Vibronic dynamics

The full quantum mechanical study of nuclear dynamics in molecules has received considerable attention in recent years. An important example of such developments is the work carried out on the prototypical systems H3 [1-5] and its isotopic variant HD2 [5-8], Li3 [9-12], Na3 [13,14], and HO2 [15-18], In particular, for the alkali metal trimers, the possibility of a conical intersection between the two lowest doublet potential energy surfaces introduces a complication that makes their theoretical study fairly challenging. Thus, alkali metal trimers have recently emerged as ideal systems to study molecular vibronic dynamics, especially the so-called geometric phase (GP) effect [13,19,20] (often referred to as the molecular Aharonov-Bohm effect [19] or Berry s phase effect [21]) for further discussion on this topic see [22-25], and references cited therein. The same features also turn out to be present in the case of HO2, and their exact treatment assumes even further complexity [18],... 

The dynamical mechanical measurements were made using a Vibron dynamic viscoelastomer, model DDV II (Toyo Instrument Co.) at two frequencies, 3.5 and 110 Hz, over the temperature range —180° to 240°C. 

Although the presented numerical approach to the coupled master equations has shown that a turnover feature can be seen in vibronic dynamics appearing in the calculated pump-probe stimulated emission spectra as a function of the energy gap between the two relevant vibronic states. It is found that vibronic quantum beats cannot be observed when the energy gap becomes larger in which situation it leads to smaller Franck-Condon overlaps between the energy conserved levels. 

Ed., Wiley, Chichester, 1997, pp. 152-278. Vibronic Dynamics of Polyatomic Molecules. 

To calculate numerically the quantum dynamics of the various cations in time-dependent domain, we shall use the multiconfiguration time-dependent Hartree method (MCTDH) [79-82, 113, 114]. This method for propagating multidimensional wave packets is one of the most powerful techniques currently available. For an overview of the capabilities and applications of the MCTDH method we refer to a recent book [114]. Additional insight into the vibronic dynamics can be achieved by performing time-independent calculations. To this end Lanczos algorithm [115,116] is a very suitable algorithm for our purposes because of the structural sparsity of the Hamiltonian secular matrix and the matrix-vector multiplication routine is very efficient to implement [6]. 

The rest of the article is organized in the following way. The basic concept of vibronic coupling is reviewed in Sect. 2. The theoretical and computational methodologies to treat the static and dynamic aspects of vibronic coupling are outlined in Sect. 3. The important findings on the vibronic dynamics of Ph, PA +, N + and... 

A vibronic dynamic problem of valence tautomerism in a single molecule was discussed in [221,222]. As a basis set we take the following states of the molecule with localized electrons arising from its four configurations ... 

Dynamic mechanical measurements were carried out on a Vibron Dynamic Viscoelastometer, Model DDV-II (Toyo Measuring Instruments Co.). The temperature range was — 160°-200°C and the frequencies used were 3.5,11, and 110 Hz. Samples were heated at a rate of 1°-2°C/ min under dry nitrogen. 

Additional insight into the vibronic dynamics can be achieved by performing time-dependent calculations. The latter allow for a more direct visualization of the coupled electronic and nuclear motions. Moreover, given only the spectrum, Eq. (31), or a small number of resonance Raman amplitudes, the information obtained from the time-dependent wavefunction differs also in principle from that of stationary spectra. 

In our early work on multimode vibronic dynamics, a fourth-order predictor-corrector method has been used to integrate the time-dependent Schrodinger equation. Later, FOD schemes and a fourth-order Runge-Kutta method have also been employed. These techniques proved to be superior to the predictor-corrector method for example, the FOD scheme was found to be 3-5 times faster than the SOD integrator (the latter... 

In concluding this subsection, we mention that both systems have been treated also by more elaborate calculations beyond the linear-plus-quadratic vibronic-coupling model. The vibronic dynamics of O3 has been... 

JAHN TELLER AND PSEUDO-JAHN TELLER INTERSECTIONS SPECTROSCOPY AND VIBRONIC DYNAMICS... 

The two theories therefore predict much different appearance kinetics for individual vibronic states of solute/solvent clusters generated by IVR and the bare chromophore molecule generated by VP. While the interpretation of wavelength and time resolved measurements does not depend on the theoretical model imposed or envisioned, the interpretation of the cw experiments is indeed highly model dependent. Thus, in the absence of temporal resolution, the assumption of only parallel or only serial relaxation processes is important for the data interpretation. The question of serial yLLi parallel processes for vibronic dynamics can in any cases be uniquely answered by time resolved studies. Indeed, we have shown zpreviously for tetrazine(Ar)i,2b and herein for aniline(Ar)i, (N2)i, (CH4)i, that the serial IVR/VP process is the appropriate one. 

In this context exact (QD) means the most exact ab initio treatment to describe the vibrational dynamics during MPI processes induced by ultrafast laser pulses which is possible and practicable with the current state-of-the-art computational methods. As already pointed out in detail, this method takes into account all three vibrational modes and only neglects the rotational degrees of freedom. The exact (QD) method can describe all laser-induced MPI processes without exception and is able to record the main features of the vibronical dynamics without the use of any fitting parameter. 

Koppel H, Cederbaum LS,DomckeW (1988) Interplay of Jeihn-Teller and pseudo-Jahn-Teller vibronic dynamics in the benzene cation. J Chem Phys 89 2023... 

Bildea I, KSppel H (2006) Multistate multimode vibronic dynamics entemglement of electronic and vibrational degrees of freedom in the benzene radical cation. J Chem Phys 124 064101... 

H. Koppel, Jahn-Teller and pseudo-Jahn-Teller intersections Spectroscopy and vibronic dynamics, in Conical Intersections, Electronic Structure, Dynamics and Spectroscopy, W. Domcke, R. Yarkony, H. Koppel, Eds., World Scientific, Singapore, 2004, pp. 429 72. 

Natural Orbitals Nonadiabatic Derivative Couplings Photochemistry Photodissociation Dynamics Valence Bond Curve Crossing Models Vibronic Dynamics in Polyatomic Molecules. 

Electronic Diabatic States Definition, Computation, and Applications Gradient Theory Photochemistry Photodisso ciation Dynamics Vibronic Dynamics in Polyatomic Molecules. 

Classical Dynamics of Nonequilibrium Processes in Fluids Integrating the Classical Equations of Motion Control of Microworld Chemical and Physical Processes Mixed Quantum-Classical Methods Multiphoton Excitation Non-adiabatic Derivative Couplings Photochemistry Rates of Chemical Reactions Reactive Scattering of Polyatomic Molecules Spectroscopy Computational Methods State to State Reactive Scattering Statistical Adiabatic Channel Models Time-dependent Multiconfigurational Hartree Method Trajectory Simulations of Molecular Collisions Classical Treatment Transition State Theory Unimolecular Reaction Dynamics Valence Bond Curve Crossing Models Vibrational Energy Level Calculations Vibronic Dynamics in Polyatomic Molecules Wave Packets. 

Under the concept vibronic coupling all phenomena are subsumed which arise from the mixing of different electronic states by nuclear displacements. Vibronic-coupling effects become important whenever there is a degeneracy or neardegeneracy of electronic states. In such cases the well-known Born-Oppenheimer adiabatic approximation usually breaks down. It is then necessary to consider nuclear motion on several coupled electronic energy surfaces, referred to as vibronic dynamics in the title of this chapter. 

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