Correlated atoms

There are several types of basis functions listed below. Over the past several decades, most basis sets have been optimized to describe individual atoms at the EIF level of theory. These basis sets work very well, although not optimally, for other types of calculations. The atomic natural orbital, ANO, basis sets use primitive exponents from older EIF basis sets with coefficients obtained from the natural orbitals of correlated atom calculations to give a basis that is a bit better for correlated calculations. The correlation-consistent basis sets have been completely optimized for use with correlated calculations. Compared to ANO basis sets, correlation consistent sets give a comparable accuracy with significantly fewer primitives and thus require less CPU time. 

Ebenstein Y, Mokari T, Banin U (2002) Fluorescence quantum yield of CdSe/ZnS nanocrystals investigated by correlated atomic-force and single-particle fluorescence microscopy. Appl Phys Lett 80 4033 1035... 

If a (full) dislocation has passed through a crystal, its surface shape is affected. If a partial dislocation has passed through a crystal, the stacking sequence is disturbed across the glide plane. If bundles of partial dislocations pass through a crystal in a certain order, they may change the crystal structure by correlated atomic displacements, for example, from fee to hep. 

First, there is the obvious objection that there may be no experimental values for the properties and systems of interest. Second (and almost as obvious) is the possibility that the experimental values are wrong. Third, the experimental values may in fact be derived from experimental measurements by a number of steps that involve assumptions or other theoretical calculations. All of these objections are important, but in one sense they are orthogonal to the real issue what if our calculations contain multiple sources of error that can cancel with one another We know already that any truncated one-particle space and truncated jV-particle space treatment has two sources of error, these two truncations. And there is no reason to suppose that the error from these two sources cannot cancel, indeed, from the early days of large-scale correlated atomic wave functions there is good evidence that they do cancel [35]. Hence even if there are absolutely reliable experimental values for the properties and molecules we want to consider, using them to calibrate theoretical methods may be useless unless we can establish whether we have a cancellation of errors or not. 

The argument so far is premised on the assumption that there is no interaction possible between the correlated atoms at the time that the measurement is done. However, should there be an undisclosed interaction between the two particles, disturbance of A, caused by the measurement could communicate itself to B, causing a simultaneous disturbance at that position as well. This interaction may result in orientation of the spin at B in a direction opposite to that of A. Not surprisingly Einstein, the father of special relativity, did not even consider such a possibility since it requires instantaneous non-local interaction. 

S. Kielich, T. Bancewicz, and S. Wozniak. Spectral distribution of scattered light by fluid mixtures of correlated atoms and molecules. Canad. J. Phys., 59 1620-1626 (1981). 

Abstract We consider a possible realization of the position- and momentum-correlated atomic pairs that are confined to adjacent sites of two mutually shifted optical lattices and are entangled via laser-induced dipole-dipole interactions. The Einstein-Podolsky-Rosen (EPR) "paradox" [Einstein 1935] with translational variables is then modified by lattice-diffraction effects. We study a possible mechanism of creating such diatom entangled states by varying the effective mass of the atoms. 

We first observe that we do not get automatically better results by simply adding polarization functions (d orbitals on O and p orbitals on H). For the lBi state, whose vertical excitation energy is well established to be around 7.4 eV (36, 37), the DZP result ( 9.1 eV) at the MP3 and CCSD levels is about 0.4 eV further away from the experiment than the DZ result ( 8.7 eV). It is thus important to employ more appropriate basis set in order to reach basis set converged results. We thus employ the ANO basis sets, resulting from correlated atomic calculations, first advocated by Almlof and Taylor (38), which are known to efficiently account for molecular correlation effects. 

These experiences have been described in literature of chemistry education for decades [6]. Only in exceptional cases has the teaching of chemistry been completely altered due to this criticism [9]. Students are not only given the atoms and correlative atomic masses based on the Daltonic model with the Periodic System of the Elements (PSE), but also important ion types (see Fig. 5.10). This special Periodic System graphically depicts and clearly arranges atoms and Ions as basic particles of matter [9] (see Fig. 5.10). Both spherical models of atoms and ions correlate to their sizes as measured by physicists. Christen [10] uses a similar system in his book for introduction to chemistry. 

Interactions involving short laser pulses have occasionally been compared to collisions, which also depend impulsively on time. Collision problems require at the outset a rather good description of the correlated atom, without which realistic predictions cannot be made. This analogy suggests that a maximum atomic physics option is required. 

These various observations suggest that the continuous diffuse scattering is a potentially useful source of unique dynamic information regarding correlated atomic displacements in a crystal. 

M. Micic, D. Hu, Y.D. Suh, G. Newton, M. Romine, H.P. Lu, Correlated atomic force microscopy and fluorescence lifetime imaging of live bacterial cells, Colloids and Surfaces B, Biointerfaces 34, 205-212 (2004)... 

As previously mentioned, in the approach that correlates atomic radii with the electronegativity it is of fundamental importance to know the atomic electron density of a given system. In this respect, a suitable treatment is based on the Slater orbital electronic picture that produces the normalized distribution functions under the radial form (Slater, 1964) ... 

Correlate atomic properties, such as ionization energy, with electron configuration, and explain how these relate to the chemical reactivity and physical properties of the alkali and alkaline earth metals (groups lA and 2A). (Section 7.7)... 

Abstract A new recursive procedure is reported for the evaluation of certain three-body integrals involving exponentially correlated atomic orbitals. The procedure is more rapidly convergent than those reported earlier. The formulas are relevant to ab initio electronic-structure computations on three- and four-body systems. They also illustrate techniques that are useful in the evaluation of summations involving binomial coefficients. 

Intriguing connections to condensed-matter physics can be found when Feshbach molecules are trapped in optical lattices. In this spatially periodic environment, a Feshbach molecule can be used both as a well-controllable source of correlated atom pairs, and as an efficient tool to detect such pairs. A recent experiment [95] shows how Feshbach molecules, prepared in a three-dimensional lattice, are converted into repulsively bound pairs of atoms when forcing their dissociation through a Feshbach ramp. Such atom pairs stay together and jointly hop between different sites of the lattice, because the atoms repel each other. This counterintuitive behavior is due to the fact that the bandgap of the lattice does not provide any available states for taking up the interaction energy. 

The interference of radiation, x-rays or neutrons, scattered from correlated atoms yields eventually experimental values of the pair correlation function g,s(r). The diffraction methods yield the intensity / of the beam of the radiation at a fixed wavelength X diffracted at various angles 0 for the defined variable k ... 

Structure factors, S. ik), for scattering from two correlated atoms i and j in the... 

Here 1(9) is the intensity of the scattered radiation at the angle 0, normalized to the instrumentation employed and to the total number of atoms in the system exposed to the radiation, c. is the concentration of the jth atom species, and is the coherent scattering amplimde from this species, and the summation extends over all the atomic species present. There are as many linear relationships between the structure factors and the intensity 1(0) as there are pairs of correlated atoms in the system and special means have to be employed to extract from than the desired information, namely the partial structure fartors S (k). 

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