Calculation of the Hyperfine Splittings of CH. Cusp Constraint of a Wavefunction

Abstract

It is shown that applying an electron–nuclear cusp constraint to a CI wavefunction is equivalent to omitting from the basis set a particular linear combination of atomic orbitals. This result is exploited in constructing cusp‐constrained wavefunctions for CH. Several small STO basis sets, a double‐zeta basis, Cade and Huo's basis, and a subset of their basis were used to calculate hyperfine couplings for CH. The last two sets were also used with cusp constraints. Reasonable results are obtained for the proton splitting using either the free atom ${\text{1s}}_H$ orbital or the ${\text{1s}}_H$ orbitals from Cade and Huo's basis. Any attempt to use optimum orbital exponents with a small basis gave unreasonable results. The cusp constraint produced little change in the results for the largest basis. Our best theoretical estimate for $a^H$ is − 18 ± 3 G. Carbon‐13 splittings are much more sensitive to the basis set. Even for the largest basis the results were still strongly affected by the cusp constraint. Our best estimate for $a^C$ is + 10 ± 15 G.