in this context that only in the case of non-Gaussian statistics of the transition
frequency fluctuations dx t
ð Þ one would obtain new physical information about the
system [232]. Because the local interactions that often dominate vibrational
dynamics, it can be expected that non-Gaussian statistics may play a significant role
in vibrational dynamics of several types of samples, especially in non-isotropic
environments, where asymmetric lineshapes are observed in the samples. However,
demonstrations of 3D IR spectroscopy in this context are rare [232]. and the
discussion will be limited to the other essential strength of 3D IR.
The second important example that has been proposed for 3D IR spectroscopy
concerns so-called (non-)Markovian dynamics in a chemical reaction. Broadly
speaking, the Markovian assumption implies that the temporal evolution of a
molecular system depends only on its current state, but not on previous events. That
is, the sample system has no ‘‘memory’’ about earlier events. In such a case,
correlation functions such as Eq. (6) would simply factorize in two lower-order
correlation functions (Eq. 7). As an example for the breakdown of this assumption,
it has been suggested that chemical reactions, which occur as fast as the solvent
relaxation around it, can become non-Markovian [245].
C 3 t 4 ; t 2
ð
Þ ¼hdx jk t 4
ð Þdx ij t 2
ð Þdx 01 0
ð Þi hdx jk t 4
ð Þdx ij 0
ð Þihdx ij t 2
ð Þdx 01 0
ð Þi ð7Þ
The potential of 3D IR spectroscopy for resolving non-Markovian dynamics in
chemical reactions has recently been explored by Hamm et al. [245]. As a model
reaction, the authors re-investigated the chemical exchange of hydrogen bond
formation/dissociation between phenol-OD/benzene in CCl 4 (see also Sect. 3.1.4)
from the perspective of Markovianity. The aim of this experiment was to test if the
OD-stretch vibration performs as a Markovian coordinate or not, i.e. if the
complexes associated/dissociated during the vibrational lifetime after initial
excitation perform spectroscopically differently as the ones that did not associate/
dissociate. As an essential result, it was found that the OD-stretch vibration is
indeed a non-Markovian coordinate. Using molecular dynamics simulations to back
up that interpretation, it could furthermore be revealed that the non-Markovian
dynamics originate from the heterogeneous structure of the mixed solvent (benzene/
CCl 4 ), which forms clusters due to the different chemical nature of the molecules
[246]. In this situation, the dynamics can be fairly complex since hydrogen bond
formation/dissociation can depend on the position of the phenol molecule in the
cluster.
The 3D IR signals of the phenol-OD/benzene system depicted in Fig. 19 have
been obtained at the indicated waiting times, where the first value is associated with
the t 2 delay and the second value with t 4 . As described in Sect. 3.1.4 the signal at
2660 cm
-1 is associated with the free phenol-OD (F) whereas the broader signal at
2630 cm
-1 is associated with the complex (C). Note that only the ground state
bleach/stimulated emission signal contributes in the considered spectral range, i.e.
no energy level diagrams of the form of Fig. 18c and d contribute to the signals. In
extension to 2D IR spectroscopy, diagonal peaks show up, but now on the bodydiagonal line, if the waiting times are (close to) zero (upper left spectrum). In
contrast to 2D IR spectroscopy, now six possibilities exist for cross peaks to show
Top Curr Chem (Z) (2017) 375:86
123
161
Reprinted from the journal
frequency fluctuations dx t
ð Þ one would obtain new physical information about the
system [232]. Because the local interactions that often dominate vibrational
dynamics, it can be expected that non-Gaussian statistics may play a significant role
in vibrational dynamics of several types of samples, especially in non-isotropic
environments, where asymmetric lineshapes are observed in the samples. However,
demonstrations of 3D IR spectroscopy in this context are rare [232]. and the
discussion will be limited to the other essential strength of 3D IR.
The second important example that has been proposed for 3D IR spectroscopy
concerns so-called (non-)Markovian dynamics in a chemical reaction. Broadly
speaking, the Markovian assumption implies that the temporal evolution of a
molecular system depends only on its current state, but not on previous events. That
is, the sample system has no ‘‘memory’’ about earlier events. In such a case,
correlation functions such as Eq. (6) would simply factorize in two lower-order
correlation functions (Eq. 7). As an example for the breakdown of this assumption,
it has been suggested that chemical reactions, which occur as fast as the solvent
relaxation around it, can become non-Markovian [245].
C 3 t 4 ; t 2
ð
Þ ¼hdx jk t 4
ð Þdx ij t 2
ð Þdx 01 0
ð Þi hdx jk t 4
ð Þdx ij 0
ð Þihdx ij t 2
ð Þdx 01 0
ð Þi ð7Þ
The potential of 3D IR spectroscopy for resolving non-Markovian dynamics in
chemical reactions has recently been explored by Hamm et al. [245]. As a model
reaction, the authors re-investigated the chemical exchange of hydrogen bond
formation/dissociation between phenol-OD/benzene in CCl 4 (see also Sect. 3.1.4)
from the perspective of Markovianity. The aim of this experiment was to test if the
OD-stretch vibration performs as a Markovian coordinate or not, i.e. if the
complexes associated/dissociated during the vibrational lifetime after initial
excitation perform spectroscopically differently as the ones that did not associate/
dissociate. As an essential result, it was found that the OD-stretch vibration is
indeed a non-Markovian coordinate. Using molecular dynamics simulations to back
up that interpretation, it could furthermore be revealed that the non-Markovian
dynamics originate from the heterogeneous structure of the mixed solvent (benzene/
CCl 4 ), which forms clusters due to the different chemical nature of the molecules
[246]. In this situation, the dynamics can be fairly complex since hydrogen bond
formation/dissociation can depend on the position of the phenol molecule in the
cluster.
The 3D IR signals of the phenol-OD/benzene system depicted in Fig. 19 have
been obtained at the indicated waiting times, where the first value is associated with
the t 2 delay and the second value with t 4 . As described in Sect. 3.1.4 the signal at
2660 cm
-1 is associated with the free phenol-OD (F) whereas the broader signal at
2630 cm
-1 is associated with the complex (C). Note that only the ground state
bleach/stimulated emission signal contributes in the considered spectral range, i.e.
no energy level diagrams of the form of Fig. 18c and d contribute to the signals. In
extension to 2D IR spectroscopy, diagonal peaks show up, but now on the bodydiagonal line, if the waiting times are (close to) zero (upper left spectrum). In
contrast to 2D IR spectroscopy, now six possibilities exist for cross peaks to show
Top Curr Chem (Z) (2017) 375:86
123
161
Reprinted from the journal