Muon transfer from the excited mesic hydrogen in the metastable 2s-state to helium nuclei

The rate of the molecular charge exchange of the excited muonic hydrogen in the 2s-state on helium nuclei is calculated. Resonance muon transfer is shown to occur with the formation of the intermediate excited complex ([(H μ)*He²⁺]2e)*. The resulting rates prove that the muon transfer from the 2s-state alone can not account for the experimental data on the muon transfer frompμ-atoms to⁴He nuclei.     

Theoretical investigation of the low-lying electronic states of the alkaline hydride BeH2+ ion: Potential energy curves, spectroscopic constants, vibrational levels, and transition dipole functions

The structure and spectroscopic properties of the alkaline hydride BeH²⁺ ion have been investigated using an ab initio approach based on nonempirical pseudopotentials and parameterized l-dependent polarization potentials. The adiabatic potential energy curves and their spectroscopic constants for the ground and seventeen excited electronic states, dissociating into Be⁺(2s, 2p, 3s, 3p, 3d, 4s, 4p, and 4d) + H⁺ and Be²⁺ + H(1s and n = 2), of ²??⁺, ²??, and ²?? symmetries have been determined. As no experimental data are available, our results are discussed and compared with the few existing theoretical calculations. A very good agreement has been found with the previous theoretical data for the ground state; however many potential energy curves for the higher excited states are presented here, for the first time. Numerous avoided crossings between electronic states for ²??⁺ and ²?? symmetries have been localized and analyzed. Their existence is related to the interaction between the electronic states and to the charge transfer process between the two ionic systems Be²⁺H and Be⁺H⁺. In addition, we have calculated the vibrational energy level spacings of the bound electronic states. Furthermore, the adiabatic transition dipole functions from the X ²??⁺ and 2²??⁺ states to the higher excited states of ²??⁺ and ²?? symmetries have been evaluated and compared with the available theoretical work. This study represents the necessary initial step towards the investigation of the charge transfer processes in collision between Be⁺-H⁺ and Be²⁺-H.     

Rotational 1 → 0 transitions in muonic helium-hydrogen molecular ions due to external Auger process

Rotational J = 1 → J = 0 transitions in (Heμh)_J muonic molecular ions (where He and h are helium and hydrogen isotopes, respectively), induced by external Auger process in collision with hydrogen isotope atoms are considered. The obtained reaction rates, normalized to liquid hydrogen density, range between 3.4 · 10¹¹ s^-1 and 11.2 · 10¹¹ s^-1 for different isotope combinations. Rotational state populations of Heμh in hydrogen isotope-helium mixtures are also calculated.     

Theoretical study of hydrated Be2+ ions

Hydrated Be²⁺ ions [Be(H₂O)_n]²⁺, n = 1−4 and 6, were examined theoretically. The structure of the hydrated ions was determined and the hydration energy estimated with and without electron correlation. The bond between the Be²⁺ ion and the oxygen of water is very strong and has the nature of a dative bond. The non-additivity of the binding energy is so profound that without taking it into account the structure and dynamics of Be²⁺ ions cannot be explained. The hydration number in water is found to be 4. The fifth and sixth water molecules prefer forming the second coordination shell to the Be²⁺ ion. The result is in agreement with X-ray analysis of the aqueous solution, but not with a recent molecular dynamics simulation. In addition, the harmonic vibrational frequencies for the complexes are evaluated and compared with some experiments.     

Treatment of Be+ ( 1 s? 1)2S Auger resonance with different decouplings of the dilated electron propagator

The diagonal 2ph-TDA and quasiparticle decouplings of the dilated electron propagator (based on an underlying bi-variational SCF) are utilized to calculate energy and width of the Be⁺(1_s ⁻¹)²S Auger resonance for the first time. Comparison with experimental and other theoretical results reveals that the renormalized infinite order diagonal 2ph-TDA decoupling seems to offer a less balanced approach to the treatment of resonances than the second-order decoupling. The diagonal quasiparticle approximation to the self energy is seen to offer an effective and economic alternative to the non-diagonal propagator calculations.     

Charge transfer and curve crossings in the [BeH2O]2+ system

Summary Diabatic and adiabatic potential energy curves have been determined for the complexation of beryllium cation with a water molecule, by means of multi-reference perturbation CI. The quasi-diabatic states correspond to Be²⁺H₂O and to nine charge transfer states (Be⁺H₂O⁺): at short beryllium-water distances the ground state is essentially Be²⁺H₂O, but at large distances several charge transfer states have lower energies. The nature of the curve crossings of the ground and lowest excited states in the [BeH₂O]²⁺ system is clarified. The changes brought about by the presence of a second water molecule are investigated.     

Calculation of the ground‐state energy and studies of other properties of exotic helium atoms with the use of boundary conditions of wave function

The minimum energy and average distance between particles of doubly muonic helium atoms Heμμ (He²⁺ + 2μ ), are calculated with the use of a wave function that satisfies boundary conditions such as the behavior of the wave function when two particles are close to each other or far away from each other. In this wave function, the muon–muon correlation in doubly muonic helium atoms is described to arrive at the correct behavior for r₁₂ tending to zero and infinity. It is shown that the obtained results are very close to the values calculated by others. Finally, to confirm the method and results, calculated values are compared with a similar electronic system, and it is shown that the small differences in the energies of Heμμ and He are due to the reduced masses, as expected. In addition to being very simple, the proposed wave function provides relatively accurate values for the energy and expectation values of r²ⁿ, emphasizing the importance of the local properties of the wave functions. © 2004 Wiley Periodicals, Inc. Int J Quantum Chem, 2005     

Decay modes of muonic lithium-hydrogen molecules

Radiative, Auger and predissociation decay modes of muonic lithium-hydrogen molecule, Liμh, (h = p, d or t is a hydrogen isotope) are considered. Results obtained for the corresponding reaction rates indicate that predissociation is a dominating decay mode for h = p, d while Auger decay dominates for h = t. The calculated conversion coefficient is significantly larger than that for helium muonic molecule and ranges between 37 and 42 (on the basis of one electron) depending on isotope composition of the molecule. Reaction rates for rotational 1 → 0 transitions in Liμh and Heμh due to inner Auger process are also calculated.     

CO inner-shell excitation studied by electron impact spectroscopy

The inner-shell excitation and decay of the CO molecule have been studied in electron impact experiments. The dipole-forbidden transition (1sσ_c)⁻¹(2pπ) ³Π has been characterized by angular resolved electron energy loss spectroscopy and its decay via the measurement of resonant Auger spectra. The contribution of the (1sσ_c)⁻¹(2pπ) ³Π state to the CO resonant Auger spectrum in the region of the “spectator transitions” has been isolated and the population of CO⁺ quartet final states has been observed.     

Vibrational relaxation of HF(υ = 3,4)

The vibrational relaxation of pure HF(υ = 3 and υ = 4) has been studied by pumping HF directly from υ = 0 to υ = 4. The relaxation rates of υ = 3 and υ = 4 were determined to be k³_T = (2.8 ± 0.4) × 10^?11 cm³ molecule^?1 s^?1 and k⁴_T = (7.2. ± 0.5) × 10^?11 cm³ molecule^?1 s^?1 at 293 K. It is shown that sigle quantum energy transfer can account for all the vibrational relaxation.     

On the metal ion selectivity of PNP-lariat ether—an insight from density functional theory calculations

The complexes of Li⁺, Na⁺, K⁺, Be²⁺, Mg²⁺, and Ca²⁺ metal cations with [N₃P₃R₄O(CH₂CH₂O)₄] (R?=?H(1), NMe₂(2), NC(NMe₂)₂(3)) PNP-lariat ethers were systematically studied in the gas phase by using density functional theory (DFT) B3LYP-D3/6-311+G(3df,2p)//B3LYP/6-31+G(d,p) method. The gas phase cation affinities were calculated to span the wide range between 64.2 and 496.1 kcal mol^?1 in order K⁺?<?Na⁺?<?Li⁺?<?Ca²⁺?<?Mg²⁺?<?Be²⁺. The structural and electronic properties of 1–3 and their complexes were investigated and effects of electron-donor substituents were analyzed. The electron-donor substituents were found to promote the cation affinity. Sidearm coordinative interaction with the crown ether-complexed metal ion has been noticed. The nature of the metal–ligand interactions was investigated using Bader’s Quantum theory of atoms in molecule. It has been found that the Be²⁺–N bonds are partly covalent in nature while other coordinate bonds are of the electrostatic nature. The electron density at the bond critical points was found to be consistent with cation affinity. Natural bond orbital analysis was performed on the optimized geometries. The results showed that the stabilization interaction energies are caused by the donation of O/N lone pair electrons to the LP* orbitals of the metal cations. The amount of charge transfer follows the cation affinity order. The largest charge transfer and associated second-order perturbation stabilization energy were observed for Be²⁺ complexes.

     

Self-quenching and electronic energy transfer of triplet molecules. The benzaldehyde-biacetyl system in the vapor phase

The triplet-triplet energy transfer from benzaldehyde to biacetyl and the competing self-quenching between triplets and ground state molecules of benzaldehyde were investigated in the dilute vapor phase by monitoring the phosphorescence (T₁(nπ^*)S_o) decay of benzaldehyde. Following excitation into the S₁(nπ^*)S₀ absorption band, a triplet self-quenching rate constant of k_SQ=(2.4±0.1) × 10⁴ s^?1 Torr^?1, corresponding to a gas-kinetic cross section of σ_SQ=0.22 A², was measured. The collision-free lifetime of the benzaldehyde triplet was found to be 2.3 ± 0.4 ms. Substitution of the aldehydic proton by deuterium reduces k_SQ by a factor of two: complete deuteration of the molecule has no further effect. Under the same excitation conditions, the energy transfer rate to biacetyl is k_ET=(2.8 ± 0.1) × 10⁶ s^?1 Torr^?1, with σ_ET = 24 A². This process is not influenced by deuteration.     

Rate constant of the gas-phase reaction between Fe atoms and CO2

The rate constant of the gas-phase reaction Fe(a ⁵ D ₄) + CO₂ at 1180–2380 K and a total gas density of (7.0–10.0) × 10^?6 mol/cm³ behind incident shock waves is k(Fe + CO₂) = 1.4 × 10^{14.0 ± 0.3}exp[?(14590 ± 1100)/T] cm³ mol^?1 s^?1, as determined by resonance atomic absorption photometry. Using thermochemical data available from the literature, the rate constant of the reverse reaction was calculated to be k(Fe + CO) = 9.2 × 10^{11.0 ± 0.3} (T/1000)^0.57exp[?(490 ± 1100)/T] cm³ mol^?1 s^?1. The results are compared with data reported earlier.     

Rotationally inelastic scattering from surfaces CO(g) + LiF(OO1)

The rotationally inelastic scattering of a supersonic, rotanonally cold (T_rot^I = 4–30 k) CO molecular beam from a clean LiF(001) surface has been investigated by VUV laser-induced fluorescence. Rotational accommodation was incomplete for surface temperatures 350 <T_s < 900 K. The degree of accommodation decreased with T_s and was independent of collision energy.     

The rate constants of the gas-phase reactions K + Cl ⇆ K+ + Cl− and KCl + M ⇆ K+ + Cl− + M from measurements in atmospheric pressure flames

Mass spectrometric studies of the ions present in H₂/O₂/N₂ flames with potassium and chlorine added have demonstrated that ionization can occur in the forward steps of K + Cl ? K⁺ + Cl^? (II), KCl + M ? K⁺ + Cl^? + M (IV), where M is any third body. Variations of [K⁺] with time in these systems have been measured and establish that the rate coefficients (in ml molecule^?1 s^?1) of the ion-producing steps are k₂ = 5 × 10^?10T^{?$\text{1}\text{2}$} exp(?10 500/T) and k₄ = 2.2 × 10⁷T^?3.5 × exp(?60 800/T). Coefficients for ion-ion recombination have been obtained from k₂ and k₄ using the equilibrium constants of (II) and (IV) and are k_?2 = 1.7 × 10^?9T^{?$\text{1}\text{2}$} and k_?4 = 1.1 × 10^?17T^?3, with each one in the ml molecule^?1 s^?1 system of units. Replacement of the N₂ in one of these flames with sufficient Ar to maintain the temperature constant leaves the measured k₂ and k_?2 unchanged, but lowers the observed k₄ and k_?4. This confirms that ion-recombination in the backward step in (II) is a two-body process, whereas in (IV) it is termolecular.     

Die Deprotonierung von Metall-Aquoionen I.: Be · aq2+ Solvatations-Isomerie

The reaction of Be · aq²⁺ with OH^? leeds not only to loss of protons by the metalaquo ion but also to structural changes in the solvation sphere. These can be studied by following the pH variations during the first decisecond after mixing the solutions of metal salt and alkali hydroxide. The equilibrium Be²⁺ ? BeOH⁺ is reached within 5 milliseconds if acid free Beryllium solutions are used. If the metal solution is strongly acidic, however, the establishment of the equilibrium needs more time because of the slowness of the process H⁺ + BeOH⁺ → Be²⁺ (k ～ 10⁵ M^?1, s^?1). The extraction of two protons produces in the first instance an unstable Be(OH) species which transforms into the stable isomer Be(OH)₂ (solvatation isomerism) in a first-order reaction of half-life of 7 ms. This isomerisation causes almost complete disappearance of BeOH⁺ from the equilibrium Be²⁺ ? BeOH⁺ ? Be(OH)₂. (KAKIHANA & SILLEN state that the relaxed solutions contain only Be²⁺, Be(OH)₂, Be₃(OH) and some Be₂OH³⁺.) The formation of the polynuclear species Be₃(OH) needs about 30 seconds to go to completion.     

Dual-level direct dynamics studies on the reactions of tetramethylsilane with chlorine and bromine atoms

The multiple-channel reactions Cl + Si(CH₃)₄ and Br + Si(CH₃)₄ are investigated by direct dynamics method. The minimum energy path is calculated at the MP2/6-31+G(d,p) level, and energetic information is further refined by the MC-QCISD (single-point) method. The rate constants for individual reaction channel are calculated by the improved canonical variational transition state theory with small-curvature tunneling correction over the temperature range 200–3,000 K. The theoretical three-parameter expression k ₁(T) = 9.97 × 10^?13 T ^0.54exp(613.22/T) and k ₂(T) = 1.16 × 10^?17 T ^2.30exp(?3525.88/T) (in unit of cm³ molecule^?1 s^?1) are given. Our calculations indicate that hydrogen abstraction channel is the major channel due to the smaller barrier height among feasible channels considered.     

Local structure and hyperfine interactions of Fe and Sn atoms in brownmillerite-like ferrite Sr2Fe1.98Sn0.02O5+x

Mössbauer spectroscopy has been applied for studying local environment of ⁵⁷Fe and ¹¹⁹Sn probe atoms within tin-doped Sr₂Fe_1.98Sn_0.02O_5+x (x?0.02) ferrite with the brownmillerite-type structure. ⁵⁷Fe Mössbauer spectra indicate no appreciable local distortions induced by the tin dopant atoms. The ¹¹⁹Sn spectra recorded below the magnetic ordering temperature (T_N) can be described as a superposition of two Zeeman sextets, which indicate that Sn⁴⁺ dopant ions are located in two non-equivalent crystallographic and magnetic sites. The observed hyperfine parameters were discussed supposing Sn⁴⁺ cations to replace iron cations in the octahedral (Sn_O) and tetrahedral (Sn_T) sublattices. It has been supposed that Sn⁴⁺ cations being stabilized in the tetrahedral sublattice complete their nearest anion surrounding up to the octahedral oxygen coordination “Sn_T⁴⁺”. Annealing of the Sr₂Fe_1.98Sn_0.02O_5+x in helium flux conditions at 950°C leads to formation of divalent Sn²⁺ cations with a simultaneous decrease of the contribution for the Sn_T⁴⁺ sub-spectrum. The parameters of combined electric and magnetic hyperfine interactions of the ¹¹⁹Sn²⁺ sub-spectrum underline that impurity atoms are stabilized in the sp³d-hybrid state in the oxygen distorted tetragonal pyramid. The analysis of the ¹¹⁹Sn spectra indicates a chemical reversibility of the processes Sn_T²⁺?Sn_T⁴⁺ within the tetrahedral sublattice of the brownmillerite-type ferrite.     

Vibrational energy exchange of the DF (ν=2) state with DF (ν=0)

The energy transfer rate for the reaction DF (ν=1) + DF (ν=1)^k_νν→ DF (ν=0) + DF (ν=2) + ΔE=91.6 cm^?1 has been studied in a combined shock-tube laser-induced fluorescence experiment at temperatures from 295 to 720°K. The rate coefficient k_νν for the exothermic reaction was found to vary as T^?1 when expressed in units of cm³/mole sec. At T=295°K, the probability of the reaction is approximately 0.2 per collision.     

Theoretical study of Na(4p2P) + Na(3s2S) and Cd(5p3P0) + Na(3s2S) collisions and their role in the energy transfer between Cd.* and Na

We have computed the cross sections for the energy transfer process Cd(5p³P₀) + Na(3s²S) → Cd(5s¹S) + Na(4p²P) and for the state changing collision Na(4p²P) + Na(3s²S) → Na(3d²D) + Na(3s²S), based on theoretical interaction potentials for the NaCd and Na2 systems, respectively. Our calculations shed light on the interpretation of experiments with laser excited Na+Cd vapour mixtures [1]. It turns out that Cd(5p³P₀), in rapid equilibrium with the doorway state Cd(5p³P₁), efficiently transfers energy to Na, populating the 4p²P state. The collisions with ground state Na cause a very fast conversion of the 4p³P₁ to the 3d²D state, from which the strongest emission is observed.