Abstract
To compute and analyze vibrationally resolved electronic spectra at zero temperature, we have recently implemented the on-the-fly ab initio extended thawed Gaussian approximation [A. Patoz et al., J. Phys. Chem. Lett. 9, 2367 (2018)], which accounts for anharmonicity, mode-mode coupling, and Herzberg-Teller effects. Here, we generalize this method in order to evaluate spectra at non-zero temperature. In line with thermo-field dynamics, we transform the von Neumann evolution of the coherence component of the density matrix to the Schrödinger evolution of a wavefunction in an augmented space with twice as many degrees of freedom. Due to the efficiency of the extended thawed Gaussian approximation, this increase in the number of coordinates results in nearly no additional computational cost. More specifically, compared to the original, zero-temperature approach, the finite-temperature method requires no additional ab initio electronic structure calculations. At the same time, the new approach allows for a clear distinction among finite-temperature, anharmonicity, and Herzberg-Teller effects on spectra. We show, on a model Morse system, the advantages of the finite-temperature thawed Gaussian approximation over the commonly used global harmonic methods and apply it to evaluate the symmetry-forbidden absorption spectrum of benzene, where all of the aforementioned effects contribute.
Highlights
Resolved electronic spectra have, for a very long time, been used to learn more about electronic and vibrational states of molecules, their potential energy surfaces, and lightinduced dynamics of nuclei.1–4 The computational methods for simulating such spectra are, an essential tool in physical chemistry.The most widespread is the global harmonic method,5–7 which employs the harmonic approximation for both ground- and excited-state potential energy surfaces
Ref. 12 has so far been used to compute vibronic spectra only scitation.org/journal/jcp in systems described with globally harmonic potential energy surfaces, where it is equivalent to the global harmonic approximation for vibronic spectra, which is much simpler because analytical expressions for C(t) exist
The effect of anharmonicity on the peak positions becomes significant for χ = 0.02, and even the thawed Gaussian approximation is inadequate
Summary
Resolved electronic spectra have, for a very long time, been used to learn more about electronic and vibrational states of molecules, their potential energy surfaces, and lightinduced dynamics of nuclei. The computational methods for simulating such spectra are, an essential tool in physical chemistry. Within the framework of the global harmonic approximation, one can account for non-Condon and finite-temperature effects.. Within the framework of the global harmonic approximation, one can account for non-Condon and finite-temperature effects.8–12 This approximation, neglects the effects of anharmonicity, which can significantly alter molecular spectra. We have been investigating the thawed Gaussian approximation (TGA), an efficient semiclassical method that accounts partially for anharmonicity and requires no initial knowledge of the potential energy surface. As a wavepacket propagation method, it has been limited to computing spectra in the zero-temperature limit, where only the ground vibrational state is populated initially. We combine the extended thawed Gaussian wavepacket propagation with the thermo-field dynamics in order to include both anharmonicity and finite-temperature effects. We apply it to evaluate the spectrum corresponding to the symmetry-forbidden electronic transition S1 ← S0 (A 1B2u ← X 1A1g) of benzene and demonstrate that the simultaneous inclusion of Herzberg–Teller, anharmonicity, and finite-temperature effects is needed to reproduce the experimental spectrum
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