Conical Intersection Of Potential Surfaces Research Articles

Photochemistry of XXI century: Paradigm change

The process of revision of the mechanisms of photochemical reactions is reviewed. The revision is characterized by the recognition of the role of conical intersections of potential surfaces in the transitions from excited to ground state. We may assume that, to date, this revision is completed.

The time-dependent Born-Oppenheimer approximation

We explain why the conventional argument for deriving the time-dependent Born-Oppenheimer approximation is incomplete and review recent mathematical results, which clarify the situation and at the same time provide a systematic scheme for higher order corrections. We also present a new elementary derivation of the correct second-order time-dependent Born-Oppenheimer approximation and discuss as applications the dynamics near a conical intersection of potential surfaces and reactive scattering.

Compensation of the electronic geometric phase by the nuclear part of the wave-function

The nuclear equation in the Born-Oppenheimer scheme for electron-ion bound states is solved by a method that ensures that the nuclear part compensates for the geometrical (Berry) phase in the electronic part and that the total wave-function is single valued. The compensation occurs in a manner that keeps the energy of the state continuous even across a `topological transition', i.e. for a change of parameters that removes the electronic degeneracy. The method ties the phase to the behaviour of the nuclear part near the conical intersection of potential surfaces. The consistency of the method is illustrated by Gedankenexperiments in a non-symmetric Jahn-Teller situation and a spin-orbit coupled doublet.

Molecular point symmetry and the phase of the electronic wave function: Tools for the prediction of critical points of potential energy surfaces

AbstractBy combining a well‐known theorem of Longuet‐Higgins on the phase changes of electronic wave functions along loops encircling a conical intersection of potential surfaces, and a recently proven “vertical symmetry theorem” on the relative distributions of point symmetry groups and potential surface critical points in configuration space, a new result is obtained, suitable for the prediction of the presence of a critical point within a domain of configurations.

A b i n i t i o studies of the low-lying electronic states of ketene

Features of the potential energy surfaces of the X̃ 1A1, 3A2(3A″), 1A2(1A″), 3A1(3A′), 1B1, and 2 1As1 low-lying electronic states of ketene have been investigated using self-consistent-field (SCF) and configuration interaction singles and doubles (CISD) methods with double zeta plus polarization (DZP) and DZP+Rydberg (DZP+R) basis sets. The DZP+R CISD vertical excitation energies are in excellent agreement with observed transition energies and suggest assignments for the X̃ 1A1→1B1 and X̃ 1A1→2 1A1 transitions in the electronic spectrum of ketene. Stationary points have been located at the DZP SCF level of theory for the first four states listed above, and SCF quadratic force constants and harmonic vibrational frequencies have been computed analytically at these stationary points. The X̃ 1A1 geometry and vibrational frequencies compare favorably with experimental values, the agreement being typical of DZP SCF results. Due to curve crossings and conical intersections of potential surfaces, the four lowest theoretical excited state surfaces have only two valid (double) minima, corresponding to 3A″ and 1A″ electronic states. At the DZP SCF geometries, Davidson-corrected CISD adiabatic excitation energies of 16 700 and 19 000 cm−1 have been obtained for the 3A″ and 1A″ states, supporting the previous experimental T0 upper bounds of Laufer and Keller. Finally, the X̃ 1A1 state is predicted to lie only 5500–7000 cm−1 below the 1A″ state at the 1A″ optimum geometry and appears to have a significant effect on the 1A″ out-of-plane frequencies.