Theoretical Description of Molecular Rydberg States: B Σ+1 and Lowest Σ+3 States of BH

Ab initio calculations, including electron correlation, have been carried out on the ${\mathrm{X\hspace{0.17em}}}^1{\Sigma }^{+}$ , ${\mathrm{B\hspace{0.17em}}}^1{\Sigma }^{+}$ , and lowest ${}^3{\Sigma }^{+}$ states of BH. The last two states can be thought of as arising from the ${\text{1σ}}^2{\text{2σ}}^2\text{3σ 4σ}$ electron configuration. A double‐zeta‐plus‐polarization and Rydberg function basis of Slater functions is used and electron correlation is considered through the use of approximate ``first‐order'' wavefunctions. Optimum wavefunctions for the ${\mathrm{B\hspace{0.17em}}}^1{\Sigma }^{+}$ state are obtained by repeated diagonalization of the density matrix arising from the second eigenvalue of the ${}^1{\Sigma }^{+}$ secular equation. For the ground state the ab initio dissociation energy is 3.27 eV, compared to Gaydon's experimental value $\text{3.54 ± 0.04\hspace{0.17em}}\mathrm{eV}$ . Other spectroscopic constants for the ${\mathrm{X\hspace{0.17em}}}^1{\Sigma }^{+}$ and ${\mathrm{B\hspace{0.17em}}}^1{\Sigma }^{+}$ states are also in good agreement with experiment. The X—B separation is calculated to be 51 770 cm<sup>−1</sup>, compared to the experimental value 52 347 cm<sup>−1</sup>. The ${\mathrm{B\hspace{0.17em}}}^1{\Sigma }^{+}$ calculations confirm the double minimum predicted by Browne and Greenawalt. The lowest ${}^3{\Sigma }^{+}$ state is predicted by the present treatment to be Rydberg‐like (with a minimum at 1.173 Å) for short internuclear separations and valencelike (repulsive) for large separations. A maximum occurs in the ${}^3{\Sigma }^{+}$ potential curve at 1.45 Å. Natural‐orbital analyses and electron density plots are used to describe the valence to Rydberg ``transition.''