A global change is a dangerous thing. When I wrote the manuscript for my L&PS (PDF) paper on quantum chemistry, I wrote both 'Quantum Chemistry' and 'Quantum Mechanics' with a capital. Pretty consistently. Then at the last moment I changed my mind. As a result, there are some annoying typos in the paper with an inconsistent capitalisation of both 'quantum', 'chemistry' and 'mechanics'.
I also noted I dropped a factor 1/2 in formula 2. The summation over 2-particle terms needs a factor 1/2, or it needs the sum changed to read that it is over i less than j.
While none of this changes the argument one little bit, I'm slightly annoyed with myself nonetheless.
