12 research outputs found
Revisiting Vertical Models To Simulate the Line Shape of Electronic Spectra Adopting Cartesian and Internal Coordinates
Vertical models for
the simulation of spectroscopic line shapes
expand the potential energy surface (PES) of the final state around
the equilibrium geometry of the initial state. These models provide,
in principle, a better approximation of the region of the band maximum.
At variance, adiabatic models expand each PES around its own minimum.
In the harmonic approximation, when the minimum energy structures
of the two electronic states are connected by large structural displacements,
adiabatic models can breakdown and are outperformed by vertical models.
However, the practical application of vertical models faces the issues
related to the necessity to perform a frequency analysis at a nonstationary
point. In this contribution we revisit vertical models in harmonic
approximation adopting both Cartesian (<b>x</b>) and valence
internal curvilinear coordinates (<b>s</b>). We show that when <b>x</b> coordinates are used, the vibrational analysis at nonstationary
points leads to a deficient description of low-frequency modes, for
which spurious imaginary frequencies may even appear. This issue is
solved when <b>s</b> coordinates are adopted. It is however
necessary to account for the second derivative of <b>s</b> with
respect to <b>x</b>, which here we compute analytically. We
compare the performance of the vertical model in the <b>s</b>-frame with respect to adiabatic models and previously proposed vertical
models in <b>x</b>- or <b>Q</b><sub>1</sub>-frame, where <b>Q</b><sub>1</sub> are the normal coordinates of the initial state
computed as combination of Cartesian coordinates. We show that for
rigid molecules the vertical approach in the <b>s</b>-frame
provides a description of the final state very close to the adiabatic
picture. For sizable displacements it is a solid alternative to adiabatic
models, and it is not affected by the issues of vertical models in <b>x</b>- and <b>Q</b><sub>1</sub>-frames, which mainly arise
when temperature effects are included. In principle the <b>G</b> matrix depends on <b>s</b>, and this creates nonorthogonality
problems of the Duschinsky matrix connecting the normal modes of initial
and final states in adiabatic approaches. We highlight that such a
dependence of <b>G</b> on <b>s</b> is also an issue in
vertical models, due to the necessity to approximate the kinetic term
in the Hamiltonian when setting up the so-called GF problem. When
large structural differences exist between the initial and the final-state
minima, the changes in the <b>G</b> matrix can become too large
to be disregarded
Duschinsky, HerzbergāTeller, and Multiple Electronic Resonance Interferential Effects in Resonance Raman Spectra and Excitation Profiles. The Case of Pyrene
We show that a recently developed
time-independent approach for
the calculation of vibrational resonance Raman (vRR) spectra is able
to describe Duschinsky and HerzbergāTeller (HT) effects acting
on a single resonant state, together with interferential contributions
arising from multiple electronic resonances, allowing us to investigate
in detail how their interplay determines both the vRR spectra at selected
wavelengths and the Raman excitation profiles. We apply this methodology
to the study of the spectra of pyrene in acetonitrile, an ideal system
since it exhibits three close-lying electronic transitions that are
bright but also subjected to HT effects. To single out the different
contributions to vRR line shapes we adopted two different adiabatic
models for resonant-state potential energy surfaces, namely, Adiabatic
Shift (only accounting from equilibrium geometry displacements) and
Adiabatic Hessian (AH, including also the Duschinsky effects), and
FranckāCondon (FC) or HT approximations for the transition
dipole. We show that, on balance, FC+HT calculations within the AH
model provide the best agreement with experiment. Moreover, our methodology
permits to individuate bands in the experimental spectra due to the
simultaneous contribution of more than one resonant state and to point
out and analyze interferential effects between the FC and HT terms
in each resonance Raman process, together with FC-HT and HT-HT interferences
between different electronic states
Modeling Solvent Broadening on the Vibronic Spectra of a Series of Coumarin Dyes. From Implicit to Explicit Solvent Models
We
present a protocol to estimate the solvent-induced broadening
of electronic spectra based on a model that explicitly takes into
account the environment embedding the solute. Starting from a classical
approximation of the solvent contribution to the spectrum, the broadening
arises from the spread of the excitation energies due to the fluctuation
of the solvent coordinates, and it is represented as a Gaussian line
shape that convolutes the vibronic spectrum of the solute. The latter
is computed in harmonic approximation at room temperature with a time-dependent
approach. The proposed protocol for the computation of spectral broadening
exploits molecular dynamics (MD) simulations performed on the soluteāsolvent
system, keeping the solute degrees of freedom frozen, followed by
the computation of the excitation properties with a quantum mechanics/molecular
mechanics (QM/MM) approach. The factors that might influence each
step of the protocol are analyzed in detail, including the selection
of the empirical force field (FF) adopted in the MD simulations and
the QM/MM partition of the system to compute the excitation energies.
The procedure is applied to a family of coumarin dyes, and the results
are compared with experiments and with the predictions of a very recent
work (Cerezo et al., <i>Phys. Chem. Chem.
Phys.</i> <b>2015</b>, <i>17</i>, 11401ā11411), where an implicit model was adopted for the solvent. The final
spectra of the considered coumarins were obtained without including <i>ad hoc</i> phenomenological parameters and indicate that the
broadenings computed with explicit and implicit models both follow
the experimental trend, increasing as the polarity change from the
initial to the final state increases. More in detail, the implicit
model provides larger estimations of the broadening that are closer
to the experimental evidence, while explicit models appear to better
capture relative differences arising from different solvents or different
solutes. Possible inaccuracies of the adopted FF that may lead to
the observed underestimation are analyzed in detail
Optical Properties of Diarylethenes with TD-DFT: 0ā0 Energies, Fluorescence, Stokes Shifts, and Vibronic Shapes
This contribution is an investigation
of both the structures and
optical properties of a set of 14 diverse, recently synthesized diarylethenes
using Time-Dependent Density Functional Theory (TD-DFT) at the ĻB97X-D/6-31GĀ(d)
level of theory. The linear response (LR) and state-specific (SS)
versions of the Polarizable Continuum Model (PCM) have been adopted
to account for the bulk solvation effects and their relative performances
were critically accessed. It is shown, for the first time in the case
of nontrivial diarylethenes, that TD-DFT provides good agreement between
the experimental absorption-fluorescence crossing points (AFCPs) and
their theoretical counterparts when a robust model accounting for
both geometrical relaxation and vibrational corrections is used instead
of the vertical approximation. On the other hand, the theoretical
estimates for the Stokes shifts based on the vertical transition energies
were found to be in disagreement with respect to experiment, prompting
us to simulate the absorption/emission vibronic band shapes. It is
proved that difficulties associated with the breakdown of the harmonic
approximation in Cartesian coordinates exist for the investigated
system, and we show how they can be at least partially overcome by
means of a vertical approach including Duschinsky effects. Our results
provide a valuable basis to rationalize the experimental vibronic
structure of both emission and absorption bands and are expected to
be a significant asset to the understanding of the optical properties
of diarylethene derivatives
First Principles Studies of the Vibrationally Resolved Magnetic Circular Dichroism Spectra of Biphenylene
We present density-functional response theory calculations
of the
one-photon absorption and magnetic circular dichroism spectral bandshapes
of biphenylene. The effects from the surrounding solvent environment
and molecular vibrations have been included. The solvent is described
by the Polarizable Continuum Model (PCM), while the vibrational structures
of the spectra have been computed including both FranckāCondon
and HerzbergāTeller contributions in the vibronic model. This
is the first study of vibronic effects on magnetic circular dichroism
spectra including non-FranckāCondon contributions. A detailed
comparison with experimental data has been performed, revealing that
the B3LYP functional in combination with PCM gives the best agreement
with experimental data. Our calculations indicate that nonadiabatic
vibronic coupling may play a role, and even small computational inaccuracies
might cause significant changes in the calculated HT term, which raises
concerns about the inclusion of HT contributions in the calculations
of vibronic MCD in systems that have close-lying excited states
Electronic Circular Dichroism in Exciton-Coupled Dimers: Vibronic Spectra from a General All-Coordinates Quantum-Dynamical Approach
We present a computational approach
of general applicability to
simulate the vibronic line shapes of absorption and electronic circular
dichroism (ECD) spectra in rigid exciton-coupled dimers based on a
time-dependent expression of the spectra and quantum dynamical calculations.
We adopt a diabatic model of interacting states localized on the monomers
whose electronic potential energy surfaces are described within harmonic
approximation, including the effect of displacements, frequency changes,
and normal-mode mixings. Spectra that fully account for the effect
of all nuclear degrees of freedom of the system are obtained through
a hierarchical representation of the Hamiltonian in blocks, defined
so that few blocks accurately describe the short-time dynamics of
the system. With this approach, on the ground of time-dependent density
functional theory calculations, we simulate the absorption and ECD
spectra of a covalent compound representing a ādimerā
of anthracene, in the spectral region of the <sup>1</sup>L<sub>a</sub> monomer transition, obtaining results in good agreement with the
experiment
Vibronic Coupling Dominates the Electronic Circular Dichroism of the Benzene Chromophore <sup>1</sup>L<sub>b</sub> band
The
alkylbenzene derivatives (<i>R</i>)-PhCHĀ(CH<sub>3</sub>)<sup>t</sup>Bu (<b>1</b>) and (<i>R</i>)-PhCHĀ(CH<sub>3</sub>)<sup>i</sup>Pr (<b>2</b>) were taken as paradigms of
chiral benzene compounds and their vibronic electronic circular dichroism
(ECD) spectrum in the <sup>1</sup>L<sub>b</sub> band region analyzed
in detail. The <sup>1</sup>L<sub>b</sub> ECD band of chiral benzene
compounds is often used to assign absolute configurations on the basis
of sector rules. However, <sup>1</sup>L<sub>b</sub> ECD bands of several
benzene derivatives are associated with a forbidden character and
show marked vibrational progressions strongly modulating their shape.
This is also true for compounds <b>1</b> and <b>2</b>,
the latter also showing a peculiar thermochromism. The low-temperature
ECD spectrum of <b>2</b> displays in fact an alternation of
positive and negative ECD maxima. Vibronic ECD calculations performed
within a TDDFT scheme allowed a full rationalization of the observed
ECD spectra of <b>1</b> and <b>2</b>. Especially in the
case of <b>2</b>, the ECD spectrum in the <sup>1</sup>L<sub>b</sub> band region results from a complex balance of FranckāCondon
and HerzbergāTeller effects, as well as of conformational factors.
Therefore, straightforward sector rules cannot be safely used to assign
the absolute configuration of even these simple derivatives
Erratum: Harmonic Models in Cartesian and Internal Coordinates to Simulate the Absorption Spectra of Carotenoids at Finite Temperatures
Erratum:
Harmonic Models in Cartesian and Internal
Coordinates to Simulate the Absorption Spectra of Carotenoids at Finite
Temperature
Harmonic Models in Cartesian and Internal Coordinates to Simulate the Absorption Spectra of Carotenoids at Finite Temperatures
When large structural
displacements take place between the ground state (GS) and excited
state (ES) minima of polyatomic molecules, the choice of a proper
set of coordinates can be crucial for a reliable simulation of the
vibrationally resolved absorption spectrum. In this work, we study
two carotenoids that undergo structural displacements from GS to ES
minima of different magnitude, from small displacements for violaxanthin
to rather large ones for Ī²-carotene isomers. Their finite-temperature
(77 and 300 K) spectra are simulated at the harmonic level, including
Duschinsky effect, by time-dependent (TD) and time-independent (TI)
approaches, using (TD)ĀDFT computed potential energy surfaces (PES).
We adopted two approaches to construct the harmonic PES, the Adiabatic
(AH) and Vertical Hessian (VH) models and, for AH, two reference coordinate
frames: Cartesian and valence internal coordinates. Our results show
that when large displacements take place, Cartesian coordinates dramatically
fail to describe curvilinear displacements and to account for the
Duschinsky matrix, preventing a realistic simulation of the spectra
within the AH model, where the GS and ES PESs are quadratically expanded
around their own equilibrium geometry. In contrast, internal coordinates
largely amend such deficiencies and deliver reasonable spectral widths.
As expected, both coordinate frames give similar results when small
displacements occur. The good agreement between VH and experimental
line shapes indicates that VH model, in which GS and ES normal modes
are both evaluated at the GS equilibrium geometry, is a good alternative
to deal with systems exhibiting large displacements. The use of this
model can be, however, problematic when imaginary frequencies arise.
The extent of the nonorthogonality of the Dushinsky matrix in internal
coordinates and its correlation with the magnitude of the displacement
of the GS and ES geometries is analyzed in detail
Insights for an Accurate Comparison of Computational Data to Experimental Absorption and Emission Spectra: Beyond the Vertical Transition Approximation
In this work we carefully investigate
the relationship between
computed data and experimental electronic spectra. To that end, we
compare both vertical transition energies, <i>E</i><sub>V</sub>, and characteristic frequencies of the spectrum like the
maximum, Ī½<sup>max</sup>, and the center of gravity, <i>M</i><sup>1</sup>, taking advantage of an analytical expression
of <i>M</i><sup>1</sup> in terms of the parameters of the
initial- and final-state potential energy surfaces. After pointing
out that, for an accurate comparison, experimental spectra should
be preliminarily mapped from wavelength to frequency domain and transformed
to normalized lineshapes, we simulate the absorption and emission
spectra of several prototypical chromophores, obtaining lineshapes
in very good agreement with experimental data. Our results indicate
that the customary comparison of experimental Ī½<sup>max</sup> and computational <i>E</i><sub>V</sub>, without taking
into account vibrational effects, is not an adequate measure of the
performance of an electronic method. In fact, it introduces systematic
errors that, in the investigated systems, are on the order of 0.1ā0.3
eV, i.e., values comparable to the expected accuracy of the most accurate
computational methods. On the contrary, a comparison of experimental
and computed <i>M</i><sup>1</sup> and/or 0ā0 transition
frequencies provides more robust results. Some rules of thumbs are
proposed to help rationalize which kind of correction one should expect
when comparing <i>E</i><sub>V</sub>, <i>M</i><sup>1</sup>, and Ī½<sup>max</sup>