Complex symbolic algebra, such as the manipulation of second-quantized operators, Slater determinants, Feynman diagrams, is inevitable and ubiquitous in quantum chemistry. Increasingly, these operations are performed by the computerized systems that can handle higher mathematical objects than just numbers and simple arithmetic. With continuous financial support from the U.S. Department of Energy (Office of Basic Energy Sciences Grant No. DE-FG02-04ER15621), we have been leading the development of the algorithms that automate the algebraic transformation and computer implementation of many-body quantum-mechanical methods for electron correlation [1–11]. They enable a whole new class of highly complex but vastly accurate methods, the manual development of which is no longer practical.
[1] S. Hirata, The Journal of Physical Chemistry A, 107, 9887–9897 (2003).
[2] S. Hirata, T. Yanai, W. A. de Jong, T. Nakajima, and K. Hirao, The Journal of
Chemical Physics 120, 3297–3310 (2004).
[3] S. Hirata, The Journal of Chemical Physics 121, 51–59 (2004).
[4] S. Hirata, P.-D. Fan, A. A. Auer, M. Nooijen, and P. Piecuch,
The Journal of Chemical Physics 121, 12197–12207 (2004).
[5] S. Hirata, The Journal of Chemical Physics 122, 094105 (2005).
[6] G. Baumgartner, A. Auer, D. E. Bernholdt, A. Bibireata, V. Choppella, D. Cociorva,
X. Gao, R. Harrison, S. Hirata, S. Krishanmoorthy, S. Krishnan, C.-C. Lam, M. Nooijen,
R. Pitzer, J. Ramanujam, P. Sadayappan, and A. Sibiryakov, Proceedings of the IEEE 93,
276–292 (2005).
[8] K. Kowalski, S. Hirata, M. Wloch, P. Piecuch, and T. L. Windus,
The Journal of Chemical Physics 123, 074319 (2005).
[9] P. Piecuch, S. Hirata, K. Kowalski, P.-D. Fan, and T. L. Windus,
International Journal of Quantum Chemistry 106, 79–97 (2006).
[10] P.-D. Fan and S. Hirata, The Journal of Chemical Physics 124, 104108 (2006).
[11] S. Hirata, Theoretical Chemistry Accounts (an invited review) (online first, 2006).