Matrix-Based Coupled Perturbed SCF D-CPSCF

Density Matrix-Based Coupled Perturbed SCF (D-CPSCF) 

In the following, we focus on the determination of the density matrix as perturbed with respect to the magnetic field (P )s whereas an extension to other perturbations is straightforward. Within a linear response formalism (only terms linear in the external perturbation are considered), we can solve for the perturbed density matrix P directly 

At this stage, it is worthwhile to consider some properties of the derivative density matrix, which can—as described in the section on density matrix-based energy gradients—be split into a sum of subspace projections (Eq. [108])  

The convergence properties of the density matrix-based equations, i.e., the number of iterations to converge P , are similar to the ones encountered for a solution in the MO space, so that the advantage of using sparse multiplications within the density-based approach allows us to reduce the scaling property of the computational effort in an efficient manner. In this way, NMR chemical shift calculations with linear-scaling effort become possible and systems with 1000 and more atoms can be treated at the HF or DFT level on today s computers.Extensions to other molecular properties can be formulated in a similar fashion. 

OUTLOOK ON ELECTRON CORRELATION METHODS EOR LARGE SYSTEMS 

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