Vibrational Dynamics and Spectroscopy of Water at Porous g-C$_{3}$N$_{4}$ and C$_{2}$N Materials

In this work, the vibrational dynamics and spectroscopy of deuterated water molecules (D$_{2}$O) mimicking dense water layers at room temperature on the surfaces of two different C/N based materials with different N content and pore size, namely graphitic C$_{3}$N$_{4}$ (g-C$_{3}$N$_{4}$) and C$_{2}$N are studied using Ab Initio Molecular Dynamics (AIMD). In particular, Time-Dependent vibrational Sum-Frequency Generation spectra (TD-vSFG) of the OD modes and also time-averaged vSFG spectra and OD frequency distributions are computed.


Introduction
Water at interfaces and on surfaces is of immense significance for it plays a role as a solvent and as a catalyst in many chemical processes [1][2][3] .In biology, interfacial water at lipid bilayers and proteins contribute to the overall biological activity and selectivity 4 .Water on semiconductor surfaces offers an alternative to conventional energy sources by means of electroor photo-catalytic water splitting.Many photo(electro)catalysts contain metals which are expensive and sometimes hazardous [5][6][7] .In contrast, recently synthesized organic materials like graphitic carbon nitride (g-C 3 N 4 ) 8-10 and C 2 N 11,12 not only have demonstrated their propensity to facilitate water-splitting, they are also easy to synthesize and non-hazardous to the environment.These quasi-two dimensional, porous, layered materials offer a large surface area, and their properties can be tuned by the C/N ratio and the size of the pores.
Nitrogen is particularly important in these materials, notably for uptake of water, as it considerably increases the hydrophilicity of the material w.r.t.graphite or graphene 12,13 .This makes these materials also interesting in a non-catalytic context, e.g., as sieves to separate liquids when acting as water-selective membranes.
Both for catalytic and non-catalytic purposes like selective adsorption and separation, a precise understanding of the interaction of water with C/N-containing porous materials is desirable.Several theoretical studies have been performed which explored the geometric and electronic structure of these carbon-based materials and how the latter is modified by water adsorption 12,13,[15][16][17][18] .Often (but not always) single-or few-layer models were studied, and low coverages using stationary models.For example, in a first-principles Density Functional Theory (DFT) study including van-der Waals corrections and employing a (3×3) periodic supercell model it was found, that a single water molecule preferentially adsorbs in a triangular pore of the g-C 3 N 4 surface, with an adsorption energy between -0.55 and -0.62 eV depending on functional 18 .The water molecule lies almost flat in the pore of the buckled g-C 3 N 4 surface, forming two hydrogen bonds with accepting N atoms of the cavity.Also cluster models using highly correlated wavefunction methods support these results 13,14 .(Note that with smaller (1×1) unit cells the surface is falsely predicted to be flat and other adsorption geometries are more stable 16 .)In Ref. 18 , by a Potential Energy Surface (PES) scan also other (metastable) adsorption sites for water were found, and barriers for lateral diffusion of water to these sites were determined -in the order of 0.2 eV.In Ref. 17 , in an attempt to go to higher-coverage situations, multi-layer systems and dynamical behaviour relevant for water-selective membranes and "molecular sieves", the diffusion of water (and ethanol) through pristine and modified g-C 3 N 4 sheets was studied using classical molecular dynamics simulations based on empirical forcefields.An inverse correlation between the diffusion coefficient of water and the lifetime of intermolecular hydrogen bonds (HBs) was found, i.e. short lifetimes caused larger diffusion coefficients (and vice versa).Diffusion coefficients (for water) on / between g-C 3 N 4 were also found to be smaller than for bulk water, and the HB-lifetime was correspondingly larger for water at / in g-C 3 N 4 compared to bulk water 17 .
In case of C 2 N, which consists of flat layers under ideal conditions and with hexagonalshaped pores slightly larger than those of g-C 3 N 4 , both periodic DFT and also cluster calculations predict a similar adsorption energy for a single H 2 O on a C 2 N monolayer as for g-C 3 N 4 .
In this case, however, the water resides above the (center of the) pore, but still forming two H-bonds to two adjacent, basic N atoms 12,13 .Beyond single-layer models for C 2 N and after loading with larger amounts of water, according to the combined experimental-theoretical work in Ref. 12 , water molecules reside between the layers, forming H-bonds with N atoms of C 2 N which are stronger than the H-bonds between different water molecules in bulk water.
The adsorption energy decreases with increasing water load.
In order to understand the interaction with and adsorption of liquid water on 2D C/Ncontaining materials better, it is necessary to consider high coverages, finite temperatures, and dynamical behaviour which will naturally arise at finite temperature.(In the studies mentioned above, this was only done within the classical MD work reported in Ref. 17 .)Our goal here is to unravel differences of the C/N material / water systems compared to bulk water or water / air interfaces, and also differences between various C/N materials.This is, in the end, a prerequisite to fully understand the performance of N-containing graphitic materials for water splitting or as sieves, and their rational design.Another motivation for our work is the mentioned observation that the H-network but also transport or chemical behaviour of water in confined spaces / at surfaces can be very different from what is observed in the bulk (see also 19,20 ).
Appropriate "fingerprints" are needed by which differences between various systems and general effects of a confining surface can be accessed.In this context, we note that the spectral signature peaks for the concerted intermolecular motion of hydrogen bonded water molecules as well as the intramolecular fluctuations of the OH (or OD) modes of water molecules can be seen in vibrational spectra, such as the infrared (IR) spectrum.In particular, the IR spectrum provides a fingerprint region to decipher the hydrogen-bond dynamics in aqueous solutions and at interfaces 3 .Nevertheless, conventional vibrational spectroscopy cannot disseminate the contribution of interfacial molecules from the bulk.Vibrational Sum Frequency Generation Spectroscopy (vSFG) enables to selectively study the structure, hydrogen-bond network and orientational profile of interfaces and surfaces [21][22][23][24][25][26][27][28] .Moreover, the temporal evolution of the interfacial molecules can be explored using Time-Dependent vSFG (TD-vSFG) [29][30][31] .
Existing theoretical studies have not explored the vibrational dynamics of water molecules on two-dimensional, N-containing graphitic materials.In the present work, we have investigated the vibrational dynamics and vSFG spectra of interfacial water on g-C 3 N 4 and C 2 N surfaces using Ab Initio Molecular Dynamics.We concentrate on surfaces in this work, using single-layer models for the 2D material, and leaving investigations of the effects of other layers and the bulk to future work.We will consider thin layers of D 2 O molecules (rather than H 2 O, for practical reasons) adsorbed on one side of the 2D layer, and analyze OD vibrations in detail.Fluctuations in the vibrational frequency of OD modes were obtained using the wavelet transform of the time-series analysis and the surface-specific Velocity Velocity Autocorrelation Function (ssVVAF) approach 32 was used to calculate the vSFG and TD-vSFG spectra of interfacial water molecules.
The paper is organized as follows.In the following section 2, we briefly outline theoretical methods and computational models.In Sec.3, we study the vibrational dynamics, timeaveraged vibrational spectroscopy and time-resolved vibrational spectroscopy, respectively.Sec.4 summarizes and concludes our work.
2 Computational Details and Models

Models
We performed AIMD simulations for D 2 O molecules adsorbed either on C 2 N or g-C 3 N 4 monolayers, using periodic supercell models.For g-C 3 N 4 , a supercell of dimension (20.4 ×20.4×24.0)Å with 126 atoms (C 54 N 72 ) was employed representing a (3×3) 2D trigonal elementary cell to model the wave-like reconstruction found elsewhere 13,18 (see Fig. 1(a) in Ref. 13 for a pictorial representation).We then adsorbed 60 D 2 O molecules on one side (the surface) of the monolayer.A snapshot resulting from an AIMD simulation (see below), is shown in Fig. 1(a).As a result, about 14 Å of vacuum separate different periodic images along z (perpendicular to the surface).C 2 N was modelled using a primitive unit cell of dimensions (8.32 × 8.32 × 20.0) Å with 18 atoms (composition C 12 N 6 ), corresponding to a 2D trigonal elementary cell, see Fig. 1(c) in Ref. 13 ).On one side of this layer, 12 D 2 O molecules were added, as shown in the form of an AIMD snapshot in Fig. 1(b).This way, a vacuum gap of around 12 Å remained between water-covered layers.

AIMD simulations
First-principles simulations of water molecules on the g-C 3 N 4 and C 2 N surfaces were performed using the Vienna Ab initio Simulation Package 33,34 (VASP, version 5.4).The inner core electrons were represented by projector augmented-wave (PAW) pseudopotentials 35,36 and valence electrons using the Perdew Becke Ernzerhof (PBE) exchange correlation functional 37 together with Grimme's D3 dispersion correction 38,39 .(For a general assessment of DFT for water, see Ref. 40 .)The plane-wave kinetic energy cutoff was set to 400 eV for both systems.For C 2 N/water, a 3×3×1 k-point grid was used for Brillouin zone sampling; for g-C 3 N 4 /water, only the Γ-point was included.
Simulations were performed in the NVT ensemble using the Nosé-Hoover thermostat 41 at 300 K with deuterium masses for hydrogen and a time step of 1 fs for integrating the equations of motion.The vibrational spectra were sampled by using single, long NVT trajectories of 45 ps length (C 3 N 4 /D 2 O) and 55 ps (C 2 N/D 2 O), respectively.D 2 O instead of H 2 O was used in order to allow for longer timesteps and total propagation times in AIMD, hence better statistics, and also to inspire experiments which are often done with deuterated water 42 .

Frequency distributions
A (time-dependent) distribution of vibrational frequencies of OD modes of water molecules on g-C 3 N 4 and C 2 N surfaces was determined using the wavelet transform of a time-series analysis.The method is well documented 43 and is based on the principle that a timedependent function (f (t)) can be expressed in terms of basis functions obtained by the translations and dilations of a mother wavelet which is represented in the so-called Morlet-Grossman form in our present study and is mathematically given as, . (2) The parameters λ and σ are assigned the values of 1 and 2 sec −1 in our present study.The coefficients of the wavelet expansion are given by the wavelet transform of f (t), i.e.
where a and b are both real quantities.Here, a > 0 is a scale parameter which is directly related to the instantaneous frequency content of the system over a small time-window centered around b. Accordingly, based on the fluctuations in the time-series f (t), the wavelet transform L ψ f (a, b) provides the vibrational frequency for the given small time-window around t = b.Since the frequency value is proportional to 1 a , the time-window narrows for high frequency (small a) and widens for low frequency (large a).The value of parameter a which maximizes the modulus of the wavelet transform of time series f at time t = b is used to calculate the most important frequency component for the given interval.
The time-series of interest in this work, f (t), is constructed as a complex function with its real and imaginary parts corresponding to fluctuations of the bond length and momentum of an OD mode projected along the OD bond, namely (possible unit factors omitted) Here, the fluctuations are defined as where q(t) denotes the instantaneous property (= r OD (t) or p OD (t)), and ⟨q⟩ the corresponding average over the trajectory.Here, r OD (t) = |r OD (t)| where r OD (t) = r O − r D is the OD bond vector for a given OD bond, obtained from atomic position vectors.Further, the momentum projected along the OD mode is given as where m D , m O are atomic masses of deuterium and oxygen, v O , v D are atom velocities, and rOD = r OD /r OD the unit vector along the OD bond.This method is then applied to all the OD modes present in a given system.4][45][46] .

Time-averaged frequency distribution
We first look at time-averaged vibrational frequency distributions P (ω) of OD modes, obtained from time-averaging the time-dependent vibrational frequencies of OD modes resulting from the wavelet transform of f (t).Practically, an averaged vibrational frequency distribution is obtained by dividing the frequency range of 2000-3000 cm −1 in equally spaced bins.
If at a given instant the frequency of an OD mode falls within a given bin, the bin height is incremented by unity.This process is repeated for each OD mode and along the entire trajectory.
The time-averaged vibrational frequency distribution of OD modes of the interfacial water on the g-C 3 N 4 surface was found to be a distribution ranging from about 2000 cm −1 to about 2900 cm −1 with a mean at 2496 cm −1 as shown in Fig. 2(a).The distribution is similar to a distribution found for bulk water at 300 K using a similar methodology (see Fig. 2(a) of Ref. 46 , for example), however, with two differences.First, the distribution in our Fig.2(a) is slightly broader, and, more importantly, a clear shoulder peak now appears in the high frequency region around 2750 cm −1 which is absent in bulk water.Closer analysis shows that this shoulder corresponds to the free or dangling OD modes, i.e., OD bonds which are not part of a H-bond network and not bound to the surface and stick out into vacuum instead.
Similarly, the average vibrational frequency of OD modes on the C 2 N surface is 2487 cm −1 (Fig. 2(b)), and the whole time-averaged distribution is similar to the other surface.Also for C 2 N, a shoulder peak in the high-frequency region around 2750 cm −1 is found, again mainly due to the free/dangling OD modes of the interfacial water.Due to the non-centrosymmetric environment at the surface, the tetrahedral hydrogen-bond network is distorted for both surfaces and thus the population of free OD modes shows an overall increment.The highfrequency shoulder is more prominently observable for g-C 3 N 4 which implies comparatively higher population of free/dangling OD modes.Interestingly, high-frequency shoulders are also a characteristic feature of vSFG (vibrational Sum Frequency Generation) spectra of other systems with interfacial water [24][25][26]42,47 .

Time-resolved frequency distribution and dynamics
Further, the temporal dynamics of the OD modes of water molecules on the surface of g-C 3 N 4 and C 2 N were studied using time-dependent joint probability distributions.The time-dependent joint probability distribution used can be expressed mathematically as Here, δ(a(t) − b) = a(t) − b in analogy to Eq.( 5), and the average is taken over all OD bonds.
The joint probability distribution gives the probability that a given OD mode which was oscillating with the vibrational frequency ω 1 evolves to a frequency ω 3 within a time interval In Fig. 3, we have plotted the distributions for the waiting times t 2 = 10, 100, 750 and 3500 fs for OD modes of water molecules on the g-C 3 N 4 surface respectively.For small waiting times, i.e., t 2 = 10 fs, the distribution is predominantly a straight line aligned along the diagonal ω 1 = ω 3 , indicating that the OD modes keep close to their initial vibrational frequency.
However, for the longer waiting times, the distribution eventually gets elongated and evolves into a spherical distribution which implies that the OD modes undergo vibrational spectral diffusion due to hydrogen bond rearrangement.Moreover, within 3.5 ps the OD modes have sampled all accessible vibrational states / frequencies (cf.Fig. 2(a)).A key observation in the time-resolved frequency distributions is that the high frequency shoulder is evidently observable at low as well as long waiting times.Further, the vibrational dephasing of the modes corresponding to the shoulder peak is seen progressing as vertical slab along 2750 cm −1 .
A similar analysis for the water molecules on the C 2 N surface corresponding to the waiting times of t 2 = 10, 100, 750 and 3500 fs is shown in Fig. 4. The vibrational dephasing follows a similar pattern, and overall differences between both surfaces seem small.To more quantitatively address this point, the temporal dynamics of the OD modes of water molecules on the g-C 3 N 4 and C 2 N surfaces is also analyzed using a frequency time correlation function (FTCF) which is given as, The time-dependent decay of the correlation function of OD modes of water molecules on the g-C 3 N 4 and C 2 N surfaces is shown in Fig. 5(a).Evidently, the decay is biphasic with short time regime which extends up to 100 fs and is governed by the ultrafast librational dynamics or concerted collective motion of water molecules 48 whereas the long time decay which extends up to a few picoseconds and is mainly attributed to the hydrogen bond rearrangement dynamics.The timescale of vibrational dephasing was determined by using a bi-expontential fitting function, The short time constant τ 0 was found to be 76 fs and the long time decay constant τ 1 was 5.7 ps for water on g-C 3 N 4 .For C 2 N, we find τ 0 = 104 fs and τ 1 = 4.4 ps.We note that for both systems the long time constant, τ 1 , is significantly longer than for bulk liquid water 46,49 .
According to Ref. 46 , a computed τ 1 for bulk D 2 O is 1.6 ps.Thus, vibrational dynamics of OD modes are slowed down in proximity of a the g-C 3 N 4 surface, and slightly less so near C 2 N.
Since frequency fluctuations of the OD modes are associated with the rearrangement of the local hydrogen bond network, we have also calculated a "hydrogen bond lifetime" using a continuous HB correlation function given as, Here, h(t) and H(t) are hydrogen bond population labels, defined as follows.For a given pair of hydrogen-bonded, different water molecules at an instant t, h(t) is assigned a value of 1 and otherwise 0. also for bulk deuterated water and for the water-vacuum interface in Ref. 50 .The H-bond lifetimes computed there are of similar length, but hard to compare quantitatively to our numbers since they were obtained with another DFT functional and with Car-Parrinello MD rather than Born-Oppenheimer MD.Still, in Ref. 50 it was found that the bulk S HB function decays faster than the interface one.Here, we have the additional effect of the porous surface and we see differences between the two surfaces, g-C 3 N 4 and C 2 N.

Vibrational Sum Frequency Generation (vSFG) spectra
Further insight into the water dynamics on the studied 2D materials, more directly accessible by experiment, comes from vibrational spectroscopy.Here we concentrate on vibrational SFG as a particularly surface-sensitive method.

Time-averaged vSFG spectra
We start with time-averaged vSFG spectra.A time-averaged vSFG spectrum provides relevant frequencies and gives information about the orientation profile of molecular dipoles at the surface/interface.The time-averaged vSFG spectrum is determined from the secondorder optical susceptibility tensor of the system, with tensor elements 27,28 Here, a, b, and c are Cartesian coordinates, α ab (t) is the (a,b)-component of the polarizability tensor at time t, µ c (0) the c-component of the dipole vector at time t = 0, and ω the frequency.Squared, summed (and weighted) components of χ 2 abc give the vSFG spectrum.Here, we concentrate on so-called ssp-polarization spectra, which we approximate by only considering a single χ 2 abc element and setting a = b = x and c = z, respectively, where x is a direction parallel to the surface and z perpendicular to it.We show real and imaginary parts of the second-order susceptibility, χ 2 xxz (ω), whereby the imaginary part can be attributed to the orientation of the interfacial molecules with respect to the surface [21][22][23] .In practice, we calculate here the ssVVAF method mentioned earlier 32,47 .Then, Eq.( 11) can be rewritten, for our D 2 O / surface vSFG problem (with only O-D stretch vibrations considered), as 32,47 Here, r OD i is the coordinate vector of an OD bond (i) as defined earlier (there are and µ ′ OD and α ′ OD are derivatives of the dipole moments and polarizabilities, respectively.A few things are worth mentioning: The ssVVAF expression ( 12) is approximate in the sense that only O-D stretch vibrations are considered.Further, we also use a parameterized (linear) version of dipole moments and polarizabilities without explicitly calculating them -in fact we also do also not include the frequency dependence of µ ′ OD and α ′ OD and set them as constants.Finally, a sometimes used "quantum correction factor" Q(ω) 32 is also neglected.Still, the approach followed here will give insight into the O-D dynamics and in particular into the dynamics of the interfacial H-bond network.The method has been shown to give for the O-H stretch region of a water / air interface, quite similar vSFG spectra compared to a non-parameterized procedure with calculated dipole moments and polarizabilities 28 .xxz .(The real part of the vSFG spectrum is similar to a conventional infrared spectrum and provides information about the frequency required to excite vibrations of the adsorbed molecules.)For D 2 O/g-C 3 N 4 , the imaginary part of the susceptibility is characterized by a broad, (mostly) negative peak for the frequency domain of 2400-2700 cm −1 which refers to the OD modes which are hydrogen-bonded with the other water molecules or with the g-C 3 N 4 surface (Fig. 6(a)).We also note a sharp positive peak for the frequency domain of 2700-2800 cm −1 , referring to free, dangling, or weakly bound OD units (with D 2 O not having four D-bonded neighbours), which are orientated away from the surface.For example, O-D bonds pointing into vacuum are of this type.Note that positive intensities refer to dominantly "upward" and negative intensities dominantly to "downward" orientations of OD bonds.We also note that the intensity of this peak remains unchanged relative to the (unsupported) pure water/air interface computed in Ref. 30 (Fig. 2 there), while the intensity of bonded, red-shifted OD modes is relatively reduced as compared to this reference.This may imply an overall reduction of contributing bonded OD bonds, relative to the free/non-bonded ones, in case of water on C/N surfaces compared to the water/air interface.This is in agreement with the frequency distribution of water molecules on g-C 3 N 4 as shown in Fig. 1(a), where the population of free/dangling OD modes is clearly visible as a high-frequency shoulder.
Further, in Fig. 6(b) the second-order susceptibility of the water molecules on the C 2 N surface is shown.The imaginary part of the second order susceptibility for this system is more similar to the pure water-air interface 30 .Namely, similar to the latter, the negativeintensity peak covering the spectral domain of 2200-2700 cm −1 for the water/C 2 N system is broader and of larger intensity (comparable to the high-frequency peak) compared to the water/g-C 3 N 4 surface.(Note that in Refs. 28,30non-deuterated water was considered so absolute oxygen-hydrogen frequencies are different.) To summarize, the vSFG spectra of OD modes on the g-C 3 N 4 and C 2 N surfaces have similar features for the high frequency region around 2700-2800 cm −1 .But for the frequency region of 2200-2700 cm −1 , the spectral intensity is depleted in the case of g-C 3 N 4 , while it is not for water/C 2 N which behaves similar to the water-air interface 28 .We attribute this behaviour to a propensity of the C 2 N material to stabilize bonded OD bonds.

Time-resolved vSFG spectra
Time-averaged vSFG spectra provide information about the orientation of molecular dipoles at the interface.Nevertheless, dynamics of these molecular dipoles cannot be studied with the conventional vSFG technique.Here, time-resolved vSFG spectra offer more insight.A time-dependent vibrational SFG spectrum can be obtained by modifying Eq.( 11) as Here, we compute the second-order susceptibility of a given vibrational oscillator provided that the oscillator was vibrating at a frequency ω ′ at a time instant t ′ .By systematically varying the value of the waiting time, T w in Eq.( 13), the delay time between a pump pulse and the overlapping IR/vis pulses which generate an SFG signal, we can obtain frequencyresolved, time-dependent susceptibilities and from there, TD-vSFG spectra 30 .It is important to note that in the given computational framework, a priori information of the instantaneous frequency of the oscillators/OD modes is needed to obtain the TD-vSFG spectrum.This information is obtained from the wavelet transform as described above.Further, Eq.( 13) can easily be rewritten in the ss-VVAF form (12), which we use in the following to compute Im χ (2) (ω; T w ) (actually, Im χ (2) (ω IR ; T w , ω pump )).
To calculate the TD-vSFG spectra of the hydrogen bonded OD modes, we have applied a broadband IR pump pulse corresponding to the frequency domain of 2200-2700 cm −1 .
Technically, this was done by computing the susceptibilities of the water molecules based on their vibrational excitation frequency within this frequency range.The imaginary parts of the second-order susceptibility of the hydrogen-bonded OD modes of the interfacial water molecules on g-C 3 N 4 corresponding to the waiting times T w = 0, 400, 2000, 3000 and 4000 fs are shown in Fig. 7(a).The spectrum for the waiting time T w = 0 fs, the "impulsive limit", is dominated by a peak with negative intensity centered around 2600 cm −1 .With increasing waiting times, e.g. for T w = 400 fs, we see a formerly shallow shoulder in the high frequency region around 2750 cm −1 growing, corresponding to the free / dangling OD modes.Further, than the bound → free interconversion (about 4 ps) in (a).This is due to the free OD modes having a strong propensity to form hydrogen bonds and stabilize.When compared to the pure water / air interface 30,31 , it is found that the hydrogen-bond inter-conversion dynamics for the bonded OD modes are overall slowed down whereas for the free OD, the timescale remains relatively unchanged in the presence of the g-C 3 N 4 surface.
Along the same lines, we have also obtained the spectra of the bonded and dangling/free OD bonds of water on the C 2 N surface as shown in Fig. 7(c) and (d).The spectra of the bonded OD modes are shown for waiting times of T w =0, 400, 2000, 5000 and 8000 fs, respectively.While the spectral features as seen in the TD-vSFG spectra are similar to previous calculations for the water / air interface 30 , a key difference is a very slow temporal evolution of the peak for the free OD modes which extends up to nearly 8 ps.
The spectra of dangling/free OD modes are shown for the waiting times T w = 0, 200, 1000, 2000 and 5000 fs respectively.Again, the free OD modes have a strong propensity to form hydrogen bonds due to which the spectral domain corresponding to the bonded OD modes proceeds mostly within 2 ps.The spectra of free OD modes of interfacial water molecules are interestingly independent of the surface, i.e., g-C 3 N 4 or C 2 N.
To summarize, we note that although the overall vibrational dynamics of OD modes on g-C 3 N 4 and C 2 N are similar according to the frequency correlation function, Fig. 5(a) (with a tendency of faster H-bond dynamics for C 2 N), the inter-conversion rates of free and bonded • The time-dependent decay of the OD frequency (measured by a frequency correlation function) is quite similar for both surfaces with a timescale of about 4 ps which is considerably slower than that of the bulk liquid (deuterated) water.Similar trends for the two studied C/N surfaces arise when analyzing the H-bond network via a H-bond measure S HB (t), which implies a slightly longer timescale for g-C 3 N 4 than for C 2 N.
• Time-independent vSFG spectra (measured by χ 2 xxz ), indicate that the dangling OD bonds, pointing upward away from the water / vacuum interface are dominant features in the spectra and are characterized by positive imaginary parts of χ 2 xxz at high frequencies."Bound" OD modes are usually of lower intensity, have negative imaginary parts of χ 2 and are red-shifted.As a difference between the two surfaces, the spectral domain around 2000-2600 cm −1 of the vSFG spectrum for D 2 O/C 2 N is marked by a stronger negative intensity peak compared to g-C 3 N 4 .
• Detailed insight into OD bond dynamics is provided by TD-vSFG spectra, with interesting trends for the two surfaces.Although the vibrational frequency correlation functions are similar, the time-resolved vSFG of bonded OD modes saturates within about 4 ps for g-C 3 N 4 whereas the same process takes nearly 8 ps for the C 2 N surface.
The "free" → "bound" interconversion is faster (∼ 2 ps) and more similar for both surfaces.Thus we can infer on the basis of slower interconversion rates for the bonded to free OD state that the C 2 N surface has a propensity to stabilize bonded OD moieties.
All of these observations imply different performance of porous C/N-containing materials in either catalysis or sieving.That key factors like pore size, C/N ratio, or the three-dimensional structure of the materials (e.g., flat or buckled) influence the vibrational dynamics of adsorbed water has been demonstrated, however, how these factors act in detail is a matter of further research.

Figure 1 :
Figure 1: Snapshots of water (D 2 O) molecules simulated on (a) a C 3 N 4 (3×3) monolayer and (b) a C 2 N monolayer.The employed unit cells are shown in side-views, with C: green, N: blue, O: red, D: white.

Figure 2 :
Figure 2: Time-averaged frequency distribution P (ω) (in arbitrary units) of the OD modes of water molecules on the (a) g-C 3 N 4 and (b) C 2 N surface.

Figure 5 :
Figure 5: (a) Frequency correlation function C ωω (t) and (b) hydrogen bond correlation function S HB (t) for OD modes of water molecules on the g-C 3 N 4 and C 2 N surfaces.

(
Time zero refers to the beginning of the segment of the trajectory into which the trajectory was divided.)Further, if the hydrogen bond between a pair of water molecules remains intact from time t = 0 till time t, H(t) is assigned a value of 1 or else 0. The water molecules are considered to be hydrogen-bonded, if the intermolecular O . . .D distance is less than 2.45 Å corresponding to the first minimum in the O • • • D pair correlation function.The temporal decay of the hydrogen bond correlation function indicates the timescale of rearrangement of the H-bond network and is shown for water (D 2 O) on g-C 3 N 4 and C 2 N surfaces in Fig.5(b).Evidently, also within this measure, the temporal decay of the S HB (t) correlation function is somewhat faster for C 2 N/water in comparison to g-C 3 N 4 /water, as can be seen by visual inspection of Fig.5(b).More quantitatively, the long hydrogen bond lifetime τ 1 , obtained from bi-exponential fits of S HB (t), are found to be τ 1 = 1.8 ps for g-C 3 N 4 and 1.3 ps for water on the C 2 N surface, respectively.Calculations of S HB (t) have been done

Figure 6 :
Figure 6: Real and imaginary parts of χ 2 xxz for D 2 O at (a) g-C 3 N 4 and (b) C 2 N surfaces.The y-axis is in arbitrary units, with the largest positive intensity of imaginary or real parts normalized to 1.

within 4 .Figure 7 :
Figure 7: Imaginary part of χ(2) (ω) at different delay times T w , computed for water on g-C 3 N 4 for (a) the H-bonded OD modes and (b) the free/dangling OD modes.For C 2 N, the same information is given in panels (c) for bonded OD modes and (d) for free/dangling OD modes respectively.Now, for y-axes arbitrary but non-normalized units are used to make the time-evolution of signal intensities visible.