Effective rotational Hamiltonian for molecules with two periodic large-amplitude motions

Groner, Peter
September 1997
Journal of Chemical Physics;9/22/1997, Vol. 107 Issue 12, p4483
Academic Journal
Starting from a general Hamiltonian for a molecule with two periodic large-amplitude motions, an effective rotational Hamiltonian is developed for bound states of the internal motions. It contains two types of matrix elements: (i) The internal motion energy, expressed as two-dimensional Fourier series, and transformed to a reference axes system. (ii) Matrix elements of rotational operators in the reference axes system multiplied by two-dimensional Fourier series. The spectroscopic parameters are the coefficients of the Fourier series (integrals of localized functions), the internal motion parameters ρ, and the angles between the vectors ρ and the reference axes. Expressions are given for cases with higher symmetry. The effectiveness of the Hamiltonian is demonstrated by fitting the rotational spectrum of the ground state of dimethylether (356 frequencies involving levels up to J=25) to experimental precision. The data of five vibrational excited states can be fit to almost the same precision.


Related Articles

  • Singularities in the spectra of random matrices. Walker, Paul N.; Sanchez, Maria Jose; Wilkinson, Michael // Journal of Mathematical Physics;Oct96, Vol. 37 Issue 10, p5019 

    Analyzes singularities in the spectra of random matrices. Singularities of the set of energy levels of a quantum Hamiltonian; Role of singularities such as minima, degeneracies, branch points and avoided crossings in physical applications.

  • Transport through modes in random media. Jing Wang; Genack, Azriel Z. // Nature;3/17/2011, Vol. 471 Issue 7338, p345 

    Excitations in complex media are superpositions of eigenstates that are referred to as 'levels' for quantum systems and 'modes' for classical waves. Although the Hamiltonian of a complex system may not be known or solvable, Wigner conjectured that the statistics of energy level spacings would be...

  • Using simultaneous diagonalization and trace minimization to make an efficient and simple multidimensional basis for solving the vibrational Schrödinger equation. Dawes, Richard; Carrington, Tucker // Journal of Chemical Physics;2/7/2006, Vol. 124 Issue 5, p054102 

    In this paper we improve the product simultaneous diagonalization (SD) basis method we previously proposed [J. Chem. Phys. 122, 134101 (2005)] and applied to solve the Schrödinger equation for the motion of nuclei on a potential surface. The improved method is tested using coupled complicated...

  • Classical, semiclassical, and quantum mechanics of a globally chaotic system: Integrability in the adiabatic approximation. Martens, Craig C.; Waterland, Robert L.; Reinhardt, William P. // Journal of Chemical Physics;2/15/1989, Vol. 90 Issue 4, p2328 

    Examines the classical, semiclassical and quantum mechanics of a chaotic Hamiltonian system. Adiabatic separation of the x and y motion; Connection between integrable approximation and the exact dynamics; Agreement between energy levels and energy spectrum.

  • The one-particle energy spectrum of weakly coupled quantum rotators. Angelescu, Nicolae; Minlos, Robert A.; Zagrebnov, Valentin A.; Zagrebnov, Valentine A. // Journal of Mathematical Physics;Jan2000, Vol. 41 Issue 1 

    The ground state of a lattice model of weakly interacting quantum rigid rotators is analyzed by the cluster expansion method applied to its Feynman-Kac representation. The Hamiltonian of the infinite crystal in the ground state is shown to have a branch of absolutely continuous spectrum...

  • Vibrational energy level statistics of small molecules. Karrlein, W. // Journal of Chemical Physics;3/1/1991, Vol. 94 Issue 5, p3293 

    A simple model Hamiltonian including kinetic coupling of adjacent bonds is chosen for investigations of the statistics of vibrational eigenenergies for a series of three- and four-atomic molecules. Depending on the coupling strength which is governed by structural characteristics of each...

  • A variational method for the calculation of rovibrational energy levels of triatomic molecules using a Hamiltonian in hyperspherical coordinates: Applications to H+3 and Na+3. Carter, Stuart; Meyer, Wilfried // Journal of Chemical Physics;2/1/1994, Vol. 100 Issue 3, p2104 

    A full variational procedure is presented for the calculation of rovibrational (J>=0) energy levels which is particularly suited for triatomic potentials that support large amplitude motions and that may be of high permutational symmetry. It is based on a kinetic energy operator expressed in...

  • Transitions and optimal self-organization in the collective motion in driven systems. Vicsek, Tama´s; Helbing, Dirk; Cziro´k, Andra´s // AIP Conference Proceedings;2000, Vol. 501 Issue 1, p273 

    Organisms moving in the same environment typically self-organize into coherently moving groups. This grouping can be successfully described using simple models of driven particles for collective motion. Here we discuss simulations of flocking and a principle related to driven motion in general...

  • Ionic excitation in dense, two-component plasmas: Effect of energy level shifts. Kitamura, Hikaru // Physics of Plasmas;Feb2004, Vol. 11 Issue 2, p771 

    Collisional excitation rates for an ion immersed in dense electron–ion two-component plasmas are formulated by taking into account shifts of ionic energy levels due to static and dynamic plasma perturbations. The theory is based on the equations of motion for density matrices combined...


Read the Article


Sorry, but this item is not currently available from your library.

Try another library?
Sign out of this library

Other Topics