Computational study of addition and abstraction reactions between

Computational study of addition and abstraction reactions between hydroxyl radical and dimethyl sulfide: a difficult case. Michael L. McKee. J. Phys. ...
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J. Phys. Chem. 1993,97, 10971-10976

10971

Computational Study of Addition and Abstraction Reactions between OH Radical and Dimethyl Sulfide. A Difficult Case Michael L. McKee Department of Chemistry, Auburn University, Auburn, Alabama 36849 Received: March 31, 1993

The addition complex between OH radical and dimethyl sulfide (DMS) could not be located unless a level of theory higher than MP2/6-31G(d) was used. At the MP2/6-31+G(2d) level, a complex was found which was bound by 9.3 kcal/mol. At the estimated QCISD(T)/6-31+G(2d,p) level the complex is 8.7 kcal/mol more stable than DMS plus OH. This is reduced to 6.0 kcal/mol with zero-point correction. The calculated binding is underestimated with respect to experiment (1 3 f 3 kcal/mol). A transition state for abstraction of a hydrogen from DMS by OH was located at the MP2/6-3 1+G(2d) level 1.8 kcal/mol higher than reactants. Complexes of C1 and Br atoms with D M S and with dimethyl sulfoxide (DMSO) could be located at much lower levels of theory. Chlorine and bromine are much more polarizable than OH, and the interaction can be viewed as a soft acid (halogen radical) interacting with a soft base (DMS or DMSO) which appears to be described adequately at lower levels of theory. On the other hand, the orbital energies of O H and DMS are similar, and binding is due to a two-center, three-electron (2c-3e) interaction.

Introduction The reaction of hydroxyl radical with dimethyl sulfide (DMS) has been the subject of recent experimental investigation.'-10 The reaction is believed to be an important atmospheric reaction" and may be the major path for removing DMS, which is a significant product of biomass decay in oceans.12 The two proposed initial pathways for the decomposition of DMS are addition of OH to the sulfur atom (eq 1) to form dimethylhydroxysulfuranyl radical (DMS-OH, 1) and the abstraction of a hydrogen by hydroxyl (eq 2) to form water plus methylthiomethyl OH + CHSSCH,

(DMS)

€

CHaS(OH)CHj (DMS-OH, 1)

(1)

CHaSCHz (2) + H20

(2)

Me2S

+ Me

-

Me$ (TS)

-

Me

+ Me2S

(4)

coordinate transition state.16 Ferris et al." used ab initio calculations at the UHF/4-3 lG* level to locate a transition state which exhibited a T-shaped molecular structure. Single-point calculations at the PMP4/4-31G* level ("P" = spin projection) plus zero-point and thermal correctionsgave an activation barrier of 13.1 kcal/mol. Again, the DMS-OH adduct (1) differs from Me3S only by replacing one methyl group with hydroxyl. The purpose of the present study is to carry out an ab initio study of the two pathways (eqs 1 and 2) at a high level of theory. In particular, the presence or absence of a stable adduct will be considered since there exists conflictingevidence in the literature.

Method radical (2). A number of kinetic studies have been carried out, All ab initio calculations have used the GAUSSIAN 92 many of which indicate that abstraction (eq 2) is importa~~t.lJ.~.~-~program s y ~ t e m s . ' ~Optimizations J~ and frequency calculations The reported activation barrier is between -0.352 and +0.274 for the DMS/OH potential energy surface were carried out at kcal/mol. 1 the MP2/6-3 1+G(2d) level since that level was required to locate A flash photolysis-resonance fluorescence study by Wine and a stable adduct for DMS-OH. Relative energies are computed co-workers' indicates that eq 1 must also be considered to explain at a base level of MP4/6-31G(2d) and improved20 by adding the the kinetic results in the presence of 0 2 (eq 3). However, a quite relative effect of increasing the sophistication of the method to MP4/6-31G(2d,p) (adding p-functions to hydrogens), MP4/6CH,S(OH)CH, (1) + 0,-products (3) 3 1+G(2d) (adding diffuse functions to all non-hydrogens), and QCISD(T)/6-3 1G(2d) (using higher level of electron correlation). recent study using neutralization-reionization mass spectrometry Approximate relative energies at the QCISD(T)/6-3 l+G(Zd,p) found no evidence for 1 as a stable intermediate. Rather, 1 was level are obtained by using eq 5, where AI3 refers to relative suggested to be a transition state in the oxidation of dimethyl sulfidewith hydroxyl radicals on the basis of ab initio calculations hE(tota1) = AE(+p/H) AE(+diff) hE(+elect corr) (UHF/6-31G(d)) which found no minimum for a stable OH 2hE(base) (5) adduct with DMS. The DMS-OH adduct (1) is an example of a 9 4 - 3 complex13 energies. Total energies are given in Table I, and the relative (three substituents around sulfur and nine valence electrons), for energies (kcal/mol) are given in Table 11. Geometric parameters which three types of bonding are known:I4(a) a pyramidal sulfur are given at the MP2/6-31+G(2d) level for relevant species in Figure 1. with a 2c-3e bond to one substituent, (b) a T-shaped sulfur with one electron in a u* orbital, or (c) a T-shaped sulfur with one Lower level optimizations (UHF/3-2 1G*)2' have been carried out for adducts of C1 and Br with dimethyl sulfide (DMS) and electron in a A* orbital. Interestingly, evidence has been dimethyl sulfoxide (DMSO). For the chlorine adducts (DMSpresented's for a T-shaped geometry for alkyldialkoxysulfuranyl C1 and DMSO-CI), single-point calculations were made at the radicals (RS(0R)z). The DMS-OH radical (1) differs from PMP2/6-31G(d) level, while for the bromine adducts (DMS-Br CH3S(OR)2only by replacing two alkoxy groups with a hydroxyl and DMSO-Br) single-point calculations were made at the and a methyl group. PMP2/3-21G*(*) level, where the standard 3-21G* basis set It is been suggested that radical displacementreactions at sulfur was supplemented with a set of d-orbitals for each carbon and (as modeled by reaction 4) may take place through a three-

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0022-3654/93/2097-10971$04.00/0

0 1993 American Chemical Society

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10972 The Journal of Physical Chemistry, Vol. 97, No. 42, 1993

McKee

TABLE I: Absolute Energies (hartrees) of Various Species Calculated at MP2/6-31+C(2d) Optimized Geometries MP2/ MP4/ MP4/ MP4/ QCISD(T)/ sym state 6-31+G(2d) 6-31G(2d) 6-31G(2d,p) 6-31+G(2d) 6-31G(2d) H K 'S -0.498 23 -0.498 23 -0.498 23 -0.498 23 -0.498 23 -39.702 98 -39.700 79 -39.699 13 -39.724 41 D3h 2A2" -39.681 06 CH3 -75.573 50 -75.571 48 -75.563 34 -75.554 46 -75,562 31 OH e,, 211 -76.251 56 -76.238 57 -76.238 26 -76.260 95 Cb 'AI -76.239 41 H2O -437.399 02 437.398 24 -437.396 14 -437.421 42 C, 2A' -437.358 60 CH3S -476.511 68 -476.560 83 -476.603 40 -476.500 51 -476.564 30 CH3SCH2 c, 2A" -476.561 07 -476.603 65 -476.568 21 -476.564 58 C1 'A -476.511 79 CH3SCH2 -477.213 40 -477.264 42 477.218 31 477.215 32 Cb 'A1 477.161 18 CH3SCH3 -552.828 74 -552.780 68 -552.772 54 -552.705 68 -552.766 00 CH3SCH3+OHTS CI 'A -552.842 45 -552.801 71 -552.784 04 -552.730 44 -552.779 71 C, 2A' CH3S(OH)CH3 a Zero-point energy in kcal/mol and number of imaginary frequencies calculated at the MP2/6-31+G(2d) level,

ZPE (NIF). 0.00 18.78 (0) 5.20(0) 13.14(0) 22.56(0) 38.48( 1) 38.93(0) 47.79(0) 51.59( 1) 55.79(0)

TABLE Ik Relative Energies (kcal/mol) of Various Species Calculated at MP2/631+G(2d) Optimized Geometries MP2/ 6-3 1+G(2d) 0.0 94.8 76.2 0.0 6.2 -22.3 -9.3

MP4/ 6-3 lG(2d) 0.0 96.7 74.1 0.0 6.1 -14.8 -2.5

MP4/ 6-3 1G(2d,p) 0.0 102.0 74.4 0.0 5.8 -16.7 -2.8

MP4/ 6-3 1+G(2d)

QCISD(T)/ 6-3 lG(2d) 0.0 95.7 73.0 0.0 3.8 -15.4 -3.4

[QCISD(T)/

6-3 1 +G(2d,p)]' 0.0 99.6 72.2 0.0 3.1 -21.3 -8.7

+ZPCb

0.0 0.0 CH3SCH3 91.2 95.3 CH~SCHZ(CI) +H 73.0 66.1 CH3S + CH3 0.0 0.0 CH3SCH3+ OH 1.8 5.7 CHiSCH3 + OH TS -18.8 -22.2 CH3SCHz (Ci) + H20 -7.5 -6.0 CHpS(OH)CH3 a Additivity approximation.20 b Zero-point correction has been calculated at the MP2/6-31+G(2d) level and weighted by a 0.95 factor. H

1

.

4

CHI 1.082

A H,

OH 0.978

ct.H

C '

H20 0.968, 104.2

H

DMS

1.817

H\C 4

\C

c

.

2

\H

4

=

1.718

around sulfur is similar in CS2 and DMS. Initial optimizations at the UHF/6-31G(d) level confirmed6 that no stable adduct between DMS and OH existed at that level. Higher level optimizations at the UMP2/6-31G(d) level gave the same results-no stable adduct present. From a consideration of the predicted bond energy of the S=C--S-OH adduct with respect to level of the UMP2/6-31+G(2d) level of theory was used to calculate the adduct. At that level, the adduct is predicted to be 9.3 kcal/mol more stable than OH plus DMS. The results for the DMS-OH adduct are quite significant in that they reveal a weakness in the G123and G224methods, which purport to give results of chemical accuracy ( f 2 kcal/mol). Both methods are based on optimizations at the MP2/6-31G(d) level with the implicit assumption, valid in the overwhelming number of cases, that the geometries at the MP2/6-31G(d) level are not significantly different than experiment. However, the DMSO H adduct does not exist at the MP2/6-31G(d) level, and thus, the G1 or G2 method would be qualitatively incorrect. The description of the two-center, three-electron bond (2o3e), which binds the OH radical to a lone pair on DMS, requires a higher level of theory for binding. In many systems, lower levels of theory may predict a minimum for unstable adducts because there exists a small reverse barrier to dissociation. Higher levels of theory may then reverse the stability of reactants and products and lead to a stable adduct. Such was the case for the OH adduct with CS2 ( S - C - S - O H ) . However, for OH plus DMS no reverse barrier exists at lower levels of theory. For the methylthiomethyl radical (2), two structures were determined. The C, structure proved to be a transition state to a lower-symmetry (but only marginally more stable) structure of C1 symmetry. The distortion is small, and the two structures are almost equivalently stable when zero-point corrections are included. The C-H and C S bond energies (at 0 K) have been determined to be 91.2 and 66.1 kcal/mol, respectively (Table 11), and can be compared to recent values of 91 2 and 74.9 f 1.5 kcal/mol, respectively, determined from vacuum-ultraviolet photodissociation and photoionization studies by Nourbakhsh et al.25 With respect to DMS plus OH, the abstraction pathway is calculated to be 22.2 kcal/mol exothermicwhich can be compared to an experimental exothermicity of 24.6 kcal/mol. The experimentalvalue (at 0 K) is determined by using-5.1,9.2, and-57.1 kcal/mol for the heats of formation26of DMS, OH, and HzO, respectively, and 34 kcal/mol for CH3SCH2.2S The activation

ACHH \ Cl

2'

H

Figure 1. Geometric parameters of species calculated at the MP2/631+G(2d) level of theory.

oxygen (exponent = 0.8). Absolute energies (hartrees) and relative energies (kcal/mol) are given in Tables I11 and IV, respectively, while geometric parameters at the UHF/3-21G1 level are given for C1 and Br adducts of DMS and DMSO in Figure 2. Additional optimizations at the UHF/6-3 lG(d)-level and single-point calculations at the PMP4/6-3 1G(d) level for the DMS-Cl adduct gave very similar results and are not reported.

Results and Discussion A recent study22 of OH plus CS2 suggests that high levels of theory are required for even qualitatively correct results. The adduct between OH and one sulfur of CS2 is less stable than fragments by 19.6 kcal/mol at the UHF/6-3 1lG(d,p)//UMP2/ 6-31G(d,p) level and is still predicted to be 3.0 kcal/mol less stable at the MP2/6-31 lG(d,p)//MP2/6-3lG(d,p) level. At the G1 level of theory, the adduct is predicted to be 5.9 kcal/mol more stable than OH plus CS2. The adduct between OH and DMS may require similar levels of theory since the environment

*

Reactions between O H Radical and Dimethyl Sulfide

The Journal of Physical Chemistry, Vol. 97, No. 42, 1993 10973

TABLE III: Total Energies at HF/f21G* Optimized Geometries

c1

2P -457.371 09 -459.447 96 -459.553 53 K -936.694 55 -931.835 34 -936.187 04 2A' DMS-C1 C, ZA' -1006.221 56 -1010.984 05 -1011.677 02 DMSO-Cl C, -474.456 98 -476.735 30 -477.120 61 DMS Ck, 'AI 'A' -548.846 67 -551.537 03 -552.111 11 DMSO CS Br K -2560.244 62 ZP -3034.709 18 2A' DMS-Br Cs -3109.096 08 2A' DMSO-Br C, a Polarization functions have been added to the 3-21G* basis set for carbon and oxygen. frequencies calculated at the HF/3-21G* level.

0.00 51.89 (0) 54.29(0) 51.22(0) 53.88(0)

-474.909 09 -414.524 62 -549.514 96 -548.945 31 -2560.351 I1 0.00 -2560.244 62 -3035.280 94 51.76(0) -3034.776 57 -3109.884 26 54.23(0) -3109.195 13 Zero-point energy in kcal/mol and number of imaginary

TABLE Ik Relative Energies (kcal/mol) of CI and Br Adducts at HF/3-21G* Optimized Geometries HF/3-21GS HF/6-31G(d) PMP2/6-31G(3) +ZPC HF/3-21G*(*)" PMP2/3-21G*(*)" 0.0 0.0 0.0 DMS + C1 0.0 DMS-Cl -4.6 -2.4 -12.8 -12.2 0.0 DMSO + C1 0.0 0.0 0.0 -3.9 0.6 -7.8 -7.4 DMSO-Cl 0.0 DMS + Br 0.0 0.0 -4.8 -4.6 -12.6 DMS-Br DMSO + Br 0.0 0.0 0.0 -3.0 -3.3 -11.0 DMSO-Br See footnote Table I. Zero-point correction has been calculated at the HF/3-21GS level and weighted by a 0.90 factor. 0 111.490

k

IOH

CH$CH2

+

OH

+

H20

= CH3S(OH)CH3 IOH

CH&OH)CH,

-

+

0.0

-10.7

otherproduds

H20

The S - 0 bond in the adduct is predicted to be very long (2.047 bond with a bond order of 0.5. The hydroxyl is interacting with an unhybridized p orbital, as shown by the OH bond, which is nearly parallel to the CSC plane and the OSC bond angle, which is close to 90' (88.7O). The CSC bond angle has opened up slightly (98.1' 99.9'), and the S-C bond has shortened slightly (1.817 1.804 A) upon adduct formation (Figure 1). The spin density (UHF/6-31+G(2d)) is located on oxygen (0.57 e-) and sulfur (0.58 e-) as expected for a 2 o 3 e O:.S bond (Table V). In the abstraction transition state, the forming OH bond is 1.375 A (42% longer than in HzO) while the breaking C H bond is 1.190 A (8% longer than in DMS), indicating an early transition state as expected for an exothermic reaction (Figure 1). The most favorable approach of the OH radical is from above the CSC plane which allows the lone pair on sulfur to stabilize the developing radical center on carbon as the hydrogen is removed. The 0-H-C angle is 166.2', and the spin density (UHF/63 1+G(2d)) is largely on oxygen (0.90 e-). The SC bond adjacent to the OH group has shortened 0.027 A in the transition state,

A), which suggests a 2c-3e

barrier for H abstraction is 1.8 kcal/mol while the OH adduct is stable by 6.0 kcal/mol. Since the stability of the S=C=S-OH adduct was underestimated by about 4 kcal/mol at the highest level of theory,zz it is reasonable to expect that the stability of the DMS-OH adduct will be underestimated by a similar amount. If so, the true adduct binding energy would be about 10 kcal/ mol, which would be in good agreement with the experimental value of 13 f 3 kcal/mol for the OH-perdeuteriodimethyl sulfide adduct.' It is not known whether the formation of the adduct is accompanied by an activation barrier. Since the adduct does not exist a t the MP2/6-31G(d) level, it would seem likely that the barrier at the MP2/6-31+G(2d) (if one exists at all) would be

0.0 -12.1

small. The abstraction pathway has a calculated barrier of 1.8 kcal/mol (at 0 K), which is about 2 kcal/mol higher than 0bserved.l92.~9~-~ There are several factors which limit the accuracy of the calculated barrier: first, the limitations of the method used to calculate the electronic energy (i.e., finite basis set and finite electron correlation); second, neglect of quantum mechanical tunneling; and third, the assumption that the position of the transition state on the potential energy surface is the same as on thevibrationally adiabatic potential.27 The first and second factors would likely reduce the barrier while the third factor would likely increase it. A reasonable estimate of the barrier might be 1.8 f 2 kcal/mol, which would be in reasonable agreement with experiment (-0.4 to +O -3 kcal/ mol). 1,2q4v7-9 It is possible that the DMS-OH complex forms without activation and that abstraction occurs from DMS as well as from the DMS-OH complex (eq 6). On the other hand, the branching ratio may favors abstraction over addition because addition has a small barrier (1-2 kcal/mol). CH3SCH3

Figure 2. Geometricparameters of speciescalculated at the HF/3-21G* level of theory for DMS, DMSO, and CI and Br adducts of DMS and DMSO.

+ZPCb

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10974 The Journal of Physical Chemistry, Vol. 97, No. 42, 1993

TABLE V Charges

Total Atomic Spin Densities and Mulliken

DMS-X, X = OH, C1, Br DMSO-X, X X (basis) X S charge“ X S -0.29 OH (6-31+G(2d)) 0.57 0.58 -0.22 0.86 0.07 CI (6-31G(d)) 0.75 0.27 Br (3-21G*(*)) 0.86 0.16 -0.12 0.88 0.06

= C1, Br chargea -0.12 4.10

a Mulliken charges calculated with the indicated basis set. For OH, the hydrogen Mulliken charge is summed together with oxygen.

TABLE VI: Frequencies (cm-I) and Intensities (km)for DMS and DMS-OH DMS MP2/ 6-31+G(2d)“ bZ 3152 (1) al 3151 (4) a2 3139 (0) bl 3130 (10) bz 3039 (19) al 3034 (22) a1 1499 (1) bz 1489 (18) bl 1487 (20) a2 1476 (0) a1 1380 (0) bz 1356 (3) a1 1063 (13) bl 1000 (6) a2 968 (0) bZ 932 (0) bz 766 (0) al 710 (3)

exptlb 2991 (5) 2991 (5) 3013 (4) 2991 (5) 2952 (6) 2916 (4) 1456 (3) 1440 (3) 1434 (4) 1446 (2) 1317 (5) 1317 (3) 1028 (3) 1005 (0) 963 (0) 972 (-4) 741 (3) 691 (3)

a1 266 (0)

286 (-6)

bl 200 (1) az 194 (0)

182 (10) 173 (12)

DMSOH MP2/6-3l+G(2dla a’3667 (15) a”3178 (0) a’3177 (1) a”3166 (0) a’ 3163 (1) a” 3050 (6) a’3048 (11) a’ 1482 (16) a” 1467 (1) a’ 1472 (6) a” 1459 (1 1) a’ 1365 (11) a” 1345 (1) a’ 1069 (13) a’994 (15) a” 961 (0) a” 944 (1) a’ 834 (38) a”773 (0) a’715 (4) a’ 475 (24) a’ 296 (8) a” 295 (22) a‘ 244 (8) a’ 181 (1) a” 160 (16) a” 45 (60)

assignt

0 - H str CHI str CH3 str CH3 str CH3 str CH3 str CH3 str CH3 def CH3 def CH3 def CH3 def CH3 def CH3 def CHI def CH3 def CH3 def CH3 def SO-H bend S-C str S-C str S-0 str CSC bend OH tors S-OH bend CH3 tors CH3 tors S-OH bend

*

a Symmetry of mode, frequency (cm-l), and intensity (km). See: Dewar, M. J. S.;Ford, G. P. J. Am. Chem. SOC.1977, 99, 1685. Experimental frequency following by percentage difference from MP2/ 6-31+G(2d) value, Le., (calc - exptl)/exptl X 100.

which is 27% of the shortening which occurs between DMS and CH3SCH2 (2). The MP2/6-3 1+G(2d) vibrational frequencies for DMS and DMS-OH are reported in Table VI. The S-C stretches and CSC bend have increased slightly upon adduct formation due to donation of charge from DMS to OH and a corresponding reduction of electrons in the sulfur lone pair which has a S-C antibonding component. The most characteristic frequencies of the DMS-OH complex are probably the 0-H stretch at 3667 cm-1, the SO-H bend at 834 cm-I, and the S-O stretch at 475 cm-I, which are all predicted to have more than average intensity in the IR spectrum. A comparison with experimental frequencies of DMS shows that the calculated frequencies are too high by an average of 1.8%. A more accurate prediction of the adduct frequenciescan be made by using the individual ratios of observedto-calculated frequencies for DMS as weighting factors for the corresponding frequencies in the adduct. The average factor (1.8%) can be used for the new frequencies. One might ask why the DMS-OH adduct is so difficult to describe by an ab initio treatment and whether other adducts of DMS, such as DMS-Cl and DMS-Br, would be equally difficult to describe. The answer to the latter question is negative, as will be shown in the section below.

McKee

Adducts of CI and Br with DMS and DMSO The OH radical interacts with a lone pair of DMS to form a 2c-3e bond. A similar interaction can be expected with DMSO, which has a lone pair similar in nature to the lone pair of DMS but lower in energy. Optimizations at lower levels failed to find a DMSO-OH adduct, which is not unexpected given earlier experience with DMS-OH. However, experimentally, it is that DMSO-OH adducts are readily formed by sonolysis or pulse radiolysis of a DMSO/water mixture. Halogen radicals, such as C1 and Br atoms, can also form adducts with DMS and In an effort to better understand the DMS-OH complex, low-level calculations have been carried out for DMS and DMSO complexes with C1 and Br. In contrast to the DMS-OH adduct, both halogen adducts are bound at all levels of theory used. At the PMP2/6-3 1G(d)/ /3-21G* level, the DMS-Cl adduct is bound by 12.2 kcal/mol, while the DMS-Br adduct is bound by 12.1 kcal/mol at the PMP2/3-2 lG* (*)//3-2 1G* level. The experimental homolytic bond strengths are 14 f 3 kcal/m01~~ for the S-Cl bond in DMSC1 and 14.6 f 1.1 kcal/moP9 for the S-Br bond in DMS-Br. The agreement is quite good. Thus, it appears that moderately low levels of theory can be used to predict halogen atom binding energies, which is in contrast to complexes with hydroxyl. A considerable amount of information exists for these C1 and Br adducts. For example, the experimental rate constant for addition of chlorine atoms to DMS is significantly larger than for OH addition to DMS.3l-33 Stickel et al.33have suggested that the addition reaction might be responsible for removing some of the DMS above Oceans where significant levels atomic chlorine could arise from the heterogeneous reaction of N205 vapor with moist NaCl(s). The complexes RzS:.X (X = OH, C1,3’-33 and Br3*)can be formed by pulse radiolysis of an aqueous solution as shown in eqs 7 and 8. The extent of formation in solution depends on the

+

R2S+ X- == R,S.=X (R,S);

(7)

+ X- + R,S:.X + R,S

relative solvation energies of ions (eq 7) as well as the stability of the symmetricion complex (eq 8). In the gas phase, the adducts will not be in equilibrium with ionic species (eqs 7 and 8) due to lack of solvation stabilization. Therefore, the stability of R2S:.X in solution and gas phase may be quite different. This can be seen in eq 9 in which the DMSO radical cation

R2SO+ + Cl-* R,S(O):.Cl (but not for Br-)

(9)

reacts with chloride to give the DMSO-Cl complex. The analogous reaction with bromide does not give the corresponding pr0duct.3~ The homolytic halogen-DMSO bond strengths are predicted to be similar (Table IV), which suggests that solvation effects play a determining role. The S-Cl bond length at the UHF/3-21GS level is 2.760 A (Figure 2), which is about 0.7-0.8 A longer than a typical S-Cl bond@ (2.0-2.1 A). At the UHF/3-21G* level the S-Br bond is predicted to be 2.961 A (Figure 2), which can be compared to 2.2-2.4 A in several compounds with S-Br bonds.@ The much longer bond lengths are indicative of a 2c-3e interaction where the bond order is 0.5. The DMSO adducts of C1 and Br have smaller binding energies than adducts with DMS due to a poorer energy match between the lone pair orbital of DMSO (lower in energy than DMS) and the orbital containing the unpaired electron in C1 and Br. The strength of a 2 o 3 e interaction falls off exponentially as the difference in the ionization potential between the two moieties increase~.~l,~2 For chlorine, the DMSO adduct is 4.8 kcal/mol

Reactions between O H Radical and Dimethyl Sulfide

The Journal of Physical Chemistry, Vol. 97, No. 42, 1993 10975

TABLE VII: Vibrational Frequencies (cm-l) Calculated at the HF/3-21G* Level for C1 and Br Adducts of DMS and DMSO dimethyl sulfoxide (DMSO) dimethyl sulfide (DMS) DMS (exptl)’ DMS-Cl DMS-Br assignt DMSO (exptl)b DMSO-CI DMSO-Br 3287 (2991) 3305 3300 a‘ CH3 str 3295 (2995) 3305 3 304 3288 (3013) 3306 3301 a’’ CH3 str 3292 (2995) 3302 3300 3278 (2991) 3294 3292 a’ CH3 str 3290 (2991) 3295 3294 3280 (2991) 3296 3294 a” CH3 str 3288 (2994) 3294 3293 3206 (2916) 3214 3213 a’ CH3 str 3208 (2934) 3212 3212 3208 (2852) 3216 3214 a” CH3 str 3205 (2935) 3209 3209 1663 (1456) 1650 1653 a’ CH3 def 1650 (1418) 1644 1645 1654 (1440) 1648 1650 a” CH3 def 1632 (1449) 1626 1627 1643 (1434) 1640 1642 a’ CH3 def 1627 (1403) 1621 1621 1653 (1446) 1636 1639 a” CH3 def 1613 (1443) 1607 1607 1550 (1317) 1550 1550 a’ CH3 def 1548 ( 1302) 1550 1550 1527 (1317) 1531 1529 a” CH3 def 1529 (1328) 1532 1532 a ’ s 4 str 1178 (1109) 1200 1196 1181 (1028) 1189 1188 a’ CH3 def 1167 (1008) 1168 1169 1107 (1005) 1081 1080 a” CH3 def 1065 (1034) 1072 1070 1031 (963) 1115 1115 a’ CH3 def 1064 (914) 1078 1075 1072 (972) 1045 1042 a” CH3 def 1023 (942) 1030 1029 784 (741) 785 785 a” C S as str 774 (694) 790 788 727 (691) 725 726 a’ C S s str 735 (688) 739 739 a’ S=O bend 401 (378) 407 405 a” S=O bend 330 (336) 339 337 288 (282) 294 292 a’ CSC bend 324 (305) 322 324 202 (182) 213 204 a’ CH3 tors 251 (c) 242 240 195 (173) 190 188 a” CH3 tors 204 (c) 199 195 170 135 S-X str 88 69 108 86 S-X bend 59 53 46 49 96 85 S-X bend See: Dewar. M. J. S.: Ford, G. P. J . Am. Chem. SOC.1977.99,1685. Horrocks, Jr., W. D.; Cotton, F. A. Spectrochim. Acta 1961,17,134. Not observed. weaker than the DMS adduct, while for bromine, the DMSO adduct is 1.4 kcal/mol weaker than the DMS adduct (Table IV). The vibrational frequencies of Cl and Br adducts of DMS and DMSO are compared in Table VII. The mode assignments of DMSO are used to order all other complexes so that crossing the table along a row reveals the change in wavenumber for a particular mode. Thus, there are gaps in the column of frequencies for DMS when a particular mode is not present, as for example a S=O stretch. Most modes remain nearly constant, even when comparing DMS modes with DMSO modes. Themodes involving C1and Br systematicallydecreaseon going from the DMS complex to the DMSO complex, which is in keeping with the smaller binding energies. The source of the difficulties with the DMS-OH adduct can be traced to the nature of the interaction. As can be seen in Table V, the spin density on O H and sulfur are nearly equal (0.57 and 0.58 a spin density, respectively), which indicates that the SOMO (singly occupied molecular orbital) of OH and the HOMO (highest occupied molecular orbital) or DMS areof similar energy and mix equally in forming the 2c-3e bond (Figure 3a). While unpaired spin density has been donated to sulfur, OH has a net gain of electrons as seen from the Mulliken charge on OH. For adducts of C1 and Br, the unpaired electron resides mostly on the halogen. Thus, less spin density is donated to sulfur accompanied by a smaller net gain of electrons (see spin density and Mulliken charge in Table V). The reason for this is that the SOMO of C1 and Br are a t higher energy than the SOMO for OH and the match with the HOMO of DMS is worse resulting in less orbital mixing in the formation of the 2 o 3 e bond (Figure 3b).4143 Another viewpoint pertaining to the stability of the adducts is the hard/soft acid/base theory extended to a SOMO/HOMO interaction rather than a LUMO/HOMO intera~tion.3~ Hydroxyl, which is not polarizable, is an example of a hard acid while DMS is an example of a soft base. Chlorine and bromine, on the other hand, are polarizable and can be described as soft acids, which interact with DMS to form a soft acid/soft base pair. The calculation of the soft acid/soft base interaction appears to be reasonable even at lower levels of theory. However, the best description of the DMS-OH interaction is a covalent 2c-3e

3a)

DMS

OH

‘’W

CI,Br LEWIS ACID

DMS LEWIS BASE

2c-3e-

Figure 3. Interaction diagram of the singly occupied orbital (SOMO)

of OH, C1, or Br with the highest occupied orbital (HOMO) of DMS. (a) The SOMO/HOMO orbital energies are similar in the DMS-OH adduct which results in an equal distribution of unpaired spin density on OH and DMS. (b) In the CI and Br adducts, the SOMO energy is higher, and the mismatch with the HOMO results in litte unpaired spin densityon DMS. The results for adductsformed with DMSO are expected to be similar. The HOMOof DMSO is lower than DMS which increases the mismatch of energies with C1 and Br and reduces the unpaired spin density on DMSO. bond, which requires a higher level of theory to be adequate. The majority of previous work on 2c-3e bonding (such as MezS:.SMe2+)& involve charged species where charge equalization was a large stabilizing factor in bond formation. Conclusions Hydroxylradicaladds to DMS to form a stablecomplex ( D M S OH) bound by 6.0 kcal/mol, which can be compared to an experimentally determined value of 13 f 3 kcal/mol. The geometry must be described at a high level of theory, which is why an earlier study failed to find a complex. While a barrier for OH addition to DMS was not determined, the barrier for hydrogen abstraction from DMS by OH was calculated to be 1.8 kcal/mol. Vibrational frequencies and IR intensities are reported for the DMS-OH complex at the MP2/6-31+G(2d) level. Lower level calculations were used to determine the binding energy of C1 and Br to DMS and DMSO. In contrast to DMSOH, the complexes are bound at all levels of theory. The DMSC1 and DMS-Br complexes have binding energies (12.2 and 12.1

10976 The Journal of Physical Chemistry, Vol. 97, No. 42, 1993

kcal/mol, respectively) in good agreement with experiment and are predicted to be more strongly bound than DMSO-Cl and DMSO-Br complexes (7.4 and 10.7 kcal/mol, respectively). Significant transfer of unpaired spin density occurs when the DMS-OH complex forms. In contrast, the unpaired electron resides predominately on the halogen in C1 and Br complexes, due to a poor orbital energy match. The stabilizing effect in these complexes can better be thought of as a soft acid (halogen atom) interacting with a soft base (DMS). The theoretical descriptionof 2c-3e bonding in the neutral complex (DMS-OH) requires substantially higher levels of theory than donor-acceptor interactions (DMS-Cl,Br). It can be concluded that interactions which are primarily 2c3e interactions between neutral fragments will, in general, require much higher levels of theory for reliable predictions.

Acknowledgment. I thank thedonors of the Petroleum Research Fund, administered by the American Chemical Society, for financial support. Computer time for this study was made availableby the Alabama Supercomputer Networkand theNSFsupported PittsburghsupercomputerCenter. I thankP. H. Wine for helpful discussions. References and Notes (1) Hynes, A. J.; Wine, P. H.; Semmes, D. H. J. Phys. Chem. 1986,90, 4148. (2) Wine, P. H.; Kreutter, N. M.; Gump, C. A,; Ravishankara, A. R. J. Phys. Chem. 1981, 85, 2660. (3) Hynes, A. J.; Wine, P. H. In Biogenic Sulfur in the Environment;

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