Atomic Partial Spins

How partial spins for open-shell molecules are determined in MPcules

Atomic partial spins can be defined similarly to atomic partial charges for molecules with unpaired electrons ("open-shell" molecules; "closed-shell" molecules with no upaired electrons have 0 net spin and therefore 0 partial spin on each atom, by definition). We currently calculate atomic partial spins using two methods: Mulliken population analysis [1] and natural atomic populations from NBO [2, 3]. While Mulliken partial charges can be unreliable, we have generally found that Mulliken partial spins are qualitatively similar to those obtained from NBO and can therefore be treated without prejudice.


  1. Mulliken, R.S., 1955. Electronic population analysis on LCAO–MO molecular wave functions. I. The Journal of chemical physics, 23(10), pp.1833-1840.

  2. Glendening, E.D., Badenhoop, J.K., Reed, A.E., Carpenter, J.E., Bohmann, J.A., Morales, C.M., Karafiloglou, P., Landis, C.R., Weinhold, F., 2018. NBO 7.0. Theoretical Chemistry Institute, University of Wisconsin, Madison.

  3. Glendening, E.D., Landis, C.R. and Weinhold, F., 2012. Natural bond orbital methods. Wiley interdisciplinary reviews: computational molecular science, 2(1), pp.1-42.

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