Symmetry Rules for Brownian Photomotors Marina L. Dekhtyar *1 , Viktor М. Rozenbaum 2 1 Institute of Organic Chemistry, National Academy of Sciences of Ukraine, Murmanskaya str. 5, Kiev, 02094, Ukraine, mdekh@mail.ru 2 Chuiko Institute of Surface Chemistry, National Academy of Sciences of Ukraine Generala Naumova str. 17, Kiev, 03164, Ukraine, vik-roz@mail.ru (Received July 29, 2013) Abstract A number of symmetry rules have been derived which govern the occurrence of directed motion and its reversals in Brownian photomotors both for individual molecules and for molecular ensembles. The exclusion principles and sufficient conditions for the photoexcited transport of molecules are found in terms of electron density distribution symmetries in the substrate and moving molecules. Thus, the most general sufficient condition for a nonzero directed velocity of a single molecule at any symmetry type of the substrate is as follows: symmetric or antisymmetric components of the molecular electron density distribution change on excitation, the remaining symmetry components not vanishing in the ground and excited states simultaneously. The exclusion principle for motion reversals (stopping points) in single-molecule transport is such that symmetric and antisymmetric components of the molecular electron density distribution change proportionally on excitation. For collective molecular transport to occur, it is sufficient that the substrate not be symmetric and that symmetric components of the molecular electron density distribution not vanish in the ground and excited states simultaneously. The symmetry relationships established offer much promise for the effective quantum-chemistry based screening and rational molecular design of light-driven nanodevices. * The author to whom correspondence should be addressed. E-mail: mdekh@mail.ru MATCH Communications in Mathematical and in Computer Chemistry MATCH Commun. Math. Comput. Chem. 71 (2014) 609-626 ISSN 0340 - 6253