Harmonic Moments Research Articles

Ab initio study on the characterization of N 2O 4 isomers

Equilibrium geometries, harmonic vibrational frequencies, infrared intensities and dipole moments have been calculated for a set of N 2O 4 isomers ( trans-ONONO 2, cis-ONONO 2, cis-perp- trans ONOONO and trans-perp- trans ONOONO) by ab initio method at the MP2 level with the 6-31G ∗ and 6-311G ∗ basis sets. The calculated results satisfactorily reproduce the available experimental vibrational spectral features of trans- and cis-ONONO 2. Calculations at the same levels indicate that two OO coupled isomers of ONOONO, namely cis-perp- trans and trans-perp- trans forms, are also true minima on the potential energy surface. Our ab initio results elucidate several trends involving relative energies, Mulliken population and bonding characteristics and suggest that two ONOONO isomers are covalently bound structures, while trans- and cis-ONONO 2 isomers may be formed by a strong mixture of covalent and ionic bonding with nonplanar structures.

The ClO4 radical: Experiment versus theory

The chlorine tetroxide radical and its anion have been investigated with unrestricted Hartree–Fock, density functional and hybrid Hartree–Fock/density functional methods, perturbation theory, and coupled cluster methods. It is predicted that the minimum on the ClO4 radical potential energy surface corresponds to the 2B2 ground electronic state, a C2v-symmetry structure. The C3v structure identified experimentally lies a few kcal mol−1 higher energetically. A Cs symmetry structure lies very close energetically to the C2v minimum at some levels of theory. Adiabatic electron affinities, equilibrium geometries, harmonic vibrational frequencies, infrared intensities, isotopic shifts, and dipole moments are presented for all methods. Comparisons with recent experimental vibrational data for the radical are made. It is predicted that the C2v equilibrium geometry of the ground state is Re(Cl–O1)=1.502 Å, Re(Cl–O2)=1.424 Å, θe1=93.6° and θe2=114.2°. The adiabatic electron affinity of the ClO4 radical is predicted to lie near 5.2 eV.

Power transmission from a vibrating body to a circular cylindrical shell through passive and active isolators

The transmission of harmonic vibratory power from a vibrating rigid body into a thin supporting cylindrical shell through multiple passive and active isolators is investigated theoretically. The model allows for the transmission of vertical and horizontal harmonic forces and moments about all three coordinate axes. Results show that over a frequency range from 0 to 200 Hz, the real power transmission into the supporting shell can be reduced substantially by employing in parallel with existing passive isolators, active isolators adjusted to provide appropriate control force amplitudes and phases.

STEADY-STATE SOLUTION OF AN ER CLUTCH AT HARMONIC LOAD

A concentric electrorheological clutch (ERC) constituting the central part of a broader system: electro-hydro-aggregate (EHA) with an electrodrive on one side and a loading machine on the other side is considered. Harmonic loading moment is taken into account. Dynamic model of EHA is presented in a dimensionless form and linearized in the vicinity of mean values of the sought steady-state solution. Due to limited extent of the paper further course of solution is described only briefly whereby averaging of variable viscosity of ER fluid is performed. As solution special Bessel, i. e., Kelvin functions and matrix calculus are utilized. Methodology of 3-level analysis is briefly described. Some results of preliminary analysis are presented. Lastly some open problems are pointed out.

Structure and spectra of the thioketenyl (HCCS) radical in its ground and first excited states obtained by ab initio coupled-cluster methods

There is recent interest in finding the HCCS radical in interstellar sources and a detailed investigation of its UV spectrum has also been reported. By using state of the art coupled-cluster (CC) based ab initio methods, such as coupled-cluster singles and doubles (CCSD) with approximate triple excitation correction (CCSD(T)), the equation-of-motion CC method for excited states (EOMEE-CC) and for ionization potential (EOMIP-CC) together with large basis sets, we present the structure, harmonic vibrational frequencies and dipole moment of the ground and first excited 2Π states. We confirm the experimental rotational constant and most of the assignment made on the vibrational structure of the UV spectrum, but we also suggest reassignments in some cases. Special attention is paid to the Renner–Teller splitting present for such 2Π states.

LINE ADMITTANCE AT THE JUNCTION OF TWO PLATES WITH AND WITHOUT FLUID LOADING

A time harmonic line force or moment is applied at the junction of two plates in welded contact, with or without unilateral fluid loading. The objective is the 2 x 2 matrix of admittances relating the applied force and moment to the deflection and rotation at the load. The structural asymmetry leads to coupling between force and rotation, and between moment and deflection, even in the absence of fluid loading. The impedance matrix is derived for sources with linear phase variation of the form e ik, y for real k y . The dry plate problem is addressed first, and displays the possibility of a resonance when the drive is in phase with a flexural Stoneley wave, which is defined here. The fluid-loaded problem is attacked by expressing the vibration of either plate and the acoustic response in the fluid as transforms, the integrands of which are derived using the Wiener-Hopf technique. It is found that the wet response shows the same general behaviour as for the dry plates, but without possibility of a structural resonance. Numerical examples are presented showing the frequency dependence of the admittance matrix for joined steel plates in water. The general theory for distinct plates under fluid loading also provides a new formula for the line admittance of a uniform plate in a fluid.

Density Functional Studies of Vibrational Properties of HCN, H2O, CH2O, CH4, and C2H4

Small molecules provide a unique testing ground for post-Hartree−Fock methods because their harmonic force constants and dipole moment derivatives are known experimentally. We have compared several density functional theory (DFT) methods with various combinations of exchange and correlation functionals such as BLYP, B3LYP, BP86, B3P86, BPW91, B3PW91, BVWN, BVWN5, and BPL in combination with several basis sets for HCH. Most density functional results provide impressive agreement with the experiment for geometries and vibrational frequencies. Methods with B3 exchange functional consistently overestimate diagonal force constants, while other methods underestimate the CH stretching force constant in HCN. However, all calculated dipole moment derivatives of HCN, including HF, DFT, and QCISD, show less accurate agreement with experiment than for vibrational frequencies. The results show a strong dependency on the choice of the basis set and on the form of the density functional. On the basis of the extensive basis set and DFT potential dependency studies on HCN, we have applied only the three most promising DFT's to a calculation of other small molecules in order to generalize what we have observed. Calculations on H2O, CH2O, CH4, and C2H4 molecules provide relatively accurate predictions of dipole moment derivatives. DFT calculations allow unequivocal sign assignments in the determination of atomic polar tensors (APT) of these molecules including a new assignment of signs of the dipole moment derivatives for C2H4 and confirming earlier assignments of the H2CO and CH4 of Person et al. These results further support DFT as a means for obtaining reasonable dipole moment derivatives.

Instability Phenomena for the Fourier Coefficients

Let P be an elliptic differential operator on a non-compact connected manifold X; suppose that both X and the coefficients of P are real analytic. Given a pair of open sets D and σ in X with σ⊂⊂ D ⊂⊂ X, we fix a sequence {ev} of solutions of Pu = 0 in D which are pairwise orthogonal under integration over both D and σ. By orthogonality is meant the orthogonality in the corresponding Sobolev spaces; we also assume a completeness of the system on σ. For a fixed y ε X/⊂, denote by kv(y) the Fourier coefficients of a fundamental solution ϕ(·, y) of P with respect to the restriction of {ev} to σ. Suppose K is a compact set in D/σ, and let f be a distribution with support on K. In this paper we show, under appropriate conditions on K, that if the moments (f, kv) decrease sufficiently rapidly in a certain precise sense, then these moments vanish identically. In the most favorable cases, it is then possible to conclude that f = 0. This phenomenon was previously noticed by the first author and L. Zalcman for analytic and harmonic moments of f.

Quantum chemical studies of the pyrrole-water and pyridine-water complexes

An ab initio quantum chemical study of the hydrogen bonded binary complexes pyrrole-water and pyridine-water is reported. The calculations were performed largely at the MP2 level of theory using basis sets of double-zeta-plus polarization functions quality and focus on properties of the complexes such as molecular geometries, energies, harmonic vibrational frequencies, dipole moments and 14N nuclear quadrupole coupling constants. Where possible, the results of the calculations are compared with experimental data. In addition, the interaction potentials are studied in some detail, specifically with regard to basis set superposition and its effect on geometries, intermolecular vibrational frequencies and binding energies. The nature of interaction, i.e., the importance of electrostatic, Pauli repulsion, polarization, charge transfer and dispersion contributions to the hydrogen bond energies, as obtained in constrained spatial orbital variation analyses, is also discussed.

Vibrational power transmission in a finite multi-supported beam

An approach based on flexural wave motion has been developed to investigate vibrational power transmission in a uniform, multi-supported beam. The method can be applied to a finite beam with multiple, different supports subjected to harmonic forces and/or moments. In addition, the method is generally applicable to beams with different end and support conditions. The effects of excitation point location, support spacing and internal damping on the input and transmission of vibrational power have been studied. Experiments on vibrational power, including input power and power transmission, have been carried out in a multi-bay beam in an “indirect” way by employing a multiple channel FFT analyzer. Comparisons between measured and predicted values are presented, and for most cases there was good agreement.

Studies on the dynamic behaviour of a cantilever beam of varying thickness subjected to an end moment

A detailed study has been conducted on the effects of different types of variations in profile and thickness on the amplitude of deflection and the dynamic of a cantilever beam subjected to a harmonic end moment. The response has been calculated for the first four modes of vibration. In each case the results obtained for different types of thickness variations are compared with those obtained for a uniform thickness beam. It is observed that considerable reduction in deflection and/or bending stress can be achieved by proper selection of the thickness variation.

Dynamic response of a two-dimensional semi-circular foundation embedded in a layered viscoelastic half-space

The dynamic response of a massless rigid strip foundation of semi-circular cross-section embedded in a uniform or layered viscoelastic half-space is considered. The foundation is subjected to external harmonic forces and moments and to plane homogeneous P-, SV- and SH-waves. Numerical results are obtained by two indirect boundary integral equation methods: a reciprocity-based approach and a version of the least squares approach. The results for a uniform half-space are tested against the exact solution for longitudinal vibrations and against earlier results for the in-plane impedance functions and for the in-plane response to plane waves. The deffects of Poisson's ratio, material attenuation and layering on the impedance functions and on the scattering coefficients (response to waves) are described in some detail. The appearance of fictitious eigen-frequencies at which the solution may fail is also discussed.

Optimized triple‐zeta Gaussian basis sets for use with relativistic effective potentials

AbstractContracted split valence 311 Gaussian basis sets optimized for the averaged relativistic effective potentials (AREP) of Christiansen et al. are developed for the main‐group elements BNe, AlAr, and GaKr. These triple‐zeta basis sets are intended for use in valence‐only molecular calculations with inclusion of correlation. The performance of the optimized basis functions is first analyzed in HF atomic calculations and compared with HF‐limit results. Molecular calculations at the HF, MP2, and CISD levels of theory are performed for some selected diatomics, using these potentials and the optimized sets supplemented by one standard d‐type polarization function. Results are reported for bond lenghts, harmonic vibrational frequencies, dipole moments, atomization energies, and ionization energies and compared with all‐electron reference calculations and experimental data. © 1994 John Wiley & Sons, Inc.

Observation of conservations laws in diffusion limited aggregation.

We repeat the numerical experiments for diffusion limited aggregation (DLA) and show that there is a potentially infinite set of conserved quantities for the long time asymptotics. We connect these observations with the exact integrability of the continuum limit of the DLA (quasi-static Stefan problem). The conserved quantities of the Stefan problem (harmonic moments) when discretized are our conserved quantities. These numerical experiments show that the exact integrability of the Stefan problem may be continued beyond the formation of cusps in the moving boundary.

Structural acoustics and vibration behavior of complex panels

Among the many mechanical parameters that influence structure-borne sound are the effects of stiffeners, added mass and complex support conditions along the structure boundaries. In the present paper, these effects are incorporated into a model of sound radiation in air from a complex, baffled, rectangular panel under harmonic point force or point moment excitation. A complex panel is thus defined as a panel which is stiffened lengthwise and widthwise by flexural-torsional beams, which carries point masses and which is elastically restrained against transverse displacement and rotation along the edges. The vibration of the panel assumes no fluid loading and is solved using the Rayleigh-Ritz method with simple polynomial trial functions. The expressions of the kinetic and strain energies associated with stiffeners, added mass and elastic boundary conditions, are detailed. A simple computation scheme is used to derive the farfield sound pressure from the transverse displacement of the panel. Numerical results are shown in terms of the mean quadratic velocity of the panel, radiated sound power and radiation efficiency for a variety of situations including force or moment excitation, simply-supported, clamped or free edges, addition of stiffeners and addition of a point mass, and are used to draw some useful guidelines in practice.

Fourier analysis of redshift-space distortions and the determination of

The peculiar velocities of galaxies distort the pattern of galaxy clustering in redshift space, making the redshift space power spectrum anisotropic. In the linear regime, the strength of this distortion depends only on the ratio $\beta \equiv f(\Omega)/b \approx \Omega^{0.6}/b$, where $\Omega$ is the cosmological density parameter and $b$ is the bias parameter. We derive a linear theory estimator for $\beta$ based on the harmonic moments of the redshift space power spectrum. Using N-body simulations, we examine the impact of non-linear gravitational clustering on the power spectrum anisotropy and on our $\beta$-estimator. Non-linear effects can be important out to wavelengths $\lambda \sim 50$Mpc/h or larger; in most cases, they lower the quadrupole moment of the power spectrum and thereby depress the estimate of $\beta$ below the true value. With a sufficiently large redshift survey, the scaling of non-linear effects may allow separate determinations of $\Omega$ and $b$. We describe a practical technique for measuring the anisotropy of the power spectrum from galaxy redshift surveys, and we test the technique on mock catalogues drawn from the N-body simulations. Preliminary application of our methods to the 1.2 Jy IRAS galaxy survey yields $\beta_{est} \sim 0.3-0.4 $ at wavelengths $\lambda \sim 30-40$Mpc/h . Non-linear effects remain important at these scales, so this estimate of $\beta$ is probably lower than the true value.

Solution of Multigroup Transport Equation in X-Y-Z Geometry by the Spherical Harmonics Method Using Finite Fourier Transformation.

Abstract A neutron multigroup transport equation in x-y-z geometry is solved by the spherical harmonics method using finite Fourier transformation. Using the first term of the Fourier series for the space variables of spherical harmonics moments, three-point finite difference like equations are derived for X-, y- and z-axis directions, which are more consistent and accurate than those derived using the usual finite difference approximation, and these equations are solved by the iteration method in each axis direction alternatively. A method to find an optimum acceleration factor for this inner iteration is described. It is shown in the numerical examples that the present method gives higher accuracy with less mesh points that the usual finite difference method.

Solution of Multigroup Transport Equation inX-Y-ZGeometry by the Spherical Harmonics Method Using Finite Fourier Transformation

Abstract A neutron multigroup transport equation in x-y-z geometry is solved by the spherical harmonics method using finite Fourier transformation. Using the first term of the Fourier series for the space variables of spherical harmonics moments, three-point finite difference like equations are derived for X-, y- and z-axis directions, which are more consistent and accurate than those derived using the usual finite difference approximation, and these equations are solved by the iteration method in each axis direction alternatively. A method to find an optimum acceleration factor for this inner iteration is described. It is shown in the numerical examples that the present method gives higher accuracy with less mesh points that the usual finite difference method.

Ammonia alane

A b initio studies employing basis sets approaching triple-ζ plus double-polarization plus f function quality are reported for AlH3NH3, AlH3, and NH3. The self-consistent-field method was employed for all basis sets; the single and double excitation configuration interaction and the comparable coupled-cluster methods were utilized with a double-ζ plus polarization functions basis set. The dissociation energy of AlH3NH3 is predicted to be 26 kcal/mol after correcting for zero-point vibrational energy, in qualitative agreement with the rough estimate of 30 kcal/mol by Haaland for Al–N bond strengths. In keeping with the dative nature of the Al–N bond, the AlH3 and NH3 moieties do not undergo large changes upon the formation of AlH3NH3. The resemblance of AlH3NH3 to the related compound BH3NH3 is quite strong. The equilibrium geometry, harmonic vibrational frequencies, infrared intensities, atomic charges, and dipole moment of ammonia alane are reported.

A systematic ab initio study of the group V trihalides MX3 and pentahalides MX5 (M = PBi, X = FI)

AbstractAb initio calculations using effective core potentials and polarized split‐valence basis sets are reported for the title compounds. The calculated geometries, vibrational frequencies, infrared intensities, harmonic force fields, dipole moments, relative energies, and barriers to pseudorotation are compared with the available experimental data for the known molecules. Predictions are made for those pentahalides that are still unknown. Trends in the calculated properties are identified and discussed.