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.     

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.     

Cross sections and rate constants for the vibrational relaxation of D2 (υ = 1,j = 0) in collisions with 4He

Fully converged quantum cross sections for ⁴He—D² (υ = 1,j = 0) vibrational relaxation were determined using the coupled-states method and a modified version of the Gordon—Secrest surface. First-order forbidden rotational transitions play a significant role, comparable to that observed previously for the He—H₂ system. At 60 K the υ = 1,j = 0 level of D₂ is predicted to relax ≈4 times slower than the corresponding level of H₂. This difference decreases with increasing temperature.     

Applications of an adiabatic rotational model to the Ar…O2 van der Waals molecule

In this paper a separation of vibrational and rotational motions is applied to describe the metastable levels of the ArO₂ van der Waals molecule. The potential energy surface is written as a sum of atom—atom pairwise Morse functions, the parameters being obtained by fitting the potential of Pirani and Vecchiocattivi at the equilibrium configuration. The results agree fairly well with experimental data about infrared absorption, assuming a J = 2 → 1 transition, where J is the quantum number associated to the total angular momentum of the complex. Also, close coupling three-dimensional calculations about the ArO₂ collision show a good agreement with some energies previously calculated. The widths for rotational predissociation have been estimated by this procedure to be of the order of 1 cm^?1.     

N-lines and chromium-pairs in the luminescence spectra of the spinels ZnAl2O4:Cr3+ and MgAl2O4:Cr3+

It is shown that the N-lines in the luminescence spectra of the two spinels ZnAl₂O₄:Cr³⁺ and MgAl₂O₄:Cr³⁺ exhibit quite similar dependencies on chromium concentration, excitation frequency, and thermal treatment of the samples. While most of these lines are structure dependent, the line N₄ at $\text{ν}{}_{\mathrm{R}}\text{?}\text{ν}\text{≈ 400}\text{cm}{}^{\mathrm{?1}}$ and two very weak lines are in both cases due to chromium-pairs. The exchange Hamiltonian H_ex = JS₁ · S₂ + j(S₁ · S₂)² used for the ground-state splitting is fitted by the parameters J = 40.9 cm^?1, j = 1.5 cm^?1 and J = 45.6 cm^?1, j = 2.0 cm^?1 for ZnAl-spinel and MgAl-spinel, respectively. The differences between the spectra of low-doped and high-doped samples are in both cases caused by the existence of a phonon sideband of the N₄-line, which is in many respects similar to the well-known phonon side band of the R-line.     

Wave packet and quasiclassical trajectory calculations for the N(D) + H2 reaction and its isotopic variants

The N(²D) + H₂(v = 0, j = 0) reaction and its HD and D₂ isotopic variants have been studied by means of quantum mechanical real wave packet and wave packet with split operator and quasiclassical trajectory methodologies on the potential energy surface of Ho et al. [J. Chem. Phys. 119 (2003) 6]. Total initial state-selected and final state-resolved reaction probabilities and product rotational distributions have been calculated for total angular momentum J = 0 in a broad range of collision energies. The real wave packet results are in very good agreement with the corresponding split operator wave packet calculations. A reasonable overall good agreement has been found between the wave packet and quasiclassical trajectory results. Integral cross-sections and thermal rate constants have been calculated from the wave packet reaction probabilities by means of standard J-shifting, refined J-shifting and uniform J-shifting methods in combination with the centrifugal sudden approximation for J > 0. Comparisons with available exact wave packet, quasiclassical trajectory and experimental results are made and discussed.     

Transfer of state multipoles in excited A 1Σ+u7Li2 following rotationally inelastic collisions with He: Experiment and theory

Circularly polarized dye laser radiation is used to prepare rotational levels j = 1 to j = 20 of the A ¹Σ⁺_u excited state of ⁷Li₂ with well defined values of the state multipoles K = 0, 1 and 2. Inelastic collisions with helium atoms populate other j levels and we have measured the circular polarisation ratio of emission, C, from these levels. C is plotted versus final j′ for each value of Δj from +2 to +18 and a family of curves is obtained which may be used as a critical test of current theories. The results are interpreted in terms of cross sections σ^K for transfer of the state multipoles under isotropic collision conditions. The observation of substantial polarisation following inelastic collision indicates that the σ^K are dominated by certain restricted scattering channels. Relative magnitudes of the multipole cross sections are calculated using the “l-dominant”, “restricted Δm_j channels” nd the Born approximation. These cross sections are then used to calculate C.     

Resonance-enhanced multiphoton ionization of molecular hydrogen via the E,F1Σg+ state: Photoelectron energy and angular distributions

Photoelectron energy and angular distributions are measured for the 2+1 multiphoton ionization process H₂ X¹Σ_g⁺ (ν = 0,J) + 2hv → E,F¹Σ_g⁺(ν_E,J_E = J) + hν → H₂⁺X²Σ_g⁺ (ν⁺) + e^?, for ν_E = 0, 1, or 2 and for J_E = 0 or 1 of the inner well of the double-minimum E,F state. Although a strong preference is found for ν⁺ = ν_E, the detailed H₂⁺ vibrational distribution does not exhibit Franck-Condon behavior, and the photoelectron angular distributions vary markedly with both the J_E value of the intermediate state and the ν⁺ value of the ion.     

Rotationally resolved (3 + 1) rempi of H 2 via the B1Σ+u state

In the paper, we compare the results of our ab initio calculations for the ro-vibrational branching ratios resulting from a (3+1) REMPI of H₂ via the B¹Σ⁺_u state with the experimental data of Pratt, Poliakoff, Dehmer and Dehmer. These results indicate that non-Franck-Condon effects are less important here than in the (3+1) REMPI of H₂ via the C¹Π_u state. We observe that the ΔJ = ±3 peaks in the photoelectron spectrum are of negligible strength and that the ratio of ΔJ = +1 to ΔJ = −1 peak is independent of the ionic vibrational state. A detailed analysis indicates that these features arise as a result of a dynamic interference between the do and dμ ionization channels and do not imply either the smallness of the d-wave or the smallness of the j_t = 3 angular momentum coupling terms.     

Measurement of state-to-state rotational transfer rates in collision of I2*(B 0u+, υ = 15, j) with 3He, 4He,Ne, Ar,H2, D2 and I2

The selective laser excitation and induced fluorescence observation technique has been used to study rotationally inelastic collisions of I₂^*(B 0_u⁺, υ = 15,j) with I₂, ³He, ⁴He, Ne, Ar, H₂ and D₂. For each collision partner, several initial rotational levels ranging from j_i = 12 up to j_i = 146 have been excited. For purely rotational transfer within the υ = 15 level, our data are perfectly consistent with energy sudden (eventually corrected) scaling laws. Thus, any thermally averaged rate constant, k(j_i → j_f), can be expressed as a function of the basis rate constants k(l → 0). Furthermore, these k(l → 0) are found to follow simple empirical fitting laws. Consequently any k(j_i → j_f) can be predicted given a set of two or three fitting parameters. Collisions with relatively heavy particles (I₂, Ar and Ne) are well described by using the inverse power fitting law k(l → 0) = b[l(l+1)]^?γ, where b = 1.7, 1.2 and 1.2×10^?10 cm³ s^?1 and γ = 1.08, 1.02 and 1.17 for I₂^*-Ne, I₂^*-Ar and I₂^*-I₂ collisions respectively. For collisions with light particles (³He, ⁴He, H₂ and D₂), k(l → 0) shows a sharp decrease with l which can be accounted for by a hybrid power-exponential fitting law k(l → 0) = b[l(l+1)]^?γ exp[-l(l+1)/l^* (l^*+1)], where b = 0.84, 0.71, 2.77 and 2.78×10^?10 cm³ s^?1l⁺ = 20.6, 23.1, 18.8 and 31.4, and γ = 0.66, 0.66, 0.78 and 0.91 for I₂^*-³He, I₂^*-He, I₂^*-H₂ and I₂^*-D₂ collisions, respectively. We confirm that the rotational transfer dynamics in heavy molecules is mainly governed by angular momentum exchange.     

Resonance in the rotational dependence of the isotope-selective reaction between IiCl(A 3Π1) and acetylene

The rotational dependence of the isotope selective reaction between IⁱCl(A ³Π_l, υ′, J′) and acetylene (C₂H₂, C₂D₂) forming the photoaddition product 1,2-iodo-chloro-ethyene was studied for ν′ = 19 and ν′ = 20. The enrichment factor in the photoproduct shows resonances for J′ = 32, ν′ = 19 and J′ = 6, υ′ = 20.     

Quantum wave packet and quasiclassical trajectory studies of the reaction H(2S) + CH(X2Π; v = 0, j = 1) → C(1D) + H2(X1 ): Coriolis coupling effects and stereodynamics

The quantum mechanics (QM) and quasiclassical trajectory (QCT) calculations have been carried out for the title reaction with the ground minimal allowed rotational state of CH (j = 1) on the 1 ¹A′ potential energy surface. For the reaction probability at total angular momentum J = 0, a similar trend of the QM and QCT calculations is observed, and the QM results are larger than the latter almost in the whole considered energy range (0.1–1.5 eV). The QCT integral cross sections are larger than the QM results with centrifugal sudden approximation, while smaller than those from QM method including Coriolis coupling for collision energies bigger than 0.25 eV. The quantum wave‐packet computations show that the Coriolis coupling effects get more and more pronounced with increasing of J. In addition to the scalar properties, the stereodynamical properties, such as the average rotational alignment factor <P₂( j′?k )>, the angular distributions P(θ_r), P(?_r), P(θ_r,?_r), and the polarization‐dependent generalized differential cross sections have been explored in detail by QCT approach. © 2013 Wiley Periodicals, Inc.     

On a simple reaction mechanism for the collision-induced dissociation He + Li2(B1Πu) → He + Li(2 2S) + Li(2 2P)

A simple reaction mechanism is suggested for the dissociation of electronically excited Li₂(B¹Π_u) in collision with rare-gas atoms. Experimental rate constants for dissociation of Li₂ in specific vibrational—rotational levels (ν1J) show an unexpected behaviour as a function of the initial molecular energy and angular momentum. We propose that raction proceeds by a transition to the ¹Π_g state of Li₂. This may dissociate more readily since it is more weakly bound and has a larger equilibrium distance than the ¹Π_u state.     

A quantum algorithm for spin chemistry: a Bayesian exchange coupling parameter calculator with broken-symmetry wave functions

The Heisenberg exchange coupling parameter J (H = −2JS_i · S_j) characterises the isotropic magnetic interaction between unpaired electrons, and it is one of the most important spin Hamiltonian parameters of multi-spin open shell systems. The J value is related to the energy difference between high-spin and low-spin states, and thus computing the energies of individual spin states are necessary to obtain the J values from quantum chemical calculations. Here, we propose a quantum algorithm, B̲ayesian ex̲change coupling parameter calculator with b̲roken-symmetry wave functions (BxB), which is capable of computing the J value directly, without calculating the energies of individual spin states. The BxB algorithm is composed of the quantum simulations of the time evolution of a broken-symmetry wave function under the Hamiltonian with an additional term jS², the wave function overlap estimation with the SWAP test, and Bayesian optimisation of the parameter j. Numerical quantum circuit simulations for H₂ under a covalent bond dissociation, C, O, Si, NH, OH⁺, CH₂, NF, O₂, and triple bond dissociated N₂ molecule revealed that the BxB can compute the J value within 1 kcal mol⁻¹ of errors with less computational costs than conventional quantum phase estimation-based approaches.

A quantum algorithm “Bayesian exchange coupling parameter calculator with broken-symmetry wave function (BxB)” enables us to calculate Heisenberg exchange coupling parameter J without inspecting total energies of individual spin states, within 1 kcal mol⁻¹ of energy tolerance.     

Exact relation between the spectrum and the eigenfunctions of a generalized Jahn-Teller hamiltonian for different parameter values

A generalized E ? ? Jahn-Teller hamiltonian with a parameter δ (δ = ?1/4 in the JT case) is studied. As in the Jahn-Teller case, the angular momentum is a constant of the motion with the eigenvaluesj + 1/2 where j is a non-negative integer. For j fixed, consider two values δ₁ = ?j/2 ?1/2 and δ₂ = ?gd₁ ?1/2. The spectrum and the eigenfunctions for δ₂ are completely determined by the spectrum and the eigenfunctions for δ₁.     

Collision rotational transfers in NaH A1Σ+ by He,Ar or H2 (and in KH A1Σ+ by H2)

The total and relative rotational transfer cross sections σ_total and σ_Ji-Jf, by collisions of NaH A¹Σ with He, Ar or H₂, are measured from υ′ = 4 and υ′ = 11, J₁′ = 6. The σ_total increase as υ′ increases. They are similar for He and H₂ but much greater for Ar especially at large υ′. In NaH A¹Σ⁺ the bond goes from covalent to ionic as υ′ increases: σ_total is very sensitive to an attractive potential due to the interaction of the permanent electric dipole moment of the molecule with the polarizability of the atom (α_Ar = 11 au, α_He = 1.37 au). The σ_Ji-Jf decrease monotonously as |J_f-J_i| increases and may be fitted by a scaling law. The variation with ΔJ depends on the colliding gas but does not change appreciably with υ′: most of the transfers could take place on the repulsive part of the interaction potential, the shape of which would not depend on υ′.     

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.     

A new energy level of the neutral tantalum atom

Investigating the hyperfine structure (hfs) of the not yet classified line λ=4160.99 Å we succeeded in the determination of the electronic angular momenta of the combining levels and in the identification of the lower level using the hfs constants of all known levels as a finger-print card-index. In this way the lower level turned out to be thea ² G _9/2 level, which has even parity. Using the energy of this level and the wavenumber of the transition it was possible to determine the energy of the (odd parity) upper level to 34716.23 ± 0.02 cm^?1. The total angular momentum quantum number amounts toJ=11/2. Additionally, it was possible to identify the line λ=3436.00 Å as a further combination with this new level.     

Elastic and inelastic angular distributions in the jz-conserving coupled states approximation for molecular collisions

An approximation scheme is described which allows the decoupling of molecular rotational j and l angular momenta in molecular collisions. With a particular choice of the interaction potential, the potential matrix couples only the molecular states of the system and in particular those in which the z-axis projection of j is conserved. Test calculations on He + H₂ for the elastic j = O → O and rotationally inelastic j = O → 2 differential cross sections are presented in the energy range 0.1 to 0.9 eV. These results are compared with the full coupled-channel cross sections and are found to be extremely accurate.