# The Role of Fermi Resonance in Formation of Valence Band of Water Raman Scattering

Authors: Sergey A. Burikov; Tatiana A. Dolenko; Victor V. Fadeev
Journal: Research Letters in Optics
 (2008)

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## Abstract

The role of Fermi resonance in formation of valence band of water Raman scattering was investigated. Simultaneous measurement of characteristics of bending and valence bands of water inD2O solutions, KBr, and KCl and using genetic algorithms in conjunction with variation methods allowed increasing accuracy of estimation of Fermi resonance coupling constant and of Fermi resonance contribution into formation of water Raman valence band.


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## Body

## 1. Introduction

Until now, mechanisms of   formation of Raman valence band of water are
not clarified. Many attempts (see, [1–6])
to determine contributions of intra-
and intermolecular interactions and Fermi resonance (FR)—resonance between symmetric valence vibration v1 and overtone of bending vibration 2v2 of water
molecule—did not lead to definite
conclusions. Under FR energy transfers from vibration v1 to overtone 2v2 [1–6] occurs.
This energy transfer can explain existence of the shoulder in low-frequency
part (in the region 3300 cm-1) of water Raman valence band. If
authors of  [6] account that FR role is not too great, that according to
calculations in [4] the contribution of FR into water Raman valence band is
unexpectedly great, and according to [7] FR does not influence the formation of
water Raman valence band. Contradiction in the opinions about the role of
FR in vibrational spectra of water is connected with absence of precise methods
of calculating frequencies and intensities of intramolecular vibrations in
spectra of liquids. Nevertheless, different models of FR are discussed in
literature [2–5], and different methods of calculation of FR quantitative
characteristics are suggested [1–9].According to
the generally received model [1–3, 5], the scheme of splitting of bands of
intramolecular vibrations due to FR is presented in Figure 1. Valence
vibrations of OH bond with
“unperturbed” frequency vu are split into symmetric vs and antisymmetric va   components due to intramolecular
interactions (V is the constant of intramolecular coupling). Due to
intermolecular interactions, vibrations
with frequencies vs, va are split into in- and
out-of-phase vibrations vs−in, vs−out and  va−in, va−out
(υs and υa are the intermolecular
coupling constants). Due to intermolecular interactions, the bending vibration v2  is split into v2−in and  v2−out (overtones 2v2−in and 2v2−out). As
frequencies of overtones of the bending vibration are closed to frequencies of
symmetric valence vibrations, it is possible that FR can take place between
pairs of vibrations of the same symmetry—(vs−in and 2v2−in) and (vs−out and  2v2−out) [1]. At the
same time, vibrations with vs−in and 2v2−out are
transformed into vibrations with vs−in′ and 2v2−in′, and vibrations with vs−out and 2v2−out are
transformed into vibrations with vs−out′ and 2v2−out′
(Figure 1).Figure 1
Model diagram of Fermi resonance in water. The vertical lines mark the
band positions; the dashed lines show the splitting.In the literature [1, 6] it is
assumed that FR is caused by anharmonicity of vibrations and from the point of
view of the perturbation theory authors describe the FR by the following system of equations:(1)R=I1/I2=(Δ+Δ0)/(Δ−Δ0),Δ=Δ02+4W2, where R is the ratio of
intensities of FR components, Δ0 is the initial splitting of
levels in absence of FR, Δ is the splitting of levels in presence of FR,  and W is the matrix
element of interaction of two vibrations, or the coupling constant of FR.The valuesΔ
and Δ0 cannot be measured experimentally. Furthermore, now there are
no precise   methods for calculating frequencies of bending and valence
vibrations without FR and in presence of FR. This is why calculation of the
coupling constant of FR W is a complicated problem.To estimate
the valueW, the authors of [3, 5] decomposed the valence band of isotropic
water Raman spectrum into components (the curves of Gaussian shape or the
components of Fourier deconvolution). If the difference of maximum frequencies
Δ of two from these components and the ratio of
their intensities R=I1/I2 are determined, the values of Δ0 and W will
be found from system(1).
According to the data of different authors,
the calculated values of W are changed in wide ambits: for H2O-97 cm−1 [3],
99.5 cm−1 [5],
36 cm−1 [6], 151 cm−1 [8],
83.5 cm−1 [9]; for solutions of LiCl (12 m)-70 cm−1 [3]. The most of obtained values W confirm the assumption about significant role of FR in
formation of water Raman valence band in comparison with intramolecular
(V=23 cm−1 [3], 32 cm−1 [5]) and intermolecular interactions (υ=96cm−1 [3], 42 cm−1 [5]).It is obvious that next steps in the discussion about
the role of FR in formation of water valence band should be connected with new
experimental approaches and new methods of spectra processing. In this paper,
parallel measurements of characteristics of valence and bending bands of water
were carried out for solutions of HDO and of KBr and KCl salts. For precision
analysis of bands, the genetic algorithms [10] were used together with
variation methods. This allowed increasing the accuracy of estimation of FR coupling constant
and of its contribution into the
formation of water Raman valence band.


## 2. Experiment

Excitation of
Raman signal was performed using argon laser radiation (wavelength 488 nm,
power 450 mW). The spectra were measured in 90° geometry using monochromator (Acton
2500i, resolution 2 cm−1) and photomultiplier (Hamamatsu H 8259-01) with photon counting
system.To
study the FR in water, the polarized and depolarized Raman bending and valence
bands of distilled water and of water in solutions of KBr, KCl salts (the
concentration range was from 0 up to 4 M with the step 0.4 M) and in solutions
of HDO (the concentration range ofH2O in D2O was from 0
up to 100 mole % with the step 5–10 mole %) were
obtained simultaneously.


## 3. Results and Discussion

Raman bending   and valence
bands of water in solutions of salts and HDO in the region
1000–3800cm−1
are presented in Figures 2 and
3. With increasing concentration of salts,
the intensity of the high-frequency region of Raman valence band increases; and
that of the low-frequency region decreases, the band shifts towards higher
frequencies.  Under this, the position of the bending band remains practically
unchanged,  and the intensity increases significantly (1.5–2 fold under high concentrations).Figure 2
Experimental
water Raman valence band of water solutions of KCl and HDO.Figure 3
Experimental bending bands of water Raman spectra in solutions of KCl
and HDO.In this
study, the method of calculation of Fermi coupling constants using formula
(1)
is suggested. This method differs from the one used previously by the
following. First, we obtained the experimental bending and valence bands of isotropic
Raman spectra of water in solutions of HDO. Therefore, at our service we had
the frequencies of overtones of bending vibrations OH groups under low
concentration of H2O in D2O, that is in absence of FR.
Second, formulas in (1), which were used by many authors [3, 5] to calculate the
Fermi coupling constants, suppose measuring of the value R—the ratio of
intensities of FR components (in [3, 5] this is the ratio of intensities of the
curves of Gaussian shape or the components of Fourier deconvolution). Such
determination of R is correct on the hypothesis that the intensity of the
low-frequency region of water Raman valence band (3250–3350 cm−1) is caused only by FR.
But the role of FR in the formation of water Raman valence band is now only
being ascertained. Therefore, calculation of the R values by the components
intensities is a procedure that is not fully correct.The
experimental bending Raman bands of water in HDO solutions
obtained in this study allowed us to calculate
the value ofW without using R. It is
calculated by
(2)Δ2=Δ02+4W2.To calculate the FR coupling constantW by (2),
it is necessary to know
the frequency of the bending vibration overtone and the frequency of the
symmetrical valence vibration without FR (unperturbed frequencies) and
in presence of FR (split frequencies).Theunperturbed frequencies were determined
from experimental water Raman spectra in solutions HDO. It is
supposed [2, 3] that in HDO
solutions with low concentration of H2O
groups, OH in molecules
HDO, and in
surrounding of D2O molecules are isolated from interactions with the
other OH groups, that is, there are no intermolecular interactions between OH
groups; and the FR is absent too. Therefore, as the unperturbed frequency of bending vibrations, the frequency of maximum of the Raman bending
band of OH groups in HDO solution
with very low concentration of H2O in D2O was choused.
According to our experimental data v2u=1640 cm−1.Theunperturbed frequency of valence vibrations was calculated as the point of intersection of
the dependences of the maximum frequencies for isotropic vmaxisotr (CH2O) valence
and
anisotropic valence vmaxanisotrop (CH2O)  Raman bands
on concentration of H2O in D2O
(Figure 4). According to data of [3],
these dependences intersect at point 3434 cm−1 at concentration 12
molar % H2O in D2O. According to our data
(Figure 4) the straight lines of the dependences vmaxisotr (CH2O)
and vmaxanisotr (CH2O)
intersect at 10% concentration of H2O in D2O in the point
vmaxu=3432 cm−1.Figure 4
Determination ofvu—crossing viso (CH2O) and vaniso (CH2O).According to
the diagram of vibrations splitting (Figure1), one can suggest that the
isotropic valence band consists of four components: the overtone of bending
vibrations, symmetric valence vibrations of molecules with C2v symmetry participating in FR, symmetric vibrations of water molecules with
another symmetry (e.g., Cs) not participating in FR, the component
corresponded to nonboned (or weekly bonded) molecules, the vibrations of which
provided the peculiarity of high-frequency shoulder of valence band (Figure 2).
Therefore, to find the split frequencies of symmetric valence vibrations
of H2O molecules, the decomposition of the isotropic valence band
into four Gaussian curves was performed.The
decomposition of the isotropic valence band into the components was performed
with the help of genetic algorithm (GA) [10] (GeneHunter add-on from Ward
Systems Group, Inc. for Microsoft Excel) in combination with the generalized
reduced gradient (GRG2) algorithm of nonlinear optimization (standard Solver
add-on to Microsoft Excel).As thesplit frequencies of the overtone of bending and symmetric valence vibrations of
water molecules, the frequencies of maximums of the first two Gaussian components
were accepted. The values of FR
coupling constants W were calculated by (2).The results of decomposition of valence bands of
isotropic water Raman spectra into Gaussian curves and the calculated FR
coupling constants for distilled water and for solutions of maximal
concentrations are presented in Table1.Table 1
The frequencies of the Gaussian components maxima and the calculated FR coupling constants for distilled
water and for solutions of maximal concentrations.
v1Gaus=2v2, cm−1v2Gaus, cm−1v3Gaus, cm−1v4Gaus, cm−1W, cm−1Distillate321133183436361154KBr,4M324133713488354139KCl,4M323333653479354838Calculations showed that at concentration of KBr and
KCl increasing from 0 up to 4 M, the FR coupling constant decreases
approximately 1.4 fold. Because of increasing frequencies of symmetric valence
vibrations of water molecules in hydrated shells of anions, the FR is relaxing.
AnionsBr−   ℵ   Cl− are negatively hydrated, so mobility of H2O molecules in hydrated
shells of these anions increases [11] (in comparison with pure water), the
hydrogen bonds between water molecules become weaker, and the frequencies of
valence vibrations increase. As the result, the detuning of frequencies of
overtone bending and symmetric valence vibrations becomes large, and FR
weakens.The obtained values of FR coupling constants show that
FR apparently makes a contribution into the forming of water Raman valence
band. However, at present the quantitative estimations are possible only with
accuracy up to tens ofcm−1.


## 4. Conclusion

In this
study, the values of FR coupling
constantsW in water and in water solutions were improved. This was
possible due to the additional experimental spectral information about
frequencies of bending and valence bands of OH groups isolated in solutions of
HDO, which allowed calculating
the value of W using only the values of frequencies of water molecules
vibrations in absence and in presence of FR. The decomposition of isotropic
Raman valence bands was performed using the modern mathematical methods (GA and
GRG2), thus increasing stability of solution of the incorrect inverse problem—decomposition
of valence band into components.



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*Source: 204828-2008-06-18.xml*