Describing potential energy surfaces PESs

The result is that, to a very good approxunation, as treated elsewhere in this Encyclopedia, the nuclei move in a mechanical potential created by the much more rapid motion of the electrons. The electron cloud itself is described by the quantum mechanical theory of electronic structure. Since the electronic and nuclear motion are approximately separable, the electron cloud can be described mathematically by the quantum mechanical theory of electronic structure, in a framework where the nuclei are fixed. The resulting Bom-Oppenlieimer potential energy surface (PES) created by the electrons is the mechanical potential in which the nuclei move. Wlien we speak of the internal motion of molecules, we therefore mean essentially the motion of the nuclei, which contain most of the mass, on the molecular potential energy surface, with the electron cloud rapidly adjusting to the relatively slow nuclear motion. 

This last equation is the nuclear Schrodinger equation describing the motion of nuclei. The electronic energy computed from solving the electronic Schrodinger equation (3) on page 163 plus the nuclear-nuclear interactions Vjjjj(R,R) provide a potential for nuclear motion, a Potential Energy Surface (PES). 

In this article, we present an ab initio approach, suitable for condensed phase simulations, that combines Hartree-Fock molecular orbital theory and modem valence bond theory which is termed as MOVB to describe the potential energy surface (PES) for reactive systems. We first provide a briefreview of the block-localized wave function (BLW) method that is used to define diabatic electronic states. Then, the MOVB model is presented in association with combined QM/MM simulations. The method is demonstrated by model proton transfer reactions in the gas phase and solution as well as a model Sn2 reaction in water. 

Before getting into a deeper analysis of the concept of resonance, we must define precisely what we understand by chemical structure . One of the most basic concepts in molecular quantum mechanics is the one of potential energy surface (PES). It allows us to define a molecular structure as an arrangement of nuclear positions in space. The definition of molecular structure depends on the validity of the Bom-Oppenheimer approximation for a given state. Actually, its validity is limited to selected portions of the entire Bom-Oppenheimer PES. When a state is described by one PES, we call it an adiabatic state. It is clear that the concept of chemical structure , depends on the existence of a previously defined molecular structure . Only adiabatic states have a molecular structure . From now on, we will always be dealing with adiabatic states. 

The last years have witnessed tremendous progress in the theoretical description of surfaces and processes on surfaces. A variety of surface properties can now be described from first principles, i.e. without invoking any empirical parameters [1], In particular, whole potential energy surfaces (PES) can nowadays be mapped out by total energy calculations based on ab initio electronic structure theory. This development has also motivated new efforts in the dynamical treatment of adsorption/desorption processes in the last decade such as the development of efficient schemes for high-dimensional quantum dynamical simulations [2, 3]. 

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. 

The Absorption Cross Section (Abs. XS or XS or a(E)) of molecules in the visible and or UV range is due to (at least one) electronic transition. At low resolution, each Abs.XS has a bell shape which can be described with very few (3 or 4, see below) parameters. This bell shape can be understood as the "reflection" of the ground state vibrational wavefunction (which can be approximated as a onedimensional or multidimensional Gaussian) on the potential energy surface (PES)... 

Owing to the complexity of zeolitic systems, most computational studies are still performed with the help of classical models. These methods use a set of potential functions to describe the potential energy surface (PES) in a manydimensional space of geometrical parameters of the system. Although the PES can be tested in terms of observables such as equilibrium atom positions, vibrational frequencies, heats of formation, and other experimental information, the PES itself is not an observable quantity. Because of that, there is no unique representation of the PES, and several coordinate systems and parameteriza-... 

The presence of these three electronic states, as well as the sizable spin-orbit (SO) splitting in the F and Cl atoms (1.15 kcaEmol for F and 2.52 kcaEmol for Cl [25]) raises two important questions (1) what is the reactivity of the excited spin-orbit state relative to that of the ground state and (2) how well is the dynamics of the reaction described by calculations on a single, electronically adiabatic potential energy surface (PES). If the reaction were to proceed adiabatically on a single PES, as would be predicted by the Bom-Oppenheimer (BO) approximation, then the excited SO state should not react.[26, 27]... 

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