Local energy minima

The Mg + dicadon [42] with AN+2 (N= 1) valence electrons has a stable structure in agreanent with the rule, but this is a local energy minimum. The linear structure is more stable because it minimizes the Coulomb repulsion. This is in contrast to the tetrahedral stmcture of the Li dication with two electrons (N= 0). The six electron systems caimot form closed-shell structures in the tetrahedron, but the two electron systems can do. 

An important difficulty of this simulation is the fact that, once the two helices are close to each other, it is very difficult to slide one with respect to the other or change their relative orientation because of steric clashes. This means that a simulation where the helix-helix distance is constrained would not be able to sample phase space efficiently but rather would remain near the local energy minimum where it started. In contrast, using ABF, the helices have the opportunity to move closer and farther apart so that their relative position can vary more freely. 

One NH3 ligand is expelled during the search of the local energy minimum. 

Semiempirical calculations indicate that there is a local energy minimum for the endoperoxide 37 with a barrier height of 6 kcalmoE corresponding to a lifetime of ca 10 s, in agreement with experimental results However, the most important result, which corroborates the hypothesis of 37 as the HEI in luminol chemiluminescence, is the state correlation between the ground state of 37 and the excited state of 3-AP. ... 

In order to circumvent this problem, one may either manipulate the initial guess or set up a constrained optimization, where the SCF iterations converge to predefined (constrained) properties. The latter was achieved in a protocol by Van Voorhis and coworkers (133-135). This approach suffers from the fact that the constrained Slater determinant may not represent a local energy minimum of the unconstrained potential energy surface. 

MNDO/3 has been applied to thiirene (5) and the isomeric carbene (5a), zwitterion (5b), heterocumulene (5c), and cyclic carbene (5d). Structure (5) is calculated to lie in a local energy minimum. 

The energy minimum with the lowest energy value on an energy surface (see energy minimum, local energy minimum). 

Type C number Localization energy Minimum Maximum Average... 

Putting Eq. (28) into Eq. (16) and identifying H with reverse field at which the magnetization state escapes the local energy minimum yields [134, 140]... 

A transition state represents an energy maximum—any small displacement leads to a more stable product. An intermediate, on the other hand, is a molecule or ion that represents a localized energy minimum—an energy barrier must be overcome before the intermediate forms something more stable. As you have seen in Chapter 3, and will see again in Chapter 22, because of this energy barrier, it is even possible to isolate these reactive intermediates (RCO+) and study their spectra. 

Semiempirical calculations have been applied to antiaromatic three-membered rings and indicate that they correspond to energy minima <1973CC688>. For example, thiirene 13 corresponds to a local energy minimum relative to the isomeric carbene 14, zwitterion 15, heterocumulene 16, and heterocyclic carbene 17. 

Finally, we feel it is worthwhile to stress one more time the importance of the kinetic inertia in the (reversible) chiral transfer and memory processes of our porphyrin systems. Inertia provides evidence that the system is trapped in an energy minimum. In the above examples the minimum is local the real minimum is that reached from the achiral system whose formation involves the same enthalpic contribution of the chiral one but a more favourable entropic contribution. In particular, the network of electrostatic interactions ensures a quite deep local energy minimum (that is a high value of EA). 

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