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The Pauli exclusion principle gives an upper bound of 1 on natural occupation numbers. Recently there has been an intriguing amount of theoretical evidence that there is a plethora of additional generalized Pauli restrictions or (in)equalities, of a kinematic nature, satisfied by these numbers. Here a numerical analysis of the nature of such constraints is effected in real atoms. The inequalities are nearly saturated, or quasipinned. For rank 6 and rank 7 approximations for lithium, the deviation from saturation is smaller than the lowest occupancy number. For a rank 8 approximation we find well-defined families of saturation conditions.

The Boson peaks are typically ascribed to an excess density of vibrational states for the small clusters. A well resolved boson peak is observed in the low-frequency portion of the spectrum. A starting point for our discussion is the behaviour of the boson peak, derived from the vibrational density of states and the temperature dependencies of the vibrational heat capacities of the re-optimized neutral gold clusters. This Boson peak is associated with the existence of intermediate range order (IRO) in the arrangements of atoms. The low frequency (Far Infrared FIR, IR-C 200-10 cm−1) containing this dominant spectral line (Boson peak) is interpreted in terms of its relationship to the amplitude and extent of the density fluctuations in atoms and is, thereby, considered a measure of the intermediate range order in these atoms. We found a systematic relation among the boson peak energy, the boson peak intensity per atom, and the zigzag-bond density; the peak energy decreases and the peak intensity increases as zigzag-bond density decreases.

The geometries and vibrational frequency of the most stable small AuN clusters with N = 3 to 20 are presented through global structure re-optimization Study. The finite-differentiation method has been implemented within the density-functional tight-binding (DFTB) approach. The desired set of system eigenfrequencies (3N-6) is obtained by a diagonalization of the symmetric positive semi definite Hessian matrix. We have observed the vibrational modes between 0.55 and 370.72 cm-1 in wavenumbers at T=0 for the small gold clusters. The effect of the range of interatomic forces was calculated, and even the very lower frequencies were occupied in some clusters.

The vibrational heat capacity Cvib of a re-optimized neutral gold cluster was investigated at temperatures 0.5-300 K. The vibrational frequency of an optimized cluster was revealed by small atomic displacements using a numerical finite-differentiation method. This method was implemented using density-functional tight-binding (DFTB) approach. The desired set of system Eigen frequencies (3N -6) was obtained by diagonalization of the symmetric positive semi definite Hessian matrix. Our investigation revealed that the Cvib curve is strongly influenced by temperature, size, and structure and bond-order dependency. The effect of the range of interatomic forces is studied; especially the lower frequencies make a significant contribution to the heat capacity at low temperatures. In addition to that, we have exactly predicted the vibrational frequencies (ωi) which occur between 0.55 to 370.72 cm-1, depending on the nanoparticle morphology at T=0 for small neutral gold clusters AuN=3-20. This result has been proved and confirmed by the size effect values. It was found that beside the particle size, geometric shape, defect structure and an increase in asymmetry of nanoparticles effects on heat capacity. Surprisingly, the Boson peaks are typically ascribed to an excess density of vibrational states for the small clusters. Finally, temperature dependencies of the vibrational heat capacities of the re-optimized neutral gold clusters have been studied for the first time.

The vibrational heat capacity Cvib of a re-optimized neutral gold cluster AuN=14 was investigated at temperatures 0.5-300/950 K. The vibrational frequency of a optimized cluster was revealed by small atomic displacements using a numerical finite-differentiation method. This method was implemented using density-functional tight-binding (DFTB) approach. The desired set of system eigenfrequencies (3N-6) was obtained by diagonalization of the symmetric positive semidefinite Hessian matrix. Our investigation revealed that the Cvib curve is strongly influenced by temperature, size and structure dependency. The effect of the range of interatomic forces is studied, especially the lower frequencies make a significant contribution to the heat capacity at low temperatures. Surprisingly, the Boson peaks are typically ascribed to an excess density of vibrational states for the small clusters. Finally, temperature dependencies of the vibrational heat capacities of the re-optimized neutral gold cluster have been studied for the first time.

Bright luminescence of Eu(II) doped into the cubic perovskites KMgH3 and mixed crystal compounds LiBaxSr(1-x)H(3) was observed and assigned to the 4f(6)5d-4f(7) emission of Eu2+. KMgH3: Eu2+ shows an extremely bright yellow emission, whereas the wavelength of the emission maximum in LiBaxSr(1-x)H(3): Eu2+ depends on the value of x and ranges from yellow to green. Furthermore, an extremely wide red shift in the emission energy is observed for the orthorhombically distorted perovskite NaMgH3: Eu2+. Additionally, we review the crystal structure of KMgH3 using density functional calculations.