1
On the Intermolecular Vibrational Coupling, Hydrogen Bonding, and
Librational Freedom of Water in the Hydration Shell of Mono- and
Bivalent Anions
Mohammed Ahmed, V. Namboodiri, Ajay K. Singh, and Jahur A. Mondal*
Radiation & Photochemistry Division, Bhabha Atomic Research Centre, Trombay, Mumbai400085, India.
Email: mondal@barc.gov.in
Supplementary Material.
1. Experimental Raman spectra of aqueous salt solutions in the OH stretch, HOH
bend, [bend+librational] combination, and librational band regions.
The experimentally recorded Raman spectrum of neat water in 150 – 4050 cm-1 region is shown
in Figure S1. The three spectral windows that bear the vibrational characteristics of water are: (i)
~ 3000 - 3700 cm-1 (OH stretch), (ii) ~ 1500 – 2500 cm-1 (HOH bend and [bend+librational]
combination band), and (iii) below 1000 cm-1 (librational bands). For better clarity of these
spectral bands, the individual bands in presence of different salts are shown in three different
Figures (S2 - S4). Figure S2 shows the area normalized Raman spectra (OH stretch) of neat
water and Na-salt solutions (0.8 mole dm-3) corresponding to different anions, such as I-, SO42-,
and CO32-. At such low concentration, the Raman spectra of salt solutions are not very different
from each other and also from that of neat water. As a result, from these experimental spectra, it
is difficult to understand the structural changes of water in the hydration shell of these ions.
However, the Raman spectrum specific to hydration water, as obtained by MCR-analysis of
these apparently similar experimental spectra, are significantly different from the Raman
spectrum of bulk water and also varies with the nature of anions.
2
Figure S1. Raman spectra of neat water in 150 4050 cm-1 region.
Figure S2. Area normalized Raman spectra of neat
water (black) and 0.8 mole dm-3 Na-salt solutions
NaI (red), Na2SO4 (green), and Na2CO3 (blue)) in
the OH stretch regions.
The area normalized Raman spectra of water in the HOH bend (~ 1640 cm-1) and combination
(bend+libration; ~2115 cm-1) band regions are shown in Figure S3 with different concentrations
of Na-salts. Similar to the OH stretch region, the position and width of IC-spectra in these
regions differ from that of bulk water, which is not so evident in the experimental spectra.
Figure S3. Area normalized Raman spectra of aqueous Na-salt solutions in the HOH bend and
combination (bend+librational) band regions. Concentration of NaI (left), Na2SO4 (middle), and
Na2CO3 (right) are mentioned in the respective graph panels.
The Raman spectrum of water in the librational band regions (400 – 1000 cm-1) are shown in the
inset of Figure S4. The librational bands are weak and buried in large background signal (dashed
line in the inset panel). Deconvolution of background subtracted spectrum (black dashed line in
Figure S4) shows two librational bands with maxima at 470 (L1) and 670 cm (L2),
respectively.1,2 The positions of these librational bands provide direct information about
3
intermolecular interactions and rotational freedom of water. However, because of weak intensity,
strong overlap with each other and with large back ground signal, direct monitoring of the
changes in librational band in presence of salt are technically difficult.
Figure S4. Background subtracted Raman spectrum (dashed line) of H2O in hindered rotational
band regions (400 – 1000 cm). Gray line is the fitted spectrum, purple and green lines are the
Gaussian component bands. Inset: Raw Raman spectrum of H2O (solid line) and background
signal (dashed line).
2. HOH bend spectrum of H2O in H2O-D2O mixture.
Similar to the OH stretch band, the HOH bend vibration of water is coupled with neighboring
water molecules. On sufficient dilution of H2O with D2O (H2O + D2O  2 HOD; K = 4), the
HOH bend vibration is decoupled with neighbors, since the bend mode of D2O (1210 cm-1) and
HOD (1450 cm-1) are energetically separated from that of H2O (1640 cm-1) (see Figure S5).
However, the bend fundamental of H2O is quite close to the weak [bend+librational]
combination band of D2O (1560 cm-1). Therefore, at low dilution, the bend fundamental of H2O
gets buried in the high frequency wing of the [bend +librational] combination band of D2O. By
applying MCR-analysis, we have retrieved the band shape of the HOH bend fundamental (MCR-
4
retrieved Raman spectrum of H2O in D2O) which is vibrationally decoupled with neighboring
oscillators in the system. The MCR-retrieved Raman spectrum of H2O in D2O, as discussed in
the main text, is blue-shifted and narrower than that of intermolecularly coupled H2O.
Figure S5. Raman spectra of neat H2O, D2O, and H2O-D2O mixtures in 1000 – 1850 cm-1
regions.
It is to be noted that, as shown in Figure S5, there are three components in H2O-D2O mixture
(i.e. bulk D2O, HOD and H2O). However, in the MCR-analysis we considered two components
such that one component corresponds to the pure D2O and the other component represents the
combined response of HOD and H2O. Since the bend frequencies of H2O (~1642 cm-1) and HOD
(1450 cm-1) are different, we can expect that the spectral response around 1640 cm-1 is purely
due to H2O.
Effect of salt concentrations on the position and width of HOH bend mode of water.
Previous experimental3,4 (IR and Raman studies of concentrated salt solutions) and theoretical5
studies have suggested that the B band of water is red-shifted in presence of weakly hydrated
anions/neutral molecules (e.g. I-, CHCl3). Apparently, these results are in disagreement with the
present Raman-MCR study, which shows blue-shift (~5 cm) of the bend mode in the hydration
shell of weakly hydrated I anion. To verify the anomaly, we reinvestigated the variation of
fwhm and position of the B band in presence of varying concentrations of Na-salts (up to 6.0M
5
for NaI). As shown in Figure S6A, the peak position gradually shifts toward higher energy with
increasing concentration (up to 2 mole dm-3) for SO4 andCO3anions. However, in the case of
I anion, the band position shifts toward higher energy with increasing concentration up to ~0.8
mole dm, and then decreases with increasing concentration up to 6.0 mole dm. The spectral
width also decreases marginally for SO4 andCO3, but that in the case of I decreases sharply
up to a concentration of 0.8 mole dm, and then decreases slowly at higher concentrations (up to
6.0 mole dm, Figure S6B). The non-monotonic variations of peak position and width (for I)
imply that there are two factors governing the position and width of the bend spectrum of
hydration water. The IC-spectrum for I, whose maximum is blue-shifted than that of bulk H2O,
but red-shifted than that of decoupled H2O (Figure 2 and table 1 in main text) also hints to the
presence of two opposing factors: one is intermolecular vibrational decoupling (causes blue-shift
of B band) and the other is weakening of H-bond strength (causes red-shifts of B band). At
lower concentration (< 0.8 mole dm), the population of weakly H-bonded as well as
vibrationally decoupled water increases with increasing concentration of I and the combined
effect is a net blue-shift of the B band. However, at higher concentration ( 0.8 mole dm) of
I, the population of weakly H-bonded water increases but not that of decoupled water, since at
high concentration there is hardly enough bulk water to be decoupled. As a result, the position of
B band is mainly governed by the H-bond strength of hydration water, which shifts toward
lower frequency with increasing I concentration.
6
Figure S6. Variation of (A) peak position and (B) width (fwhm) of the HOH bend spectrum of
water with concentration of Na-salts.
Evidence of intermolecular decoupling in the hydration shell: Comparison of Cl - correlated
spectrum as well as isotopically diluted water with the polarized Raman spectra of bulk
H2O.
Role of intermolecular coupling on the vibrational band shapes (e.g. OH stretch band and HOH
bend) of water is quite evident from the comparison of polarized (isotropic and anisotropic)
Raman spectra of water. For example, the isotropic and anisotropic Raman spectra significantly
differ from each other as well as from the unpolarized Raman spectrum of water, especially in
the red region on the OH stretch band (< 3400 cm-1). The isotropic Raman spectrum was
4
4
calculated as 𝐼𝑖𝑠𝑜 = (𝐼 − 3 𝐼 ) and aniosotropic Raman spectrum, as 𝐼𝑎𝑛𝑖𝑠𝑜 = 3 𝐼 , where 𝐼 and
𝐼 are the parallel and perpendicular spectra recorded by placing a laminated film polarizer
(Thorlabs) in front of the collection optical fiber.6 As shown in Figure S7, the 3250 cm-1 band is
very prominent in the isotropic spectrum, whereas the same is largely reduced in the anisotropic
one.7 In fact, the anisotropic Raman spectrum is similar to the Raman spectrum (unpolarized) of
isotopically diluted water (H2O/D2O = 1/19; v/v; red dotted curve). These results indicate that the
7
3250 cm-1 band is dominated by the vibrational response of intermolecularly coupled water
molecules. Therefore, a decrease of intensity in 3250 cm-1 region, as observed in the MCRretrieved anion correlated spectra (see the main text; Cl- correlated spectrum is shown in Figure
S7 (gray curve) for the reference), indicates a reduced intermolecular coupling of water in the
hydration shell. Moreover, as shown in the inset of Figure S7, in the HOH bend region too, the
perpendicular Raman spectrum (𝐼 ) is narrower and blue-shifted from those of the parallel (𝐼 )
and unpolarized Raman spectra. The ion-correlated spectra also show similar changes (discussed
in the main text) and hence assignable to the intermolecular decoupling of water in the hydration
shell.
Figure S7. Unpolarized (black dashed curve) and polarized (isotropic (blue) and anisotropic
(green)) Raman spectra of H2O in the OH stretch region. Unpolarized Raman spectrum of
isotopically diluted water (H2O/D2O = 1/19; v/v; red dotted curve) and Cl--correlated spectrum
of H2O (gray curve; obtained by MCR analysis) are shown for comparison. Inset: V-polarized
(𝐼 ), H-polarized (𝐼 ) and unpolarized Raman spectra of H2O in the HOH bend region.
Multivariate Curve Resolution (MCR) Analysis.
The background corrected area normalized Raman spectra are arranged in to the rows of a
matrix, X. The first row corresponds to the spectrum of neat water and the other rows contain the
8
spectra of aqueous salt solutions with varying concentration of salt. The data matrix 𝑋 of size
𝑚 × 𝑛 can be written as
[𝑋]𝑚×𝑛
𝑥11
𝑥21
=[ ⋮
𝑥𝑚1
𝑥12
𝑥22
⋮
𝑥𝑚2
⋯
⋯
⋱
⋯
𝑥1𝑛
𝑥2𝑛
⋮ ]
𝑥𝑚𝑛
As a result, the columns of 𝑋 can be regarded as vectors in the space of concentration profiles;
and the rows can be thought of as vectors in the space of spectral profiles. In multivariate curve
resolution (MCR) analysis, the objective is to extract the linearly independent spectral
components from the data matrix X. In order to do so, the data matrix is decomposed by singular
value decomposition (SVD).8
[𝑋]𝑚×𝑛 = [𝑈]𝑚×𝑟 [Σ]r×r [𝑉 𝑇 ]𝑟×𝑛
(1)
The singular value decomposition gives two sets of singular vectors 𝒖’s (columns of the matrix
𝑈) and 𝒗’s (columns of the matrix 𝑉) which are eigen vectors of the matrices 𝑋𝑋 𝑇 and 𝑋 𝑇 𝑋
respectively. Since both these matrices are symmetric (𝐴𝑇 = 𝐴), their eigen vectors can be
chosen orthonormal. Since 𝒖’s and 𝒗’s constitute the columns 𝑈 and 𝑉, orthogonality
gives 𝑉 𝑇 𝑉 = 𝐼 = 𝑈 𝑇 𝑈. The singular vectors 𝑣1 , 𝑣2 , … , 𝑣𝑟 are in the row space of X and the
singular vectors 𝑢1 , 𝑢2 , … , 𝑢𝑟 are in the column space of 𝑋. Since the row space of X contains
information about the spectral profile, 𝒗’s constitute the basis vectors for the spectral profile.
Similarly 𝒖’s constitute the basis vectors for the column space, i.e., the concentration profile.
The rank (r) of the data matrix 𝑋 gives the number of independent spectral components
contained in 𝑋 so that there will be 𝑟 significant singular values (𝜎’s) in the diagonal matrix Σ.
Accordingly, the singular value decomposition can be expanded as:
[𝑋]𝑚×𝑛 = [𝑈]𝑚×𝑟 [Σ]r×r [𝑉 𝑇 ]𝑟×𝑛 = [𝑢1
⋯
𝑢𝑟 ] [
𝜎1
⋱
𝑣1𝑇
][ ⋮ ]
𝜎𝑟 𝑣𝑟𝑇
or
𝑋 = 𝑢1 𝜎1 𝑣1𝑇 + 𝑢2 𝜎2 𝑣2𝑇 + ⋯ + 𝑢𝑟 𝜎𝑟 𝑣𝑟𝑇
(2)
9
Arranging the singular values in descending order 𝜎1 ≥ 𝜎2 ≥ ⋯ ≥ 𝜎𝑟 > 0, the SVD gives the
rank-one (component wise) pieces of the data matrix 𝑋 in the order of importance. The
expansion in equation (2) can be rearranged as
𝑋 = 𝑐1 𝑠1𝑇 + 𝑐2 𝑠2𝑇 + ⋯ + 𝑐𝑟 𝑠𝑟𝑇 = 𝐶𝑆 𝑇
(3)
Where, 𝑐𝑖 = 𝑢𝑖 are the concentration components; and 𝑠𝑖𝑇 = 𝜎𝑖 𝑣𝑖𝑇 are the component spectra.
𝐶 is the matrix with the concentration profile vectors (𝑐𝑖 ) as columns and 𝑆 is the matrix with
component spectra (𝑠𝑖 ) as columns.
In the present case of diluted salt solutions, it is likely that the data matrix X contains two
independent spectral components: (i) bulk water and (ii) the hydration water of the solute as well
as the intramolecular vibrational bands (if any) of the solute. Hence, the number of significant
singular values (𝜎’s) is expected to be two. Thus after SVD, two most prominent singular values
are retained and the rest of the singular values, usually very small, are assumed to be due to
experimental noise.9,10 Thus, the equation (2) can be rewritten as
𝑋 = 𝑢1 𝜎1 𝑣1𝑇 + 𝑢2 𝜎2 𝑣2𝑇 + 𝐸 = 𝑐1 𝑠1𝑇 + 𝑐2 𝑠2𝑇 + 𝐸 = 𝐶`𝑆`𝑇 + 𝐸
(4)
Where, 𝐸 is the experimental noise matrix. The initial estimates of C` and S`, obtained from the
SVD, were further improved by alternating least square fitting (ALS) method. The lease square
method solves two least square problems simultaneously.
Given the spectra matrix 𝑆, the concentration matrix 𝐶 can be estimated as:
𝐶 = 𝑋𝑆(𝑆 𝑇 𝑆)−1
(5)
And, given the concentration matrix, the spectra matrix can be estimated as:
𝑆 = 𝑋 𝑇 𝐶(𝐶 𝑇 𝐶)−1
(6)
The ALS algorithm iteratively solves equations (5) and (6) such that ‖𝑋 − 𝐶𝑆 𝑇 ‖ = 𝐸 is
minimized. The validity of the method was checked by comparing the component spectrum of
bulk water obtained by MCR method and the experimentally recorded pure water spectrum.
Moreover, the MCR method was applied to simulated spectral data matrix (Figure S8), and it
observed that the MCR-retrieved spectra closely resemble to the simulated input spectra of the
solvent in the bulk and in the solvation shell.
10
Figure S8. Retrieval of spectral components by MCR analysis of simulated mixed spectral data.
It is assumed that the vibrational response of a solvent in the solvation shell of a solute is
different from that in bulk; and the simulated spectra of solvent in bulk (black) and in the
solvation shell (purple) of a solute are shown by solid lines. The mixed spectra are the response
of the solvent in presence of a solute which does not have vibrational bands in the shown spectral
window. At low concentration of solute, the mixed spectra are the combined response of bulk
and solvation shell solvent molecules such that the contribution of solvation shell increase
gradually with increasing concentration of solute: mixed spectrum_1 (99% bulk + 1% solvation
shell), mixed spectrum_2 (98% bulk + 2% solvation shell), mixed spectrum_1 (97% bulk + 3%
solvation shell), mixed spectrum_1 (96% bulk + 4% solvation shell), respectively. Inset: The
MCR-retrieved spectra of the solvent in bulk (green dashed line) and in the solvation shell
(orange dashed line) are compared with the respective simulated spectra (solid lines).
References.
1
2
3
4
5
6
7
G. E. Walrafen, J. Chem. Phys. 36 (4), 1035 (1962).
D. S. Venables, K. Huang, and C. A. Schmuttenmaer, J. Phys. Chem. B 105 (38), 9132
(2001).
J. J. Max, S. Blois, A. Veilleux, and C. Chapados, Can. J. Chem. 79, 13 (2001).
R. E. Weston Jr, Spectrochim. Acta 18 (9), 1257 (1962).
K. A. Sharp, M. Bhupinder, M. Eric, and M. V. Jane, J. Chem. Phys. 114 (4), 1791
(2001).
G. Kabisch, J. Mol. Struct. 77, 219 (1981).
A. Sokołowska, J. Raman Spectrosc. 22 (1), 31 (1991).
11
8
9
10
G. Strang, Introduction to Linear Algebra,. (Wellesley-Cambridge Press., 2009).
J. H. Jiang, Y. Liang, and Y. Ozaki, Chemometrics and Intelligent Laboratory Systems
71, 1 (2004).
R. Tauler, Chemometrics and Intelligent Laboratory Systems 30 (1), 133 (1995).