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The curvature of the conical intersection seam: an approximate second-order analysis

We present a method for analyzing the curvature (second derivatives) of the conical intersection hyperline at an optimized critical point. Our method uses the projected Hessians of the degenerate states after elimination of the two branching space coordinates, and is equivalent to a frequency calculation on a single Born-Oppenheimer potential-energy surface. Based on the projected Hessians, we develop an equation for the energy as a function of a set of curvilinear coordinates where the degeneracy is preserved to second order (i.e., the conical intersection hyperline). The curvature of the potential-energy surface in these coordinates is the curvature of the conical intersection hyperline itself, and thus determines whether one has a minimum or saddle point on the hyperline. The equation used to classify optimized conical intersection points depends in a simple way on the first- and second-order degeneracy splittings calculated at these points. As an example, for fulvene, we show that the two optimized conical intersection points of C2v symmetry are saddle points on the intersection hyperline. Accordingly, there are further intersection points of lower energy, and one of C2 symmetry - presented here for the first time - is found to be the global minimum in the intersection space

© Journal of Chemical Physics, 2004, vol. 121, núm. 23, p. 11562-11571

American Institute of Physics

Author: Paterson, Martin J.
Bearpark, Michael J.
Robb, Michael A.
Blancafort San José, Lluís
Date: 2004
Abstract: We present a method for analyzing the curvature (second derivatives) of the conical intersection hyperline at an optimized critical point. Our method uses the projected Hessians of the degenerate states after elimination of the two branching space coordinates, and is equivalent to a frequency calculation on a single Born-Oppenheimer potential-energy surface. Based on the projected Hessians, we develop an equation for the energy as a function of a set of curvilinear coordinates where the degeneracy is preserved to second order (i.e., the conical intersection hyperline). The curvature of the potential-energy surface in these coordinates is the curvature of the conical intersection hyperline itself, and thus determines whether one has a minimum or saddle point on the hyperline. The equation used to classify optimized conical intersection points depends in a simple way on the first- and second-order degeneracy splittings calculated at these points. As an example, for fulvene, we show that the two optimized conical intersection points of C2v symmetry are saddle points on the intersection hyperline. Accordingly, there are further intersection points of lower energy, and one of C2 symmetry - presented here for the first time - is found to be the global minimum in the intersection space
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Citation: Paterson, M.J., Bearpark, M.J., Robb, M.A., i Blancafort, L. (2004). The curvature of the conical intersection seam: an approximate second-order analysis. Journal of Chemical Physics, 121 (23), 11562-11571. Recuperat 23 març 2011, a http://link.aip.org/link/doi/10.1063/1.1813436
ISSN: 0021-9606 (versió paper)
1089-7690 (versió electrònica)
Document access: http://hdl.handle.net/10256/3288
Language: eng
Publisher: American Institute of Physics
Collection: Reproducció digital del document publicat a: http://dx.doi.org/10.1063/1.1813436
Articles publicats (D-Q)
Is part of: © Journal of Chemical Physics, 2004, vol. 121, núm. 23, p. 11562-11571
Rights: Tots els drets reservats
Subject: Algorismes
Enllaços químics
Energia de superfície
Estructura molecular
Optimització matemàtica
Algorithms
Chemical bonds
Mathematical optimization
Molecular structure
Surface energy
Title: The curvature of the conical intersection seam: an approximate second-order analysis
Type: info:eu-repo/semantics/article
Repository: DUGiDocs

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