Franck-Condon Models for Simulating the Band Shape of Electronic Absorption Spectra

Agglomeration compaction promotes corrosion of gold nanoparticles

Engineered nanoparticles are increasingly being used in various areas of human activity. However, the degradation mechanism of nanobodies in harsh environments is still a puzzle for theory and experiment. We report here the results of optical spectroscopy and nanoparticle tracking analysis, quantifying agglomeration and sizing of 50 nm citrate stabilized gold nanoparticles (GNPs) in HCl solutions containing H2O2. The mechanism of a consecutive corrosion reaction of GNPs is discussed within the framework of the near-field approach. We found that the disappearance of single nanoparticles from a suspension does not occur due to their dissolution per se, but is a consequence of the formation of aggregates. The neutralization of electrostatic shielding at high ionic strength allows gold nanoparticles to approach the subnanometer distance within the region of capping defects, at which the Casimir and van der Waals attractive forces dominate. It is suggested that electric field fluctuations in the confined space between highly conductive gold nanoparticles cause complexant-stimulated loss of metal from the core in the contact area. Going beyond the charge screening limitations by constraining the reaction space and reducing the double electrical layer thickness allows for chemical processes flow along otherwise not accessible reaction pathways.

Unravelling the Origin of the Vibronic Spectral Signatures in an Excitonically Coupled Indocarbocyanine Cy3 Dimer

The indocarbocyanine Cy3 dye is widely used to probe the dynamics of proteins and DNA. Excitonically coupled Cy3 dimers exhibit very unique spectral signatures that depend on the interchromophoric geometrical orientation induced by the environment, making them powerful tools to infer the dynamics of their surroundings. Understanding the origin of the dimeric spectral signatures is a necessity for an accurate interpretation of the experimental results. In this work, we simulate the vibronic spectrum of an experimentally well-studied Cy3 dimer, and we explain the origin of the experimental signatures present in its linear absorption spectrum. The Franck-Condon harmonic approximations, among other tests, are used to probe the factors contributing to the spectrum. It is found that the first peak in the absorption spectrum originates from the lower energy excitonic state, while the next two peaks are vibrational progressions of the higher energy excitonic state. The polar solvent plays a crucial role in the appearance of the spectrum, being responsible for the localized S1 minimum, which results in an increased intensity of the first peak.

FCclasses3: Vibrationally-resolved spectra simulated at the edge of the harmonic approximation

We introduce FCclasses3, a code to carry out vibronic simulations of electronic spectra and nonradiative rates, based on the harmonic approximation. Key new features are: implementation of the full family of vertical and adiabatic harmonic models, vibrational analysis in curvilinear coordinates, extension to several electronic spectroscopies and implementation of time-dependent approaches. The use of curvilinear valence internal coordinates allows the adoption of quadratic model potential energy surfaces (PES) of the initial and final states expanded at arbitrary configurations. Moreover, the implementation of suitable projectors provides a robust framework for defining reduced-dimensionality models by sorting flexible coordinates out of the harmonic subset, so that they can then be treated at anharmonic level, or with mixed quantum classical approaches. A set of tools to facilitate input preparation and output analysis is also provided. We show the program at work in the simulation of different spectra (one and two-photon absorption, emission and resonance Raman) and internal conversion rate of a typical rigid molecule, anthracene. Then, we focus on absorption and emission spectra of a series of flexible polyphenyl molecules, highlighting the relevance of some of the newly implemented features. The code is freely available at http://www.iccom.cnr.it/en/fcclasses/.

Predicting the Electronic Absorption Band Shape of Azobenzene Photoswitches

Simulations based on molecular dynamics coupled to excitation energy calculations were used to generate simulated absorption spectra for a family of halide derivatives of azobenzene, a family of photoswitch molecules with a weak absorption band around 400-600 nm and potential uses in living tissue. This is a case where using the conventional approach in theoretical spectroscopy (estimation of absorption maxima based on the vertical transition from the potential energy minimum on the ground electronic state) does not provide valid results that explain how the observed band shape extends towards the low energy region of the spectrum. The method affords a reasonable description of the main features of the low-energy UV-Vis spectra of these compounds. A bathochromic trend was detected linked to the size of the halide atom. Analysis of the excitation reveals a correlation between the energy of the molecular orbital where excitation starts and the energy of the highest occupied atomic orbital of the free halide atom. This was put to the test with a new brominated compound with good results. The energy level of the highest occupied orbital on the free halide was identified as a key factor that strongly affects the energy gap in the photoswitch. This opens the way for the design of bathochromically shifted variants of the photoswitch with possible applications.

Metal complexes of benzimidazole-derived as potential anti-cancer agents: synthesis, characterization, combined experimental and computational studies

In this study, a series of 14 Cu (II), Zn (II), Ni (II) and Ag (I) complexes containing bis-benzimidazole derivatives were successfully designed and synthesized from 2-(1H-benzimidazole-2-yl)-phenol derivatives and corresponding metal salt solutions. The compound structures were identified by FT-IR, ¹H-NMR, powder X-ray diffraction and ESI-MS analyses, and the presence of the metal in the complexes was confirmed by ultraviolet-visible spectroscopy and ICP optical emission spectrometry. Electronic structure calculations were also carried out to describe the detailed structures in addition to the electronic absorption spectra of the ligands. The cytotoxic activity of the complexes was evaluated against three human cancer cell lines: lung (A549), breast (MDA-MB-231) and prostate (PC3) cancer cells. All complexes inhibited anti-proliferative cancer cells better than free ligands, especially Zn (II) and Ag (I) complexes, which are most sensitive to MDA-MB-231 cells. In addition, showing the growth inhibition of three cancer cell lines with IC₅₀ < 10.4 µM, complexes C₁ , C₃ and C₁₄ could be considered potential multi-targeted anti-cancer agents.

Metal complexes of benzimidazole-derived as potential anti-cancer agents: synthesis, characterization, combined experimental and computational studies

In this study, a series of 14 Cu (II), Zn (II), Ni (II) and Ag (I) complexes containing bis-benzimidazole derivatives were successfully designed and synthesized from 2-(1H-benzimidazole-2-yl)-phenol derivatives and corresponding metal salt solutions. The compound structures were identified by FT-IR, ¹H-NMR, powder X-ray diffraction and ESI-MS analyses, and the presence of the metal in the complexes was confirmed by ultraviolet-visible spectroscopy and ICP optical emission spectrometry. Electronic structure calculations were also carried out to describe the detailed structures in addition to the electronic absorption spectra of the ligands. The cytotoxic activity of the complexes was evaluated against three human cancer cell lines: lung (A549), breast (MDA-MB-231) and prostate (PC3) cancer cells. All complexes inhibited anti-proliferative cancer cells better than free ligands, especially Zn (II) and Ag (I) complexes, which are most sensitive to MDA-MB-231 cells. In addition, showing the growth inhibition of three cancer cell lines with IC₅₀ < 10.4 µM, complexes C₁ , C₃ and C₁₄ could be considered potential multi-targeted anti-cancer agents.

Modeling the Electronic Absorption Spectra of the Indocarbocyanine Cy3

Accurate modeling of optical spectra requires careful treatment of the molecular structures and vibronic, environmental, and thermal contributions. The accuracy of the computational methods used to simulate absorption spectra is limited by their ability to account for all the factors that affect the spectral shapes and energetics. The ensemble-based approaches are widely used to model the absorption spectra of molecules in the condensed-phase, and their performance is system dependent. The Franck–Condon approach is suitable for simulating high resolution spectra of rigid systems, and its accuracy is limited mainly by the harmonic approximation. In this work, the absorption spectrum of the widely used cyanine Cy3 is simulated using the ensemble approach via classical and quantum sampling, as well as, the Franck–Condon approach. The factors limiting the ensemble approaches, including the sampling and force field effects, are tested, while the vertical and adiabatic harmonic approximations of the Franck–Condon approach are also systematically examined. Our results show that all the vertical methods, including the ensemble approach, are not suitable to model the absorption spectrum of Cy3, and recommend the adiabatic methods as suitable approaches for the modeling of spectra with strong vibronic contributions. We find that the thermal effects, the low frequency modes, and the simultaneous vibrational excitations have prominent contributions to the Cy3 spectrum. The inclusion of the solvent stabilizes the energetics significantly, while its negligible effect on the spectral shapes aligns well with the experimental observations.

Effect of extended defects on photoluminescence of gallium oxide and aluminum gallium oxide epitaxial films

In this work, a systematic photoluminescence (PL) study on three series of gallium oxide/aluminum gallium oxide films and bulk single crystals is performed including comparing doping, epitaxial substrates, and aluminum concentration. It is observed that blue/green emission intensity strongly correlates with extended structural defects rather than the point defects frequently assumed. Bulk crystals or Si-doped films homoepitaxially grown on (010) β-Ga₂O₃ yield an intense dominant UV emission, while samples with extended structural defects, such as gallium oxide films grown on either (-201) β-Ga₂O₃ or sapphire, as well as thick aluminum gallium oxide films grown on either (010) β-Ga₂O₃ or sapphire, all show a very broad PL spectrum with intense dominant blue/green emission. PL differences between samples and the possible causes of these differences are analyzed. This work expands previous reports that have so far attributed blue and green emissions to point defects and shows that in the case of thin films, extended defects might have a prominent role in emission properties.

How to Predict Excited State Geometry by Using Empirical Parameters Obtained from Franck-Condon Analysis of Optical Spectrum

Excited state geometries of molecules can be calculated with highly reliable wavefunction schemes. Most of such schemes, however, are applicable to small molecules and can hardly be viewed as error-free for excited state geometries. In this study, a theoretical approach is presented in which the excited state geometries of molecules can be predicted by using vibrationally resolved experimental absorption spectrum in combination with the theoretical modelling of vibrational pattern based on Franck-Condon approximation. Huang-Rhys factors have been empirically determined and used as input for revealing the structural changes occurring between the ground and the excited state geometries upon photoexcitation. Naphthalene molecule has been chosen as a test case to show the robustness of the proposed theoretical approach. Predicted 1B_2u excited state geometry of the naphthalene has similar but slightly different bond length alternation pattern when compared with the geometries calculated with CIS, B3LYP, and CC2 methods. Excited state geometries of perylene and pyrene molecules are also determined with the presented theoretical approach. This powerful method can be applied to other molecules and specifically to relatively large molecules rather easily as long as vibrationally resolved experimental spectra are available to use.

Multiscale Modeling of Electronic Spectra Including Nuclear Quantum Effects

Theoretical prediction of electronic absorption spectra without input from experiments is no easy feat, as it requires addressing all of the factors that affect line shapes. In practice, however, the methodologies are limited to treat these ingredients only to a certain extent. Here, we present a multiscale protocol that addresses the temperature, solvent, and nuclear quantum effects as well as anharmonicity and the reconstruction of the final spectra from individual transitions. First, quantum mechanics/molecular mechanics (QM/MM) molecular dynamics is conducted to obtain trajectories of solute-solvent configurations, from which the corresponding quantum-corrected ensembles are generated through the generalized smoothed trajectory analysis (GSTA). The optical spectra of the ensembles are then produced by calculating vertical transitions using time-dependent density-functional theory (TDDFT) with implicit solvation. To obtain the final spectral shapes, the stick spectra from TDDFT are convoluted with Gaussian kernels where the half-widths are determined by a statistically motivated strategy. We have tested our method by calculating the UV-vis spectra of a recently discovered acridine photocatalyst in two redox states. Vibronic progressions and broadenings due to the finite lifetime of the excited states are not included in the methodology yet. Nuclear quantization affects the relative peak intensities and widths, which is necessary to reproduce the experimental spectrum. We have also found that using only the optimized geometry of each molecule works surprisingly well if a proper empirical broadening factor is applied. This is explained by the rigidity of the conjugated chromophore moieties of the selected molecules, which are mainly responsible for the excitations in the spectra. In contrast, we have also shown that other parts of the molecules are flexible enough to feature anharmonicities that impair the use of other techniques such as Wigner sampling.

Vibronic and Environmental Effects in Simulations of Optical Spectroscopy

Including both environmental and vibronic effects is important for accurate simulation of optical spectra, but combining these effects remains computationally challenging. We outline two approaches that consider both the explicit atomistic environment and the vibronic transitions. Both phenomena are responsible for spectral shapes in linear spectroscopy and the electronic evolution measured in nonlinear spectroscopy. The first approach utilizes snapshots of chromophore-environment configurations for which chromophore normal modes are determined. We outline various approximations for this static approach that assumes harmonic potentials and ignores dynamic system-environment coupling. The second approach obtains excitation energies for a series of time-correlated snapshots. This dynamic approach relies on the accurate truncation of the cumulant expansion but treats the dynamics of the chromophore and the environment on equal footing. Both approaches show significant potential for making strides toward more accurate optical spectroscopy simulations of complex condensed phase systems.

Herzberg-Teller Effect on the Vibrationally Resolved Absorption Spectra of Single-Crystalline Pentacene at Finite Temperatures

The line shape of an electronic spectrum conveys the coupling between electronic and vibrational degrees of freedom. In the present study, the light absorption spectra of single-crystalline pentacene were measured by polarized UV-vis microscopy at 77, 185, and 293 K. The vibronic coupling encoded in each spectrum was resolved by the Herzberg-Teller theory that considers the contributions from the Franck-Condon (FC) factor, Franck-Condo/Herzberg-Teller (FC/HT) interference, and Herzberg-Teller (HT) coupling. Specifically, excitation energies, electronic transition dipole moments, and their nuclear gradients were evaluated by the GW method to ensure numerical accuracy, while the computationally efficient density function theory was employed to determine the optimized structures and vibrational normal modes. For every pair of electronic transition and normal mode that gives rise to a strong vibronic transition intensity, we examined their spatial characteristics by projecting them onto the three crystal axes. It was found that all normal modes strongly coupled to the lowest-lying a-polarized electronic transitions oscillate along axis a, whereas none of their counterparts for the lowest-lying b-polarized electronic transitions is predominantly along axis b. This notable difference on the alignment between the electronic transition and molecular vibration could help the directional control of charge dissociation and/or spin separation. Moreover, a significant variance of the destructive FC/HT interference was discovered with increasing temperatures that can well explain the a-polarized fading tableland near 650 nm. Finally, the importance of HT coupling was corroborated by comparing its intensity with those of FC factor and FC/HT interference. Taken all together, the vibrational dependence of the electronic wave function is critical to resolve the light absorption spectra of single-crystalline pentacene and its temperature effects, facilitating the systematic design of functional optical materials based on pentacene and its derivatives.

Methyl substitution effects on the non-adiabatic dynamics of benzene: lifting three-state quasi-degeneracy at conical intersections

Previously, theoretical calculations on the non-adiabatic dynamics of benzene from the S₂ state have indicated that the S₂/S₁ and S₁/S₀ conical intersections (CIs) facilitate ballistic nuclear wavepacket motion from S₂ to S₀ (fast channel) and branching to S₁ (slow channel). In this paper, we present time-resolved photoelectron spectra of benzene and its methyl-derivatives (toluene and o-xylene) measured with a vacuum-UV laser, which clearly reveal both the fast and slow channels. The extremely short propagation time of the wavepacket between the two CIs of benzene indicates that the two are in close proximity to each other, while methyl substitution extends the propagation time and decreases the branching ratio into the fast channel. The results suggest that the quasi-degeneracy of the three states in benzene is lifted by the geometrical shifts of the CIs by methyl substitution.

Optical signatures of pentacene in soft rare-gas environments

Acenes and pentacene (Pc), in particular, are promising candidates for organic dyes with interesting properties important for solar light to energy conversion. We present a combined experimental and computational study of Pc in an ultracold environment that allows for high resolution optical spectroscopy. The spectra and their vibrational substructure are interpreted with the help of density functional theory calculations. While there are only slight changes within superfluid helium as compared to vacuum, the neon surface shows more prominent effects. Additional vibrational coupling by neon modes leads to broadening as well as the emergence of new features, like the otherwise symmetry forbidden out-of-plane butterfly mode.

Assessment of MC-PDFT Excitation Energies for a Set of QM/MM Models of Rhodopsins

A methodology for the automatic production of quantum mechanical/molecular mechanical (QM/MM) models of retinal-binding rhodopsin proteins and subsequent prediction of their spectroscopic properties has been proposed recently by some of the authors. The technology employed for the evaluation of the excitation energies is called Automatic Rhodopsin Modeling (ARM), and it involves the use of the complete active space self-consistent field (CASSCF) method followed by a multiconfiguration second-order perturbation theory (in particular, CASPT2) calculation of external correlation energies. Although it was shown that ARM is capable of successfully reproducing and predicting spectroscopic property trends in chromophore-embedding protein sets, practical applications of such technology are limited by the high computational costs of the multiconfiguration perturbation theory calculations. In the present work we benchmark the more affordable multiconfiguration pair-density functional theory (MC-PDFT) method whose accuracy has been recently validated for retinal chromophores in the gas phase, indicating that MC-PDFT could potentially be used to analyze large (e.g., few hundreds) sets of rhodopsin proteins. Here, we test this theory for a set of rhodopsin QM/MM models whose experimental absorption maxima (λ a max) have been measured. The results indicate that MC-PDFT may be employed to calculate λ a max values for this important class of photoresponsive proteins.

The importance of nuclear quantum effects in spectral line broadening of optical spectra and electrostatic properties in aromatic chromophores

In this work, we examine the importance of nuclear quantum effects on capturing the line broadening and vibronic structure of optical spectra. We determine the absorption spectra of three aromatic molecules indole, pyridine, and benzene using time dependent density functional theory with several molecular dynamics sampling protocols: force-field based empirical potentials, ab initio simulations, and finally path-integrals for the inclusion of nuclear quantum effects. We show that the absorption spectrum for all these chromophores are similarly broadened in the presence of nuclear quantum effects regardless of the presence of hydrogen bond donor or acceptor groups. We also show that simulations incorporating nuclear quantum effects are able to reproduce the heterogeneous broadening of the absorption spectra even with empirical force fields. The spectral broadening associated with nuclear quantum effects can be accounted for by the broadened distribution of chromophore size as revealed by a particle in the box model. We also highlight the role that nuclear quantum effects have on the underlying electronic structure of aromatic molecules as probed by various electrostatic properties.

Excitation spectra of retinal by multiconfiguration pair-density functional theory

Retinal is the chromophore in proteins responsible for vision. The absorption maximum of retinal is sensitive to mutations of the protein. However, it is not easy to predict the absorption spectrum of retinal accurately, and questions remain even after intensive investigation. Retinal poses a challenge for Kohn-Sham density functional theory (KS-DFT) because of the charge transfer character in its excitations, and it poses a challenge for wave function theory because the large size of the molecule makes multiconfigurational perturbation theory methods expensive. In this study, we demonstrate that multiconfiguration pair-density functional theory (MC-PDFT) provides an efficient way to predict the vertical excitation energies of 11-Z retinal, and it reproduces the experimentally determined absorption band widths and peak positions better than complete active space second-order perturbation theory (CASPT2). The consistency between complete active space self-consistent field (CASSCF) and KS-DFT dipole moments is demonstrated to be a useful criterion in selecting the active space. We also found that the nature of the terminal groups and the conformations of retinal play a significant role in the absorption spectrum. By considering a thermal distribution of conformations, we predict an absorption spectrum of retinal that is consistent with the experimental gas-phase spectrum. The location of the absorption peak and the spectral broadening based on MC-PDFT calculations agree better with experiments than those of CASPT2.

Vibronic relaxation energies of acene-related molecules upon excitation or ionization

Effective-mode Franck–Condon parameters evaluation for excited state ionization from the corresponding excitation and ground-state ionization values leads to substantial errors.