0.5b -31.05+0.4b -48.08 ( 0.05b -33.4 ( 1.2,c -33.0,d -31.3e -56.12 ( 0.2b -65.5 ( 2.1f -74.1 ( 0.9f
a Unscaled zero-point vibrational energy. b The enthalpies of formation are taken from ref 35, and the uncertainties are evaluated from the values quoted by Cox and Pilher (Thermochemistry of Organic & Organometallic Compounds; Academic Press: London, New York, 1970). c Estimated from ∆Hf°298 (CH3OO) ) 2.70 ( 0.80 kcal/mol (ref 33) with ∆Hf°298 (H) equal to 52.1 ( 0.01 kcal/mol and DH°(CH3OO-H) equal to 88.2 ( 0.4 kcal/mol. This value is used in isodesmic reactions to calculate the enthalpies of formation of the three ethyl hydroperoxides. d Reference 9. e Reference 20. f Estimated in this work; see text.
TABLE 6: Reaction Energies (kcal/mol) and Theoretical Enthalpies of Formation (kcal/mol) ∆H°rxn(HF/ 6-31G*)a
∆H°rxn(MP2/6-31G** //HF/6-31G*)a
R1 R4
-2.65 0.06
-6.02 -0.08
R2 R5
-6.97 1.00
-13.48 -0.04
R3 R6
-3.71 6.01
-13.26 4.08
∆Hf°298 (C2H5-xClxOOH) (HF)b (MP2)c CH3CH2OOH -38.4 ( 1.4 -41.8 ( 1.4 -41.4 ( 1.5 -41.5 ( 1.5 CH3CHClOOH -49.2 ( 1.8 -55.7 ( 1.8 -49.8 ( 3.4 -50.9 ( 3.4 CH3CCl2OOH -50.3 ( 1.7 -59.8 ( 1.7 -53.4 ( 2.2 -55.3 ( 2.2
comparison
-40.2,c -41.3d -49.2e
a The energies of reactions include the scaled (0.9) zero-point energy correction. b By use of the energies of reactions calculated at HF/6-31G*/ /6-31G* and the enthalpies of formation listed in Table 5, the enthalpy of formation of CH3OOH used in the calculation is 33.2 kcal/mol. Using MP2/6-31G**//HF/6-31G* energies. Values in bold are recommended. c Reference 17. d Evaluated from the experimentally determined value of ∆Hf°298(CH3CH2OO), -5.19 kcal/mol (ref 54), and the average bond energy D°(ROO-H), 88.2 kcal/mol (ref 34). e Evaluated from the experimentally determined value of CH3CHClOO, -13.8 kcal/mol (ref 55), and the average bond energy D°(ROO-H), 88.2 kcal/mol (ref 34).
reaction schemes for CH3CHClOOH and CH3CCl2OOH at the MP2/6-31G**//HF/6-31G* level of theory. ∆Hf°298(CH3CHClOOH) was calculated to be -50.9 ( 3.4 kcal/mol using ∆H°rxn(R5) ) -0.04 kcal/mol and ∆Hf°298(CH3CHClOH) ) -65.5 ( 2.1 kcal/mol. This is consistent with the value of -49.2 kcal/mol evaluated from the experimentally determined ∆Hf°298(CH3CHClOO), -13.1 kcal/mol,55 and the average bond enthalpy DH°(ROO-H) ) 88.2 kcal/mol.34 The value of ∆Hf°298(CH3CHClOOH) obtained using reaction R2 is -55.7 ( 1.8 kcal/mol. ∆Hf°298(CH3CCl2OOH) was calculated to be -55.3 ( 2.2 kcal/mol using ∆H°rxn(R6) ) 4.08 kcal/mol and ∆Hf°298(CH3CCl2OH) ) -74.1 ( 0.9 kcal/mol. It is determined to be -59.8 ( 1.7 kcal/mol using reaction R3. No other data for ∆Hf°298(CH3CCl2OOH) are currently available for comparison. Thermodynamic Properties. Thermodynamic properties of the three title molecules are listed in Table 7. Pitzer and Gwinn’s method and tables56-58 are commonly used to calculate the contributions of hindered internal rotors to thermodynamic functions. This approach is applicable only for a sinusoidal hindered potential. Therefore, one needs to select an “average barrier” when this method is used for nonsinusoidal potentials like those of chlorinated alkyl hydroperoxides. This approximation introduces errors in thermodynamic properties. Table 8 illustrates the scale in the deviation of entropies and heat capacities contributed from hindered rotators when calculated using Pitzer and Gwinn’s approximation. The use of Pitzer and Gwinn’s approach in this case may lead to significant errors in the determination of hindered rotor contributions to entropies (-1.10 to +1.69 cal mol-1 K-1) and heat capacities (-0.76 to +0.18 cal mol-1 K-1 for Cp300 and -1.14 to +0.69 cal mol-1 K-1 for Cp500).
Comparison of MNDO/AM1 and PM3 Molecular Geometries and Vibrational Frequencies. A comparison of molecular geometries and vibrational frequencies calculated using ab initio at the MP2/6-31G* level of theory and the semiempirical MO methods, AM1 and PM3, is also performed. The results indicate that the O-O bond length is ca. 12% (-0.18 Å) underestimated by AM1, and slightly overestimated (ca. 3%, +0.03 Å) by PM3, compared to the those optimized at the MP2/ 6-31G* level, which are close to the experimentally determined re,O-O value, 1.452 Å.43 The C-O bond lengths differ only slightly when calculated by the MP2/6-31G*, AM1, and PM3 methods. PM3 gives a more accurate C-O bond length with less than 1.2% deviation (absolute value), and the C-O bond lengths of AM1 are from 1.7 to 3.8% too long. Vibrational contribution to the entropy (S°298,vib) and heat capacity (Cp500,vib) determined using AM1 and PM3 methods is also compared to those obtained from the scaled frequencies determined at the HF/6-31G*. The mean deviation of S°298,vib for the three molecules from AM1 is -0.75 cal mol-1 K-1 and +0.40 cal mol-1 K-1 from PM3. The mean deviation of Cp500,vib for the three molecules from AM1 is -1.03 cal mol-1 K-1 and +0.63 cal mol-1 K-1 from PM3. PM3 appears to be a preferred alternative for the calculation of entropies and heat capacities for chlorinated alkyl hydroperoxides among these two semiempirical methods. Summary Ab initio calculations were performed on the CH3CH2OOH, CH3CHClOOH, and CH3CCl2OOH molecules using the Gaussian92 system of programs at the RHF/6-31G* and MP2/6-31G* levels of theory. Results show that it is important to include
8248 J. Phys. Chem., Vol. 100, No. 20, 1996
Lay et al.
TABLE 7: Ideal Gas Phase Thermodynamic Propertiesa for CH3CH2OOH, CH3CHClOOH, and CH3CCl2OOH ∆Hf°298b TRVe C-Cf C-Og O-Oh total comparison: Bensoni TRV C-C C-O O-O total TRV C-C C-O O-O total
S°298c
Cp300c
-41.5
62.99 4.25 5.72 3.18 76.14
14.05 2.13 2.25 1.37 19.79
-39.10
76.66
20.08
Cp500
Cp600
Cp800
Cp1000
Cp1500
CH3CH2OOHd (a) 18.07 21.94 2.18 2.09 2.24 2.15 1.44 1.51 23.93 27.69
Cp400
25.33 1.95 2.04 1.57 30.88
30.73 1.69 1.82 1.63 35.88
34.75 1.50 1.66 1.63 39.54
40.97 1.26 1.39 1.52 45.14
24.19
27.70
30.62
35.53
38.80
28.32 2.16 3.57 1.86 35.91
33.18 1.95 3.61 1.79 40.53
36.71 1.74 3.33 1.73 43.50
42.11 1.41 2.53 1.57 47.62
31.66 2.20 2.29 1.78 37.94
35.90 2.02 2.09 1.67 41.68
38.89 1.81 1.85 1.56 44.11
43.40 1.46 1.26 1.36 47.48
-50.9
69.12 3.97 3.40 2.73 79.22
17.24 2.00 2.33 1.80 23.37
CH3CHClOOHj (b) 21.42 25.16 2.19 2.22 2.83 3.29 1.90 1.89 28.33 32.57
-55.3
74.63 3.89 4.91 3.11 86.55
21.08 1.96 2.79 1.86 27.69
CH3CCl2OOHk (c) 25.30 28.81 2.17 2.23 2.53 2.39 1.87 1.84 31.87 35.27
a
Thermodynamic properties are referred to a standard state of an ideal gas of pure enantiomer at 1 atm. Three torsional frequencies are not included in the calculations of entropies and heat capacities. Instead, the contributions from hindered rotations about the C-C, C-O and O-O bonds are included. b In kcal mol-1. c In cal mol-1 K-1. d CH3CH2OOH symmetry number: 3. Main moments of inertia (g cm2): 2.1607 × 10-38, 2.0135 × 10-38, 2.7509 × 10-39. Scaled frequencies (with three torsional frequencies excluded, in cm-1): 293, 481, 804, 868, 1002, 1087, 1153, 1174, 1263, 1383, 1405, 1423, 1466, 1481, 1484, 2892, 2898, 2936, 2955, 2966, 3661. e The sum of contributions from translations, external rotations, and vibrations. f Contribution from internal rotation about the C-C bond. The reduced moments of inertia are calculated about the C-C bond to be 2.98, 3.08, and 3.11 amu Å2 for a, b, and c, respectively. g Contribution from internal rotation about the C-O bond. The reduced moments of inertia are calculated about the C-O bond to be 17.22, 24.95, and 25.96 amu Å2 for a, b, and c, respectively. h Contribution from internal rotation about the O-O bond. The reduced moments of inertia are calculated about the O-O bond to be 0.86, 0.87, and 0.87 amu Å2 for a, b, and c, respectively. j The values are calculated according to the procedure and groups values from ref 20. i CH3CHClOOH symmetry number: 3. Main moments of inertia (g cm2): 3.9142 × 10-38, 2.4814 × 10-38, 1.691 × 10-38. Scaled frequencies (with three torsional frequencies excluded, in cm-1): 305, 316, 430, 518, 632, 890, 1009, 1068, 1122, 1167, 1300, 1359, 1416, 1428, 1464, 1469, 2909, 2977, 2989, 3019, 3652. k CH3CCl2OOH symmetry number: 3. Main moments of inertia (g cm2): 4.6623 × 10-38, 3.8942 × 10-38, 3.5485 × 10-38. Scaled frequencies (with three torsional frequencies excluded, in cm-1): 269, 288, 299, 352, 406, 549, 563, 734, 924, 1066, 1099, 1132, 1194, 1413, 1439, 1462, 1465, 2922, 2995, 3009, 3651.
TABLE 8: Comparison of Pitzer & Gwinn’s Method (PG) and the Method Used in This Study for Calculation of Thermodynamic Properties of Molecules with Hindered Rotors Vmeanb (kcal/mol)
Ir a (amu Å2) C-Od
17.22
PGe this workf
O-Og
0.86
PG this work
C-O
24.95
O-O
0.87
PG this work PG this work
C-O
25.96
O-O
0.87
PG this work PG this work
nc
CH3CH2OOH 4.23 3 CH3CHClOOH 6.94 1 8.98
3
8.72
1
CH3CCl2OOH 8.00 3 5.48
1
S°298 (cal/mol K)
Cp300 (cal/mol K)
Cp500
5.58 5.72
2.21 2.25
2.30 2.15
2.08 3.18
1.95 1.37
2.20 1.51
5.09 3.40 1.86 2.73
2.00 2.33 1.87 1.80
2.15 3.29 2.11 1.89
5.25 4.91 2.34 3.11
2.03 2.79 2.04 1.86
2.11 2.39 2.28 1.84
a Reduced moments of inertia are calculated about the rotational bonds C-O and O-O, based on the molecular geometries of aSTS, bSTS, and cSTS optimized at the MP2/6-31G* level of theory. b Arithmetic mean of rotational barriers. c Number of potential maxima. d Contribution from internal rotation about the C-O bond. e The method and tables by Pitzer and Gwinn, ref 58. f Method used in this work, by summation over the energy levels obtained by direct diagonalization of the Hamiltonian matrix of hindered internal rotations; see text. g Contribution from internal rotation about the O-O bond.
the perturbation approach in the theoretical determination of the geometry of alkyl hydroperoxides. The barriers for internal rotations obtained using MP2/6-31G*//MP2/6-31G* and MP2/ 6-31G**//HF/6-31G* are similar. The barriers for the internal rotations about the C-C bond increase with the increase of chlorine substitution on the R-carbon: 3.27 kcal/mol in a, 4.26 kcal/mol in b, and 4.58 kcal/mol in c. The internal rotations about the C-O bond present more complex potential energy
curves with the following maximum rotational barriers (in order of a, b, c): 6.36, 12.50, and 8.50 kcal/mol. The internal rotational barriers about the O-O bond, which occur at the C-O-O-H cis conformation, are (in order of a, b, c) 6.94, 8.72, and 5.48 kcal/mol. All values of barriers reported above are calculated at the MP2/6-31G*//MP2/6-31G* level of theory. Enthalpies of formation for these three molecules were calculated using isodesmic reactions. Standard entropies (S°298)
R-Chlorinated Ethyl Hydroperoxides and heat capacities (Cp(T)’s, 300 e T/K e 1500) were calculated using the rigid-rotor-harmonic-oscillator approximation based on parameters obtained from the ab initio studies. Contributions from hindered rotors were calculated by summation over the energy levels obtained by direct diagonalization of the Hamiltonian matrix of hindered internal rotations. Use of Pitzer and Gwinn’s tables for the internal rotation about C-O bonds and O-O bonds of the three title species leads to significant errors (from -0.9 to +1.8 cal mol-1 K-1) in internal rotor contributions to the entropies. Enthalpies of formation were calculated to be ∆Hf°298(CH3CH2OOH) ) -41.5 ( 1.5 kcal mol-1, ∆Hf°298(CH3CHClOOH) ) -50.9 ( 3.4 kcal mol-1, and ∆Hf°298(CH3CCl2OOH)) -55.3 ( 2.2 kcal mol-1. Entropies (S°298) are calculated to be 76.1, 79.2, and 86.6 cal mol-1 K-1 for CH3CH2OOH, CH3CHClOOH, and CH3CCl2OOH, respectively. Results from semiempirical MO calculations with the AM1 and PM3 Hamiltonians were also compared to the ab initio results. The comparisons show that the molecular parameters obtained by the PM3 method are in better agreement with ab initio results than those by AM1. Acknowledgment. The authors acknowledge funding from the NJIT-MIT USEPA Northeast Research Center and the USEPA MIT-CALTECH-NJIT Research Center on Airborne Organics and the generous grant of computer time from Pittsburgh Supercomputing Center and New Jersey Institute of Technology. This work was also partially supported by the Hazardous Substance Management Research Center, an advanced technology center of the New Jersey Commission on Science and Technology and a National Science Foundation Industry/University Cooperative Research Center. The valuable comments from an anonymous reviewer are acknowledged. References and Notes (1) Hughes, K. J.; Halford-Maw, P. A.; Lightfoot, P. D.; Tura´nyi, T.; Pilling, M. J. Symp. (Int.) Combust., [Proc.] 1992, 24, 645. (2) Fenter, F. F.; Catoire, V.; Lesclaux, R.; Lightfoot, P. D. J. Phys. Chem. 1993, 97, 3530. (3) Fenter, F. F.; Lightfoot, P. D. J. Phys. Chem. 1993, 97, 5313. (4) Sahetchian, K. A.; Rigny, R.; Tardieu de Maleissye, Symp. (Int.) Combust., [Proc.] 1992, 24, 637. (5) Niki, H.; Maker, P. D.; Savage, C. M.; Breitenbach, L. P. J. Phys. Chem. 1982, 86, 3825. (6) (a) Wallington, T. J.; Gierzak, C. A.; Ball, J. C.; Japar, S. M. Int. J. Chem. Kinet. 1989, 21, 1077. (b) Wallington, T. J.; Japar, S. M. Chem. Phys. Lett. 1990, 166, 495. (c) Ibid. 1990, 167, 513. (7) Wallington, T. J.; Dagaut, P. Chem. ReV. 1992, 92, 667. (8) Wu, F.; Carr, R. W. J. Phys. Chem. 1992, 96, 1743. (9) Benassi, R.; Folli, U.; Sbardellati, S.; Taddei, F. J. Comput. Chem. 1993, 4, 379. (10) WMO Global Ozone Research and Monitoring Project. Report No. 20, 1989. (11) Chen, Y; Tschuikow-Roux, E. J. Phys. Chem. 1992, 96, 7266. (12) Cohen, N; Benson, S. W. J. Phys. Chem. 1987, 91, 162. (13) Stull, D. R.; Prophet, H. JANAF Thermochemical Tables, 2nd ed. (NSRDS-NBS37); U.S. Goverment Printing Office: Washington, DC, 1970. (14) Benson, S. W.; Shaw, R. In Organic Peroxides; Swern, D., Ed.; Wiley-Interscience: New York, London, 1970; Vol. 1. (15) Kozolov, N. A.; Rabinovich, Tr. Khim. Khim. Tekhnol. 1964, 2, 189; Chem. Abstr. 1965, 63, 6387. (16) Stathis, E. C.; Egerton, A. C. Trans. Faraday Soc. 1940, 36, 606. (17) Benson, S. W. J. Chem. Phys. 1964, 40, 1007. (18) Baldwin, A. C. Thermochemistry of Peroxides. In The Chemistry of Functional Groups, Peroxides; Patai, S., Ed.; John Wiley & Sons: New York, 1983; Chapter 3. (19) Cox, J. D.; Pilcher, G. Thermochemistry of Organic and Organometallic Compounds; Academic Press: London, 1970. (20) Benson, S. W. Thermodynamic Kinetics, 2nd ed.; Wiley-Interscience: New York, 1976.
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