Symmetry-adapted density fitting in auxiliary density functional theory

Abstract

The working equations for the variational fitting of the Coulomb potential in finite systems with symmetry-adapted auxiliary functions are derived and presented. The computationally efficient construction of the symmetry transformation matrix from symmetry equivalent atoms and function transformation matrices is discussed in details. We show that for totally symmetric electron densities only the totally symmetric parts of the fitting equation systems in auxiliary density functional theory have to be solved. This approach is validated on test molecules with point group symmetries $$C_{\infty v},\, C_{2v},\, C_{3v},\, C_{s},\, O_h,\, T_{d},\, D_{5d},\, D_{5h} ,\, D_{6h}$$ and $$I_h$$ for Hartree-Fock, the local density approximation, the generalized gradient approximation and hybrid functionals. In all cases, the self-consistent field energy differences between the converged unconstrained and symmetry-adapted density fitting is well below $$1\,$$ kcal/mol. The large reduction in the dimensionality of the corresponding linear equation systems is explored in the calculation of giant fullerenes in $$I_h$$ symmetry. For these systems, the symmetry-adapted density fitting using truncated eigenvalue decomposition is computationally more efficient than the recently introduced iterative density fitting with the Krylov subspace method MINRES. This illustrates the computational advantage of symmetry-adapted density fitting.