Quantum dynamics of dissociative adsorption of H2 and D2: The time-dependent wave packet method

A time-dependent quantum wave packet method was used to study the dynamics of dissociative adsorption of H₂ and D₂ on a flat and static surface. The molecule-surface interaction is described using a modified London-Eyring-Polanyi-Sato (LEPS) type potential for the H₂/Ni(100) system. The three-dimensional (3-D) dissociation probabilities were calculated for different initial rovibrational states as a function of initial incident energies. Our results show that the dissociation of the diatomic rotational states whose quantum numbers satisfyj+m = odd is forbidden at low energies for the homonuclear H_z and D₂ due to the selection rule. The effect of the rotational orientation of diatoms on adsorption predicts that the in-plane rotation (m = j) is more favorable for dissociation than the out-of-plane rotation (m = 0). Enhanced dissociation for vibrationally excited molecules and the significant enhancement of the dissociation probability of H2 when compared to D₂ were explained reasonably in terms of quantum mechanical zero-point energies, the tunneling effect and the reflection from an activation barrier. Project supported by the National Natural Science Foundation of China (Grant No. 19694033) and partially by the Science Foundation for Overseas Chinese Scholars and Students, administered by the State Education Commission of China (Grant No. 1992), by the State Key Laboratory of Theoretical and Computational Chemistry of Jilin University at Changchun (Grant No. 98011, and by the Natural Science Foundation of Shandong Province (Grant No. Y96B03022)     

On m-changes in atom-rigid-rotor collissions: influence of an initial rotation

Reorientation of the angular momentum of a diatomic molecule in collisions with atoms is investigated using classical mechanics. A factorisation formula for cross sections for rotational excitation is given. The factorisation allows the calculation of the state-specific cross section d σ (j′ m′ ← jm)/dΩ once the m-averaged cross sections d σ (j″← 0 )/dΩ for all possible j″ are known. The approach is applied to the Na₂-He system.     

Comparison of classical mechanics and the coupled states approximation for Li+-CO scattering on an ab initio calculated CI potential energy surface

The dynamics of rotational excitation on an ab initio calculated CI rigid rotor potential energy surface for Li⁺-CO are investigated using classical mechanics and the quantum mechanical coupled-states (CS) approximation. Transition probabilities out of the j = 0 initial level are calculated for various impact parameters between b = 0 and 40a_o for 1 eV collisions. The classical results agree well with the average of Δj-even and Δj-odd quantum transition probabilities except for a few lower impact parameters where CS seems to underestimate the large Δ transitions. No propensity rule is observed for the preference of the Δj-even versus Δj-odd transitions as might have been expected.     

Semiclassical treatment of ro-vibrational relaxation in the large j limit. Application to CO + 4He collisions

A semiclassical model for the vibrational relaxation of a diatomic molecule in collision with an atom is presented in the coupled-state framework in the large j limit. Our model realizes an exact quantum resolution of the rotational dynamics, the vibrational dynamics being integrated within a first-order perturbational perturbed-stationary-state approach. The application to CO + ⁴He confirms an appreciable role of the rotational energy transfers which produce an increase of the rate constant by a factor of ≈ 2.5.     

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.     

Distorted-wave calculations for the three dimensional chemical reaction H + H2(v ⩽ 2, j = 0) → H2(v′ ⩽ 2, j′, mj) + H

Calculations of the vibrational—rotational product state population distributions and differential cross sections for the chemical reaction H + H₂(v ? 2, j = 0) → H₂(v′ ? 2, j′, m_j) + H have been carried out on the Porter—Karplus potential energy surface. The vibrationally-adiabatic-distorted-wave (VADW) method has been used. The relative rotational product distributions, differential cross sections and the helicity m_j, dependences of these quantities for the v = 0 reaction agree well with accurate close-coupling results. The absolute integral cross sections are considerably smaller than the accurate quantum values, however. The calculations for the v = 1 reaction agree with the findings of previous sudden quantum, limited close-coupling and quasiclassical theoretical studies and experiments that product H₂(v′ = 1) is more likely to be produced than H₂(v′ = 0). For the reaction with v = 2, it is found that at high translational energies product H₂(v′ = 2) is favoured over H₂(v′ = 1) or H₂(v′ = 0). The VADW differential cross sections for the v = 1 and v = 2 reactions have a similar shape to those of the v = 0 reaction, with backward peaking when summed over all m_j states. The relative rotational distributions for the v = 2, j = 0 → v′ = 2, j and v = 1, j = 0 → v′ = 1, j reactions are also similar to those obtained for the v = 0, j = 0 → v′ = 0, j reaction, with low rotational excitation.     

Dynamical tunneling through a chaotic region

It is shown that a non-vibrating diatomic molecule (i.e. a rigid rotor) in the presence of a strong laser field changes its hindered rotational motion (which on the average is in resonance with the oscillating time dependent field) from anti-clockwise to clockwise (hindered) rotational motion. This transition is classically forbidden and is another example of a quantum mechanical tunneling phenomenon occurring due to the time-reversal symmetry of the Hamiltonian. Classically, the two stable rotational modes are separated by an extended chaotic region in phase space. The Husimi representation of the quasienergy states of the time-periodic quantum system enables us to localize wave packets inside the classical stability islands. The effect of the field and the molecular parameters on the perioid of this oscillation is obtained from the quasienergy splittings without the need to carry out long time dependent computations. An analytical analysis of the dynamical tunneling using an extended version of the (t,t) formalism recently developed (J. Chem. Phys.99, 4590 (1993)) is in remarkable agreement with the numerical results.Member of the Minerva center of non-linear physics of complex systems at the Technion     

Close-coupling elastic and inelastic integral and differential cross sections for Li+ + H2 collisions

The quantum mechanical close-coupling formalism is applied to the study of elastic and rotationally inelastic Li⁺ + H₂ collisions making use of the Kutzelnigg-Staemmler-Hoheisel potential energy surface. Integral and differential cross sections for j = 0 → 0 and j = 0 → 2 are obtained in the collision energy range 0.2 to 0.9 eV and for j = 1 → 1 and j = 1 → 3 at 0.6 eV. A rainbow structure is observed in both the elastic and inelastic angular distributions and a quenching of the fast oscillations is found in the cross sections for j = 1 initially compared to the case j = 0 initially. At 0.6 eV. the calculated quantum mechanical angular distributions are compared to those from a classical trajectory calculation using the same surface and to the experimental ones. The dynamics of rotational excitation in the Li⁺ + H₂ system is contrasted to rotational excitation in systems for which the atom-diatom interaction is predominantly repulsive.     

Classical trajectory study of rotationally inelastic scattering of two HF molecules

Classical trajectory calculations of the partial opacities and integral cross sections for rotationally inelastic collisions of HF—HF were carried out for the j₁ = 0,j₂ = 0 → (11), (02), (22) transitions at initial relative translational energies of 500, 1000, and 8000 cm^?1 and for the (11) → (02) transition at 1000 cm^?1. Three different methods of relating the initial and final quantum rotational levels to classical distributions were used. The results were compared to the quantum calculations of DePristo and Alexander. It was found that the classical method using a random distribution of initial rotational energies was in poor agreement with the quantum results, while the other two methods which assigned definite classical energies to the quantum levels were in good agreement with the quantum results.     

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.     

Classical and quantum mechanics of diatomic molecules in tilted fields

We investigate the classical and quantum mechanics of diatomic molecules in noncollinear (tilted) static electric and nonresonant linearly polarized laser fields. The classical diatomic in tilted fields is a nonintegrable system, and we study the phase space structure for physically relevant parameter regimes for the molecule KCl. While exhibiting low-energy (pendular) and high-energy (free-rotor) integrable limits, the rotor in tilted fields shows chaotic dynamics at intermediate energies, and the degree of classical chaos can be tuned by changing the tilt angle. We examine the quantum mechanics of rotors in tilted fields. Energy-level correlation diagrams are computed, and the presence of avoided crossings quantified by the study of nearest-neighbor spacing distributions as a function of energy and tilting angle. Finally, we examine the influence of classical periodic orbits on rotor wave functions. Many wave functions in the tilted field case are found to be highly nonseparable in spherical polar coordinates. Localization of wave functions in the vicinity of classical periodic orbits, both stable and unstable, is observed for many states.     

Sudden approximation relations between tensorial cross sections for the collision of two diatomic molecules

We demonstrate relations between tensorial cross sections for the collision between two diatomic molecules, one of which does not rotate during the collision. The demonstration relies on a factorisation of the S matrix. A numerical example is presented for the rotational excitation problem of CO by H₂ (j = 1) molecules     

Experimental determination of the mj distribution in inelastic scattering of Na2 by He

The orientational distribution of Na₂ molecules scatterd by He has been determined in a molecules beam experiment. At large angle scattering where inelastic collisions are dominant, a high degree of alignment has been observed. This alignment depends strongly on the rotational quantum number J after scattering. The J dependence can be explained by assuming that during collisions m_j is conserved when the quantization axis is chosen parallel with the geometric apse.     

Photophysics and photochemical dynamics of methylanisole molecules in a supersonic jet

The fluorescence excitation, dispersed fluorescence and hole burning spectra, and fluorescence lifetimes of jet-cooled o-, m-, and p-methylanisoles (MA) were measured. The low-frequency ring methyl internal rotational bands observed for their S₀ and S₁ states were assigned. In the case of m-MA, the rotational isomers of cis and trans conformers, which arise from the orientation of the OCH₃ group with respect to the CH₃ group, were assigned by hole-burning spectroscopy. The observed level energies and relative intensities of the methyl internal rotation were reproduced by a calculation using a free rotor basis set. Furthermore, their potentials in the S₀ and the S₁ states were determined. The potential barrier heights for the S₀ states of m- and p-MA were quite low, suggesting that the methyl groups are freely rotating, while changing from S₀ to S₁ states, the potential barrier height increases. The potential barrier heights of o-MA drastically decreased in going from S₀ to S₁ states. The decrease would be due to the hydrogen bonding between O atom and one H atom of the methyl group. The torsional bands of the methoxy group (–OCH₃) were also observed for p- and o-MA. The –OCH₃ modes are found to couple with the level of the e species for the methyl internal rotation.Fluorescence lifetimes (τ_f) of the methyl internal rotational bands in the S₁ states of o-, m-, and p-MA were measured in order to investigate the photochemical dynamics. The values of the nonradiative rate constant (k_nr) were estimated from the τ_f values and Franck–Condon factors. The k_nr values drastically increased with the excitation of methyl internal rotation. Accordingly, the methyl internal rotation should enhance the nonradiative process, presumably intersystem crossing (ISC). The enhancement should be caused by the increase of the state density (ρ) effectively coupled with triplet manifolds. The drastic increase in the ρ value should be caused by level mixing. In addition, the methyl internal rotational motion may enhance the increase of the coupling matrix elements through the vibronic coupling between the excited singlet states. The remarkable rotational quantum species dependence on the ISC rate constant (k_ISC) value clearly appeared in m-MA. The dependence should result from the difference of the ρ value between a₁ and e species, since the e species are doubly degenerate. The species dependence was apparently related to the potential barrier height, suggesting that the large barrier height should have an influence on the ρ value of the triplet states.     

Measurements of the hyperfine dimer spectrum for H2-Ne,H2-Ar,H2-Kr by the magnetic beam renosance technique

Measurements are performed on ortho H₂(I = 1, j = 1, vibrational ground state)-X dimers with X = Ne, Ar, Kr; the dimers H₂-X occur in their van der Waals stretch ground state. The dimer end-over-end rotational states (quantum number L) are investigated for L ?2. The rf hyperfine-transition frequencies are measured, 30 ? v ? 600 kHz. Combining our results with scattering data from the Göttingen group, for H₂Ne the full potential could be described with high accuracy. For the other systems, a simple molecular parameter is derived pertaining to the dimer system. As our spectroscopy mainly permits a sensitive probing of the well region, new scattering data are needed to determine accurate model potentials over the full range.     

Dynamically based fitting law for thermal rate coefficients in rotational relaxation

An earlier analytical, approximative result for the semi-classical, sudden limit of energy dependent j_o → j cross sections of rotational relaxation of homonuclear, diatomic molecules perturbed by an atom has been integrated to obtain dynamical fitting of temperature dependent rate coefficients. The result can be written by using two parameters, k_jjo = [(2j + 1)/(2j_o + 1)] ^1/2a (lj - 1]^?1 ? b), where the parameters a and b are given from the assumed intermolecular potential, The reduced mass for the collisions and the temperature. A comparison with several experimental results proves the validity of the above expression and gives some statements about the intermolecular potentials for the systems considered.     

Absolute quantum yield measurements for the formation of oxygen atoms after UV laser excitation of SO2 at 222-4 nm

The dynamics of formation of oxygen atoms after UV photoexcitation of SO₂ in the gas-phase was studied by pulsed laser photolysis-laser-inducedfluorescence ‘pump-and-probe’ technique in a flow reactor. SO₂ at room-temperature was excited at the KrCl excimer laser wavelength (222.4 nm) and O(³P_j) photofragments were detected under collision-free conditions by vacuum ultraviolet laser-induced fluorescence. The use of narrow-band probe laser radiation, generated viaresonant third-order sum-difference frequency conversion of dye laser radiation in Krypton, allowed the measurement of the nascent O(³P_j=2,1,0) fine-structure state distribution:n _j=2/n_j=1/n_j=0 = (0.88 ± 0.02)/(0.10 ± 0.01)/(0.02 ± 0.01). Employing NO₂photolysis as a reference, a value of Φ₀(³P) = 0.13 ± 0.05 for the absolute O(³P) atom quantum yield was determined. The measured O(³P) quantum yield is compared with the results of earlier fluorescence quantum yield measurements. A suitable mechanism is suggested in which the dissociation proceeds via internal conversion from high rotational states of the initially excited SO₂(~C¹B₂ (1, 2, 2) vibronic level to nearby continuum states of the electronic ground state.     

Theory and spectroscopy of an incarcerated quantum rotor: The infrared spectroscopy,inelastic neutron scattering and nuclear magnetic resonance of H2@C60 at cryogenic temperature

The supramolecular complex, H₂@C₆₀, represents a model of a quantum rotor in a nearly spherical box. In providing a real example of a quantum particle entrapped in a small space, the system cuts to the heart of many important and fundamental quantum mechanical issues. This review compares the predictions of theory of the quantum behaviour of H₂ incarcerated in C₆₀ with the results of infrared spectroscopy, inelastic neutron scattering and nuclear magnetic resonance. For H₂@C₆₀, each of these methods supports the quantization of translational motion of H₂ and the coupling of the translational motion with rotational motion and provides insights to the factors leading to breaking of the degeneracies of states expected for a purely spherical potential. Infrared spectroscopy and inelastic neutron scattering experiments at cryogenic temperatures provide direct evidence of a profound quantum mechanical feature of H₂ predicted by Heisenberg based on the Pauli principle: the existence of two nuclear spin isomers, a nuclear spin singlet (para-H₂) and a nuclear triplet (ortho-H₂). Nuclear magnetic resonance is capable of probing the local lattice environment of H₂@C₆₀ through analysis of the H₂ motional effects on the ortho-H₂ spin dynamics (para-H₂, the nuclear singlet state, is NMR silent). In this review we will show how the information obtained by three different forms of spectroscopy join together with quantum theory to create a complementary and consistent picture which strikingly shows the intrinsically quantum nature of H₂@C₆₀.     

The phase modulated semiclassical sudden approximation. Study of the transitions υ = 1, j → υ = 0 j′ in the pH2 + He4 system

A modified version of the semiclassical sudden approximation is presented. The expressions retain the attractive simplicity of the original sudden theory approximations but they take into account, due to a phase modulation, the adiabaticity modifications which are produced by the transitions between the rotational states. The comparison between the calculated total ro-vibrational and the close coupling cross sections for the couple pH₂ + He ⁴ gives satisfactory agreement. The influence of the non rigidity of the rotator and the role of the intramolecular anharmonicity are studied. The strong influenced of the υ = 2 state on the one quantum transitions (υ = 1, j) → (υ = 0, j′) can also be seen.