Abstract
We report measurement and modeling of two-dimensional (2D) electronic spectra of a silicon naphthalocyanine (SiNc) in benzonitrile, a system for which the polarization anisotropy reveals passage through a square-symmetric Jahn-Teller conical intersection in ∼100 fs [D. A. Farrow, W. Qian, E. R. Smith, A. A. Ferro, and D. M. Jonas, J. Chem. Phys. 128, 144510 (2008)]. The measured 2D Fourier transform (FT) spectra indicate loss of electronic coherence on a similar timescale. The 2D spectra arising from femtosecond vibronic dynamics through the conical funnel are modeled by full non-adiabatic treatment of the coupled electronic and vibrational dynamics for a pair of un-damped Jahn-Teller active vibrations responsible for both electronic decoherence and population transfer. Additional damped Jahn-Teller active modes that can cause only decoherence or population transfer are treated with analytical response functions that can be incorporated into the numerical non-adiabatic calculation by exploiting symmetry assignment of degenerate vibronic eigenstates to one of two electronic states. Franck-Condon active totally symmetric modes are incorporated analytically. The calculations reveal that these conical intersection dynamics alone are incapable of destroying the coherence of the initially prepared wavepacket on the experimentally observed timescale and predict an unobserved recurrence in the photon echo slice at ∼200 fs. Agreement with the experimental two-dimensional electronic spectra necessitates a role for totally symmetric vibrational dynamics in causing the echo slice to decay on a ∼100 fs timescale. This extended model also reproduces the ∼100 fs ultrafast electronic anisotropy decay in SiNc when an "asymmetric solvation mode" with a small stabilization energy of ∼2 cm(-1) is included. Although calculations show that inhomogeneities in the energy gap between excited states can broaden the anti-diagonal 2D lineshape, the anti-diagonal width is dominated by totally symmetric vibrational motions in SiNc. For this shallow conical intersection, the non-adiabatic dynamics destroy electronic coherence more slowly than they destroy electronic alignment.
Highlights
The quantum description of molecules usually begins by solving the electronic Schrodinger equation for fixed nuclear coordinates, generating energy eigenvalues that are considered as adiabatic electronic potential energy surfaces on which the rotation-vibration Schrodinger equation is solved.1 In the adiabatic approximation, electronic and vibrational motions are separable, and slow vibrational motion is confined to a single adiabatic potential energy surface corresponding to the electronic quantum state
We have presented two-dimensional electronic spectra of silicon naphthalocyanine (SiNc), a system known to have a shallow conical “funnel” between the degenerate singly excited electronic states
The analytic response functions that use symmetric and asymmetric dephasing functions for damped vibrations in our model are well-described with the adiabatic theory of Refs. 56 and 57 and require the rigorous symmetry-based distinction between the vibronic eigenstates developed here so that they can be combined with the numerical response function for the nonadiabatic dynamics
Summary
The quantum description of molecules usually begins by solving the electronic Schrodinger equation for fixed nuclear coordinates, generating energy eigenvalues that are considered as adiabatic (or Born-Oppenheimer) electronic potential energy surfaces on which the rotation-vibration Schrodinger equation is solved. In the adiabatic approximation, electronic and vibrational motions are separable, and slow vibrational motion is confined to a single adiabatic potential energy surface corresponding to the electronic quantum state. When two adiabatic potential energy surfaces of polyatomic molecules intersect, the neighborhood around the intersection resembles the vertex of a right-circular double cone through which the two conical surfaces smoothly connect with each other.. When two adiabatic potential energy surfaces of polyatomic molecules intersect, the neighborhood around the intersection resembles the vertex of a right-circular double cone through which the two conical surfaces smoothly connect with each other.2 At these points of “conical intersection,” the electronic energy gap is zero. A conical intersection or nearly missed intersection is called a “conical funnel” if changes in quantum state occur faster than vibrational relaxation Such “sudden” changes in the electronic quantum state can result in fast reactions driven by the new electronic state. When these non-adiabatic changes lead to a rapid relaxation of photoexcited molecules to ground state products, the organic photochemistry concept of a “funnel” comes into play. Conical intersections are believed to be both common and responsible for some of the fastest chemical processes, with lower dimensional hypersurfaces of intersecting conical intersections playing a role in some reactions. Conical intersections play an essential role in biological reactions such as the isomerization of retinal, the primary step in vision, intramolecular proton transfer reactions, and solar light harvesting reactions. A well-developed framework for the coupled vibrational and electronic dynamics near a conical intersection has been used for many computational studies. This framework shows that every conical intersection involves two crucial coordinates, one which
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