Lowest energy configuration for

Fig. 30 Lowest energy configurations for glycine on Cu(100). a Homochiral c(4x2) glycine layer, as indicated by the rectangular cell. Also shown is the (-Jl x V2)45° unit cell, b Heterochiral (4 x 2)pg structures of glycine on Cu(100). Ignoring the handedness, the molecules form a (2x2) grid on the surface. Reprinted in part with permission from [67]. Copyright (2005) American Chemical Society...

Redondo and Goddard28 first reported that the lowest energy configuration for a dimer in a small silicon cluster model, SigH, shown in Figure la, is the symmetric geometry. 

A different approach to the stability of hydride nanoparticles is bottom-up, using computational techniques to construct equilibrium (lowest energy) configurations for the clusters, nanoparticles or thin films of the metal and corresponding hydride, and evaluate the difference in stability between the two as a function of particle size. Although the possibilities are rapidly increasing, these calculations are still limited to small cluster sizes due to computational restraints. As a relevant example we vhll only briefiy discuss various types of calculations for the case of the ionic hydrides MgH2 and NaH. 

This behavior is summarized by Hund s rule (named for the German physicist F. H. Hund), which states that the lowest-energy configuration for an atom is the one having the maximum number of unpaired electrons allowed by the Pauli principle in a particular set of degenerate orbitals. 

Energies of the lowest lying sextet, quartet and doublet states were calculated for each of the heme units studied. The geometries of the complexes were taken from crystal structures and simplified to unsubstituted porphyrins. The orientations of the porphyrin macrocycles were such that the pyrrole nitrogens were on the x- and y-axes. The choice of the lowest energy configurations for each state was as follows ... 

The sextet state configuration is unique. The choice of the lowest energy configuration for the doublet and quartet states was confirmed by comparisons of the relative energies of various quartet and doublet configurations, obtained by assignment of unpaired electron(s) to different iron d orbitals, in some representative complexes. It is also corroborated by a recent detailed study of... 

Using a central field approximation in which it is assumed that each electron moves independently in an average spherically symmetric potential, it is possible to solve for the energies of the different configurations. Calculations of this type show that the / -configuration is the lowest energy configuration for the trivalent lanthanides and actinides. 

The expected lowest energy configuration for the valence shell is now... 

Fig. 23 Lowest energy configuration for two Pd atoms in surface sites (black disks), linked by a Cu chain along the close-packed direction in the overlayer (large grey disks).

Fig. 29 Lowest energy configurations for two Au atoms (black disks) in a Cu(lOO) surface. Large grey disks and open circles denote Cu(0) and Cu(S) atoms, respectively.

Carbon is the next element and has six electrons. Two electrons occupy the Is orbital, two occupy the 2s orbital, and two occupy 2p orbitals. Since there are three 2p orbitals with the same energy, the mutually repulsive electrons will occupy separate 2p orbitals. This behavior is summarized by Hund s rule (named for the German physicist F. H. Flund) The lowest energy configuration for an atom is the one having the maximum number of unpaired electrons allowed by the Pauli principle in a particular set of degenerate orbitals. By convention, the unpaired electrons are represented as having parallel spins (with spin "up"). 

In the independent electron approximation, the lowest-energy configuration for helium is Is. Let us write the various conceivable spin combinations for this configuration. They are... 

Since ls 2s is the lowest-energy configuration for which we can write an antisymmetrized wavefunction, this is the ground state configuration for hthium in this independent-electron approximation. 

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