J. Phys. Chem. 1995,99, 2646-2655
2646
Bound States of HeHCN: Ab Initiu Calculation and High-Resolution Spectroscopy Stephen Drucker, Fu-Ming Tao, and William Klemperer" Department of Chemistry, Haward University, Cambridge, Massachusetts 021 38 Received: September 7, 1994; In Final Form: October 27, 1994@
Several rotational levels in the lowest excited bending state of HeHCN have been observed at hyperfine resolution by electric resonance spectroscopy near 100 GHz. The observed transitions correlate to the j = 1 0 transition in the limit of free internal rotation. The ground state has been characterized by using millimeter wavehicrowave double resonance. One-photon transitions in the ground state are not observable using electric 0 and J = 2 1 resonance, due to poor focusing of the nominally j = 0 levels. Ground-state J = 1 transitions were measured at 15 893.6108(41) and 31 325.2443(82) MHz, respectively. Quadrupole coupling constants eqJQ were determined to be 0.11 18(15) MHz for J = 1 and 0.199( 12) MHz for J = 2. We have calculated rovibrational energies and wave functions arising from an ab initio intermolecular potential, calculated at the MP4 level using a large basis set containing bond functions. The potential is characterized by a well depth of 25 cm-' at the centers of mass separation R = 4.27 A. The global minimum occurs at the collinear He-H-C-N configuration, and the minimum energy rises monotonically, with large angular-radial coupling, as the HCN orientation angle 8 increases from 0 to n. Calculated and observed transition frequencies, including hyperfine structure, agree to within 10%. We have used the calculated Coriolis interaction energy to deperturb the measured ground-state spectroscopic constants. This procedure permits estimates of vibrationally averaged structural parameters. We find, for the ground state, (R-2)-"2 = 4.23 A. Very large amplitude radial motion results from zero-point energy that is 75% of the 25-cm-' well depth. The hyperfine data reflect very weak anisotropy in the potential, with (P2(cosO)) = 0.092 (J = 1) and (P2(cos8)) = 0.1 15 ( J = 2). These values are very close to (P~(cos8))= 0, characteristic of a free internal rotor. The centrifugal distortion of eqJQ indicates that, as in the other rare gas-HCN complexes, significant angular-radial coupling causes the HCN to align with the intermolecular axis in the rotating complex.
-
+
I. Introduction Molecular complexes of helium have been of singular importance following tge production of He12 by Levy et al.' and their observation of the laser-induced fluorescence spectrum of the B X visible transition. The very low quenching efficiency of helium allowed a detailed study of the vibrational predissociation of the complex, and this certainly stimulated broad theoretical developments.2 Subsequent studies of Hehalogen complexes provided further opportunity to ascertain the ground-state intermolecular potential by mapping the fragment halogen rotational di~tribution.~ The structures of the complexes of He with HF? HC1; C 0 5 and C026 have been determined by rotation-vibration spectroscopy, and intermolecular potentials for these species have been obtained. Theoretical studies of helium complexes have also been very successful. Electron structure calculations for the potential energy surfaces of HeHF' and HeC08 are in good agreement with observation. The quality of the calculations is high enough that direct comparison of observed and calculated energy levels is feasible. Empirical and ab initio surfaces also agree well. In all cases, the binding energies are quite low; only a small number of bound states are predicted to exist. The low binding energy and relatively small mass of He require that the dynamics be quantal, since a large fraction of the probability density is outside the classical region. Helium complexes and helium collisions have provided a rich opportunity to study nonclassical behavior. Stuart Rice sought displays of this behavior very early, in considering the verylow-temperature He-molecule collisions that provide the vibrational relaxation in an adiabatic expansion s o ~ r c e .The ~
-
@
Abstract published in Advance ACS Abstracts, February 1, 1995.
+
necessity of accurate intermolecular potentials for helium collisions was stressed as a requirement for a reliable estimation of novel relaxation. In this paper, we consider the HeHCN complex. A paucity of helium complexes has been studied at the high spectral resolution required for the accurate measurement of nuclear hyperfine structure. Furthermore, the rare gas-HCN complexes in particular have shown quite complex dynamical behavior. The HeHCN complex is the most loosely bound rod-ball complex. In this work, we therefore hope to gain some appreciation of the dynamics of such a system by combining an electron structure calculation with observations using microwave and millimeter spectroscopy. The minimum energy configuration, Le., equilibrium geometry, of the rare gas-HCN complexes is almost certainly linear. However, the angular rigidity for all of them is low. Rotational spectroscopy of the complexes of HCN with &,lo Ar,",12and NeI3 shows an increasingly larger bending amplitude as well as larger centrifugal distortion. The angles obtained from the quadrupole coupling constant are 26.8" for KrHCN, 31.0" for ArHCN, and 46.8" for NeHCN. By use of a pseudodiatomic model, we may express the centrifugal distortion with the useful parameter y = (D/B)1'2= 2B/o (since D = 4 B 3 / 0 2 ) . We note y = 6.30 x for KrHCN, 1.03 x for ArHCN, and y = 2.15 x for NeHCN. The isotope effect observed is dramatic for both KrDCN ( y = 4.83 x loF3)and ArDCN ( y = 8.04 x while for NeDCN, y = 2.04 x which is virtually identical to the value for NeHCN. These effects have been studied in most detail for ArHCN and have been shown to be the result of barrier penetration together with large angular radial coupling, Le., a minimum energy path along which the center-of-mass separation R
0022-3654/95/2099-2646$09.00/0 0 1995 American Chemical Society
J. Phys. Chem., Vol. 99, No. 9, 1995 2647
Bound States of HeHCN decreases drastically as the angle 6 in the Jacobian coordinates changes from 0 to nl2. Since the barrier penetration ceases to be important in NeHCN, it is unlikely to play a role in HeHCN. We may anticipate, therefore, a large centrifugal distortion but expect that the study of HeDCN is not especially important. The nonrigidity expected in HeHCN, as well as the importance of measuring the low-frequency vibrational excitations, set a course for this investigation which is different from previous studies. The intermolecular potential energy surface was calculated by ab initio electron structure theory. The calculated bound-state energies and wave functions were used as a guide during the course of spectral searches to ascertain observability criteria and to assign observed lines. Finally, the results of the bound-state calculation were used to estimate Coriolis contributions to the rovibrational energy. This has permitted extraction of structural information from fitted spectroscopic constants.
11. Theoretical Method A. Ab Znitio Computation. The basis set for the present calculation of the HeHCN potential energy surface is [7s5p3d, 5s3p]-{3s3p}, a combination of the nucleus-centered set [7s5p3d, 5s3pl and the bond function set ( 3 ~ 3 ~ )The . nucleuscentered set for C or N is 7s5p3d, which is contracted from Huzinaga and Klobukowski's well-tempered Gaussian set 1 4 ~ 1 0 p ~and ~ 3 'extended ~ with three sets of d-type polarization functions (the Gaussian exponents are Q(C) = 1.252, 0.313, 0.0783; &(N) = 1.826,0.4565,0.1141). The nucleus-centered set for H or He is 5s3p, which is contracted from Huzinaga's 1 0 ~ and ' ~ extended with three sets of p-type polarization functions (a,(H) = 1.28,0.32,0.08; a,(He) = 2.56,0.64,0.16). The set of bond functions (3s3p) consists of three sets of uncontracted s- and p-type functions (a, = a, = 0.9, 0.3, O.l), all centered at the midpoint between the helium nucleus and the HCN center of mass. Molecular energies were computed by complete fourth-order Moller-Plesset perturbation theory (MP4) with frozen-core approximation. The intermolecular energy between He and HCN is given as a difference between the total energy of the complex, EH~HCN, and the sum of the monomer energies, E H ~ EHCN.The full counterpoise (CP) method" was used for the correction of basis set superposition error. The HCN unit is fixed at its !round-state vibrationally averaged geometry with rCH = 1.064 A and TCN = 1.156 It is assumed to be linear, and the bending of HCN is not considered here. All the calculations were carried out by using the GAUSSIAN 92 package.l9 B. Parametrization of the ab Znitio Surface. The calculated points on the HeHCN potential were fitted to an analytical model potential. The model follows closely the ArHCl potential by Hutson20 and incorporates the simplifying constraints introduced by Cohen and Saykally21 in fitting the ArH20 potential. The HeHCN potential is given as a sum of the exponential repulsion (Vrep), induction (Vind). and dispersion (vdlsp) energies:
+
Here D,(R) is a Tang and Toennies damping function n
Cv ~ ) ~ / m !
DJR) = 1 - e-PR
The induction and dispersion energy expansions, eqs 3 and 4, are truncated at n = 9. All the &dependent terms, A(@, /I(@, RreAe), and are expanded in a series of Legendre polynomials, Pn(cos
e(@,p(@,
X@ = DPA(C0S e>
(6)
i
ep.
where f = A , #?, R,f, C:d, or The expansion is truncated at A = 3. In order to further limit the number of parametersfi to vary in a least-squares fit, several constraints are placed on the analytical potential. First, the induction energy is completely fixed using the experimentalmultipole moments for HCN (UHCN = 3.00 D22and OHCN = 3.495 B23)and dipole polarizability of (n = 6, 7) He (aHe = 0.2048 A3 24). Second, some of the coefficients in the dispersion energy expansion are zero by symmetry; specifically, =e;p =
=
=0
(7)
Third, the reference distance &de)) is constrained to be the radial minimum (R,) along the 8 angle,
v(R,,e)
= -€(e)
(8)
where €(e)is the well depth at R,(@ and is expanded in a series of Legendre polynomials with A 5 3. The first derivative of the potential with respect to R is required to be zero at the minimum;
TIR=Rm =0
(9)
Equations 8 and 9 permit a nonlinear transformation of the potential parameters C d e ) , C9(0), and A(0) from @(e),e ( @ , and C8(@ =
where
where
(3)
(5)
m=O
Drucker et al.
2648 J. Phys. Chem., Vol. 99, No. 9, 1995
TABLE 1: Convergence of J = 0 Bound-State Energies Using the Collocation Method basis set size"
even
odd
Note that R, in the above expressions is a function of the 8 angle. All these constraints leave 13 remaining parameters to vary in the least-squares fit. We emphasize the comment by Cohen and Saykally" that the (n = 6-9) coefficients should be interpreted with care and that any changes in c 6 and C7 are easily compensated for by corresponding changes in c&? and Cg with no effect on the potential in the region of interest. C. Bound-State Calculations. To calculate the bound-state energies and wave functions, a form of the collocation method adapted for rotating systems was used. This approach was developed by Peet and YangZ5and has been fully implemented by Cohen and Saykally" in a computer program used for calculating bound states of the ArH20 complex. We have used this program for the HeHCN problem, making only minor modifications to enable the use of locally installed library routines. Though the program was originally written for complexes containing an atom and a CzV monomer, it was possible to use the same code for calculating HeHCN bound states by excluding monomer k 0 states from the basis set. The ab initio potential, as parametrized above, was used in the rovibrational Hamiltonian:
*
H = - - ti'-
a' + b d 2 + -(ti2 j
2P aR2
+
- j)2 V(R,O) (17)
2pR'
Here, j is the HCN angular momentum (expressed in bodyfixed coordinates), p is the pseudodiatomic reduced mass for the complex,Aandpois the HCN ground-state rotational constant. Expanding (J - j)2,the Hamiltonian may be written as a zeroorder term plus a Coriolis contribution:
2515
2516
2517
2518
energy, cm-'
-6.4132 -2.8878
-6.4118 -2.8851
-6.4116 -2.8846
-6.4115 -2.8845
basis set size energy, cm-'
3117 -6.4466 -2.9370
3217 -6.4477 -2.9391
3317 -6.4485 -2.9407
3417 -6.4490 -2.9417
a
Notation as defined in text.
chosen points in the coordinate space.25 This converts the differential equation into an algebraic equation, which can be solved by standard matrix methods if the number of collocation points is the same as the number of basis functions. As in variational methods, convergence is achieved by increasing the size of the basis set. In the collocation technique, convergence occurs most rapidly by optimizing the radial interval in which the quadrature points are specified. This is an important consideration if collocation is used as part of an iterative fitting procedure. However, computational efficiency is not the highest priority in the present application, because the bound states only need to be calculated a single time. Accordingly, we have chosen the radial interval somewhat arbitrarily, by fixing the lower boundary at 2.9 8, and increasing the total width by 1 8, for every six radial functions included in the basis set. Table 1 shows the results of convergence tests for J = 0 bound states. We employ the notation NRINe, where NR designates the number of radial basis functions used and Ne specifies the highest order of Legendre polynomial appearing in the angular basis. Convergence within 0.001 cm-' was reached at the 33/7 basis. This level of uncertainty is more than adequate for the dynamics calculation, since errors up to 10% are expected in the ab initio calculation of points on the potential. The size of NR required for convergence is similar to that observed by Peet and Yang in their calculation of highly excited stretching states of ArHCl.27 Large radial excursions are expected for these states, necessitating a larger basis set to span the radial space. Similar large amplitude motion is expected for all of the HeHCN bound states, given a well depth of only about 25 cm-I.
111. Theoretical Results
p r= - -Q
2pR2
A
*
J
+j L ) A ? .
+ +
The collocation routine was used to solve 9, with the Coriolis term treated variationally. The wave functions were expanded in a basis set formed as the direct product of angular and radial bases, The angular functions are simultaneous eigenfunctions of J2, j2,and J,. The radial functions were taken to be the eigenfunctions of the one-dimensional Hamiltonian
-h2 d2 H,,= -+ V(R) 2P dR2
where V(R)was chosen such that the eigenvectors span the radial space of the full two-dimensional potential surface. The onedimensional Hamiltonian was solved variationally using a basis of 40 Gaussian functions distributed evenly between 2.8 and 8.7 A, following the prescription of Hamilton and Light26with the parameter c = 0.5. The collocation method is a quadrature scheme in which the the Schrodinger equation is forced to be correct at suitably
A. Potential Energy Surface. Table 2 presents the values of the HeHCN interaction energy at various values of R and 8, with the corresponding deviations in the least-squares fit to the analytical model potential given by eqs 1-4. Table 3 gives the parameters of the model potential from the least-squares fit. Figure 1 shows the minimum separation (R,) and minimum energy (V,) as functions of the angle 8 from the fitted potential. The HeHCN potential energy surface exhibits a single minimum energy V, = -25.3 cm-' at R = 4.27 A, 8 = 0", corresponding to a collinear He-H-C-N configuration. The minimum energy rises monotonically as 8 varies from 0" to 180". The minimum energy at 8 = 90" is 6.7 cm-' above the global minimum, and at 8 = 180°, it is 8.9 cm-I above the global minimum. This indicates that the potential has the highest anisotropy around the He-H-C-N configuration, and the energy linearly increases between the T-shaped configuration and the least stable linear He-N-C-H configuration. Considerable radial-angular coupling is present in the HeHCN potential, as shown by the R,-8 curve in Figure 1. This is expected for a complex containing a polyatomic linear molecule. The minimum separation first decreases from Rm = 4.27 8, at 8 = 0" to R, = 3.59 8, at 8 = 90" and then increases
Bound States of HeHCN
J. Phys. Chem., Vol. 99, No. 9, 1995 2649
TABLE 2: Points on the ab Initio Potential Surface Used in the Least-Squares Fit ab initio ab initio energy R, 8, 8, deg energy, cm-' fit energy, cm-' 0 0 0 0 45 45 45 45 90 90 90 90 90 90 135 135 135 135 180 180 180 180 180
3.969 4.234 4.498 4.763 3.704 3.969 4.234 4.763 3.250 3.440 3.704 3.969 4.234 4.763 3.704 3.969 4.234 4.763 3.704 3.969 4.234 4.498 4.763
-9.43 -24.91 -22.66 -16.90 -18.60 -21.50 -17.61 -9.37 -3.00 -16.16 -17.91 -14.71 -11.00 -5.73 -15.29 - 16.96 -13.91 -7.57 +2.67 -14.77 -15.87 -12.90 -9.64
0.04 0.25 -0.25 0.07 -0.49 0.13 -0.03 0.21 0.04 0.48 0.10 -0.28 -0.26 0.05 -0.62 0.14 0.01 0.27 -0.02 0.45 -0.18 -0.21 0.01
TABLE 3: Parameters Obtained from the Least-Squares Fit of the ab Initio Potential Po,
A-'
€0,
cm-'
€1,
cm-I
cm-' cm-I R i , 8, €2,
€3,
RL, 8,
R i , 8, R i , 8,
hartree a$
elp, hartree ao6 hartree, e:p, hartree
aO7
aO7
4.78 19.3 3.49 1.47 0.973 3.79 0.0192 0.395 0.065 19.4 0.342 16.3 -0.460
to R , = 4.09 8, at 8 = 180". This behavior is characteristic of rare gas-HCN systems and is not seen in rare gas-HX systems. There is no ab initio or experimental potential for HeHCN available for a direct comparison to our present calculations. Comparisons with known potentials of other systems may be useful. First, our well depth of 25.3 cm-' for HeHCN might be underestimated by about lo%, as expected from the similar calculations on rare gas and other complexes such as HeC0,8 ArHF, ArH20, and ArNH3.31332The underestimate appears to be systematic and is mainly attributed to the insufficient correlation treatment by the MP4 theory. After taking this error into account, the HeHCN well depth is comparable to those for other He-molecule complexes. For example, the HeCO potential has a well depth of 22.5 cm-I 33 (our MP4 calculations gave a value of 20.5 cm-' x). Also, the HeHF potential has a well depth of 35 cm-' (~emiempirical~) or 39.2 cm-' (ab initio7), similar to the estimate of 41.0 cm-I for HeC02.6 The potential well depth appears to be slightly greater for the He complexes with molecules containing secondrow atoms. For example, the well depth was estimated to be over 40 cm-' for HeC123,34and over 60 cm-I for HeC1F.35 The HeHCN potential anisotropy appears to be unique in all of the known helium complexes. The HeC033,8and HeC02 complexes have only one potential minimum, at the T-shaped configuration, while the HeHF ~ o m p l e xhas ~ . ~two minima, at the linear He-H-F and linear He-F-H configurations with
4.3 4.1 3.9 3.7 3.5 -16
-18 -20
-22 -24 -26
i 45
0
90
135
180
e (") Figure 1. Radial minimum distance R, and energy V , as functions of the angle 8.
an energy difference of about 4 cm-I and a large barrier at the T-shaped configuration. Both of the HeCl2 and HeClF complexes have three potential minima, at the T-shaped and two linear configuration^.^^^^,^^ The potential anisotropy of HeHCN may be very similar to that of ArHCN. Early experimental results for the ArHCN complex were analyzed on the basis of a model potential that had two minima, at the linear b H C N and T-shaped configuration^."^^^ A barrier near 45", in conjunction with strong angular-radial coupling, could explain the unusual dependence of the centrifugal distortion constant on isotopic substitution. However, no T-shaped minimum is evident from ab initio calculation^.^^^^^ A detailed ab initio potential energy surface for ArHCN, similar to the present HeHCN surface, was used to obtain rovibrational energies which are in good agreement with experimental observations.' 1,39,40 B. Bound-State Calculation. Figure 2 is an energy level diagram showing the HeHCN bound states calculated from the ab initio potential using a 34/7 basis set. The level pattern shows that the HCN monomer's rotational spacing (2bo = 88.6 GHz) is not seriously altered by the effect of potential anisotropy. Hence, the qualitative features of the dynamics are most clearly described by using a space-fixed reference frame. (Body-fmed coordinates were used in the bound-state calculation only for their convenience in expressing the potential.) In spacefixed coordinates, the Hamiltonian is
3
The operators and represent the angular momentum of the pseudodiatomic complex and the HCN subunit, respectively. In the absence of anisotropy,j and 1 are good quantum numbers, with j establishing the pattern of "bending vibrational " levels and 1 imparting rotational structure. The total angular momentum, J = 1 j, is, of course, also conserved, though J is not a pattern-forming quantum number. In the zero anisotropy limit, a given j , I level will have degenerate J states ranging from J =ll-jl toJ=Il+jl. If the actual anisotropy is finite but very small compared to the monomer's rotational spacings (as in HeHCN), then the j ,
+
Drucker et al.
2650 J. Phys. Chem., Vol. 99, No. 9, I995 ---------
0.00
-1.58 -1.62 -1.88
-2.61 -2.67 -2.94 -3.20
~
___ ___ ~
-5.00
-5.96 -6.45
~
~
~
Energy (c”
~
ground-state rotational levels. This ensures that interactions with t h e j = 1 states cause the ground-state levels to shift downward in energy. While the dipole matrix elements connecting rotational levels within the ground state are nonvanishing, we expect one-photon pure rotational transitions to be unobservable in our spectrometer, since these states are nonfocusing. The above arguments, when applied to the excited vibrational levels asymptotically connected to j = 1, show that these levels have positive Stark coefficients and, therefore, are focusing.
dissociation limit
-
1 1 1
2 2 2
+ + t -
1 1 1 1
1 1 1 2 1 0 0 1
+
2 3 1
0
2
2
- 0
1
1
IV. Experiment
+ o o o P
J
~
J
)
Figure 2. Bound-state energies of HeHCN, calculated from the ab initio potential.
1 quantum numbers serve as approximate labels. J is still a rigorously good quantum number, as is the parity under inversion of space-fixed coordinates, p = (-ly’+‘. As seen in Figure 2, the anisotropy lifts the J degeneracy associated with a particular j , 1 level forj, 1 > 0. Because the monomer rotation is essentially decoupled from the molecular axis, the space-fixed projection of j is nearly conserved. This is in contrast to semirigid complexes such as ArHCN or ArHCl, in which Z and 17 labels usefully”1-40 describe the lowest bending states in terms of the body-fixed projection of j . When a body-fixed basis is used to calculate these states in HeHCN, the characteristic rotational pattems are distorted beyond recognition by the II-Z Coriolis interaction. The bound-state calculation has been a very helpful guide in our spectroscopic studies, both in predicting spectral features and in identifying the most feasible experimental approaches. Of particular relevance to our experiments is the Stark effect of the energy levels. The Fraser-type spectrometefl2 utilizes a multipole focuser. For a molecule to be focused onto the detector, it must be in a quantum state with a positive Stark effect, i.e., a state whose energy increases with electric field. The observability of a transition then depends upon the difference in the Stark effect of the two radiatively connected levels, as well as the population of the levels. While the Stark effect of all of the levels may be calculated directly in terms of the intermolecular potential and dipole moment surfaces, it is useful to have a qualitative picture. Since the polarizability of helium is virtually zero, the dipole moment surface is determined entirely by the orientation of the HCN submolecule. In the space-fixed basis mj 1 m,), the matrix elements of the Stark effect are (j mj I~HcNEI j f 1 mj)dn. ( E = E,, E, = Ey = 0). The composition of the ground vibrational state of HeHCN is primarily j = 0. The strongest Stark interaction is, therefore, with j = 1 basis states. The admixture of j = 1 in the ground state is small enough that the overall Stark effect for these rotational levels is dominated by connections to the lowest bending states (primarilyj = 1). These states are about 7 times higher in frequency than the spacing between
Rovibrational spectra of HeHCN were recorded by using a Fraser-type spectrometer which has been described in detail previously.40 The only modification for the present experiments is that a 1.6-millimeter-diametercircular disk used as a beamstop was replaced with a 0.7-millimeter-diameter stopwire, to increase the solid angle of the molecular beam reaching the detector. HeHCN is formed in a supersonic expansion of roomtemperature helium containing 0.35% HCN. The gas expands at a stagnation pressure of 5 atm through a 40-pm circular nozzle. The millimeter wave radiation source is a Gunn oscillator (J. E. Carlstrom Co.), optimized for the range 85-115 GHz and phase locked (XL-Microwave) to a PTS Model 120 synthesizer. The output power from the Gunn oscillator varies between 15 and 40 mW, depending on frequency. This power level is about 20 dB greater than necessary to saturate single hyperfine components of the observed rovibrational transitions in HeHCN or the J = 1 0 transition in HCN. The excessive power is exploited to produce 2 MHz line broadening, thereby permitting large frequency increments (typically 200-400 M z ) to be used while searching for new lines. A Hewlett-Packard 8672A synthesizer is employed as a microwave source for millimeter wave/microwave doubleresonance experiments. Synthesized radiation from 2 to 37 GHz is obtained by using a commercial doubler with a 10-dB amplifier (Avantek) operating in the range 18-40 GHz. Power of 1 mW is sufficient to observe HeHCN pure rotational transitions. We fist attempted to observe pure rotational transitions within the ground vibrational state, as was readily done in ArHCN.’] We estimated the HeHCN rotational constant to be 7-9 GHz. This estimate relied on preliminary results from ab initio calculations, as well as extrapolation of measured rotational constants for NeHCNI3 and ArHCN.” The latter was guided by the rotational constants of HeHX? NeHX,44,45 and ArHX46s47 (X = C1 or F). We unsuccessfully searched for the J = 1 0 transition in the region 13-20 GHz. The microwave power was adequate to saturate the J = 1 0 transition if the vibrationally averaged dipole moment was at least 0.8 D. The absence of the J = 1 0 signal suggests that no component of J = 1 is focusable, because J = 0, being the lowest level, necessarily exhibits a negative Stark effect. We conclude from the apparently poor focusing of groundstate J = 1 molecules that the Stark effect strongly connects the ground state (nominallyj = 0) with the lowest bending states (j = 1). We expect the latter to be shifted upward in energy by this Stark interaction and be focusable in our electrostatic hexapole. As discussed above, the ab initio results lead to the same prediction, and we decided that a search for j = 1 0 transitions would be most profitable. The search began at the frequency of the HCN J = 1 0 line, 88.6 GHz, and included the region up to 115 GHz. Transitions were observed at 101.4 and 105.8 GHz.
-
-
-
-
-
-
J. Phys. Chem., Vol. 99, No. 9, 1995 2651
Bound States of HeHCN
TABLE 5: Ground-State Double-Resonance Transitions in HeHCN
3c2
J', F' J' F'
-J , F J
F
~
obsd - calcd,
v , MHz ~
1 1 1 2 2
1 0 1 15 893.475(15) 2 0 1 15 893.635(15) 0 0 1 15 893.890(15) 1 1 0 31 325.140(30) 2 1 1 31 325.210(30)
2
3
1 2 31 325.265(30)
MHz
millimeter wave pump(s), MHz 101 432.880 101 432.241 101 432.457 101 432.457 101 432.880 105 795.257 101 432.241
+0.004 -0.004 +O.OOO +O.OOO +O.OOO
-0.001
a Uncertainties quoted are larger than the resolution of the microwave source due to excessive Doppler broadening.
1014320
Figure 3. G,l) = (1, 1)
-
1014325
1014330
frequency (MHz)
(0, 1) R(1) transition. This scan is a result of 54 averages over 65 min at a resolution of 10 kHz and a time constant of 0.3 s. The hyperfine components are labeled F' F".
-
TABLE 4: Observed Millimeter Wave Transition Frequencies in HeHCN J', F'
-
J". F"
J'
F'
J"
F"
v , MHz ~
obsd - calcd, MHz
2 2 2
3 1 1
1 1 1 2 2
2 0
101 432.241(10) 101 432.457(10) 101 432.880(10) 105 795.257(10) 105 795.365(10)
+o.ooo
a
I 2
-0.002 f0.002
Uncertainty is the frequency increment
The 101.4-GHz transition is shown at high resolution in Figure 3. The I4N nuclear quadrupole hyperfine structure is well resolved, and the frequencies of the individual components are listed in Table 4. The relative intensities reflect not only the partitioning of oscillator strength among the hyperfine components but also the instrumental factors arising from the dependence of focusing on the total angular momentum F = I J. Consequently, not all hyperfine components have been observed. A lower state J assignment of 1 was ascertained by double resonance with the ground-state J = 1 0 and J = 2 1 transitions. The double-resonance results are discussed in detail below. For the transition at 105.8 GHz, two hyperfine components were observed, at frequencies listed in Table 4. Double resonance with the ground-state J = 2 1 transition establishes a J" = 2 assignment. The two millimeter wave transitions were observed as an increase of the molecular beam intensity reaching the detector. This confirms that the excited state is preferentially focused in the hexapole field. At 35 kV, breakdown occurs within the hexapole, which limited the optimization of the HeHCN signals with respect to focuser voltage. Searches for HeHCN transitions were conducted using a focuser voltage of 34 kV. It is possible that other transitions could be observed if a higher voltage were attainable. It is noteworthy that a focusing voltage of only 26 kV is required to optimize the HCN J = 1 0 transition. The necessity of using significantly larger voltages for HeHCN reflects the dilution of j = 1 character in the bending state and the larger energy gap between strongly interacting levels. Although the direct search for pure rotational transitions was unsuccessful, several have been observed using millimeter wave/ microwave double resonance. In these experiments, the unmodulated millimeter wave source is used to populate a rovibrational level of t h e j = 1 manifold, while the microwave source is swept over a pure rotational resonance. As discussed above, molecules in the bending states are preferentially focused onto the detector, so a microwave transition can be detected if
+
-
+
+
-
it changes the population distribution within the vibrationally excited state. This technique permits observation of pure rotational transitions occurring in the ground state, despite our inability to detect ground-state molecules directly. The results from the double-resonance experiments are given in Table 5. Each of the indicated microwave transitions was recorded while the millimeter-wave source was locked to the frequency of a single hyperfine component of either the 101.4GHz or the 105.8-GHz line. The experimental uncertainty cited for these spectra is about 5 times the resolution available from the microwave synthesizer. The measurement precision is diminished by excessive Doppler broadening (170 kHz for 16GHz radiation and 330 kHz for 31-GHz radiation), resulting from the use of open waveguide in transmitting the microwave radiation. (Rectangular line shapes were observed with a calculated width of 3.2 x lo5 c d s , which is nearly twice the terminal velocity of the helium carrier gas in the molecular beam. This shows the microwave radiation is almost isotropic within the resonance region.) In contrast, the millimeter-wave radiation is transmitted by a standard-gain horn and focused into the molecular beam by a Teflon lens. In one-photon millimeter-wave spectra, observed line widths of about 80 kHz at 101 GHz are due to much more modest Doppler broadening produced by rapid focusing of the directed radiation beam. The hyperfine structure of the microwave transitions is well resolved, despite the excessive line widths. The high resolution is available because the millimeter-wave pump selects only one F level as the initial or final state of the microwave transition. Moreover, in each of the cases reported in Table 5, a single allowed transition was observed. Thus, although these lines are excessively broadened, none are superimposed. The observed hyperfine structure confirms that the transitions at 15.9 and 31.3 GHz occur in the same vibrational state. With the assignments J = 1 0 and J = 2 1, respectively, it is possible to fit quadrupole coupling constants eqJQ and hyperfine-free line centers to better than experimental precision. The hyperfine structure has been corroborated by the results of Gutow~ky$~ who recorded the J = 1 0 transition directly by using a Fourier transform microwave spectrometer at the frequency observed here in double resonance. Individual hyperfine frequencies reported here agree with those measured by Gutowsky, within experimental error. A third microwave transition has been observed at 3 1.1 GHz. Combination differences involving this line and those at 3 1.3 and 101.4 GHz were used to predict a transition occurring at 101.2 GHz. The latter had not been located in the initial search but was subsequently observed with appreciable signal averaging. Figure 4 shows the observed lines, with J assignments where possible. Also indicated a r e j and 1 labels specifying the basis states to which the observed levels correlate in the isotropic limit. The upper state j , 1 assignments are established by rigorous parity selection rules and a A1 = 0 propensity rule. +
+
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Drucker et al.
2652 J. Phys. Chem., Vol. 99, No. 9, 1995
written in body-fixed coordinates, to analyze the spectral results. The basis set for thjs analysis is conventionally taken to be the eigenfunctions of €#‘, with the Coriolis term treated perturbatively. The molecular constants so obtained characterize basis states of definite lKJ,i.e.,Z and I7 states. We follow this general approach for HeHCN but reiterate that the weak anisotropy gives rise to extreme Coriolis mixing between the lowest ll and Z bending states, having high-order effects even on the ground state. Because observations of the bending states have been limited, we will rely on the results of the bound-state calculation to “deperturb” the empirically determined constants and facilitate the description of a pure Z-Le., rotationless-ground state. The observation of the ground state J = 1 0 and J = 2 1 transitions allows us to fit the hyperfine-free line centers to the effective Hamiltonian:
31.1-
101.4
-
,
I
I I,
t
,
15.9
+
0
2
2
-
0
1
1
101.2
I
31.3-
