Potential energy, molecular

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. 

Morgan J D III and Simon B 1980 Behavior of molecular potential energy curves for large nuclear separations/nf. J. Quantum Chem. 17 1143... 

THE CRUDE BORN-OPPENHEIMER ADIABATIC APPROXIMATION OF MOLECULAR POTENTIAL ENERGIES... 

J. N, Murrell, S. Carter, S. C. Farancos, P. Huxley, and A. J, C. Varandas, Molecular Potential Energy Functions, John Wiley Sons, Tnc., Chichester, 1984. 

HypcrC. hcm provides calculations IhaL explore molecular potential energy surfaces. Indeed, most of computational chemistry relates in one way or another to molecular potential energy surfaces, the topography of the surface and motion on the surface. 

Cee M L and M Page 1993. Computing Reaction Pathways on Molecular Potential Energy Surfaces. In Lipkowitz K B and D B Boyd (Editors). Reviews in Computational Chemistry Volume 4. New York, VCH Publishers, pp. 35-65. 

E. Kracka, T. H. Dunning, Jr., Advances in Molecular Electronic Structure Theory Calculation and Characterization of Molecular Potential Energy Surfaces T. H. Dunning, Jr. Ed., 129, JAI, Greenwich (1990). 

CM Becker. Principal coordinate maps of molecular potential energy surfaces. J Comput Chem 19 1255-1267, 1998. 

Sketch the qualitative molecular potential energy curves for the N—N bond on one graph for N2H4, N2, and N,. ... 

Once the mechanisms of dynamic processes are understood, it becomes possible to think about controlling them so that we can make desirable processes to occur more efficiently. Especially when we use a laser field, nonadiabatic transitions are induced among the so-called dressed states and we can control the transitions among them by appropriately designing the laser parameters [33 1]. The dressed states mean molecular potential energy curves shifted up or down by the amount of photon energy. Even the ordinary type of photoexcitation can be... 

During the last decades, a large body of structural information has been derived from gas-electron diffraction studies. The corresponding results are nearly exclusively reported in the literature in terms of r distances, or the equivalent thermal average intemuclear distances, which are denoted r. The r distances are defined by the relation, r = r — If. Alternative methods for interpreting gas-electron diffraction data are possible, for example, in terms of -geometries5, but they are currently too complex to apply in routine stmctural analyses, because they require detailed information on the molecular potential energy surface which is not usually available. 

Michael L. McKee and Michael Page, Computing Reaction Pathways on Molecular Potential Energy Surfaces. 

Fig. 3.2 A schematic of a molecular potential energy curve with three stationary points two local minima (32 E/dq2 > 0) and one transition state (32 E/dq2 < 0).

Representing the molecular potential energy as an analytic function of the nuclear coordinates in this fashion implicitly invokes the Born-Oppenheimer approximation in separating the very fast electronic motions from the much slower ones of the nuclei. 

In this study, we assume that crystal structures will have the lowest possible total of intra- and inter-molecular potential energy. However, the partitioning of the potential energy between intra- and inter-molecular terms will vary among crystal structures, distorting the glucose residues away from the shape of lowest energy in a way that will reflect more-or-less random... 

A general theory of quantitatively comparing molecular shapes using common overlap steric volume(33-36) and, more recently, descriptors derived from superimposed molecular potential energy fields of pairs of molecules(37) has been derived and tested. This theory allows a "marriage between Hansch analysis and conformational analysis. 

We can put this on a somewhat clearer mathematical footing by expanding die full molecular potential energy in a multi-dimensional Taylor expansion, which is a generalization of the one-dimensional case presented as Eq. (2.1). Thus... 

The molecular potential energy surface is one of the most important concepts of physical chemistry. It is at the foundations of spectroscopy, of chemical kinetics and of the study of the bulk properties of matter. It is a concept on which both qualitative and quantitative interpretations of molecular properties can be based. So firmly is it placed in the theoretical interpretation of chemistry that there is a tendency to raise it above the level of a concept by ascribing it some physical reality. 

The molecular potential energy is an energy calculated for static nuclei as a function of the positions of the nuclei. It is called potential energy because it is the potential energy in the dynamical equations of nuclear motion. 

How sensitive is the computed control field to fluctuations in the field source and to uncertainties in the molecular potential-energy surface ... 

Fig. 8. Electrostatic molecular potential-energy maps for cytosine in the ring plane (top) and in the plane perpendicular to the ring plane and passing through atoms as indicated (bottom).244...

The optimization of minima and saddle points of a function in many variables is reviewed. Emphasis is on methods applicable to the calculation of electronic wave functions (ground and excited states) and the optimization of minima and transition states of molecular potential energy surfaces. 

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