T. N. Rescigno

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 molecular nitrogen: A moment analysis of discrete-basis-set calculations in the static-exchange approximation

Theoretical investigations of photoexcitation and ionization cross sections in molecular nitrogen are reported employing the recently devised Stieltjes–Tchebycheff moment-theory technique in the static-exchange approximation. The coupled-channel equations for photoabsorption are separated approximately by identifying the important physically distinct excitation processes associated with formation of the three lowest electronic states of the parent molecular ion. Approximate Rydberg series and pseudospectra of transition frequencies and oscillator strengths are constructed for the seven individual channel components identified using Hartree–Fock ionic core functions and normalizable Gaussian orbitals to describe the photoexcited and ejected electrons. Detailed comparisons of the theoretically determined discrete excitation series with available spectral data indicate general accord between the calculated and observed excitation frequencies and oscillator strengths, although there are some discrepancies and certain Rydberg series have apparently not yet been identified in the measured spectra. The total Stieltjes–Tchebycheff vertical photoionization cross section obtained from the discrete pseudospectra is in excellent agreement with recent electron–ion coincidence measurement of the cross section for parent–ion production from threshold to 50 eV excitation energy. Similarly, the calculated vertical partial cross sections for the production of the three lowest electronic states in the parent molecular ion are in excellent accord with the results of recent electron–electron coincidence and synchrotron–radiation branching ratio measurements. The origins of particularly intense resonancelike features in the discrete and continuum portions of the photoabsorption cross sections are discussed in terms of excitations into valencelike molecular orbitals. Small discrepancies between theory and experiment are attributed to specific autoionization processes and channel couplings not included in the calculations. In contrast to previously reported model or local potential studies, the present results employ the full nonlocal and nonspherical molecular Fock potential in ab initio photoabsorption calculations. The excellent agreement obtained between theory and experiment in molecular nitrogen suggests that highly reliable photoabsorption cross sections for diatomic molecules can be obtained from Hilbert space calculations and the Stieltjes–Tchebycheff method in the static-exchange approximation under appropriate conditions.

Applicability of self‐consistent field techniques based on the complex coordinate method to metastable electronic states

Hartree–Fock theory is applied to resonance states of an atomic Hamiltonian under the complex coordinate transformation. It is concluded that for shape resonances restricted Hartree–Fock theory provides a useful and practical approach to the problem of computing the complex resonance energy. Numerical results are presented for the low‐energy 2P shape resonance in e–Be scattering. With properly chosen basis functions the resonance energy obtained in these calculations is practically independent of the phase of the complex scaling parameter for a wide range of values. Application of this technique to molecular resonances is discussed. The widths of Feshbach resonances cannot be obtained from the theory in its present form, but it is suggested that a complex coordinate form of multiconfiguration self‐consistent field theory may be appropriate for that case.

Potential energy curves for diatomic zinc and cadmium

Molecular electronic structure theory has been applied to the low‐lying electronic states of Zn2 and Cd2. Gaussian basis sets of size Zn  (13s 9p 5d) and Cd  (15s 11p 7d) have been optimized in atomic calculations on the ground 1S and excited 3P electronic states. The general contraction scheme of Raffenetti has been used to reduce these primitive Gaussian bases to size Zn  (5s 4p 1d) and Cd  (6s 4p 2d) without any degradation in the atomic SCF energies. Following X 1Σ+g ground state SCF calculations, full configuration interaction was performed for the four valence electrons. The resulting potential energy curves for Zn2 and Cd2 are, with some notable exceptions, qualitatively similar. In the case of Cd2, we have obtained potential curves which include spin–orbit coupling and have carried out a detailed analysis of the fluorescence intensity from the first 1u (3Σ+u) excited state.

Application of complex coordinate SCF techniques to a molecular shape resonance: The 2Πg state of N2−

The lifetime and level width of the metastable 2Πg state of N2− are calculated using restricted Hartree‐Fock theory.(AIP)

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.

Theoretical study of the 400 eV core‐excited valence states of N2

We show that accurate transition energies for the 1s core‐valence excited 1Πu and 1Πg states of N2 can be obtained from limited configuration–interaction calculations using localized 1σ orbitals. Generalized oscillator strengths are also obtained for these states and comparisons with recent experimental findings are made.

The Complex Kohn Variational Method

Though substantial progress has been made in the theoretical study of electron collisions with molecules and molecular ions, most work has been restricted to diatomic or linear targets. Electron- and photon-molecule collision cross sections are needed in such diverse areas such as advanced laser development, pollution control, the design of highspeed space re-entry vehicles, the manufacture of semiconductor devices and plasma driven chemical synthesis. For example, the photoionization of polyatomic radicals, which plays an important role in combustion1, requires a description of electron scattering from a polyatomic molecular ion. Such studies are scarce. In the area of plasma enhanced chemical vapor deposition and etching2, studies indicate a subtle interplay between the neutrals, ions, electrons, and the surface. A critical lack of fundamental cross sections is hindering our understanding of these processes. Reliable theoretical methods are exceptionally important because of the extreme difficulty of experiments in this area.

Interchannel coupling and ground state correlation effects in the photoionization of CO

We describe a general procedure for applying the complex Kohn variational method to the calculation of molecular photoionization cross sections and asymmetry parameters. In this initial application of the method, we examine the effects of interchannel coupling and ground state correlation on the X 2Σ+(5σ−1), A 2Π(1π−1), and B 2Σ+(4σ−1) partial photoionization cross sections and asymmetry parameters for the CO molecule. We find that the dominant effect of interchannel coupling is to remove a spurious π→π* resonance feature from the continuum that appears at the frozen‐core Hartree–Fock level. We also find that it appears to be important to combine the effects of final channel coupling with a correlated initial target state to achieve quantitatively correct cross sections.