Electronic ground state energy

Oppenlieimer potential which is defined as the electronic ground-state energy for nuclear configuration T, including the niiclear-niiclear repulsion. 

Just as in classical statistical mechanics, the different pictures of electronic changes are related by Legendre transforms. The state function for closed systems in the electron-following picture is just the electronic ground-state energy, /i v AT The total differential for the energy provides reactivity indicators for describing how various perturbations stabilize or destabilize the system,... 

Figure 9.1 Schematic illustration of a CPMD trajectory along a single spatial coordinate. The smooth curve denotes the exact electronic ground state energy, while the symbols indicate the electronic energy calculated by the CPMD method at each time step of an MD simulation.

Finally, for the electronic contribution qielec, it is generally only necessary to consider the first term (contribution from electronic ground-state energy level E0) in the quantum sum over states, namely,... 

The density functional methods were, in the views of many, legitimized by the introduction of the first Hohenberg-Kohn theorem [10]. The consequence of this celebrated theorem is that for a non-degenerate ground state and a given external potential, v(r), the electronic ground state energy can be expressed as... 

Figure 11 2 4. The MgB2 electronic ground state energy/unit cell as the function of the displacement f. The electronic energy of the undistorted structure is the reference value - 0 eV. The dependence is harmonic over the studied range of the displacements, and is identical for all studied types of the distortions. At the displacement E= 0.005/atom, the lower splitoff c band has just sank below EF, and the ground state energy has been destabilized by 12 meV...

Finally, the electronic partition function is considered. The zero of energy is chosen as the electronic ground-state energy. The spacings between the electronic energy levels are, normally, large and only the first term in the partition function will make a significant contribution that is,... 

Note that in Eq. 8-24 we have used the typical approximation to factorize the partition function [28,32] and hence Qv,s, Qv are the (quantum) vibrational partition functions of the solvent and solute molecule, respectively, and U = + AUvfi with < > the system potential energy (i.e., electronic ground state energy surface) and NUv,o the system vibrational ground state energy shift from a reference value [28,32], typically negligible. 

The electronic ground-state energy /i TV, v for a given average number of electrons N and the external potential v of the BO approximation is also the functional of the grand-canonical ensemble density [123] ... 

Now let us take two interacting water molecules. First, let us ask how many minima we can find on the electronic ground-state energy hypersurface. Detailed calculations have shown that there are two such minima (see Fig. 7.9). The global minimum corresponds to the configuration characteristic for the hydrogen bond (cf. p. 863). One of the molecules is a donor, and the other is an acceptor of a proton (Fig. 7.9a). A local minimum of smaller stability appears when one of the water molecules serves as a donor of two protons, while the other serves as an acceptor of them called the bifurcated hydrogen bond," (Fig. 7.9b). 

Let us try to write down a general expression for the electronic ground-state energy of the system under consideration. Obviously, we have to have in it the kinetic energy of the electrons, their interaction with the nuclei, and their repulsion among themselves. However, in the DFT... 

Starting from the energy functional E p], see Eq. (5), the first task is to compute the electronic ground-state energy t/, which depends parametrically on the ionic coordinates (Ri), and to define one point on the Bom-Oppenheimer surface of the system... 

Charge-separated states (electrons, positive ions, negative ions) and physical quantities that describe their behavior and reactions are seriously affected by the density and nature of the medium. Thus, the electron energy 8, the quasifree (excess) electron "ground state" energy V, the electron drift velocity w, the electron mobility y, the cross sections for electron scattering electron capture [Pg.284]

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