Adiabatic potential energy surfaces cross section

The adiabatic potential energy surface below the intersection point possesses three equivalent minimum regions. One of these surface minima is seen in the cross section in Figure 3 and is labeled as point Min. The three minima on the surface are separated by three saddle-point transition states. Point TS in the Figure 3 cross section is the transition state between the two other... 

In this section, we introduce the model Hamiltonian pertaining to the molecular systems under consideration. As is well known, a curve-crossing problem can be formulated in the adiabatic as well as in a diabatic electronic representation. Depending on the system under consideration and on the specific method used, both representations have been employed in mixed quantum-classical approaches. While the diabatic representation is advantageous to model potential-energy surfaces in the vicinity of an intersection and has been used in mean-field type approaches, other mixed quantum-classical approaches such as the surfacehopping method usually employ the adiabatic representation. 

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. 

We return finally in this section to the question of avoided crossings in potential energy surfaces. We have already noted in section 2 that diabatic potentials may be a more suitable basis for a dynamical calculation than adiabatic. By expanding on the relationship between the two we will be able to introduce the concept of analytic continuation of adiabatic surfaces into complex coordinate space which has proved useful for some dynamical problems. 

Figure 2.1(a) above illustrates the potential energy surface for a diabatic electron transfer process. In a diabatic (or non-adiabatic) reaction, the electronic coupling between donor and acceptor is weak and, consequently, the probability of crossover between the product and reactant surfaces will be small, i.e. for diabatic electron transfer /cei, the electronic transmission factor, is transition state appears as a sharp cusp and the system must cross over the transition state onto a new potential energy surface in order for electron transfer to occur. Longdistance electron transfers tend to be diabatic because of the reduced coupling between donor and acceptor components this is discussed in more detail below in Section 2.2.2. 

Figure 6. The dependence of the harrier height on the Jacobi angle y for the potential energy surfaces used in the present cross section calculations for O + H2 and O + HCl (DCl) reactions (—) pure electronic barrier (—) vibrationally adiabatic barrier (v = 0) [21].

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... 

ABSTRACT. Calculation of the rate constant at several temperatures for the reaction +(2p) HCl X are presented. A quantum mechanical dynamical treatment of ion-dipole reactions which combines a rotationally adiabatic capture and centrifugal sudden approximation is used to obtain rotational state-selective cross sections and rate constants. Ah initio SCF (TZ2P) methods are employed to obtain the long- and short-range electronic potential energy surfaces. This study indicates the necessity to incorporate the multi-surface nature of open-shell systems. The spin-orbit interactions are treated within a semiquantitative model. Results fare better than previous calculations which used only classical electrostatic forces, and are in good agreement with CRESU and SIFT measurements at 27, 68, and 300 K. ... 

---