Electric Field Effect on Condensed-Phase Molecular Systems. VII

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Electric Field Effect on Condensed-Phase Molecular Systems. VII. Vibrational Stark Sensitivity of Spatially Oriented Water Molecules in an Argon Matrix Youngwook Park, Jong Hyeon Lim, Jin Yong Lee, and Heon Kang J. Phys. Chem. C, Just Accepted Manuscript • Publication Date (Web): 27 Mar 2019 Downloaded from http://pubs.acs.org on March 27, 2019

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The Journal of Physical Chemistry

Revised version

Electric Field Effect on Condensed-Phase Molecular Systems. VII. Vibrational Stark Sensitivity of Spatially Oriented Water Molecules in an Argon Matrix

Youngwook Park,† Jong Hyeon Lim,‡ Jin Yong Lee,*,‡ Heon Kang*,† †Department

of Chemistry, Seoul National University, 1 Gwanak-ro, Seoul 08826, South

Korea ‡Department

of Chemistry, Sungkyunkwan University, Suwon 16419, South Korea

Abstract The susceptibility of a water molecule to electric fields provides fundamental and essential information for understanding the vibrational spectra of water clusters and condensed-phase water. In this study, the Stark sensitivities for the ν2 bending and ν1 symmetric stretching vibrations of water molecule were experimentally determined. The water molecules isolated in the solid Ar matrix were spatially oriented in the direction of the externally applied field (~108 V m−1) in the laboratory frame by using the ice film nanocapacitor method. The signature of the field-induced reorientation of water molecules was observed with reflection-absorption infrared spectroscopy. The Stark sensitivities of the D2O vibrations were determined from the field-induced change of vibrational frequencies of the spatially oriented D2O molecules. The Stark sensitivity of the D2O bending vibration was much larger than that of the symmetric stretching vibration, and the two normal modes showed the opposite signs. Isotope dependence of the Stark sensitivity of the bending vibration was also observed by investigating HDO and H2O molecules. An ab initio calculation was conducted to elaborate on the observed characteristics of the Stark sensitivity of water vibrations.

Introduction 1

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Vibrational spectroscopy has been widely used for elucidating the structure and dynamics of condensed-phase water.1 The vibrational spectrum of bulk water contains rich and complicated information about the H-bonding structure and dynamics of water molecules, intra- and intermolecular vibrational couplings, as well as electrostatic interactions. Extensive theoretical studies have been conducted to understand and simulate the vibrational spectrum of water in condensed phases.2-6 To construct the spectrum of water, it is important to understand the susceptibility of molecular vibrations to electric fields originating from intermolecular Hbonding and electrostatic interactions. Several researchers have studied the field susceptibility, or Stark sensitivity (∆𝜇), of the OH (or OD) stretching vibration of water, mostly by theoretical calculations. Andrés et al.7 and Hermansson8 studied the Stark sensitivity of decoupled OH stretching vibration of water monomer in external electric fields using ab initio computation methods. Skinner and coworkers9 investigated the OH or OD stretching band of dilute HDO in liquid D2O or H2O using electronic structure calculations and liquid water simulations. From a linear empirical relationship observed between the calculated hydroxyl stretching frequencies and the electric fields from the solvent, they deduced the values of |∆𝜇(OH)| and |∆𝜇(OD)| to be 2.36 and 1.65 cm−1/(108 V m−1), respectively. Sen et al.10 obtained similar Stark sensitivity values for decoupled OH and OD stretching vibrations in water clusters. Recently, J. H. Lim et al.11 reported the Stark sensitivity of decoupled OD vibration of water monomer, dimer, and tetramer. The results indicated that the Stark sensitivity significantly increases with cluster size due to hydrogen bonding; for free OD, |∆𝜇(OD)| = 0.1–0.7 cm−1/(108 V m−1) and for bonded OD, |∆𝜇(OD)| = 1.5–2.7 cm−1/(108 V m−1). Experimental approaches to determine the vibrational Stark sensitivity of water have been very limited. Shin et al. experimentally measured the Stark sensitivity of OH or OD stretching vibration of dilute HDO in D2O or H2O crystalline ice; |∆𝜇(OH)| = 10–16 cm−1/(108 V m−1) and |∆𝜇(OD)| = 6.4–12 cm−1/(108 V m−1).12 These values are significantly larger as compared to those of water clusters10-11 or liquid water obtained by theoretical calculations.9 Boxer and coworkers used vibrational Stark spectroscopy to measure the Stark sensitivities of OH and OD stretching of 2,6-di-t-butylphenol in toluene, which were determined as |∆𝜇(OH)| = 2.3 ± 0.3 cm−1/(108 V m−1) and |∆𝜇(OD)| = 1.4 ± 0.2 cm−1/(108 V m−1).13 Most of the studies published to date have reported the Stark sensitivity of decoupled hydroxyl vibrations, for example, the OD (or OH) vibration of dilute HDO in bulk H2O (or 2


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D2O). To the best of our knowledge, there have been no previous experimental measurements or theoretical calculations of the Stark sensitivity of the normal modes of water. In particular, despite extensive studies on vibrational Stark effects, the field susceptibility of the bending vibration has neither been reported nor discussed for water and other molecules, except for the case of CH2 bending vibration of matrix-isolated formaldehyde.14 The present work reports the first experimental measurement of Stark sensitivity of the symmetric stretching and bending vibrations of a water molecule. The measurement was made possible by spatially orienting the water molecules that were isolated in a solid Ar matrix using strong (< 2 × 108 V m−1) external electric fields provided by the ice film nanocapacitor method.14-15 The spectral features of the field-driven reorientation and Stark response of the matrix-isolated water molecules were observed by reflection-absorption infrared spectroscopy (RAIRS). Because the transition moment of a vibrational mode is a vector quantity with specific direction in the molecule-fixed frame, the direction of the vibrational transition moment of the field-oriented molecules is well defined with respect to the direction of the applied field in the laboratory frame. Under this condition, both the magnitude and sign of the Stark sensitivities of the vibrational modes can be measured by using a polarized IR beam. The present experiment revealed a clear difference in the Stark response of the symmetric stretching and bending vibrations of the water molecule. In addition, we studied the origin of different Stark responses of the stretching and bending modes of water using ab initio calculations.

Experimental details The experiments were performed in an ultrahigh vacuum (UHV) chamber, which has been described in detail elsewhere.14-15 The sample was prepared on a cold Pt(111) substrate (about 10 K) by sequential deposition of the corresponding gaseous species that were introduced into the UHV chamber through variable leak valves. H2O (Milli-Q) and D2O (Aldrich, 99 atom% D) were purified by freeze-pump-thaw cycles. Ar gas was used directly from commercially available gas cylinders. The film of matrix-isolated D2O (H2O) was prepared by co-adsorption of D2O (H2O) and Ar gases in a predetermined pressure ratio (1:1000–1:200). The sample had a stacked structure of an Ar film (288–960 ML thickness; ML = monolayer; 1 ML = 1.1 × 1015 molecules cm−2) containing D2O (H2O) molecules, which was sandwiched between two spacer 3



layers (96–120 ML each) of pure Ar films. The Ar film was capped with an amorphous H2O (D2O) film (25 ML). To avoid spectral overlap between the capping ice film and matrixisolated water molecules, the former was composed of water isotopologue different from the latter. The thickness of the complete sample was 290–710 nm. A dc electrostatic field was applied across the film using the ice film nanocapacitor method, which has been described previously in detail.16 The field strength was increased by the deposition of Cs+ ions on the capping ice film and decreased by spraying low energy (roughly 3 eV) electrons on the Cs+-deposited film.17-18 The strength of the applied field across the film was estimated from the film voltage measured with a Kelvin probe. All measured values of field strength given in this article are the macroscopic field strength (F0), estimated simply by dividing the film voltage with the thickness of the film. The actual strength of the field (F) that a matrix-isolated water molecule experiences can be expressed as 𝐹 = 𝑐𝑙𝑜𝑐𝑎𝑙𝐹0, with the local field correction factor 𝑐𝑙𝑜𝑐𝑎𝑙 estimated to be in the range of 1–2.14, 19 Reflection-absorption infrared spectroscopic (RAIRS) measurements were conducted using a Fourier transform infrared (FTIR) spectrometer with a liquid nitrogen-cooled mercurycadmium-telluride detector in grazing angle reflection geometry (85°). An incident IR beam was p-polarized by a wire grid polarizer. The RAIR spectra were averaged 256 times with a spectral resolution of 1 cm−1. The sloped baselines of all spectra, caused by the increasing negative reflection-absorbance with increasing wavenumber,20-21 were corrected for better visualization.

Results and Discussion When a water molecule is isolated in a solid Ar matrix as a monomer, it behaves as a nearly free-rotor.22-23 Figure 1(a) shows the RAIR spectrum of D2O molecules isolated in Ar matrix (referred to as ‘D2O@Ar’) in the absence of an externally applied field. Features at around 1190 cm−1 are rotation-vibration transitions in the ν2 bending region, predominantly 111-000 (1194.9 cm−1) and 110-101 (1185.4 cm−1) in the notation of JKaKc, where J is the quantum number of total rotational angular momentum and Ka and Kc are the total angular momentum components on the principal axes a and c, respectively. The position of the transitions matches well with the previous assignments.22 Transitions in the stretching vibration region were not 4


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observed in the spectrum, because of the weaker oscillator strengths as compared to those of the bending vibration. The broad band at 1660 cm−1 corresponds to the bending mode of the bulk H2O layer, which was overlaid onto the Ar matrix sample to construct the ice film nanocapacitor.16

(a) Zero field

111-000 and 110-101 of 2(D2O) 2(D2O)

(b) F0 = 3.8 × 107 V m-1

Absorbance

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


1(D2O)

2(H2O)

0.005

2(HDO)

(c) Difference spectrum [(at F0 = 3.8 × 107 V m-1) - (at zero field)]

3000

2000

1000 -1

Wavenumber (cm )

Figure 1. RAIR spectra of D2O monomer isolated in the solid Ar matrix (D2O@Ar). (a) Absorbance spectrum at zero field. (b) Absorbance spectrum under F0 = 3.8 × 107 V m−1. The positions of symmetric stretching (ν1) and bending (ν2) vibrations are marked on the spectrum. Bending vibration of H2O and HDO isolated in the matrix were also observed. The broad band at 1660 cm−1 is the bending mode of the bulk H2O layer, which is part of the ice film nanocapacitor used for applying an electric field. (c) Difference absorbance of (b) and (a). Disappearance of the ro-vibrational peaks of matrix-isolated D2O is evident in the difference spectrum.

When the external field was applied, the peak at around 1175 cm−1 drastically increased in the D2O bending region, as shown in Figure 1(b). This peak corresponds to the band center of the ν2 bending mode of matrix-isolated D2O. The increase in the intensity of this 5



peak was accompanied by the disappearance of existing rotation-vibration transitions, which is more clearly seen in the difference spectrum as dips at higher frequencies (1194.9 and 1185.4 cm−1) (Figure 1(c)). The removal of the rotational features and emergence of the peak at the band center is a characteristic signature of the pendularization of a free-rotor induced by the intense external electric field which is collinear with the radiative field of infrared light.24-25 The increase in the intensity of the band center of the ν1 symmetric stretching mode of D2O is not evident in Figure 1, owing to the small oscillator strength of the vibration. It will be shown shortly that this feature appeared more clearly for the sample with a larger D2O content (see Figure 3). Increase in the intensity of the bending peaks at 1589 and 1399 cm−1 of H2O and HDO, respectively, which were isotopic impurities of water incorporated into the sample, was also observed.22 Figure 2 shows the sequence of field-induced spectral changes in the ν2 bending vibration region of D2O@Ar. At zero field, the water monomer showed the rotation-vibration transitions at 1194.9 and 1185.4 cm-1 as a nearly free rotor, assigned as 111-000 and 110-101, respectively. The 212-101 transition, which is expected to appear at 1204 cm−1,22 was not clearly observed. Since the temperature of the matrix was maintained at a cryogenic temperature (about 10 K), it is reasonable that the strongest rotation-vibration transition is 111-000. Note that the nuclear permutation statistics results in the weight ratio of 000(ortho, I=0,2):101(para, I=1) = 6:3. Removal of the rotation-vibration transitions at a stronger field was clearly seen in the spectra. The 111-000 transition became blue-shifted, broadened, and eventually disappeared above 1.9 × 107 V m−1. This behavior is analogous to the field-induced change of the R(0) transition of HCl monomer isolated in an Ar matrix15 and can be rationalized by the changes in the rotational energy levels, perturbed by external electric fields.26-28 The change of 110-101 transition was harder to identify because of the weaker intensity, but it can be said that the peak of 110-101 also disappeared when a strong field was applied. Along with these changes in the rotation-vibration transitions, the peak at band center (1174.6 cm−1, gray dashed vertical line in Figure 2) increased tremendously at stronger field, as mentioned above as a signature of field-driven pendularization of D2O molecules in the Ar matrix. At stronger fields, the band center peak position was slightly blue-shifted. It can be noted that without the spatial orientation of D2O molecules by the external field, the intensities of ν1 and ν2 vibrations were very weak, which has been a major obstacle to IR spectroscopic investigation of the Stark 6


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sensitivity of these bands in past research efforts.

111-000 110-101

0.005

F0 (× 107 V m-1) 3.8

Absorbance

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


2.7 1.9 1.1 0.5 0 1200

1180 1160 -1 Wavenumber (cm )

Figure 2. Series of RAIR spectra of the ν2 bending vibration of D2O@Ar as a function of the externally applied field strength. The positions of ro-vibration transitions (111-000 and 110-101) and band center are marked with the gray dotted lines and gray dashed line, respectively.

The spectral changes at stronger external fields are shown in Figure 3. The spectra were obtained with the films having larger D2O content for an increased signal-to-noise ratio of the spectra. Since there exists a trade-off between the film thickness and maximum field strength applicable with the ice film nanocapacitor method, to prepare a sample with a larger D2O content, the density of D2O in the matrix had to be increased. This inevitably resulted in the formation of D2O dimer, trimer, and larger clusters isolated in the matrix. These cluster peaks were identified by comparing the zero-field spectrum in Figure 3 with those from previous research on matrix-isolated D2O samples.22 The two peaks of the dimer (‘D-acceptor’ 7



at 1177.2 cm−1 and ‘D-donor’ at 1188.2 cm−1) and the trimer peak (1183.4 cm−1) are marked in the bending region in Figure 3.

1 band center

2 band center

0.002

0.01

F0 (× 107 V m-1) 12.3

Absorbance

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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7.9

3.3 1.5 d

2670

2660

2650

//

1200 Wavenumber (cm-1)

t

d

1180

0 1160

Figure 3. Series of RAIR spectra of the ν1 symmetric stretching and ν2 bending vibrations of D2O@Ar recorded at stronger fields. The spectra were obtained from three separate experiments performed under similar conditions. The spectral intensities of the separate experiments were rescaled, so that the spectra had the same intensity for the D2O monomer band at the same field strength. The peak positions of the ν1 and ν2 band center of the D2O monomer in the matrix are marked with gray dashed lines (2657.7 cm−1 and 1174.6 cm−1, respectively). The features marked with ‘d’ and ‘t’ in the ν2 bending region are the absorption bands of D2O dimer and trimer, respectively, in the matrix. The corresponding multimer bands in the ν1 symmetric stretching region appeared below 2620 cm−1, which are not shown in the figure for the sake of clarity.

As the field became stronger, the peaks at the band center of both ν1 symmetric stretching and ν2 bending vibrations became more and more intense. This is a signature of D2O molecules being dipole-reoriented toward the external field direction. With stronger fields, the 8


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molecules are more oriented along the field direction. This results in an increase in the intensity of the ν1 symmetric stretching and ν2 bending vibrations whose transition dipoles are parallel (or anti-parallel) with the permanent dipole of the molecule. Note that the external field direction is collinear with the polarization of infrared light in the instrument.14-16 The intensity became saturated as the field strength approached the strongest, indicating the asymptotic perfect reorientation of matrix-isolated D2O molecules. This feature is clearly seen in Figure 4. In the experiments where the field strength was decreased, it was found that the field-induced spectral changes of matrix-isolated D2O monomer were reversible. This indicates that the reorientation of D2O molecule is reversible with respect to the field strength, which is reasonable considering that a water molecule isolated in the solid Ar matrix is a nearly free rotor at zero field.

1.2

2 band center 1 band center

1.0

Normalized Intensity

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


0.8 0.6 0.4 0.2 0.0

0

5

10

15

F0 (× 107 V m-1)

Figure 4. Plot of relative peak intensities of the band center of bending and symmetric stretching vibrations of D2O@Ar as a function of external field strength. Data points from three separate experiments are shown overlapped. The peak intensity here indicates the area of the peak, which was obtained by integrating the band. Because of the overlap of the bending vibration peak of the D2O monomer and the D-acceptor peak of the D2O dimer at high fields (see Figure 3), the contribution of the D-acceptor peak was numerically subtracted from the 9



integration, assuming that the D-acceptor peak did not change significantly under the external fields. The peak area is shown normalized with respect to the largest area obtained at 1.3 × 108 V m−1.

At the high field region in Figure 3, the ν1 symmetric stretching peak was red-shifted and the ν2 bending blue-shifted with the stronger field. This unidirectional shift with field is a characteristic feature of the vibrational Stark effect of oriented molecules.14-15, 29 Figure 5 is the plot of the peak position of both ν1 and ν2 as a function of external field strength. A linear response was observed above 5 × 107 V m−1, where the intensity of the peaks indicated an asymptotic full orientation of the molecules. The slope of linear response includes information on the Stark sensitivity (∆𝜇) of the vibration. We mention in passing that the Stark response is contributed by both ortho- and para-D2O molecules, but these two components could not be distinguished in the band origin peak because of limited spectral resolution of the present experiment. Since the measured field is the macroscopic field (F0), which has a relation with the actual field (F) that a water molecule experiences inside the matrix by 𝐹 = 𝑐𝑙𝑜𝑐𝑎𝑙𝐹0,14, 19 the slope of the plot in Figure 5 is the Stark sensitivity multiplied by the local field correction factor, 𝑐𝑙𝑜𝑐𝑎𝑙 ∆𝜇. For convenience, however, this quantity is referred to as the ‘uncorrected’ Stark sensitivity and denote by the symbol without 𝑐𝑙𝑜𝑐𝑎𝑙 in the notation, for instance, ∆𝜇2(D2 O) for the ν2 bending vibration of D2O.

10


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1 sym. stretch: -0.33 ± 0.07 cm-1/(108 V m-1)

2657.6 2657.4 2657.2

//

Peak Wavenumber (cm-1)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


2 bend: +2.0 ± 0.2 cm-1/(108 V m-1)

1178 1177 1176 1175 0

5

10 F0 (× 107 V m-1)

15

Figure 5. Plot of the peak wavenumber of the band center of bending and symmetric stretching vibrations of D2O@Ar as a function of the field strength. Data points from seven separate experiments are shown overlapped. The Stark sensitivities of the two vibrations derived from the slope of the plot are indicated. The standard deviation of the measured sensitivity values mostly originated from the uncertainty in field strength measurement, about 10%. The ν1 mode had a larger uncertainty due to the larger dispersion of data points.

The linear fit of Figure 5 gave the ‘uncorrected’ Stark sensitivities of ν1 symmetric stretching and ν2 bending vibrations, ∆𝜇1(D2O) = −0.33 ± 0.07 cm−1/(108 V m−1) and ∆𝜇2(D2 O) = +2.0 ± 0.2 cm−1/(108 V m−1). The magnitude of ∆𝜇2(D2O) is about six times larger than that of ∆𝜇1(D2O), indicating that the bending vibration of D2O molecule is significantly more susceptible to electrostatic field than symmetric stretching vibration. The sign of ∆𝜇1(D2O) and ∆𝜇2(D2O) is opposite, which implies that the transition dipole moments of those vibrations are anti-parallel. The Stark sensitivities of other water isotopologues (H2O and HDO) could also be measured with the same approach. Those of the bending vibration were determined to be ∆𝜇2( H2O) = +3.3 ± 0.3 cm−1/(108 V m−1) and ∆𝜇2(HDO) = +2.9 ± 0.3 cm−1/(108 V m−1) (Supporting Information Figure S1). The Stark sensitivity of the symmetric stretching vibration 11



of H2O, however, was not obtained because this peak was extremely weak for H2O as compared to D2O, even when the bending vibrational peak of H2O appeared with similar or larger intensity than that of D2O under strong fields. Presumably, the symmetric stretching peak of H2O was weak because of the optical effect in the RAIRS measurement of an Ar film, which gave the greater negative absorbance at higher wavenumbers.20-21 To account for the experimental observations, the Stark sensitivities of water monomer (D2O) were theoretically obtained by ab initio calculations. Here, the electric field was applied parallel to the dipole moment direction of the D2O molecule to simulate the field-orientation of the molecules in the experiment. The Stark sensitivities were derived from harmonic vibrational frequencies. The calculations were performed at the coupled cluster singles and doubles (CCSD) level of theory30 with augmented correlation-consistent polarized valence triple- (aug-cc-pVTZ) basis set. The CCSD method is known to produce one of the most accurate results for vibrational frequencies31 and Stark shifts.32 All calculations were performed using the Gaussian 09 suite of programs.33 The computational results for the Stark sensitivities of 1 symmetric stretching and 2 bending were ∆𝜇1(D2O) = −0.065 cm−1/(108 V m−1) and ∆𝜇2(D2O) = +0.31 cm−1/(108 V m−1), respectively. The Stark sensitivity of the bending mode is five times larger than the symmetric stretching mode with an opposite sign. This ratio is in good agreement with the experimentally determined |∆𝜇2(D2O)|/|∆𝜇1(D2O)| = 6 ± 1.3. To understand the reason why Stark sensitivity of bending vibration is so large and why it has an opposite sign to that of symmetric stretching mode, the Stark sensitivities were decomposed into geometric and electronic terms as described in a previous work.11 The geometric and electronic terms were derived from the Stark shifts caused by nuclear and electronic structure changes, respectively, under the influence of an applied electric field. Figure 6 shows the calculated total Stark sensitivity (∆𝜇tot) and its geometric and electronic terms (∆𝜇geom and ∆𝜇elec) for the bending and symmetric stretching modes of D2O molecule. The most distinctive difference between the Stark sensitivities of bending and symmetric stretching modes is that the ∆𝜇geom values had opposite signs. The symmetric stretching mode had a negative value of ∆𝜇geom because the O-D bond length became longer under the electric field, as seen in Supporting Information Figure S2. The longer O-D bond 12


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also affected the bending vibrational frequency toward red-shift, but the decrease in the bond angle under the influence of electric field outweighed the effect of O-D bond elongation and led to a blue-shift (positive ∆𝜇geom). In contrast to ∆𝜇geom, ∆𝜇elec had a positive sign for both vibrational modes. Because both ∆𝜇geom and ∆𝜇elec of the bending mode were positive, its total Stark sensitivity was greater than that of the symmetric stretching mode. In the studies of vibrational Stark effect of simple chromophore structures like CO and CN, the vibrational frequency shifts have been explained in terms of the change in the expectation value of the dipole moment upon vibrational excitation.34-37 When the applied field strength is moderate (~106 V m−1), such as for the conditions employed in liquid He droplet experiments,38 the fieldinduced change of molecular geometric and electronic structures may have negligibly small effects on the observed frequency shifts. For example, according to the data shown in Figure S2 in Supporting Information, electric field with the strength of 106 V m−1 is expected to alter the O-D length of water by only 2 × 10−7 Å and the D-O-D angle by 2 × 10−4 degree. Therefore, the dipole moment change upon vibrational excitation may be relatively more important under these conditions.

tot

-1

0.2

8

0.3

0.1

-1

 (cm /(10 V m ))

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


geom elec

0.0 -0.1 -0.2

bending

sym. stretching

Figure 6. Calculated values of ∆𝜇tot, ∆𝜇geom, and ∆𝜇elec of the bending and symmetric stretching modes of D2O molecules.

13



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The Stark sensitivities of other water isotopologues (HDO and H2O) were also calculated at the same level of theory, CCSD, and the results are listed in Table 1. The magnitude of the Stark sensitivity of vibrations was larger for HDO and H2O than D2O, which is consistent with the experimental observation. For the bending mode, the magnitudes of ∆𝜇geom and ∆𝜇elec for HDO were 1.25 and 1.29 times larger, respectively, than those of D2O, and those of H2O were 1.42 and 1.38 times larger. For the symmetric stretching mode, the magnitudes of ∆𝜇geom and ∆𝜇elec for H2O were 1.59 and 1.31 times larger than those of D2O. These scale factors are related to the difference in the reduced mass (𝑚red). In general, the vibrational frequency is inversely proportional to the square root of reduced mass of a normal mode (𝜈 ∝ 1/ 𝑚red). Since the reduced mass is independent of the electric field, Stark sensitivity is expected to have the same relationship (Δ𝜇 ∝ 1/ 𝑚red). A relationship between the Stark sensitivities of these isotopologues, therefore, would be given as ) =

𝑚red,HDO⋅∆𝜇(HDO) =

𝑚red,D2O⋅∆𝜇(D2O

𝑚red,H2O⋅∆𝜇(H2O), assuming the same force constants for the

isotopic systems. Based on this relationship, the theoretical scaling factors for the Stark sensitivity of a normal mode of HDO and H2O with respect to D2O could be estimated by using the reduced mass of the specific normal mode for different isotopologues, which is: ∆𝜇2(HDO) = 1.31×∆𝜇2(D2O), ∆𝜇2(H2O) = 1.45×∆𝜇2(D2O) for the bending mode and ∆𝜇1(H2O) = 1.44×∆𝜇1(D2O) for the symmetric stretching mode. These scaling factors, which are estimated based solely on the reduced mass obtained from the vibrational analysis,39 well explain the isotopic difference in the ∆𝜇 values determined by the ab initio calculations. They also seem to show a reasonable agreement with the experimentally observed isotopic effect: ∆𝜇2(HDO)/ ∆𝜇2(D2O) = 1.45 ± 0.21 and ∆𝜇2(H2O)/∆𝜇2(D2O) = 1.65 ± 0.23 for the bending vibration.

14


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Table 1. Calculated ∆𝜇geom and ∆𝜇elec of bending and symmetric stretching modes for D2O, HDO, and H2O molecules. The values in parentheses are relative magnitudes with respect to their correspondence of D2O. ∆𝝁 (cm−1/(108 V m−1))

D2O

HDO

H2O

∆𝜇geom

0.17 (1)

0.22 (1.25)

0.25 (1.42)

∆𝜇elec

0.14 (1)

0.18 (1.29)

0.19 (1.38)

Symmetric

∆𝜇geom

-0.12 (1)

-

-0.19 (1.59)

stretching

∆𝜇elec

0.056 (1)

-

0.073 (1.31)

Bending

While the relative magnitude of Stark sensitivity (namely, relative Stark sensitivity scaling between the bending and symmetric stretching vibrations of D2O, or that between the bending vibrations of H2O, HDO, and D2O) showed a good agreement between the experimental and theoretical results, the absolute magnitude showed a large discrepancy between the experiment and calculation. The calculated Stark sensitivities were about six times smaller than the ‘uncorrected’ Stark sensitivities obtained from experiments. The discrepancy may be attributed to the matrix effect in the experiment. The matrix-isolated water molecule is strongly confined inside the cavity of the matrix. Also, there is uncertainty in the estimated local field strength. The tendency that a lower Stark sensitivity is obtained in the calculation is consistent with previous reports that the theoretical Stark sensitivity of CN chromophore is almost an order of magnitude lower than the experimental values when the solvent effect is excluded.36, 40 Also, in our previous study of water monomer and clusters up to octamer using the second-order Møller-Plesset perturbation (MP2) theory, the Stark sensitivity of O-D stretching frequency significantly increases with the cluster size, such that the Stark sensitivity of octamer becomes close to the experimental value of bulk ice, while that of monomer is an order of magnitude lower.12 We emphasize that the main purpose of the present calculation is to understand the origin of relative difference in Stark responses of the bending and stretching vibrations of water under the influence of external electric field.

15



Conclusion In this study, Stark sensitivities of the normal modes (ν2 bending and ν1 symmetric stretching vibrations) of water molecules isolated in the Ar matrix were measured by orienting the molecules with strong external fields and observing the field-induced changes of the vibrational frequencies. The bending and symmetric stretching vibrations of water had Stark sensitivities of opposite signs. The Stark sensitivity of the bending vibration of D2O was six times larger in magnitude than that of the symmetric stretching vibration. The quantum calculations revealed that the critical difference in Stark sensitivity between the bending and symmetric stretching vibrations originated from molecular geometry changes induced by the field rather than electronic perturbations. Isotopic difference was observed in the Stark sensitivity of the bending vibration of water, which could be understood in terms of the reduced mass of the normal mode. If these individual molecular properties in vibrational Stark response are extended to a bulk water system, it can be inferred that the bending vibrational frequency in the spectrum of bulk water is more susceptible to electrostatic fields originating from the neighbor molecules, while the hydroxyl stretching frequency changes primarily with the hydrogen bonding structure of water, and is relatively less susceptible to the environmental field.

Supporting Information. The PDF file of Supporeting Information is available free of charge on the ACS Publications website at DOI: Figures S1 and S2. AUTHOR INFORMATION Corresponding Authors * To whom correspondence should be addressed. E-mail: [email protected] (J.Y.L.), [email protected] (H.K.), Tel: +82 2 875 7471, Fax: +82 2 889 8156 Notes The authors declare no competing financial interests. 16


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ACKNOWLEDGMENT This work was supported by Samsung Science and Technology Foundation (SSTF-BA130104).

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TOC Figure

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Electric Field Effect on Condensed-Phase Molecular Systems. VII

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