Schematic representation of potential energy surface

Figure 6.4. Schematic representation of potential energy surfaces S, and S, as well as So->S, excitation (solid arrows) and nuclear motion under the influence of the potential energy surfaces (broken arrows) a) in the case of an avoided crossing, and b) in the case of an allowed crossing (adapted from Michl, 1974a).

Figure 6.3. Schematic representation of potential energy surfaces of the ground state (S ) and an excited state (S, or T,) and of various processes following initial excitation (by permission from IVfichl, 1974a).

Figure 10. Schematic representation of potential energy surfaces for linear and bent dissociation.

Figure 6. Schematic representation of tip-to-surface interactions in SFM. (a) potential energy as a function of separation distance (b,c) net force and force gradient, respectively. The repulsive and attractive force regimes have been defined.

Figure Al.6.10. (a) Schematic representation of the three potential energy surfaces of ICN in the Zewail experiments, (b) Theoretical quantum mechanical simulations for the reaction ICN ICN [I--------------...

Fig. 13.5. Schematic representation of the potential energy surfaces of the ground state (S ,) and the excited state (.5,) of a nonadiabatic photoreaction of reactant R. Depending on the way the classical trajectories enter the conical intersection region, different ground-state valleys, which lead to products P and can be reached. Reproduced from Angew. Chem. Int. Ed. Engl. 34 549 (1995) by permission of Wiley-VCH.

Figure 5.7. Schematic representation of the definitions of work function O, chemical potential of electrons i, electrochemical potential of electrons or Fermi level p = EF, surface potential %, Galvani (or inner) potential

Figure 7, Schematic representation of the 1-TS (solid) and 2-TS (dashed) (where TS = transition state) reaction paths in the reaction Ha + HbHc Ha He + Hb- The H3 potential energy surface is represented using the hyperspherical coordinate system of Kuppermann [54], in which the equilateral-triangle geometry of the Cl is in the center (x), and the linear transition states ( ) are on the perimeter of the circle the hyperradius p = 3.9 a.u. The angle is the internal angular coordinate that describes motion around the CL...

Figure 1.1 Schematic representation of a well known catalytic reaction, the oxidation of carbon monoxide on noble metal catalysts CO + Vi 02 —> C02. The catalytic cycle begins with the associative adsorption of CO and the dissociative adsorption of 02 on the surface. As adsorption is always exothermic, the potential energy decreases. Next CO and O combine to form an adsorbed C02 molecule, which represents the rate-determining step in the catalytic sequence. The adsorbed C02 molecule desorbs almost instantaneously, thereby liberating adsorption sites that are available for the following reaction cycle. This regeneration of sites distinguishes catalytic from stoichiometric reactions.

Fig. 6 Stepwise and concerted electron transfer and bond breaking. Schematic representation of the potential energy surface, (a) Stepwise process, a > 0.5. (b) Concerted process, a < 0.5. (Adapted from Andrieux et ai, 1985.)...

Figure 2.1 Schematic representation of the ground and electronic excited potential energy surfaces (PESs) and the corresponding absorption spectra of the parent molecule, resulting from the reflection of different initial wavefunctions on a directly dissociative PES (a) absorption from a vibrationless ground state consists of a broad continuum and (b) absorption from a vibrationally excited state shows that extended regions are accessed, leading to a structured spectrum with intensities of the features being dependent on the Franck-Condon factors. Reproduced with permission from Ref. [34]. Reproduced by permission of lOP Publishing.

Fig. 13. Top Schematic representation of the two components of the Jahn-Teller-active vibrational mode for the E e Jahn-Teller coupling problem for octahedral d9 Cu(II) complexes. Bottom Resulting first-order Mexican hat potential energy surface for showing the Jahn-Teller radius, p, and the first-order Jahn-Teller stabilization energy, Ejt.

Fig. 35. Schematic representation of the first-order potential energy surface for T0e vibronic coupling. The two components of the eg vibrational mode are shown on the left.

Fig. 9.1. Left-hand side Representation of an elastic potential energy surface. It has the general form (6.35) with coupling strength parameter e = 0. In case (a), the equilibrium bond distance in the electronic ground state equals the equilibrium separation of the free BC fragment. The heavy arrows schematically indicate two representative trajectories starting at the respective FC points. Right-hand side The corresponding final state distributions.

Figure 9. Schematic representation of upper portion of potential eneigy surface for merging of substitution mechanisms. A Sjsj 1 mechanism. No nucleophilic solvation in transition state ion pair intermediate (possibly nudeophilically solvated) B Sn2 (intermediate). Transition state is nudeophilically solvated by solvent (SOH) intermediate is a nudeophilically solvated ion pair (see Fig. 8) C Classical Sn2. No energy minimum. In curves A and B, the second transition state may be of higher energy than the first in cases where internal return is important.

Figure 14. Schematic representation of direct and precursor-mediated processes on a surface [129, 130]. Processes occurring along the surface normal are plotted along the abszissa. The processes are correlated with the potential energy diagram of Fig. 7(b) (ex = extrinsic precursor, in —intrinsic precursor, nc = number of impinging particles from the gas phase, a and a" are fractions of trapped molecules, p = probabilities. p"m = migration probability along the surface).

Fig. 12 A schematic representation of the consecutive locations Li on the potential energy surface and the range of fragments detected for each location. Adapted from [15]...

Figure 2.5. Schematic representation of electronic potential energy surfaces 1, consecutive conformational and solvatational equilibrium processes with the essential change in the nuclear coordinates Q and the standard Gibbs energy AG0 2, consecutive non-equilibrium processes with small changes in Q and AG0 3, 4, equilibrium (full line) and non-equilibrium (broken line) processes in the normal and inverted Marcus regions respectively. (Likhtenshtein, 1996) Reproduced in permission.

Figure 8. Schematic representation of chemical potential energy surfaces. Counting of states below reaction barrier for both reactants and products gives a minimal estimate of numbers of coupled equations to be solved.

Figure 1 Schematic representation of a potential energy surface with two minima. The larger width of the higher-energy minimum B (leading to greater flexibility compared with the narrower lower-energy minimum A) could result in a lower free energy for conformation B that fluctuates about the higher-energy minimum.

Fig. x.4. Schematic representation of the motion in phase space of the internal coordinates of a critically energized molecule with a single possible mode of decomposition. Bounding surface is one of constant potential energy. 

Fig. 3. Schematic representation of the energetic path followed along a polymerization reaction of the monomer M catalyzed by a catalytic centre h (such as a transition metal site or a basic surface center). The precursor species are indicated as F M, while l- M represent oligomers/polymers. The activation energy barriers for each step (A i) are represented. Also the energy barrier Afi) associated with the polymers release is represented in the perpendicular direction, as this step can potentially occur for each M insertion. In contrast to the cases displayed in Fig. 2, in this case A , > > A i (unpublished).

The following discussion makes frequent use of such one-dimensional cross sections through potential energy surfaces. The reaction coordinate Q used as the abscissa often remains unspecified in schematic representations. Caution is required in interpreting such cross sections. What appears as a minimum, barrier, or saddle point in one cross section may look quite different in another one. A typical example is a maximum of a reaction profile, which appears as a minimum in a cross section perpendicular to the reaction coordinate. 

Figure 4.1. Schematic representation of Born-Oppenheimer potential energy surfaces. Using the photochemical nomenclature, the ground-state surface of a closed-shell system, which is the lowest singlet surface, is labeled So, followed by S Sj, etc. in order of increasing energies. The triplet surfaces are similarly labeled T, Tj,...

Figure 4.3. Schematic representation of adiabatic and diabatic (nondiabatic) potential energy surfaces S and S, (adapted from Michl, 1974a).

Figure 5.22. Schematic representation of the potential energy surfaces for excimer formation and of the difference between monomer fluorescence and excimer fluorescence (adapted from Rehm and Weller, 1970a).

Figure 5.37. Schematic representation of the potential energy surfaces of hot excited-state reactions.

Figure 6.8. Schematic representation of the potential energy surfaces relevant for the photochemical conversion of 1,4-dewarnaphihalcnc to naphthalene. Radiative and nonradiative processes postulated are shown and probabilities with which each path is followed are given (by permission from Wallace and Michl, 1983).

Figure 7.24. Schematic representation of energies of stationary points for the Norrish type 11 reaction of butanal. The diagram corresponds to a projection of multidimensional potential energy surfaces into a plane. The two energies given for the biradical on the S, suiface correspond to a geometry optimized for So (front bottom) and optimized for S, (middle rear), respectively. A broken...

From the schematic representation in Figure 7.56 it is seen that chemiluminescence can be described as a reverse photochemical reaction. Chemiluminescence is afforded by a transition from the ground-state potential energy surface to an isoenergetic vibrational level of an excited-state surface and... 

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