Vibrational Spectra Of Diatomic Molecules Research Articles

Quasi-Exactly Soluble Potentials and Deformed Oscillators

It is proved that quasi-exactly soluble potentials corresponding to an oscillator with harmonic, quartic and sextic terms, for which the n+1 lowest levels of a given parity can be determined exactly, may be approximated by WKB equivalent poten- tials corresponding to deformed anharmonic oscillators of SUq(1,1) symmetry, which have been used for the description of vibrational spectra of diatomic molecules. This connection allows for the immediate approximate determination of the levels of the same parity lying above the fewest n+1 known levels, as well as of all levels of the opposite parity. Such connections are not possible in the cases of the q-deformed oscillator, the Q-deformed oscillator, and the modified Pöschl-Teller potential with SU(1,1) symmetry.

QUANTUM ALGEBRAIC SYMMETRIES IN NUCLEAR AND MOLECULAR PHYSICS

The first realizations of quanttun algebraic symmetries in nuclear and molecular spectra are presented. Rotational spectra of even-even nuclei are described by the quantum algebra SUq(2). The two parameter formula given by the algebra is equivalent to an expan- sion in terms of powers of j(j + 1), similar to the expansion given by the Variable Moment of Inertia (VMI) model. The moment of inertia parameter in the two models, as well as the small parameter of the expansion, are found to have very similar numerical values. The same formalism is found to give very good results for superdeformed nuclear bands, which are closer to the classical SU(2) limit, as well as for rotational bands of diatomic molecules, in which a partial summation of the Dunham expansion for rotation-vibration spectra is achieved. Vibrational spectra of diatomic molecules can be described by the q-deformed anhannonic oscillator, having the symmetry Uq(2)>Oq(2). An alternative de- scription is obtained in terms of the quantum algebra SUq(1,1). In both cases the energy formula obtained is equivalent to an expansion in terms of powers of (v+½) , where ν is the vibrational quantum number, while in the classical ST(1,1) case only the first two powers appear. In all cases the improved description of the empirical data is obtained with q being a phase (and not a real number). Further applications of quantum algebraic symmetries in nuclei and molecules are discussed.

Approximate analytical solutions of the stationary radial Schrödinger equation with new anharmonic potentials

For a high accuracy description of bond-stretching vibrations of diatomic molecules new analytic five and six-parameter potential energy functions have been proposed. These potentials include parameters that can be determined with the use of a direct fit to measured energy level spacings. The corresponding stationary radial Schrödinger equations with these potential energy functions are solved analytically, in an approximate scheme for zero total angular momentum. It is found that the wave functions for bound states can be expressed in terms of the Jacoby polynomial. The analytical expressions for purely vibrational energy levels have been derived within the algebraic approach. The potentials presented can be very useful for theoretical spectroscopic studies to reproduce the vibrational spectra of diatomic molecules.

An Optimized Algebraic Basis for Molecular Potentials

The computation of vibrational spectra of diatomic molecules through the exact diagonalization of algebraically determined matrices based on powers of Morse coordinates is made substantially more efficient by choosing a properly adapted quantum mechanical basis, specifically tuned to the molecular potential. A substantial improvement is achieved while still retaining the full advantage of the simplicity and numerical light-weightedness of an algebraic approach. In the scheme we propose, the basis is parametrized by two quantities which can be adjusted to best suit the molecular potential through a simple minimization procedure.

A Uqp(u1,1) Model for Vibrational Molecular Spectra

A Uqp(u1,1) model is presented for describing vibrational spectra of diatomic molecules. The model is tested on the vibrational spectra in the X1Σg+ state of H2 obtained through the Rydberg-Klein-Rees method.

A qp-DEFORMED ANHARMONIC OSCILLATOR WITH THE Uqp(U2) ⊃ Uqp(O2) SYMMETRY AND ITS APPLICATION TO VIBRATIONAL MOLECULAR SPECTRA

A qp-deformed anharmonic oscillator with the Uqp(U2) ⊃ Uqp(O2) symmetry is presented for describing vibrational spectra of diatomic molecules. The energy formula is tested on the vibrational spectra in the state [Formula: see text] of H2 obtained through the Rydberg-Klein-Rees (RKR) method.

Connection between q-deformed anharmonic oscillators and quasi-exactly soluble potentials

It is proved that quasi-exactly soluble potentials (QESPs) corresponding to an oscillator with harmonic, quartic and sextic terms, for which the n + 1 lowest levels of a given parity can be determined exactly, may be approximated by WKB equivalent potentials corresponding to deformed anharmonic oscillators of SU q (1,1) symmetry, which have been used for the description of vibrational spectra of diatomic molecules. This connection allows for the immediate approximate determination of all levels of the QESPs.

U q (4)⊇O q(4) description of diatomic molecules: Vibrational spectra

Quantum-deformed algebra (q-DA) of the O(4) dynamical symmetry of the U(4) group is studied in respect of the vibrational spectra of diatomic molecules. It is shown that, as in the case of the U(6) group for nuclei, the q-deformation parameter in Uq(4)⊇Oq(4) must also be complex for any meaningful gain in going from the classical to the q-deformed algebra. Application is made to the ground electronic state (X 1Σ+g) of the H2 molecule.

Q-deformed vibron model for diatomic molecules.

A deformed version of the vibron model for diatomic molecules is constructed. Both the O(4) and U(3) dynamical symmetries of the model are rewritten, using the concept of complementary subalgebras, in a more convenient form, which is subsequently deformed. The present model unifies the so far independent successful quantum-algebraic approaches to rotational and to vibrational spectra of diatomic molecules. In addition, the method can be used for the construction of deformed versions of the U(5) and O(6) limits of the interacting boson model of nuclear structure.

Comment on "Generalized deformed oscillators for vibrational spectra of diatomic molecules"

Comment on "Generalized deformed oscillators for vibrational spectra of diatomic molecules"

Reply to "Comment on 'Generalized deformed oscillators for vibrational spectra of diatomic molecules' "

We point out that the condition imposed on the deformation parameters by the preceding Comment [Pan, Phys. Rev. A 50, 888 (1994)] does not affect the validity of the fits of the commented work [Bonatsos and Daskaloyannis, Phys. Rev. A 46, 75 (1992)]. Furthermore, we point out a way of avoiding both the condition on the parameters and the appearance of negative norm states simultaneously.

Generalized deformed oscillators for vibrational spectra of diatomic molecules.

Using deformed bosons, we construct generalized anharmonic oscillators suitable for the description of vibrational spectra of diatomic molecules. One of them gives the same spectrum as the modified P\oschl-Teller potential, i.e., the first two terms of the Dunham expansion, while the other is a q deformation of the first, corresponding to summing all terms of the Dunham expansion for vibrational molecular spectra.

WKB equivalent potentials for q-deformed anharmonic oscillators

WKB equivalent potentials giving the same spectra as the q-deformed anharmonic oscillators with symmetries U q (2) ⊃ O(2) and SU q (1, 1), which have been used for the description of vibrational spectra of diatomic molecules, are determined. In both cases the shape of the WKB equivalent potentials resembles the modified Pöschl—Teller potential and the Morse potential, which are connected by a known transformation.

Classical potentials for q-deformed anharmonic oscillators.

Classical potentials giving the same spectrum as the q-deformed anharmonic oscillators having the symmetries ${\mathrm{U}}_{\mathit{q}}$(2)\ensuremath{\supset}O(2) and ${\mathrm{SU}}_{\mathit{q}}$(1,1), which have been used for the description of vibrational spectra of diatomic molecules, are determined in analytic form. The potentials found here are somewhat wider than the corresponding classical anharmonic potentials obtained in the limit q\ensuremath{\rightarrow}1, while their Taylor expansions are similar to the expansion of the modified P\"oschl-Teller potential, which is connected to the Morse potential through a known transformation.

The q-deformed oscillator model and the vibrational spectra of diatomic molecules

A model of a q-oscillator with quantum group symmetry H q (4) is put forward. The representations of the q-oscillator algebra H q (4) and solutions to the quantum q-oscillator system are provided. We find that the energy spectrum of the q-oscillator bears the essential properties of the observed spectra of diatomic molecules. When the parameters are determined phenomenologically, the spectrum of the q-oscillator coincides with the infrared, vibrational Raman spectra and vibrational structure of electronic transitions of the diatomic molecule.

SUq(1,1) description of vibrational molecular spectra

The SUq(1,1) quantum algebra is used for the description of vibrational spectra of diatomic molecules for which SU(1,1) is used in the classical approach. While in the classical case only the first two terms of the empirical Dunham expansion occur, in the quantum case all terms are obtained. The improved description of the empirical data is obtained with q being a phase (and not a real number), in agreement with the situation occurring in the q-rotor (having the symmetry SUq(2)) used for the description of rotational spectra of molecules and nuclei.

Quantum algebraic description of vibrational molecular spectra

Vibrational spectra of diatomic molecules can be described in terms of the q-deformed anharmonic oscillator. The Hamiltonian has the U q (2) ⊃ O q (2) symmetry, where q is the parameter measuring its deviation from the usual U(2) ⊃ O(2) symmetry. The energy formula obtained is equivalent to an expansion in terms of powers of (υ + 1 2 , where υ is the vibrational quantum number, and corresponds to summing a Dunham expansion for vibrational molecular spectra.

Vibrational excitation intensities of molecules adsorbed on metal surfaces

We use electrodynamic theory modifed by density functional calculations to investigate the intensity of the vibrational spectra of diatomic molecules adsorbed on metallic surfaces.

Vibrational excitation intensities of molecules adsorbed on metal surfaces

Abstract We use electrodynamic theory modifed by density functional calculations to investigate the intensity of the vibrational spectra of diatomic molecules adsorbed on metallic surfaces.

A generalization of the morse potential for diatomic molecules

To describe the vibrational spectra of diatomic molecules the potential curve V (r) is approximated by a sum of three Morse functions. This approach has the advantage of being more flexible than the simple Morse potential while preserving the correct asymptotical behavior: V (∞ = const. Furthermore, such a sum potential can give rise to a small threshold above dissociation energy, as it occurs, e.g., in the C 1 Π u state of H2 due to dipole-dipole resonance forces. As the Schrödinger equation cannot be solved exactly for this potential the energy eigenvalues are calculated by means of perturbation theory taking into account fourth-order corrections relative to the harmonic (zeroth) approximation. In connection with the approximate term formula a general procedure for fitting the parameters of the generalized Morse potential to spectroscopic constants is presented and applied to various molecules (N 2 , NO, O 2 , and I 2 ). The resulting potential curves are in good agreement with RKR curves, even for higher vibrational states where the simple Morse potential fails.