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Multi-dimensional energy surfaces

Crespos C, Collins MA, Pljper E, Kroes GJ (2003) Multi-dimensional energy surface determination by modified Shepherd interpolation for a molecule-surface reaction H2 -t Pt (111). Chem Phys Lett 376 566-575... [Pg.103]

The curvature about the minima is an expression of molecular flexibility, which can be ascertained, in principle at least, from knowledge of the molecular vibrations. From a more general viewpoint, the reaction profile must be regarded as a more or less complicated curve on a multi-dimensional energy hyper-surface. [Pg.174]

For multi-dimensional potential energy surfaces a convenient measure of the gradient vector is the root-mean-square (RMS) gradient described by... [Pg.300]

For k(r) we shall assume at first, as in (19), that the reaction is adiabatic at the distance of closest approach, r = a, and that it is joined there to the nonadiabatic solution which varies as exp(-ar). The adiabatic and nonadiabatic solutions can be joined smoothly. For example, one could try to generalize to the present multi-dimensional potential energy surfaces, a Landau-Zener type treatment (41). For simplicity, however, we will join the adiabatic and nonadiabatic expressions at r = a. We subsequently consider another approximation in which the reaction is treated as being nonadiabatic even at r = a. [Pg.239]

More recently, Yang and Thompson implemented this type of sensor in FI manifolds, which they consider ideal environments for relating the sensor s hydrodynamic response to the analyte s concentration-time profile produced by the dispersion behaviour of sample zones. Network analysis of the sensor generates multi-dimensional information on the bulk properties of the liquid sample and surface properties at the liquid/solid interface. The relationship between acoustic energy transmission and the interfacial structure, viscosity, density and dielectric constant of the analyte have been thoroughly studied by using this type of assembly [171]. [Pg.144]

Multi dimensional quantum mechanical calculations are needed for the quantitative description of the effects discussed above. Rigorously stated, such calculations are very laborious. In this connection, considerable attention has been paid during the last two decades to the development of simplified methods for resolving the multi-dimensional problems. We refer, for instance, to the method of classic S-matrix [60] and the quantum-mechanical method of the transition state [61]. The advantage of these methods is the use of realistic potential energy surfaces the shortcoming is the fact that only... [Pg.49]

The confluence of theory and experiment achieved in recent years has greatly deepened our understanding of molecular photodissociation. At this point, however, it is important to underline that the cornerstone of realistic dynamical investigations is a multi-dimensional potential energy surface (PES). The interrelation between PESs on one hand and the various dissociation cross sections on the other hand is one prominent topic of this book and therefore we think it is useful to elucidate some qualitative aspects of PESs before we start with the development of the dynamical concepts. [Pg.18]

We will not discuss the actual construction of potential energy surfaces. This monograph deals exclusively with the nuclear motion taking place on a PES and the relation of the various types of cross sections to particular features of the PES. The investigation of molecular dynamics is — in the context of classical mechanics — equivalent to rolling a billiard ball on a multi-dimensional surface. The way in which the forces i fc(Q) determine the route of the billiard ball is the central topic of this monograph. In the following we discuss briefly two illustrative examples which play key roles in the subsequent chapters. [Pg.20]

Figures 1.12 and 1.13 readily explain, without quantitative calculation, some key features of the photodissociation of H2O through excitation in the A and in the B absorption bands. Multi-dimensional potential energy surfaces are the cornerstones for a trustworthy analysis of molecular dynamics. Knowing the general topology of the PES often suffices for a qualitative explanation of the main experimental observations. However, in order to perform realistic calculations we need potential energy surfaces which are as accurate and complete as possible. Figures 1.12 and 1.13 readily explain, without quantitative calculation, some key features of the photodissociation of H2O through excitation in the A and in the B absorption bands. Multi-dimensional potential energy surfaces are the cornerstones for a trustworthy analysis of molecular dynamics. Knowing the general topology of the PES often suffices for a qualitative explanation of the main experimental observations. However, in order to perform realistic calculations we need potential energy surfaces which are as accurate and complete as possible.
Although the theory of photodissociation has not yet reached the level of sophistication of experiment, major advances have been made in recent years by many research groups. This concerns the calculation of accurate multi-dimensional potential energy surfaces for excited electronic states and the dynamical treatment of the nuclear motion on these surfaces. The exact quantum mechanical modelling of the dissociation of a triatomic molecule is nowadays practicable without severe technical problems. Moreover, simple but nevertheless realistic models have been developed and compared against exact calculations which are very useful for understanding the interrelation between the potential and the nuclear dynamics on one hand and the experimental observables on the other hand. [Pg.431]

When desorption takes place from a metal surface, many hot charge carriers are generated in the substrate by laser irradiation and are extended over the substrate. Then, the desorption occurs through substrate-mediated excitation. In the case of semiconductor surfaces, the excitation occurs in the substrate because of the narrow band gap. However, the desorption is caused by a local excitation, since the chemisorption bond is made of a localized electron of a substrate surface atom. When the substrate is an oxide, on the other hand, little or no substrate electronic-excitation occurs due to the wide band gap and the excitation relevant to the desorption is local. Thus, the desorption mechanism for adsorbed molecules is quite different at metal and oxide surfaces. Furthermore, the multi-dimensional potential energy surface (PES) of the electronic excited state in the adsorbed system has been obtained theoretically on oxide surfaces [19, 20] due to a localized system, but has scarcely been calculated on metal surfaces [21, 22] because of the delocalized and extended nature of the system. We describe desorption processes undergoing a single excitation for NO and CO desorption from both metal and oxide surfaces. [Pg.292]

Quantum chemical calculations provide the values of a multi-dimensional potential at the mesh points of a grid. Several coordinates are varied step by step and to each set of all these coordinates there is a corresponding number. However, we need a potential energy function which is analytic if possible, continuous and differentiable in any order. At the mesh points of the grid the values of this function are to be as close as possible to the computed ones. In addition, the values of the derivatives of this function with respect to any coordinate must be physically possible on the limiting contour surrounding the region of the potential surface studied. This is very im-... [Pg.12]

Automatic searches of conformational hyperspace may be requested using the multi-level bond rotation algorithm described above. A selection is made for a uniform sequential scan, a random scan, or a multi-dimensional minimization search of the conformational energy surface. (As indicated above, prototype versions of CAMSEQ/M provide only the sequential scan mode.)... [Pg.359]


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