Potential energy surface minima

Can it exist at all Like tetra-t-butyltetrahedrane this is a potential energy surface minimum and lacks frequencies below 500 cm corresponding to vibrations of the tetrahedrane nucleus, indicating (cf tetra-t-butyltetrahedrane, above) a secure minimum. Such calculations would have provided, prior to its synthesis, good evidence that the molecule can exist. 

Some of the earliest ab initio calculations on tetrahedrane are by Kollmar, who also refers to earlier semiempirical work [59], Can it exist B3LYP/6-3IG calculations (e.g. by the author) show a potential energy surface minimum with no vibrations below 500 cm for deformation of the C4 nucleus (in fact no vibrations at all below 500 ). This indicates a robust minimum on the potential energy surface. 

In the case of nitrogen the question is whether five fluorine atoms can be squeezed on to a nitrogen atom. Although calculations predict NF5 to be a potential energy surface minimum, there is enough doubt about the ability of ab initio calculations to accurately handle molecular size (related somewhat to nonbonded interactions [10]) for one to be less than fully confident that this compound will be synthesized. 

Figure 13 shows the cross section for insertion events whose minimum energy was nearly that of the potential energy surface minimum. The cross section for abstraction includes only those reactions whose minimum energy was nearly that of products. Owing to the use of these more restrictive definitions, the excitation functions for insertion and abstraction do not necessarily sum to the overall excitation function but any discrepancy is always quite small. 

Figure Al.6.26. Stereoscopic view of ground- and excited-state potential energy surfaces for a model collinear ABC system with the masses of HHD. The ground-state surface has a minimum, corresponding to the stable ABC molecule. This minimum is separated by saddle points from two distmct exit chaimels, one leading to AB + C the other to A + BC. The object is to use optical excitation and stimulated emission between the two surfaces to steer the wavepacket selectively out of one of the exit chaimels (reprinted from [54]).

The combination is in this case an out-of-phase one (Section I). This biradical was calculated to be at an energy of 39.6 kcal/mol above CHDN (Table ni), and to lie in a real local minimum on the So potential energy surface. A normal mode analysis showed that all frequencies were real. (Compare with the prebenzvalene intermediate, discussed above. The computational finding that these species are bound moieties is difficult to confimi experimentally, as they are highly reactive.)... 

Figure 3. Low-energy vibronic spectrum in a. 11 electronic state of a linear triatomic molecule, computed for various values of the Renner parameter e and spin-orbit constant Aso (in cm ). The spectrum shown in the center of figure (e = —0.17, A o = —37cm ) corresponds to the A TT state of NCN [28,29]. The zero on the energy scale represents the minimum of the potential energy surface. Solid lines A = 0 vibronic levels dashed lines K = levels dash-dotted lines K = 1 levels dotted lines = 3 levels. Spin-vibronic levels are denoted by the value of the corresponding quantum number P P = Af - - E note that E is in this case spin quantum number),...

At minimum of the lower sheet of potential energy surface. 

At minimum of the conical intersection on the upper sheet of potential energy surface. Rotation about the axis perpendicular to the plane of the molecule. 

To carry out ageometry optimization (minimi/atioiT), IlyperCh em starts with a set of Cartesian coordinates for a molecule and tries to find anew set of coordinates with a minimum potential energy. Yon should appreciate that the potential energy surface is very complex, even for a molecule containing only a few dihedral an gles. 

Transition stale search algorithms rather climb up the potential energy surface, unlike geometry optimi/.ation routines where an energy minimum is searched for. The characterization of even a simple reaction potential surface may result in location of more than one transition structure, and is likely to require many more individual calculations than are necessary to obtain et nilibrinm geometries for either reactant or product. 

Characterize a potential energy surface for acertain niimberof atoms, i.e., detect all the local energy minima, the global minimum on the surface, and all the transition states between different minima. 

In the chapter on reaction rates, it was pointed out that the perfect description of a reaction would be a statistical average of all possible paths rather than just the minimum energy path. Furthermore, femtosecond spectroscopy experiments show that molecules vibrate in many dilferent directions until an energetically accessible reaction path is found. In order to examine these ideas computationally, the entire potential energy surface (PES) or an approximation to it must be computed. A PES is either a table of data or an analytic function, which gives the energy for any location of the nuclei comprising a chemical system. 

MEP (IRC, intrinsic reaction coordinate, minimum-energy path) the lowest-energy route from reactants to products in a chemical process MIM (molecules-in-molecules) a semiempirical method used for representing potential energy surfaces... 

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