Distance geometry potential surface

The potential surfaces of the ground and excited states in the vicinity of the conical intersection were calculated point by point, along the trajectory leading from the antiaromatic transition state to the benzene and H2 products. In this calculation, the HH distance was varied, and all other coordinates were optimized to obtain the minimum energy of the system in the excited electronic state ( Ai). The energy of the ground state was calculated at the geometry optimized for the excited state. In the calculation of the conical intersection... 

Trioxirane is a cyclic isomer of ozone but whereas trioxirane has six 7f-electrons, ozone has only four. The relative positions of trioxirane and ozone on the O3 potential surface are of some interest and we have therefore carried out additional calculations in which the geometries of both species were optimized with the 4-31G basis set. This basis set gives more reasonable values of the 0—0 distances (1.468 A in hydrogen peroxide compared with the experimental value of 1.475 A, 1.476 A in trioxirane, and 1.255 A in ozone compared with the experimental value of 1.277 A). Using the 4-31G optimized geometries, ozone is calculated to be 18.0 kcal/mol more stable than trioxirane at the 6-31G level. Distortions Dsn -> Cz ) from the 4-3IG optimized structure for trioxirane lead to an increase in (4-3IG) energy, i.e. the cycUc structure is a local potential minimum in the 4-31G surface for O3 under a Czv symmetry constraint. 

HF, while keeping the structure of the HF wave function as far as possible. In its fully variational form, it may yield a smooth potential surface with any kind of geometry, including extremely large bond distances, and it is free from the intruder-state problem (unfortunately, this does not hold for approximately optimized APSG). 

The LS state is characterised by the adiabatic potential surface i LS(r) having a minimum ifo.Ls at a certain geometry (metal-ligand distances rLS) with some definite curvature (the second derivative representing a force constant /LS). Within this nearly parabolic function a set of vibration levels e, LS occurs, the lowest one corresponding to the zero-point vibration, e0LS. The HS state differs in these characteristics in such a way that the relationships... 

The existence of a surface charge o will result in an electric potential dependent on the distance to the surface, and related to a through Poisson s equation. is not easy to measure directly, but the problem of evaluating it as a function of 0 and the distance from the surface (x) has long been solved at least for simple surface geometries 3> decreases very quickly as a fimction of x (it becomes negligible within a few tens of A in realistic situations). 

A detailed analysis [159] shows that the link atom correction S ink can become unphysical for geometries far away from equilibrium (e.g., for distances approaching zero). The potential surface for geometry optimizations is therefore defined as... 

Geometry optimization of the proposed mimetic is included as part of the design analysis to ensure the feasibility of the desired molecular conformation. MM and semiempirical quantum mechanical methods have been used most extensively for these purposes. Conformational analysis of the proposed mimetic allows the determination of an energy profile for the molecule under consideration. This has been used by researchers to assess where the desired conformation for the mimetic resides on the molecular potential energy surface. Monte Carlo, MD, and distance geometry-based conformational search techniques have been employed extensively to sample conformational space. Computational methods that attempt to approximate the efifects of aqueous solvation on the conformational profile of the mimetic are being used more frequently as part of these efforts. 

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