Nora H. Sabelli

MCSCF calculations for six states of NaH

Ab initio multiconfiguration self‐consisting‐field calculations are reported for the energies, electronic wavefunctions, and one‐electron properties of the X1Σ+, A1Σ+, B1Π, a3Σ+, b3Π, and c3Σ+ states of NaH over a wide range of internuclear distances. In these calculations, only the two valence electrons are correlated. Three states (X1Σ+, A1Σ+, and b3Π) were found to be bound, with the following dissociation energies and internuclear separations (with known experimental values in parentheses): De (X1Σ+) = 1.878 (2.12±0.20) eV, Rmin (X1Σ+) = 3.609 (3.566) bohr; De (A1Σ+) = 1.203 (1.41±0.20) eV, Rmin (A1Σ+) = 6.186 (6.062) bohr; and De (b3Π) = 0.109 eV, Rmin (b3Π) = 4.458 bohr.

Transition moments, band strengths, and line strengths for NaH

Electronic transition moments, as functions of internuclear separation, are calculated for the A1Σ+ → X1Σ+, B1Π → X1Σ+, B1Π → A1Σ+, c3Σ+ → a3Σ+, b3Π → a3Σ+, and b3Π → c3Σ+ transitions in NaH from ab initio molecular wavefunctions. Reduced line strengths, band strengths, band oscillator strengths, and band Einstein coefficients are calculated for the observed A1Σ+ → X1Σ+ transition, and are compared to experimental band intensities. Also calculated are Franck–Condon factors and R centroids, and the effects of various approximations used in treating experimental data are analyzed.

A new method for computing properites of negative ion resonances with application to 2Σ+u states of H−2

A new method for computing properties of negative ion resonances is reported. The first step is to carry out a CI calculation of the lowest 15 or so states of proper symmetry of the negative ion system. A Feshbach projection‐operator technique is then used to project out the various resonances from the CI states. The projection is based on the assumption that resonances have small expectation values for the one‐electron operator z2 and continuum states have large values. The energies, energy widths, and lifetimes of the resonances are then straightforward to calculate. The method has been applied to the 2Σ+u states of H−2. Two resonances reported here have been seen by other workers, but a third, which lies 5.8 eV above the v=0 level of H2, has not been identified before. The implication of this resonance for electron‐hydrogen scattering experiments is discussed.

Rotation–vibrational analysis for three states of NaH and NaD

We have carried out a rotation–vibrational analysis for the X1Σ+, A1Σ+, and b3Π states of NaH and NaD using accurate ab initio calculated potential curves. The calculated values of Be, αe, Re, ωe, and ωexe (with known experimental values in parentheses) are NaH X1Σ+ : Be = 4.748 (4.886) cm−1, αe = 0.126 (0.129) cm−1, Re = 3.625 (3.562) bohr, ωe = 1183.17 (1172.2) cm−1, and ωexe = 21.23 (19.72) cm−1; NaD X1Σ+ : Be = 2.475 (2.5575) cm−1, αe = 0.0474 (0.0520) cm−1, Re = 3.624 (3.565) bohr, ωe = 826.60 (826.10) cm−1 and ωexe = 9.44 cm−1; NaH b3Π : Be = 3.533 cm−1, αe = 0.853 cm−1, Re = 4.202 bohr, ωe = 419.39 cm−1 and ωexe = 50.25 cm−1; NaD b3Π: Be = 1.763 cm−1, αe = 0.265 cm−1, Re = 4.294 bohr, ωe = 311.95 cm−1 and ωexe = 28.68 cm−1. The anomalous behavior of the Bv′s and ΔGv+1/2′s of the A1Σ+ state is satisfactorily reproduced by these calculations: for NaH, Bv (max ) = 1.9717 (1.941) cm−1 at v = 6 (6) and ΔGv+1/2 (max) = 381.37 (360.3) cm−1 at v = 9 (8); for NaD, Bv (max) = 1.0274 (1.012) cm−1 at v = 8 (8)...

Frozen core approximation, a pseudopotential method tested on six states of NaH

A pseudopotential formulation, more appropriately called the frozen core approximation (FCA), is presented in detail. This FCA is tested by performing MCSCF calculations on the six low lying states, X1Σ+, A1Σ+, a3Σ+, c3Σ+, B1Π, and b3Π of NaH. The results obtained are compared with those of an analogous previous MCSCF calculation on these states without the use of FCA, i.e., with all orbitals optimized. It is found that energies are obtained rather accurately with FCA; however, calculated molecular properties are affected more strongly and the shapes of the potential curves appear to be distorted somewhat by FCA. It is argued that no pseudo‐ or model‐potential calculation can give errors less than FCA unless the potential is made valence shell dependent. This, however, would be analogous to a full calculation, and the savings due to a pseudopotential approximation would be lost.

Simple semiempirical potential energy surfaces for the reaction of alkali metal atoms with the bromine molecule

Potential energy surfaces for the reactions of the alkali metals M (Li, Na, K, Rb, and Cs) with Br2 are computed using a simple semiempirical procedure. The calculations show that there is a vibrational barrier between M+Br2 and M++Br2− along the Br–Br coordinate which plays an important role in the reaction. A potential well exists for all angles of approach of the metal to the molecule; this M+Br2− species is lower in energy than any product channel. The calculated ionic/covalent coupling matrix elements between M+Br2 and M++Br2− agree well with the experimental values.

SCF study of the lowest 2Σ+u resonance of H−2

A novel technique for computing properties of negative ion resonances is reported. The system is initially embedded in a spherical cage of charge +1. This lowers the energy of the resonance below the energies of the neutral molecule–free electron states, so the ground state SCF wave function corresponds to the pure resonance. The energy of the resonance is then determined by removing the cage, freezing the wave function, and computing the expectation value of the correct Hamiltonian. The negative ion basis set can be optimized at each value of R if desired. Results of SCF and projected (localized) SCF computations are reported for the 2Σ+u state of H−2. Satisfactory agreement with the complex SCF calculations of McCurdy and Mowrey is obtained. The projected SCF wave functions form a useful basis for a configuration–interaction computation.

A theoretical investigation of 2Σ+u resonance states of H−2

We have applied a new method for computing properties of molecular negative ion resonances to calculate the potential curves of the first three 2Σ+u states of H−2. The energy widths and lifetimes of the resonances are also calculated. The first and third resonances correlate to H+H− asymptotes at R=∞, but the second resonance disappears near R=6.0 a.u. The resonance properties are shown to be insensitive to variations in the basis set. The results are compared to recent calculations on this system.

Calculation of the far‐wing line broadening of the sodium D line induced by collisions with hydrogen atoms

Using ab initio potential curves and electronic transition moments we have calculated the far wings of the sodium D line emission spectrum broadened by collisions with hydrogen atoms. A classical–statistical model was used for this calculation. The calculated spectrum has two satellite peaks, one at 9683 cm−1, whose intensity diminishes with increasing temperature, and one at 21 641 cm−1, whose intensity increases with increasing temperature.