Rice was born on 10 July 1960 in Cambridge, England. She earned a bachelors degree in mathematics and chemistry from Royal Holloway, University of London in 1981, winning the Martin Holloway Prize as that years best honours finalist in her subject. She completed her Ph.D. in theoretical chemistry at the University of Cambridge in 1985, under the supervision of Nicholas C. Handy.
After postdoctoral research with Henry F. Schaefer III at the University of California, Berkeley, and a year as a research fellow of Newnham College, Cambridge, she joined IBM Research in 1988.