Microwave Spectrum and Structure of a Hydrogen ... - ACS Publications

measured for purines and pyrimidines using X-ray crystallog- raphy.20 This discrepancy ... Gordy and Cook21 present a method of relating the quadrupol...
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7451

J. Phys. Chem. 1993,97, 7451-7457

Microwave Spectrum and Structure of a Hydrogen-Bonded Pyrrole-Water Complex' Michael J. Tubergen, Anne M. Andrews,' and Robert L. Kuczkowski' The Department of Chemistry, The University of Michigan, Ann Arbor, Michigan 48109-1055 Received: February 22, 1993; I n Final Form: May 3, 1993

Twelve a-type rotational transitions of a pyrrole-water van der Waals complex were observed using a Fouriertransform microwave spectrometer; these transitions were split into doublets by an internal motion of the complex. Microwave spectra were recorded for the 15Nisotopomer and the triply deuterated complex as well as the normal isotopic species. The spectra of these isotopomers were found to be consistent with a structure in which the pyrrole acts as a proton donor. Quadrupole hyperfine structure of the normal isotopic species was assigned and discussed in terms of the electronic environment of the 14Nnucleus. Stark effect splittings of the 15Nsubstituted complex were measured and fit to obtain pa = 4.35 (6) D. Likely pathways for the internal motion are discussed in terms of spin statistical weights and model potentials calculated using the STO-3G and 6-31G basis sets.

Introduction Binary complexes have received much study lately as part of a general effort to understand the basic forces governing solvation and other intermolecular interactions. A rich variety of topics have been addressed for these complexes including the determination of equilibrium structures, the analysis of the spectroscopic effects of internal motions (such as rotations or inversions of the two monomer units), and the modeling of the intermolecular potential. Fourier-transform microwave spectroscopy2 has been shown to be an excellent method for determining both the equilibrium structures and the internal motions of complexes formed in supersonic expansions, while ab initio calculations predict minimum-energy structures and can be used to generate intermolecular potential surfaces. It is interesting, therefore, to compare theresultsof theab initiocalculations with the structures that are determined from microwave spectroscopy. Studiesof water complexeswith small molecules found in larger biological systems are particularly interesting because hydrogen bonding is a fundamental interaction in biochemistry. Experiments and ab initio calculations on this important class of complexes may help determine the importance of hydrogen bonding in governing the structure of larger biomolecules. One recent paper has reported the microwave spectra and structures of the formamide-water and formamidemethanol complexes.3 The spectra were consistent with structures in which the water and methanol are doubly hydrogen bound to the formamide;Le., the formamide donates and accepts a hydrogen bond in these complexes. These structures agree with the ab initio calculations of Jasien and Stevens! Pyrrole is a five-membered heterocyclic aromatic ring found as a component of many larger ring systems in biomolecules. Pyrrole is of interest because it can act both as a proton donor (the proton attached to the nitrogen) to water and as a proton acceptor (to the r-electron cloud, as in benzenewater5). When our study was initiated, ab initio calculations carried out at the STO-3G level6 for the pyrrole-water complex had predicted that the proton donor form was energetically favored by 6.72 kcal/ mol (2350cm-1,0.291 eV) overthegeometryin which thepyrrole Ir-electron cloud forms two hydrogen bonds with the water. We undertook a spectroscopic experiment in order to observe one or both of these complexes. This paper presents the microwave spectra observed for the complex in which the pyrrole serves as the proton donor. Three f Current address: Molecular Physics Division, National Institute of Standards and Technology, Gaithersburg, MD 20899.

0022-3654/93/2097-145 1S04.00IO

different isotopically substituted complexes were measured including the normal species. All transitions were split into doublets by an internal motion. The experimentalresults for the structure and internal motion are compared to the previous ab initio calculations, calculations we performed using the Gaussian90 program package: and calculations published8 after the referees' comments were received. In addition, the nuclear quadrupole and Stark effect splittings were measured.

Experimental Section Spectra were obtained using a Balle-Flygare type Fouriertransform microwave spectr~meter~.~ operatingfrom 4 to 18 GHz. Typical line widths, in the absence of quadrupole splitting, are found to be 30 kHz, and the accuracy of the center frequencies is f 4 kHz. The microwave cavity is straddled by two 50 cm X 50 cm steel mesh grids placed 30 cm apart and to which up to 10 000 V of opposite polarity can be applied for Stark effect experiments. The electric field for each Stark measurement was calibrated by measuring the shift of the 1 0 transition of OCS (0.715 21 Dlo). The sample gas mixture was prepared by placing several millilitersof pyrrole liquid (pyrrole-14N,Aldrich; pyrrole-15N(99% 'SN),MSD Isotopes) in the bottomofaone 1-Lglassbulb.mole1-d was prepared by repeated washings of pyrrole in DzO; its isotopic purity was found to be 98% by mass spectrometry. The pyrrole was degassed on a vacuum line with several freezepump thaw cycles. Water vapor (or D20 vapor for the pyrrole-l-dDzO complex) was then added to the pyrrole sample until the total pressure equilibrated near 20Torr. This mixture was diluted to 1.6 atm with argon and expanded into the spectrometer through a modified Bosch fuel injector which served as the pulsed valve. When the sample was prepared in this way, we found that it could be diluted many times with argon without significant loss of signal intensity. Accurate measurements of the quadrupole splittings were accomplished using a pulsed valve mounted in one of the mirrors of the cavity, so that the expansion traveled along the axis of the cavity. This produced Doppler doublets for each quadrupole component split by about 50 kHz,while the line widths of each component decreased to less than 10 kHz. In this way, the small splittings arising from the 14N nuclear electric quadrupole hyperfine structure could be resolved. +

R€&ts MicrowaveSpectrum. Before searching for lines, rough spectral predictions were made based on models in which the pyrrole acts 0 1993 American Chemical Societv

7452 The Journal of Physical Chemistry, Vol. 97, No. 29, 1993 as the proton donor (hereafter, extended conformation) and in which the ?r-electron cloud of the pyrrole acts as the proton acceptor (hereafter, stacked conformation). Both structures were predicted to be near prolate tops with a-type rotational lines. In addition to an a-component of the dipole moment, the stacked conformation was predicted to have some dipole moment component along the b symmetry axis, allowing the observation of b-type transitions as well. The stacked complex was also predicted to be a more prolate asymmetric top than the extended conformation, so the Kp= 1 asymmetry splittings were expected to be much smaller for a stacked complex than for an extended one. Lastly, the stacked conformation was predicted to have a larger B rotational constant than the extended one, shifting the a-type spectrum to higher frequencies. One ambiguity in both structures was the exact orientation of the water with respect to the pyrrole. The extendedconformation, for example, could have the planes of the water and pyrrole aligned either parallel, crossed, or at some intermediate dihedral angle; a similar uncertainty existedforthestackedcomplex. The positionsofthe water protons were expected to have only a minor effect on the rotational constants and microwave spectrum of the complex, so this ambiguity did not change our basic predictions about the microwave spectra for the two possible structures. After extensive searching, a weak a-type spectrum was found for the normal isotopic species. Twelve rotational transitions were eventually found (see Table I), each split 1-3 MHz by a tunnelingmotion with smaller 14Nquadrupole hyperfinestructure superimposed on each tunneling component. No b- or C-type transitions were found within several hundred megahertz of the positions predicted from the a-type spectrum. The higher frequency doublet members were consistently more intense than the lower frequencydoublet members. Using the nozzle mounted in the cavity mirror, the quadrupole splittings could be resolved and assigned; the resulting fit of the hyperfine structure yielded the hyperfine constants shown in Table 11. Line centers of the higher frequency doublet components were calculated from the fit of the quadrupole structure and fit to A, B, C, DJ, DJK,and dl (see Table 11) using the Watson S-reduction P representation. Only six of the weaker, lower frequency doublet components were analyzed for hyperfine splittings (all the rotational transitions were observed to consist of doublets, however), and these line centerswere only fit to three rotationalconstants. These rotational constants and quadrupole coupling constants are listed in Table 11. Nine rotational transitionsfrom the pyrr~le-~~N-water complex (see Table 111) were found shifted 2 MHz to lower frequencies than the correspondingtransitions of the normal isotopic species. This small isotope shift indicates that the nitrogen atom is very close to the center-of-massand that the complex is in the extended conformation (see below). Again, each rotational line was split into doublets, the upper doublet member being more intense. The tunneling splittings for the two isotopomers were found to be the same for the three transitions where a direct comparison can be made (404-303, 414-313, 413-312). Upper and lower doublet members were fit separately to the Watson S-reduction Hamiltonian;valuesobtained for the rotational and centrifugaldistortion constants are reported in Table 11. The absence of a nuclear quadrupole moment in pyrrole-15Nwater allowed Stark effect splittings to be measured without complicating hyperfine splittings. The observed Stark effects of six components from the higher frequency doublet member of three transitions (shown in Table IV) were fit to a, b and c dipole components using second-order Stark coefficients calculated from the rotational constants. These coefficients were checked by diagonalization of an energy Hamiltonian containing the rigid rotor and Stark effect matrix elements to ensure that AvlE2wasconstant over the measurement range. The transitions were chosen to include ones which were reasonably sensitive to

lw

Tubergen et al.

TABLE I: Measured Hyperfine Components for the Pyrrole-Water Complex

lower freq

tunneling doublet

higher freq

tunneling doublet transition freq oh-calc freq obs-calc Jkfi-J’kfi F’-Fff (MHz) (kHz) (MHz) (kHz) 6053.252. -24.6* 6054.193. 0.5. -1.7d 6053.721 1-1 6052.776 0.9 2.4 6054.173 3-2 6053.230 3.7 -1.0 2-1 6053.266 -1.6 6054.207 1-0 6053.460 -5.5 -1.7 6054.405 2-2 6053.548 5.9 -1 .o 6054.482 5811.906 -34.5 -1.8 5813.177 1-1 5810.966 -2.7 0.2 58 12.244 3-2 5811.810 0.2 5813.084 2.5 1-0 -8.5 5813.292 2-1 5812.137 2.1 2.3 58 13.408 0.5 2-2 5812.560 3.6 5813.832 -11.2 6306.309 0.1 6307.037 5.9 1-0 6305.502 4.5 6306.227 2-2 6305.838 0.0 0.3 6306.569 3-2 6306.287 -5.9 2.4 6307.024 2- 1 -3.9 6307.262 1-1 1.7 6307.972 -1.9 9065.900 4-3 4.6 9065.885 2- 1 -6.1 9065.924 3-2 1.5 9065.924 -0.3 87 15.944 4-3 2.4 87 15.898 3-2 1.2 8716.007 2-1 8716.007 -3.6 9456.619 0.0 3-3 -1.9 9456.226 2- 1 9456.499 0.4 4-3 1.2 9456.616 3-2 9456.681 0.3 12057.851 -5.7 12059.295 2.0 5-4 12057.831 -0.3 12059.275 -1.1 3-2 12057.853 1.3 12059.299 2.6 4-3 12057.880 -1 .o -1.5 12059.324 1161 1.811 26.3 2.3 11614.256 5-4 11611.778 -2.4 0.1 11614.226 4-3 11611.844 3.2 1.9 11614.288 3-2 11611.844 -0.8 -2.0 11614.288 12599.996 14.6 0.0 12601.342 3-2 12599.948 -1.4 12601.294 -0.9 5-4 12599.966 2.1 0.8 12601.340 4-3 12600.026 -0.7 12601.372 0.1 15028.726 -0.7 6-5 15028.706 0.7 4-3 2.9 15028.718 5-4 -0.1 15028.763 5-5 -3.5 15029.165 -1 .o 14506.838 6-5 14506.818 1.5 4-3 14506.857 0.1 5-4 -1.6 14506.857 15739.358 0.0 5-5 15739.024 -0.9 4-3 15739.332 1 .o 6-5 1.2 15739.356 5-4 15739.378 -1.1 44 -0.2 15739.776 a Fitted linecenters from quadrupolehyperfine structure. Transition frequencies calculated using A, B, and C from Table 11, column 2 and DJ, DJK, and dl from Table 11, column 3. cTransition frequencies calculated using the rotational constants from Table 11, column 3. Calculated hyperfine splittings from quadrupole coupling constants in

Table 11.

the p b and pc components (by a factor of 10 larger compared to bI). This fitting procedure resulted in pa2 = 18.97 D2, fib2 = 4.05 D2,and k2= 0.05 D2. The results for Pb2 and k 2are consistent with values of zero for Pb and pc. When the experimental data (Avs,k I 1 MHz) and sensitivity of these transitions to pb and k were considered, the values for the dipole

The Journal of Physical Chemistry, Vol. 97, No. 29, 1993 7453

Hydrogen-Bonded Pyrrole-Water Complex

TABLE Ik Rotational Constants, Second Moments, Centrifugal Distortion Constants, and Quadrupole Coupling Constants for pyrrole-Water Isotopic Species I4N

1 *N

set 1"

set 2'

set 1

set 2 8948.82(17) 1638.259(1) 1391.434(1) 0.592(4) 58.8(2) -0.130(3) 307.6092(11) 55.5982(11) 0.8763( 11)

A/MHz 90694 2) 8948.79(39) 9032.44(37) B/MHz 1638.358(31) 1638.557(1) 1638.146(1) C/MHz 1391.169(31) 1391.624(1) 1391.049(1) 0.576(8) 0.571(8) Dr/wZ 58.9(4) 60.7(4) DrK/mZ -0.139(6) -0.132(5) dilwz Pu/amu A2 308.01(6) 307.5566(17) 307.9315(23) Pbb/amu A2 5 5.27(6) 55.6013(17) 55.3764(23) P,/amu A2 0.46(6) 0.8728(17) 0.5752(23) xu/MHz 0.917(5) 0.915(3) Xbb/MHZ 1.415(7) 1.409(3) xof/MHz -2.332(9) -2.324(4) a Sets 1 and 2 are the lower and higher frequency tunneling doublets, respectively.

TABLE IIL Frequencies of the Pyrr~lel~N-Water and Pyrroie-1-6D~OComplexes transition 15Nlow obs - ale lSNhigh obs - ale Jk&-J'k& freq (MHz) (WZ) freq (MHz) (kw 303-202 313-212 312-211 404-303 414-3 1 3 413-312

9 063.188 8 712.767 9 453.938 12 055.951 1 1 610.086 12 597.842 15 024.980 14 501.728 15 735.114

505-404 515-414 514-413

0.5 -0.9 0.8 -0.6 1.3 -1.1 0.2 -0.5 0.4

9 064.460 8 714.645 9 454.998 12 057.394 1 1 612.525 12 599.185 15 026.390 14 504.683 15 736.673

6w-505 616-5 15 615-514

0.1 -0.1 0.6 -0.1 0.1 -0.8 0.0 -0.1 0.3

pyrrole-1-d D2O (MHz) 8 331.060 8 038.500 8 651.800 1 1 088.300 10 712.900 1 1 530.550 13 829.100 13 382.400 14 404.800 16 549.650 16 049.538 17 272.965

I4N-D3 8849.(26) 1493.505(38) 1288.990(38)

336.67(17) 55.40(17) 1.71 (17)

ob - calco 380 388 197 256 198 112 178 -953 4 -9 5 26 1 -384

Calculated transition frequencies from rotational constants in Table 11.

TABLE Iv: Summary of the Stark Effect Splittings Observed for the Higher Frequency Tunneling Doublets of Selected Pyrr~le-l~N-Water Transitions (Av/t2) X lo5 (obs-cald) X 105 transition lM MHz/(V/cm)* MHz/(V/cm)2 303-202

0

404-303

1 0 1

413-3 12

2 0

-4.08 (8) -1.03 (10) -1.45 (6) -0.89 (2) 0.75 (1) -0.82 (5)

-0.06 0.10 0.01 0.00 -0.07 0.04

Calculatedvalues using pa = 4.35 D, p b = 0, = 0and the rotational constants in Table 11. components were determined as pa = 4.35 (6) D, = 0.0 (2) D, and = 0.0 (2) D. A comparison of the observed Stark effect to the one calculated for these dipole values is given in Table IV. Finally, the Stark shifts of several 1A4l lobes of the weaker, lower frequency doublet members were found to be the same as observed for the corresponding lobes of the upper doublet members, although the low intensityof these transitions prevented a complete Stark shift analysis. The rotational constants and microwave spectrum of pyrroleI-d-DzO were predicted from a structural fit of the rotational constants for the normal and 15N isotopic species. Pyrrole-ld-D20 was chosen over other deuterated samples to minimize deuterium/hydrogen exchange of the labile water and pyrrole nitrogen protons (deuterons). Twelve rotational transitions were found; most transitions exhibited extensive splitting from deuterium and nitrogen nuclear quadrupole hyperfine effects as well as the tunneling splitting. The line shapes were very complicated, so no assignment was made for the hyperfine components of each rotational transition. Instead, approximate line centers (*lo0 kHz) were used to fit the rotational transitions to a rigid rotor Hamiltonian. The resulting values for the rotational constants are listed in Table 11. Searches were made to locate the spectra

of other partially deuterated isotopomers. While some transitions were found, the line intensities were very weak (due to extensive splitting as well as hydrogen/deuterium exchange problems) and the efforts were unfruitful. Structure. The center-of-mass of the extended conformation is expected to lie very close to the pyrrole nitrogen, so '5N substitution will result in only small changes to the rotational constants and therefore will not shift the spectrum of the l*N isotopomer far from the normal species isotopomer. The centerof-mass of the stacked complex lies out of the pyrrole plane and farther from the pyrrole nitrogen (about 1.3 A for a stacked structure similar to the reported benzene-water structure), so 15Nsubstitution will have a large effect on the spectrum of a stacked pyrrolewater complex. The observation of a very small '5N isotope shift (2 MHz) in the spectrum of pyrrole-water is consistent only with the extended conformation of the complex. Furthermore, the experimentally determined rotational constants match the rotational constants estimated for the extended structure better than those from the stacked conformation. A stacked structure similar to that reported for benzene-water predicts that A = 4480 MHz and B C = 2355 MHz ( K = -0.997), while an extended structure with a 2-A hydrogen bond predicts A = 8870 MHz, B = 1670 MHz, and C = 1410 MHz ( K = -0.930); these differences in the estimated rotational constants will be reflected in the Jvalues and asymmetry spacings observed in the spectrum. As shown in Table 11, the measured rotational constants ( K = -0.935) agree better with an extended conformation of the complex. To quantitatively determine the structure of the pyrrole-water complex,variables describing the relative orientation of the water and pyrrole monomers were least-squares fit to the B and C rotational constants of the three isotopomers and the A rotational constant of the 15N isotopomer; the A rotational constants of the normal and deuterated isotopomers were omitted from the fit because they were less well determined from the a-type spectrum

Tubergen et al.

7454 The Journal of Physical Chemistry, Vol. 97, No. 29, 1993

TABLE V: Sllmmvy and Comparison of the Structural Fitting

exptl results

/

-u -R+

Figure 1. Geometrical parameters used to describe the structure of the

pyrrole-water complex: R is the distance between the centers-of-mass of the pyrrole (labeled X,) and the water, 0, is the tilt angle of the plane of the water, 0, is the tilt angle of the plane of the pyrrole, and @ is the dihedral angle between the plants of the two monomer units (@ = 0 when the planes of the water and pyrrole are crossed).

A b

A

Figure 2. Diagrams of the two likely orientations of the monomer planes. Figure 2A depictsthe casewhere the monomer planesarecrossed (crossed orientation, @ = O O ) , while Figure 2B depicts the case where the water hydrogens are symmetric about the uc plane (hinge orientation, @ = 90O). The a and b inertial axes are also shown in the figure.

that was found. Monomer structures were takeR from refs 11 and 12 and were assumed to be unchanged upon complexation. Six structural parameters are needed to describe the relative orientation of the two monomers, but we considered only the parameters shown in Figure 1:R,the length of the intermolecular line joining the two monomer centers-of-mass; 8,, the angle between R and the Cz axis of water; $,a similar angle for pyrrole; and ip, a dihedral angle about R. We neglected the parameters +w and 4p,which are dihedral angles about the C2 axes of water and pyrrole, respectively. +p is degenerate with ip in the limit of OP = 0, which should be approximately correct for the complex structure in which the pyrrole acts as the proton donor. In the fitting procedure, ip and 4, were fmed to define either of the symmetric structures shown in Figure 2. The water protons in Figure 2A are symmetric about the ab plane (crossed orientation, becausethe planes of water and pyrrole are crossed), but in Figure 2B they are symmetric about the ac plane (hinged orientation). Initially R,e,, and OP were fit to the moments of inertia, but it was found that the value of OP did not converge. 8, was then fixed at Oo for both thecrossed and hingedorientations,and thevariables R and 8, were fit to the rotational constants obtained from the less intense, lower-frequency set of tunneling doublets. These constants are believed to be the ground-state values and less perturbed by the tunneling motion (see below). The results of the least-squares fitting are compared in Table V. The values of the parameters R and 0, are similar for the crossed and hinged structures and areconsistent with the presence of an intermolecular hydrogen bond. 0, is approximately 40' for both structures, indicating that the oxygen end of the water is closest to the pyrrole. Likewise, the value obtained for R,4.2 A, is much greater than expected for a stacked complex similar to benzene-water (R = 3.3 A)4. The fitted values for the centerof-mass separation differ by less than one percent for the two structures under consideration. The crossed and hinge structures,

AIMHz BIMHz CIMHz

zi

&"A (W-I

amu A2

c r d

structure

9069. 8935.104 1638.358 1636.851 1391.169 1392.234 37.3(4.6) 4.20 15( 18) 3.0283(37) 0.393

symmetric cross

8970.933 1638.901 1394.586

hinged structure

8928.013 1641.067 1388.320 ob 41.5(13.2) 4.1962(26) 4.2026(55) 3.0095(26) 3.0326(116) 0.777 1.240

planar structure 8970.933 1645.072 1390.149

ob 4.1962(47) 3.0095(47) 1.428

a See Figure 1 for parameter definition. AI = 4(calc.) - Ii(obs.) for each isotopic species. b Held fixed.

however, do not fit the moments of inertia equally well, since (AZ), is 3 times greater for the hinged structure than for the crossed orientation. The moments were also fit to crossed and hinged structures with 8, fixed at zero. These fits are also listed in Table V. The (AI), for the crossed structure is again significantly better than for the hinged structure, but comparable to the hinged structure fit with 8, = 37O. The large (AZ), for the hinged structure with 8, = 0 (water and pyrrole coplanar) eliminates this configuration as plausible. The (AZ), for the hinged structure (8, = 37') and crossed structure (8, = Oo) are poorer than the crossed structure (8, = 37') butarenotlargeenough toexcludetheseasequilibrium configurations given that the large amplitude vibrational motions may contaminate the moments of inertia. Thecrossedstructurewiththelowest (AZ),(8, = 37')predicts values for the dipole moment components of pa = 3.24 D,pb = 1.12 D, and pc = 0 D. The large discrepancybetween the observed and predicted values for pa (>1 D) can be attributed in part to polarization induced by the hydrogen bond. The largediscrepancy between the observed and predicted values for pb (=l.l D) is more perplexing as it is not readily rationalized by polarization effects. The same remarks apply to the hinged structure (8, = 37') upon interchanging pb and pc. Alternatively, a crossed structure with 8, = ' 0 (symmetric cross) predicts pa = 3.62 D, pb = pc = 0 D, in better agreement with the dipole moment data. However, the inertial fit, (AI),, deterioratesfor this configuration (see Table V). Another possibilityis that theequilibrium structure for the complex is consistent with 8, # Oo, but that the water tunnels between equivalent crossed (or hinged) configurations by an inversion and/or internal rotation process with a barrier low enough to result in an average value of pb = cc, = 0. In summary, the moment of inertia and dipole moment eliminate stacked and coplanar structures; they areonly consistent with the pyrrole acting as a proton donor to the water oxygen. The precise orientation of the water hydrogens is ambiguous. Their location on average is consistent with 8, = ' 0 based on the dipole data. The inertial data suggest a crossed structure with 8, = 37O. The dipole moment is probably a more reliable indicator for the average structure than the moment of inertia fits. Largeamplitude vibrational effects can contaminate the moments of inertia significantly, making it troublesometo locate the hydrogen atoms by fitting the moments of inertia. Tunneling Doublets. The observed spectrum of the pyrrolewater displays spectroscopicsplittings usually associated with an internal tunneling process. An alternative explanation for the splittingsisthat they ariseas therotationalspectrumofapopulated vibrational state of the complex. The doublet members of the pyrrole-15N-water complex 303-&2 transition were recorded using both argon and an 80% nwn/20% helium gas mix for the expansion;the relative intensity of the doublet members was found to be independent of carrier gas. Since the cooling properties of the expansion depend on the carrier gas, a change in the carrier gas would be expected to affect the relative populations of (and the relative intensities of rotational spectra arising from) the ground and excited vibrational states. The splittings, therefore,

Hydrogen-Bonded Pyrrole-Water Complex are more consistent with tunneling doublets than an excited vibrational state. It is not straightforward to obtain insight on the tunneling pathway from the small frequencysplittings between the doublets. One can infer from the low residuals obtained upon fitting each set of transitions independently that the tunneling process is hindered by a barrier. The second-order Stark effects observed for both states also suggest that the tunneling motion does not arise from a nearly free internal rotation. The relative intensities of the doublet members from the 404303and 414-3 13 transitions were measured, since intensity patterns can often provide insight on nuclear spin statistical weights. In principle, these spin weights can be different depending on the presence or absence of various processes which exchange equivalent fermions (hydrogen nuclei). We measured the relative intensities in the pyrrole-15N-water system to avoid the complicated quadrupole splitting pattern associated with the l4N species. The relative intensities were measured by recording the signal-to-noiseratio for 9-1 1 spectra for both doublet members; our data acquisitionprogram estimates signal-to-noiseasthe ratio of the largest peak in the early portion of the free induction decay to the largest peak in the last 10% of the recorded time domain-the free induction decay signal generally decays below the noise level by this time. The relationship between the pump frequency, transition frequency, and cavity frequency was the same for both sets of measurements. Following this procedure, we found the relative intensities of the doublet members to be 1:2 for the 404-303 transition and 1:4 for the 414-313 transition with an estimated accuracy of f20%. Someconclusionscan bedrawnfrom theobservationofdoublets and from the approximate intensity ratio of the doublet members. In the limit of a rigid structure with C, symmetry (e, = Oo) only one tunnelingmotion is possible (torsion about the hydrogen bond); two tunneling states (observed as doublets) would arise from this tunneling process. If the complex has an equilibrium point group symmetry of C, (hinged or crossed, 8, # OO), there can be more than one internal motion and more than two tunneling states could arise (resulting in quartets). However, since only doublets are observed, only one tunneling motion is presumably present for the limiting C, or C, structures. Based on the observed relative intensities of the doublet pairs, it is unlikely that internal rotation of pyrrole or inversion of the H 2 0 (along the coordinate )e, are the origin of the doublets in the C, limiting structure. The internal rotation of pyrrole leads to spin statistical weights for the ground and excited states of 10:6. The inversion tunneling pathway results in spin weights of 28:36. These spin weights do not seem compatible with the observed relative intensities, which range between 1:2 and 1:4. On the other hand, internal rotation of water about its CZaxis in a C, limiting structure leads to a 1:3 ground state:excited state spin weight ratio. Also, an internal rotation about the hydrogen bond of either the C, or C, limiting structures exchanges 3 pairs of hydrogens (1 pair on water and 2 pairs on pyrrole). The permutation-inversion group for these exchanges is Ga and results in spin weights of 10:18 or 6:30 depending on whether K p is even or odd. The spin weights of either of these internal motions are consistent with the observed intensities, considering the large uncertainty in the measurements. Ab Initio. To gain further insight into the structure and internal motion of the pyrrole-water complex, ab initio calculations were performed at the Hartree-Fock level using the Gaussian90 program package.' The intermolecular separation, R, and Ow were optimized using both STO-3G and 6-31G basis sets for the crossed and hinged structures; again, the monomer structures were taken from refs 11 and 12. The minimal STO-3G basis set was chosen initially for comparison to earlier computations on the pyrrole-water complex.6 Values for R and Ow obtained with this basis set are very similar for the crossed and hinged

500ri-7

The Journal of Physical Chemistry, Vol. 97, No. 29, 1993 7455

-

v-

400

a

p

W

-180

-90

0

90

180

Angle (degrees)

Figure 3. Potential energy curves for the pyrrole-water complex along the intermolecular coordinates described by 0, and 3 generated using Gaussian90 and the STO-3G basis set. geometries" (R = 3.844 A and 3.843 A, RON= 2.670 A and 2.67 1A, e, = 40° and 43O, respectively)and also agree reasonably with the previously published results. It is interesting that the tilt angle of the water plane, 0, ir 40°, predicted by the Slatertype orbitals is consistent with the value obtained by fitting the experimentally determined rotational constants, but the length of the hydrogen bond (and the center-of-mass separation) is predicted to be much shorter than the length obtained from fitting the experimental data. On the other hand, the 6-31G basis set was found to model the intermolecular separation and dipole moment data better. As was found with the Slater orbitals, the crossed and hinged geometries optimized to similar values of Or and R using the 6-31G basis set14(R = 4.134 and 4.163 A, RON = 2.944 and 2.974 A, e, = 0' and 3.9O, respectively). The crossed geometry was found to be the minimum-energy structure using either basis set, although the relative energy of the two structures differs markedly between the STO-3G and 6-3 1G basis sets.I'J4 In summary, the optimized structures from the ab initio calculations confirm the basic hydrogen-bonded structure derived from the rotational constants and suggest a crossed configuration. The optimizedgeometrieswere used to map out potential energy curves along the tunneling pathways described in the previous section. These potential energy curves may provide further insight into the origin of the tunneling doublets, since tunneling doublets appear when two (or more) equivalent structures of a complex can be interconverted along a pathway which contains a barrier. Energy curves along the coordinates Ow and CP calculated using the basis set STO-3G are shown in Figure 3; similar curves calculated with the 6-31G basis set are presented in Figure 4. In both figures the curve depicting the potential energy along Ow was calculated using the structure in which the pyrrole and water planes are crossed. The STO-3G basis set predicts two equivalent structures at Ow = f40° and separated by a 116-cm-1 barrier at 0, = 0'. As discussed above, the 6-3 1G basis set does not predict two minima along the Ow coordinate, since the optimized geometry was found to have 8, = Oo. The barrier to internal rotation of the water about the hydrogenbond (described by CP) was calculated for a C, limiting structure using STO-3G and for a C, limiting structure using 6-31G (C, and C, correspond to the optimized structures for STO-3G and 6-31G, respectively). In both cases the barriers were found to be small, 42 cm-I for C, and 187 cm-' for C,, and were found to occur when the planes of the pyrrole and water are aligned in the hinge-likestructure (planar structure for C,). Finally, the barrier to internal rotation of the water about its C2 axis was considered for the C, limiting structure. This barrier was found to be 1700 cm-l using STO-3G and 890 cm-1 using 6-31G (e, was fixed at 40' for both calculations; if Ow = Oo, as in the optimized 6-31G structure, this pathway would

Tubergen et al.

1456 The Journal of Physical Chemistry, Vol. 97,No. 29, 1993 500

TABLE VI: Comparison of the Bonding Characteristics L Pyrrole-Water Obtained from Quadrupole Analysis for Pyrrole and xu/MHz XW/MHZ xco/MHz C(NH)

pyrrole 1.400(8)'

pyrrole-wa ter 0.9 15 1.409

1.300(8)"

-2.799(11)"

-2.324

0.24b

-1 80

-90 Angle

0 90 (degrees)

180

Figure 4. Potential energy curves for the pyrrole-water complex along the intermolecular coordinates described by e, and 0 generated using Gaussian90 and the 6-31G basis set.

be degenerate with the coordinate described by a). The barrier to internal rotation of water occurs when the water and pyrrole are coplanar. An internal rotation Hamiltonian was used to estimate the J-dependence of the tunneling splittings for water as the This method neglected the variation in the top moment of inertia with internal rotation angle. Nevertheless, splittings of the right order of magnitude should be obtained when the top motion involves only the water protons. Using twofold barriers for both the C, and CZ,limiting structures, the Hamiltonian gave splittings ranging from 0.3 to 15 MHz ( J = 1-2) for internal rotation about the hydrogen bond or the C2 axis of the water (Cs,8, = 37") for barriers of 10-200 cm-I. The calculated splittings were very sensitive to the structure assumed, Le., the orientation of the top axis relative to the principal inertial axes. This sensitivity along with the approximate Hamiltonian precludes any fiim conclusions except that barriers in this range are consistent with the observed splittings. While revising this manuscript for comments from the referees, a full geometry optimization ab initio study of pyrrole-water was published! These results were consistent with our work. HartreeFock level calculations with the 6-31G* basis set predicted a crossedstructure with 8, = 5.9" and RON= 3.064A. Calculations at the MP2 level predicted a C, crossed structure with 8, = 35.8" and RON= 2.971 A. Potential energy surfaceswere not described, so a comparison to the barriers and tunneling processes discussed in this study was not possible.

Discussion These experiments were undertaken to observe the microwave spectrum of at least one of the two possible hydrogen-bonded structures of the pyrrole-water complex. The spectrum analyzed in this paper corresponds to the complex structure in which the pyrrole acts as a proton donor. This conformer is considerably more stable than a r-hydrogen bonded pyrrole-water dimer according to ab initio studies.6.8 The determination of this structure will help characterize the important RIN-H- - -0 hydrogen-bonding interaction, since no previous gas-phase structures have been determined for a complex exhibiting this type of hydrogen bond. Using the N-H bond distance from the pyrrole monomer, the hydrogen bond in this complex is calculated to be 2.02 A. Previous gas-phase studies of carbon monoxide-water,16 ethylene-water,17 and cyclopropane-water18 have reported hydrogen bond lengths of 2.41,2.48, and 2.34 A, respectively. The pyrrole-water N-0 distance (3.025 A) is in better agreement with the 0-0 distance reported for the water dimerlg (2.98 A), so the pyrrole-water structure seems to be consistent with the

0.466

c-

O.2gb

0.32

0.48 0.34 From Aust. J. Phys. 1974,27, 143-146. See text for definitionsof i, rC,and c-. Calculated according to the method of ref 21.

rii

*E

formation of a relatively strong hydrogen bond. Interestingly, the gas-phase hydrogen bond in pyrrole-water is longer than the 1.77 A mean distance of the R2NH- -OH2 hydrogen bonds measured for purines and pyrimidines using X-ray crystallography.20 This discrepancy probably arises from other intermolecular interactions present in crystalline samples and highlights the difficulty of comparing hydrogen bonding in different environments. The exact orientation of the water protons is not unambiguously determined from the inertial data or the dipole moment results. Considering the contamination of the moments of inertia from large-amplitude vibrational effects, the upper bound uncertainty limits for pb and pc, and the ab initio calculations which prefer a crossed structure, it is reasonable to conclude that the crossed structure is the preferred configuration. Some information about internal dynamics and electronic effects is contained in the 14N quadrupole coupling constants. The internal tunneling of the complex apparently does not mix the elements of the quadrupole tensor Xbb and xa as much as the internal motions of other systems. In the ~yclopropane-H2~~0 system,18 for example, a free rotation about the hydrogen bond makes Xbb and xEcnearly equal and intermediate between the Xbb and xa values expected from a rigid complex. The measured values of Xbb and xoc for the pyrrole-water complex are quite different from each other, indicating that the internal motion does not mix the b and c components of the quadrupole coupling tensor as much as the internal motion of ~ y c l o p r o p a n e H 2 ~ ~ 0 . In the ~yclopropane-H2~~0 system the internal motion can be described as a rotation of either the water or the cyclopropane about the intermolecular hydrogen bond. Because of its greater mass, the relative orientation of the cyclopropanewill determine the projection of the 170quadrupole coupling tensor onto the inertial axes and internal rotation about the hydrogen bond will mix Xbb and xW.In the pyrrole-water complex, the quadrupolar nucleus, 14N, is located in the more massive pyrrole moiety; assuming that the potential barriers are similar,the internal motion of thewater withrespect to thepyrroledw not mix the projections of the quadrupole tensor as much as in the cyclopropane-water system. In a rigid pyrrole-water complex the values of Xaa, Xbbt and xa would be expected to be very similar to the quadrupole coupling constants measured for the pyrrole monomer since the inertial axes of the complex do not rotate very much from those in pyrrole. In fact, sizable changes are observed, particularly in xaa(Table VI). In weakly bound complexes a deviation from the expected x's often arises from large-amplitude motions of the complexing partners. There is no single angle, 8, representing an average vibrational amplitude angle which will transform the pyrrole x's into those of the complex, although a value of about 20° can reasonably approximate the values measured for xaaand xcc. Given that pyrrole is 3.7 times more massive than water, this value seems to be unrealistically large to attribute the changes in the x's as arising predominantly from the vibrational averaging effects. An alternative explanationfor the change in pyrrole quadrupole coupling constants upon complexation with water is that the

-

Hydrogen-Bonded Pyrrole-Water Complex intermolecular hydrogen bond changesthe electronic environment of the nitrogen nucleus. Gordy and Cook21present a method of relating the quadrupole coupling constants of pyrrole to a description of the bonding by the nitrogen; similar treatments have been carried out for indole22and carbazole.23 We have analyzed the coupling constantsfor pyrrolewater and more recent constants for pyrrole24 in the same way; these results are summarized and compared in Table VI. As one might expect, the ionic character of the pyrrole N-H bond, i,,(NH), displays a large change upon complexation, increasingby 33%. Similarly, the amount of negative charge on the nitrogen, c-, increases by 20%. These changes are consistent with the formation of the hydrogen bond involving the nitrogen proton. The *-bonding character of the p z orbital (rC)appears to change only slightly upon complex formation. It is interesting that the recent publications on the ab initio calculations for the pyrrolewater complex reports a lengthening of the pyrrole N-H bond upon complex formation, which would suggest significant relaxation effects of the charge distribution around the nitrogen as well. However, this analysis of the quadrupole coupling constants has not been found to be generally applicableto all hydrogen-bonded nitrogen complexes (e.g., in NH3-HCCH25 and NH3-HCN,26 the NH3 nitrogen quadrupole coupling constants do not reflect the increase in the hydrogen-bonding interactionstrength). Very likely the large change from the quadrupole coupling constants of pyrrole arises from a combinationof electronic and vibrational effects. Finally, an estimateofthe relativestrengthoftheintermolecular bond is often derived from the centrifugal distortion constant DJ using a pseudodiatomic mode1.27 In this model, the force constant of the intermolecular stretching mode, k,, can be related to DJ by

k, = 16?r2B3p/DJ where p is the reduced mass of the complex. The force constant for pyrrolewater is estimatedto be 0.28 mdyn/A with a harmonic frequency of 180 cm-l. Using a Lennard-Jones 6-12 (LJ 6-12) potential to describe the intermolecular interaction, the binding energy of the complex is estimated to be 3500 cm-l. For comparison, the binding energy from the ab initio calculations (see refs 13 and 14) is about 2950 cm-' in the STO basis, 2400 cm-l in the 6-3 1G basis, and 2021 cm-1 from the 6-3 1G+ MP2/ BSSE calculation.* The pseudodiatomic binding energy of pyrrole-Ar28 is only 300 cm-', and the same method yieldsI8 e = 731 and 1640 cm-* for the hydrogen-bonded systems cyclopropanewater and formamidewater, respectively. It seems unlikely that the binding energy of pyrrolewater is so much greater than for formamide-water, especially since the formamidewater complex contains two intermolecular hydrogen bonds. One assumption made in estimating the binding energy is that the intermolecular interaction is described by a LJ 6-12 potential. The LJ 6-12 potential poorly describes interactions which are fairly strong (trimethylamine-sulfur dioxideZ9for example) and underestimates the binding energy. The discrepancies in the estimated binding energies for the hydrogen-bonded complexes probably arises from a poor representation of the intermolecular potentials by the LJ 6-12 model.

The Journal of Physical Chemistry, Voi.97, No. 29, 1993 7457 Conclusions Rotational spectra were recorded for three isotopomers of a hydrogen-bonded pyrrolewater complex. The rotational constants indicate that pyrrole is acting as a proton donor and that the hydrogen bond is 2.02 A. Tunneling splittings were observed for the rotational transitions; analysis of the doublet intensity patterns and models of the potential barriers suggest a crossed structure with a hindered internal rotation about the hydrogen bond. Acknowledgment. This work was supported by a grant from the National Science Foundation. The assistance of Dr. Kurt Hillig I1with the ab initio calculationsis gratefully acknowledged. References and Notes (1) DedicatedtoProfessor HansBockontheoccasionofhis65thbirthday. (2) Balle, T. J.; Flygare, W. H. Rev.Sci Imtrum. 1981, 52, 33. (3) Lovas, F. J.; Suenram, R. D.; Fraser, G. T.; Gillies, C. W.; Zozom, J. J. Chem. Phys. 1988,88, 722. (4) Jasien, P. G.; Stevens, W. J. J. Chem. Phys. 1986,84, 3271. (5) (a) Gotch, A. J.; Zwier, T. S.J . Chem. Phys. 1992, 96, 3388. (b) Suzuki, S.;Green, P. G.; Bumgarner, R. E.; Dasgupta, S.;Goddard, W. A,, 111; Blake, G. A. Science 1992, 257, 942. (6) Del Bene, J. E.; Cohen, I. J . Am. Chem. Soc. 1978, 100, 5285. (7) Gaussian90, Revision I; Frisch, M. J.; Head-Gordon, M.; Trucks, G. W.; Foresman, J. B.; Schlegel, H. B.; Raghavachari, K.; Robb, M.; Binkley, J. S.;Gonzalez, C.; Defrees, D. J.; Fox, D. J.; Whiteside, R. A,; Seeger, R.; Melius, C. F.; Baker, J.; Martin, R.L.; Kahn, L. R.; Stewart, J. J. P.; Topiol, S.;Pople, J. A. Gaussian, Inc., Pittsburgh PA, 1990. (8) Nagy, P. I.; Durant, G. J.; Smith, D. A. J . Am. Chem. Soc. 1993, 115, 2912. (9) Hillig, K. W., 11; Matos, J.; Scioly, A.; Kuczkowski, R. L. Chem. Phys. Ltt. 1987, 133, 359. (10) Tanaka, K.; Ito, H.; Harada, K.; Tanaka, T. J . Chem. Phys. 1984, 80, 5893. (1 1) Nygaard, L.; Nielsen, J. T.; Kirchheiner, J.; Maltesen, G.; Rastrup Andersen, J.; Sorensen, G. 0. J . Mol. Srrucr. 1969, 3, 491. (12) CRC Handbook, 51st ed.; CRC Press: Boca Raton, FL; p F157. (13) Using the STO-3G basis set, the calculated energies for the initial monomer structures are pyrrole = -206.224 12 au and water = -74.963 10 au. The calculated energy of the crossed structure is -281.200 72 au and the energyofthe hingestructureis-281,200 53 au. Theenergydifferencesbetween the conformers is 0.1 19 kcal/mol. (14) Using the 6-31G basis set, the calculated energies for the initial monomer structures are pyrrole = -208.729 05 au and water = -75.983 96 au. The calculated energy of the crossed structure is -284.724 40 au and the energyofthehiestructureis-284.723 55 au. Theenergydifferencesbetween the conformers is 0.533 kcal/mol. (15) Andrews, A. M.; Taleb-Bendiab, A.; LaBarge, M. S.;Hillig, K. W., 11; Kuczkowski, R. L. J . Chem. Phys. 1990,93, 7030. (16) Yaron, D.; Peterson, K. I.; Zolandz, D.; Klemperer, W.; Lovas, F. J.; Suenram, R. D. J . Chem. Phys. 1990,92, 7095. (17) Peterson, K. I.; Klemperer, W. J . Chem. Phys. 1986, 85, 725. (18) Andrews, A. M.; Hillig, K. W., 11; Kuczkowski, R. L. J. Am. Chem. Sot. 1992, 114, 6765. (19) Dyke, T. R.; Mack, K. M.; Muenter, J. S.J . Chem. Phys. 1977,66, 498; Odutola, J. A.; Dyke, T. R. J. Chem. Phys. 1980, 72, 5062. (20) Jeffrey, G. A.; Saenger, W. Hydrogen Bonding in Biological Structures: SDrinner: Berlin. 1991: D 130. (21) Gordy, f.; Cook, R.L. Microwave Molecular Spectra; Wiley: New York, 1984; pp 772-776. (22) Suenram, R. D.; Lovas, F. J.; Fraser, G. T. J . Mol. Spectrosc. 1988,

-I ?-? , AI7 . . -. I

(23) Suenram, R. D.; Lovas, F. J.; Fraser, G. T.; Marfey, P. S.J. Mol. Struct. 1988, 190, 135. (24) Bolton. K.; Brown, R. D. Ausr. J . Phys. 1974, 27, 143. (25) Fraser, G. T.; Leopold, K. R.; Klemperer, W. J. Chem. Phys. 1984, 80, 1423. (26) Fraser,G.T.;Leopold,K.R.;Nelson,D.D., Jr.;Tung,A.;Klemperer, W. J. Chem. Phys. 1984,80, 3073. (27) Millen, D. J. Can. J . Chem. 1985, 63, 1477. (28) Bohn, R. K.; Hillig, K. W., II; Kuczkowski, R. L. J . Phys. Chem. 1989, 93, 3456. (29) Oh, J. J.; LaBarge, M. S.;Matos, J.; Kampf, J. W.; Hillig, K. W., 11; Kuczkowski, R.L. J. Am. Chem. SOC.1991,113,4732.