J. Phys. Chem. 1994,98, 2231-2235
2231
ARTICLES Microwave Spectrum and Structure of the Argon-Formic Acid van der Waals Complex Ioannis 1. Ioannou and Robert L. Kuczkowski' Department of Physics and Department of Chemistry, The University of Michigan, Ann Arbor, Michigan 481 09- I055 Received: November 15, 1993'
The argon-formic acid van der Waals dimer was studied by Fourier transform microwave spectroscopy. The structure was found to be planar (or very nearly so), with the argon attracted to the acidic hydrogen and carbonyl oxygen. This was determined from assigning the rotational spectrum of three isotopic species: normal, AreDCOOH, and Ar*H13COOH. The distance from the argon to the carbonyl oxygen was 3.71(3) A, to the acidic hydrogen 2.81(3) A, and to the center of mass of formic acid 3.732(2) A. The deuterium quadrupole coupling constants were determined for the formic acid-dl (DCOOH) complex as xu = 135(2) kHz, Xbb = -75(2) kHz. The dipole moment was also determined as p = 1.305(1) D. An induction model was employed to explain the decrease in the dipole moment compared to free formic acid. A dispersive model was used to rationalize the structural data. The binding energy of the dimer was estimated to be 144.4(2) cm-1 from centrifugal distortion data and a Lennard-Jones potential.
Introduction
Formic acid is the simplest organic acid. The electric field produced by the carbonyl and hydroxyl groups which characterize the acid function should markedly influence its van der Waals interactions. To explore this matter, we initiated a study of the dimers between formic acid and other simple organic species such as methanol and formamide using pulsed supersonic nozzle methods and Fourier transform microwave spectroscopy (FTMW). There appear to be no previous high-resolution spectroscopic studies of a formic acid containing dimer.' Reactivity and sample-handling problems have hindered our investigation of the HCOOH.CH30H and HCOOH.HCONH2 systems. However, in these studies transitions were observed which mixing experiments showed were arising from the Ar-HCOOH complex. This system seemed interesting in its own right. Argon can serve as a simple, spherical probe of the electric fields around formic acid. Moreover, the system appeared to be a good example to test the predictive power of a simple model recently employed to rationalize the structures of a number of van der Waals complexes which contain a rare gas.2 This paper reports on the microwave spectrum and structure of the ArSHCOOH complex. Experimental Sample. Several drops of formic acid (ACS grade, Fisher Co.) were added to a 1-L bulb which was pressurized to 1-1.5 atm with dry argon. This material was expanded through a modified Bosch fuel injection valve with a 1-mm orifice under supersonic expansion conditions to form the dimers. The transitions for Ar-DCOOH were obtained similarly using 98% deuteriumenriched formic acid-dl + 5% H2O (Cambridge Isotope Laboratories). The transitions arising from the H W O O H isotope were observed in natural abundance (13C, 1.1%). Spectrometer. The spectrum from 8 to 14 GHz was obtained using a Balle-Flygare pulsed FTMW spectrometer described previously.3 One more line below 8 GHz was observed with a newly constructed FTMW spectrometer. Stark effects were
* Abstract published in Advance ACS Abstracrs, February 1,
1994.
0022-3654/94/2098-223 1S04.50/0
obtained by applying electric potentials up to 6000 V with opposite polarity to two wire-mesh parallel plate screens separated by about 30 cm which straddled the Fabry-Perot cavity. Maximum Stark shifts ranged from 2.9 MHz for the 101-110 transition to 3.1 MHz for the 2l1-202 transition. The electric fields were calibrated using SO2 ( p = 1.633 05 D).4 Timing of the gas and MW pulses was adjusted so that Doppler doublets were not observed. The axis of gas expansion was ordinarily perpendicular to the cavity axis. Line widths about 25 kHz (fwhm) were obtained except for the Ar-DCOOH transitions which were broadened about 50 kHz due to unresolved deuteriumquadrupolecoupling. Thelinecentersof the transitions were estimated to be accurate to f 4 kHz except for the unresolved ArSDCOOH transitions which have uncertainties of f 10 kHz. For several APDCOOH transitions, the quadrupole splitting was resolved using a nozzle expansion oriented collinear with the cavity axis. This produced sharp Doppler doublets (fwhm 10 kHz) separated by about 50 kHz with uncertainties of f 4 kHz.
Results and Discussion Spectra. The spectrum was characterized by strong 6-type and weak a-type transitions. The transitions of the normal isotopic species aregiven in Table 1. They were fit with the A-type Watson reduction Hamiltonians (Prepresentation) including threequartic centrifugal distortion terms. The constants obtained are given in Table 2. Seven b-type transitions were measured for the Ar-HWOOH and APDCOOH species. They are given in Table 3. The Ar-DCOOH assignment was confirmed by the quadrupole splitting patterns for four transitions (see Table 4). These transitions are also reported in Table 3 with the quadrupole perturbation removed. The Ar.H13COOH transitions were located using isotope shift predictionsand confirmed by the inertial defect (see below). These transitions were fit to an A-type Watson Hamiltonian holding the centrifugal distortion constants fixed at the values for the normal species. This is not likely to be a good approximation for the Ar-DCOOH species and probably introduces errors in the A, B, and C constants of hO.1 MHz. This reduces somewhat the utility of these constants in accurately 0 1994 American Chemical Society
2232 The Journal of Physical Chemistry, Vol. 98, No. 9, 1994
TABLE 1: Rotational Transitions of Argon-Formic Acid transition ob^ (MHz) Au (kHz) 13 575.548 16 493.103 9 516.818 13 103.679 10 656.837 10 863.074 1 1 177.824 1 1 607.489 12 160.437 12 846.809 13 678.168 9 355.007 9 669.760 9 057.830 12 457.636 12 887.296 12 072.002 5 978.929
11 1-000 212--10l 606-515 707-616 1 Io-101 211-202 312-303 4 I 3-404 514-505
615-606 716-707 303-202 312-21 1 3 I 3-21 2 404-303 413-3 12 414-313 505-414
TABLE 5: Principal Axis Coordinates and Structural Parameters for Argon-Formic Acid coordinates laol' ladb lbol Ibsl Icd Ic,l argon 0 0 carbon 2.148 2.145 0.100 b 2 < 0 0 0.068 hydrogen (H,) 3.245 3.327 0.057 b2< 0 0 0.327 structural parameters distances (A) R,& H-Ar O,bn,I-Ar Ondd-Ar
-4 3
-3 4 -4 -1 1
~
4 1
angles (deg)
-4
1 3
8 -3 -6 -3
12 115.8112(64) 1638.8824(50) 1440.4048(37)
12094.087(16) 1604.834(12) 1414.5192(93)
13 0.778
31 0.582
13 555.736 16 435.362 10 675.008 10 875.406 1 1 181.092 1 1 598.096 12 134.323
514-505
13 508.101 16 335.994 10 679.187 10871.184 1 1 163.848 1 1 562.720 12 075.076
TABLE 4 Deuterium Nuclear Quadrupole Splittings for Ar-DCOOH (MHz) J f ~ i r ~ , o F' J f f K ~ ~ p K ~ ~ OF f f v0bsa AS 111 111
111
1 IO 1 IO 1 IO 212 212 212
1 2 0 2 2 1 1 2 3
101 101 101
1 1 1 1 2 0 1 1 2
000
000 000 101 101
101
212
1
101
0
211 211
2 3 1
202 202 202
2 3 1
211
13 508.082 13508.104 13 508.139 10 679.158 10 679.197 10679,238 16 335.945 16335.914 16 335.996 16 336.047 10871.168 10 871.188 10 871.200
2.81(3)
C-O-Ar
168(3)
103(3)
~~~~
3.71(3)
3.76(3)
I,(calc) - I,(exp). b Kraitchmansubstitutioncoordinates(r,)? Distance between the centers-of-massof Ar and HCOOH.
5 0
TABLE 3 Rotational Transitions (MHz) of Argon-Formic Acid Isotopic Species Ar.HWOOH AreDCOOH 111-000
3.732(2)
0-H-Ar
~
ro coordinates from least-squares fitting of nine Ps;co coordinates held at zero (planarity assumed). AIm = 0.37 amu A2 where AI =
a The centrifugal distortion constants were held fixed at the values of the normal isotope. The uncertainties in parenthesesare 1 u. Au = u0k - ucplc A = I, - I b - In;so-called inertial defect.
212-101 1 IO-lOl 211-202 312-303 413404
~
a
TABLE 2 Spectroscopic Constants for Argon-Formic Acid Isotopomers Ar-HCOOH Ar-H13COOHa Ar.DCOOHa 12 116.629(3)b 1663.5226(7) 1459.3817(5) 17.41(1) 199.2(2) 2.173(4) 4.5 0.787
Ioannou and Kuczkowski
0 -1 1 2 0 -2 0 -1 0 1
-1 0 1
Calculated unperturbed frequencies can be found in Table 3. Au = uok - ucrlc (in kHz), where uulc is calculatedwith the coupling constants 135(2) kHz. Xbb = -75(2) kHz, x e c = -60(2) kHz. xaa a
locating the D atom in the complex. However the effect of large amplitude vibrations on the rotational constant is probably a more serious source of uncertainty on the derived structure ultimately. The derived rotational constants are given in Table 2. Dipole Moment. The Stark coefficients (AulE2) were measured for eight components arising from four transitions. The values
are given in the supplementary material Table S1 (see paragraph a t the end of this article). The transitions were selected to be sensitive to the three possible dipole components. The eight equations were least-squares fit to determine the three unknowns (pa2, pbz, pf2) using the perturbation coefficients calculated from the rotational constants in Table 2. This resulted in the values /pal= 0.086(1) D, Ipd = 1.302(1) D and Ipd = 0.018(37) D. It is seen that pa and Nb are well determined while pc is small and undetermined. The data are consistent with pc I 0.1 D. The overall dipole moment is p = 1.305(1) D with the uncertainty estimated by considering various systematic errors which arise in the measurementse6 This value can be compared to the value of 1.423 D for formic acid.' A discussion of the magnitude and orientation of the dipole moment of the complex will be given after the structure analysis. Structure. There are several indications that the complex is planar. The absence of a measurable p, is consistent with this configuration. The small positive value for the inertial defect (A = Z, - Zb - la,Table 2) is typical for a planar species. It is a result of vibration-rotation effects from the low-frequency in-plane vibrational modes.* A Kraitchman substitution calculation of the coordinates of the carbon and the hydrogen (H,) attached to it using the isotopic shift data is also informative (Table 9 . 9 The imaginary values for the b coordinates and small positive values for the c coordinates indicate that these values are small, possibly zero. These coordinates have large uncertainties (-0.1 A) arising from the neglect of vibrational effects on the rotational constants which preclude any precise determination of their values. The a coordinates are large however and probably accurate to f0.05 A. The large difference between them of 1.18 A is essentially the C-H bond distance and implies that H,, and C lie almost collinear along the a inertial axis. This would not be true unless the Ar lay in or close to the formic acid plane. Nevertheless, it cannot be shown rigorously that the complex is planar unless contributions to the rotational constants for vibrational effects are computed. This requires a knowledge of the vibrational potential function which is not presently available. Thus, the present constants and dipole moment data cannot definitively eliminate a nonplanar structure with the argon atom as much as 20° out of the formic acid plane. However, the absence of inversion tunneling splittings expected for such a nonplanar form and the lack of any compelling positive evidence for nonplanarity leads us to conclude that a planar structure is the most plausible conformation based on the present evidence. A more general approach to determine the structure of the complex is to fit the rotational constants to obtain the coordinates of the argon atom. If the structure of formic acid is unchanged upon complexation,lOJl the three coordinates locating the argon relative to the center-of-mass of formic acid can be determined from the constants. If the argon is constrained to lie in the formic acid plane, only the a and b principal axes coordinates of the argon are needed. If two of the rotational constants of the normal isotopic species are used to determine these coordinates, it can
Argon-Formic Acid van der Waals Complex Argon
The Journal of Physical Chemistry, Vol. 98, No. 9, 1994 2233
- formic acid
STRUCTURE I
n
Figure 1. Structure of argon-formic acid in the principal axis system.
be shown that four structures are found, differing in the ab quadrant of the monomer principal axes system occupied by the argon. This ambiguity is partially removed if all nine rotational constants are fit for the three isotopic species. In this case the data are consistent only with the argon positioned on the acid hydrogen side of the formic acid. However, two very similar structuresare found, one of which is listed in Table 5 and illustrated in Figure 1. The second structure is nearly the same with the argon b coordinatechanging its sign, positioning the argon in the upper ab quadrant in Figure 1. The standard deviation of these fits is AZr,, = 0.36 amu A2 (AZ = Zx(obs) - Zx(calc)). The uncertainties in Table 5 are the statistical uncertainties(1 a) arising from fitting nine equations and are sufficient to encompass both structural fits. The relationship of these parameters and uncertainties to a well-defined quantity such as the equilibrium (re) or average (rr) parameters is difficult to estimate. It seems reasonable to suggest that the three distances involving Ar in the table are within 10.1 A of the equilibrium values. The argonoxygen and argon-hydrogen distances compare well with expected values. The argon-oxygen distance based on the sum of their van der Waals radii is 3.40 The Ar-H distance in Ar-HCl is estimated to be 2.742 8113 at the linear configuration. Deuterium Quadrupole Coupling. The deuterium nuclear electric quadrupole moment produced hyperfine splittings in the low-J transitions (Table 4). These were analyzed to obtain the quadrupole coupling constants along the inertial axis xUu= 135(2) kHz, Xbb = -75(2) kHz, xcc = -60(2) kHz. The D-C bond is almost aligned with the a axis and the quadrupole tensor is nearly cylindrically symmetric,14indicating that xu,, xbb, and xcc correspond approximately to xss, xxx, x,,,, respectively in the principal axis system of the quadrupole tensor. These can be compared with the respective values estimated for free DCOOH, xzz = 166 kHz, xxx = x,,,, = -83 kHz.14 It is seen that the cylindrical symmetry of the electric field gradients has been perturbed in the complex, and all three coupling constants have decreased. The qualitative agreement is nevertheless consistent with the derived structure. The decreases are believed to arise largely from vibrational averaging effects and are given by equation
where 8i represents the amplitudeof vibration and the index stands for the quadrupole tensor axes. The observed values lead to average amplitudes of vibration estimated as 15' and 25' for the in-plane and out-of-plane soft modes of the complex which are mostly averaged over the x and y axes, respectively. The differences in the values suggest a complicated vibrational averaging motion. Electrostatic and Dispersive Analysis. Dimers of argon with a polar molecule can have a larger or smaller dipole moment than the free molecule. The change arises almost entirely from the induced moment in the argon and whether it adds or subtracts in the complex. Since in the complex is large and pn is small,
STRUCTURE I1 aHCOOH
I
bdimer
I
Figure 2. Argon-formic acid dipole moment and formic acid dipole moment, projected in the monomer and dimer principal axes systems. The vector difference, Ap, has been translated to the argon site, where is also projected. The the electric field from the formic acid (EHCOOH) magnitude and direction for f i n d u d calculated from the electric field, agree better with Ap for structure I+ than II+. See also Table 6.
TABLE 6 Comparison of the Estimated Induced Dipole Moment ( p w ) to the Difference between the Monomer and Dimer Dipole Moment (Ap,) Calculated from Measured Values ~~~
~
configurationa I+ I11+ II-
pajndb
Pb.ind
&a
APb
-0.1530 -0.1530 -0.1628 -0.1628
-0.1163 -0.1163 -0.0738 -0.0738
-0.1028 -0.1028 -0.1028 -0.1028
-0.0806 -0.1715 -0.2525 -0.3434
The sign represents the two possible orientations of p, of the dimer. I and I1 refer to the two structures consistent with the inertial data. Configurations I+ and L are in best agreement (see text, Electrostatic Analysis), with structure I+ preferred by the authors. Both dipole components evaluated from electric fields calculated for the HCOOH monomer at the site of the argon in the dimer.
it is reasonable for the induced dipole in argon to be predominantly oriented along pb and to reduce the value from formic acid. This assumes that the field lines arising from the dipole moment of formic acid make the primary contribution to the polarization of argon. A more sophisticated way to interpret this is to calculate the induced moment in the argon using an electric field at this site estimated from an ab initio calculation. This procedure has been effective in rationalizing the dipole moments in several other argon c o m p l e x e ~ .The ~ ~ electric fields E, = 0.005 437 au and Eb = 0.004 1 3 1 au were obtainedfrom a GAUSSIAN9016calculation at the HF/6-311G** level, using the published HCOOH structure.1° The stability of the calculations with change of the basis set was verified by using different basis sets, with less than 5% discrepancy for the higher order ones. The field is reported in the monomer principal axis system. This gave induced dipole moments of po,ind = -0.1 530 D and pb,ind = -0.1 163 D, using the literature polarizability for argon,17 compared to the measured values of Ap, = -0.1088 D and Apb = -0.0806 D, from differences of the dimer dipole moment to the monomer one. The dipole moments of formic acid, argon, and the complex are illustrated in Figure 2. The direction of the dipole moment in HCOOH was previously determined, based on isotopic shift effects on the dipole
2234 The Journal of Physical Chemistry, Vol. 98, No. 9, 1994 moment components.18 However, a later remeasurement’ of p for HCOOH based on laser Stark spectroscopy was found to be outside the error bars of the earlier work, raising questions about the earlier conclusion regarding the direction. We have chosen in Figure 2 the direction for HCOOH and ArmHCOOH which are best consistent with the induced moments measured for the dimer and with the field calculation. This supports a direction forpbin HCOOH which is opposite to theoneinitiallypublished.l* Table 6 contains the components of the induced dipole moment along the a and b monomer axes, calculated at the HF/6-3 11G** level, along with the difference between the monomer and dimer dipole moments, for the two possible hydrogen-bonded structures (I and 11) combined with the two possible orientations of the a dipole of the dimer along its axis (+ or -), which is also ambiguous due to its size. Good coincidence is found only for structure I (thestructurelistedinTable 5 and Figure l), with theacomponent of the dimer oriented toward the positive axis. Reasons for discrepancies between pind calculated this way and the measured Ap’s are discussed elsewhere-see, for example, ref 6. Kisiel has proposed a simple dispersive model to analyze the structures of about 30 rare gas van der Waals complexes.2 Its qualitative and even quantitative predictions were quite successful for most of the examples, with the exception of linear dimers, which usually involve molecules with acidic hydrogens. It employs a potential function which consists of a dispersive attractive part and a hard-spheres repulsive part. The first is of the form
Ioannou and Kuczkowski TABLE 7: Experimental and Model Distances (A) of Argon from Selected Formic Acid Atoms distance
model“
exptl
Ar-Ha&d Ar-C Ar-Omrbonyi
2.66 3.94 3.48
2.8 1 4.15 3.71
Dispersive model.*
Several argon-formic acid distances are compared with the experimental values in Table 7. The argon is attracted strongly to the acidic hydrogen and carbonyl oxygen. The repulsive contributions are not very large but obviously must become a factor in destabilizing the structure should Ar move closer to any interaction center. It is gratifying that the Ar is located in the general area found experimentally after adjusting the Kisiel model with some plausible assumptions. However, further adjustments in the model’s parameters are necessary to find a set which will better approximate the experimental structure and give a minimum of energy for that structure. Binding Energy. Using a simple model where the dimer is viewed as a diatom stretching along &, we can determine the stretching force constant if we consider the formic acid to be an “atom”. In that case the stretching force constant is given in terms of AJ as19
n.
where the covalent radii (r-) are used as a measure of the atomic polarizability in the P attractive term and the sum extends over all atoms of the monomer and argis the rare-gas polarizability. The repulsive term is represented by
where p is the reduced mass of the system,fis the stretching force constant, I&the rotational inertia perpendicular to the-diatomic” axis, Be is the rotational constant that corresponds to it, we is the stretching frequency, and the subscript e represents equililibrium values. If we use the AJ and B of the fit, then
f, = 0.01483(11) mdyn/A where A , c, and d a r e shape factors defined in the original paper to analytically approximate the hard-sphere repulsion, and srg,i is the sum of the vdW radii of the rare gas and any one of the atoms of the monomer. The computer program based on the model is parametrized to search for a minimum energy structure, according to the above prescription. When this model was applied to formic acid using the recommended values for singly bonded covalent and vdW radii, a nonplanar structure resulted with the Ar about 3.0 A out of the plane. However, better agreement with the planar structure in Table 5 could be obtained by making some plausible adjustments to the model and these radii. First, according to the model, a large repulsive center was placed at the midpoint of the carbonyl bond in order to account for the increased exchange repulsion due to the high electronic density of the carbonyl. The vdW radius at this steric center was chosen as the average of the C and 0 standard vdW radii. Also, the vdW radii at C and 0 were reduced by the difference of the C-0 and C - 0 standard bonds, as prescribed by the model. Finally, the acid hydrogen vdW size was reduced to compensate for the loss of electronic density to the neighboring oxygen. The amount of reduction was determined by trial and error, starting from rvdw = 1.20 A, the formal vdW radius of hydrogen. As this parameter decreased, the argon moved closer to the plane near the site expected. The best agreement with experiment occurred at fvdw = 0.6 A for an almost planar configuration. A further reduction in rvdw to 0.5 A resulted in a completely planar complex; however, the Ar was even closer to HCOOH. The atom locations, radii, and E,,, and E,, terms for the rvdw = 0.6 A calculation are listed in Table S 2 (supplementary material).
os= 34.30(53) cm-’
These values are comparable to similar systems like Ar-HCI, where the force constant for stretching is calculated to be 0.01 17 mdyn/A.20 Furthermore, one can calculate t, the binding energy for the pseudodiatomic model, considering the potential to be a 6-12 Lennard-Jones type. This gives
and for theargon-formicacidcasec = 144.4(2) cm-1, ascompared to Ar-HC1 where t = 126.3 cm-I. Summary
The spectral data have shown that the argon-HCOOH complex is planar or nearly planar. The argon atom is approximately equidistant from the carbonyl and hydroxyl oxygen atoms. The hydrogen atom is quiteclose to the argon (2.81 A). The structure suggests that both the carbonyl oxygen and acidic hydrogen interact attractively with the argon. This position for the argon is not predicted by the simple Kisiel interaction model, which works well for many other simpler argonacid systems. However, adjustments in the covalent and vdW radii used in the model and introduction of a repulsive center a t the midpoint of the carbonyl bond were proposed which lead to more stable structures, in line with the experimental results. It appears that with additional calibration structures, the Kisiel model can be revised to better handle these more complex acidic systems. Acknowledgment. We would like to acknowledge NSF for funding of this research and Prof. Z. Kisiel for providing us with
Argon-Formic Acid van der Waals Complex a program to perform the dispersive calculations and for some helpful discussions. Supplementary Material Available: Stark effect data and dispersive modeling data (2 pages). Ordering information is given on any current masthead page. References and Notes (1) Novick, S.E.Bibliography of RotarionalSpectra of Weakly Bound Complexes; Department of Chemistry, Wesleyan University, Middletown, CT, 1992. (2) Kisiel, Z.J . Phys. Chem. 1991, 95, 7605. (3) Hillig, K. W., 11; Matos, J.; Scioly, A.; Kuczkowski, R. L. Chem. Phys. Lett. 1987,133, 359. (4) Patel, D.; Margolese, D.; Dyke, T. R. J . Chem. Phys. 1979,70,2740. (5) Watson, J. K. G.J. Chem. Phys. 1967,46, 1935. (6) Andrews, A. M.; Nemes, L.; Maruca, S. L.; Hillig, K. W. 11; Kuczkowski, R. L.; Muenter, J. S . J. Mol. Spectrosc. 1993,160, 422. (7) Kuze, H.; Kuga, T.; Shimizu, T. J . Mol. Spectrosc. 1982, 93, 248. (8) Oka,T.; Morino, Y. J . Mol. Spectrosc. 1961,6,472.
The Journal of Physical Chemistry, Vol. 98, No. 9, 1994 2235 (9) Kraitchman, J. Am. J. Phys. 1953, 21, 17. (10) Davis, R. W.; Robiette, A. G.;Gerry, M. C. L.;Bjamov, E.; Winnewisser, G.J. Mol. Spectrosc. 1980,81, 93. (11) Ioannou, I. I. Ph.D. Thesis, University of Michigan, 1993. (12) Bondi, A. J. Phys. Chem. 1964,68,441. (13) Hutson, J. M. J . Chem. Phys. 1988, 89, 4550. (14) Ruben, D. J.; Kukolich, S.G. J . Chem. Phys. 1974,60, 100. (15) (a) Oh, J. J.; Hillig, K. W. 11; Kuczkowski, R. L.;Bohn, R. K. J. Phys. Chem. 1990,94,4453. (b) Taleb-Bendiab, A.; LaBarge, M. S.;Lohr, L. L.;Taylor, R. C.; Hillig, K. W. 11; Kuczkowski, R. L.J . Chem. Phys. 1989, 90, 6949. (16) Frisch, M. J.; Head-Gordon, M.; Trucks, G. W.; Formman, 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. .I. P.; Topiol, S.;Pople, J. A. Gaussian 90, Reuision I; Gaussian, Inc.: Pittsburgh, PA, 1990. (17) Orcutt, R. H.; Cole, R. H. J . Chem. Phys. 1967,46, 697. (18) Kim, H.; Keller, R.; Gwinn, W. D. J . Chem. Phys. 1962,37,2748. (19) Gordy, W.; Cook, R. L. Techniques of Chemistry. Microwave Molecular Spectra, 3rd 4.; Wiley-Interscience: New York, 1984;Vol. 18, Chapter 8. (20) Novick, S. E.;Janda, K. C.; Holmgren, S. L.; Waldman, M.; Klemperer, W. J . Chem. Phys. 1976,65, 1114.
