Efficient calculation of ROA tensors with analytical gradients and fragmentation.

We present the results of calculations of Raman optical activity spectra of sizable systems from optical tensors of the fragments, the tensors calculated by an analytic approach at the time-dependent Hartree-Fock level of theory. The analytic approach permits large basis sets which, together with the limited geometrical extent of the fragments, obviates the need for the use of London-type orbitals. The implementation of the analytical gradient approach is formulated in the atomic orbital basis by using the elements of the density matrix as variational parameters. This makes the approach directly applicable to linear scaling methods. We do not solve the response equations for the geometrical distortions of the nuclei but determine instead the second-order perturbed densities with respect to the electromagnetic field perturbations. The number of perturbed density matrices that needs to be determined is thus independent of the number of nuclei, making the approach applicable to fragments with many nuclei and with good quality basis sets. Compared to numerical differentiation schemes, the analytical approach is about 10 times faster even for moderately sized molecules.