Rotational inelasticity in high-energy H2H2 collisions

Rotational cross sections for transitions in the H₂H₂ system have been calculated for energies up to ≈ 2.0 eV and for rotor levels up to j = 11 in the effective potential approximation. The cases of para H₂-para H₂, ortho H₂-ortho H₂ and ortho H₂-para H₂ are considered. Correlations and trends in the cross sections have been examined, and it is shown that the high-energy collisions are dominated by coupling effects. The results of this analysis also suggest that the collision process may be profitably viewed as a diffusion of probability among the levels.     

Rotation-vibration-translation energy transfer in laser excited Li2 (B1Πu)

Using the method of laser fluorescence, inelastic collisions with rare gas atoms of electronically excited ⁷Li₂ molecules in the υ = 2 and 4 levels were studied. Vibrational transitions ranging from Δ = +2 to ?4 were observed. The simultaneous rotational transitions were completely resolved, and detailed rate constants k_{Δυ, ΔJ} for specific collision- induced quantum jumps Δυ, ΔJ were determined. The effect of secondary rotational relaxation was eliminated by an extrapolation to zero pressure. By integration over ΔJ, rate constants k_Δυ, were found. They are, within the error limits, independent of the collision partner and on the initial υ (2 or 4) and depend rather weakly on Δυ. These findings are compared with theoretical results from various methods, generally based on a collinear collision model. The apparent disagreement in all respects suggests strongly the importance of rotational degrees of freedom in the collision. Experimental evidence for this is the large amount of V — R transfer observed, which about equals the V — T transfer. The mean cross sections σ(Δυ) for specific vibrational transitions Δυ range between 6 and 15 A², among the largest ever observed.     

Validity of the coupled states approximation for molecular collisions

The process of rotational excitation in the body-fixed frame is examined in detail. Physical arguments are presented to justify the coupled states approximation which involves a diagonalization of the body-fixed centrifugal potential. Cross sections for rotational transitions in HeHCN and in ArN₂ collisions are reported and are compared to exact close coupling cross sections. The coupled states method is found to maintain its high accuracy for the extremely strong-coupling HeHCN system and also for the large Δj transitions in the ArN₂ system even when many partial waves are required. General rules are given for the applicability of this approach in terms of the strength and the position of the anisotropy in the potential energy surface.     

Rotational energy transfer in the NO A 2Σ+(v' = 0) state with He and Ar

Rotational energy transfer cross sections are determined for NO (A ²Σ⁺, v' = 0, N' = 0, 7, and 15) +He and NO (A ²Σ⁺, v' = 0, N' = 0) +Ar by the two-color, double-resonance ionization method. Rotational jumps up to ΔN' = 8 take place as a single collision event. The cross sections determined are discussed in terms of the IOS and ECS scaling laws.     

List of subjects

Elastic and inelastic cross sections for well specified m_j-states have been investigated in exact quantum mechanical calculations for H₂—inert gas systems using realistic potentials. The influence of different approximations like the neglect of closed channels and the distorted wave approximation is investigated, especially also in the orbiting resonances of H₂Ar. Compensations of effects of the repulsive and attractive part of the intermolecular potential are found in many cross sections. The diffraction pattern in the inelastic differential cross sections is shown to depend only on k′_j, the wave number of the final state.     

Inelastic collisions between 4He and H2: Study of dynamical approximations

We report a detailed study of the convergence and accuracy of HeH₂ rotationally and ro-vibrationally inelastic cross sections, determined within both the coupled states (CS) and effective potential (EP) formalisms. Two different potential surfaces were used. CS total cross sections appear insensitive to the specific choice of centrifugal barrier. Although the CS results are more accurate, the EP method reproduces the important qualitative features of the various inelastic processes. In addition, with the counting-of-states correction, the EP cross sections for ro-vibrationally inelastic transitions out of low-lying rotational levels agree with the CS values to within a factor of two, with only few exceptions.     

A complete decoupling of Faddeev-like equations for three arrangement systems; applications to HH2 collision

A complete decoupling of time-dependent Faddeev-like equations for three identical particles is presented in terms of an operator formalism. No restriction to pairwise additive interaction needs to be made. Our decoupled equations can be looked at as being a generalization of the special decoupled versions of Faddeev and Lovelace in so far as they include all irreducible representations of the permutation group S₃. Thus, the new equations also apply to three composite particles of any spin. An application is made for the system composed of three H-atoms. In particular we show how the cross sections of ortho—para transitions are directly related to the transition operators obtained from the decoupled equations.     

Total reactive cross section for K + Br2 in the energy range of 0–4 eV

3-D classical trajectory calculations were performed using diabatic as well as adiabatic potential energy surfaces. Non-adiabatic transitions were allowed and localized at the avoided crossing of the two adiabatic surfaces. The transition probability was calculated according to the Landau—Zener formalism. The total cross sections for the reaction K + Br₂ → KBr + Br were calculated and compared with experimental data. The total cross sections, calculated with the aid of adiabatic potential energy surfaces, were, contrary to those with diabatic surfaces, in very good agreement with the measured total reactive cross sections over the whole energy range of 0–4 eV.     

Observed adiabatic corrections to the born-oppenheimer approximation for diatomic molecules with ten valence electrons

Using millimeter-wave (mw) spectroscopy pure rotational transitions were measured with very high precision in several vibrational states for many compounds of the group III/VII and IV/VI diatomic molecules. The spectra were fitted to the usual Dunham expansion adopting the normal mass relations for the Y_lk except for Y₀₁ in order to combine all data of different isotopes for the same compound. For Y₀₁ the atomic mass relation given by Watson is used which introduces phenomenological parameters Δ₀₁^A, Δ₀₁^B for molecule AB taking the adiabatic and nonadiabatic corrections to the Born-Oppenheimer approximation into account. All observed spectra are well described by such a procedure. From these calculations the correction parameters Δ₀₁^A, Δ₀₁^B were obtained with an accuracy of ≈ 10% or better. Using known values of the rotational gJ factor and of the electric dipole moment the nonadiabatic part was calculated and with this result the adiabatic part was evaluated from Δ₀₁ for each atom. The adiabatic correction does not change very much for one specific atom by varying the chemical counterpart and in general it is less than 30% of the total correction for this class of molecules. The only exceptions are InI and the Tl and Pb compounds for which the adiabatic corrections are obtained ten to hundred times larger than those of the other compounds. No explanation is known for this behavior in the published literature.     

A study of reorientation effects in CsF—Ar using approximate quantum methods

The EB (exponential Born) and IOS (infinite order sudden) methods are used to calculate a variety of j → j′ and jm → j′m′ integral cross sections and j → j′ differential cross sections for CsF—Ar at E_cm = 87.7 meV. Inelastic rotational cross sections are found to depend primarily on the odd long range parts of the interaction potential. The jm → j′m′ integral cross sections for the quantization axis parallel to the initial relative velocity vector are found to approximately obey the selection rule “Δj + Δm = even” and cross sections for which the orientation of the rotor is left unchanged (i.e. 11 → 11, 11 → 22, and 11 → 33 transitions) are strongly favored over those which are changed for low lying rotational states. Good agreement between the IOS and EB methods is found for most of the scattering quantities calculated.     

Collisional energy transfer involving molecules in 1II electronic states: fully quantum study of collisions of Li2(B1IIu) with He and Ne

Infinite-order-sudden (IOS), coupled-states (CS) and close-coupled (CC) calculations for collisions of Li₂ (B¹II_u) with He and Ne are reported, based on a representation of the potential energy surfaces introduced by Poppe. We explore the range of validity of the CS and IOS approximations and analyse the quantum interference effects in the integral cross sections. For both homonuclear and heteronuclear molecules in ¹II electronic states we discuss, within the IOS approximation, when asymmetries will exist in the cross sections for upward (J → J + ΔJ), as compared to downward (J → J - ΔJ) transitions. In addition, also within the IOS approximation we show that the J → J + ΔJ across sections will not be invariant with respect to the A-doublet level of the initial state. The CC cross sections are compared with previous and current experimental results. Good agreement is found for the magnitude of both the integral cross sections and the cross section asymmetries. The present study as well as previous experimental investigations show that the asymmetry pattern appears to be extremely sensitive to the interaction potential.     

A semiclassical model of polarisation forces in atomic scattering

Low-energy elastic, differential and integral, collision cross sections for electron scattering from rare gas atoms are calculated using a simplified model treatment of the short-range polarisation forces already applied successfully to helium atoms (De Fazio et al., 1994). Static and exchange contributions to the total interaction are treated exactly, while a global semiclassical model provides a simple procedure for the short-range damping of all the long-range adiabatic terms which asymptotically lead to the polarisation forces. The results are compared with several available experimental findings for Ne and Ar atoms. The higher order terms in the perturbation expansion are found to have little effect on the cross sections and then only at low energies and in the small-angle region.Von Humboldt Stiftung Forschungspreisträger (1992)     

Two-photon absorption properties of two-dimensional π-conjugated chromophores: combined experimental and theoretical study

The two-photon absorption (TPA) properties of four TPEB [tetrakis(phenylethynyl)benzene] derivatives (TD, para, ortho, and meta) with different donor/acceptor substitution patterns have been investigated experimentally by the femtosecond open-aperture Z-scan method and theoretically by the time-dependent density-functional theory (TDDFT) method. The four compounds show relatively large TPA cross sections, and the all-donor substituted species (TD) displays the largest TPA cross-section σ(2) = 520 ± 30 GM. On the basis of the calculated electronic structure, TD shows no TPA band in the lower energy region of the spectrum because the transition density is concentrated on particular transitions due to the high symmetry of the molecular structure. The centrosymmetric donor-acceptor TPEB para shows excitations resulting from transitions centered on D-π-D and A-π-A moieties, as well as transition between the D-π-D and A-π-A moieties; this accounts for the broad nature of the TPA bands for this compound. Calculations for two noncentrosymmetric TPEBs (ortho and meta) reveal that the diminished TPA intensities of higher-energy bands result from destructive interference between the dipolar and three-state terms. The molecular orbitals (MOs) of the TPEBs are derivable with linear combinations of the MOs of the two crossing BPEB [bis(phenylethynyl)benzene] derivatives. Overall, the characteristics of the experimental spectra are well-described based on the theoretical analysis.     

Spin—orbit and vibronic perturbations on the chiroptical spectra of dissymmetric pseudo-tetragonal metal complexes

The influence of spin—orbit and vibronic interactions upon the chiroptical properties of nearly degenerate dd transitions in metal complexes of pseudo-tetragonal symmetry is investigated. A model system is considered in which three nearly degenerate dd excited states are coupled via both spinorbit and vibronic interactions. Vibronic interactions among the three nearly degenerate dd electronic states are assumed to arise from a pseudo-Jahn—Teller (PJT) mechanism involving three different vibrational modes (each nontotally symmetric in the point group of the undistorted model system).A vibronic hamiltonian is constructed (for the excited states of the model system) which includes linear coupling terms in each of the three PJT-active vibrational modes as well as a linear coupling term in one totally symmetric mode of the system and a spin—orbit interaction term. Wavefunctions and eigenvalues for the spin—orbit/vibronic perturbed excited states. of the model system are obtained by diagonalizing this hamiltonian in a basis constructed of uncoupled vibrational and electronic (orbital and spin) wavefunctions.Rotatory strengths associated with transitions to vibronic levels of the perturbed system are calculated and “rotatory strength spectra” are computed assuming gaussian shaped vibronic spectral components. Calculations are carried out for a number of vibronic and spin—orbit coupling parameters and for various splitting energies between the interacting electronic states. The calculated results suggest that chiroptical spectra associated with transitions to a set of nearly degenerate dd excited states of a chiral transition metal complex cannot be interpreted directly without some consideration of the effects introduced by spin—orbit and vibronic perturbations. These perturbations can lead to substantial alterations in the sign patterns and intensity distributions of rotatory strength among vibronic levels derived from the interacting electronic states and it is generally not valid to assign specific features in the observed circular dichroism spectra to transitions between states with well-defined electronic (orbital and spin) identities.Our theoretical model is conservative with respect to the total (or net) rotatory strength associated with transitions to levels derived from the three interacting electronic states; the vibronic and spin—orbit coupling operators are operative only within this set of states. That is, the total (or net) rotatory strength associated with these transitions remains invariant to the vibronic and spin—orbit coupling parameters of the model.     

The Franck—Condon principle for radiationless transitions in molecules and a selection rule for morse oscillators

The Franck—Condon (FC) principle for the tunnel radiationless transition (RT) is formulated. It reads that the RT occurs at constant values of the nuclear coordinates q* and of the classical momenta p*. However, unlike the optical transitions, q* and p* take non-physical values since the tunnel RT is a classically forbidden process. As a result of energy conservation, the potential surfaces of two given electronic states cross with one another at the nuclear configuration q*. It is concluded that the electronic-orbital selection rules and the numerical values of the purely electronic matrix elements are governed by the configuration q* rather than by the equilibrium nuclear configuration as was supposed previously. The configuration q* for the T₁ → S₀ intersystem crossing in aromatic hydrocarbons is described in terms of a large displacement of only one H atom from its equilibrium position along the CH bond (perhaps, there is also some out-of-plane displacement). Using the FC principle, it is found that the anharmonicity of the local CH bond vibrations results in a strong dependence of the T₁ → S₀ intersystem crossing rates upon the sign of the CH bond-length change between two given electronic states, Δq = R_T1 - R_S0. Namely, the following “selection rule” holds: these RTs are allowed at Δq < 0 and they are forbidden at Δq > 0, the prohibition factor being of the order of 10²–10⁴. Finally, an oscillatory dependence of the FC factors upon Δq is explained, using the FC principle, in terms of quantum interference in the total transition probability, of which the amplitude is a sum of the transition amplitudes due to different crossing points q*. The interference effects are believed to be insignificant for RTs in molecules with large energy gaps and so they are eliminated in the usual manner by adding up the partial probabilities rather than the partial amplitudes. The classical FC factor thus obtained smoothly depends upon Δq (and upon other parameters as well). This procedure also provides an analytical continuation of the FC factor to non-integral quantum numbers.     

Polarization in elastic scattering: close-coupling studies on ArN2

We present the results of close-coupling calculations of m_j-dependent differential and integral cross sections forj₁ = 2 → j₂ = 2 rotationally elastic ArN₂ collisions. Two potential surfaces were used with differing long-and short-range anisotropies. If the anisotropy is long-ranged the scattering of an isotropic beam results in a significant angle dependent polarization of the elastically scattered products. To a certain extent this reflects a selective loss of m_j-state population due to rotationally inelastic transitions. For quantization along the initial relative velocity vector or perpendicular to the scattering plane, the depolarization of an initially m_j-state selected beam vanishes in the forward direction and is significantly less than the statistical limit at all angles, which indicates a dynamical conservation of the direction of the molecular rotational angular momentum. By contrast, in the helicity frame depolarization is much more pronounced. The oscillatory structure present in the rotationally inelastic differential cross section does not appear to be quenched by the interference between various m → m′ transitions.     

Collision dynamics of excited NaK. I. Reactive KNaK and elastic HeNaK collisions

The collision dynamics of excited NaK have been studied using the technique of circularly polarised laser fluorescence. A very unusual m-dependent rate is observed for KNaK* reactive or quenching collisions which is different depending on whether the initial excitation is via Q or P, R transitions. A model is presented attributing this to the spatial distribution of the ¹Π Λ-doublet components and the influence of the nuclear function. Elastic HeNaK collisions are observed and a reorientation cross section for f = 30 was evaluated. This was found to have an upper limit of 0.3 Ų. Comparison of this with HeLi₂ reorientation cross sections indicate that the presence of a permanent dipole moment has little effect on the reorientation rate in rare gas-alkali dimer collisions.     

Quantum mechanical calculations for the H2O + hnu --> O(1D) + H2 photodissociation process

Quantum mechanical wavepacket calculations for the photodissociation of water in the second absorption band are presented. Using O + H2 Jacobi coordinates, partial cross sections for the O(1D) + H2 channel are calculated for different initial rotational states. Conical intersection and Renner-Teller effects are included. The branching ratios for the four accessible dissociation channels at 121.6 nm are in good agreement with experiment (J. Chem. Phys. 1982, 77, 2432). The calculations predict significant rotational and vibrational excitation of the H2 fragments. Photodissociation of ortho and para water produces predominantly, but not exclusively, ortho and para H2 fragments, respectively.