A Microscopic Interpretation of PumpâProbe Vibrational Spectroscopy

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

A Microscopic Interpretation of Pump-Probe Vibrational Spectroscopy Using ab initio Molecular Dynamics Dominika Lesnicki, and Marialore Sulpizi J. Phys. Chem. B, Just Accepted Manuscript • DOI: 10.1021/acs.jpcb.8b04159 • Publication Date (Web): 25 May 2018 Downloaded from http://pubs.acs.org on May 25, 2018

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The Journal of Physical Chemistry

A Microscopic Interpretation of Pump-Probe Vibrational Spectroscopy using ab initio Molecular Dynamics Dominika Lesnicki and Marialore Sulpizi∗ Institute of Physics, Johannes Gutenberg University Mainz, Staudingerweg 7, 55099 Mainz, Germany E-mail: [email protected] Phone: +49 6131 39 23641. Fax: +49 6131 39 25441 Abstract What happens when extra vibrational energy is added to water? Using non equilibrium molecular dynamics simulations, also including the full electronic structure, and novel descriptors, based on projected VDOS, we are able to follow the flow of excess vibrational energy from the excited stretching and bending modes. We find that the energy relaxation, mostly mediated by a stretching-stretching coupling in the first solvation shell, is highly heterogeneous and strongly depends on the local environment, where a strong hydrogen bond network can transport energy with a time scale of 200 fs, while a weaker network can slow down the transport with a factor 2-3.

Introduction Time-resolved pump-probe vibrational spectroscopy is a major tool to investigate both time scales and relaxation pathways of the vibrational energy relaxation processes. 1–3 In these 1

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experiments, a vibrational mode is excited using a laser pulse with a specific frequency, and subsequently vibrational spectra are recorded over a wide spectral window as a function of the time delay after the excitation. As the most important and most investigated compound on earth, water has been subject of intense research by time resolved vibrational experiments aiming to understand the structure and dynamics of its hydrogen bond network. In particular, 2D-IR spectroscopy for the bulk 4–6 and more recently 2D-SFG 7,8 to selectively address interfaces, have highlighted a picture of a very dynamical, heterogeneous fluid, characterized by sub-picosecond energy relaxation. In order to obtain the microscopic picture behind the experimental results, computer simulations can be used either to calculate the 2D-IR response function 9,10 or to directly simulate the excitation event. 11–13 In particular following the pioneering work of Hynes and coworkers 14–16 force field-based atomistic simulations have been used to simulate a ‘classical’ vibrational excitation localized on a single water molecule. More recently a collective excitation using a Langevin friction thermostat to produce classical excitation has been also employed. 17 In this last work substantial differences with the experimentally observed timescales emerge, possibly due to the used force field. A collective excitation using a momentum swapping approach has been used also in a recent work, in combination with ab initio molecular dynamics, however on a very small system composed of only 32 water molecules. 11 In the case of an heterogeneous liquid, as water, 18 an approach which includes the full electronic structure and is capable of describing polarization (also including electronic polarization) is certainly the optimal choice. The advantage of electronic structure based simulations is also the possibility to automatically include anharmonicity and coupling among system’s modes. The use of an electronic structure-based approach is particularly crucial in the case of interfaces, e.g. solid/liquid interfaces, where a force field may be available for the bulk liquid and bulk solid, but is not necessarily transferable to the interface or capable of describing e.g. surface rearragment/ reconstruction in the presence of the liquid. The drawback is the cost associated to a direct calculation of a typical response function, 2


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requiring a very long sampling, as well as the difficulty to analyze the relaxation in terms of molecular contributions, as for example when collective excitations are produced. In addition to the above mentioned work, where the relaxation dynamics is purely classical (although eventually driven by an electronic structure -based Hamiltonian), hybrid quantum/classical perturbative approaches have been also applied to vibrational relaxation. Such methods, pioneered by Rey and Hynes 19 and Lorentz and Skinner 20,21 are based on the Landau-Teller theory in a perturbative treatment, where only some of the vibrational modes are treated quantum mechanically, while others are treated classically and act as a thermal bath. 22–25 Vibrational Molecular Dynamics Quantum Transition (MDQT) has been also used within the framework of hybrid quantum/classical methods and applied to vibrational relaxation of the H2 O bending in water 26,27 and of the OD stretching fundamental of HOD in H2 O 28 The idea of this work is to use Density Functional Theory (DFT)-based molecular dynamics (MD) simulations to realize a vibrational excitation localized on a single water molecule and to follow the excess energy relaxation to the surrounding environment using newly derived descriptors based on projected vibrational density of states (VDOS). Although the VDOS descriptors are similar to those presented in Refs., 12,29 where a gaussian pulse is applied to the all simulation box, our excitations are localized in space on a single water molecule and projected on the local normal modes. The simulation of a localized vibrational excitation will permit to analyze the energy transfer in space, as well as in time. Such a single molecule resolution, which is not yet achieved in experiments, permits to analyze the experimental data and to understand the microscopic origin of the observed relaxation time scales. Anticipating our results, we are able not only to reproduce the time scale observed in the 2D-IR experiments, but also to identify the main energy channels for the transfer. In the case of the stretching mode, a major role is played by the coupling with other OH stretching modes on the neighboring waters. Our approach permits, for the first time, to describe the heterogeneity in the vibrational relaxation time observed in the experiments 18 and to 3



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correlate the relaxation time scales with the local hydrogen bond structure. In the case of the bending excitation the energy relaxation is faster, as actually found in the experiments, 30–35 and mainly occurs through the coupling of the bending mode to the libration and stretching modes of the excited molecules, as well as through the coupling of the bending mode with the bending modes of the waters in the first solvation shell.

Methods We now turn to the description of our approach. Starting from a given configuration extracted from an equilibrium ab initio molecular dynamics trajectory of water in the condensed phase, the vibrational excitation is obtained by adding to a given water molecule extra kinetic energy according to a given symmetry, namely according to a symmetric (antisymmetric) stretching, or bending mode as below:

gs ex ~vH = ~vH + δv ~xij ij ij

(1)

gs ex are the velocity of a given hydrogen atom i belonging to water and ~vH where ~vH ij ij

molecule j in the vibrationally excited and ground state, respectively. ~xij is the component of the given normal mode, on the atom i. For the excitation of the symmetric stretching the vectors ~xij are unit vectors along the two OHi bonds, while in the case of the excitation of the bending ~xij are unit vectors orthogonal to each of the OHi bonds. The value of δv is chosen such that the temperature of the overall simulation box is increased by 1.5 K. This not only is close to the increment in the temperature of the sample in typical pump-probe experiments, but also ensures that the excitation is not strongly perturbing, or even disrupting, the local hydrogen bond network. Despite the fact that the excitation energy is the single initial mode is quite high, we can show that the chosen value guarantees that the obtained excitation spectrum still remains very close to the VDOS spectrum obtained from the equilibrium simulation at room temperature. A comparison of the excitation spectrum at 1.5 K and the 4


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equilibrium VDOS spectrum is reported in Fig.S1 of the Supporting Information. Assigning the excess velocity according to a given mode automatically also select the frequency of the excitation. This is discussed more extensively below and proven by the excitation frequency distribution, which indeed is localized in the frequency. The extra kinetic energy, added to a given molecule, drives, instantaneously, the system out of the equilibrium and the subsequent relaxation process is followed within NVE trajectories using descriptors, which permit to follow the excess energy redistribution among given modes. In particular, the time evolution of the excess vibrational energy can be described as the difference between the power spectrum calculated in the vibrationally excited (or non equilibrium) state and that calculated in the ground (or equilibrium) state, 12,29,36 according to: ∞

Z

Z

ex

P (ω, t) dω −

I(t) =

∞

P gs (ω, t) dω.

(2)

0

0

where Z P (ω, t) = t

t+∆t

*

+ X

vi (t)vj (t + τ ) e−iωτ dτ.

(3)

ij

is the Fourier transform of the velocity-velocity autocorrelation function calculated at a given time t and vi (t) is the velocity of atom i at time t and ∆t the time window over which the correlation function is computed (see Supporting Information for details). In order to monitor how the excess energy is redistributed among different water molecules and among different vibrational modes, the velocities in Eq. 3 are projected along the normal modes of a single gas-phase water (see the Supporting Information). This use of the local normal modes is new and was not already presented in the work of Refs. 12,29,36 In this way the stretching, bending, and libration component of the total energy descriptor I(t) can be obtained, which allows to monitor, as function of time, how the energy of a given mode (band) decreases, respectively increases. Moreover summing over a selected subset of 5



molecules the excess energy can be localized in space providing the possibility to spatially follow the energy flow as it leaves the excited molecule and redistribute to the environment. As a starting point we considered a 50 ps AIMD trajectory in the NVT ensemble at 330K (Nose-Hoover thermostat) from which 10 snapshots were extracted every 5 ps in order to ensure that velocities are decorrelated. From each of these 10 snapshots 128 non equilibrium trajectories were started where, in turn, one of the water molecules is (classically) promoted to a vibrationally excited state. In this way a total of 1280 excitations (non equilibrium trajectories) are obtained for the stretching and the bending excitation, respectively. The localization of the vibrational excitation on different molecules will permits to sample different local hydrogen bond environments, which all together will be representatative of the average bulk water dynamics. The BLYP functional 37,38 , also including Grimme (D3) correction for dispersion, 39 the norm-conserving Goedecker-Teter-Hutter (GTH) pseudopotentials 40 and the TZV2P basis set were used. Such level of theory has been shown to provide an accurate description of structural and dynamical properties of liquid water. 41 The slightly elevated temperature has been shown to reproduce the liquid structure at 1 g/cm3 . 42 A charge-density cutoff of 280 Ry was employed for the real-space grid with density smoothing. The simulation cell contained 128 H2 O molecules with 1.0 g/cm3 density. Periodic boundary conditions were employed. All the simulations were performed with the CP2K code. 43

Results and discussion Figure 1 shows the distribution of the excitation frequencies (excitation spectrum), defined as the distribution of the frequency of the maximum of I(t). For both the symmetric stretching (panel A) and the bending excitation (panel B) a gaussian distribution is obtained, centered around 3380 cm−1 , respectively 1632 cm−1 which is consistent with the infrared absorption spectra of bulk water. 18,44

6


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60 Excitation frequency distribution

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


A

80

50 40

B

60

30

40

20 20

10 0

3000 3250 3500 3750 -1 ω (cm )

0

1400 1600 1800 2000 -1 ω (cm )

Figure 1: Frequencies distribution obtained for the stretch excitation (A) and bend excitation (B) at initial time (black, dot) and their gaussian fits (black, plain).

The excess vibrational energy in each mode I(t) is monitored along the 1 ps long NVE runs. Figure 2 shows the time evolution of the excess energy defined by Eq. 2 of the excited OH stretch (A) and excited bend (B) (red lines). From a single exponential fit a relaxation time constant of 225 fs for the stretch and 145 fs for the bend are obtained, in good agreement with experiments ( 200-270 fs, 170-260 fs for stretching and bending respectively) . 30–35,45

In Figure 2 the intensity I(t) for the accepting modes are also reported. In the case of stretching excitation, we find that the excess energy rapidly transfers to the stretch of the first (blue line, 20% of the initial excess energy) and second solvation shell (green line, %10 of the initial excess energy). This stretch-to-stretch channel is the major localized contribution to the energy relaxation. This finding is in agreement with the assumption which is often used to interpret the experimental data, 46 namely that the initial energy is transferred to other stretching modes of close frequency (and only subsequently to the bending) and also with force field -based simulations of Saito’s group. 12 We also find a small energy transfer to the bending (lower than %10 of the excess energy). We should stress here that DFT-based MD simulations do naturally include resonance among 7



different vibrational modes, and therefore also the coupling between stretching and bending, although in a classical description of the statistical properties and of the dynamics, and therefore cannot account for purely quantum mechanical effects as the Fermi resonance. How to reinstate and compute this purely quantum feature of the spectra is beyond the scope of the present paper and still an open issue within the computational spectroscopy community. For the bending excitation, part of the energy is transferred to the libration mode on the excited molecule and on the first shell ( 10% each). A comparable fraction of the energy is also transferred to higher energy modes, namely to the stretching mode of the excited water molecule. (∼ 10% of the total excess energy). This transfer to the higher energy modes (namely to the stretching) is classically possible, and also quantum mechanically possible if the excitation involves two or more quanta. A key result of our analysis is that the vibrational energy relaxation is not homogeneous, namely the relaxation time constant strongly depends on the frequency of the excitation. In particular faster relaxation times are associated to the lower frequency of excitation, while longer relaxation times are associated to higher excitation frequencies. In Fig. 3 the computed relaxation time (red dots) i is reported as function of the frequency of excitation and compared to analogous quantities (black dots) extracted from 2D-IR experiments in bulk water. 18 A remarkably good agreement is found between simulations and experiments. What is the microscopic origin of the different relaxation time scales? A closer analysis of the hydrogen bond network (see the Supporting Information) around the vibrationally excited molecule reveals that the faster relaxation, associated to the lower frequency side of the excitation spectrum, occurs for those water molecules involved into a stronger hydrogen bond network. In particular the relaxation time nicely correlates with the number of hydrogen bonds in the first solvation shell (black, plus symbols in Fig. 3). The idea that the relaxation time correlates with the number of water in the first solvation shell is also discussed in the work of Saito, 12 (where faster relaxation time is found for water molecules surrounded by 8


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1 ex stretching mode ex bending mode

A

st

1 shell stretching mode

0.8

nd

I / norm

2 shell stretching mode

0.6

0.4

0.2

0 0

0.2

0.4

0.6

0.8

1

t (ps)

ex bending mode ex stretching mode ex libration mode st 1 shell libration mode

B 0.8

I / norm

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

0.2

0.4

0.6

0.8

1

t (ps)

Figure 2: Time evolution of the excess energy of the OH stretch (A) and bend (B) of the excited molecule (red, plain) and its exponential fit (red, dash) normalized by the initial value at t = 0.05 ps. 4-5 neighbours, while slower relaxation was found in the case of 3 neighbours), and it can be traced back to the work of Ohmine and Saito in 1999. 47 However a quantitative correlation as shown by our Fig. 3, as well as the direct comparison to the experiments is reported here for the first time. The correlation between relaxation time, frequency of excitation and number of hydrogen bonds makes clearly sense if we consider that the main pathway for the energy relaxation is the coupling of the stretching mode of the excited molecule to the stretching modes of the water molecules in its first solvation shell. Experimental pump-probe experiments have permitted in the last few years to extract information on the modulation of the OH oscillator frequency, also called spectral diffusion. This is typically obtained from the center line slope (CLS) method or from the nodal line 9



3800 3 -1

Excitation frequency (cm )

3.2

3600

3.4 N

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

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3400

3.6 3.8

3200 4 0

100

200

300 400 τ (fs)

500

600

Figure 3: Relaxation times τ of the OH stretch vibration of bulk as a function of the OH stretch frequency obtained via simulation (red, circle symbol) and experiment 18 (black, circle symbol). Values of τ are obtained averaging Eq. 3 over a window of wex = 50 cm−1 . τ is obtained from a single exponential fit. The excess energy on the lower frequency side of the OH stretch decays faster than that on the higher frequency side. Experimental data from Ref. 18 are included. Number of HB formed by the excited water molecule as a function of the OH stretch frequency (black, plus symbol). to extract the frequency-frequency correlation function (FFCF). For bulk water spectral diffusion has been reported to be very fast, namely 50-150 fs. 4,6,30 The spectral diffusion can be directly obtained in our approach from the time decay of the FFCF defined by

Cω (t) = hδω(t)δω(0)i / δω(0)2

(4)

where δω(t) = ωmax (t) − ω ¯ max (t) is the fluctuation from the average frequency at time t. The average of Eq. 4 is over the initial time and over the two OH groups of the excited water molecule. The results of the frequency-frequency correlation are shown in Fig. 4. A fast exponential decay of 115 fs and 44 fs are found for the excited stretching (black curve) and bending (red curve) modes respectively, in agreement with experiments. 4,6,30 This is faster than that obtained in Refs. 11 where the frequency of excitation was set to 3600 cm−1 only, and in Ref. 48 where a classical force field was used. We also observe that for the 10


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lower-frequency modes a longer lifetime is obtained. 1

0.8

0.6 Cω

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


0.4

0.2

0 0

0.2

0.4

0.6

0.8

1

t (ps)

Figure 4: Frequency-frequency correlation function as function of time. A single exponential fit provides a lifetime of 115 fs and 44 fs for the excited stretch (black curve) and bend (red curve) respectively. In summary, vibrational energy relaxation is investigated in a novel approach which includes a full electronic structure description of bulk water. The vibrational excitation is introduced in the classical approximation and selectively addressing a single water molecule. Using novel descriptors, based on projected VDOS, we are able to provide an interesting new picture of the energy relaxation in water. For both the stretching and the bending excitation we obtain relaxation time scales in very good agreement with those experimentally measured. In the case of stretching we demonstrate that the relaxation is the result of the coupling of the excited stretching mode to the stretching modes of the OH groups in the first solvation shell. Coupling to the bending plays instead a minor role. We also show how the relaxation is highly heterogeneous. Energy relaxation from the stretching can be as fast as 200 fs for frequencies in the range of 3100-3300 cm−1 , and more then twice slower (500 fs) for the higher frequencies (3500 cm−1 ). The different time scales correlate with the strength and number of hydrogen bonds in the first solvation shell, being therefore a very sensitive probe 11



of the local environment. Finally we are also able to reproduce the spectral diffusion, which overall is quite fast, in the range of 115 fs.

Conclusions Our finding provide the first accurate molecular picture behind the vibrational energy relaxation in water, which explicitly take into account the full electronic structure of the system. The remarkable good agreement obtained with the experiments provides strong support in favor of the highlighted mechanisms behind the process. Our results also have also strong implication for the computational chemistry community aiming to describe chemical reactions in water, as they strongly confirm the need to explicitly include water molecules to quantitatively take into account the local heterogeneous water structure and its ability to dissipate energy, which strongly depends on the local environment. As future steps in our research the impact of nuclear quantum effects 49 on VER will certainly be investigated.

Supporting Information Available • Projection along the normal modes of the transient vibrational spectra. • Definition of the hydrogen bond network.

Acknowledgement This work was supported by the Deutsche Forschungsgemeinschaft (DFG) TRR 146, project A4. All the calculation were performed on the supercomputer of the High Performance Computing Center (HLRS) of Stuttgart (grant 2DSFG). The authors thank M.P. Gaigeot, E.H.G. Backus, J. Hunger and Y. Nagata for very interesting discussions.

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(35) Pakoulev, A.; Wang, Z.; Pang, Y.; Dlott, D. D. Reply to: Comment on: Vibrational relaxation and spectral diffusion following ultrafast OH stretch excitation of water, by H.J. Bakker, A.J. Lock, D. Madsen. Chemical Physics Letters 2004, 385, 332 – 335. (36) Jeon, J.; Hsieh, C.-S.; Nagata, Y.; Bonn, M.; Cho, M. Hydrogen bonding and vibrational energy relaxation of interfacial water: A full DFT molecular dynamics simulation. The Journal of Chemical Physics 2017, 147, 044707. (37) Becke, A. D. Density-functional exchange-energy approximation with correct asymptotic behavior. Phys. Rev. A 1988, 38, 3098–3100. (38) Lee, C.; Yang, W.; Parr, R. G. Development of the Colle-Salvetti correlation-energy formula into a functional of the electron density. Phys. Rev. B 1988, 37, 785–789. (39) Grimme, S.; Antony, J.; Ehrlich, S.; Krieg, H. A consistent and accurate ab initio parametrization of density functional dispersion correction (DFT-D) for the 94 elements H-Pu. The Journal of Chemical Physics 2010, 132, 154104. (40) Goedecker, S.; Teter, M.; Hutter, J. Separable dual-space Gaussian pseudopotentials. Phys. Rev. B 1996, 54, 1703–1710. (41) Lin, I.-C.; Seitsonen, A. P.; Tavernelli, I.; Rothlisberger, U. Structure and Dynamics of Liquid Water from ab Initio Molecular Dynamics-Comparison of BLYP, PBE, and revPBE Density Functionals with and without van der Waals Corrections. Journal of Chemical Theory and Computation 2012, 8, 3902–3910. (42) Schmidt, J.; VandeVondele, J.; Kuo, I.-F. W.; Sebastiani, D.; Siepmann, J. I.; Hutter, J.; Mundy, C. J. Isobaric-Isothermal Molecular Dynamics Simulations Utilizing Density Functional Theory: An Assessment of the Structure and Density of Water at NearAmbient Conditions. The Journal of Physical Chemistry B 2009, 113, 11959–11964.

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Page 18 of 19

Page 19 of 19

Graphical TOC Entry 3600

50

-1

40 30 20 10 0

3

3000

3500 ω (cm ) -1

3.2 3400

3.4 3.6 3.8

3200 0

200 400 τ (fs)

19

H-bond number

60 frequency (cm )

frequency distribution

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


4 600


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