A local picture associated with a triply degenerate vibrational mode: vibrational and rovibrational local states

A symmetrized basis adapted to the study of some vibrational excited states of spherical top molecules is proposed. This basis, consistent with the Cartesian picture associated with a three-dimensional mode, is then tested numerically through various XY₆ and XY₄ molecules. In addition, some simulations, made with ²³⁸UF₆ and a simplified version of an effective Hamiltonian, clearly show that the method can be further extended through the construction of a symmetrized local rovibrational basis.     

Refined local mode analysis of the stretching vibrational levels of C2D2

Dideuteroacetylene, C₂D₂, is a remarkable species for which the stretch-bend separability of the vibrational states is such that all the experimentally known stretching levels can be reproduced with an rms of 1.1 cm^?1 by using a simple stretching coordinate Hamiltonian model. The only two levels which deviate significantly from the calculations point out the effect of the 1/244 stretch-bend resonance previously identified. The local mode parameters retrieved from the fit of the experimental levels allow for a very satisfactory prediction of the available energy levels of the ¹²C¹³CD₂ species. A comparison between the local mode and normal mode approaches is presented.     

Potential models for quarkonia

In this paper I discuss what we can learn about quarkonium dissociation from lattice-potential based models. Special emphasis is given to results obtained in agreement by different models, and to the relevance of lattice QCD for potential models. Future directions are also discussed.     

Non-Gaussian statistical models for scattering calculations

Abstract

In calculating the properties of waves scattered by random media it is almost always assumed that variations of the media constitute a joint Gaussian process. In this paper two alternative models are investigated. It is shown that whilst some features of the statistics of the scattered waves are more sensitive to the spectrum of the fluctuations in the medium than to the basic statistical model, in general significantly different properties are predicted using the alternative models.     

Non-Gaussian statistical models for scattering calculations

In calculating the properties of waves scattered by random media it is almost always assumed that variations of the media constitute a joint Gaussian process. In this paper two alternative models are investigated. It is shown that whilst some features of the statistics of the scattered waves are more sensitive to the spectrum of the fluctuations in the medium than to the basic statistical model, in general significantly different properties are predicted using the alternative models.     

Simplified models for vibrational energy transfer in proteins

We consider the transfer of vibrational energy in proteins and derive a simplified model for the resonant energy exchange between different vibrational modes. We use the parameters of an earlier study [K. Moritsugu, et al., Phys. Rev. Lett. 85 (2000) 3970 ] to compare our predictions with the results of the molecular dynamics simulations, and reveal an excellent agreement.     

Fibre mode expansion for 2-D waveguide calculations

A numerical method is introduced which is devised to calculate the lower-order modes of optical waveguides with two-dimensional transverse index profiles embedded in a homogeneous cladding medium. We propose a method based on a series expansion using guided modes of an optical fibre. To test the method, it is applied to a three-layer optical-fibre and the results are compared with the exact analytical solutions. The error in the calculation of the modal effective indices is found to be less than 10−6. This method allows the modelling of symmetric 2 × 2 completely fused fibre couplers. Effective indices and polarization corrections are compared with results obtained by the field correction method. The adiabaticity criterion is calculated for these couplers. This revised version was published online in November 2006 with corrections to the Cover Date.     

Quantum-mechanical calculations and analysis of vibrational modes in lead magnoniobate

The vibrational modes in lead magnoniobate have been calculated using the frozen phonon method. It has been shown that lead atoms participate in two radically different vibrational modes, namely, a nonpolar antiferrodistortive mode, which involves the antiphase motion of some lead atoms with respect to other lead atoms, and a polar mode, which includes the polar motion of lead atoms with respect to other atoms of the lattice. The nontrivial properties of lead magnoniobate have been discussed in terms of the unity and conflict of these modes.     

Three-nucleon calculations for local potentials with the quasiparticle method

The three-nucleon system for energies below the breakup threshold is investigated with the help of the quasiparticle method. Two types of local potentials are used, namely purely attractive Yukawa potentials and the soft-core potentials of Malfliet and Tjon. The results obtained are compared with those of other calculations employing different methods.Presented at the symposium Theory of lightest nuclei, Liblice, Czechoslovakia, May 1974.     

Multiloop calculations of effective action for local composite operators

Effective action for local composite operators is described for both the standard loop expansion formulation and an improved two-particle irreducible formulation. Rules for calculating multiloop contributions to the effective action are given in both formulations and are exemplified in the Gross-Neveu model in the large-N limit. Calculation of the exact effective action in the Gross-Neveu model is considerably simplified in the improved formulation. Results obtained from the conventional auxiliary field method, like dynamical symmetry breaking, non-classical solitions, etc., can all be obtained in the present formulation by dealing with the composite operators directly without introducing auxiliary fields. The present method can be applied to models in which the auxiliary field method is difficult to implement.     

Hamiltonian description and 6D calculations on the ammonia vibrational levels

In this work, a Hamiltonian formalism and a 6D vibrational calculation procedure is described and implemented, designed for the exploration of vibrational motion in ammonia (and any XH₃ molecule). The 6D potential energy surface of ammonia was modelled in simple analytical form (including the inversion potential) at the planar, totally symmetric (D_3h) reference configuration. Using the described method (which is an adaptation of the formalism, previously developed and applied to benzene), 6D calculations were carried out on the vibrational level system of ammonia ¹⁴NH₃, at the lower levels of vibrational excitation. On the basis of the satisfactory agreement between the calculated and the experimentally measured vibrational frequencies, the values of some important harmonic and anharmonic force constants, characterizing the ammonia PES were determined.     

Ab initio calculations of vibrational energies and wave-functions of triatomic molecules

A method is developed for the ab initio treatment of non-infinitesimal vibrations of triatomic molecules. The orientation of the moving system of axes fixed to the molecule is defined in a way that differs somewhat from that normally used. The transformation from internal coordinates into normal coordinates is accomplished by a combined diagonalization and numerical integration procedure; the vibrational functions themselves are expanded into products of one-dimensional harmonic oscillator functions. The method is applied to the calculation of vibrational levels of two states in HCN and deviation from the results obtained using the uncoupled harmonic approximation is discussed.     

Improved combined wave number eigenvalue equations method for band structure calculations of metal photonic crystal

We provide the combined wave number eigenvalue equations (CWNEE) method based upon the plane-wave expansion (PWE) method to calculate and optimize the band structures of the two-dimension (2D) photonic crystals (PhCs). Compared with the traditional PWE methods for the metal PhCs, the band structures can be obtained directly using the CWNEE method, and not any extra procedures are needed to handle the folded band structures. The comparison between the CWNEE method and FDTD method in accuracy and time-consuming has been analyzed, and the results show that the CWNEE method is reliable and accurate. With the CWNEE method and the Bisection-Particle Swarm Optimization method, we optimize the large gap–midgap ratio of the 2D square lattice of square metal rods and circular metal rods. Unlike many traditional PWE method, the CWNEE method can directly calculate the band structure in the arbitrary given frequency range, and it is quite useful for calculating the defect mode of photonic crystal cavity.     

A theoretical investigation of vibrational fine structure accompanying core ionization in hydrogen cyanide and acetylene

Non-empirical calculations at the STO-4.31G level are reported on the ground-state and core-ionized states of HCN and H ₂C ₂. An analysis of the changes in bond lengths and force constants for the normal modes involving stretching vibrations allows direct computation of the overall band profiles for the core-ionized levels. The distinct asymmetries arising from the vibrational excitations accompanying core ionizations suggest that the experimental investigations of these systems would be eminently worthwhile.     

The muonium adduct to biacetyl – ab initio calculations and vibrational averaging

The room temperature muon‐electron hyperfine coupling constant of the 2‐muoxy‐3‐ketobut‐2‐yl radical formed by Mu addition to biacetyl (butane‐2,3‐dione) is the smallest thus far measured in any radical, with A^\prime_μ\simeq 0.7 MHz (R.M. Macrae, C.J. Rhodes, K. Nishiyama and K. Nagamine, Chem. Phys. Lett, submitted). Calculations on this radical using the ROHF, UHF, and B/PW 91 formalisms are presented, with averaging performed over the C–O torsional mode using an expansion in free internal rotation eigenfunctions. UHF and B/PW 91 give similar predictions of the dependence of A^\prime_μ on the torsional angle \gamma, but are strikingly different in their predictions of the torsional energetics. This difference is traced to spin contamination in the UHF wavefunction. UHF disagrees with both ROHF and B/PW 91 in its structural predictions, yielding excessive electron delocalisation into the central C–C bond. Vibrational corrections lead to a small |A^\prime_μ| with a weak temperature‐dependence, and suggest that the radical may twist from the trans geometry of the parent compound into the energetically more favourable intramolecularly H‐bonded cis structure. This revised version was published online in August 2006 with corrections to the Cover Date.     

Variational calculations of vibrational energy levels for XY4 molecules 1. Stretching states

A variational method for calculating excited stretching states of symmetric tetrahedral pentaatomic molecules is presented based on the use of Radau coordinates and Morse oscillator-like basis functions. Symmetry is used both to reduce the size of the secular matrix to be diag-onalized and to calculate the potential energy matrix elements over a reduced grid of quadrature points. Test results are presented for methane, silane and germane. For CH₄, stretch-bend coupling is found to be significant, whereas it is less important for the more strongly local mode SiH₄ and GeH₄ molecules. Converged results are obtained for stretching states significantly higher than considered in previous calculations. These states will be used to represent stretching motions in a fully coupled stretch-bend calculation.     

Bipolaronic states in doped polyacetylene from electronic and vibrational densities of states by negative eigenvalue theorem

It is shown that the negative eigenvalue theorem is a useful numerical tool for the calculation of the electronic density of states for disordered one-dimensional systems in the Hueckel approximation. Application is made to the case of doped polyacetylene when a random distribution of centro-symmetrical defects is considered.