Algebraic Treatment of a Three-Oscillator System: Applications to Some Molecular Models

Boujut, V.; Michelot, F.

doi:10.1006/jmsp.1997.7317

Cited by 3 publications

(1 citation statement)

References 20 publications

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“…An algebraic and unified treatment in the framework of the u(2) and u(3) Lie theory and boson representation has been proposed in Refs. [61][62][63][64] to build symmetrized powers for all point groups admitting two and three dimensional irreps. Another tensorial formalism has been reviewed in Ref.…”

Section: Construction Of γ-Covariant Polynomialsmentioning

confidence: 99%

Group-theoretical formulation of an Eckart-frame kinetic energy operator in curvilinear coordinates for polyatomic molecules

Rey

2019

The Journal of Chemical Physics

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Section: Construction Of γ-Covariant Polynomialsmentioning

confidence: 99%

Group-theoretical formulation of an Eckart-frame kinetic energy operator in curvilinear coordinates for polyatomic molecules

Rey

2019

The Journal of Chemical Physics

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Using nested tensor train contracted basis functions with group theoretical techniques to compute (ro)-vibrational spectra of molecules with non-Abelian groups

Rey,

Carrington

2024

The Journal of Chemical Physics

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In this paper, we use nested tensor-train contractions to compute vibrational and ro-vibrational energy levels of molecules with five and six atoms. At each step, we fully exploit symmetry by using symmetry adapted basis functions obtained from an irreducible tensor method. Contracted basis functions are determined by diagonalizing reduced dimensional Hamiltonian matrices. The size of matrices of eigenvectors, used to account for coupling between groups of coordinates, is reduced by discarding rows and columns. The size of the matrices that must be diagonalized is thus substantially reduced, making it possible to use direct eigensolvers, even for molecules with five and six atoms. The symmetry-adapted contracted vibrational basis functions have been used to compute J = 0 energy levels of the CH3CN (C3v) and J > 0 levels of CH4.

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Algebraic treatment of some systems with spin-like interactions with applications in quantum optics and vibronic spectroscopy

Michelot¹

2006

J. Phys. A: Math. Gen.

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Algebraic Treatment of a Three-Oscillator System: Applications to Some Molecular Models

Cited by 3 publications

References 20 publications

Group-theoretical formulation of an Eckart-frame kinetic energy operator in curvilinear coordinates for polyatomic molecules

Group-theoretical formulation of an Eckart-frame kinetic energy operator in curvilinear coordinates for polyatomic molecules

Using nested tensor train contracted basis functions with group theoretical techniques to compute (ro)-vibrational spectra of molecules with non-Abelian groups

Algebraic treatment of some systems with spin-like interactions with applications in quantum optics and vibronic spectroscopy

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