Resonance Raman and vibronic absorption spectra with Duschinsky rotation from a time-dependent perspective: Application to β-carotene

Nonadiabatic Photodynamics of Amantadine and1-Cyanoadamantane Cations

Cations of diamondoids and derivatives thereof have recently become the subject of experimental, spectroscopic studies due to their potential role in astrochemistry. In particular, their electronic spectra and photoinduced dynamics trigger great interest. Here, we report on computational investigations of two nitrogen-containing derivatives of the adamantane cation (Ada+,C 10 H 16 + ${{\rm{C}}_{10} {\rm{H}}_{16}^+ }$ ), the amantadine cation (Ama+,C 10 H 15 NH 2 + ${{\rm{C}}_{10} {\rm{H}}_{15} {\rm{NH}}_2^+ }$ and the 1-cyanoadamantane cation (Ada-CN+, C10H15CN+). Specifically, we study electronic (vibrationally resolved) spectra and nonadiabatic molecular dynamics (modeled using the surface hopping approach based on semiempirical electronic structure theory) of these radical cations. The internal conversion time constants as well as reactive relaxation outcomes (cage-opening and hydrogen loss) are compared for the two derivatives and also with the case of Ada+ [29] Remarkably, we find a longer ground-state recovery time for Ada-CN+ than for Ama+ (for the same excitation energy window), despite a smaller excitation energy for the former. Thus, a static energy gap law cannot be used to rationalize nonadiabatic dynamics and excited state lifetimes in this case: Dynamics and details of the couplings between several states play a decisive role.

Nonadiabatic Vibrational Resonance Raman Spectra from Quantum Dynamics Propagations with LVC Models. Application to Thymine

We present a viable protocol to compute vibrational resonance Raman (vRR) spectra for systems with several close-lying and potentially coupled electronic states. It is based on the parametrization of linear vibronic coupling (LVC) models from time-dependent density functional theory (TD-DFT) calculations and quantum dynamics propagations of vibronic wavepackets with the multilayer version of the multiconfiguration time-dependent Hartree (ML-MCTDH) method. Our approach is applied to thymine considering seven coupled electronic states, comprising the three lowest bright states, and all vibrational coordinates. Computed vRR at different excitation wavelengths are in good agreement with the available experimental data. Up to 250 nm the signal is dominated by the lowest HOMO → LUMO transition, whereas at 233 nm, in the valley between the two lowest energy absorption bands, the contributions of all the three bright states, and their interferences and couplings, are important. Inclusion of solvent (water) effects improves the agreement with experiment, reproducing the coalescence of vibrational bands due to CC and C═O stretchings. With our approach we disentangle and assess the effect of interferences between the contribution of different quasi-resonant states to the transition polarizability and the effect of interstate couplings. Our findings strongly suggest that in cases of close-lying and potentially coupled states a simple inclusion of interference effects is not sufficient, and a fully nonadiabatic computation should instead be performed. We also document that for systems with strong couplings and quasi-degenerate states, the use of HT perturbative approach, not designed for these cases, may lead to large artifacts.

Franck-Condon spectra of unbound and imaginary-frequency vibrations via correlation functions: a branch-cut free, numerically stable derivation

Molecular electronic spectra can be represented in the time domain as auto-correlation functions of the initial vibrational wavepacket. We present a derivation of the harmonic vibrational auto-correlation function that is valid for both real and imaginary harmonic frequencies. The derivation rests on Lie algebra techniques that map otherwise complicated exponential operator arithmetic to simpler matrix formulae. The expressions for the zero- and finite-temperature harmonic auto-correlation functions have been carefully structured both to be free of branch-cut discontinuities and to remain numerically stable with finite-precision arithmetic. Simple extensions correct the harmonic Franck-Condon approximation for the lowest-order anharmonic and Herzberg-Teller effects. Quantitative simulations are shown for several examples, including the electronic absorption spectra of F2, HOCl, CH2NH, and NO2.

Efficient simulation of resonance Raman spectra with tight-binding approximations to Density Functional Theory

Resonance Raman spectroscopy has long been established as one of the most sensitive techniques for detection, structure characterization and probing the excited-state dynamics of biochemical systems. However, the analysis of resonance Raman spectra is much facilitated when measurements are accompanied by Density Functional Theory (DFT) calculations which are expensive for large biomolecules. In this work, resonance Raman spectra are therefore computed with the Density Functional Tight-Binding (DFTB) method in the time-dependent excited-state gradient approximation. To test the accuracy of the tight-binding approximations, this method is first applied to typical resonance Raman benchmark molecules like β-carotene and compared to results obtained with pure and range-separated exchange-correlation (xc) functionals. We then demonstrate the efficiency of the approach by considering a computationally challenging heme variation. Overall, we find that the vibrational frequencies and excited-state properties (energies and gradients) which are needed to simulate the spectra are reasonably accurate and suitable for interpretation of experiments. We can therefore recommend DFTB as a fast computational method to interpret resonance Raman spectra.

Excited state geometry of β-carotene influenced by environments: the nature and decisive role of solvent revealing by two-dimensional resonance Raman correlation spectroscopy

Resonance Raman scattering can be used to investigate the ground and excited state information of carotenoid. It is known that the Dushinsky rotation can significantly influence the resonant Raman intensity of β-carotene (β-car). The excited state geometry revealed by the double components feature of the C = C stretching vibrational modes and the environmental dependence of the Raman intensity for each component remain unknown. We explore the influence of environmental factors on the relative intensity of these two C = C stretching vibration modes and perform two-dimensional resonance Raman correlation analysis to reveal the changes on β-car excited state geometry. The results show that the relative wavelength difference between the 0-0 absorption and the excitation is the key factor that decides the intensity ratio of the two components and that the intensity of each mode is modulated by environmental factors. This modulation is closely related to the excited state geometry and dynamics, effective conjugation length, and electron-phonon coupling constant. It also shows that the asynchronous cross-peaks in the two-dimensional resonance Raman correlation spectrum (2DRRCOS) can effectively characterize the degree of the varied electron-phonon coupling with the changing conditions. These results are not only complementary to the research on the excited states of carotenoids but also applicable to investigate the environmental dependence of Raman intensity for a lot of π-conjugated molecules.

Role of Explicit Solvation in the Simulation of Resonance Raman Spectra within Short-Time Dynamics Approximation

In short-time dynamics approximation, relative resonance Raman (RR) intensity of a vibrational mode primarily depends on the magnitude of square of the excited-state gradient along the corresponding normal coordinate, ground-state normal mode eigenvector, and harmonic vibrational wavenumbers. In this study, through simulation of RR spectra of guanosine-5'-monophosphate (GMP) in two ππ* singlet excited states, we analyze how the explicitly hydrogen-bonded local solvation structure of the chromophore dictates intensities of the RR active modes in an unprecedented manner. We show that the accuracy of the structural model of solvated chromophore plays a decisive role in determining an optimal theoretical method for prediction of the Franck-Condon region of the ππ* excited states. 9-Methylguanine (9-meG) in complex with six water molecules (9-meG·6H₂O) is found out to be the most accurate one for describing GMP in two different bright electronic states. We find that explicit hydrogen-bonded water molecules strongly influence computed RR intensities of GMP by modulating both the ground-state normal mode vectors and the excited-state energy gradients. We find that simultaneous inclusion of six explicit waters to describe the solute-solvent interaction near all hydration sites is essential for reliable prediction of the features of RR spectra in L_b and B_b electronic states of GMP.

Vibrationally Broadened Optical Spectra of Selected Radicals and Cations Derived from Adamantane: A Time-Dependent Correlation Function Approach

Diamondoids are hydrogen-saturated molecular motifs cut out of diamond, forming a class of materials with tunable optoelectronic properties. In this work, we extend previous work on neutral, closed-shell diamondoids by computing with hybrid density functional theory and time-dependent correlation functions vibrationally broadened absorption spectra of cations and radicals derived from the simplest diamondoid, adamantane, namely, the neutral 1- and 2-adamantyl radicals (C₁₀H₁₅), the 1- and 2-adamantyl cations (C₁₀H₁₅⁺), and the adamantane radical cation (C₁₀H₁₆⁺). For selected cases, we also report vibrationally broadened emission, photoelectron, and resonance Raman spectra. Furthermore, the effect of the damping factor on the vibrational fine-structure is studied. The following trends are found: (1) Low-energy absorptions of the adamantyl radicals and cations, and of the adamantane cation, are all strongly red-shifted with respect to adamantane; (2) also, emission spectra are strongly red-shifted, whereas photoelectron spectra are less affected for the cases studied; (3) vibrational fine-structures are reduced compared to those of adamantane; (4) the spectroscopic signals of 1- and 2-adamantyl species are significantly different from each other; and (5) reducing the damping factor has only a limited effect on the vibrational fine-structure in most cases. This suggests that removing hydrogen atoms and/or electrons from adamantane leads to new optoelectronic properties, which should be detectable by vibronic spectroscopy.

Vibrational Relaxation in Carotenoids as an Explanation for Their Rapid Optical Properties

We propose the ultrafast S₂ (1B_u) to S₁ (2A_g) "electronic internal conversion" observed in carotenoids to be a vibrational relaxation of the 1B_u state. This suggestion arises from comparing excited-state geometries computed with the CAM-B3LYP density functional to the ground states; it is found that each conjugated atom moves less than 5 pm in, for example, violaxanthin. However, the changes of excitation energies are large, ranging from 0.4 to 1.2 eV. This is connected to the size of the conjugated system: while each atom contributes only 0.02-0.06 eV, the sum amounts to the observed shift. Additional analysis of computational data is provided from new or already published calculations. As the mechanism may be valid for all linear polyenes, the model has implications that go beyond the presented case of carotenoids. Finally, four sets of experimental data on carotenoids published elsewhere are reinterpreted. The model predicts near-infrared (IR) absorptions and transient femtosecond IR spectra within 0.1 eV accuracy.

Time-Dependent Formulation of Resonance Raman Optical Activity Spectroscopy

In this work, we extend the theoretical framework recently developed for the simulation of resonance Raman (RR) spectra of medium-to-large sized systems to its chiral counterpart, namely, resonance Raman optical activity (RROA). The theory is based on a time-dependent (TD) formulation, with the transition tensors obtained as half-Fourier transforms of the appropriate cross-correlation functions. The implementation has been kept as general as possible, supporting adiabatic and vertical models for the PES representation, both in Cartesian and internal coordinates, with the possible inclusion of Herzberg-Teller (HT) effects. Thanks to the integration of this TD-RROA procedure within a general-purpose quantum-chemistry program, both solvation and leading anharmonicity effects can be included in an effective way. The implementation is validated on one of the smallest chiral molecule (methyloxirane). Practical applications are illustrated with three medium-size organic molecules (naproxen-OCD₃, quinidine and 2-Br-hexahelicene), whose simulated spectra are compared to the corresponding experimental data.

Assessment of Franck-Condon Methods for Computing Vibrationally Broadened UV-vis Absorption Spectra of Flavin Derivatives: Riboflavin, Roseoflavin, and 5-Thioflavin

We address the performance of the vertical and adiabatic Franck-Condon (VFC/AFC) approaches combined with time-independent or time-dependent (TI/TD) formalisms in simulating the one-photon absorption spectra of three flavin compounds with distinct structural features. Calculations were done in the gas phase and in two solvents (water, benzene) for which experimental reference measurements are available. We utilized the independent mode displaced harmonic oscillator model without or with frequency alteration (IMDHO/IMDHO-FA) and also accounted for Duschinsky mixing effects. In the initial validation on the first excited singlet state of riboflavin, the range-separated functionals, CAM-B3LYP and ωB97xD, showed the best performance, but B3LYP also gave a good compromise between peak positions and spectral topology. Large basis sets were not mandatory to obtain high-quality spectra for the selected systems. The presence of a symmetry plane facilitated the computation of vibrationally broadened spectra, since different FC variants yield similar results and the harmonic approximation holds rather well. Compared with the AFC approach, the VFC approach performed equally well or even better for all three flavins while offering several advantages, such as avoiding error-prone geometry optimization procedures on excited-state surfaces. We also explored the advantages of curvilinear displacements and of a Duschinsky treatment for the AFC spectra in cases when a rotatable group is present on the chromophore. Taken together, our findings indicate that the combination of the VFC approach with the TD formalism and the IMDHO-FA model offers the best overall performance.

Vibrationally resolved optical spectra of modified diamondoids obtained from time-dependent correlation function methods

Optical properties of modified diamondoids have been studied theoretically using vibrationally resolved electronic absorption, emission and resonance Raman spectra. A time-dependent correlation function approach has been used for electronic two-state models, comprising a ground state (g) and a bright, excited state (e), the latter determined from linear-response, time-dependent density functional theory (TD-DFT). The harmonic and Condon approximations were adopted. In most cases origin shifts, frequency alteration and Duschinsky rotation in excited states were considered. For other cases where no excited state geometry optimization and normal mode analysis were possible or desired, a short-time approximation was used. The optical properties and spectra have been computed for (i) a set of recently synthesized sp(2)/sp(3) hybrid species with C[double bond, length as m-dash]C double-bond connected saturated diamondoid subunits, (ii) functionalized (mostly by thiol or thione groups) diamondoids and (iii) urotropine and other C-substituted diamondoids. The ultimate goal is to tailor optical and electronic features of diamondoids by electronic blending, functionalization and substitution, based on a molecular-level understanding of the ongoing photophysics.

Resonance Femtosecond-Stimulated Raman Spectroscopy without Actinic Excitation Showing Low-Frequency Vibrational Activity in the S2 State of All-Trans β-Carotene

Raman scattering with stimulating femtosecond probe pulses (FSR) was used to observe vibrational activity of all-trans β-carotene in n-hexane. The short-lived excited electronic state S2 was accessed in two ways: (i) by transient FSR after an actinic pulse to populate the S2 state, exploiting resonance from an Sx ← S2 transition, and (ii) by FSR without actinic excitation, using S2 ↔ S0 resonance exclusively and narrow-band Raman/broad-band femtosecond probe pulses only. The two approaches have nonlinear optical susceptibilities χ((5)) and χ((3)), respectively. Both methods show low-frequency bands of the S2 state at 200, 400, and ∼600 cm(-1), which are reported for the first time. With (ii) the intensities of low-frequency vibrational resonances in S2 are larger compared to those in S0, implying strong anharmonicities/mode mixing in the excited state. In principle, for short-lived electronic states, the χ((3)) method should allow the best characterization of low-frequency modes.

A spectroscopic study of the cis/trans-isomers of penta-2,4-dienoic acid attached to gold nanoclusters

We simulate how one can spectroscopically discriminate between cis/trans isomers of a molecular switch attached to gold nanoclusters.

A general time-dependent route to resonance-Raman spectroscopy including Franck-Condon, Herzberg-Teller and Duschinsky effects

We present a new formulation of the time-dependent theory of Resonance-Raman spectroscopy (TD-RR). Particular attention has been devoted to the generality of the framework and to the possibility of including different effects (Duschinsky mixing, Herzberg-Teller contributions). Furthermore, the effects of different harmonic models for the intermediate electronic state are also investigated. Thanks to the implementation of the TD-RR procedure within a general-purpose quantum-chemistry program, both solvation and leading anharmonicity effects have been included in an effective way. The reliability and stability of our TD-RR implementation are validated against our previously proposed and well-tested time-independent procedure. Practical applications are illustrated with some closed- and open-shell medium-size molecules (anthracene, phenoxyl radical, benzyl radical) and the simulated spectra are compared to the experimental results. More complex and larger systems, not limited to organic compounds, can be also studied, as shown for the case of Tris(bipyridine)ruthenium(II) chloride.

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

We present an effective time-independent implementation to model vibrational resonance Raman (RR) spectra of medium-large molecular systems with the inclusion of Franck-Condon (FC) and Herzberg-Teller (HT) effects and a full account of the possible differences between the harmonic potential energy surfaces of the ground and resonant electronic states. Thanks to a number of algorithmic improvements and very effective parallelization, the full computations of fundamentals, overtones, and combination bands can be routinely performed for large systems possibly involving more than two electronic states. In order to improve the accuracy of the results, an effective inclusion of the leading anharmonic effects is also possible, together with environmental contributions under different solvation regimes. Reduced-dimensionality approaches can further enlarge the range of applications of this new tool. Applications to imidazole, pyrene, and chlorophyll a1 in solution are reported, as well as comparisons with available experimental data.