Electronic energy minimum

Above with electron energy Minimum detectable Minimum detectable... 

Figure 2.1 State diagram (commonly called Jabfonski diagram) depicting molecular states and photophysical processes. The vertical position of the thick horizontal lines represents the electronic energy minimum. Vibrational energy levels are shown as thin lines. The width of the horizontal lines and their position along the abscissa are chosen merely to avoid congestion in the graphical diagram and have no physical connotation...

This means that in almost all cases the experimenters investigate molecules close to the minimum of the electronic energy (minimum of PES). What happens to the electronic structure for other configurations of the nuclei is a natural question, sometimes of great importance (e.g., for chemical reactions). Only computational chemistry opens the way to see what would happen to the energy and to the electronic density distribution if... 

All m oleciilar orbitals are com biiiations of the same set of atom ic orbitals they differ only by their LCAO expansion coefficients. HyperC hem computes these coefficients, C p. and the molecular orbital energies by requiring that the ground-state electronic energy beat a minimum. That is, any change in the computed coefficients can only increase the energy. 

Calculated transition structures may be very sensitive to the level of theory employed. Semi-empirical methods, since they are parametrized for energy minimum structures, may be less appropriate for transition state searching than ab initio methods are. Transition structures are normally characterized by weak partial bonds, that is, being broken or formed. In these cases UHF calculations are necessary, and sometimes even the inclusion of electron correlation effects. 

At the energy minimum, each electron moves in an average field due to the Other electrons and the nuclei. Small variations in the form of the orbitals at this point do not change the energy or the electric field, and so we speak of a self-consistent field (SCF). Many authors use the acronyms HF and SCF interchangeably, and I will do so from time to time. These HF orbitals are found as solutions of the HF eigenvalue problem... 

The self-consistent field function for atoms with 2 to 36 electrons are computed with a minimum basis set of Slater-type orbitals. The orbital exponents of the atomic orbitals are optimized so as to ensure the energy minimum. The analysis of the optimized orbital exponents allows us to obtain simple and accurate rules for the 1 s, 2s, 3s, 4s, 2p, 3p, 4p and 3d electronic screening constants. These rules are compared with those proposed by Slater and reveal the need for the screening due to the outside electrons. The analysis of the screening constants (and orbital exponents) is extended to the excited states of the ground state configuration and the positive ions. 

Equation (22) shows that since electrode potentials measure electronic energies, their zero level is the same as that for electronic energy. Equation (22) expresses the possibility of a comparison between electrochemical and UHV quantities. Since the definition of 0 is6 the minimum work to extract an electron from the Fermi level of a metal in a vacuum, the definition of electrode potential in the UHV scale is the minimum work to extract an electron from the Fermi level of a metal covered by a (macroscopic) layer of solvent. ... 

The Mg + dicadon [42] with AN+2 (N= 1) valence electrons has a stable structure in agreanent with the rule, but this is a local energy minimum. The linear structure is more stable because it minimizes the Coulomb repulsion. This is in contrast to the tetrahedral stmcture of the Li dication with two electrons (N= 0). The six electron systems caimot form closed-shell structures in the tetrahedron, but the two electron systems can do. 

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