Molecules electronic potential energy

In the following, we shall demonstrate techniques for calculating the electronic potential energy terms up to the second order. For simplicity, we shall study the case of H2 molecule, the simplest multi-electron diatomic molecule. 

As for the theoretical treatment, we could only try to include the eleetrostatie solute-solvent interaetions and, in faet, we corrected the electronic potential energies for the solvation effeets by simply adding as calculated according to the solvaton model [eq. (2)]. The resulting potential curves are to be seen as effective potentials at equilibrium, i.e. refleeting orientational equilibrium distributions of the solvent dipoles around the eharged atoms of the solute molecule. In principle, the use of potentials thus corrected involves the assumption that solvent equilibration is more rapid than internal rotation of the solute molecule. Fig. 4 points out the effects produced on the potential... 

The total electronic potential energy of a molecule depends on the averaged electronic charge density and the nonlocal charge-density susceptibility. The molecule is assumed to be in equilibrium with a radiation bath at temperature T, so that the probability distribution over electronic states is determined by the partition function at T. The electronic potential energy is given exactly by... 

This formula can be simplified. The first term on its RHS is = Vne — specifically, the total nuclear-electronic potential energy of the molecule [Eq. (4.5)] stripped of all the individual core nuclear-electronic interactions V. Next, we decompose V ... 

Electron attachment to O2 has been investigated in supercritical hydrocarbon fluids at densities up to about 10 molecules/cm using the pulsed electric conductivity technique [110], and the results have been explained in terms of the effect of the change in the electron potential energy and the polarization energy of 2 in the medium fluids. In general, electron attachment to O2 is considered to be a convenient probe to explore electron dynamics in the condensed phase. 

In Ref. [4] we have studied an intense chirped pulse excitation of a molecule coupled with a dissipative environment taking into account electronic coherence effects. We considered a two state electronic system with relaxation treated as diffusion on electronic potential energy surfaces with respect to the generalized coordinate a. We solved numerically equations for the density matrix of a molecular system under the action of chirped pulses of carrier frequency a> with temporal variation of phase [Pg.131]

The angle brackets remind us that these energy terms are quantum-mechanical average values or expectation values each is a functional of the ground-state electron density. Focussing first on the middle term, the one most easily dealt with the nucleus-electron potential energy is the sum over all 2n electrons (as with our treatment of ab initio theory, we will work with a closed-shell molecule which perforce has an even number of electrons) of the potential corresponding to attraction of an electron for all the nuclei A ... 

Figure 4 Difference Vnn—Vee between nuclear-nuclear and electron-electron potential energy against total kinetic energy T for light molecules. Energies are in Hartree units...

From eqn (6.30) it is clear that the virial of the electronic forces, which is the electronic potential energy, is totally determined by the stress tensor a and hence by the one-electron density matrix. The atomic statement of the virial theorem provides the basis for the definition of the energy of an atom in a molecule, as is discussed in the sections following Section 6.2.2. 

Equations (48) and (50) show that the formation of a stable diatomic molecule from the free atoms is characterized by an increase of the mean electronic kinetic energy and a relatively more important decrease of the mean electronic potential energy. According to the above discussion, the chemical bond would result from the diminution of the mean potential energy of the electrons at the equilibrium distance, this effect would prevail over the augmentation of T and V ... 

The model Hamiltonian of Section II captures some of the essential features of the electronic and vibrational structure of polyatomic molecules, like benzene and 5ym-triazine, that have both nondegenerate and degenerate, Jahn-Teller active, electronic levels. In this section interference experiments are described which will be sensitive to the geometric phase development accompanying adiabatic nuclear motion on either of the electronic potential energy surfaces in the Jahn-Teller pair. 

It is well known that for heavy atoms the effect of the finite nucleus charge distribution has to be taken into account (among other effects) in order to describe the electronic structure of the system correctly (see e.g. (36,37)). As a preliminary step in the search for the effect of the finite nuclei on the properties of molecules the potential energy curve of the Th 73+ has been calculated for point-like and finite nuclei models (Table 5). For finite nuclei the Fermi charge distribution with the standard value of the skin thickness parameter was adopted (t = 2.30 fm) (38,39). 

In spite of recent advances in computer technology and electronic structure theory, only for the simplest molecules can potential energy surfaces be calculated with spectroscopic accuracy by employing purely ab initio approaches (2). For more complicated systems, empirical approaches are often used to invert spectra from experimental observables (3-10). This process is shown schematically by following the arrows up in Fig. 1. This new potential can then be used to predict the spectroscopy and dynamics for previously unobserved states and thereby help direct future experiments (11,12). This latter process corresponds to following the down arrows in Fig. 1. 

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