Minimum energy point

Information about critical points on the PES is useful in building up a picture of what is important in a particular reaction. In some cases, usually themially activated processes, it may even be enough to describe the mechanism behind a reaction. However, for many real systems dynamical effects will be important, and the MEP may be misleading. This is particularly true in non-adiabatic systems, where quantum mechanical effects play a large role. For example, the spread of energies in an excited wavepacket may mean that the system finds an intersection away from the minimum energy point, and crosses there. It is for this reason that molecular dynamics is also required for a full characterization of the system of interest. 

Figure 1.9 A plot of energy versus internuclear distance for two hydrogen atoms. The distance between nuclei at the minimum energy point is the bond length.

These discrepancies result (a) from the harmonic approximation used in all calculations [to,- (theory) > v, (exp)], (b) the known deficiencies of minimal and DZ basis sets to describe three-membered rings [polarization functions are needed to describe small CCC bond angles a>,(DZ + P) > w,(DZ) > to,(minimal basis)] and (c) the need of electron correlated wave functions to correctly describe the curvature of the potential energy surface at a minimum energy point [ [Pg.102]

The shift transformation method yields expressions for the vibronic state at a point on the trough of minimum-energy points (see Ref. [29] and references therein). We know that Q i, (> and Q are vibrations and therefore, the unitary shift transformation operator U will only act on these three phonon coordinates. The generalised vibronic states allowing for phonon excitations can be written in... 

The above procedures yield expressions for the states at a single point on the trough of minimum-energy points. As all of these points are equivalent, the total states of the system must be an integral... 

Fig. 3.6 Variation of the energy of a molecule with separation of nonbonded atoms or groups. Atoms/ groups A and B may be in the same molecule (as indicated here) or the interaction may be intermolecular. The minimum energy occurs at van der Waals contact. For small nonpolar atoms or groups the minimum energy point represents a drop of a few kJ mol-1 ( m in = —1.2 kJ mol-1 for CH4/CH4), but short distances can make nonbonded interactions destabilize a molecule by many kJ mol-1...

If the makeup gas to the ammonia synthesis loop is absolutely free of catalyst poisons, such as H2O and C02, it can flow directly to the ammonia synthesis converter. This leads to the most favorable arrangement from a minimum energy point of view. This can be accomplished by allowing the gas that leaves the methanation step to pass through beds of molecular sieves to remove water and traces of C02 74... 

Figure 9 Conformational energy contour map of N-acetyl-N -methylalanine amide, for x1 = 60°. Locations of minima are indicated by the filled circles. The contour lines are labeled with energy in kcal/mol above the minimum-energy point at (4>,

Thus, for a given diabatic state, z is the free energy difference between the minimum energy point and the point corresponding to the minimum energy of the other state. The effective z value for the two-state system can be taken as the arithmetic mean of z, and z/ [47] (i.e., one-half of the Stokes shift for the optical ET process). 

For model 20m, the ring at the minimum-energy points could assume... 

Model 21m also had three different types of ring at the minimum-energy points two envelopes with axial and equatorial side-chains (21m-i and 21m-ii) and one boat with the equatorial side-chain (21m-iv). The axial/equatorial ratio was 59 41, and the free energy difference was almost zero. This may be due to the cyclopropyl ring that is syn to the side-chain. The axial side-chain would be repulsive to the cyclopropyl ring. 

Table 2 shows the relative energy of each minimum-energy conformer of models lm, 20m and 21m and the side-chain axial/equatorial ratios. At the minimum-energy points, the ring in lm was one of two types an... 

Considering the structural properties of hirudin in the free and bound state and the steric requirements at the S2 site of thrombin, we shaved the Vail side chain with Ala or replaced it with tm-butylglycine (/Bug) (Figure 9-2). In fact, both Val and /Bug have comparable side-chain volume [36] and strong P-forming propensities [37], with minimum energy points at ( )/ / = -90°, 100° for Val and ( )/ / = -130°,... 

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