Large Electron Transfer Rate Effects from the Duschinsky Mixing of Vibrations

Quantum dynamics of the photoinduced charge separation in a symmetric donor–acceptor–donor triad: The role of vibronic couplings, symmetry and temperature

The photoinduced charge separation in a symmetric donor–acceptor–donor (D–A–D) triad is studied quantum mechanically using a realistic diabatic vibronic coupling model. The model includes a locally excited DA*D state and two charge-transfer states D+A−D and DA−D+ and is constructed according to a procedure generally applicable to semirigid D–A–D structures and based on energies, forces, and force constants obtained by quantum chemical calculations. In this case, the electronic structure is described by time-dependent density functional theory, and the corrected linear response is used in conjunction with the polarizable continuum model to account for state-specific solvent effects. The multimode dynamics following the photoexcitation to the locally excited state are simulated by the hybrid Gaussian-multiconfigurational time-dependent Hartree method, and temperature effects are included using thermo field theory. The dynamics are connected to the transient absorption spectrum obtained in recent experiments, which is simulated and fully assigned from first principles. It is found that the charge separation is mediated by symmetry-breaking vibrations of relatively low frequency, which implies that temperature should be accounted for to obtain reliable estimates of the charge transfer rate.

Theoretical investigation of [Ru(bpy)2(HAT)]2+ (HAT = 1,4,5,8,9,12-hexaazatriphenylene; bpy = 2,2'-bipyridine): Photophysics and reactions in excited state

In this article, Density Functional Theory based calculations, including dispersion corrections, PBE0(D3BJ)/Def2-TZVP(-f), were performed to elucidate the photophysics of the [Ru(bpy)₂(HAT)]²⁺ complex in water. In addition, the thermodynamics of the charge and electron transfer excited state reactions of this complex with oxygen, nitric oxide and Guanosine-5'-monophosphate nucleotide (GMP) were investigated. The first singlet excite state, S₁, strongly couples with the second and third triplet excited states (T₂ and T₃) giving rise to a high intersystem crossing rate of 6.26 × 10¹¹ s^-1 which is ∼10⁶ greater than the fluorescence rate decay. The thermodynamics of the excited reactions revealed that all electron transfer reactions investigated are highly favorable, due mainly to the high stability of the triply charged radical cation ²PS^•3+ species formed after the electron has been transferred. Excited state electron transfer from the GMP nucleotide to the complex is also highly favorable (ΔG_sol = -92.6 kcal/mol), showing that this complex can be involved in the photooxidation of DNA, in line with experimental findings. Therefore, the calculations allow to conclude that the [Ru(bpy)₂(HAT)]²⁺ complex can act in Photodynamic therapy through both mechanisms type I and II, through electron transfer from and to the complex and triplet-triplet energy transfer, generating ROS, RNOS and through DNA photooxidation. In addition, the work also opens a perspective of using this complex for the in-situ generation of the singlet nitroxyl (¹NO^-) species, which can have important applications for the generation of HNO and may have, therefore, important impact for physiological studies involving HNO.

Simulation of Ab Initio Optical Absorption Spectrum of β-Carotene with Fully Resolved S0 and S2 Vibrational Normal Modes

The electronic absorption spectrum of β-carotene (β-Car) is studied using quantum chemistry and quantum dynamics simulations. Vibrational normal modes were computed in optimized geometries of the electronic ground state S₀ and the optically bright excited S₂ state using the time-dependent density functional theory. By expressing the S₂-state normal modes in terms of the ground-state modes, we find that no one-to-one correspondence between the ground- and excited-state vibrational modes exists. Using the ab initio results, we simulated the β-Car absorption spectrum with all 282 vibrational modes in a model solvent at 300 K using the time-dependent Dirac-Frenkel variational principle and are able to qualitatively reproduce the full absorption line shape. By comparing the 282-mode model with the prominent 2-mode model, widely used to interpret carotenoid experiments, we find that the full 282-mode model better describes the high-frequency progression of carotenoid absorption spectra; hence, vibrational modes become highly mixed during the S₀ → S₂ optical excitation. The obtained results suggest that electronic energy dissipation is mediated by numerous vibrational modes.

Multimode two-dimensional vibronic spectroscopy. I. Orientational response and polarization-selectivity

Two-dimensional Electronic-Vibrational (2D EV) spectroscopy and two-dimensional Vibrational-Electronic (2D VE) spectroscopy are among the newest additions to the coherent multidimensional spectroscopy toolbox, and they are directly sensitive to vibronic couplings. In this first of two papers, the complete orientational response functions are developed for a model system consisting of two coupled anharmonic oscillators and two electronic states in order to simulate polarization-selective 2D EV and 2D VE spectra with arbitrary combinations of linearly polarized electric fields. Here, we propose analytical methods to isolate desired signals within complicated spectra and to extract the relative orientation between vibrational and vibronic dipole moments of the model system using combinations of polarization-selective 2D EV and 2D VE spectral features. Time-dependent peak amplitudes of coherence peaks are also discussed as means for isolating desired signals within the time-domain. This paper serves as a field guide for using polarization-selective 2D EV and 2D VE spectroscopies to map coupled vibronic coordinates on the molecular frame.

Generalized Analytic Approach for Determination of Multidimensional Franck-Condon Factors: Simulated Photoelectron Spectra of Polynuclear Aromatic Hydrocarbons

An enhanced generalized analytic approach for determination of multidimensional Franck-Condon Factors (FCFs) enables efficient computational prediction of photoelectron spectra for large-dimensional systems. Incorporation of the automated assignment of Cartesian coordinate handedness and coordinate superposition between the ground and excited electronic states satisfies the Eckart conditions and allows evaluation of the Duschinsky effect. The model shows excellent agreement with experiments for the determination of FCFs and photoelectron spectra of a series of increasing dimensions polynuclear hydrocarbons (PAHs), including naphthalene, anthracene, phenanthrene, and pyrene. In addition, a high-resolution prediction of the PES for the 84-dimensional PAH corannulene provides motivation for an additional experimental study. For FCFs, coordinate transformation between the initial and final states rather than the dimension of the systems more greatly influences the complexity of the spectral band shapes.

Resonant catalysis of thermally activated chemical reactions with vibrational polaritons

Interaction between light and matter results in new quantum states whose energetics can modify chemical kinetics. In the regime of ensemble vibrational strong coupling (VSC), a macroscopic number [Formula: see text] of molecular transitions couple to each resonant cavity mode, yielding two hybrid light-matter (polariton) modes and a reservoir of [Formula: see text] dark states whose chemical dynamics are essentially those of the bare molecules. This fact is seemingly in opposition to the recently reported modification of thermally activated ground electronic state reactions under VSC. Here we provide a VSC Marcus-Levich-Jortner electron transfer model that potentially addresses this paradox: although entropy favors the transit through dark-state channels, the chemical kinetics can be dictated by a few polaritonic channels with smaller activation energies. The effects of catalytic VSC are maximal at light-matter resonance, in agreement with experimental observations.

Photoinduced charge transfer rate of Cy3/C60 blend material

The rates of charge separation and charge recombination of the cyanine dye/C₆₀ heterojunction solar cell in an external electric field were provided using the Marcus and Marcus-Levich-Jortner formalisms. The vibrational mode as another influencing factor was also introduced into the rate expression for the planar heterojunction solar cell. Detailed theoretical analysis of the excited-state of the Cy3/C₆₀ blend was achieved using density functional theory and time-dependent density functional theory. The Gibbs free energy was regulated by an external electric field, while the reorganisation energy presented the opposite conclusion. Frequency analysis was utilised to demonstrate the energy stability of the obtained structures. The rate calculated using the Marcus formalism was greater than that obtained by the Marcus-Levich-Jortner formalism. Consideration of the calculated rates in all vibration modes and at different external electric field strengths indicated that vibrational mode and external electric field played important roles in determining the rates of charge separate and charge recombination, which could provide a more accurate theoretical rate for organic photovoltaic devices.

Q-model of electrode reactions: altering force constants of intramolecular vibrations

A theory of redox reactions involving electron transfer between a metal electrode and a molecule in solution is formulated in terms of two types of nuclear coordinates of the thermal bath: electrostatic polarization of the medium and local low-frequency vibrations. The polarization fluctuations follow Gaussian statistics. In contrast, the vibrational coordinate is allowed to change its force constant between two oxidation states of the reactant, which is projected onto non-Gaussian fluctuations of the reactant's electronic states. A closed-form analytical theory for the electrode redox reactions is formulated in terms of three reorganization energies: the reorganization energy for the electrostatic polarization of the medium and two internal (vibrational) reorganization energies for the reduced and oxidized states of the reactant. The theory predicts asymmetry between the cathodic and anodic branches of the electrode current driven by the corresponding difference in the vibrational force constants.

Vibronic quantized tunneling controlled photoinduced electron transfer in an organic solar cell subjected to an external electric field

In this work, vibration-resolved photoinduced electron transfer of an organic conjugated D⋯A system subjected to an external electric field was theoretically investigated.

Deep proton tunneling in the electronically adiabatic and non-adiabatic limits: comparison of the quantum and classical treatment of donor-acceptor motion in a protein environment

Analytical models describing the temperature dependence of the deep tunneling rate, useful for proton, hydrogen, or hydride transfer in proteins, are developed and compared. Electronically adiabatic and non-adiabatic expressions are presented where the donor-acceptor (D-A) motion is treated either as a quantized vibration or as a classical "gating" distribution. We stress the importance of fitting experimental data on an absolute scale in the electronically adiabatic limit, which normally applies to these reactions, and find that vibrationally enhanced deep tunneling takes place on sub-ns timescales at room temperature for typical H-bonding distances. As noted previously, a small room temperature kinetic isotope effect (KIE) does not eliminate deep tunneling as a major transport channel. The quantum approach focuses on the vibrational sub-space composed of the D-A and hydrogen atom motions, where hydrogen bonding and protein restoring forces quantize the D-A vibration. A Duschinsky rotation is mandated between the normal modes of the reactant and product states and the rotation angle depends on the tunneling particle mass. This tunnel-mass dependent rotation contributes substantially to the KIE and its temperature dependence. The effect of the Duschinsky rotation is solved exactly to find the rate in the electronically non-adiabatic limit and compared to the Born-Oppenheimer (B-O) approximation approach. The B-O approximation is employed to find the rate in the electronically adiabatic limit, where we explore both harmonic and quartic double-well potentials for the hydrogen atom bound states. Both the electronically adiabatic and non-adiabatic rates are found to diverge at high temperature unless the proton coupling includes the often neglected quadratic term in the D-A displacement from equilibrium. A new expression is presented for the electronically adiabatic tunnel rate in the classical limit for D-A motion that should be useful to experimentalists working near room temperature. This expression also holds when a broad protein conformational distribution of D-A equilibrium distances dominates the spread of the D-A vibrational wavefunction.

A momentum-conserving Franck-Condon approximation: theory and application to the photodissociation of Li2+ in an intense laser field

A new, computationally efficient approximation to calculating matrix elements between vibrational-electronic states that does not assume stationary nuclei is introduced. The approach emphasizes the importance of the conservation of nuclear momenta. The calculated quantities can be used wherever equivalent quantities from standard Franck-Condon treatments can be used. The new method is illustrated by a time-dependent perturbation theory description of the photodissociation of the Li(2) (+) molecular cation in an intense laser field (I=0.9x10(12) W/cm(2)), which was previously identified in a detailed study of the electronic structure [Khait et al., J. Chem. Phys. 122, 094111 (2005)] as likely to have unusual sensitivity to the initial vibrational state in dynamics. The current study confirms this speculation and shows this to be a specific instance of a situation in which nuclear dynamics during an electronic optical transition cannot be ignored.

Fluorescence spectroscopy of jet-cooled chiral (±)-indan-1-ol and its cluster with (±)-methyl- and ethyl-lactate

The laser-induced fluorescence excitation, dispersed fluorescence, and IR-UV double resonance spectra of chiral (+/-)-indan-1-ol have been measured in a supersonic expansion. Three low energy conformers of the molecule have been identified, and the ground state vibrational modes of each conformer are tentatively assigned with the aid of quantum chemistry calculations. The frequencies of the nu(OH) and nu(CH) stretch modes of the two most abundant conformers have been measured by fluorescence dip IR spectroscopy and have been used for their assignment. The dispersed fluorescence spectra clearly indicate the coupling of low-frequency modes, as was seen in other substituted indanes such as 1-aminoindan and 1-amino-2-indanol. (R)- and (S)-indan-1-ol distinctly form different types of clusters with (R)- and (S)- methyl- and ethyl-lactate. Both hetero- and homochiral clusters are characterized by complex spectra which exhibit a progression built on low-frequency intermolecular modes.

Franck−Condon Simulations of Clusters: Phenol−Nitrogen

Multidimensional Franck-Condon simulations of the resonance enhanced multiphoton ionization (REMPI) and mass-analyzed threshold ionization (MATI) spectra of phenol-nitrogen are obtained from CASSCF, MRCI, and SACCI optimized geometries. In the REMPI simulations, the results are unsatisfactory, as the transitions associated with intermolecular modes are widely underestimated and much less intense than those associated with intramolecular modes. Conversely, the simulations of the MATI spectra show a good similarity to experiment. The best simulations are obtained in both instances from the SACCI optimized geometries. Furthermore, the simulations suggest that the two most prominent Franck-Condon envelopes present in the MATI spectra are due to the sigma and sigma + ngamma' combination bands in accord with the assignments of the MATI spectra of the analogous phenol-carbon monoxide cluster.

The Use of Multidimensional Franck−Condon Simulations to Assess Model Chemistries: A Case Study on Phenol

Multidimensional Franck-Condon simulations of the dispersed fluorescence spectra of phenol generated with geometries obtained from the highly correlated post-Hartree-Fock methods CASSCF, MRCI, and SACCI are presented. While the simulations based on CASSCF and MRCI optimized geometries are very similar to each other and fail to reproduce the experimentally measured intensities faithfully, the simulations obtained from SACCI optimized geometries are very close to the experimental spectra. The code developed for the multidimensional Franck-Condon simulations is described. It is shown that the integral storage problem common to the evaluation of multidimensional Franck-Condon integrals can be overcome by saving all quantities needed to disk. This strategy allows the code to run on computers with limited resources and is very well suited for application to molecules with a very large number of vibrational modes.

Hydrogen bond-induced vibronic mode mixing in benzoic acid dimer: A laser-induced fluorescence study

Laser-induced dispersed fluorescence spectra of benzoic acid dimer in the cold environment of supersonic jet expansion have been reinvestigated with improved spectral resolution of measurements. The spectra are analyzed with the aid of the normal mode vibrations of the dimer calculated by the ab initio quantum chemistry method at the DFT/B3LYP/6-311+G(*) (*) level of theory. The analysis reveals that the low-frequency intermolecular hydrogen bond modes are mixed extensively with the carboxyl as well as aromatic ring vibrations upon electronic excitation. The mode mixing is manifested as the complete loss of mirror symmetry relation between the fluorescence excitation and dispersed fluorescence spectra of the S(1) origin, and appearance of large number of cross-sequence transitions when the DF spectra are measured by exciting the low-energy vibrations near the S(1) origin. The cross-sequence bands are found in all the cases to be the combinations of two nontotally symmetric fundamentals consisting of one of the intermolecular hydrogen bond modes and the other from the aromatic ring and carboxyl group vibrations. The implications of this mode mixing on the excited state dynamics of the dimer are discussed.

Excited state charge-transfer dynamics study of poplar plastocyanin by ultrafast pump-probe spectroscopy and molecular dynamics simulation

We have applied ultrafast pump-probe spectroscopy to investigate the excited state dynamics of the blue copper protein poplar plastocyanin, by exciting in the blue side of its 600-nm absorption band. The decay of the charge-transfer excited state occurs exponentially with a time constant of approximately 280 fs and is modulated by well visible oscillations. The Fourier transform of the oscillatory component, besides providing most of the vibrational modes found by conventional resonance Raman, presents additional bands in the low frequency region modes, which are reminiscent of collective motions of biological relevance. Notably, a high frequency mode at approximately 508 cm(-1), whose dynamics are consistent with that of the excited state and already observed for other blue copper proteins, is shown to be present also in poplar plastocyanin. This vibrational mode is reproduced by a molecular dynamics simulation involving the excited state of the copper site.

The theory of electron transfer reactions: what may be missing?

Molecular dynamics simulations are presented for condensed-phase electron transfer (ET) systems where the electronic polarizability of both the solvent and the solute is incorporated. The solute polarizability is allowed to change with electronic transition. The results display notable deviation from the standard free energy parabolas of traditional ET theories. A new three-parameter ET model is applied, and the theory is shown to accurately model the free energy surfaces. This paper presents conclusive evidence that the traditional theory for the free energy barrier of ET reactions requires modification.

Calculation of triplet-triplet energy transfer rates from emission and absorption spectra. The quenching of hemicarcerated triplet biacetyl by aromatic hydrocarbons

The kinetics of triplet-triplet (T-T) energy transfer have been analysed with a view to linking theories of chemical reactions (involving the rupture and formation of bonds) with theories of processes, such as electron transfer or energy transfer, which preserve chemical bonding. As for the latter, our analysis does not support the claim that, of the two rival expressions for T-T energy transfer, both rooted in the golden rule, only one is applicable to electron transfer or T-T transfer. Though the two expressions do reflect different standpoints, the distinction is eroded by the assumption of a delta-function distribution for the vibrational spectrum. It is shown that theories of chemical reactions also furnish estimates of Franck-Condon factors; rates of chemical reactions and chemical processes are both related to the properties (strengths and lengths) of the reactive bonds, but differ in the mode of energy dissipation. The relationship between the rates of reactions and processes presents new possibilities for a unified view of chemical reactivity.