High-accuracy ab-initio quantum chemistry by means of an SU(2) x U(1) invariant matrix product state Ansatz: the static second hyperpolarizability

We have implemented the single-site density matrix renormalization group algorithm for the variational optimization of SU(2) \times U(1) (spin and particle number) invariant matrix product states for general spin and particle number symmetric fermionic Hamiltonians. This class also includes non-relativistic quantum chemical systems within the Born-Oppenheimer approximation. High-accuracy ab-initio finite field results of the longitudinal static polarizabilities and second hyperpolarizabilities of one-dimensional hydrogen chains are obtained with the algorithm. A comparison with other methods is made.