Time-Frequency Analysis of Classical Trajectories of Polyatomic Molecules

Vela-Arevalo, Luz V.; Wiggins, Stephen

doi:10.1142/s0218127401002766

Cited by 119 publications

(155 citation statements)

References 11 publications

(23 reference statements)

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“…The O-D stretching vibrational spectrum was calculated based on continuous wavelet transformation of the trajectories as introduced by Vela-Arevalo and Wiggins (47). The vibrational frequency of an individual O-D bond at a given moment is obtained through a time series analysis of the O-D distance.…”

Section: Methodsmentioning

confidence: 99%

“…The electric field on an H atom depends on the positions, orientation, and point atomic charges of water molecules in the vicinity. To verify this relationship, we calculated the electric field on D atoms using the Hirshfeld's point atomic charges (46) and the corresponding frequencies of the O-D stretching mode ν OD for short segments of the ab initio MD trajectory using the continuous wavelet transformation method (47). A remarkably simple linear relationship is seen to exist between the ν OD frequency (i.e., H-bond strength) and the projection of the electric field along the H-bond vector D .…”

Section: Ir Spectroscopy Of Water Molecules In the Neighborhood Of Pumentioning

confidence: 99%

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Origin of hydrophobicity and enhanced water hydrogen bond strength near purely hydrophobic solutes

Grdadolnik

Merzel

Avbelj

2016

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

196

145

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Hydrophobicity plays an important role in numerous physicochemical processes from the process of dissolution in water to protein folding, but its origin at the fundamental level is still unclear. The classical view of hydrophobic hydration is that, in the presence of a hydrophobic solute, water forms transient microscopic "icebergs" arising from strengthened water hydrogen bonding, but there is no experimental evidence for enhanced hydrogen bonding and/or icebergs in such solutions. Here, we have used the redshifts and line shapes of the isotopically decoupled IR oxygen-deuterium (O-D) stretching mode of HDO water near small purely hydrophobic solutes (methane, ethane, krypton, and xenon) to study hydrophobicity at the most fundamental level. We present unequivocal and model-free experimental proof for the presence of strengthened water hydrogen bonds near four hydrophobic solutes, matching those in ice and clathrates. The water molecules involved in the enhanced hydrogen bonds display extensive structural ordering resembling that in clathrates. The number of ice-like hydrogen bonds is 10-15 per methane molecule. Ab initio molecular dynamics simulations have confirmed that water molecules in the vicinity of methane form stronger, more numerous, and more tetrahedrally oriented hydrogen bonds than those in bulk water and that their mobility is restricted. We show the absence of intercalating water molecules that cause the electrostatic screening (shielding) of hydrogen bonds in bulk water as the critical element for the enhanced hydrogen bonding around a hydrophobic solute. Our results confirm the classical view of hydrophobic hydration.hydrophobic hydration | hydrogen bonding | IR spectroscopy | electrostatic screening | ab initio molecular dynamics D espite its great importance in numerous phenomena, the origin of hydrophobicity remains one of the most disputed topics in science (1-5). Experimental studies have shown that small purely hydrophobic solutes (alkanes and noble gases) in water increase the order (6, 7) and restrict the mobility (8) of neighboring water molecules. There are several opposing views on how to explain these data. The classical view is that a solute modifies water structure by forming transient, semiordered clathrate-like clusters ("icebergs"; used here only as a loose term) around it, arising from enhanced water hydrogen bonding (H bonding) (6, 7). This enhancement is brought about by either strengthening (9) or increasing the number of water to water H bonds (10). The classical view explains the characteristic changes in the thermodynamic variables of hydrophobic hydration (positive ΔG, ΔC p , negative ΔS, and ΔH) and the restricted mobility of water molecules observed by NMR (8). Neutron diffraction (11, 12) and extended X-ray absorption fine structure (EXAFS) (13) studies, however, show that the water molecules around small purely hydrophobic molecules do not differ significantly from those in pure liquid water. According to the dynamic view, the hydrophobic solute causes slowdown of t...

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Section: Methodsmentioning

confidence: 99%

Section: Ir Spectroscopy Of Water Molecules In the Neighborhood Of Pumentioning

confidence: 99%

Origin of hydrophobicity and enhanced water hydrogen bond strength near purely hydrophobic solutes

Grdadolnik

Merzel

Avbelj

2016

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

196

145

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“…However, from the tunneling perspective it is crucial to determine dynamically relevant part of the static web at E ≈Ē. This "dynamical web" is determined via a wavelet based local frequency analysis [17] of the Hamiltonian eq. 3.…”

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confidence: 99%

Resonance-assisted tunneling in three degrees of freedom without discrete symmetry

Keshavamurthy

2005

Phys. Rev. E

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We study dynamical tunneling in a near-integrable Hamiltonian with three degrees of freedom. The model Hamiltonian does not have any discrete symmetry. Despite this lack of symmetry we show that the mixing of near-degenerate quantum states is due to dynamical tunneling mediated by the nonlinear resonances in the classical phase space. Identifying the key resonances allows us to suppress the dynamical tunneling via the addition of weak counter-resonant terms.Tunneling is a phenomenon that is forbidden by classical mechanics but allowed by quantum mechanics. In general, any flow of quantum probability between (approximately) equivalent yet classically disconnected regions constitutes tunneling. The classical regions could be disconnected due to barriers in coordinate space, momentum space or, more generally, in the classical phase space. In the cases where tunneling occurs despite the absence of obvious energetic barriers it is called dynamical tunneling [1]; the barriers now arise due to certain exact or approximate constants of the motion and hence are naturally identified in the underlying classical phase space. Considerable theoretical [1,2,3,4,5,6,7,8,9,10] and experimental [11] works have established that tunneling between quantum states localized on two symmetryrelated regions in the phase space can be strongly influenced by the classical stochasticity (chaos-assisted tunneling[2]) and/or by the intervening nonlinear resonances (resonance-assisted tunneling [6]). In the former case, phase space is mixed regular-chaotic and the splittings show marked dependence on the nature of the chaotic states which couple to the tunneling doublets [2,3,4]. In the latter case with near-integrable phase space, the splittings depend delicately on the various resonance islands bridging the degenerate states [5,6,7,8,9,10]. Clearly, a quantitative semiclassical theory, still elusive, requires one to identify key structures in the phase space on which the theory is to be based. In this regard there is increasing evidence [9,10] that the classical nonlinear resonances might play a central role in near-integrable as well as mixed phase space situations.However, most of the studies thus far have been on two degrees of freedom (dof) systems with discrete symmetries [12]. Does the resonance-assisted tunneling viewpoint hold in systems with three or more dof which lack discrete symmetries? The main motivation for our study comes from suggestions[8] put forward in the molecular context -can dynamical tunneling provide a route for mixing between near-degenerate states and hence energy flow between regions supporting qualita- * Permanent address: Department of Chemistry, Indian Institute of Technology, Kanpur, U.P. 208016, India.tively different types of motion? In addition, notwithstanding the difficulties associated with visualizing the multidimensional phase space, dynamics in three or more dof has features that cannot manifest in the systems studied up until now [13]. In this letter we attempt to understand dynamical tunneling in a...

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“…Interestingly much more efforts have been made in celestial mechanics 45 with fewer applications in atomic physics 46 and molecular systems 48 . Recently Arevalo and Wiggins 47,49 have proposed a technique for performing time-frequency analysis (LFA) which include strongly chaotic trajectories as well by using wavelet analysis. Applications to various systems demonstrated the advantages of a wavelet based LFA in understanding phase space transport 49 .…”

Section: Introductionmentioning

confidence: 99%

Intramolecular vibrational energy redistribution in DCO (X̃²A′): Classical-quantum correspondence, dynamical assignments of highly excited states, and phase space transport

Semparithi

Keshavamurthy

2003

Phys. Chem. Chem. Phys.

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Intramolecular dynamics of highly excited DCO ( X 2 A ′ ) is studied from a classical-quantum correspondence perspective using the effective spectroscopic Hamiltonian proposed recently by Tröllsch and Temps (Z. Phys. Chem. 215, 207 (2001)). This work focuses on the polyads P = 3 and P = 4 corresponding to excitation energies Ev ≈ 5100 cm −1 and 7000 cm −1 respectively. The majority of states belonging to these polyads are dynamically assigned, despite extensive stochasticity in the classical phase space, using the recently proposed technique of level velocities. A wavelet based time-frequency analysis is used to reveal the nature of phase space transport and the relevant dynamical bottlenecks. The local frequency analysis clearly illustrates the existence of mode-specific IVR dynamics i.e., differing nature of the IVR dynamics ensuing from CO stretch and the DCO bend bright states. In addition the role of the weak Fermi resonance involving the CO stretch and DCO bend modes is investigated. A key feature of the present work is that the techniques utilized for the analysis i.e., parametric variations and local frequency analysis are not limited by the dimensionality of the system. This study, thus, explores the potential for understanding IVR in larger molecules from both time domain and frequency domain perspectives.

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Time-Frequency Analysis of Classical Trajectories of Polyatomic Molecules

Cited by 119 publications

References 11 publications

Origin of hydrophobicity and enhanced water hydrogen bond strength near purely hydrophobic solutes

Origin of hydrophobicity and enhanced water hydrogen bond strength near purely hydrophobic solutes

Resonance-assisted tunneling in three degrees of freedom without discrete symmetry

Intramolecular vibrational energy redistribution in DCO (X̃²A′): Classical-quantum correspondence, dynamical assignments of highly excited states, and phase space transport

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Time-Frequency Analysis of Classical Trajectories of Polyatomic Molecules

Cited by 119 publications

References 11 publications

Origin of hydrophobicity and enhanced water hydrogen bond strength near purely hydrophobic solutes

Origin of hydrophobicity and enhanced water hydrogen bond strength near purely hydrophobic solutes

Resonance-assisted tunneling in three degrees of freedom without discrete symmetry

Intramolecular vibrational energy redistribution in DCO (X̃2A′): Classical-quantum correspondence, dynamical assignments of highly excited states, and phase space transport

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Product

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Intramolecular vibrational energy redistribution in DCO (X̃²A′): Classical-quantum correspondence, dynamical assignments of highly excited states, and phase space transport