Prospects of Using High-Intensity THz Pulses To Induce Ultrafast

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A: New Tools and Methods in Experiment and Theory

On the Prospects of Using High-Intensity THz Pulses to Induce Ultrafast Temperature-Jumps in Liquid Water Pankaj Kr. Mishra, Vincent Bettaque, Oriol Vendrell, Robin Santra, and Ralph Welsch J. Phys. Chem. A, Just Accepted Manuscript • DOI: 10.1021/acs.jpca.8b00828 • Publication Date (Web): 18 May 2018 Downloaded from http://pubs.acs.org on May 19, 2018

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The Journal of Physical Chemistry

On the Prospects of Using High-Intensity THz Pulses to Induce Ultrafast Temperature-Jumps in Liquid Water Pankaj Kr. Mishra,†,‡ Vincent Bettaque,¶ Oriol Vendrell,§ Robin Santra,†,‡,¶ and Ralph Welsch∗,† †Center for Free-Electron Laser Science, DESY, Notkestraße 85, D-22607 Hamburg, Germany ‡The Hamburg Centre for Ultrafast Imaging, University of Hamburg, Luruper Chaussee 149, D-22761 Hamburg, Germany ¶Department of Physics, University of Hamburg, Jungiusstraße 9, D-20355 Hamburg, Germany §Department of Physics and Astronomy Aarhus University, DK-8000 Aarhus C, Denmark E-mail: [email protected]

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ACS Paragon Plus Environment

The Journal of Physical Chemistry 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

Abstract Ultrashort, high-intensity THz pulses, e.g., created at free-electron laser facilities, allow for direct investigation as well as the driving of intermolecular modes in liquids like water and thus will deepen our understanding of the hydrogen bonding network. In this work, the temperature-jump (T-jump) of water induced by THz radiation is simulated for ten different THz frequencies in the range from 3 to 30 THz and five different pulse intensities in the range from 1 × 1011 to 5 × 1012 W/cm2 employing both ab initio molecular dynamics (AIMD) and force field molecular dynamics (FFMD) approaches. The most efficient T-jump can be achieved with 16 THz pulses. Three distinct T-jump mechanisms can be uncovered. For all cases, the T-jump mechanism proceeds within tens of femtoseconds (fs). For frequencies between 10 and 25 THz most of the energy is initially transferred to the rotational degrees of freedom. Subsequently, the energy is redistributed to the translational and intramolecular vibrational degrees of freedom within a maximum of 500 fs. For the lowest frequencies considered (7 THz and below), translational and rotational degrees of freedom are heated within tens of fs as the THz pulse also couples to the intermolecular vibrations. Subsequently, the intramolecular vibrational modes are heated within a few hundred fs. At the highest frequencies considered (25 THz and above), vibrational and rotational degrees of freedom are heated within tens of fs and energy redistribution to the translational degrees of freedom happens within several hundred fs. Both AIMD and FFMD simulations show a similar dependence of the T-jump on the frequency employed. However, the FFMD simulations overestimate the total energy transfer around the main peak and drop off too fast towards frequencies higher and lower than the main peak. These differences can be rationalized by missing elements, such as the polarizability, in the TIP4P/2005f force field employed. The feasibility of performing experiments at the studied frequencies and intensities as well as important issues such as energy efficiency, penetration depth and focusing are discussed.

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1

Introduction

Liquid water is ubiquitous on earth and is the universal solvent in which most of the chemical and biochemical processes take place. 1 It is the most studied liquid in chemistry, physics and biology and many efforts have been devoted to understanding both the equilibrium as well as the dynamical properties of liquid water and of reactive processes taking place in water. Along these lines, temperature jump (T-jump) experiments have been used for a long time to investigate the kinetics of chemical reactions in water. 2–5 Employing femtosecond lasers, ultrafast T-jump experiments have been carried out to investigate the fast kinetics of fundamental steps in chemical reactions, 6–10 and fundamental aspects of the hydrogenbond dynamics and energy transfer in liquid water. 11–18 However, most of these studies have focused on pumping water with infrared (IR) lasers that are in resonance with the intramolecular vibrational modes of liquid water 6,7,9,12–15,17,19,20 around 3400 cm−1 , or on exciting dissolved dye molecules with ultraviolet-visible (UV/VIS) lasers 10 that subsequently transfer their electronic energy to heat up the solvent. These techniques have allowed Tjumps on the order of tens to few hundreds of Kelvin on a timescale ranging from tens of picoseconds (ps) 6,17 to several nanoseconds (ns). 21 With the advent of ultrashort, high-intensity THz pulses, the possibility of ultrafast Tjumps of water by directly coupling to the low frequency intermolecular modes has been discussed. 22–26 The intermolecular dynamics of liquids, e.g., intermolecular vibrations and librations, manifest in the THz regime. They are particularly interesting for water as they include the dynamics of the hydrogen bonding network, which is still not well understood and is thought to cause many of the anomalous properties of water, such as compressibility, density maximum and heat capacity. 27 Applied THz pulses create a torque on the rotational motion of water molecules, which will orient the dipoles of the water molecules along the polarization direction of the THz pulse, 28 transfer energy to the intermolecular modes and perturb the equilibrium arrangement formed by the hydrogen bonding network. Particularly interesting for discussing the T-jump of liquid water pumped with THz pulses 3



is the coupling of different low frequency modes to each other as well as the coupling of the low frequency modes to intramolecular vibrational modes. Through experimental 12,29–31 and theoretical 32–36 investigations it has been established that energy redistribution between inter- and intramolecular modes in liquid water occurs on time scales of tens to hundreds of femtoseconds (fs). Perturbation of one of the librations of a water monomer is followed by energy transfer to the neighboring water molecules on the timescale of a few tens of fs. 36 The last decade has seen tremendous advances in THz laser technology. Various ways are now established to create short, high-intensity THz pulses. 37–40 Low-frequency THz pulses in the regime from 0.1 to 3 THz are created using optical rectification in nonlinear crystals, such as LiNbO3 , reaching a field strength of more than 1 MV/cm and pulse duration of a few ps. 28,41–47 THz pulses in the range of about 2 to 10 THz can be efficiently created from table top sources using organic crystals like DSTMS or DAST. 48,49 These pulses can reach field strengths of up to 80 MV/cm with a duration of several hundred fs. 50,51 Pulses from organic crystals can get as short as 130 fs in full width at half maximum (FWHM) while maintaining field strengths of about 0.3 MV/cm. 52,53 Also pulses beyond 10 THz have been created with organic crystals at field strengths of up to 0.5 MV/cm. 54 THz fields beyond 10 THz can be efficiently generated with difference-frequency generation in GaSe crystals with field strength surpassing 100 MV/cm. 55,56 High-intensity THz pulses reaching up to tens of MV/cm and spanning the frequency range from 0.1 to 30 THz with pulse lengths of tens of fs to several ps can be created using free-electron laser (FEL) facilities 40,57,58 such as FLASH, 59,60 LCLS, 61 PAL-FEL, 62 FERMI, 63,64 or TELBE. 65 The highest field strength, up to 200 MV/cm, can be achieved by creating coherent transition radiation from relativistic electron bunches passing through Beryllium foils. 66 However, these pulses typically have a very broad spectral width of tens of THz. THz pulses with very broad energy ranges and field strengths of tens of MV/cm can also be obtained from laser-plasma interactions. 67–69 Various of these short, high-intensity THz pulses have been used to pump low frequency motions and to investigate the subsequent dynamics in water and other liquids. 28,52,53,70–76

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Strongly pumping the low frequency motions of solvents like water might also offer a path towards dynamical, time-resolved studies of thermal reactions in solution. By ultrafast Tjumps and heating of the surrounding medium, e.g., water, and subsequent energy transfer from that medium to the reaction partners, the thermal reactions might be triggered and then studied in a time resolved manner. To study the ultrafast THz-induced T-jump process of water computationally, both ab initio molecular dynamics (AIMD) and force field based molecular dynamics (FFMD) approaches have been employed. 22–26,77 However, several of these studies focused on low frequency pulses of 3 THz only. 22–24 Two other works 25,26 studied the T-jump of water and heavy water due to picosecond long, lower intensity pulses employing FFMD simulations. The THz-induced T-jump was studied for frequencies in the range from 0.1 to 30 THz and a maximum T-jump of 260 K was found for a 15 THz pulse with an intensity of 6×1010 W/cm2 and a FWHM of 1 ps. 25,26 A clear peak in the frequency-dependent T-jump curve was found around 15 THz, which was attributed to the case where the THz field is in resonance with the hindered rotational motions of water. 25,26 Away from the resonance a fast decrease in Tjump capabilities of the THz field was found. In order to support the design of experiments on high-intensity THz heating of water, we present in the present work an extensive study of the THz-induced T-jump of liquid water by ultrashort, high-intensity THz pulses in the frequency range from 3 to 30 THz employing both AIMD and FFMD simulations. The article is organized as follows. In Sec. 2 the computational methods are described and the parameters for the THz pulses are given. Sec. 3 presents and discusses the results and compares the results obtained from AIMD and FFMD simulations. A detailed discussion of the experimental feasibility of THz-induced T-jumps is given in Sec. 4 and the main conclusions are presented in Sec. 5.

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2 2.1

Computational Details Ab Initio Molecular Dynamics Simulations

Ab initio molecular dynamics (AIMD) simulations are performed with the CP2K molecular dynamics package. 78 The ab initio density functional calculations employ the quickstep module, 79 the Perdew-Burke-Ernzerhof (PBE) functional 80 together with the GeodeckerTeter-Hutter (GTH) pseudopotential. 81 The Gaussian plane waves method 82 is employed with a cutoff of 400 Ry and the TZV2P basis set. 79 All AIMD simulations employ 256 water molecules and periodic boundary conditions. The small number of water molecules that has to be used in the AIMD simulations due to the numerical cost of the simulations does not significantly influence the investigation of THz-induced T-jump processes as was shown in a recent study, where simulation boxes with 128 to 8265 water molecules were studied employing force fields. 25 Initial conditions are sampled from a long, canonical (NVT) trajectory at a temperature of 300 K and a density of 1 g/cm3 . The Nose-Hoover thermostat 83,84 is used to maintain the temperature. A total of ten initial conditions are sampled with a time separation of 300 fs. Subsequently, each set of initial conditions was propagated for 0.5 ps in the presence of the THz pulses and without any thermostat and for another 1 ps under NVE conditions without the THz pulse, which, for the situation considered, has negligible strength after 500 fs. The Berry-phase approach 85,86 is used to include the electric field under periodic boundary conditions when solving the self-consistent electronic structure equations.

2.2

Force Field Molecular Dynamics Simulations

Force field based molecular dynamics (FFMD) simulations are performed with the Largescale Atomic/Molecular Massively Parallel Simulator (LAMMPS) 87 employing periodic boundary conditions. The flexible TIP4P/2005f 88,89 water force field is used. TIP4P/2005f uses a Morse type potential to describe O-H bonds and a harmonic potential to describe H-O-H bending. Initial conditions for a simulation box of 1024 water molecules are sampled from a 6


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long MD trajectory computed under canonical (NVT) conditions at a temperature of 300 K and a density of 1 g/cm3 . The Nose-Hoover thermostat 83,84 is used to maintain the temperature. Five different sets of initial conditions are sampled with a 1 ps time separation to avoid artificial correlations between each sampled phase space point. Subsequently, each set of initial conditions is propagated for 2.0 ps in the presence of the THz pulses and without any thermostat. For all FFMD trajectory propagations the velocity-Verlet algorithm is used with a time step of 1 fs. A cut-off radius of 15 ˚ A is used for the calculation of the shortrange Lennard-Jones interactions and the Particle-Particle-Particle-Mesh technique is used to calculate the electrostatic interaction.

2.3

THz Field Parameters

Each THz pump pulse is considered as a time-dependent electric field in the simulations, the pulse profile being given by

E(t) = ε(t) uz cos(2πν t + φ),

(1)

where ε(t) = A exp{−t2 /2σ 2 } is a Gaussian envelope with A the maximum electric field amplitude. The pulse width is σ = 91 fs, which results in a full width at half maximum (FWHM) for the pulse intensity of 150 fs. The polarization direction uz of the electric field is always set to uz = (0, 0, 1) and φ is the carrier-envelope phase, which is set to π/2. In the present work, frequencies ν in the far-infrared region, ν = {3, 7, 10, 13, 16, 19, 22, 25, 28, 30} THz, and peak pulse intensities of I = {1 × 1011 , 5 × 1011 , 1 × 1012 , 3 × 1012 , 5 × 1012 } W/cm2 are considered. For the different intensities, the peak field amplitude is set to A = {0.0868, 0.194, 0.274, 0.475, 0.614} V/˚ A, respectively.

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2.4

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Energy Analysis

The energy gain of bulk water due to the THz pulse is analyzed on the basis of decomposing (m)

2 (t)) of each water monomer m in terms of its the total kinetic energy (EK (t) = 12 Mam Vm (m)

(m)

(m)

translational energy (ET (t)), rotational energy (ER (t)) and vibrational energy (EV (t)) components. This is achieved in Cartesian coordinates by, (m) ET (t)

(m)

=

ER (t) =

|

P

X am

Ma Va (t)|2 P m m , 2 am Mam

am

(2)

j2am (t) , 2Mam |xam (t)|2

jam (t) = Mam (xam (t) × vam (t)),

(3)

and (m)

(m)

(m)

(m)

EV (t) = EK (t) − ET (t) − ER (t),

respectively. xam (t) ≡ Xam (t) − Xm (t) and vam (t) ≡ Vam (t) − Vm (t) define the position and velocity of atom a in monomer m relative to the center of mass position Xm (t) and velocity Vm (t) of the monomer, respectively. The kinetic energy per water monomer related (m)

to vibrational motion EV (t) corresponds to the remaining three intramolecular coordinates. The mean kinetic energy per monomer at time t is obtained as M 1 X (m) hEX i(t) = E (t), M m=1 X

with X = K, T, R, V,

(4)

with M the total number of water molecules in the simulation box. The instantaneous temperatures for each subset of coordinates are connected to the corresponding mean kinetic

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energies by the relation 3 hEX i(t) = kB TX (t), 2

(5)

where X = T (translational energy), R (rotational energy) and V (vibrational energy) and 9 hEK i(t) = kB TK (t) 2

(6)

for the total kinetic energy. Please note that these are instantaneous temperatures, which are for analysis purposes only, and no assumption about equilibration is made in this context. The average T-jump ∆T¯ = T¯f − T¯i is calculated from the initial and final temperatures T¯i and T¯f obtained from averaged initial and final energies hE¯K,i i and hE¯K,f i calculated as Zi 1 X ¯ hEK,i i = hEK i(tmin + (j − 1)∆t), Zi j=1

1 hE¯K,f i = Zf

Z X

hEK i(tmin + (j − 1)∆t),

(7)

(8)

j=Z−Zf

with tmin = −250 fs the start time of the propagation, Z the total number of time steps taken and Zi =20 and Zf =100 are two appropriately chosen constants. Please note that in the simulations and the analysis all nuclei are treated classically, which may result in some inaccuracies of the energy transfer rate, in particular for the intramolecular vibrational modes. Additionally, the energy profiles obtained by the procedure explained above are fitted to analytic functions to obtain a more consistent picture of the THz-induced T-jump process. The instantaneous temperature for each intensity and frequency is fitted to a sigmoidal function 1 TX (t) = T0 + ∆T 2

t − t0 1 + tanh , τ

9


(9)


where T0 represents the temperature at t = 0, ∆T the T-jump at the end of the trajectory, τ the timescale for the T-jump and t0 the shift of the strongest T-jump from the center of the pulse. The fitting procedure is independently performed for the average T-jump obtained for each set of initial conditions and the resulting parameters are averaged. Error bars for the quantities are then obtained as standard deviations of the obtained parameters.

3

Results and Discussion

3.1

Frequency- and Intensity-Dependent Temperature Jump 1800

11

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2

I = 1×10 W/cm I = 5×1011 W/cm22 12 I = 1×1012 W/cm2 I = 3×1012 W/cm2 I = 5×10 W/cm

(a)

1600 1400

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2

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— ∆ TK / K

11

I = 1×10 W/cm I = 5×1011 W/cm22 12 I = 1×1012 W/cm2 I = 3×1012 W/cm2 I = 5×10 W/cm

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(c)

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(d)

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1200 — ∆ TR / K

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Figure 1: (a): Average T-jump (∆T¯K ) for different pumping frequencies ν and intensities I obtained from AIMD simulations. (b) - (d): Considering only translational (∆T¯T ), rotational (∆T¯R ) and vibrational (∆T¯V ) motion, respectively. The average T-jump ∆T¯ (see Eq. 7) calculated from AIMD for all frequencies and intensities considered is plotted in Fig. 1a. The average T-jump resembles in shape the far-IR 10


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spectrum known for bulk water. 90 The T-jump peaks around 16 THz with a shoulder around 25 THz. It drops off towards lower and higher frequencies. The maximal ∆T¯ achieved in this study is 1500 ± 100 K for a 16 THz pulse with an intensity of 5 × 1012 W/cm2 . The general shape of the curve is largely independent of the intensity. However, the shoulder around 25 THz is more pronounced at lower intensities (1 × 1012 W/cm2 and below). No significant difference for contributions from the different motions, i.e., translational, rotational and vibrational kinetic energy, is found for the final T-jump (see panels b-d in Fig. 1).

1000

ν = 3 THz ν = 16 THz ν = 22 THz ν = 30 THz

fit, β=1.4 fit, β=1.3 fit, β=0.9 fit, β=0.8

500 — ∆ TK / K

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


100 50

10 5x10

11

12

12

1x10 3x10 intensity / W/cm2

12

5x10

Figure 2: Average T-jump as a function of the intensity applied for different frequencies ν considered. Solid lines give the fit of the data to a power law, ∆T¯K (I) = αν I βν . The scaling of the T-jump with respect to the applied intensity is depicted in Fig. 2 for a subset of frequencies. For all frequencies considered in this work the total T-jump as a function of the applied intensity can be fit well with a power law; ∆T¯K (I) = αν I βν . By fitting the power law to the data, a value of βν ≈ 1.3 to 1.4 is obtained for frequencies below 19 THz. This indicates that the heating process starts to be non-linear for the highest 11



intensities employed in this work. This is in agreement with a rough estimate that around 6 to 10 photons need to be absorbed per water molecule to achieve the ∆T¯ presented in this work for frequencies below 19 THz and I = 5 × 1012 W/cm2 . For frequencies above 20 THz a slightly sublinear scaling is found with βν ranging from 0.9 to 0.8, indicating small saturation effects. From Fig. 2 it can also be seen that the slope of the intensity dependent heating curves is quite different for the different frequencies. This corroborates the analysis above, that very different temperature gains and efficiencies can be achieved depending on the applied frequency.

3.2

Time-Resolved THz-Induced Temperature-Jump Mechanism

In the following the time-resolved THz-induced T-jump mechanism of liquid water is investigated in more detail for three different frequencies, ν = 7, 16, 28 THz, showing distinct T-jump processes. Fig. 3 displays the total, translational, rotational and vibrational temperature per water molecule as a function of time calculated from AIMD trajectories for ν = 16 THz and different intensities. The overall time-dependent temperature depicted in Fig. 3a follows a sigmoidal curve and can be very well fitted by the function defined in Eq. 9. The final T-jump obtained through the fitting, ∆T , matches well the T-jump obtained by averaging the initial and final time steps (∆T¯, Eq. 7) as presented in Figs. 1 and 2. The fitting parameter τ in Eq. 9 can be interpreted as a timescale for the T-jump process. More than 75% of the T-jump process is achieved in the time interval of 2τ around the center time t0 , [t0 − τ, t0 + τ ]. For ν = 16 THz, a τ of around 70 fs is found, well in line with the FWHM of 150 fs for the pulses employed. The timescale is nearly independent of the applied intensities within the error bars of the calculations presented. Similar timescales and dependencies are found for all other frequencies employed (see supporting information (SI)). The time traces of the individual components, i.e., translational, rotational and vibrational motion, presented in Fig. 3 b-d (ν = 16 THz), reveal the T-jump dynamics. Both 12


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I = 1×1011 W/cm22 I = 5×1011 W/cm2 I = 1×1012 W/cm 12 I = 3×1012 W/cm22 I = 5×10 W/cm

Data Data Data Data Data


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Figure 3: (a) Average kinetic temperature (TK ) per water monomer as a function of time for a 16 THz pulse with different intensities. Symbols give the data obtained from the simulation and broken lines the fit to the function given in Eq. 9. t = 0 corresponds to the center of the THz pulse envelope and the profile of the employed pulse is shown as a gray line. (b) - (d): Considering only translational (TT ), rotational (TR ) and vibrational (TV ) motion, respectively.

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the translational and vibrational T-jump follow a sigmoidal curve, but on a longer timescale than the total T-jump process (τT > 200 fs and τV ≈ 140 fs). The rotational T-jump does not match a simple sigmoidal curve. It shows a very fast T-jump, which overshoots the final T-jump by about 50%, and a subsequent decay of energy lost to other degrees of freedom. It can be fit by a function describing this two step mechanism by a sigmoidal function for the initial T-jump due to the THz pulse and an exponential decay of that energy into the other degrees of freedoms:

TR (t) =

T00

t − t00,2 t − t00 1 0 0 0 + θ t − t0,2 ∆T2 exp − − 1 , (10) + ∆T 1 + tanh 2 τ0 τ20

with θ(x) the Heaviside step function, t00,2 the start time for the energy redistribution, τ20 the timescale of the energy redistribution and ∆T 02 the amount of energy lost to the other degrees of freedom. For ν = 16 THz and I = 5 × 1012 W/cm2 , the timescale for the initial rotational T-jump is τ 0 = 72 fs, well in line with the total T-jump mechanism. The timescale for the energy loss into other degrees of freedom is τ20 = 232 fs, which fits roughly to the timescale for T-jump of the other two degrees of freedom. The initial rotational T-jump is ∆T 0 = 2907 K, but ∆T 02 = 1373 K of energy is lost to the other degrees to freedom subsequently (see Fig. 4). Due to the fast redistribution of energy from the rotational degrees of freedom to the other degrees of freedom it is not possible to quantitatively determine how much energy is deposited into each degree of freedom directly by the THz pulse, but at least 45% of the energy transferred from the THz pulse goes into rotational motion initially. A slightly different T-jump mechanism is found for the lowest frequencies considered as depicted for ν = 7 THz in Fig. 5. Here the pulse also couples to the intermolecular vibrations. Thus, additionally to an ultrafast T-jump of the rotational degrees of freedom, the translational degrees of freedom show a very fast T-jump (τT ≈ 40 − 70 fs). The intramolecular vibrations are again heated due to energy transfer from the other degrees of freedom on a timescale of τV ≈ 90 − 150 fs.

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I = 1×1011 W/cm22 I = 5×1011 W/cm2 I = 1×1012 W/cm2 I = 3×1012 W/cm I = 5×1012 W/cm2

Fit Fit Fit Fit Fit


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Figure 4: Same as 3c, but the fit is done with the function given in Eq. 10.

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Figure 5: (a) Average kinetic temperature (TK ) per water monomer as a function of time for a 7 THz pulse with different intensities. Symbols give the data obtained from the simulation and broken lines the fit to the function given in Eq. 9 of the main text. t = 0 corresponds to the center of the THz pulse envelope and the profile of the employed pulse is shown as a gray line. (b) - (d): Considering only translational (TT ), rotational (TR ; fit to Eq. 10) and vibrational (TV ) motion, respectively.

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For high frequencies, e.g., ν = 28 THz, the intramolecular vibrations are heated significantly by the pulse and show a fast T-jump process (τV ≈ 30 − 70 fs) as well as an initial T-jump higher than the final T-jump as can be seen in Fig. 6. However, the effect is smaller than for the rotational degrees of freedom. For the higher frequency cases the translational degrees of freedom are heated by energy transfer from the other degrees of freedom on a timescale of τT ≈ 200 − 400 fs. Please note that for the cases where the T-jump of the internal vibrational degrees of freedom is important in our simulations the nuclear quantum effects may influence the energy transfer process, which are neglected in this work. Inclusion of nuclear quantum effects is beyond the scope of this work, but the approximate ring-polymer molecular dynamics approach 91–93 might offer an efficient way to partially account for them. The T-jump mechanism can be summarized as follows. The THz pulse couples directly to the dipole of the water molecules, exerts a torque on them 28 and thus deposits energy into the rotational degrees of freedom heating them up very quickly. At frequencies between 10 and 22 THz, the T-jump of the translational and vibrational degrees of freedom is only partially due to coupling to the THz pulse and mostly due to energy transfer from the heated rotational degrees of freedom. However, at ν = 7 THz (and also at 3 THz) the pulse also couples to the intermolecular vibrations and thus the translational degrees of freedom are also heated up very fast. The results are in very good agreement with the T-jump process previously analyzed for ν = 3 THz, which also finds very fast heating of both translational and rotational degrees of freedom and a slightly delayed heating of the vibrational degrees of freedom. 22,23,94 However, a slightly lower T-jump of ∆T¯ = 600 ± 100 K at an intensity of 5×1012 W/cm2 is found in the present work, compared to 740 K in previous work. 22,23,94 At high frequencies (ν = 25 THz and above) the pulse additionally couples to the vibrational degrees of freedom, thereby quickly heating them in addition to the fast T-jump of the rotations. However, it should be stressed that nuclear quantum effects can play some role in this process, which are neglected here. Details on all frequencies not shown in the main

17




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text can be found in the SI.

3.3

Comparison of Ab Initio MD and Force Field MD

On-the-fly AIMD simulations are computationally very demanding limiting the number of initial conditions that could be used in this study. A result of this limitation is the noticeable statistical error bars in the results presented above. While the results presented above still show significant differences for the different frequencies and intensities employed, a cheaper way of obtaining qualitatively or quantitatively similar results would be advantageous. Thus, we also performed FFMD simulations to assess their performance and accuracy to describe ultrafast THz-induced T-jumps in water. The final T-jump (∆T¯) and its translational (∆T¯T ), rotational (∆T¯R ), and vibrational (∆T¯V ) components as obtained from FFMD simulations for an intensity of 3×1012 W/cm2 are presented in Fig. 7 and compared to the AIMD results. The shape and resonance position of the frequency-dependent T-jump curve obtained from FFMD simulations are in good agreement with previous studies, which used the TIP3P and the SPC/E force fields. 25,26 The FFMD simulations show a similar overall dependence of the T-jump on frequency as the AIMD simulations, but several deviations can be observed. The peak in the FFMD simulations is shifted to slightly lower frequencies, but increased in height. Away from the main peak, the T-jump drops faster in the FFMD simulations than in the AIMD simulations, in particular towards higher frequencies. Similar patterns are seen for the translational and rotational degrees of freedom (panel b and c in Fig. 7) and even stronger for the T-jump of the intramolecular vibrational degrees of freedom (Fig. 7d). Similar deviations are also seen for lower intensities (see SI). The overestimation of the total energy uptake around the main peak might follow from the underestimation of the strength in the hydrogen bonding network in the force field as well as from deficiencies of fixed partial charges to properly describe the coupling of the electric field to the individual molecules. The stronger drop in energy uptake away from the main peak in the FFMD simulations compared to AIMD simulations can be rationalized by 19



the lack of polarizability in the TIP4P/2005f force field employed. At lower and higher frequencies the laser pulse is not directly resonant with the hindered rotations and the coupling of the laser pulse is not only described by interaction with fixed partial charges, but more subtle effects like charge transfer and coupling of the laser pulse to the polarizability become more important. These effects are completely neglected by the FFMD simulations. The underestimation of the far-IR spectrum around 3 THz for force fields is well known, 74,95–98 in particular, for non-polarizable force fields. 95,96 The differences in T-jump of the vibrational degrees of freedom shows the deficiencies of the TIP4P/2005f force field in describing the vibrational modes and, in particular, their coupling to the rotational and translational degrees of freedom. Please note that simulations performed with TIP4P/2005f at an intensity of 5×1012 W/cm2 mostly failed as at T-jumps resulting from fields that strong some water molecules start to break apart and sample geometries which the force field was not designed for. Thus, the highest intensity considered for the FFMD simulations was 3×1012 W/cm2 .

4

Prospects of THz-Induced Temperature Jumps in Water and Experimental Considerations

As discussed in the introduction, there is a manifold of ways to generate THz pulses at the frequencies and intensities employed in this work. In this section, several experimental considerations regarding the THz-induced T-jump of water will be discussed. The THz pulses can typically be focused down to roughly the diffraction limit and thus, nearly optimal intensities can be achieved for a given pulse energy. 99–101 However, this is not the case for the THz radiation with the highest possible field strength generated at FELs from coherent transition radiation, which limits the intensity at the target that can be reached by these sources at the moment. 58,66 THz pulses generated at FELs using undulators can suffer from instabilities due to the length of the electron bunch. Synchronization of FEL generated THz pulses with optical (probe-)pulses is a difficult problem and thus timing uncertainties, so20


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called timing jitter, might arise in pump-probe experiments at these sources. On the other hand, FELs can produce XUV and x-ray (probe-)pulses perfectly synchronized with the THz radiation from the same source, which cannot be done with laser based THz radiation. Thus, depending on the actual experimental setup and probe to be used, the different THz radiation sources have varying advantages and disadvantages. We note, however, that timing jitter problems can be partially circumvented employing machine learning techniques 102 or advanced hardware solutions. 103–105 The energy efficiency for generating THz pulses varies widely by the method of generation. Generating THz pulses employing non-linear crystals has an overall energy efficiency of about 5 to 0.5 %. 37,39 The overall energy efficiency of FEL generated THz light is, however, below 0.01 %. 39,40 Therefore, the generation of THz light is at least an order of magnitude less efficient than the generation of mid-IR light, which has an efficiency of ≈ 50%. For the most promising frequencies for heating, around 15 to 25 THz, the prospects are currently worse and the generation of THz light is at least two orders of magnitude less efficient than the generation of mid-IR light. Thus, a viable way forward to achieve the most efficient, ultrafast T-jump of bulk water might be to push forward with mid-IR lasers exciting the intramolecular vibrational modes of water directly. Fast energy redistribution on the timescale of a few hundred fs would allow for a fast T-jump. 14,31,106,107 However, two additional points need to be considered. First, as water absorbs IR light very efficiently at the resonance frequencies of the vibrations, penetration depths of only few µm can be reached, whereas THz light is absorbed less and some tens of µm are possible. 108 Therefore, a spatially more uniform T-jump can be achieved with THz light than with IR light. Second, exciting the vibrational modes directly will not allow for dynamical, time-resolved studies of thermal reactions as the IR light might also excite specific vibrational modes of the solute, which greatly influences the reaction dynamics observed. Thus, for progress in that direction, THz light remains promising.

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5

Conclusion

In this paper the ultrafast THz-induced temperature jump (T-Jump) process of water was investigated in detail. Ab initio molecular dynamics (AIMD) and force field molecular dynamics (FFMD) simulations were performed for ten different THz frequencies in the range from 3 to 30 THz and for five different pulse intensities in the range from 1 × 1011 to 5 × 1012 W/cm2 . The most efficient frequency for THz-induced T-jumps of water is 16 THz. It was shown that T-jumps of over 1000 K are possible. A detailed analysis of the time-resolved T-jump in the studied parameter range revealed three distinct T-jump processes. At frequencies between 10 and 22 THz, the rotational degrees of freedom are heated up within tens of fs. Due to coupling of the rotations to the translational and vibrational degrees of freedom, the latter are heated within some hundreds of fs. At lower frequencies, the THz pulse couples to both the rotational and translational degrees of freedom heating them up within tens of fs. Intramolecular vibrational modes are then heated due to energy transfer from rotations and translations. At higher frequencies, the intramolecular vibrational modes are heated rapidly along with the rotational degrees of freedom. In this case the translational degrees of freedom are heated indirectly. Comparison of AIMD and FFMD simulations revealed inaccuracies in the TIP4P/2005f force field, which was employed here. The T-jump maximum is slightly shifted to lower frequencies. The T-jump curve drops of too fast away from the maximum, which is due to the missing polarizability and the fixed partial charge model in the force field employed. The pulse frequencies and intensities employed in this work are reachable by modern THz pulse generation methods and work to investigate the THz-induced T-jump process of water experimentally is under way. (private communications)

Acknowledgement This work has been supported by the excellence cluster The Hamburg Centre for Ultrafast Imaging - Structure, Dynamics and Control of Matter at the Atomic Scale of the Deutsche 23



Forschungsgemeinschaft (DFG). We are grateful to Franz Kärtner, Peter Zalden, Nikola Stojanovic, Sergio Carbajo, and Gerhard Gr¨ ubel for helpful discussions. This work was partially performed on the computational resource ForHLR II at the Karlsruhe Institute of Technology (KIT) funded by the Ministry of Science, Research and the Arts BadenW¨ urttemberg and DFG.

Supporting Information Available Time-dependent T-jump curves for different frequencies, comparison of FFMD and AIMD at different intensities and T-jump timescales. This information is available free of charge via the Internet at http://pubs.acs.org

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Prospects of Using High-Intensity THz Pulses To Induce Ultrafast

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