Theoretical Methods for Rovibrational States of Floppy Molecules

Bačić, Zlatko; Light, John C.

doi:10.1146/annurev.pc.40.100189.002345

Cited by 847 publications

(220 citation statements)

References 69 publications

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“…The T-R energy levels and wave functions of the Hamiltonian in equation (2.1) are obtained utilizing the efficient computational methodology that originated in our group [19,24]. The final Hamiltonian matrix, its size drastically reduced by the sequential diagonalization and truncation procedure [25], is diagonalized, yielding the T-R eigenstates which are numerically exact for the five-dimensional PES used. The parameters extracted from the IR spectra of HD@C 60 [7], listed in table 1, give the rotational constant B 0 = 44.53 cm −1 (5.521 meV) for HD in the ground vibrational state v = 0.…”

Section: Theorymentioning

confidence: 99%

HD in C ₆₀ : theoretical prediction of the inelastic neutron scattering spectrum and its temperature dependence

Lawler

et al. 2013

Phil. Trans. R. Soc. A.

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One contribution of 13 to a Theo Murphy Meeting Issue 'Nanolaboratories: physics and chemistry of small-molecule endofullerenes' . We report rigorous quantum calculations of the inelastic neutron scattering (INS) spectra of HD@C 60 , over a range of temperatures from 0 to 240 K and for two incident neutron wavelengths used in recent experimental investigations. The computations were performed using our newly developed methodology, which incorporates the coupled five-dimensional translation-rotation (T-R) eigenstates of the guest molecule as the initial and final states of the INS transitions, and yields highly detailed spectra. Depending on the incident neutron wavelength, the number of computed INS transitions varies from almost 500 to over 2000. The low-temperature INS spectra display the fingerprints of the coupling between the translational and rotational motions of the entrapped HD molecule, which is responsible for the characteristic splitting patterns of the T-R energy levels. INS transitions from the ground T

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Section: Theorymentioning

confidence: 99%

HD in C ₆₀ : theoretical prediction of the inelastic neutron scattering spectrum and its temperature dependence

Lawler

et al. 2013

Phil. Trans. R. Soc. A.

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“…A special mention is due to those based on the discrete variable representation ͑DVR͒ method. 8 In this energy regime, the interpretation of corresponding wave functions in simple terms is much more difficult. For moderate excitation energies choosing an adequate ͑curvilinear͒ coordinate system 9 can help.…”

Section: ͓S0021-9606͑96͒03316-6͔mentioning

confidence: 99%

Transition from order to chaos in molecular wave functions and spectra

Arranz

Borondo

Benito

1996

The Journal of Chemical Physics

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In this Communication we describe how the transition from regularity to classical chaos in molecular Hamiltonian systems shows up at the quantum level in the structure of the corresponding wave functions and spectra. By changing the value of ប we show how the scars result from combinations of regular wave functions. © 1996 American Institute of Physics. ͓S0021-9606͑96͒03316-6͔In the early stages of vibrational spectroscopy typical studies were only concerned with low lying vibrational states in which the nuclei move in a localized region around the minimum of the Born-Oppenheimer potential energy surface ͑PES͒. Anharmonic terms, responsible for the overtone and combination frequencies, were considered only as weak perturbations. 1 In this regime, the intramolecular dynamics are completely regular and the spectra consist ͑at least in the ideal case͒ of a progression of bands, corresponding to the different excitations of each normal mode, that can easily be assigned, due to the lack of irregularities. The corresponding wave functions exhibit a very regular nodal pattern 2 and quantum numbers can also, in principle, be assigned easily. Special care has to be exerted in the presence of classical resonances since they have a profound influence on the nodal structure of wavefunctions, as was demonstrated in the work of DeLeon, Davis, and Heller. 3 At higher levels of excitation the dynamics of molecular systems change very much, and the interactions between normal modes 4 cause the structure of the spectra to be more complicated. The KAM theorem dictates that more and more regular tori are destroyed as energy increases, rendering a multitude of resonant chains of islands, overlapping bands of stochasticity and embedded cantori. 5 Nonlinear interactions among normal modes lead to irreversible intramolecular vibrational energy flow, which is controlled by all those classical structures. Also, the rate of many intramolecular processes, such as isomerization, unimolecular decomposition, etc., is determined by this intramolecular vibrational relaxation ͑IVR͒. 6 Modern spectroscopy has broadened this horizon by the introduction of new techniques, such as IR overtone excitation, multiphonon excitation, stimulated emission pumping or electron photodetachment, 7 in which extensive regions of the PES, sometimes very far from the equilibrium geometries, are probed. On the theoretical side, efficient methods have been developed to calculate accurately the eigenvalues and eigenfunctions of the vibrationally excited states involved. A special mention is due to those based on the discrete variable representation ͑DVR͒ method. 8 In this energy regime, the interpretation of corresponding wave functions in simple terms is much more difficult. For moderate excitation energies choosing an adequate ͑curvilinear͒ coordinate system 9 can help. On the other hand, for very high vibrational energies some wave functions appear localized on periodic orbits ͑POs͒ of the system. This effect, known as ''scarring'', has received much attention in t...

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“…They exploit the structure of the basis, the quadrature grid, and the kinetic energy operator (KEO). For molecules with more than five atoms, vectors representing wavefunctions and the vector representing the PES on the quadrature grid [4,30,31] are so large that they require too much memory. In the rest of this chapter, I therefore review methods that obviate the need to store large vectors.…”

Section: Introductionmentioning

confidence: 99%

Iterative Methods for Computing Vibrational Spectra

Carrington

2018

Mathematics

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I review some computational methods for calculating vibrational spectra. They all use iterative eigensolvers to compute eigenvalues of a Hamiltonian matrix by evaluating matrix-vector products (MVPs). A direct-product basis can be used for molecules with five or fewer atoms. This is done by exploiting the structure of the basis and the structure of a direct product quadrature grid. I outline three methods that can be used for molecules with more than five atoms. The first uses contracted basis functions and an intermediate (F) matrix. The second uses Smolyak quadrature and a pruned basis. The third uses a tensor rank reduction scheme.

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Theoretical Methods for Rovibrational States of Floppy Molecules

Cited by 847 publications

References 69 publications

HD in C ₆₀ : theoretical prediction of the inelastic neutron scattering spectrum and its temperature dependence

HD in C ₆₀ : theoretical prediction of the inelastic neutron scattering spectrum and its temperature dependence

Transition from order to chaos in molecular wave functions and spectra

Iterative Methods for Computing Vibrational Spectra

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Theoretical Methods for Rovibrational States of Floppy Molecules

Cited by 847 publications

References 69 publications

HD in C 60 : theoretical prediction of the inelastic neutron scattering spectrum and its temperature dependence

HD in C 60 : theoretical prediction of the inelastic neutron scattering spectrum and its temperature dependence

Transition from order to chaos in molecular wave functions and spectra

Iterative Methods for Computing Vibrational Spectra

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Product

Resources

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HD in C ₆₀ : theoretical prediction of the inelastic neutron scattering spectrum and its temperature dependence

HD in C ₆₀ : theoretical prediction of the inelastic neutron scattering spectrum and its temperature dependence