Hello all,

I am confused about how this "steepest ascent" analysis is equivalent to the zero-flux surface, critical point analysis originally proposed by Bader. Intuitively, this connection makes sense considering the topology of ATOMS (only maxima), but does not make sense to me considering any general topology. A formal analysis, as described in Bader's original book, connects the saddle points together to form the atom surface. May someone point me to a paper or reference with this discussion?

--Thank you for the clarification!

## Connection to original Bader theory

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### Re: Connection to original Bader theory

You are absolutely correct that there is some distinction between our approach and how it is described by Bader. Much of the original theory deals with the topology of the paths connecting critical points in the electron density, and an interpretation of the bonding in terms of this analysis. Our approach is more utilitarian: we find the Bader volumes but do not (yet) determine the critical points or their connectivity. The critical points, however, do lie on the boundary of the volumes that we determine (by steepest ascent). A student in the group is working on a subsequent determination of the critical points, the local curvatures at these points, and their connectivity.