Direct analytic SCF second derivatives and electric field properties

Abstract The direct SCF method (recomputation of two-electron integrals) has been extended to the analytic second derivatives of the SCF energy. Since the use of direct rather than conventional methods adds a step which scales in cost with the fourth power of molecular size to a calculation which overall scales with the fifth power, this is an ideal case for the direct approach. The direct second derivative calculation must, however, be organized somewhat differently than the direct SCF itself in order to performed the O (N5) steps with the same efficiency as the conventional procedure. Additionally, certain classes of third derivatives, including the hyperpolarizability and the nuclear coordinate derivatives of the polarizability, can be handled directly. The result is a method which requires only O(N3) external storage (or main memory), is only 30% slower than the conventional method even for small cases (e.g., 16 atoms and 100 basis functions) and enables the prediction of vibrational spectra and electric field properties for much larger systems than was previously possible.

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