Equilibrium Interatomic Distances Research Articles

Cohesive energy, phonon spectra, and thermodynamic properties of elements with the structures A1, A2, A3, A4—Al, Cu, V, Ti, Mg, Si, and Sn

The dependences of the cohesive (atomization) energy on the interatomic distance for elements Al, Cu, Ti(A2), V, Mg, Ti(A3), Si, and Sn are calculated using methods based on the Thomas-Fermi-Dirac-Gambosh statistical atomic theory. The obtained dependences are approximated by the Mie-Gruneisen potential. The phonon spectra calculated on the basis of the Born-Karman model and the Born-Karman-Blackman-de Lunay approach are used to determine the temperature dependences of the specific heat, free energy, and internal energy of the elements under investigation. The calculated cohesive energy, equilibrium interatomic distances, and temperature dependences of the specific heat agree with the experimental data.

Large Clusters with Cadmium Sulfide Cores Simulation of Thiolate Ligands on the Surface by Ab Initio MO LCAO Calculation

Inorganic cores MnXm(M=Cd, Zn, Cu, etc.; X=S, Se, Te) in the semiconductor clusters produced in solutions with protection by X-containing ligands provide the main physical properties of clusters. However, the external ligand shell is more important in the chemical respect. An effect of the ligand type is considered for a series of CdnSm–R clusters (n=4, 17 and m=3, 28, respestively, R=H, CH3, CH2OH, C2H4OH) on the basis of ab initio quantum-chemical calculations. Under conservation of local tetrahedral symmetry, the ligand protection strongly influences equilibrium interatomic distances and electronic density distribution. Energies of the first allowed electronic transition for the Cd4S13 species are too high to be fitted in the quantum confinement, while Cd17S28 clusters reveal the value close to the experimental one, which depends on the type of termination.

LARGE CLUSTERS WITH CADMIUM SULFIDE CORES: SIMULATION OF THIOLATE LIGANDS ON THE SURFACE BY Ab Initio MO LCAO CALCULATION

Inorganic cores M n X m (M=Cd, Zn, Cu, etc.; X=S, Se, Te) in the semiconductor clusters produced in solutions with protection by X-containing ligands provide the main physical properties of clusters. However, the external ligand shell is more important in the chemical respect. An effect of the ligand type is considered for a series of Cd nSm– R clusters (n=4, 17 and m=3, 28, respestively, R=H, CH3, CH2OH, C2H4OH) on the basis of ab initio quantum-chemical calculations. Under conservation of local tetrahedral symmetry, the ligand protection strongly influences equilibrium interatomic distances and electronic density distribution. Energies of the first allowed electronic transition for the Cd4S13 species are too high to be fitted in the quantum confinement, while Cd17S28 clusters reveal the value close to the experimental one, which depends on the type of termination.

Symmetry of generalized mean-square vibration amplitudes and their effect on mean and equilibrium bond lengths in benzene, pyridine, and N-oxypyridine

Symmetry properties of generalized mean-square vibration amplitudes for plane six-membered rings belonging to the C2v and D6h symmetry groups are investigated. Corrections to average and equilibrium interatomic distances in benzene, pyridine, and N-oxypyridine are calculated. The character of the corrections in the series of these molecules and their deuterosubstituted analogs is investigated.

Lattice Dynamics of FCC–Cryocrystals with Many–Parametric Impurities

The vibrational characteristics of the FCC–cryocrystals with substitutional impurities have been analyzed. A “non–central” impurity atom in environment of the “central” host atoms is considered. The difference between equilibrium interatomic distances $$\widetilde{r_0 }$$ and r 0 of the impurity and host atoms, respectively, causes their non–central interaction. A very strong dependence of the impurity frequency spectra on the ratio $$\widetilde{r_0 }/r_0 $$ is shown. The range of the values of this ratio which corresponds to dynamical stabitity of the system under consideration is determined.

Vibrationally resolved Si 2p photoabsorption spectrum of SiF 4

A high-resolution study of the Si 2p photoabsorption spectrum of gas-phase SiF 4 is reported. In the excitation region of the Rydberg orbitals, vibrational substates from symmetric stretching vibrational modes were resolved, which were described on the basis of a Franck-Condon analysis resulting in vibrational energies and equilibrium interatomic distances of the core-excited molecule. The natural lifetime width of the Si 2p core excitation amounts to 85 meV, a value that is substantially larger than the theoretically predicted one.

Chemical Bonding in Mn Clusters, MnNand Mn+N(N=2–7)

Electronic states of the neutral and cationic Mn N clusters for N =2–7 are calculated by the spin-polarized density functional method. For neutral clusters, the equilibrium interatomic distances are 20% or more larger than that of the bulk crystal, and the characteristics of the electronic structure remain the same as those of an isolated atom. Atoms consisting of the neutral clusters are bonded non-metallically. For smaller cationic Mn N + clusters ( N =2–4), similar situations exist although the 3 d -4 s mixing increases. For larger cationic Mn N + clusters ( N =5–7), the equilibrium interatomic distances are less than 90% of the value of the bulk crystal. The 3 d levels broaden in energy and constitute band-like structure, and the 4 s metallic bonding occurs. This change from non-metallic to metallic bonding in the cationic clusters seems to correspond to the magic number 5 which is observed in the cationic clusters.

Atomic bonding of neutral and cationic Mn clusters

By using the spin-polarized DV-Xα-LCAO method, electronic states of neutral and cationic Mn N clusters (N=2∼5) are calculated to study atomic bonding of Mn clusters. For the neutral Mn2 cluster, the equilibrium interatomic distance is much larger than that of the bulk crystal. The 3d-derived states are nearly half-filled, and the 4s-derived states are almost fully occupied,i.e. the electronic configuration is close to that of the isolated atom. These indicate that the Mn2 cluster is bound by the van der Waals force. The same situation is true for the larger neutral clusters while the equilibrium interatomic distance becomes smaller and thes-d mixing becomes larger. For the cationic clusters, the behaviors tend to become metallic. The equilibrium interatomic distances are smaller and thes-d mixings are larger than those of the corresponding neutral clusters. However, the Mn 2 + and Mn 4 + clusters still remain the van der Waals characters. Contrary to these clusters, the Mn 5 + cluster, whose interatomic distance is smaller than that of the bulk crystal, shows strong metallic bonding. These results seem to correspond to the magic number observed on the mass spectroscopy of cationic Mn clusters.

Proposed universal interatomic potential for elemental tetrahedrally bonded semiconductors.

Based on the idea that bonding energies of many substances can be modeled by pairwise interactions moderated by the local environment, we propose a new universal interatomic potential for tetrahedrally bonded materials. We obtain two basic relationships linking equilibrium interatomic distances and cohesive energies to the coordination number for a large range of phases of silicon. The relationships are also valid for germanium and carbon, covering, in the latter case, double and triple carbon-carbon bonds, where \ensuremath{\pi} bonding is important. Based on these ideas we discuss the construction of the universal interatomic potential for these three substances. This potential, which uses very few parameters, should be useful, particularly for surface studies.

Interatomic potentials of HgXe van der Waals complex formed in supersonic jets as studied by laser induced fluorescence spectroscopy

The laser induced fluorescence spectra of HgXe formed in a supersonic free jet of a He/Xe/Hg mixture were observed to determine the interatomic potentials between Hg and Xe in the X 10+, A 30+, and B 31 states. The dissociation energies for the X, A, and B states are 254, 1457, and 172 cm−1, respectively, with the equilibrium interatomic distances of 4.25, 3.25, and 4.47 Å for the respective states. It is found that the potential shape for the X and B states can be represented in good approximation by a Morse function, though this function may not reproduce the potential for the A state especially in the vicinity of high vibrational levels (v′>16).

Structural dynamics of melanin investigated by Rayleigh scattering of Mössbauer radiation

AbstractMeasurements of Rayleigh scattering of Mössbauer radiation (RSMR) have been performed on synthetic L‐Dopa melanin as a function of the scattering vector, Q, and temperature, T, and are compared with the results of X‐ray diffraction analyses. The data obtained allow us to derive a radial distribution function for the atomic positions not affected by the dynamic disorder and determined only by the distribution of equilibrium interatomic distances. The mean‐square atomic displacements, <u2>, derived from the RSMR measurements, evidence a strong anisotropy of the atomic vibrations: even at room temperature, <u2> reaches fairly high values for off‐plane displacements, as compared with those for motions within the planes of the structure. A connection is suggested between the observed dynamics and the biological screening action of melanins.

A study of the ground states and ionization energies of H2, C2, N2, F2, and CO molecules by the variational cellular method

Self-consistent calculations for the ground state potential curves and ionization energies are reported for the molecules H2, C2, N2, F2, and CO, using the recent proposed variational cellular method. For all these molecules the results are quite good. The calculated binding energies, equilibrium interatomic distances, and energy ionization spectra are in excellent agreement with the available experimental findings.

Self-consistent calculation of the electronic structure ofN2and CO by the variational cellular method

In this paper the variational cellular method is extended to the self-consistent calculation of diatomic molecules. This extension is based on a new variational expression for the total molecular energy the extremum of which defines the one-electron potential of the Schr\"odinger equation. The method was tested in the calculation of ${\mathrm{N}}_{2}$ and CO and the results are very good: the binding energy and the equilibrium interatomic distances were calculated to be within less than 10% of the known experimental results.

Molecular structure and vibrational potential function of HgI 2: electron diffraction study

For the first time in electron diffraction structure analysis of polyatomic molecules the direct parameterization of an intensity function on force constants and equilibrium interatomic distances is applied. Following this procedure, all harmonic valence force constants of the HgI 2 molecule and the equilibrium interatomic distance HgI in the harmonic approximation have been determined by gas-phase electron diffraction assuming the equilibrium geometry to be linear. On the basis of vibrational frequencies calculated from the force constants thus obtained, a critical analysis of available spectroscopic data is given. By combined use of electron diffraction and most reliable spectroscopic data treated as independent observables the best values for harmonic valence force constants are obtained. The anharmonicity in the bending vibrational potential is also examined. It is shown that, to a good approximation, the bending vibration may be regarded as being harmonic at least for small vibrational quantum number values.

Third-order energy using CNDO/2 and INDO Hamiltonian approximations in the modified PCILO method

The perturbative configuration interaction using strictly localized molecular orbitals, called the modified PCILO method has been applied in this communication for the calculations of the energy terms of 15 small molecules up to the third order of the perturbation theory. For this method the use of the Rayleigh-Schrodinger many-body perturbation theory with the Moller-Plesset type of the Hamiltonian partitioning is characteristic. On the CNDO/2 and INDO level of approximations the strictly localized molecular orbitals have been constructed by solving the modified 2 x 2 Roothaan's equations. From the zeroth order ground-state wave function the charge distributions, dipole moments and carbon 13-proton nuclear spin-spin coupling constants have been calculated. Results show that the chemical formula, represented with the zeroth order of the perturbation theory, is a good order of the approximation for the study of the molecule. For diatomic molecules the equilibrium interatomic distances and harmonic force constants have been calculated up to the third order of the perturbation theory. The second order of the perturbation theory provides results which are very near to the MO-LCAO-SCF calculations. The main advantage of the PCILO method lies in much saving of the computing time.

Trends of force constants in diamond and sphalerite-structure crystals

The dependence of force constants (ν 2μ) on equilibrium interatomic distances are analysed for the following three diamond-like crystal groups: IV–IV, III–V and II–VI. We have considered the models due to Varshni and Anderson and arrived at a simpler relation. It is found that the force constants are presented as a function of interatomic distances within an accuracy of ≈ 3%. The model constants are evaluated by least-squares fitting of available experimental data, and the parameters, along with the relative merits of the models, are presented.

An improved Hellmann‐type pseudopotential for atoms and molecules

AbstractThe concept of pseudopotentials offers much attractiveness for the quantum mechanical evaluation of the physical properties of atoms and molecules. The ideas of Hellmann, in which the repulsive and fermion character of inner electrons can be mimicked by an experimentally fitted, exponentially damped potential term, are especially attractive. Unfortunately, it is found that such a simple expression can only be used in a very limited number of cases, such as for the alkali metals, and even then fails for the simple case of lithium.The present study shows that the Hellmann idea can readily be extended by including a second “shielded potential” term evaluated from tabulated previous Hartree‐Fock calculations. The new expression for the model pseudopotential is both simple and effective. With it, the inner potential of any of the alkali metal atoms, including lithium, can be represented so that calculation of the molecular properties of the metal dimers can be accomplished. Calculations for Li2, Na2, and K2 show the binding energies and equilibrium interatomic distances to be quite well given, in agreement with both chemical experience and spectroscopic evidence.

Influence of deviations of the equilibrium interatomic distances from the vegard rule on the heats of formation of inorganic solid solutions

Influence of deviations of the equilibrium interatomic distances from the vegard rule on the heats of formation of inorganic solid solutions

The Structure and Internal Motion of Hexachloroethane

The equilibrium interatomic distances and their average amplitudes of vibration were determined for C2Cl6 by means of the microphotometer method in electron diffraction. Internal rotation was investigated, and the interdependence of the effects of the torsional mode and other modes of vibration on the gauche Cl–Cl distance is presented graphically.

Compressibilities, Force Constants, and Interatomic Distances of the Elements in the Solid State

Available data for the compressibilities of crystalline elements are used to calculate the force constants for the assumed Hooke's law interactions between adjacent atoms. On comparison of these constants and the equilibrium interatomic distances it is found that for many substances there holds the relation discovered by Badger for diatomic gas molecules: a linear relation between the reciprocal of the cube root of the force constant and the interatomic distance, for elements of a given row in the periodic table. Deviations from this relation are in the direction of increased compressibility. They are explained as resulting from changes in bond type (that is, in electronic structure) that permit the crystal to adjust itself to the increased pressure.