109
vibrational Sgectroscopy, 5 (1993) 109-117
Elsevier Science Publishers B.V., Amsterdam
Infrared absorption in hydrogen-bonded complexes
and absorption of an excess electron
in hydrogen-bonded solvents
H. Abramczyk
Instituteof Applied Radiation Chemistry, Technical University, Wr6blewskiego 15, 93-590 t&if (Poland)
(Received 3rd September 1992)
Abstract
A comparison was made between the theories of IR absorption in hydrogen-bonded complexes and near-IR and
visible absorption of an excess electron in hydrogen-bonded solvents. The near-IR and visible absorption spectra of
excess electrons in water, alcohols, amines and alkanes were calculated in terms of electron-vibron coupling. The
role of the hydrogen bond on electron stabilization and solvation is discussed.
Keywords: Infrared spectrometry; Excess-electrons; Hydrogen-bonded complexes; Hydrogen-bonded solvents; Infrared absorption
The IR absorption spectrometry of hydrogenbonded (H-bonded) complexes and near-IR and
visible absorption of an excess electron have many
common features. It will be shown that the theoretical formalism to describe the band broadening mechanisms is very similar in both instances.
Moreover, the vibrational dynamics of H bonds
play an important role in localization, electron
attachment, stabilization and solvation of an excess electron generated by radiolysis or photoionization in H-bonded solvents.
COMPARISON BETWEEN THEORIES OF IR ABSORPTION IN HYDROGEN-BONDED COMPLEXES AND
NEAR-IR AND VISIBLE ABSORPTION OF AN EXCESS
ELECTRON IN HYDROGEN-BONDED SOLVENTS
Various theoretical approaches have been proCorrespondenceto: H. Abramczyk, Institute of Applied Radiation Chemistry, Technical University, Wr6blewskiego 15, 93590 tidi (Poland).
posed to understand the origin of most of the
characteristic spectroscopic properties of IR absorption in H-bonded complexes. The various
theoretical approaches used in the treatment of
the stretching mode v&XI31 in H-bond complexes
may be classified as the weak coupling limit [l-5]
and strong coupling limit [6-81.
The weak coupling of the system to the bath is
treated through perturbation theory and it can be
used only for weak H-bonded complexes. For
medium-strong and strong H-bonded complexes
the interactions are sufficiently strong that the
vibrational relaxation (dephasing) cannot generally be treated through perturbation theory. In
the strong coupling limit, the Hamiltonian in the
excited vibrational state depends linearly (or
non-linearly) on the external coordinate Q coupled to the internal vibrational mode q. This term
is called the strong coupling term.
In the strong coupling method, the hamiltonian is diagonalized by performing a canonical
transformation.
For weak coupling of an H-
0924~2031/93/$06.00 0 1993 - Elsevier Science Publishers B.V. All rights reserved
110
bonded system to a bath, the cumulant expansion
approach is usually used, assuming that the coupling is a purely classical stochastic Gaussian
process for which the cumulant expansion may be
truncated beyond second order.
Substantial progress has been made in elucidating the physical nature of this coupling. Two
main relaxation mechanisms have been proposed.
One of these considers broadening mechanism of
the band as the direct dipolar interaction of the
dipole moment of the complex to the local fluctuating electric field produced by the solvent dipoles
as proposed Zundel and co-workers 191,or of the
dipole moment of the proton donor and the dipole
moment produced by the H bond as proposed
Abramczyk [S,lO] in the complex regarded as a
non-rigid supermolecule. The other is an indirect
relaxation mechanism caused by the anharmonic
coupling of the high-frequency V&X-H) stretching mode to the low-frequency hydrogen bridge
vibration V-(X-H ***Y) [l-4,7-8]. The IR band
shape of the mode is controlled by the dynamics
of the bridge motion (X-H ***Y).
Both the weak and strong coupling theories
can be classified according to the level of approximation in treating the dynamics of the bridge.
Bratos 111assumed that the time dependence of
the coupling of the vV mode to the envinroment
(bath) is suppressed (static limit). The X . **Y
bridge is regarded as a Brownian oscillator obeying the Langevin equation in the model of
Robertson and Yanvood [3] or the generalized
Langevin equation in the model of Sakun [4]. The
interaction of the oscillator with bath is ignored,
so that the X. . . Y length is allowed to oscillate
without damping in the gas phase in the
Marechal-Witkowski model [7].
More recently, an approach by Boulil et al.
[ill has been reported, which is a fully quantum
mechanical theory and the coupling to the bath is
decribed as intermolecular resonance energy exchange with the molecules of the inert solvent
(bath). This model is able to connect the
Marechal-Witkowski
approach in the gas phase
and the theories in the liquid phase.
For medium-strong and strong H-bonded complexes it is believed that additional IR band-shaping mechanisms are efficient: Fermi resonances
H. Abramczyk /Vii. Spectrosc. 5 (1993) 109-117
between vs and combinations or overtones (e.g.,
the doubly excited in-plane hydrogen bending
and the doubly excited out-of-plane hydrogen
bending), mechanical and electrical anharmonicity of the mode itself, a double-well potential
governing the motion of the proton stretching
vibration, causing tunnelling of the proton to the
acceptor Y.
The theoretical aspects of strong H-bonded
complexes have been discussed in several papers
[2,12]. The IR band shape theories of strong H
bonds could explain not only the facts that the
band is very broad, much more intense and shifted
to lower wavenumbers compared with the position of the free band, but also a well defined
structure, especially Evans windows and A, B and
C bands. Bratos and Ratajczak [2] have shown
that Fermi resonances results in the A, B and C
bands whereas Hofacker et al. [13] have pointed
out that the theoretical intensities for this mechanism for carboxyhc acids deviate drastically from
the experimental intensity pattern.
Recently, a model has been proposed [14] that
is intended to cover the gap between weak and
strong H-bonded complexes. A model was presented in which the IR band shape theories for
weak and strong H bonds becomes the particular
cases of the general description. It is assumed
that the proton motion occurs in a single- or
double-potential well and is accompanied by the
anharmonic
coupling to the low-frequency
stretching mode of the bridge vJX-H ***Y).
The streching mode V&XI-I) is coupled to the
V-(X-H . **Y) mode and the strong coupling limit
theory has been used to describe this interaction.
The low-frequency
mode vJX-H
- ** Y) is
damped by the environment undergoing intermolecular resonant energy exchange with the
molecules of the solvent. The interaction between
the vJX-H . **Y) and the environment is responsible for the time evolution of the coupling
strength between v&XII) and vJX-H ***Y).
Both the potential well shape and the strength of
the coupling are randomly modulated with time.
The two lowest states of a potential well are
weakly coupled to the solvent (Markowian approach). The fluctuations of the potential well
and the vibrational energy levels arising from the
111
H. Abramczyk/ Kb. Spectmsc. 5 (1993) 109-117
direct coupling to the environment are described
by the stochastic Liouville equation.
This physical mechanism underlying the IR
V&XI-I)absorption band width with a fully quantum mechanical description and discussion in
terms of “Franck-Condon
progression” is in
analogy with the case of vibronically broadened
electronic bands in molecules. This analogy is
even greater for the case of electronic absorption
of an excess electron trapped in a solvent. Recently, an absorption band-shape theory of an
excess electron in condensed media has been
proposed [15]. The theoretical details can be
found elsewhere [15-201. Here an outline is presented of the analogy between the IR band
broadening of the vibrational mode v&XII) and
visible band broadening of an excess electron
(Table 1).
If one considers an electronic transition tz = 0
+ 1 of an excess electron and a vibrational motion u = 0 + 1 in an adiabatic approximation, it is
stated that in both instances similar theoretical
formalism can be used. The fast motion of an
electron coordinate r is coupled with the slow
motion of vibration 4 of the molecule being a
trapping site or belonging to the cavity that has
been formed around the electron. However, this
vibrational motion, which is slow in comparison
with an electron, becomes the fast motion 4 for
the H bond, because it is coupled with the lowfrequency mode of the hydrogen bridge Q.
Additional mechanisms of band broadening
are also similar: the direct dephasing of electronic frequencies due to the statistical variety of
an electron environment plays the same role as
the direct dephasing of vibrational frequencies of
vibrational bands. Tunnelling, although it cannot
be excluded, seems not to influence the band
widths much in either instance. Band broadening
due to the different potential wells of the ground
and an excited state (different frequencies in the
ground and excited states) can be formally de-
TABLE I
Analogy between solvent-broadened vibrational line shape in H-bonded complexes and vibronically broadened electronic band
profile of an excess electron
Fundamental
transition
Fast motion
Slow motion
Fast motion
states
Coupling
mechanism
Additional band
broadening mechanisms
Excess electron
H-bonded complex
e- . . . X-H
4
e
X-H
4
n = 0 + 1 of electrons
u = 0 --) 1 of X-H vibration
rektrons= r
9
Electron eigenfunctions:
W, 41, Mr, 4)
Energy eigenvalues:
E,(q), -q(q)
=o
-_=O
q of vs (X-H)
... Y
Q
Vibrational eigenfunctions:
$o(g, Q>,4&r, Q>
Energy eigenvalue:
4,(Q), J%(Q)
=o
-_=O
a4
aQ
(a) Direct dephasing of electron
(a) Direct dephasing of
states by solvent
vibrational states by solvent
(b) Tunnelling of an excess
(b) Tunnelling of proton
electron
(c) Fluctuations during transition due to
different potential wells in the ground
and the first excited states
112
scribed in both instances as a fluctuation with
time of the parameters characterizing the energy
potential well in which the transition occurs.
THE INFLUENCE OF HYDROGEN BONDING ON THE
LOCALIZATION, ELECTRON ATTACHMENT, STABILIZATION, SOLVATION, DYNAMICS OF THE LOCALIZATION AND SPECTROSCOPIC PROPERTIES OF AN
EXCESS ELECTRON IN HYDROGEN BOND-FORMING
MATRICES
Despite much experimental and theoretical interest, the influence of H bonding on the localization, electron attachment, stabilization, solvation,
dynamics of the localization and spectroscopic
properties in bulk liquid ammonia, water and
other matrices and also in small clusters remains
unclear. The theoretical calculations should be of
help in finding the sites of preferential attachement within a molecular cluster and to establish
whether an electron forms the cavity with the
electron in the centre through breaking the existing H-bond structure, is attached to pre-existing
groups of the molecules with free OH or NH
bonds or does not break the H-bond structure
being attached as an additional electron in the
diffuse solvent anionic complex.
In order to answer these questions, three main
structures have been considered for the H-bonded
solvents: the electron localized in the cavity
[21,28]; the solvated diffise anionic complex [29341; and the polaron [351.
The structures with the electron in the cavity
are currently most favoured but the question remains of what the structure of the cavity is and
what the sites of preferential attachement within
a molecular cluster are. In the framework of the
cavity models, dipole-oriented [22,28,36] and H
bond-oriented [37-421 structures have been considered for H-bond solvents. Alcohols seem to
ignore the H-bond, creating a dipole-oriented
cavity [28]. In contrast, the H bond-oriented cavities seem to exist in water, ammonia and amines
[23,27,38-421. Experimental electron spin resonance results [241, molecular dynamic simulations
and some ab initio calculations [22,33,34,40,41,43]
suggest that six protons in OH or NH bonds are
H. Abramczyk / Vii. Spectrosc. 5 (1993) 109-l I7
directed towards the electron localized at the
centre of the (H,O);
or @WI,& cavity. The
results of Newton [221 showed that the cavity
seems to be formed by the free OH or NH groups
and fully H-bonded molecules do not appear to
offer especially favourable trapping sites.
The theoretical calculations are consistent with
the nozzle beam studies [44] where an increase in
signal intensity at n = 6 is observed. However,
most unexpected is the detection of (H,O);
dimers [44], because it seemed that only larger
clusters are required for both water and ammonia
for trapping of the electron.
Despite ab initio results for the electron in the
negatively charged clusters which depend strongly
on the diffuseness of the basis set, a few marked
differences in the structure of the hydrated and
ammoniated electron can be observed: the size 06
the cavity for NH, is calculated to be 3.9 A
whereas that for water is 2.6 8, [22]; the breathing
force constant of the e,
cavity is markedly
smaller than that of the e& cavity; the ammoniated electron is calculated to be appreciably less
strongly bound than the hydrated electron or
even unbound electron relative to the isolated
electron and six ammonia molecules [221; the
electron spin density on the proton in water is
positive whereas in ammonia it is negative [2223,361; and ammonia clusters of any size do not
form well-bound excess electron surface states
1391.
A second problem is the role of H-bond interactions on the dynamics of the electron localization and stabilization. Barnett et al. [39] investigated by molecular simulation experiments very
early stages following excess electron injection in
ammonia and water. They started from the system in which an electron is initially attached to
an equilibrated neutral cluster in the ground electronic state in the pre-existing trapping sites due
to the process of multi-phonon non-radiative
transitions [45] or as a result of the charge-induced polarization [46-481. The H-bond interactions play a role in the first stage of the dynamic
of excess electron migration (0.15-4 ps for the
ammonia clusters and 0.15-l-2 ps for water) during the reorganization in the vicinity of the electron with the NH or OH bonds pointing to the
H. Abramczyk/V%.
113
Spectrosc. 5 (1993) 109-117
centre of the excess electron as a final result. In
the next step, migration of the electron towards
the centre of the cluster occurs, characterized by
polaron-like dynamic evolution. The processes of
the excess electron migration are slower in ammonia than in water. The question arises of what
the major interaction is that is responsible for the
equilibrium structures suggested by molecular dynamics simulations and electron spin resonance
of the solvated electron in H-bonded solvents.
Clark and Illing 1231 suggested that the major
interaction, apart from the spin polarization, is H
bonding with the localized electron as a donor to
the antibonding a& or a& orbitals in water
and ammonia.
RESULTS AND DISCUSSION
As mentioned in the Introduction, a theory of
the absorption spectrum of an excess electron has
recently been proposed [151. The theoretical development considers the contribution to the absorption band profile from the coupling of the
excess electron with the vibrational intramolecular modes of the matrix, inhomogeneous broadening due to the statistical variety of trapping sites
and tunnelling. The vibrational coupling between
the excess electron and the solvent molecules
modifies the equilibrium structure by the selective attachement to the intramolecular vibrational
modes of the molecules forming the trap (in
terms of the “cavity” or the “solvated anion”
model). The vibrational coupling is treated in the
framework of the strong coupling limit theory.
Theoretical spectra were calculated in the visible and near-IR range of the electron solvated in
water, alcohols, ammonia, amines, ethers and
alkanes. The comparison between the theory and
experiment suggests that the coupling between
the excess electron and the intramolecular modes
of the solvent plays the dominant role on the
absorption bands of the excess electron in both
the visible and the near-IR regions. The model
generates the peak position, the width and the
asymmetry of the visible (equilibriated) spectra of
the solvated electron in water, methanol, ammo-
go-4(l.md-‘.mi’
I
1
---~.-----..-
0
. . .._- _ .__. _ _.___.__ __.___.___
‘c
1.0
2.0
I ev )
3.0
Fig. 1. Visible absorption spectrum of water at 300 K: solid
line, experiment; dashed lines, theory; coupling with the vibrational modes; (1) torsional V, (710 cm-‘); (2) bending IQ,
(1595 cm-‘); (3) stretching vs (3600 cm-‘).
nia, methylamine, trimethylamine, propane and
3-methylpentane with good accuracy.
It has been shown that the band widths arise
from the combination of the vibronic bands due
to the coupling of the electron with the lowfrequency modes: torsional vt or bending vt,
modes. Some of the results are given in Figs. 1-5.
In matrices that form H bonds, an excess electron
is coupled with the torsional mode, at 710 cm-r
for water, 320 cm-’ for ammonia and 370 cm-’
for methylamine. The only exception is methanol,
a
1.0
2.0
3.0
I eV
I
Fig. 2. Visible absorption spectrum of methanol at 298 K:
solid line, experiment; dashed lines, theory; coupling with the
vibrational modes; (1) stretching v&OH) at 3679 cm-‘; (2)
bending v,JCOH) at 1345 cm-‘; (3) stretching v&H) at 3000
cm-‘; (4) bending vt,(CH) at 1450 cm-‘; (5) stretching I&O)
at 1050 cm-‘.
H. Abramczyk / Vii. Spectrosc. 5 (1993) 109-117
0.5
1.0
IeV)
15
Fig. 3. Absorption spectrum of ammonia at 203 K: solid line,
experiment; dashed lines, theory; coupling with the vibrational
modes; (1) symmetric stretching v, at 3298 cm-‘; (2) symmetric bending vb at 1070 cm-‘; (3) asymmetric stretching vS at
3380 cm-‘; (4) asymmetric bending vt, at 1658 cm-‘; (5)
torsional vt at 320 cm-t.
where the electron is coupled with the bending
mode v,(C-OH) at 1345 cm-‘. In non-H-bonded
solvents an excess electron is coupled with the
bending modes lying at low frequencies: The
v,(C-N-C)
mode at 365 cm-’ for trimethylamine, v,(C-O-C)
at 440 cm-’ for diethyl
ether, v,(C-C-O)
at 596 cm-i for tetrahydrofuran, v,(CCC) at 323 cm-’ for propane-d, and
v,(CCC> at 444 cm-’ for 3-methylpentane. From
this selective attachment deductions can be made
about the geometry of the cavity or the preferential sites on an anion.
9.0
t
c’
‘..,
jj6.0.
I,.,
‘..,
Lu=
>O
F
4: _13.0_ j
i$
::’
k
.: :f,-yi_
...
i....,,
....‘..,
‘...,
“.,......,_,
O 0 ‘,
0.5
I”
(eV)
Fig. 4. Absorption profiles of the electron solvated in diethyl
ether at 211 K. Dotted line, experiment; solid line, theory;
coupling with the bending mode v,(COC) at 440 cm-‘.
IeV 1
Fig. 5. Absorption profiles of the electron solvated in tetrahydrotitran at 211 K: dashed line, experiment; solid line, theory;
coupling with the bending mode v&OC) at 596 cm-‘.
It is well known that in H-bond complexes the
stretching vS and the torsional vt modes are the
most sensitive on H-bond interaction. Taking this
fact into account, it was concluded that the absorption spectra in water, ammonia and methylamine should be ascribed to the electrons in H
bond-oriented
cavities, whereas in alcohols,
ethers, alkanes and trimethylamine to the electrons in dipole-oriented
cavities. The vibronic
bands are broadened by the coupling of the intramolecular modes ut or v,, with the lowfrequency modes of the bath. In H-bonded matrices these are the modes of the hydrogen bridges.
It was found that the inhomogeneous broadening
due to the distribution of solvent environments
plays a minor role on the band shapes. The
short-time dynamics probed by the spectral band
shape is not affected by tunnelling.
The results linked to the near-IR absorption
(transient band) led to the conclusion that the IR
spectra of excess electrons in alcohols have a
different origin to those in water and aqueous
glasses. In alcohols there are two kinds of trapped
electrons, which are distinctly different in nature.
The visible-absorbing electrons are associated
with the OH traps in alcohol matrices [coupling
H. Abramczyk / Wb. Spectrosc.
0.6
‘7
04
...’
II
,._.;”
05
f’
,,./
,?
k
o,3 6
p
/
i
!
.Y’
/
.I’
0.2
0.1
115
. ..+..
/
KY*;:
“.
‘;..
\,
\
.__..
2
‘A.
.
‘1
‘...Y.
.:.
‘1
‘X...
‘x.,‘..
‘1
“...:,..
%.
‘.__ .
“..._ ._
‘X ....._. _-- ____
3
1’
t
10
20
3.0
eV
Fig. 6. IR absorption spectrum of ethanol at 77 K: solid line, experiment; dashed lines, theory; coupling with the vibrational modes;
(1) stretching v&CH) at 3000 cm-’ in shallow alkyl trap; (2) stretching vS(OH) at 3660 cm-’ in deep hydroxyl trap; (3) stretching
v&OH) at 3660 cm-’ in shallow trap (presolvated electron).
with the bending mode YJOH)] whereas the IRabsorbing electrons are trapped in the alkyl group
(coupling with the CH stetching modes) (Fig. 6).
The distinction between the two, kinds of
trapped electrons has been indicated by many
workers [49-521 and the present results support
their conclusions. In contrast, the IR absorption
in water has a different origin. There is only one
kind of trap in water, the OH trap. The visible
band is associated with the electron coupled with
I
10
the torsional mode vt (710 cm-‘) whereas the IR
band is due to the electron in the same trap
coupled to the stretching mode v&OH) (at 3651
cm-’ for H,O and 2660 cm-’ for D,O). The
coupling with v&OH) or v,(OD) becomes weaker
with time when an electron reaches the stages
closer to equlibrium, which results in a decrease
in the IR absorption.
Strong evidence in favour of this interpretation
is the failure to detect IR absorption in H,O at
*
20
31)
eV
Fig. 7. IR and visible absorption spectrum of water at 77 IQ coupling with the vibrational modes; (1) stretching u&OD) at 2660
cm-‘; (2) stretching vs(0I-I) at 3651 cm-‘; (3) torsional vt at 710 cm-‘.
116
low temperatures in contrast to D,O matrices.
This seemed suprising because the molecular
structures including the ability to form H bonds
are very similar in both matrices and the depth of
the electron potential well should be nearly the
same. The model is able to explain it on the basis
of the different vibrational properties of protiated and deuterated matrices.
It has been shown that the absorption in the
near-IR region for the coupling with v&OH) is
much weaker than in D,O for the coupling with
v,(OD). It should be stressed that the differences
between H,O and D,O are not the result of any
arbitrary change in parameters. The results in
Fig. 7 were calculated for the same set of molecular properties. The only different parameter that
causes the different spectrometric behaviour of
H,O and D,O is the frequency of the vibrational
stretching mode v&OH) (at,,, = 3651 cm-’ for
H,O and 2660 cm-’ for D,O) which was taken
from IR experiments. Hence the isotope effect on
the absorption spectra is not the result of any
arbitrary reparametrization,
but comes from the
coupling between the excess electron with the
same mode v&OH) having different frequencies
on deuteration.
The vibrational coupling of the electron is able
not only to explain the appearance of the IR-absorbing band in D,O and its absence in H,O
matrices at low temperatures, but also to reproduce the difference in the band widths and the
peak positions of the visible bands in H,O and
D,O. Further evidence in favour of this interpretation is the finding that the conversion em + evis
is observed in alcohols and but not or to a much
lesser extent in water. The conversion in alcohols
is possible due to the different traps responsible
for the IR and visible absorption. In water there
exists only one kind of trap, which means that the
idea of conversion loses its sense.
Conclusions
The results provide strong arguments [16-201
that the dynamics of the excess electron are governed by vibrational properties of matrices in
which the electron is trapped. It has been indicated which vibrational modes are coupled with
H. Abratnczyk / Vii. S’ctrosc. 5 (1993) 109417
an excess electron in typical matrices. It has been
shown that in H-bonded matrices the vibrational
modes which are the most sensitive on H-bond
formation, i.e., the stretching mode V, and the
torsional mode vt, are coupled with an electron.
The coupling with the high-frequency stretching
mode u, determines the absorption of the transient band in the near-IR region whereas coupling with the low-frequency torsional mode vt
determines the absorption of the equilibrium band
in the visible range. This suggests that an electron
is involved in some kind of H-bond interaction
with the solvent molecules forming an H-bonded
trap.
In other matrices dipolar interactions between
the solvent molecules and an electron seems to
determine the spectrometric properties of the
absorption bands of an electron. In this instance
the electron is coupled with the vibrational modes,
which strongly modifies the dipole moments of
the molecules like bending modes. However, many
details, some of which are fundamental, remain
to be elucidated. The critical point is not that a
fit of the experimental spectra is achieved, but
what physical insight about the band shape can
be gained from this theory in its present form. In
addition, the experimentally measured spectra of
the solvated electron were readily reproduced in
the past by a wide range of sometimes mutually
exclusive ad hoc models. Further work on the
applications of the theory to a variety systems is
necessary to establish whether its derived parameters show physically sensible trends and to clarify its physical implications concerning the band
shape.
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