Potential surface adiabatic

Figure 1. Adiabatic potential surfaces (a) for the linear E x e case and (b) for a state with linear Jahn-Teller coupling and spin-orbit coupling to a state,...

Finally, we note that there are some situations, of which the dynamical Jahn-Teller and Renner-Teller effects are the classic examples, where the nuclear coupling terms are important in any electronic basis 18). Adiabatic potential surfaces may still be defined but the resulting molecular eigenstates cannot be identified with any one surface. 

Fig. 85 Energetic relationships in the spin-crossover systems. Left-, the two adiabatic potential surfaces for the low-spin and the high-spin state centre thermodynamics of the unimolecular reaction right the van t Hoff plot...

As an effect of the linear and quadratic vibronic integrals the adiabatic potential surface stays no longer paraboloid-shaped. It exhibits an additional warping with several local minima and saddle points out of the reference high-symmetry configuration Q0. 

We have not explicitly included the nuclear motions (molecular vibrations) so far, the fact being frequently misunderstood. This is the second stage the lowest sheet of the adiabatic potential surface, Etp, adopts the role of potential energy in solving the electron-nuclear Schrodinger equation containing explicitly the kinetic energy of nuclei... 

For JT problems of higher dimensions such as that for the T (e t2) problem, the adiabatic potential V is complicated and cannot be written down in an analytical form. However, in such problems, the least action path can be approximated by the minimum energy path (or path of steepest descent) on the adiabatic potential surface. It is the path for which the tangent to it is parallel to the gradient of the APES. 

In the master formula for the analysis of the pseudo-Jahn-Teller effect, the total curvature of the adiabatic potential surface, K, is partitioned in a so-called non vibronic part K0 and the vibronic one Kv, namely K = K0 + Kv, with... 

The surface-hopping trajectories obtained in the adiabatic representation of the QCLE contain nonadiabatic transitions between potential surfaces including both single adiabatic potential surfaces and the mean of two adiabatic surfaces. This picture is qualitatively different from surface-hopping schemes [2,56] which make the ansatz that classical coordinates follow some trajectory, R(t), while the quantum subsystem wave function, expanded in the adiabatic basis, is evolved according to the time dependent Schrodinger equation. The potential surfaces that the classical trajectories evolve along correspond to one of the adiabatic surfaces used in the expansion of the subsystem wavefunction, while the subsystem evolution is carried out coherently and may develop into linear combinations of these states. In such schemes, the environment does not experience the force associated with the true quantum state of the subsystem and decoherence by the environment is not automatically taken into account. Nonetheless, these methods have provided com-... 

In this sense, the control of electronic transitions of wavepackets using short quadratically chirped laser pulses of moderate intensity is a very promising method, for two reasons. First, only information about the local properties of the potential energy surface and the dipole moment is required to calculate the laser pulse parameters. Second, this method has been demonstrated to be quite stable against variations in pulse parameters and wavepacket broadening. However, controlling of some types of excitation processes, such as bond-selective photodissociation and chemical reaction, requires the control of wavepacket motion on adiabatic potential surfaces before and/or after the localized wavepacket is made to jump between the two adiabatic potential energy surfaces. 

In order to discuss the JT distortion on the adiabatic potential surface we define a vector Rjt as the vector given by the displacements of the atoms from the high symmetry point defined by the Rhs- The JT radius, Rjp is given by the length of the distortion vector between the high symmetry and the minimum energy configuration. 

Fig. 10 Snapshots of Cr(CO)5 wavepacket dynamics on the lowest and first excited adiabatic potential surfaces and right panels). The contours show the two-dimensional Jahn-Teller surface in the space of the (Qj, Q2) pair of Jahn-Teller active coordinates, shown to the left...

Fig. 1 The adiabatic potential surface of an electronic Eg state due to the linear vibronic interaction with a vibrational mode top) the mexican hat-shaped curve on the left is modified by higher order coupling terms, yielding a three minima-refinement, which is shown in a cross section perpendicular to the energy axes on the right. The potential surface, resulting from Tg Eg coupling (amidst), leads to an analogous three-well-structure already in first order - each of these corresponding to a tetragonal polyhedron distortion along one of the three molecular axes. The vibrational ai and e modes are shown on the bottom (adopted from [2])...

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