This article explores the place of computation in the history of quantum theory by examining the development of several approximation methods to solve the Schröödinger equation without using empirical information, as these were worked out in the years from 1927 to 1933. These ab initio methods, as they became known, produced the results that helped validate the use of quantum mechanics in many-body atomic and molecular systems, but carrying out the computations became increasingly laborious and difficult as better agreement between theory and experiment was pursued and more complex systems were tackled. I argue that computational work in the early years of quantum chemistry shows an emerging practice of theory that required human labor, technological improvement (computers), and mathematical ingenuity.