Which online resources are available for job search at the Ph.D. level in the computational chemistry field?
One of the best resources for jobs in computational chemistry (not limited to PhD level positions) is the job section of the Computational Chemistry List.
Another place where I've regularly seen relevant postings is the "Computational Chemists" group on LinkedIn.
If you are based in Europe, or would consider a position in Europe, I strongly recommend the CCP5 mailing-lists for this purpose. I also second the advice about the Computational Chemistry List, these are the two places I post job openings for my own group.
In the UK, all academic positions open are posted to jobs.ac.uk, making it really invaluable for job search.
Finally, some journals have a job listings section as well, such as Nature jobs, Science Careers. The learned society of your field might also have job listing, as e.g. the Royal Society of Chemistry or the ACS’s Chemistry jobs listing.