Super-atoms

At such cold temperatures, atoms start to do strange things. This state of matter is called a condensate because it is formed by a sort of condensation of atoms. Under normal temperatures, atoms exist in their own bit of space. Near absolute zero, these atoms condense and clump together and form what scientists call a super atom. 

Not surprisingly, these super atoms give rise to some unusual properties of BECs, many of which are not entirely understood. One of the most interesting properties is the ability of these liquids to spontaneously flow out of their containers. 

Chen, C.-J., Liu, Z.-J., Rose, J. R, Rosenbaum, G., and Wang, B. C. (2001). Low resolution sulfur super atom phasing for proteins containing disulfide bonds. Acta Crystallogr. Section D, submitted. 

There comes a time in the validation process when the surviving super-atoms will be transformed into general molecules by the specification of all possible sets of alkyl radicals, of unknown inner structure, which have to be attached to the free valences of the superatoms. To which of the free valences each possible alkyl radical may belong is not important at this point. The atoms of the superatom under consideration are subtracted from the empirical formula so far inferred, leaving the number of carbon atoms which must be distributed in all possible wajrs among the free valences of the superatom. For example, if the inferred elemental composi-... 

Another important electronic structure principle is the maximum hardness principle " (MHP) which may be stated as, There seems to be a rule of nature that molecules arrange themselves to be as hard as possible . Numerical verification of this principle has been made in several physico-chemical problems such as molecular vibrations , internal rotations , chemical reactions" , isomer stability , pericyclic reactions and Woodward-Hoffmann rules , stability of magic clusters , stability of super atoms ", atomic shell structure" , aromaticity , electronic excitations , chaotic ionization, time-dependent problems like ion-atom collision and atom-field interaction " etc. 

The development of the super-atom model for the description of electronic properties of metal clusters arose from the attempt to understand and interpret experimental data by W. Schulze and co-workers Figure 1.1 shows the absorption of small silver particles... 

Figure 1.1 Optical absorption of small silver particles Ag embedded in argon at low temperatures, according to Ref. [11]. The huge absorption hump is a collective electronic oscillation localized at the interface Ag/Ar. This figure historically gave the impact for the development of the super-atom model for metal clusters. For large clusters a broad, damped peak is observed, whereas for small clusters the line is fragmented...

Two features of the jellium description of the super-atom model are experimentally confirmed ... 

Once again a crystal is a compound of atoms or assemblies of atoms ordered in space this because the atoms and the atomic orbital are the quantum fundament of the compounds of the super-atomic (yet nano-) matter. 

The PS CG beads consisted these m and r diads as super-atoms as shown in Fig. 4. The centres of the beads were set on methylene carbon atom. The beads were two types m and r. Accordingly the CG force field have three different bond types corresponding to the three undistinguishable triads (mm, mr and rr), six angle types (mmm, mmr, mrm, mrr, rmr, and rrr). All these combinations are depicted schematically in Fig. 5 with the help of modified Fisher projection. 

In the example of the substituted benzoic acids, all matrices are equalized in size by condensing all the atoms of S into a super-atom , that is a collection of nuclei and their associated atomic basins that are taken as one self-contained group. The idea of a super-atom implements the concept of pmning the branches introduced by Pye and Poirier [27, 28]. 

The number of localized electrons within the super-atom S is the sum of the localized electrons in each composing atom plus the number of electrons delocalized within the group (that is between the constituent atoms). Thus, we define the localization index of the super atom [21] ... 

It is non-coincidental that Eq. (3.18) bears a striking resemblance to Eq. (3.7) since at the limit where the super-atom is enlarged to consist of the full molecule... 

On the other hand, the number of electrons shared between the super-atom S and an atom k outside of S is given by the sum of the delocalization indices of every atom within S to that atom [21] ... 

Sumar 1, Ayers PW, Matta CF (2014) Electron localization and delocalization matrices in the prediction of pKa s and UV-wavelengths of maximum absorbance of p-benzoic acids and the definition of super-atoms in molecules. Chem Phys Lett 612 190-197... 

In a meso-scale model, a group of atoms is often replaced by a single interaction center. This center is usually the size of a monomer in a polymer and it is often called a super-atom. Because the super-atoms are the only interaction centers in a meso-scale simulation, they are required to carry the information of the interactions between the real atoms in their local geometrical arrangements that are imposed by the chemistry of the polymer. 

Figure 2 Various anchor sites for the super-atoms of polystyrene. Reprinted from Computers and Chemical Engineering Volume 29, Q. Sun and Roland Faller, Systematic Coarse-Graining of Atomistic Models for Simulation of Polymeric Systems, pp. 2380-2385, Copyright (2005) with permission from Elsevier.

Coarse-graining techniques are based on the idea of effective interaction potentials between super-atoms. The larger-scale model is calibrated against the smaller-scale model, which is considered to be more reliable and is used as a gold standard. Thus, any deficiencies of the small-scale model are carried over to the large-scale model. 

One of the earliest approaches of systematic mapping was attempted by Tschop et al. Their technique begins with a detailed quantum chemical calculation of a few monomers of the system to obtain energetically favorable local conformations and their relative energies. Those quantum chemically determined distributions are then used to perform single-chain Monte Carlo simulations in a vacuum. The corresponding distributions of super-atom bond... 

Figure 3 The bond angle potential on the meso-scale for polystyrene obtained by the Iterative Boltzmann Method. The angle is defined by three consecutive super-atoms...

In principle, the mapping onto simple models assigns a computationally cheap interaction potential to a set of super-atoms. With respect to optimization, this mapping is just the initial step before any further refinement is carried out. In this vein, the polymer models can be similar to one another, in which case, we can get a good mapping or we can rely on vastly different polymer models with poor mapping qualities and, as such, have essentially nothing to do with each other. 

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