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Microwave and tunable far-infrared laser spectroscopy of OCH2O: investigation of the water tunneling potential
Volume 176, number
I
CHEMICAL PHYSICS LETTERS
4 January 199 1
Microwave and tunable far-infrared laser spectroscopy of OC-H20: investigation of the water tunneling potential R.E. Bumgarner, Sakae Suzuki, Paul A. Stockman, Peter G. Green and Geoffrey A. Blake ’ Division
ofGeological and Planetary Sciences, CaliJbrnia Institute of Technology, 170-25 Pasadena, CA 91125, USA
Received 20 August 1990
The K,=O- I rotation-tunneling bands of 0’%-H20 and O’*C-D*O have been measured in the region between 400 and 600 GHz. Two bands for each isotopomer were observed corresponding to AK,= I, &type rotational transltions in the A and B water
tunneling states. Each band was fit independently using a Watson A-reduced Hamiltonian yielding all three rotational and several distortion constants per band. The effective A-rotational constants, A*, contain a contribution due to water tunneling. Assuming the tunneling splittings are the same in I$=0 and K,= 1, A*(A state) -A*(B state) =2u,, where v, is the tunneling splitting. We obtain tunneling splittings of 16.684 GHz for 0 “C-H20 and I .O12 GHz for 0 ‘*C-DzO. These measurements are in good agreement with the predictions of Yaron et al. (J. Chem. Phys. 92 ( 1990) 7095). Effective one-dimensional potentials have been employed to place constraints on the hydrogen bond geometry, to model the measured tunneling splittings, and to predict higher
frequency vibration-rotation-tunneling transitions.
Hydrogen bound and van der Waalsbound species have been the subject of intense study for many decades. This is due to the important role weak intermolecular interactions play in a wide variety of physical and chemical processes. For example, bulk properties such as deviations from the ideal gas law, melting and boiling points, and solubilities are governed primarily by the strength and nature of intermolecular interactions. With the wide variety of new spectroscopic techniques available to study dimers and higher order weakly bound polymers, it is now becoming possible to extract accurate intermolecular potential energy surfaces for a variety of systems. In particular, far-infrared (FIR) spectroscopic measurements which directly probe the intermolecular motions [ l-91, along with higher frequency measurements which probe intermolecular motions in combination with vibrational or electronic excitation in the. monomers [ 10-161, are providing a wealth of information on intermolecular potentials. We began our investigation of OC-HZ0 both to
’ Packard
Fellow, Sloan
Investigator. 0009-2614/9
Fellow and
Presidential
Young
provide an example of the simplest type of rod-top system (diatom-triatom) and as part of a larger program to study interactions of important atmospheric molecules with water, In this initial report on OCHzO, we present the spectroscopic constants obtained from extensive microwave and FIR spectral measurements on 0 12C-H20 and 0 “C-D20. A more complete account, including spectroscopicdata for the singly deuterated and carbon-13 substituted speciesalong with the results of ab initio calculations on the dimer, will be published at a later date. The water/carbon monoxide dimer has been the subject of a previous microwave study by Yaron et al. [ 171. They obtained u-type, Kp=O spectra of 0 “C-H20, 0 ‘?C-HDO, 0 “C-D20, 0 ‘3C-H20, 0 13C-HD0 and 0 12C-H2l’0. In the dimers containing H20 or D20, two sets of rigid-rotor-like transitions per isotopomer were observed, indicative of a water tunneling motion. Resolved proton-proton spin-spin interactions allowed separate water spin states to be uniquely assignedto the different sets of rotational transitions. Yaron et al. noted that the u-dipole moment of the A tunneling state (the spatially symmetric state) is
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always higher than that of the B state (spatially antisymmetric). By assuming that the tunneling path is a rotation about the c axis of water (i.e. remains planar), and that at the barrier both hydrogens are pointing towards the CO, the dipole moment differences could be attributed to the nodal character of the rovibrational wave functions near the barrier. That is, the antisymmetric tunneling state has a node at the barrier and will therefore have a lower probability of sampling dimer geometries in this region. This results in the symmetric tunneling state having a slightly larger average projection of the water monomer dipole moment onto the a axis. By modeling the small differences in the dipole moments of the symmetric and antisymmetric tunneling states, Yaron et al. arrived at a barrier to tunneling of 210(20) cm-‘. They also predicted (prior to our measurement) tunneling splittings of 17 ( 1) GHz for OC-Hz0 and 1.1 ( I ) GHz for OC-D20. Fig. 1 shows an energy level diagram for the Kg= 0 and K,= 1 states including the effect of the water large
H \,-k
c-o
E(HOH-CO)
E(DOD-CO) 360
240
4 January 199 I
amplitude motion. Each K, level is split into two tunneling components. Since the total wave function for OC-H,O must be anti-symmetric with respect to exchange of the protons, the symmetric water spin function pairs with the spatially symmetric tunneling state in Kp=O and the spatially anti-symmetric function in K,= 1. This leads to intensity ratios of 3: 1, B: A. For D20, similar arguments lead to spin weights of 6:3, A:B. Using our previously described microwave spectrometer [ 181, we have extended the measurement of a-type AJ= 1, Kp=O transitions to 75 GHz. The microwave measurements allowed the beam conditions to be adjusted for maximum dimer production using transitions well predicted from the work of Yaron et al., and provided ground state data useful for combination difference assignments in the FIR. FIR b-type spectra in the ranges between 348 and 660 GHz were obtained with a tunable laser sideband cluster spectrometer similar in construction to the UC Berkeley instrument [ 3 1, and which will be described in detail in ref. [ 191. The observed FIR bands are shown in fig. 1. Each set of transitions was fit independently to a standard A-reduced Watson Hamiltonian yielding the spectroscopic constants reported in table 1. The effective A-rotational constants, A*, obtained from such a lit contain contributions due to tunneling. If we assume that the tunneling splittings, v,, in Kp=O and 1 are equal, then A*(Astate)-A*(Bstate)s2v, and
(GHz)
120
v (DOD) = 351 GHz
B A
0 U K=O
0 K=l
Fig. 1. Schematic energy level diagram of the observed K,= 0 and K,= 1 rotation-tunneling states of the water/carbon monoxide dimer. Tunneling splittings have been exaggerated for clarity, especially for D,O. Arrows mark the observed transitions.
124
A*(Astate)+A*(Bstate)=?(A+d,), where A is the structural rotational constant. The (A+&)? and tunneling splittings calculated with this assumption are 577916.6 and 16683.6 MHz for 0 “C-H20 and 352255.4 and 1012.9 MHz for 0 ‘*C-D20. Our measurements of the Kp= O- 1 rotation-tunneling transitions confirm that the tunneling motion is about the c axis of water in that “top-to-bottom” and “bottom-to-top” selection rules are observed (see fig. 1). The measured tunneling splittings are in surprisingly good agreement with the predictions of the simple non-periodic one-dimensional tunneling potential of Yaron et al. To investigate the range of tun-
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CHEMICALPHYSICSLETTERS
Table I Spectroscopic constants for 0 ‘*C-H20 and 0 “C-D*O. Reported errors are one standard deviation of the fit. Unreported constants were held fixed at zero. The last line is the number of transitions included in the fit 0 ‘*C-H20
A*(MHz) B(MHz) C(MHz) A,K(MHz) A, (kHz) 8, @Hz) HJK(kHz1 h,K@Hz) & (Hz) h, (Hz)
0 “C-DZO
A state
B state
A state
B state
594600.280(89) 2762.1849(39) 2736.0710(39) -25.1925(31) 20.474(12) 0.520(15) -3.980(20)
561233.01(11) 2759.9769(73) 2741.0376(73) -20.?986(43) 20.416( 15) 1.154(54) -3.838(32)
353268.37(58) 2632.111(79) 2606.343(84) -3.231(46) 19.9(11)
351242.53(22) 2631.455(26) 2606.380(27) -3.519(18) 14.456(37)
47
1.26(21) SO
-6.8( 1.2) 5.8( 1.2) 0.238(39) 28
-11.1(43) 0.0479( 13) 23
neling potentials consistent with the data, we have modeled the observed tunneling splittings using a potential of the form V= I,( f V,) [ 1 - cos( no) 1, and the c-moments of inertia of HZ0 and DzO in the kinetic energy part of the tunneling Hamiltonian. We pick 0 to be the angle which the b axis of H20 makes with the a axis of the complex. 8=0” corresponds to both hydrogens pointing towards to OC, while 8= 55.5” corresponds to a hydrogen on the a axis #‘. A two term, V, t VZpotential of the above form can be fit to the two tunneling splittings assuming both H,O and 40 rotate in the same potential. Such a parametrization is quite restrictive in the range of potential shapes one can obtain. For example, the equilibrium angle, Beg,for such a two term potential is determined solely by - V,/4V,=cos &,. The two term potential which fits both tunneling splittings is V,=745.00 and V’,= -493.21 cm-‘. For thispotential, 0,,=67.8”. We have also investigated a range of V, + Vz t V, term potentials in an effort to see if it is possible to decrease &., toward a more linear hydrogen bond and still fit the tunneling splittings. With three terms in the potential, at least one more piece of data or one more constraint must be used. We have sampled the three term potential parameter space by selecting
values of S,, and Vat 180”, and by fitting V, to the tunneling splitting in H20. V,= V( 180” ) - V,, and the choice of 0, fixes the value of V,. We varied V( 180” ) from 400 to 1100 cm-’ and 0,, from 58” to 67”. The chosen upper range for V( 180”) is well above the ab initio binding energy of 923 cm-’ calculated at the MP2/6-31G* level [ 201, while the lower limit is set somewhat more arbitrary at roughly twice the expected tunneling barrier. For a given choice of &,, we find that the barrier height which reproduces the Hz0 tunneling splitting varies by less than 5% throughout the entire range of V( 180”) sampled. Further constraints can be placed on 0,, by consideration of the nuclear hypertine constants. The proton spin-spin constant in the anti-symmetric tunnelingstate ofOC-H,O, S,,= 19.5(2) kHz [ 171, places a fairly tight lower bound on the value of 0,, The spin-spin value in the dimer is given by 33.072(P,(cos$))kHz, where 33.072 kHz is the spin-spin value calculated for the average structure of water [ 2 I] #*and $Jis the angle between the a axis of the dimer and the line connecting the protons. In the limit of planarity, (P2(cos@))=1/2(P,(cos 0) ) . Since out of plane averaging can only reduce the value of (P,(cos 4) ), the spin-spin con-
RI
“2
The angle at this position is not 104.5’/2, since we are rotating about the center of mass (c.m.) of the HZ0 and L H-c.m.H=l II” forH20. For D20, L D-c.m.-D= 116.5”.
Note that different definitions of the spin-spin constant are in common use, resulting in a factor of 4 difference between one definition and the other.
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stant of the dimer therefore requires that the effective value of theta, 8*, calculated from the Pz projection be larger than 58.5”. Tunneling reduces 13* from the value of 19,~so that 0,, must also be larger than 58.5 ‘. We find that the minimum .9,, for a three term potential of the above form which reproduces the HZ0 tunneling splitting and the spin-spin constant is 62.5’. Larger values of &., are also consistent with the data provided some out-of-plane averaging reduces the value of ( P2( cos 4) ). The values of V,, V, and r/, which reproduce the Hz0 and D,O tunneling splittings for &= 62.5” are given in table 2. The most significant structural conclusion of Yaron et al. [ 171 was that the equilibrium hydrogen bond angle C-H-O was bent by approximately 11’ and thus that &.,~64.0” in our coordinate system. The conclusion of a bent hydrogen bond was that imposed by a symmetrical vibrational averaging model in which the spin-spin constant for OC-HZ0 and the deuterium quadrupole for OC-DOH could only be brought into agreement by averaging around a bent angle - provided the tunneling potential remains constant. As noted in the above discussion, the spin-spin constant of OC-Ha0 combined with a knowledge of the water tunneling splitting also requires that the equilibrium angle is bent. Hence, the non-linear hydrogen bond determined by Yaron et al. is not simply an artifact of averaging OC-HZ0 and OC-DOH in identical potentials, but is required by the HZ0 data alone. Potential parameters which reproduce both the HZ0 and D20 tunneling splittings at &,=64’ are also provided in table 2. As noted by Yaron et al., electrostatic models predict considerably less tilt in the hydrogen bond than is required by the available data. At this point it is useful to discuss sources of model error. In addition to the limited range of potential Table 2 Three term potentials which reproduce both the H,O and D20 tunneling splittings
0 ;; (cm-l) V2 (cm-‘) V3 (cm-‘) barrier height (cm-‘)
126
Potential A
Potential B
62.5” 6 10.070 -357.339 - 113.082 229.6
64.0” 684.280 -418.850 - 72.284 217.7
4 January1991
shapes available with a three term potential of the above form, there are two other obvious sources of possible error. The first is that the moment of inertia which should be used in the kinetic energy part of the Hamiltonian may not be simply the c-moment of inertia of water. This could result from a slightly nonplanar tunneling path, a path in which the intermolecular distance changes as a function of 0 (bendstretch coupling), or a tunneling path involving a slight rotation of the OC molecule. If the O-C-O angle is slightly bent at equilibrium, as predicted from the ab initio calculations of Reed et al. [20], exchange of the hydrogens would require motion of the OC subunit. Also, even for simpler threefold internal rotations of methyl or substituted methyl groups, it is not uncommon that the observation of several internal rotation states requires that the moment of inertia of the tunneling subunit be fit to a slightly different value than that expected from the structure alone. A second source of possible error are couplings and interactions with other vibrational modes. Note that for OC-DOH, only the D-bound form is observed in molecular beam conditions and that the calculated intermolecular bond lengths for water-carbon monoxide decrease with increasing mass of the subunits [ 171. Similar effects are typical for weakly bound dimers and are indicative of changes in effective onedimensional potentials due to reduced zero-point vibrational motion in other modes. Also, even for a given isotopomer, Coriolis couplings to other modes could effect the measured tunneling splittings. In principle, the above possible sources of error could be eliminated or reduced with more complicated models. However, there is currently not enough spectroscopic data to separate these effects. We are presently exploring methods to calculate high level ab initio potentials for dimers and algorithms which combine experimental data with ab initio calculations to generate quantitative intermolecular potential energy surfaces, and will report on these efforts in the future. At this time it seems more reasonable to acquire the spectra of higher internal rotation states than to further model the potential with the currently available data. In table 3 we therefore present the energies of the first four internal rotation states for 0 ‘2C-Hz0 calculated with the two potentials given in table 2. These predictions should aid in
CHEMICALPHYSICS LETTERS
Volume 176,number 1
Table 3 Predicted transitions using the potentials in table 2. Frequencies are in cm-‘. For a-dipole transitions, the frequency given is just the difference in the tunneling energy levels. For b-dipole transitions, A+ d, was added to the difference.Transitions marked with an asterisk correspond to the observed FIR bands. Quantum numbers for the transitions are given as ( m, K,)- (m’,K; ) where m is the internal rotation quantum number (m, &)-(m’, Kb)
Potential A
Potential B
Dipole
(O,O)-(l,l)’
19.833 18.721 114.5 145.4 133.2 125.6
19.833 18.721 110.2 141.6 128.9 121.8
b b
(1, OHO, 1)’ (O,OH-l,O)
(O,O)-(:,I ) (1,0)-(-l, 1) (~,OW,O)
f b
a
searches for transitions accessing the higher energy internal rotation states. Observation of such transitions will much more tightly constrain the complex geometry and tunneling potential. The authors wish to thank Dr. David Yaron for numerous helpful discussions throughout the course of this work and for providing a copy of ref. [ 171, prior to publication. REB would like to acknowledge the support of a Bantrell Fellowship administered by the California Institute of Technology. This work was
supported in part by grants from the Packard and Sloan Foundations, the Caltech Beckman Institute and the NSF (CHEM-8957228). Acknowledgement is also made to the Donors of the Petroleum Research Fund, administered by the .4merican Chemical Society, for partial support of this work.
4 January 199I
References [ I] M.D. Marshall, A. Charo, H.O. Leung and W. Klemperer, J. Chem. Phys. 83 (1985) 4924. [2] D. Ray, R.L. Robinson, D.H. Gwo and R.J. Saykally, J. Chem.Phys.84 (1986) 1171. [ 31 K.L. Busarow,GA. Blake,K.B. Laughlin,R.C. Cohen, Y.T. Lee and R.J. Saykally,J. Chem. Phys. 89 ( 1988) 1268. [41 R.C. Cohen, K.L. Busarow, K.B. Laughlin, G.A. Blake, M. Havenith, Y.T. Lee and R.J. Saykally,J. Chem. Phys. 89 (1988) 4494. [ 51G.A. Blake,K.L. Busarow,R.C. Cohen, K.B. Laughlin,Y.T. Lee and R.J. Saykally,J. Chem. Phys. 89 (1988) 6577. [ 61 N. Mozzen-Ahmadi, A.R.W. McKellar and J.W.C. Johns, Chem. Phys. Letters I5 I ( 1988) 318. [ 71 KL. Busarow,R.C. Cohen, G.A. Blake,K.B. Laughlin,Y.T. Lee and R.J. Saykally,J. Chem. Phys. 90 (1989) 3937. [81 G.A. Blakeand R.E. Bumgamer, J. Chem. Phys. 91 (1989) 7300. [ 91 R.C. Cohen, K.L. Busarow, Y.T. Lee and R.J. Saykally,J. Chem. Phys. 92 (1990) 169; R.C. Cohen and R.J. Saykally,J. Phys. Chem., in press. [IO] D.H. Levy, Advan. Chem. Phys. 47 (1981) 323, and references therein. [ I I ] A.W. Castleman Jr. and R.G. Keesee, Ann. Rev. Phys. Chem. 37 (1986) 525, and references therein. [ 121D.J. Nesbit, in: Structure and dynamics of weakly bound molecular complexes, ed. A. Weber (Reidel, Dordrecht, 1987) p. 107,and references therein. [ 131J.W. Bevan, in: Structure and dynamics of weakly bound molecular complexes, ed. A. Weber (Reidel, Dordrecht, 1987) p. 149. [ 141N. Ohashi and A.S. Pine, J. Chem. Phys. 81 (1984) 73. [ 151R.E. Miller, Science 240 ( 1988) 447. [ 161A.R.W. McKellar, J. Chem. Phys. 92 (1990) 3261. [ 171D. Yaron, K.I. Peterson, D. Zolandz, W. Klemperer, F.J. Lovas and R.D. Suenram, J. Chem. Phys. 92 ( 1990) 7095. [ 181R.E. Bumgamer and G.A. Blake, Chem. Phys. Letters I61 (1989) 308. [ 191G.A. Blakeand R.E Bumgamer, to be published. [201A.E. Reed, F. Weinhold, L.A. Curtiss and D.J. Pochatko, J. Chem. Phys. 84 (1986) 5687. [21] M.D. Harmony, V.W. Laurie, R.L. Kuczkowski, R.H. Schwendeman,D.A. Ramsay, F.J. Lovas,W.J. Lafferty and A.G. Maki, J. Phys. Chem. Ref. Data 8 (I 979) 619.
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CHEMICAL PHYSICS LETTERS
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Microwave and tunable far-infrared laser spectroscopy of OC-H20: investigation of the water tunneling potential R.E. Bumgarner, Sakae Suzuki, Paul A. Stockman, Peter G. Green and Geoffrey A. Blake ’ Division
ofGeological and Planetary Sciences, CaliJbrnia Institute of Technology, 170-25 Pasadena, CA 91125, USA
Received 20 August 1990
The K,=O- I rotation-tunneling bands of 0’%-H20 and O’*C-D*O have been measured in the region between 400 and 600 GHz. Two bands for each isotopomer were observed corresponding to AK,= I, &type rotational transltions in the A and B water
tunneling states. Each band was fit independently using a Watson A-reduced Hamiltonian yielding all three rotational and several distortion constants per band. The effective A-rotational constants, A*, contain a contribution due to water tunneling. Assuming the tunneling splittings are the same in I$=0 and K,= 1, A*(A state) -A*(B state) =2u,, where v, is the tunneling splitting. We obtain tunneling splittings of 16.684 GHz for 0 “C-H20 and I .O12 GHz for 0 ‘*C-DzO. These measurements are in good agreement with the predictions of Yaron et al. (J. Chem. Phys. 92 ( 1990) 7095). Effective one-dimensional potentials have been employed to place constraints on the hydrogen bond geometry, to model the measured tunneling splittings, and to predict higher
frequency vibration-rotation-tunneling transitions.
Hydrogen bound and van der Waalsbound species have been the subject of intense study for many decades. This is due to the important role weak intermolecular interactions play in a wide variety of physical and chemical processes. For example, bulk properties such as deviations from the ideal gas law, melting and boiling points, and solubilities are governed primarily by the strength and nature of intermolecular interactions. With the wide variety of new spectroscopic techniques available to study dimers and higher order weakly bound polymers, it is now becoming possible to extract accurate intermolecular potential energy surfaces for a variety of systems. In particular, far-infrared (FIR) spectroscopic measurements which directly probe the intermolecular motions [ l-91, along with higher frequency measurements which probe intermolecular motions in combination with vibrational or electronic excitation in the. monomers [ 10-161, are providing a wealth of information on intermolecular potentials. We began our investigation of OC-HZ0 both to
’ Packard
Fellow, Sloan
Investigator. 0009-2614/9
Fellow and
Presidential
Young
provide an example of the simplest type of rod-top system (diatom-triatom) and as part of a larger program to study interactions of important atmospheric molecules with water, In this initial report on OCHzO, we present the spectroscopic constants obtained from extensive microwave and FIR spectral measurements on 0 12C-H20 and 0 “C-D20. A more complete account, including spectroscopicdata for the singly deuterated and carbon-13 substituted speciesalong with the results of ab initio calculations on the dimer, will be published at a later date. The water/carbon monoxide dimer has been the subject of a previous microwave study by Yaron et al. [ 171. They obtained u-type, Kp=O spectra of 0 “C-H20, 0 ‘?C-HDO, 0 “C-D20, 0 ‘3C-H20, 0 13C-HD0 and 0 12C-H2l’0. In the dimers containing H20 or D20, two sets of rigid-rotor-like transitions per isotopomer were observed, indicative of a water tunneling motion. Resolved proton-proton spin-spin interactions allowed separate water spin states to be uniquely assignedto the different sets of rotational transitions. Yaron et al. noted that the u-dipole moment of the A tunneling state (the spatially symmetric state) is
I /$ 03.50 0 1991 - Elsevier Science Publishers B.V. (North-Holland)
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always higher than that of the B state (spatially antisymmetric). By assuming that the tunneling path is a rotation about the c axis of water (i.e. remains planar), and that at the barrier both hydrogens are pointing towards the CO, the dipole moment differences could be attributed to the nodal character of the rovibrational wave functions near the barrier. That is, the antisymmetric tunneling state has a node at the barrier and will therefore have a lower probability of sampling dimer geometries in this region. This results in the symmetric tunneling state having a slightly larger average projection of the water monomer dipole moment onto the a axis. By modeling the small differences in the dipole moments of the symmetric and antisymmetric tunneling states, Yaron et al. arrived at a barrier to tunneling of 210(20) cm-‘. They also predicted (prior to our measurement) tunneling splittings of 17 ( 1) GHz for OC-Hz0 and 1.1 ( I ) GHz for OC-D20. Fig. 1 shows an energy level diagram for the Kg= 0 and K,= 1 states including the effect of the water large
H \,-k
c-o
E(HOH-CO)
E(DOD-CO) 360
240
4 January 199 I
amplitude motion. Each K, level is split into two tunneling components. Since the total wave function for OC-H,O must be anti-symmetric with respect to exchange of the protons, the symmetric water spin function pairs with the spatially symmetric tunneling state in Kp=O and the spatially anti-symmetric function in K,= 1. This leads to intensity ratios of 3: 1, B: A. For D20, similar arguments lead to spin weights of 6:3, A:B. Using our previously described microwave spectrometer [ 181, we have extended the measurement of a-type AJ= 1, Kp=O transitions to 75 GHz. The microwave measurements allowed the beam conditions to be adjusted for maximum dimer production using transitions well predicted from the work of Yaron et al., and provided ground state data useful for combination difference assignments in the FIR. FIR b-type spectra in the ranges between 348 and 660 GHz were obtained with a tunable laser sideband cluster spectrometer similar in construction to the UC Berkeley instrument [ 3 1, and which will be described in detail in ref. [ 191. The observed FIR bands are shown in fig. 1. Each set of transitions was fit independently to a standard A-reduced Watson Hamiltonian yielding the spectroscopic constants reported in table 1. The effective A-rotational constants, A*, obtained from such a lit contain contributions due to tunneling. If we assume that the tunneling splittings, v,, in Kp=O and 1 are equal, then A*(Astate)-A*(Bstate)s2v, and
(GHz)
120
v (DOD) = 351 GHz
B A
0 U K=O
0 K=l
Fig. 1. Schematic energy level diagram of the observed K,= 0 and K,= 1 rotation-tunneling states of the water/carbon monoxide dimer. Tunneling splittings have been exaggerated for clarity, especially for D,O. Arrows mark the observed transitions.
124
A*(Astate)+A*(Bstate)=?(A+d,), where A is the structural rotational constant. The (A+&)? and tunneling splittings calculated with this assumption are 577916.6 and 16683.6 MHz for 0 “C-H20 and 352255.4 and 1012.9 MHz for 0 ‘*C-D20. Our measurements of the Kp= O- 1 rotation-tunneling transitions confirm that the tunneling motion is about the c axis of water in that “top-to-bottom” and “bottom-to-top” selection rules are observed (see fig. 1). The measured tunneling splittings are in surprisingly good agreement with the predictions of the simple non-periodic one-dimensional tunneling potential of Yaron et al. To investigate the range of tun-
Volume 176,number 1
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CHEMICALPHYSICSLETTERS
Table I Spectroscopic constants for 0 ‘*C-H20 and 0 “C-D*O. Reported errors are one standard deviation of the fit. Unreported constants were held fixed at zero. The last line is the number of transitions included in the fit 0 ‘*C-H20
A*(MHz) B(MHz) C(MHz) A,K(MHz) A, (kHz) 8, @Hz) HJK(kHz1 h,K@Hz) & (Hz) h, (Hz)
0 “C-DZO
A state
B state
A state
B state
594600.280(89) 2762.1849(39) 2736.0710(39) -25.1925(31) 20.474(12) 0.520(15) -3.980(20)
561233.01(11) 2759.9769(73) 2741.0376(73) -20.?986(43) 20.416( 15) 1.154(54) -3.838(32)
353268.37(58) 2632.111(79) 2606.343(84) -3.231(46) 19.9(11)
351242.53(22) 2631.455(26) 2606.380(27) -3.519(18) 14.456(37)
47
1.26(21) SO
-6.8( 1.2) 5.8( 1.2) 0.238(39) 28
-11.1(43) 0.0479( 13) 23
neling potentials consistent with the data, we have modeled the observed tunneling splittings using a potential of the form V= I,( f V,) [ 1 - cos( no) 1, and the c-moments of inertia of HZ0 and DzO in the kinetic energy part of the tunneling Hamiltonian. We pick 0 to be the angle which the b axis of H20 makes with the a axis of the complex. 8=0” corresponds to both hydrogens pointing towards to OC, while 8= 55.5” corresponds to a hydrogen on the a axis #‘. A two term, V, t VZpotential of the above form can be fit to the two tunneling splittings assuming both H,O and 40 rotate in the same potential. Such a parametrization is quite restrictive in the range of potential shapes one can obtain. For example, the equilibrium angle, Beg,for such a two term potential is determined solely by - V,/4V,=cos &,. The two term potential which fits both tunneling splittings is V,=745.00 and V’,= -493.21 cm-‘. For thispotential, 0,,=67.8”. We have also investigated a range of V, + Vz t V, term potentials in an effort to see if it is possible to decrease &., toward a more linear hydrogen bond and still fit the tunneling splittings. With three terms in the potential, at least one more piece of data or one more constraint must be used. We have sampled the three term potential parameter space by selecting
values of S,, and Vat 180”, and by fitting V, to the tunneling splitting in H20. V,= V( 180” ) - V,, and the choice of 0, fixes the value of V,. We varied V( 180” ) from 400 to 1100 cm-’ and 0,, from 58” to 67”. The chosen upper range for V( 180”) is well above the ab initio binding energy of 923 cm-’ calculated at the MP2/6-31G* level [ 201, while the lower limit is set somewhat more arbitrary at roughly twice the expected tunneling barrier. For a given choice of &,, we find that the barrier height which reproduces the Hz0 tunneling splitting varies by less than 5% throughout the entire range of V( 180”) sampled. Further constraints can be placed on 0,, by consideration of the nuclear hypertine constants. The proton spin-spin constant in the anti-symmetric tunnelingstate ofOC-H,O, S,,= 19.5(2) kHz [ 171, places a fairly tight lower bound on the value of 0,, The spin-spin value in the dimer is given by 33.072(P,(cos$))kHz, where 33.072 kHz is the spin-spin value calculated for the average structure of water [ 2 I] #*and $Jis the angle between the a axis of the dimer and the line connecting the protons. In the limit of planarity, (P2(cos@))=1/2(P,(cos 0) ) . Since out of plane averaging can only reduce the value of (P,(cos 4) ), the spin-spin con-
RI
“2
The angle at this position is not 104.5’/2, since we are rotating about the center of mass (c.m.) of the HZ0 and L H-c.m.H=l II” forH20. For D20, L D-c.m.-D= 116.5”.
Note that different definitions of the spin-spin constant are in common use, resulting in a factor of 4 difference between one definition and the other.
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CHEMICALPHYSICSLETTERS
Volume 176. number 1
stant of the dimer therefore requires that the effective value of theta, 8*, calculated from the Pz projection be larger than 58.5”. Tunneling reduces 13* from the value of 19,~so that 0,, must also be larger than 58.5 ‘. We find that the minimum .9,, for a three term potential of the above form which reproduces the HZ0 tunneling splitting and the spin-spin constant is 62.5’. Larger values of &., are also consistent with the data provided some out-of-plane averaging reduces the value of ( P2( cos 4) ). The values of V,, V, and r/, which reproduce the Hz0 and D,O tunneling splittings for &= 62.5” are given in table 2. The most significant structural conclusion of Yaron et al. [ 171 was that the equilibrium hydrogen bond angle C-H-O was bent by approximately 11’ and thus that &.,~64.0” in our coordinate system. The conclusion of a bent hydrogen bond was that imposed by a symmetrical vibrational averaging model in which the spin-spin constant for OC-HZ0 and the deuterium quadrupole for OC-DOH could only be brought into agreement by averaging around a bent angle - provided the tunneling potential remains constant. As noted in the above discussion, the spin-spin constant of OC-Ha0 combined with a knowledge of the water tunneling splitting also requires that the equilibrium angle is bent. Hence, the non-linear hydrogen bond determined by Yaron et al. is not simply an artifact of averaging OC-HZ0 and OC-DOH in identical potentials, but is required by the HZ0 data alone. Potential parameters which reproduce both the HZ0 and D20 tunneling splittings at &,=64’ are also provided in table 2. As noted by Yaron et al., electrostatic models predict considerably less tilt in the hydrogen bond than is required by the available data. At this point it is useful to discuss sources of model error. In addition to the limited range of potential Table 2 Three term potentials which reproduce both the H,O and D20 tunneling splittings
0 ;; (cm-l) V2 (cm-‘) V3 (cm-‘) barrier height (cm-‘)
126
Potential A
Potential B
62.5” 6 10.070 -357.339 - 113.082 229.6
64.0” 684.280 -418.850 - 72.284 217.7
4 January1991
shapes available with a three term potential of the above form, there are two other obvious sources of possible error. The first is that the moment of inertia which should be used in the kinetic energy part of the Hamiltonian may not be simply the c-moment of inertia of water. This could result from a slightly nonplanar tunneling path, a path in which the intermolecular distance changes as a function of 0 (bendstretch coupling), or a tunneling path involving a slight rotation of the OC molecule. If the O-C-O angle is slightly bent at equilibrium, as predicted from the ab initio calculations of Reed et al. [20], exchange of the hydrogens would require motion of the OC subunit. Also, even for simpler threefold internal rotations of methyl or substituted methyl groups, it is not uncommon that the observation of several internal rotation states requires that the moment of inertia of the tunneling subunit be fit to a slightly different value than that expected from the structure alone. A second source of possible error are couplings and interactions with other vibrational modes. Note that for OC-DOH, only the D-bound form is observed in molecular beam conditions and that the calculated intermolecular bond lengths for water-carbon monoxide decrease with increasing mass of the subunits [ 171. Similar effects are typical for weakly bound dimers and are indicative of changes in effective onedimensional potentials due to reduced zero-point vibrational motion in other modes. Also, even for a given isotopomer, Coriolis couplings to other modes could effect the measured tunneling splittings. In principle, the above possible sources of error could be eliminated or reduced with more complicated models. However, there is currently not enough spectroscopic data to separate these effects. We are presently exploring methods to calculate high level ab initio potentials for dimers and algorithms which combine experimental data with ab initio calculations to generate quantitative intermolecular potential energy surfaces, and will report on these efforts in the future. At this time it seems more reasonable to acquire the spectra of higher internal rotation states than to further model the potential with the currently available data. In table 3 we therefore present the energies of the first four internal rotation states for 0 ‘2C-Hz0 calculated with the two potentials given in table 2. These predictions should aid in
CHEMICALPHYSICS LETTERS
Volume 176,number 1
Table 3 Predicted transitions using the potentials in table 2. Frequencies are in cm-‘. For a-dipole transitions, the frequency given is just the difference in the tunneling energy levels. For b-dipole transitions, A+ d, was added to the difference.Transitions marked with an asterisk correspond to the observed FIR bands. Quantum numbers for the transitions are given as ( m, K,)- (m’,K; ) where m is the internal rotation quantum number (m, &)-(m’, Kb)
Potential A
Potential B
Dipole
(O,O)-(l,l)’
19.833 18.721 114.5 145.4 133.2 125.6
19.833 18.721 110.2 141.6 128.9 121.8
b b
(1, OHO, 1)’ (O,OH-l,O)
(O,O)-(:,I ) (1,0)-(-l, 1) (~,OW,O)
f b
a
searches for transitions accessing the higher energy internal rotation states. Observation of such transitions will much more tightly constrain the complex geometry and tunneling potential. The authors wish to thank Dr. David Yaron for numerous helpful discussions throughout the course of this work and for providing a copy of ref. [ 171, prior to publication. REB would like to acknowledge the support of a Bantrell Fellowship administered by the California Institute of Technology. This work was
supported in part by grants from the Packard and Sloan Foundations, the Caltech Beckman Institute and the NSF (CHEM-8957228). Acknowledgement is also made to the Donors of the Petroleum Research Fund, administered by the .4merican Chemical Society, for partial support of this work.
4 January 199I
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