Franck–Condon principle

Summary

The Franck–Condon principle (named for James Franck and Edward Condon) is a rule in spectroscopy and quantum chemistry that explains the intensity of vibronic transitions (the simultaneous changes in electronic and vibrational energy levels of a molecule due to the absorption or emission of a photon of the appropriate energy). The principle states that during an electronic transition, a change from one vibrational energy level to another will be more likely to happen if the two vibrational wave functions overlap more significantly. Overview The Franck–Condon principle has a well-established semiclassical interpretation based on the original contributions of James Franck. Electronic transitions are relatively instantaneous compared with the time scale of nuclear motions, therefore if the molecule is to move to a new vibrational level during the electronic transition, this new vibrational level must be instantaneously compatible with the nuclear positions and momenta of t

Official source

https://en.wikipedia.org/wiki/Franck%E2%80%93Condon_principle

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Understanding the elementary steps involved in a chemical reaction forms the cornerstone of physical chemistry research. One way to deepen this understanding is by studying chemical and physical processes using linear and nonlinear spectroscopic techniques. However, the outcomes of such experiments can be difficult to decipher due to the interweaving of several effects. Therefore, in order to help experimentalists to disentangle such spectra, the role of theorists is to develop efficient tools that are able to accurately describe molecular systems. The starting point of such tools is solving the time-dependent Schrödinger equation. In this thesis, after implementing geometric integrators, which are based on a combination of the split-operator algorithm and Magnus expansion, for the exact nonadiabatic quantum dynamics of a molecule interacting with a time-dependent electromagnetic field, we derive and implement these geometric integrators for the time-dependent perturbation theory, the Condon, rotating-wave, and ultrashort-pulse approximations, as well as every possible combination thereof. As verified in several model systems, these integrators exactly preserve the geometric invariants, and achieve an arbitrary prescribed order of accuracy in the time step and an exponential convergence in the grid spacing. We also explore in more detail the ultrashort-pulse approximation and derive an analytical expression for the combination with the time-dependent perturbation theory; this expression significantly accelerates numerical calculations. We show that in the limit of the zero pulse width, the d-pulse approximation is recovered. We illustrate the performance of the introduced approximations, using a three-dimensional model of pyrazine, in which it is essential to go beyond the d-pulse limit in order to describe the dynamics correctly. The high-order algorithms are also applied to the photodissociation dynamics of iodomethane (CH3I), following its excitation to the A band. We implement a general split-operator with both discrete-variable and finite-basis representations that can treat one non-Cartesian, such as angular coordinate. To test the effect of various degrees of freedom and of the nonadiabatic dynamics, we apply these algorithms to one-, two-, and three-dimensional models of iodomethane, both in the presence and in the absence of nonadiabatic couplings. A full quantum calculation is, however, limited to problems with low dimensionality (approximately ten degrees of freedom). Beyond this, one must seek an affordable balance between computational efficiency and physical accuracy and can employ, for example, semiclassical methods that are based on classical trajectories. A simple semiclassical approximation that can treat larger systems and requires only local knowledge of the potential is the on-the-fly ab initio thawed Gaussian approximation. We implement a generalization of the method that goes beyond the Franck-Condon approximation and treats Herzberg-Teller active molecules. Our method is used to compute absorption spectra of phenyl radical and of benzene, for which the Herzberg-Teller contribution is essential.

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In this work, new spectroscopic techniques have been developed to measure electric dipole moments of highly excited rovibrational states of small polyatomic molecules in the gas phase. These techniques make use of lasers arid of microwave synthesizers. They enable one to measure the change on a molecular system caused by applying an external electric field, which is called Stark effect and from this, extract the dipole moment. The first technique, called microwave Stark spectroscopy, makes use of microwave-optical double resonance combined to either laser induced fluorescence or vibrational predissociation detection. The second approach, called Stark induced quantum beat spectroscopy, relies on the time evolution of a coherently prepared molecular wavepacket in an electric field, using either electronic photodissociation or laser induced fluorescence for detection. These techniques have been applied to H2C0, HOCl, HDO, and H20 for whom the electric dipole moment have been measured for several highly excited rovibrational states of the ground electronic state. Using these experimental measurements, the dependence of the dipole moment vector, both in orientation and in magnitude, on the vibrational excitation is discussed. Moreover the experimental data are used to test ab initio calculations potential energy and dipole moment surfaces and to establish critical benchmarks for future improvements. Due to the rarity of dipole moment data for highly excited vibrational states and their central role in transition intensities, intermolecular forces and collisions, these measurements are of special importance for chemical and energy transfer processes in atmospheric sciences, combustion studies, planetology, or more generally in the whole quantitative spectroscopy field, where transitions intensities are at least as important as line frequency positions.

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