Equilibrium Geometric Parameters Research Articles

Theory of the banded domain structure in coarse-grained ferroelectric ceramics

Abstract A theory of the banded domain a-structures in tetragonal ferroelectric ceramics is presented. The mechanical sources of internal stresses appearing on the grain and band boundaries at a phase transition are modelled by arrays of wedge disclinations and continuously distributed fictitious dislocations. With the aid of the disclination and dislocation models the ceramic elastic energy due to the internal stress field is evaluated. This result is used to calculate the equilibrium geometric parameters of the banded domain structure which minimize the internal energy of a coarse-grained ceramic. The dependencies of the equilibrium parameters on the grain size are discussed. The influence of external static and low-frequency electric fields on the banded domain structure is also considered on the basis of an energetic approach. The amplitudes of reversible displacements are calculated for the 90° domain walls inside bands and for the band boundaries consisting of alternating stripes of 90° and 180° wal...

Conformation of 1,3,2,6-dioxaphosphazocines according to data obtained by molecular mechanics method

The molecular mechanics method has been used to determine the equilibrium geometric parameters of 39 conformations of the 1,3,2,6-dioxaphosphazocine molecule, among which the preferred form is the boat-boat (BB) conformer with C and O atoms at the vertices. The role of the anomeric effect in stabilizing the axial orientation of the P-S bond has been evaluated quantitatively in various conformers on the 1,3,2,6-dioxaphosphazocine molecule.

Calculation of the geometrical parameters of iminoxy radicals by the unrestricted Hartree-Fock-Roothaan method

1. The approach considered can determine the equilibrium geometrical parameters of iminoxyl H2CNO. to within 0.02 A and 2° for the bond lengths and valence angles, respectively. 2. On forming the radical H2CNO. from the parent oxime the bond length r(N-O) decreases by 0.2 A, the angle CNO increases by about 15°, and the structural characteristics of the fragment H2C=N- remain practically unchanged.

Ab initio studies of simple compounds of 3d metals

A critical analysis is made of results from ab initio calculations of the potential surfaces of equilibrium geometric parameters and the relative energy characteristics of simple and complex compounds of 3d elements with closed shells.

Second-order perturbation approach to anharmonic analysis of molecules by electron diffraction: Part III. Morse-like potential function of SnCl 2, SnBr 2, SnI 2, Ga 2O and Tl 2O

A practical procedure based on a second-order perturbation intensity equation derived in Part II of this series is developed for analysis of diffraction data from bent symmetric triatomic molecules in terms of the molecular potential function. With this procedure, diffraction data for SnCl 2, SnBr 2, SnI 2, Ga 2O and Tl 2O obtained earlier were re-interpreted and the equilibrium geometrical parameters, harmonic force constants and Morse-like anharmonic parameters for both distances were determined. The frequencies of vibration were also evaluated and compared with spectroscopic and estimated values reported in the literature.

Estimation of equilibrium structure and anharmonicity by use of changes in the rz structure by isotopic substitution and vibrational excitation : I. General formulation and application to OCl 2

A general formulation is presented on the differences in the average ( r z ) structure caused by isotopic substitution and vibrational excitation; the differences in the average structure for both bonded and nonbonded atomic pairs are represented as linear combinations of quadratic average values of the Cartesian displacement coordinates. This method is applicable to a joint analysis of spectroscopic and electron diffraction data so that the equilibrium geometrical parameters and effective anharmonic constants for polyatomic molecules can be estimated even when only a limited number of rotational constants for isotopic species and vibrationally excited states are available. Its application to OCl 2 molecule as an example is discussed.

Geometry and electronic structure of (CO)3NiCH2. A model transition-metal carbene

The first application of nonempirical molecular electronic structure theory to a realistic transition metal carbene complex is reported. The system chosen was (CO){sub 3}NiCH{sub 2}, methylene (tricarbonyl) nickel(0). All studies were carried out at the self-consistent-field (SCF) level. A large and flexibly contracted basis set was chosen, labeled Ni(15s 11p 6d/11s 8p 3d); C,O(9s 5p/4s 2p); H(5s/3s). In addition, the importance of methylene carbon d functions was investigated. The critical predicted equilibrium geometrical parameters were R [Ni-C (methylene)]=1.83 {Angstrom}, {theta}(HCH)=108°. The sixfold barrier to rotation about the Ni-C (methylene) axis is small, ~o.2 kcal. The electronic structure of (CO){sub 3}NiCH{sub 2} is discussed and compared with those of the naked complex NiCH{sub 2} and the stable Ni(CO){sub 4} molecule.

MRD-CI calculations for the structure and stability of the hsin-hnsi isomers

Ab initio SCF and CI calculations are employed to determine the equilibrium geometrical parameters (bond lengths, stretching force constants and rotational constants B e) for the two isomers HSiN and HNSi. It is found that HNSi is bound relative to H( 2S) + SiN( 2Σ +) by 122 kcal mole −1, whereby the SiN( 2π) state is predicted to lie only 13 kcal mole −1 above SiN( 2Σ +). The HNSi isomer is calculated to be more stable than HSiN by 68 kcal mole −1 (CI treatment) and it is found that only a small barrier exists for angular inter-conversion between the two linear forms. A discussion of these results in the light of similar findings for other HAB systems containing first- and second-row atoms is presented Finally it is concluded on the basis of the present calculations that neither HNSi nor HSiN is a likely source for the observed interstellar molecular line U 81.5 ( J = 2 → 1).

An INDO-UHF Molecular Orbital Study of the Conformations and Electronic Structures of Some σ-Type Radicals

Abstract The equilibrium geometric parameters determined for XC=Y radicals (HC=O, CH3C=O, NH2C=O, and HC=CH2) are not characterized by their bond lengths but by their X–C–Y angles, which are wide compared with the angles in their parent molecules (XHC=Y). The %s character of the a orbitals on the C atom in XHC=Y was found to be conserved in the %s character and the s-orbital spin density of the same atom in XC=Y radicals: there are linear relationships between them. Some notable features of the unpaired-electron distribution on the frameworks of XC=Y radicals are also discussed in connection with the electronic properties of the σ radicals.

Conformations and electronic properties of alkyl peroxides, alkylperoxy radicals and alkoxy radicals

The equilibrium geometric parameters have been determined for peroxides (H 2O 2, CH 2O 2H, and CH 3O 2CH 3), alkylperoxy radicals (HO 2, CH 3O 2), and C 2H 5O 2), and alkoxy radicals (HO, CH 3O, and C 2H 5O) by means of the semiempirical MINDO/2' method. The predicted bond lengths were found to be more reasonable than those estimated by the CNDO/2 and INDO methods, but the bond angles were predicted too large because of the insufficient parametrizations for such heteroatoms as oxygen. The electronic properties of the above species are also discussed in connection with their physicochemical constants.

SCF-CI studies of correlation effects on hydrogen bonding and ion hydration

Previous single-determinant Hartree-Fock studies on the equilibrium structures and stabilities of H2 O, H3 O+ as well as of the monohydrated ionic systems Li+ · H2O, F− · H2O and the hydrogen bonded water dimer, H2 O · HOH, are extended by large scale configuration interaction calculations including all the possible single and double excitations arising from the canonical set of Hartree-Fock molecular orbitals. The correlation energy effects on the equilibrium geometrical parameters of the systems under consideration are found to be quite small. The contributions of the correlation energy to the total binding energies of the weakly interacting composed systems are obtained to be of the order of 1 kcal/mole, leading to a considerable increase of the hydrogen bond strength in F− · H2O and H2O · HOH and to a small decrease of the binding energy in Li+ · H2 O. The observed strengthening of the hydrogen bonding interaction due to correlation is shown to be partly compensated by the change in the vibrational zero-point energy of the composed systems compared to the non-interacting subsystems. Approximate force constants corresponding to the intersystem vibrations in Li+ · H2O, F− · H2 O, and H2O · HOH are deduced from the calculated potential curve data on the SCF and the CI level of accuracy.