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Methodology : development of Canonical Perturbation Theory |
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![](images_ressources/coin_bleu_h.png) |
2D representation of the 3D potential energy surface of HCN (the CN distance is fixed at equilibrium value r0), showing the two
minima (HCN and CNH) and the minimum energy path (MEP) linking them
through the saddle. Energy contours are separated by 1000 cm-1. |
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Plot of the 1D potential curve for the pure bending states (v1=v3=0)
of HCN/CNH, obtained by applying CPT to the 3D ab initio surface, and
corresponding wave functions. |
![Puce](images_ressources/coin_bleu.png) |
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Until recently, physicists were unable to compute the exact spectra of most systems, because this requires the diagonalization
of (usually) large Hamiltonian matrices. Fortunately, theoretical tools like Van Vleck's Canonical Perturbation Theory (CPT), which
allow a precise determination of quantum spectra without direct diagonalization, were derived very early and played a fundamental role
in the development of quantum mechanics.
Although modern computers now make it possible to calculate the whole spectrum of small molecules, CPT is still an interesting tool
in the field of molecular physics. Indeed, CPT basically consists of a series of canonical (or unitary) transformations, which are aimed
at rewriting the Hamiltonian of the system in terms of as complete as possible a set of good quantum numbers (or corresponding classical
constants of the motion). These Hamiltonians are in turn very convenient starting points for the investigation of the non-linear
dynamics of these systems, especially when they are subjected to semi-classical quantization.
We adapted CPT to the study of
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highly excited vibrational states of molecules with a single equilibrium position (semi-rigid molecules)
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highly excited vibrational states of molecules with several equilibrium positions (floppy molecules)
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highly excited vibrational states of molecules with several coupled electronic surfaces (non-adiabatic dynamics)
This provided us a deep understanding of the non-linear dynamics of small molecules, like for example bifurcations,
monodromy, and non-adiabatic dynamics. We also showed that CPT leads to the
definition of meaningful local modes for intra-molecular vibrational energy redistribution (IVR) studies. |
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Related articles (suggested
ones in red) : |
50 - |
On the application of canonical perturbation theory up to the dissociation threshold
S. Buyukdagli and M. Joyeux,
Chem. Phys. Lett. 412 (2005) 200-205
[Abstract]
[Ask for an electronic reprint by email] |
49 - |
Intramolecular dynamics along isomerization and dissociation pathways
M. Joyeux, S. Yu. Grebenshchikov, J. Bredenbeck, R. Schinke and S.C. Farantos,
Adv.Chem. Phys. 130 (2005) 267-303
[full text]
copyright : Wiley ([Book abstract]) |
48 - |
Study of vibrational energy localization and redistribution in hydrogen peroxide H2O2 at low energy
M. Joyeux,
J. Chem. Phys. 122 (2005) 074303 (1-8)
[full text]
copyright : The American Institute of Physics ([Abstract]) |
42 - |
Canonical perturbation theory versus Born-Oppenheimer-type separation of motions : the vibrational dynamics of C3
J. Robert and M. Joyeux,
J. Chem. Phys. 119 (2003) 8761-8762 (note)
[full text]
copyright : The American Institute of Physics ([Abstract]) |
38 - |
Canonical perturbation theory for highly excited dynamics
M. Joyeux and D. Sugny,
Can. J. Phys. 80 (2002) 1459-1480 (tutorial article)
[full text]
copyright : NRC Research Press ([Abstract]) |
35 - |
A local diabatic representation of non-Born-Oppenheimer dynamics
M. Joyeux, D. Sugny and M. Lombardi,
Chem. Phys. Lett. 352 (2002) 99-105
[Abstract]
[Ask for an electronic reprint by email] |
34 - |
A new canonical perturbation procedure for studying nonadiabatic dynamics
D. Sugny and M. Joyeux,
Chem. Phys. Lett. 337 (2001) 319-326
[Abstract]
[Ask for an electronic reprint by email] |
32 - |
Investigation of the vibrational dynamics of the HCN-CNH isomers through high order canonical perturbation theory
D. Sugny, M. Joyeux and E.L. Sibert,
J. Chem. Phys. 113 (2000) 7165-7177
[full text]
copyright : The American Institute of Physics ([Abstract]) |
29 - |
On the application of canonical perturbation theory to floppy molecules
D. Sugny and M. Joyeux,
J. Chem. Phys. 112 (2000) 31-39
[full text]
copyright : The American Institute of Physics ([Abstract]) |
25 - |
Gustavson's procedure and the dynamics of highly excited vibrational states
M. Joyeux,
J. Chem. Phys. 109 (1998) 2111-2122
[full text]
copyright : The American Institute of Physics ([Abstract]) |
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