Molecular potential local

It is necessary to note that fluorescence characteristics demonstrate remarkable sensitivity to variations of physicochemical parameters of the environment. Therefore, such parameters as polarity, viscosity, temperature, electric potential, local electric field, pressure, pH, etc., can be registered successfully using the modem sensitive apparatus for fluorescence detection [1, 4—12]. As a consequence, fluorescent molecules are used successfully as molecular probes to study the local characteristics of physicochemical, biochemical and biological systems. 

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).

Primary quantity measured local interactions (magnetic, electric field gradient) atomic, molecular potentials... 

The harmonic approximation reduces to assuming the PES to be a hyperparaboloid in the vicinity of each of the local minima of the molecular potential energy. Under this assumption the thermodynamical quantities (and some other properties) can be obtained in the close form. Indeed, for the ideal gas of polyatomic molecules the partition function Q is a product of the partition functions corresponding to the translational, rotational, and vibrational motions of the nuclei and to that describing electronic degrees of freedom of an individual molecule ... 

K.C. Thompson, M.J.T. Jordan, M.A. CoUins, Polyatomic molecular potential energy surfaces by interpolation in local internal coordinates, /. Chem. Phys. 108 (20) (1998) 8302-8316. 

The same procedure can be applied for derivatives from other representations. Electronic properties obtained by differentiation are usually classified by its dependence on the position. Global properties have the same value everywhere, such as the chemical potential, hardness and softness. Electron density, Fukui function and local softness change throughout the molecule, and they are called local properties. Finally, kernel properties depend on two or more position vectors, like the density response and softness kernels. Global parameters describe molecular reactivity, local properties provide information on site selectivity, while kernels can be used to understand site activation. 

XANES (X-ray Absorption Near-Edge Strueture) is X-ray absorption spectroscopy for the lower energy region than EXAFS (Extended X-ray Absorption Fine Structure). It is sensitive to the local atomic arrangement around the absorbing atom and to the chemical states because the low energy electrons emitted through the photoabsorption are affected by details of the molecular potential (1). 

Based on the —> AIM theory, TAE descriptor methodology encodes the distributions of electron density based on molecular properties, such as kinetic energy density, —> molecular electrostatic potential, local average ionization potentials, —> Fukuifunctions, electron density gradients, and second derivatives, in addition to the density itself [Breneman, Thompson et al., 1995 Song, Breneman et al., 2002 Breneman, Bundling et al., 2003]. 

The optimization of ah initio Born-Oppenheimer potential energy surfaces is an important subject in quantum chemistry. Methods for the efficient localization and characterization of stationary points of the molecular potential energy surface are an essential tool in studies of molecular structure and reactivity. Of particular importance are methods for the determination of minima and first-order saddle points, corresponding to molecular equilibrium structures and transition states. 

In the first case, the time T oc during which an electron remains at a certain site becomes larger than or comparable to the time Topt of vibration of an optical (intramolecular short-wavelength vibrations) phonon, and therefore the transport of electrons can take place only through an uncorrelated hopping -type motion between these localized states. This means that during the application of perturbation theory, the zeroth-order Hamiltonian contains the molecular potential plus the electron-vibration interaction and one must treat as a perturbation the intermolecular potential, which earlier gave rise to the formation of Bloch functions. The transport thus becomes a diffusion process and the mobility is determined by the Einstein relation n = ed/k T, where the... 

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