Molecular potential adiabatic states

Before getting into a deeper analysis of the concept of resonance, we must define precisely what we understand by chemical structure . One of the most basic concepts in molecular quantum mechanics is the one of potential energy surface (PES). It allows us to define a molecular structure as an arrangement of nuclear positions in space. The definition of molecular structure depends on the validity of the Bom-Oppenheimer approximation for a given state. Actually, its validity is limited to selected portions of the entire Bom-Oppenheimer PES. When a state is described by one PES, we call it an adiabatic state. It is clear that the concept of chemical structure , depends on the existence of a previously defined molecular structure . Only adiabatic states have a molecular structure . From now on, we will always be dealing with adiabatic states. 

It is convenient to treat intense electromagnetic field problems in the dressed molecular states picture (see review by Giusti-Suzor, et al, (1995)). This picture allows one to think about intense field problems in a framework that closely resembles the weak field, diabatic or adiabatic states picture that is the primary focus of this book. In the dressed states picture the photon energy is added to, or subtracted from, the field-free potential energy curves. One obtains field-dressed potential curves. 

As an example of the effect of an intense laser on chemical reactions, a possible control of nonadiabatic transition of Na - - Cl by modulating its avoided crossing is studied [425], Figure 8.3 shows the potential curves that cross each other between the lowest covalent and ionic adiabatic states. The calculation is in the level of RHF/CISD/6-31G, with 26 molecular orbitals, 91 CSFs, and 13 core orbitals. The target was set to the qualitatively correct description of only the sigma states, without careful attention to the two lowest Ft states. In doing so, we chose the core orbitals up to the second highest occupied molecular orbitals. 

In this calculation, the potential energy surface (PES) for Cs -Os bond dissociation of 5 -dTMPH in vertical and adiabatic states was calculated using both compact (6-31G ) and diffuse (6-31++G ) basis sets. At each step on the PES, the singly occupied molecular orbital (SOMO)... 

Two colliding atoms approach on tire molecular ground-state potential. During tire molasses cycle witli tire optical fields detuned only about one line widtli to tire red of atomic resonance, tire initial excitation occurs at very long range, around a Condon point at 1800 a. A second Condon point at 1000 takes tire population to a 1 doubly excited potential tliat, at shorter intemuclear distance, joins adiabatically to a 3 potential, drought to be die... 

In this chapter, we look at the techniques known as direct, or on-the-fly, molecular dynamics and their application to non-adiabatic processes in photochemistry. In contrast to standard techniques that require a predefined potential energy surface (PES) over which the nuclei move, the PES is provided here by explicit evaluation of the electronic wave function for the states of interest. This makes the method very general and powerful, particularly for the study of polyatomic systems where the calculation of a multidimensional potential function is an impossible task. For a recent review of standard non-adiabatic dynamics methods using analytical PES functions see [1]. 

The adiabatic picture developed above, based on the BO approximation, is basic to our understanding of much of chemistry and molecular physics. For example, in spectroscopy the adiabatic picture is one of well-defined spectral bands, one for each electronic state. The smicture of each band is then due to the shape of the molecule and the nuclear motions allowed by the potential surface. This is in general what is seen in absorption and photoelectron spectroscopy. There are, however, occasions when the picture breaks down, and non-adiabatic effects must be included to give a faithful description of a molecular system [160-163]. 

The expressions (75) and (77) can he used to extract the parameters ki, k2, ki2, s l, s 2, and (2 from the mean adiabatic potential and the difference of the adiabatic potentials for two components of the electronic state spatially degenerate at linear molecular geomehy. 

In Chapter VI, Ohm and Deumens present their electron nuclear dynamics (END) time-dependent, nonadiabatic, theoretical, and computational approach to the study of molecular processes. This approach stresses the analysis of such processes in terms of dynamical, time-evolving states rather than stationary molecular states. Thus, rovibrational and scattering states are reduced to less prominent roles as is the case in most modem wavepacket treatments of molecular reaction dynamics. Unlike most theoretical methods, END also relegates electronic stationary states, potential energy surfaces, adiabatic and diabatic descriptions, and nonadiabatic coupling terms to the background in favor of a dynamic, time-evolving description of all electrons. 

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