Rotational spectra and structures of the C6H6-HCN dimer and Ar3-HCN tetramer

Article abstract of DOI:10.1063/1.469579

A comparative study has been made of the rotational properties of C6H6-HCN and Ar3-HCN, observed with the Balle/Flygare pulsed beam, Fourier transform microwave spectrometer.C6H6-HCN is found to be a prolate symmetric top and Ar3-HCN an oblate one, both with the H in the middle.The rotational constants B₀, D_J, and D_JK of the parent species are 1219.9108(4) MHz, 1.12(3) kHz, and 18.32(8) kHz for C6H6-HCN,and 886.4878(1) MHz, 10.374(2) kHz, and 173.16(1) kHz for Ar3-HCN.Rotational constants are reported for the isotopic species C6H6-H13CN, -HC15N, and 13CC5H6-HC15N, and for Ar3-HC15N and -DCN.Analysis of the 14N hyperfine interaction χ finds its projection on the figure axis to be -4.223(4) MHz in C6H6-HCN and -1.143(2) in Ar3-HCN.They correspond to average projection angles θ between the HCN and figure axes of 15.2 deg and 45.3 deg, respectively.A pseudodiatomic analysis of the rotational constants gives the c.m. to c.m. distance to be 3.96 Angstroem in C6H6-HCN and 3.47 Angstroem in Ar3-HCN.While the rotational properties of C6H6-HCN are normal those of Ar3-HCN display a long list of abnormalities .They include a J-dependent χ(14N) similar to that of Ar-HCN; a very large projection angle θ, large centrifugal distortion including higher-order terms in H_J and H_JK; splitting of the K=3 transitions into J-dependent doublets; and the ready observation of an excited vibrational state.These behavior differences are related qualitatively to the interaction surfaces for the two clusters, calculated with the molecular mechanics for clusters (MMC) model, and discussed.The potential minimum for C6H6-HCN is smooth, circular, steep except for a flat bottom, and deep (1762 cm^-1).That for Ar3-HCN is tricuspid, with large gullies, and shallow (507 cm^-1).In addition to the dispersion forces, the dominant interaction forming C6H6-HCN is between the benzene quadrupole moment and the HCN dipole moment, a strong 4-2 potential.That in Ar3-HCN is polarization of the spherical Ar by the HCN dipole and quadrupole moments, a weak 0-2,4 potential.

Full text of DOI:10.1063/1.469579

Rotational spectra and structures of the C6H6–HCN dimer and Ar3–HCN tetramer
H. S. Gutowsky, E. Arunan, T. Emilsson, S. L. Tschopp, and C. E. Dykstra
Citation: The Journal of Chemical Physics 103, 3917 (1995); doi: 10.1063/1.469579
View online: http://dx.doi.org/10.1063/1.469579
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Rotational spectra and structures of the C6H6–HCN dimer
and Ar3–HCN tetramer
H. S. Gutowsky, E. Arunan,a) T. Emilsson, and S. L. Tschopp
Noyes Chemical Laboratory, University of Illinois, Urbana, Illinois 61801
C. E. Dykstra
Department of Chemistry, Indiana University-Purdue University Indianapolis, 402 N. Blackford Street,
Indianapolis, Indiana 46202
͑Received 1 May 1995; accepted 1 June 1995͒
A comparative study has been made of the rotational properties of C6H6–HCN and Ar3–HCN,
observed with the Balle/Flygare pulsed beam, Fourier transform microwave spectrometer.
C6H6–HCN is found to be a prolate symmetric top and Ar3–HCN an oblate one, both with the H in
the middle. The rotational constants B0, DJ , and DJK of the parent species are 1219.9108͑4͒ MHz,
1.12͑3͒ kHz, and 18.32͑8͒ kHz for C6H6–HCN, and 886.4878͑1͒ MHz, 10.374͑2͒ kHz, and
173.16͑1͒ kHz for Ar3–HCN. Rotational constants are reported for the isotopic species
C6H6–H13CN, -HC15N, and 13CC5H6–HC15N, and for Ar3–HC15N and -DCN. Analysis of the 14N
hyperfine interaction ␹ finds its projection on the figure axis to be Ϫ4.223͑4͒ MHz in C6H6–HCN
and Ϫ1.143͑2͒ in Ar3–HCN. They correspond to average projection angles ␪ between the HCN and
figure axes of 15.2° and 45.3°, respectively. A pseudodiatomic analysis of the rotational constants
gives the c.m. to c.m. distance to be 3.96 Å in C6H6–HCN and 3.47 Å in Ar3–HCN. While the
rotational properties of C6H6–HCN are ‘‘normal,’’ those of Ar3–HCN display a long list of
‘‘abnormalities.’’ They include a J-dependent ␹͑14N͒ similar to that of Ar–HCN; a very large
projection angle ␪; large centrifugal distortion including higher-order terms in HJ and HJK ; splitting
of the Kϭ3 transitions into J-dependent doublets; and the ready observation of an excited
vibrational state. These behavioral differences are related qualitatively to the interaction surfaces for
the two clusters, calculated with the molecular mechanics for clusters ͑MMC͒ model, and discussed.
The potential minimum for C6H6–HCN is smooth, circular, steep except for a flat bottom, and deep
͑1762 cmϪ1͒. That for Ar3–HCN is tricuspid, with large gullies, and shallow ͑507 cmϪ1͒. In addition
to the dispersion forces, the dominant interaction forming C6H6–HCN is between the benzene
quadrupole moment and the HCN dipole moment, a strong 4-2 potential. That in Ar3–HCN is
polarization of the spherical Ar by the HCN dipole and quadrupole moments, a weak 0–2,4
potential. © 1995 American Institute of Physics.
I. INTRODUCTION
proved understanding of them substantially so the same ap-
proach is applied here to C6H6–HCN and Ar3–HCN.
Our report is primarily on Ar3–HCN, the third member
of the Arm –HCN series we have looked at. The first was
Ar–HCN in which we found the 14N quadrupole interaction
In recent studies of weakly bound ‘‘rod and ball sys-
tems,’’ HCN has become the favored rod for exploring how
molecular size and shape affect gas-phase intermolecular in-
teractions and small-cluster properties. A striking example of
the results being obtained in this area1 is the strong coupling
found in the quasilinear Ar–HCN dimer between radial and
bending motions of the HCN. Moreover, in the rare gas
series2 Rg-HCN, the motional coupling is weaker in Kr–
HCN and much stronger in Ne–HCN. This is in accord with
the MMC ͑molecular mechanics for clusters͒ model,3 which
was used to predict the potential energy surfaces ͑PES͒ for
the dimers. The stability of the Rg-HCN increases with the
polarizability of the Rg, giving MMC values of 21, 37, 85,
and 108 cmϪ1 with He, Ne, Ar, and Kr as the rare gas.
Moreover, the PES are systematically shallower and more
isotropic for the smaller Rg, accounting, at least qualita-
tively, for the mobile internal dynamics of Ar–HCN and
Ne–HCN.2 Comparison of the Rg-HCN members has im-
constant ␹ to be J dependent because of the radial-angular
aa
coupling in its centrifugal distortion.4 The dimer is now rela-
tively well understood,1 except possibly for pairs of very
weak KÞ0 transitions5 approximately symmetrical about the
Kϭ0, Jϭ1→2, and 2→3 transitions of the linear species.
Also, Ar2–HCN was found to be a T-shaped asymmetric top
with C2v symmetry,6 similar to Ar2–H2O7 and Ar2–HX with
XϭF,Cl.8,9 However, the rms deviation of the fit for
Ar2–HCN is poor ͑300 kHz͒ and the centrifugal distortion
and inertial defect are huge, indicating significant deviations
from the conventional asymmetric top model.10
Our results for Ar3–HCN exhibit a similar pattern, al-
though less extreme. The projection of ␹͑N͒ onto the figure
axis (c) is found to be J dependent, but only a third that of
the Ar–HCN dimer. Similarly, the centrifugal distortion is
large but not huge. On the other hand, the hydrogen halide
analogs,11,12 Ar3–HX, exhibit ‘‘normal behavior,’’ as do the
dimers13,14 and trimers,8,9 Ar–HX and Ar2–HX. This implies
a͒
Current address: Department of Chemistry, Indian Institute of Technology,
Kanpur, India 208 016.
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Gutowsky et al.: C6H6–HCN dimer and Ar3–HCN tetramer
TABLE I. Rotational transition frequencies observed and fitted for the symmetric top 15N, parent, and 13C isotopic species of C6H6–HCN.
C6H6–HC15N
C6H6–HCNb
Observed
Residuea
Observed
Residue
J→J ,K
͑MHz͒
͑kHz͒
J→J ,K
͑MHz͒
͑kHz͒
Ј
Ј
0→1,0
1→2,0
1
2369.3786
4738.7306
4738.6620
7108.0332
7107.9263
7107.6056
9477.2579
Ϫ0.3
Ϫ1.3
1.5
0→1,0
2439.8169
4879.6066
4879.5352
7319.3425
7319.2352
7318.9032
Ϫ0.3
Ϫ0.8
1.1
1→2,0
1
2→3,0
1
Ϫ0.2
0.0
2→3,0
Ϫ1.1
1.6
1
2
2
0.5
0.6
3→4,0
0.4
C6H6–H13CNb
1
2
9477.1148
9476.6867
0.0
0.2
c
c
c
0→1,0
1→2,0
1
2406.9657
4813.9017
4813.8357
3
9475.9718
11 846.3783
11 846.1997
11 845.6649
11 844.7729
11 843.5233
Ϫ0.9
Ϫ0.2
Ϫ0.3
0.2
4→5,0
1
2
3
4
0.4
0.0
aResidueϭobserved-calculated.
bLine centers determined by fitting 14N hfs.
cFitted exactly to give B0 , DJ , and DJK
.
III. RESULTS AND ANALYSIS
that the oddball behavior of Arm –HCN requires the rod-like
character of the HCN, but it leaves unexplored the role of the
three-fold symmetric PES generated by the Ar3 and HCN
interaction. Therefore we extended our work to the benzene-
HCN dimer, which proved to be a normal symmetric top.
These results suggest that the unusual behavior of
Arm –HCN requires a PES characteristic of both the rare gas
and HCN. We have sought to identify such properties for
Ar3–HCN by comparing the results of MMC calculations of
the PES for C6H6–HCN with those for Ar3–HCN. The de-
tails and outcome of this approach are presented below.
A. Benzene–HCN dimer
1. Search, hfs, and rotational constants
As mentioned in the Introduction, the benzene–HCN
dimer was investigated to see what light it might shed on the
dynamical peculiarities attributable to the size and shape of
the HCN in the Rg-HCN dimers.1,2 The C6H6–HX ͑XϭF,Cl͒
dimers are known to be symmetric tops, with the HX along
the benzene C6 axis, the H end nearest the benzene face.17,18
However, in C6H6–N2, the N2 is found to be parallel to the
ring, centered on the C6 axis, and exhibiting internal rotation
against a small barrier.19 Nonetheless, MMC calculations for
C6H6–HCN by Augspurger and Dykstra20 gave a PES with a
sharp global minimum when the HCN is on the benzene C6
axis, favoring a benzene–HX structure. So a search was
made, centered on the B0 of 1180 MHz predicted for the
axially symmetric equilibrium structure.
Symmetric top transitions were readily found for the par-
ent species, C6H6–HC14N, with a B0 of 1220 MHz, and mea-
surements were extended to several isotopic species with the
results given in Tables I–IV. The frequencies for low J,K are
listed in Table I for the HCN parent, 15N, and 13C species. In
the case of the parent and 13C isotopomers, the frequencies
are the unperturbed line centers obtained by fitting the 14N
II. EXPERIMENT
The rotational spectra were observed with the Balle/
Flygare Mark II pulsed nozzle, Fourier transform microwave
spectrometer, which has been described previously.15,16 The
benzene-HCN dimer was generated by using a gas mixture
of 0.1% HCN ͑Fumico͒ in a carrier gas of neon ‘‘first run’’
͑70% Ne and 30% He͒, with 4% of the carrier gas diverted
through a bubbler containing benzene at an ambient tempera-
ture. The argon was obtained from Liquid Air and the neon
first run from MG Industries. The isotopic species of HCN
with 13C or 15N were synthesized from the enriched KCN
͑Isotec͒ precursor by standard methods. DC14N was prepared
by reacting KCN with D3PO4, the latter by dissolving P2O5
in D2O ͑Sigma͒. The Ar3–HCN was formed with a gas mix-
ture of 0.25% HCN in a carrier gas of 50% argon and 50%
neon first run. Backing pressures of 1.3 and 1.0 atm were
used for the benzene–HCN and Ar3-HCN, respectively. Both
of the clusters produced the strongest signals with a 0.3 ␮s
microwave pulse. The frequencies measured usually have a
standard deviation of less than a kHz, provided that any hy-
perfine structure ͑hfs͒ is fully resolved.
quadrupolar hyperfine structure ͑hfs͒. In the fitting, ␹ ͑N͒
aa
was found to be independent of J. A more complex example
of hfs fitting is given in Table II that describes the combined
effects of the 14N and the much smaller D quadrupole inter-
actions on the Jϭ0→1 transition of C6H6–DC14N. Table III
gives the transition frequencies for low J͑0,1,2͒ observed at
natural abundance for the asymmetric top species
13CC5H6–HC15N.
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Gutowsky et al.: C6H6–HCN dimer and Ar3–HCN tetramer
3919
TABLE II. The 14N and D hyperfine structure observed and fitted for the
Jϭ0→1 transition of C6H6–DCN.
TABLE IV. Rotational and hyperfine interaction constants obtained for sev-
eral isotopic species of C6H6–HCN by fitting the assigned frequencies in
Tables I–III.
Observed
Residue
F ,F→FЈ ,F
͑MHz͒
͑kHz͒
Isotopic
species
Ј
B0
͑MHz͒
DJ
͑kHz͒
DJK
͑kHz͒
␹ ͑N͒
aa
͑MHz͒
1
1
1,2→1,1
1,2→1,2
1,1→1,0
1,0→2,1
1,2→2,3
1,1→2,2
1,2→0,1
2426.9722
2427.0031
2427.0577
2428.2355
2428.2582
2428.2993
2430.1683
Ϫ0.8
Ϫ3.0
4.8
2.2
0.9
a
C6H6–HCN
C6H6–HC15N
C6H6–H13CN
C6H6–DCNb
1219.9108 ͑4͒ 1.12 ͑3͒
1184.6916 ͑1͒ 1.074 ͑2͒ 17.845 ͑5͒
1203.4853
1214.028
18.32 ͑8͒
Ϫ4.223 ͑4͒
•••
Ϫ4.226 ͑7͒
Ϫ4.220 ͑6͒
•••
1.24
16.5
c
Ϫ4.8
0.7
13CC5H6–HC15N 1179.0339 ͑2͒ 1.059 ͑3͒ 17.65 ͑4͒
aFound to be independent of J.
bOnly the Jϭ0→1 transition was analyzed. From it ␹͑D͒ was found to be
206 ͑10͒ kHz.
c(B0ϩC0)/2 for the asymmetric top. The rotational constants are A0ϭ2823
͑7͒; B0ϭ1181.7168 ͑1͒; C0ϭ1176.3513 ͑2͒ MHz.
The rotational and quadrupolar coupling constants found
in the various fittings are summarized in Table IV. The line
centers and hfs were fitted in the usual manner with the
Hamiltonian
quadrupole coupling constant from its value ␹ in the free
0
monomer. For an axially symmetric interaction, the coupling
HϭHRϩHQ ,
͑1͒
constant ͑␹ ͒ observed in the dimer is then given by the
gg
in which HR is the semirigid rotor contribution,
HRϭB0J2ϪDJJ4ϪDJKJ2K2,
projection of ␹0 onto the inertial axis with the transition mo-
ment,
͑2͒
and HQ is the quadrupole interaction of 14N and of D, when
present. HQ was treated by standard methods21 with the basis
set FϭJϩIN for 14N species and with JϩIDϭF1 and
F1ϩINϭF for C6H6–DC14N.
␹
ϭ ␹ /2͒ 3 cos2 ␪ Ϫ1 ,
͑3͒
͑
Ј
͗
͘
gg
0
where ␪Ј is the instantaneous angle. By averaging over ␪Ј,
one obtains
1/2
␪ϭarccos cos2 ␪
,
͑4͒
Ј
͗
͘
2. Structural analysis
which is an operational definition of the HCNs ‘‘floppiness.’’
The basic symmetry of the C6H6–HCN dimer given in
Fig. 1 is established by the symmetric top spectra observed
for the dimers between the four linear isotopic species of
HCN and the D6h benzene. The finding of J→Jϩ1 transi-
tions for all K states with KрJ is consistent with the spin
statistics of the benzene protons. The orientation of the HCN
along the C6 axis is given by the relative values of B0 in
Table IV for the 13C and 15N isotopomers. The value of B0 is
1184.7 MHz for 15N and 1203.5 MHz for 13C, indicating that
the nitrogen is significantly farther away from the benzene
than the carbon is. So the H end is closest to the benzene as
in the C6H6–HX dimers.17,18
With this approach and the reported value22 of Ϫ4.7079
MHz for ␹ ͑14N͒ in free HCN, the experimental value of
0
Ϫ4.223 for ␹ in Table IV corresponds to a ␪ of 15.2°.
aa
The dimers with DCN or D13CN exhibit hfs from the
small ␹ ͑D͒, which further splits the components caused by
0
14N. The combined effects are relatively simple for the
Jϭ0→1 transition, where ␹ ͑D͒ splits two of the three
aa
␹ ͑14N͒ components into close triplets, giving a seven line
aa
hfs, as shown in Table II for C6H6–DCN. This enables one,
in principle, to test the assumption that a quadrupole interac-
tion in a monomer is unaffected by dimer formation. If so,
the application of Eq. ͑4͒ to ␹ ͑D͒ and ␹ ͑N͒ for a given
aa
aa
This leaves to be determined the two structural features
shown in Fig. 1. They are ␪ and R, where ␪ is the angular
displacement between the HCN axis and the figure axis of
the dimer and R is the center of mass ͑c.m.͒ to c.m. separa-
tion of the two monomers. The value of ␪ is usually esti-
mated by assuming that dimer formation does not change a
isotopomer should yield the same value of ␪. However,
␹ ͑D͒ is small in free DCN, approximately 207͑4͒ kHz.4
0
Moreover, the accuracy of ␹ ͑D͒ from the fits for Jϭ0→1
aa
of C6H6–DCN and C6H6–D13CN, is modest, respectively,
206͑10͒ kHz in Table II and 198͑8͒ kHz in a fit not given.
The results for ␹ ͑D͒ correspond to a ␪ of 7.3° compared
aa
TABLE III. Rotational transition frequencies observed and fitted for the nearly prolate 13CC5H6–HC15N.
Observed
͑MHz͒
Residue
͑kHz͒
Observed
͑MHz͒
Residue
͑kHz͒
Transition
Transition
000→101
111→212
101→202
110→211
212→313
221→322
220→321
202→303
2358.0626
4710.6660
4716.0898
4721.3967
7065.9273
7073.6672
7073.7194
7074.0366
Ϫ1.2
Ϫ0.1
0.7
Ϫ0.4
Ϫ0.1
1.1
211→312
313→414
331→432
330→431
322→423
321→422
303→404
414→515
7082.0241
9421.1024
9430.7561
9430.7561
9431.4267
9431.5568
9431.8695
11 776.1635
0.2
Ϫ0.3
Ϫ0.3
Ϫ0.4
0.7
Ϫ0.6
Ϫ0.3
0.3
0.7
Ϫ0.7
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Gutowsky et al.: C6H6–HCN dimer and Ar3–HCN tetramer
With a value for ␪ in hand, the pseudodiatomic expression is
convenient,
IbϭIb C H ͒ϩ I HCN͒/2 1ϩcos2 ␪͒ϩ␮ R2,
͓ ͑ ͔͑
͑5͒
͑
6
6
d
where ␮ is the reduced mass of the dimer as a diatomic
d
species. Substitution in Eq. ͑5͒ of the B0’s for the dimer
͑Table IV͒, the benzene monomer ͑5688.9186 MHz͒,23 and
for HC14N ͑44 315.9757 MHz͒,24 with a value of 15.2° for ␪,
gives a value of 3.959 Å for R.
Isotopic substitution of a nucleus on the symmetry axis
of the dimer changes B0 by an amount depending on its
distance ai from the c.m. of the dimer,
IbЈϭIbϩ␮sa2i ,
͑6͒
where ␮ is the reduced mass for substitution.10 Application
s
of this approach to the B0’s for the 13C and 15N species of
HCN with 14N as parent, gives aC and aN to be 2.388 and
3.531 Å, respectively, with the HCN c.m. at 2.976 Å. This
result shows that the hydrogen of the HCN is pointed at the
benzene ring. We note also that aNϪaCϭ1.146 Å, which is
appreciably shorter than the C–N bond distance of 1.1551 Å
in free HCN.24 Their ratio corresponds to a projection angle
␪ of 7.2°. The a value for the HCN c.m. enables us to find
the position of the C6H6 c.m. ͑Ϫ1.030 Å͒ by the first moment
condition, and thereby determine R to be 4.006 Å. Also, the
position of the C6H6 c.m. is at aC in C6H6–HC14N.
FIG. 1. Molecular geometry of the benzene–HCN symmetric top. Two in-
termolecular coordinates are determined, the c.m. to c. m. distance R and the
average magnitude ␪ of the angle between the HCN axis and the a axis.
Also, r is defined as the separation between the benzene c.m. and the pro-
jection of the hydrogen in HCN upon the a axis, while ␾ describes the
rotational angle of the HCN about the a axis.
with the 15.2° from ␹ ͑N͒, the difference perhaps due to a
aa
differential effect of dimer formation on ␹ ͑D͒ and
aa
␹ ͑14N͒.
aa
Two methods can be applied for determining R, the
Further evidence on the state of the benzene was found
from a substitution analysis of the three rotational constants
pseudodiatomic18 and the substitution10 approximations.
TABLE V. The observed and fitted 14N hfs for the Jϭ0→1 to Jϭ6→7 transitions of Ar3–HCN.
Transition
Observed
Residue
Transition
Observed
Residue
J→J ,K/F→F
͑MHz͒
͑kHz͒
J→J ,K/F→F
͑MHz͒
͑kHz͒
Ј
Ј
Ј
Ј
0→1,0
1→1
1→2
1→0
1→2,0
2→2
0→1
1→2
2→3
1→1
2→3,0
3→3
1→2
2→3
3→4
2→2
3→4,3a
3→4
4→5
2→3
3→4,0
4→4
2→3
3→4
4→5
3→3
4→5,3a
1772.6488
1772.9915
1773.5053
0.0
0.1
0.0
4→5
8844.3218
8844.5121
8844.5573
0.0
Ϫ0.1
0.0
5→6
3→4
4→5,0
5→5
3545.2759
3545.3344
3545.6180
3545.6452
3546.1922
0.3
Ϫ0.4
Ϫ0.6
0.8
8859.3116
8859.6944
8859.7056
8859.7157
8860.1915
0.2
Ϫ1.0
Ϫ0.4
1.0
3→4
4→5
5→6
Ϫ0.1
4→4
0.1
5→6,3a
5→6
5317.4374
5317.7527
5317.8042
5317.8232
5318.3244
0.2
Ϫ0.6
Ϫ0.4
0.7
10 610.7318
10 610.8441
10 610.8635
0.5
Ϫ1.3
0.8
6→7
4→5
0.1
5→6,0
6→6
4→5
5→6
6→7
5→5
6→7,0
7→7
5→6
6→7
7→8
6→6
10 628.5244
10 628.9237
10 628.9288
10 628.9385
10 629.4099
Ϫ0.5
Ϫ0.8
0.3
1.4
Ϫ0.4
7076.6821
7077.0467
7077.1834
Ϫ0.2
0.9
Ϫ0.7
7088.8655
7089.2307
7089.2482
7089.2626
7089.7470
Ϫ0.1
0.0
0.1
0.1
Ϫ0.1
12 396.2683
12 396.6803
12 396.6803
12 396.6904
12 397.1615
0.1
Ϫ0.1
Ϫ0.2
1.1
Ϫ0.8
aThe frequencies given for Kϭ3 transitions are the averages of close doublets, the splitting increasing with J as shown in detail in Table VII for Ar3–HC15N.
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Gutowsky et al.: C6H6–HCN dimer and Ar3–HCN tetramer
3921
TABLE VI. Rotational transition frequencies observed and fitted for the
symmetric tops Ar3–HCN and Ar3–HC15N.a,b
TABLE VII. Doublet frequencies observed for the Kϭ3 transitions of
Ar3–HC15N.a
Ar3–HC15N
Transition
3Ϫ
3ϩ
⌬
Ar3–HCN
J→J
͑MHz͒
͑MHz͒
͑kHz͒
Ј
Observed
Residuec
Observed
Residue
3→4
4→5
5→6
6→7
7→8
8→9
9→10
6 949.8609
8 685.5147
10 419.9813
12 153.0145
13 884.3841
15 613.8644
17 341.2300
6 949.8609
8 685.5285
10 420.0056
12 153.0600
13 884.4595
15 613.9746
17 341.3821
0
J→J ,K
͑MHz͒
͑kHz͒
͑MHz͒
͑kHz͒
Ј
13.8
24.3
45.5
75.4
110.2
152.1
0→1,0
1→2,0
2→3,0
3→4,3
0
1 772.9343
3 545.6196
5 317.8078
7 076.9570
7 089.2521
8 844.4606
8 859.7077
10 610.8120
10 628.9314
0.2
0.1
0.0
Ϫ0.3
Ϫ0.1
0.5
0.1
Ϫ0.2
Ϫ0.1
1 741.5312
3 482.8067
5 223.5591
6 949.8609
6 963.5330
8 685.5216
8 702.4727
10 419.9934
10 440.1253
12 153.0372
12 176.2394
13 884.4218
13 910.5672
15 613.9195
15 642.8654
17 341.3060
17 372.8953
2.9
3.8
3.7
Ϫ1.8
2.2
Ϫ4.7
0.0
Ϫ1.2
Ϫ1.6
2.5
Ϫ2.5
4.7
Ϫ2.6
3.3
Ϫ1.1
Ϫ4.7
3.1
4→5,3
aThe lower- and higher-frequency components are arbitrarily labeled 3Ϫ and
0
3ϩ. ⌬ is the splitting between them.
5→6,3
0
6→7,3
than the 1.396 Å reported23 for free benzene, implying there
is little or no tilt of the benzene in the dimer to foreshorten
bC .
0
12 396.6843
0.0
7→8,3
0
8→9,3
0
9→10,3
0
B. Ar3–HCN tetramer
1. Search, hfs, and rotational constants
aDue to the presence of the three equivalent spin-zero Ar nuclei, only Kϭ3n
levels are observed.
Our first attempts to find rotational transitions of
Ar3–HCN were more than five years ago. They were
prompted by the unusual properties of the Ar–HCN dimer
compared with those of the Arm –HX species ͑mϭ1,2,3;
XϭF,Cl͒.1 In particular, the Ar3–HX tetramers are nice,
semirigid symmetric tops in which the HX has large bending
amplitudes ͑40° and 37°͒ with respect to the C3 axis. The
search for such an Ar3–HCN symmetric top, with the same
Ar to c.m. HCN distance ͑4.34 Å͒, as in the Ar–HCN dimer,
was unsuccessful, even though the approach worked for
Ar3–HX. Subsequent work on Ar2–HCN found an Ar to
HCN c.m. distance 0.18 Å shorter than that in the dimer.6 A
renewed, more intensive search on this basis led to the re-
sults now reported.
bThe Kϭ3 lines show doubling attributable to centrifugal distortion. Their
average is given here.
cHJ and HJK terms are needed to fit the transitions to experimental accuracy.
See the text.
͑Table IV͒ for the asymmetric top 13CC5H6–HC15N, using
C6H6–HC15N as the parent.10 The results are approximate
because of the large uncertainty in A0. The analysis gives the
a and b positions for the C in benzene to be 1.035 and 1.404
Å. Because of the isotopic substitution, the 1.035 Å for aC
with 15N as the parent is on the short side, compared with the
1.030 Å from the first moment analysis for the 14N isoto-
pomer as a parent. The 1.404 Å for bC is somewhat larger
Once its transitions were found, identification of the tet-
ramer was straightforward. The Arm –͑HCN͒ composition
n
was confirmed by observing the disappearance of a transition
when the neon first run was substituted as the carrier gas and
when HCN was removed from the argon carrier. The ob-
served transitions ͑Tables V and VI͒ consist of the J,K pro-
gressions predicted by Eq. ͑2͒ for the symmetric top shown
in Fig. 2, except that transitions are observed only for K
TABLE VIII. J dependence of ␹ ͑N͒ in the Ar3–HC14N cluster for Kϭ0
cc
levels.
1/2
cosϪ1͗cos2 ␪͘
␹
cc
J
͑MHz͒
͑deg͒
0
1
2
3
4
5
6
7
Ϫ1.143a
45.28
45.28
45.24
45.16
45.09
45.09
44.99
44.87
Ϫ1.142͑2͒
Ϫ1.147͑2͒
Ϫ1.157͑2͒
Ϫ1.166͑5͒
Ϫ1.167͑5͒
Ϫ1.178͑2͒
Ϫ1.193͑2͒
FIG. 2. Molecular geometry of the Ar3–HCN symmetric top. The coordi-
nates used correspond to those in Fig. 1 for the benzene–HCN dimer. How-
ever, here the figure axis is the c axis.
a
0
0
␹ is extrapolated from the fit to ␹cc(J)ϭ␹ccϩD J(Jϩ1) in which D is
␹
␹
found to be Ϫ0.878 kHz.
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3922
Gutowsky et al.: C6H6–HCN dimer and Ar3–HCN tetramer
TABLE IX. Rotational and hyperfine interaction constants obtained for several isotopic species of Ar3–HCN by fitting the assigned frequencies.
Constant
Units
Ar3–HCN
Ar3–H13CNa
Ar3–HC15N
Ar3–DCNb
B0
DJ
DJK
HJ
MHz
kHz
kHz
Hz
886.4878͑1͒
10.374͑2͒
173.156͑7͒
0.87͑2͒
876.2129͑2͒
9.665͑7͒
870.7873͑4͒
10.830͑6͒
192.57͑4͒
0.77͑3͒
876.5933͑2͒
8.44͑1͒
179͑1͒
HJK
Hz
MHz
74.8͑1͒
Ϫ1.143͑2͒
85.6͑3͒
c
␹
͑N͒
Ϫ1.187͑5͒
•••
Ϫ1.42͑1͒
cc
aOnly the Kϭ0 transitions were measured, from Jϭ1→2 to Jϭ3→4.
bThe Jϭ1→2 to Jϭ4→5 transitions were measured. The D hfs was not sufficiently resolved for analysis.
cThe ␹ ͑N͒ reported is for the Jϭ0→1 transition.
cc
ϭϮ3n for integer n. This behavior is characteristic of sym-
metric tops with a three-fold symmetry axis interchanging
identical Iϭ0 nuclei.21 Argon is spin zero so the symmetry
requirements are met by an equilateral Ar3 having the HCN
on its C3 axis with three-fold or higher axial symmetry.
ference reflects the weak intermolecular interactions of the
tetramer versus the strong covalent bonding in CHF3
3. ␹cc(N) and its J dependence
Larger species such as Ar4–HCN and Ar3–͑HCN͒ are ruled
2
As pointed out for the benzene–HCN dimer in connec-
out by their much smaller predicted B0. The orientation and
vibrational bending of the HCN are considered later.
The transitions of the parent isotopic species, including
their 14N hyperfine structure, are listed in Table V. The hfs
was fitted separately for each transition, in the same manner
tion with Eqs. ͑3͒ and ͑4͒, ␹ ͑N͒ enables one to estimate the
cc
average bending amplitude of the HCN with respect to the
figure axis. Also, the J dependence of ␹͑N͒ in clusters con-
taining HCN is a sensitive indicator of coupling in the PES
between stretching and bending of its van der Waals
coordinates.1,4,29 Therefore, particular care was taken in gath-
ering and analyzing the hf data for 14N in the parent species
͑Table V͒.
Good results were obtained for ␹(J) in the Kϭ0 levels.
However, for Kϭ3 we observed only the three ⌬Fϭ1 com-
ponents, which are closed spaced and give relatively inaccu-
rate values of ␹͑N͒. The findings for the Kϭ0 levels are
given in Table VIII for Jϭ0 through Jϭ7. Three transitions
were fitted for Kϭ3 ͑Jϭ3–6͒, yielding ␹͑N͒ values consis-
tent with the more reliable Kϭ0 findings. The latter were
fitted by the equation
as for C6H6–HCN, with the line center, and ␹cc(J) of the 14
N
as adjustable parameters. The line centers obtained are listed
in Table VI, along with those observed directly for the hfs–
free transitions of the 15N containing species. Less extensive
measurements, not given, were also made for the
Ar3–H13CN and Ar3–DCN isotopic species.
For transitions above Jϭ3→4, the Kϭ3 component was
found to be split into a doublet, the splitting increasing rap-
idly with J. The splittings for Ar3–HC15N are uncomplicated
by the 14N hfs, and are given in Table VII; its splitting is 152
kHz for Jϭ9→10. Another noteworthy feature of the tet-
ramer is that ␹cc(N) is J dependent, as shown by the results
in Table VIII for the Kϭ0 levels of the parent species. The
rotational constants determined by fitting the line centers of
the four isotopomers to Eq. ͑2͒ are summarized in Table IX.
␹
J͒ϭ␹ 0͒ϩD J Jϩ1͒.
͑9͒
͑
͑
͑
cc
cc
␹
From the fit, D was found to be Ϫ0.878 kHz, and ␹ ͑0͒ to
␹
cc
be Ϫ1.143 MHz, which corresponds to an average angle ␪
between the c axis and the HCN axis of 45.3°. The J depen-
dence corresponds to a small decrease in ␪ from 45.3 to
44.9° as J increases from 0 to 7.
2. Splitting of K؍3 levels
The splitting of the Kϭ3 transitions is attributable to a
nonvanishing off-diagonal matrix element
K͉H͉KϮ6 in
͗ ͘
the rotational Hamiltonian of a C3v symmetric top. This pos-
sibility was pointed out some time ago by Watson,26 and its
observation was reported very recently for high-J ͑у29͒
transitions of CHF3.27,28 The first-order splitting is given by
4. Structural analysis
The dynamic state of HCN in the Ar3–HCN symmetric
top of Fig. 2 is difficult to describe in conventional terms.
Therefore we have resorted to escape clauses like ‘‘apparent
structure.’’ For example, the rotational constants for the iso-
topic species in Table IX enable one to obtain the substitu-
tion positions along the c axis of the carbon and nitrogen
atoms, cC and cN . They prove to be 2.590 and 3.222 Å,
respectively.
⌬␯ϭ12h3 JϪ1͒J Jϩ1͒ Jϩ2͒ Jϩ3͒.
͑7͒
͑
͑
͑
͑
However, in the reported cases as well as here, a second-
order term is needed. This may be accomplished by replacing
h3 with
h ϭh0ϩ␦h J Jϩ1͒.
͑8͒
͑
3
3
3
Their difference, 0.632 Å, should be the on average pro-
jection over the bending oscillations of the 1.155 Å C–N
bond. But the difference found corresponds to a projection
The results of this approach are seen in Table VII, which
includes the splittings observed and the residues of their fit.
The values found for h30 and ␦h3 are 0.461 and Ϫ4.04ϫ10Ϫ3
Hz, respectively. They are two and five orders of magnitude
larger than those reported27,28 for CHF3. Presumably this dif-
angle ␪ of 56.8° while that from the observed ␹ ͑N͒ is only
cc
45°. Moreover, the difference is far too large to be attributed
to charge redistribution of the HCN by cluster formation.30
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Gutowsky et al.: C6H6–HCN dimer and Ar3–HCN tetramer
3923
ity search for it in the parent species. The values obtained for
DJ and HJ are both negative and comparable for the two
isotopomers.
It appears that the two sets of transitions are from an
excited vibrational state of the Ar3–HCN, a more extensive
study of which is underway.31 However, at this time it is
noteworthy that substitution analysis of the B’s in Table X
for the excited state shows only a modest decrease of 0.007
Å in its cN , implying that the excitation does not have a large
effect on the c.m. location of the HCN.
TABLE X. Kϭ0 transition frequencies and rotational constants for an ex-
cited state of Ar3–HCN and Ar3–HC15N.
Ar3–HCNa
Ar3–HC15N
Observed
Transition
Observed
Residue
Residue
J→J
͑MHz͒
͑kHz͒
͑MHz͒
͑kHz͒
Ј
1→2
2→3
3→4
4→5
5→6
6→7
7→8
3560.3506
5340.8625
7121.4086
8902.0477
10682.7197
12463.3212
14243.6882
Ϫ104
26
3497.4231
5246.3338
6995.4364
8744.7192
10 494.1188
12 243.5152
13 992.7427
Ϫ11
Ϫ5
6
10
2
45
28
Ϫ12
Ϫ37
18
Ϫ13
5
C. MMC calculations
The results presented thus far exhibit some interesting
features of the two clusters. Both clusters are symmetric
tops, one with a six-fold axis, the other three-fold. Their
geometry, given in Figs. 1 and 2, has the HCN in equivalent
positions. But here the similarities end. DJ and DJK are an
order of magnitude larger for the cluster with Ar3 than with
benzene. Moreover, Ar3–HCN requires sixth-order HJ and
HJK centrifugal distortion terms. Finally, the benzene–HCN
dimer is a well-behaved symmetric top while Ar3–HCN has
at least four unusual features. The average bending angle ␪
for the HCN is three times larger ͑45°͒ than in the dimer. The
rms dev.
48
8
Rotational constants
B͑MHz͒
DJ͑kHz͒
HJ͑Hz͒
890.09͑1͒
Ϫ3.0͑3͒
Ϫ19.͑2͒
874.331͑2͒
Ϫ3.52͑5͒
Ϫ19.1͑4͒
aThe frequencies given are for the middle line of the three component 14N
hfs.
value found for ␹ ͑N͒ is J dependent in Ar3–HCN, but not
cc
Also, although the H end of the HCN is closest to the Ar3,
the B0 for Ar3–DCN is very close to that of Ar3–H13CN.
In any event, we have employed Eq. ͑5͒ with
Ib͑Ar3–HCN͒, Ib͑Ar3͒, and ␪͑14N͒ to determine R for the
cluster. Here Ib͑Ar3͒ is simply 2mAr͑l/2͒2, where l is the
Ar–Ar distance. Both R and l are not determinable, and l is
taken to be 3.85 Å.12 On this basis, R is found to be 3.47 Å.
The substitution approach gives a value of 3.43 Å. Calcula-
tion of Ic͑Ar3–HCN͒ with these parameters shows that the
tetramer is a near spherical, oblate top. The a and c axes in
Fig. 2 interchange to give a prolate top when lр3.80 Å,
which seems unlikely. If so, it would change the labels in our
assignments, but not modify their content.
in the dimer. The Kϭ3 transitions of Ar3–HCN are split into
J-dependent doublets by centrifugal distortion, and an ex-
cited vibrational state was found. These differences should
be reflected in the potential energy surfaces for the clusters,
which we consider in this section.
To examine the primary features of the potential surfaces
of the two complexes, model potential calculations were car-
ried out using the molecular mechanics for clusters
approach.3 MMC generates potentials for weak interaction
between two or more closed shell species as a function of
intermolecular coordinates. The potential energy consists of
two additive elements, one associated with electrical interac-
tion and one associated with all other contributions treated
collectively. The electrical interaction is obtained by com-
plete solution of mutual, multipolar hyperpolarization equa-
tions using electrical properties for the interacting species
obtained from ab initio calculation. The other term is an
atom–atom Lennard-Jones ͑‘‘6–12’’͒ potential, with empiri-
cal parameters that are transferable with each monomer; it
corresponds to dispersion and exchange repulsion.
5. An excited state
In the course of characterizing the parent species, a set
of weak transitions was found at frequencies just above the
Kϭ0 lines of the parent, with a B of 890.1 MHz, instead of
886.5. Moreover, the spacings of the transitions are larger at
higher J and each transition has three hf components, ex-
tending over 340 kHz for Jϭ1→2 but coalescing at higher
J’s to a single line for Jϭ7→8. The hfs appears to be the
three ⌬Fϭ1 components predicted for the Kϭ0 transitions
of a near symmetric top with a single Iϭ1 nucleus ͑14N͒.21
They could not be fitted as a symmetric top.
The frequencies of the central hf components are given
in Table X for the Jϭ1→2 through Jϭ7→8 transitions for
the parent species. Also listed are the corresponding, readily
found, hf-free frequencies for the 15N species. Both sets were
fitted with the standard three-term equation10 in B, DJ , and
HJ . The fit is mediocre for the parent species, probably be-
cause of the approximate line centers. But the fit for the 15N
species has a more reasonable rms deviation of 8 kHz. The
Jϭ0→1 transition was not found, in spite of a high sensitiv-
1. C6H6–HCN dimer
The MMC electrical representation for HCN includes its
first three permanent moments, its dipole, dipole–
quadrupole, and quadrupole polarizability, and its dipole hy-
perpolarizability. The electrical representation of benzene is
a set of six equivalent point dipoles (0.890D) placed along
the C–H bonds ͑0.503 Å from carbon͒ and six equivalent,
anisotropic dipole polarizability tensors assigned to the six
carbon centers.32 Electrical interaction among the benzene
electrical centers is not allowed; that is, there is no intramo-
lecular interaction energy. This representation yields good
correspondence with the true permanent charge field at van
der Waals separation distances both in plane, at the edges of
benzene, and above the benzene plane.33 Also, the simple
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3924
Gutowsky et al.: C6H6–HCN dimer and Ar3–HCN tetramer
representation of the polarization response by carbon atom
dipole polarizabilities is effective, in that the net molecule
dipole polarizability is reproduced and the molecule-centered
quadrupole polarizability is rather well reproduced.33
Figure 3͑a͒ is a plot of the contours of the MMC poten-
tial energy for HCN above the benzene ring as in Fig. 1. The
plot was generated for a grid of b-c positions, where the
benzene ring defines the b-c plane, with aϭ0, bϭ0, and
cϭ0 being the inversion center of benzene. For each grid
point calculation, HCN was positioned above the benzene
ring with b-c coordinates fixed. Then its altitude ͑a coordi-
nate͒ and orientation angles were energy optimized. This
generates the potential surface slice for an HCN moving
above the benzene plane at its optimum height and orienta-
tion. The results are presented in Figs. 3͑b͒ and 3͑c͒ for the
same b-c grid as in Fig. 3͑a͒. The contours in Fig. 3͑b͒ are
for the optimum c.m. separation between HCN and benzene,
while those in Fig. 3͑c͒ are for the optimum angle ␪ between
the HCN and a axes.
gon atoms than with benzene. With allowance for the 290
cmϪ1 Ar/Ar interaction that for Ar/HCN is only ϳ200 cmϪ1
The contours display a C3 symmetry and are not circular.
HCN prefers to be in the middle of the triangle, and if dis-
placed from that position, it prefers to go between two ar-
gons rather than directly at any one of them.
The equilibrium distance between the HCN c.m. and that
of Ar3 is plotted in Fig. 4͑b͒ for the grid. The contours depict
a tricuspid surface with a small, relatively flat, central mini-
mum. From it radiate the three easy paths, one between each
pair of argons, alternating with the steeper climbs directly
toward an argon. The angle ␪ between the HCN and c axes is
given in Fig. 4͑c͒. The equilibrium state has the HCN per-
pendicular to the Ar3 plane, hydrogen end pointed at the
triangle center. But as the HCN is moved away from the
.
Key features of these plots are their smoothness and the
essentially circular form of the contours. The six bond di-
poles representing the charge field of benzene interacting
with the first three permanent moments of HCN do not give
rise to ‘‘bumps’’ at or between carbon centers, even though
the benzene electrostatic potential displays a small degree of
six-fold ‘‘lumpiness’’, especially at closer separations.33 The
nonelectrical part of the potential also has a six-fold symme-
try axis, but at the optimum interaction distances of the grid,
the potential energy does not noticeably reflect the positions
of the carbons or hydrogens; it is nearly circular. For water–
benzene clusters,32,34 MMC potential surfaces show nearly
circular contours, though they are not quite as smooth as
those in Fig. 3. Basically, benzene interacts with other mol-
ecules mostly like a smooth disk, even at relatively short
range ͑3 Å͒.
Another noteworthy feature of the potential energy sur-
face in Fig. 3͑a͒ is its form, which is that of a bowl with a
partly flattened bottom. The change in potential energy for
HCN to move within the ring of carbon atoms is, at most, 65
cmϪ1. But for it to move from the carbon ring to the hydro-
gens requires 300 cmϪ1. This is clearly a potential having a
flat bottom within the carbon ring and then steep sides out-
ward. The same feature has been found for benzene and
HCl.33
2. Ar3–HCN tetramer
MMC calculations were made first on a cluster of three
argon atoms, giving an equilateral structure with an equilib-
rium interaction energy of 290 cmϪ1. Interaction of a fixed
Ar3 with the HCN was then calculated, predicting an equi-
librium symmetric top structure as given in Fig. 2 and found
previously11,12 for Ar3–HX ͑XϭF,Cl͒. Plots are shown in
Fig. 4 of the results corresponding to those in Fig. 3 for
C6H6–HCN. The grid employed is in the a-b plane, parallel
to the plane of Ar3. The plots exhibit three-fold symmetry
about the axis equidistant from the three argons. The center
of the Ar3 triangle is taken to be the origin of the grid.
The potential energy contours in Fig. 4͑a͒ show that
HCN interacts much more weakly with the ring of three ar-
FIG. 3. MMC potential energy surface for the benzene–HCN dimer. ͑a͒
Contours of the potential energy in cmϪ1. Steps between contours are 50
cmϪ1. The energy at each b-c point is the optimum for an HCN with its c.m.
at that point. The orientation and a coordinate were relaxed. The positions of
the atomic centers of benzene are shown. ͑b͒ Contours of the optimum
distance in Å between the mass centers of HCN and benzene. ͑c͒ Contours
of the optimum angle ␪ between the HCN and a axis.
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Gutowsky et al.: C6H6–HCN dimer and Ar3–HCN tetramer
3925
FIG. 4. MMC potential energy surface for the Ar3–HCN cluster. ͑a͒ Contours of the potential energy in cmϪ1. There are 10 cmϪ1 steps between contours. The
energy at each a-b point is the optimum for an HCN with its c.m. at that point; the HCN orientation and c coordinate were relaxed. The positions of the argons
are indicated; they were kept fixed. If the argons are also relaxed, the equilibrium E is 507 cmϪ1. ͑b͒ Contours of the optimum distance in Å between the c.m.
of HCN and of Ar3 . ͑c͒ Contours of the optimum angle ␪ between the HCN and c axis.
center of the grid, and farther from the Ar3 plane, it flattens
out, becoming more nearly parallel to that plane.
the optimum orientation somewhat, accounting for ␪ becom-
ing smaller at higher J.
Comparison of Figs. 4͑a͒ and 4͑c͒ for Ar3–HCN reveals
that the energy (E) and optimum orientation ͑␪͒ are corre-
lated in an interesting, opposed way. To illustrate this, we
calculated curves wherein the HCN was displaced to a-b
positions 3.5 Å from the center of the triangle. These posi-
tions, of course, lie in a circle about the c axis, and we use
the angle ␾ ͑Fig. 2͒ to designate the location around the
circle. Figure 5 is a plot of E and ␪ as a function of ␾,
showing that where the potential is lowest, ␪ is at its greatest
value.
As a final interrogation of the Ar3–HCN potential, we
calculated a surface slice similar to that of Fig. 4͑a͒, except
that the altitude ͑c coordinate͒ was increased by 0.05 Å. That
is, at each a-b grid point, the c coordinate was fixed at 0.05
Å greater than the optimum. Then only the orientation of the
HCN was reoptimized. The potential energy contours ob-
tained in this way are a little different from those in Fig. 4͑a͒
because this small amount of ‘‘raising up’’ from the Ar3
plane has little effect on the energy. However, it does affect
When compared with those in Fig. 4͑c͒, the central con-
tours for ␪ less than 20° shift outward when the HCN is 0.05
Å higher than optimum. Thereby, the region of the surface
with an optimum ␪ of less than 20° expands with increasing
R. So, centrifugal stretching of the HCN away from the Ar3
plane should be accompanied by a reduction in the optimum
value of ␪, as observed. This is presented in Fig. 6 in a
different way. Here we follow first the circle of a-b points of
Fig. 5, but then again with the c coordinate set at 0.05 Å
longer than the optimum for each point. For every choice of
␾, we find ␪ to be visibly smaller when the HCN is pulled
out by 0.05 Å.
IV. DISCUSSION
The advent of the Balle/Flygare pulsed nozzle FTMW
spectrometer has enabled a rapidly increasing number of
FIG. 6. A plot indicating the effect of centrifugal distortion on the orienta-
tion ␪ of the HCN in Ar3–HCN. The upper part, ␪(c), is a 120° section of
the 3.5 Å curve in Fig. 5, giving ␪ as a function of ␾ at the optimum
distance between the Ar3 and HCN c.m. ␪͑cϩ0.05͒ is the value of the ␪
recalculated for a c coordinate 0.05Å greater than the optimum.
FIG. 5. Circular slices of the MMC potential energy E and the HCN opti-
mum orientation angle ␪ from Figs. 4͑a͒ and 4͑c͒ for Ar3–HCN. The values
of E and ␪ are given for a circle of radius 3.5 Å about the Ar3 c.m. as a
function of the angle ␾ by which the HCN is rotated about the c axis.
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3926
Gutowsky et al.: C6H6–HCN dimer and Ar3–HCN tetramer
row, stretching from the C3 axis to between a pair of argon
atoms, while the multipole interaction path is distributed
much more evenly, helped by the C6 symmetry of benzene.
By-and-large, the MMC interaction surfaces are consis-
tent with experiment. Both clusters are predicted to be sym-
metric tops per Figs. 1 and 2, as found. The larger interaction
energy for C6H6–HCN, 1762 vs 507 cmϪ1, implies it should
be less readily deformed, and, in fact, its DJ and DJK ͑1.1
and 18 kHz͒ are an order of magnitude smaller than those for
Ar3–HCN. In addition, when one considers the structural
parameters, R and ␪, other differences appear.
TABLE XI. Comparison of structural properties observed for C6H6–HX
dimers.
␪
B0
DJ
DJK
ra
Dimer
͑MHz͒
͑kHz͒
͑kHz͒
͑Å͒
͑deg͒
C6H6–HFb
C6H6–HCld
C6H6–HCNe
2048.540
1237.684
1219.911
3.1
1.22
1.12
74
13.4
18.0
2.25
2.32
2.41
22c
23.0
15.2
aC6H6 c.m. to H distance.
bReference 17.
dReference 18, 35Cl.
eThis research.
cFor DF.
The C6H6–HCN dimer is relatively well behaved as
clusters go. MMC predicts an equilibrium C6H6 c.m. to HCN
c.m. distance R of 3.89 Å. The experimental value from the
pseudodiatomic approximation is 3.96 Å. The significantly
larger experimental value is attributable to zero point vibra-
tional averaging over the very flat potential minimum in Fig.
3. The value of ␪ obtained from the 14N hfs is 15.2°. This
may be small compared with the averaging required for R. In
any case, the C6H6–HCN interaction surface is qualitatively
similar to that for say the C–F bond in CH3–F. The main
difference is that the 4–2 ͑quadrupole–dipole͒ interaction is
an order of magnitude weaker than the C–F bond.
When one turns to Ar3–HCN major anomalies appear.
The pseudodiatomic approximation for R is 3.47 Å, which is
much smaller than the MMC 0–2,4 ͑sphere-dipole, quadru-
pole͒ prediction of 3.79 Å for the equilibrium R. Also, the
value of 45.3° obtained for ␪ from the 14N hfs is much larger
than expected from the MMC surface in Fig. 4͑c͒. The proxi-
mate cause of these aspects is our treatment of the Ar3 as
rigid and tilt free. The approximations of this assumption are
aggravated by the complexities of the weak 0–2,4 interac-
tion, which are a large fraction of the total interaction. Nu-
merical vibrational averaging to test such possibilities is be-
yond the scope of the present work. However, our finding of
an excited vibrational state is indicative of low-frequency
zero-point modes, which could have a considerable effect on
the apparent structure.
dimers and small clusters to be studied in remarkable detail.
A fascinating consequence is the evolving realization that the
rich variety of dynamic structures found in small clusters far
exceeds the more limited domain of conventional chemically
bonded species. Also, comparative studies such as the
present one are feasible and are beginning to reveal the com-
plexities of the weak interaction state.1
Our choice of C6H6–HCN and Ar3–HCN for compari-
son was based in part on the in-the-lab feeling that although
both clusters were likely to be symmetric tops, they would
differ significantly. However, it was fortuitous that the elec-
trical properties of argon and benzene differ as sharply as
they do. The argons are electrically spherical, so they have
no permanent electric moments, and the weak interactions
͑507 cmϪ1͒ forming Ar3–HCN are primarily polarization of
the argons by the large HCN dipole and quadrupole mo-
ments. In contrast, benzene has a nonspherical charge distri-
bution with a large electric quadrupole moment. It is also
more polarizable than Ar3. Therefore, the interaction forming
C6H6–HCN is relatively very strong ͑1762 cmϪ1͒ and largely
an electrical multipole interaction between the C6H6 quadru-
pole and the HCN dipole/quadrupole. Then too, in both clus-
ters there are the dispersion forces, which depend on atomic
species and cluster geometry.
The difference in interaction type affects not only the
strength of the interaction but also its directionality. In fact,
comparison of the interaction surfaces in Figs. 3 and 4 finds
them strikingly different. Those of C6H6–HCN have the six-
fold atomic axis as a Cϱ axis with cylindrical symmetry,
while those of Ar3–HCN have C3 symmetry, with some of
the elements rotated by 60°. These differences arise because
the lowest-energy polarization paths in Ar3–HCN are nar-
Table XI compares some rotational properties of
C6H6–HCN with those reported a decade ago for the HF and
HCl counterparts.17,18 The three dimers are symmetric tops
with quite similar properties. The interaction in all three
cases is primarily a strong 4–2, a quadrupole–dipole type.
The HCN does have an appreciable quadrupole moment, but
the 4–4 interaction of C6H6–HCN augments the 4–2 sur-
face.
A more extensive comparison is given in Table XII for
the Ar3–HCN cluster. It includes the tetramers with HF and
HCl, and the Ar2–HCN trimer and Ar–HCN dimer. The re-
markable feature here is that the clusters containing both Ar
and HCN have exceptionally active internal dynamics, while
those with only one or the other are relatively well behaved.
The same applies to the Ar2–HX and Ar–HX trimers and
dimers not included in the table ͑XϭF,Cl͒.8,9,13,14
Of particular interest is the fact that Ar3–HF and
Ar3–HCl tetramers are relatively well behaved, but
Ar3–HCN exhibits ‘‘unusual’’ behavior. This demonstrates
that the differences between them arise from differences be-
tween HCN and HF/HCl. Inspection of the MMC model
TABLE XII. Comparison of structural properties observed for Arm –HX
clusters.
␪
B0
DJ
DJK
ra
Cluster
͑MHz͒
͑kHz͒
͑kHz͒
͑Å͒
͑deg͒
Ar3–HFb
1188.212
843.90
886.488
1756.610f
1609.837
6.85
2.33
Ϫ5.75
1.82
173.16
Ϫ1.199g
•••
2.07
2.34
2.29
2.35
2.68
41.0
36.9
45.3
39.3
31.0
Ar3–HClc
Ar3–HCNd
Ar2–HCNe
Ar–HCNh
10.37
Ϫ6.538g
173.14
aArm c.m. to H distance.
bReference 11.
eReference 6.
f(AϩB)/2.
cReference 12.
gThese are ␶ and ␶ in MHz.
1
2
dThis research.
hReference 35.
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Gutowsky et al.: C6H6–HCN dimer and Ar3–HCN tetramer
3927
shows that the differences found in the PES for the tetramers
are largely size effects. HCN is a larger, longer molecule
than HF/Cl and cannot get as close to the argons, which
makes the interactions weaker and affects the balance among
the various dispersion and electrostatic interactions.
9 T. D. Klots, C. Chuang, R. S. Ruoff, T. Emilsson, and H. S. Gutowsky, J.
Chem. Phys. 86, 5315 ͑1987͒.
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This view is supported not only by the present work, but
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Chem. Phys. 87, 4383 ͑1987͒.
6
4
for Ar2–HCN and -HF and for Ar–HCN and -HF. An im-
portant element of the Ar/HCN interaction is its weakness. If
the equilibrium interaction energy is only 100 cmϪ1, varia-
tions in the surface cannot be much of an impediment to
internal motions. This is evident in the dependence on the
rare gas of properties for the Rg-HCN dimers ͑RgϭNe, Ar,
Kr͒. Kr, which is the most polarizable, gives an almost nor-
mal ‘‘strong’’ Kr–HCN dimer. Ne, least polarizable, has a
very shallow and isotropic potential surface and extremely
mobile internal dynamics. Such behavior is no doubt typical
of clusters formed by weak interactions, weak in this context
being a pair interaction the order of a hundred cmϪ1 or so.
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ACKNOWLEDGMENTS
22 A. G. Maki, J. Phys. Chem. Ref. Data 3, 221 ͑1974͒.
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C.E.D. from the Theoretical and Computational Chemistry
Program of the National Science Foundation ͑CHE-94
03545͒, and by a grant to H.S.G. from the Experimental
Physical Chemistry Program ͑CHE-94 13380͒.
23
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