Basis set truncation further clarifies vibrational coherence spectra

Tracking the conical intersection dynamics for the photoinduced Jahn-Teller switch of a Mn(iii) complex

Octahedral Mn(iii) ions predominantly exhibit an axially elongated Jahn-Teller (JT) distortion, which is responsible for their large uniaxial magnetic anisotropy. As a result, they are often used in the synthesis of single-molecule magnets (SMMs). Modulation of the JT distortion using femtosecond laser pulses could offer a route to controlling the magnetisation direction, and therefore is promising for the development of data storage devices that work on ultrafast timescales. Photoinduced switching of the distortion from an axially elongated to an axially compressed structure has been demonstrated for various Mn(iii) complexes. However, the dynamics around the region of the conical intersection for the photoinduced JT switch remains unclear. Here, ultrafast transient absorption spectra were recorded for solutions of tris(2,2,6,6-tetramethyl-3,5-heptanedionato)manganese(iii) (Mn(dpm)3) in ethanol to further explore the dynamics of the photoinduced JT switch. We observe the generation of a vibrational wavepacket on the excited state surface, which has a frequency of approximately 155 cm-1 and encompasses a JT-active vibrational mode. This coherent motion is maintained after passage through the conical intersection back to the ground state, which launches wavepackets along the ground state potential energy surface (PES) with frequencies of approximately 180 and 110 cm-1 that we assign to the elongated and compressed state, respectively. Inspection of the relative phases of the frequencies reveals phase shifts that are consistent with a one-mode reaction coordinate, and passes through the conical intersection at 1/4 and 3/4 of the excited state vibrational period. Our results provide direct insights into the non-adiabatic dynamics of Mn(iii) complexes, which can be used to guide the synthesis of optically controlled SMMs.

Vibrational coherences in half-broadband 2D electronic spectroscopy: Spectral filtering to identify excited state displacements

Vibrational coherences in ultrafast pump-probe (PP) and 2D electronic spectroscopy (2DES) provide insights into the excited state dynamics of molecules. Femtosecond coherence spectra and 2D beat maps yield information about displacements of excited state surfaces for key vibrational modes. Half-broadband 2DES uses a PP configuration with a white light continuum probe to extend the detection range and resolve vibrational coherences in the excited state absorption (ESA). However, the interpretation of these spectra is difficult as they are strongly dependent on the spectrum of the pump laser and the relative displacement of the excited states along the vibrational coordinates. We demonstrate the impact of these convoluting factors for a model based upon cresyl violet. A careful consideration of the position of the pump spectrum can be a powerful tool in resolving the ESA coherences to gain insights into excited state displacements. This paper also highlights the need for caution in considering the spectral window of the pulse when interpreting these spectra.

Theoretical model of femtosecond coherence spectroscopy of vibronic excitons in molecular aggregates

When used as pump pulses in transient absorption spectroscopy measurements, femtosecond laser pulses can produce oscillatory signals known as quantum beats. The quantum beats arise from coherent superpositions of the states of the sample and are best studied in the Fourier domain using Femtosecond Coherence Spectroscopy (FCS), which consists of one-dimensional amplitude and phase plots of a specified oscillation frequency as a function of the detection frequency. Prior works have shown ubiquitous amplitude nodes and π phase shifts in FCS from excited-state vibrational wavepackets in monomer samples. However, the FCS arising from vibronic-exciton states in molecular aggregates have not been studied theoretically. Here, we use a model of vibronic-exciton states in molecular dimers based on displaced harmonic oscillators to simulate FCS for dimers in two important cases. Simulations reveal distinct spectral signatures of excited-state vibronic-exciton coherences in molecular dimers that may be used to distinguish them from monomer vibrational coherences. A salient result is that, for certain relative orientations of the transition dipoles, the key resonance condition between the electronic coupling and the frequency of the vibrational mode may yield strong enhancement of the quantum-beat amplitude and, perhaps, also cause a significant decrease of the oscillation frequency to a value far lower than the vibrational frequency. Future studies using these results will lead to new insights into the excited-state coherences generated in photosynthetic pigment-protein complexes.

Vibrational response functions for multidimensional electronic spectroscopy in nonadiabatic models

The interplay of nuclear and electronic dynamics characterizes the multidimensional electronic spectra of various molecular and solid-state systems. Theoretically, the observable effect of such interplay can be accounted for by response functions. Here, we report analytical expressions for the response functions corresponding to a class of model systems. These are characterized by coupling between the diabatic electronic states and the vibrational degrees of freedom, resulting in linear displacements of the corresponding harmonic oscillators, and by nonadiabatic couplings between pairs of diabatic states. In order to derive the linear response functions, we first perform the Dyson expansion of the relevant propagators with respect to the nonadiabatic component of the Hamiltonian, then derive and expand with respect to the displacements the propagators at given interaction times, and finally provide analytical expressions for the time integrals that lead to the different contributions to the linear response function. The approach is then applied to the derivation of third-order response functions describing different physical processes: ground state bleaching, stimulated emission, excited state absorption, and double quantum coherence. Comparisons between the results obtained up to sixth order in the Dyson expansion and independent numerical calculation of the response functions provide evidence of the series convergence in a few representative cases.

Vibrational response functions for multidimensional electronic spectroscopy in the adiabatic regime: A coherent-state approach

Multi-dimensional spectroscopy represents a particularly insightful tool for investigating the interplay of nuclear and electronic dynamics, which plays an important role in a number of photophysical processes and photochemical reactions. Here, we present a coherent state representation of the vibronic dynamics and of the resulting response functions for the widely used linearly displaced harmonic oscillator model. Analytical expressions are initially derived for the case of third-order response functions in an N-level system, with ground state initialization of the oscillator (zero-temperature limit). The results are then generalized to the case of Mth order response functions, with arbitrary M. The formal derivation is translated into a simple recipe, whereby the explicit analytical expressions of the response functions can be derived directly from the Feynman diagrams. We further generalize to the whole set of initial coherent states, which form an overcomplete basis. This allows one, in principle, to derive the dependence of the response functions on arbitrary initial states of the vibrational modes and is here applied to the case of thermal states. Finally, a non-Hermitian Hamiltonian approach is used to include in the above expressions the effect of vibrational relaxation.

Characterizing Mode Anharmonicity and Huang-Rhys Factors Using Models of Femtosecond Coherence Spectra

Femtosecond laser pulses readily produce coherent quantum beats in transient-absorption spectra. These oscillatory signals often arise from molecular vibrations and therefore may contain information about the excited-state potential energy surface near the Franck-Condon region. Here, by fitting the measured spectra of two laser dyes to microscopic models of femtosecond coherence spectra (FCS) arising from molecular vibrations, we classify coherent quantum-beat signals as fundamentals or overtones and quantify their Huang-Rhys factors and anharmonicity values. We discuss the extracted Huang-Rhys factors in the context of quantum-chemical computations. This work solidifies the use of FCS for analysis of coherent quantum beats arising from molecular vibrations, which will aid studies of molecular aggregates and photosynthetic proteins.

Vibronic dynamics resolved by global and target analysis of ultrafast transient absorption spectra

We present a methodology that provides a complete parametric description of the time evolution of the electronically and vibrationally excited states as detected by ultrafast transient absorption (TA). Differently from previous approaches, which started fitting the data after ≈100 fs, no data are left out in our methodology, and the "coherent artifact" and the instrument response function are fully taken into account. In case studies, the method is applied to solvents, the dye Nile blue, and all-trans β-carotene in cyclohexane solution. The estimated Damped Oscillation Associated Spectra (DOAS) and phases express the most important vibrational frequencies present in the molecular system. By global fit alone of the experimental data, it is difficult to interpret in detail the underlying dynamics. Since it is unfeasible to directly fit the data by a theoretical simulation, our enhanced DOAS methodology thus provides a useful "middle ground" where the theoretical description and the fit of the experimental data can meet. β-carotene in cyclohexane was complementarily studied with femtosecond stimulated Raman spectroscopy (FSRS). The fs-ps dynamics of β-carotene in cyclohexane in TA and FSRS experiments can be described by a sequential scheme S2 → hot S1 → S1' → S1 → S0 with lifetimes of 167 fs (fixed), 0.35, 1.1, and 9.6 ps. The correspondence of DOAS decaying concomitantly with hot S1 and the Species Associated Difference Spectra of hot S1 in TA and FSRS suggest that we observe here features of the vibrational relaxation and nuclear reorganization responsible for the hot S1 to S1 transition.

Signatures of Vibrational and Electronic Quantum Beats in Femtosecond Coherence Spectra

Femtosecond laser pulses can produce oscillatory signals in transient-absorption spectroscopy measurements. The quantum beats are often studied using femtosecond coherence spectra (FCS), the Fourier domain amplitude, and phase profiles at individual oscillation frequencies. In principle, one can identify the mechanism that gives rise to each quantum-beat signal by comparing its measured FCS to those arising from microscopic models. To date, however, most measured FCS deviate from the ubiquitous harmonic oscillator model. Here, we expand the inventory of models to which the measured spectra can be compared. We develop quantum-mechanical models of the fundamental, overtone, and combination-band FCS arising from harmonic potentials, the FCS of anharmonic potentials, and the FCS of a purely electronic dimer. This work solidifies the use of FCS for identifying electronic coherences that can arise in measurements of molecular aggregates including photosynthetic proteins. Furthermore, future studies can use the derived expressions to fit the measured FCS and thereby extract microscopic parameters of molecular potential-energy surfaces.