Dimethyl Sulfide–Dimethyl Ether and Ethylene Oxide–Ethylene Sulfide

Sep 29, 2015 - The ground-state rotational spectra of the dimethyl sulfide–dimethyl ether (DMS–DME) and the ethylene oxide–ethylene sulfide (EOâ...
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Dimethyl Sulfide−Dimethyl Ether and Ethylene Oxide−Ethylene Sulfide Complexes Investigated by Fourier Transform Microwave Spectroscopy and Ab Initio Calculation Yoshiyuki Kawashima,* Yoshio Tatamitani, and Takayuki Mase Department of Applied Chemistry, Faculty of Engineering, Kanagawa Institute of Technology, Atsugi, Kanagawa 243-0292, Japan

Eizi Hirota The Graduate University for Advanced Studies, Hayama, Kanagawa 240-0193, Japan S Supporting Information *

ABSTRACT: The ground-state rotational spectra of the dimethyl sulfide−dimethyl ether (DMS−DME) and the ethylene oxide−ethylene sulfide (EO−ES) complexes were observed by Fourier transform microwave spectroscopy, and atype and c-type transitions were assigned for the normal, 34S, and three 13C species of the DMS−DME and a-type and btype transitions for the normal, 34S, and two 13C species of the EO−ES complexes. The transition frequencies measured for both the complexes were analyzed by using an S-reduced asymmetric-top rotational Hamiltonian. The rotational parameters thus derived for the DMS−DME were found to be consistent with a structure of Cs symmetry with the DMS bound to the DME by two C−H(DMS)···O and one S···H−C(DME) hydrogen bonds. Some high-Ka lines were found to be split, and we have interpreted these splittings in terms of internal rotations of the two methyl groups of the DMS and of the “free”, i.e., outer group, of the DME. Some forbidden transitions were also observed in cases where Ka = 3 levels were involved, for the DMS−DME complex in the internal-rotation E state. The barrier height, V3, to internal rotation of the CH3 in the DME thus derived is smaller than that of the DME monomer, while the V3 of the CH3 groups in the DMS is nearly the same as that of the DMS monomer. For the EO−ES complex, the observed data were interpreted in terms of an antiparallel structure of Cs symmetry with the EO bound to the ES by two C−H(ES)···O and two S···H−C(EO) hydrogen bonds. An attempt was also made to observe a-type transitions of the DMS dimer without success. We have applied a natural bond orbital analysis to the DMS−DME and EO−ES to calculate the stabilization energy CT (= ΔEσσ*), which was correlated closely with the binding energy as found for other related complexes.

I. INTRODUCTION

A molecular beam is normally generated by diluting the sample molecules with pressurized rare gases; hence, complexes consisting of a rare gas atom attached to a molecule are formed in the beam. Many such examples of rare gas atom−molecule complexes have been detected and studied extensively in previous contributions. The interaction between the constituents in these cases is primarily dispersion forces, often referred to as van der Waals interactions, which are weakest among the intermolecular interactions. In cases where one rare gas atom is attached to a molecule, the rare gas atom tends to occupy multiple sites, two or, in rare cases, three equivalent positions, and the tunneling paths can be traced by spectroscopic observations. The nitrogen molecule and carbon monoxide seem to behave in a way similar to the cases of rare gases, although both the molecules are not spherically symmetric and

The advent of a conventional method for preparing molecules in beam form during the 1970s, combined with high-resolution spectroscopic methods such as microwave spectroscopy, has made it possible for us to explore the structure and dynamics of molecular complexes in detail and has thus opened various new research areas; one good example is intermolecular interactions. Imperfections of gaseous samples have been well-known to arise from weak intermolecular interactions, which mainly consist of dispersion forces and are hence attractive in most cases and inversely proportional to the sixth power of the intermolecular distance. Scattering experiments have also made some contributions to the understanding of intermolecular interactions. In sharp contrast with these traditional approaches, high-resolution spectroscopic investigations on atomic and molecular complexes have yielded a completely new type of information, namely, the potential energy surfaces at close separation of atoms and/or molecules under study. © XXXX American Chemical Society

Received: August 16, 2015 Revised: September 28, 2015

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three weak hydrogen bonds.7 They reported that the V3 barrier to “free” DME methyl group internal rotation to be 2.2 kcal/ mol (785.4 cm−1), which is smaller than that of the monomer, 2.6 kcal/mol (951.7 cm−1).8 In the present study, we investigated the DMS dimer, the heterodimer of DME and DMS, and the heterodimer of EO and ES. We report here the results of FTMW spectroscopy and ab initio calculations.

thus induce anisotropy in their interactions with other molecules through their internal rotational angular momenta. Because the interactions are as weak as those in the cases of rare gas complexes, the intracomplex motions tend to be of large amplitude and often prohibit us from analyzing their highresolution spectra. The other extreme limit of interactions, i.e. the strongest one, is exemplified by the hydrogen bond, which has already been well established in many molecular systems, and has attracted much attention because of its important roles played in many areas, in particular, in biological systems. The hydrogen bond is normally formed between a hydrogen and an electronegative atom in a molecule and is naturally active also between separate atoms and/or molecules, as the strongest means of producing complexes. There exist a large variety of interactions between the two limits of the weak van der Waals and the strong hydrogen bond, and we should try to determine not only a simple scale of strength, but also many kinds of additional measures to match the diversity of intermolecular interactions and to systematize them. As one possible efficient way of achieving such a goal, we have decided to employ various types of molecules, which result in a variety of intermolecular interactions. We have paid particular attention to molecules of high symmetry because they are expected to provide us with information on intermolecular interactions clearly and also in a systematic way. As such examples we have selected the dimethyl ether (DME) and dimethyl sulfide (DMS) pair and a similar pair of ethylene oxide (EO) and ethylene sulfide (ES). The systems consisting of these molecules will also involve hydrogen bonds, but often deviating from ideal linear arrangements. The four molecules contain either an O or an S atom, which has lone pair electrons and induces a unique type of directivity in the interactions. The four molecules can rotate about their own 2-fold axis in the complex, as in the cases of the N2 and CO rotations about the perpendicular axis, which induce internal rotational angular momenta coupled with the overall rotation of the entire complex. These “internal” rotations may be regarded as an intracomplex motion, following the well-known example of the stretching motion between two component molecules. A significant number of complexes have already been investigated by a few groups including ours, by using Fourier transform microwave (FTMW) spectroscopy, as listed below: CO−EO,1 CO−ES,1 CO−DME,2 CO−DMS,3 CO2−EO,1 CO2−ES,1 N2−EO,4 H2CO−DME,5 and H2CO−DMS.5 We have also applied a natural bond orbital (NBO) analysis to the complexes to calculate the stabilization energy CT (= ΔEσσ*), which we found was closely correlated with the binding energies EB. Legon examined the structures of the EO−HX and ES−HX (X = F, Cl, and Br) complexes and explained the structures and binding energies derived in terms of the hydrogen bond between the lone pair electrons in the O of the EO or in the S of the ES and the H of the HX, which is referred to as the n-pair model.6 We have reported that the Ar, CO, and CO2 are located along the lone pair electron of the O atom of the EO or the S atom of the ES (see Figure 6 of ref 1). The stabilization energy CT of the complexes containing DME and/or DMS is two and a half times larger than the EB (see Figure 6 of ref 5). In the cases of the H2CO−DME and H2CO−DMS complexes, the CT is four times larger than the EB because H2CO is a strong acceptor.5 Tatamitani et al. reported the microwave spectra of the DME dimer, which consists of weak, improper, C−O···H−C hydrogen bonds and has a structure of Cs symmetry with two monomers bound by

II. EXPERIMENTAL SECTION The rotational spectra of the DMS dimer were searched for in the frequency region from 7 to 22 GHz, while those of the DMS−DME and EO−ES complexes were observed in the frequency region from 4 to 24 GHz, by using a Balle−Flygare type FTMW spectrometer,9 which was described previously.10 Samples of DME, DMS, and ES, 99% pure, commercially available from Aldrich Co., and of EO, 99% pure, from Nippon Fine Gas Co., were employed without further purification. The DMS dimer spectra were searched for by using a sample of DMS diluted with Ar to 1.0%, whereas a one-to-one mixture of DME and DMS and of EO and ES, each diluted with Ar to 0.5% ∼ 1.0%, were introduced in an evacuated Fabry−Perot cavity of the FTMW spectrometer through a 0.8 mm diameter orifice of a General Valve Series 9 pulsed nozzle, at a repetition rate of 2 Hz and at the backing pressure of approximately 5 atm. We integrated the signals 30∼1000 times to get a good signal-to-noise ratio for the frequency measurements. The uncertainty of the frequency measurement was typically 2 kHz, and the resolution achieved was about 5 kHz. III. AB INITIO CALCULATIONS To obtain preliminary information on the structure and the dynamics of the DMS−DME and the EO−ES complexes, we have carried out ab initio molecular orbital calculation at the level of MP2 with basis sets 6-311++G(d,p) using the Gaussian 09 package.11 The optimized structures of the two complexes thus obtained are displayed in Figures 1 and 2, respectively, along with the principal inertial axes.

Figure 1. Optimized geometries of the DME−DMS and DMS−DME heterodimers calculated at the MP2/6-311++G(d,p) level of theory. The oxygen atom is shown in red, the sulfur atom in yellow, and the carbon atom in black, while the hydrogen atom is indicated by a small sphere.

We have chosen the following convention for the naming of the component molecules, namely, the molecule with its molecular plane perpendicular to the heavy-atom skeleton of the complex: the a−c and a−b plane for the DMS−DME and EO−ES complexes, respectively, appears first, i.e., at the lefthand side of the name (DMS and EO, in the present examples, respectively). The most stable configuration of the DMS−DME displayed in Figure 1a is of Cs symmetry, and the next stable one, DME− B

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bonds, as in the case of the DME dimer, with the rotational constants A, B, and C of 3607.3, 799.2, and 788.4 MHz, respectively, and the dipole-moment components μa, μb, and μc of 1.76, 0.66, and 0.00 D, respectively. We thus expected that the dimer closely approximates a prolate symmetric top and yields a-type R-branch transitions at every 1500 MHz. Many rotational lines were observed for a DMS and Ar mixture in the frequency region from 7 to 14 GHz. When the absorption lines of the DMS monomer,8 its isotopologues, and the Ar−DMS complexes15 were removed from the observed spectra, 42 lines remained unassigned in this region. Replacement of Ar by Ne as a buffer gas confirmed 38 among 42 lines could be ascribed to the Ar−DMS, leaving only four. Thus, the DMS dimer spectra could not be identified in this frequency region. B. Rotational Spectra of the DMS−DME Complex. The ab initio calculation indicated that the two complexes, DMS− DME and DME−DMS (or, probably better to say, the two lowest-energy conformations of the complex), would exhibit atype R-branch transitions at every 2070 and 2125 MHz, respectively, because both of these heterodimers were close to prolate symmetric top molecules. Many rotational lines were in fact observed for a DME, DMS, and Ar mixture in the frequency region from 7 to 14 GHz. After the absorption lines of the DME16,17 and DMS8 monomers, their isotopologues, and the Ar−DME18,19 and Ar−DMS15 complexes were removed from the observed spectra, we identified a-type Rbranch series: J = 3 ← 2 up to 7 ← 6, which appeared at every 2.0 GHz and closely approximated the symmetric-top pattern. This observation was followed by detection of c-type R-branch transitions: 211 ← 101 and 312 ← 202 at 7195.94 and 9222.43 MHz, respectively, but no b-type transitions were observed. The a-type transitions of the 34S species were observed and assigned under natural abundance. The two carbon atoms of the DMS are equivalent in the most stable conformation of the DMS−DME complex; hence, the corresponding 13C species have natural abundance of about 2%. On the other hand, the two 13C species, one with the 13C atom in the inner and the other in the outer position of the DME, are both of 1% natural abundance. Finally, we assigned 104 a-type R-branch transitions and 50 c-type R-branch transitions for the normal species of the DMS− DME complex, with J spanning from 1 to 12 and Ka from 0 to 6, and the 36 a-type R-branch transitions for the 34S and 13 C(DMS) species, with J spanning from 2 to 10 and Ka from 0 to 2, except for the inner-13C and outer-13C species, for which Ka was limited from 0 to 1. Almost all a-type transitions, including Ka = 2 and/or 3, and c-type transitions showed small splittings due to internal rotation of the methyl groups. We discuss these CH3 internal rotation splittings in a following section. A list of the measured lines is available as Supporting Information in Table S1. The assigned transitions were analyzed by using an asymmetric-top rotational Hamiltonian of S-reduced form. Three rotational and five centrifugal distortion constants were thus determined, except for DK of the 34S and 13C (DMS) and for DJK, DK, d1, and d2 of the two 13 C (DME) species, which were fixed to the values of the normal species. All the derived constants are listed in Table 2, along with the values calculated by MP2/6-311++G(d,p) for comparison. We have attempted to detect rotational lines of the second conformer: DME−DMS without success, presumably because of higher energy and also a too small a-type dipole moment component.

Figure 2. Optimized geometries of the antiparallel and perpendicular EO−ES heterodimers calculated at the MP2/6-311++G(d,p) level of theory. The colors of the atoms are the same as those in Figure 1.

DMS, has no symmetry with all three dipole-moment components finite because one of the methyl groups of the DMS is located outside the plane, as shown in Figure1b. In a similar way, the MP2/6-311++G(d,p) optimized structures of the most stable, antiparallel EO−ES and of the second-lowest energy, perpendicular ES−EO complexes, are displayed in Figure 2a and 2b, respectively, both being of Cs symmetry. The binding energies calculated with MP2/6-311++G(d,p) of the DMS−DME and EO−ES complexes are listed in Table 1, Table 1. Calculated Dissociation Energies (De), Counterpoise (CP) Corrections for the Basis Set Superposition Errors, Zero-Point Vibrational Energy (ΔZPV) Corrections, Predicted Rotational Constants, and Dipole Moment Components of the DMS−DME, DME− DMS, EO−ES, and ES−EO Complexes, Obtained by the MP2/6-311++G(d,p) Level of Theory DMS−DME Figure 1a De (kJ mol−1) CP (kJ mol−1) ΔZPV (kJ mol−1) D0 = De+ΔZPV (kJ mol−1) D0+50%CP (kJ mol−1) Ae (MHz) Be (MHz) Ce (MHz) μa (D) μb (D) μc (D) Rcm (Å)

DME−DMS Figure 1b

EO−ES Figure 2a

ES−EO Figure 2b

20.5 9.8 3.6 16.9

17.9 9.5 3.0 14.9

22.4 8.6 3.0 19.4

19.4 7.5 2.9 16.5

12.0

10.2

15.1

12.8

4129.7 1044.6 1025.3 2.72 0.00 0.69 3.880

4671.0 1097.3 1026.7 0.48 0.52 1.27 3.453

5259.2 1447.4 1374.0 1.28 0.33 0.00 3.442

6162.4 1231.7 1131.5 2.33 0.44 0.00 3.483

where the basis set superposition errors (BSSE) calculated with the counterpoise correction method12 and the zero-point vibrational energy corrections are also included. According to ref 13, the counterpoise correction tends to overestimate the BSSE derived with small basis sets, and a 50% counterpoise correction has been known to give empirically a better estimate for the dissociation energies. Therefore, we assumed the counterpoise correction to be 50% in the present study, as in fact is widely adopted in the microwave spectroscopy community.14 The absence of imaginary vibrational frequencies indicates that the four eigenstates mentioned above all exist in stable minima.

IV. RESULTS A. Rotational Spectra of the DMS Dimer. The ab initio calculation predicted that the DMS dimer has a structure of Cs symmetry with two monomers bound by three weak hydrogen C

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Table 2. Rotational and Centrifugal Distortion Constants of the DMS−DME, DMS(34S)−DME, DMS(13C)−DME, DMS− DME(inner 13C), and DMS−DME(Outer 13C), in Comparison with the Values Calculated by MP2/6-311++G(d,p)a A (MHz) B (MHz) C (MHz) DJ (kHz) DJK (kHz) DK (kHz) d1 (kHz) d2 (kHz) σb (kHz) N(a‑type)c N(c‑type)c |as(X)| (Å) |bs(X)| (Å) |cs(X)| (Å) a

DMS−DME

DMS(34S)−DME

DMS(13C)−DME

DMS−DME(inner 13C)

DMS−DME(outer 13C)

calculated

4173.47059 (34) 1007.505687 (64) 984.464897 (64) 1.05199 (21) 0.8998 (16) 6.717 (33) 0.01502 (25) 0.02665 (16) 2.9 104 50

4163.85 (30) 991.46914 (14) 969.68348 (13) 1.02362 (30) 0.721 (19) (6.717) 0.01526 (43) 0.02450 (28) 1.2 36 − 1.9982 0.0455 i 0.3844

4098.68 (25) 1003.21626 (17) 977.31362 (16) 1.03561 (38) 1.039 (23) (6.717) 0.01255 (53) 0.02582 (34) 1.5 36 − 1.3587 1.3719 0.5928

4122.65 (49) 998.18576 (11) 978.44018 (11) 1.02693 (62) (0.8998) (6.717) (0.01502) (0.02665) 1.9 24 − 1.7839 0.1143 i 1.2358

4157.99 (35) 987.178637 (87) 965.795426 (86) 1.01814 (50) (0.8998) (6.717) (0.01502) (0.02665) 1.5 24 − 3.1540 0.1505 0.6651

4060.66 1027.57 1010.04 0.8381 0.7380 5.2710 0.0153 0.0424

The number in parentheses denotes 3σ. bStandard deviations. cNumber of fitting transitions.

Table 3. Rotational and Centrifugal Distortion Constants of the EO−ES, EO−ES(34S), EO(13C)−ES, and EO−ES(13C) and Substituted Coordinates of the S atom, the Two C Atoms in the Normal Species of the EO−ES Complex, in Comparison with the Values Calculated by MP2/6-311++G(d,p)a A (MHz) B (MHz) C (MHz) DJ (kHz) DJK (kHz) DK (kHz) d1 (kHz) d2 (kHz) σb (kHz) N(a‑type)c N(b‑type)c |as(X)| (Å) |bs(X)| (Å) |cs(X)| (Å) a

EO−ES

EO−ES(34S)

EO(13C)−ES

EO−ES(13C)

calculated

5220.98990 (36) 1400.07588 (12) 1327.28939 (12) 1.492372 (82) 5.5353 (32) −5.018 (37) −0.07990 (91) 0.00321 (51) 2.4 57 30

5153.551 (54) 1383.36664 (21) 1307.92462 (20) 1.46719 (69) 5.334 (21) (−5.018) −0.0811 (10) (0.00321) 1.3 28 − 1.4895 0.8127 0.0547 i

5185.677 (49) 1380.29971 (19) 1310.78474 (18) 1.45215 (63) 5.362 (10) (−5.018) −0.07476 (92) (0.00321) 1.2 28 − 2.1614 0.3748 0.7306

5154.704 (50) 1389.91440 (10) 1317.43226 (10) 1.45905 (71) 5.496 (12) (−5.018) −0.0784 (10) (0.00321) 1.3 28 − 1.4578 0.8476 0.7375

5225.97 1395.51 1326.22 1.2787 5.4742 −4.7481 −0.0608 0.0148

The number in parentheses denotes 3σ. bStandard deviations. cNumber of fitting transitions.

C. Rotational Spectra of the EO−ES Complex. Both the EO−ES antiparallel and the ES−EO perpendicular structures, optimized by ab initio calculations, suggested a-type R-branch transitions, approximately at every 2820 and 2360 MHz, respectively, because both the heterodimers were predicted to be close to prolate symmetric tops with sizable dipole-moment components along the a axis. Many rotational lines were observed for an EO, ES, and Ar mixture in the frequency region from 7 to 14 GHz. After removing the absorption lines of the EO20 and ES21 monomers, their isotopologues, and the Ar− EO22,23 and Ar−ES24 complexes from the observed spectra, we readily identified the a-type J = 3 ← 2 transition near 8.2 GHz and extended the observation to the a-type R-branch series from J = 2 ← 1 up to 8 ← 7, which appeared at every 2.73 GHz and closely approximated the symmetric-top pattern. This observation was followed by detection of b-type R-branch transitions: 111 ← 000, 212 ← 101, and 313 ← 202 transitions at 6548.27, 9202.78, and 11821.22 MHz, respectively. According to the ab initio calculation, the ES−EO is less stable than the EO−ES by 250 cm−1, and in fact we could have detected only spectra of the EO−ES complex in the frequency region from 7 to 14 GHz. The two carbon atoms in the EO are equivalent, as

are those in the ES, in the EO−ES complex; thus, the two types of the 13C species of the EO−ES have the natural abundance of about 2%. Finally, we assigned 57 a-type R-branch transitions and 30 b-type R-branch transitions for the normal species, with J spanning from 1 to 8 and Ka from 0 to 5, and 28 a-type Rbranch transitions for the 34S and two 13C species, with J spanning from 1 to 8 and Ka from 0 to 3. A list of the measured lines is available as Supporting Information in Table S2. The measured transition frequencies were analyzed by using an asymmetric-top rotational Hamiltonian of S-reduced form. Three rotational and five centrifugal distortion constants were determined, except for DK and d2 fixed to the values of the normal species for the 34S and 13C isotopic species, and the constants thus obtained are listed in Table 3, along with the corresponding values calculated by MP2/6-311++G(d,p) for comparison. The agreement between the observed and calculated molecular parameters is satisfactory.

V. DISCUSSION A. Molecular Structures of the DMS−DME and EO−ES Complexes. The planar moment of inertia Pbb = (Iaa + Icc − Ibb)/2 obtained for the DMS−DME was 66.4167 uÅ2, which is D

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Figure 3. Observed and calculated splittings of the internal rotation of the DMS−DME; 1038 ← 937 and 1037 ← 936.

very close to the sum of the two planar moments: Paa = (Ibb + Icc − Iaa)/2 of the DMS monomer (63.1620 uÅ2)8 and Pcc = (Iaa + Ibb − Icc)/2 of the DME (3.2073 uÅ2).8 This result clearly indicates the observed complex to be the DMS−DME (see Figure 1a). No b-type transitions were detected, as expected from the fact that the a−c plane is the symmetry plane of the complex. The rotational constants of this complex led to the distance Rcm between the centers of mass of the two component molecules by assuming the following equation to hold:

The rotational constants derived for the EO−ES led to the distance Rcm between the centers of mass of the two component molecules, Rcm, to be 3.518 Å, by assuming the following equations to hold: Icc(EO−ES) = Iaa(EO) + Ibb(ES) + μR cm(EO−ES)2

which is quite close to an ab initio calculated value, 3.442 Å (Table 1). The rs coordinates of the S and C atoms in the ES and the C atom in the EO were calculated by the Kraitchman equation, and are listed in Table 3. The c-coordinate of the S atom of the ES was derived to be imaginary, as listed in Table 3, and was set to zero in further structural calculations. These structural data are consistent with the spectral data; no c-type transitions were observed. The rs C−S and C−C bond distances and the angle C−S−C in the ES and the C−C bond distance in the EO were derived to be 1.817 and 1.475 Å, 47.9°, and 1.461 Å, respectively, which are close to 1.815 (3), 1.494 (3) Å, 48.3 (1)°, respectively, of the ES monomer26 and to 1.463 (2) Å of the EO monomer.20 B. Internal Rotations of the Methyl Groups in the DMS−DME. The a-type R-branch transitions of J = 3←2 up to 7←6 with Ka = 2 and of J = 7←6 up to 12←11 with Ka = 3 and also some c-type R- and Q-branch transitions of the DMS− DME were found split into several components, as exemplified by the 1038 ← 937 and 1037 ← 936 transitions shown in Figure 3. These splittings were presumably caused by combinations of the CH3 internal-rotation/overall rotation coupling and the Ktype doubling. The two transitions of Figure 3 are split into 6 components, indicating that not only the internal rotation of the free methyl group of the DME but also that of the two methyl groups of the DMS are responsible for the splittings. An ab initio calculation predicts that the V3 internal rotation barriers are 910.0 and 950.3 cm−1, respectively, for the outer and inner methyl group of the DME and 744.4 cm−1 for the two methyl groups of the DMS. Because the DMS−DME complex is close to a symmetric top and shows splittings only for Ka = 2 or 3 rotational transitions, the a components of the methyl internal-rotation first-order terms must be dominant in splitting. We have attempted to analyze the observed splittings by assuming the DMS and DME CH3 group contributions to be additive, while neglecting possible couplings among the CH3

Ibb(DMS−DME) = Iaa(DMS) + Icc(DME) + μR cm(DMS−DME)2 (1)

where Ibb(DMS−DME), Iaa(DMS), and Icc(DME) denote the moment of inertia about the b-axis of the DMS−DME, that about the a-axis of the DMS, and that about the c-axis of the DME, respectively. μ designates the reduced mass of the DMS−DME μ=

m(DMS) m(DME) m(DMS) + m(DME)

(3)

(2)

and Rcm(DMS−DME) represents the distance between the centers of the mass of the two component molecules. The Rcm thus obtained is 3.970 Å, which is close to the ab initio calculated value of 3.880 Å (Table 1). The rs coordinates of the S and C atoms in the DMS−DME complex were calculated using the Kraitchman equation25 and are listed in Table 2. The b-coordinates of the S atom of the DMS and of the two carbon atoms of the DME were set to zero in further structural calculations. The derived rs C−S bond distance and the bond angle C−S−C are 1.783 Å and 101.3°, respectively, which are close to the 1.801 (1) Å and 99.0 (1) °, respectively, of the monomer.8 The planar moment of inertia Pcc = (Iaa + Ibb − Icc)/2 obtained for the EO−ES complex is 38.50140 uÅ2 and very close to the sum of the planar moments of the inertia Paa = (Ibb + Icc − Iaa)/2 of the EO: 19.43150 uÅ2 and the Pbb = (Iaa + Icc − Ibb)/2 of the ES: 19.63938 uÅ2. This result indicates that the observed complex is the EO−ES (see Figure 2a), consistent with the fact that no c-type transition was observed. We have concluded that the observed complex has the a−b plane as the symmetry plane. E

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Figure 4. Observed allowed and forbidden transitions: 634 ← 624 and 633 ← 625 of the DMS−DME.

groups, and have forwarded the analysis in three steps, as described in the following. The first step considers the internal rotation of only the “free” (i.e., outer) methyl group of the DME, which is not bound by hydrogen bonds, as shown in Figure 1a. Some of the transitions of the DMS−DME were found split into only two (A and E) components. The K-type doublings become as small as the internal-rotational splittings when K reaches 3, and then the internal rotation splittings become discernible and even some forbidden transitions are observed. Examples are 634 ← 624 and 633 ← 625 shown in Figure 4, where forbidden transitions clearly appear. The analysis of the observed spectra was carried out by using the XIAM program of Hartwig and Dreizler,27 resulting in three rotational and five centrifugal distortion constants, in addition to the potential barrier V3 to CH3 internal rotation. The parameter ρ was fixed to a value calculated by assuming the methyl moment of inertia Iα to be 3.191 uÅ2, and the two angles, δ and ε, which denote the angle between the CH3 internal-rotation axis and the principal inertial axis, a, of the complex and the angle between the CH3 internalrotation axis, projected on the b-c plane, and the inertial axis, b, respectively, could not be determined because of high correlation of these two angles with V3 and were thus fixed to 22.6° and 90.0°, respectively, as ab initio calculated using MP2/6-311++G(d,p). All the molecular parameters derived are summarized in Table 4. A list of the measured rotational lines is available as Supporting Information in Table S3. The V3 barrier height to internal rotation of the DME free methyl group in the DMS−DME thus determined is 918.51 (42) cm−1, which is smaller than that of the monomer (951.72 (70) cm−1),8 but larger than that of DME dimer (785.4 (52) cm−1),7 Ar−DME (778 (1) cm−1),19 and CO−DME (772 (2) cm−1).2 The second step was directed to the splittings caused by the two equivalent methyl tops of the DMS. There are four internal rotation states, designated by the two symmetry species, the left-hand side for the negative combination of the two internal rotation angles and the right-hand side for the positive one: AA, EE, AE, and EA. The AA state contributes only tiny secondorder terms, and the rotational lines in this state will almost coincide with those of the A state of the DME free CH3 group. The analysis of the splittings was carried out as in the case of the DME free CH3 internal rotation, and the molecular parameters thus derived are listed in Table 4. A list of the measured rotational lines is available as Supporting Information

Table 4. Rotational and Centrifugal Distortion Constants of the DMS−DME and Internal Rotation Parameters of the Free and Two Equivalent Methyl Group in the DMS−DMEa

A0 (MHz) B0 (MHz) C0 (MHz) DJ (kHz) DJK (kHz) DK (kHz) d1 (kHz) d2 (kHz) F (GHz) λa(O−CH3) λb (O−CH3) λc (O−CH3) λa(S-CH3) λb (S-CH3) λc (S-CH3) s V3(O−CH3) (cm−1) V3(S-CH3) (cm−1) σ (kHz) a

V3 of the free methyl group

V3 of the two methyl groups

4173.46875 (21) 1007.506242 (37) 984.464466 (36) 1.05227 (12) 0.89970 (91) 6.778 (19) 0.01483 (15) 0.026752 (92) 159.21b 0.923081b 0.0b 0.384606b − − − 75.08 918.51 (42) − 2.9

4173.46766 (26) 1007.505719 (50) 984.464700 (55) 1.05289 (19) 0.9022 (17) 6.669 (24) 0.01504 (26) 0.02667 (15) 159.21b − − − 0.342348b 0.765279b ± 0.545110b 61.81 − 744.96 (53) 3.9

The number in parentheses denotes 3σ. bFixed.

in Table S4. The V3 barrier, 744.96 (53) cm−1, is close to those of the monomer [752.3 (70) cm−1],8 Ar−DMS [736.17 (32) cm−1],15 and CO−DMS [745.5 (30) cm−1].3 The third step is a combined analysis of the spectral splittings due to internal rotation of both the two CH3 groups of the DMS and the free CH3 of the DME. Some transitions with Ka = 2 and/or 3 of the DMS−DME complex were observed split into as many as six components. Among the four CH3 groups in the complex, the inner one in the DME, which is closely located to the S atom of the DMS, will be subjected to the highest potential barrier V3 among the four and, in addition, its internal-rotation axis makes an angle with the a-principal inertial axis of the complex as large as 88.77°. Hence, this CH3 group is ignored hereafter, and attention is paid to the remaining three CH3: the two in the DMS and the one free in the DME. A molecular system containing two equivalent CH3 groups, of both C2v (like DME) and Cs (such as the present complex) F

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The Journal of Physical Chemistry A symmetry, has been studied by a few groups in detail.28 We start with the result on the latter case, a Cs molecule. Its symmetry group can be expressed by a direct product of the two symmetry groups: C3− × C3v+, where the former applies to the 1/2(α1 − α2) internal rotation angle and the latter to 1/ 2(α1 + α2). Each symmetry operation may be expressed by a product of those of the two groups, in such a way as EE, 2EC3, and so on, resulting in 18 in total, and accordingly, the symmetry species are again expressed by a product of those of the two groups, six in number, as shown in the character table (See Table 5). The statistical weight is calculated by ignoring

Δ(J , K ) = [A − (B + C)/2]bK (J + K ) ! /{8K − 1(J − K ) ! [(K − 1) ! ]2 }, b = (C − B)/(2A − B − C)

The a-type R-branch transition J + 1 ← J, K ← K frequencies, for example, are given by ν(J + 1 ← J , K ← K , ± ← ± ) = (B + C)(J + 1) 1 + centrifugal corrections ± {[(Q aK )2 + Δ(J + 1, K )2 ]1/2 2 − [(Q aK )2 + Δ(J , K )2 ]1/2 }

Table 5. Character Table of Two-Top Molecule AA1 AA2 AE EA1 EA2 EE

2EC3

3Eσv

2C3E

4C32

6C3σv

1 1 2 2 2 4

1 1 −1 2 2 −2

1 −1 0 2 −2 0

1 1 2 −1 1 −2

1 1 −1 −1 1 1

1 −1 0 −1 −1 0

ν(J + 1 ← J , K ← K , ± ← ∓ ) = (B + C)(J + 1) 1 + centrifugal corrections ± {[(Q aK )2 + Δ(J + 1, K )2 ]1/2 2 1 2 2 1/2 ± [(Q aK ) + Δ(J , K ) ] (7) 2

For the internal rotation A symmetry state, Qa = 0; thus, the ordinary K-type doublet appears, whereas the E symmetry state yields a doublet with a smaller K splitting located between the two A state K-type doublet components, in addition to the forbidden lines located outside the K-type doublet of the A state. The transition frequencies of the c-type R-branch and Qbranch K + 1 ← K transitions follow the selection rules ± ← ± and ± ← ∓ , respectively. It should be noted that both the AA and EA species do not produce the first-order term because Qa does not exist and/or is canceled out in these two states. We thus obtain the following first-order contributions of CH3 internal rotation shown in Table 6, where QS and QO denote the first-order terms due to

symmetry operations containing σv, namely by considering the group C3− × C3+. The number of the nuclear spin functions, 8 for each CH3 and 64 in total, leads to the relative statistical weights: 2:1:1:4 for the AA: AE: EA: EE species. As noted above, the DMS−DME complex we are studying involves three CH3, i.e., it consists of the free CH3 attached to a two-top Cs system. Therefore, we combine the symmetry operations of this additional CH3 group of the DME with those of the Cs system (the superscript O is attached to the added operations, when necessary, to discriminate the new ones from those of the Cs starting system) as follows: EEE ,

2EEC3 ,

3EEσv ,

2EC3E ,

4EC3 ,

Table 6. Eight States of the Internal Rotation of Three Methyl Groups, Their First-Order Splittings, and Their Relative Intensities

6EC3σv ,

2C3OEE , 4C3OEC3 , 6C3OEσv , 4C3OC3E , 8C3OC32 , 12C3OC3σv , 3σv OEE , 6σv OEC3 ,

(6)

Those for the forbidden transitions ± ← ∓ are

EE

2

(5b)

9σv OEσv , 6σv OC3E , 12σv OC32 , 18σv OC3σv

To derive the statistical weight, we ignore the symmetry operations, which involve σv and/or σvO, and we end up with the following weights for the eight symmetry species: AAA 2, AAE 1, AEA 1, AEE 4,

state

first-order term, Qa

relative intensity

AAA + AEA AAE AEE EAA + EEA EAE EEE

0 2QS QS QO 2QS + QO QS + QO

3 1 4 3 1 4

EAA 2, EEA 1, EEA 1, EEE 4

the two CH3 in the DMS and to the free CH3 in the DME, respectively, and both are given by eq 5a. It should be noted that QS contains the contributions of the two CH3 groups and hence must be multiplied by 2. The two terms QO and QS can then be estimated to be −0.0459 and −0.0472, respectively, by using λa of 0.923081 and 0.342348 and V3 of 918.51 (42) [910.0] and 744.96 (53) [744.4] cm−1, respectively; where the values of V3 are obtained by a preliminary analysis (i.e., the first and second steps, respectively) of the observed spectra, along with the ab initio calculated values in square brackets. The two terms, QO and QS, were determined by using the observed deviations from the corresponding line frequencies of the AAA state to be −0.059 (36) and −0.0448 (15), respectively. Unfortunately, the presently available spectral resolution is far from satisfactory for determining all the internal-rotation parameters precisely, and we certainly need to take into account possible couplings among methyl groups in the spectral

As already explained, the observed splittings originate from the interplay between the first-order contribution of the methyl group internal rotation and the molecular asymmetry. The eigenvalues of the K-type doublets of a near prolate symmetric top like the DMS−DME complex are given by E(J , K )± = ±

1 (B + C)J(J + 1) + centrifugal terms 2

1 [(Q aK )2 + Δ(J , K )2 ]1/2 2

(4)

where Qa denotes the first-order term of the methyl internal rotation and Δ(J,K) represents the molecular asymmetry splitting:29 Q a = 4(hλa /8π 2rIaa)⟨p⟩

(5a)

where r = 1 − ∑g=a,cλg Iα/Igg and 2

G

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Table 7. Calculated Intermolecular Distance (Rcm), Estimated Binding Energy (EB), Calculated Stabilization Energy of the Charge Transfer (CT), and Corrected Dissociation Energy (D0 + 50% CP) of the DMS−DME, EO−ES, and Their Related Complexes parameter

Rcm (Å)

ks (N m−1)

EB (kJ mol−1)

CT (kJ mol−1)

D0+50%CP (kJ mol−1)

ref

Ar−DME Ar−DMS CO−DME CO−DMS CO2−DME H2CO−DME H2CO−DMS (DME)2 DMS−DME Ar−EO CO−EO CO2−EO N2−EO EO−ES Ar−ES CO−ES CO2−ES

3.583 3.80 3.682 3.789 3.255 3.102 3.200 3.837 3.970 3.61 3.61 3.259 3.467 3.518 3.79 3.80 3.471

2.3 2.0 1.4 2.7 10.9 6.5 7.9 5.3 5.6 1.5 3.3 8.0 2.1 9.7 2.1 3.2 6.9

2.5 2.4 1.6 3.3 9.7 5.2 6.7 4.7 7.3 1.6 3.6 7.1 2.1 10.0 2.5 3.9 7.1

2.5 2.1 8.4 8.8 24.3 27.9 35.4 13.8 19.5 1.9 8.8 14.1 6.5 17.9 2.0 11.0 13.5

1.28 1.19 4.27 3.94 9.23 9.9 10.5 10.1 12.0 0.93 4.34 5.98 4.26 15.1 1.42 4.42 4.51

18, 19 14 2 3 38 5 5 7 this work 22, 23 1 1 4 this work 24 1 1

5 against the binding energy, EB, which indicates the two quantities ΔEσσ* and EB run closely parallel. Figure 5 shows that the complexes containing EO and/or ES are located on the blue line, where the CT stabilization energies are approximately twice as large as the EB, while the complexes containing DME and/or DMS complexes, except for those containing Ar, are located on the red line, where CT is about two and half times larger than EB. The difference between the two groups is ascribed to the fact that the ionization potentials of DME (Ip = 9.0 eV) and DMS (Ip = 8.7 eV) are lower than those of the EO (Ip = 9.7 eV) and ES (Ip = 9.4 eV); thus, DME and DMS behave as slightly stronger electron donors than EO and ES. We have recently investigated the H2CO−DME and H2CO− DMS complexes and have found that the CT’s are four times larger than the EB in these complexes. The DMS−DME complex shown in Figure 1a is more stable than the DME− DMS shown in Figure 1b, and this difference in the stability may be explained by the n-pair model,6 that is, in the DMS− DME complex the two lone pair electrons of the O atom of the DME form two weak hydrogen bonds with the two H atoms of the DMS and the lone pair electron of the S atom one weak hydrogen bond with the H atom of the inner methyl group of the DME. However, the lone pair electrons of the S atom of the DMS cannot form hydrogen bonds to the two H atoms of the DME because the lone pair electrons are located perpendicular to the a−c plane. According to the MP2/6-311++G(d,p) calculation, the stabilization energy due to CT from the DME to the DMS in the DMS−DME complex is calculated to be 9.8 kJ/mol, while the CT from the DMS to the DME in the DME−DMS complex is only 5.7 kJ/mol. D. Isotopic Effects on the DMS−DME Complex. The spectral intensities of the DMS−DME inner-13C species were observed to be larger than those of the DMS−DME outer-13C species by a factor of 1.6. We have previously discovered much more conspicuous examples for the CO2−EO and CO2−ES complexes; spectra of the inner OC18O−EO/ES complexes were stronger than those of the outer 18OCO−EO/ES1 by a factor of 2, and similarly the inner N15N−EO showed rotational spectra stronger than those of the outer 15NN−EO by a factor of 2.4 This sort of observation applies also to the 15N14N−

analysis. The agreement between the observed and calculated internal-rotation splittings thus still remain in semiquantitative stage, as demonstrated by an example shown in the lower part of Figure 3. C. Intermolecular Stretching Force Constant, Binding Energy, and CT Stabilization Energy of the DMS−DME and EO−ES Complexes, and Comparison of the Corresponding Parameters with Those of the Related Complexes. We have estimated the stretching force constant, k s , and binding energy, E B , by using the following equations:30−33 ks =

EB =

16π 4μ2 R cm 2[3B4 + 3C 4 + 2B2 C 2] hDJ

1 ksR cm 2 72

(8)

(9)

The EB and ks thus obtained are listed in Table 7 and are compared with those of related complexes. The NBO model has been shown to be very useful in explaining the hydrogen bonding in the X−H···Y system, where the charge delocalization takes place between the lone pair of the donor Y and the antibonding σ*(X−H) orbital of the acceptor. The energy lowering caused by this electron delocalization may be estimated by the second-order perturbation theory. We have thus evaluated the stability of van der Waals complexes due to charge transfer. We have carried out an NBO analysis on the DMS−DME and the EO− ES complexes by an ab initio molecular orbital method at the level of MP2/6-311++G(d,p) using Gaussian 09. This stabilization energy, ΔEσσ*, is given by34 ΔEσσ * = −2

⟨σ |F |̂ σ *⟩2 εσ * − εσ

(10)

where F̂ is the Fock operator and εσ and εσ* are the zerothorder NBO orbital energies. The stabilization energy, ΔEσσ*, is obtained as the sum of all the energy terms which exceed 0.05 kcal/mol (= 0.21 kJ/mol). The total CT stabilization energy, ΔEσσ*, thus calculated and listed in Table 7, is plotted in Figure H

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Figure 5. Relationship between the binding energy, EB, and the charge-transfer stabilization energy, CT. The following symbols are used: circle for DME, triangle for DMS, square for EO, and diamond for ES; Ar, CO, CO2, and N2 are shown by blue, violet, green, and orange, respectively.

HOH and 14N15N−HOH complexes,35 followed by the N2− CO2 of a T-shaped structure in which the OCO forms the cross of the T,36 and also by the CO2-propylene oxide37 and the CO2−DME38 complexes. The dissociation energy will be larger for heavier species, and repeated dissociation and reformation of the complexes at initial processes of the molecular beam expansion will result in a distribution in which the heavier species are more populated. The zero-point vibration energy was calculated to be 0.84 and 0.59 cm−1, respectively, for the inner and outer conformers of the DMS−DME by using the MP2/6-311++G(d,p) and MP2/aug-cc-pvTZ basis sets. If the beam temperature was as low as 1∼2 K, the Boltzmann distribution of the outer species was estimated to be nearly half

of the inner one, in conformity with the observed relative intensities of their rotational spectra.

VI. CONCLUSIONS We have found the hetero dimers DMS−DME and EO−ES by using an FTMW spectrometer, but we could not detect the other species: the DME−DMS and the DMS dimer. The reason for this failure is that the DME−DMS is less stable than the DMS−DME and the DMS dimer has a very weak binding interaction between the components. The isotopomers of the DMS−DME, 34S and three 13C species, indicate the structure of the complex to be of Cs symmetry with the DMS bound to the DME by two C−H(DMS)−O and one S−H−C(DME) I

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The Journal of Physical Chemistry A hydrogen bonds. The isotopomers of the EO−ES, 34S and two 13 C species, indicate the structure of the complex to be of antiparallel Cs symmetry with the EO bound to the ES by two C−H(ES)−O and two S−H−C(EO) hydrogen bonds. We have interpreted the observed splittings of some DMS−DME high-Ka transitions in terms of internal rotations of the two methyl groups of the DMS and of the free, i.e., outer group, in the DME. The observed internal-rotation barriers V3 are not much different from those in the monomers. We require more accurate data to find correlation between V3 and CT, if any. We have applied an NBO analysis to the DMS−DME and EO−ES to calculate the stabilization energy, CT (= ΔEσσ*), which we found is closely correlated with the binding energy, EB, as for other related complexes.

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jpca.5b07984. Measured rotational transition frequencies of the normal and isotopomer species of the DMS−DME complex (Table S1) (PDF) Measured rotational transition frequencies of the normal and isotopomer species of the EO−ES complex (Table S2) (PDF) Internal rotation splittings for the DMS−DME complex (Table S3) (PDF) Internal rotation splittings for the DMS−DME complex (Table S4) (PDF)

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Phone:+81 46 291-3095. Fax: +81 46 242-8760. Notes

The authors declare no competing financial interest.

■ ■

ACKNOWLEDGMENTS We thank Dr. Yoshiro Osamura for his advice in carrying out the MO calculations. REFERENCES

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K

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