Variational Approaches to Vibration‐Rotation Spectroscopy for Polyatomic Molecules

Carney, G. D.; Sprandel, Ludwig Leo; Kern, C. W.

doi:10.1002/9780470142561.ch6

Cited by 299 publications

(117 citation statements)

References 100 publications

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“…, {m}) gives the so-called vibrational SCF (VSCF) method. 16,17 At the other extreme, the partition ({1, 2, . .…”

Section: The Vmfci Methodsmentioning

confidence: 99%

“…2,15 In the latter references, its general equations were reported, but the publication of systematic test calculations has been postponed to the present article. As its name might suggest, the VMFCI method encompasses both the vibrational self-consistent field (VSCF) method 16,17 and the vibrational configuration interaction (VCI) method as particular cases. However, it is much more general and flexible than these two methods.…”

Section: Introductionmentioning

confidence: 99%

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The VMFCI method: A flexible tool for solving the molecular vibration problem

Cassam-Chenaı̈

Liévin

2006

J Comput Chem

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The present article introduces a general variational scheme to find approximate solutions of the spectral problem for the molecular vibration Hamiltonian. It is called the "vibrational mean field configuration interaction" (VMFCI) method, and consists in performing vibrational configuration interactions (VCI) for selected modes in the mean field of the others. The same partition of modes can be iterated until self-consistency, generalizing the vibrational self-consistent field (VSCF) method. As in contracted-mode methods, a hierarchy of partitions can be built to ultimately contract all the modes together. So, the VMFCI method extends the traditional variational approaches and can be included in existing vibrational codes based on the latter approaches. The flexibility and efficiency of this new method are demonstrated on several molecules of atmospheric interest.

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“…, {m}) gives the so-called vibrational SCF (VSCF) method. 16,17 At the other extreme, the partition ({1, 2, . .…”

Section: The Vmfci Methodsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

The VMFCI method: A flexible tool for solving the molecular vibration problem

Cassam-Chenaı̈

Liévin

2006

J Comput Chem

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“…32,44 In the VCI method, a variational self consistent field (VSCF) procedure is adopted to find the solution of the vibrational Schroedinger equation. 52,53 The ansatz for the vibrational wavefunction is given by the direct product of unidimensional functions. The application of the variational principle to the eigenstates equation for this ansatz brings a set of equations coupled through a mean-field potential for each unidimensional eigenfunction.…”

Section: First Principles Semiclassical Molecular Dynamics Of Formmentioning

confidence: 99%

Fighting the curse of dimensionality in first-principles semiclassical calculations: Non-local reference states for large number of dimensions

Ceotto

Tantardini

Aspuru‐Guzik

2011

The Journal of Chemical Physics

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Semiclassical methods face numerical challenges as the dimensionality of the system increases. In the general context of the theory of differential equations, this is known as the “curse of dimensionality.” In the present manuscript, we apply the recently-introduced multi-coherent states semiclassical initial value representation (MC-SC-IVR) approach to extend the applicability of first-principles semiclassical calculations. The proposed strategy involves the use of non-local coherent states with the goal of increasing accuracy in the Fourier transforms, and on the other hand, allows for the selection of peaks of different frequencies. The ability to filter desired peaks is important for analyzing the power spectra of complex systems. The MC-SC-IVR approach allows us to solve a 19-dimensional test system and to resolve on-the-fly the power spectra of the formaldehyde molecule with very few classical trajectories.

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“…The corresponding wave function is found by a variational method in Eckart coordinates for a total angular momentum Jϭ0. 19,21 The Hamiltonian used in the variational calculation can be written as 22,23 In order to find the eigenvalues and eigenfunctions of the Hamiltonian of the electronic ground state, the wave function is expanded in a direct product basis of single-particle functions,…”

Section: A Calculation Of the Initial Wave Packetmentioning

confidence: 99%

A 2 A 2 ←X 2 B 1 absorption and Raman spectra of the OClO molecule: A three-dimensional time-dependent wave packet study

Lou

Nyman

2005

The Journal of Chemical Physics

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2 A 2 potential energy surface better reproduces the detailed structures of the absorption spectrum at long wavelength, while the revised surface of the A 2 A 2 state, consistent with the work of Xie and Guo, better reproduces the overall shape and the energies of the vibrational levels. Both surfaces of the A 2 A 2 state can reasonably reproduce the experimental Raman spectra but neither does so in detail for the numerical model employed in the present work.

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Variational Approaches to Vibration‐Rotation Spectroscopy for Polyatomic Molecules

Cited by 299 publications

References 100 publications

The VMFCI method: A flexible tool for solving the molecular vibration problem

The VMFCI method: A flexible tool for solving the molecular vibration problem

Fighting the curse of dimensionality in first-principles semiclassical calculations: Non-local reference states for large number of dimensions

A 2 A 2 ←X 2 B 1 absorption and Raman spectra of the OClO molecule: A three-dimensional time-dependent wave packet study

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