Showing papers on "Normal coordinates published in 2004"

A study of the mode-selective trans--cis isomerization in HONO using ab initio methodology.

Abstract: Ab initio calculations on the six-dimensional cis–trans double minimum potential energy surface of the electronic ground state of the HONO molecule were performed using a coupled cluster approach. An analytic fit to the data points was established. The interconversion barrier was calculated to be 4105 cm−1. The nuclear motion problem was solved variationally using a full six-dimensional Hamiltonian in internal coordinates. The eigenstates up to about 3650 cm−1 were tentatively assigned by harmonic quantum numbers. The assignment was based on the mean values of the internal coordinates of the six-dimensional eigenfunctions and on a comparison of the eigenenergies with those calculated by second-order perturbation theory from a full quartic force field in dimensionless normal coordinates. In cold matrices the trans- and the cis-OH ν1 stretching modes and the first trans- and cis-NO 2ν2 stretching overtones lead to isomerization. In the isolated molecule these modes (J=0) were found to be entirely localized. However, several overtones of the ν4 ONO bending and ν5 N–O stretching, which are close in energy to the OH stretch and combined with the torsional mode, were found to be strongly cis–trans delocalized.

Newton-like methods for numerical optimization on manifolds

Abstract: Many problems in signal processing require the numerical optimization of a cost function, which is defined on a smooth manifold. Especially, orthogonally or unitarily constrained optimization problems tend to occur in signal processing tasks involving subspaces. In this paper we consider Newton-like methods for solving these types of problems. Under the assumption that the parameterization of the manifold is linked to so-called Riemannian normal coordinates our algorithms can be considered as intrinsic Newton methods. Moreover, if there is not such a relationship, we still can prove local quadratic convergence to a critical point of the cost function by means of analysis on manifolds. Our approach is demonstrated by a detailed example, i.e., computing the dominant eigenspace of a real symmetric matrix.

The vibrations and tunnelling of malonaldehyde on a Møller–Plesset surface

Abstract: The vibrations and tunnelling motion of malonaldehyde have been studied in their full dimensionality using an internal coordinate path Hamiltonian. In this representation there is one large amplitude internal coordinate s and 3N − 7 (=20) normal coordinates Q which are orthogonal to the large amplitude motion at all points. It is crucial that a high accuracy potential energy surface is used in order to obtain a good representation for the tunneling motion; we use a Moller–Plesset (MP2) surface. Our methodology is variational, that is we diagonalize a sufficiently large matrix in order to obtain the required vibrational levels, so an exact representation for the kinetic energy operator is used. In a harmonic valley representation ( s, Q ) complete convergence of the normal coordinate motions and the internal coordinate motions has been obtained; for the anharmonic valley in which we use two- and three-body terms in the surface (s, Q 1, Q 2), we also obtain complete convergence. Our final computed stretchin...

Symmetric quantum Weyl algebras

Abstract: We study the symmetric powers of four algebras: q-oscillator algebra, q-Weyl algebra, h-Weyl algebra and U(sl 2 ). We provide explicit formulae as well as combinatorial interpretation for the normal coordinates of products of arbitrary elements in the above algebras.

Isotope effects on nuclear magnetic shieldings calculated by including zero-point vibration corrections: the VMF approach

Abstract: As a minimal dynamic correction the ‘zero-point vibration’, ZPV, was included in the ab initio calculation of the isotropic magnetic shielding of 13C, 19F, 29Si, 31P, and 35Cl in some molecules including the references of NMR spectroscopy (f.i. CFCl3, CH3–NO2, and TMS). In contrast to most previous works the ZPV correction is not based on gradients of internal coordinates, but uses derivatives obtained by ‘vibration mode following’ (VMF, the coordinates of the gradients describing the magnetic shielding hypersurface are the normal coordinates of the ground state vibration motion). The vibrational corrections obtained at the applied DFT level of theory are slightly smaller than those reported for MP2 calculations. Isotope effects computed with the ZPV/VMF correction are in reasonable agreement with experimental data. Contributions from individual vibration modes to the zero-point correction show that rotational motions have a large effect.

The Gravitational Field of Massive Non-Charged Point Source in General Relativity

Abstract: Utilizing various gauges of the radial coordinate we give a description of static spherically symmetric space-times with point singularity at the center and vacuum outside the singularity. We show that in general relativity (GR) there exist a two-parameters family of such solutions to the Einstein equations which are physically distinguishable but only some of them describe the gravitational field of a single massive point particle with nonzero bare mass $M_0$. In particular, the widespread Hilbert's form of Schwarzschild solution, which depends only on the Keplerian mass $M

Rotational oscillations of a molecular chain with quadrupolar interaction

Abstract: Molecular chains with rotational degree of freedom in the plane of an adsorbing surface and quadrupolar interaction between linear molecules are investigated theoretically. It is found that alternation ordering of the molecules is preferable. Equations of rotational movement are derived and solved for linear oscillations. It is shown that dispersion relation has two optic branches of rotational excitations. The normal coordinates are found to be strongly dependent on dispersion. In the long wave limit normal coordinates are symmetric and antisymmetric. The heat capacity of the molecular chain is found at low temperature. (© 2004 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)

Gravitational Field Equations on and off a 3-Brane World

Abstract: The effective gravitational field equations on and off a 3-brane world possessing a Z_{2} mirror symmetry and embedded in a five-dimensional bulk spacetime with cosmological constant were derived by Shiromizu, Maeda and Sasaki (SMS) in the framework of the Gauss-Codazzi projective approach with the subsequent specialization to the Gaussian normal coordinates in the neighborhood of the brane. However, the Gaussian normal coordinates imply a very special slicing of spacetime and clearly, the consistent analysis of the brane dynamics would benefit from complete freedom in the slicing of spacetime, pushing the layer surfaces in the fifth dimension at any rates of evolution and in arbitrary positions. We generalize the SMS effective field equations on and off a 3-brane to the case where there is an arbitrary energy-momentum tensor in the bulk. We use a more general setting to allow for acceleration of the normals to the brane surface through the lapse function and the shift vector in the spirit of Arnowitt, Deser and Misner. We show that the gravitational influence of the bulk spacetime on the brane may be described by a traceless second-rank tensor W_{ij}, constructed from the "electric" part of the bulk Riemann tensor. We also present the evolution equations for the tensor W_{ij}, as well as for the corresponding "magnetic" part of the bulk curvature. These equations involve the terms determined by both the nonvanishing acceleration of normals in the nongeodesic slicing of spacetime and the presence of other fields in the bulk.

Fedosov supermanifolds: II. Normal coordinates

Abstract: The study of recently introduced Fedosov supermanifolds is continued Using normal coordinates, properties of even and odd symplectic supermanifolds endowed with a symmetric connection respecting given sympletic structure are studied

The Hopf Algebra of Renormalization, Normal Coordinates and Kontsevich Deformation Quantization

Abstract: Using normal coordinates in a Poincar\'e-Birkhoff-Witt basis for the Hopf algebra of renormalization in perturbative quantum field theory, we investigate the relation between the twisted antipode axiom in that formalism, the Birkhoff algebraic decomposition and the universal formula of Kontsevich for quantum deformation.

Application of the DVR method to the vibration-rotation spectrum of N2O: derivation of the dipole moment derivatives in Radau coordinates

Abstract: The rovibrational line intensities of the N 2 O molecule in its ground electronic state have been used to determine its dipole moment derivatives using a fitting procedure. The wavefunctions calculation have been made using a Discrete Variable Representation method in Radau coordinates and an available potential energy surface. The resulting dipole moment derivatives are compared to previous ones obtained using normal coordinates approach.

Determination of the parameters of multidimension vibration Hamiltonian of CH3NH2 from quantum chemical data

Abstract: The two large-amplitude motions—NH2 wagging and CH3 internal rotation—take place in methylamine, CH3NH2. The complete set of potential and kinematic coupling constants, characterizing the Hamiltonian of a nonrigid molecule CH3NH2 with two large-amplitude coordinates, is derived from standard quantum chemical data for the equilibrium geometries, normal frequencies, and eigenvectors in the ground and transition states. The reconstruction of the Hamiltonian is made via the following steps: classification of the generalized coordinates according to the irreducible representations of the group of the nonrigid molecular model; linear transformation of the ground-state normal coordinates into the frame of the transition state taking into account the Eckart conditions; and perturbative solution of the inverse vibrational problem. It is shown that the consideration of interactions of large-amplitude vibrations with transfer ones significantly affects the parameters of 2-D potential. © 2003 Wiley Periodicals, Inc. Int J Quantum Chem, 2004

Regular and anomalous torsional splitting patterns: a trend in ethane-like molecules and general perspectives

Abstract: It is shown that torsional Coriolis coupling can alter the torsional splittings in molecules with hindered internal rotation. Splitting patterns that would occur in the absence of any vibrational contribution to the torsional angular momentum, with reference to a molecular axis system (IAM), are called regular. It is shown that different sets of vibrational coordinates, corresponding to vibrational states with different splitting patterns, can be defined for modes normal to the internal rotation axis. The forms of normal coordinates appropriate to basis vibrational states with regular and inverted splitting patterns are identified. It is found that in normal coordinates appropriate to vibrational states with regular torsional splitting patterns, the relative orientation of the displacements of pairs of atoms belonging to different molecular moieties is independent of the internal rotation angle, and relative displacements normal to the internal rotation axis can be cis or trans at any conformation. On the contrary, in normal coordinates appropriate to vibrational states with inverted torsional splitting patterns the relative orientation of such displacements changes by π(cis-trans interchange) upon half the internal rotation converting two neighbor equivalent conformations (as in a staggered-eclipsed conformational conversion). The formation of the actual torsional splitting patterns in degenerate vibrational states of CH3CH3-type molecules depends on the joint effect of torsional Coriolis and head-tail coupling. The torsional Coriolis operator can tune pairs of levels to resonance for the action of typical head-tail coupling operators (torsion-dependent vibrational operators), depending on the values of the torsional Coriolis coefficients, generating vibrational states with either regular or inverted torsional splitting patterns and affecting the splitting magnitude. It is shown that operators with a sin3τ-type torsional dependence favor the formation of inverted splitting patterns. In less symmetric molecules torsional Coriolis coupling affects the torsional splitting patterns by the same mechanism as in CH3CH3-type molecules, but the torsion-dependent operators are different and their action is expected to be less effective. Typical anomalous perpendicular splitting patterns can be predicted for non-degenerate modes localized in a single molecular moiety, normal or with a component normal to the internal rotation axis, having fixed orientation in that moiety (as the C=O or C-H stretchings of acetaldehyde). Adopting a barrier-hindered torsional basis, where the lower torsional levels can be seen as vibrational states with quantum numbers vτ exhibiting tunneling splitting, one finds that all operators generating matrix elements with Δvτ=±1, or in general odd, work toward the formation of inverted splitting patterns, generating anomalous patterns.© (2004) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.

The Hopf Algebra of Renormalization, Normal Coordinates and Kontsevich Deformation Quantization

Abstract: Using normal coordinates in a Poincare–Birkhoff–Witt basis for the Hopf algebra of renormalization in perturbative quantum field theory, we investigate the relation between the twisted antipode axiom in that formalism, the Birkhoff algebraic decomposition and the universal formula of Kontsevich for quantum deformation.

Vibrational spectra and molecular structural investigation of quiniodochlor

Abstract: A normal coordinate analysis on quiniodochlor has been carried out with a systematic set of symmetry coordinates following Wilson's F-G Matrix method. The potential constants evaluated for the molecule are found to be in good agreement with literature values thereby confirming the vibrational assignments. To check whether the chosen set of vibrational frequencies contribute maximum to be potential energy associated with the normal coordinates of the molecule, the potential energy distribution has been evaluated.

Investigation of anharmonicity of normal vibrational modes in [Sb2S3]2cluster

Abstract: Theoretical investigation of the vibrational spectrum based on a chain model of the cluster with two Sb2S3 molecules in a cell is presented. For this purpose, symmetric and normal coordinates along the z (c) axis have been formed. The dependence of total energy E(�z) upon normal coordinates has been defined for four infrared and five Raman modes. The anharmonicity of these modes has been evaluated by calculating a ratio of quasi-harmonic e and harmonic frequencies !0.