Potential eneigy surface

At both minima and saddle points, the first derivative of the energy, known as the gradient, is zero. Since the gradient is the negative of the forces, the forces are also zero at such a point. A point on the potential eneigy surface where the forces are zero is called a stationary point All successful optimizations locate a stationary point, although not always the one that was intended. 

Fisher, J.J. Koyanagi, G.K. McMahon, T.B. The C2H7 Potential Eneigy Surface a Fourier Transform Ion Cyclotron Resonance Investigation of the Reaction of Methyl Cation with Methane. Int. J. Mass Spectrom. 2000, 795/796,491-505. 

R. Schinke In the case of HNO and HO2, we calculated the number of states and simply extrapolated this number into the continuum. We believe that this is the best what can be done, provided a global potential eneigy surface and full dimensionality dynamics calculations for this potential are available. Because of the much smaller number of states, for HCO this procedure is less well defined. In our final analysis (Ref. 33 of our paper in this volume) we tested the extrapolation from the bound to the continuum region and an estimation of the density of states based on a Dunham expansion of the term energies and found that both recipes give essentially the same result. 

Figure 9. Schematic representation of upper portion of potential eneigy surface for merging of substitution mechanisms. A Sjsj 1 mechanism. No nucleophilic solvation in transition state ion pair intermediate (possibly nudeophilically solvated) B Sn2 (intermediate). Transition state is nudeophilically solvated by solvent (SOH) intermediate is a nudeophilically solvated ion pair (see Fig. 8) C Classical Sn2. No energy minimum. In curves A and B, the second transition state may be of higher energy than the first in cases where internal return is important.

Alexander, M. H. (1993) Adiabatic and Approximate Diabatic Potential Eneigy Surfaces for the B... H2 van der Waals Molecule, J. Chem. Phys. 99, 6014-2026. 

The observed vibration frequencies of a molecule depend on two features of the molecular structure the masses and equilibrium geometry of the molecule and the potential eneigy surface, or force field, governing displacements from equilibrium. These are described as kinetic and potential effects, respectively for a polyatomic molecule the form and the frequency of each of the 3N—6 normal vibrations depend on the two effects in a complicated way. The object of a force field calculation is to separate these effects. More specifically, if the kinetic parameters are known and the vibration frequencies are observed spectroscopically, the object is to deduce the potential eneigy surface. A major difficulty in this calculation is that the observed frequencies are often insufficient to determine uniquely the form of the potential energy surface, and it is necessary to use data on the frequency shifts observed in isotopically substituted molecules or data on vibration/rotation interaction constants observed in high resolution spectra in order to obtain a unique solution. 

Figure 5.40. The distribution of electron density (charge density) p for an atom the nucleus is at the origin of the coordinate system, (a) Variation of p with distance from the nucleus. Moving away from the nucleus p decreases from its maximum value and fades asymptotically toward zero, (b) Variation of —p with distance from the nucleus —p becomes less negative and approaches zero. The —p picture is useful for molecules (Fig. 5.41) because it makes clearer analogies with a potential eneigy surface, (c) A 4D picture (p vs. x, y, z) of the variation of p in an atom the density of the dots (number of dots per unit volume) indicates qualitatively electron density p in various regions.

In Ref. [4] we have studied an intense chirped pulse excitation of a molecule coupled with a dissipative environment taking into account electronic coherence effects. We considered a two state electronic system with relaxation treated as diffiision on electronic potential eneigy surfaces with respect to the generalized coordinate a. We solved numerically equations for the density matrix of a molecular system under the action of chirped pulses of carrier frequency a> with temporal variation of phase... 

Fig. 16.3 Orientational features of the rigid rotor potential eneigy surfaces for six different angles (y = 0°, 11°, 25.3°, 39.7°, 68.5°, and 90.0°) without the three-body effects...

Ab initio Study of the Potential Eneigy Surface and Stability... 

The subscripted i terms are reduced masses. The use of mass scaled coordinates casts the 3 body coUinear problem into that of a single particle moving on a potential eneigy surface skewed by the angle p,... 

A suitable definition of the RP of potential eneigy surfaces is necessary to ensure that the reaction theories based on it will possess sufficiently high quality. Thus, we have to consider three important fields of research ... 

In case of partially saturated systems the compounds (28, 29), do not appear as stable species on the MP2/6-3 lG(d) potential eneigy surface. The approach of proton leads to spontaneous ring opening via C -O and C -O bond breaking for compounds (28) and (29), respectively [75]. Formation of caibonium ion intermediates also has been shown for monomoleeular transformation of fluorooxirane [73], ehlo-rooxirane [76], and styrene oxide [77]. 

Of special interest are the eneigy barriers for given reactions, and in principle, calculation of the potential eneigy surfaces can provide these quantities. In practice, the majority of studies report one-point calculations on SCF-minimized geometries. Generally, calculations for gas-phase Sj 2 reactions use the model dqncted for the identity reaction ... 

Thompson KC, Jordan MJT, Collins MA (1998) Polyatomic molecultir potential eneigy surfaces by interpolation in local internal coordinates. J Chem Phys 108 8302-8316... 

Varandas AJC (2004) Modeling and interpolation of global multi-sheeted potential eneigy surfaces. In Domcke W, Yarkony DR, Koppel H (eds), Conictd Intersections. World Scientific, Singapore p 205... 

Valero R, Andersson S (2012) Quantitative integral cross sections for the H + CO2 —> OH + CO reaction from a density functional theory-based potential eneigy surface. Phys Chem Chem Phys 14 16699... 

Bowman JM, Czako G, Fu B (2011) High-dimensional ab initio potential eneigy surfaces for reaction dynamics calculations. Phys Chem Chem Phys 13 8094... 

Lu Z, Hu Q, Oakman JE, Continetti RE (2007) Dynamics on the HOCO potential eneigy surface studied by dissociative photodetachment of HOCO and DOCO. J Chem Phys 126 194305... 

Chen J, Xu X, Zhang D (2013) An accurate global potential eneigy surface for the OH + CO —> H + CO2 reaction using neural networks. J Chem Phys 138 221104... 

Mielke SL, Lynch GC, Tmhlar DG, Schwenke DW (1993) A more accurate potential eneigy surface and quantum mechanical cross section calculations for the F -F H2 reaction. Chem Phys Lett 213(1) 10... 

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