B. V. McKoy

Theoretical studies of photoexcitation and ionization in H2O

Theoretical studies are reported of the complete dipole excitation and ionization spectrum in H_2O employing Franck–Condon and static‐exchange approximations. Large Cartesian Gaussian basis sets are used to represent the required discrete and continuum electronic eigenfunctions at the ground‐state equilibrium geometry, and previously devised moment‐theory techniques are employed in constructing the continuum oscillator‐strength densities from the calculated spectra. Detailed comparisons are made of the calculated excitation and ionization profiles with recent experimental photoabsorption studies and corresponding spectral assignments, electron impact–excitation cross sections, and dipole (e, 2e)/(e, e+ion) and synchrotron‐radiation studies of partial‐channel photoionization cross sections. The various calculated excitation series in the outer‐valence (1b(^−1)_1, 3a(^−1)_1, 1b(^−1)_2) region are found to include contributions from valence‐like 2b_2 (σ*) and 4a_1(γ*) virtual orbitals, as well as appropriate nsa_1, npa_1, nda_1, npb_1, npb_2, ndb_1, ndb_2, and nda_2 Rydberg states. Transition energies and intensities in the ∼7 to 19 eV interval obtained from the present studies are seen to be in excellent agreement with the measured photoabsorption cross section, and to provide a basis for detailed spectral assignments. The calculated (1b(^−1)_1)X(^ 2)B_1, (3a_1(^−1))^2A_1, and (1b_2(^−1))(^2)B_2 partial‐channel cross sections are found to be largely atomic‐like and dominated by 2p→kd components, although the 2b_2(σ*) orbital gives rise to resonance‐like contributions just above threshold in the 3a_1→kb_2 and 1b_2→kb_2 channels. It is suggested that the latter transition couples with the underlying 1b_1→kb_1 channel, accounting for a prominent feature in the recent high‐resolution synchrotron‐radiation measurements. When this feature is taken into account, the calculations of the three outer‐valence channels are in excellent accord with recent synchrotron‐radiation and dipole (e, 2e) photoionization cross‐sectional measurements. The calculated inner‐valence (2a_1(^−1)) cross section is also in excellent agreement with corresponding measured values, although proper account must be taken of the appropriate final‐state configuration‐mixing effects that give rise to a modest failure of the Koopmans approximation, and to the observed broad PES band, in this case. Finally, the origins of the various spectral features present in the measured 1a_1 oxygen K‐edge electron energy‐loss profile in H_2O are seen to be clarified fully by the present calculations.

Photoabsorption in carbon monoxide: Stieltjes–Tchebycheff calculations in the separated‐channel static‐exchange approximation

Theoretical investigations of total and partial‐channel photoabsorption cross sections in carbon monoxide are reported employing the Stieltjes–Tchebycheff (S–T) technique and separated‐channel static‐exchange calculations. Pseudospectra of discrete transition frequencies and oscillator strengths appropriate for individual excitations of each of the six occupied molecular orbitals are constructed using Hartree–Fock core functions and normalizable Gaussian orbitals to describe the photoexcited and ejected electrons. Use of relatively large basis sets of compact and diffuse functions insures the presence of appropriate discrete Rydberg states in the calculations and provides sufficiently dense pseudospectra for the determination of convergent photoionization cross sections from the S–T technique. The calculated discrete vertical electronic excitation spectra are in very good agreement with measured band positions and intensities, and the partial‐channel photoionization cross sections are in correspondingly g...

Photoexcitation and ionization in molecular oxygen: Theoretical studies of electronic transitions in the discrete and continuous spectral intervals

Theoretical studies of valence-electron (1πg, 1πu, 3σg) photoexcitation and ionization cross sections in molecular oxygen are reported employing separated-channel static-exchange calculations and the Stieltjes–Tchebycheff moment-theory technique. As in previously reported investigations of photoexcitation and ionization in small molecules following this approach, canonical Hartree–Fock orbitals, large Gaussian basis sets, and many-electron eigenstates of correct symmetry are used in defining appropriate noncentral static-exchange potentials and in computations of the appropriate discrete and continuum transition strengths. It is particularly important in molecular oxygen to incorporate the appropriate ionic parentages of the various photoionization multiplet states in order to obtain the correct partial-channel cross sections. The calculated discrete series associated with 1πg excitation are found to be in good agreement with available experimental assignments and previously reported theoretical studies, and the predicted states associated with 1πu and 3σg excitations are in general accord with assignments for the higher series based on spectral and quantum-defect analysis. Although the observed photoelectron spectra and photoionization cross sections are relatively complex, the calculated total vertical electronic photoabsorption cross section and the partial-channel photoionization cross sections for production of X 2πg, a 4πu, A 2πu, 2 2πu, 3 3IIu, b 4∑g-, and B 2∑g-, ionic states are found to be in good accord with recent synchrotron radiation, line-source, electron-impact, and (e,2e) dipole oscillator-strength measurements when proper account is taken of the parentages of the various multiplet states. The partial-channel cross sections exhibit resonancelike structures that can be attributed to contributions from diabatic valencelike virtual states that appear in the appropriate photoionization continua, rather that in the corresponding discrete spectral intervals. These features in the dipole spectrum of molecular oxygen are discussed and are contrasted and compared with the results of previously reported related studies in molecular nitrogen and carbon monoxide.

Photoexcitation and ionization in acetylene

Theoretical studies are reported of photoexcitation and ionization processes in the acetylene molecule. The calculations performed employ Franck—Condon and static-exchange approximations, and implicitly invoke vibrational and rotational closure. Detailed comparisons with recent spectral assignments, electron-impact excitation studies, and total and partial-channel cross-sectional measurements indicate that the theoretical results provide a useful first approximation to the complete dipole excitation/ionization spectrum of C_2H_2. The calculated discrete spectra are seen to include contributions from virtual 4σ_g(n/σ^*) and 1π_g(π^*) orbitals, which appear an valence interlopers in the 1π_u→ nsσ_g, 2σ_u → nsσ_g, 1σ_u → nsσ_g and 2σ_u → ndπ_g, 1σ_u → ndπ_g Rydberg series, respectively, in good accordance with spectral measurements. By contrast, the 3σ_u(σ^*) virtual valence orbital gives rise to prominent diabatic resonance features above threshold in the 3σ_g → kσ_u, 2σ_g → kσ_u, and 1σ_g → kσu cross-sections, results that are in good quantitative accordance with corresponding experimental studies. Prominent features in the measured (1π_u^(−1))X^2Π_u partial cross-section, which is in good accordance with the present values, are attributed to autoionization 2σ_u → 1π_g(π^*) and 4σ_g(n/σ^*) intravalence transitions.

Experimental and theoretical studies of the valence-shell photoion1zation cross sections of acetylene: strong autoionization in the (1πu−1) X2Πu partial channel

Experimental studies of photoionizaiion cross sections in acetylene reveal the presence of a strong resonance in the (1π_u^(−1) X^2Π_u partial channel that is attributed on the basis of corresponding theoretical studies to autoionization of the valence (2σ_u^(−1)1π_g) b^1Π_u and (2σ_u^(−1)4σ_g)^1Σ_u^+ states.

Photoexcitation and ionization in molecular fluorine: Stieltjes–Tchebycheff calculations in the static‐exchange approximation

Theoretical investigation of outer (1pig, 1piu, 3sigmag) and inner (2sigmau, 2sigmag) valence-shell electronic photoexcitation and ionization cross sections in molecular fluorine are reported employing separated-channel static-exchange calculations and Stieltjes–Tchebycheff (S–T) moment-theory techniques. The discrete vertical electronic 1pig excitation series are found to be in good agreement with recent spectral assignments and previously reported theoretical studies, and those for 1piu, 3sigmag, 2sigmau and 2sigmag excitations are in general accord with position and intensity estimates based on quantum-defect analysis. Certain of the partial-channel photoionization cross sections in F2 are seen to exhibit resonancelike features similar to those reported recently in related S–T studies of photoionization in N2, CO, and O2. The resonances can be attributed to valencelike and pre-Rydberg diabatic states that cross the outer limbs of appropriate Rydberg series and corresponding ionic-state potential curves as functions of internuclear coordinate, giving rise to large continuum transition intensities at the ground-state equilibrium internuclear separation. In contrast to the situation in N2, CO, and O2, however, there is no evidence of a resonance like sigma-->sigma* feature in the 3sigmag-->ksigmau photoionization channel in F2. Rather, this resonance in F2 appears as a strong N-->Vg transition below the 3sigmag ionization threshold, and the corresponding partial-channel photoionization cross section is seen to be structureless. Although experimental studies of partial-channel photoionization cross sections are apparently unavailable for comparison, the calculations reported here should provide reliable approximations to the dipole excitation/ionization spectra in F2, and are helpful in understanding and clarifying the dependences of photoionization spectra in light diatomic molecules on shell occupancy and equilibrium internuclear separation when compared with the results of previous studies of photoionization in N2, CO, and O2.

Photoabsorption in formaldehyde: Intensities and assignments in the discrete and continuous spectral intervals

Theoretical investigations of total and partial‐channel photoabsorption cross sections in molecular formaldehyde are reported employing the Stieltjes–Tchebycheff (S–T) technique and separated‐channel static‐exchange (IVO) calculations. Vertical one‐electron dipole spectra for the 2b_2(n), 1b_1(π), 5a_1(σ), 1b_2, and 4a_1 canonical molecular orbitals are obtained using Hartree–Fock frozen‐core functions and large basis sets of compact and diffuse normalizable Gaussians to describe the photoexcited and ejected electrons. The calculated discrete excitation spectra provide reliable zeroth‐order approximations to both valence and Rydberg transitions, and, in particular, the 2b_2(n) →nsa_1, npa_1, npb_2, and nda_2 IVO spectra are in excellent accord with recent experimental assignments and available intensity measurements. Convergent (S–T) photoionization cross sections in the static‐exchange (IVO) approximation are obtained for the 15 individual partial channels associated with ionization of the five occupied molecular orbitals considered. Resonance features in many of the individual‐channel photoionization cross sections are attributed to contributions from valencelike a_1σ^∗ (CO), a_1σ^∗ (CH), and b_2σ^∗ (CH)/π_y^∗ (CO) molecular orbitals that appear in the photoionization continua, rather than in the corresponding one‐electron discrete spectral intervals. The vertical electronic cross sections for ^1A_1→^1B_1, ^1B_2, and ^1A_1 excitations are in generally good accord with previously reported CI (S–T) predictions of continuum orbital assignments and intensities, although some discrepancies due to basis‐set differences are present in the ^1B_1 and ^1B_2 components, and larger discrepancies apparently due to channel coupling are present in the ^1A_1→^1A_1 cross section. Partial‐channel vertical electronic cross sections for the production of the five lowest parent‐ion electronic states are found to be in general agreement with the results of very recent synchrotron‐radiation photoelectron branching‐ratio measurements in the 20 to 30 eV excitation energy interval. Most important in this connection is the tentative verification of the predicted orderings in intensities of the partial‐ channel cross sections, providing support for the presence of a strong ka_1σ^∗ (CO) resonance in the (5a_1^(−1))^2A_1 channel. Finally, the total vertical electronic cross sections for absorption and ionization are in general accord with photoabsorption measurements, photoionization–mass–spectrometric studies, and the previously reported CI (S–T) calculations. Although further refined calculations including vibrational degrees of freedom and autoionization line shapes are required for a more precise quantitative comparison between theory and experiment, the present study should provide a reliable zeroth‐order account of discrete and continuum electronic dipole excitations in molecular formaldehyde.

Rotationally resolved energy-dispersive photoelectron spectroscopy of H2O: Photoionization of the C̃(0,0,0) state at 355 nm

Measured and calculated rotationally resolved photoelectron spectra for photoionization of low rotational levels of the C^1B_1 Rydberg state of water are reported. This is the first example of rotationally resolved photoionization spectra beyond the special cases of H_2, high-J levels, and threshold spectra. These spectra reveal very nonatomiclike behavior and, surprisingly, the influence of multiple Cooper minima in the photoelectron matrix elements.

Photoexcitation and ionization in ozone: Stieltjes–Tchebycheff studies in the separated‐channel static‐exchange approximation

Theoretical studies are reported of total and partial-channel photoexcitation/ionization cross sections in ozone employing Stieltjes–Tchebycheff (S–T) techniques and the separated-channel static-exchange approximation. As in previously reported investigations of excitation and ionization spectra in diatomic and polyatomic molecules employing this approach, vertical electronic dipole transition spectra for the twelve occupied canonical Hartree–Fock symmetry orbitals in ozone are constructed using large Gaussian basis sets, appropriate computational methods, and noncentral static-exchange potentials of correct molecular symmetry. Experimental rather than Koopmans ionization potentials are employed when available in construction of transition energies to avoid the incorrect ionic-state orderings predicted by Hartree–Fock theory, and to insure that the calculated series have the appropriate limits. The spectral characteristics of the resulting improved-virtual-orbital discrete excitation series and corresponding static-exchange photoionization continua are interpreted in terms of contributions from valencelike 7a1(sigma*), 2b1(pix*), and 5b2(sigma*) virtual orbitals, and appropriate diffuse Rydberg functions. The 2b1(pix*) valence orbital apparently contributes primarily to discrete or autoionizing spectra, whereas the 7a1(sigma*) and 5b2(sigma*) orbitals generally appear in the various photoionization continua. Moreover, there is also evidence of strong 2p-->kd atomiclike contributions to ka2 final-state channels in the photoionization continua. The calculated outer-valence-shell 6a1, 4b2, and 1a2 excitation series are compared with electron impact–excitation spectra in the 9 to 13 eV interval, and the corresponding partial-channel photoionization cross sections are contrasted and compared with the results of previously reported studies of photoionization in molecular oxygen. The intermediate- and inner-valence-shell excitation series and corresponding photoionization cross sections are in general accord with quantum-defect estimates and with the measured electron-impact spectra, which are generally unstructured above ~22 eV. Of particular interest in the intermediate-valence-shell spectra is the appearance of a strong sigma-->sigma* feature just above threshold in the 3b2-->kb2 photoionization cross section, in qualitative agreement with previously reported studies of the closely related 3sigmag-->ksigmau cross section in molecular oxygen. Finally, qualitative comparisons are made of the calculated K-edge excitation and ionization spectra in ozone with recently reported photoabsorption studies in molecular oxygen.

The equations-of-motion method for F2: Transition energies, oscillator strengths and born cross sections

The equations-of-motion method has been used to study various electronic states of F_2. The transition energies have been found in both the random phase approximation (RPA) and higher random approximation (HRPA) using single particle—hole components in the excitation operators. We have also computed generalized oscillator strengths (Born cross sections) for the scattering of high energy electrons by F_2.