Surface, hypothetical potential energy

Figure 5-2. A hypothetical potential energy surface for the reaction A -I- BC —> AB -I- C.

Figure 1. Schematic diagram of a hypothetical potential energy hyper-surface for (ABCD)+, constructed to illustrate the main features which relate and control the production of isomeric forms and the isomerization between those forms.

A depiction of a hypothetical potential energy surface for a reacting system as a function of two chosen coordinates (c.g., the lengths of two bonds being broken). Such diagrams are useful in assessing structural effects on transition states for stepwise or concerted pathways. An example of More O Ferrall-Jencks diagrams for j8-elimina-tion reactions is shown below. 

Figure 3 A hypothetic potential-energy surface for a system with two internal degrees of freedom. A, B, C, and D mark different local total-energy minima...

Fig. 1. Hypothetical potential energy surface for the oxygen-binding processes of hemoglobin to show relationship between chemical coordinate and conformation coordinate. See text.

Figure 3. Hypothetical potential energy surface for the collinear reaction A + BC AB + C. The solid lines are equipotentials and the dashed line is the reaction path (31).

Hypothetical potential energy surface for cyclopropane isomerization based on the group increments method. 

AMI Calculations of the potential energy surface of the photoisomerization of the hypothetical (V-imide 6 (R1 = CHO R2 = H) have been reported.78... 

There have a number of computational studies of hypothetical RMMR species [10-13, 40, 411. The simplest compounds are the hydrides HMMH. Some calculated structural parameters and energies of the linear and trans-bent metal-metal bonded forms of the hydrides are given in Table 1. It can be seen that in each case the frans-bent structure is lower in energy than the linear configuration. However, these structures represent stationary points on the potential energy surface, and are not the most stable forms. There also exist mono-bridged, vinylidene or doubly bridged isomers as shown in Fig. 2... 

Figure 6.34 shows potential energy curves for a hypothetical diatomic molecule X2, which approaches a surface, coming from the right-hand side of the diagram. First... 

Figure 1 Relative positions of the potential energy (E) surfaces of the electronic states involved in a hypothetical chemiluminescent reaction as a function of intemuclear separation (r). P and P represent the ground and lowest electronically excited singlet states of the product of the reaction, respectively. R represents the ground electronic state of the reactant. AH is the enthalpy of the dark reaction while AHa is its enthalpy of activation. AH is the enthalpy of activation of the photoreaction, hv denotes the emission of chemiluminescence.

Molecules are never motionless, even at the ground vibrational state they perform vibrations. It is only in the minimum position of the potential energy surface where a molecule would be motionless and this is a hypothetical state. Although it does not exist, it is a well-defined reference structure and... 

Fig. 2. Potential energy surface of a hypothetical collection of atoms.

To a good approximation, substitution of one isotope for another does not alter the potential energy surface. The electronic structure, and thus all binding forces, remain the same. All differences are attributable solely to the change in mass, which manifests itself primarily in the frequencies of vibrational modes. For a hypothetical model of a small mass m attached to a much larger mass by a spring of force constant k, the classical vibrational frequency is given by 49... 

Potential energy surfaces or profiles are descriptions of reactions at the molecular level. In practice, experimental observations are usually of the behaviour of very large numbers of molecules in solid, liquid, gas or solution phases. The link between molecular descriptions and macroscopic measurements is provided by transition state theory, whose premise is that activated complexes which form from reactants are in equilibrium with the reactants, both in quantity and in distribution of internal energies, so that the conventional relationships of thermodynamics can be applied to the hypothetical assembly of transition structures. 

The central concept of mode-selective chemistry is illustrated in Fig. 1, which depicts the ground and excited state potential energy surfaces of a hypothetical triatomic molecule, ABC. One might wish, for example, to break selectively the bond between atoms A and B to yield products A+BC. Alternatively, one might wish to activate that bond so that in a subsequent collision with atom D the products AD+BC are formed. To achieve either goal it is necessary to cause bond AB to vibrate, thereby inducing motion along the desired reaction coordinate. 

At the same time, many theoretical calculations have been carried out over the last two decades to find new polynitrogens. Computational studies have been able to assist and encourage experimental work to find and identify unknown polynitrogens by providing information about molecular structures and kinetic stabilities on the potential energy surface with respect to N2. Many hypothetical structures of polynitrogens (from N4 to N60) have been predicted by quantum-mechanical calculations, which have led to the... 

The reason we work with the derivatives is related to the fact that the mode displacements are measured from their instantaneous, t = 0, position rather than some hypothetical harmonic minimum (48). We know that the global potential energy surface of a liquid is far from harmonic, so such a minimum would be a rather unphysical construct. What happens instead is that our modes do obey simple harmonic dynamics, but subject to somewhat unusual initial conditions (49) ... 

In die hypothetical case of a perfectly homogeneous surface, there is no variation of uniform surface, which gives rise to energy wells of the same depth. Now, the potential energy profiles corresponding to mobile and localized adsorption are shown respectively in Figures 1.4b and 1.4c. In the former case, there is a random distribution of... 

Figure 1.4. Distribution of adsorbed molecules on hypothetical surfaces (left) and corresponding variations of potential energy (right). M, mobile L, localized. Adsorbate-adsorbate interactions are not taken into account.

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