Showing papers on "Normal coordinates published in 1979"
TL;DR: In this article, two methods for calculating polyatomic Franck-Condon integrals are reported, one using a coordinate transformation on the normal coordinates of both the ground and excited electronic states and the other using contact transformation perturbation theory to construct a representation of the vibrational wavefunctions.
Abstract: Two methods for calculating polyatomic Franck–Condon integrals are reported. The first method uses a coordinate transformation on the normal coordinates of both the ground and excited electronic states. This transformation effectively removes any Duschinsky mixing and allows the multidimensional Franck–Condon integral to be written as a sum of integrals each of which is a product of one‐dimensional harmonic oscillator overlap integrals. The second method uses contact transformation perturbation theory to construct a representation of the vibrational wavefunctions. With this representation, the calculation of a polyatomic Franck–Condon integral involves evaluation of matrix elements exclusively within the ground electronic state vibrational manifold. Application of both methods is made to the A0n vibronic series of the 1A1g→1B2u symmetry‐forbidden electronic transition of benzene. Relative intensities calculated by either method agree well with observed values. However, the computational efficiencies of th...
87 citations
TL;DR: In this article, an extension of the affinity, metric, and geodesic equations in Fermi normal coordinates to higher order is presented, with an iteration scheme for higher orders.
Abstract: Fermi normal coordinates about a geodesic form a natural coordinate system for the nonrotating geodesic (freely falling) observer. Expansions of the affinity, metric, and geodesic equations in these coordinates in powers of proper distance normal to the geodesic are calculated here to third order, fourth order, and third order, respectively. An iteration scheme for calculation to higher orders is also given. For generality, we compute the affinity and the geodesic equations in an arbitrary affine manifold, and compute the metric in a Riemannian manifold with arbitrary signature.
49 citations
TL;DR: In this paper, the absolute Raman intensities and depolarization ratios of all the fundamental bands of CH2Cl2, CD2CL2 and CHDCl2 have been measured in the gas phase.
Abstract: The absolute Raman intensities and depolarization ratios of all the fundamental bands of CH2Cl2, CD2Cl2 and CHDCl2 have been measured in the gas phase. These experimental data have been included in a refinement of the vibrational potential function of the dichloromethanes. A detailed description is made of the use of the bond polarizability approach. Explicit expressions for the derivatives of the molecular polarizability with respect to the symmetry coordinates are given in terms of the zeroth- and first-order electro-optical parameters of the theory. Good agreement is found between experimental and calculated intensities. The refined electro-optical parameters compare quite well with those obtained from methane, chloroform and carbon tetrachloride. The derivatives of the molecular polarizability with respect to the normal coordinates are also given.
44 citations
TL;DR: In this paper, an asymmetric rotor molecule in a vibrational state (v 1 v 2 v 2 … vN ) and a rotational states (J τ) is considered, where terms in the expansion up to those quartic in the reduced normal coordinates are taken into account.
Abstract: Molecular properties depend on the state of rotation and vibration. As a result of recent experimental developments such a dependence has been detected by several techniques for a variety of molecular properties of a large number of compounds. By expanding the property P as a power series in the reduced normal coordinates it is possible to derive an expression relating P to the state of rotation and vibration. In the present paper this is done for an asymmetric rotor molecule in a vibrational state (v 1 v 2 … vN ) and a rotational state (J τ). Terms in the expansion of P up to those quartic in the reduced normal coordinates are taken into account. The expression is of the form where Pe (0) is the value of the property at equilibrium, P J τ , Ai J τ and Bij depend on the parameters describing the potential energy surface and the property surface, and a superscript J τ denotes a dependence on rotational state through the quantities ⟨J τ|Πα 2|J τ⟩ where Πα denotes the rotational angular momentum about a prin...
32 citations
TL;DR: In this article, the force field reported in this paper gives such a satisfactory frequency fit that it should provide a good starting point for the explanation of the peculiar band widths of 1.4−dihalobutyne−2.
Abstract: Force constants and normal modes were evaluated using an overlay technique for CH3CCH, CH3CCD, CD3CCH, CD3CCD, CH2FCCH, CH2ClCCH, CH2BrCCH CH3CCCH3, CH3CCCH2Cl, CH3CCCH2Br, CH2FCCCH2F, CH2ClCCCH2Cl and CH2BrCCCH2Br. Particular attention has been given to diagonal and off‐diagonal force constants related to linear bending coordinates. The force field reported in this paper gives such a satisfactory frequency fit that it should provide a good starting point for the explanation of the peculiar band widths of 1,4‐dihalobutyne‐2.
14 citations
TL;DR: In this article, it is shown how to reduce probability densities calculated from vibrational wave functions of polyatomic molecules to one-dimensional radial distribution functions derived from diffraction experiments.
Abstract: It is shown how to reduce N‐dimensional probability densities calculated from vibrational wave functions of polyatomic molecules to one‐dimensional radial distribution functions. Such distributions are, in principle, derivable from diffraction experiments. In this initial treatment, anharmonicity and nonlinearities in transformations between normal coordinates and internuclear distances are neglected. Illustrative calculations are given for H2O, CF3Cl, and SF6 in various vibrational states or thermal distributions among vibrational states. Possible applications are briefly discussed.
14 citations
TL;DR: In this paper, the cubic and quartic anharmonic potential energy functions for XY6 molecules of Oh symmetry in terms of normal coordinates are given, and a standard form, introduced by Hecht, is related to the tensor formalism developed for the potential energy of tetrahedral XY4 molecules.
Abstract: We give the cubic and quartic anharmonic potential energy functions for XY6 molecules of Oh symmetry in terms of normal coordinates. The numbers of independent cubic and quartic potential constants are 22 and 92, respectively. A standard form, introduced here, is related to the tensor formalism developed for the potential energy of tetrahedral XY4 molecules by Hecht.
11 citations
15 Jan 1979
TL;DR: In this paper, the GF-Wilson eigenvalue problem and the parameters of the generalized coupled oscillator model involving long-range interactions have been obtained separately for each mode for finite chains (n -paraffins, fatty acids, and glymes).
Abstract: New repeat unit normal coordinates for the analysis of the defect polymer vibrational spectra are suggested. Relations between the valence force field for the GF-Wilson eigenvalue problem and the parameters of the generalized coupled oscillator model involving long-range interactions have been obtained separately for each mode. The results of the application of this model to most modes of finite chains ( n -paraffins, fatty acids, and glymes) seem to be quite satisfactory. The applicability of the proposed model is discussed.
10 citations
TL;DR: In this article, a set of vibrational coordinates which are not the normal coordinates but which have the simpliest possible vibration is defined, and explicit expressions in these coordinates for general, planar and linear molecules are presented.
4 citations
TL;DR: In this article, two methods for calculating polyatomic Franck-Condon integrals are reported, one using a coordinate transformation on the normal coordinates of both the ground and excited electronic states and the other using contact transformation perturbation theory to construct a representation of the vibrational wavefunctions.
Abstract: Two methods for calculating polyatomic Franck–Condon integrals are reported. The first method uses a coordinate transformation on the normal coordinates of both the ground and excited electronic states. This transformation effectively removes any Duschinsky mixing and allows the multidimensional Franck–Condon integral to be written as a sum of integrals each of which is a product of one‐dimensional harmonic oscillator overlap integrals. The second method uses contact transformation perturbation theory to construct a representation of the vibrational wavefunctions. With this representation, the calculation of a polyatomic Franck–Condon integral involves evaluation of matrix elements exclusively within the ground electronic state vibrational manifold. Application of both methods is made to the A0n vibronic series of the 1A1g→1B2u symmetry‐forbidden electronic transition of benzene. Relative intensities calculated by either method agree well with observed values. However, the computational efficiencies of th...
1 citations
TL;DR: In this paper, the force field reported in this paper gives such a satisfactory frequency fit that it should provide a good starting point for the explanation of the peculiar band widths of 1.4−dihalobutyne−2.
Abstract: Force constants and normal modes were evaluated using an overlay technique for CH3CCH, CH3CCD, CD3CCH, CD3CCD, CH2FCCH, CH2ClCCH, CH2BrCCH CH3CCCH3, CH3CCCH2Cl, CH3CCCH2Br, CH2FCCCH2F, CH2ClCCCH2Cl and CH2BrCCCH2Br. Particular attention has been given to diagonal and off‐diagonal force constants related to linear bending coordinates. The force field reported in this paper gives such a satisfactory frequency fit that it should provide a good starting point for the explanation of the peculiar band widths of 1,4‐dihalobutyne‐2.
TL;DR: In this article, the generalized Lucas polynomials were used to expand the molecular vibration-rotation hamiltonian in terms of the scalar invariants of the inverse of the moment of inertia tensor.
Abstract: The Watson version of the molecular vibration-rotation hamiltonian is expanded in terms of the scalar invariants of the inverse of the moment of inertia tensor using the generalized Lucas polynomials. The resultant expansion consists of the matrices I, , 2 with coefficients depending on the normal coordinates. This is in contrast to the usual expansion as a power series in the matrix .