Fabrizio Santoro

Effective method to compute Franck-Condon integrals for optical spectra of large molecules in solution

The authors present a new method for the computation of vibrationally resolved optical spectra of large molecules, including the Duschinsky [Acta Physicochim. URSS 7, 551 (1937)] rotation of the normal modes. The method automatically selects the relevant vibronic contributions to the spectrum, independent of their frequency, and it is able to provide fully converged spectra with a quite modest computational time, both in vacuo and in condensed phase. Starting from the rigorous time-dependent expression they discuss indeed in which limits the spectrum of a molecule embedded in a solvent, described as a polarizable continuum, can be computed in a time-independent formalism, defining both nonequilibrium and equilibrium limits. In these cases the polarizable continuum model provides a suitable description of the solvent field. By computing the absorption spectra of anthracene in gas phase and of coumarin C153 in gas phase and cyclohexane, and the phosphorescence spectrum of the unsubstituted coumarin in ethanol they show that the method is fast and efficient.

Effective method for the computation of optical spectra of large molecules at finite temperature including the Duschinsky and Herzberg–Teller effect: The Qx band of porphyrin as a case study

The authors extend their recent method for the computation of vibrationally resolved optical spectra of large molecules, including both the Duschinsky rotation and the effect of finite temperature in the framework of the Franck-Condon (FC) approximation, to deal with the more general case of the Herzberg-Teller (HT) model, where also the linear dependence of the transition dipole moment on the nuclear coordinates is taken into account. This generalization allows us to investigate weak and vibronically allowed transitions by far extending the range of application of the method. The calculation of the spectra of sizable molecules is computationally demanding because of the huge number of final vibrational states that must be taken into account, and the inclusion of HT terms further increases the computational burden. The method presented here automatically selects the relevant vibronic contributions to the spectrum, independent of their frequency, and it is able to provide fully converged spectra with a modest computational requirement. The effectiveness of the method is illustrated by computing the HT absorption and fluorescence Q(x) spectra of free-base porphyrin both at T=0 K and at room temperature, performing for the first time an exact treatment of vibrations in harmonic approximation. Q(x) spectra are compared to experiments and FC/HT interferences are analyzed in detail.

Effective method to compute vibrationally resolved optical spectra of large molecules at finite temperature in the gas phase and in solution

The authors present a new method for the computation of vibrationally resolved optical spectra of large molecules, including the Duschinsky rotation of the normal modes and the effect of thermal excitation. The method automatically selects the relevant vibronic contributions to the spectrum, independently of their frequency, and it is able to provide fully converged spectra with moderate computational times, both in vacuo and in solution. By describing the electronic states in the frame of the density functional theory and its time-dependent extension, they computed the room temperature absorption spectra of coumarin C153 and trans-stilbene in cyclohexane and the phosphorescence spectrum of porphyrazine in gas phase, showing that the method is fast and efficient. The comparison with experiment for trans-stilbene and coumarin C153 is very satisfactory, confirming the progress made toward a reliable method for the computation and interpretation for the optical spectra of large molecules.

Tracking the excited-state time evolution of the visual pigment with multiconfigurational quantum chemistry

The primary event that initiates vision is the photoinduced isomerization of retinal in the visual pigment rhodopsin (Rh). Here, we use a scaled quantum mechanics/molecular mechanics potential that reproduces the isomerization path determined with multiconfigurational perturbation theory to follow the excited-state evolution of bovine Rh. The analysis of a 140-fs trajectory provides a description of the electronic and geometrical changes that prepare the system for decay to the ground state. The data uncover a complex change of the retinal backbone that, at ≈60-fs delay, initiates a space saving “asynchronous bicycle-pedal or crankshaft” motion, leading to a conical intersection on a 110-fs time scale. It is shown that the twisted structure achieved at decay features a momentum that provides a natural route toward the photoRh structure recently resolved by using femtosecond-stimulated Raman spectroscopy.

Quantum Mechanical Studies on the Photophysics and the Photochemistry of Nucleic Acids and Nucleobases

The photophysics and photochemistry of DNA is of great importance due to the potential damage of the genetic code by UV light. Quantum mechanical studies have played a key role in interpretating the results of modern time-resolved pump-probe spectroscopy, and in elucidating the main photoactivated reactive paths. This review provides a concise, complete picture of the computational studies carried out, approximately, in the past decade. We start with an overview of the photophysics of the nucleobases in the gas phase and in solution. We discuss the proposed mechanisms for ultrafast decay to the ground state, that involve conical intersections, consider the role of triplet states, and analyze how the solvent modulates the photophysics. Then we move to larger systems, from dinucleotides to single- and double-stranded oligonucleotides. We focus on the possible role of charge transfer and delocalized or excitonic states in the photophysics of these systems and discuss the main photochemical paths. We finish with an outlook on the current challenges in the field and future directions of research.

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, EV, and characteristic frequencies of the spectrum like the maximum, ν(max), and the center of gravity, M(1), taking advantage of an analytical expression of M(1) 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 ν(max) and computational EV, 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 0.1-0.3 eV, i.e., values comparable to the expected accuracy of the most accurate computational methods. On the contrary, a comparison of experimental and computed M(1) and/or 0-0 transition frequencies provides more robust results. Some rules of thumbs are proposed to help rationalize which kind of correction one should expect when comparing EV, M(1), and ν(max).

Influence of base stacking on excited-state behavior of polyadenine in water, based on time-dependent density functional calculations

A thorough study of the excited-state properties of the stacked dimers and trimers of 9-methyladenine in B-DNA conformation has been performed in aqueous solution by using time-dependent density functional calculations and the solvent polarizable continuum model, and results were compared with experimental results on polyadenine oligomers. The effect of base stacking on the absorption and emission spectra is fully reproduced by our calculations. Although light absorption leads to a state (SB) delocalized over several nucleobases, excited-state geometry optimization indicates that SB subsequently evolves into a state in which the excitation is localized on a single base. Analysis of the excited-state potential energy surfaces shows that SB can easily decay into the lowest energy excited state, SCT, which is a dark excimer produced by intermonomer charge transfer between two stacked bases. The subpicosecond features of the time-resolved experiments are interpreted in terms of ultrafast decay from SB. After localization, two easy, radiationless decay channels are indeed open for SB: (i) ground-state recovery, according to the same mechanisms proposed for isolated adenine and/or (ii) decay to SCT. Our calculations suggest that the slowest part of the excited-state dynamics detected experimentally involves the SCT state.

Computing the inhomogeneous broadening of electronic transitions in solution: a first-principle quantum mechanical approach

Starting from Marcuss relationship connecting the inhomogeneous broadening with the solvent reorganization energy and exploiting recent state-specific developments in PCM/TD-DFT calculations, we propose a procedure to estimate the polar broadening of optical transitions. When applied to two representative molecular probes, coumarin C153 and 4-aminophthalimide, in different solvents, our approach provides for the polar broadening values fully consistent with the experimental ones. Thanks to these achievements, for the first time fully ab initio vibrationally resolved absorption spectra in solution are computed, obtaining spectra for coumarin C153 in remarkable agreement with experiments.

An artificial molecular switch that mimics the visual pigment and completes its photocycle in picoseconds

Single molecules that act as light-energy transducers (e.g., converting the energy of a photon into atomic-level mechanical motion) are examples of minimal molecular devices. Here, we focus on a molecular switch designed by merging a conformationally locked diarylidene skeleton with a retinal-like Schiff base and capable of mimicking, in solution, different aspects of the transduction of the visual pigment Rhodopsin. Complementary ab initio multiconfigurational quantum chemistry-based computations and time-resolved spectroscopy are used to follow the light-induced isomerization of the switch in methanol. The results show that, similar to rhodopsin, the isomerization occurs on a 0.3-ps time scale and is followed by <10-ps cooling and solvation. The entire (2-photon-powered) switch cycle was traced by following the evolution of its infrared spectrum. These measurements indicate that a full cycle can be completed within 20 ps.

Comparison of vertical and adiabatic harmonic approaches for the calculation of the vibrational structure of electronic spectra

The calculation of the vibrational structure associated to electronic spectra in large molecules requires a Taylor expansion of the initial and final state potential energy surface (PES) around some reference nuclear structure. Vertical (V) and adiabatic (A) approaches expand the final state PES around the initial-state (V) or final-state (A) equilibrium structure. Simplest models only take into account displacements of initial- and final-state minima, intermediate ones also allow for difference in frequencies and more accurate models introduce the Dushinsky effect through the computation of the Hessians of both the initial and final state. In this contribution we summarize and compare the mathematical expressions of the complete hierarchy of V and A harmonic models and we implement them in a numerical code, presenting a detailed comparison of their performance on a number of prototypical systems. We also address non-Condon effects through linear expansions of the transition dipole as a function of nuclear coordinates (Herzberg-Teller effect) and compare the results of expansions around initial and final state equilibrium geometries. By a throughout analysis of our results we highlight a number of general trends in the relative performance of the models that can provide hints for their proper choice. Moreover we show that A and V models including final state PES Hessian outperform the simpler ones and that discrepancies in their predictions are diagnostic for failure of harmonic approximation and/or of Born-Oppenheimer approximation (existence of remarkable geometry-dependent mixing of electronic states).