Fourier Transform Microwave Spectrum of the Nitrogen Molecule

Article pubs.acs.org/JPCA

Fourier Transform Microwave Spectrum of the Nitrogen Molecule− Ethylene Oxide Complex: Intracomplex Motions Yoshiyuki Kawashima* 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 rotational spectra of the N2−ethylene oxide (EO) complex were measured in the frequency region from 4 to 27 GHz by Fourier transform microwave spectroscopy, paying particular attention to intracomplex motions. The isotopologues with enriched 15N2 or 15NN as a moiety were also investigated. We have observed spectra of a strong/weak pair for each of the ortho and para states of the 14N2−EO and 15N2−EO species, which indicated that the complex existed in four distinct states. We interpreted, on the basis of the observed relative intensities, that these states were generated primarily by the exchange of the nitrogen atoms of the N2 moiety, followed by that of the two CH2 groups in the EO molecule. The 15 NN−EO species was found to consist of two isomers, one with the 15N in the inner expressed as N15N−EO and the other in the outer position designated as 15 NN−EO, and the spectra of both isomers were accompanied by one weak set of satellites. The observed spectra were rotationally assigned by using sum rules and were analyzed by the asymmetric-rotor program of S-reduction, with the standard deviation of less than 10 kHz. We have found some of the molecular parameters like A, DJK, and DK to be correlated between the two pairs of the spectra, and also, to much less extent, between the strong and weak members. The differences in these molecular parameters between the four sets were explained by the first-order Coriolis interaction between the “ground” and “excited” states generated by a combination of the two internal motions corresponding to the exchanges of the equivalent atoms and/or groups in the N2 and EO constituents of the complex. These internal motions were simulated by the 2-fold internal rotations of the two moieties. We have carried out ab initio molecular orbital calculations at the level of MP2 with basis sets 6-311++G(d,p), aug-ccpVDZ, and aug-cc-pVTZ, to complement the information on the intracomplex motions obtained from the observed rotational spectra.

I. INTRODUCTION A number of high-resolution spectroscopic studies have already been carried out on molecular complexes and have clarified the structures of the complexes at energy minima, often plural, and the intracomplex movements of the constituents. The information thus obtained on complexes has contributed much to our understanding the intermolecular potential, in particular that in close proximity of the constituents, which had been most uncertain in the intermolecular potential. Nevertheless, our knowledge on the intermolecular interactions is still far from satisfactory; we certainly have to scrutinize in detail the data hitherto obtained from high-resolution spectroscopic studies from various points of view and have to supply data on new complexes, to make our knowledge on the intermolecular potential more comprehensive and systematic. One way to attain such a goal will be applying our highresolution spectroscopic tools to the complexes properly chosen. In one of our previous publications, we reported such an attempt: microwave spectroscopic studies on the four complexes: CO−EO, CO−ES, CO2−EO, and CO2−ES, where © 2013 American Chemical Society

EO and ES denote ethylene oxide and ethylene sulfide, respectively, both being selected because of their high symmetry.1 In this paper we cited the previously reported data on Ar−EO, Ar−ES, Ar−DME, Ar−DMS, CO−DME, CO−DMS, and CO2−DME for comparison, where DME and DMS stand for dimethyl ether and dimethyl sulfide, respectively, again selected on the basis of their high symmetry. The high symmetry of the constituents will give us clues to disclose important trends hidden in the intermolecular potential. A few important examples are, however, still missing from the list of the studied complexes and are waiting for detailed studies to be carried out. Good examples include the complexes of the high-symmetry moieties mentioned above: EO, ES, DME, and DMS, attached to a nitrogen molecule. The Special Issue: Terry A. Miller Festschrift Received: August 21, 2013 Revised: October 9, 2013 Published: October 11, 2013 13855

dx.doi.org/10.1021/jp408349r | J. Phys. Chem. A 2013, 117, 13855−13867

The Journal of Physical Chemistry A

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described previously.8 A sample of EO 99% pure, commercially available from Nippon Fine Gas Co. was employed without further purification. Enriched samples of 15N2 and 15NN were purchased from Shoko Tsusyo Co. A mixture of EO/N2, diluted with Ar to 0.4% and 1.6% for the two components, respectively, was 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 3−5 atm. We scanned the frequency region mentioned above, while integrating the signals 30−1000 times to get a good signal-tonoise ratio for the frequency measurements. The uncertainty of the frequency measurement was typically 2 kHz, and the resolution achieved was about 5 kHz.

nitrogen molecule deserves a particular attention in this respect, because its high symmetry is quite different in a sense from that of the four C2v molecules. The exchange of the two nitrogen atoms will produce two different eigenstates and will provide us with unique information on the intracomplex motions. Besides the two main isotopologues, which involve either 14N2 or 15N2 as a constituent, the species with one 15N atom and one 14N atom will give us additional information on the structure of the complex. A large number of the N2-complexes have already been investigated, as listed below with their equilibrium structure form in parentheses: Rg−N2,2−6 N2−CO,7,8 N2−CO29 (T-shaped) HX−N2,10−13 HCCH−N2,14 N2−HCN,15 N2−H2O16 (linear or quasi-linear) N2−OCS17 (parallel or slipped parallel) N2−O3,18 N2−SO218 (nonplanar) As a matter of convenience, we shall transfer a convention on ortho and para modifications introduced for the homonuclear diatomic molecule to the present study: “The modifications with the greater statistical weight is called the ortho modification and that with the smaller weight the para modification.”19 Xu et al.7 and Kawashima et al.8 reported two sets of the a-type K = 0 and 1 transitions for N2−CO and assigned them to the ortho and para species. They found that the nuclear quadrupole coupling constants of the nitrogen atoms were drastically different for the ortho and para species and these findings were ascribed to large-amplitude motions in the complex. Frohman et al. observed two sets of the a-type K = 0 transitions for N2−CO2 and explained them to be caused by the exchange of the nitrogen atoms in a T-shape structure, where the OCO acted as a cross of the T.9 Leung et al. reported four sets of the a-type K = 0 transitions for N2−H2O and concluded that the structure consisted of a nearly linear N−N··· HO linkage with N···H of 2.42 (4) Å and N···H−O angle of 169°.16 The larger splitting of the four sets was ascribed to tunneling of the H2O and the smaller splitting to the nitrogen exchange. Connelly et al. reported that the N2−O3 and N2− SO2 complexes showed two sets of rotational spectra and they interpreted these sets to be caused by the exchange of the nitrogen atoms, supplemented by a remark that the antisymmetric nuclear spin states were absent due to the zero nuclear spin quantum number of 16O.18 They claimed that they identified three tunneling pathways, although no information was obtained on the N2 tunneling frequency. It is interesting to note that the intensities of the rotational spectra of the two isomeric forms of the 15N14N isotopomer were different by a factor of 2 for the N2−H2O and N2−CO2 complexes and were explained by the zero-point energy being a little smaller in one conformer (inner) than in the other (outer). We have carried out a preliminary Fourier transform microwave study on the N2−DME and 15N2−DME complexes and have detected four sets of the spectra, two of them being subjected to larger centrifugal distortion than the other two. We have also detected two isomers for the (15N14N)−DME species. In the present study we focused attention to the N2−EO complex, to compare the results with those of the N2−DME.

III. AB INITIO CALCULATIONS To obtain a preliminary information on the structure and the dynamics of the N2−EO complex, we have carried out an ab initio molecular orbital calculation at the level of MP2 with basis sets 6-311++G(d,p), aug-cc-pvDZ, and aug-cc-pvTZ using the Gaussian 09 package.22 The MP2/6-311++G(d,p) optimized structure of the complex is displayed in Figure 1 along

Figure 1. Optimized geometries of the N2−EO calculated at the MP2/ 6-311++G(d,p) level of theory. The oxygen atom is shown in red, the nitrogen atom in blue, and the carbon atom in black, and the hydrogen atom is indicated by a small sphere.

with the principal inertial axes. The binding energies calculated with MP2/6-311++G(d,p), aug-cc-pvDZ, and aug-cc-pvTZ are listed in Table 1, where the basis set superposition errors (BSSE) calculated with the counterpoise correction method23 and the zero-point vibrational energy corrections are also included. According to ref 24, the counterpoise correction tends to overestimate the BSSE derived with small basis sets. It has been known that a 50% counterpoise correction gives empirically a better estimate for the dissociation energies, so we assumed the counterpoise correction to be 50% in the present study, which has been widely adopted in the microwave spectroscopy community. When the aug-cc-pvTZ basis set was employed, the b- and c-axes were exchanged, because the present complex is very close to the prolate symmetric-top limit, the asymmetry parameter κ being −0.9995. The absence of imaginary vibrational frequencies indicates that the four eigenstates exist in stable minima.

IV. OBSERVED SPECTRA AND ROTATIONAL ASSIGNMENT A. Overview of the Rotational Spectra of the N2−EO Complex. Many rotational lines were observed for an EO, N2, and Ar mixture in the frequency region from 5 to 20 GHz. After removing the absorption lines of the EO monomer,25 its

II. EXPERIMENTAL SECTION The rotational spectrum of the N2−EO complexes was observed in the frequency region from 3.8 to 27 GHz by using a Balle-Flygare type FTMW spectrometer,20,21 which was 13856



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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 N2−EO Complex, Obtained by the MP2/6-311++G(d,p), MP2/aug-cc-DZ, and MP2/aug-cc-TZ Levels of Theory MP2/ aug-cc-DZ

MP2/ aug-cc-TZ

−7.96 4.44 1.48 −6.48

−8.63 3.63 2.04 −6.59

−7.81 1.96 1.96 −5.85

−4.26 12594.04 2093.545 2087.655 1.062 2.098 0.000 3.440 56.28

−4.78 12478.529 2121.087 2116.795 0.936 2.051 0.000 3.434 49.50

−4.87 12707.03 2144.724 2140.230 0.933 1.990 0.000 3.434 49.54

MP2/6-311++G(d,p) De/kJ mol−1 CP/kJ mol−1 ΔZPV/kJ mol−1 D0 = De + ΔZPV/ kJ mol−1 D0 + 50% CP/kJ mol−1 A0a/MHz B0a/MHz C0a/MHz μa/D μb/D μc/D Rcm/Å θa(N2)b/deg

complicated because of the nuclear quadrupole coupling of the two nitrogen atoms, of dense K structures caused by the very small asymmetry parameter of the complex, and of the presence of satellites, one for each of the two main sets. Use of an enriched sample of nitrogen containing an equal amount of 15 N and 14N gave the spectra of 15NN−EO, N15N−EO, 15N2− EO, and N2−EO. The J = 1 ← 0 transitions observed for this sample are displayed in Figure 2; it should be noted that the band c-axes are exchanged for some of the isotopic species. B. Assignment and Analysis of the Rotational Spectra of the 15N2−EO Complex. We initiated the detailed spectroscopic studies with the 15N2−EO species, because this isotopomer is free of complications due to the nitrogen hyperfine structure. Immediately after the start of searching the rotational spectra, we realized that the K = 1 ← 0 Q-branch series appeared at higher frequencies as we went to higher J, which meant that the b-type selection rules applied to this species. In other words, the symmetry plane is the ab plane. We confirmed the assignment by using sum rules among the observed line frequencies. Each transition was found to consist of two main components, each being accompanied by a weaker one separated from the main by several hundred kilohertz, and we shall hereafter refer these strong and weak components to as s and w, respectively. According to the nuclear spin statistical weight, the calculation of which is described below, the spectra of the ortho state is expected to be stronger than those of the para state, and thus we assigned the b-type J = 1 ← 0 transition near 14 846 MHz to the ortho state and the one near 14 917 MHz to the para state (Figure 2). Finally, we assigned 28 a-type R-branch and 9 b-type Q-branch and 19 b-type R- and P-branch transitions for the ortho state, with J spanning from 0 up to 9 and Ka from 0 to 3, and 27 a-type and 28 b-type transitions for the weak satellite set of the ortho state. For the para state, 24 atype and 25 b-type transitions were assigned for the main set and 24 a-type and 24 b-type transitions for the accompanying set. A list of the measured lines is available as Supporting

a

Included the contributions of the centrifugal distortion constants. Angle between the inertial a-axis and the internal-rotation axis of the N2. b

isotopologues, and the Ar−EO complex26,27 from the observed spectra, we identified two sets of a-type R-branch series: J = 2 ← 1 up to 5 ← 4, which appeared every 4.0 GHz and closely approximated the symmetric-top pattern. This observation was followed by the detection of two sets of c-type R-branch transitions: 110 ← 000 at 15 046 and 15 132 MHz and 211 ← 101 transition at 19 096 and 19 182 MHz, and of two sets of the ctype Q-branch Ka = 1 ← 0 transition at 10 996 and 11 082 MHz. The spectra of the normal species were quite

Figure 2. J = 1 ← 0 transitions of the N2−EO, 15N2−EO, and 15NN−EO complexes: the 110 ← 000 transition of the ortho and para states of the N2− EO and of the 15NN(outer)−EO and the 111 ← 000 transition of the ortho and para of the 15N2−EO and of the N15N(inner)−EO. 13857



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Table 2. Rotational and Centrifugal Distortion Constants of the Ortho and Para States of 15N2−EOa parameter

ortho (s)

ortho (w)

para (s)

para (w)

A/MHz B/MHz C/MHz DJ/kHz DJK/kHz DK/kHz d1/kHz d2/kHz HJ/kHz HJK/kHz HKJ/kHz σb/kHz Na‑typec/− Nb‑typec/− relative intensityd/−

12898.4216 (13) 1948.94773 (30) 1947.94545 (22) 13.4793 (69) −28.466 (57) −472.56 (25) 0.2398 (11) 0.1209 (14) −0.0002 (49) −0.02812 (93) −1.2290 (51) 2.6 28 28 1.00

12898.1298 (18) 1948.94510 (45) 1947.94571 (33) 13.484 (10) −29.402 (84) −514.50 (37) 0.2426 (17) 0.1190 (21) −0.0001 (76) −0.0242 (15) −1.3480 (79) 3.5 27 28 0.58 (17)

12970.6845 (11) 1950.01758 (21) 1948.23583 (16) 13.7554 (49) 84.633 (66) 1035.76 (24) 0.3224 (12) 0.1305 (10) −0.0002 (100) 0.01571 (93) 1.4053 (97) 1.6 24 25 0.35 (11)

12970.3171 (17) 1950.01459 (37) 1948.23614 (28) 13.7536 (85) 83.31 (11) 976.97 (41) 0.3237 (20) 0.1335 (17) −0.0001 (165) 0.0155 (16) 1.233 (16) 2.6 24 24 0.22 (10)

a The number in parentheses denotes 3σ. bStandard deviations. cNumber of fitting transitions. dAverage relative intensities for the four sets, normalized to that of the ortho (s).

Figure 3. 110 ← 000 transition of the ortho and para states of the N2−EO. Both transitions consist of one strong and one weak component splitting by several hundred kilohertz. Small splittings show Doppler doublets.

transition 110 ← 000 displayed in Figure 3. The group, which appeared around 15 132 MHz, obviously consists of many more components than that around 15 046 MHz, and thus the former was assigned to the ortho and the latter to the para. As is the case of 15N2−EO, both the ortho and para transitions consist of one strong and one weak component split by several hundred kilohertz, again referred to as s and w, whereas the rotational selection rules are a-type and c-type, at variance with the 15N2−EO case, namely the symmetry plane is the ac plane. We have assigned 24 a-type R-branch and 7 c-type Q-branch and 15 c-type R- and P-branch rotational transitions for the strong component of the ortho state with J spanning from 0 up to 7 and Ka from 0 to 2, 24 a-type and 21 c-type rotational transitions for the weak component, as listed in Table S2 (Supporting Information). We have also assigned 24 a-type Rbranch and 6 c-type Q-branch and 15 c-type R- and P-branch

Information in Table S1. The assigned transitions were analyzed by using an asymmetric-top rotational Hamiltonian of S-reduced form. The weight for weak satellite lines was reduced to 0.5, when they were overlapped by strong main band lines. Three rotational and eight centrifugal distortion constants thus determined for the four sets of the 15N2−EO complex are listed in Table 2. The observed relative intensities are also given in Table 2, where the intensities of the ortho (s) spectra were taken as the standard. C. Assignment and Analysis of the Rotational Spectra of the N2−EO Complex. In view of the complications of the spectra of the parent isotopomer, we advanced the assignment step by step by applying sum rules to the observed frequencies, where the strongest components among those of the rotational transition were employed. The transitions, composed of many lines, were assigned to the ortho state. An example is the c-type 13858



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Table 3. Rotational, Centrifugal Distortion, and Nuclear Quadrupole Coupling Constants of the Ortho and Para States of N2− EOa

a

parameter

ortho (s)

ortho (w)

para (s)

para (w)

A/MHz B/MHz C/MHz DJ/kHz DJK/kHz DK/kHz d1/kHz d2/kHz HJ/kHz HJK/kHz HKJ/kHz χaa/MHz χbb − χcc/MHz σ/kHz Na‑type/− Nc‑type/− θa(N)b/deg

13108.53118 (80) 2025.48936 (16) 2024.16723 (19) 14.8249 (66) 101.407 (52) 1074.03 (19) 0.31608 (96) 0.13410 (79) −0.000041 (79) 0.01810 (74) 1.4642 (80) 0.0398 (10) 4.2017 (18) 3.3 130 134 55.04

13108.0955 (12) 2025.48990 (26) 2024.16314 (31) 14.819 (10) 99.597 (77) 1002.76 (29) 0.3131 (18) 0.1365 (11) −0.00006 (12) 0.0192 (11) 1.202 (i2) 0.0379 (15) 4.0923 (26) 4.4 130 107 55.02

13020.6982 (14) 2025.09860 (29) 2022.80500 (35) 14.486 (12) −29.794 (95) −553.38 (33) 0.2239 (22) 0.1248 (16) 0.00007 (15) −0.0384 (14) −1.318 (i5) 0.0281 (25) 4.2177 (43) 4.6 75 75 54.95

13020.3600 (13) 2025.09866 (31) 2022.80083 (38) 14.464 (13) −30.813 (94) −604.05 (34) 0.2179 (24) 0.1204 (17) −0.00028 (15) −0.0301 (15) −1.517 (15) 0.0498 (25) 4.2178 (44) 4.3 76 68 55.11

The number in parentheses denotes 3σ. bAngle between the a inertial axis and the internal-rotation axis of the N2.

Table 4. Rotational, Centrifugal Distortion, Nuclear Quadrupole Coupling Constants, and the Substituted Coordinates of the N Atoms of N15N(inner)−EO and 15NN(outer)−EOa N15N(inner)−EO

a

15

NN(outer)−EO

parameter

s

w

s

w

A/MHz B/MHz C/MHz DJ/kHz DJK/kHz DK/kHz d1/kHz d2/kHz HJ/kHz HJK/kHz HKJ/kHz χaa/MHz χbb − χcc/MHz σ/kHz Na‑type/− Nb‑type/− Nc‑type/− θa(N)b/deg |a(N)|/Å |b(N)|/Å |c(N)|/Å

12980.44086 (90) 1995.62727 (21) 1995.22741 (16) 14.0455 (58) 39.861 (59) 382.53 (23) 0.2689 (15) 0.1335 (11) −0.000016 (61) −0.00812 (87) 1.115 (11) 0.0550 (13) −4.3124 (13) 3.6 74 71

12980.1084 (13) 1995.62371 (37) 1995.22756 (27) 14.0416 (98) 38.712 (96) 332.16 (36) 0.2742 (26) 0.1343 (16) 0.00005 (10) −0.0072 (13) 0.978 (18) 0.0498 (22) −4.3031 (22) 3.9 70 67

13022.4059 (12) 1975.83419 (24) 1975.05350 (32) 14.2147 (89) 34.018 (92) 158.81 (31) −0.2690 (23) 0.1236 (17) −0.000245 (97) −0.0096 (13) 1.277 (17) −0.0557 (21) 4.1727 (21) 5.4 77

13022.0331 (17) 1975.83360 (34) 1975.04942 (46) 14.195 (12) 32.79 (12) 103.83 (47) −0.2714 (33) 0.1244 (21) 0.00002 (13) −0.0136 (17) 1.234 (23) −0.0668 (31) 4.1807 (31) 5.1 71

55.15 1.8820 0.0 0.5046

55.11 1.8821 0.0 0.5050

82 54.32 2.4921 0.0 0.4071

71 54.23 2.4921 0.0 0.4071

The number in parentheses denotes 3σ. bAngle between the a inertial axis and the internal-rotation axis of the N2.

species containing one 15N atom exhibited two separate sets of rotational spectra, which were assigned to the N15N−EO inner and 15NN−EO outer (see Figure 1 for the definition of the N(inner) and N(outer)) species. It is interesting to note that the observed Q-branch transitions of the N15N−EO and 15 NN−EO species followed the b-type and c-type selection rules, respectively. It is also worth noting that the b-type transitions of the N15N−EO species were observed stronger than the c-type ones of the 15NN−EO, as is exemplified in Figure 2. The relative intensities of the two isomers are discussed in the last section. The spectra of the two isomers were found accompanied by one set of satellites, separated from

rotational transitions for the strong component of the para state and 24 a-type and 21 c-type rotational transitions for the weak component of the para state, where J spanned from 0 up to 7 and Ka from 0 to 2, as listed in Table S3 (Supporting Information). We wrote a program, by which we analyzed the observed spectra including the hyperfine structures caused by the two equivalent N atoms. Three rotational, eight centrifugal distortion constants, and two nuclear electric quadrupole coupling constants were thus determined for the four sets, as listed in Table 3. D. Assignment and Analysis of the Rotational Spectra of the N15N(inner)−EO and 15NN(outer)−EO. The isotopic 13859



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internal motion are not extensive, except for tunneling, and thus the internal rotation can be employed to simulate the internal motion, that is, the exchanges of the equivalent atoms and/or groups of atoms by permutation. We have calculated the potential energy surface (PES) using MP2/6-311++G(d,p), by treating the N2 and EO internal motions as internal rotations, and the resulting PES is displayed in Figure 4.

the main by several hundred kilohertz, and the main and satellite were referred again to as s or w, respectively. We assigned the observed transition frequencies using sum rules, as in the case of the 15N2−EO, and finally we assigned 24 a-type and 8 b-type Q-branch and 14 b-type R- and P-branch rotational transitions for the stronger set of the N15N−EO inner species, with J spanning from 0 up to 8 and Ka from 0 to 2, and 24 a-type and 7 b-type Q-branch and 14 b-type R- and Pbranch rotational transitions for the weaker set of the same species, as listed in Table S4 (Supporting Information). For the 15 NN−EO outer isomer, 24 a-type and 7 c-type Q-branch and 14 c-type R-branch rotational transitions were observed for the stronger component, with J spanning from 0 up to 8 and Ka from 0 to 2, and the 24 a-type and 7 c-type Q-branch and 14 ctype R-branch rotational transitions of the weaker component, as listed in Table S5 (Supporting Information). The assigned transitions were analyzed by using an asymmetric-top rotational Hamiltonian of S-reduced form. Because the asymmetry parameter of the two isomers is very close to the symmetrictop limit κ = −1, care had to be taken to determine χaa unambiguously. We thus initially estimated χaa from the 101 ← 000 transition: 0.046 (28) and −0.0503 (43) MHz, respectively, for the N15N (inner)−EO and 15NN (outer)−EO species. Then all the observed transitions were analyzed simultaneously while giving proper weights to overlapped lines, as listed in Tables S4 and S5 (Supporting Information). Three rotational, eight centrifugal distortion constants, and two nuclear electric quadrupole coupling constants thus determined are listed in Table 4.

Figure 4. Potential energy surface for the two-dimensional internal rotation in the N2−EO complex, calculated by using MP2/6-311+ +G(d,p). Contours are drawn relative to the energy value of the most stable configuration with the scale in every 8 cm−1 from 0 to 166 cm−1; the energy values were calculated by optimizing the internal rotation angles of N2 and EO, τ and θ, respectively, as in Figure 1. The four most stable configurations are indicated by I, II, III, and IV. States I, II, III, and IV are completely equivalent, as mentioned in the text.

V. INTERNAL DYNAMICS A. Internal-Rotation Model. The experimental data obtained in the present study clearly indicate that the N2− EO complex exists in at least four distinct states. We may easily conceive of permutation of the two nitrogen atoms in the N2 moiety and of the two methylene groups in the EO constituent. The four states may be derived from the two types of permutation combined, or even from one set. Both of the constituents, N2 and EO, belong to a G4 group, and its character table is shown in Table 5. Here the permutation

Both of the N2 and EO internal rotations are 2-fold, namely the 180° rotation will bring the configuration back to the original one. In the case of the N2 internal rotation, for which τ denotes the internal-rotation angle coordinate, the potential function V(τ) thus satisfies the following condition:

V (τ ) = V (τ + π )

Table 5. Character Table of G4a

(1a)

Therefore, the Fourier series of V(τ) must consist of only even terms: spin weight

G4

E

(12)

(ab)

(12)(ab)

eigenfunction

A1 A2 B1 B2

1 1 1 1

1 1 −1 −1

1 −1 1 −1

1 −1 −1 1

|1⟩ |2⟩ |3⟩ |4⟩

15

N2−EO 10 6 30 18

14

V (τ ) =

N2−EO 60 36 30 18

∑ Vk cos(2kτ)

(1b)

where k denotes an integer or zero. The equilibrium structure of the complex calculated by a MP2 ab initio method belongs to Cs symmetry, as shown in Figure 1, so that only cosine terms are retained in eq 1b. The eigenfunctions are given, provided that the origin of τ is set to 0 at the equilibrium configuration as shown in Figure 5a, by

a

(12) and (ab) denote the exchange operations of the N atoms in the N2 moiety and of the CH2 groups in the EO, respectively, see Figure 1.

operation is designated as (12), where 1 and 2 denote the two nitrogen atoms in the N2 and the second permutation operation is designated as (ab), where a and b denote the two CH2 groups in the EO. Permutation may be replaced by a sort of internal rotation, although the paths where the two groups of atoms actually take are difficult to specify in detail and the atoms can deviate from the paths of the internal rotation. Fortunately, the rotational spectra of the present complex closely approximate a rigid-rotor pattern, which indicates that the excursions of atoms during the

Us , σ= 0(τ ) =

∑ Cn′ cos(2nτ)

Us , σ= 1(τ ) =

∑ Cn″ cos[(2n + 1)τ ]

(n = 0, 1, 2, ...)

(2a)

(n = 0, 1, 2, ...) (2b)

Ua , σ= 1(τ ) =

∑ Sn″ sin[(2n + 1)τ ]

(n = 0, 1, 2, ...) (2c)

Ua , σ= 0(τ ) = 13860

∑ Sn′ sin(2nτ)

(n = 1, 2, ...)

(2d)



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Figure 5. Potential energy functions for the two internal rotations of the N2 and EO moieties in the N2−EO complex, shown in (a) and (b), respectively.

matrix elements between |s, σ = 0⟩ and |a, σ = 0⟩ and between |a, σ = 1⟩ and |s, σ = 1⟩, and thus the Coriolis interaction does not explain the observed variations in A and DK. We conclude that the one-dimensional internal-rotation model does not account for the observed four sets of the spectra. C. Two-Dimensional Internal-Rotation Model. Because the one-dimensional internal-rotation model fails to reproduce the observed spectra, we turn to a two-dimensional potential energy surface as depicted in Figure 4, where the abscissa and ordinate coordinates are θ and τ, which describe the EO and N2 internal rotations, respectively. There are four equilibrium positions on the plane: (θ, τ) = I (0, 0), II (0, π), III (π, 0), and IV (π, π). These potential minima are completely equivalent, and I and II are connected by a tunneling motion along the τ coordinate, as are III and IV. In a similar way, I and III are combined through the second tunneling path along the θ coordinate, and II and IV behave in an exactly same way. When two equivalent states are connected by a tunneling, one of them becomes the symmetric state and the other the antisymmetric state with respect to the coordinate, and the two are separated by the tunneling matrix element t. This situation may be formally expressed by a 2 × 2 matrix, which has the identical unperturbed energy in the two diagonal blocks and −t/2 in the off-diagonal block. The present two-dimensional problem is thus represented by the schematic potential energy surface of Figure 4, and the energy matrix is explicitly given in eq 4.

and the eigenvalues approximately satisfy the relations

Es , σ = 0 ≈ Es , σ = 1

(3a)

Ea , σ = 0 ≈ Ea , σ = 1

(3b)

The potential energy function for the EO internal rotation is displayed in Figure 5b, where the coordinate is the angle θ. The former potential function yields the following parameters for 15N2−EO: Es , σ = 0 = 14.510685 cm−1 Es , σ = 1 − Es , σ = 0 = 375.754 MHz Ea , σ = 0 = 41.190896 cm−1 Ea , σ = 0 − Ea , σ = 1 = 9438.108 MHz

Es, σ= 1 = 14.523219 cm−1 Ea, σ= 1 = 40.876075 cm−1 Us, σ= 0(τ ) = 0.744 + 0.914 cos(2τ ) + 0.237 cos(4τ ) + 0.0344 cos(6τ ) + ... Ua, σ= 0(τ ) = 1.292 sin(2τ ) + 0.568 sin(4τ ) + 0.088 sin(6τ ) + ... Us, σ= 1(τ ) = 1.314 cos(τ ) + 0.513 cos(3τ ) + 0.094 cos(5τ ) + ... Ua, σ= 1(τ ) = 0.982 sin(τ ) + 0.989 sin(3τ ) + 0.239 sin(5τ ) + ...

B. Critical Comparison of a One-Dimensional InternalRotation Model against the Experimental Data. Even if one internal rotation, e.g., the N2 one, yields four low-lying eigenstates: s, σ = 0, s, σ = 1, a, σ = 0, and a, σ = 1, as shown above. However, the nuclear spin statistical weight is determined by proper symmetry operations: E and (12), and for the 15N2−EO, the two σ = 0 states are given the weight of 1 and the two σ = 1 the weight of 3, which do not reproduce the observed relative intensities of the four observed sets of the spectra. In addition the two a states are higher in energy than the two s states by a few tens of cm−1, further making the discrepancy between the predicted and observed relative intensities larger. The internal-rotation model will yield Coriolis interaction terms, a most important one of which is related to the rotation about the a inertial axis and is approximately expressed as −2(A + ρ2F)Jap, where ρ = IN/Ia, IN denotes the moment of inertia of the N2, F = (h/8π2)(1/rIN), and r = 1 − ρ. The angular momentum p of the internal rotation has finite

This matrix is diagonalized by the unitary matrix: ⎡1 1 1 1⎤ ⎢ ⎥ 1 1 −1 −1⎥ /2 U=⎢ ⎢1 −1 1 −1⎥ ⎢⎣1 −1 −1 1⎥⎦

(5)

to obtain the four eigenvalues and eigenfunctions, as given by E1 = E0 − (t1 + t 2)/2 |1⟩ = [|I⟩ + |II⟩ + |III⟩ + |IV⟩]/2 (6a) 13861



Article

E2 = E0 − (t1 − t 2)/2 |2⟩ = [|I⟩ + |II⟩ − |III⟩ − |IV⟩]/2

C(0): Us , σ= 0(τ ) =

∑ Cn′cos(2nτ)

C(1): Us , σ= 1(τ ) =

∑ Cn″ cos[(2n + 1)τ ]

(n = 0, 1, 2, ...)

(6b)

E3 = E0 + (t1 − t 2)/2 |3⟩ = [|I⟩ − |II⟩ + |III⟩ − |IV⟩]/2

(9a)

(n = 0, 1, 2, ...) (9b)

(6c)

S(1): Ua , σ= 1(τ ) =

E4 = E0 + (t1 + t 2)/2 |4⟩ = [|I⟩ − |II⟩ − |III⟩ + |IV⟩]/2

∑ Sn″ sin[(2n + 1)τ ]

(n = 0, 1, 2, ...) (9c)

(6d)

It should be noted that the I ± II pair and also the III ± IV pair correspond to the (s, σ = 0), (s, σ = 1) pair of the N2 onedimensional internal-rotation model. Similarly, the I ± III pair and the II ± IV pair correspond to the corresponding pair in the EO one-dimensional model. On the other hand, the higherenergy (a, σ = 1), (a, σ = 0) pair of the one-dimensional internal-rotation model is ignored for a moment, in view of their higher eigenvalues. The four eigenstates of eqs 6 belong to a G4 group, which consists of four symmetry operations: the identity E, the exchange (12) of the two nitrogen atoms in the N2 moiety, the exchange (ab) of the two methylene groups in the EO, and finally (12)(ab). The G4 character table is given in Table 5. We may think of an expanded version of this group, namely G8, which includes an operation corresponding to a reflection on the symmetry plane; the ab plane for the 15N2−EO species. However, the G4 group is sufficient to calculate the nuclear spin weight. For the 15N2−EO species, the nuclear spin functions of the 15 N2 are reduced to (3A1 + B1), whereas the nuclear spin functions of the four hydrogens in the EO to (10A1 + 6A2), and the total nuclear spin functions are given by

S(0): Ua , σ= 0(τ ) =

∑ Sn′ sin(2nτ)

(n = 1, 2, ...)

(9d)

Then the four states of eqs 6 are rewritten as E1(A1) [N2 , C(0); EO, C(0)] −t1″ /2 − t 2″ /2

(10a)

E 2(A 2) [N2 , C(0); EO, C(1)] −t1″ /2 + t 2″ /2

(10b)

E3(B1) [N2 , C(1); EO, C(0)] +t1″ /2 − t 2″ /2

(10c)

E4(B2) [N2 , C(1); EO, C(1)] +t1″ /2 + t 2″ /2

(10d)

where the tunneling parameters are attached double primes, to clearly indicate that they are associated with the “ground” state. A schematic energy diagram is shown in Figure 6.

(3A1 + B1) × (10A1 + 6A 2) = (30A1 + 18A 2 + 10B1 + 6B2)

(7)

On the other hand, the total wave function must belong to B1. In a similar way, we may calculate the total nuclear spin functions of the 14N2−EO species as follows: (6A1 + 3B1) × (10A1 + 6A 2) = (60A1 + 36A 2 + 30B1 + 18B2)

(8)

and the eigenfunction as a whole belongs to A1. Thus we derive the nuclear spin weights for the eigenstates of the N2−EO and 15 N2−EO complexes and show the result in Table 5. Therefore, we assign the four sets of the spectra observed for the 15N2−EO species as follows: ortho (s) → E3 (B1 symmetry) ortho (w) → E4 (B2 symmetry) Figure 6. Schematic energy diagram for the ground and the excited states of the two internal rotations in the N2−EO complex. The red and blue lines indicate that the levels connected by these lines are Coriolis interacting through ςN2 and ςEO, respectively.

para (s) → E1 (A1 symmetry) para (w) → E 2 (A 2 symmetry)

D. Variations of a Few Molecular Constants among the Four Detected States. To explain the small, but characteristic, variations of a few molecular constants like A and DK among the four states, we take into account the two upper states of the one-dimensional internal rotation, namely the (a, σ = 1), (a, σ = 0) pair states, in the two-dimensional analysis. For the sake of brevity, we call the four states of eqs 2 as follows:

We then introduced eight “excited” states in the discussion, one-half of which involve the N2 moiety excited and are located at ΔN above the ground state and the other half of which contain the EO excited at ΔE, namely E5 [N2 , S(1); EO, C(0)] ΔN − t1′/2 − t 2″ /2 13862

(11a)


The Journal of Physical Chemistry A E6 [N2 , S(1); EO, C(1)] ΔN − t1′/2 + t 2″ /2

Article

ΔE /2 + ( −t 2″ + t 2′)/4 − t1″ /2

(11b)

E 7 [N2 , S(0); EO, C(0)] ΔN + t1′/2 − t 2″ /2

(11c)

E8 [N2 , S(0); EO, C(1)] ΔN + t1′/2 + t 2″ /2

(11d)

− [(ΔE + t 2′/2 + t 2″ /2)2 /4 + (Q a EJa + Q bEJb )2 ]1/2 = −t1″ /2 − t 2″ /2 − (Q a EJa + Q bEJb )2 /(ΔE + t 2′/2 + t 2″ /2) + (Q a EJa + Q bEJb )4 /(ΔE + t 2′/2 + t 2″ /2)3 + ...

E 9 [N2 , C(0); EO, S(1)] ΔE − t1″ /2 − t 2′/2 E10 [N2 , C(0); EO, S(0)] ΔE − t1″ /2 + t 2′/2

E2 state Interaction with E8

(12b)

−t1″ /2 + t 2″ /2 − (Q a NJa + Q bNJb )2

E11 [N2 , C(1); EO, S(1)] ΔE + t1″ /2 − t 2′/2

(12c)

E12 [N2 , C(1); EO, S(0)] ΔE + t1″ /2 + t 2′/2

(12d)

/(ΔN + t1′/2 + t1″ /2) + (Q a NJa + Q bNJb )4 /(ΔN + t1′/2 + t1″ /2)3 + ...

−t1″ /2 + t 2″ /2 − (Q a EJa + Q bEJb )2 /(ΔE − t 2′/2 − t 2″ /2) + (Q a EJa + Q bEJb )4 /(ΔE − t 2′/2 − t 2″ /2)3 + ...

+t1″ /2 − t 2″ /2 − (Q a EJa + Q bEJb )2

energy difference

Q a NJa + Q bNJb

ΔN + t1′/2 + t1″ /2

(13a)

/(ΔE + t 2′/2 + t 2″ /2) + (Q a EJa + Q bEJb )4

E10−E1 Q a EJa + Q bEJb

ΔE + t 2′/2 + t 2″ /2

(13b)

/(ΔE + t 2′/2 + t 2″ /2)3 + ...

E8−E 2 Q a NJa + Q bNJb

ΔN + t1′/2 + t1″ /2

(13c)

Interaction with E5

E 9−E 2 Q a EJa + Q bEJb

ΔE − t 2′/2 − t 2″ /2

(13d)

+t1″ /2 − t 2″ /2 − (Q a NJa + Q bNJb )2


ΔE + t 2′/2 + t 2″ /2

(14a)

/(ΔN − t1′/2 − t1″ /2) + (Q a NJa + Q bNJb )4

Q a NJa + Q bNJb

ΔN − t1′/2 − t1″ /2

(14b)

/(ΔN − t1′/2 − t1″ /2)3 + ...


ΔE − t 2′/2 − t 2″ /2

(14c)

Q a NJa + Q bNJb

ΔN − t1′/2 − t1″ /2

(14d)

E6−E4

(17b)

+t1″ /2 + t 2″ /2 − (Q a EJa + Q bEJb )2 /(ΔE − t 2′/2 − t 2″ /2) + (Q a EJa + Q bEJb )4 /(ΔE − t 2′/2 − t 2″ /2)3 + ...

(18a)

Interaction with E6 +t1″ /2 + t 2″ /2 − (Q a NJa + Q bNJb )2

ΔN /2 + ( − t1″ + t1′)/4 − t 2″ /2

/(ΔN − t1′/2 − t1″ /2) + (Q a NJa + Q bNJb )4

− [(ΔN + t1′/2 + t1″ /2)2 /4 + (Q a NJa + Q b NJb )2 ]1/2

/(ΔN − t1′/2 − t1″ /2)3 + ...

= − t1″ /2 − t 2″ /2 − (Q a NJa + Q b NJb )2 /(ΔN + t1′/2 + t1″ /2) + (Q a NJa + Q b NJb )4 /(ΔN + t1′/2 + t1″ /2) + ...

(17a)

E4 state Interaction with E11

We treat the Coriolis interaction by a second-order perturbation, by assuming the Q (Coriolis) parameters to be much smaller than the energy difference ΔN or ΔE between the two eigenstates under interaction. The corrections are calculated as follows. E1 state Interaction with E7

3

(16b)

E3 state Ineraction with E12

matrix element

E5−E3

(16a)

Interaction with E9

The tunneling parameter in the excited state is designated by a single prime as t′. A schematic energy diagram including the “excited” states is also shown in Figure 6. The excited and ground states, which are coupled by the Coriolis interactions, are listed below. It is to be noted that the interactions take place about the a- and b-axes in the case of the 15 N2−EO, whereas they are about the a- and c-axes in the 14 N2−EO species. Therefore, the list given below applies to the 15 N2−EO, and for the 14N2−EO, Qb and Jb are to be replaced by Qc and Jc, respectively.

E 7−E1

(15b)

(12a)

(18b)

The differences in the A and DK constants are obtained from the correction terms in Qa2 and Qa4, respectively. (1) The 1(s)−2(s) pair, i.e., the E3−E1 pair, and the 3(w)− 4(w) pair, i.e., the E4−E2 pair

(15a)

Interaction with E10 13863



Article

Table 6. Calculated Bond Distance, Rcm, Estimated Binding Energy, EB, Calculated Stabilized Energy of the Charge Transfer (CT), and Corrected Dissociation Energy, D0 + 50% CP, of the N2−EO and Their Related Complexes complexes

Rcm/Å

EB/kJ mol−1

ks/N m−1

CT/kJ mol−1

|D0 + 50% CP|/kJ mol−1

ref

N2−EO CO−EO CO2−EO Ar−EO N2−DME CO−DME CO2−DME Ar−DME N2−H2O N2−CO N2−CO2 N2−O3 Ar−N2

3.596 3.61 3.259 3.606 3.45 3.68 3.255 3.53 3.498 3.440 3.442 3.582 3.865

2.14 3.6 7.1 1.6 0.7−1.2 1.6 9.7 2.5 2.72 2.52 2.80 3.86 0.98

2.13 3.3 8.0 1.5 0.7−1.2 1.4 10.9 2.3 2.65 2.55 2.84 3.61 0.79

6.82 8.77 14.06 1.92

4.26 4.34 5.98 0.93

8.37 24.27 2.47

4.27 9.23 1.28

this work 1 1 26 unpublished data 36 37 38 16 7, 8 9 18 39

where the last column gives the values of section VA and VIA, to demonstrate the validity of the Coriolis interaction model. Equations 20 are also simplified in the same way:

− (Q a NJa + Q b NJb )2 /(ΔN − t1′/2 − t1″ /2) + (Q a NJa + Q b NJb )4 /(ΔN − t1′/2 − t1″ /2)3 + (Q a NJa + Q b NJb )2 /(ΔN + t1′/2 + t1″ /2) 4

3

− (Q a NJa + Q b NJb ) /(ΔN + t1′/2 + t1″ /2)

→ ΔA = − Q a N 2(t1′ + t1″)/[ΔN 2 − (t1′/2 + t1″ /2)2 ] (19a) 4

2

2 3

/[ΔN − (t1′/2 + t1″ /2) ]

(19b)

(2) The 1(s)−3(w) pair, i.e., the E3−E4 pair, and the 2(s)− 4(w) pair, i.e., the E1−E2 pair 2

2

(23a)

ΔDK = +3Q aE 4(t 2′ + t 2″)/ΔE 4

(23b)

(t 2′ + t 2″) = +3(ΔA)2 /ΔDK

(24a)

Q a E/ΔE = [ΔDK /3ΔA]1/2

(24b)

or

2

→ ΔDK = − Q a N (t1′ + t1″)[3ΔN + (t1′/2 + t1″ /2) ] 2

ΔA = + Q aE 2(t 2′ + t 2″)/ΔE 2

The observed molecular constants of the 1(s)−3(w) pair and the 2(s)−4(w) pair, listed in Table 2, lead to

2

→ ΔA = + Q aE (t 2′ + t 2″)/[ΔE − (t 2′/2 + t 2″ /2) ] (20a)

1(s)−3(w)

→ ΔDK = + Q aE 4(t 2′ + t 2″)[3ΔE 2 + (t 2′/2 + t 2″ /2)2 ] 2

2 3

/[ΔE − (t 2′/2 + t 2″ /2) ]

ΔA /MHz (20b)

ΔA = − Q aN (t1′ + t1″)/ΔN

2

which, when inserted in eqs 24, led to (t 2′ + t 2″)/MHz 6.0769 6.7891 Q a E/ΔE

(21a)

ΔDK = −3Q aN 4(t1′ + t1″)/ΔN 4

(21b)

(t1′ + t1″) = −3(ΔA)2 /ΔDK

(22a)

Q a N/ΔN = [ΔDK /3ΔA]1/2

(22b)

The observed molecular constants of the 1(s)−2(s) pair and the 3(w)−4(w) pair, listed in Table 2, lead to

ΔA /MHz

3(w)−4(w)

−72.2312(74) −72.1590(74)

ΔDK /MHz −1.5050(17)

−1.4884(18)

When these data were inserted in eqs 22, we obtained (t1′ + t1″)/MHz 10400.025 10495.003 9513.862 Q a N/ΔN

0.2200 0.2323

VI. DISCUSSION A. Molecular Structure, Intermolecular Stretching Force Constant, Binding Energy, and the Stabilization Energy through CT of the N2−EO Complexes, and Comparison with the Corresponding Parameters of Related Complexes. The b- and c-axes are easily exchanged in the N2−EO upon some isotope substitution, because the asymmetry parameter κ is quite close to a symmetric-top limit: −0.9995. The following molecular structure parameters make the complex a near prolate symmetric top; the angle between the line connecting the centers of mass of the two constituents and the bisecting line of the COC angle in the EO is about 54°, and the latter line is nearly parallel to the N2 molecular axis. The planar moment Pcc was determined to be 19.4895 u Å2 for the N2−EO, which was close to the Paa moment 19.4315 u Å2 of the EO monomer,25 indicating that the structure of the N2− EO complex consisted of the N2 moiety lying in the plane bisecting the COC angle and perpendicular to the COC plane

or

1(s)−2(s)

0.2941(89) 0.3663(55)

ΔDK /MHz 0.0427(21) 0.05929(132)

Because the excited − ground state energy difference ΔN is much larger than the tunneling splitting t1, we may simplify eqs 19 as follows: 2

2(s)−4(w)

0.0834014 0.0829186 0.1133611 13864



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of the EO, in consistence with no c-type or b-type transitions being detected. The rotational constants of this complex led to the distance between the centers of mass of the two component molecules, Rcm of 3.596 Å, by assuming the following equations to hold: Icc(N2−EO) = I(N2) + Iaa(EO) + μ[R cm(N2−EO)]2

EB =

(25)

χgg (14N ) = 1/2χ0 (14 N)⟨3 cos2 θg − 1⟩av

1.8237 Å

2.4340 Å

bs

−0.4444 Å

0.3970 Å

cs

0.0 Å

0.0 Å

IN

6.5443921 u Å ρ = IN/Ia = 0.1674958

IEO 32.527580 u Å r = 1 − ρ = 0.8325042

F = 92760.165 MHz = 3.094146 cm−1 Fρ2 = 2602.372 MHz

These data were employed to check the observed values of (t1′ + t1″) and QaN/ΔN, as described above. As commented there, the agreement is fair. The direction cosines of the internal rotation axes of the N2 and EO moieties at the equilibrium configuration are λa

λb

N2 0.8318 0.5551 EO 0.4269 0.9043

The effect of the a-type Coriolis interaction is thus expected to be smaller for the EO than for the N2, in qualitative agreement with the observed data. We have estimated the stretching force constant ks and the binding energy EB by using the following equations:30−33 ks =

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

(28)

The brackets indicate averaging over the large-amplitude vibrational motions, and θg is the instantaneous angle between the N2 molecular axis and the g-principal axis of the complex. Equation 28 assumes that the coupling constant of the free monomer is not significantly changed upon complex formation, and we thus employed χ0 (14N) to be equal to the free N2 value: −5.370 MHz.34 The values of the θg calculated from the diagonal tensor χaa of the 15NN−EO and N15N−EO complexes are listed in Table 4: 54.61° for the 15NN−EO and 55.14° for the N15N−EO, in good agreement with the molecular structure data obtained for the N2−EO complex. Agreement holds also with θa obtained for the ortho (s), ortho (w), para (s), and para (w) states of the N2−EO in Table 3. C. NBO Analysis of N2−EO and CO−EO. The NBO model has been shown very useful for explanation not only of the hydrogen bond in the X−H···Y systems in terms of the charge delocalization and but also of the stability of van der Waals complexes by small amounts of charge transfer (CT) from the bonding and lone-pair electron orbitals to the antibonding orbitals, in other words in terms of intermolecular donor−acceptor interactions. We have carried out an NBO analysis on the N2−EO by using ab initio molecular orbital method at the level of MP2/6-311++G(d,p) using Gaussian 09. The stabilization energies via CT thus obtained for the N2−EO are listed in Table 6 and are compared with those of the CO− EO; the two results are widely different. In the case of the CO− EO the main stabilization energies originate from the lone pair of the O atom of the EO to the CO antibonding orbital of the CO, whereas in the case of the N2−EO the similar contribution to the NN antibonding of the N2 is very small. The large stabilization energies are derived by the charge transfer from the NN bonding of N2 to the Rydberg orbital of the O atom of EO in the N2−EO complex. The total stabilization energy of the charge transfer is 6.82 kJ mol−1 for the N2−EO, which is considerably smaller than 8.77 kJ mol−1 for the CO−EO.1 D. Isotopic Effects on the N2−EO Complex. The observed intensities of the inner N15N−EO were larger by a factor of 2 than those of the outer 15NN−EO. Similar observations have been reported for the 15N14N−HOH and 14 15 N N−HOH complexes,16 followed by a recent example the N2−CO2 of a T-shaped structure, with the OCO forming the

outer N

as

(27)

The EB and ks thus obtained are listed in Table 6, along with the calculated stabilized energy of the charge transfer CT and the dissociation energy E0 + 50% CP, and these data are compared with those of related complexes. Table 6 shows that the dissociation energy E0 + 50% CP is approximately twice as large as the EB for the N2−EO. The binding energy obtained by the quantum chemical calculation is larger than the experimental value. Accordingly, the calculated bond distance between the N2 and EO moieties is shorter and the estimated rotational constants are larger than the experimental data. B. Nitrogen Nuclear Electric Quadrupole Coupling Constants of the N2−EO Complex. The nuclear quadrupole coupling constants χgg in weakly bound complexes may be estimated from the coupling constant χ0 of the free N2 molecule, projected onto the principal inertial axis g of the complex,

The bond distance Rcm on related complexes are given for comparison in Table 6. The rs coordinates of the N atoms in the N2−EO or 15N2− EO complex were calculated by the Kraitchman equation.28 The b-coordinates of the two nitrogen atoms of the N2 were either imaginary or very small, as listed in Table 4, and were set to zero in further structural calculations. These data are consistent with the spectral data; no b-type or c-type transitions were observed for the 14N2−EO and 15NN(outer)−EO or the 15 N2−EO and N15N(inner)−EO species, respectively. The calculated bond distance rs of the NN for the N2−EO and 15 N2−EO are 1.0970 and 1.0408 Å, respectively, which is a little shorter than r0(NN) = 1.100 071 Å, calculated for the free N2 molecule B0 constant listed in Huber and Herzberg,29 and the angles between the N−N bond and the a-axis for the N2− EO and 15N2−EO are 56.21° and 54.10°, respectively. We have calculated some parameters relevant to the internal rotation of the N2 moiety. The total moment of inertia about the a-axis of the complex Ia was 39.071 972 u Å2 from the average value of the A rotational constants observed for the stronger components of the ortho and para states of the 15N2− EO. We have obtained a set of rs structure parameters of the 15 N2−EO, of which the coordinates of the inner and outer nitrogen atoms were employed to derive some parameters pertinent to internal rotation: inner N

1 ksR cm 2 72

(26) 13865



Article

cross of the T,9 and also by a study on the CO2−propylene oxide.35 Frohman et al.9 found that the intensities of the rotational transitions of the 14N15N−CO2 were at least twice as large as those of the 15N14N−CO2. These observations were rationalized if a wide-amplitude bending motion of the N2 group took place about a pivot point, which was further away from CO2 than the center of mass of the N2. If this was the case, the reduced mass of the N2 bending would be greater in 14 15 N N−CO2 than in 15N14N−CO2, and the 14N15N−CO2 would be lower in energy in the van der Waals potential well, gaining more populations and greater intensities. The dissociation energy of the heavier species would be larger, and repeated dissociation and reformation of the clusters at the initial phase of the molecular beam expansion will lead to a distribution in which the heavier species is 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 N2−EO by using the MP2/6-311++G(d,p) and MP2/augcc-pvTZ basis sets. If the beam temperature was as low as 1−2 K, the Boltzmann distribution of the outer conformer was estimated nearly half of the inner conformer, in conformity with the observed relative intensities of the rotational spectra. E. Comments on the Related Study on the N2−O3 and N2−SO2 Complexes. Connelly et al.18 derived and analyzed the rotational spectra of the N2−O3 and N2−SO2 by paying particular attention to the internal motions. They detected two sets of rotational spectra, which they assigned to the symmetric and antisymmetric states arising from the tunneling motion of the N2 moiety. Their treatment is very close to the present one, except for one important point; they included the concerted motion. This tunneling path can be included easily in the present treatment, namely we only need to fill the two vacant off-diagonal blocks of the matrix eq 4 with −t3/2, which is equivalent to Connelly et al.’s νC. The matrix is easily diagonalized to give the eigenvalues:

consist of two isomers, one with the 15N in the inner and the other in the outer position (see Figure 1 for the definition of the N(inner) and N(outer)), and the spectra of both species were accompanied by one weaker satellite. The observed spectra were assigned by using sum rules and were analyzed by the asymmetric-rotor program of S-reduction, with the standard deviation of less than 10 kHz. We have found an interesting correlation for some molecular parameters like A, DJK, and DK between the two main sets of the spectra, and also, to much less extent, between the strong and weak members. These differences in the molecular parameters between the four sets were explained by the first-order Coriolis interaction between the “ground” and “excited” states generated by a combination of the two internal motions: exchanges of the equivalent atoms and/or groups in the N2 and EO constituents of the complex. These internal motions could be simulated by the 2-fold internal rotations of the two moieties. We have also carried out ab initio molecular orbital calculations at the level of MP2/6311++G(d,p), aug-cc-pVDZ, and aug-cc-pVTZ using the Gaussian 09 package. The calculated rotational constants of the N2−EO were found to be larger than those of the experimental values. It is clear that the calculated binding energy of the N2−EO are larger than the experimental value and the calculated bond distance between the N2 and EO moieties is shorter than the experimental value, because the correction dissociation energy D0 + 50% CP is twice as large as the estimated binding energy, 2.14 kJ mol−1.

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ASSOCIATED CONTENT

S Supporting Information *

Measured rotational transition frequencies for (Table S1) 15 N2−EO species, (Table S2 and S3) the ortho and para states of the normal species of the N2−EO complex, respectively (Table S4) N15N−EO species, and (Table S5) 15NN−EO species. This material is available free of charge via the Internet at http://pubs.acs.org.

E1 = E0 − (t1 + t 2 + t3)/2 |1⟩ = [|I⟩ + |II⟩ + |III⟩ + |IV⟩]/2 (29a)

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E2 = E0 − (t1 − t 2 − t3)/2 |2⟩ = [|I⟩ + |II⟩ − |III⟩ − |IV⟩]/2 (29b)

AUTHOR INFORMATION

Corresponding Author

*Y. Kawashima: e-mail, [email protected]; phone, +81 46 291-3095; fax, +81 46 242-8760.

E3 = E0 + (t1 − t 2 + t3)/2 |3⟩ = [|I⟩ − |II⟩ + |III⟩ − |IV⟩]/2 (29c)

Notes

The authors declare no competing financial interest.

E4 = E0 + (t1 + t 2 − t3)/2 |4⟩ = [|I⟩ − |II⟩ − |III⟩ + |IV⟩]/2 (29d)

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ACKNOWLEDGMENTS We thank Dr. Yoshihiro Osamura for his advice in carrying out the MO calculations and Emeritus Professor Masaru Ishida of Tokyo Institute of Technology for his financial support in purchasing enriched 15N2 and 15NN gas samples and Miss Eriko Kawase for her help in observing spectra of N2−EO at the earlier stage. Thanks are due to Dr. Koichi Yamada for discussions on the internal motions.

Because the 16O atoms in the O3 and SO2 moieties have the nuclear spin quantum number of zero, only two eigenstates E1 and E3 exist. As eqs 29 show, the two parameters t1 and t3 behave in the same way in these two states. Therefore, unless we include species with some appropriate oxygen isotopes in the study, it is impossible to determine t1 and t3 separately. The data on the N2−SO2 complex can be analyzed by using eqs 21.

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VII. CONCLUSIONS We have studied the N2−EO complex by Fourier transform microwave spectroscopy and have observed two strong/weak pair spectra for the 14N2−EO and 15N2−EO species, indicating that the complex existed in four distinct states. We interpreted, on the basis of the observed relative intensities, that these states were generated primarily by the exchange of the nitrogen atoms of the N2 moiety and followed by that of the two CH2 groups in the EO molecule. The 15NN−EO species were found to

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Fourier Transform Microwave Spectrum of the Nitrogen Molecule

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