Potential energy curves diabatic

Figure 2. Intersecting harmonic energy curves for the reaction A+BC- AB+C is the sum of the bond extensions of AB and BC at the transition state and e is the resonance energy at the crossing point d is the horizontal distance of the potential energy curves (diabatic curves) which cross at the top of the reaction energy barrier.

Fig. 1. Schematic potential energy curves for a neutral transition metal atom (M) inserting into the H-R bond of a hydrocarbon. Diabatic curves are shown as dashed lines, adiabatic curve shown as a solid line.

Figure 4. Diabatic (solid lines) and adiabatic (dashed lines) potential-energy curves of Model IVa. The Gaussian wave packet indicates the initial preparation of the system at time t = 0.

Figure 1. Diabatic potential energy curves for Nal with an expanded view of the adiabatic potential curves, e, and Ej, near the diabatic curve crossing.

Figure 3. Computed potential energy curves for the diabatic and adiabatic state in the [HsN-H-NH ] system in the gas phase using 6-31G(d) basis set. The HF and MOVE energy profiles are overlapping.

Historically the first application of symmetry to potential energy surfaces was to prove the so-called non-crossing rule. In its simplest form this may be stated as potential energy curves for states of diatomic molecules of the same symmetry do not cross . We have already seen in section 2 that this should be qualified to apply to adiabatic curves, as in some situations it may be convenient to define diabatic curves wdiich do cross. 

Figure 1 Left Enol-keto tautomerism in salicylaldimine (SA) and normal mode displacements for skeleton modes 1 4 and 1/30. Middle H/D diabatic potential energy curves Ua(Qu) for mode i/u (lowest states ground state, bolding and stretching fundamental, first bolding overtone arrows indicate laser excitation). Right two-dimensional (Qj4,Q3o) cuts through the adiabatic PES (obtained upon diagonalizing the field-free part of Eq. (1)) which has dominantly H/D stretching character but includes state and mode couplings (contours from 0 to 7400 cm-1).

Figure 30. Schematic representation of potential energy curves for adiabatic (a, b) and diabatic (c) photoreactions. (Reprinted with permission from Ref. 33).

Let us consider a typical situation as sketched in Figure 7.5. V and V2 represent the (diabatic) potential energy curves (or surfaces) of two... 

An intriguing example which highlights the idea of femtosecond chemistry is the photodissociation of Nal (Rose, Rosker, and Zewail 1988 Rosker, Rose, and Zewail 1988). Figure 16.6 illustrates the potential energy curves involved in the fragmentation. The pump pulse excites Nal to a covalent state which, in the diabatic picture, correlates with Na +... 

Fig. 7. Diabatic ab initio potential energy curves for 1 + O2. These calculations correspond to a fixed 0-0 distance of 2.287 bohr and a Jacobi angle of 50°.

Figure 2. (a) Schematic illustration of the adiabatic (solid) and diabatic (dashed) vibrational free energy curves as functions of the solvent coordinate Zp for a symmetric single proton transfer reaction, (b) Potential energy curves as functions of the proton coordinate r, for three specific values of the solvent coordinate Zp indicated in (a). 

The results obtained in our laboratory as well as by other experimentalists [3, 4] have inspired a considerable amount of theoretical work on this system [2, 5-8], Archirel and Levy [7] have calculated a set of potential energy surfaces for the states N2 (X) + Ar, N2(A) + Ar, and N2 + Ar+(2P) as well as the couplings between these surfaces using a novel computational technique. From their results they developed a set of diabatic vibronic potential energy curves, and they assumed that transitions could occur when two curves crossed. Cross sections were computed using either the Demkov or Landau-Zener formula, as appropriate, and good agreement was obtained with the experimental values in most cases. Nikitin et al. [8] have taken a somewhat similar approach to this system. They estimated the adiabatic vibronic interaction curves for this system, and they assumed that transitions... 

Electromagnetic Field-Dressed Diabatic and Adiabatic Potential Energy Curves. 177... 

Table 3.1 summarizes the different types of potential energy curves and the specific terms in H that are neglected in order to define the diabatic, adiabatic, relativistic-adiabatic, and relativistic-diabatic basis functions. 

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. 

Figure 3.12 Field-dressed potential energy curves for HJ interacting with a 532nm laser field. The field-dressed diabatic curves are shown as full lines. The field-dressed adiabatic curves, shown as dotted and dashed curves, correspond respectively to laser intensities of 1 x 1013 W/cm2 and 4 x 1013 W/cm2 (from Giusti-Suzor, et al., 1995).

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