Morse Oscillator Model Research Articles

Nonchaotic laser pulse dissociation through deformed tori.

We consider the nonlinear classical dynamics of a diatomic molecule under the action of a laser field in the framework of the driven Morse oscillator model. We investigate the influence of the dipole function and the laser field on the deformations of the surviving, invariant tori. For intense and high-frequency fields, some invariant tori traverse the separatrix of motion, visiting both the bound and unbound regions of the interatomic potential. Based on this fact, we propose the use of appropriately designed laser pulses to induce dissociation of trajectories on such invariant tori. This mechanism constitutes a controlled nonchaotic route for dissociation, which is an alternative to chaotic multiphoton dissociation and to chirped pulse dissociation.

Classical theory for asymmetric in-plane atom surface scattering

In-plane atom surface scattering perturbation theory within a generalized Langevin equation formalism is proposed to account for the asymmetry found in angular distributions of heavy rare gas atoms scattered by corrugated surfaces. We show that when the surface corrugation is represented in terms of the first two (sine) Fourier components, one finds an asymmetric angular distribution. This asymmetry reflects the ratchetlike form of the effective corrugation. Adding in higher-order terms can also increase the number of rainbow scattering angles. Three rainbows are found for a second-order sine term in the corrugation, four symmetrically spaced rainbow angles are found when adding in a second-order cosine term to the corrugation. Analytic expressions for the angular distribution are derived in terms of a Morse oscillator model. The theory accounts well for the asymmetry and predicts its disappearance as the incident scattering angle is increased. It also features a decrease in the distance between the rainbow angles as the angle of incidence is increased and as the incident energy is increased. The theory is successfully applied to the experimental results of Kondo et al. [Eur. Phys. J. D 38, 129 (2006)] for the scattering of Ar on LiF(100) and the results of Amirav et al. [J. Chem. Phys. 87, 1796 (1987)] for the scattering of Xe on Ge(100) and Ar and Kr on Ag(100).

A finite-difference implementation of the Caldeira–Leggett master equation

The Caldeira-Leggett master equation for dissipative quantum dynamics has predominantly been implemented in phase space, where it plays the role of a quantum Fokker-Planck equation. Here we demonstrate the feasibility of a pure coordinate space implementation in the case of intermediate damping strength and temperature, for times long enough to observe thermal equilibration. After a thorough numerical investigation of the analytically solvable harmonic oscillator case, a Morse oscillator model is studied. This is a case in which a quantal phase space approach would be difficult to implement and we show how analytical results for thermal averages are reproduced to a surprisingly high degree.

Solution of the fully-mixed-state problem: Direct deperturbation analysis of theAΣ+1–bΠ3complex in a NaCs dimer

Laser-induced fluorescence (LIF) spectra $(4)\phantom{\rule{0.2em}{0ex}}^{1}\ensuremath{\Sigma}^{+}\ensuremath{\rightarrow}A\phantom{\rule{0.2em}{0ex}}^{1}\ensuremath{\Sigma}^{+}--b\phantom{\rule{0.2em}{0ex}}^{3}\ensuremath{\Pi}$ and collisionally enhanced $A\phantom{\rule{0.2em}{0ex}}^{1}\ensuremath{\Sigma}^{+}--b\phantom{\rule{0.2em}{0ex}}^{3}\ensuremath{\Pi}\ensuremath{\rightarrow}X\phantom{\rule{0.2em}{0ex}}^{1}\ensuremath{\Sigma}^{+}$ LIF spectra measured by Fourier transform spectrometer with the resolution of $0.03--0.05\phantom{\rule{0.3em}{0ex}}{\mathrm{cm}}^{\ensuremath{-}1}$ provided about 1160 term values of the $e$-symmetry rovibronic levels of the fully mixed $A\phantom{\rule{0.2em}{0ex}}^{1}\ensuremath{\Sigma}^{+}$ and $b\phantom{\rule{0.2em}{0ex}}^{3}\ensuremath{\Pi}$ states of a NaCs molecule. Direct deperturbation treatment of the experimental data field, covering rotational quantum numbers $J∊[5,151]$ of the $A\text{\ensuremath{-}}b$ complex in the energy region $E∊[10577,13668]\phantom{\rule{0.3em}{0ex}}{\mathrm{cm}}^{\ensuremath{-}1}$, was accomplished in the framework of the inverted channel-coupling approach by means of the $4\ifmmode\times\else\texttimes\fi{}4$ Hamiltonian constructed on Hund's coupling case $(a)$ basis functions. The nonequidistant spin-orbit splitting of the $b\phantom{\rule{0.2em}{0ex}}^{3}\ensuremath{\Pi}_{\ensuremath{\Omega}=0,1,2}$ substates and the indirect coupling $A\phantom{\rule{0.2em}{0ex}}^{1}\ensuremath{\Sigma}^{+}--b\phantom{\rule{0.2em}{0ex}}^{3}\ensuremath{\Pi}_{\ensuremath{\Omega}=1}$ matrix element were introduced in the Hamiltonian phenomenologically to account for the regular perturbations by remote states manifold. The expanded Morse oscillator model was used to approximate both potential energy curves of the mutually perturbed states and spin-orbit coupling matrix elements as an analytical function of internuclear distance. Overall 31 fitting parameters have been required to reproduce 98% of experimental term values with a standard deviation of $0.006\phantom{\rule{0.3em}{0ex}}{\mathrm{cm}}^{\ensuremath{-}1}$, which is consistent with the uncertainty of the experiment. The term values deperturbation analysis was confirmed by a calculation of relative intensity distributions in the $A--b\ensuremath{\rightarrow}X$ LIF progressions. The predicted probabilities for both weakly and strongly perturbed levels agree with their experimental counterparts within the accuracy of measurements. The evaluated nonadiabatic $A\text{\ensuremath{-}}b$ wave functions were applied for a prediction of radiative lifetimes of the $A\text{\ensuremath{-}}b$ complex as well as transition probabilities of the $a\ensuremath{\rightarrow}A--b\ensuremath{\rightarrow}X$ cycle proposed in Stwalley, Eur. Phys. J. D 31, 221 (2004), for efficient transformation of ultracold molecules to their absolute ground level ${v}_{X}=0$; ${J}_{X}=0$.

Vibrational overtones quenching of near infrared emission in Er3+ complexes

Erbium organic complexes are receiving increasing attention in view of their application in polymeric telecommunication devices, but their use is limited by small emission quantum yield. Non-radiative deactivation of near IR (NIR) transition in Er3+ organic complexes is discussed on the basis of the electronic–vibrational energy transfer. Relevant transition matrix elements necessary to predict quenching effects exerted by various bonds located in the Er3+ coordination sphere are evaluated on the basis of an anharmonic Morse oscillator model and expressed as analytical functions of the fundamental vibrational intensities. The latter are calculated on the basis of various ‘ab initio’ quantum chemical methods, which yield intensity values close to the experimental measurements. Quenching effects in complexes containing a number of common ligands are evaluated and discussed, and a strategy to design highly efficient NIR emitters is proposed.

Theoretical study of multiphoton processes in diatomic molecules

AbstractWe investigate multiphoton processes in diatomic molecules. We adopt the Morse oscillator model for the vibrational state of molecules and simulate the population transfer between vibrational levels caused by molecule–laser interaction. The ground‐state energy is calculated by the quadratic configurational interaction (QCISD) level ab initio molecular orbital calculation, and the potential energy curve of the ground state is fitted by the Morse potential curve to evaluate the discrete vibrational levels. An intense laser field generally causes the nonlinear optical processes in molecules, such as multiphoton excitation and ionization. We investigate the 1‐, 2‐, 3‐, and 4‐photon absorption processes in H2 and OH molecules in relation to the laser intensity in the picosecond (ps) regime. We also apply the stimulated Raman adiabatic passage (STIRAP) method to the efficient generation of the highly vibrational excited state, using a couple of the simultaneous 2‐photon absorption processes as the Stokes and pump processes. © 2005 Wiley Periodicals, Inc. Int J Quantum Chem, 2005

Multimode transitions of the tetrahedralMO4units(M=Si,Ge,Ti)in sillenite single crystals

Multimode transitions of the tetrahedral unit modes in ${\mathrm{Bi}}_{12}{\mathrm{SiO}}_{20}$ (BSO), ${\mathrm{Bi}}_{12}{\mathrm{GeO}}_{20}$ (BGO), ${\mathrm{Bi}}_{12}{\mathrm{TiO}}_{20}$ (BTO), and mixed $(1\ensuremath{-}x)\mathrm{BSO}\ensuremath{\cdot}x\mathrm{BGO}$ sillenite crystals have been studied using Fourier transform infrared absorption spectroscopy, with a resolution as fine as 0.04 ${\mathrm{cm}}^{\ensuremath{-}1}$ in the 600--3500-${\mathrm{cm}}^{\ensuremath{-}1}$ wave number and 9--300-K temperature ranges. Up to four-mode transitions (overtones of the F mode and combinations of F and A modes) were detected in BGO, BSO, and BTO, and up to three-mode transitions in the mixed crystals. The F-mode anharmonicity parameter, evaluated in the framework of the Morse oscillator model, was in the range 0.003--0.006. The A-mode anharmonicity was found to be still lower. Fine structures of the F-mode absorption were observed and attributed to the LO-TO splitting of the F mode; in the case of BSO, additional structures due to the natural abundance of Si isotopes were detected. The transitions monitored in the mixed crystals were well described by a two-mode behavior. The temperature dependence of the line position and width was studied as well. ``Red'' and ``blue'' shifts were observed for different lines: the results were analyzed by considering thermal expansion and anharmonicity effects.

Vibrational coherent states for Morse oscillator

For the one-dimensional Morse oscillator we have built a set of creation and annihilation operators and established the corresponding coherent states. The average values of some observables in these coherent states have been calculated and their time evolution established. In order to study the strong vibrations of di-atomic molecules we use a three-dimensional Morse oscillator model and its dynamic group. For this system we have built the coherent states and calculated the dynamic modifications of the refractive index of the molecules, as the result of interaction with a laser beam.

Dissociation of diatomic molecules by elliptically polarized chirped pulses

The effects of the rotational degrees of freedom in the photodissociation dynamics of diatomic molecules by a chirped laser pulse is studied. In general, the inclusion of rotational degrees of freedom reduces the efficiency of the chirping excitations relative to that found for nonrotating molecules. However, using classical 2D and 3D rotating Morse oscillator models we demonstrate that field polarization can cause dramatic enhancements of the dissociation probabilities, with circularly polarized chirped pulses inducing dissociation in rotating molecules almost as efficiently as that previously seen for nonrotating Morse oscillators. We suggest reasons for such improvement in efficiency and discuss the validity of the bucket dynamics model for rotating Morse oscillators.

Kinematical bounds on optimization of observables for quantum systems

Upper and lower kinematical bounds for the expectation values of arbitrary observables of driven quantum systems in mixed states are derived, and criteria for their attainability established. The results are applied to the problem of maximizing the energy of a laser-driven four-level Morse oscillator model for HF, as well as a four-level harmonic-oscillator model.

Near-infrared spectra of Ba(NO2)2•X2O (X = H,D) at 10 K. A local-mode approach

The fundamental and overtone vibrational spectra of Ba(NO2)2•X2O (X=H,D) have been interpreted using the local mode model. The calculated parameters are consistent with the structure, which has one strong hydrogen bond and one weak bifurcated hydrogen bond. Evidence for Fermi resonance between stretch and bend features having similar energies is discussed. Evidence for the breakdown of the simple Morse oscillator model, which was quite successful for [Formula: see text] hydrogen bonds, is also presented. Keywords: overtone, spectra, near-infrared, hydrates, local-mode model.

Spectral consequences of periodic orbit bifurcations of AB 2 stretching vibrational modes

Analysis of the kinetically coupled Morse oscillator model of Thiele and Wilson is used to relate abrupt changes in the qualitative character of the stretching vibrational spectra of AB 2 species to the loss of stability of the symmetric stretching periodic orbit above a certain energy threshold. A new uniform asymptotic solution of the relevant Hill's equation yields novel scaling relations that govern the dependence of the stability parameters on the mass ratio ( m A/ m B) and the reduced energy ( E/ D), scaled with respect to the dissociation energy. Crudely simulated dispersed emission spectra are used to illustrate the quantum mechanical consequences of the theory with particular reference to recent experiments on CS 2.

Anharmonic effects on lattice vibration modes of sillenites

Abstract High resolution FTIR absorption spectroscopy in the 600–3500 cm−1 wavenumber and 9–300 K temperature ranges was applied to study multi-phonon transitions of the tetrahedral unit modes in BSO, BGO, BTO and mixed BSO-BGO sillenite crystals. Up to four-phonon (overtones of the F mode and combination of F and A modes) transitions were detected in BGO, BSO, and BTO and up to three- in the mixed crystals. The F mode anharmonicity, evaluated in the framework of the Morse oscillator model, was in the range 0.0024–0.0056. Fine structures due to Si-isotopes were observed in BSO. The two- and three-phonon transitions in the mixed crystals were well described by a two-mode behaviour.

Intramolecular dynamics from a statistical analysis of vibrational levels: Application of two coupled Morse oscillator models to the HCN molecule.

Two local-mode model Hamiltonians containing stretch-stretch couplings have been utilized to obtain the vibrational energy levels of the HCN molecule for the purpose of studying them statistically. The effect of the kinetic coupling has been clearly obtained from the statistical analysis which includes nearest-neighbor level-spacing distributions (NNLSD) and the ${\mathrm{\ensuremath{\Delta}}}_{3}$ statistics of Dyson and Mehta. For NNLSD, a pronounced tendency towards the Wigner distribution has been found. The role of isotopic masses in the statistical properties of the vibrational spectra has also been elucidated. Comparison has been made between the results obtained from the two models. Correlation has been found between a transition to chaos (utilizing Poincar\'e sections and Lyapunov exponents) through classical mechanics and the above statistical behavior of the spectra.

Control of quantum dynamics by a locally optimized laser field. Multi-photon dissociation of hydrogen fluoride

We present a theoretical method for laser-control of a quantum system with open channels. The framework is based on the local optimization theory proposed in a previous paper (J. Chem. Phys. 100 (1994) 5646). The optimization theory is extended by introducing an optimization parameter q(ϵ) relevant to a continuum channel with kinetic energy ϵ. As an example of application, the control theory is used in multi-photon dissociation of hydrogen fluoride in the ground electronic state. The optimized laser field is analyzed with the help of a window Fourier transform and is shown to approximate a sequence of linear chirped pulses with different chirping rates. Such a form of the optimized laser field originates from the breakdown of the selection rule for optical transition in a Morse oscillator model. The time variation of multi-photon processes in the presence of the optimized laser field and a dissociation fraction are calculated based on the nuclear wave packet theory.

Propagation of molecular constant variations into Franck-Condon type integrals

Approximate analytical expressions connecting statistical variations in rotational- vibrational molecular constants ( Be, ωe and ωe Xe) with changes in Franck-Condon type integrals ƒ n,m = 〈χ n| f|χ m〉 and the matrix elements of the form r k n,m = 〈χ n| r k|χ m〉 〈χ n|χ m〉 have been obtained by applying the rules of error propagation to Morse and Morse-Pekeris oscillator models of internuclear potential. The accuracy of the formulae are tested on the A − X and B − X systems of CO molecule by comparing with exact numerical results. The validity conditions for resulting relations as well as the opportunity to use them in the case of RKR potential model are discussed.

Classical strong-field dissociation dynamics for linear triatomic molecules: Application of a coupled Morse oscillator model to HCN.

Classical strong-field dissociation dynamics for linear triatomic molecules: Application of a coupled Morse oscillator model to HCN.

Resonant short-pulse effects on nuclear motion in the electronic ground state

We investigate several approximate treatments of the pulse propagators describing the effects of electronically resonant ultrashort light pulses on the states of molecules in condensed phases, including the classical Franck approximation and a quadratic Hamiltonian treatment. Using a Morse oscillator model of iodine, we examine the effects of the initial form and motion of the pump-induced nuclear density matrix increment on pump-probe signals. We also clarify the conditions of high temperature and short-pulse duration under which the contribution of nuclear dynamics in the electronic ground state to a pump-probe signal will bear a definite sign.

Anharmonicity on the Cu(110)-(2×1)O surface

We have studied the temperature-dependent energy shift of surface vibrations on the Cu(110)-(2×1)O reconstructed surface using high-resolution electron energy loss spectroscopy. Interatomic bonds involved in the observed vibrations were extracted from phonon slab calculations. The measured energy shifts can be directly related to the anharmonicity of the potentials between the vibrating atoms by using a simple Morse oscillator model. By comparing to bulk phonon measurements, we find that both the oxygen-copper and copper-copper bonds at the surface have bulk-like anharmonicity. This is in contrast to the clean surface where strong anharmonicity is observed.

ChemInform Abstract: A Force Field Analysis of the Methyl Radical X2A′′ 2 State Stretching Potential Using the Local Mode‐Coupled Morse Oscillator Model

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