Theoretical studies of photoexcitation and ionization in H_2O

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 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

On the electron affinity of the oxygen atom

The electron affinity (EA) of oxygen is computed to be 1.287 eV, using 2p electron full configuration-interaction (CI) wave functions expanded in a 6s5p3d2f Slater-type orbital basis. The best complete active space self-consistent field - multireference CI (CASSCF-MRCI) result including only 2p correlation is 1.263 eV. However, inclusion of 2s intrashell and 2s2p intershell correlation increases the computed EA to 1.290 at the CASSCF-MRCI level. At the full CI basis set limit, the 2s contribution to the electron affinity is estimated to be as large as 0.1 eV. This study clearly establishes the synergistic effect between the higher excitations and basis set completeness on the electron affinity when the 2s electrons are correlated

Benchmark full configuration-interaction calculations on HF and NH2

Full configuration-interaction (FCI) calculations are performed at selected geometries for the 1-sigma(+) state of HF and the 2-B(1) and 2-A(1) states of NH2 using both DZ and DZP gaussian basis sets. Higher excitations become more important when the bonds are stretched and the self-consistent field (SCF) reference becomes a poorer zeroth-order description of the wave function. The complete active space SCF - multireference configuration-interaction (CASSCF-MRCI) procedure gives excellent agreement with the FCI potentials, especially when corrected with a multi-reference analog of the Davidson correction

Accurate ab initio calculations which demonstrate a 3 Pi u ground state for Al2

The spectroscopic parameters and separations between the three low-lying X 3 Pi u, A 3 Sigma g -, and a 1 Sigma g + states of Al2 are studied as a function of both the one-particle and n-particle basis set. Approximate correlation treatments are calibrated against full Cl calculations correlating the six valence electrons in a double-zeta plus two d-function basis set. Since the CASSCF/MRCI 3 Pi u to 3 Sigma g - separation is in excellent agreement wtih the FCI value, the MRCI calculations were carried out in an extended (20s13p6d4f)/(6s5p3d2f) gaussian basis. Including a small correction for relativistic effects, the best estimate is that 3 Sigma g - state lies 174/cm above the 3 Pi u ground state. The 1 Sigma g + state lies at least 2000/cm higher in energy. At the CPF level, inclusion of 2s and 2p correlation has little effect on D sub e, reduces T sub e by only 26/cm, and shortens the bond lengths by about 0.02 a sub o. Further strong support for a 3 Pi u ground state comes from the experimental absorption spectra, since both observed transitions can be convincingly assigned as 3 Pi u yields 3 Pi g. The (2) 3 Pi g state is observed to be sensitive to the level of correlation treatment, and to have its minimum shifted to shorter rho values, such that the strongest experimental absorption peak probably corresponds to the 0 yields 2 transition

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

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 good accord with recent electron–electron (e,2e) coincidence, synchrotron-radiation, and line-source branching-ratio measurements. Predicted resonance features in the X, B, O2s−1, and carbon K-shell channels are in particularly good agreement with the positions and intensities in the measured cross sections. A modest discrepancy between experiment and theory in the A-channel cross section is tentatively attributed to channel-coupling mechanisms associated with opening of the 1pi shell. The total vertical electronic S–T photoionization cross section for parent-ion production is in excellent agreement with recent electron–ion coincidence measurements. Comparisons are made between ionization processes in carbon monoxide and in the previously studied nitrogen molecule, and similarities and differences in the respective cross sections are clarified in terms of conventional molecular-orbital theory

Theoretical studies of the potential surface for the F - H2 greater than HF + H reaction

The F + H2 yields HF + H potential energy hypersurface was studied in the saddle point and entrance channel regions. Using a large (5s 5p 3d 2f 1g/4s 3p 2d) atomic natural orbital basis set, a classical barrier height of 1.86 kcal/mole was obtained at the CASSCF/multireference CI level (MRCI) after correcting for basis set superposition error and including a Davidson correction (+Q) for higher excitations. Based upon an analysis of the computed results, the true classical barrier is estimated to be about 1.4 kcal/mole. The location of the bottleneck on the lowest vibrationally adiabatic potential curve was also computed and the translational energy threshold determined from a one-dimensional tunneling calculation. Using the difference between the calculated and experimental threshold to adjust the classical barrier height on the computed surface yields a classical barrier in the range of 1.0 to 1.5 kcal/mole. Combining the results of the direct estimates of the classical barrier height with the empirical values obtained from the approximation calculations of the dynamical threshold, it is predicted that the true classical barrier height is 1.4 + or - 0.4 kcal/mole. Arguments are presented in favor of including the relatively large +Q correction obtained when nine electrons are correlated at the CASSCF/MRCI level

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

Atomic spectral-product representations of molecular electronic structure: metric matrices and atomic-product composition of molecular eigenfunctions

Recent progress is reported in development of ab initio computational methods for the electronic structures of molecules employing the many-electron eigenstates of constituent atoms in spectral-product forms. The approach provides a universal atomic-product description of the electronic structure of matter as an alternative to more commonly employed valence-bond- or molecular-orbital-based representations. The Hamiltonian matrix in this representation is seen to comprise a sum over atomic energies and a pairwise sum over Coulombic interaction terms that depend only on the separations of the individual atomic pairs. Overall electron antisymmetry can be enforced by unitary transformation when appropriate, rather than as a possibly encumbering or unnecessary global constraint. The matrix representative of the antisymmetrizer in the spectral-product basis, which is equivalent to the metric matrix of the corresponding explicitly antisymmetric basis, provides the required transformation to antisymmetric or linearly independent states after Hamiltonian evaluation. Particular attention is focused in the present report on properties of the metric matrix and on the atomic-product compositions of molecular eigenstates as described in the spectral-product representations. Illustrative calculations are reported for simple but prototypically important diatomic (H_2, CH) and triatomic (H_3, CH_2) molecules employing algorithms and computer codes devised recently for this purpose. This particular implementation of the approach combines Slater-orbital-based one- and two-electron integral evaluations, valence-bond constructions of standard tableau functions and matrices, and transformations to atomic eigenstate-product representations. The calculated metric matrices and corresponding potential energy surfaces obtained in this way elucidate a number of aspects of the spectral-product development, including the nature of closure in the representation, the general redundancy or linear dependence of its explicitly antisymmetrized form, the convergence of the apparently disparate atomic-product and explicitly antisymmetrized atomic-product forms to a common invariant subspace, and the nature of a chemical bonding descriptor provided by the atomic-product compositions of molecular eigenstates. Concluding remarks indicate additional studies in progress and the prognosis for performing atomic spectral-product calculations more generally and efficiently