[en] A continuous path connecting two SCF trial functions can be defined in a variety of ways. We introduce one which is, in a sense, the minimal path between these states. Corresponding occupied and virtual orbital pairs are defined. Variation of the SCF energy along the minimal path is fitted by a cubic polynomial using information supplied by the normal SCF calculation. The cubic fit is usually found to be an excellent approximation to the true energy function. Interpolation, or extrapolation, along the path effectively overcomes problems due to use of a poor initial trial function, and always converges. The final approach to convergence can be slow. Various acceleration methods, applicable to the end-game problem, have been proposed in the literature. Our interpolation method insures convergence when combined with almost any of these alternative methods for the closed-shell problem