We model the evolving time- dependent electronic structure of a solid- state quantum gate as it performs basic quantum operations. Our time- dependent configuration- interaction method follows the evolution of two donor electron spin qubits interacting with a third, optically excited, control spin in an applied magnetic field, a possible realization of the basic component of a proposed quantum information processor. We identify unitary operations which approximately disentangle the control spin, and use them to construct high-accuracy two- electron operations that are locally equivalent to CNOT, SWAP and root SWAP operations. From our evaluation of the accuracy of a set of candidate gates we estimate the residual entanglement of the control electron and overall gate operation times. These results attest to the feasibility of the silicon- based quantum gates proposed by Stoneham, Fisher and Greenland.