Analytical photoion spectroscopy applied to dissociative single and double photoionization of diatomic molecules (H2, N2, O2, CO,and NO)

This work reports the principle, advantage, and limitations of analytical photoion spectroscopy which has been applied to dissociative photoionization processes for diatomic molecules such as H₂, N₂, CO, and NO. Characteristic features observed in the differential photoion spectra are summarized with a focus on (pre)dissociation of(i) multielectron excitation states commonly observed in the inner valence regions,(ii) shape resonances, and(iii) doubly charged parent ions. Possible origins for negative peaks in the differential spectra are discussed. This spectroscopy is applied to the reported photoion branching ratios for D₂ (and H₂ at high energies). The main findings are as follows: (1) The direct dissociation of theX ²Σ _g ⁺ (1sσ _g ) state of D ₂ ⁺ , the two-electron excited state¹Σ _u ⁺ (2pσ _u 2sσ _g ) of D₂, and the²Σ _u ⁺ (2pσ _u ) state of D ₂ ⁺ appear clearly in the differential spectrum, as previously observed for H₂. (2) Decay of H ₂ ⁺ (D ₂ ⁺ ) to H⁺ (D⁺) above 38 eV is due to the direct dissociation of highly excited states of H ₂ ⁺ (D ₂ ⁺ ) such as the²Σ _g ⁺ (2sσ _g ) and high-lying Rydberg states converging on H ₂ ²⁺ (D ₂ ²⁺ ). (3) In the ionization continuum of H ₂ ²⁺ (D ₂ ²⁺ ) peculiar dissociation pathways are observed. The differential photoion spectra for O₂ derived from the reported photoion branching ratios are also presented. The (pre)dissociation of theb ⁴Σ _g ^? ,B ²Σ _g ^? , III²Π _u ,²Σ _u ^? , and^2,4Σ _g ^? states of O ₂ ⁺ appears as the corresponding positive values in the spectra in accord with previous observations. Some other dissociation pathways possibly contributing to the spectra are discussed including dissociative double ionization.     

The interaction of metastable helium atoms with alkali atoms

Using crossed beams of ground state alkali atoms A (A = Li, Na, K, Rb, Cs) and metastable He(2³ S), He(2¹ S) atoms, we have measured the energy spectra of electrons resulting in the respective Penning ionization processes at: thermal collision energies. The data are interpreted to yield the well depthD _e ^* of the²Σ interaction potentials as follows: He(2³ S)+A:D _e ^* (A=Li)=868(20) meV;D _e ^* (Na)=740(25) meV;D _e ^* (K)=591(24) meV;D _e ^* (Rb)=546(18) meV;D _e ^* (Cs)=533(18) meV. He(2¹ S)+A:D _e ^* (Li)=330(17) meV;D _e ^* (Na)=277(24) meV;D _e ^* (K)=202(23) meV;D _e ^* (Rb)=219(18) meV;D _e ^* (Cs)=277(18) meV. The well depth for He(2³ S)+A(²Σ) is always close to 80% of the well depth for Li(2s)+A(X ¹Σ). The ionization cross sections for He(2¹ S)+A are about 3 to 4 times larger than those for He(2³ S)+A.     

Stability of Au 2 2+ : metastability through an excited state?

We discuss the stability of doubly charged Auclusters. From a calculation using semi-empirical linear combination of atomic-orbitals (LCAO) method, we conclude that Au ₂ ²⁺ in an excited state (³Σ _u ⁺ or¹Σ _u ⁺ ) is metastable with an energy barrier of about 0.3 eV. In the ground state (¹Σ _g ⁺ ) Au ₂ ²⁺ is unstable, except for small values of Δ(=ε _s ?ε _d ) (difference between thes andd atomic energy levels of Au), when a very shallow minimum appears in the binding energy curve. These results are critically discussed and compared with those obtained by different calculations.     

Photofragmentation of cluster ions: the visible photoabsorption spectrum of Ar2N 2 +

The absolute cross section for photodissociation of Ar₂N ₂ ⁺ was measured as a function of wavelength in the 470–550 nm range. A structureless broad band was observed; the cross section has a maximum of ～ 210 × 10^?18 cm² at ～ 500 nm. The measurement of the photofragment time-of-flight spectrum shows that(1) N ₂ ⁺ , Ar⁺ and Ar ₂ ⁺ are produced in the photodissociation of Ar₂N ₂ ⁺ in the wavelength range studied, and that(2) the observed visible absorption band is ascribable to a parallel-type transition of Ar₂N ₂ ⁺ , which possibly retains a linear geometry.     

Photofragment spectroscopy of N 2 + in the near UV

Photofragment spectroscopy of N ₂ ⁺ has been studied in the wavelength range 343–404 nm using an excimer-pumped dye laser with a spectral resolution of 0.2 cm^?1. The observed bands are assigned to transitions from thev″=23?26 levels of theX ²Σ _g ⁺ state to highlying rovibrational levels (v′≈46–48) of theB ²Σ _u ⁺ state, forming quasibound (predissociating) states above the dissociation limit N⁺(³ P)+N(⁴ S ⁰). Measurement of the photofragment kinetic energies allows to establish an absolute energy scale for the transitions with respect to the dissociation limit. Molecular constants for the lower and upper states of the observed transitions are determined. The measurements allow the first direct determination of the N ₂ ⁺ dissociation energyD ₀ ⁰ (N ₂ ⁺ ). Some high-resolution (0.04 cm^?1) measurements show the fine-structure splitting and lifetime broadening of the excitation lines.     

Metastable decay of rare gas cluster ions: mechanism and kinetics

Metastable decay of cluster ions has been discovered only recently. It was noted that one has to take this metastable decay into account when using mass spectrometry to probe neutral clusters, because ion abundance anomalies in mass spectra of rare gas and molecular clusters are caused by delayed metastable evaporation of monomers following ion production. Moreover, it was found that(i) the individual metastable reaction rates k depend strongly on cluster size and cluster ion production pathways and that(ii) there exists experimental evidence (k=k(t)) and a theoretical prediction that a given mass selected cluster ion generated by electron impact ionization of a nozzle expansion beam will comprise a range of metastable decay rates. In addition, it was discovered that metastable Ar cluster ions which lose two monomers in the μs time regime decay via sequential decay series Ar _n ⁺ *→Ar _n?1 ⁺ *→Ar _n?2 ⁺ * with cluster sizes 7≤n≤10 andn=3 (similar results were obtained recently in case of N₂ cluster ions). Conversely, the dominant metastable decay channel of Ar ₄ ⁺ * into Ar ₂ ⁺ was found to proceed predominantly via a single step fissioning process.     

High resolution spectroscopy of the 13Σ g + (b) ← 13Σ u + (x) transition of Na2

Rotational-vibrational transitions of the triplet system 1³Σ _g ⁺ ← 1³Σ _u ⁺ of the Na₂ molecule have been investigated around $\bar v = 13970 cm^{ - 1} $ by Doppler-free polarization spectroscopy in a heat pipe and by resonant two-step photoionization in a collimated cold argon beam, seeded with sodium vapor. The fine- and hyperfine structure of the transitions is partly resolved. The analysis of the measured spectra and a theoretical discussion of the expected multiplet structure yields the rotational constantsB′ _v (v′=17)=0.0866(4) cm^?1 for the upper andB″ _v (v″=0)=0.0533(4) cm^?1 for the lower state. The difference Δb=b(³Σ _u )?b(³Σ _g ) of the hyperfine coupling constantsb turns out to be Δb=80 MHz.     

Analysis of bound-free fluorescence and improved characterization of the electronic and spectroscopic properties of the 11Σ u + state of Cl2

Synchrotron radiation is used to selectively excite the chlorine molecule in the VUV spectral range. Stationary fluorescence spectra of the 1¹Σ _u ⁺ state are observed following primary excitation of 1¹Σ _u ⁺ and 2¹Σ _u ⁺ . The bound-free part of the spectra is analysed with the aid of quantum mechanical computer simulations. A potential energy curve is constructed which is an approximation of the adiabatic double well potential energy curve of the 1¹Σ _u ⁺ state. The inner well is characterized byT _e =(73428±50) cm^?1,r _e =(1.85 ± 0.05) Å; for the outer well holdT _e =(64631±50) cm^?1,r _e =(2.57±0.05) Å, ω _e =(261±5) cm^?1, ω _e x _e =(0.668±0.01) cm^?1 (³⁵Cl₂;v′<30). The potential energy curve is successfully checked with fluorescence excitation spectra. Within the error limits, the results of a former synchrotron radiation study are verified. It is ruled out, that the Cl₂ “γ-state” recently observed with laser spectroscopic methods, can be attributed to the outer well of 1¹Σ _u ⁺ .     

Simulating the experimental vacuum ultraviolet radiation of rare-gases plasma

Experimental excimer continua emitted by electric discharge plasma of krypton and xenon were interpreted as the ¹ Σ _u ⁺ → ¹ Σ _g ⁺ bound-free transitions. The relative populations of the lower vibrational levels of the ¹ Σ _u ⁺ state were derived fitting experimental spectra with the theoretical ones.     

Direct measurement of the N 2 + dissociation energy

The accuracy for the direct measurement of the dissociation energy of the N ₂ ⁺ B²Σ _u ⁺-state was significantly improved by using frequency doubled laser light, which enables the authors to excite from lowerv″-levels and additionally to calibrate the fundamental laser wavelength with an iodine cell. The obtained value is:D ₈(N ₂ ⁺ )=70248±6 cm^?1.     

Activation parameters of supercritical and gas-phase β-pinene thermal isomerization

New data on enthalpy and entropy contributions to the energy barrier of β-pinene thermal isomerization were obtained. The rate of β-pinene conversion is higher in supercritical EtOH (P = 120 atm) than in the gas phase (P ≤ 1 atm, without solvent, or for inert carrier gas N₂) at equal temperatures. The highest activation energy E _Σ of total β-pinene conversion is also observed in reactions in the supercritical (sc) condition. Activation parameters ΔH _Σ ^# , ΔS _Σ ^# , and ΔG _Σ ^# depend strongly on the reaction pressure. Thus, at P ≤ 1 atm (gas-phase reaction) the values of ΔS _Σ ^# are negative, while at sc conditions at P = 120 atm is positive. The linear dependences lnk _Σ0 ? E _Σ and ΔS _Σ ^# ? ΔS _Σ ^# indicate an isokinetic relation (IKR) and enthalpy-entropy compensation effect (EEC). The isokinetic temperature was calculated (T _iso = 605.5 ± 22.7 K). It was shown that elevation of temperature reduces the value of ΔG _Σ ^# (T) upon sc thermolysis only, whereas in all gas-phase reactions ΔG _Σ ^# (T) increases. At equal reaction temperatures, the greatest values of K _eq ^# (T) proved to be typical for thermolysis in sc-EtOH. We hypothesize that the rate of total β-pinene conversion increases dramatically due to a considerable shift in equilibrium toward higher concentrations of activated complex y _TS ^# . A detailed analysis of activation parameters shows that the IKR and EEC coincide, evidence of a common mechanism of β-pinene conversion observed under different reaction conditions, including thermolysis in sc-EtOH.     

Observations and spectral simulations of the7Li2 21 Σ u + →X 1 Σ g + transition

The⁷Li₂ 2¹ Σ _u ⁺ →X ¹ Σ _g ⁺ electronic transition has a bound-bound and a bound-free part due to the double minimum nature of the upper 2¹ Σ _u ⁺ state. We have studied this transition both experimentally and by performing spectral simulations. When inner well was excited the bound-free part at 4525 Å was observed due to the collisions between Li ₂ ^* and argon. We found that when levels above the barrier are excited the bound-free emission is strongly affected by collisional relaxation of Li ₂ ^* by Li atoms. Conditions for the observation of the bound-free part are discussed.     

Bemerkung zur Rayleigh-Schrödinger-Störungstheorie

The time-independent Hamiltonians ? ₀ and ?=? ₀ + V have a discrete spectrum, eigenvalues, and eigenvectors E _s ^(o) , ¦s〉^(o) resp. E _s, ¦s〉. If the RS perturbation theory can be applied here then an operator \(\mathfrak{p}\) with the property $$\left| s \right\rangle ^{(n + 1)} = \frac{1}{{n + 1}}\mathfrak{p}\left| s \right\rangle ^{(n)} , E_s^{(n + 1)} = \frac{1}{{n + 1}}\mathfrak{p}E_s^{(n)} $$ exists where ¦s〉⁽ⁿ⁾ and E _s ⁽ⁿ⁾ denote the n-th order corrections of perturbation theory if E _s ^(o) is nondegenerate. In the case of degeneracy the operation \(\mathfrak{p}\) remains defined and can always be used todetermine perturbation corrections of quantum mechanical expressions which are invariant in zerothorder under transformations of the basis in degenerate subspaces of ? ₀. The equations $$\left| s \right\rangle = \sum\limits_n^{0,\infty } {\left| s \right\rangle ^{(n)} = e^\mathfrak{p} \left| s \right\rangle ^{(0)} } , E_s = \sum\limits_n^{0,\infty } {E_s^{(n)} } = e^\mathfrak{p} E_s^{(0)} $$ correspond to a basis transformation where nondegenerate eigenvectors ¦s∝> ^(o) and eigenvalues E _s ^(o) of ? ₀ transform into eigenvectors ¦s∝> and eigenvalues E _s of ?. Examples show the usefulness of this formulation.     

Multi-reference configuration interaction calculations on the systems Xe 2 + and Xe 3 +

Potential curves for the ground (²Σ _u ⁺ ) and the three lowest excited states of the Xe ₂ ⁺ dimer ion (²Π _g ,²Π _u ,²Σ _g ⁺ ) have been calculated using pseudopotentials in MRD-CI (multi-reference single anddouble excitationconfigurationinteraction) calculations. Spin-orbit interaction — leading to the six states 1.(1/2) _u , 1.(3/2) _g , 1.(3/2) _u , 1.(1/2) _g , 2.(1/2) _u , 2.(1/2) _g — has been taken into account using a semiempirical technique [1]. Subsequently, starting with a relaxed Xe ₂ ⁺ ion in its ground state, the potential energy surface for the system Xe-Xe ₂ ⁺ was studied. We found that the collinear approach of the Xe atom leads to the most stable geometry. This is a linear symmetric molecule with bond lengths of 6.38 bohr. In the bestT-shaped structure, the Xe atom is 7.83 bohr away from the midpoint of the Xe ₂ ⁺ (r=6.1 bohr) dimer. The calculated binding energy of 0.25 eV for the equilibrium structure of the Xe ₃ ⁺ molecule (i.e. the linear symmetric geometry), is in very good agreement with experimental results of 0.27 ± 0.02 eV [2].     

Effect of solvation on the dynamics of H + CH3 association

The gas phase association of CH₃ with the HAr₂ cluster to form a vibrationally/rotationally excited CH ₄ ^* molecule is used as a model to study microscopic solvation dynamics. A potential energy surface for the reactive system is constructed from a previously fitted H + CH₃ ab initio potential and 12-6 Lennard-Jones Ar-Ar, Ar-C, and Ar-H potentials. Classical trajectory calculations performed with the chemical dynamics computer program VENUS are used to investigate the CH₃ + HAr₂ → CH ₄ ^* + Ar₂ reaction dynamics. Reaction is dominated by a mechanism in which the CH₃ “strips” the H-atom from HAr₂ during large impact parameter collisions. For a large initial relative translational energy the CH₃ + HAr₂ → CH ₄ ^* + Ar₂ cross section is the same as that for H + CH₃ association, so that HAr₂ acts like a “heavy” H-atom. However, at a low initial relative translational energy, the long-range Ar₂—CH₃ attractive potential apparently makes the CH₃ + HAr₂ association cross section larger than that for H + CH₃. Partitioning of energy to the CH ₄ ^* and Ar₂ products is consistent with a stripping mechanism. The initial and final relative translational energies are nearly identical and the CH ₄ ^* rotational energy is controlled by the initial CH₃ rotational energy. The velocity and orbital tilt scattering angles, θ(v _i ,v _f ) and θ(l _i ,l _f ), respectively, are consistent with the stripping mechanism. On average only a small amount of the product energy is partitioned to Ar₂ vibration/rotation and CH ₄ ^* + Ar₂ relative translation.     

The nature of molecular oxygen binding and activation in Mn-O2 complex

Non-empirical calculations of CASSCF energies, electric dipole moments, Einstein coefficients, matrix elements of the operator of spin-orbital interaction between states of different multiplicity in a model complex ^6,8[Mn-O₂] of C _2v symmetry have been made in 3-21G, 6-31G, 6-31G** basis sets. The crosssections of the potential energy surface (PES) of the ground and excited states were built. It is found that oxygen bonding to manganese is possible when excited atoms of manganese collide with molecular oxygen, singlet oxygen with Mn[⁶ S _5/2] atoms, or in a close contact O₂[X³Σ _g ^? ] + Mn[⁶ S _5/2] and is determined by charge transfer states ^6,8CTS(Mn⁺O ₂ ^? ). Mechanisms of singlet oxygen activation/deactivation are determined by a considerably increased probability of electric dipole transitions b ¹Σ _g ⁺ ?a ¹Δ_g, a ¹Δ_g?X³Σ _g ^? , b ¹Σ _g ⁺ ?X³Σ _g ^? induced in oxygen in the collision process.     

Adiabatic channel study of the capture of nitrogen and oxygen molecules by an ion: effect of nuclear symmetry and spin-spin interaction

Within the adiabatic channel treatment of ionmolecule capture we have calculated the low temperature capture rate constants of N₂(¹Σ _g ⁺ ) and O₂(³Σ _g ^? )in collisions with positive and negative ions. In both cases, the charge-quadrupole and the anisotropic charge-induced dipole interactions produce noticeable deviations from the Langevin rate constant. The rate constants calculated with account for the anisotropic interaction, in addition, are substantially affected by nuclear symmetry; in the case of O₂(³Σ _g ^? ), the fine-structure spin-spin interaction strongly manifests itself in the rate constants.     

Towards understanding the stability of the H*4 (C3v ) cluster

As a first attempt to study the stability of the H*₄ (C_3v ) cluster we have used the MRD-CI method and a medium size basis set to calculate various sections of the potential energy surfaces of its ground and first excited states. We show that these correlate to the (X ¹Σ _g ¹ X ¹Σ _g ⁺ ) and (X ¹Σ _g ⁺ B ¹Σ _u ⁺ ) states of the two H₂ constituents respectively. Finally, we report on the calculation of the diabatic matrix elements of the vibronic interaction in the region of the avoided crossing which is crucial to the stability of H ₄ ⁺ .