Charles F. Bender

Potential Energy Surface Including Electron Correlation for F + H2 → FH + H: Refined Linear Surface

A priori quantum mechanical calculations have been carried out at about 150 linear geometries for the fluorine plus hydrogen molecule system. An extended basis set of Gaussian functions was used, and electron correlation was treated explicitly by configuration interaction. Comparison with the experimental activation energy and exothermicity suggests that the theoretical potential surface is quite realistic.

INTERACTION POTENTIAL BETWEEN TWO RIGID HF MOLECULES

As a prelude to the study of energy transfer in the HF–HF system, the potential energy surface for the interaction of two rigid HF molecules has been calculated within the ab initio self‐consistent‐field framework. An H(4s 1p/2s 1p), F(9s 5p 1d/4s 2p 1d) basis set of contracted Gaussian function was employed. The number of unique points on the surface is greatly reduced by symmetry, and only 294 points were required to give a fairly complete description of the four‐dimensional surface. Parts of the surface are illustrated by a series of contour maps. Some preliminary attempts to fit the surface to an analytic form are described. The equilibrium geometry of (HF)2 is predicted.

Potential Energy Surface Including Electron Correlation for the Chemical F + H2 → FH + H I. Preliminary Surface

Rigorous quantum mechanical calculations have been carried out for about 150 linear and 200 non‐linear geometries for the FH2 system. The contracted Gaussian basis set used consisted of four s and two p functions on fluorine and two s functions on hydrogen. The barrier height and exothermicity are poorly predicted by single configuration self‐consistent‐field calculations. However, the 214‐configuration correlated results are in qualitative agreement with experiment (low barrier height and substantial exothermicity). The reaction coordinate is discussed, and pictures of the potential surface are presented. A second series of calculations is being carried out with a larger basis set. These latter calculations yield nearly quantitative agreement with experiment for both the barrier height and exothermicity.

Model studies of chemisorption. Interaction between atomic hydrogen and beryllium clusters

The interaction between hydrogen atoms and Be metal clusters has been studied by ab initio electronic structure theory. Self‐consistent‐field (SCF) calculations have been carried out using both minimum and larger basis sets of contracted Gaussian functions. Both spatially restricted and unrestricted SCF methods were used, and different results were obtained in several cases. Reasons for the choice of this particular model system are discussed. Clusters as large as ten Be atoms have been considered, as have four different sites for the approach of the H atom. The electronic structure is discussed on the basis of predicted orbital energies and Mulliken atomic populations.

Avoided intersection of potential energy surfaces: The (H+ + H2, H + H2+) system

Nonempirical electronic structure calculations have been carried out on the two lowest 1A1 states of H 3+. When one proton is infinitely separated from the other two, these 1A1 potential surfaces cross each other. The nature of this avoided intersection is examined by means of potential curves, contour diagrams, and perspective plots. Surface hopping is discussed within a Landau‐Zener‐Stuckelberg (LZS) framework and the LZS assumptions concerning the surfaces are shown to be reasonable near the avoided intersection. Ab initio LZS parameters are compared with those obtained from the semiempirical diatomics‐in‐molecules surfaces of Preston and Tully. The agreement is good, better than might have been anticipated.

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.

C2υ Potential Energy Surfaces for Seven Low‐Lying States of CH2

Ab initio calculations have been carried out at 28 C2υ geometries for the lowest 1A1, 1A2, 3A2, 1B1, 3B1, 1B2, and 3B2 states of CH2. The basis set used was of the contracted Gaussian type with four s and two p functions on carbon and two s functions on hydrogen. In all calculations except 1A1 the SCF configuration plus all singly and doubly excited configurations were included (holding the K shell frozen), and the iterative natural orbital procedure was used to obtain an optimum set of orbitals. For the 1A1 state a two configuration SCF calculation was used as the starting point for the configuration interaction calculations. In a preliminary communication we predicted the triplet ground state of CH2 to be bent, and this prediction has since been justified experimentally by Bernheim et al. and by Wasserman et al. For the 1A1 state the ab initio geometry is r = 1.13 A, θ = 104°, compared to experiment, r = 1.11 A, θ = 102°. For the 1B1 state the predicted geometry is r = 1.09 A, θ = 144°, as opposed to ex...

Electronic Splitting between the 2B1 and 2A1 States of the NH2 Radical

Theoretical calculations are reported for the ground and first excited states of NH2. A contracted Gaussian basis of four s, two p, and one d functions is centered on the nitrogen atom, while for hydrogen two s and one p functions are used. Both self‐consistent‐field (SCF) and multiconfiguration first‐order wave‐functions have been computed, the latter using the iterative natural‐orbital method. Two new theoretical ideas were tested and found useful: (a) Bunges partitioning of degenerate spaces and (b) a procedure for generating uniform sets of starting orbitals for multiconfiguration calculations. For the 2B1 state the SCF, CI, and experimental geometries are θ=105.4°, r=1.019 A; θ=102.7°, r=1.055 A; θ = 103.3± 0.5, r=1.024± 0.005 A. The analogous results for the 2A1 state are θ=141.9°, r=0.997 A; θ144.7°, r=1.010 A; θ = 144± 5, r=0.97–1.00 A. For the upper 2A1 state the barrier to linearity is 1370 cm−1 in the SCF approximation, 1030 cm−1 from the correlated wavefunctions, and 770± 100 cm−1 experimenta...

Theoretical assignments of the low-lying electronic states of carbon dioxide

Abstract Extensive configuration interaction calculations (1000 to 1500 determinants) have been carried out for the six low-lying valence states of carbon dioxide in order to provide reliable assignments for the transitions to these states. In addition, Hartree—Fock calculations were performed on the lowest five (singlet and triplet) Rydberg states and the 2 Π g state of the positive ion. These results yield an accurate description of the excited states of carbon dioxide and provide for definitive assignments of the transitions observed by optical and electron impact studies (for the five states known experimentally, the calculations agree to within 0.2 eV of the experimental transition energies).