Eckart ro-vibrational Hamiltonians via the gateway Hamilton operator: Theory and practice.

@article{Szalay2017EckartRH,
  title={Eckart ro-vibrational Hamiltonians via the gateway Hamilton operator: Theory and practice.},
  author={Viktor Szalay},
  journal={The Journal of chemical physics},
  year={2017},
  volume={146 12},
  pages={
          124107
        }
}
  • V. Szalay
  • Published 7 January 2017
  • Physics
  • The Journal of chemical physics
Recently, a general expression for Eckart-frame Hamilton operators has been obtained by the gateway Hamiltonian method [V. Szalay, J. Chem. Phys. 142, 174107 (2015) and V. Szalay, J. Chem. Phys. 143, 064104 (2015)]. The kinetic energy operator in this general Hamiltonian is nearly identical to that of the Eckart-Watson operator even when curvilinear vibrational coordinates are employed. Its different realizations correspond to different methods of calculating Eckart displacements. There are at… 
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References

SHOWING 1-10 OF 68 REFERENCES

Aspects of the Eckart frame ro-vibrational kinetic energy operator.

  • V. Szalay
  • Physics
    The Journal of chemical physics
  • 2015
TLDR
It is shown analytically, by term by term comparison, that the Eckart KEOs obtained by employing Pickett's method and the gateway Hamiltonian method are equivalent, and the general, exact ro-vibrational Eckart frame KEO is unique.

Numerical and exact kinetic energy operator using Eckart conditions with one or several reference geometries: Application to HONO.

TLDR
This work has adapted Dymarsky and Kudin's approach to obtain a kinetic energy operator in curvilinear coordinates using a numerical but exact procedure without resorting to finite differences for the study of molecular systems with several minima, for which several Eckart reference geometries are required.

Computing rovibrational levels of methane with curvilinear internal vibrational coordinates and an Eckart frame.

TLDR
No previous calculation of rovibrational levels of methane includes as many levels as the one presented in this paper, which is demonstrated by calculating a large number of converged J = 10 methane rovibational levels in the Tetradecad polyad.

Understanding nuclear motions in molecules: Derivation of Eckart frame ro-vibrational Hamiltonian operators via a gateway Hamiltonian operator.

  • V. Szalay
  • Physics
    The Journal of chemical physics
  • 2015
TLDR
The new Hamiltonian is shown to provide easy access to Eckart frame ro-vibrational Hamiltonians with exact Tˆ given in terms of any desired set of vibrational coordinates.

Automatic differentiation method for numerical construction of the rotational-vibrational Hamiltonian as a power series in the curvilinear internal coordinates using the Eckart frame.

TLDR
The results show that very high accuracy and quick convergence can be achieved even with moderate expansions if curvilinear coordinates are employed, which is important for applications involving large polyatomic molecules.

Rovibrational spectroscopy using a kinetic energy operator in Eckart frame and the multi-configuration time-dependent Hartree (MCTDH) approach.

TLDR
A method is developed to introduce in a systematic way the Eckart frame for the expression of the kinetic energy operator (KEO) in the polyspherical approach, which leads to a faster convergence especially for large J states and vibrationally excited states.

A novel discrete variable representation for quantum mechanical reactive scattering via the S-matrix Kohn method

A novel discrete variable representation (DVR) is introduced for use as the L2 basis of the S‐matrix version of the Kohn variational method [Zhang, Chu, and Miller, J. Chem. Phys. 88, 6233 (1988)]

Eckart-Sayvetz conditions revisited.

  • V. Szalay
  • Mathematics
    The Journal of chemical physics
  • 2014
TLDR
It is shown that vibrational displacements satisfying the Eckart-Sayvetz conditions can be constructed by projection of unconstrained displacements by means of linear and non-orthogonal transformation.

A general discrete variable method to calculate vibrational energy levels of three‐ and four‐atom molecules

TLDR
A general variational method to calculate vibrational energy levels of polyatomic molecules without dynamical approximation based on a Lanczos algorithm, which does not require storage of the Hamiltonian matrix.
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