Urea In Water: Structure, Dynamics and Vibrational Echo

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B: Liquids, Chemical and Dynamical Processes in Solution, Spectroscopy in Solution

Urea In Water: Structure, Dynamics and Vibrational Echo Spectroscopy from First Principles Simulations Deepak Ojha, and Amalendu Chandra J. Phys. Chem. B, Just Accepted Manuscript • DOI: 10.1021/acs.jpcb.9b01904 • Publication Date (Web): 23 Mar 2019 Downloaded from http://pubs.acs.org on March 23, 2019

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The Journal of Physical Chemistry

Urea In Water: Structure, Dynamics and Vibrational Echo Spectroscopy from First Principles Simulations Deepak Ojha† and Amalendu Chandra∗ Department of Chemistry, Indian Institute of Technology Kanpur, India 208016. Abstract Aqueous solution of urea at concentration of 4.0 M is studied by using ab initio molecular dynamics simulation. The radial and spatial distribution functions reveal no significant disruption of the local solvent structure by urea even at such a rather high concentration. While the static structural features are not altered in any significant manner, the translational, rotational and vibrational dynamics are found to show noticeable slowing down. The diffusion coefficient of urea is found to be three times lower than that of bulk water molecules. Similarly, orientational relaxation of water molecules in the solvation shell of urea is found to be about 5.0 ps which is significantly higher than the average value of 3.8 ps found for all water molecules. The vibrational dynamics is investigated through calculations of frequency time correlation function (FTCF), joint frequency probability and frequency-structure correlation functions. The timescale of vibrational spectral diffusion as determined from FTCF is found to be 2.7 ps which is higher than the known calculated timescale of ∼2 ps for spectral diffusion of pure water for similar levels of calculations. The third order polarization and the corresponding vibrational echo intensity of OD modes are calculated within the Condon and second-order cumulant approximations. The timescales of loss of correlation in vibrational echo spectrum are calculated from the time dependence of the slope of 3-pulse photon echo (S3PE) function. The timescales obtained from S3PE are found to be in agreement with the FTCF. The slowing down of vibrational, translational and rotational dynamics mean that urea affects the properties of water from a dynamical perspective.

————————————– ∗ †

E-mail: [email protected] Present address: Dynamics of Condensed Matter and Center for Sustainable Systems De-

sign, Department of Chemistry, Paderborn University, Warburger Str. 100, 33098 Paderborn, Germany

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1

Introduction

Aqueous solutions of urea have been extensively studied using several experiments and simulations 1–11 . Urea has a lot of biological significance because it is known to lead to the denaturation of proteins 12 . The solubility of hydrocarbons also increases in aqueous solutions containing urea in comparison to that in the pure water 13 . Further, urea as a solute is an example of an overall electrically neutral molecule having both hydrophilic and hydrophobic moieties 14–16 . In order to understand the mechanism of processes like the denaturation of protein in presence of urea, we need to identify how the local solvent structure gets modified on the dissolution of urea. In this regard, there has been several studies to illustrate the effects of urea dissolution on the local hydrogen bond network of water. 1–18 . While many of the studies have concluded that urea exists essentially as a non-perturbative solute 19–21 in water, there has also been some studies which have classified urea as slightly “structure maker” 22,23 or as slightly “structure breaker” 7,12,24 . A recent simulation study found that an increase of the urea mole fraction in water leads to lowering of the overall tetrahedrality of the system and hence identified urea as a structure breaker 7 . Similarly, neutron diffraction studies found that the second solvation shell of water gets reduced significantly on urea dissolution 25,26 . Based on the depletion of the second coordination shell’s peak of water, it was inferred that it disrupts the local hydrogen bond network of aqueous solutions 25,26 . However, another study based on simulation and Kirkwood-Buff analysis found that the excess self-association in water marginally increased with an increase of urea concentration 22 . Further, based on the temperature and concentration-dependent absorption coefficients of urea-water mixtures in the THz range of 50-350 cm−1 , a recent study concluded that urea-water solution remains predominantly ideal 9 . A dielectric spectroscopic study 20 also concluded that urea remains weakly associated with water and is neither a structure maker nor a structure breaker. The dielectric spectroscopic study was carried out over a wide range of frequencies for aqueous urea solutions of concentration varying from 0.5 to 9.0 M 20 . These conclusions have also been affirmed by NMR 21 and calorimetry 19 based experiments. Further, it is also known that the activity coefficient of urea is remarkably constant for its entire molar solubility range which implies that energetics of the solutions remains 2


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rather similar on the addition of urea 27 . The vibrational spectrum of an aqueous solution is known to be sensitive to the local solvent structure and its temporal evolution. 28–33 Thus, the effects of the dissolution of urea on hydrogen bond network of water can be interpreted in terms of changes in the linear absorption spectrum of OD modes of urea-water solutions 28,29 . An infrared absorption spectroscopic study of dilute (10 %) HOD in H2 O with urea-D4 of 5 M concentration found no significant change in the spectrum 29 . This also means that the hydrogen-bonded network of water is not significantly modified by dissolution of urea. Similarly, the effects of increase in the urea concentration on the absorption spectrum of the CO stretch of urea-H4 in H2 O and urea-D4 in D2 O have also been reported 30 . It concluded that the CO stretch absorption spectrum also does not undergo any significant changes with increasing urea concentration. Further, there has also been an ultrafast spectroscopic study of urea in water with concentration varying from 0 to 8 M 8 . It was found that although the structure is not affected by the urea concentration, the reorientational dynamics gets slowed down with increasing concentration of urea. This phenomenon was interpreted in terms of a two-component model where most of the molecules were found to undergo reorientational motion with a timescale of 2.5 ps and a small fraction of water molecules which form doubly hydrogen-bonded complex with urea undergoing reorientational motion with a significantly slower timescale. On the simulation side, there have been many molecular dynamics studies on the structure and dynamics of urea-water solutions 4–7,15,16,18 . A recent study has also looked at the vibrational spectrum of OD and CO stretches of water and urea of urea-water mixtures using empirical electric field maps 11 . The reorientational dynamics was also studied by calculating the polarization anisotropy and orientational correlation functions 11 . While the dynamics was found to slow down, it was also found that the population of doubly hydrogen-bonded water molecules with urea was extremely small. Thus, the observed slowing down of reorientational dynamics was attributed mainly to the excluded volume effects where the urea molecules block the available sites for the reorientational motion of water molecules that are present in the solvation shells. We are not aware of any theoretical study of the structure, dynamics, vibrational spectral diffusion and vibrational echo spectra of aqueous urea solution

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from first principles simulations. Such a study is presented here. In the current study, we present an ab initio molecular dynamics simulation study of a 4 M solution of urea in water and analyze the structure, reorientational dynamics, frequency probability distribution, frequency structure correlation and also the frequency fluctuation dynamics using time correlation function approach along with vibrational echo spectroscopic calculations. We have calculated the vibrational echo intensity within the Condon and second-order cumulant approximations. We note that a previous first principles simulation study looked at the infrared spectrum of liquid water directly from Wannier dipole dynamics 34 . However, the non-linear spectroscopic calculations involve four-point correlation functions whose statistical convergence is slow and require significantly large simulation run length. Thus, we restrict to the Condon approximation in the present study and assume transition dipole moment to be constant for all calculations. We note that most of the previous simulation studies have calculated the vibrational echo spectra for an isolated OD/OH mode of HOD present in H2 O or D2 O 35–38,40–43 . In the current study, however, we have simulated deuterated urea in D2 O and analyzed each OD mode as a local mode. Further, contributions of the resonant coupling and fast population relaxation 44–48 are not considered in our spectral calculations, thus the present study can be viewed as the vibrational spectral diffusion study of an isolated OD mode in a urea-water solution.

2

Theoretical Formulation

In the present section, we describe briefly the theoretical formulation for calculation of the non-linear response functions for third order polarization generated in a system on irradiation of three consecutive electric field pulses. The overall polarization induced on irradiation of electric field pulses may be expressed as a Taylor series expansion, P(r, t) =

n X

Pn (r, t).

(1)

i=1

Nonlinear spectroscopic techniques like 3PEPS and 2D-IR are used to experimentally determine the third order polarization i.e P3 (r, t). Within the linear response theory, the third order polarization is given as the convolution of the applied electric field with the third order 4


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response of the system i.e. 3

P (t) =

Z 0

∞

dt3

Z 0

∞

dt2

Z

∞

0

dt1 R3 (t1 , t2 , t3 )Ea (t1 )Eb (t2 )Ec (t3 ).

(2)

Here, P 3 (t) is third order polarization, Ei are the applied electric field and R3 (t1 , t2 , t3 ) is the third order response function. In the present work, we have assumed the externally applied field to be delta pulses. Therefore, the polarization is determined by calculating the response functions as given below. These response functions are shown within the Condon approximation which implies that the transition dipole moment µ10/21 is independent of nuclear degrees of freedom. A more detailed theoretical discussion in available in the literature 49–53 . When three electric field pulses with propagation vectors k1 , k2 and k3 are irradiated sequentially on a system, an echo (as measured in 3PEPS/2D-IR) is generated due to constructive interference in the rephasing direction and free induction decay (FID) in the non-rephasing direction. In the equations presented below, the time delay between the first and second pulse is denoted as t1 , between second and third pulse is referred to as t2 and the time delay from third pulse irradiation onwards is denoted as t3 . We ignore the rotational and excited state lifetime effects in the present study. The response functions for the polarization generated in the rephasing (RP) and nonrephasing (NP) directions are expressed as follows 49–54 ,

R1 (t3 , t2 , t1 ) = R2 (t3 , t2 , t1 ) = µ410 exp (−ihω10 it3 + ihω10 it1 )hϕRP (t3 , t2 , t1 )i ,

(3)

R4 (t3 , t2 , t1 ) = R5 (t3 , t2 , t1 ) = µ410 exp (−ihω10 it3 − ihω10 it1 )hϕN P (t3 , t2 , t1 )i ,

R3 (t3 , t2 , t1 ) = −µ210 µ221 exp (−ihω21 it3 + ihω10 it1 )hψRP (t3 , t2 , t1 )i , 5


(4)

(5)


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R6 (t3 , t2 , t1 ) = −µ210 µ221 exp (−ihω21 it3 − ihω10 it1 )hψN P (t3 , t2 , t1 )i .

(6)

where ϕRP (t3 , t2 , t1 ) = exp [i

dτ δω10 (τ ) − i

0

ϕN P (t3 , t2 , t1 ) = exp [−i

ψRP (t3 , t2 , t1 ) = exp [i

t1

Z

0

t1

Z

ψN P (t3 , t2 , t1 ) = exp[−i

t1

Z

0

t1

Z 0

t1 +t2

dτ δω10 (τ ) − i

dτ δω10 (τ ) − i

t1 +t2 +t3

Z

(7)

t1 +t2 +t3

Z

dτ δω10 (τ )] ,

t1 +t2

(8)

t1 +t2 +t3

Z

dτ δω10 (τ ) − i

dτ δω10 (τ )] ,

t1 +t2

Z

dτ δω21 (τ )] ,

(9)

t1 +t2 +t3

t1 +t2

dτ δω21 (τ )] .

(10)

Here, Ri=1...6 are the third order response functions, µ10 and µ21 correspond to the transition dipole moment for the vibration excitation corresponding to 0 − 1 and 1 − 2 transitions. Further, ω10 and ω21 are the vibrational frequencies of the mode in the ground and first excited states. In integrated three pulse echo peak shift (3PEPS) experiments, the intensity along the rephasing direction integrated over t3 is measured. The expression of the integrated intensity is given by

I(t1 , t2 ) =

Z

∞

0

3 2 X dt3 Ri (t1 , t2 , t3 ) .

(11)

i=1

The peak shift t∗1 (t2 ) for a given t2 is defined as the value of t1 for which the echo intensity exhibits a maximum. An alternative to the extraction of frequency correlation function from the integrated echo is the calculation of the initial slope of the integrated three-pulse echo intensity, known as the short-time slope of 3-pulse echo or S3PE, which can be mathematically expressed as

S(t2 ) = 6

∂I(t1 , t2 ) |t1 =0 . ∂t1


(12)

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The normalized frequency time correlation function is then given by 55–59 C(t2 ) =

3

S(t2 ) . S(0)

(13)

Ab initio Simulations

Ab initio molecular dynamics simulations were performed by using the method of Car and Parrinello 60,61 and the CPMD code 62 . The system was chosen such that the effects of urea molecules on the local structure, dynamics and vibrational spectral dynamics of liquid water may be explored for a rather high concentration of urea. The concentrated solution corresponding to the molarity of 4 M was prepared by dissolving nine molecules of urea in a box of 99 D2 O at 300 K. The box length was determined from the known experimental density of the solution 63 . The electronic structure of the system was represented by Kohn-Sham formulation of density functional theory 64 within plane-wave basis set. The norm-conserving atomic pseudopotentials of Troullier-Martins 65 type were employed for the inner core electrons and the plane wave expansion of the orbitals was truncated at the kinetic energy cut-off of 80 Ry. The electronic orbitals were assigned the fictitious mass of 800 au and the coupled equations of motion were integrated with a time step of 5 au. We have used the BYLP-D2 functional 66–70 in the current simulations. In this functional, the dispersion corrections into the BLYP 66,67 functional are incorporated using the D2 scheme of Grimme 68–70 . The initial configuration of the system was obtained from classical molecular dynamics simulations using AMBER03 forcefield 71 . Moreover, the configuration henceforth obtained from classical simulation exhibited a unifrom mixture of urea in water and was found to be devoid of any aggregation among urea molecules. The classical simulations were then followed by further equilibration in NVT ensemble through ab initio molecular dynamics for 15 ps. Subsequently, the production run was carried out for a duration of 50 ps for calculations of various structural, dynamical and spectral properties.

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4

Results and Discussions

4.1

Structure around the Solute

The effects of urea on the solvent structure can be analyzed using radial distribution functions. We calculated the radial distribution functions of oxygen-oxygen, hydrogen-hydrogen and oxygen-hydrogen correlations of water molecules. Based on these distribution functions, we conclude that aqueous urea solution is slightly less structured as compared to pure water. This can be affirmed by comparing the inter-particle distribution functions of the current system (urea-water) with that of pure water which are obtained from AIMD simulations using same protocols and also shown in Fig.1(a) 52 . Further, we calculated the radial distribution functions for nitrogen of urea (Nu ) with oxygen (Ow ) and hydrogen atoms (Dw ) of water molecules which are shown in Fig. 1(b). For the latter, the first shoulder appears at a distance beyond 2.45 ˚ A which implies that water does not donates any hydrogen bond to the nitrogens of urea (Nu ). However, there exists a sharp peak at 1.8 ˚ A for the oxygen of urea i.e. Ou with hydrogens of water (Dw ) and a moderate hump for hydrogens of urea (Du ) with oxygen of water (Ow ) in the solvent-solute radial distribution functions. We infer that the oxygen (Ou ) of urea accepts a hydrogen bond from water. The moderate hump for hydrogens of urea (Du ) with the oxygen of water (Ow ) implies that water accepts a weak hydrogen bond from N − D of urea. With respect to the carbon atom of urea (Cu ), the water molecules are oriented with hydrogens pointing toward them and oxygens pointing away from carbon. This is illustrated in the radial distribution functions of the carbon atom of urea with respect to hydrogen and oxygen atoms of surrounding water molecules. It is found that the first peak of the radial distribution function of carbon of urea molecules (Cu ) with hydrogen atoms of water (Dw ) is located at 2.7 ˚ A, whereas the first peak of the corresponding correlation between the carbon of urea molecules (Cu ) and oxygen of water (Ow ) appears at 3.7 ˚ A. The interaction between urea and water is resolved further in the angular domain by calculating the angularly resolved interparticle distance distributions of C − O · · · D − O and N − D · · · O − D as shown in Fig. 2. For first case, the distance shown is between Ou and Dw and the angle refers to the angle formed by vectors corresponding to C − O mode of urea

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and O − D mode of water. Similarly, for the second distribution, the distance between Ow and Du is calculated and the angle refers to angle formed by vectors corresponding to N − D mode of urea and O − D mode of water. We observe that the C − O is hydrogen bonded to water molecules preferentially at an angular orientation of 60◦ . Unlike C − O, urea does not interact strongly with water via its N − D modes. The radial distribution functions on angular resolution show a uniform angular spread. We have also calculated the coordination numbers for respective solute and solvent radial distribution functions which are included in Table.1. The coordination numbers of nitrogen of urea with oxygen and hydrogen of water are found to be 1.73 and 1.43, respectively. We see that the first minima and the coordination of nitrogen with oxygen and hydrogen atoms of water are similar and comparable with each other. Moreover, the angularly resolved inter-particle distribution for hydrogens of N − D modes of urea (Nu ) with oxygen of water (Ow ) also shows no-preferential orientation of water. It implies that there is no preferentially specific orientation of water molecules around the nitrogens of urea. The oxygen of urea forms about one hydrogen bond with water molecules as can be seen from the corresponding coordination number of 0.77. Further, we explored the overall distributions of the solute and solvent molecules around each other using spatial distribution functions (SDF) and the results are shown in Fig.3(a) and Fig 3.(b). We observe that the isosurface of water’s density around water remains largely intact and its tetrahedral network is not significantly influenced by urea’s presence. For further support, we have also shown in Fig 3.(c) the SDF of water around water for a system comprising of 108 D2 O simulated using same protocols 52 . Further, the number density of urea around water is comparatively low and predominantly beyond the first solvation shell. Similarly, in case of urea, we find that urea shows a reasonable distribution of both the solute and solvent molecules. However, a noticeable ring-like distribution of water around oxygen of urea shows distinct hydrogen-bond led interaction between urea and water. These features also reveal a prominent hydrogen bond between urea’s oxygen and hydrogens of water. All the SDF calculations were done using the TRAVIS software 72 . Based on the structural analysis described above, we conclude that the urea does not affect the local solvent structure of water

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very significantly.

4.2

Translational Diffusion of Water and Urea

We have also looked at the translational dynamics of urea and water molecules in the solution. The diffusion coefficients are calculated from the slope of mean square displacements 73 , E 1 D |r (t) − r (0)|2 . t→∞ 6t

D = lim

(14)

The mean square displacements of urea and water molecules are shown in Fig.4. The diffusion coefficient of urea molecules in the solution is found to be 0.35 × 10−5 cm2 sec−1 . The diffusion coefficient of water molecules in the solution is found to be 0.97×10−5 cm2 sec−1 . The current results of diffusion coefficients are in line with those of previous simulations 74 which also reported a much slower diffusion of urea than that of water in aqueous urea solution.

4.3

Rotational Relaxation of Water

Further, we have investigated the orientational relaxation of water molecules present in the urea solution. The orientational correlation function 73 is defined as, ˆ e(0) ˆ Pl e(t). 2 D h iE , Cl (t) = ˆ e(0) ˆ Pl e(0). D

h

iE

(15)

where Pl is the Legendre polynomial of rank l and eb(t) denotes the unit vector along the molecular dipole. The timescale of orientational relaxation is obtained as the time integral of the orientational correlation function. We have calculated the orientational correlation function for water molecules present in specific solvation shells of carbon, oxygen and nitrogen atoms of a urea molecule. A water molecule is said to be in solvation shell if the inter-atomic distance between oxygens of water and respective atoms of urea is less than the location of the first minima of their respective radial distribution functions. We find that the water molecules in close proximity of urea have slower orientational relaxation as compared to the bulk water. While the orientational relaxation timescale for all water molecules present in aqueous urea 10


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solution is 3.8 ps, the rotational timescales of water molecules in the solvation shells of oxygen, carbon, and nitrogen of urea are found to be 5.01, 4.85 and 4.84 ps, respectively. Further, the rotational relaxation timescale of water molecules in pure water 52 was found to be 2.9 ps which is also faster than the timescale for the aqueous urea solution. The time-dependent decay of the orientational correlation functions is shown in Fig.5. We note that earlier experimental and simulation studies have also reported a similar slowing down of rotational dynamics of water in aqueous urea solutions 8,9,11 .

4.4

Vibrational Frequencies and their Fluctuation Dynamics

The instantaneous fluctuations in vibrational frequencies in the ground state are calculated from the trajectory obtained from ab initio molecular dynamics using the wavelet method of time-series analysis 75–77 . The method has been described in details in the literature for calculations of vibrational frequencies of water in aqueous medium 52–54,78 . We apply the method over all the OD modes present in the system and get the timedependent fluctuations in vibrational frequencies over the entire simulation time period. The fluctuations corresponding to higher vibrational level excitations are calculated by modeling the OD modes as Morse oscillators 79 . The details of such calculation have been discussed in our earlier studies 52–54 . The energy eigenvalues of the Morse oscillator 79 can be determined analytically and are given by,

Ev = (v + 1/2)hν − (v + 1/2)2 xe hν ,

(16)

where the anharmonicity constant xe is equal to ν/4De , where De is the bond dissociation energy and ν is the harmonic oscillation frequency which is related to the curvature of the potential at its minimum 79 . Following our previous work 52–54 , we determine the anharmonicity parameter of an OD mode at a given time instant using the fixed value of De i.e. dissociation energy and the vibrational frequency obtained from the wavelet method. With both the anharmonicity parameter and dissociation energy known, we calculate the vibrational fre-

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quencies corresponding to the higher excitations which are expressed as ω10 = (E1 − E0 )/hc and ω21 = (E2 −E1 )/hc. The instantaneous fluctuations in ω10 and ω21 and the anharmonicity (∆ = ω10 − ω21 ) for a section of the trajectory are shown in Fig.6. While the radial distribution functions revealed that the time-averaged local solvent structure is not significantly perturbed on the dissolution of urea in water, we have also looked at the effects of urea on vibrational dynamics of OD vibrational modes of the solvent. The distribution of vibrational frequencies of all OD modes present in the system is shown in Fig.7. The mean frequency of stretch of OD modes is found to be 2370 cm−1 for the solution of urea in water. The average frequency of stretch of OD modes for pure water as calculated from ab initio simulations was also found to be 2370 cm−1 which implies that the static distribution of vibrational frequencies of OD modes is not affected by the presence of urea molecules. Our findings are in agreement with the terahertz experimental studies which have shown that the total absorption coefficient of aqueous urea solutions is nearly independent of urea concentration 9 . We have also looked at the vibrational frequency distribution of the CO and ND stretch modes of urea molecules as shown in Figs. 7(b) and 7(c). The mean frequency of the CO stretch is 1430 cm−1 and of the ND stretch is 2420 cm−1 . Further, we have calculated the time-dependent two-dimensional joint probability distributions of vibrational frequencies of OD modes 52,80 . The time-dependent evolution of the frequency probability distributions gives qualitative time scale of spectral diffusion. It is known theoretically that beyond the timescales of vibrational spectral diffusion, shape of 2D-IR spectrum and frequency probability distribution are similar 80 . We calculate the probability distribution for four waiting times of t2 = 30 fs, 1 ps, 2 ps and 3 ps and the results are shown in Fig.8. At short times, the distribution is essentially elliptical around the diagonal but as the waiting time increases, the pattern gradually becomes widened and it becomes essentially spherical by 3 ps. This modification in distribution pattern means that all the local solvent structures are sampled. Further, we have also calculated the joint probability distributions of CO modes for the waiting times of t2 = 12, 120, 240 and 1000 fs as shown in Fig 9. We find that the distribution of CO modes undergoes faster relaxation and by 1 ps the distribution is completely spherical. Similar probability distribution results for the ND

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modes of urea molecules are shown in Fig. 10. The distribution plots are shown corresponding to the waiting times t2 = 12 fs, 300 fs, 1 ps and 2 ps respectively. As the distribution becomes spherical by 2 ps, the timescale of spectral diffusion in ND modes is calculated to be around 2 ps. We also determined the time-averaged frequency-frequency cross-correlation between the OD modes of nearest water molecules to the CO modes and also with ND modes of urea molecules. The results are shown in Fig. 11 (a) and (b), respectively. We observe that the vibrational modes of OD are not strongly coupled with either CO or ND modes of urea as seen from the cross-correlation distributions. The frequency-time correlation function (FTCF) has been used extensively to calculate the timescales at which different processes contributing to vibrational spectral diffusion occur. Several experiments have extracted the observables like peak shift 81 and slope of nodal line (SNL) 82 which capture the extent of loss of frequency correlation in a system. The FTCF of OD stretch modes of water, CO and ND modes of urea are shown in the Fig.12. The frequency correlation function shows a biphasic decay with a short timescale decay extending up to 100 fs and a long timescale decay which decays in the time range of a few picoseconds. In order to extract the timescales corresponding to the loss of frequency correlation, we use a biexponential fit of the following kind,

f (t) = a0 exp(−

t t ) + (1 − a0 )exp(− ). τ0 τ1

(17)

The short timescale is found to be 81 fs which can be attributed to the fast librational motions seen through terahertz spectroscopy. The timescale for longer decay, in general, corresponds to the hydrogen bond rearrangement dynamics. The longtime decay is found to be 2.71 ps which is comparatively higher than the value of 1.92 ps for the pure water as calculated from recent ab initio simulation study 52 . Interestingly, it implies that while the time-averaged frequency distribution is not influenced by the urea molecules, the timedependent vibrational spectral dynamics is slowed down in presence of urea. Further, the short timescale obtained from the biexponential fit to the FTCF of ND modes is 91 fs and the longer timescale is 1.53 ps. We obtained a very fast decay for the correlation loss in the vibrational frequency of CO modes as shown in Fig. 12. The longer timescale for the decay 13



obtained from the biexponential the fit is 1.12 ps. In order to correlate the decay of FTCF of OD modes with the instantaneous fluctuations in the local hydrogen bond network, we have calculated the time-dependent decay of instantaneous fluctuation in intermolecular RO···O for water molecules i.e. hδRO···O (0).δRO···O (t)i as shown in Fig. 13. The timescale of decay of the local structural correlation was determined using the biexponential fit. The longer timescale of decay was found to be 3.1 ps which is in close agreement with the timescale of decay of FTCF of OD modes. Further, another interesting feature of local structure correlation decay is the presence of an initial oscillatory pattern which is also reported in several vibrational echo experiments. This oscillatory kink in the correlation functions can be predominantly attributed to the underdamped motion of H-bonded O · · · O pairs. The spatial-correlations in vibrational frequencies of OD, CO and ND modes are also studied through the frequency-structure correlation maps as shown in Fig. 14. The spatial correlations between the vibrational frequency of an OD mode and the RO−H···O and RO···O distances and θO−H···O angle show that the frequency fluctuations are modulated by the modification in the local hydrogen bond network. Although there exists a hydrogen bond between the carbonyl oxygen of urea with the hydrogen of water, the modulations in CO mode vibrational frequency are not significantly correlated with the RC−O···H and RC−O···O distances and θC−O···H−O angle. This clearly implies that the correlation loss in frequency fluctuations of CO mode are not governed by the local hydrogen bond network reorganization. Similarly, in case of ND modes, it is seen that the vibrational frequency fluctuations are not strongly correlated with the RN −D···H−O and RN −D···O distances and θN −D···O angle. Thus, the hydrogen bonded interactions between urea and water are not found to be strong enough to significantly enhance the urea-water intermolecular local structure.

4.5

Echo Intensity and S3PE

Heterodyned three-pulse photon echo peak shift (3PEPS) spectroscopic technique has been used extensively to obtain the frequency correlation decay 81 . Theoretically, several alternatives have been proposed to extract frequency correlation decay from integrated echo inten-

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sity 56,57 . The slope of 3-pulse photon echo (S3PE) is defined as the slope of echo intensity at time t = 0 and, within the impulsive limits, it has been shown that the S3PE is well suited over 3PEPS to determine the frequency correlation 57 . In the present work, we have determined the integrated echo intensity and S3PE within the Condon and second-order cumulant approximations. The integrated echo intensity along the rephasing direction as a function of time t1 calculated within the Condon and cumulant approximations are shown in Figs. 15 (a) and (b), respectively. It is quite evident that as the population time increases, the intensity shows a surge and then gradually decays. Further, the time-dependent decay of the normalized S3PE for the Condon and second order cumulant approximations are shown in Fig. 15(c). The timescales of frequency correlation loss are calculated using a biexponential fit. The values of the longer timescale of decay are found to be 3.2 ps and 2.7 ps for the cumulant and Condon approximations, respectively. We note that while the cumulant approximation predicts a slightly slower dynamics, the results for the Condon approximation are in very good agreement with that of FTCF. Further, the timescales of decay of S3PE for pure water are around 1.91 and 1.87 ps 52 for the cumulant and Condon approximations, respectively, which also support the overall slowing down of the vibrational spectral diffusion of OD modes in aqueous urea solutions.

5

Discussion

In the present section, we discuss our findings in the context of existing and future experimental studies. We note that earlier THz 9 , NMR 21 and dielectric spectroscopic studies 20 have shown that urea does not affect the liquid water characteristics in any significant manner. Also, a polarization-resolved mid-infrared pump-probe spectroscopic study of concentrated aqueous urea solutions has shown that orientational relaxation of water is slowed down in presence of urea. Nevertheless, the decaying bleach of OD vibration was found to be independent of urea concentration 8 . The effects of urea on hydrogen bond structure and its rearrangement can be analyzed using vibrational spectroscopy or more specifically its dynamical aspects can be explored through third order non-linear vibrational spectroscopic experiments like 2D-IR or 3PEPS. To the best of our knowledge, no experimental study is

15



available in the literature where the effects of urea dissolution on water dynamics has been studied using 3PEPS or 2D-IR. In the present work, we have presented theoretical calculations of such nonlinear spectroscopic observables which, we hope, would encourage such non-linear vibrational spectroscopic experiments on water-urea systems. Here, we have shown that the vibrational spectral diffusion in aqueous urea solution gets slower compared to that in pure water. While the existing classical simulations of water-urea systems have demonstrated noticeable slowing down in the translational and reorientational dynamics of water, the effects of urea dissolution on vibrational dynamics of water has not yet been fully explored. Since the translational, rotational and vibrational degrees of freedom are not necessarily coupled in any simple manner, earlier results of translation and rotational dynamics cannot be readily generalized to describe or extrapolate vibrational spectral diffusion in aqueous urea solutions. In addition to the calculations of the vibrational frequency correlation functions (FTCF), we have also calculated the S3PE for urea solution at the levels of Condon and cumulant approximations which also affirm a noticeably slower vibrational spectral diffusion. Further, we have also studied the vibrational dynamics of CO and ND modes of urea through calculations of FTCF and joint probability distributions. We find that both the ND and CO modes show a biexponential decay which is faster than that of OD modes of water. Further, frequency cross-correlations of the CO-OD and ND-OD modes show that the fluctuation dynamics of the ND and CO modes are fairly uncorrelated to OD mode vibrations. Similarly, the frequency-structure correlation functions for CO and ND modes also support that fluctuations in CO and ND modes are not significantly influenced by local solvent structural fluctuations. We note, that real-time experimental studies involving 3PEPS/2D-IR of CO and ND modes would be able to affirm their correlations to surrounding dynamical structure of water. Further, the channels of vibrational spectral diffusion for CO and ND modes are also not fully understood yet. Experimental work in this direction would be able to predict the effects of urea on water dynamics including the correlations of the CO and ND mode fluctuations with the hydrogen bonded dynamical structure of water.

16


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6

Summary

In the present work, we have investigated the structure, dynamics and nonlinear vibrational spectrum of a 4 M solution of urea in water through ab initio molecular dynamics simulation. We have explored the intermolecular structure of the solute and solvent using various radial and spatial distribution functions. The local solvent structure is found to be not much perturbed despite the high concentration of urea. Further, there is no enhanced aggregation of water around urea as seen from urea’s radial distribution functions. These inferences are further supported by the calculations of spatial distribution functions of urea and water. Based on the static radial distribution functions, it can be said that urea is neither structure maker nor structure breaker. However, the translational dynamics of the solution is slowed down considerably as the diffusion coefficient of urea molecules is found to be slower by three times compared to that of water. Further, the timescale of orientational relaxation of water molecules in the solvation shell of urea is found to be around 5 ps, whereas the orientational relaxation time of all OD modes in aqueous urea solution is 3.8 ps. The slowing down of rotational dynamics of water molecules in the solvation shell of urea is predominantly because of the hindered rotation in solute’s neighborhood. The vibrational frequency distribution of OD modes in urea solution is indistinguishable from that of pure water. The joint probability distributions give a qualitative timescale of 3 ps for vibrational spectral diffusion. The timescale of decay of the slower component of FTCF gives a timescale of 2.7 ps. The slope of 3-pulse photon echo (S3PE) of integrated intensity of OD modes calculated within the Condon and second-order cumulant approximations also give similar timescales. Thus, we infer that while the static structure of solvent is not significantly perturbed by urea, the translational, vibrational and orientational dynamics undergo noticeable slowing down in presence of urea. We finally note that the current ab initio simulations were performed by using the dispersion corrected BLYP-D2 functional 68–70 . This functional was employed in many earlier ab initio simulations of aqueous systems 83–88 and it was shown to provide significantly improved description of the structure, dynamics and phase diagram of aqueous systems compared to those obtained with the corresponding BLYP functional 66,67 without any dispersion correc17



tion. We also note in this context that there are also other dispersion correction schemes such as DFT-D3 like BLYP-D3 66,67,70 , revPBE-D3 70,89 , DFT-vdw 90 , DFT-TS 91 etc, which have been used in ab initio simulations of water and other hydrogen bonded systems. It would be worthwhile to carry out a study of the comparative performance of these different dispersion correction schemes for aqueous urea solutions.

Acknowledgement We gratefully acknowledge the financial support from Science and Engineering Research Board (SERB) and Council of Scientific and Industrial Research (CSIR), Government of India.

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Table 1. Location of the first minimum of radial distribution functions and coordination numbers of different atoms of urea with the hydrogen and oxygen atoms of surrounding water. Atom pair rmin Coordination Number N and Dw 4.56 1.71 N and Ow 4.29 1.43 Ow and Du 2.55 0.40 Ou and Dw 2.50 0.77 Cu and Dw 3.13 0.46 Cu and Ow 4.85 1.85

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2

3.5 O w -O w O -D

3

w

N u -O w

1.8

N u -D w

w

O w -D u

1.6

D w -D w

2.5

O u -D w

1.4

Cu -O w Cu -D w

1.2 g(r)

2 g(r)

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


1.5

1 0.8 0.6

1

0.4 0.5 (a)

0

2

3

4

5

0.2 0

(b)

1

2

3

4

5

6

Fig.1 (a) Interatomic pair correlation functions of water molecules in 4.0 M aqueous urea solution. (In dotted line) Interatomic pair correlation functions of pure water with same nomenclature as for 4.0 M aqueous urea solution. (b) Interatomic pair correlation functions of different atoms of urea with oxygen and hydrogen atoms of water in the same solution.

29



Fig.2 Joint probability distributions of hydrogen bond angle and hydrogen bond distance for the (left) C − O and (right) N − D modes of urea.

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(a)

(b)

(c)

Fig.3 (a) Spatial distribution function of water (purple) and urea (green) molecules around water, (b) spatial distribution function of water (purple) and urea (green) molecules around urea in 4.0 M urea solution, (c) spatial distribution function of water around water for pure water.

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10 Urea Water

8

6

4

2

0

0

2

4

6

8

10

12

14

Time (ps)

Fig.4 Mean square displacements of water and urea molecules in 4.0 M aqueous urea solution.

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1 water in N

0.9

water in C

u

shell shell

u

0.8

water in O

0.7

all water molecules pure water

u

shell

0.6 C 2 (t)

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


0.5 0.4 0.3 0.2 0.1 0 0

1

2

3

4

5

6

7

8

Time (ps)

Fig.5 Oreintational correlation functions of water molecules present in the solvation shell of nitrogen, carbon, and oxygen atoms of urea and also averaged over all OD modes present in the aqueous urea solution and also of pure water.

33



Frequency (cm−1)

1800 ω10

2000

(a)

ω

21

2200 2400 2600 2800 20

20.5

21

21.5

22

22.5 23 Time (ps)

23.5

24

24.5

25

250

(b) ∆ (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

Page 34 of 44

200

150

100 0

5

10

15

20

25 30 Time (ps)

35

40

45

50

Fig.6. (a) Fluctuations in 0 → 1 and 1 → 2 vibrational transition frequencies of an OD oscillator in the 4.0 M urea solution over a selected segment of the trajectory. (b) Instantaneous fluctuations in the anharmonicity ∆ over the entire simulation trajectory of the same system.

34


Page 35 of 44

P(ω)

(a)

2000

2100

2200

2300

2400 2500 −1 ω (cm )

2600

2700

2800

P(ω)

(b)

1300

1350

1400

1450 ω (cm−1)

1500

1550

1600

2200

2300

2400 ω (cm−1)

2500

2600

2700

(c)

P(ω)

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


2100

Fig.7. Frequency distributions of (a) OD oscillators, (b) CO oscillators, and (c) ND oscillators in the 4.0 M aqueous urea solution.

35



2800

2800

t = 30 fs

t = 1 ps

ω3 ( cm−1)

2

2600

2600

2400

2400

2200

2200

2000 2000

2200

2400 −1 2600

ω1 ( cm )

2800

2

2000 2000

2200

2400−1 2600

2800

2400−1 2600

2800

ω1 (cm )

2800

2800

t2= 2 ps ω3 ( 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

Page 36 of 44

2600

2600

2400

2400

2200

2200

2000 2000

2200

2400−1 2600

ω1 (cm )

2800

t2= 3 ps

2000 2000

2200

ω (cm ) 1

Fig.8. Joint probability distributions of finding frequencies ω1 and ω3 at a time gap of t2 of an OD mode in the 4.0 M aqueous urea solution.

36


Page 37 of 44

1500

1500 t2 = 120 fs

1400

ω3 (cm−1)

ω3 (cm−1)

t2 = 12 fs

1300

1200 1200

1300 1400 −1 ω1 (cm )

1500

1400

1300

1200 1200

1500

t = 1000 fs

t2 = 240 fs

ω3 (cm−1)

2

1400

1300

1200 1200

1300 1400 −1 ω1 (cm )

1500

1500

ω3 (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


1400

1300

1200 1200 1300 1400 ω1 (cm−1)

1500

1300 1400 ω1 (cm−1)

1500

Fig.9. Joint probability distributions of finding frequencies ω1 and ω3 at a time gap of t2 of a CO mode in the aqueous urea solution.

37



2800

2800 t2 = 300 fs

t2 = 12 fs

2600

ω3 (cm−1)

ω3 (cm−1)

2600

2400

2400 2200

2200 2000 2000 2200 2400−1 2600 2800 2000 2200 2400−1 2600 2800 ω1 (cm ) ω1 (cm ) 2800

2800 t2 = 1 ps

t2 = 2 ps

2600 ω3 (cm−1)

2600 ω3 (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

Page 38 of 44

2400 2200

2400 2200

2000 2000 2000 2200 2400−1 2600 2800 2000 2200 2400−1 2600 2800 ω1 (cm ) ω1 (cm )

Fig.10. Joint probability distributions of finding frequencies ω1 and ω3 at a time gap of t2 of an ND mode in the aqueous urea solution.

38


Page 39 of 44

1600

2800 (b)

(a) 2700 1550 2600 (cm -1 )

(cm -1 )

1500

1450

ND

CO

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


2500 2400 2300

1400 2200 1350 2100 1300 2000

2200

2400 OD

(cm

-1

2600

2800

2000 2000

)

2200

2400 OD

2600 (cm -1 )

2800

Fig.11 Time averaged cross correlation probability distribution (a) of ωCO with ωOD , (b) ωN D with ωOD .

39



1 0.9 0.8 0.7 0.6 C(t)

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

Page 40 of 44

0.5 0.4 0.3 0.2 0.1 0

0

0.5

1

1.5

2

2.5

3

Time (ps)

Fig.12. Time dependence of the correlation function of frequency fluctuations of OD, CO and ND stretch modes in the aqueous urea solution.

40


Page 41 of 44

1

0.8

C rOO (t)

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


0.6

0.4

0.2

0

0

0.5

1

1.5

2

2.5

3

Time (ps) Fig.13. Time dependence of the correlation function of RO···O fluctuations for OD stretch modes in the aqueous urea solution.

41



Fig.14. Frequency-structure correlation between (a) OD modes and RO−D···O , (b) OD modes and RO···O , (c) OD modes and θO−D···O , (d) CO modes and RC−O···D−O , (e) CO modes and RC−O···O , (f) CO modes and θC−O···D−O (g) ND modes and RN −D···D−O , (h) ND modes and RN −D···O and (i) ND modes and θN −D···D−O .

42


Page 42 of 44

Page 43 of 44 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


Fig. 15. Time dependence of the integrated echo intensity of vibrational echo spectroscopy of OD stretch in the aqueous urea solution calculated within (a) second order cumulant and (b) Condon approximations, (c) Time dependence of the S3PE of vibrational echo spectrum of OD stretch in aqueous urea solution calculated within the second order cumulant and Condon approximations.

43



TOC Figure

44


Page 44 of 44

Urea In Water: Structure, Dynamics and Vibrational Echo

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