Vibration-rotation spectroscopy of molecules trapped inside C60

A simple model is developed to treat the energy levels and spectroscopy of diatomic molecules inside C 60. The C 60 cage is treated as spherically symmetric, and the coupling to the C 60 vibrations is ignored. The remaining six degrees of freedom correspond to the vibrations and rotations of the diatomic molecule and the rattling vibration of the molecule inside the cage. By using conservation of angular momentum, we can remove two of these motions and simplify the calculations. The resulting energy levels are simple and can be labeled by a set of quantum numbers. The IR and Raman spectra look like those of gas-phase diatomic molecules at low temperatures. At higher temperatures, hot bands due to the low-frequency rattling mode appear, and the spectrum becomes congested, looking like a solution spectrum.     

Dynamics of adsorption: A model calculation for HD activated adsorption

We have recently developed a model potential for the interaction of a diatomic molecule with a rigid solid surface. In this note, we report some results of classical trajectory studies designed to simulate the adsorption of a diatomic molecule. Model potentials with different barrier heights are used and a variety of different initial conditions for the incident molecule are studied. In common with gas-phase results, we find that translational energy is most effective in surmounting early barriers and enhancing adsorption.     

Study of the vibrational characteristics of the homonuclear diatomic nuclear schrödinger equation with a numerov method using a number of empirical potential functions

Many empirical potential energy functions have been modeled to represent the potential energy function of a diatomic molecule along whole range of internuclear distance coordinate, whereby one can determine certain molecular constants. Here we employ various potential functions such as Morse, Rydberg, Varshni(II), Varshni(III), Varshni(VI), Pöschl-Teller, Hulburt-Hirschfelder, Lippincott, Frost-Musulin, Linnet, and Rosen-Morse, and the Numerov method to solve the nuclear Schrödinger equation for F2, as an example of a homonuclear diatomic molecule. Herewith, the vibrational and vibration-rotation energy levels are obtained and excellent accuracy is achieved. The potential of employing the Numerov method in engineering physics computations is emphasized.     

Simplistic classical probabilistic model of superexcited states of molecules

The decay processes in the superexcited state of a molecule are investigated theoretically in terms of a classical trajectory method. The simplest model of a diatomic molecule is considered. Particular attention is payed to the branching ratio for preionization and predissociation, and to the energy distribution of the ejected electrons. New formulas of practical use are derived for these two quantities.     

Localized states in molecular auger spectra

The influence of the degree of localization of the two final holes on the Auger spectra of a simple diatomic molecule is analysed in detail and cases where such effects may be observed experimentally are discussed. The results are compared with studies of the valence band Auger spectra of solids.     

Bifurcations as dissociation mechanism in bichromatically driven diatomic molecules

We discuss the influence of periodic orbits on the dissociation of a model diatomic molecule driven by a strong bichromatic laser fields. Through the stability of periodic orbits, we analyze the dissociation probability when parameters, such as the two amplitudes and the phase lag between the laser fields, are varied. We find that qualitative features of dissociation can be reproduced by considering a small set of short periodic orbits. The good agreement with direct simulations demonstrates the importance of bifurcations of short periodic orbits in the dissociation dynamics of diatomic molecules.     

Preparation and resolution of molecular states by coherent sequences of phase-locked ultrashort laser pulses

We study the application of nonlinear wave packet interferometry to the preparation and resolution of the overlaps of nonstationary nuclear wave functions evolving in an excited electronic state of a diatomic molecule. It is shown that possible experiments with two phase-locked ultrashort pulsepairs can be used to determine a specific vibrational wave packet state in terms of coherent states of the ground electronic state. We apply this scheme to an idealized molecule with harmonic potential energy surfaces and to the X <-- B transition states of the iodine molecule. Our results indicate that this scheme is very promising as a potential tool to quantum control.     

Wellenfunktionen und Terme des Systems Atom/zweiatomiges Molekül bei großen intermolekularen Abständen

Zusammenfassung Wellenfunktionen des Systems Atom/homonukleares zweiatomiges Molekül werden konstruiert und ihr Symmetrieverhalten wird untersucht; dabei sind Atom und Molekül beide bahn- und spinentartet. Die erhaltene Klassifizierung der Zustände des dreiatomigen Systems bei großen Atom-Molekül-Abständen ist der für zweiatomige Moleküle aus verschiedenen Atomen analog und basiert auf der Näherungssymmetrie des eingeführten effektiven Hamilton-Operators des Systems. H _eff enthält Spin-Bahn-, Coulomb-, Dispersions- und Austauschwechselwirkung. Man erhält allgemeine Ausdrücke für die Matrixelemente von H _eff. Die Matrixelemente der Austauschwechselwirkung werden mit Hilfe einer Einzentrennäherung für das Molekül aus zwei gleichen Kernen berechnet.

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Wave-functions and terms of the system atom/diatomic molecule in the case of large intermolecular distances

Wavefunctions of the system atom/homonuclear diatomic molecule are constructed, and their symmetry behaviour is examined; both atom and molecule can be degenerate with respect to spin and orbital. The classification of the states of the triatomic system with large atom-molecule distances is analogous to that of diatomic molecules consisting of different atoms, and is based on the approximate symmetry of the effective Hamiltonian of the system. H _eff contains spin-orbit, Coulomb, dispersion, and exchange interactions. General expressions for the matrix elements of H _eff are obtained. The matrix elements of the exchange interaction are calculated with the aid of a one centre approximation for a molecule with two equal nuclei.

     

A nonlinear Hamiltonian describing the rovibrational states of diatomic molecules

Summary On the basis of the deformable body model and harmonic potential approximation a nonlinear quantum-mechanical Hamiltonian describing rovibrational states of diatomic molecules has been derived. The obtained formula is applied in evaluation of molecular constants and for prediction of rovibrational and rotational spectra of the selected two-atomic systems giving quite satisfactory reproduction of the data values using only two molecular and one semiempirical parameters. This additional parameter is responsible for the change of curvature of internuclear potential in the excited rotational states, and may be viewed as an indicator of molecular susceptibility to rotation induced dissociation of a molecule.     

A numerical solution of the pair equation of a model two‐electron diatomic system

It has been well‐documented that about 90% of the total correlation energy of atomic systems can be obtained by solving so‐called pair equations. For atoms, this approach requires solving partial differential equations (PDE) in two variables. In case of a diatomic molecule, we face devising a method for treating PDEs in five variables. This article shows how a well‐established finite difference method used to solve Hartree–Fock equations for diatomic molecules can be extended to solve numerically a model two‐electron Schrödinger equation for such systems. We show that using less than 100 grid points in each variable, it is possible to obtain the total energy of the helium atom and hydrogen molecule with a chemical accuracy and the S energy of the helium atom and hydride ion as accurately as the best results available. © 2015 Wiley Periodicals, Inc.     

Trajectory calculation results on the orientation of a diatomic molecule in collision with an atom

Orientational effects in collisions between a diatomic molecule and a noble gas atom are studied by classical trajectory calculations. A preferable ”perpendicular orientation“ of the molecule is found at the moment of closest approach of the atom. This orientational effect is more pronounced in collisions with heavy atoms.     

Potential energy surfaces for the interaction of atomic and diatomic hydrogen with lithium metal clusters

In this paper a modified CNDO/2 method is used to study the interaction of hydrogen atoms and molecules with molecular clusters simulating the (100) surface of solid lithium metal. The modification, described in an earlier papers, involves rescaling bicentric CNDO/2 energy contributions with known diatomic bond energies. Potential energy curves are calculated for six attack points by the hydrogen atom on the surface, and for one attack point by the molecule. The results indicate that in both atom and molecule forms hydrogen penetrates the surface and that the molecule most likely dissociates.     

Mechanism for collision-induced transitions between Λ-doublets in 1Π molecules: Reduction to a single scattering potential

The theory is presented for rotational excitation of ¹Π molecules by collisions with rare gas atoms. It is shown that collision dynamics are described by the two electronic potential energy surfaces which correlate with the electronically degenerate Λ components (doublets) in the diatomic molecule. Because the ±Λ degeneracy can alternatively be described as being in the rotational rather than in the electronic degree of freedom, one can reformulate the collision dynamics in terms of a single effective electronic potential which then depends on Φ, the angle of rotation about the diatomic axis. The form of this Φ dependence is found to be identical to that postulated to explain experimental data for collisional transfer of laser-induced fluorescence.     

Application of potential constants: Empirical determination of molecular energy components for diatomic molecules

The potential (force) constant of a diatomic molecule is applied to determine the molecular energy components such as the electronic kinetic (T) and electrostatic potential (V) energies. The theoretical framework of the method is constructed from T and V representations of the quantum mechanical virial theorem. To confirm the utility of the method developed here, the calculated molecular energy components of diatomic molecules are compared with available Hartree-Fock data. It is concluded that the present method is simple and powerful for evaluating the molecular energy components of various diatomic molecules.     

Time-Dependent quantum theory. IV. Effect of lattice relaxation on the optical spectra

The absorption and emission spectra of a diatomic “molecule” connected to an unstrained linear crystal are calculated for the circumstance where the diatomic undergoes a change of equilibrium internuclear separation in the electronic transition. The expansion (or contraction) of the diatomic results in a frequency dependent line-width in the customary Lorentzian expression, and is manifested in the absorption spectrum as an asymmetric tailing to the blue, and in the emission spectrum as an asymmetric tailing to the red. The interaction of the diatomic with the lattice also produces a blue-shift of the absorption spectrum and a red-shift of the emission spectrum. An important consequence of the asymmetry is the apparent loss of integrated intensity of the line. The striking similarity, both in the width and the over-all shape, of the emission line calculated here with those observed in the Vegard–Kaplan band of N₂ dissolved in rare gas crystals is discussed.     

Molecular basis set generation: Accurate slater basis sets for LiH− ground and excited state and Li2− ground state

A procedure for generating basis sets for diatomic molecule electronic structure calculations is described. In essence, this procedure maps the results of nearly exact numerical Hartree–Fock calculations into basis set form. Two applications of the procedure are proposed: (a) generation of very high accuracy basis sets, and (b) investigation of basis sets for unusual systems. The latter application is illustrated by some results for diatomic anions.     

Kinetic energy release in fragmentation processes following electron emission: a time-dependent approach

A time-dependent approach for the kinetic energy release (KER) spectrum is developed for a fragmentation of a diatomic molecule after an electronic decay process, e.g., Auger process. It allows one to simulate the time-resolved spectra and provides more insight into the molecular dynamics than the time-independent approach. Detailed analysis of the time-resolved emitted electron and KER spectra sheds light on the interrelation between wave packet dynamics and spectra.     

Lie algebraic approach to multiphoton excitation of diatomic molecules in intense laser fields

The quadratic anharmonic oscillator Lie algebraic model is used to study the multiphoton transition of the diatomic molecule placed in intense laser fields. The multiphoton excitation of vibration and vibration‐rotation of diatomic molecules in intense laser fields are discussed. In the pure vibration transition we calculate the transition probability versus the frequency of the laser fields for the CO molecule. We also investigate the roles of rotational motion in multiphoton processes and compare with pure vibration for the LiH molecule. The influences of the angular quantum number l and the molecular orientations in laser fields on the multiphoton processes are discussed. The averaged absorb energy changing with the laser field's frequency is calculated. ©1999 John Wiley & Sons, Inc. Int J Quant Chem 71: 201–207, 1999     

On the direct calculation of the time evolution of excited molecular states in the presence of nonadiabatic interactions

The possibility is explored of calculating the time evolution of a given initial molecular state, in the presence of sufficiently strong nonadiabatic interactions, with a fully quantum-mechanical approach. Two methods are presented. The first one is based on the determination of the molecular eigenstates, with expansion of the nuclear wavefunctions on a Hermite basis. The second method is based on the Padé 1,1 approximation of the time evolution operator and on a finite difference representation of the time-dependent nuclear wavefunctions. Both methods are applied to simple models of a diatomic molecule.     

Nonadiabatic transitions in chemical reactions. A comparison between exact and approximate collinear calculations

The quantum mechanical study of nonadiabatic transitions during a reactive collision of an atom and a diatomic molecule is extended. The constant coupling term used in our previous work is replaced by a gaussian-type function to simulate the fact that the interaction becomes stronger as the two interacting surfaces become closer. the two surfaces are assumed to be one above the other but shifted along the vibrational coordinate. It is found that when the coupling is not too strong, the nuclear process taking place on the original adiabatic surface can be decoupled from the electronic process which is responsible for the transitions between the two surfaces. It is established that the strength of the coupling is defined in terms of the area under the coupling function and its width. Dependence on the latter is in general expected to be much stronger than on the former.