This paper investigates the efficiency of the implicit restart Lanczos and simple (without reorthogonalization) Lanczos algorithms, as eigensolvers for large scale computations in molecular and chemical physics. Using the cardioid billiard and the hydrogen cyanide/hydrogen isocyanide (HCN/HNC) molecule as model systems we demonstrate superior efficiency of implicit restart Lanczos compared to the simple Lanczos algorithm. A modified implementation of implicit restart Lanczos is also presented which works with a smaller Krylov space-with associated savings in memory-and can handle larger basis sets than the usual implicit restart Lanczos. It also enables getting all eigenpairs of a matrix, or all eigenvalues below a threshold (where the number of such is not known before hand), which is more difficult with the usual implicit restart algorithm.