Energy single states

In an ideal Bose gas, at a certain transition temperature a remarkable effect occurs a macroscopic fraction of the total number of particles condenses into the lowest-energy single-particle state. This effect, which occurs when the Bose particles have non-zero mass, is called Bose-Einstein condensation, and the key to its understanding is the chemical potential. For an ideal gas of photons or phonons, which have zero mass, this effect does not occur. This is because their total number is arbitrary and the chemical potential is effectively zero for tire photon or phonon gas. 

Configuration Interaction (or electron correlation) adds to the single determinant of the Hartree-Fock wave function a linear combination of determinants that play the role of atomic orbitals. This is similar to constructing a molecular orbital as a linear combination of atomic orbitals. Like the LCAO approximation. Cl calculations determine the weighting of each determinant to produce the lowest energy ground state (see SCFTechnique on page 43). 

Examine atomic charges and the electrostatic potentit map for the lower-energy transition state. Which atom appear to be most electron rich in each Is the negativ charge concentrated on a single atom in the transition stat or delocalized Add this charge information (either or 5- ) to the molecular structure for the transition stat which you drew previously. 

The first term in this equation describes the suppression of the probability of the fluctuation with the correlator Eq. (3.22) (the weight />[//(a)] of the disorder configuration is exp (— J da/2 (x))), while the second term stems from the condition that the energy c+[t/(x)] of the lowest positive-energy single-electron state for the disorder realization t/(x) equals c. The factor /< is a Lagrange multiplier. It can be shown that the disorder fluctuation //(a) that minimizes A [//(a)] has the form of the soliton-anlisolilon pair configuration described by [48] ... 

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