Potential-energy surface reduced-dimension

The topic of this review, reactions at metal surfaces, has been in general treated in a similar way to gas-phase reactivity. High level ab initio electronic structure methods are used to construct potential energy surfaces of catalytically important surface reactions in reduced dimensions. Once a chemically accurate potential surface is available, quantum or classical dynamics may be carried out in order to more deeply understand the microscopic nature of the reaction. 

A normal-mode representation of the Hamiltonian for the reduced system involves the diagonalization of the projected force constant matrix, which in turn generates a reduced-dimension potential-energy surface in terms of the mass-weighted coordinates of the reaction path [64] ... 

In the photochemistry of benzene, the so-called channel 3 represents a well-known decay route along which fluorescence is quenched above a vibrational excess of 3000 cm [57], The decay takes place through a prefulvenic conical intersection characterized by an out of plane bending [52,58] and results in the formation of benzvalene and fulvene. The purpose of this study is to find distinct radiationless decay pathways that could be selected by exciting specific combinations of photoactive modes in the initial wavepacket created by a laser pulse. For this, we carry out quantum dynamics simulations on potential energy surfaces of reduced dimension, using the analysis outlined above for the choice of the coordinates. 

The potential surface in a (3N - 6>dimensional space is reduced by the above assumption to a surface in one or two dimensions, respectively. As the molecule reproduces its configuration by a rotation of the top through 2ir/3, we know that the potential energy is periodic in 2tr/3. A mathematical description of such a periodic potential-energy surface is a one- or two-dimensional Fourier series. The most general form of a one-dimensional Fourier series with the internal rotation angle a as the variable may be reduced to... 

In a bulk semiconductor, photoexcitation generates electron-hole pairs which are weakly bounded by Coulomb interaction (called an exciton). Usually one can observe the absorption band of an exciton only at low temperature since the thermal energy at room temperature is large enough to break up the exciton. When the exciton is confined in an energy potential, the dissociation probability reduces and the overlap of the electron and hole wavefunction increases, which is manifested by a sharper absorption band observable at room temperature. This potential can be due to either a deformation in the lattice caused by an impurity atom or, in the present case, the surface boundary of a nanocluster. The confinement of an exciton by an impurity potential (called bound exciton) is well known in the semiconductor literature [16]. There is considerable similarity in the basic physics between confinement by an impurity potential and confinement by physical dimension. The confinement effects on the absorption cross section of a nanocluster are discussed in Section II. 

This equation is remarkable, since it describes a general form to express the relation among surface energies, chemical potential and dimension Z. For a spherical particle, Z = Rp and op = 3, (42) reduces to... 

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