Abstract.
The reaction path (RP) is an important concept of theoretical chemistry. We generalize the definition of the Newton trajectory (NT), as an RP, to Newton leaves in a higher dimensional subspace of the configuration space. Our standpoint is that of Bofill and Anglada [(2001) Theor. Chem. Acc. 105:436], who used a “reduced potential energy surface” for finding an RP. An NT follows an RP curve where the gradient is always a pointer to a fixed direction. More generally, a Newton leaf is a subspace of coordinates where the gradient can move in a subspace of directions. We report some known mathematical properties of Newton leaves. We explain the construction of Newton leaves with the example of a 3D test surface in ℝ4 [W.Quapp et al. (1998) Theor. Chem. Acc. 100:285], because three coordinate dimensions are the smallest number of dimensions one needs at least to understand a Newton leaf in contrast to the known NTs.
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Acknowledgement The work was made possible through financial support of the Deutsche Forschungsgemeinschaft. The authors thank D. Heidrich for stimulating discussions.
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Hirsch, M., Quapp, W. Newton leaves on potential energy surfaces. Theor Chem Acc 113, 58–62 (2005). https://doi.org/10.1007/s00214-004-0608-x
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DOI: https://doi.org/10.1007/s00214-004-0608-x