Potential energy surface of a molecule

Molecular mechanics is a simple technique for scanning the potential energy surface of a molecule, molecular ion, crystal lattice, or solvate. The model is based on chemical and physical principles. The resulting functions are parameterized on the basis of experimental data. That is, the potential energy surface is computed not by thorough theoretical expressions but by using functions whose parameters are derived empiri-... 

Molecular mechanics is a simple technique for scanning the potential energy surface of a molecule, molecular ion, crystal lattice or solvate. The model is based on a set of functions which may or may not be based on chemical and physical principles. These functions are parameterized based on experimental data. That is, the potential energy surface is not computed by fundamental theoretical expressions but by using functions whose parameters are derived empirically by reproducing experimentally observed data. Molecular mechanics then is, similar to a neural network, completely dependent on the facts that it has been taught. The quality of results to be obtained depends on the choice of the experimental data used for the parameterization. Clearly, the choice of potential energy functions is also of some importance. The most common model used is loosely derived from... 

In a recent paper [112], taking hydrogen peroxide and its isotopomers as the natural starting example, we examined the tools of fhis investigation, where we employed quantum chemistry to describe the potential energy surface of a molecule with a floppy bond. For this prototypical simple system, we have exploited or-... 

Origin of kinetic isotope effects. By virtue of the Born-Oppenheimer approximation, which states that the motions of electrons and of nuclei can be considered separately, the potential energy surface of a molecule does not vary with the isotopic nature of nuclei moving on it. This makes isotopic substitution a uniquely valuable probe of mechanism, since, unlike electronic substituent effects, the probe does not alter what is being investigated. 

The determination of minima and saddle points on the potential-energy surface of a molecule plays an important role (Schaefer and Miller, 1977, Chapter 4) in describing the electronic structure and chemical reactivity of molecules. In this section, we show how such stationary points on a molecule s potential energy surface may be found by using an approach similar to that employed in Section 5.B. We first consider how the electronic Hamiltonian changes when the nuclear positions are changed from an initial set of positions, to R, i.e., R - R + u. The electron-nuclear interaction is the only term in the Hamiltonian that depends explicitly on the nuclear position. Performing a Taylor expansion of this potential about the point R, we obtain... 

Energy is central to the understanding of chemistry. The potential energy surface of a molecule defines chemical structure and reactivity. A diatomic dissociation curve has two ends, one at the equilibrium distance Re and another one at the dissociation limit R oo. For determining a dissociation energy both counts. 

Ab initio molecular orbital calculations, by giving the potential energy surface of a molecule at its minimum energy conformations, provide a complete vibrational... 

A force field is a set of equations that describes the potential energy surface of a molecule under the Bom-Oppenheimer approximation. These equations are ordinarily formulated using classical (Newtonian) mechanics and electrostatics. Many different force fields have been designed for a variety of different purposes. They have much in common, but they also have many differences. The following force fields are discussed in this encyclopedia ... 

Now, we examine the effect of vibronic interactions on the two adiabatic potential energy surfaces of nonlinear molecules that belong to a degenerate electronic state, so-called static Jahn-Teller effect. 

Fig. 1.2 The potential energy (r) of two isolated atoms as a function of the distance r between their centres. The curve for the potential energy (z) of a molecule as a function of its distance z from the surface of a solid is similar in general shape to this curve.

The third principle relates to the set of equations which describe the potential energy surface of the molecule. These potential energy equations, derived primarily from classical physics, contain parameters optimized to obtain the best match between experimental data and/or theoretical results for a training set of compounds. Once the parameters are evaluated for a set of structures (as diverse as possible), they are fixed and then used unmodified for other similar (and usually larger) compounds. As a first approximation, these parameters must be transferable from one structure to another for this method to work and be generally applicable. 

The potential energy of water molecule is a function of three parameters, i.e. ru r2 and angle 0. A plot of the complete potential energy surface of a water molecule, therefore, will be four dimensional. Since we are limited to three dimensions for plotting functions, we cannot draw the entire potential... 

Molecules are never motionless, even at the ground vibrational state they perform vibrations. It is only in the minimum position of the potential energy surface where a molecule would be motionless and this is a hypothetical state. Although it does not exist, it is a well-defined reference structure and... 

Dependent Band Model for Lanthanide Compounds and Conditions for Interconfiguration Fluctuations J. N Murrell The Potential Energy Surfaces of Polyatomic Molecules J-A-Duffy Optical Electron ativity and Nephelauxetic Effect in Oxide Systems Application to Conducting, Semi-Conducting and Insulating Metal Oxides... 

Given some overall strategy of what you hope to accomplish with the calculations, you need to decide which conformation(s) of your reactant(s) to use. A potential energy surface of nontrivial molecules will have many hills and valleys. The deepest valley is called the global minimum, as mentioned earlier. Without some other basis for selecting a conformation, many chemists will want to use the global minimum conformation. However, most pertinent is the conformation a molecule adopts at the time of reaction. This may or may not be the global minimum. You may need to use your chemical intuition to choose the most relevant conformation. Sometimes, you will need to explore several different conformations. 

The central concept of mode-selective chemistry is illustrated in Fig. 1, which depicts the ground and excited state potential energy surfaces of a hypothetical triatomic molecule, ABC. One might wish, for example, to break selectively the bond between atoms A and B to yield products A+BC. Alternatively, one might wish to activate that bond so that in a subsequent collision with atom D the products AD+BC are formed. To achieve either goal it is necessary to cause bond AB to vibrate, thereby inducing motion along the desired reaction coordinate. 

DIM Diatomics in molecules. A semiempricial method used to construct potential energy surfaces of polyatomic molecules from the energy of the diatomic fragments. 

If, 2 3 are electronic orbital functions for a molecule with internal coordinates Q and Hamiltonian H then the potential energy surfaces of the molecule are eigenvalues of the matrix given in equation 10 ... 

Medium effects can be divided into two classes those that directly modify the potential energy surfaces of the molecule, such as polarity or hydrogen bonding capacity, affecting through strong solvation in particular the (n,ji ) as opposed to the ( r, r ) state energies, and those that operate in a more subtle manner. Examples of the latter are microscopic heat conductivity. 

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