Intermolecular vibrations of phenol–(H2O)3 and d 1 -phenol–(D2O)3
in the S 0 and S 1 states
Thomas Bürgi, Martin Schütz,a) and Samuel Leutwyler
Institute für anorganische, analytische und physikalische Chemie, Freiestr. 3, CH-3000 Bern 9, Switzerland
~Received 18 April 1995; accepted 11 July 1995!
We report a combined spectroscopic and theoretical investigation of the intermolecular vibrations of
supersonic jet-cooled phenol•~H2O!3 and d 1 -phenol•~D2O!3 in the S 0 and S 1 electronic states.
Two-color resonant two-photon ionization combined with time-of-flight mass spectrometry and
dispersed fluorescence emission spectroscopy provided mass-selective vibronic spectra of both
isotopomers in both electronic states. In the S 0 state, eleven low-frequency intermolecular modes
were observed for phenol•~H2O!3 , and seven for the D isotopomer. For the S 1 state, several
intermolecular vibrational excitations were observed in addition to those previously reported. Ab
initio calculations of the cyclic homodromic isomer of phenol•~H2O!3 were performed at the
Hartree–Fock level. Calculations for the eight possible conformers differing in the position of the
‘‘free’’ O–H bonds with respect to the almost planar H-bonded ring predict that the ‘‘up–down–
up–down’’ conformer is differentially most stable. The calculated structure, rotational constants,
normal-mode eigenvectors, and harmonic frequencies are reported. Combination of theory and
experiment allowed an analysis and interpretation of the experimental S 0 state vibrational
frequencies and isotope shifts. © 1995 American Institute of Physics.
I. INTRODUCTION
Hydrogen bonding to water molecules has been of considerable interest both experimentally and theoretically, and
is important for understanding a large variety of fundamental
phenomena in physics and chemistry, such as ionic and molecular solvation, phase changes, structure of ice and protein
folding, to name a few. Using molecular-beam techniques,
isolated cold H-bonded complexes and clusters can be synthesized, allowing direct analysis of cluster properties such
as geometry, vibrational structure, dissociation energy, and
dynamics.
Among the most thoroughly examined systems are the
phenol•~H2O!n clusters, due to their model character; phenol
is the simplest aryl alcohol, and its hydrogen-bonding interactions with water are prototypical for related aromatic and
heteroaromatic molecules. The S 1 excited state of phenol–
water complexes has been investigated intensively by resonant two-photon ionization ~R2PI! and laser induced fluorescence ~LIF! measurements.1–11 On the other hand,
intermolecular vibrations in the ground electronic state are
less well investigated. This information is especially desirable, since ab initio calculations of the electronic groundstate intermolecular potential energy surface ~IPES! are feasible, and can be compared directly to the experimental
results. Close interaction between and comparison of experiment and high-level theoretical calculations are crucial, both
for the analysis and interpretation of the experimental results,
as well as for improving and calibrating models for
hydrogen-bonding interactions. Several spectroscopic techniques have been used to study vibrational spectra of
phenol•~H2O!n clusters in the S 0 electronic ground state.
Cluster ion dip spectroscopy ~CID! was first used by Ebata
a!
Present address: Department of Theoretical Chemistry, University of Lund,
Sweden.
and co-workers,7 who reported CID spectra for phenol•H2O
in the frequency range 500–3500 cm21. Later, Stanley and
Castleman8,12 also obtained spectra for the phenol•~H2O!n
n53,4 clusters in the frequency range 500–1300 cm21. Intermolecular modes were observed only as combination
bands with intramolecular vibrations. Felker and
co-workers13 applied ionization-loss stimulated Raman spectroscopy ~ILSRS! to study complexation-induced frequency
shifts of intramolecular vibrations in phenol•H2O. Tanabe
et al. have observed the high-frequency O–H stretching vibrations of phenol•~H2O!n , n51 – 3 clusters by IR-UV
double-resonance spectroscopy.14
We have previously studied the binary phenol•H2O and
d 1 -phenol•D2O complexes using two color resonant two
photon ionization ~R2PI! and dispersed fluorescence techniques in combination with ab initio calculations.9,15 Detailed insight into the vibrational structure and the intermolecular PES of that complex was obtained for both the S 0 and
S 1 electronic states.
The phenol•~H2O!2 cluster is difficult to study spectroscopically due to fast intersystem crossing in the S 1 electronic state, resulting in a low fluorescence quantum yield
and short fluorescence lifetime tfl'6 ns.6 The R2PI spectrum
of that complex exhibits a broad, poorly structured origin
band;5,16 ab initio calculations predict a triangular cyclic
structure. Several conformers, differing only in the H atom
positions of the ‘‘free’’ O–H bonds with respect to the plane
defined by the three oxygen atoms, were located on the
IPES,17 in analogy to the water trimer ~H2O!3 .18 To our
knowledge, no experimental ground-state intermolecular
spectrum is available for phenol•~H2O!2 up to now.
The phenol•~H2O!3 cluster has a longer fluorescence
lifetime tfl'18 ns, reflecting a higher quantum yield. Stanley
and Castleman8 reported R2PI and CID spectra of the
phenol•~H2O!3 cluster. In the S 1 excited state, one hydrogenbond bending and one stretching mode were assigned. For
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Burgi, Schutz, and Leutwyler: Vibrations of phenol•(H2O)3
the S 0 ground state an intermolecular stretching mode at 189
cm21 was observed in combination with intramolecular vibrations. Recently, Schmitt et al.10 reported fluorescence excitation and hole-burning spectra of phenol•~H2O!3 . They
observed several bands in the S 1 excited state and showed,
that the main features in the excitation spectra belong to one
isomer. A H-bond stretching mode at 186 cm21 was assigned.
From a different point of view, phenol•~H2O!3 can be
regarded as the phenyl-substituted analog of ~H2O!4 , and it is
expected that the structures and intermolecular vibrational
modes are closely related. Small cyclic water clusters are
structurally nonrigid in several intermolecular coordinates,
and exhibit unusual large-amplitude vibrational motions. For
the water trimer and tetramer, torsional tunneling and pseudorotation motions have recently been investigated by
theory18 –23 and for the trimer, by far-infrared absorption
experiments.24,25 A better understanding of these motions is
important for understanding rotational reorientation and dielectric relaxation processes in bulk water.
In this study we report both experimental and computational results on phenol•~H2O!3 and d 1 -phenol•~D2O!3 . We
have measured R2PI and high resolution dispersed fluorescence spectra and performed ab initio calculations at the selfconsistent field ~SCF! level. The results of the calculations
allow us to assign a large part of the intermolecular transitions in the dispersed fluorescence spectra. Section II presents the experimental methods, Sec. III the theoretical results, and Sec. IV the experimental results and discussion.
II. EXPERIMENTAL METHODS
Phenol ~Fluka p.a.! was used as received. d 1 -phenol was
produced by mixing 1 g of phenol and 15 ml of D2O
~99.8%!. After stirring for 5 min and centrifuging, the liquid
d 1 -phenol layer was directly used as the sample. The
phenol•~H2O!3 @d 1 -phenol•~D2O!3!# complexes were formed
in a supersonic beam expansion by flowing neon carrier gas
at a 1.5 bar backing pressure through a bubbler containing
H2O ~D2O! held at 218 °C, followed by a sample holder
containing phenol ~d 1 -phenol! at 40–50 °C.
For the R2PI measurements the excitation laser ~,25
mJ! and ionization laser ~'1 mJ! pulses were overlapped and
crossed the skimmed molecular beam 160 mm from the
nozzle. For excitation, the frequency doubled output of a dye
laser ~FL 2002, Coumarin 153! pumped by the third harmonic output ~355 nm! of a Nd:YAG ~Quanta-Ray DCR-2A!
laser was used. The secod harmonic output ~532 nm! of the
same Nd:YAG laser pumped a second dye laser ~LPD 3002,
Pyridine 1!, the frequency doubled output of which served as
ionization beam. The resulting cluster were mass-analyzed in
a linear Wiley–McLaren time-of-flght ~TOF! mass spectrometer.
For the dispersed fluorescence experiments the excitation laser beam ~'200 mJ/pulse! crossed the molecular beam
10 mm from the nozzle. The emitted radiation was collected
with a spherical mirror and a quartz lens and dispersed in a
1.0 m SPEX 1704 monochromator, using a spectral bandpass
of '4 cm21. The molecular beam apparatus and TOF have
been described previously.26
6351
An advantage of dispersed fluorescence measurements
over ion dip spectra is the possibility to measure transitions
below 500 cm21, i.e., in the frequency range of the intermolecular vibrational fundamentals. Also, in contrast to the ion
dip method, dispersed fluorescence spectroscopy is
background-free, resulting in a better signal/noise ratio.
III. THEORETICAL RESULTS AND DISCUSSION
A. Cluster geometry
Full geometry optimizations were performed at the
Hartree–Fock SCF level with the 6-31G(d,p) basis set using
the GAUSSIAN-92 program package.34 Several minima were
located on the PES corresponding to structures differing only
in the positions of the free H atoms with respect to the O
atoms. The most stringent optimization criteria were used in
26
GAUSSIAN-92 ~very tight option, 10
a.u. for the norm of the
gradient!. At the stationary points analytical second derivatives were calculated and a normal coordinate analysis was
performed, yielding harmonic frequencies and eigenvectors.
A large number of distinct minima exist on the IPES of
phenol•~H2O!3 . In analogy to the cyclic S 4 symmetric water
tetramer,23,27–31 one possible arrangement is a fourmembered cyclic homodromic structure, with each molecule
acting both as a single H-bond donor and single acceptor. Six
heterodromic hydrogen-bonded networks exist with one H2O
acting as a double H-bond donor and one of the other molecules ~phenol or H2O! as a double acceptor. Heterodromic
networks with two water molecules as double H-bond donors
are conceivable, but are probably less stable. Pyramidal cluster structures with two water molecules acting as double donors and single acceptors and the remaining water molecule
as well as phenol acting as single donor and double acceptor
are also conceivably stable, in analogy to the pyramidal isomer postulated for ~H2O!4 .27,29 Other possible structure types
involve hydrogen bonding of one H2O molecule to the p
system of the aromatic ring, as in the benzene•~H2O!n complexes and clusters.32
For any of these hydrogen-bonded networks, several
conformers may exist, differing only in the positions of the
‘‘free’’ ~non-H-bonded! hydrogen atoms. Theoretical characterization of all these minima on the intermolecular PES is
beyond our current computational resources. However, ab
initio calculations on ~H2O!4 ~Refs. 23,30,31! predict the S 4
homodromic cyclic structure to be the most stable, with other
networks lying at considerably higher energy, by 8 –14
kcal/mol.29 This implies that the global minimum of
phenol•~H2O!3 has an analogous structure. Unfortunately, no
experimental structure determination of R–O–H•~H2O!3
type clusters has been performed up to now.
We hence restricted the search for minimum-energy
structures of phenol•~H2O!3 to the homodromic cyclic
hydrogen-bonded network. Four stable conformers were
found, which differ in the positions of the free hydrogen
atoms of the H2O molecules with respect to the
O•••O•••O•••O ~O4! ring plane. The deepest minimum at the
SCF level corresponds to the structure shown in Fig. 1,
which is analogous to the S 4 symmetric ~H2O!4 structure.
The phenyl and the hydrogen bonded ring are mutually in-
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Burgi, Schutz, and Leutwyler: Vibrations of phenol•(H2O)3
6352
TABLE II. Overview of structural parameters of the (Udud) conformer of
phenole•~H2O!3 , calculated at the SCF level using the 6-31G(d,p) basis set
~distances in Å, angles in deg!. See Fig. 1 for the atom numbering scheme.
Distances
r~O–H! phenol
r b ~O–H!a
r f ~O–H!b
r~C–O!
R~O••O!c
0.957
0.956/0.954/0.951
0.943/0.943/0.943
1.353
2.784/2.811/2.838/2.900
Angles
a~C–O–H! phenol
a~H–O••O!d
a~O••O••O!e
111.82
7.05/9.52/9.10/12.12
92.33/89.05/89.39/88.34
Dihedral angles
b~C2 –C1 –O1 –H1!
b~O1••O2••O3••O4!
4.39
352.67
Torsional angles
t1~C1 –O1••O2••O3!g
t2,3,4~H–O••O••O!f,g
48.99
262.22/62.92/263.32
a
‘‘Bound’’ O–H distances: O2 –H2/O3 –H3/O4 –H4 .
‘‘Free’’ O–H distances: O2 –H5/O3 –H6/O4 –H7 .
O•••O distances: O1••O2/O2••O3/O3••O4/O4••O1 .
d
H–O•••O angle: H1 –O1••O2/H2 –O2••O3/H3 –O3••O4/H4 –O4••O1 .
e
O•••O•••O angle: O1••O2••O3/O2••O3••O4/O3••O4••O1/O4••O1••O2 .
f
H–O•••O•••O dihedral angle: H5 –O2••O3••O4/H6 –O3••O4••O1/H7 –
O4••O1••O2 .
g
Dihedral angles-180°, in correspondence with earlier work ~Refs. 18, 23!.
b
c
FIG. 1. Calculated minimum-energy structure and conformation of the
lowest-energy (Udud) conformer of phenol•~H2O!3 , viewed from above.
The numbering scheme is sequential along the O–H•••O direction of the
hydrogen-bonds, and is used to define the structure parameters in Table II.
clined. In a notation introduced in our work on ~H2O!3 ~Ref.
18! and continued for the water tetramer,23 the conformer
shown in Fig. 1 is denoted (Udud), meaning that the phenyl
ring is Up and the free hydrogen atoms of the first, second,
and third water molecule are down, up, and down, respectively, relative to the O4 ring, as shown in Fig. 1. The capitalized letter refers to the position of the phenyl ring. The
other torsional conformers, which differ in the position of the
free H-atoms or the phenyl ring relative to the O4-plane are
calculated to be at least 0.5 kcal/mol less stable than (Udud)
at the SCF level, using the above-mentioned basis. These
other conformers will be discussed elsewhere.33 For simplicity in all of the following, we will assume that (Udud) is the
relevant conformer, although this cannot be proved by our
experimental results.
Rotational constants calculated for the r e structure are
given in Table I for phenol•~H2O!3 and d 1 -phenol•~D2O!3 .
Note, that experimental rotational constants might differ considerably from these, due to the zero-point amplitude of several low-frequency large-amplitude vibrations ~see below!.
Centrifugal distortion effects might also be anomalously
large, due to the very low force constants for the torsional
modes ~see below!.
TABLE I. Rotational constants ~MHz! for the (Udud) conformer of
phenol•~H2O!3 and d 1 -phenol•~D2O!3 calculated at the SCF level using the
6-31G(d,p) basis set.
phenol•~H2O!3
d 1 -phenol•~D2O!3
A
B
C
1926.38
1770.46
505.84
475.96
428.02
402.56
Some important structural parameters are compiled in
Table II. Comparing intramolecular structural parameters for
bare phenol and phenol•~H2O!n n51,2,3 at the same level of
theory, one notices a steady increase in the phenolic O–H
bond length from 0.943 Å in bare phenol15 to 0.949 Å,9,15
0.953 Å,17 and 0.957 Å for phenol•~H2O!n n51, 2, and 3,
respectively. This can be interpreted as incremental solvation
effect. Looking at the intramolecular water O–H bond
lengths for phenol•~H2O!3 in Table II, it can be seen, that the
‘‘bound’’ O–H bond lengths r b ~O–H! differ slightly, while
the ‘‘free’’ O–H bond lengths r f ~O–H! are virtually identical
for the three water molecules.
The hydrogen-bond lengths increase sequentially around
the O4 ring; the shortest distance, R~O•••O!52.784 Å, is
from the phenol oxygen to the first H2O ~see Table II!, while
the longest O•••O distance ~2.900 Å! is from the third water
molecule to the phenol oxygen acting as a H-acceptor. This
result is qualitatively consistent with the fact that phenol has
higher gas-phase acidity than water, leading to a relatively
strong phenol–O–H•••OH2 and a relatively weak H–O–
H•••O–phenol hydrogen bond, respectively.
Comparing the phenol–O–H•••OH2 hydrogen bond
lengths in the series phenol•~H2O!n , n51 – 3, a decrease
from R~O•••O!52.906 Å for n51,9,15 to 2.819 Å for n52,17
and to 2.784 Å for n53 is predicted. This trend can be
ascribed to three- and higher many-body contributions,
mainly the mutually reenforcing polarization interactions.
The H–O•••O angles, as defined in Table II and Fig. 1,
measure the nonlinearity of the hydrogen bonds; for a linear
hydrogen bond this angle would be 0°. The deviation from
linearity ranges from 7.1° to 12.1°, with the strongest hydrogen bond ~phenol donor! being the most linear and the weakest hydrogen bond ~phenol acceptor! showing the largest deviation from linearity. In phenol•H2O the deviation from
linearity is 3.3°,9,15 while for phenol•~H2O!2 the deviations
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1995
129.194.8.73
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Dec
10:10:40
Burgi, Schutz, and Leutwyler: Vibrations of phenol•(H2O)3
range from 15.8° to 25.9°,17 showing that there is considerably more ring strain in phenol•~H2O!2 , than in
phenol•~H2O!3 .
The O4 ring is not exactly planar, but the dihedral angle
b~O1••O2••O3••O4! is only 7.3°. Likewise, the phenolic
O–H group is not coplanar with the phenyl ring; the deviation from coplanarity is given by the dihedral angle
b~C2 –C1 –O1 –H1!54.4°. The torsional angles t1 and t2,3,4
measure the inclination of the phenyl ring and the free O–H
groups, respectively, relative to the hydrogen bonded ring. A
value of 0° implies coplanarity with the O4 ring. O–H bonds
with values larger than 0° lie above ~up! the hydrogen
bonded ring. The calculated inclinations of the three O–H
groups are between 62.2° and 63.3°, while the corresponding
value for the more voluminous phenyl group is only 49.0°.
Finally, it should be noted that the predicted (Udud)
minimum-energy-structure is chiral; there is an enantiomer,
denoted (Dudu), of equal energy. The direct enantiomerization motion carries each constituent of the cluster from a
torsional ‘‘up’’ to a ‘‘down’’ position, or vice versa. Hence
the interconversion can be largely described by a path in the
intermolecular torsional angle subspace spanned by
b~C1 –O1••O2••O3! and the three b~H–O••O••O!’s. The
enantiomerization pathways for phenol•~H2O!3 , of which
several may exist, have not yet been examined. The situation
may be analogous to cyclic homodromic ~H2O!4 , which has
recently been studied by ab initio computations at a very
high level.23 There, the lowest-energy pathway for enantiomerization proceeds through a series of single torsional
‘‘flips,’’ i.e., the path from (udud)→(uuud)→(uu pd) ~a
transition structure!→(uudd) ~a local minimum!→(pudd)
~a second transition structure!→(dudd)→(dudu). For
phenol•~H2O!3 , the (Uddu) conformer, which is analogous
to the (uddu) or (uudd) conformer of ~H2O!4 , is also a
local minimum at the SCF level.
B. Interaction energy
The binding energies D e were calculated as the difference between the minimum energy of the complex and the
subunits, each fully optimized at the SCF level. For the calculation of zero point vibrational energies ~ZPE! and dissociation energies D 0 , the intramolecular harmonic vibrational
frequencies were scaled by 0.9, while intermolecular frequencies remained unscaled. Correlation energy contributions to the binding energy were estimated as the energy
difference between complex and subunits, each at the SCF
optimized geometry, using second-order Møller–Plesset perturbation theory. The basis set superposition error ~BSSE!
was calculated by applying the full counterpoise ~CP!
procedure.35 For this, each monomer ~phenol or water! was
calculated both in the complete tetramer and monomer basis
sets, at the optimized geometry in the phenol•~H2O!3 cluster.
Table III gives the calculated stabilization energies at the
SCF and at the counterpoise ~CP! corrected SCF1MP2 levels, and the individual BSSE energy contributions for
phenol•~H2O!3 and d 1 -phenol•~D2O!3 . These energies are
compared to those of cyclic S 4 symmetric ~H2O!4 , evaluated
at the same level of theory. At the SCF level, the total stabilization energy of phenol•~H2O!3 is 2D e 528.85 kcal/mol,
6353
TABLE III. Binding energies D e and dissociation energies D 0 ~kcal/mol! of
phenol•~H2O!3 , d 1 -phenol•~D2O!3 and ~H2O!4 , calculated at the SCF optimum geometry using the 6-31G(d, p) basis set. The SCF and MP2 binding
energy contributions, and respective BSSE contributions are also given.
phenol•~H2O!3
SCF energy
MP2 energy
BSSE~SCF!
BSSE~MP2!
Totala
a
d 1 -phenol•~D2O!3
~H2O!4
2D e
2D 0
2D e
2D 0
2D e
2D 0
28.85
8.44
24.59
24.21
28.49
21.35
28.85
8.44
24.59
24.21
28.49
23.04
29.06
7.60
24.61
23.98
28.07
20.25
20.99
22.68
19.26
D e 5SCF1MP21BSSE~SCF!1BSSE~MP2!; D 0 5D e 2zero-point-energy.
or 7.21 kcal/mol per hydrogen bond. At the same level of
calculation, the stabilization energy for phenol•H2O is
2D e 57.25 kcal/mol, and for ~H2O!4 , the 2D e ~2D e per
H-bond! is 29.06 ~7.27! kcal/mol, which, per H-bond, are
both slightly higher. However, for ~H2O!2 the calculated H
bond energy is much lower, 2D e 55.54 kcal/mol.9 This
comparison implies that ~i! the phenol–O–H•••OH2 hydrogen bond is stronger than a HO–H•••OH2 bond by about 1.7
kcal/mol; ~ii! many-body effects on the hydrogen-bond energy ~mainly mutual polarization energy! are important for
both phenol•~H2O!3 and ~H2O!4 , being on the order of about
20%; ~iii! the many-body effects are larger for ~H2O!4 than
for phenol•~H2O!3 , and hence larger for the smaller cluster.
The ZPE correction amounts to 26% and 30% of the
binding energy for phenol•~H2O!3 and ~H2O!4 , respectively.
The lower ZPE correction for phenol•~H2O!3 relative to
~H2O!4 is a consequence of the larger reduced masses for
phenol•~H2O!3 modes, leading to a larger dissociation energy
2D 0 for phenol•~H2O!3 . It should be noted that consideration of anharmonicity will reduce the ZPE, and hence the
calculated binding energy 2D 0 will increase. Since anharmonicity is very important for intermolecular vibrations of
rotational parentage, as has been shown for the ~H2O!3
cluster,18,22–25 the correction of 2D 0 due to anharmonicity
might be considerable, i.e., several 100 cm21. The Møller–
Plesset second-order correlation energy was calculated at the
SCF geometry; the contribution to the hydrogen bond energy
is 29% for phenol•~H2O!3 which is slightly higher than for
phenol•~H2O ~26%!. On the other hand the total BSSE ~SCF
1MP2! is of the same order, so that correlation correction
and BSSE cancel quite closely. The uncorrected SCF binding
energy and the counterpoise and correlation corrected values
differ by only 1.2% for phenol•~H2O!3 and 3.4% for ~H2O!4 ,
similar to the finding in our earlier work on phenol•H2O.9
C. Intermolecular vibrations
Eighteen intermolecular normal modes arise from complexation of phenol with three H2O molecules. Table IV
compiles the calculated harmonic frequencies and reduced
masses for phenol•~H2O!3 and d 1 -phenol•~D2O!3 for the
(Udud) conformer. Figs. 2–5 display the calculated eigenvectors for twelve intermolecular modes. The labels n 91 ,
n 92 , etc. are given according to increasing vibrational frequency. The calculated intermolecular harmonic vibrational
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J. Chem.
Phys., Vol.
No.
15,2013
15 October
1995
129.194.8.73
On: 103,
Fri, 13
Dec
10:10:40
Burgi, Schutz, and Leutwyler: Vibrations of phenol•(H2O)3
6354
TABLE IV. Calculated intermolecular harmonic frequencies ~cm21! and reduced masses ~amu! of
phenol•~H2O!3 and d 1 -phenol•~D2O!3 at the SCF 6-31G(d, p) level.
phenol•~H2O!3
Description
mutual ring motion
mutual ring motion
mutual ring motion
O–O–O–O ring def.
O–O–O–O ring def.
ph-O•••H–O–H stretch, s 91
ph-O–H•••OH2 stretch, s 29
torsion t 91
H2O•••H–O–H stretch, s 39
torsion t 92
H2O•••H–O–H stretch, s 49
torsion t 93
out-of-plane libration
out-of-plane libration
out-of-plane libration
in-plane libration
in-plane libration
in-plane libration
d 1 -phenol•~D2O!3
Mode
Freq.
Red. mass
Mode
Freq.
Red. mass
n 91
n 29
n 93
n 94
n 95
n 96
n 97
n 98
n 99
n 910
n 911
n 913
n 914
n 915
n 916
n 921
n 923
n 929
21.3
29.6
45.7
69.3
74.6
153.2
190.7
195.9
217.1
233.4
237.6
296.4
327.4
404.7
433.3
643.4
750.0
948.3
5.41
4.15
5.35
7.02
4.92
5.70
4.54
1.13
6.06
1.13
4.44
1.21
1.10
1.09
1.07
1.14
1.06
1.13
n 91
n 29
n 93
n 94
n 95
n 97
n 99
n 96
n 910
n 98
n 912
n 911
n 913
n 915
n 916
n 919
n 920
n 924
20.5
28.7
44.1
67.3
71.0
148.4a
183.2
139.2
205.2
168.5
224.7a
218.4
233.0
297.4
319.6
491.5b
543.1
676.0b
5.83
4.36
5.60
7.31
5.31
4.66
5.02
2.40
5.82
2.23
3.12
3.30
2.83
2.32
2.47
3.00
2.24
3.20
a
Coupled to a torsional coordinate.
Coupled to intramolecular mode.
b
frequencies range from 20 to 950 cm21 for phenol•~H2O!3
and from 20 to 680 cm21 for d 1 -phenol•~D2O!3 , while the
lowest intramolecular mode appears at 266 cm21. This
means that inter- and intramolecular fundamentals overlap
over a sizeable range, from '250 to 950 cm21 ~250 to 680
cm21 for the deuterated species!.
The calculated modes can be categorized based on both
frequencies and eigenvectors. Modes n 91 – n 93 shown in Fig. 2,
are motions of the phenyl ring relative to the H-bonded O4
ring, displacing as two entities against each other. n 91 is a
‘‘butterfly’’ mode, n 92 is characterized by mutual twisting of
the two rings, and in n 93 the H-bonded ring and phenyl ring
move like a pair of cogwheels, while the mutual torsional
angle of the two rings remains approximately constant. The
first group of vibrations is further characterized by large reduced masses and small deuteration shifts.
Modes n 94 and n 95 shown in Fig. 3, are ring deformations
of the hydrogen-bonded O4 ring; n 94 is an in-plane, n 95 an
out-of-plane distortion. This group of vibrations is of translational parentage, i.e., the motions of the cluster constituents
are predominantly translational, not rotational. They exhibit
large reduced masses and small deuteration shifts. Similar
modes were calculated for ~H2O!4 .23
The next group of vibrations ~n 96 , n 97 , n 99 , and n 911! consists of the four hydrogen-bond stretching vibrations, also
denoted s 91 – s 94 . They are shown in the lower part of Fig. 3
and in Fig. 4. Interestingly, a relatively large frequency gap
opens between the highest-frequency member of the ring deformation family and the lowest-frequency mode of the
H-bond stretching family. This gap extents from 75 to 150
cm21 for phenol•~H2O!3 . Again, the H-bond stretching
modes have large reduced masses, and the deuteration shifts
are moderate, i.e., ranging from 3.1% to 5.5%. The four
stretching modes are somewhat delocalized, i.e., usually two
or three H-bond stretches are involved in the same mode.
Nevertheless, the lowest frequency stretching mode s 91 @at
153.2 cm21 for phenol•~H2O!3# has the largest amplitude in
that H-bond in which the phenol O atom acts as hydrogen
acceptor, ~‘‘phenol acceptor stretch’’!. This is in good agreement with this being the longest of the four H-bonds in the
ring, and with phenol being a much weaker H acceptor than
donor. The stretching mode s 92 has a large component in the
phenol–O–H•••OH2 bond ~‘‘phenol donor stretch’’!, and is
almost 40 cm21 higher in energy than the phenol acceptor
stretch. The other two H-bond stretching modes s 93 and s 94
have dominant amplitudes in the H-bonds between the water
molecules.
Note that there are large atomic displacements associated
with the phenol moiety particularly for the hydrogen-bond
stretching modes, as can be seen in Figs. 3 and 4. The major
component of these atomic displacements can be understood
as rigid-body rotation and/or translation of the phenol moiety
with only minor intramolecular distortions, as is clearly seen,
for, e.g., the s 92 normal mode in Fig. 4, in which the phenol
molecule rotates around an axis perpendicular to the benzene
ring. These large atomic displacements of the phenol moiety
results from the constraints of zero overall linear and angular
momentum for normal coordinates ~the Eckart–Sayvetz conditions!.
Three torsional mode eigenvectors n 98 , n 910 , and n 913 ,
also denoted t 91 , t 92 , and t 93 , are shown in Fig. 5. The parentage of these eigenvectors is in the free-molecule rotations
of the individual water molecules, with the local rotation
axes approximately parallel to the axis of the H-bonded O–H
bond, and with large amplitudes on the free H or D atoms.
These modes are analogous to the torsional normal modes in
the S 4 asymmetric cyclic water tetramer,23 but due to the
much lower symmetry in the phenol•~H2O!3 cluster, there is
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6355
TABLE V. Observed frequencies ~cm21! and intensities relative to the origin for phenol•~H2O!3 and
d 1 -phenol•~D2O!3 in the S 0 and S 1 states. For assignments, see text.
phenol•~H2O!3
Assignment
S0
origin
n 91
n 29
2• n 91
n 39
n 91 1 n 93
n 94
n 59
s 91
s 29
s 93
v 19 1 s 39
2• s 29
S1
origin
n 18
2• n 81
n 82
n 83
n 84
s 28
d 1 -phenol•~D2O!3
Frequency
Intensity
0.0b
18.0
28.6
35.6
43.5
60.8
70.4
83.0
90.7
99.3
104.4
116.9
124.0
135.7
159.8
193.4
215.2
100.0
4.2
5.8
5.5
3.2
2.0
5.7
9.6
6.7
4.8
3.2
2.7
1.7
1.6
2.9
24.2
3.7
289.8
379.0
1.7
3.4
0.0
100.0
11.3
19.4
24.6
40.0
9.8
8.0
12.7
4.8
58.7
65.0
70.9
75.4
80.0
186.9
2.2
2.1
0.9
0.9
1.0
1.0
a
Frequency
Intensitya
0.0c
17.8
100.0
23.9
35.3
9.2
70.7
2.7
93.7
108.4
121.6
125.9
158.9
179.1
199.5
216.5
244.6
6.3
4.0
2.6
2.6
1.6
5.7
6.8
2.1
2.1
0.0
8.0
11.6
21.0
25.7
100.0
7.2
19.0
4.7
13.9
34.4
46.4
50.3
55.2
2.3
2.1
3.0
4.4
a
Relative to the electronic origin.
Absolute frequency 36 261 cm21.
c
Absolute frequency 36 293 cm21.
b
no one-to-one correspondence. The frequencies overlap with
the H-bond stretches, and are very sensitive towards deuteration, with deuteration shifts of 26.3%–28.9%. In contrast to
all modes discussed above, the torsional modes have small
reduced masses. It has been shown for ~H2O!3 ~Ref. 18! and
~H2O!4 ~Ref. 23! that for this type of coordinate the harmonic
description may be insufficient or even totally wrong; due to
the large rms vibrational amplitudes strongly anharmonic
parts of the potential are sampled, and hence the true frequencies may be considerably lower than the harmonic estimate. Thus, in ~D2O!3 the anharmonic torsional frequencies
are up to a factor of 8 lower than the harmonic values! The
frequencies of these torsional modes are especially sensitive
to the relative energies of the other low energy torsional
conformers and the barrier heights between them.33 Although
the shape and symmetry of the potential energy surface
~PES! in the torsional coordinates is quite different for
~H2O!3 and phenol•~H2O!3 , the problem is similar; anhar-
monic multidimensional quantum calculations are necessary
for reliable predictions of torsional frequencies.
The last two families of intermolecular normal modes
~not shown! are librational modes ~rotational parentage! with
small reduced masses and large deuteration shifts. In modes
n 914 , n 915 , and n 916 for phenol•~H2O!3 and n 913 , n 915 , and n 916
for d 1 -phenol•~D2O!3 the local rotational axes of the water
molecules are parallel to the H-bonded ring, and perpendicu9 , n 23
9 , and
lar for the remaining intermolecular modes n 21
n 929 ~n 919 , n 920 , and n 924!.
For several modes, harmonic mode scrambling occurs
upon deuteration, i.e., the orientation of the eigenvectors
changes between phenol•~H2O!3 and d 1 -phenol•~D2O!3 .
Harmonic mode scrambling is especially evident between
stretching and torsional coordinates in n 97 and n 912 of
d 1 -phenol•~D2O!3 , see Table IV. Furthermore, for n 919 and
n 924 of the deuterated cluster, mixing of inter- and intramo-
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1995
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6356
Burgi, Schutz, and Leutwyler: Vibrations of phenol•(H2O)3
FIG. 2. Calculated vibrational eigenvectors and harmonic frequencies for
the lowest-frequency normal modes n 19 , n 29 , and n 39 of phenol•~H2O!3 . All
three modes are characterized by mutual motions of the phenyl group relative to the entire hydrogen-bonded network: n 19 is a ‘‘butterfly’’ motion, n 29 is
a twist around the phenolic O–H bond, and n 93 is a disrotatory or cogwheellike motion. Atomic displacement vectors for a given mode are represented
by rods.
lecular modes occurs, as indicated in Table IV.
The normal mode eigenfrequencies of the other conformers are generally similar, although the eigenvectors can
differ substantially, as will be discussed in Ref. 33. Hence it
is difficult to assign conformers on the basis of the vibrational frequencies only.
IV. EXPERIMENTAL RESULTS AND DISCUSSION
A. R2PI spectra of phenol–(H2O)3 and d 1 -phenol–(D2O)3
Figure 6 shows the R2PI spectra of the phenol•~H2O!3
and d 1 -phenol•~D2O!3 clusters close to the electronic origins,
at 36 261 and 36 293 cm21; these were scaled to equal
height. A number of intermolecular vibrational bands are observed up to 50 cm21 above the origin bands. Table V compiles the frequencies ~relative to the origin! and the relative
intensities of the observed bands. Schmitt et al.10 have
shown by LIF hole-burning experiments that the most prominent bands of the phenol•~H2O!3 cluster belong to the same
isomer. Compared to their LIF excitation spectra we find
somewhat different band intensities in our R2PI spectra, especially with respect to the band at 11.3 cm21. Interestingly,
FIG. 3. Calculated vibrational eigenvectors and harmonic frequencies for
the lowest-frequency normal modes n 94 to n 96 of phenol•~H2O!3 . The first
two modes are deformations of the hydrogen bonded four-membered ring,
n 96 is the hydrogen-bond stretching mode s 91 .
for some vibrations the Franck–Condon factors seem to be
higher for the deuterated species, while the reverse was true
for the phenol•H2O complex.9
The phenol•~H2O!3 band at 0001186.9 cm21 was previously assigned as a stretching mode by Stanley and Castleman and by Schmitt et al.10,8 This band is very weak, in
contrast to the situation in the phenol•H2O complex where
the H-bond stretching excitation is the strongest intermolecular band in the R2PI spectrum.9 In the hole burning spectra
of Schmitt and co-workers10 however, the 186.9 cm21 band
is of comparable intensity to the low frequency bands, which
dominate the R2PI spectrum. This is an indication that IVR
occurs on a time scale of the laser pulse width ~'7 ns! at the
energy of this stretching mode at 186.9 cm21 above the origin. Based on the calculated deuteration shifts for the S 0
state, a corresponding stretching excitation is expected at
'180 cm21 for the deuterated species, but no evidence for
such a band can be seen in the R2PI spectrum of
d 1 -phenol•~D2O!3 . In fact, no bands at all are observed
above '55 cm21 for the deuterated cluster, which implies
that efficient nonradiative channels are available at very
small excess energies.
A direct correlation of the bands in the R2PI spectra of
phenol•~H2O!3 and d 1 -phenol•~D2O!3 is possible, but not unambiguous. The three lowest-frequency bands of
phenol•~H2O!3 at 11.3 cm21, 19.4 cm21, and 24.6 cm21 seem
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Burgi, Schutz, and Leutwyler: Vibrations of phenol•(H2O)3
FIG. 4. Calculated vibrational eigenvectors and harmonic frequencies for
the normal modes n 97 , n 99 , and n 911 of phenol•~H2O!3 , the hydrogen-bond
stretching modes s 29 , s 39 , and s 49 . Note that although the stretching motions are somewhat delocalized, the main stretching deformations can be
associated mainly with one or two of the H-bonds in each case.
to have counterparts in the R2PI spectrum of d 1 phenol•~D2O!3 at the same or slightly higher frequencies
~11.6, 21.0, and 25.7 cm21!. If this correlation is correct, then
the deuteration shifts are small, implying large reduced
masses. This, together with the very low absolute frequencies
implies that these three bands are due to mutual ring motions. i.e., the S 1 state analogs of n 91 to n 93 , cf. Fig. 2. The
small frequency increases upon deuteration could arise from
harmonic mode scrambling in the excited state.
The lowest-frequency band of the d 1 -phenol•~D2O!3
spectrum at 8.0 cm21 has no obvious match in the
phenol•~H2O!3 spectrum. The existence of a second conformer or isomer cannot be ruled out at this stage, and will
be further investigated via hole-burning experiments.
A weak band is observed 6.8 cm21 below the electronic
origin of phenol•~H2O!3 . Since the lowest-frequency intermolecular vibrations in the S 0 and S 1 states are at 18 cm21
~see below! and 11.3 cm21, respectively, and the difference is
6.7 cm21, we assign this as the 111 sequence band of the
lowest-frequency intermolecular vibration n1 . The intensity
of this band is '1.5% of that of the electronic origin. Assuming that the Franck–Condon factor of the 000 and the 111
bands are equal, this implies a vibrational cluster temperature
of T vib'6 K. A tentative assignment for the bands in the S 1
6357
FIG. 5. Calculated vibrational eigenvectors and harmonic frequencies for
the normal modes n 98 , n 910 , and n 913 of phenol•~H2O!3 . These torsional
modes t 19 , t 29 , and t 39 are dominated by hindered internal rotations of the
H2O molecules around their respective H-bonded O–H bonds.
spectra of phenol•~H2O!3 and d 1 -phenol•~D2O!3 ~see Table
V! is based on similarities with the respective S 0 spectra, and
is given after the discussion of the dispersed fluorescence
spectra at the end of the next section.
B. Dispersed fluorescence spectra of phenol–(H2O)3
and d 1 -phenol–(D2O)3
The dispersed fluorescence emission spectra of
phenol•~H2O!3 and d 1 -phenol•~D2O!3 in the frequency range
0– 400 cm21 were obtained at '4 cm21 monochromator
bandpass, and are given in Fig. 7. Table V compiles the
frequencies as well as the relative intensities of the observed
bands and the assignment as discussed below. The origin
bands of phenol•~H2O!3 and d 1 -phenol•~D2O!3 were scaled
to equal height, and are off scale by a factor of 4, in order to
bring out the relatively weak intermolecular bands. There is
no contribution of scattered light to the origin bands, so that
the relative intensities of the emission bands are proportional
to Franck–Condon ~FC! factors for the corresponding transitions.
The dispersed emission spectra of phenol•~H2O!3 and
d 1 -phenol•~D2O!3 look strikingly different. This is unexpected, given the small deuteration effects, the similarities of
calculated frequencies and reduced masses ~see Table IV!.
We conclude that harmonic mode scrambling between the
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Burgi, Schutz, and Leutwyler: Vibrations of phenol•(H2O)3
FIG. 6. R2PI spectra of phenol•~H2O!3 and d 1 -phenol•~D2O!3 in the vicinity
of their electronic origins. Band positions relative to the respective electronic origins are given above the spectra.
two isotopomers must be strong, as well as normal mode
rotation between the ground and excited states ~Dushinskii
rotation!.
1. Frequency range 0 – 50 cm21
At low frequencies, four bands appear in the spectrum of
phenol•~H2O!3 , with intensities 3%– 6% of the origin transition. Based on the ab initio calculations discussed above we
assign the bands at 18.0, 28.6, and 43.5 cm21 to the fundamental transitions of n 91 , n 92 , and n 93 , respectively. The band
at 35.6 cm21 is assigned as 2 • n 91 . The FC factor for 2 • n 91 is
higher than the FC factor for the fundamental n 91 , but this
may be due to a Fermi resonance with n 92 . The calculated
harmonic frequencies for n 91 , n 92 , and n 93 are slightly higher
than the observed frequencies, by 18.3%, 3.5%, and 5.0%,
respectively. The fact that all three mutual ring twisting
modes n 91 , n 92 , and n 93 are moderately active in the spectrum
implies a slight geometric rearrangement of the orientation
of the phenyl ring relative to the O•••O•••O•••O ring upon
electronic excitation.
For d 1 -phenol•~D2O!3 only two bands occur, at 17.8 and
35.3 cm21, but these are the most intense in the spectrum,
with relative intensities of 24% and 9%, respectively. Based
on the frequency we assign the 17.8 cm21 band as n 91 . Given
the large FC factor for n 91 , an overtone of '7% intensity is
expected, and we assign the 35.3 cm21 band as 2 • n 91 . This
implies that bands corresponding to n 92 or n 93 are weak in the
spectrum of d 1 -phenol•~D2O!3 . As mentioned above, this ob-
FIG. 7. Dispersed fluorescence emission spectra of phenol•~H2O!3 and
d 1 -phenol•~D2O!3 , excited at their respective electronic origins ~see Fig. 6
and Table V!, using a monochromator bandpass of 4 cm21. Peak frequencies
relative to the respective electronic origins are given above the spectra.
servation can be rationalized by harmonic mode scrambling
between the n 19 , n 29 , and n 39 modes of phenol•~H2O!3 and
d 1 -phenol•~D2O!3 . The deuteration shift is very small for
n 19 , as was predicted by the calculations.
2. Frequency range 50 – 150 cm21
The weak band at 60.8 cm21 in the phenol•~H2O!3 spectrum is assigned as the combination band of the low frequency ring vibrations n 91 1 n 93 , which borrows intensity
from the nearby 70.4 cm21 band. This band as well as its
counterpart for d 1 -phenol•~D2O!3 at 70.7 cm21 are assigned
as one of the O•••O•••O•••O ring deformation modes n 94 or
n 95 . The calculated harmonic values for these two modes are
69.3 and 74.6 cm21 for phenol•~H2O!3 and 67.3 and 71.0
cm21 for d 1 -phenol•~D2O!3 , respectively. The calculated frequencies for n 94 and n 95 bracket the observed frequencies and
our assignment of the 70.4 cm21 band for phenol•~H2O!3 to
n 94 is tentative. The band at 70.7 cm21 for d 1 -phenol•~D2O!3
is broad, and might consist of two vibrational transitions corresponding to n 94 and n 95 .
In the 75–150 cm21 range a number of band appear in
the fluorescence spectra of both phenol•~H2O!3 and
d 1 -phenol•~D2O!3 , while the ab initio calculations predict a
gap in this range, as mentioned above. An assignment for the
band at 83.0 cm21 in the phenol•~H2O!3 spectrum to n 95 ~calculated at 74.6 cm21! is possible. A different interpretation is
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6359
based on the torsional modes t 91 , t 92 , and t 93 . As noted
above, the harmonic treatment completely fails for these
modes in ~H2O!3 and ~D2O!3 ,18 giving much too large frequencies. Furthermore, in both ~H2O!3 and ~D2O!3 several
torsional bands with frequencies between 80–100 cm21 have
been observed in the FIR.24,25
3. Frequency range 150 – 400 cm21
The most prominent band in the phenol•~H2O!3 spectrum appears at 193.4 cm21 with a relative intensity of
24.2%. We assign this band to the stretching vibration s 92 ,
described above as the phenol donor stretch with a calculated
harmonic frequency of 190.7 cm21. That this intermolecular
vibration is the most active mode in the fluorescence spectrum is not surprising, since the electronic transition is located in the phenol moiety and a displacement along the
intermolecular stretching mode involving the first H2O molecule is expected. As for the stretching vibration of
phenol•H2O,9 the calculated harmonic value at the SCF level
with the 6-31G(d,p) basis set reproduces the observed frequency very well; for phenol•~H2O!3 the observed frequency
~193.4 cm21! is slightly higher than the calculated harmonic
frequency ~190.7 cm21! with a relative deviation of only
1.4%. The band at 379.0 cm21 is attributed as the overtone
band of this stretch, 2• s 92 .
Weaker bands at 159.8 and 215.2 cm21 are observed in
the spectrum of phenol•~H2O!3 with relative intensities of
2.9% and 3.7%, respectively. We assign these two bands to
further stretching vibrations s 91 and s 93 . s 91 is the lowest
frequency stretching vibration of the cluster and described as
the phenol acceptor stretching vibration in Sec. III C. The
agreement with the calculated harmonic values is quite good;
for s 91 ~calculated 153.2 cm21! the difference between observed and calculated frequency is 4.1%, and for s 93 ~calculated 217.1 cm21! the difference is only 0.9%.
Figure 8 shows the dispersed fluorescence spectrum for
phenol•~H2O!3 in the frequency range 0–240 cm21, together
with a stickplot of some calculated harmonic fundamentals.
The assignment are those discussed above, and the agreement between the experimental and calculated harmonic frequencies is evident.
For d 1 -phenol•~D2O!3 , two moderately strong bands are
observed at 199.5 and 179.1 cm21 in the H-bond stretching
region. Based on the calculated frequencies and deuteration
shifts we assign the band at 179.1 cm21 as the phenol donor
stretching vibration s 92 ~calc. 183.2 cm21!. The deuteration
shift is therefore 7.4%, compared to a calculated shift of
3.9%. The band at 199.5 cm21 is assigned as s 93 , giving an
observed and calculated deuteration shifts of 7.3% and 5.5%,
respectively.
The intensity pattern for the two bands is different for
the undeuterated and deuterated cluster. In the former most
of the intensity is in the phenol donor stretching band s 92 ,
while in the latter case both bands ~s 92 and s 93 ! are of comparable intensity. This again indicates that harmonic mode
scrambling is important between these two modes in
phenol•~H2O!3 and d 1 -phenol•~D2O!3 . The weak band at
158.9 cm21 in the d 1 -phenol•~D2O!3 spectrum might be the
counterpart to the 159.8 cm21 band of phenol•~H2O!3 , which
FIG. 8. A comparison of the experimental fluorescence emission spectra of
phenol•~H2O!3 ~top! with a subset of the calculated harmonic S 0 state intermolecular frequencies ~bottom!. The assignment of the individual bands is
given above the spectra ~see Tables IV and V!.
we assigned as the phenol acceptor stretching mode s 91 . Finally the weak band at 216.5 cm21 in the d 1 -phenol•~D2O!3
spectrum is assigned to the combination band n 91 1 s 93 ~see
Table V!.
A comparison of S 0 state vibrational frequencies with S 1
state frequencies is possible for several intermolecular
modes. On the basis of the S 0 state assignments ~see also
Table V!, it seems acceptable to assign the excited-state
bands at 11.3, 24.6, and 40.0 cm21 to the analogous n 81 ,
n 82 , and n 83 vibrations, respectively. This would imply that n3
decreases by about 10% upon electronic excitation, while n1
decreases by almost 40%. For d 1 -phenol•~D2O!3 the bands at
11.6 and 25.7 cm21 can be assigned to n 81 and n 82 , respectively, while there is no obvious assignment for n 83 , in contrast to phenol•~H2O!3 . For the bands at 19.4 and 21.0 cm21
in the R2PI spectra of phenol•~H2O!3 and d 1 -phenol•~D2O!3 ,
respectively, a possible assignment is to the 2 • n 81 mode,
which borrows intensity from n 82 by Fermi resonance, and is
therefore shifted to the lower energy. The band at 55.2 cm21
in the spectrum of d 1 -phenol•~D2O!3 is possibly the S 1 counterpart to the S0 band at 70.7 cm21, and is tentatively assigned to the n 84 vibration. For phenol•~H2O!3 the weak band
at 58.7 cm21 is assigned to n 84 .
The general decrease in frequencies upon electronic excitation shows that the large-amplitude butterfly and twisting
mutual ring modes n12n3 and O4 ring deformation n4 of the
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Burgi, Schutz, and Leutwyler: Vibrations of phenol•(H2O)3
cluster become softer, and for n1 , much softer. Note, however, that there is little geometry change along these coordinates, since the Franck–Condon factors are ,0.1. Similarly,
if the S 0 band at 193.4 cm21 and the S 1 excitation band at
186.9 cm21 are due to the same hydrogen-bond stretch s2 , a
very small ~3.4%! decrease in frequency occurs.
These findings are in qualitative agreement with the observation that the electronic spectral red shifts are small, being dn5292.4 cm21 for phenol•~H2O!3 and dn5255.4
cm21 for d 1 -phenol•~D2O!3!. Comparing to phenol•H2O,
with a spectral shift dn52350 cm21, the spectral shifts are
seen to be smaller in the larger cluster.
These spectral shifts reflect the change of cluster dissociation
energy
D0
upon
electronic
excitation,
dn 5D 0 (S 0 )2D 0 (S 1 ). The relative change in dissociation
energy is thus only '1% for phenol•~H2O!3 , and even
smaller, only 0.4%, for d 1 -phenol•~D2O!3 . The latter conforms with the observation that the S 1 ↔S 0 spectra of
phenol•~H2O!3 and especially of d 1 -phenol•~D2O!3 exhibit
low intensity in the intermolecular vibrations. Hence both the
cluster geometry and the cluster binding energy are very
similar in both electronic states.
V. CONCLUSIONS
Extensive experimental data are presented on the lowfrequency intermolecular vibrations of supersonically jetcooled phenol•~H2O!3 and d 1 -phenol•~D2O!3 in the S 0 and
S 1 states, using dispersed fluorescence emission and twocolor resonant two-photon ionization spectroscopies. In parallel, quantum chemical ab initio calculations on this cluster
were performed; following structural optimizations at the
SCF level, single-point MP2 calculations were made at the
SCF optimum geometry. The energies were counterpoisecorrected for basis set superposition error at both SCF and
MP2 levels.
The calculations predict that the lowest-energy
hydrogen-bonding network is the cyclic homodromic cluster
with four sequential O–H•••O hydrogen bonds. Of the eight
distinct conformers conceivable for this cyclic structure, the
lowest-energy one is predicted to have the ‘‘free’’ phenyl
group or O–H bonds in the Up–down–up–down or (Udud)
conformation. The hydrogen-bonded ring is unstrained, since
the deviation of the hydrogen bonds from linearity is small,
with angles a~H–O•••O! between 7.0° and 12.1°. The calculated well depth and dissociation energy at the SCF1MP2
level, corrected for basis set superposition error, are
D e 528.49 kcal/mol and D 0 520.94 kcal/mol @22.68 kcal/
mol for d 1 -phenol•~D2O!3#. Per hydrogen bond, these values
amount to 7.12 and 5.24 kcal/mol ~5.67 kcal/mol!, respectively.
Based on the H-bond lengths, the strength of the individual hydrogen bonds decreases sequentially around the
ring; the shortest hydrogen-bond has R~O1•••O2!52.78 Å,
between phenol as a H donor and the first water molecule
acting as an acceptor, while the longest H-bond between the
third water molecule and the phenol O atom acting as a
H-bond acceptor has R~O3•••O4!52.90 Å, being 0.12 Å
longer. There is significant correlation between hydrogen
bond angles a~H–O•••O! and hydrogen bond lengths
R~O•••O!; the H-bond nonlinearity increases with increasing
R~O•••O! distance. This cluster structure is chiral, and hence
exists as a pair of enantiomers, (Udud) and (Dudu). The
tunneling splitting which results from interconversion between the two enantiomers is expected to be below our experimental resolution of '0.2 cm21.
Normal mode eigenvectors and harmonic frequencies
were determined from analytical SCF second derivatives.
The intermolecular vibrational modes fall into several distinct classes; in sequence of increasing frequency, these are
~i! relative motions of the phenyl and O4 rings ~20– 45
cm21!; ~ii! deformation modes of the hydrogen-bonded
O•••O•••O•••O ring, ~65–75 cm21!; ~iii! hydrogen-bond
stretches, interspersed with ~iv! torsional modes, in the range
150–300 cm21; ~v! out-of-plane librations ~320– 430 cm21!;
and ~vi! in-plane librations ~640–950 cm21!. The torsions
and librational modes exhibit significant deuteration shifts,
while for the other modes these are very small. For the torsional modes, the predicted harmonic frequencies may not be
relevant, due to the strong anharmonic couplings expected
for these modes, by analogy with the ~H2O!3 and ~H2O!4
clusters.
The intermolecular vibrational bands associated with the
S 1 ←S 0 electronic origin of both phenol•~H2O!3 and
d-phenol•~D2O!3 are narrow and well-resolved; this is in
stark contrast with the observed electronic origins of the
smaller homologous clusters phenol•~H2O!2 ~Refs. 4 – 6, 16!
and d 1 -phenol•~D2O!2 .16 For the h-isotopomer, the main intermolecular vibrational bands belong to the same
isomer/conformer,10 but this is not yet clear for the
d 1 -phenol•~D2O!3 spectrum.
Both isotopomers exhibit a very rich dispersed fluorescence spectrum in the frequency range 0–250 cm21, following excitation at the electronic origin. Many intermolecular
vibrational bands could be assigned, based on the normal
coordinate analysis for the most stable (Udud) cyclic conformer. The observed fundamentals were grouped into three
classes; ~i! the n 91 , n 92 , and n 93 mutual ring torsion modes of
the phenyl and hydrogen-bonded rings; ~ii! the n 94 and possibly n 95 O4 ring deformation modes; ~iii! s 91 , s 92 , and s 93 ,
i.e., three out of four hydrogen-bond stretching modes. For
all of these modes, the agreement of theoretically predicted
frequencies with observed frequencies is very satisfactory.
None of the intermolecular modes of rotational parentage
~torsions, librations! was clearly identified. In the S 1 ↔S 0
electronic transitions, the displacements along all of the intermolecular vibrational coordinates are modest or small, implying small structural changes upon electronic excitation.
Similarly, the change in intermolecular binding energy upon
electronic excitation is small, on the order of 0.5%–1%.
Further spectroscopic investigations will address the
identification of other conformers, which are expected on the
basis of ab initio calculations, but have not yet been identified, and the further elucidation of some of the vibrational
assignments.
ACKNOWLEDGMENT
This work was supported by the Schweiz. Nationalfonds
~Project No. 20-33’879.92!.
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Phys., Vol.
No.
15,2013
15 October
1995
129.194.8.73
On: 103,
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Dec
10:10:40
Burgi, Schutz, and Leutwyler: Vibrations of phenol•(H2O)3
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This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to IP:
J. Chem.
Phys., Vol.
No.
15,2013
15 October
1995
129.194.8.73
On: 103,
Fri, 13
Dec
10:10:40