J. A. Stephens

Rotationally resolved photoelectron spectroscopy of the 2Σ- Rydberg states of OH: the role of Cooper minima

We have measured rotationally resolved photoelectron spectra of the OH radical using (2+1) resonance enhanced multiphoton ionizationspectroscopy via the D  ^2Σ^−(3pσ) and 3 ^2Σ^−(4sσ) Rydberg states. For the D  ^2Σ^−(3pσ) state, we observe primarily ΔN=even distributions of ionic rotational states, in contrast to the ΔN=odd distribution expected for ionization of a 3pσ Rydberg electron. The observations are described quantitatively by ab initio calculations which predict a Cooper minimum in the 3pσ→kπ(l=2) channel, whose occurrence determines the ΔN=even ion rotational distribution. In contrast, the 3 ^2Σ^−(4sσ) photoelectron spectra reveal a broad distribution in rotational levels, arising from greater l mixing in the higher Rydberg orbital and much weaker Cooper minima in the continuum.

Rotationally resolved photoelectron spectra in resonance enhanced multiphoton ionization of Rydberg states of NH

Results of combined theoretical and experimental studies of photoelectron spectra resulting from (2+1) resonance enhanced multiphoton ionization (REMPI) via the f ^1Π(3pσ), g ^1Δ(3pπ), and h ^1Σ^+(3pπ) Rydberg states of NH are reported. The overall agreement between these calculated and measured spectra is encouraging. Strong ΔN=N+−N’=even peaks, particularly for ΔN=0, are observed in these spectra. Low‐energy Cooper minima are predicted to occur in the l=2 wave of the kπ(^1Σ^+), kπ(^1Σ^−), and kπ(^1Δ) photoelectron channels for the f state, the kπ(^1Δ), kδ(^1Π), and kδ(^1Φ) channels for the g state, and the kπ(^1Σ^+) and kδ(^1Π) channels for the h state of NH. Depletion of the d wave (l=2) contributions to the photoelectron matrix element in the vicinity of these Cooper minima subsequently enhances the relative importance of the odd l  waves. The observed ΔN transitions are also affected by strong l  mixing in the electronic continuum induced by the nonspherical molecular potential. Interference of continuum waves between degenerate ionization channels also determines the spectral pattern observed for photoionization of the f ^1Π state of NH. Photoelectron angular distributions and the angular momentum compositions of photoelectron matrix elements provide further insight into the origin of these Cooper minima.

Shape-resonance-induced non-Franck–Condon effects in (2+1) resonance enhanced multiphoton ionization of the C 3Πg state of O2

We show that strong non-Franck–Condon effects observed in (2+1) resonance enhanced multiphoton ionization of the C 3Pig state of O2 are due to the ksigmau shape resonance previously observed in single-photon studies of diatomic molecules. Calculated vibrational branching ratios for the v=2,3 levels of the C 3Πg state are in reasonable agreement with experiment. Certain discrepancies remain in comparing theoretical results with the measured spectra, and possible electron-correlation effects which underly this are discussed.

Effects of Cooper minima in resonance enhanced multiphoton ionization‐photoelectron spectroscopy of NO via the D 2Σ+ and C 2Π Rydberg states

Cooper minima are predicted to occur in the 3pσ→kσ(l=2) and 3pσ→kπ(l=2) channels in the resonance enhanced multiphoton ionization of NO via the D  ^2Σ^+(3pσ) Rydberg state. The low energy kσ(l=2) Cooper minimum leads to the observed ΔN = N^+ − N’=0 photoelectron peak, in addition to the ΔN = ±1, ±3 peaks seen in the rotational spectra. The Cooper minima are accompanied by significant l mixing in the continuum due to the nonspherical molecular potential and result in a strong dependence of rotational branching ratios and angular distributions on photoelectron kinetic energy. A Cooper minimum is also predicted in the 3pπ→kδ(l=2) channel for photoionization of the C  ^2Π(3pπ) Rydberg state. The effect of this Cooper minimum on photoelectron spectra and photoelectron angular distributions is also investigated.

Orbital evolution and promotion effects in the photoionization dynamics of 2Σ− Rydberg states of OH

In this paper, we discuss the photoionizationdynamics of the D ^2Σ^−(1π^23pσ) and 3 ^2Σ^−(1π^24sσ) Rydberg states of OH, emphasizing the critical role that Rydberg orbital evolution plays at intermediate to larger internuclear distances in determining vibrational and rotational molecular ion distributions. The orbital evolution process is discussed in terms of diabatic and adiabatic molecular states, united atom–separated atom correlation rules, and quantum defect functions. Vibrationally resolved photoelectron spectra and angular distributions for resonance enhanced multiphoton ionization (REMPI) of OH via the D  ^2Σ^−(1π^25σ) and 3 ^2Σ^−(1π^26σ) Rydberg states are considered as examples. The results and conclusions are relevant to vibrationally and rotationally resolved REMPI studies of all first‐row molecular hydrides, due to the similarity of their electronic structure and correspondence to their associated united atom.

Shape resonance and non‐Franck–Condon effects in (2+1) resonant enhanced multiphoton ionization of O2 via the C 3Πg state

We report vibrationally resolved photoelectron angular distributions for photoionization of the C3Πg Rydberg state of O2. Comparison is made with recent experimental measurements of angular distributions which employ (2+1) resonant enhanced multiphoton ionization of the C3Πg state. The present theory treats the process as single-photon ionization from an unaligned Rydberg state, and qualitatively accounts for much of the observed trends. Non-Franck–Condon effects induced by the kσu shape resonance lead to a substantial dependence of the angular distributions on the vibrational state of the X2Πg ion. Discrepancies between our theoretical results and experiment are qualitatively discussed and tentatively attributed to residual electron correlations.

Vibrational state dependence of ionic rotational branching ratios in resonance enhanced multiphoton ionization of CH

We show that rapid evolution of a Rydberg orbital with internuclear distance in a resonance enhanced multiphoton ionization (REMPI) process can have a profound influence on the production of molecular ions in alternative rotational states. This is illustrated by calculations of ionic rotational branching ratios for (2+1′) REMPI via the O11 (20.5) branch of the E′ ^2Σ^+(3pσ) Rydberg state of CH. The rotational propensity rule for ionization changes from ΔN=odd (ΔN=N_+−N_i) at lower vibrational excitation, as expected from the ΔN+l=odd selection rule, to ΔN=even at higher vibrational levels. This effect is expected to be quite general and should be most readily observable in diatomic hydrides.

Non-Franck-Condon effects in photoionization of the 3 3Π Rydberg state of NH

Strong non‐Franck–Condon behavior is predicted to occur in the vibrationally resolved photoionization spectra of NH for (3+1) resonance enhanced multiphoton ionization processes via the 3 ^3Π Rydberg state. The non‐Franck–Condon effects are interpreted on the basis of rapid orbital evolution, Cooper minima, and internuclear distance dependence of the dipole transition moment and cross sections. A Cooper minimum occurs in the 5σ→kπ channel at small internuclear distances, where NH resembles its united atom, oxygen. The iterative Schwinger variational method and multiplet‐specific ion potentials are employed in the calculation of the photoelectron continuum wave functions. Cross sections and asymmetry parameters for photoionization of the NH ground state leading to the X  ^2Π, a  ^4Σ^−, and A  ^2Σ^− ions are also reported.

Photoionization of the valence orbitals of OH

We report the results of studies of the photoionization cross sections and asymmetry parameters for the 3σ and 1π levels of OH, corresponding to the production of the A ^3Π, c ^1Π, a ^1Δ, b ^1Σ+, and X ^3Σ− molecular ions. The calculations employed multiplet‐specific Hartree–Fock potentials and numerical photoelectron continuum orbitals, obtained using the iterative Schwinger variational method. Noticeable nonstatistical behavior of the cross sections is seen, mainly for the 1π level, although deviations are not as pronounced as in other open‐shell systems. Comparison with fragmentary experimental data is encouraging, although synchrotron radiation studies are needed to fully assess the accuracy of the calculated cross sections.

Studies of molecular Rydberg states by Schwinger variational-quantum defect methods : application to molecular hydrogen

An ab initio electronic structure technique has been developed to study highly excited states of molecules by combining Schwinger variational methods of collision theory with generalized quantum defect theory. The technique exploits methods of scattering theory to study the region of highly excited Rydberg levels below and across ionization thresholds for molecules. The reaction matrix K, which describes the interaction of the Rydberg electron with the ionic core, is found at arbitrary negative electron energies by employing an unbounded Coulomb Green’s function in the Lippmann–Schwinger equation for the electronic wave function. Quantal conditions are imposed to obtain discrete molecular energy levels, associated Rydbergwave functions, and quantum defect functions, all as a function of the internuclear distance. Results within the static‐exchange approximation for the ^(1,3)Σ^+_u(1σ_gnσ_u ) and ^(1,3)Π_u(1σ_gnπ_u) Rydberg states of H_2, for n=2–20 and R=1.2–5.0 a_0, are presented and discussed.