### Abstract

Topological relations among the number of critical points of various orders (zero order are minima, first order are saddle points, etc.) are presented, which are invariants of the actual periodic (hyper)surfaces considered. The principal results involve the Betti numbers, the minimum number of critical points of a given order that must be present, and the Euler characteristic, based on an alternating sum rule involving the number of critical points of each order. Several conformational potential energy (hyper)surfaces are analyzed in terms of these relationships, including two containing lines of degeneracy and degenerate critical points.

Original language | English |
---|---|

Pages (from-to) | 127-135 |

Number of pages | 9 |

Journal | Journal of Molecular Structure: THEOCHEM |

Volume | 94 |

Issue number | 1-2 |

DOIs | |

Publication status | Published - Jun 1983 |

### ASJC Scopus subject areas

- Biochemistry
- Condensed Matter Physics
- Physical and Theoretical Chemistry

## Fingerprint Dive into the research topics of 'Topological properties of conformational potential energy surfaces'. Together they form a unique fingerprint.

## Cite this

*Journal of Molecular Structure: THEOCHEM*,

*94*(1-2), 127-135. https://doi.org/10.1016/0166-1280(83)80164-X