Dr. Dayhoff's graduate research career began with a Ph.D. in quantum chemistry, under Prof. George Kimball, in the Columbia University Department of Chemistry. She was a Watson Computing Laboratory Fellow in 1947-48, allowing her to use the computing resources of the laboratory.  In her thesis research, she pioneered the application of mass data processing equipment to theoretical chemistry. She devised a method of applying punched-card machines to the calculation of molecular resonance energies of several polycyclic organic molecules. Due to the amount of calculation required, such calculations were considered infeasible with hand operated calculators. The machines she used were regarded as high technology in 1947, shortly before the emergence of programmable computers. The process was iterative and required manually carrying cards from one type of machine to another (4 types), as no single machine could do the whole iteration. Convergence was slow and several months could be required for a result.

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