Using the relation to chemical hardness we develop an efficient density functional perturbation scheme for the analytic computation of the nuclear gradients of frontier orbital energies. The method is applied to activate three model chemical reactions with biradicaloid transition states, namely ethylene isomerisation, 2 + 2 cycloaddition of ethylene and disrotatory cyclisation of butadiene. Approximate reaction paths are generated by controlled variation of the energy gap between the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO). (C) 2002 Elsevier Science B.V. All rights reserved.