of 21
Computational Design of Molecular Probes for Electronic Pre-
Resonance Raman Scattering Microscopy
Jiajun Du
†,‡
,
Xuecheng Tao
†,‡
,
Tomislav Begušić
,
Lu Wei
†Division of Chemistry and Chemical Engineering, California Institute of Technology, Pasadena,
California 91125, USA
Abstract
Recently developed electronic pre-resonance stimulated Raman scattering (epr-SRS) microscopy,
in which the Raman signal of a dye is significantly boosted by setting the incident laser
frequency near the electronic excitation energy, has pushed the sensitivity of SRS microscopy
close to that offered by confocal fluorescence microscopy. Prominently, the maintained narrow
line-width of epr-SRS also offers high multiplexity that breaks the “color barrier” in optical
microscopy. However, detailed understandings of the fundamental mechanism in these epr-SRS
dyes still remain elusive. Here, we combine experiments with theoretical modeling to investigate
the structure-function relationship, aiming to facilitate the design of new probes and expanding
epr-SRS palettes. Our ab initio approach employing the displaced harmonic oscillator (DHO)
model provides a consistent agreement between simulated and experimental SRS intensities of
various triple-bond bearing epr-SRS probes with distinct scaffolds. We further review two popular
approximate expressions for epr-SRS, namely the short-time and Albrecht A-term equations, and
compare them to the DHO model. Overall, the theory allows us to illustrate how the observed
intensity differences between molecular scaffolds stem from the coupling strength between the
electronic excitation and the targeted vibrational mode, leading to a general design strategy for
highly sensitive next-generation vibrational imaging probes.
Graphical Abstract
tbegusic@caltech.edu; lwei@caltech.edu.
Contributed equally to this work
Supporting Information Available
Computational and experimental details, connection between short-time and Albrecht equations, Duschinsky and Herzberg–Teller
effects on the absorption spectra of MARS probes, analysis of the 0-0 transition energy, comparison between the simulated and
experimental transition dipole strengths
HHS Public Access
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. Author manuscript; available in PMC 2023 November 26.
Published in final edited form as:
J Phys Chem B
. 2023 June 08; 127(22): 4979–4988. doi:10.1021/acs.jpcb.3c00699.
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Introduction
Over the last one and half decades, stimulated Raman scattering (SRS) microscopy has
emerged as an important vibrational bio-imaging modality complementary to standard
fluorescence microscopy. Although SRS has enhanced the otherwise weak spontaneous
Raman transition by up to 10
8
-fold through stimulated emission amplification,
1
-
3
its current
sensitivity of non-resonant probes is still largely limited to micromolar to millimolar range,
4
restricting probing the rich chemical information of dilute biomolecules
in vivo
, which
is usually in the nanomolar to low micromolar range. This sensitivity gap has proven to
be successfully tackled by customized Raman probes.
4
Among numerous Raman probes,
some of the most sensitive ones up to date are the pyronin-based electronic pre-resonance
(epr) enhanced Manhattan Raman scattering (MARS) dyes.
5
When the pump wavelength
is tuned to be close to the electronic excitation energy, i.e. under the epr condition,
the vibrational mode coupled to the electronic state would be selectively amplified with
enhanced SRS signals. By carefully tuning the absorption of the dyes (660–790 nm) to
moderately close to the laser wavelength (800~900 nm), SRS intensities of the triple bonds
(nitriles or alkynes) when conjugated into the conjugation systems of these dyes have
been found to be pre-resonantly enhanced by up to 10
4
folds (detection limit down to
250 nM) with a well-maintained high signal-to-background ratio. Since the invention of
MARS dyes, numerous exciting imaging applications have been achieved. The MARS dyes
enable super-multiplexed (>20 channels) vibrational imaging by taking advantage of the
narrow linewidth of Raman peaks (peak width about 10 cm
−1
, ~50–100 times narrower
than fluorescent peaks) from triple bonds in the cell-silent region (1800–2800 cm
−1
) where
there are no background signals from endogenous molecules.
5
-
7
These ideas inspired the
design of multi-functional Raman probes including photo-switchable, photo-activatable, and
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turn-on enzymatic probes.
8
-
12
They also paved the way for all-far-field single-molecule
Raman spectroscopy and imaging without plasmonic enhancement by stimulated Raman
excited fluorescence (SREF).
13
Thus the superb vibrational properties and versatility of epr
MARS dyes are widely recognized, making them essential for a wide range of vibrational
spectroscopy and imaging. However, these dyes are still the only set of triple-bond bearing
epr-SRS dyes until now and the principle of designing such strong Raman probes is still
inconclusive. This has largely restricted the development of new epr-SRS scaffolds to
further increase the sensitivity and expand the multiplexity, a central topic in the current
development of SRS imaging. While the Albrecht A-term pre-resonance approximation
equation was previously adopted to fit the dependence of epr-SRS signals with a single
parameter of laser detuning, the treatment ignored the structure dependent factors as it
assumes all frequency-independent factors as a constant.
5
The necessity to rationally explore
and design new epr-SRS scaffolds hence sets a high demand for a more systematic theory to
understand and predict the dependence of the epr-SRS signals on molecule structures (i.e., a
structure-function relationship).
Indeed, our initial screening of molecular candidates for new epr-SRS probes revealed that
the structure related factors play a crucial role. For example, a series of pyrrolopyrrole
cyanine (PPCy) dyes were originally identified by us to be promising candidates of
epr-SRS probes. PPCy dyes are neutral and have two nitrile groups in the conjugation
system with adjustable absorption between 680 and 800 nm.
14
The absorption spectrum
of one of those dyes, namely the PPCy-10a molecule (Figure 1A, blue), almost overlaps
with that of MARS2237 (Figure 1A, red), one of the well-validated MARS dyes. The
absorption maximum and molar extinction coefficient of these two molecules are also very
close, implying that a similar epr-SRS signal should be expected based on the detuning
and oscillator strength dependence implied from the full Albrecht A-term pre-resonance
approximation equation.
15
However, as a stark difference to MARS2237, which presented a
clear and sharp epr-SRS peak, we barely see any epr-SRS signal from the nitrile groups of
PPCy-10a under the same measurement conditions (Figure 1A). This observation points
out that it is not effective enough to identify novel epr-SRS probes only through the
experimentally measured absorption quantities. Instead, it indicates that the epr-SRS process
relies heavily on the specific molecular structures. To decipher the structure-dependent
factors underlying this vibronic process, we turn to quantum chemistry methods, which
provide access to parameters that cannot be obtained from experiments.
Theory
Theoretical tools that can accurately and reliably predict Raman intensity could greatly
help us understand the key factors involved in epr-SRS. Although established computational
methods for simulating resonance and pre-resonance Raman spectra exist,
16
-
25
they have
been largely used for simulating the full spectra of individual molecules. Here, we explore
an alternative task, in which we compare the intensities of a single peak, corresponding
to the nitrile (C
N) or alkyne (C
C) bond stretch, in the pre-resonance Raman spectra of
multiple large molecules (50–100 atoms). Theoretically, the SRS signal intensity is
26
,
27
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I
0
1
(
ν
̄
)
ρλ
α
0
1
(
ν
̄
)
(
ω
I
)
ρλ
2
,
(1)
where 0 and 1 denote the ground and first excited vibrational states of mode
ν
̄
in the
electronic ground state,
α
0
1
(
ν
̄
)
(
ω
I
)
is the frequency-dependent polarizability matrix element
between these vibrational states,
ω
I
is the incident light frequency, and
ρ
and
λ
are the
polarizations of the incident and scattered lights. In eq 1, we omit the prefactor that depends
on the incident light (pump) frequency and the Stokes pulse intensity because these factors
cancel out when the SRS intensity is reported with respect to a standard reference. The
conventional frequency-domain approach formulates the polarizability through the Kramers-
Heisenberg-Dirac (KHD) equation
28
,
29
α
0
1
(
ν
̄
)
(
ω
I
)
ρλ
= −
1
n
ψ
1
(
ν
̄
)
μ
ρ
ψ
n
〉〈
ψ
n
μ
λ
ψ
0
(
ν
̄
)
ω
I
ω
n
+
ω
0
(
ν
̄
)
+
ψ
1
(
ν
̄
)
μ
λ
ψ
n
〉〈
ψ
n
μ
ρ
ψ
0
(
ν
̄
)
ω
I
+
ω
n
ω
1
(
ν
̄
)
,
(2)
which involves a sum over all vibrational states
ψ
n
(with energies
ω
n
of the excited
electronic state that is near resonance with the incident light.
ω
0
(
ν
̄
)
and
ω
1
(
ν
̄
)
correspond
to the energies of the ground and first excited vibrational states of the mode of interest
(
ν
̄
)
,
respectively.
μ
ρ
=
μ
ε
S
,
μ
λ
=
μ
ε
I
are the projections of transition dipole moment
μ
along
the scattered and incident light polarizations, respectively, and
γ
is the dephasing parameter.
In the remainder, we will assume the Condon approximation,
μ
μ
(
q
) ≈
μ
(
q
eq
)
, in which
the coordinate dependence of the transition dipole moment is neglected.
q
eq
denotes the
ground-state equilibrium geometry.
Time-domain approach, popularized by Heller and Tannor,
30
,
31
offers an efficient
alternative to evaluating the above sum-over-states formula. Here, the frequency-dependent
polarizability is written as the half-Fourier transform
α
0
1
(
ν
̄
)
(
ω
I
)
ρλ
=
i
μ
λ
μ
ρ
0
C
(
t
)Γ(
t
)
e
I
t
dt
+
0
C
(
t
)Γ(
t
)
e
i
(
ω
I
ω
(
ν
̄
)
)
t
dt
(3)
of the time correlation function
C
(
t
) = 〈
ψ
1
(
ν
̄
)
e
iH
e
t
∕ ℏ
ψ
0
(
ν
̄
)
e
0
(
ν
̄
)
t
,
(4)
where
H
e
is the excited-state Hamiltonian, and we denote
ω
(
ν
̄
)
=
ω
1
(
ν
̄
)
ω
0
(
ν
̄
)
for simplicity.
Γ(
t
)
is the dephasing term in its more general form; for example,
Γ(
t
) =
e
γt
corresponds
to the Lorentzian lineshape in the KHD expression (eq 2). In words, the computation of
C
(
t
)
requires the time propagation of a quantum wavepacket
ψ
(
t
)〉 = exp( −
iH
e
t
∕ ℏ) ∣
ψ
0
(
ν
̄
)
in the excited electronic state, which is computationally costly for molecular Raman probes
with a typical size of 50–100 atoms, even with, for example, trajectory-guided Gaussian
wavepacket approaches.
32
-
43
In fact, the number of ab initio computations in the excited
electronic state should be minimized to allow for efficient analysis of relatively large
molecules.
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The displaced harmonic oscillator (DHO) model
19
offers a practical way to approximate the
time propagation in the excited state. Within this model, it is assumed that the ground and
excited potential energy surfaces can be sufficiently accurately represented as two harmonic
potentials with equal force constants (with frequencies
ω
(
ν
)
but different minima. Note that
ν
represents an arbitrary mode, and is distinguished from
ν
̄
, the mode of interest that gives the
Raman signal. In this case, the time correlation function of eq 4 simplifies into
C
DHO
(
t
) = −
Δ
ν
̄
2
(1 −
e
(
ν
̄
)
t
)
ν
e
−(1 −
(
ν
)
t
e
(
ν
)
t
ν
2
∕ 2
e
i
(
δ
+
ω
I
)
t
.
(5)
Δ
ν
is the dimensionless distance between the ground- and excited-state minima along mode
ν
and is expressed within the vertical gradient model
21
as
Δ
ν
=
1
ω
(
ν
)
f
ν
2
ω
(
ν
)
,
(6)
where
f
ν
is the gradient of the excited-state potential energy with respect to the mass-scaled
normal mode
ν
(see Figure 1B) evaluated at the ground-state equilibrium geometry. The
dimensionless displacement parameters
Δ
ν
are directly related to the well-known Huang–
Rhys factors
S
ν
= Δ
ν
2
∕ 2
In eq 5,
δ
=
ω
eg
ω
I
is the difference (detuning) between the vertical
excitation frequency
ω
eg
and the incident light frequency. Equation 3 is combined with the
approximations in eqs 5 and 6 to provide the major simulation protocol for this study. In
addition, because the laser frequency is sufficiently close to the vertical excitation gap, only
the resonant part (first term on the right-hand side of eq 3) was computed.
Finally, we close the review of the methods by pointing out that two simple but useful
expressions can be further derived from eq 5 under the pre-resonance conditions. First,
following Heller, Sundberg, and Tannor,
26
,
31
a short-time expansion of the time correlation
function
C
DHO
(
t
)
leads to
C
ST
(
t
) = −
is
ν
̄
te
s
2
t
2
∕ 2 −
i
(
δ
+
ω
I
)
t
,
(7)
where
s
ν
= Δ
ν
ω
(
ν
)
2
and
s
2
= ∑
ν
s
ν
2
. Substituting eq 7 into the first (resonant) term of eq 3
yields the short-time expression for the SRS intensity
I
0
1
(
ν
̄
), ST
μ
4
s
ν
̄
2
2
s
4
0
te
t
2
∕ 2 +
s
dt
2
,
(8)
where we used
ρλ
μ
ρ
2
μ
λ
2
=
μ
4
and introduced the dipole strength
μ
2
= ∑
ρ
=
x
,
y
,
z
μ
ρ
2
. Alternatively,
the large detuning limit can be applied directly to the KHD formula in the frequency
domain, which leads to the well-known Albrecht A-term equation but now with calculable
structure-dependent factors
15
,
44
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I
0
1
(
ν
̄
), Albrecht
4
μ
4
s
ν
̄
2
2
ω
I
2
+
ω
eg
2
(
ω
I
2
ω
eg
2
)
2
2
μ
4
s
ν
̄
2
2
δ
4
.
(9)
The first part of eq 9 corresponds to the most common form that includes both resonant
and non-resonant terms, whereas the final right-hand side expression is an approximate form
assuming
δ
ω
eg
. Although more approximate than eq 5, the short-term and Albrecht’s
expressions provide additional insight into the origins of strong pre-resonance Raman
signals. For example, Albrecht’s expression reveals a strong
(1 ∕
δ
4
)
dependence of the
Raman intensity on the detuning, which is otherwise hidden in the more accurate equation.
However, it neglects the impact of spectator modes, i.e., modes that are not directly excited
by the scattering event, which are still accounted for in the short-time expansion formula (eq
8) through a collective vibrational parameter
s
2
that depends on all mode displacements.
Methods
Computational details
Practical implementation of the simulation protocol involves three quantum chemistry
calculations for each molecule, namely the (a) ground-state vibrational modes and
frequencies (or Hessian), (b) electronic transition dipole moment, and (c) excited state
gradient, all evaluated at the ground-state equilibrium geometry (i.e., Franck-Condon point).
The excited-state Cartesian forces are then transformed into the normal-mode coordinates
obtained from the diagonalization of the mass-scaled Hessian of the ground electronic
state. We assumed the validity of the Condon approximation, in which the transition dipole
moment is a constant evaluated at a single molecular geometry, in our case the Franck-
Condon point. In addition, within the DHO model, the excited state frequencies and normal
modes were approximated by those of the ground state, i.e., the changes in the frequencies
(mode distortion) and normal modes (Duschinsky effect) between the ground and excited
electronic states were neglected.
45
The DHO and Condon approximations were validated on
the electronic absorption spectra of several dyes (see Sec. 4 of the Supporting Information).
We performed the quantum-chemical calculations with the ORCA software package
46
,
47
and computed the Raman intensities from the aforementioned analytical expressions in a
separate Python code. Further details of ab initio simulations are available in Sec. 1 of the
Supporting Information.
Raman intensities were computed using mixed computational and experimental data.
Namely, to avoid the computational errors in evaluating the vertical excitation gap, we
estimated this energy from the experimental spectra. Since most of the probes exhibit
absorption spectra that are dominated by the 0–0 transition
48
(see Sec. 5 of the Supporting
Information), we assumed that the wavelength of maximum intensity,
λ
max
, corresponds
to this transition, i.e.,
λ
0 − 0
λ
max
. Then, within the DHO model, we could recover the
experimental estimate of the vertical excitation energy as
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ω
eg,exp
=
ω
0 − 0
+
1
2
ν
ω
ν
Δ
ν
2
,
(10)
where
ω
0 − 0
is the 0-0 transition frequency. Computational data was used for all other
parameters, including the transition dipole moments (analyzed in Sec. 6 of the Supporting
Information). After evaluating the time correlation function
C
(
t
)
within the DHO model (eq
5), we used a Gaussian dephasing
Γ(
t
) =
e
−Θ
2
t
2
∕ 2
in eq 3 to account for the inhomogeneous
broadening of the lineshape
18
,
24
in the solution.
Θ
was set to 250 cm
−1
, which was
consistent with the broadening used in the electronic absorption spectra simulations.
Experimental details
There are two independent laser systems of different fundamental wavelengths for
measuring epr-SRS signals of the molecules, providing different detuning for the same
molecule. One has a fundamental wavelength of 1031.2 nm (2 ps pulse width, 80 MHz
repetition rate) and the other one has a fundamental wavelength of 1064.2 nm (6 ps pulse
width, 80 MHz repetition rate). The different fundamental wavelengths (used as the Stokes
beam) of the two laser systems provide different pump wavelengths for the same molecule.
For the Raman peak of triple bond around 2200 cm
−1
, 1031.2 nm fundamental laser sets
the pump wavelength to be around 840 nm and 1064.2 nm fundamental laser sets the pump
wavelength to be around 860 nm. For example, the Raman peak for the nitrile bond of
MARS2228 is 2228 cm
−1
, thus the pump wavelength is either 838.5 nm (when the Stokes
beam is 1031.2 nm) or 860.2 nm (when the Stokes beam is 1064.2 nm). Details of the two
laser systems are given in Sec. 2 of the Supporting Information. A 10 mM aqueous EdU
sample is measured under each laser system as a benchmark reference sample to correct the
dependence of non-resonant Raman cross section on the wavelength.
Results and Discussion
With the computational approach in hand, we first validate it by comparing the theoretical
and experimental SRS intensities of molecules with various scaffolds. For the benchmark,
we searched for candidates based on the criteria that the molecules strongly absorb in the
epr-SRS region (660–790 nm) and that the nitrile and alkyne groups are directly conjugated
to the
π
-system. Fortunately, there are several molecule scaffolds fitting into our criteria,
although not many. In addition to the pyronin (O/C/Si Rhodamine) scaffold presented
in MARS dyes and PPCy dyes we introduced earlier, there are other scaffolds such as
coumarin,
49
bodipy
50
and pyrrolopyrrole
51
(see Table 1). We synthesized the molecules and
measured their absorption and epr-SRS signals. The data of some of the MARS dyes were
adapted from previous reports.
5
,
6
It is noteworthy that we report epr-SRS measurements
from two independent laser systems, providing different detuning for the same molecules
(see Supporting Information Sec. 2 for details). The pump wavelength is tuned to be around
840 nm or 860 nm for the triple bond and the corresponding experimental results are shown
in Table 2. Each laser system used EdU as the reference substance.
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Figure 2 compares the measured epr-SRS intensities (red bars) of nitrile and alkyne probes
with the simulated intensities (blue bars) from the DHO theory described above. Data from
two SRS laser systems with different pump wavelengths (around 860 nm and 840 nm) are
shown. A consistent agreement is seen between experiment and theory across magnitudes of
SRS intensities on all scaffolds. It is clear that our computational approach remains robust
for laser setups with different detunings. Details of the computational quantities involved
in the epr-SRS intensity calculations (including vertical excitation wavelength, detuning
frequency, transition dipole strength, Raman mode displacement, Raman mode frequency,
epr-SRS signal strength) are reported in the Table S1 of the Supporting Information.
Furthermore, when the comparison is performed at a quantitative level in the inset, the
presence of a linear trend in the figure reinforces the ability of our simple theoretical
approach to identify high-intensity epr-SRS probes. A linear regression of the data gives
a slope of 0.67 or 1.11 rather than 1, illustrating also the limitations of our approach.
Admittedly, a number of approximations enter the simulations, including the DHO model
for the time-correlation function and (TD)DFT level of electronic structure theory. Most of
the calculated values (normalized to the strongest epr-SRS probe in each group) are within
or close to the experimental standard error of about 10% (see Figure S1 of the Supporting
Information). Yet, our calculations deviate more on the intensities of alkyne dyes: they
largely overestimate the SRS intensities of the alkynyl pyronin dyes C-MARS2190 and C-
MARS2143, while they underestimate the intensity of PADBP-9. Whereas in conventional
simulations of a single resonance Raman spectrum the effects of detuning and transition
dipole strength are only moderate, e.g., the spectra are typically scaled to the highest
peak, here these factors play an important role because different molecules exhibit
different detunings and transition dipole strengths. Since the epr-SRS intensity depends
strongly on these parameters, even seemingly acceptable quantum-chemical errors can
lead to discrepancies between theory and experiment. Furthermore, C-MARS2190 and
C-MARS2143 exhibit a strong asymmetry between absorption and emission spectra (see
Figure S5 of the Supporting Information), which implies that the independent-mode DHO
model is not valid for these molecules. In Sec. 4 of the Supporting Information, we
show that mode-coupling (Duschinsky) and non-Condon effects are not much stronger
than in several other (nitrile-based) probes. We believe that aggregation effects,
52
which
have already been reported in these molecules,
53
could be responsible for the distorted
absorption and fluorescence spectra, as well as for the discrepancy between theoretical and
experimental Raman intensities.
More importantly, the theoretical approach allows us to analyze the effect of the vibrational
mode displacement
Δ
ν
̄
, a key factor that enters the SRS intensity expression but cannot
be easily accessed from experiments.
54
,
55
To this end, we revisit the opening example of
Figure 1A. In Figure 3 we show the highest occupied molecular orbitals (HOMOs) and
lowest unoccupied molecular orbitals (LUMOs) of PPCy-10a and MARS2237, as well as
the corresponding parameters related to the vibrational mode displacement between the
ground and excited electronic states. The
π
π
electronic transition leads to a strong
electron density generation on the C
N vibration for MARS2237 but not for PPCy-10a
(Figure 3, comparing the HOMO-LUMO difference in the connected dashed-gray boxes).
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As we see from the
Δ
ν
̄
values, the C
N bond in MARS2237 has to stretch more to reach the
equilibrium position when electronically excited, leading to a stronger SRS signal for this
mode. The large difference in the epr-SRS signal strengths for the two probes then becomes
straightforward according to eq 5, despite the fact that they exhibit similar characteristic
absorption properties.
Figure 3 also reveals that simply adding more nitrile groups does not necessarily increase the
overall SRS intensity. The specific comparison of MARS2237 (containing one nitrile) and
PPCy-10a (containing two nitriles) is an extreme example. Additionally, in the third column
of Figure 3 we present the FC-10 molecule, which contains three nitrile groups. Here, in
contrast to PPCy-10a, all C
N bonds are coupled to the electronic
π
system of the dye and
participate in the electronic transition. However, the coupling is weaker than in MARS2237,
as demonstrated by the values of the dimensionless displacement parameter
Δ
ν
̄
. Interestingly,
in the normal mode basis, there are only two modes with non-zero displacement. We explain
this by the fact that the two C
N bonds labeled “b” and “c” in Figure 3 are equally displaced
in the excited electronic state. Therefore, their symmetric linear combination forms a normal
mode that is displaced and Raman active, whereas their antisymmetric combination is not.
Figure 4 compares the SRS intensities of several probes simulated with the full DHO
expression and two approximate expressions, the short-time expansion (eq 8) and Albrecht
A-term (eq 9) formulas. As expected, both expressions are less accurate than the DHO
method. Since the overall computational cost of the three approaches is almost the same and
is contained mostly in the required quantum chemistry calculations, the DHO expression is
recommended over the other two when a quantitative agreement is needed. Nevertheless,
the qualitative trends in the intensity strength are exactly reproduced. Therefore, we can
use these simpler and more interpretable expressions to seek design principles for highly
sensitive pre-resonance Raman probes.
Detuning (
δ
=
ω
eg
ω
I
), transition dipole moment (
μ
), and the Raman mode displacement
(
Δ
ν
̄
) are the three factors that are highlighted in the Albrecht A-term formula (eq 9). The
epr-SRS intensity increases steeply with an increase in either the transition dipole moment
or the reciprocal of the detuning to the fourth order. Molecular probes with strong oscillator
strengths are always preferred, while one carefully chooses the detuning, i.e. optimal
pre-resonance regime, to tip the balance between high Raman signal strength and signal-to-
background ratio, as discussed in the previous experimental work.
5
To better illustrate the
principles derived from the theoretical analysis, in Table 3 we present an example where
three structural isomers of (9CN-)MARS2228 are proposed and investigated as potential
molecular probe candidates. The isomers, for which the nitrile group is attached at various
positions on the conjugated aromatic ring, have not been reported before in the literature
and are proposed here. Among the four molecules, the 9CN- substituted one exhibits
the lowest-energy absorption maximum, leading to the smallest detuning and, hence, the
strongest SRS intensity when the pump laser is consistently fixed at 838 nm. 9CNThe 9CN-
isomer also exhibits the strongest vibrational displacement and can, therefore, be expected
to provide a stronger SRS signal even if the detuning is fixed to the same value for different
molecules, i.e., even if the pump laser can be freely tuned for each molecule. An example
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of such calculations is shown in the bottom row of Table 3. Combining all of these factors
together, it is not surprising that MARS2228 is listed as one of the most sensitive epr-SRS
Raman probes to date. And as a pre-screening step, our computation may greatly facilitate
the development of new epr-SRS scaffolds.
We can similarly analyze the differences between the nitrile- and alkyne-based probes. For
example, the alkyne MARS2190 probe exhibits a weaker SRS signal than its nitrile-based
structural analog bearing a similar chromophore (Si-pyronin), the MARS2225 probe (see
Table 1 for structures and Figure 2 for intensities). Here, the displacement factors of around
0.146 for MARS2225 and 0.154 for MARS2190 cannot explain this discrepancy. In fact,
in this case, we can explain the difference between the nitrile and alkyne dyes through
their absorption properties, namely the dipole strength and detuning. Specifically, if we
neglect the displacement factor, the ratio of their Raman intensities within the Albrecht
approximation is
I
MARS2225
I
MARS2190
≈ 4.12
, which agrees well with the experimental
value of 303/73
4.15 (see Table 2, pump laser at 860 nm).
The Albrecht A-term equation considers the contribution to the Raman intensity solely from
the specific vibrational mode. In contrast, the short-time expansion is useful when analyzing
the influence of other (spectator) vibrational modes. More specifically, eq 8 can be rewritten
as
I
0
1
(
ν
̄
), ST
=
I
0
1
(
ν
̄
), Albrecht
1
ξ
4
0
te
t
2
∕ 2 +
it
ξ
dt
2
,
(11)
where the second part of the expression depends only on
ξ
=
s
δ
, a dimensionless factor
that involves the displacement of all modes, including spectator modes.
When
ξ
approaches zero, the impact of the spectator modes on the Raman intensity becomes
negligible, i.e., the
ξ
-dependent term becomes 1 (see Figure S2), which corresponds to
the relatively-large-detuning limit of Albrecht.
44
On the other hand,
I
0
1
(
ν
̄
), ST
I
0
1
(
ν
̄
), Albrecht
reaches
its optimum at
ξ
≈ 0.43
, for which the short-time expansion gives roughly three times
stronger intensity than Albrecht equation. That is to say, once the electronic transition
properties associated with the Raman mode of interest are optimally tuned, additional fine
functionalization of the spectator modes could further enhance the spectral intensity (see
Supporting Information Sec. 3 for further discussion). However, as seen from Table 3, it is
recognized as a mild effect compared with the aforementioned three key factors and is not
expected to be the first target in the optimization protocol.
Conclusion
To conclude, we have demonstrated that theoretical modeling can elucidate the chemical
principles behind vastly different epr-SRS signals from different molecular scaffolds. The
computational protocol is both robust and efficient in predicting the epr-SRS intensities
and could lead towards a rational design of new epr-SRS scaffolds. Importantly, it allows
us to decompose the final SRS intensity into three key factors, namely the (a) detuning,
(b) transition dipole strength, and (c) vibrational mode displacement. We showed that the
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strength of vibronic coupling of the specific chemical bond can be visualized by the electron
density distribution during the electronic transition in the epr-SRS setting. In addition, we
analyzed the applicability of approximate Albrecht and short-time expressions, which can
explicitly separate these parameters. Overall, although not as accurate as the full DHO
model, these approximate formulas are still useful because of their interpretability. By
combining them with quantum chemistry computations, we could analyze the effect of
all relevant molecular properties, including the vibrational mode displacement parameters,
which are not necessarily observable in experiments.
This work provides a fundamental step towards a computationally or data-driven
methodology of epr-SRS probe design, ensuring efficient utilization of experimental efforts
by avoiding traditional trial-and-error procedures. In our simulations, we have observed
that the relative values of the transition dipole strength and vibrational mode displacement
parameters can be sufficiently accurately modeled from quantum chemistry calculations
at the TDDFT level of theory, whereas the detuning cannot. This implies two possible
strategies for future work. In a purely computational approach, explicitly correlated
electronic structure methods could be used for determining the vertical excitation energy
to high accuracy in order to minimize the error in the detuning parameter. Alternatively, in
a hybrid, experimental and computational data-driven approach, experimentally available
electronic absorption spectra could be used for a range of existing dyes that do not
necessarily contain a nitrile or alkyne group. Then, different isomers of such dyes with
a nitrile or alkyne substitution could be computationally screened for strong vibrational
mode displacement, assuming that the absorption maximum is red-shifted in a predictable
way
6
after the addition of these functional groups. This opens new avenues for designing
next-generation highly-sensitive epr-SRS palettes, driving the detection limit down to the
ultimate single-molecule level. In either case, our work presents the necessary theoretical
and computational basis for future design strategies.
Supplementary Material
Refer to Web version on PubMed Central for supplementary material.
Acknowledgement
L.W. acknowledges support from NIH Director’s New Innovator Award (GM140919). T.B. acknowledges financial
support from the Swiss National Science Foundation through the Early Postdoc Mobility Fellowship (grant number
P2ELP2-199757). We thank Dr. Martin J. Schnermann for sharing the FC10 dye. The computations presented here
were conducted in the Resnick High Performance Computing Center, a facility supported by Resnick Sustainability
Institute at the California Institute of Technology.
References
(1). Ploetz E; Laimgruber S; Berner S; Zinth W; Gilch P Femtosecond stimulated Raman microscopy.
Appl. Phys. B 2007, 87, 389–393.
(2). Freudiger CW; Min W; Saar BG; Lu S; Holtom GR; He C; Tsai JC; Kang JX; Xie XS Label-free
biomedical imaging with high sensitivity by stimulated Raman scattering microscopy. Science
2008, 322, 1857–1861. [PubMed: 19095943]
Du et al.
Page 11
J Phys Chem B
. Author manuscript; available in PMC 2023 November 26.
Author Manuscript
Author Manuscript
Author Manuscript
Author Manuscript
(3). Ozeki Y; Dake F; Kajiyama S; Fukui K; Itoh K Analysis and experimental assessment of the
sensitivity of stimulated Raman scattering microscopy. Opt. Express 2009, 17, 3651–3658.
[PubMed: 19259205]
(4). Du J; Wang H; Wei L Bringing Vibrational Imaging to Chemical Biology with Molecular Probes.
ACS Chem. Biol 2022, 17, 1621–1637. [PubMed: 35772040]
(5). Wei L; Chen Z; Shi L; Long R; Anzalone AV; Zhang L; Hu F; Yuste R; Cornish VW; Min W
Super-multiplex vibrational imaging. Nature 2017, 544, 465–470. [PubMed: 28424513]
(6). Miao Y; Qian N; Shi L; Hu F; Min W 9-Cyanopyronin probe palette for super-multiplexed
vibrational imaging. Nat. Commun 2021, 12, 4518. [PubMed: 34312393]
(7). Shi L; Wei M; Miao Y; Qian N; Shi L; Singer RA; Benninger RK; Min W Highly-multiplexed
volumetric mapping with Raman dye imaging and tissue clearing. Nat. Biotechnol 2022, 40,
364–373. [PubMed: 34608326]
(8). Lee D; Qian C; Wang H; Li L; Miao K; Du J; Shcherbakova DM; Verkhusha VV; Wang LV; Wei L
Toward photoswitchable electronic pre-resonance stimulated Raman probes. J. Chem. Phys 2021,
154, 135102. [PubMed: 33832245]
(9). Ao J; Fang X; Miao X; Ling J; Kang H; Park S; Wu C; Ji M Switchable stimulated Raman
scattering microscopy with photochromic vibrational probes. Nature communications 2021, 12,
1–8.
(10). Shou J; Ozeki Y Photoswitchable stimulated Raman scattering spectroscopy and microscopy.
Optics Letters 2021, 46, 2176–2179. [PubMed: 33929447]
(11). Fujioka H; Shou J; Kojima R; Urano Y; Ozeki Y; Kamiya M Multicolor activatable Raman
probes for simultaneous detection of plural enzyme activities. J. Am. Chem. Soc 2020, 142,
20701–20707. [PubMed: 33225696]
(12). Kawatani M; Spratt SJ; Fujioka H; Shou J; Misawa Y; Kojima R; Urano Y; Ozeki Y; Kamiya M
9-Cyano-10-telluriumpyronin derivatives as red-light-activatable Raman probes. Chemistry–An
Asian Journal 2022,
(13). Xiong H; Shi L; Wei L; Shen Y; Long R; Zhao Z; Min W Stimulated Raman excited fluorescence
spectroscopy and imaging. Nat. photonics 2019, 13, 412–417. [PubMed: 32607124]
(14). Fischer GM; Isomäki-Krondahl M; Göttker-Schnetmann I; Daltrozzo E; Zumbusch A
Pyrrolopyrrole cyanine dyes: A new class of near-infrared dyes and fluorophores. Chem. Eur.
J 2009, 15, 4857–4864. [PubMed: 19296481]
(15). Asher SA UV resonance Raman studies of molecular structure and dynamics: applications
in physical and biophysical chemistry. Annu. Rev. Phys. Chem 1988, 39, 537–588. [PubMed:
3075468]
(16). Kumble R; Rush TS; Blackwood ME; Kozlowski PM; Spiro TG Simulation of Non-Condon
Enhancement and Interference Effects in the Resonance Raman Intensities of Metalloporphyrins.
J. Phys. Chem. B 1998, 102, 7280–7286.
(17). Bailey SE; Cohan JS; Zink JI Interference effects of multiple excited states in the resonance
Raman spectroscopy of CpCoCOD. J. Phys. Chem. B 2000, 104, 10743–10749.
(18). Petrenko T; Neese F Analysis and prediction of absorption band shapes, fluorescence band
shapes, resonance Raman intensities, and excitation profiles using the time-dependent theory of
electronic spectroscopy. J. Chem. Phys 2007, 127, 164319. [PubMed: 17979350]
(19). Petrenko T; Neese F Efficient and automatic calculation of optical band shapes and resonance
Raman spectra for larger molecules within the independent mode displaced harmonic oscillator
model. J. Chem. Phys 2012, 137, 234107. [PubMed: 23267471]
(20). Egidi F; Bloino J; Cappelli C; Barone V A Robust and Effective Time-Independent Route to
the Calculation of Resonance Raman Spectra of Large Molecules in Condensed Phases with
the Inclusion of Duschinsky, Herzberg–Teller, Anharmonic, and Environmental Effects. J. Chem.
Theory Comput 2014, 10, 346–363. [PubMed: 26550003]
(21). Baiardi A; Bloino J; Barone V A general time-dependent route to Resonance-Raman
spectroscopy including Franck-Condon, Herzberg-Teller and Duschinsky effects. J. Chem. Phys
2014, 141, 114108. [PubMed: 25240346]
(22). Rao BJ; Gelin MF; Domcke W Resonant Femtosecond Stimulated Raman Spectra: Theory and
Simulations. J. Phys. Chem. A 2016, 120, 3286–3295. [PubMed: 26910808]
Du et al.
Page 12
J Phys Chem B
. Author manuscript; available in PMC 2023 November 26.
Author Manuscript
Author Manuscript
Author Manuscript
Author Manuscript
(23). Quincy TJ; Barclay MS; Caricato M; Elles CG Probing Dynamics in Higher-Lying Electronic
States with Resonance-Enhanced Femtosecond Stimulated Raman Spectroscopy. J. Phys. Chem.
A 2018, 122, 8308–8319. [PubMed: 30256101]
(24). de Souza B; Farias G; Neese F; Izsák R Efficient simulation of overtones and combination bands
in resonant Raman spectra. J. Chem. Phys 2019, 150, 214102. [PubMed: 31176338]
(25). Mattiat J; Luber S Time Domain Simulation of (Resonance) Raman Spectra of Liquids in the
Short Time Approximation. J. Chem. Theory Comput 2021, 17, 344–356. [PubMed: 33269589]
(26). Tannor D. Introduction to Quantum Mechanics: A Time-Dependent Perspective; University
Science Books, 2006; Chapter 14.
(27). Schatz GC; Ratner MA Quantum mechanics in chemistry; Courier Corporation, 2002.
(28). Kramers HA; Heisenberg W Über die streuung von strahlung durch atome. Z. Phys 1925, 31,
681–708.
(29). Dirac PAM The quantum theory of dispersion. Proc. R. Soc. A 1927, 114, 710–728.
(30). Lee S-Y; Heller EJ Time-dependent theory of Raman scattering. J. Chem. Phys 1979, 71, 4777–
4788.
(31). Heller EJ; Sundberg R; Tannor D Simple aspects of Raman scattering. J. Phys. Chem 1982, 86,
1822–1833.
(32). Rohrdanz MA; Cina JA Probing intermolecular communication via lattice phonons with time-
resolved coherent anti-Stokes Raman scattering. Mol. Phys 2006, 104, 1161–1178.
(33). Makhov DV; Shalashilin DV Simulation of the effect of vibrational pre-excitation on the
dynamics of pyrrole Simulation of the effect of vibrational pre-excitation on the dynamics of
pyrrole photo-dissociation. J. Chem. Phys 2021, 154, 104119. [PubMed: 33722013]
(34). Worth GA; Lasorne B Gaussian Wave Packets and the DD-vMCG Approach. In Quantum
Chemistry and Dynamics of Excited States; Gonzáles L, Lindh R, Eds.; John Wiley & Sons, Ltd,
2020; Chapter 13, pp 413–433.
(35). Conte R; Ceotto M Semiclassical Molecular Dynamics for Spectroscopic Calculations. In
Quantum Chemistry and Dynamics of Excited States; Gonzáles L, Lindh R, Eds.; John Wiley &
Sons, Ltd, 2020; Chapter 19, pp 595–628.
(36). Bonfanti M; Petersen J; Eisenbrandt P; Burghardt I; Pollak E Computation of the S1 S0 vibronic
absorption spectrum of formaldehyde by variational Gaussian wavepacket and semiclassical IVR
methods. J. Chem. Theory Comput 2018, 14, 5310–4323. [PubMed: 30141930]
(37). Werther M; Grossmann F Apoptosis of moving nonorthogonal basis functions in many-particle
quantum dynamics. Phys. Rev. B 2020, 101, 174315.
(38). Werther M; Choudhury SL; Grossmann F Coherent state based solutions of the time-dependent
Schrödinger equation: hierarchy of approximations to the variational principle. Int. Rev. Phys.
Chem 2021, 40, 81–125.
(39). Curchod BFE; Martínez TJ Ab Initio Nonadiabatic Quantum Molecular Dynamics. Chem. Rev
2018, 118, 3305–3336. [PubMed: 29465231]
(40). Prlj A; Begušić T; Zhang ZT; Fish GC; Wehrle M; Zimmermann T; Choi S; Roulet J; Moser
J-E; Vaníček J Semiclassical Approach to Photophysics Beyond Kasha’s Rule and Vibronic
Spectroscopy Beyond the Condon Approximation. The Case of Azulene. J. Chem. Theory
Comput 2020, 16, 2617–2626. [PubMed: 32119547]
(41). Vaníček J; Begušić T Ab Initio Semiclassical Evaluation of Vibrationally Resolved Electronic
Spectra With Thawed Gaussians. In Molecular Spectroscopy and Quantum Dynamics; Marquardt
R, Quack M, Eds.; Elsevier, 2021; pp 199–229.
(42). Begušić T; Vaníček J Efficient semiclassical dynamics for vibronic spectroscopy beyond
harmonic, Condon, and zero-temperature approximations. CHIMIA 2021, 75, 261. [PubMed:
33902792]
(43). Begušić T; Tapavicza E; Vaníček J Applicability of the Thawed Gaussian Wavepacket Dynamics
to the Calculation of Vibronic Spectra of Molecules with Double-Well Potential Energy Surfaces.
J. Chem. Theory Comput 2022, 18, 3065–3074. [PubMed: 35420803]
(44). Albrecht AC On the Theory of Raman Intensities. J. Chem. Phys 1961, 34, 1476–1484.
Du et al.
Page 13
J Phys Chem B
. Author manuscript; available in PMC 2023 November 26.
Author Manuscript
Author Manuscript
Author Manuscript
Author Manuscript
(45). Hassing S; Mortensen OS The roles of vibronic coupling and the Duschinsky effect in resonance
Raman scattering. J. Mol. Spec 1981, 87, 1–17.
(46). Neese F; Wennmohs F; Becker U; Riplinger C The ORCA quantum chemistry program package.
J. Chem. Phys 2020, 152, 224108. [PubMed: 32534543]
(47). Neese F. Software update: the ORCA program system, version 4.0. Wiley Interdiscip. Rev.
Comput. Mol. Sci 2017, 8, 73–78.
(48). Kostjukov VV Excitation of rhodamine 800 in aqueous media: a theoretical investigation. J. Mol.
Model 2022, 28, 52. [PubMed: 35112197]
(49). Matikonda SS; Ivanic J; Gomez M; Hammersley G; Schnermann MJ Core remodeling leads to
long wavelength fluoro-coumarins. Chem. Sci. 2020, 11, 7302–7307. [PubMed: 34123014]
(50). Majumdar P; Yuan X; Li S; Le Guennic B; Ma J; Zhang C; Jacquemin D; Zhao J
Cyclometalated Ir (III) complexes with styryl-BODIPY ligands showing near IR absorption/
emission: preparation, study of photophysical properties and application as photodynamic/
luminescence imaging materials. J. Mater. Chem. B 2014, 2, 2838–2854. [PubMed: 32261478]
(51). Zhou Y; Ma C; Gao N; Wang Q; Lo P-C; Wong KS; Xu Q-H; Kinoshita T; Ng DK
Pyrrolopyrrole aza boron dipyrromethene based two-photon fluorescent probes for subcellular
imaging. J. Mater. Chem. B 2018, 6, 5570–5581. [PubMed: 32254967]
(52). Hestand NJ; Spano FC Expanded theory of H-and J-molecular aggregates: the effects of vibronic
coupling and intermolecular charge transfer. Chem. Rev 2018, 118, 7069–7163. [PubMed:
29664617]
(53). Pastierik T; Sebej P; Medalova J; Stacko P; Klán P Near-infrared fluorescent 9-
phenylethynylpyronin analogues for bioimaging. J. Org. Chem 2014, 79, 3374–3382. [PubMed:
24684518]
(54). Lee J; Crampton KT; Tallarida N; Apkarian V Visualizing vibrational normal modes of a single
molecule with atomically confined light. Nature 2019, 568, 78–82. [PubMed: 30944493]
(55). Xu J; Zhu X; Tan S; Zhang Y; Li B; Tian Y; Shan H; Cui X; Zhao A; Dong Z et al. Determining
structural and chemical heterogeneities of surface species at the single-bond limit. Science 2021,
371, 818–822. [PubMed: 33602852]
Du et al.
Page 14
J Phys Chem B
. Author manuscript; available in PMC 2023 November 26.
Author Manuscript
Author Manuscript
Author Manuscript
Author Manuscript
Figure 1:
(A)
Absorption and SRS spectra of MARS2237 (red) and PPCy-10a (blue). SRS intensities
are reported relative to EdU (RIE) values,
ε
stands for the molar extinction coefficient.
(B)
Scheme of the electronic pre-resonance stimulated Raman scattering (epr-SRS) process, in
which the incident (pump) light with frequency
ω
I
excites the vibrational mode
ν
̄
from its
ground to the first excited vibrational state. The pump pulse is detuned by
δ
from the vertical
excitation frequency between the ground and first excited electronic states of the molecule.
The scattering process is stimulated by a Stokes (probe) pulse of frequency
ω
S
and proceeds
through a coupling between the vibrational and electronic degrees of freedom, controlled by
the dimensionless displacement parameter
Δ
.
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Figure 2:
Comparing the measured and computed epr-SRS spectral intensities for near-infrared triple
bond dyes with pump lasers at around 860 (left) and 840nm (right). Experimental values
are reported in Table 2. The theoretical values are obtained with the DHO formula (see
eqs 3, 5-6).The insets quantitatively compare the intensities on the log
10
scale, and a linear
regression (dashed gray) of the data gives the slopes of 0.67 (left, R
2
= 0.95) and 1.11 (right,
R
2
= 0.88).
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Figure 3:
Epr-SRS process is strong for vibrational modes that are coupled to the electronic transition.
π
π
electronic transition (as indicated by the HOMO and LUMO orbitals) induces strong
electron density generation on the C
N bond for MARS2237 but not for PPCy-10a. As
a result, MARS2237 exhibits significantly larger Raman mode displacement
ν
̄
)
, hence
the 100 times stronger signal intensity for the epr-SRS Raman peak associated with the
C
N vibration. The FC-10 molecule, shown in the last column exhibits two relatively
strong vibrations even though it contains three nitrile groups, which can be ascribed to the
symmetric (Raman active) and antisymmetric (inactive) linear combinations of the stretch
vibrations corresponding to the two groups labeled b and c.
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Figure 4:
epr-SRS intensities simulated through the two approximate expressions—short-time
expansion (eq 8) and Albrecht A-term (eq 9) formulas—compared with those simulated
through the DHO equation (same as in Figure 2, 860 nm pump) and with the experiment.
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