Approximate factorization of molecular potential surfaces. I. Basic approach

Madsen, Dorte; Pearman, Ryan; Gruebele, Martin

doi:10.1063/1.473253

Cited by 46 publications

(62 citation statements)

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“…For the vibrational Hamiltonian, the factorized normal mode surface was therefore used (12,18,19). A related method also has been reported by Bullock et al (20) Our approach provides a very compact representation of the PES in terms of ladder operators…”

Section: Model and Computationsmentioning

confidence: 99%

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Intramolecular vibrational dephasing obeys a power law at intermediate times

Gruebele

1998

Proc. Natl. Acad. Sci. U.S.A.

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Experimental intramolecular vibrational dephasing transients for several large organic molecules are reanalyzed. Fits to the experimental data, as well as full numerical quantum calculations with a factorized potential surface for all active degrees of freedom of f luorene indicate that power law decays, not exponentials, occur at intermediate times. The results support a proposal that power law decays describe vibrational dephasing dynamics in large molecules at intermediate times because of the local nature of energy f low.The standard description for the time evolution of pure vibrational dephasing in large isolated molecules (intramolecular vibrational relaxation or redistribution; IVR) is based on the Golden Rule formulae:P͑t͒ ϭ e Ϫk I VR t .[1b]Eq. 1 was successfully applied to radiationless transitions by Jortner and coworkers (1) and to IVR by Freed (2). Some limitations of Eq. 1 as applied to pure dephasing were clear early on (3): it does not properly represent the t ϭ 0 rolloff due to a finite (although large) number of participating eigenstates; it does not represent the quantum beats, which arise even in large molecules at low vibrational energy; and it does not describe the leveling-off of P(t) at a value greater than zero due to the finite size of molecular state space (4). However, it is generally thought that Eq. 1b adequately describes the dynamics of a sufficiently large and highly excited molecule (''statistical limit'') on all but the longest time scales. For a general manifold of coupled states, Eq. 1 is a result of first order perturbation theory, where V rms is an average over individual couplings V 0i from the bright state ͉0Ͼ to a prediagonalized manifold {͉iϾ}. It can be systematically augmented by a perturbation expansion (2), but such a treatment is difficult to connect to standard molecular parameters. The prediagonalized manifold {͉iϾ} offers no additional insights or practical time savings compared with full diagonalization because V rms or its generalizations are not related to known spectroscopic parameters (e.g., cubic potential constants) in a simple fashion (5). Hence, there has been an ongoing discussion, both experimental (6) and theoretical (5,(7)(8)(9)(10), that Eq. 1a should be represented in terms of local molecular parameters rather than the total density of states tot . There has been much less focus on the question of whether the IVR process can be globally described by an exponential rate law at all (11). This latter question will be considered in this paper.In 1993, a landmark paper by Schofield and Wolynes (11) introduced a different description of IVR time evolution, which emphasizes the local nature of energy flow through state space. By introducing a size scaling law for quantum transport in the molecular state space, they concluded that vibrational dephasing is better represented by a power lawThe coefficient ␦ was proposed to vary from 2 near the IVR threshold, to ᏺ Ϫ 1 for a molecule with ᏺ vibrational modes well beyond the IVR threshold. Power law d...

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Section: Model and Computationsmentioning

confidence: 99%

“…The second line is the result of fitting the first line to two prototype organic molecules from ref. 18, combined with the fact that V (3) ϰ…”

Section: Model and Computationsmentioning

confidence: 99%

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Intramolecular vibrational dephasing obeys a power law at intermediate times

Gruebele

1998

Proc. Natl. Acad. Sci. U.S.A.

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“…In general, one finds that low-order anharmonic interactions are strongest 3,7,8 . They are noted here ij/mn, indicating that quanta of vibrational modes i and j are exchanged for quanta of modes m and n. Among them are Fermi interactions…”

Section: Introductionmentioning

confidence: 99%

Vibration–rotation alchemy in acetylene (¹²C₂H₂), at low vibrational excitation: from high resolution spectroscopy to fast intramolecular dynamics

et al. 2010

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“…Equation (4) describes a Raman process, where phonons are transferred from one reservoir to the other by scattering through the intermediate states of the molecule. The linear coupling coefficients, T , scale as the square root of the product of the frequencies of the coupled modes [6],…”

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Thermal conduction through a molecule

Buldum¹,

Leitner²,

Çiraci³

1999

Europhys. Lett.

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The quantum features of phononic thermal conduction through a molecule between two reservoirs have been studied in the weak-coupling limit. As opposed to ballistic heat transfer through a uniform bridge or atomic chain strongly coupled to reservoirs investigated earlier, thermal conductance in the present case shows a nonlinear temperature dependence that is sensitive to the mode frequencies of the molecule.

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Approximate factorization of molecular potential surfaces. I. Basic approach

Abstract: Articles you may be interested inCorrelated ab initio investigations on the intermolecular and intramolecular potential energy surfaces in the ground electronic state of the O 2 − ( X Π g 2 ) − HF ( X Σ + 1 ) complex

Cited by 46 publications

References 20 publications

Intramolecular vibrational dephasing obeys a power law at intermediate times

Intramolecular vibrational dephasing obeys a power law at intermediate times

Vibration–rotation alchemy in acetylene (¹²C₂H₂), at low vibrational excitation: from high resolution spectroscopy to fast intramolecular dynamics

Thermal conduction through a molecule

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Approximate factorization of molecular potential surfaces. I. Basic approach

Abstract: Articles you may be interested inCorrelated ab initio investigations on the intermolecular and intramolecular potential energy surfaces in the ground electronic state of the O 2 − ( X Π g 2 ) − HF ( X Σ + 1 ) complex

Cited by 46 publications

References 20 publications

Intramolecular vibrational dephasing obeys a power law at intermediate times

Intramolecular vibrational dephasing obeys a power law at intermediate times

Vibration–rotation alchemy in acetylene (12C2H2), at low vibrational excitation: from high resolution spectroscopy to fast intramolecular dynamics

Thermal conduction through a molecule

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Vibration–rotation alchemy in acetylene (¹²C₂H₂), at low vibrational excitation: from high resolution spectroscopy to fast intramolecular dynamics