- Email: [email protected]
Tunnelling rate and barrier to the transfer of the protic group in dimethylether–HCl
Chemical Physics Letters 394 (2004) 262–265 www.elsevier.com/locate/cplett
Tunnelling rate and barrier to the transfer of the protic group in dimethylether–HCl Paolo Ottaviani a, Walther Caminati
a,*
, Biagio Velino b, Juan C. Lo´pez
c
a
Dipartimento di Chimica ÔG. CiamicianÕ dellÕ Universita`, Via Selmi 2, I-40126 Bologna, Italy Dipartimento di Chimica Fisica e Inorganica dellÕ Universita`, Viale Risorgimento 4, I-40136 Bologna, Italy Departamento de Quı´mica-Fı´sica y Quı´mica-Inorga´nica, Facultad de Ciencias, Universidad de Valladolid, E-47005 Valladolid, Spain b
c
Received 7 June 2004; in final form 22 June 2004 Available online 27 July 2004
Abstract In dimethylether–HCl, the HCl group is tunnelling between the two lone pairs of the ether oxygen at a rate of 8182(7) MHz, through a barrier of 69 cm1, as deduced from the free jet millimetre wave absorption spectrum. 2004 Elsevier B.V. All rights reserved.
Hydrogen chloride is a strong proton donor, so that it is not a surprise that many of its molecular complexes with proton acceptors have been investigated with several theoretical and experimental techniques, in order to obtain information on the shape and energetics of the involved hydrogen bonds. The most precise data have been undoubtedly obtained by rotationally resolved spectroscopies: the moments of inertia give the shape of the complex, while vibrational doubling of lines or centrifugal distortion effects give information on the potential energy surface describing the intermolecular motions. Detailed information has been obtained in this way on the adduct with water [1], while the studies of complexes of HCl with small organic molecules such as cyclic ethers or sulphides [2–10], supplied mainly information on the structure and conformation of the complex. More interestingly, spectra due to both axial and equatorial adducts of HCl with tetrahydropyran [11], trimethylene sulphide [12] and pentamethylene sulphide [13] have been assigned and measured. In these cases, however, no splitting due to the transfer of the *
Corresponding author. Fax: +39 051 2099456. E-mail addresses: [email protected], caminati@ciam. unibo.it (W. Caminati). 0009-2614/$ - see front matter 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.cplett.2004.07.010
HCl protic group between two equivalent lone pairs of the oxygen (or sulphur) atom, has been observed. Viceversa, a doubling of lines due to the tunnelling of HF has been observed for 2,5-dihydrofuran–HF [14] and dimethylether–HF [15]. Dimethylether (since now on DME) is the simplest open chain ether. The COC angle is larger than in most of cyclic ethers; correspondingly the two oxygen lone pairs are expected to be closer to each other. This factor can greatly change the internal dynamics (the HCl motions) of its complex with HCl, with respect to the HCl-cyclic ether adducts. A supersonic jet experiment has already been performed on DME–HCl, but it was mainly concerned with the HCl stretching mode IR spectrum [16]. In the same paper the dissociation energy of the complex has been estimated by DFT calculations. It has been found that the complex is strongly bound, with the dissociation energy in the range 9–11 kcal/mol. For the reasons mentioned above we decided to investigate the DME–HCl complex (see Fig. 1) by free jet millimetre-wave absorption spectroscopy. The Stark modulated free jet millimetre-wave absorption spectrometer used in this study has already been described elsewhere [17]. Commercial samples of DME (Aldrich) and HCl (Rivoira) have been used without further puri-
P. Ottaviani et al. / Chemical Physics Letters 394 (2004) 262–265
263
Table 1 Experimental transition frequencies (MHz) of DME HCl J 0 ðKa0 Kc0 Þ J 00 ðKa00 Kc00 Þa
DME H35Cl 0
Fig. 1. Drawn of DME HCl with significant structural parameters used through the text.
fication. The conditions were optimised for the 1:1 adduct formation flowing separately DME and a mixture of 3% of HCl in argon at the entrance of the nozzle and at pressure of 30 and 500 mbar, respectively. We used a home made nozzle with a diameter of 0.13 mm. The first estimates of the rotational constants of the complex were obtained by attaching HCl to DME in a configuration similar to that observed for oxirane–HCl [3]. The effective r0 geometry of DME [18] has been assumed to remain unaltered in the complex. 68 lines of four la-R-type bands, with J in the range 15–18 have been measured. They were belonging to two separate vibrational states, arising from the inversion of HCl. In addition, three lc-transitions, very broadened of the unresolved 35Cl nucleus quadrupole effects, have been measured. The experimental frequencies are listed in Table 1 for both tunnelling states. They have been fitted together using PickettÕs coupled Hamiltonian [19,20] in the S reduction and Ir representation [21], according to, X CD int H¼ ðH R with i ¼ 0; 1 ð1Þ i þ Hi Þ þ H i
and H int ¼ DE þ ½F ac þ F acJ J ðJ þ 1Þ þ F acK K 2 ðP a P c þ P c P a Þ ð2Þ R
CD
where H and H are the rotational and centrifugal distortion terms, DE is the energy difference between the two tunnelling substates, Fac is the rotation–vibration coupling parameter between the two states, and FacJ and FacK take into account its dependence from the
(1) la-transitions 16(1,15)–15(1,14) 16(2,14)–15(2,13) 16(3,14)–15(3,13) 16(3,13)–15(3,12) 16(4,13)–15(4,12) 16(4,12)–15(4,11) 16(5,12)–15(5,11) 16(5,11)–15(5,10) 16(6)–15(6) 17(0,17)–16(0,16) 17(1,17)–16(1,16) 17(1,16)–16(1,15) 17(2,16)–16(2,15) 17(2,15)–16(2,14) 17(3,15)–16(3,14) 17(3,14)–16(3,13) 17(4,14)–16(4,13) 17(4,13)–16(4,12) 17(5,13)–16(5,12) 17(5,12)–16(5,11) 17(6)–16(6) 17(7)–16(7) 18(0,18)–17(0,17) 18(1,18)–17(1,17) 18(1,17)–17(1,16) 18(2,17)–17(2,16) 18(2,16)–17(2,15) 18(3,16)–17(3,15) 18(3,15)–17(3,14) 18(4,15)–17(4,14) 18(4,14)–17(4,13) 18(5,14)–17(5,13) 18(5,13)–17(5,12) 18(6)–17(6) 18(7)–17(7)
(2) lc-transitions 4(4)–3(3) 5(4)–4(3)
+
59944.68 61622.10 59782.00 60841.59 59897.59 60006.68 59774.00 59778.69 59671.95 59887.76 63389.81 62218.66 65414.14 63477.59 64821.28 63660.52 63825.41 63528.43 63536.97 63410.62 63323.04 63285.17 63183.86 66797.83 65743.30 69165.76 67157.62 68811.00 67422.03 67664.15 67285.51 67300.03
0
59984.29 61548.00 59764.45 60744.71 59869.69 59967.76 59753.93 59758.14 59659.68 60001.57 59860.33 63445.80 62257.39 65343.51 63461.14 64707.47 63628.62 63777.00 63504.28 63511.79 63395.32 63315.04 63407.38 66868.55 65789.80 69100.47 67143.00 68682.33 67386.29 67603.55 67256.73 67269.58
67051.02
67040.67
0–0+
0+–0
76114.0
60089.0 63814.0
DME H37Cl 0+
0
61816.41 60621.83 63620.48 61774.05 62941.23 61917.59 62048.91 61792.72 61799.07 61685.86 61605.98 61730.22 61615.10 65156.90 64063.97 67289.24 65362.48 66811.28 65576.22 65769.21
61866.14 60659.98 63554.10 61761.69 62843.79 61892.86 62011.17 61775.48 61781.14 61676.59 61603.41 61848.92 61727.09 65221.67 64109.55 67227.02 65351.79 66699.15 65547.93 65721.83 65423.90
65322.85 65231.87
65311.10 65227.17
a Only Ka is indicated in the notation when transitions are doubly overlapped due to the near prolate degeneracy of the involved levels.
centrifugal distortion. Besides the rotational constants we could determine five centrifugal distortion parameters. The results of the fit are summarised in Table 2. The vibrational spacing between the v = 0, 1 levels (DE = 8182 MHz) indicates a low barrier to the HCl tunnelling motion. The rotational spectrum of the isotopomer with 37Cl has also been measured and the transition frequencies are listed in Table 1, while the derived spectroscopic constants are reported in Table 2. ˚ 2, for The planar moments of inertia Pbb (47.556 uA v = 0), which gives the extension of the masses out of the ac plane, are just slightly higher than the Paa value
264
P. Ottaviani et al. / Chemical Physics Letters 394 (2004) 262–265
Table 2 Spectroscopic constants of DME HCl DME H35Cl
A (MHz) B (MHz) C (MHz) DJ/kHz DJK (kHz) d1 (kHz) d2 (kHz) HJK (Hz) DE (MHz) Fac/(MHz) FacJ/(kHz) FacK/(kHz) Nd r/(MHz)e a b c d e
DME H37Cl
v=0
v=1
v=0
v=1
9467.9(3)a 2007.250(8) 1721.84(1) 6.829(8) 77.1(4) 0.687(5) 0.232(2) 26(2) 8182(7) 171.96(9) 6.8(4) 151(9) 81 0.10
9454.5(3) 2011.463(6) 1725.356(8) 5.99(2) 85.6(8)
9469.5(5) 1949.47(2) 1678.98(2) 6.45(1) 72.5(1) 0.66(2) 0.206(1) [26]b 8060c 167.14(6) [6.8] [151] 70 0.09
9453.9(6) 1953.48(2) 1682.43(2) 5.70(1) 81.9(1)
Errors in parenthesis are in units of the last digit. Data in square brackets fixed at the values of the 35Cl species. Fixed to the value obtained from flexible model calculations. Number of transitions in the fit. Standard deviation of the fit.
˚ 2, suggesting that HCl lies in the of DME, 47.047 uA plane of symmetry of DME perpendicular to the COC plane. The small increase is imputable to an opening of the COC angle upon formation of the complex [15], as confirmed by quantum chemical calculations (see below). The substitution coordinates [22] of the Cl atom, with jbj @ 0, confirm such a result. A partial r0 geometry has been obtained from the six available rotational constants, leading to the values shown in Table 3: only the four parameters (R, s, h and a) of Fig. 1 have been adjusted. The measured DE vibrational spacing and the value of the angle a can be used to determine the HCl tunnelling pathways. These data are not sufficient, however, to find all the potential energy and structural relaxation parameters required for this purpose. For this reason we performed some ab initio calculations in order to have
Table 3 Partial effective r0 structural parameters and substitution rs coordi˚ and ) nates of the Cl atom in DME HCl (A RH O (1) Partial r0 structure r0 1.766 1.742 ab initioa jaj (2) Cl rs coordinates Exptl. 1.957(3) Calc.b 1.959 a b
a
h
s
112.4 111.5
172.8 172.6
42.9 48.1
jbj
jcj
rCl
0.08(6) 0.0
0.06(6) 0.03
1.960(3) 1.959
MP2/6-311++G**. From the above r0 structure.
an indication on the preferred pathways and on the main structural relaxation. MP2 calculations were performed with the GAUSSIAN 98 suite of programs [23]. We found the stationary points with the 6-31G** basis, and then optimised them by using the 6-311++G** basis. The most stable geometry is in agreement with the experimental evidences, with HCl in the rv plane, perpendicular to the OCO plane, of the DME monomer. The transition state energy was calculated to be 116 cm1, while some structural parameters undergo a considerable structural relaxation. Our data allow for the determination of an experimental value of the barrier. We used for this purpose a 1D flexible model [24] which allows to calculate vibrational and rotational wavefunctions and eigenvalues. The following potential energy function has been adopted: 2 2
V ðsÞ ¼ B½1 ðs=se Þ ;
ð3Þ
where B is the barrier to inversion and se is the equilibrium value of the inversion angle (see Fig. 1). The relaxations of the following parameters as a function of s have been also taken into account, according to the ab initio calculations mentioned above
hðsÞ= ¼ 180:0 þ 7:1ðs=se Þ;
ð4aÞ
2
aðsÞ= ¼ 113:6 1:2ðs=se Þ ;
ð4bÞ 2
˚ ¼ 1:800 0:033ðs=se Þ ; RðsÞ=A
ð4cÞ ˚ where 7.1, 1.2 and 0.033 A are the changes of h, a and R in going from s = 0 to s = se. The experimental DE splitting of 8182 MHz has been obtained when B = 69 cm1 and se = 42.9. This value is ca. half of that (116 cm1) obtained with the ab initio calculations mentioned above. The model value of the DE splitting for the 37Cl isotopomer is 8060 MHz. In the flexible model calculations the a coordinate has been considered in the ±110 range and solved into 41 mesh points [24]. We found, with the present investigation, the rate and the tunnelling barrier for the transfer of a full protic group between two equivalent lone pairs as those of a molecule as common as DME.
Acknowledgements We thank the support given by the azione integrata Italia Spagna (HI-2000-0092 in Spain, It294-2001 in Italy). P.O., B.V. and W.C. thank the Ministero dellÕ Istruzione, dellÕUniversitaÕ e della Ricerca, and the University of Bologna (ex 60% and funds for special topics) for financial support. J.C.L. would like to thank the Direccio´n General de Investigacio´n – Ministerio de Ciencia y Tecnologı´a (Grant BQU2003-03275) for financial support.
P. Ottaviani et al. / Chemical Physics Letters 394 (2004) 262–265
References [1] A.C. Legon, L.C. Willoughby, Chem. Phys. Lett. 95 (1983) 459; Z. Kisiel, B.A. Pietrewicz, P.W. Fowler, A.C. Legon, E. Steiner, J. Phys. Chem. A 104 (2000) 6970. [2] A.C. Legon, C.A. Rego, L. Wallwork, Angew. Chem. Int. Ed. 29 (1990) 72. [3] A.C. Legon, C.A. Rego, L. Wallwork, J. Chem. Phys. 97 (1992) 3050. [4] S. Antolinez, J.C. Lopez, J.L. Alonso, Chem. Phys. Lett. 334 (2001) 250. [5] A.C. Legon, J.C. Thorn, Chem. Phys. Lett. 227 (1994) 472. [6] S. Antolinez, J.C. Lopez, J.L. Alonso, Chem. Phys. Lett. 323 (2000) 130. [7] S. Antolinez, A. Lesarri, J.C. Lopez, J.L. Alonso, Chem. Eur. J. 6 (2000) 3345. [8] C.M. Evans, A.C. Legon, Chem. Phys. 198 (1995) 119. [9] J.C. Lopez, J.L. Alonso, F.J. Lorenzo, V.M. Raya, J.A. Sordo, J. Chem. Phys. 111 (1999) 6363. [10] M.E. Sanz, J.C. Lopez, J.L. Alonso, J. Phys. Chem. A 102 (1998) 3681. [11] S. Antolinez, J.C. Lopez, J.L. Alonso, Angew. Chem. Int. Ed. 38 (1999) 1772.
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[12] M.E. Sanz, A. Lesarri, J.C. Lopez, J.L. Alonso, Angew. Chem. Int. Ed. 40 (2001) 935. [13] M.E. Sanz, J.C. Lopez, J.L. Alonso, Chem. Eur. J. 5 (1999) 3293; S. Antolinez, J.C. Lopez, J.L. Alonso, Chem. Phys. Lett. 323 (2000) 130. [14] J.C. Lopez, S. Blanco, A. Lesarri, M.E. Sanz, F.J. Lorenzo, J.L. Alonso, J. Chem. Phys. 114 (2001) 9421. [15] P. Ottaviani, W. Caminati, B. Velino, S. Blanco, A. Lesarri, J.C. Lo´pez, J.L. Alonso, Chem. Phys. Chem. 5 (2004) 336. [16] P. Asselin, P. Soulard, M.E. Alikhani, J.P. Perchard, Chem. Phys. 249 (1999) 73. [17] S. Melandri, W. Caminati, L.B. Favero, A. Millemaggi, P.G. Favero, J. Mol. Struct. 352/353 (1995) 253. [18] F.J. Lovas, K. Lutz, H. Dreizler, J. Phys. Chem. Ref. Data 8 (1979) 1051. [19] H.M. Pickett, J. Chem. Phys. 56 (1972) 1715. [20] H.M. Pickett, J. Mol. Spectr. 148 (1991) 371. [21] J.K.G. Watson, in: J.R. Durig (Ed.), Vibrational Spectra and Structure, vol. 6, Elsevier, New York/Amsterdam, 1977, p. 1. [22] J. Kraitchmann, Am. J. Phys. 21 (1953) 17. [23] M.J. Frisch et al., GAUSSIAN 98, Revision A.7, Gaussian Inc., Pittsburgh, PA, 1998. [24] R. Meyer, J. Mol. Spectrosc. 76 (1979) 266.
Tunnelling rate and barrier to the transfer of the protic group in dimethylether–HCl Paolo Ottaviani a, Walther Caminati
a,*
, Biagio Velino b, Juan C. Lo´pez
c
a
Dipartimento di Chimica ÔG. CiamicianÕ dellÕ Universita`, Via Selmi 2, I-40126 Bologna, Italy Dipartimento di Chimica Fisica e Inorganica dellÕ Universita`, Viale Risorgimento 4, I-40136 Bologna, Italy Departamento de Quı´mica-Fı´sica y Quı´mica-Inorga´nica, Facultad de Ciencias, Universidad de Valladolid, E-47005 Valladolid, Spain b
c
Received 7 June 2004; in final form 22 June 2004 Available online 27 July 2004
Abstract In dimethylether–HCl, the HCl group is tunnelling between the two lone pairs of the ether oxygen at a rate of 8182(7) MHz, through a barrier of 69 cm1, as deduced from the free jet millimetre wave absorption spectrum. 2004 Elsevier B.V. All rights reserved.
Hydrogen chloride is a strong proton donor, so that it is not a surprise that many of its molecular complexes with proton acceptors have been investigated with several theoretical and experimental techniques, in order to obtain information on the shape and energetics of the involved hydrogen bonds. The most precise data have been undoubtedly obtained by rotationally resolved spectroscopies: the moments of inertia give the shape of the complex, while vibrational doubling of lines or centrifugal distortion effects give information on the potential energy surface describing the intermolecular motions. Detailed information has been obtained in this way on the adduct with water [1], while the studies of complexes of HCl with small organic molecules such as cyclic ethers or sulphides [2–10], supplied mainly information on the structure and conformation of the complex. More interestingly, spectra due to both axial and equatorial adducts of HCl with tetrahydropyran [11], trimethylene sulphide [12] and pentamethylene sulphide [13] have been assigned and measured. In these cases, however, no splitting due to the transfer of the *
Corresponding author. Fax: +39 051 2099456. E-mail addresses: [email protected], caminati@ciam. unibo.it (W. Caminati). 0009-2614/$ - see front matter 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.cplett.2004.07.010
HCl protic group between two equivalent lone pairs of the oxygen (or sulphur) atom, has been observed. Viceversa, a doubling of lines due to the tunnelling of HF has been observed for 2,5-dihydrofuran–HF [14] and dimethylether–HF [15]. Dimethylether (since now on DME) is the simplest open chain ether. The COC angle is larger than in most of cyclic ethers; correspondingly the two oxygen lone pairs are expected to be closer to each other. This factor can greatly change the internal dynamics (the HCl motions) of its complex with HCl, with respect to the HCl-cyclic ether adducts. A supersonic jet experiment has already been performed on DME–HCl, but it was mainly concerned with the HCl stretching mode IR spectrum [16]. In the same paper the dissociation energy of the complex has been estimated by DFT calculations. It has been found that the complex is strongly bound, with the dissociation energy in the range 9–11 kcal/mol. For the reasons mentioned above we decided to investigate the DME–HCl complex (see Fig. 1) by free jet millimetre-wave absorption spectroscopy. The Stark modulated free jet millimetre-wave absorption spectrometer used in this study has already been described elsewhere [17]. Commercial samples of DME (Aldrich) and HCl (Rivoira) have been used without further puri-
P. Ottaviani et al. / Chemical Physics Letters 394 (2004) 262–265
263
Table 1 Experimental transition frequencies (MHz) of DME HCl J 0 ðKa0 Kc0 Þ J 00 ðKa00 Kc00 Þa
DME H35Cl 0
Fig. 1. Drawn of DME HCl with significant structural parameters used through the text.
fication. The conditions were optimised for the 1:1 adduct formation flowing separately DME and a mixture of 3% of HCl in argon at the entrance of the nozzle and at pressure of 30 and 500 mbar, respectively. We used a home made nozzle with a diameter of 0.13 mm. The first estimates of the rotational constants of the complex were obtained by attaching HCl to DME in a configuration similar to that observed for oxirane–HCl [3]. The effective r0 geometry of DME [18] has been assumed to remain unaltered in the complex. 68 lines of four la-R-type bands, with J in the range 15–18 have been measured. They were belonging to two separate vibrational states, arising from the inversion of HCl. In addition, three lc-transitions, very broadened of the unresolved 35Cl nucleus quadrupole effects, have been measured. The experimental frequencies are listed in Table 1 for both tunnelling states. They have been fitted together using PickettÕs coupled Hamiltonian [19,20] in the S reduction and Ir representation [21], according to, X CD int H¼ ðH R with i ¼ 0; 1 ð1Þ i þ Hi Þ þ H i
and H int ¼ DE þ ½F ac þ F acJ J ðJ þ 1Þ þ F acK K 2 ðP a P c þ P c P a Þ ð2Þ R
CD
where H and H are the rotational and centrifugal distortion terms, DE is the energy difference between the two tunnelling substates, Fac is the rotation–vibration coupling parameter between the two states, and FacJ and FacK take into account its dependence from the
(1) la-transitions 16(1,15)–15(1,14) 16(2,14)–15(2,13) 16(3,14)–15(3,13) 16(3,13)–15(3,12) 16(4,13)–15(4,12) 16(4,12)–15(4,11) 16(5,12)–15(5,11) 16(5,11)–15(5,10) 16(6)–15(6) 17(0,17)–16(0,16) 17(1,17)–16(1,16) 17(1,16)–16(1,15) 17(2,16)–16(2,15) 17(2,15)–16(2,14) 17(3,15)–16(3,14) 17(3,14)–16(3,13) 17(4,14)–16(4,13) 17(4,13)–16(4,12) 17(5,13)–16(5,12) 17(5,12)–16(5,11) 17(6)–16(6) 17(7)–16(7) 18(0,18)–17(0,17) 18(1,18)–17(1,17) 18(1,17)–17(1,16) 18(2,17)–17(2,16) 18(2,16)–17(2,15) 18(3,16)–17(3,15) 18(3,15)–17(3,14) 18(4,15)–17(4,14) 18(4,14)–17(4,13) 18(5,14)–17(5,13) 18(5,13)–17(5,12) 18(6)–17(6) 18(7)–17(7)
(2) lc-transitions 4(4)–3(3) 5(4)–4(3)
+
59944.68 61622.10 59782.00 60841.59 59897.59 60006.68 59774.00 59778.69 59671.95 59887.76 63389.81 62218.66 65414.14 63477.59 64821.28 63660.52 63825.41 63528.43 63536.97 63410.62 63323.04 63285.17 63183.86 66797.83 65743.30 69165.76 67157.62 68811.00 67422.03 67664.15 67285.51 67300.03
0
59984.29 61548.00 59764.45 60744.71 59869.69 59967.76 59753.93 59758.14 59659.68 60001.57 59860.33 63445.80 62257.39 65343.51 63461.14 64707.47 63628.62 63777.00 63504.28 63511.79 63395.32 63315.04 63407.38 66868.55 65789.80 69100.47 67143.00 68682.33 67386.29 67603.55 67256.73 67269.58
67051.02
67040.67
0–0+
0+–0
76114.0
60089.0 63814.0
DME H37Cl 0+
0
61816.41 60621.83 63620.48 61774.05 62941.23 61917.59 62048.91 61792.72 61799.07 61685.86 61605.98 61730.22 61615.10 65156.90 64063.97 67289.24 65362.48 66811.28 65576.22 65769.21
61866.14 60659.98 63554.10 61761.69 62843.79 61892.86 62011.17 61775.48 61781.14 61676.59 61603.41 61848.92 61727.09 65221.67 64109.55 67227.02 65351.79 66699.15 65547.93 65721.83 65423.90
65322.85 65231.87
65311.10 65227.17
a Only Ka is indicated in the notation when transitions are doubly overlapped due to the near prolate degeneracy of the involved levels.
centrifugal distortion. Besides the rotational constants we could determine five centrifugal distortion parameters. The results of the fit are summarised in Table 2. The vibrational spacing between the v = 0, 1 levels (DE = 8182 MHz) indicates a low barrier to the HCl tunnelling motion. The rotational spectrum of the isotopomer with 37Cl has also been measured and the transition frequencies are listed in Table 1, while the derived spectroscopic constants are reported in Table 2. ˚ 2, for The planar moments of inertia Pbb (47.556 uA v = 0), which gives the extension of the masses out of the ac plane, are just slightly higher than the Paa value
264
P. Ottaviani et al. / Chemical Physics Letters 394 (2004) 262–265
Table 2 Spectroscopic constants of DME HCl DME H35Cl
A (MHz) B (MHz) C (MHz) DJ/kHz DJK (kHz) d1 (kHz) d2 (kHz) HJK (Hz) DE (MHz) Fac/(MHz) FacJ/(kHz) FacK/(kHz) Nd r/(MHz)e a b c d e
DME H37Cl
v=0
v=1
v=0
v=1
9467.9(3)a 2007.250(8) 1721.84(1) 6.829(8) 77.1(4) 0.687(5) 0.232(2) 26(2) 8182(7) 171.96(9) 6.8(4) 151(9) 81 0.10
9454.5(3) 2011.463(6) 1725.356(8) 5.99(2) 85.6(8)
9469.5(5) 1949.47(2) 1678.98(2) 6.45(1) 72.5(1) 0.66(2) 0.206(1) [26]b 8060c 167.14(6) [6.8] [151] 70 0.09
9453.9(6) 1953.48(2) 1682.43(2) 5.70(1) 81.9(1)
Errors in parenthesis are in units of the last digit. Data in square brackets fixed at the values of the 35Cl species. Fixed to the value obtained from flexible model calculations. Number of transitions in the fit. Standard deviation of the fit.
˚ 2, suggesting that HCl lies in the of DME, 47.047 uA plane of symmetry of DME perpendicular to the COC plane. The small increase is imputable to an opening of the COC angle upon formation of the complex [15], as confirmed by quantum chemical calculations (see below). The substitution coordinates [22] of the Cl atom, with jbj @ 0, confirm such a result. A partial r0 geometry has been obtained from the six available rotational constants, leading to the values shown in Table 3: only the four parameters (R, s, h and a) of Fig. 1 have been adjusted. The measured DE vibrational spacing and the value of the angle a can be used to determine the HCl tunnelling pathways. These data are not sufficient, however, to find all the potential energy and structural relaxation parameters required for this purpose. For this reason we performed some ab initio calculations in order to have
Table 3 Partial effective r0 structural parameters and substitution rs coordi˚ and ) nates of the Cl atom in DME HCl (A RH O (1) Partial r0 structure r0 1.766 1.742 ab initioa jaj (2) Cl rs coordinates Exptl. 1.957(3) Calc.b 1.959 a b
a
h
s
112.4 111.5
172.8 172.6
42.9 48.1
jbj
jcj
rCl
0.08(6) 0.0
0.06(6) 0.03
1.960(3) 1.959
MP2/6-311++G**. From the above r0 structure.
an indication on the preferred pathways and on the main structural relaxation. MP2 calculations were performed with the GAUSSIAN 98 suite of programs [23]. We found the stationary points with the 6-31G** basis, and then optimised them by using the 6-311++G** basis. The most stable geometry is in agreement with the experimental evidences, with HCl in the rv plane, perpendicular to the OCO plane, of the DME monomer. The transition state energy was calculated to be 116 cm1, while some structural parameters undergo a considerable structural relaxation. Our data allow for the determination of an experimental value of the barrier. We used for this purpose a 1D flexible model [24] which allows to calculate vibrational and rotational wavefunctions and eigenvalues. The following potential energy function has been adopted: 2 2
V ðsÞ ¼ B½1 ðs=se Þ ;
ð3Þ
where B is the barrier to inversion and se is the equilibrium value of the inversion angle (see Fig. 1). The relaxations of the following parameters as a function of s have been also taken into account, according to the ab initio calculations mentioned above
hðsÞ= ¼ 180:0 þ 7:1ðs=se Þ;
ð4aÞ
2
aðsÞ= ¼ 113:6 1:2ðs=se Þ ;
ð4bÞ 2
˚ ¼ 1:800 0:033ðs=se Þ ; RðsÞ=A
ð4cÞ ˚ where 7.1, 1.2 and 0.033 A are the changes of h, a and R in going from s = 0 to s = se. The experimental DE splitting of 8182 MHz has been obtained when B = 69 cm1 and se = 42.9. This value is ca. half of that (116 cm1) obtained with the ab initio calculations mentioned above. The model value of the DE splitting for the 37Cl isotopomer is 8060 MHz. In the flexible model calculations the a coordinate has been considered in the ±110 range and solved into 41 mesh points [24]. We found, with the present investigation, the rate and the tunnelling barrier for the transfer of a full protic group between two equivalent lone pairs as those of a molecule as common as DME.
Acknowledgements We thank the support given by the azione integrata Italia Spagna (HI-2000-0092 in Spain, It294-2001 in Italy). P.O., B.V. and W.C. thank the Ministero dellÕ Istruzione, dellÕUniversitaÕ e della Ricerca, and the University of Bologna (ex 60% and funds for special topics) for financial support. J.C.L. would like to thank the Direccio´n General de Investigacio´n – Ministerio de Ciencia y Tecnologı´a (Grant BQU2003-03275) for financial support.
P. Ottaviani et al. / Chemical Physics Letters 394 (2004) 262–265
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