Ab initio study of the energy hypersurface of uneven sulfuranes

18 November 1994

ELSEVlER

CHEMICAL PHYSICS LETTERS

Chemical Physics Letters 230 ( 1994) 203-208

Ab initio study of the energy hypersurface of uneven sulfuranes. Dissociation of HCl from Cl-SH (OH)-Cl G&bor I. Csonka a, Michel Loos b, ArpBd Kucsman

c, Imre G. Csizmadia

d

aDepartment oflnorganic Chemistry, Technical University ofBudapest, 1521 Budapest, Hungary b Laboratoire de Chimie Thkorique, UA 510 CNRS, C’niversitCde Nancy-I, B.P. 239, 54506 Vandoeuvre-les-Nancy Cedex, France ’ Department of Organic Chemistry. Eiitvas University, Pdzmciny PPter s&&y 2, II 17 Budapest, Hungary ‘Department of Chemistry, University of Toronto, Toronto, Ontario, Canada M5S IAI’ Received 25 May 1994; in final form 5 September 1994

Abstract The MP2/6-3 11G(d) level of theory has been applied to answer the question of how the geometry and total energy changes with respect to lengthening of the S-Cl bond in Cl-SH(OH)-Cl. The results predict that the title compound would readily dissociate forming HC1 and Cl-S (H)O. The dissociation energy is calculated at the G2 (MP2) and CCSD (T) /6-3 11G(d) levels of theory with zero-point and basis set corrections. Our finding that the sulfurane structure is trapped at a high energy minimum relative to the HCl and SH(O)Cl component molecules implies that sulfurane synthesis from those components is energetically an uphill process.

1. Introduction The principle of conformationally induced doubly degenerate unevenness in sulfuranes has been introduced recently [ 11. The results of theoretical studies showed that it is possible to find a pair of degenerate structures in which the two apical bond lengths are different in a constitutionally symmetric molecule. The following examples HS-SH2-SH [ 11, ClS(OH)2-C1 and CI-S(NH2)2-Cl [2], have been published so far. This appears to be a conformationally induced trans-effect (TE) reported earlier [ 31 for Se and Te but not for S compounds, in which collinear or nearly collinear trans bonds of homoligands L-Z-L have unequal lengths. In a previous study [4] at the RHF level of theory for the energy hypersurface of the Cl-S( H)X-Cl molecules (X=OH or NH*) it was found that unevenness in the S-Cl ( 1) and S-Cl (2) bond lengths

occurs depending on the rotation of the OH and NH2 groups. The existence of this unevenness has been confirmed at higher levels of theory [ 5 1. In this Letter we wish to concentrate on the following questions. How do the molecular geometry and the total energy of Cl-SH(OH)-Cl change with respect to SCl stretching? What are the best theoretical estimates for the dissociation energy of the Cl-S(H)OH-Cl molecule to form HCl and Cl-S (H)O?

2. Theoretical

methods

The geometry of the title compound was fully optimized (except the fixed S-CI( 1) bond length) at selected points of the energy hypersurface with a series of ab initio calculations. A transition structure optimization was also performed and its result was characterized by frequency analysis. In these calcu-

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G.I. Csonka et al. / Chemical Physics Letters 230 (1994) 203-208

204

lations we used triple-split-valence plus polarization 6-31 lG(d) basis sets [ 61 at the MP2 correlated level of theory [ 71. This basis set involves five d orbitals [ 81 an the McLean-Chandler ( 12s 9p) + [ 6s 5p] basis sets [ 91 for sulfur and chlorine atoms. To estimate the dissociation energy we apply G2 (MP2) theory [ lo]. G2 (MP2) theory, described in ref. [lo], is based on MP2=FU/6-31G(d) ’ geometries. Energies are calculated at the QCISD (T) / 6-311G(d, p) level with corrections. In G2(MP2) theory the basis set extension correction is obtained at the MP2 level

Because there is no change in the number of (Yand j3 electrons for the chemical reaction discussed in this Letter the difference in HLCs (AE(HLC)) is zero. Thus we will not use the HLC terms explicitly. We use the same zero-point corrections as in G (MP2 ) theory. The total energy calculated with CCSD theory with triple excitations using MP2 basis set correction (CT2 ) is given by

AE(MP2)=E(MP2/6-311

We replace the QCISD (T) term of G2 (MP2) theory with a CCSD( T) term because the QCI is an approximation to the CC equations where some quadratic, cubic and higher order terms are excluded. It is easier to implement and to carry out the QCI methods than the CC methods, however the latter is theoretically more precise. It should be noted that in our case the QCISD(T) and CCSD(T) perform equally well. We do not include the p polarization functions for the hydrogens in the basis set at the CCSD(T) level. This is advantageous computationally for the hydrogen containing molecules. We shall show that the MP2 correction accounts well for this basis set effect at much lower computational cost. The ab initio calculations were carried out using the GAUSSIAN 92 computer program [ 121 on a Silicon Graphics R4000 Indigo workstation.

-E(MP2/6-31

lG(d,

+G(3df,

2p))

p)) .

(1)

A higher-level correction (HLC ) to account for remaining basis set deficiencies is added. This is (in millihartree)E(HLC)=-O.l9n,-4.81ng,wheren, and ng, are the number of cx and /I valence electrons respectively, with n,> ns The value of -4.8 1 was chosen to give the smallest absolute deviation from experiment for a set of 125 well established experimental values. Finally, the energy E(0) is obtained by adding the zero-point correction (E(ZPE)), obtained from scaled (0.893) HF/6-31G(d) wavenumbers. The total G2 (MP2 ) energy is given by E(O)=E(QCISD(T)/6-31 +AE(MP2)

+E(HLC)

lG(d, +E(ZPE)

p)) .

lG(d))

.

+AE’ (MP2) +E(ZPE)

.

(4)

(2)

In this Letter we suggest replacing the MP2=FU/ 6-31G(d) geometries with the MP2=FC/6-31G(d) geometries. The use of valence electrons only (FC=frozen core) instead of all the electrons provides a substantial savings in computational time and disk storage during the geometry optimization. We also suggest calculating the energies at the CCSD (T) / 6-3 11G (d) level [ 11 ] then adding correction terms. The basis set extension correction is obtained at the MP2 level

-E(MP2/6-31

E,,,(O)=E(CCSD(T)/6-311G(d))

(3)

’ The following abbreviation is used: FU=full; MP2=F’U/63 I G (d) imply that all possible excitations were used within the second-order Meller-Plesset perturbation theory.

3. Results and discussion Fig. 1 illustrates an MP2/6-3 11G (d) potential energy curve cross section of the potential energy hypersurface associated with the dissociation of the ClSH(OH)-Cl molecule. The two apical chlorine atoms are numbered as shown in Fig. 1. Clearly, the Cl ( 1) atom is closer to the OH proton than the Cl( 2) atom. The unevenness is due to the fact that the syn and anti C, symmetry conformations of the title compound were found to be transition states and a pair of asymmetric conformations were degenerate energy minima (see Fig. 2 in Ref. [ 5 ] ) . Our previous calculations [ 5 ] at MP2/6-31 lG(d)/MP2/631 lG(d) and CCSD(T)/6-31 lG(d)//MP2/6-

205

G.I. Csonka et al. / Chemical Physics Letters 230 (1994) 203-208

Cl(l) H p 0

z.

.-~~--~~~____.. H I-

s

AE(dissoc)

\

Cl(2) 3

./

H-BONDED COMPLEX

+ HCl I ElSSE"2kcalhml

fl

Fig. 1. Potential energy curve for the dissociation of Cl-SH(OH)-Cl to HS(O)CI+HCI computed at the MP2/6-31 lG(d) level of theory. This is a cross section of the potential energy hypersurface along the S-Cl ( 1) parameter with all other parameters optimized. The S-Cl( 1) distance is a convenient parameter for graphical presentation and it is not meant to be interpreted as a reaction coordinate. A vibrational analysis shows that the most important geometry change in the transition structure is the O-H and H-Cl distance change at nearly constant S-Cl( I ) distance. The optimized transition structure is marked by a cross at S-CI( 1) = 288.09 pm.

3 11 G(d) levels of theory supported the earlier RHF results [ 41 in this respect. Table 1 shows the optimized geometric parameters and the total energy as a function of the selected SCl( 1) distances at the MP2/6-31 IG(d) level of theory. This study may shed some light on the consequences of the geometrical unevenness existing in the title compound. If the S-Cl ( 1) bond length is forced below 235 pm, then the S-Cl(2) bond length becomes longer than its equilibrium distance (2 19.67

pm). In contrast, as the S-Cl( 1) distance lengthens beyond 235 pm, the S-Cl( 2) bond length shortens. A dramatic change occurs if the S-Cl ( 1) distance is allowed to stretch above 290 pm, when the O-H bond breaks and two separate molecules, HS(O)Cl and HCI, are formed. The optimized transition structure is indeed close to this point (S-Cl( I ) =288.09 pm in Table 1). The barrier height was found to be 10.64 kcal/mol relative to the sulfurane structure (Table 1 ). If, after the transition structure, we fix the

G.I. Csonka et al. / Chemical Physics Letters 230 (1994) 203-208

S-Cl ( 1) distance at 3 10 pm and we let relax the rest of the geometrical parameters, then further full optimization would lead to two separate molecules as shown by the geometrical changes and the considerably lower energy of the molecule. To obtain a reliable prediction for the dissociation energy we performed a series of high-level calculations. First we optimized the structures of HCl and HS(O)CI at the MP2/6-31 lG(d) level. The dissociation energy calculated at this level of theory ( - 8.05 kcal/mol) is nearly identical with the - 8.00 kcal/mol stabilization energy found at 310 pm SCl ( 1) distance (Table 1) . Next we reoptimized the geometries at MP2=FC/ 6-3lG(d) level for the CT2 and G2(MP2) studies described below. The two nearly identical MP2 results in Tables 1 and 2 ( - 8.05 and - 8.09 kcal/mol) show that the different choice of equilibrium geometries (MP2/6-31G(d) and MP2/6-3lG(d), respectively) has only a minor effect on the calculated dissociation energy. Table 2 shows that the CCSD(T)/6-31lG(d) energy difference ( - 7.84 kcal/mol) is close to the corresponding results obtained by MP2. This means that the MP2 is satisfactorily converged in this case. If we correct the CCSD( T) energy, then our predicted CT2 dissociation energy is -7.30 kcal/mol at 0 K (Eq. (4) ). The results obtained by our basis set study given in Table 2 shows that the calculated dissociation energy is sensitive to the basis set used. However, the effect is small beyond the 6-311 +G(2d, p) level of theory and the computational cost increases rapidly. To check our prediction for the dissociation energy we performed a QCISD (T ) /6-3 11 G (d, p) calculation necessary for G2 (MP2) theory (Table 2). This level of theory yields reliable dissociation energies [ lo]. The G2(MP2) dissociation energy is - 7.68 kcal/mol (Eq. (2) ). The fairly good agreement between the two predicted dissociation energies shows that our prediction is reliable. This good agreement is partly due to the fact that the energetic correction of the basis set extension from (d) to (d, p) at the MP2 level (-2.05 kcal/mol) is nearly equal to the QCISD (T) energy change ( - 2.14 kcal/mol ). Consequently, the error of this approximation is less than 0.1 kcal/mol, and this small error justifies the validity of the omission of the p polarization functions in the computer time demanding QCISD (T) method.

201

G.I. Csonka et al. / Chemical Physics Letters 230 (1994) 203-208 Table 2 Calculated total energies tion energies (kcal/mol)

(hartree) and zero-point vibrational energies for HCI, Cl-S(H)0 for the Cl-S(H)OH-Cl+HCl+Cl-S(H)OH-Cl reaction a

and Cl-S(H)OH-Cl

molecules

and dissocia-

HCl

Cl-S(H)0

Cl-SH(OH)-Cl

&E(diss.)

CCSD(T)/6_311G(d) MP2/6-31 lG(d) MP2/6-31 lG(d, p) MP2/6-311 +G(2d, p) MP2/6-311 +G(3df, p) MP2/6-311+G(3df, 2p)

- 460.24513 -460.22658 -460.24400 -460.26487 -460.29712 -460.29874

-932.92718 -932.88737 -932.90156 -932.99096 -933.08496 -933.08612

-1393.16041 -1393.10106 - 1393.12938 - 1393.24616 - 1393.3729 - 1393.37617

- 7.84 - 8.09 - 10.14 -6.07 -5.75 -5.45

QCISD(T)/6-31 QCISD(T)/6-31

-460.24577 -460.26336

-932.92842 -932.94324

- 1393.16123 - 1393.19022

hE(ZPE)

IG(d) lG(d, p)

0.00649

b HF/6-31G(d)

’ Frozen core results calculated b Corrected with 0.893.

in the MP2/6-3

IG(d)

equilibrium

Another reason for the good agreement is that the QCISD(T)/6-31 lG(d) and CCSD(T)/6-31 lG(d) results agree well with each other (Table 2 ) . As was noted earlier, the MP2 calculations are satisfactorily converged in this case yielding -7.54 kcal/mol for the dissociation energy with the 6-3 1 1 + G( 3df, 2p) basis set and with ZPE correction. In conclusion we may say that the stereoelectronic effects previously referred to as conformational induction [ 1,2,4] are in fact stabilizing the asymmetric molecular conformation relative to the possible C, symmetric syn and anti conformations. This is a preparatory step toward the dissociation of the ClSH(OH)-Cl molecule. Biirgi and Dunitz [ 13-l 51 have already shown that the relative positions of reactive moieties in the crystalline state are in fact along the direction that one expects from reactants in the early stages of a given reaction. This phenomenon was also observed for the gas phase structures [ 161. In the present case the Cl-SH( OH)-Cl molecule may dissociate in a number of possible ways. The distortion of the title compound already indicates the direction of one particular dissociation mode leading to HCl and SH(O)Cl. The fact that the sulfurane structure is trapped at a high-energy minimum relative to the HCl and SH (0) Cl component molecules implies that sulfurane synthesis is energetically an uphill process. Thus the addition of the HCl to the S=O double bond, unlike the addition of the HCl to the C=C double bond, is energetically unfavorable. The implication of this

0.01773

0.02756

I

-8.13 - 10.27 -2.09

geometries.

observation is that sulfurane synthesis requires special considerations, where the reactant states are higher on the energy (enthalpy) scale than the product sulfurane itself leading to an exothermic reaction.

Acknowledgement The authors are indebted to Dr. P. Csaszar for providing expert technical skills while preparing this manuscript. The financial support of the Hungarian Research Foundation (OTKA I/3 No. 644 and 2244) is acknowledged. The continuous financial support of the Natural Sciences and Engineering Research Council (NSERC) is gratefully acknowledged.

References [ I] M. Loos? J.-L. Rivail, A. Kucsman and LG. Czismadia, J. Mol. Struct. THEOCHEM 230 ( 199 1) 143. [2] M. Loos, J.-L. Rivail, A. Kucsman and LG. Csizmadia, Phosphorus Sulfur Silicon 74 ( 1993 ) 44 1. [3] 0. Knopp, S.C. Choi and D.C. Hamilton, Can. J. Chem. 10 ( 1992) 2574. [ 41 E.A. Innes, I.G. Csizmadia, J.-L. Rivail, M. Loos and A. Kucsman, submitted for publication. [ 51 G.I. Csonka, M. Loos, A. Kucsman and I.G. Csizmadia, J. Mol. Struct. THEOCHEM, in press. [ 6 ] R. Krishnan, J.S. Binkley, R. Seeger and J.A. Pople, J. Chem. Phys. 72 ( 1980) 650; D.J. DeFrees, J.S. Binkley and A.D. McLean, J. Chem. Phys. 80 (1984) 3720.

208

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[ 7 ] R. Krishnan, M.J. Frisch and J.A. Pople, J. Chem. Phys. 72 ( 1980) 4244, and references therein. [8] A. Rauk and LG. Czismadia, Can. J. Chem. 46 (1968) 1205. [ 91 A.D. McLean and G.S. Chandler, J. Chem. Phys. 72 ( 1980) 5639. [ lo] L.A. Curtiss, K. Raghavachari and J.A. Pople, J. Chem. Phys. 98 (1993) 1293. [ 111 J. Ciiek, J. Chem. Phys. 45 (1966) 4256; J. Paldus, J. &ek and I. Shavitt, Phys. Rev. A 5 ( 1972) 50; J.A. Pople, R. Krishnan, H.B. Schlegel and J.S. Binkley, Intern. J. Quantum Chem. I4 ( 1978) 545; G.D. Purvis and R.J. Bartlett, J. Chem. Phys. 76 (1982) 1910; J.A. Pople, M. Head-Gordon and K. Raghavacahri, J. Chem. Phys. 87 (1987) 5968;

G.E. Scuseria and H.F. Schaefer III, J. Chem. Phys. 90 (1989) 3700. [ 12 ] M.J. Frisch, G. W. Trucks, M. Head-Gordon, P.M.W. Gill, M.W. Wong, J.B. Foresman, B.G. Johnson, H.B. Schlegel, M.A. Robb, E.S. Replogle, R. Gomperts, J.L. Andres, K. Raghavachari, J.S. Binkley, C. Gonzalez, R.L. Martin, D.J. Fox, D.J. DeFrees, J. Baker, J.J.P. Stewart and J.A. Pople, GAUSSIAN 92, Revision C (Gaussian, Pittsburgh, 1992 ). [ 131 H.B. Bhrgi, Angew. Chem. 87 (1975) 461. [ 141 R.E. Rosentield Jr., R. Parthasarathy and J.D. Dunitz, J. Am. Chem. Sot. 99 ( 1977) 4860. [ 151 D. Britton and J.D. Dunitz, Helv. Chim. Acta 63 (1980) 1068. [ 16 ] J.G. Angyan, R.A. Poirier, A. Kucsman and I.G. Csizmadia, J. Am. Chem. Sot. 109 (1987) 2237.