Potential energy surface schematic

Figure 8. Two-dimensional potential energy surfaces (schematic) for (a) early and (b) late barrier (B) of dissociation of H2 on a transition metal surface.

Potential energy surface Schematic two- or three-dimensional representation of the total potential energy of a chemical system as a function of internuclear coordinates. 

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.

Fig. 13.11. A schematic drawing of the potential energy surfaces for the photochemical reactions of stilbene. Approximate branching ratios and quantum yields for the important processes are indicated. In this figure, the ground- and excited-state barrier heights are drawn to scale representing the best available values, as are the relative energies of the ground states of Z- and E -stilbene 4a,4b-dihydrophenanthrene (DHP). [Reproduced from R. J. Sension, S. T. Repinec, A. Z. Szarka, and R. M. Hochstrasser, J. Chem. Phys. 98 6291 (1993) by permission of the American Institute of Physics.]...

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 55. Two-dimensional coupled potential energy surfaces and the wavepacket motion, (a) Si — S2 surfaces and (b) Si — So surfaces. The black, gray, and white circles and dotted lines indicate the locations of the FC region. Si - S2 conical intersection minimum, 5MR Si — So conical intersection minimum, and seam lines, respectively. The solid arrows indicate the schematic wavepacket pathway in the case of natural photoisomerization starting from the vibrational ground state. Taken from Ref. [49].

Figure 4. Schematic potential energy surface for the reaction of FeO" " with methane. The sohd line indicates the sextet surface the quartet surface is shown with a dotted line, in each case leading to the production of Fe + CH3OH. The dashed line leads to formation of FeOET + CH3. The pathway leading to the minor FeCH2" + H2O channel is not shown. Schematic structures are shown for the three minima the [OFe CHJ entrance channel complex, [HO—Fe—CH3] insertion intermediate, and Fe" (CH30H) exit channel complex. See text for details on the calculations on which the potential energy surface is based.

Figure 1. Schematic of the radial cuts of the ground- and excited-state potential energy surfaces at the linear and T-shaped orientations. Transitions of the ground-state, T-shaped complexes access the lowest lying, bound intermolecular level in the excited-state potential also with a rigid T-shaped geometry. Transitions of the linear conformer were previously believed to access the purely repulsive region of the excited-state potential and would thus give rise to a continuum signal. The results reviewed here indicate that transitions of the linear conformer can access bound excited-state levels with intermolecular vibrational excitation.

It is likely that the above schematic view of the potential energy surface would be relevant for the mixed valence Donnor Acceptor Donnor (DAD) architectures such as ... 

Let us consider the possible relations of LS and HS potential energy surfaces as shown schematically in Fig. 9. As long as the zero-order or diabatic surfaces are considered, the eleetrons remain localized on the particular spin state, no eleetron transfer being possible. In order that a conversion between the LS and HS state takes place, electronic coupling of the states is required. This coupling effectively removes the degeneracy at the interseetion of the zero-order surfaces... 

Figure 5.1. Schematic potential energy surfaces for the photoelectron spectroscopy experiment. Labels in parentheses refer to negative ion photoelectron spectroscopy.

Fig. 24. Schematic C iv potential energy surfaces for the methoxy radical as a function...

Fig. 25. Schematic C%v potential energy surfaces for the CH3S radical as a function of C—S bond length. (From Hsu et a/.,163 Cui et a/.,161 and Bise et a/.164)...

Fig. 28. Schematic of potential energy surfaces of the vinoxy radical system. All energies are in eV, include zero-point energy, and are relative to CH2CHO (X2A//). Calculated energies are compared with experimentally-determined values in parentheses. Transition states 1—5 are labelled, along with the rate constant definitions from RRKM calculations. The solid potential curves to the left of vinoxy retain Cs symmetry. The avoided crossing (dotted lines) which forms TS5 arises when Cs symmetry is broken by out-of-plane motion. (From Osborn et al.67)...

Fig. 3. Schematic potential energy surfaces for reaction of FeH+, CoH+, and NiH+ with CH4 (93).

Figure 6.2 Schematic diagram of the potential energy surfaces for the reduced and the oxidized state.

Figure 11 Simplified two-dimensional schematic of a multidimensional potential energy surface as a function of its configurational degrees of freedom. The landscape topology is specified by the density, whereas the system s elevation on the landscape is dictated by temperature. Reprinted with permission from Ref. 6.

Fig. 2.5 Schematic diagram of a potential energy surface for a collinear reaction A + BC — AB + C.

Fig. 5.1 A schematic projection of the 3n dimensional (per molecule) potential energy surface for intermolecular interaction. Lennard-Jones potential energy is plotted against molecule-molecule separation in one plane, the shifts in the position of the minimum and the curvature of an internal molecular vibration in the other. The heavy upper curve, a, represents the gas-gas pair interaction, the lower heavy curve, p, measures condensation. The lighter parabolic curves show the internal vibration in the dilute gas, the gas dimer, and the condensed phase. For the CH symmetric stretch of methane (3143.7 cm-1) at 300 K, RT corresponds to 8% of the oscillator zpe, and 210% of the LJ well depth for the gas-gas dimer (Van Hook, W. A., Rebelo, L. P. N. and Wolfsberg, M. /. Phys. Chem. A 105, 9284 (2001))...

The energy term in the Boltzmann factor may be considered as the size of the barrier along a potential energy surface for a system of reactants going to products, as shown schematically in Fig. 2.1. The state of the reacting species at this activated energy can be regarded as some intermediate complex that... 

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.)...

Eigure 4.1 shows a schematic of an excited-state potential energy surface and superimposed on it is a wavepacket, which is the initial wavepacket for a photodissociation process. An analysis line is drawn perpendicular to the contour lines in the asymptotic region of the surface, where there is no longer any substantial interaction between the separating fragments and the contour... 

Figure 4.1. Schematic diagram of an excited-state potential energy surface showing an initial wavepacket for a photodissociation calculation and indicatng its path toward the dissociation products. The line marked Roo is the analysis line. ...

Figure 4.3. The initial wavepacket superimposed on an Li+HF potential energy surface. Also shown (in a schematic manner) is the analysis line, marked R o, in the product channel. In an actual calculation the analysis line would be placed at a much larger value of the product scattering coordinate.

An example of the application of transition state theory to atmospheric reactions is the reaction of OH with CO. As discussed earlier, this reaction is now believed to proceed by the formation of a radical adduct HOCO, which can decompose back to reactants or go on to form the products H + COz. For complex reactions such as this, transition state theory can be applied to the individual reaction steps, that is, to the steps shown in reaction (15). Figure 5.3 shows schematically the potential energy surface proposed for this reaction (Mozurkewich et al., 1984). The adduct HOCO, corresponding to a well on the potential energy surface, can either decompose back to reactants via the transition state shown as HOCO./ or form products via transition state HOCO,/. ... 

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. 4. Schematic drawing of the potential energy surfaces for the CPMD simulations. PES of Sellmann-type complexes (left) PES of Schrock-type complex (right).

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