At Henry's suggestion, I wrote to Jacob Bigeleisen. He replied:*
How did I get into isotope chemistry? In 1943 I worked at SAM Laboratory at Columbia U (Manhattan Project). My initial assignment was to look for isotope shifts in the electronic spectra of uranium compounds (principally uranyl ion). The purpose of this research was to examine the feasibility of a photochemical separation of the uranium isotopes for military purposes. It was a small project. It was here that I became acquainted with Maria Mayer. She worked on the theory of the spectra. I did experiments and consulted with her regularly about my results and her results. The project was reviewed in July 1943 by James B. Conant and Richard C. Tolman, two high officials in the war time science effort. They brought along as an advisor E.B. Wilson, Jr., the outstanding spectroscopist and quantum chemist from Harvard. The Committee found our work very interesting, but recommended that it be discontinued. The time schedule for any practical application of a photochemical process was inconsistent with the plans for the production of a weapon. People like Urey favored a small scale continuing effort as part of scientific intelligence. Was this a path the Germans could be following?
The dozen or so people working on the project were reassigned in September. I was assigned to write up the work of the project as a final report, which was issued under the name of H.C. Urey. Maria Mayer went to the hospital in October 1943 for gall bladder surgery. In late November an assistant of Urey's (one of his former graduate students) Isidor Kirschenbaum came to see me. He said 'you know all about spectra of uranium compounds.' I said I didn't know everything; what was known, I knew. He said: 'Here is this formula. Put in the information about all uranium compounds and give me the results. We are interested in the possible chemical separation of the uranium isotopes. What we would be particularly interested in would be a volatile compound, which dissociates in the vapor. We have reason to believe that this would be very favorable.' I asked: 'How do you know this?' He said he could not tell me. I looked at the formula he gave me. It was the Urey-Greiff equation. I told him that I was not familiar with that whole field and I would have to study it out before I put numbers into the equation. He then said: 'Don't you know there is a war on?' He reported to Urey that I was not a very cooperative person.
Well I studied out the Urey-Greiff equation. There are a lot of factors. For uranium compounds, I could see that we did not know some of the factors; for some of the factors the number was of the order +1.001; for some of the factors the number was -1.001. With the computing facilities available then (desktop mechanical calculators) one could get any final answer from +1.00x to -1.00x from the Urey-Greiff equation. So, I decided I would look into a different approach. In chemistry and most of physics, one does not measure absolute quantities. One measures differences. Would it be possible to calculate differences directly instead of absolute quantities and then subtract the two to get the isotope effect? I started on this approach and I completed the zero point energy and the Boltzmann excitation terms.
On Monday after Thanksgiving 1943 Maria Mayer returned to work. She asked me how I was coming along with the final report. I told her I was not working on it. 'What was I doing?' she asked. I explained the problem to her and showed her my progress. This was a general type of problem she was thoroughly familiar with. In collaboration with George E. Kimball and Walter Stockmayer, she had calculated the isotope effect in the reaction HD + H2O = H2 + HDO. This reaction was used to produce heavy water at a plant in Trail B.C. and in Norway.) She was also familiar with the general subject since she and her husband, Joe Mayer, had just written a book on statistical mechanics. I had studied this book as a graduate student. She found my approach very interesting, very sensible and very promising. She then volunteered by asking me whether she could join me in working on this project. I said sure, that would be great. So she did and by the end of the day we completed the derivation of the Bigeleisen-Mayer equation.  We then made a number of predictions of systems that would be hopeless for uranium isotope separation and pointed to potential interesting avenues. An experimental program was then organized under Clyde Hutchinson. I worked on that for about a half a year.
Urey was too occupied to look into what we had done. His deputies either did not understand or did not believe that a green Ph.D. new to the field could simplify the Urey-Greiff equation to the point where meaningful calculations could be made. There was a lot of secrecy and people were not told everything they needed to know to make the best progress. In April I became involved in determining the structure of UF6 by spectroscopic means. I did the experiments at American Cyanamid in Stamford, Conn., where they had outstanding spectroscopic equipment. I worked on the analysis of the the spectra with Maria Mayer, who had tried two years earlier in collaboration with Edward Teller to predict the vibrational structure of UF6 from first principles! I told Maria Mayer when I started on that project that it was an experimental project, not one for calculation. She asked me whether I could do it (determine the Raman spectrum). She took out of her drawer the infra-red spectrum which had been measured by John Turkevich at Princeton. Neither she, Turkevich nor Edward Teller were able to decipher the infra-red spectrum of UF6. While Maria Mayer and I worked on the analysis of the spectra, from which we deduced unequivocally the regular octahedral structure, in contrast to the electron diffraction results of Simon Bauer, she told me that she had written a summary report of our work on the theory of isotope effects in equilibria and our calculations relevant to uranium isotope separation.
She prepared this report at the request of Martin Kilpatrick, Urey's deputy to whom we reported. The reason for this was that Edward Teller was to make one of his regular consulting visits from Los Alamos. Kilpatrick showed Teller Maria Mayer's report of our work. Teller had also worked on this problem (there is a 1938 paper by Herzfeld and Teller). He told Kilpatrick that the work was correct and first class. Kilpatrick reported to Maria Mayer that Teller approved of the work. Fine. That made her furious. She said to me: 'They trust Edward Teller and not me.'
Regards to Henry. Pass this message on to him.
* Bigeleisen wrote to me in longhand. I transcribed it here. I supplied the links as well in case anyone was interested.
 Bigeleisen later retold a reporter about this amazing moment when he was briefly overwhelmed by Maria Mayer's brilliance:
She looked at my work and asked 'why don't you finish it up by taking out the classical part?' Without a pause, she wrote the simplified equation, saying 'Now you have it; it's all done.' I didn't immediately understand what she meant when she said to cut out the classical part. I went home. I worked on it, and eventually I got the same result.