P. W. Langhoff

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...

Stieltjes imaging of photoabsorption and dispersion profiles

Variational and moment‐theory techniques for the construction of accurate approximations to photoabsorption and dispersion profiles in atoms and molecules are described and applied to simple atomic systems. It is shown that appropriately defined principal pseudostates, when employed in ab initio variational calculations, furnish the discrete transition frequencies and oscillator strengths that provide so‐called principal representations of spectral moments. The Tchebycheff‐Stieltjes‐Markoff moment theory ensures that the principal frequencies and strengths furnish the information necessary for constructing convergent images of both the discrete and continuum portions of photoabsorption profiles. Evaluation of the appropriate principal value integrals results in convergent Stieltjes images of the associated photodispersion profiles. Detailed applications in the cases of the negative hydrogen ion and atomic hydrogen show that the Stieltjes imaging procedure is rapidly convergent for both the discrete and co...

Correlation of molecular valence‐ and K‐shell photoionization resonances with bond lengths

A theoretical study of the relationship between interatomic distances and the spectral positions of valence‐ and K‐shell σ* photoionization resonances is reported for a selected series of molecules. Three‐dimensional graphical representations of the occupied and virtual‐valence σ‐symmetry orbitals of these compounds reveal their striking similarity to the wave functions of a particle in a cylindrical well, substantiating qualitative notions long employed in free‐electron molecular orbital (FEMO) approximations. Accordingly, the molecular potential along the symmetry axis in these compounds is modeled after a finite square well, with a depth approximately equal to the energy of the lowest σ‐symmetry valence molecular orbital and a width determined from analogies to FEMO theory. Calculated minimal‐basis‐set molecular‐orbital energies for both occupied and virtual states are seen to correlate accurately with the simple square‐well energy level formula (π2 /2)(n2/l 2 ) when measured in Hartree atomic units fr...

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.

Theoretical studies of photoionization in C2H2, C2H4, and C2H6: correlation of prominent spectra features with CC and CH antibonding orbitals

Studies are reported of outer-valence-, inner-valence-, and K-shell photoionization cross sections in C2H2, C2H4, and C2H6 employing 2 methods particularly appropriate for descriptions of resonant partial channels. Calculations in the static-exchange approximation are found to give results in good agreement with corresponding measured values. Prominent spectral features in the cross sections correlate well with the positions and strengths of Mulliken N → Vσ charge-transfer excitations involving CC and CH antibonding (σ*) virtual valence molecular orbitals. Accordingly, such excitations are seen to account for the origins and natures of the resonance features in these compounds, clarifying their spectral variations in terms of CC bond distances and the numbers of CH bonds. The presence of both CC and CH antibonding (σ* orbitals makes interpretation of the photoionizat cross sections of C2H2, C2H4, and C2H6 particularly interesting, complicating somewhat the 1/l2 variation in the spectral positions of resonance features with effective bond lengths that is common in linear compounds.

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

Theoretical investigations employing configuration‐interaction calculations and recently devised moment‐theory techniques are reported of the vertical electronic dipole excitation and ionization spectra in molecular formaldehyde. A double‐zeta basis of contracted Gaussian‐lobe functions, supplemented with appropriate polarization, diffuse, and bond functions, is employed in the construction of Fock spectra in C2v symmetry for X 1A1 and (n→π*)3A2 states near the ground‐state equilibrium geometry. The 50 occupied and virtual Fock orbitals obtained in each case are used in configuration‐interaction calculations of 200‐term eigenvectors of appropriate symmetry for each of the principle‐axis polarization directions, and for the lowest‐lying molecular ionic states. The ionization energies, discrete vertical transition frequencies and oscillator strengths, and associated approximate configurational assignments obtained are in general accord with experimental determinations and with the results of previously repo...

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.

Feshbach–Fano formalism in Hilbert space: Application to shape resonances in molecular photoionization

An explicit Hilbert‐space formulation of Feshbach–Fano theory is described which is particularly well suited for treating the problem of shape resonances in molecular photoionization. The prepared states of Fano and Cooper are employed to resolve the irreducibly infinite degeneracy of molecular electronic continua that arises from the noncentral nature of molecular (body‐frame) potentials. Previously defined L2 Stieltjes states generated employing appropriate test functions are shown to converge to these prepared states, avoiding prior construction of the associated degenerate channel functions. A novel choice of zeroth‐order state particularly suitable for applications of the L2 Feshbach–Fano method to molecular shape resonances is introduced and shown to avoid many of the difficulties associated with more conventional treatments employing resonance scattering theory. Specifically, the energy of this zeroth‐order state is seen to be a weighted average over the correct photoionization cross section, the a...