## Vibrational energy relaxation of the

## OH-stretch in methanol and HOD

### Master's thesis

### January 2014

### Student: G.J. Hoeve

### Daily supervisor: Drs. R. Tempelaar Supervisor: Dr. T.L.C Jansen

### Supervisor: Dr. M.S. Pchenitchnikov

Abstract

The vibrational dynamics of the OH-stretch vibration are investigated by a combined theoretical and
experimental approach. We try to develop a model for the OH-stretch relaxation by use of the surface
hopping method. Most attention is being paid to the relaxation in diluted HOD in D2O. We look for
signatures of the ’hot ground state’ in the 2D spectrum, a result of local heating upon relaxation. Our
findings indicate that this is in principle possible in this system with a surface hopping model, but the
simple model in this work turns out to insufficient. The outcome is compared with 2D-spectra obtained
by real-life experiments on this system. Furthermore the temperature dependent linear spectra and
vibrational relaxation of the same mode in diluted methanol in partly deuterated methanol (CH3OD)
is studied by the use of pump-probe experiments. We find blueshift of 0.7 cm^{−1}K^{−1}of the OH-stretch
peak in the first experiment, and a relaxation time of 0.6 ps in the pump-probe measurements.

### Contents

1 Introduction 3

2 Theory 5

2.1 vibrational states in liquid water and alcohols . . . 5

2.2 Surface Hopping . . . 8

2.3 Pump-probe spectroscopy . . . 10

2.4 2D spectroscopy . . . 12

2.5 Brownian oscillator model . . . 13

3 Nummerical Simulations 15 3.1 Model 1: local heating of ensembles . . . 15

3.2 Model 2: relaxation with rate equation . . . 17

3.3 Model 3: relaxation described by surface hopping . . . 19

3.4 Model 4 . . . 20

3.5 Model 5 . . . 20

4 Experiments 24 4.1 Design . . . 24

4.1.1 Temperature dependent linear spectrum of methanol . . . 24

4.1.2 Preparation of the sample . . . 24

4.1.3 Laser . . . 25

4.2 Results . . . 25

4.2.1 Temperature dependent linear spectrum . . . 25

4.2.2 Pump probe measurements in open air . . . 26

4.2.3 Pump probe measurements in nitrogen box . . . 27

4.2.4 Effect of nitrogen protection . . . 27

5 Conclusions and Outlook 29

### 1 Introduction

Water has been an interesting research topic for centuries, due to its importance for biological systems, and its remarkable physical properties, like a melting temperature that, given the molecular mass of water, is surprisingly high, and an increasing density upon melting. Most of the phenomena can be explained to a large extent by the intermolecular structure of water, in particular the formation of hydrogen bonds between the molecules. Each molecule can donate two hydrogen bonds with the hydrogen atoms, and accept two with the unbounded electron pairs on the oxygen atom. Therefore, the intermolecular bonds are exceptionally strong compared to other molecular substances, where the much weaker Van der Waals forces are the dominating bonding mechanism, leading to a high melting point. Also, the low density in the solid state is caused by inefficient packing in a crystal structure that is based on solidified hydrogen bonds. Upon melting, only 13% of the hydrogen bonds are broken [35], so also in the liquid phase hydrogen bonds are important for the intermolecular structure. At higher temperatures, bonds can be broken and reformed with the same or different molecule, leading to very complex dynamics on the molecular scale [18]. Hydrogen bonds can be best described as dipole/dipole interactions[20], but there are also claims that covalent forces play a role[32]. Whatever the exact nature of hydrogen bonds is, it is clear that they have profound influence on the behaviour on the scale of individual molecules of liquids in which they are formed.

Hydrogen bonds can be formed not only in water, but in any molecule that contains polar groups. One of the strongest, which also often occurs in nature is the OH-group. If the group is bound to a carbon atom in a carbon based molecule, the molecule is called an alcohol. Alcohols have the experimental advantage that they have, besides their polar OH group, also a nonpolar side, which makes them soluble in nonpolar liquids. When an alcohol is solved in a nonpolar solvent like CCl4, alcohol will form clusters of size 5-10 molecules that are connected with hydrogen bonds[3]. This cluster structure is interesting because it creates small hydrogen bond networks that are easier to analyse than bulk alcohol, and also provides additional information that would disappear in the sea of complex signatures that appear in big networks[3].

When studying hydrogen bonds, one usually looks at intra-molecular processes that strongly depend on the hydrogen bonds formed by the molecule. One very important process is the OH-stretch vibration, the oscillation of the OH valance bond length, which can be thought of as the lighter proton moving with respect to the O atom, in the potential well generated by the molecule. Hydrogen bonding of the proton will lead to broadening of the well, and therefore to a lower vibrational energy[11]. Depending on the strength (or the length: the shorter, the stronger) of the hydrogen bond, the reduction in energy can be 10 percent or more in a strongly hydrogen bound compound like water (fig. 1). The strong dependence of the energy of the OH-stretch vibration on the hydrogen bonds, has lead researchers in the field to use observations on the absorption in the energy region of the OH-stretch as a preferred method to study the structure and dynamics of the hydrogen bond in water[30] and in methanol[16, 22].

Besides all these interesting static properties of the OH-stretch vibration, hydrogen bonds also influences how an excited state evolves in time. Upon excitation of the OH-stretch, the molecule will eventually relax to the ground state. How fast it relaxes depends on the availability of intermediate states, and the coupling between them and the OH-stretch excited state[23]. The strength of the coupling depends on how close in frequency the states are: energy transfer occurs faster in the situation of maximum resonance; the relaxation is the fastest if there is some overlap in the energy distributions of the previously excited mode and the accepting mode[7]. Since the frequency of the OH-stretch vibration depends on the local environment, so does the lifetime of the excited state. When it relaxes, the energy will be transferred to low frequency modes, or heating of the local environment[23].

A major experimental challenge when studying the dynamics of hydrogen bonds in alcohols, and the interaction with the OH-stretch vibrational excitation, is the short time scale (often subpicosecond) on which the many processes take place. Therefore, until recently it was only possible to study the static properties of the hydrogen bond structures. The development of ultrafast lasers enabled time resolved spectroscopy, which opened a new window, since it allowed researchers to study transient behaviour at a sub-picosecond timescale by use of Pump-probe and 2D spectroscopic techniques[11]. Especially 2D spectroscopy is interesting here, since it shows the correlations between frequencies over time.

2DIR and pump probe spectroscopy are both set up in such a way that one can study the spectrum after

Figure 1 (left): Measurements of Yeremenko on the OH-stretch absorption in three different systems. Figure from ref[34].

Figure 2 (right): 2D-plot of measurements on dilute
HOD in H_{2}O by Tokmakoff's group. Figure from
their paper: ref[25]

initial excitation of the system. In figure 2 we see the evolution of the OD stretch in HOD, measured by
Tokmakoff et al. After 3.2 ps a negative absorption peak, indicating induced absorption, emerges around
an absorption frequency 2600 cm^{−1}. This is ascribed to the effects of the local heating process that follows
relaxation.

It is an interesting challenge to describe local heating and the effects it has on the 2D spectra by a numerical simulation. A full quantum mechanical treatment of all the modes involved is not computationally feasible, but we do have to incorporate some quantum mechanics, since it is the quantization of the energy levels that leads to the branching of the molecular environment in ’hot’ and ’cold’, which is responsible for the signatures that we are looking for. Surface hopping offers a solution[33], using classical mechanics to describe the environment of the molecule, and the Schrodinger equation for the relevant intramolecular vibrations. The difficulty is the question how the quantum part of the model communicates with the classical part[8].

In this research I have aimed to develop a mixed quantum/classical model that consistently describes
the vibrational energy relaxation of the OH-stretch in HOD/D_{2}O mixtures, while at the same time trying
to reproduce experimental observations on consecutive local heating in a numerical simulation. I employed
the surface hopping formalism in a few slightly different models, in which the quantum mechanical part
consists of the OH-stretch, and in some models also the bend overtone, the first relaxation step of OH in
HOD as proposed by Lindner et al.[23]. The classical part consisted of either one or two coordinates, that
represent the average effect of the local environment on the hydrogen bond strength. I have tried and partly
succeeded to obtain a hot ground state signature by a numerical simulation. Additionally, I have performed
Pump-probe measurements on methanol and explain the result with the model.

### 2 Theory

### 2.1 vibrational states in liquid water and alcohols

Linear spectra

Absorption spectra are a useful way to extract information from a sample. The absorbed wavelengths correspond to transition energies between states in the sample. Where electronic transitions typically absorb in the visible/near UV, absorption in the infrared is an indicator of (intramolecular) vibrational transitions.

At even lower frequencies the lowest energy states can be found, intramolecular rotations, and intermolecular transitions[35].

One vibrational transition of particular interest in this research is the excitation of the stretch vibration of
the O-H valence bond. It absorbs in the mid-infrared (MIR), in a frequency range from 3000-4000 cm^{−1}; the
exact frequency depends strongly on the particular environment. The varying bond length can be modeled
as the movement of the lighter hydrogen nucleus in the electrostatic potential of the rest of the molecule,
and the environment. The position of the bottom of this potential is the bond length in equilibrium. Near
the bottom, the potential can be approximated by a harmonic potential:

Vh(r) = ^{1}_{2}mω^{2}(r − r0)^{2}

(1) The Schrödinger equation yields a discrete set of eigenenergies and eigenfunctions for this potential. These are the eigenstates of the OH-stretch vibration. In a harmonic potential the eigenenergies are equidistant, so the energy difference between two adjacent states is always[21]:

∆E = ~ω

(2) Because the actual potential is not exactly harmonic, usually an anharmonicity α(n) is subtracted for the higher excited states (fig. 4).

When the hydrogen atom forms a hydrogen bond with a neighboring molecule, apart from increasing the OH valence bond length, the hydrogen bond also broadens the potential in which the hydrogen nucleus moves. A wider potential leads to a smaller difference between energy levels, so the hydrogen bond causes a red shift in the OH-stretch absorption. The stronger the hydrogen bond is, the stronger the shift.

Figure 3: Linear spectrum of diluted H-methanol in D-
methanol for different temperatures ranging from 15^{◦}to 55^{◦}.
Figure by Lin et al.[22]

The strong influence of the hydrogen bond on the OH-stretch absorption spectrum can be seen from comparison of the spectra of liquid methanol with the spectra in the gas phase, where no hydrogen bonds are formed:

the OH-stretch peak shifts from 3400 cm^{−1}
in the liquid phase to 3682 cm^{−1} in the gas
phase[Herzberg, p334-5]. Another way to see
this is in the spectra of phenol in CCl_{4} so-
lution with different concentrations. At low
concentrations the benzenol molecules are iso-
lated, and no hydrogen bonds will form. At
higher concentrations small hydrogen bonded
clusters will form, and the frequency decreases
[3].

In order to better understand the effect of the hydrogen bond on the behaviour of the

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Figure 4: Comparison of the energy levels in the potential well without hydrogen bond, and with hydrogen bond. The formation of a hydrogen bond causes widening of the potential well for the OH-stretch vibration, which leads to reduction of the excitation energy.

OH-stretch, let us examine the mid-infrared spectrum range of water more closely than we did in the
introduction. We see in figure 5(a) that the absorption band due to OH-stretch excitation in water has a
FWHM of more than 200 cm^{−1} at room temperature; this inhomogeneous broadening (from a static point
of view) is a result of the varying strength of hydrogen bonds. The absorption peak of liquid water around
3400 cm^{−1} can be divided in three components: two strong peaks from the symmetric and antisymmetric
stretch. The third peak originates from coupling with the overtone (Fermi resonance) of the H-O-H bend,
that happens to be around the same frequency[34, 6]

When we compare this to the MIR spectrum of HOD in figure 5(b), we notice two differences, which will
be important later. Because of the isotopic substitution the bend overtone lies somewhat lower in HOD,
around 2900 cm^{−1}. Also, since the symmetry of the molecule is broken, the splitting in the OH-stretch
peak disappears. This allows us to study the frequency of the OH-stretch in more detail. Furthermore, also
in the case of HOD in D2O, where the OH-stretch peak is non-degenerate, the peak is asymmetric. On
the low frequency side the OH group is strongly hydrogen bound, and the broadening is dominated by the
fluctuations in the hydrogen bond strength, which is a single oscillator, therefore the spectrum is Lorentzian
on that side. The weak hydrogen bound oscillators are subject to multiple degrees of freedom (DOF) that
affect the frequency to more or less equal extent, which, as dictated by the central limit theorem, leads to a
Gaussian line shape, which is indeed what we see on the blue side of the OH absorption peak. The width
of the bend peak may be smaller than the OH-stretch peak, it is still considerable; this is also caused by
hydrogen bonding, but the influence is opposite: where the hydrogen bond formation will lead to decrease of
the stretch frequency, the frequency of the bend excitation increases as the hydrogen bond strengthens[24].

Besides inhomogeneous broadening, vibrational transitions in a liquid also exhibit homogeneous broad- ening, related to the intrinsic frequency distribution of the stretch; that means that the natural lifetime can be estimated from the linear spectral width if it is dominated by the natural linewidth[11]. In the case of hydrogen bonded systems, the inhomogeneous broadening is much larger, so in order to determine vibrational lifetimes in those systems, one needs to employ more advanced spectroscopic techniques, such as pump-probe (section 2.3).

temperature dependence

The temperature influences the line shape of the isolated OH-stretch hydrogen bonded liquids. Palamerev
and Georgiev measured on diluted HOD in D_{2}O in a temperature range from 20 till 90^{◦}C[28], and they got
similar results as Lin et al., who performed measurements on diluted H-methanol (CH_{3}OH) in D-methanol

frequency (cm^{-1})
a)

b)

### c)

Figure 5: Vibrational absorption spectra of water (a), diluted HOD in D2O (b), and the proposed vibrational energy relaxation mechanism of the OH-stretch in water by Lindner et al. Figure (a) and (b) by Wang et al.[34], figure (c) by Lindner et al.[23].

(CH_{3}OD)[22]. In both systems increase of the temperature caused a blue shift in the OH-stretch absorption
band of approximately 1 cm^{−1}K^{−1} in diluted H-methanol in D-methanol, and 0.8 cm^{−1}K^{−1} in water. The
explanation for this result lies in the effect of the temperature on the hydrogen bonds. Thermic energy
means kinetics on molecular scale, if the molecules involved in the hydrogen bond formation have higher
relative velocities/more complicated movement, than the hydrogen bond strength will become weaker, and
the red shifting effect of the hydrogen bonds on the spectrum is reduced.

vibrational energy relaxation

When a vibrational state is excited, it will decay after some time. Usually, this vibrational energy relaxation (VER) will not be directly to the ground state by emitting a photon of the same frequency as the excitation energy, because often there are faster trajectories available, which exploit the presence of intermediate close(r)-to-resonance states. This relies on the fact that transitions go much faster when the energy gap is smaller, since the coupling between those states is stronger.

Note that the intermediate states do not necessarily have to be a singly excited state. The bend overtone plays an important role in the vibrational energy relaxation of the OH-stretch in water. Lindner et al.

investigated the relaxation trajectory of water, and they concluded that the energy relaxes through the bend overtone, which then splits over two fundamental bend excitations. After that, the energy flows through libra- tions to low frequency (intermolecular states), which is merely a quantum description of thermalization[23].

This mechanism cannot be directly transferred to diluted HOD in D2O. First this trajectory is less favorable
in diluted HOD/D2O, because the overtone can not split into two fundamental excitations, as there is less
often another HOD molecule in the direct neighborhood. Second, the frequencies of the involved vibrations
and their distributions are slightly different. The gap between 3400 cm^{−1} of the hydroxyl stretch, and 2925
cm^{−1} for the bend overtone, is too large for fast direct transfer. But there is a small overlap, and we know
that in strongly hydrogen bound molecules, the bend overtone frequency is on the blue side of the spectrum
and the stretch frequency on the red side. This means that for those molecules the energy gap becomes
smaller. This greatly favors fast relaxation. According to Nienhuys et al., the energy is predominantly
dumped in the hydrogen bond[27]. However, Tokmakoff et al. investigated the VER of diluted HOD in D2O
more comprehensively, and concluded that the strongly hydrogen bonded molecules relax through the bend
overtone, followed by either the deuteroxyl stretch around 2500 cm^{−1} or the bend fundamental, while the
weaker bound molecules relax through other paths, like hydrogen bond vibrations[7].

### 2.2 Surface Hopping

Figure 6: three ways of incorporating quan- tum mechanics into molecular dynamics: Mean field approximation(a), ’naive’ surface hopping(b), fewest switches surface hopping(c). Figure by K.

Drukker[8]

Simulations of large scale quantum phenomena are hard to implement in practice, because analytical solutions of the Schrödinger equation do generally not exist, and a numerical treatment requires too much calculation time. Therefore, several strategies have been devel- opped that can reduce calculation time by treating part of the system classically. The light and fast parts of the system are treated quantum mechanically, and the heavy and slow parts classically. The challenge we face is how the classical part of the system communicates with the quantum mechanical part. This way, classical notions like temperature can be projected on the quan- tum world, resulting in a Boltzmann distribution in the occupation of the states, or wave functions. The sep- aration of the system in two parts leads to a situation where each part propagates according to its own laws (classical or quantum mechanically), while experiencing a potential generated by the other part.

The first thing we need to consider is how to describe the potential generated by the slow DOF that acts on the quantum system. Since the potential that the fast DOF experiences changes only slowly, we can assume that that quantum system adjusts itself instantaneously.

If this so called adiabatic approximation is used, then the prefactors remain the same, only the basis (i.e. what the prefactors represent) changes.

The second thing to consider is the more compli- cated question how to describe the quantum potential that acts on the classical system. Let’s for the sake of simplicity take a vibrational monomer, with ground state |g > and excited state |e >. The classical system experiences a potential Eg or Ee when the quantum system is in the ground state or excited state, respec- tively. These potentials, that have the classical coor- dinates as variables, are called potential surfaces, gen- erated by the quantum system. The classical system evolves on the surface that corresponds to the quantum state. There are different ways to deal with the situa- tion, where the quantum system is in a superposition state cg|g > +ce|e >. The most straightforward way is the mean field, or Ehrenfest, approach.

Within the Ehrenfest approach the slow DOF expe- riences a potential that is averaged over a all members of the ensemble, such that the quantum force becomes:

F_{q}=< ψ|∇_{R}H|ψ >ˆ _{n}

which can be implemented trivially into the classical propagation of the slow DOF.

Since the Ehrenfest approach uses the ensemble average energy of the monomer, it does not account for the quantization of its energy. In a low-energy system that will be very close to the ground state potential, little information of molecular dynamics in the environment of higher quantum states is obtained. And in high energy systems, the average potential describes the influence of neither of the surfaces on the behaviour of the classical coordinates correctly[8]. This can be fixed when simulating an ensemble by setting the potential on one of the potentials generated by the quantum mechanical eigenstates of the fast DOF, with probabilities according to the projections of their wave functions in the eigenstates of the instantaneous Hamiltonian. This way surface hopping does take the quantization into account, by setting the quantum force:

Fq=

∇REe with a probability |ce|^{2}

∇REg with a probability |cg|^{2}

(3) Now if the probabilities in equation(3) would be generated by naively drawing a random number on each time step, and then take the limit to infinitesimal time step, the result would effectively be the same as that from the Ehrenfest approach. Tully solved this problem by introducing the fewest switches algorithm[33].

At each time step during the numerical simulation, it is not the probability to be on another surface that determines if a hop takes place, but the change in probability, compared to the previous time step. As a result, monomers that propagate on any potential surface stay on that surface for a rather long time, which allows us to really study the behaviour of the classical coordinates on that potential. The algorithm is further designed such that the statistics of the occupied potential surfaces of large ensembles resembles the statistics of the corresponding eigenfunctions at all times[33].

From the time dependent Schrödinger equation we have:

HˆP

j

cj|φj ≥ i~_{δt}^{δ} P

j

cj|φj >

Multiplying from the left by < φk|, and introducing Vkj is the energy difference between state k and j gives:

P

j

cjVkj= i~P

j

< φk|_{δt}^{δ}cjφj>

= i~P

j

< φ_{k}|φjc˙_{j} > + < φ_{k}|cjφ˙_{j} >

= i~( ˙ck+P

j

cj< φk| ˙φj >),

which gives the expression for the time derivative of ck:

˙

ck = −P

j

cj(^{i}

~Vkj+ < φk|^{δφ}_{δt}^{j} >)

Fewest switches surface hopping is suited for any number of states, and any number of classical degrees of freedom. It can be simplified for the case with only two potential surfaces. Since de occupation of the

potential surfaces of state φk must keep pace with ck, the hopping probability peg from the excited state
surface Veto the ground state surface Vg in a two-state system is peg=|cg˙|^{2}= 2<( ˙cgc^{∗}_{g}) =

2<(cec^{∗}_{g}) < φg|^{δφ}_{δt}^{e} >,

and vice versa. Using these probabilities ensures that the hopping rate keeps track with the quantum mechanical probabilities to be in a certain state.

Each time step, a random number is drawn to determine wether a hop takes place or not, according to the probability above. In case of a hop, if the new state has a lower energy (call it a hop down) the energy difference is translated into an increase of the kinetic energy of the classical coordinates. If the new state has a higher energy (hop up) then the energy difference is taken out of the classical system. If there is not enough classical energy available, then the hop does not take place. There are two ways to treat these forbidden hops: either the momentum of the classical coordinates is inverted, or not. One can think of a classical particle rolling uphill to a higher potential level, but not having enough kinetic energy, and rolling back. The obvious objection would be that it violates conservation of momentum, but we in the surface hopping approach momentum conservation is already given up from the start, and analysis based on path integrals offers arguments for momentum inversion. In many cases, as in this research, it does not affect the general results of the simulations. In the numerical models described in this thesis the first option is used.

### 2.3 Pump-probe spectroscopy

Pump probe spectroscopy is an experimental technique that gives information about dynamical processes in a sample. It is designed such that one can follow the energy trajectory from an excited state.

The procedure is as follows: first the linear transmission spectrum of the sample is measured to obtain the reference spectrum Iof f(ω). After that the sample is excited by a laser pulse with a well-defined frequency(i.e.

narrow distribution), then after a waiting time that we call t2for future purposes, the transmission spectrum Ion(ω) is measured. When we calculate the first order differential intensity, there are contributions from 3 pathways:

The first pathway is the ground state bleach (GB): absorption at the frequency ω10is bleached by previous excitation of that frequency, leading to an increase in transmission intensity at ω10.

The second pathway is stimulated emission (SE): previous absorption of ω10 gives rise to an additional stimulated emission at that frequency, leading to an increase in transmission intensity at ω10.

The third pathway is excited state absorption (EA): previously excited states can be doubly excited with
a frequency ω21. The first pulse creates those singly excited states, leading to a decrease in transmission
signal at ω_{21}.

Here the assumption is made that there is no decay of the signal during t_{2}. However, there are two
ways a signal can decay after a time t_{2}. The relaxation of the excited mode to the ground state, second the
reorientation of the excited molecules with respect to the laser beam.

polarization dependence

The second effect is a consequence of the fact that the amount of absorption is proportional to the inner product between the interaction dipole moment that depends on the polarization of the beam and the dipole moment of the excitation. Since the molecules that were excited are in majority along the polarization direction of the pump beam, after some time their dipole directions are randomized which leads to a decay of the signal.

The response function for a large number of randomly oriented dipoles

R(≡ _{I}^{I}

0) = Z

Ω1

Z

Ω2

< µP· µt(Ω1) >^{2}< µp· µt(Ω2) >^{2}dΩ1dΩ2,

(4)
where Ω_{1} and Ω_{2} is the spherical orientation of the dipole during the first and second pulse respectively; µ_{t}
is the transistion dipole of the oscillator.

In a setup where the probe pulse follows immediately after the pump pulse, Ω1 = Ω2, and with a polarization angle α between the two pulses, equation (4) gives[11, 14]:

R = _{15}^{1}

2 cos^{2}(α) + 1

(5) In a setup where the probe pulse follows after a very long waiting time, long enough for the excited dipoles to be isotropically distributed, the response is independent of the angle between the pump and probe pulse[11, 14]:

R = ^{1}_{9}

(6) In the case we are only interested in the relaxation rate, we want to remove the effect of reorientation.

All we have to do is find an angle α such that the response before and after reorientation is the same:

1

15(2 cos^{2}(αm) + 1) = ^{1}_{9} gives[11, 14]:

α_{m}= arccos(^{√}^{1}

3) ≈ 54.7^{◦}

(7) The angle αm is called the magic angle. With pump and probe beam polarized at a relative angle αm the decay of the signal during t2 is pure relaxation, and contains no contributions from reorientation.

When you have information from parallel and perpendicular polarization, using eq. (5) you can calculate both the isotropic (from relaxation) and anisotropic (from reorientation) contributions separately:

Riso= ^{2}_{3}R_{⊥}+^{1}_{3}R_{k}

(8)

Raniso= R_{k}− R_{⊥}

(9) pumpprobe diagrams

It may be useful here to introduce the concept of optical density, which is a measure of the amount of absorption:

OD(ω) = log _{I}

0(ω)
I_{of f}(ω)

,

Figure 7: Eight possible pathways in 2D spectroscopy with relaxation during t2included

in which I(ω) is the transmission spectrum without sample. This definition makes the OD linear with the sample’s thickness and concentration. The differential optical density is calculated likewise:

∆OD = log_{I}

of f(ω)
I_{on}(ω)

A pump-probe diagram is a 2 dimensional plot, with on one axis the absorption spectrum at a given time after excitation, and on the other axis the waiting time between the two pulses. Then after increasing t2, the procedure is repeated, including the reference spectrum. Then t2 is stepwise increased, and each time the differential spectrum is calculated. Together this gives a plot of the differential signal as function of t2

and the absorption frequency ω.

### 2.4 2D spectroscopy

2D spectroscopy is a different spectroscopic technique, which compared to pump-probe spectroscopy, focusses less on the dependence of the absorption spectrum on the waiting time, but instead on the dependence on the pump frequency. The procedure is as follows: between the 1st and 2nd/2nd and 3rd/3rd and 4th interaction between the transition dipole and the EM-field, there is a time t1/t2/t3. This procedure gives rise to six Feynman diagrams that contribute to the signal (fig. 7).

One scans over t1 and t3, while keeping t2 constant, and then takes the Fourier transform to obtain the
signal dependence on the (corresponding) frequencies ω1 and ω3. When multiple 2D spectra for different
t_{2} are taken together, a movie is obtained, that gives information of where (to which state) energy moves
after initial excitation of a certain state. This is why it is an important tool in the study of energy transfer
mechanisms in solids and liquids.

When t_{2} is set close to zero, each excited dipole will give a signal at the excitation frequency, or in the
range of its natural line width. The negative signal from the GB and SE will be very close to the diagonal.

But after a time t2homogenous broadening sets in, and the SE/GB peak is in the area with the homogeneous width around the diagonal. So if t2= 0, one will see a narrow peak around the diagonal, with a with related to the natural line width, and a length related to the inhomogeneous line width.

If there is an overtone of the transition ω, the excited dipole will absorb at a slightly lower energy ω − α.

This will be visible in the same way as in pump probe spectroscopy to a peak with the same shape, but redshifted by α.

In practice α is often of the order of the homogeneous width, and therefore the peaks interact, as t2> 0. At
first, the slope between the two is 45^{◦}with respect to the vertical direction, after homogenization is complete,
the line between the peaks will be vertical. This way the time required for homogenization/frequency
correlation time can be estimated from the 2D spectra.

Energy transfer is visible through the emergence of cross peaks: off-diagonal negative peaks at [ω1, ω3]
means energy is transfered from a state with energy ω_{1} to a state with (usually lower) energy ω_{3}.

The spectra show the differential signal between the absorption with and without previous excitation.

Besides bleaching of the ground state, and the emergence of a stimulated emission signal at the central frequency (both positive), there will also be a nagative signal originating from the transition from the singly to the doubly excited state, of which the corresponding frequency is usually a little red shifted with respect to the one belonging to the fundamental transition. One of the interesting processes in this field is that the energy that is dumped in the molecular environment after relaxation between the pulses influences the local dynamics. Generally, the effective heating will increase the kinetic energy of the molecules, and therefore the fluctuations in the forces between neighbouring molecules, which will cause the local structure to dissolve on a shorter timescale[11]. The increase in fluctuations will also lead to broadening of the absorption peak.

Since we look at the differential signal, we subtract the original absorption peak of the ’cold ground state’

from this broader ’hot ground state’ (HGS) signal. The net result is two small peaks of the opposite sign on the side of the main GB/SE peak. Such a signature of a hot ground state in an HOD/D2O solution has been observed by Tokmakoff’s group (fig. 2). More information on 2D spectroscopy can be found in the excellent book on the subject by Hamm and Zanni[11]

correlation function

We saw that the formation of hydrogen bonds causes static inhomogeneous broadening. But as time passes, hydrogen bonds break and are (re)formed, strengthen and weaken, and the absorption frequency changes accordingly, such that after some time there is no memory of the initial frequency. This last notion of memory can be quantified by correlation formula:

corr_{ν}(t) = ^{<(ν(t}^{0})−<ν>_{t})·(ν(t_{0}+t)−<ν>_{t})>_{n}

<ν^{2}>t ,

where < ... >_{n} denotes the ensemble average, and < ... >_{t} the time average[11, 25].

### 2.5 Brownian oscillator model

A simple classical model to describe small motions in a liquid is the brownian oscillator model. In this model, a particle is confined in a harmonic potential, i.e. it experiences a force FH = −kx, where k is the

’spring constant’ of the system, related to the classical eigenfrequency of the harmonic potential ω =pk/m,

m is the mass of the oscillator, and x its position w.r.t. the centre of the potential well. In addition the
oscillator experiences two more forces: the first is a damping force Fd= γ ˙x, and the second a random force
F_{R} induced by the temperature of the environment. The latter is each time step randomly chosen from a
Gaussian distribution of with mean zero, and width (standard deviation):

∆FR=

q2k_{B}T γm

∆t

(10) where ∆t is the time step in the simulation. The result in a Gaussion distribution for x and ˙x with standard deviations:

∆x =pkbT /k

(11) and

∆ ˙x =pk_{b}T /m = ∆x · ω

(12) which corresponds to an energy of kbT per degree of freedom in equilibrium[25]. The correlation function of a brownian oscillator is given by:

corrν(t) = corrν(0) · e^{t/t}^{c}

(13) with tc being the correlation time:

t_{c} = γ · m/k

(14)

### 3 Nummerical Simulations

We investigate the effect of vibrational energy relaxation on the linear, pump probe and 2D spectra through numerical simulations. We will discuss five different models in increasing order of complexity. Through relaxation of the OH-stretch excitation the energy will be dumped into the environment of the molecule.

This will give rise to a local increase in temperature, which will change the absorption spectrum, giving rise
to a ground state contribution to the spectrum. The addition of the HGS signal to the GB, SE and EA
signals may result in a total spectrum that looks like the results of Tokmakoff and Skinner[26] and Dwayne
Miller[17]. Model 1 investigates the linear spectrum after a waiting time equal to the relaxation time for
different temperature rises, considering an ensemble of dimers. This way we hope to get out an estimate for
the amount of energy that needs to contribute to local heating in order to produce the experimental results. In
model 2 (and further) we sample each dimer individually, and we model the local heating implicitly through
the (classical) motion of a one-coordinate system that represents the local environment. The vibrational
energy relaxation is still modeled by a rate equation as in model 1. In model 3 another complication is added
by substituting the rate equation by surface hopping. Since it turns out that the relaxation in model 3 is
much slower than any experimentally observed relaxation by orders of magnitude, we try to mimic the actual
relaxation process of the OH-stretch relaxation, but that depends on the particular system. Since we try to
reproduce the results of Tokmakoff et al.[26] on diluted HOD in D_{2}O, and the relaxation mechanism of that
system has been studied in the past[23, 7], we focus on that system by introducing in model 4 an intermediate
level that represents the bend overtone. The relaxation via the bend overtone as an intermediate state speed
does speed up the relaxation to more realistic values ( 1 ps), but the average energy that is dumped into the
environment upon relaxation of a dimer is now much less than before, and not enough to create the observed
spectral feature of the hot ground state. Therefore we complicate the classical subsystem in model 5 in order
to store the energy for a longer time.

### 3.1 Model 1: local heating of ensembles

The oscillators are treated as an ensemble, and we only deal with the averages and expectation values.

Henceforth, we will use the notation G(µ, σ) for a Gaussian distribution with mean µ and standard deviation
σ. We assume the vibrational energy is distributed as G(ω0, βT ), i.e. the spectral width is proportional to the
temperature, and the peak frequency is independent of the temperature. This choice for the temperature
dependence of the absorption spectrum may seem a bit odd, considering the experimentally determined
relation as discussed in section 2.1; but in the brownian oscillator model (section 2.5) the spectrum depends
on the temperature in this way, and our primary purpose in this section is to investigate the conditions under
which we can obtain a HGS signature within the brownian oscillator model. The system consists initially of
excited isolated monomers, that relax to the ground state during t_{2}with a rate τ_{r}^{−1}. The excited monomers
generate identical GB and SE spectra, and an EA spectrum that is red shifted with respect to the GB and
SE spectra with an anharmonicity α=150 cm^{−1}, and has double amplitude. The monomers that relaxed
back to the ground state at time tau create an HGS signal, with the same amplitude (per monomer) and
central frequency the same as the GB/SE signal, but the frequency distribution is broader:

στ= β(T0+ (T1− T0)e^{−(t}^{2}^{−τ )})/τc,

(15)
where τ_{c}act as the cooling down time of the direct environment monomer, T_{0}is the equilibrium temperature
of the local environment, and T1is the temperature of the environment of the monomer right after it relaxed
to the ground state. The four contributions GB, SE, EA and HGS are added to get the total spectrum I:

I = GB + SE + EA + HGS

###

^{}

###

###

###

###

Figure 8: The normalized spectra including HGS after: (a) t2= 500 fs, (b) t2 = 1 ps, (c) t2= 4 ps, (d) t2

= 8 ps, with τr = 600 fs (a),(b),(c), and τr = 1.2 ps (d), for various amounts of energy dumped into the
hydrogen bond after relaxation: red = 20 cm^{−1}, cyane = 50 cm^{−1}, blue = 200 cm^{−1}, magenta = 800 cm^{−1}
and green = 3400 cm^{−1}

I = G(ω0, βT0) + (1 − e^{t}^{2})G(ω0, βT0) − 2(1 − e^{t}^{2})G(ω0− α, βT0) −

t_{2}

Z

0

e^{−τ /τ}^{r}G(ω0, στ)dτ

(16)
We apply this model to the relaxation of the OH-stretch in diluted HOD in D_{2}O. We set τ_{r} = 0.6
ps, based on the reported relaxation time of this system[7]. Some of the energy will be dumped into the
hydrogen bond, leading to a broadening of the HGS signal, and stay there for a time t_{2}− τ . We can only
see something significant if the rate at which energy is dumped into the environment is larger than the rate
at which is dissapears: τc> τr, so we set τc = 1.2 ps. The peak energy ω0= 3400cm^{−1}, T0was set at ’room
temperature’ (300 K), and β = 0.378 cm^{−1}K^{−1}, which makes σ0 = 113 cm^{−1}. The parameter that is still
free is T1 in eq. 11, which is related to the increase in temperature due to relaxation of the monomer. Now
we ask ourselves the question: how much of the energy has to go into the hydrogen bond in this scenario,
to create a HGS signature in the spectra at a certain waiting time t2? Figure 8 shows slices of pump probe
spectra that result from this model at waiting times 0.5 ps, 1 ps and 4 ps, for 5 different magnitudes of
dumped energy.

These results show that the dump of energy in this model will always lead to a HGS signature, if t2 is large enough, in the case of τr = 1.2 ps. In figure 8(d) one can see the result for a smaller τr: there will be a HGS peak visible, but only after a very long waiting time.

The conclusion is that even when the energy remains preserved in the hydrogen bond for times as short as 300 fs we can still get the desired result in the 2D-simulations if we let the waiting time be long enough.

However, the signal will be very weak in absolute terms, probably smaller than the statistical error.

### 3.2 Model 2: relaxation with rate equation

Here we consider the OH-stretch transition as a spatially isolated monomer, with Hamiltonian

H =ˆ 0 g g ω(t)

,

(17)
with ω(t) = ω0+ λ · x. ω0is fixed at 3350 cm^{−1}, and the coupling term g also fixed at 150 cm^{−1}. x behaves
like a one dimensional brownian oscillator that stands for the influence of the environment, i.e. all hydrogen
bonds and other forces that may affect the transition energy. In the model described in section 2.5, k =
1.1175 kg mol^{−1}ps^{−2}, m = 5 g mol^{−1}, T = 300 K, and γ = 50^{−1}. This results in a Gaussian distribution for
x, with σ_{x}= 0.047 nm. The coupling term between the classical system and the quantum system λ = 2400
cm^{−1} nm^{−1}, such that the width in the molecular basis (and approximately in the diagonal basis) σ_{ω}= 114
cm^{−1}. The classical eigenfrequency

qk

m = 15 ps^{−1} is somewhat smaller than ^{γ}_{2}, which makes the classical
oscillation slightly overdamped. During t1 and t3 we make the adiabatic approximation, that is: when the
quantum system is in a certain coherence, say,|0 >< 1|, is stays there even when the basis changes due to
change of x. The result is that the second pulse creates a population |1 >< 1| or |0 >< 0|. Each time
step during t2, if the quantum oscillator is in the excited state, there is a fixed probability of relaxation,
corresponding to a relaxation time of 200 fs. When the oscillator relaxes to the ground state, the energy

~ω(t) is dumped into the classical system by boosting the velocity ˙x along the direction in which x is already
moving. If in the excited state during t_{2}, the quantum force is taken into account:

Fq= _{δx}^{δ} < ψ| ˆH|ψ >= ^{λ}_{2}

1 + √ ^{ω(t)}

4g^{2}+ω(t)

(18)

### a)

### b)

Figure 9: All the interactions among the subsystems that play a role in Model 2 (a), and in Model 3 (b) Between brackets the part of the simulation that interaction is in effect.

1

0

-1

ω_{1}

ω_{1}

a) b)

Figure 10: the spectrum generated by Model 2 with τr = 200 fs after t2 = 200 fs(a), and with τr = 600 fs
after t_{2}= 600 fs.

Figure 10(a) shows the 2D spectrum after 200 fs. This corresponds with the average relaxation time,
thus the part of the monomers that has relaxed to the ground state and dumped its energy in the system, is
approximately 1 −^{1}_{e} ≈ 0.63. The small negative signal near 3600 cm^{−1}is the HGS signature we are looking
for. This result shows that it is in principle possible to create a HGS signature within this model, given the
right parameters.

Since a relaxation time of 200 fs is rather short for an excited OH-stretch, we take a look at the situation with a relaxation time of 600 fs. Now we need a longer waiting time before we expect enough monemers to relax in order to see a HGS signature. Figure 10(b) shows the 2D spectrum after 600 fs, all other parameters kept the same. As we see, there is no negative peak at the blue side visible. After 1.5 fs there is still nothing.

After 8 ps the complete spectrum is weak compared to the noise.

To sum up, we have shown in this section that, although it is in principle possible to generate a HGS signature with this model, we probably will need a shorter relaxation time than 600 fs, or we must find a way to store the energy in the classical system for a longer time.

### 3.3 Model 3: relaxation described by surface hopping

Now we want to treat the vibrational energy relaxation in a more natural way. We employ surface hopping to describe the classical motion, using the same surfaces as in Model 2, and instead of a rate equation relaxation parameter, hopping is now implemented using the fewest switches algorithm, as described in section 2.2. All parameters are kept the same as the previous model.

This model turns out to result in hardly any hops after 200 fs (< 0.1%). We can try to increase the
hopping rate by changes the fundamental parameters: the classic-quantum coupling term λ, the curvature
of the classical potential (’spring constant’) k, the effective mass m, and the damping parameter γ, without
changing the known observables of the OH-stretch absorption in water: the frequency correlation time of
220 fs, and the fact that the correlation function is monotonically decreasing, indicating overdamping, the
spectral FWHM of 180 cm^{−1}, and negligible Stokes shift. Within these limitations, the only freedom we
have is multiplying m and k by the same number a (leaving the classical eigenfrequency invariant), and λ

by a^{2}. This turns out not to affect the hopping rate. The explanation for the low hopping rate is the high
energy gap that needs to be bridged. Because the hopping probability scales with the inverse of the energy
gap, hops take place at positions where the surfaces are close to each other[8]. So this shows that, according
to the surface hopping model, direct relaxation from the excited OH-stretch state to the ground state is a
very slow process in isolation.

### 3.4 Model 4

To speed up the relaxation process we introduce an intermediate level. Following Lindner et al., who proposed
the bend overtone as a likely candidate for such an intermediate level[23], we make the bend overtone the
accepting mode. The frequency for the bend overtone is in our model ωbend(t) = 2925cm^{−1}− λ2x. After
a hop from the OH-stretch excited state to the bend overtone, the difference in energy is accepted by the
hydrogen bond. The bend overtone is assumed to decay infinitely fast, and all energy that is released in the
second relaxation step is dumped in modes that do not affect the OH-stretch frequency[23]. Thus after a
hop down, it is not possible to hop back up again. Monomers that are in the ground state after the second
pulse, will stay there during t_{2} in this simulation. The Hamiltionian for the first relaxation step, described
by surface hopping, becomes:

H =ˆ ωbend(t) g g ωstretch(t)

(19)

The result is a much faster relaxation that is more in correspondence with measurements. The relaxation time is now of the order of 1 ps, and can be increased by a factor 2 or 3 by reducing the coupling term g. A difference with the previous models is that we gain much less energy for each hop. At most hops, the energy is only little above 2g, at the minimum of the energy gap (fig. 12(c)).

In figure 12(d) the classical energies of the three trajectories are shown; it turns out that the energy from the dumps is less than the Stokes shift. As a result, even with this model that incorporates the bend overtone transition, we cannot see a hot ground state in the 2D spectrum. The strong deviations during the first 100 fs are a result of the effect that the non-equillibrium situation of the excited state immediately after excitation - it needs to adjust to the newly introduced Hellmann-Feymnan force - has on the directional preference of the surface hopping condition.

### 3.5 Model 5

Now we try to keep the energy in the classical system for a longer time after relaxation to the bend overtone.

To that end we introduce a second classical oscillator between our original one and the bath. This allows us to store the energy from relaxation longer in the classical system before we lose it to dissipation in the bath, without having to change the correlation time or overdampedness of the classical coordinate that gives feedback to the OH-stretch frequency, as explained in figure 11(b).

For this scheme to do its job, which is keeping the energy in the system for a longer time, without disturbing the statistics on the stretch and bend frequencies, we need the following properties: We want the energy to flow slower into the heat bath, so we want γ to become smaller. If we want the second oscillator overdamped, the eigenfrequency of the second oscillatorq

k2

m_{x} must be smaller than γ. The result is a very
slowly moving x2, thus the interaction force on x1 is experienced as a moreless constant force, such that x1

is underdamped. So we need x2 to be underdamped. It turns out to be impossible to create overdamped motion in x1. Underdamped motion leads to fringes in the spectrum (fig. 13), which is in contrast with experiment. I could not find a suitable set of parameters to remove the fringes from the linear spectrum.

In conclusion, we did not succeed in obtaining a satisfying model for the OH-stretch relaxation with the use of surface hopping.

### a)

### b)

Figure 11: All the interactions in Model 4 (a), and Model 5 (b)

a) b)

t2(ps)

t2(ps)

c) d)

Figure 12: The relaxation speed in Model 4 for different coupling terms g between the ground state and the excited state in the Hamiltonian (a), population relaxation during t2 time for two different coupling strengths (b), histogram of the ammount of energy dumped into the classical coordinate upon relaxation from the OH-stretch to the HOD-bend overtone (c), the average energies of the classical oscillators. The HGB should result from the E −− > G trajectory, but as this figure shows, there is not significantly more energy in that part of the system compared to the GB (d).

2000 2500 3000 3500 4000 4500
Wavelength (cm^{-1})

Figure 13: The linear spectrum of an harmonic oscillator coupled to an underdamped oscillator as in Model 5

Figure 14: a. Large beaker with the sample. b. Perastaltic Pump.

c. Smaller beaker to smoothen the pumping process. d. The smaller beaker is placed 30cm above the jet, such that the sam- ple flows from the bottom exit of the small beaker to the tripod with the jet. e. drop jet, drips back into the larger beaker.

### 4 Experiments

In order to be able to apply the model described in section 3.1 to diluted H-methanol in D-methanol, we
need the temperature dependence of the linear spectrum of that system. Therefore we measured the linear
spectra at temperatures from room temperature up until a temperature rise of 30^{◦}C. The results can be
found in section 4.2.1. We performed pump probe measurements on the same system, from which we got an
estimate of the vibrational relaxation time of the OH-stretch mode. Unfortunately, our measurement time,
and therefore the number of realisations, was limited by the rapid absorption of water vapour from the air
by the sample during the experiments, which lead to the complete absorption of the laser light in the region
around 3350 cm^{−1}. In an attempt to keep the concentration of H-methanol low for longer time, we tried to
shield the sample from air contact; first by surrounding the two areas in our setup where there was contact
between air and the sample with nitrogen, later we built a box around the entire setup and purged it with
nitrogen (section 4.1.4). We repeated the measurements from section 4.2.2 again in section 4.2.4.

### 4.1 Design

4.1.1 Temperature dependent linear spectrum of methanol

For the measurements on the temperature dependence of the linear spectrum of methanol, we prepared a solution of methanol in D-methanol in 1:1000 volume ratio. The linear MIR spectrum was measured in an infrared spectrometer, using a short path length cuvette with variable thickness. We used the shortest thickness, which was approximately 50 micrometers. Between measurements, the cuvette with the sample was heated outside the spectrometer with the use of a heat gun, while the temperature was measured simultaneously on the front and backside of the cuvette with an alcohol thermometer and an electronic thermometer.

4.1.2 Preparation of the sample

For the pump probe measurements, we used a method originally developed by Mathies’ and Bradforth’s groups[31], which has the advantage that the sample stays at the same temperature during the measurement.

This is important in this project, since we want to see the effect of local heating through vibrational energy relaxation, we do not want the sample to heat directly from absorption of the laser.

Figure 15: Optical path of the laser beam generation, by use of sapphire, Barium Borate(BBO) and potassium titanyl phosphate(KTP) crystals

We prepared 20-30 milliliters of the sample in a beaker, which was closed afterwards with a piece of rubber, with three holes in it. The liquid in the beaker was connected via a tube through one of the holes to the top of another beaker which was placed 30 cm higher. The sample was pumped upwards to the second beaker using a peristaltic pump. On top of this beaker we placed a lid with a small hole in it, in order to maintain atmospheric pressure, while minimizing air contact. A second tube was connected to an opening near the bottom of the higher beaker to transport the liquid methanol to a wire in order to create a drop jet. The first beaker was positioned under the wire, such that the sample dripped into the beaker via a funnel through a second hole in the rubber, and could be recycled. Once a stable drop jet was created, the spectrum was measured by placing the jet in the crossing of the pump and probe beams.

In order to slow down the absorption of water, to increase the time we can use the sample for our measurements, we surround the two spots in our experiment where there is air contact with gaseous nitrogen:

through the unused third hole in the rubber piece on top of the main beaker we put a tube to blow nitrogen into the beaker. Since all the holes are now being used, there was a small pressure through the funnel, creating a slow flow of nitrogen around the jet, decreasing the contact with water vapor there. Also in order to minimize diffusion from water vapor into the second beaker, we put a bag over the beaker, and a second tube would blow nitrogen into the bag. Later we replaced the tube into the beaker and the bag by a box around the entire setup, with only holes for the laser beams in and out.

4.1.3 Laser

The laser signal was generated by a Ti:Sapphire laser, and via various nonlinear crystals a MIR beam is
created centered around 3250 cm^{−1}, and a FWHM of approximately 200 cm^{−1} (fig. 15). The central
frequency could be tuned within the range of 100 cm^{−1}, as well as the width, which was always made as
broad as possible. The pump probe measurements were performed in scans consisting of 1000 spectra at a
50 Hz rate for each waiting time.

### 4.2 Results

4.2.1 Temperature dependent linear spectrum

The relation between the temperature and linear spectra of H-methanol in D-methanol solution is presented
in fig 16. The shape of the signal is quite bumpy, which we blame on the presence of water vapour in
the spectrometer, the OH-stretch of which absorbs in the same region. In order to determine the peak
position we made Gaussian fits to the spectra, including a linear correction to compensate for the overlap
with the CH-peak around 2900cm^{−1}. The results are in qualitative agreement with measurements by Lin
et al. [22](fig. 3). The peak frequency of the OH absorption undergoes a blueshift of 0.7 cm^{−1}K^{−1}, where
Lin observed a blueshift of 1 cm^{−1}K^{−1}. The explanation for this observation is that the hydrogen bonds get

a) b)

Figure 16: Linear MIR-spectra of diluted H-methanol in D-methanol for various temperatures with Gaussian fits (a), and comparison to measurements by Lin et al. from figure 3 (b)

weaker as the temperature increases, diminishing their redshifting effect on the OH-stretch absorption peak.

In both experiments the spectral width did not change significantly in the measured temperature range. We also saw agreement in the lowering of the peak intensity, which we assign to non-Condon effects. Schmidt and co-workers already showed that incorporation of non-Condon effects into their model for the related system of HOD/D2O improve the approximation of experimental results in that system[29].

4.2.2 Pump probe measurements in open air

We measured the pump probe spectrum with parallel polarization between pump and probe pulse. Using
formula (8) in section 2.3, from the parallel and perpendicular polarized (4 scans each) we obtained the
pure relaxation signal. The result is displayed in fig. 17(a). The measurements were performed at room
temperature. We can clearly see the SE and GB signal(red), which was found to peak around 3340 cm^{−1}.
Figure 17(b) shows a cutthrough at that frequency. We can conclude that the relaxation time of the OH-
stretch excitation is approximately 550 fs. In comparison: Fecko and co-workers measured a two stage decay
of the same relaxation in diluted HOD in D2O, with relaxation times of 50 fs and 1400 fs[9]. Also the EA
state is visible around 3170 cm^{−1}(blue). The EA signal is however too weak to estimate a decay time. The
two blue areas on both sides of the red peak, around τ2=0 are a result of direct interaction between the
pump and probe pulses.

A problem that occurred during these measurements was the rapid increase of the optical thickness.

After 20 minutes of measuring there was no signal measured behind the sample. Measurements in a linear
spectrometer show an increase in absorption around 3350 cm^{−1}, which we assigned to absorption of water
by the methanol solution due to the open structure, which would by isotopic substitution increase the H-
methanol concentration. The concentration of H-methanol increased by a factor 5 during the measurement
(fig. 19(a)). As a result, we were not able to perform multiple repetitions of the experiment under the same
conditions without refreshing the sample, which was undesirable for practical purposes.

t_{2}(fs)

(cm^{-1})

Figure 17: Pump probe spectra in the parallel polarization (left) and perpendicular polarization (right), and
cut through of the isotropic component of the pp-spectrum at ν=3340 cm^{−1}fitted with an exponential decay
with τr=552 fs. There is an offset of 0.011

4.2.3 Pump probe measurements in nitrogen box

In order to avoid absorption of water from the air by the sample, we built a nitrogen purged box around the
area where there was contact between methanol and air, and performed the measurements again, this time
during 3 hours, to get a total of 67 scans. The polarization angle was set at 52.7^{◦}, close to the magic angle
(eq.7), such that the measured spectrum is approximately isotropic. The corresponding pump probe plot
can be seen in fig. 18. We could not observe a hot ground state in this spectrum. The observed lifetime of
the excited state is the same as in the previous measurement. The blue area that results from the excited
state absorption peaks at a frequency well below 3150 cm^{−1}, from which we conclude that the anharmonicity
of the OH-stretch in H-methanol is at least 200 cm^{−1}.

4.2.4 Effect of nitrogen protection

Figure 19(b) shows the effect of nitrogen protection of the methanol-air contact, and of the nitrogen box.

We compare the speed in OD increase of the sample while measuring between the partly nitrogen protection and the nitrogen box. Additionally, we measured the same with the methanol solution kept in the beaker, without the pumping system and jet, for the solution in open air and the partly nitrogen protection by taking samples and measure with the linear spectrometer in the short pathway cuvette. With the methanol solution kept in the nitrogen box we saw no significant change after one hour.

From figure 19(b) it appears that at first there is a rapid increase in the OD of the nitrogen protected sample. We assign this to residual OH in the system before the experiment, particularly in the wire mecha- nism, that could not be cleaned between measurements. The long term trend seems to be that absorption is slowed down significantly by the bag and nitrogen flow around the jet, which is again slowed down more by the replacement by the box. Finally, we can conclude from the difference between absorption of the samples in rest, and during the experiment that the intense contact around the jet is mainly responsible for the absorption of water.

_{} _{}

(cm^{-1}) (cm^{-1})

Figure 18: The pump probe spectrum for liquid methanol. On the horizontal axis is the waiting time in fs.

a) b)

Figure 19: Absorption spectra taken before and after the pump-probe measurement, showing an increase in absorption in the OH region in the original situation in open air (a), and comparison of absorption speed of water by D-methanol under different circumstances. Partly nitrogen protected means by the bag around the small beaker, and an nitrogen upstream from the main beaker around the jet (b)