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Competing factors on the frequency separation between the OH stretching modes in water
Journal of Molecular Liquids 205 (2015) 42–45
Contents lists available at ScienceDirect
Journal of Molecular Liquids journal homepage: www.elsevier.com/locate/molliq
Competing factors on the frequency separation between the OH stretching modes in water Chao Zhang a,⁎, Leonardo Guidoni b,c,⁎⁎, Thomas D. Kühne a a b c
Institute of Physical Chemistry and Center for Computational Sciences, Johannes Gutenberg University Mainz, Staudinger Weg 7, D-55128 Mainz, Germany Sapienza — Università di Roma, Physics Department, P.le A. Moro 5, 00185 Rome, Italy Department of Physical and Chemical Sciences, University of L'Aquila, Via Vetoio, 67100 L'Aquila, Italy
a r t i c l e
i n f o
Available online 1 October 2014 Keywords: Vibrational spectroscopy Ab initio molecular dynamics Inhomogeneous broadening Interfacial water Biological water
a b s t r a c t Recent simulations demonstrated that the inhomogeneous broadening as observed in the vibrational spectra of liquid water at ambient conditions can be viewed as a large vibrational splitting of symmetric and asymmetric OH stretching modes, due to the asymmetry of the local hydrogen-bonding network [J. Phys. Chem. Lett., 2013, 4(19), pp 3245–3250]. In this work, we show that the finite temperature and the liquid phase do not only modulate the local hydrogen-bonding asymmetry of water molecules, but also the intramolecular coupling strength. These two factors compete together in the determination of the overall magnitude of the frequency separation between the two OH stretching modes in water at ambient conditions. © 2014 Elsevier B.V. All rights reserved.
1. Introduction Water is commonly regarded as the matrix of life because of its fundamental role in maintaining and facilitating the various functions of biomolecules [1]. In addition to its biological functions, in the age of the so-called hydrogen economy, water can be also considered as the substrate to clean production of hydrogen fuel by water splitting, a beneficial alternative to the replacement of fossil fuels and other nonrenewable energy sources [2a,2b]. Many aspects of the anomalous properties of liquid water, such as the high boiling temperature and density maximum at 4 °C, are directly related to the ability of water molecules to form hydrogen bonds (HBs) with neighboring molecules [3]. It has been long accepted that a water molecule in the liquid phase at ambient conditions is bonded, on average, to four neighbors in a distorted tetrahedral configuration [4,5], based on a wide range of experimental and computational studies [6–10]. However, this traditional picture has been questioned based on data from X-ray absorption spectra [11], where “rings and chains” structure of liquid water was implied and debated [5,12]. Recently, ab initio molecular dynamics (MD) simulations coupled with energy
⁎ Corresponding author. ⁎⁎ Correspondence to: L. Guidoni, Department of Physical and Chemical Sciences, University of L'Aquila, Via Vetoio, 67100 L'Aquila, Italy. E-mail addresses: [email protected] (C. Zhang), [email protected] (L. Guidoni).
http://dx.doi.org/10.1016/j.molliq.2014.09.049 0167-7322/© 2014 Elsevier B.V. All rights reserved.
decomposition analysis have revealed that although the geometric distortions are not large enough to justify the drastic “chain and ring” model, the majority of water molecules in liquid water exhibit a significant instantaneous asymmetry in terms of their HB strengths [13–15]. On the other hand, it is well known that the vibrational O-H stretching modes of water molecules are sensitive to their local environments [7]. Indeed, Raman and infrared (IR) spectra of liquid water exhibit a large red shift in the frequencies of O-H stretching modes compared to those in the gas phase. In particular, IR spectra have a board continuum that spans the whole range from 3000 cm−1 to 3700 cm−1, while Raman spectra show isosbestic points, which suggests the existence of different kinds of water molecules [16]. This socalled inhomogeneous broadening of vibrational spectra has been attributed to a variety of factors, such as intermolecular vibrations [17–23], hydrogen bonding configurations [24,25], bending overtone [26], as well as coupling of symmetric and asymmetric local modes [27] and charge fluctuations [28]. Previously, we have revealed the intertwined connection between the local hydrogen-bonding asymmetry and the frequency splitting of the OH stretching vibrations [29], by combining ab initio MD [30,31], effective normal mode analysis [32,33] and energy decomposition analysis based on absolutely localized molecular orbitals [34]. It was shown that the instantaneous local hydrogen-bonding asymmetry entails a decoupling of two O-H bonds in effective O-H stretching modes v1 and v3. Liquid water at ambient conditions, modeled at density functional theory (DFT) level, exhibited the characteristics of an asymmetric environment with an average degree of decoupling of fd = 0.82 and a splitting between the two OH stretching modes of Δω13 = 137 cm−1. Such
C. Zhang et al. / Journal of Molecular Liquids 205 (2015) 42–45
43
Table 1 Vibrational splitting 〈Δω13〉 of water monomer in gas phase and in liquid water at 300 K, for the case of a symmetric hydrogen-bonding environment, i.e. 〈fd〉 ≈ 0. Simulation systems System A: Water monomer in gas phase at 300 K System B: Water monomer in liquid water at 300 K a
hΔω13 icalc: f d ≈0 (cm−1)
hΔω13 i exp : f d ≈0 (cm−1)
103
99 Ref. [48]
Water monomer isolated in D2O cubic ice.
large value of decoupling fd means that the two effective normal modes are either localized on one OH bond or on the other, at variance with the symmetric fd = 0 case, where two modes are delocalized on both bonds as symmetric and asymmetric stretchings. The consequent increase of the frequency splitting can explain the inhomogeneous broadening as observed in the vibrational spectra of liquid water. Although the fd parameter can fairly explain the broadening of the spectra in liquid water, the asymmetry of the environment is not the only factor regulating the splitting Δω13. O-H bonds in water molecules are coupled through intra- and inter-molecular interactions. The intramolecular coupling is composed of a momentum coupling between two O-H bonds sharing the same oxygen atom and a potential coupling term [22]. In several reports, it has been suggested that the intramolecular coupling strength plays also a role in frequency splitting [19a,19b, 22,23]. In this work, by analyzing the ab initio MD data, we show that in liquid water fd is increased with respect to the gas phase. At the same time, the intramolecular coupling kintra is sensitive to environmental changes and reversely modulating Δω13 in liquid phase. The rest of the article is organized as follows. Section 2 describes how to extract the information on the local hydrogen-bonding asymmetry from finite temperature vibrational analysis and details of the corresponding ab initio MD simulations. Section 3 shows the evidence and interpretation of the competing factors fd and kintra to determine the vibrational splitting Δω13 from our simulations. Section 4 provides our main conclusions. 2. Method and simulations For the purpose to establish a connection between the local hydrogen-bonding asymmetry and the vibrational splitting, we have introduced the descriptor fd, which explores the degree of decoupling between the O-H1 and O-H2 vibration modes in water [29]: fd ¼
X i¼v1 ;v3
jC iO‐H1 −C iO‐H2 j 2ðC iO‐H1 þ C iO‐H2 Þ
ð1Þ
where CiO ‐ H1 and CiO ‐ H2 are contributions of the O-H1 and O-H2 bonds to the stretching mode i (v1 and v3 are the symmetric and asymmetric stretching modes, respectively). These coefficients can be obtained from the effective normal mode vj of each water molecule [35–37] by minimizing the following functional evaluated on the data obtained by molecular dynamics: Ω
45 a, Ref. [49]
54
ðnÞ
¼
X β Z j
2π
2n v
dωjωj P j ðωÞ−
β 2π
Z
2 n v dωjωj P j ðωÞ
ð2Þ
with respect to vj. Herein, β is the inverse temperature, n is an integer constant and P v j the vibrational density of states (VDOS) of vj. In finite temperature dynamics, the VDOS include all information about the molecular vibrations in a system, such as thermal fluctuations and anharmonicities [32,33,35]. It has been shown that for n = 2 this method is equivalent to a normal mode analysis performed with the thermally averaged Hessian matrix [32]. As demonstrated in our previous work [29], when all water molecules are in a full symmetric hydrogen bonding environment, fd = 0,
and when the water molecules are in a fully asymmetric hydrogen bonding environment fd = 1. Therefore, fd plays the role of an order parameter for describing the local hydrogen-bonding asymmetry. By fitting the ab initio MD data, it was shown that vibrational splitting of the stretching modes and the descriptor fd are connected by the following relation: Δω13 ∝ (1 + f2d) [29]. Based on a simple coupled harmonic oscillators model, it was further suggested that the vibrational splitting of the stretching modes is proportional to the spring constant connecting the two oscillators k′: Δω13 ∝ k ' [29]. It is worth to note that in our simple coupled harmonic oscillators model, k1 and k2 are in analogy with force constants for O-H single bonds and k′ is in analogy with the force constant kintra for the intra O-H bonds coupling. Two ab initio simulations were performed to probe the relationship between Δω13, fd and kintra: water monomer at 300 K (system A) and liquid water at 300 K (system B). The simulation box for the gas– phase system (systems A) was set to 15.7 Å × 15.7 Å × 15.7 Å and a Poisson solver for isolated systems was employed [38]. For system B, a periodic simulation cell consisting of 128 light water molecules with a density of 0.9966 g/cm3 was employed. The nuclear forces had been calculated within the framework of DFT using the Perdew–Burke– Ernzerhof (PBE) exchange and correlation functional [39], as implemented in the CP2K suite of programs [40,41]. For both systems, we took advantage of the efficient and accurate second-generation Car– Parrinello MD simulation method [31a,31b]. More details and comments on the employed basis sets, pseudopotential [42], van der Waals correction [43–45] and elevated temperature effects [46] could be found elsewhere [29]. Statistics for systems A and B had been accumulated for 20 ps and 80 ps, respectively. In order to deconvolute the relation between Δω13 and fd, we subdivided the ab initio MD trajectories of each water molecule in system B into 2 ps windows, which correspond roughly to the HB lifetime in liquid water [47] and less than the HB lifetime (6.99 ps) and water residence time (7.25 ps) as determined in our previous simulations [9,29]. The distribution of the dipole moments of the water molecules has been calculated using the centers of the maximally localized Wannier functions [48]. 3. Results and discussion The focus of the following analysis is to disentangle the effects responsible for the frequency splitting Δω13 of the OH stretching vibrations. In gas phase simulation (system A), we have analyzed separately the vibrational density of state of the symmetric stretching mode v1 and the asymmetric stretching mode v3 which are non-overlapping (Fig. 1A) with Δω13 ≈ 103 cm−1. Temperature effects only leads to a Lorentzian-like line shape broadening of the vibrational peaks. The two O-H bonds are fully coupled in these modes, as indicated by a calculated 〈fd〉 ≈ 0.01. On the contrary, in liquid water (system B), the two effective normal modes are significantly decoupled. The VDOS of the two v1 and v3 modes are calculated for each water molecule and for each short 2 ps dynamics; the sum of these spectra is reported in Fig. 1B and represents the overall decomposition of the liquid water spectra into the two vibrational modes. At variance with gas phase, the inhomogeneous broadening leads to a significant overlapping between the vibrational density of states of v1 and v3. The overall vibrational splitting 〈Δω13〉 is about 137 cm−1, in comparison with a large 〈fd〉 of about 0.82, as shown before [29].
44
C. Zhang et al. / Journal of Molecular Liquids 205 (2015) 42–45
water [29]. Indeed, as shown in the follow-up analysis here, the distribution of the dipole moment of water molecules for fd ≈ 1 and Δω13 N 400 cm−1 is shifted to a lower value by about 0.25 D, comparing to the case of fully symmetric water molecules in the bulk (Fig. 2). Such reduction of the dipole moment resembles what has been reported for interfacial water molecules in water–vapor systems [53]. 4. Conclusions
Fig. 1. A) Vibrational spectra of stretching modes v1 and v3 decomposed by effective normal mode analysis for water monomer in gas phase at 300 K; B) vibrational spectra of stretching modes v1 and v3 decomposed by effective normal mode analysis for water molecules in liquid water at 300 K. The corresponding spectral sum of v1 and v3 as well as the full vibrational density of states (VDOS) are also shown.
Considering that 〈fd〉 changes from nearly 0 in the gas phase to 0.82 in liquid water, the increase of 〈Δω13〉 by merely 34 cm−1 due to the condensed phase environment appears to be rather small. One way to explain this effect is to attribute the moderate increase of 〈Δω13〉 to the fact that Δω13 depends quadratically rather than linearly on fd, i.e. Δω13 ∝ (1 + f2d) [29]. Nevertheless, even taking this into account, 〈Δω13〉 should increase by roughly 66 cm−1 instead of just 34 cm− 1 when switching the environment from gas phase to liquid water. This fact suggests that also the intramolecular coupling kintra should be sensitive to environmental changes and reversely modulating Δω13 in liquid phase. As shown for a simple coupled harmonic oscillators model in our previous study [29], Δω13 is proportional to kintra, for the case of a symmetric hydrogen-bonding environment (fd ≈ 0). This provides a simple way to gauge the change of kintra from the gas to the condensed phase. In our liquid water simulations, we have split the dynamics of single water molecules into 2 ps-long time slices. The anisotropy of the environment has been calculated for each molecule and for each time slice, showing that there is a large variation of the fd parameter, ranging from 0 to 1. We have selected only the pieces of trajectories where fd ≈ 0 and calculated the corresponding frequency splitting hΔω13 ij f d ≈0 . Interestingly, in the gas phase, hΔω13 ij f d ≈0 is roughly twice as large as in liquid water (See Table 1.). This is in good agreement with experiment [49, 50]. Indeed, reductions of hΔω13 ij f d ≈0 due to the environmental effect have been noticed before by Torii [19], who calculated Raman and transient IR spectra of liquid water [19a,19b] and in numerical simulations by Buch and co-workers on cage clusters [22] and the liquid/vapor interface [23]. These results lead to the evidence that the intramolecular coupling kintra is sensitive to environmental changes and reversely modulating Δω13 in liquid phase. However, the caution that should be taken here is that the splitting Δω13 does not only depend on a potential energy coupling term but also depends on a momentum coupling term [22, 51]. This means that a more realistic model beyond coupled harmonic oscillators is needed in order to fully quantify the environmental modulation of kintra and therefore Δω13. It is also interesting to focus on the blue region of the spectra. In this region, as also evident from the shoulder in Fig. 1B, there is the vibrational peak of dangling O-H bonds of water molecules at 3600 cm−1, which are commonly observed for top-layer interfacial water molecules [52]. That corresponds to the asymmetric descriptor fd ~ 1 in liquid
To summarize, our simulations show that the vibrational splitting Δω13 does not only depend on the local hydrogen-bonding asymmetry as characterized by fd, but also on the intramolecular coupling strength kintra. These two factors compete with each other in the determination of the overall magnitude of the frequency separation between the two OH stretching modes in water at ambient conditions. At finite temperature, ab initio MD simulations show that fd increases in the liquid water with respect to the gas phase. In the meanwhile, the intramolecular coupling kintra is sensitive to environmental changes and reversely modulating Δω13 in liquid phase. For fd ≈ 1 and Δω13 N 400 cm−1, it is found that the distribution of the dipole moment of water molecules shifts to a lower value by about 0.25 D, with respect to the case of fully symmetric water molecules in the bulk. This resembles interfacial water molecules in water– vapor systems. Further investigations would focus on determining the variation of force constants for O-H single bonds (k1 and k2) and for the intra O-H bonds coupling (kintra) in response to the modulations of hydrogenbonding environments directly from ab initio simulations. As pointed out before, this calls for a more realistic model including the momentum coupling [22] in order to fully quantify kintra and its contribution to Δω13. The parameters of such realistic model might be also determined in the future using ab initio molecular dynamics trajectories through force matching techniques [54]. Acknowledgments C.Z. and T.D.K. gratefully acknowledge the Gauss Center for Supercomputing (GCS) for providing computing time through the
Fig. 2. Dipole moment distributions of water molecules in liquid water according to the local hydrogen-bonding asymmetry. fd ≈ 0.0 and 〈Δω13〉 ≈ 50cm−1 represents the fully symmetric water molecules in the bulk; fd ≈ 1.0 and Δω13 N 400cm−1 represents the interfacial water-like water molecules. Both distributions are normalized with the same bin size and range.
C. Zhang et al. / Journal of Molecular Liquids 205 (2015) 42–45
John von Neumann Institute for Computing (NIC) on the GCS share of the supercomputer JUQUEEN at the Jülich Supercomputing Centre (JSC). Financial support from the Graduate School of Excellence MAINZ and the IDEE project of the Carl-Zeiss Foundation is kindly acknowledged. L.G. acknowledges funding provided by the European Research Council project no. 240624.
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Contents lists available at ScienceDirect
Journal of Molecular Liquids journal homepage: www.elsevier.com/locate/molliq
Competing factors on the frequency separation between the OH stretching modes in water Chao Zhang a,⁎, Leonardo Guidoni b,c,⁎⁎, Thomas D. Kühne a a b c
Institute of Physical Chemistry and Center for Computational Sciences, Johannes Gutenberg University Mainz, Staudinger Weg 7, D-55128 Mainz, Germany Sapienza — Università di Roma, Physics Department, P.le A. Moro 5, 00185 Rome, Italy Department of Physical and Chemical Sciences, University of L'Aquila, Via Vetoio, 67100 L'Aquila, Italy
a r t i c l e
i n f o
Available online 1 October 2014 Keywords: Vibrational spectroscopy Ab initio molecular dynamics Inhomogeneous broadening Interfacial water Biological water
a b s t r a c t Recent simulations demonstrated that the inhomogeneous broadening as observed in the vibrational spectra of liquid water at ambient conditions can be viewed as a large vibrational splitting of symmetric and asymmetric OH stretching modes, due to the asymmetry of the local hydrogen-bonding network [J. Phys. Chem. Lett., 2013, 4(19), pp 3245–3250]. In this work, we show that the finite temperature and the liquid phase do not only modulate the local hydrogen-bonding asymmetry of water molecules, but also the intramolecular coupling strength. These two factors compete together in the determination of the overall magnitude of the frequency separation between the two OH stretching modes in water at ambient conditions. © 2014 Elsevier B.V. All rights reserved.
1. Introduction Water is commonly regarded as the matrix of life because of its fundamental role in maintaining and facilitating the various functions of biomolecules [1]. In addition to its biological functions, in the age of the so-called hydrogen economy, water can be also considered as the substrate to clean production of hydrogen fuel by water splitting, a beneficial alternative to the replacement of fossil fuels and other nonrenewable energy sources [2a,2b]. Many aspects of the anomalous properties of liquid water, such as the high boiling temperature and density maximum at 4 °C, are directly related to the ability of water molecules to form hydrogen bonds (HBs) with neighboring molecules [3]. It has been long accepted that a water molecule in the liquid phase at ambient conditions is bonded, on average, to four neighbors in a distorted tetrahedral configuration [4,5], based on a wide range of experimental and computational studies [6–10]. However, this traditional picture has been questioned based on data from X-ray absorption spectra [11], where “rings and chains” structure of liquid water was implied and debated [5,12]. Recently, ab initio molecular dynamics (MD) simulations coupled with energy
⁎ Corresponding author. ⁎⁎ Correspondence to: L. Guidoni, Department of Physical and Chemical Sciences, University of L'Aquila, Via Vetoio, 67100 L'Aquila, Italy. E-mail addresses: [email protected] (C. Zhang), [email protected] (L. Guidoni).
http://dx.doi.org/10.1016/j.molliq.2014.09.049 0167-7322/© 2014 Elsevier B.V. All rights reserved.
decomposition analysis have revealed that although the geometric distortions are not large enough to justify the drastic “chain and ring” model, the majority of water molecules in liquid water exhibit a significant instantaneous asymmetry in terms of their HB strengths [13–15]. On the other hand, it is well known that the vibrational O-H stretching modes of water molecules are sensitive to their local environments [7]. Indeed, Raman and infrared (IR) spectra of liquid water exhibit a large red shift in the frequencies of O-H stretching modes compared to those in the gas phase. In particular, IR spectra have a board continuum that spans the whole range from 3000 cm−1 to 3700 cm−1, while Raman spectra show isosbestic points, which suggests the existence of different kinds of water molecules [16]. This socalled inhomogeneous broadening of vibrational spectra has been attributed to a variety of factors, such as intermolecular vibrations [17–23], hydrogen bonding configurations [24,25], bending overtone [26], as well as coupling of symmetric and asymmetric local modes [27] and charge fluctuations [28]. Previously, we have revealed the intertwined connection between the local hydrogen-bonding asymmetry and the frequency splitting of the OH stretching vibrations [29], by combining ab initio MD [30,31], effective normal mode analysis [32,33] and energy decomposition analysis based on absolutely localized molecular orbitals [34]. It was shown that the instantaneous local hydrogen-bonding asymmetry entails a decoupling of two O-H bonds in effective O-H stretching modes v1 and v3. Liquid water at ambient conditions, modeled at density functional theory (DFT) level, exhibited the characteristics of an asymmetric environment with an average degree of decoupling of fd = 0.82 and a splitting between the two OH stretching modes of Δω13 = 137 cm−1. Such
C. Zhang et al. / Journal of Molecular Liquids 205 (2015) 42–45
43
Table 1 Vibrational splitting 〈Δω13〉 of water monomer in gas phase and in liquid water at 300 K, for the case of a symmetric hydrogen-bonding environment, i.e. 〈fd〉 ≈ 0. Simulation systems System A: Water monomer in gas phase at 300 K System B: Water monomer in liquid water at 300 K a
hΔω13 icalc: f d ≈0 (cm−1)
hΔω13 i exp : f d ≈0 (cm−1)
103
99 Ref. [48]
Water monomer isolated in D2O cubic ice.
large value of decoupling fd means that the two effective normal modes are either localized on one OH bond or on the other, at variance with the symmetric fd = 0 case, where two modes are delocalized on both bonds as symmetric and asymmetric stretchings. The consequent increase of the frequency splitting can explain the inhomogeneous broadening as observed in the vibrational spectra of liquid water. Although the fd parameter can fairly explain the broadening of the spectra in liquid water, the asymmetry of the environment is not the only factor regulating the splitting Δω13. O-H bonds in water molecules are coupled through intra- and inter-molecular interactions. The intramolecular coupling is composed of a momentum coupling between two O-H bonds sharing the same oxygen atom and a potential coupling term [22]. In several reports, it has been suggested that the intramolecular coupling strength plays also a role in frequency splitting [19a,19b, 22,23]. In this work, by analyzing the ab initio MD data, we show that in liquid water fd is increased with respect to the gas phase. At the same time, the intramolecular coupling kintra is sensitive to environmental changes and reversely modulating Δω13 in liquid phase. The rest of the article is organized as follows. Section 2 describes how to extract the information on the local hydrogen-bonding asymmetry from finite temperature vibrational analysis and details of the corresponding ab initio MD simulations. Section 3 shows the evidence and interpretation of the competing factors fd and kintra to determine the vibrational splitting Δω13 from our simulations. Section 4 provides our main conclusions. 2. Method and simulations For the purpose to establish a connection between the local hydrogen-bonding asymmetry and the vibrational splitting, we have introduced the descriptor fd, which explores the degree of decoupling between the O-H1 and O-H2 vibration modes in water [29]: fd ¼
X i¼v1 ;v3
jC iO‐H1 −C iO‐H2 j 2ðC iO‐H1 þ C iO‐H2 Þ
ð1Þ
where CiO ‐ H1 and CiO ‐ H2 are contributions of the O-H1 and O-H2 bonds to the stretching mode i (v1 and v3 are the symmetric and asymmetric stretching modes, respectively). These coefficients can be obtained from the effective normal mode vj of each water molecule [35–37] by minimizing the following functional evaluated on the data obtained by molecular dynamics: Ω
45 a, Ref. [49]
54
ðnÞ
¼
X β Z j
2π
2n v
dωjωj P j ðωÞ−
β 2π
Z
2 n v dωjωj P j ðωÞ
ð2Þ
with respect to vj. Herein, β is the inverse temperature, n is an integer constant and P v j the vibrational density of states (VDOS) of vj. In finite temperature dynamics, the VDOS include all information about the molecular vibrations in a system, such as thermal fluctuations and anharmonicities [32,33,35]. It has been shown that for n = 2 this method is equivalent to a normal mode analysis performed with the thermally averaged Hessian matrix [32]. As demonstrated in our previous work [29], when all water molecules are in a full symmetric hydrogen bonding environment, fd = 0,
and when the water molecules are in a fully asymmetric hydrogen bonding environment fd = 1. Therefore, fd plays the role of an order parameter for describing the local hydrogen-bonding asymmetry. By fitting the ab initio MD data, it was shown that vibrational splitting of the stretching modes and the descriptor fd are connected by the following relation: Δω13 ∝ (1 + f2d) [29]. Based on a simple coupled harmonic oscillators model, it was further suggested that the vibrational splitting of the stretching modes is proportional to the spring constant connecting the two oscillators k′: Δω13 ∝ k ' [29]. It is worth to note that in our simple coupled harmonic oscillators model, k1 and k2 are in analogy with force constants for O-H single bonds and k′ is in analogy with the force constant kintra for the intra O-H bonds coupling. Two ab initio simulations were performed to probe the relationship between Δω13, fd and kintra: water monomer at 300 K (system A) and liquid water at 300 K (system B). The simulation box for the gas– phase system (systems A) was set to 15.7 Å × 15.7 Å × 15.7 Å and a Poisson solver for isolated systems was employed [38]. For system B, a periodic simulation cell consisting of 128 light water molecules with a density of 0.9966 g/cm3 was employed. The nuclear forces had been calculated within the framework of DFT using the Perdew–Burke– Ernzerhof (PBE) exchange and correlation functional [39], as implemented in the CP2K suite of programs [40,41]. For both systems, we took advantage of the efficient and accurate second-generation Car– Parrinello MD simulation method [31a,31b]. More details and comments on the employed basis sets, pseudopotential [42], van der Waals correction [43–45] and elevated temperature effects [46] could be found elsewhere [29]. Statistics for systems A and B had been accumulated for 20 ps and 80 ps, respectively. In order to deconvolute the relation between Δω13 and fd, we subdivided the ab initio MD trajectories of each water molecule in system B into 2 ps windows, which correspond roughly to the HB lifetime in liquid water [47] and less than the HB lifetime (6.99 ps) and water residence time (7.25 ps) as determined in our previous simulations [9,29]. The distribution of the dipole moments of the water molecules has been calculated using the centers of the maximally localized Wannier functions [48]. 3. Results and discussion The focus of the following analysis is to disentangle the effects responsible for the frequency splitting Δω13 of the OH stretching vibrations. In gas phase simulation (system A), we have analyzed separately the vibrational density of state of the symmetric stretching mode v1 and the asymmetric stretching mode v3 which are non-overlapping (Fig. 1A) with Δω13 ≈ 103 cm−1. Temperature effects only leads to a Lorentzian-like line shape broadening of the vibrational peaks. The two O-H bonds are fully coupled in these modes, as indicated by a calculated 〈fd〉 ≈ 0.01. On the contrary, in liquid water (system B), the two effective normal modes are significantly decoupled. The VDOS of the two v1 and v3 modes are calculated for each water molecule and for each short 2 ps dynamics; the sum of these spectra is reported in Fig. 1B and represents the overall decomposition of the liquid water spectra into the two vibrational modes. At variance with gas phase, the inhomogeneous broadening leads to a significant overlapping between the vibrational density of states of v1 and v3. The overall vibrational splitting 〈Δω13〉 is about 137 cm−1, in comparison with a large 〈fd〉 of about 0.82, as shown before [29].
44
C. Zhang et al. / Journal of Molecular Liquids 205 (2015) 42–45
water [29]. Indeed, as shown in the follow-up analysis here, the distribution of the dipole moment of water molecules for fd ≈ 1 and Δω13 N 400 cm−1 is shifted to a lower value by about 0.25 D, comparing to the case of fully symmetric water molecules in the bulk (Fig. 2). Such reduction of the dipole moment resembles what has been reported for interfacial water molecules in water–vapor systems [53]. 4. Conclusions
Fig. 1. A) Vibrational spectra of stretching modes v1 and v3 decomposed by effective normal mode analysis for water monomer in gas phase at 300 K; B) vibrational spectra of stretching modes v1 and v3 decomposed by effective normal mode analysis for water molecules in liquid water at 300 K. The corresponding spectral sum of v1 and v3 as well as the full vibrational density of states (VDOS) are also shown.
Considering that 〈fd〉 changes from nearly 0 in the gas phase to 0.82 in liquid water, the increase of 〈Δω13〉 by merely 34 cm−1 due to the condensed phase environment appears to be rather small. One way to explain this effect is to attribute the moderate increase of 〈Δω13〉 to the fact that Δω13 depends quadratically rather than linearly on fd, i.e. Δω13 ∝ (1 + f2d) [29]. Nevertheless, even taking this into account, 〈Δω13〉 should increase by roughly 66 cm−1 instead of just 34 cm− 1 when switching the environment from gas phase to liquid water. This fact suggests that also the intramolecular coupling kintra should be sensitive to environmental changes and reversely modulating Δω13 in liquid phase. As shown for a simple coupled harmonic oscillators model in our previous study [29], Δω13 is proportional to kintra, for the case of a symmetric hydrogen-bonding environment (fd ≈ 0). This provides a simple way to gauge the change of kintra from the gas to the condensed phase. In our liquid water simulations, we have split the dynamics of single water molecules into 2 ps-long time slices. The anisotropy of the environment has been calculated for each molecule and for each time slice, showing that there is a large variation of the fd parameter, ranging from 0 to 1. We have selected only the pieces of trajectories where fd ≈ 0 and calculated the corresponding frequency splitting hΔω13 ij f d ≈0 . Interestingly, in the gas phase, hΔω13 ij f d ≈0 is roughly twice as large as in liquid water (See Table 1.). This is in good agreement with experiment [49, 50]. Indeed, reductions of hΔω13 ij f d ≈0 due to the environmental effect have been noticed before by Torii [19], who calculated Raman and transient IR spectra of liquid water [19a,19b] and in numerical simulations by Buch and co-workers on cage clusters [22] and the liquid/vapor interface [23]. These results lead to the evidence that the intramolecular coupling kintra is sensitive to environmental changes and reversely modulating Δω13 in liquid phase. However, the caution that should be taken here is that the splitting Δω13 does not only depend on a potential energy coupling term but also depends on a momentum coupling term [22, 51]. This means that a more realistic model beyond coupled harmonic oscillators is needed in order to fully quantify the environmental modulation of kintra and therefore Δω13. It is also interesting to focus on the blue region of the spectra. In this region, as also evident from the shoulder in Fig. 1B, there is the vibrational peak of dangling O-H bonds of water molecules at 3600 cm−1, which are commonly observed for top-layer interfacial water molecules [52]. That corresponds to the asymmetric descriptor fd ~ 1 in liquid
To summarize, our simulations show that the vibrational splitting Δω13 does not only depend on the local hydrogen-bonding asymmetry as characterized by fd, but also on the intramolecular coupling strength kintra. These two factors compete with each other in the determination of the overall magnitude of the frequency separation between the two OH stretching modes in water at ambient conditions. At finite temperature, ab initio MD simulations show that fd increases in the liquid water with respect to the gas phase. In the meanwhile, the intramolecular coupling kintra is sensitive to environmental changes and reversely modulating Δω13 in liquid phase. For fd ≈ 1 and Δω13 N 400 cm−1, it is found that the distribution of the dipole moment of water molecules shifts to a lower value by about 0.25 D, with respect to the case of fully symmetric water molecules in the bulk. This resembles interfacial water molecules in water– vapor systems. Further investigations would focus on determining the variation of force constants for O-H single bonds (k1 and k2) and for the intra O-H bonds coupling (kintra) in response to the modulations of hydrogenbonding environments directly from ab initio simulations. As pointed out before, this calls for a more realistic model including the momentum coupling [22] in order to fully quantify kintra and its contribution to Δω13. The parameters of such realistic model might be also determined in the future using ab initio molecular dynamics trajectories through force matching techniques [54]. Acknowledgments C.Z. and T.D.K. gratefully acknowledge the Gauss Center for Supercomputing (GCS) for providing computing time through the
Fig. 2. Dipole moment distributions of water molecules in liquid water according to the local hydrogen-bonding asymmetry. fd ≈ 0.0 and 〈Δω13〉 ≈ 50cm−1 represents the fully symmetric water molecules in the bulk; fd ≈ 1.0 and Δω13 N 400cm−1 represents the interfacial water-like water molecules. Both distributions are normalized with the same bin size and range.
C. Zhang et al. / Journal of Molecular Liquids 205 (2015) 42–45
John von Neumann Institute for Computing (NIC) on the GCS share of the supercomputer JUQUEEN at the Jülich Supercomputing Centre (JSC). Financial support from the Graduate School of Excellence MAINZ and the IDEE project of the Carl-Zeiss Foundation is kindly acknowledged. L.G. acknowledges funding provided by the European Research Council project no. 240624.
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