Introduction

The Second Derivatives (SD) program analytically calculates the Hessian matrix, from which the infrared IR frequencies and intensities can be obtained.

The SD program requires that a previous ADF Kohn-Sham calculation be done on the molecule of interest and that the corresponding TAPE21 be saved.

Currently, the SD program is about 3 to 4 times faster than the older numerical second derivatives (in ADF) for molecules that lack symmetry. If symmetry can be taken advantage of, then SD is only slightly faster than the older numerical code. Like the older numerical code, SD can be run in parallel.

Linear-scaling techniques have been introduced into the SD code, but as yet these have not been thoroughly tested.

The SD program can calculate gradients, dipole derivatives, vibrational frequencies and IR intensities. The first half of the output from the SD program is unique to SD, but the second half is identical to the output from a frequency run using the older numerical second derivatives code in ADF.

Unfortunately, SD still only works with the Xα xc-potential, although work is in progress to extend this to general gradient approximations (GGAs).

The requirements on the numerical integration seem to be less strict than for the numerical difference implementation in ADF itself. However, for heavier nuclei, it seems advisable to choose a higher accsph value than general accint value (typically 2 higher). Please check the INTEGRATION keyword in the ADF User's Guide for details on how to specify this.

The SD implementation can be combined with the ZORA treatment for relativistic effects. Some examples are discussed in the Examples document.

NOTE: At the moment the integration accuracy for SD is independent of that of ADF and should be input in the run file, prior to the SD block. To do this use the ADF key-word integration N where N is the integration accuracy required (default 4.0). See the SD example runs for more detail.