Abstract

Evaluation of symmetry-forbidden or weakly-allowed vibronic spectra requires treating the transition dipole moment beyond the Condon approximation. To include vibronic spectral features not captured in the global harmonic models, we have recently implemented an on-the-fly ab initio extended thawed Gaussian approximation, where the propagated wavepacket is a Gaussian multiplied by a linear polynomial. To include more anharmonic effects, here we represent the initial wavepacket by a superposition of three independent Gaussian wavepackets—one for the Condon term and two displaced Gaussians for the Herzberg–Teller part. Application of this ab initio “three thawed Gaussians approximation”to vibrationally resolved electronic spectra of the phenyl radical and benzene shows a clear improvement over the global harmonic and Condon approximations. The orientational averaging of spectra, the relation between the gradient of the transition dipole moment and nonadiabatic coupling vectors, and the details of the extended and three thawed Gaussians approximation are discussed.

Highlights

  • Electronic spectroscopy lies at the core of modern physical chemistry; has it been the driving force in developing first insights into the atomic and molecular structure [1, 2], but it is the method of choice for unraveling essential chemical and physical processes

  • Since the anharmonicity of the excited-state potential of the phenyl radical is shown to influence the spectrum more than the Herzberg–Teller contribution [32], this system is suited for further investigation using the 3TGA, which is intended for treating the anharmonicity of the Herzberg–Teller active modes

  • We have presented the 3TGA, constructed by replacing the Herzberg–Teller part of the initial wavepacket with two displaced Gaussians, in order to describe electronic spectra beyond the Condon approximation and anharmonicity effects beyond the single-trajectory extended thawed Gaussian approximation (ETGA)

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Summary

INTRODUCTION

Electronic spectroscopy lies at the core of modern physical chemistry; has it been the driving force in developing first insights into the atomic and molecular structure [1, 2], but it is the method of choice for unraveling essential chemical and physical processes. The extended thawed Gaussian approximation (ETGA) [32, 33], propagates a Gaussian wavepacket multiplied by a general polynomial in nuclear coordinates using a local harmonic approximation, i.e., the secondorder expansion of the potential about the center of the wavepacket Such a wavepacket, is wider than a simple Gaussian wavepacket, which raises the question whether more than a single guiding classical trajectory should be used to correctly account for the anharmonicity of the potential energy surface. We present the on-the-fly ab initio implementation of an alternative method for treating Herzberg–Teller spectra beyond the Condon approximation This semiclassical method is based on the thawed Gaussian approximation, yet, unlike the extended TGA, resolves the initial Herzberg–Teller wavepacket into three well-defined Gaussians and propagates them independently. The matrix product will use no special notation; it will be expressed by a juxtaposition of the matrices (as in AB)

Time-dependent approach to spectroscopy
Orientational averaging of the spectrum
Condon and Herzberg–Teller approximations for the transition dipole moment
Extended thawed Gaussian approximation
Three thawed Gaussians approximation
Ab initio implementation
COMPUTATIONAL DETAILS
Absorption spectrum of the phenyl radical
Absorption spectrum of benzene
Norm conservation and fidelity
CONCLUSION
Full Text
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