Linear Triatomic Molecules Research Articles

Infrared multiphoton dissociation calculation of a model linear triatomic

In a previous paper, we reported preliminary results on the multiphoton dissociation of a linear triatomic molecule. This model consists of a dissociative mode (ν 3) coupled non-linearly to an IR inactive harmonic mode (ν 1). We present here extensive calculations of the dissociation probability as a function of the laser frequency for different pulses of constant fluence. It is shown that dissociation occurs at frequencies either very red-shifted from the ν 3 IR active absorption band or located at the ν 2 and ν 3 bands (due to a 2:1 Fermi resonance). A Hose—Taylor analysis reveals that in the former case excitation proceeds through an anharmonic ladder, while a harmonic one is used in the latter case. In both cases essentially Q states are populated during the excitation process. The dissociation process has been dealt with explicitly by using metastable states to represent the continuum. It is shown that the actual structure of the continuum, due to the presence of Feshbach resonant states, has no real influence on the dissociation probability. Fragment analysis for the ABC → nhw A + BC dissociation process has been performed and shows only a slight departure from statistical distributions, except at very high intensities.

Electron correlation in alkaline-earth atoms.

Conditional probability distributions for the valence electrons of alkaline-earth atoms in their ground and valence excited states are constructed using large-basis Sturmlan configuration-interaction wave functions for two electrons in frozen, effective-core potentials. The distributions indicate that the ground states of Be, Mg, Ca, Sr, and Ba, and the valence excited states of Be, are much more like linear triatomic molecules, akin to doubly excited He, than like independent-particle systems such as the ground states of He and He-like ions.

Floquet theory analysis of stable and unstable motion

Floquet theory is applied to the stability analysis of linear triatomic molecules having local Morse bonding potentials. We identify conditions for the existence of a symmetric mode and analyze its stability as a function of the energy and symmetric to antisymmetric normal mode frequency ratio. In the stable region we apply a special phase normalization to the Floquet eigenvalues that allows us to identify factors in the Floquet index with a red-shifted generalized antisymmetric mode frequency. Instabilities set in when the ratio of this frequency to the symmetric mode frequency is integer or half-integer. Analytic forms for Poincaré surfaces of section valid for the linearized theory are derived and compared with actual trajectory intersections for both stable and unstable cases. In the stable (quasiperiodic) cases, surfaces corresponding to different sections are ellipses with varying eccentricity but constant area. Hyperbolas are obtained in unstable cases.

Calculation of average distance and amplitude parameters for linear symmetric triatomic molecules in the ground and low-lying excited vibrational states

Using the effective harmonic oscillator (EHO) method the average distance and amplitude parameters for CO 2 and CS 2 in the ground and several low-lying excited vibrational states have been estimated from the spectroscopic force fields. For reference, similar calculations were also performed by a perturbation theory of first- and second-order. In calculations due account was given for anharmonicity and nonlinearity in transformations between internal distances and normal coordinates. The trends exhibited by calculated quantities are discussed and the behaviour of CO 2 and CS 2 upon increasing the excitation within the individual modes is considered.

Role of Feshbach resonances in the infrared multiphoton dissociation of small molecules

Calculations on the infrared multiphoton dissociation of a model linear triatomic molecule are reported. The molecule has 51 bound states and dissociation occurs after absorption of at least ten photons. The dissociation probability is computed within the quantum framework of the optical potential method [C. Leforestier and R. E. Wyatt, J. Chem. Phys. 78, 2334 (1983)] in conjunction with the complex extension of Floquet theory. For any given frequency, an analysis of the molecule in interaction with the laser field is presented, which permits us to follow the entire excitation path up to the continuum. This analysis shows that excitation into the continuum proceeds primarily through Feshbach resonant states. The role of these resonant states in the dissociation of polyatomic systems is discussed.

Spectroscopic constants evaluated by numerical contact transformation

Following previous work a program has been written to evaluate spectroscopic information from anharmonic force-fields in linear triatomic molecules, using numerical contact transformations. The scheme is found to be accurate and convenient and is compared favourably with matrix diagonalization and with semi-classical methods. Extension to larger molecules has not been undertaken but appears to be straightforward.

Computer simulation of molecular orientational order: the Kerr effect in carbon disulphide

We have performed a molecular dynamics computer simulation on the liquid state of the linear triatomic molecule, carbon disulphide. On the time-scale of a few picoseconds, the reorientation of these molecules in response to an external electric field has been followed explicitly. The failure of a classical orientational diffusion model to reproduce the results of the simulation is observed for high fields. A simple modification of the diffusion model is found to restore most of its qualitative predictive power.

Semiclassical spectral quantization: Application to two and four coupled molecular degrees of freedom

Semiclassical quantization of the quasiperiodic vibrational motion of molecules is usually based on Einstein–Brillouin–Keller (EBK) conditions for the quantization of the classical actions. Explicit use of the EBK conditions for molecular systems of K degrees of freedom requires K quantization conditions. Therefore, explicit use of the EBK conditions becomes increasingly difficult if not impossible for polyatomic systems of three or more degrees of freedom. In this paper we propose a semiclassical quantization method which makes explicit use of phase coherence of the de Broglie wave associated with the trajectory rather than the EBK conditions. We show that taking advantage of phase coherence reduces the K quantization conditions to a single quantum condition—regardless of the number of degrees of freedom. For reasons that will become obvious we call this method ‘‘spectral quantization.’’ Polyatomic vibrational wave functions and energy eigenvalues are generated from quasiperiodic classical trajectories. The spectral method is applied to an ABA linear triatomic molecule with two degrees of freedom and to an anharmonic model of the molecule cyanoacetylene. The usefulness of the technique is demonstrated in this latter calculation since the cyanoacetylene model will have four coupled vibrational degrees of freedom.

The effect of anharmonic vibration and centrifugal distortion on nuclear shielding in linear triatomic molecules: NNO and CO2

The temperature dependence of the mean bond displacement in linear triatomic molecules NNO and CO2 have been determined using the well-established anharmonic force fields for these molecules. The results are applied to explain the temperature dependence of the nuclear shielding observed in the zero-pressure limit for the 15N and 13C nuclei in 15N15NO and 13CO2. By fitting the observed σ0(T)−σ0(300 K) for T=250–350 K, empirical values of (∂σ/∂Δr)e=−220 ppm/Å (CO2), −1030 ppm/Å (NN*O), and −5190 ppm/Å (N*NO) are obtained. These derivatives are discussed in comparison to similar molecular types. The average shielding for the vibrational states (000) and (0110) are calculated for both 15N nuclei in NNO and compared with values obtained from experimental spin-rotational constants. The empirical derivatives are also used to calculate NMR isotope shifts from the mass-dependent 〈Δr〉.

Supermultiplet structures of doubly excited states of H-below the N=6 hydrogen threshold

Some doubly excited resonances in electron-hydrogen scattering converging on the N=6 hydrogen threshold are calculated by a method of complex-coordinate rotation. Hylleraas-type wavefunctions are used for L=0 and L=1 resonances, and products of Slater orbitals for states with L>or=2. Both states with parities (-1)L and (-1)(L+1) are calculated. Resonance parameters for states with 'supermultiplet' quantum number I=0 are reported. Present results indicate that the doubly excited H- atom exhibits characters similar to those of a linear XYX triatomic molecule.

Application of scaling theory to vibrational relaxation in linear anharmonic triatomic molecules

The energy-corrected-sudden (ECS) scaling theory is extended to vibrational relaxation in the collisions of anharmonic linear triatomic molecules with atoms. Application is made to the collisions of He atoms with 12C 16O2, 14C 16O2, and 12C 18O2. By combining the rate constants for the (0110 → 0000) transitions, calculated using the vibrational close-coupling rotational infinite-order-sudden (VCC-IOS) method, with the ECS scaling theory, we predict rate constants for the transitions (1000 → 0110), (0220 → 0110) and (0200 → 0110). These agree very well with the rate constants computed directly using the VCC-IOS technique. This comparison presents a particularly severe test of the accuracy of the ECS scaling theory for anharmonic polyatomics since Fermi resonance effects are large for the 1000 and 0200 levels in CO2.

Calculation of the vertical ionization potentials of XBO and XBS molecules (X = H, F and Cl) by perturbation corrections to Koopmans' theorem

Vertical ionization potentials of the linear triatomic molecules, HBO, FBO, ClBO, HBS, FBS, and ClBS are computed by applying Rayleigh-Schrödinger perturbation corrections to Koopmans' theorem. Comparison with the experimental data for the XBS molecules gives us confidence that our theoretical values for the ionization potentials will greatly assist in the identification of the, as yet, unobserved photoelectron spectra of the XBO species.

Photodissociation of triatomic molecules: Rotational scattering effectsa)

An exact quantum method for calculating the state-to-state direct photodissociation probabilities for arbitrary (linear or bent) triatomic molecules is presented. It is shown that this method, which requires the accumulation of Franck–Condon overlap integrals between the initial state and a scattering state satisfying arbitrary scattering boundary conditions, is equivalent to the solution of the driven equations of Band, Freed, and Kouri. For both HCN and ICN the effects of variation of the final state potential on the vibrational and rotational distributions of the CN fragments are examined. Agreement of our exact calculations with the approximate calculations of Morse and Freed is very good.

Fluids of hard diatomic molecules. II

We consider fluids of hard diatomic molecules composed of two fused hard spheres of unequal diameter. The orientation average of the Mayer f function and the second virial coefficient B2 are calculated exactly by analytic integration in closed form. The calculation uses a decomposition of f(12) into five terms. The only difficult term is integrated in tetrahedral coordinates. Agreement with previous numerical results for B2 is excellent. Two of the five terms make small to moderate contributions to B2, depending on the molecular parameters. This supports the view that the decomposition is a useful device in formulating approximate theories. The integrals evaluated for the diatomic case are used to obtain B2 and the orientation-averaged f(12) exactly for a class of linear symmetric triatomic molecules.

Monte Carlo study of the hard triatomic molecular systems

Equilibrium behaviour of the linear and non-linear hard triatomic molecule systems was studied by the Monte Carlo simulation technique at the packing fractions of 0·4533 and 0·3988. From these simulations the site-site distribution functions were determined and their contact values used to evaluate the compressibility factor. The comparison of pseudoexperimental and theoretical values of the compressibility factor is given.

Representation of one-dimensional motion in a morse potential by a quadratic hamiltonian

A representation of the algebraic hamiltonian for the anharmonic Morse oscillator as a quadratic form, H = T1ω( 1 2 P 2 + 1 2 Q 2), where P and Q are operators is derived. The commutator of P and Q is an operator that tends to i (times the identity operator) in the harmonic limit. Coherent states and anharmonic normal modes for a linear triatomic molecule are discussed as potential applications.

High-resolution laser excitation spectra of linear triatomic molecules: Analysis of the B2Σ +- X2Σ + system of SrOH and SrOD

Single-mode cw dye laser excitation spectra of the (0, 0 0, 0)-(0, 0 0, 0), (1, 0 0, 0)-(1, 0 0, 0), (0, 1 1, 0)-(0, 1 1, 0) bands of the 611- to 607-nm system of SrOH and SrOD were observed and assigned. The spectrum is consistent with a 2Σ- 2Σ system where the molecule is linear in both electronic states. The rotational analysis is obtained by measuring P- R separations in the excitation spectrum. A technique which greatly aided in the spectral assignment that utilizes a monochromator as a bandpass filter in obtaining excitation spectra is described. A new spin-rotation constant, γ (+) - γ (−), was found necessary to fit the l-type doubling of the (0, 1 1, 0) mode in B 2Σ + of SrOH. This new constant is assumed to arise from two 2 Σ 1 2 vibronic states, split by Renner-Teller interaction, of the (0, 1 1, 0) mode of A 2Π. From a perturbation treatment of this electronic interaction, ϵω 2 of the (0, 1 1, 0) mode of A 2Π was found to be 14 cm −1. The linear structure of SrOH and SrOD in both electronic states is consistent with the model, in the one-electron approximation, in that the transition involves the promotion of the unpaired 5 s to the 5 p orbital localized on the strontium.

Anharmonic corrections for linear triatomic molecules subject to the Rennet-Teller effect

The effects of vibrational anharmonic terms and of the gK -correction on the energy levels of a triatomic molecule in a degenerate electronic state are considered. The electronic wavefunctions are described using the approach first suggested in the original paper of Renner. Formulae for the anharmonic corrections in a number of different situations are derived. For an electronic Π state the corrections are given in the form where i runs over the various contributions and x 1, x 2, … depend on the anharmonic force constants. The functions Fi can be determined numerically (see equations (4.3) and 4.7)). For the case without spin-orbit interaction the Fi s are given explicitly to first order in ∈ in table 1. Further-more, the same results apply for levels with |K|=v 2+1 even if the spinorbit interaction is not negligible. Explicit results for levels with |K|<v 2 including spin-orbit interaction are given in tables 2 and 3. The cases with larger values for Λ (2, 3, …) are also considered. The energy level formulae for a Δ state differ from those derived earlier by Merer and Travis. In particular, the small separation between the vibronic Φ and Π levels with v 2=1 is now found to be 4gK . The additional terms that arise from end-over-end rotation of the molecule are discussed in § 6.

Exact asymptotic form of the site-site direct correlation function for linear triatomic molecules

(1982). Exact asymptotic form of the site-site direct correlation function for linear triatomic molecules. Molecular Physics: Vol. 46, No. 3, pp. 665-670.

Inverse vibrational distributions of photofragments

The matrix element describing the transition from a bound to an unbound state in photodissociation of a linear triatomic molecule is found to yield an inverse vibrational distribution when the recoil energy of the photofragment is less than or comparable to the internal energy.