44
D. Ghosh et al.
within the bandwidth of the femtosecond excitation pulses, each mode will have
their own responses. Therefore, it is important to consider all the energetic pathways
available during the experiment along with the spectral signature of each of the pathways. Although there are different ways of creating these light-matter interactions,
as discussed in the experimental set-up section, the underlying principle remains the
same.
As mentioned above, different Liouville pathways are involved when a chemical
system interacts with multiple infrared pulses [10]. However, the interactions of the
three IR pulses with the sample and the subsequent generation of the 2D IR signal
can be qualitatively understood with a three-level energy diagram (v = 0, 1 and 2).
With the molecules starting in the ground vibrational state, the first pulse excites the
molecules to generate a coherence between the ground state (v = 0) and the first
excited state (v = 1). The second pulse comes after time interval τ (coherence time)
and transfers this coherence into a population of either of the two vibrational states.
The third pulse, coming at an interval of T w (waiting time) after the second pulse,
creates another coherence either between v = 0 to v = 1 or v = 1 to v = 2 states. After
the three pulses interact with the sample, a signal field, encoded with the molecular
response of the system, is emitted from the sample, and reads out the final oscillating
frequencies.
In a typical 2D IR experiment, T w is fixed while τ is scanned; each value of
τ producing a spectrum as detected by the MCT array detector. The 2D IR data
from a single experiment at constant T w thereby consists of a 2D array of time (τ )
and frequency. Numerical Fourier transform of the acquired data along the time (τ )
axis produces the 2D IR spectrum. A two dimensional spectrum is constructed with
oscillating frequencies of the first coherence (denoted by ω τ ) on one axis and that of
the final coherence (denoted by ω t or ω m ) on the other axis. The responses can be
observed as peak pairs in the 2D IR spectrum. Depending on the states involved in the
coherence, the 2D IR spectrum consists of a negative diagonal peak due to emission
involving 0–1 transition (ground state bleach or excited state emission) and a positive
off-diagonal peak due to emission involving 1–2 transition (excited state absorption).
The off diagonal peak is red-shifted from diagonal peak by the anharmonicity of the
vibrational probe. The intensity of the diagonal and off-diagonal peak decreases
with increasing waiting time and is directly related to the vibrational lifetime of the
vibrational mode being excited during the experiment. The axis is also identified as
a pump and probe axis based on the analogy to the pump-probe spectroscopy.
It should be noted that a three level system has been considered because
femtosecond IR pulses are limited by broad bandwidth and can in turn excite both
ground and the first excited states. However, this simple understanding of the 2D IR
spectrum in terms of a diagonal and an off diagonal peak is limited for a single vibrational mode and the simplest of experimental geometries. Presence of multiple vibrational modes within the bandwidth of the excitation pulses would lead to multiple
diagonal peak pairs. This will be discussed in detail in the next section of the article.
In addition, vibrational coupling, chemical exchange, and population transfer, if
present, would lead to cross peaks in the 2D IR spectrum. Some of these cases will
be discussed in the latter part of this article.
D. Ghosh et al.
within the bandwidth of the femtosecond excitation pulses, each mode will have
their own responses. Therefore, it is important to consider all the energetic pathways
available during the experiment along with the spectral signature of each of the pathways. Although there are different ways of creating these light-matter interactions,
as discussed in the experimental set-up section, the underlying principle remains the
same.
As mentioned above, different Liouville pathways are involved when a chemical
system interacts with multiple infrared pulses [10]. However, the interactions of the
three IR pulses with the sample and the subsequent generation of the 2D IR signal
can be qualitatively understood with a three-level energy diagram (v = 0, 1 and 2).
With the molecules starting in the ground vibrational state, the first pulse excites the
molecules to generate a coherence between the ground state (v = 0) and the first
excited state (v = 1). The second pulse comes after time interval τ (coherence time)
and transfers this coherence into a population of either of the two vibrational states.
The third pulse, coming at an interval of T w (waiting time) after the second pulse,
creates another coherence either between v = 0 to v = 1 or v = 1 to v = 2 states. After
the three pulses interact with the sample, a signal field, encoded with the molecular
response of the system, is emitted from the sample, and reads out the final oscillating
frequencies.
In a typical 2D IR experiment, T w is fixed while τ is scanned; each value of
τ producing a spectrum as detected by the MCT array detector. The 2D IR data
from a single experiment at constant T w thereby consists of a 2D array of time (τ )
and frequency. Numerical Fourier transform of the acquired data along the time (τ )
axis produces the 2D IR spectrum. A two dimensional spectrum is constructed with
oscillating frequencies of the first coherence (denoted by ω τ ) on one axis and that of
the final coherence (denoted by ω t or ω m ) on the other axis. The responses can be
observed as peak pairs in the 2D IR spectrum. Depending on the states involved in the
coherence, the 2D IR spectrum consists of a negative diagonal peak due to emission
involving 0–1 transition (ground state bleach or excited state emission) and a positive
off-diagonal peak due to emission involving 1–2 transition (excited state absorption).
The off diagonal peak is red-shifted from diagonal peak by the anharmonicity of the
vibrational probe. The intensity of the diagonal and off-diagonal peak decreases
with increasing waiting time and is directly related to the vibrational lifetime of the
vibrational mode being excited during the experiment. The axis is also identified as
a pump and probe axis based on the analogy to the pump-probe spectroscopy.
It should be noted that a three level system has been considered because
femtosecond IR pulses are limited by broad bandwidth and can in turn excite both
ground and the first excited states. However, this simple understanding of the 2D IR
spectrum in terms of a diagonal and an off diagonal peak is limited for a single vibrational mode and the simplest of experimental geometries. Presence of multiple vibrational modes within the bandwidth of the excitation pulses would lead to multiple
diagonal peak pairs. This will be discussed in detail in the next section of the article.
In addition, vibrational coupling, chemical exchange, and population transfer, if
present, would lead to cross peaks in the 2D IR spectrum. Some of these cases will
be discussed in the latter part of this article.