We study charge exchange in slow atomic collisions within the framework of the advanced adiabatic approach [Grozdanov and Solov'ev, Phys. Rev. A { 42}, 2703 (1990)]. In this approach, nonadiabatic transitions near hidden or avoided crossings are related to branch points connecting adiabatic potential curves at complex values of the internuclear distance. A program package has been developed that automatically takes into account all relevant nonadiabatic transition amplitudes for the calculation of charge-transfer cross sections. The present method allows the inclusion of a large number of molecular-orbital basis functions and turns out to be extremely fast. As an example, partial and total cross sections are calculated for charge exchange in slow O+H(1{ s}) collisions. The results are compared to previous theoretical and experimental data.