Potential energy surfaces stationary points, localization

Local Minimum. A Stationary Point on a Potential Energy Surface. Chemically, a local minimum corresponds to an isomer. 

Optimization algorithms are often used to find stationary points on a potential energy surface, i.e., local and global minima and saddle points. The only place where they directly enter MD is in the case of Born-Oppenheimer AIMD, in order to converge the SCF wavefunction for each MD step. It is immediately obvious that the choice of optimization algorithm crucially affects the speed of the simulation. 

Fig. 1.1 (a) In traditional quantum chemical methods the potential energy surface (PES) is characterized in a pointwise fashion. Starting from an initial geometry, optimization routines are applied to localize the nearest stationary point (minimum or transition state). Which point of the PES results from this procedure mainly depends on the choice of the initial configuration. The system can get trapped easily in local minima without ever arriving at the global minimum struc-... 

Stationary Point. A point on a Potential Energy Surface for which all energy first derivatives with respect to the coordinates are zero. Local Minima and Transition States are stationary points. 

The stationary point in octahedral symmetry is a genuine minimum on potential energy surface of SFg. This does not eliminate the possibility of the existence of local minima of lower symmetry with lower energy (which would increase the value of electron affinity). 

An obvious candidate for a stable noncyclic carbenium ion is the tert-butyl cation observed in superacidic media. Even if the proton affinity of isobutene (Table 22.1) does not make it very likely that tert-butyl cations will exist in zeolites, several quantum chemical studies have localized stationary points for tert-butyl cations in zeolite and found that they are less stable than the adsorption complex, but are similar in stability to surface butoxides. Because of technical limitations vibrational analysis, which could prove that this cation is a local minimum on the potential energy surface, that is a metastable species, have only recently been made. Within a periodic DFT study of isobutene/H-FER a complete vibrational analysis for all atoms in the unit cell was made [48], and as part of a hybrid QM/MNDO study on an embedded cluster model of isobutene/H-MOR a vibrational analysis was made with a limited number of atoms [49]. Both reached the... 

Density functional theory was also applied to this problem. The cumulenic Dg, form IS turned out to be a minimum structure at the B-LYP level of DFT using a 6-31G basis set, while the fully symmetrical structure 13 is 2.4 kcal/mol higher in energy. Unfortunately, it was not possible to localize a polyacetylenic structure with the DFT methods used. The same trend holds for Cjo and Cj4, other candicates for Htickel aromaticity the and D-j symmetrical cumulenic structures are minima on the potential energy surface polyacetylenic isomers are not stationary points using DFT methods. 

In the present work, we report DFT calculations of hydrocarbons adsorption on Au2o cluster [4]. All calculations were carried out with the nonempirical local PBE (Perdew—Burke—Ernzerhof) functional, which we have used earlier in the study of gold complexes [5]. Calculations were performed with a PRIRODA software [6]. The basis set with the SBK pseudopotential was used [7]. In this pseudopotential, the outer electronic shells are described by the following basis sets H [311/1], C [311/311/11] and Au [51111/51111/5111]. The types of stationary points on potential energy surfaces were determined from analysis of Hessians. The second derivatives were calculated analytically. 

Figure 1.1. Prototypical potential energy surface of a simple system (a) and of a complex system (b). In a simple, low-dimensional system, dynamical bottlenecks for transitions between long-lived stable states most often coincide with saddle points on the potential energy surface. Locating these stationary points reveals the reaction mechanism. In a typical complex system, the potential energy surface is rugged and has countless local minima and saddle points. Nevertheless, there can be well-defined long-lived stable states and rare transitions between them. Such transitions can occur via a multitude of different transition pathways.

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