Hartree-Fock and hybrid density functional theory calculations of static properties at the complete basis set limit via finite elements. II. Diatomic molecules

Although deceivingly simple, diatomic molecules exhibit a rich chemistry and thereby may be used for accurate benchmarks of theoretical methods. We present the implementation of a diatomic finite element solver in the HelFEM program, which can be employed for benchmark calculations on diatomic systems. A basis set of the form $B_{n}(\mu)Y_{l}^{m}(\nu,\phi)$ is used, where $(\mu,\nu,\phi)$ are transformed prolate spheroidal coordinates, $B_{n}(\mu)$ are finite element functions, and $Y_{l}^{m}$ are spherical harmonics, which allows for an arbitrary level of accuracy. HelFEM supports nonrelativistic Hartree-Fock (HF) and density functional (DF) theory calculations, including hybrid DFs that aren't available in other program packages. Hundreds of functionals at the local density approximation (LDA), generalized gradient approximation (GGA) as well as the meta-GGA level through an interface with the Libxc library. Finite electric fields are also supported, enabling access to electric properties. We introduce a powerful tool for adaptively choosing the basis set by using the core Hamiltonian as a proxy for its completeness. The program and the novel basis set procedure are demostrated by reproducing the restricted HF limit energies of 66 diatomic molecules with excellent agreement. Then, the electric properties of the BH and N2 molecules under finite field is studied, again yielding excellent agreement with previous HF limit values for energies, dipole moments, and dipole polarizabilities, even though the calculations of the present work employed over two orders of magnitude fewer parameters for the wave function. Finally, HF, LDA, GGA, and meta-GGA calculations of the atomization energy of N2 are performed, demonstrating the superb accuracy of the present approach.