In Part I (Mol. Phys. 35, 1681 (1978)) we used results from the Xα scattered wave (XαSW) method for guiding the parametrisation of the complete neglect of differential overlap (CNDO) method for clusters of silver, and we proposed the extension of this approach to other heavier elements for which CNDO schemes are not well developed. The main purpose of the present paper is to test this approach for the elements aluminium to sulphur for which more information is available. XαSW calculations have been made for the molecular clusters Al7, Si5H12, and P4, and comparisons made with experiment and with other calculations where possible. The charge distributions and transition-state energies, along with information obtained previously for S8 by Salahub et al., have been used to derive new parameters (designated CNDO/HM) for the elements aluminium to sulphur essentially following the procedure in Part I. Calculations using these parameters have then been tested against an XαSW calculation made here for an Al10 cluster (which simulates the (111) surface of aluminium), and against other calculations made previously for P8, P4S3, SiH4, PH3, H2S, and SO2. Comparisons are also made with results from the CNDO/2 scheme. Generally the CNDO/HM procedure seems at least as successful as CNDO/2.