Chemical Bonding as a Bosonic Quantum Condensate

From the December 22, 1995 when the Science magazine declared the Bose condensate as the molecule of the year , the Bose-Einstein condensation (BEC, in short), basically viewed as the macroscopic occupation of the same single-particle state in a many-body systems of bosons, had received new impetus both at theoretical and experimental levels in searching and comprehending new states of matter (Anderson et al., 1995 Ketterle, 2002). However, with the ever increasing number of experiments revealing quantum phase transitions at atomic scales (Yukalov, 2004), the need for accurate models for this new state of matter became imperative. Yet, although powerful variational and perturbation methods are available (Kleinert et al., 2004), a basic approach, centered on the key object of BEC - die bosonic gas density / - it is not yet systematically developed and implemented (Vetter, 1997). 

The DFT affirmed themselves as a formal theory able to encompasses great deal of universality through its density based functional relationship with the total number of particle in a system (Parr Yang, 1989 March, 1992 Dreizler Gross, 1990 Putz, 2012a) 

While generalizing the custom quantum normalization condition Eq. (1.155) allows extending the universality class from fermions to 

However, at the level of the quantum equations they accomplish, the fermionic case produced the equivalent for the Schrodinger equation, under the form of the so called Kohn-Sham equation for the mono-electronic 

Equation (1.159) has as the eigen-spectra the mono-orbital chemical potentials (ju) produced through the specific Kohn-Sham potential 

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