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Bond strengths of the gas-phase cluster ions X− (CS2)n (X = F, Cl, Br and I)
Volume 208, number$6
CHEMICAL PHYSICS LETTERS
18June 1993
Bond strengths of the gas-phase cluster ions X-(C$), (X=F, Cl, Brand I) Kenzo Hiraoka, Susumu Fujimaki, Kazuo Aruga Faculty OfEngineering, Yamanashi University, Takeda-4, Kofir 400, Japan
and
Shinichi Yamabe Department of Chemistry, Nara University ofEducation, Takabatake-cho, Nara 630, Japan
Received 31 July 1992; in final form 13 April 1993
Thermodynamic quantities, AH:_ ,,* and AS:_ ,,“, for the clustering reactions, X-(CSI),_,+CSz=X-(CS,),, X=F, Cl, Br and I, were measured with a pulsed electron-beam high-pressure mass spectrometer. A large binding energy, 35.0 kcal/mol, for F-...CS2 has been obtained, whereas those for other X-...C!& species are approximately 7-9 kcal/mol. Except the &, F-(CS2), geometry, linear X- (C!&), geometries are found, arising from the Sd’-Cd-G?’ electronic nature and an effective polarization of “soft” atoms.
1. Introduction
Carbon disulfide is an industrially important reagent and is known to undergo nucleophilic attacks from hard bases. For instance, potassium ethoxide ( C2H50-K+ ) reacts with CS2 in ethanol to yield potassium xanthate (C,H,OCS-K' ). It is tempting to examine the gas-phase solvation strength toward halide ions systematically, because the X-...CS2 interaction is thought to depend significantly on the kind of X ( =F, Cl, Br or I). Is the carbon atom of CS2 always a target for all halide ions? CS2 is isovalent with carbon dioxide CO1. It is of thermochemical interest to compare the X-...C02 and X-...C!$ bonding patterns. In order to provide solvent-free basic data, we have determined the binding energies of the cluster ions of X- (CS,) n by observing the equilibria of the gasphase clustering reaction x-(C&).-I
+cs*=x-(cs2),
.
(1)
To check the experimental binding energies derived from the van’t Hoff plots and to obtain structural information, ab initio calculations on X - ( CS, ) ,, ( n = I
and 2) were also carried out. Obtained energies and structures are analyzed in terms of the size of ions and the electronic nature of CS2.
2. Experimental and computational methods The experiments were made with a pulsed electron-beam high-pressure mass spectrometer. The general experimental procedures were similar to those described in our previous paper [ 11. Briefly, the buffer gas N2 was purified by passing it through a dry-ice acetone cooled 3A molecular sieve trap. CS2 and electron capture agents, NF3, CCL,, CH2Br2 and CHJ producing the ions F-, Cl-, Br- and I-, respectively, were introduced into the 0.5-3 Torr of N2 carrier gas through flow controlling stainless steel capillaries. The pressures of NF3, CC&, CH2Br2 and CHJ introduced into the N2 buffer gas were z 50, x 1, 1 X 10m3and x 1 mTorr, respectively. The equilibrium constants were independent of the change of CSZ pressure in the range of lo-50 mTorr. Structures of X- (C$), (n = 1 and 2) are fully optimized with ab initio MO calculations of the 3-
0009-2614/93/.$ 06.00 0 1993 Elsevier Science Publishers B.V. All rights reserved.
491
Volume 208, number 5,6
CHEMICAL PHYSICS LETTERS
18 June 1993
2 1+ G basis set where + means a diffuse sp orbital
on all atoms. The orbital exponents are 0.0438 (C), 0.0405 (S), 0.1076 (F), 0.0438 (Cl), 0.060 (Br) and 0.054 (I), respectively. Exponents of Br and I are obtained by minimizing total energies of bromide and iodide ions. Other exponents (of C, S, F and Cl) of diffuse orbitals are taken from the literature [2]. The F-...C$ cluster (n= 1) is expected to have a large binding energy, and there are large lobes on sulfur atoms. Consequently, the basis-set superposition error (BSSE) involved in the F...C semi-covalent bond would be significant. 3SSE is corrected by the counterpoise method [ 31. Also, the energies are re-evaluated with a more accurate method, i.e. MP2/DZP geometry optimization plus a counterpoise correction. MP2 is the second-order Msller-Plesset perturbation [ 41, and DZP is the Huzinaga-Dunning basis set [ 5 ] augmented with 6d orbitals of exponents, 0.75(C), 0.90(F) and 0.532(S), and a set of sp diffuse orbitals of the abovementioned exponents. For RHF/3-2 1 +G optimized geometries of X- ( CS2) ,, vibrational analyses have been made to check whether they correspond to stable species or to saddlepoints. Four X-(CS2), clusters (X=F, Cl, Br and I) are confirmed to be at the energy minima. Subsequently, entropy changes, A.!& (T=298.15 K and P= 1 atm) are evaluated theoretically_ All the ab initio calculations are performed using GAUSSIAN 90 [ 61 installed at the CONVEX C-220 computer. Except the 3-2 1+ G basis set of Br and 1 [ 71, basis sets are those implemented in the GAUSSIAN 90.
3. Experimental results The results for the experimentally measured equilibrium constants for reaction ( 1) are displayed in the van? Hoff plots in fig. 1, The lower limits of the temperatures for the measurements of the equilibrium constants correspond to the start of the condensation of CS2 or electron capture agents on the wall of the ion source. In table 1, the enthalpy and entropy changes for reaction ( 1) obtained from fig. 1 are summarized. For comparison, thermochemical data of the following reaction [ 1 ] are also displayed in table 1: 492
16’1 103,
1.5
2.0*
2.5 .
3.0 a
3.5 .
4.08
4.5.
5.0 1
5.5 .
$1 y*‘“pp _
-
7, i y
1.5
2.5
3.0
3.5
4.0
,j 4.5
5.0
5.5
6.0
8
6.0
BilCS*ln
102. IO’-
2
/
loo.
10-l1.5* 103. _-
20
6.0 ,
’
2.0 1..
’
2.5
’
3.0
/ *
3.5 11
’
40
3
4.5 I1
’
5.0
5.5 I.
’
1
I-(CSzh
IO2
g, 1.5
,
,
,
2.0
2.5
3.0
,I
,J<, 3.5
lOOO/
4.0
4.5
5.0
5.5
6.0
T(K)
Fig. 1. Van’t Hoff plots of the gas-phase clustering reactions, Integer number in the figure X-(CS,)“-, +C&=X-(C&),,. stands for the value of n.
x-(co~),_~+co*=x-(co~),.
(2)
In fig. 1, the plot for X =F with n= 1 is isolated in the high-temperature region. This indicates covalent bond formation in the complex of F- and CS2. The observed sharp drop of -AH:_,, with n=2 for X = F is due to the drastic change of the nature of bonding of F- ( CS2), from covalent to electrostatic with n= 1+2. The values -ME_ ,,- with na2 for X=F are smaller than those for other halide ions, arising from the charge delocalization in FCS, and make the subsequent electrostatic interaction with CS2 ligands less favorable than other halide ion clusters X-(C$), (n32) (see section 5). In our laboratory, the bond energies of halide ions with various solvent molecules M have been measured, M=H20 [8], CH$N [8], CsHs [9], CsF6 [lO,ll],COz [l] andN20 [12].Itwasfoundthat the thermochemical stabilities of the cluster ions
18 June 1993
CHEMICAL PHYSICS LETTERS
Volume 208, number 5,6
Table 1 Thermochemical data, w_,,” in kcal/mol and -a_ ,.a in Wmol K of the gas-phase clustering reaction (l), X - (C&).--I +CSZ= are computed with RHF/3-21 +G, and that in X-(CS& (X=F, Cl, Br and I). Underlined numbers in -AH& and -ti~_,,~ -~_,,~intheparentheseswith (n-l,n)=(O, I)forX=FiswithMP2/DZP//MP2/DZP.DatainsquarebracketsareforX-(C02). in reaction ( 2 ) for comparison (ref. [ 11) (n-l,n)
x F
@,I )
(192)
(233) (334)
Br
Cl
-AK-,,
-A%.”
35.0+ 1.5 W?(G) E(C& f32.04) (C2”) [32.3] 6.71 kO.2 2.12(n) m(b) 3.60(c) w(d) 17.31 05.4 17.21 l5.81
28.2 f 3.0 23.74 126.71
lS.3k2.0
[ 18.21
17 ” [22.6] [20.3]
-W-r,
I
-As:-,..
- MlI- 1.r
-hs:-1.m
-A&
877f0.2 2.73( C,) 7.11(&h) i7.61
13.9 f 2.0 13.63 18.50 [18.21
8.3 + 0.2 1.87G”) 5.24(Cm!A) t6.71
13.0+ 2.0 12.22 17.00 [16.51
7.4+0.2 1.56(G) 4.41(Cccb) l4.71
16.7+2.0 11.3L 16.27 [13.4]
7.74kO.2 7.36(D,,) i7.21
20.4 2 2.0
6.75 kO.2 w(Dmb) l4.61
21.7f2.0
[ 20.81
l4.51
18.41
14.31
[ 19.01
7.18kO.2 16.81 a6.8 [ a6.41
IS.8 + 2.0
7.3kO.2 E(D,)
[ 19.01
16.01
21.3f2.0
1.1
-AK,,
[ 22.41 23 a) [24’)]
*r Entropy value assumed.
X- (M), are generally in the order of F- > Cl- = Br- r I-, i.e. the stabilities of X- (M),, for Cland Br- are of the same order and those for I- are smaller. For example, as shown in square brackets of table 1, the bond energies of X- ( CO1), are in the order Cl- 2 Br- > I-. In contrast to the previously observed general trend, the -ALri_ ,,” values of reaction ( I) for X =Cl, Br and I are much closer to each other as shown in table 1. In addition, the bond energies of I - (CS,), are larger than those of I- (CO,), and close to those for Cl- (CO,),. These experimental results may be explained by the hard and soft acids and bases concept (HSAB) due to Pearson [ 13 1. This states that a soft base prefers to combine with a soft acid rather than a hard acid. The polarizabilities [ 141 of F-, Cl-, Br- and I- are x 1.2, ~3, z 4.5 and ~7 A3 and those of CO2 and C!$ are 2.59 and 8.08 A3, respectively. The larger polarizabilities of I- and CS2 result in the favorable soft base-soft acid interaction in I-...C&
4. Computational results In section 3, the following two results have been described: ( 1) The F-...CS, binding energy is large, 35.0 kcal/ mol. In contrast, the F-(CSz)...C& energy is the smallest, 6.71 kcal/mol, with n=2 in table 1. (2) The X- (C&),_ ,..CS, binding energies (X = Cl, Br, and I) are similar, 7-9 kcal/mol. These almost constant values suggest that the clustering bonds are quite different from that in F- (CSz )“. (3) For the four halide ions, the X-...C$ bond is stronger than the X-...C02 bond [ 11. In order to explain these experimental results, ab initio geometries and binding energies are calculated. Fig. 2 exhibits fully optimized geometries of X- (CS,) ,_For all halide ions, two isomers, Cm,.,and CzV,are obtained. While Ct, geometries are as expected prior to calculations, Csohones are noticeable in consideration of the absence of the X-...O==C=O linear cluster [ 11. The stability of two isomers is compared. For X = F, the expected xanthate-type CzV geometry is much better than the Cmh one in table 493
Volume 208, number $6
CHEMICAL PHYSICS LETTERS
Fig. 2. Two isomers (C,, and C,,) of the X- (CS2)1cluster optimized with RHF/3-21 +G. For X= F, MPZ/DZP geometric parameters are given in parentheses. The GS bond length of the free carbon disulfide is computed to be 1.581 A. I. On the contrary, other halide ions than F- are found to prefer Cmh to CZV. Four isomers a, b, c and d of F-(CS2)2 are investigated on the basis of the CZVgeometry of F- (CS,)I. After geometry optimization, they are obtained as shown in fig. 3. The model a is found to be of C, symmetry and the other three are of CZ, symmetry. In these geometries of n=2, the n= 1 structure is almost unperturbed, which shows that the F- (CS,) ,_..C& interaction is weak and electrostatic. In fact, computed binding energies of n= 1+ 2 are small, 2.12 (a), 5.14 (b), 3.60 (c) and 6.91 kcal/ mol (d) in table 1. The model d is best among four isomers, indicating that the fluorine atom in F- ( CSZ)1 is the most attractive site for not carbon but sulfur of the second C!$. Optimized geometries of X- ( CS2) Z (X= Cl, Br and I) are displayed in fig. 4. Although no symmetry
494
18June1993
assumption on the n = 2 geometries is made, most stable geometries are found to be of DoDhsymmetry. Thus, the slow decay of binding energies of X- (C$), (X=Cl, Br and I) in table 1 with n is explicable’in terms of symmetric structures. The n= 3 geometries may be of Dsh symmetry and the n=4 ones may be of Td symmetry. Fig. 5 exhibits net charges of CS2 and X- (CL&), (X=F and Cl) together with those of COZ and X-(C02),. While the carbon atom of CO1 is cationic, that of CS2 is anionic. This is in accord with the fact that the signs of the quadrupole moments of CO2 (-4.3x 10ez6 esu cm2) and C!$ (1.8~ 1O-24 esu cm’) are opposite [ 151. This difference is reflected in the contrast of the CZVX-(C02)1 versus the Cmh X- ( CSZ), for X=Cl, Br and I. Although F- ( COa) I and F- ( CS2), are found to be of CZV symmetry, the net charges on the carbon atom are different. The ( - 1) charge dispersal is more extensive in FCS: , leading to the larger -AJ& , and the smaller - AZ& of F- (CS,), than those of F- (CO,),. Next, the cationic carbon in CO2 and sulfur atoms in CS2 are bound to Cl-, respectively, Besides this evident electrostatic force, a large charge polarization in sulfur atoms of Cl-...S=C=S is found. According to HSAB, the combination of soft acids and bases induces the effective polarization. The linear geometry of X-...S=C=S (X = Cl, Br and I ) may undergo this interaction. Computed energies are compared with observed in table 1. The difference bevalues of -MI]_,,, tween two computed energies, 38.33 and 32.02 kcal/ mol of F -...C$ means that the electron-correlation effect on the binding energies works in the strongly interacting system to some extent. Since the counterpoise method tends to overcompensate the BSSE [ 161 (e.g., +7.33 kcal/mol with RHF/3-21 tG), 32.02 plus a few kcal/mol is a reasonable theoretical binding energy and is close to -AH:,, = 35.0 kcal/ mol. While computed energies of X = F and Cl are in good agreement with - AH:_ ,,,, values, those of X = Br and I are a few kcal/mol smaller than the observed ones. This small disagreement as well as the slightly larger computed ( 1,2) binding energies than the (0, 1) ones for X=Cl, Br and I is probably owing to the imbalance of the 3-21 +G basis set between the large halide ions and the sulfur atom.
18 June 1993
CHEMICAL PHYSICS LETTERS
Volume 208, number 5-6
(b)
(d) Fig. 3. Four isomers of the F- (CS2)2 cluster. b, c, and d are found to be of Czvsymmetry.
(4.43
6’3.47)
(4.70) (LWI
c
l-)
P
CLr----c W”‘l
(.0086)
W.m
l-o.9si“.. I b ML&m(4.47)
Fig. 5. Mulliken atomic net charges (positive, cationic) of carbon &sulfide, X-(COz), and X-(CS2), (X=F and Cl) computed with RHF/6-3 1G. Since basis sets including diffuse functions (i.e. 3-21 +G) tend to give unreasonable charges, the 63 1G basis set is adopted. Underlined numbers in parentheses of Cl-...C02and Cl-...C& denote atom-atom bonding populations. 5. l&h
Fig.4. Geometries of X-(CS& (X&l, Brand I) optimized with RHF/3-21 +G. Three clusters are computed to be of DoDh symmetry.
Concluding remarks
This work has dealt with the gas-phase clustering reaction of halide ions and carbon disulfide. A strong F-...CS2 bond is formed through the effective charge dispersal in the cluster. The stability of the potassium xanthate may be ascribed to this charge delo495
Volume 208, number 5,6
CHEMICAL PHYSICS LETTERS
calization. Other halide ions than F- are linked with S=C=S linearly with 9-7 kcal/mol binding energies. This linearity is ascribed to the polarization stabilization between “soft” atoms.
Acknowledgement We would like to express our appreciation for the financial support of the Morino Foundation for Molecular Science and the Grant-in-Aid in part for Scientific Research on Priority Area “Theory of Chemical Reactions’* from the Japanese Ministry of Education. We also thank the Information Processing Center of Nara University of Education for the allotment of CPU time on the CONVEX C-220 computer.
References [ I] K. Hiraoka, S. Mizuse and S. Yamabe, J. Chem. Phys. 87 (1987) 3647.
[ 2 ] T. Clark, J. Chandrasekhar, G.W. Spitznagel and P. van R. Schleyer, J. Comput. Chem. 4 (1983) 294.
[ 31 S.F. Boys and F. Bernardi, Mol. Phys. 19 (1970) 553.
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[4] W.J. Hehre and J.A. Pople, I. Am. Chem. Sot. 94 ( 1972) 690 1, and references therein to earlier theoretical work. [ 5 ] S. Huzinaga, J. Chem. Phys. 42 ( 1964) 1293; T.H. Dunning, J. Chem. Phys. 53 (1970) 2823; 55 (1971) 716. [6] M.J. Frisch, M. Head-Gordon, G.W.Truck.5, J.B. Foresman, H.B. Schlegel, K. Raghavachari, M. Robb, J.S. Binkley, C. Gonzalez,D.J. DeFrees, D.J. Fox, R.A. Whiteside, R. Seeger, C.F. Melius, J. Raker, R.L.Martin,L.R. Kahn, J.J.P. Stewart, S. Topiol and J.A. Pople, GAUSSIAN 90, Revision (Gaussian Inc., Pittsburgh, PA, 1990). [7 ] K.D. Dobbs and W.J. Hehre, J. Comput. Chem. 7 ( 1986) 359. [8] K. Hiraoka, S. Mizuse and S. Yamabe, J. Phys. Chem. 92 (1988) 3943. (91 K. Hiraoka, S. Mizuse and S. Yamabe, Chem. Phys. Letters 147 (1988) 174. [lo] K. Hiraoka, S. Mizuse and S. Yamabe, J. Phys. Chem. 9 1 (1987) 5294. [ 111 K. Hiraoka, S. Mizuse and S. Yamabe, J. Chem. Phys. 86 (1987) 4102. [ 121 K. Hiraoka, S. Fujimaki, K. Aruga and S. Yamabe, to be published. [ 131 R.G. Pearson, J. Chem. Educ. 45 (1968) 58. [ 141 R.J.W. Ix Fbvre, Advan. Phys. Org. Chem. 3 (1963) 1. [15]D.E.StrogrynandA.P.Strogryn,Mol.Phys. 11 (1966) 371. [ 161K. Morokuma and K. Kitaura, in: Chemical applications of atomic and molecular electrostatic potentials, eds. P. Politzer and D.G. Truhlar (Plenum Press, New York, 1981)
CHEMICAL PHYSICS LETTERS
18June 1993
Bond strengths of the gas-phase cluster ions X-(C$), (X=F, Cl, Brand I) Kenzo Hiraoka, Susumu Fujimaki, Kazuo Aruga Faculty OfEngineering, Yamanashi University, Takeda-4, Kofir 400, Japan
and
Shinichi Yamabe Department of Chemistry, Nara University ofEducation, Takabatake-cho, Nara 630, Japan
Received 31 July 1992; in final form 13 April 1993
Thermodynamic quantities, AH:_ ,,* and AS:_ ,,“, for the clustering reactions, X-(CSI),_,+CSz=X-(CS,),, X=F, Cl, Br and I, were measured with a pulsed electron-beam high-pressure mass spectrometer. A large binding energy, 35.0 kcal/mol, for F-...CS2 has been obtained, whereas those for other X-...C!& species are approximately 7-9 kcal/mol. Except the &, F-(CS2), geometry, linear X- (C!&), geometries are found, arising from the Sd’-Cd-G?’ electronic nature and an effective polarization of “soft” atoms.
1. Introduction
Carbon disulfide is an industrially important reagent and is known to undergo nucleophilic attacks from hard bases. For instance, potassium ethoxide ( C2H50-K+ ) reacts with CS2 in ethanol to yield potassium xanthate (C,H,OCS-K' ). It is tempting to examine the gas-phase solvation strength toward halide ions systematically, because the X-...CS2 interaction is thought to depend significantly on the kind of X ( =F, Cl, Br or I). Is the carbon atom of CS2 always a target for all halide ions? CS2 is isovalent with carbon dioxide CO1. It is of thermochemical interest to compare the X-...C02 and X-...C!$ bonding patterns. In order to provide solvent-free basic data, we have determined the binding energies of the cluster ions of X- (CS,) n by observing the equilibria of the gasphase clustering reaction x-(C&).-I
+cs*=x-(cs2),
.
(1)
To check the experimental binding energies derived from the van’t Hoff plots and to obtain structural information, ab initio calculations on X - ( CS, ) ,, ( n = I
and 2) were also carried out. Obtained energies and structures are analyzed in terms of the size of ions and the electronic nature of CS2.
2. Experimental and computational methods The experiments were made with a pulsed electron-beam high-pressure mass spectrometer. The general experimental procedures were similar to those described in our previous paper [ 11. Briefly, the buffer gas N2 was purified by passing it through a dry-ice acetone cooled 3A molecular sieve trap. CS2 and electron capture agents, NF3, CCL,, CH2Br2 and CHJ producing the ions F-, Cl-, Br- and I-, respectively, were introduced into the 0.5-3 Torr of N2 carrier gas through flow controlling stainless steel capillaries. The pressures of NF3, CC&, CH2Br2 and CHJ introduced into the N2 buffer gas were z 50, x 1, 1 X 10m3and x 1 mTorr, respectively. The equilibrium constants were independent of the change of CSZ pressure in the range of lo-50 mTorr. Structures of X- (C$), (n = 1 and 2) are fully optimized with ab initio MO calculations of the 3-
0009-2614/93/.$ 06.00 0 1993 Elsevier Science Publishers B.V. All rights reserved.
491
Volume 208, number 5,6
CHEMICAL PHYSICS LETTERS
18 June 1993
2 1+ G basis set where + means a diffuse sp orbital
on all atoms. The orbital exponents are 0.0438 (C), 0.0405 (S), 0.1076 (F), 0.0438 (Cl), 0.060 (Br) and 0.054 (I), respectively. Exponents of Br and I are obtained by minimizing total energies of bromide and iodide ions. Other exponents (of C, S, F and Cl) of diffuse orbitals are taken from the literature [2]. The F-...C$ cluster (n= 1) is expected to have a large binding energy, and there are large lobes on sulfur atoms. Consequently, the basis-set superposition error (BSSE) involved in the F...C semi-covalent bond would be significant. 3SSE is corrected by the counterpoise method [ 31. Also, the energies are re-evaluated with a more accurate method, i.e. MP2/DZP geometry optimization plus a counterpoise correction. MP2 is the second-order Msller-Plesset perturbation [ 41, and DZP is the Huzinaga-Dunning basis set [ 5 ] augmented with 6d orbitals of exponents, 0.75(C), 0.90(F) and 0.532(S), and a set of sp diffuse orbitals of the abovementioned exponents. For RHF/3-2 1 +G optimized geometries of X- ( CS2) ,, vibrational analyses have been made to check whether they correspond to stable species or to saddlepoints. Four X-(CS2), clusters (X=F, Cl, Br and I) are confirmed to be at the energy minima. Subsequently, entropy changes, A.!& (T=298.15 K and P= 1 atm) are evaluated theoretically_ All the ab initio calculations are performed using GAUSSIAN 90 [ 61 installed at the CONVEX C-220 computer. Except the 3-2 1+ G basis set of Br and 1 [ 71, basis sets are those implemented in the GAUSSIAN 90.
3. Experimental results The results for the experimentally measured equilibrium constants for reaction ( 1) are displayed in the van? Hoff plots in fig. 1, The lower limits of the temperatures for the measurements of the equilibrium constants correspond to the start of the condensation of CS2 or electron capture agents on the wall of the ion source. In table 1, the enthalpy and entropy changes for reaction ( 1) obtained from fig. 1 are summarized. For comparison, thermochemical data of the following reaction [ 1 ] are also displayed in table 1: 492
16’1 103,
1.5
2.0*
2.5 .
3.0 a
3.5 .
4.08
4.5.
5.0 1
5.5 .
$1 y*‘“pp _
-
7, i y
1.5
2.5
3.0
3.5
4.0
,j 4.5
5.0
5.5
6.0
8
6.0
BilCS*ln
102. IO’-
2
/
loo.
10-l1.5* 103. _-
20
6.0 ,
’
2.0 1..
’
2.5
’
3.0
/ *
3.5 11
’
40
3
4.5 I1
’
5.0
5.5 I.
’
1
I-(CSzh
IO2
g, 1.5
,
,
,
2.0
2.5
3.0
,I
,J<, 3.5
lOOO/
4.0
4.5
5.0
5.5
6.0
T(K)
Fig. 1. Van’t Hoff plots of the gas-phase clustering reactions, Integer number in the figure X-(CS,)“-, +C&=X-(C&),,. stands for the value of n.
x-(co~),_~+co*=x-(co~),.
(2)
In fig. 1, the plot for X =F with n= 1 is isolated in the high-temperature region. This indicates covalent bond formation in the complex of F- and CS2. The observed sharp drop of -AH:_,, with n=2 for X = F is due to the drastic change of the nature of bonding of F- ( CS2), from covalent to electrostatic with n= 1+2. The values -ME_ ,,- with na2 for X=F are smaller than those for other halide ions, arising from the charge delocalization in FCS, and make the subsequent electrostatic interaction with CS2 ligands less favorable than other halide ion clusters X-(C$), (n32) (see section 5). In our laboratory, the bond energies of halide ions with various solvent molecules M have been measured, M=H20 [8], CH$N [8], CsHs [9], CsF6 [lO,ll],COz [l] andN20 [12].Itwasfoundthat the thermochemical stabilities of the cluster ions
18 June 1993
CHEMICAL PHYSICS LETTERS
Volume 208, number 5,6
Table 1 Thermochemical data, w_,,” in kcal/mol and -a_ ,.a in Wmol K of the gas-phase clustering reaction (l), X - (C&).--I +CSZ= are computed with RHF/3-21 +G, and that in X-(CS& (X=F, Cl, Br and I). Underlined numbers in -AH& and -ti~_,,~ -~_,,~intheparentheseswith (n-l,n)=(O, I)forX=FiswithMP2/DZP//MP2/DZP.DatainsquarebracketsareforX-(C02). in reaction ( 2 ) for comparison (ref. [ 11) (n-l,n)
x F
@,I )
(192)
(233) (334)
Br
Cl
-AK-,,
-A%.”
35.0+ 1.5 W?(G) E(C& f32.04) (C2”) [32.3] 6.71 kO.2 2.12(n) m(b) 3.60(c) w(d) 17.31 05.4 17.21 l5.81
28.2 f 3.0 23.74 126.71
lS.3k2.0
[ 18.21
17 ” [22.6] [20.3]
-W-r,
I
-As:-,..
- MlI- 1.r
-hs:-1.m
-A&
877f0.2 2.73( C,) 7.11(&h) i7.61
13.9 f 2.0 13.63 18.50 [18.21
8.3 + 0.2 1.87G”) 5.24(Cm!A) t6.71
13.0+ 2.0 12.22 17.00 [16.51
7.4+0.2 1.56(G) 4.41(Cccb) l4.71
16.7+2.0 11.3L 16.27 [13.4]
7.74kO.2 7.36(D,,) i7.21
20.4 2 2.0
6.75 kO.2 w(Dmb) l4.61
21.7f2.0
[ 20.81
l4.51
18.41
14.31
[ 19.01
7.18kO.2 16.81 a6.8 [ a6.41
IS.8 + 2.0
7.3kO.2 E(D,)
[ 19.01
16.01
21.3f2.0
1.1
-AK,,
[ 22.41 23 a) [24’)]
*r Entropy value assumed.
X- (M), are generally in the order of F- > Cl- = Br- r I-, i.e. the stabilities of X- (M),, for Cland Br- are of the same order and those for I- are smaller. For example, as shown in square brackets of table 1, the bond energies of X- ( CO1), are in the order Cl- 2 Br- > I-. In contrast to the previously observed general trend, the -ALri_ ,,” values of reaction ( I) for X =Cl, Br and I are much closer to each other as shown in table 1. In addition, the bond energies of I - (CS,), are larger than those of I- (CO,), and close to those for Cl- (CO,),. These experimental results may be explained by the hard and soft acids and bases concept (HSAB) due to Pearson [ 13 1. This states that a soft base prefers to combine with a soft acid rather than a hard acid. The polarizabilities [ 141 of F-, Cl-, Br- and I- are x 1.2, ~3, z 4.5 and ~7 A3 and those of CO2 and C!$ are 2.59 and 8.08 A3, respectively. The larger polarizabilities of I- and CS2 result in the favorable soft base-soft acid interaction in I-...C&
4. Computational results In section 3, the following two results have been described: ( 1) The F-...CS, binding energy is large, 35.0 kcal/ mol. In contrast, the F-(CSz)...C& energy is the smallest, 6.71 kcal/mol, with n=2 in table 1. (2) The X- (C&),_ ,..CS, binding energies (X = Cl, Br, and I) are similar, 7-9 kcal/mol. These almost constant values suggest that the clustering bonds are quite different from that in F- (CSz )“. (3) For the four halide ions, the X-...C$ bond is stronger than the X-...C02 bond [ 11. In order to explain these experimental results, ab initio geometries and binding energies are calculated. Fig. 2 exhibits fully optimized geometries of X- (CS,) ,_For all halide ions, two isomers, Cm,.,and CzV,are obtained. While Ct, geometries are as expected prior to calculations, Csohones are noticeable in consideration of the absence of the X-...O==C=O linear cluster [ 11. The stability of two isomers is compared. For X = F, the expected xanthate-type CzV geometry is much better than the Cmh one in table 493
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Fig. 2. Two isomers (C,, and C,,) of the X- (CS2)1cluster optimized with RHF/3-21 +G. For X= F, MPZ/DZP geometric parameters are given in parentheses. The GS bond length of the free carbon disulfide is computed to be 1.581 A. I. On the contrary, other halide ions than F- are found to prefer Cmh to CZV. Four isomers a, b, c and d of F-(CS2)2 are investigated on the basis of the CZVgeometry of F- (CS,)I. After geometry optimization, they are obtained as shown in fig. 3. The model a is found to be of C, symmetry and the other three are of CZ, symmetry. In these geometries of n=2, the n= 1 structure is almost unperturbed, which shows that the F- (CS,) ,_..C& interaction is weak and electrostatic. In fact, computed binding energies of n= 1+ 2 are small, 2.12 (a), 5.14 (b), 3.60 (c) and 6.91 kcal/ mol (d) in table 1. The model d is best among four isomers, indicating that the fluorine atom in F- ( CSZ)1 is the most attractive site for not carbon but sulfur of the second C!$. Optimized geometries of X- ( CS2) Z (X= Cl, Br and I) are displayed in fig. 4. Although no symmetry
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assumption on the n = 2 geometries is made, most stable geometries are found to be of DoDhsymmetry. Thus, the slow decay of binding energies of X- (C$), (X=Cl, Br and I) in table 1 with n is explicable’in terms of symmetric structures. The n= 3 geometries may be of Dsh symmetry and the n=4 ones may be of Td symmetry. Fig. 5 exhibits net charges of CS2 and X- (CL&), (X=F and Cl) together with those of COZ and X-(C02),. While the carbon atom of CO1 is cationic, that of CS2 is anionic. This is in accord with the fact that the signs of the quadrupole moments of CO2 (-4.3x 10ez6 esu cm2) and C!$ (1.8~ 1O-24 esu cm’) are opposite [ 151. This difference is reflected in the contrast of the CZVX-(C02)1 versus the Cmh X- ( CSZ), for X=Cl, Br and I. Although F- ( COa) I and F- ( CS2), are found to be of CZV symmetry, the net charges on the carbon atom are different. The ( - 1) charge dispersal is more extensive in FCS: , leading to the larger -AJ& , and the smaller - AZ& of F- (CS,), than those of F- (CO,),. Next, the cationic carbon in CO2 and sulfur atoms in CS2 are bound to Cl-, respectively, Besides this evident electrostatic force, a large charge polarization in sulfur atoms of Cl-...S=C=S is found. According to HSAB, the combination of soft acids and bases induces the effective polarization. The linear geometry of X-...S=C=S (X = Cl, Br and I ) may undergo this interaction. Computed energies are compared with observed in table 1. The difference bevalues of -MI]_,,, tween two computed energies, 38.33 and 32.02 kcal/ mol of F -...C$ means that the electron-correlation effect on the binding energies works in the strongly interacting system to some extent. Since the counterpoise method tends to overcompensate the BSSE [ 161 (e.g., +7.33 kcal/mol with RHF/3-21 tG), 32.02 plus a few kcal/mol is a reasonable theoretical binding energy and is close to -AH:,, = 35.0 kcal/ mol. While computed energies of X = F and Cl are in good agreement with - AH:_ ,,,, values, those of X = Br and I are a few kcal/mol smaller than the observed ones. This small disagreement as well as the slightly larger computed ( 1,2) binding energies than the (0, 1) ones for X=Cl, Br and I is probably owing to the imbalance of the 3-21 +G basis set between the large halide ions and the sulfur atom.
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(b)
(d) Fig. 3. Four isomers of the F- (CS2)2 cluster. b, c, and d are found to be of Czvsymmetry.
(4.43
6’3.47)
(4.70) (LWI
c
l-)
P
CLr----c W”‘l
(.0086)
W.m
l-o.9si“.. I b ML&m(4.47)
Fig. 5. Mulliken atomic net charges (positive, cationic) of carbon &sulfide, X-(COz), and X-(CS2), (X=F and Cl) computed with RHF/6-3 1G. Since basis sets including diffuse functions (i.e. 3-21 +G) tend to give unreasonable charges, the 63 1G basis set is adopted. Underlined numbers in parentheses of Cl-...C02and Cl-...C& denote atom-atom bonding populations. 5. l&h
Fig.4. Geometries of X-(CS& (X&l, Brand I) optimized with RHF/3-21 +G. Three clusters are computed to be of DoDh symmetry.
Concluding remarks
This work has dealt with the gas-phase clustering reaction of halide ions and carbon disulfide. A strong F-...CS2 bond is formed through the effective charge dispersal in the cluster. The stability of the potassium xanthate may be ascribed to this charge delo495
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calization. Other halide ions than F- are linked with S=C=S linearly with 9-7 kcal/mol binding energies. This linearity is ascribed to the polarization stabilization between “soft” atoms.
Acknowledgement We would like to express our appreciation for the financial support of the Morino Foundation for Molecular Science and the Grant-in-Aid in part for Scientific Research on Priority Area “Theory of Chemical Reactions’* from the Japanese Ministry of Education. We also thank the Information Processing Center of Nara University of Education for the allotment of CPU time on the CONVEX C-220 computer.
References [ I] K. Hiraoka, S. Mizuse and S. Yamabe, J. Chem. Phys. 87 (1987) 3647.
[ 2 ] T. Clark, J. Chandrasekhar, G.W. Spitznagel and P. van R. Schleyer, J. Comput. Chem. 4 (1983) 294.
[ 31 S.F. Boys and F. Bernardi, Mol. Phys. 19 (1970) 553.
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[4] W.J. Hehre and J.A. Pople, I. Am. Chem. Sot. 94 ( 1972) 690 1, and references therein to earlier theoretical work. [ 5 ] S. Huzinaga, J. Chem. Phys. 42 ( 1964) 1293; T.H. Dunning, J. Chem. Phys. 53 (1970) 2823; 55 (1971) 716. [6] M.J. Frisch, M. Head-Gordon, G.W.Truck.5, J.B. Foresman, H.B. Schlegel, K. Raghavachari, M. Robb, J.S. Binkley, C. Gonzalez,D.J. DeFrees, D.J. Fox, R.A. Whiteside, R. Seeger, C.F. Melius, J. Raker, R.L.Martin,L.R. Kahn, J.J.P. Stewart, S. Topiol and J.A. Pople, GAUSSIAN 90, Revision (Gaussian Inc., Pittsburgh, PA, 1990). [7 ] K.D. Dobbs and W.J. Hehre, J. Comput. Chem. 7 ( 1986) 359. [8] K. Hiraoka, S. Mizuse and S. Yamabe, J. Phys. Chem. 92 (1988) 3943. (91 K. Hiraoka, S. Mizuse and S. Yamabe, Chem. Phys. Letters 147 (1988) 174. [lo] K. Hiraoka, S. Mizuse and S. Yamabe, J. Phys. Chem. 9 1 (1987) 5294. [ 111 K. Hiraoka, S. Mizuse and S. Yamabe, J. Chem. Phys. 86 (1987) 4102. [ 121 K. Hiraoka, S. Fujimaki, K. Aruga and S. Yamabe, to be published. [ 131 R.G. Pearson, J. Chem. Educ. 45 (1968) 58. [ 141 R.J.W. Ix Fbvre, Advan. Phys. Org. Chem. 3 (1963) 1. [15]D.E.StrogrynandA.P.Strogryn,Mol.Phys. 11 (1966) 371. [ 161K. Morokuma and K. Kitaura, in: Chemical applications of atomic and molecular electrostatic potentials, eds. P. Politzer and D.G. Truhlar (Plenum Press, New York, 1981)