Intramolecular vibrational dynamical barrier due to extremely irrational couplings

The intramolecular vibrational dynamics due to extremely irrational couplings is demonstrated by contrast to the resonance couplings, for the three-mode case of H分子物理学 分子内振动弛豫 甚高频无理耦合 共鸣 振动动力学intramolecular vibrational relaxation, extremely irrational couplings, resonanceProject supported by the National Natural Science Foundation of China (Grant No~20373030) and the Foundation for Key Program of Ministry of Education, China (Grant No~306020) and the Specialized Research Fund for the Doctoral Program of Higher Educatio2007-03-04The intramolecular vibrational dynamics due to extremely irrational couplings is demonstrated by contrast to the resonance couplings, for the three-mode case of H2O as an example. The extremely irrational couplings are shown to impose such strong hindrance to intramolecular vibrational relaxation （IVR） that they act as barriers. They restrict the direct action/energy transfer between the two stretching modes, though they allow the transfer between a stretching and a bending modes. In contrast, the resonance is more mediated by the bending mode and leads to chaotic IVR. It is also shown that there is a region in the dynamical space in which resonance and extremely irrational couplings coexist.     

Interpretation of the IR spectral intensity anomaly of HCN by potential energy surface bifurcation along a normal mode

Stable normal IR modes vibrate in a convex basin of the potential energy surface (PES). The change to locally concave equipotential lines in a higher energy normal mode direction is interpreted as a possible reason for irreversible and rotation controlled internal vibrational energy redistribution (IVR) during excitation of that normal mode. In hydrogen cyanide (HCN) such an IVR process already occurs in the CN fundamental μ₁. The concept is proven by an explanation of the spectroscopic data: The disturbed IR absorption, the very high intensity in the neighbouring Q-branch of the bending overtone 3v¹₂, the emerging of only higher J lines in the R branch of μ₁, the intensity anomaly in the further state (1, 1¹, 0), and the nearly normal behaviour of the DCN μ₁ band.     

Extremely slow intramolecular vibrational redistribution: Direct observation by time-resolved raman spectroscopy in trifluoropropyne

We have studied the dynamics of intramolecular vibrational redistribution (IVR) from the initially excited mode v₁ ≈ 3330 cm⁻¹ (acetylene-type H-C bond) in H-C≡C-CF₃ molecules in the gaseous phase by means of anti-Stokes spontaneous Raman scattering. The time constant of this process is estimated as 2.3 ns—this is the slowest IVR time reported so far for the room-temperature gases. It is suggested that so long IVR time with respect to the other propyne derivatives can be explained by a larger defect, in this case, of the Fermi resonance of v₁ with v₂ + 2v₇—the most probable doorway state leading to IVR from v₁ to the bath of all vibrational-rotational states with the close energies. In addition, it is shown that the observed dynamics is in agreement with a theoretical model assuming strong vibrational-rotational mixing.     

Modelling rotations,vibrations, and rovibrational couplings in astructural molecules – a case study based on the H+5 molecular ion

One-dimensional (1D) and two-dimensional (2D) models are investigated, which help to understand the unusual rovibrational energy-level structure of the astronomically relevant and chemically interesting astructural molecular ion H⁺₅. Due to the very low hindering barrier characterising the 1D torsion-only vibrational model of H⁺₅, this model yields strongly divergent energy levels. The results obtained using a realistic model for the torsion potential, including the computed (near) degeneracies, can be rationalised in terms of the model with no barrier. Coupling of the torsional motion with a single rotational degree of freedom is also investigated in detail. It is shown how the embedding-dependent rovibrational models yield energy levels that can be rationalised via the 2D vibrational model containing two independent torsions. Insight into the complex rovibrational energy level structure of the models and of H⁺₅ is gained via variational nuclear motion and diffusion Monte Carlo computations and by the analysis of the wavefunctions they provide. The modelling results describing the transition from the zero barrier limit to the large barrier limit should prove to be useful for the important class of molecules and molecular ions that contain two weakly coupled internal rotors.     

Dynamical aspects and the role of IVR for the reactivity of noble metal clusters towards molecular oxygen

Here, we present the dynamical aspects and the role of internal energy redistribution (IVR) in the reactivity of noble metal clusters towards O₂. We show on the example of Ag₃O₂ ^- / Ag₃O₂ / Ag₃O₂ ⁺ that NeNePo spectroscopy carried out under zero electron kinetic energy (ZEKE) conditions can be a powerful tool to investigate the geometry relaxation and IVR induced by photodetachment in real time. Furthermore, we demonstrate that difference in the reactivity of Ag₆ ^- and Au₆ ^- towards O₂ can be attributed to different nature of the IVR process. Dissipative IVR in Ag₆ ^- favors fast complex stabilization, whereas resonant IVR found for Au₆ ^- might be an important factor determining the catalytic activity of Au₆ ^- cluster in the CO oxidation.     

Hydrogen bonding in homochiral dimers of hydroxyesters studied by Raman optical activity spectroscopy

Spectroscopic analysis of homochiral dimerization is important for the understanding of the homochirality of life and enantioselective catalysis. In this paper, (S)‐methyl lactate and related molecules were studied to provide detailed structural information on hydrogen bonding in homochiral dimers of chiral α‐hydroxyesters through the experimental and theoretical study of Raman optical activity. Different homochiral dimers can be distinguished by comparing their simulated Raman optical activity spectra with the experimental results. Hydrogen bonding motions are decoded with the aid of vibrational motion analysis, which are apparently involved in vibrational motions below 800 cm^–1. A common feature related to the chain‐bending mode also indicates the absolute configuration of methyl lactate and related molecules. The differing behavior of electric dipole–electric quadrupole invariants (β(A)²) compared with the electric dipole–magnetic dipole invariant (β(G′)²), suggests that the intermolecular hydrogen bonding motion behaves differently from the intramolecular one in the asymmetric molecular electric and magnetic fields. These results may help understand hydrogen‐bonded self‐recognition and other dynamical features in chiral recognition. Copyright © 2011 John Wiley & Sons, Ltd.     

A vibrational characterisation of the O/A1(111) system: a reassignment of HREELS data

In light of recent STM measurements of the O/A1(111) system, we reassign the dipole active modes observed at low coverage to resolve discrepancies between the interpretation of Strong, Firey, deWette and Erskine [Phys. Rev. B 26 (1982) 3483], invoking subsurface oxygen, and a variety of other studies which find no evidence for surface oxygen. The STM results, which show that very small island sizes are stabilized over an exposure range up to ∼ 200 L with a total coverage ≤ 0.2 ML, are incompatible with the assumption of long range periodicity required for lattice dynamical modeling. The consequence is that vibrational modes polarized parallel to the surface may become dipole active. Within an Al₃O cluster model appropriate to exposures ≤ 3 L where most oxygen atoms are isolated species in three-fold hollow sites, the strong feature at 584 cm⁻¹ (72 meV) is still attributed to top-layer oxygen motion perpecdicular to the surface (the symmetric Al₃O stretch) but the second intense feature at 480 cm⁻¹ (60 meV) is assigned to the umbrella mode involving predominantly Al motion parallel to the surface rather than the motion of two AlO layers moving perpendicular to the surface out of phase with each other. The lowest frequency mode near 224 cm⁻¹ (28 meV) derives from the frustrated translation of the cluster perpendicular to the surface. At higher exposures (> 10 L) where multiple oxygen islands begin to appear, totally symmetric combinations of the E-derived asymmetric Al₃O stretching motion polarised nominally parallel to the surface become dipole allowed and can be assigned to the loss at 850 cm⁻¹ (105 meV), which was previously attributed to subsurface oxygen.     

采用二维坐标和变分方法计算磷烷阳离子的伞型振动

提出一个新的二维变分方法计算PH₃⁺(X²A₂")的对称伸缩振动(v1)和伞形振动(v2). 因为采用了对称化的笛卡尔坐标,所以动能项变得简单,同时伞形振动模式也能得到很好的反映. 相比采用经常使用的一维模型计算伞形振动,这个二维模型不需要约化质量的假设,同时也考虑了v1和v2振动模式之间的相互作用. 用二维模型对PH₃⁺首次进行了计算, 前七个能级的理论值和实验值的平均相对误差小于3 cm^{-1. 用相同的方法也计算了NH₃,结果没有PH₃+理想,说明这个方法有一定的局限性.}     

Energy transfer processes in linear triatomic molecule-solid surface collisions

The semiclassical stochastic trajectory method is extended to the study of rotational and vibrational transitions for linear triatomic molecules colliding with non-rigid solid surfaces. Rotational and vibrational motion are treated by quantum mechanics, translational motion by classical mechanics, and surface atom motion by the classical generalized Langevin equation. Self-consistent coupling of all motions is enforced via Ehrenfest's theorem. Calculations of the kinetic energy and gas temperature dependence of trapping probabilities, vibrational relaxation probabilities and final vibrational state distributions are presented for the CO₂-Ag(111) system at surface temperatures of 0 and 600 K. The trapping probabilities are greatly enhanced by the rotational motion and also vary to some degree with the initial vibrational state of the CO₂. Total vibrationally inelastic probabilities are on the order of 10⁻² for a single collision event with an initial state (00°1). For the initial state (01¹0) these are much larger, ~ 10⁻¹, due to the nature of bending mode motion. In conjunction with the large trapping probabilities, the mechanism of vibration to vibration, rotation, translation, phonon energy transfer can provide vibration relaxation probabilities in the range of those measured experimentally. A pseudo-selection rule for conservation of vibrational angular momentum is found.     

Intramolecular vibrational relaxation in aromatic molecules. 2: An experimental and computational study of pyrrole and triazine near the IVR threshold

The threshold region of vibrational energy redistribution (IVR) presents a great experimental and computational challenge for organic molecules with more than 10 degrees of freedom. The density of states ρ_tot is high and requires high resolution measurements over a wide range to cover all relevant timescales experimentally. Yet ρ_tot is sufficiently low that IVR quantities like the initial relaxation time τIVR or the number of participating states N_eff are very sensitive to the coupling structure. To highlight the competing effects of molecular symmetry and mode localization on the accessible density of states, this work complements a study of benzene (Callegari, A., Merker, U., Engels, P., Srivastava, H. K., Lehmann, K. K., and Scoles, G., 2000, J. chem. Phys., 113, 10583) by measuring the CH overtone spectra of pyrrole (C₄H₄NH) and 1,2,3-triazine (C₃N₃H₃) using eigenstate-resolved double-resonance spectroscopy. Large scale computations of IVR dynamics were undertaken, applying filter diagonalization to analytically fitted fourth-order ab initio force fields. With an overall adjustment to the anharmonicity of the potential, the modelled N_eff and τ_IVR agree with the experimental quantities within a factor of 2 to 3, which is reasonable for a rate theory in the threshold regime. The models also correctly predict the experimentally observed trends of τ_IVR and N_eff for the two molecules, and provide insight into the highly off-resonant coupling mechanism, which yields very sharp linewidths.     

Hamiltonian description and 6D calculations on the ammonia vibrational levels

In this work, a Hamiltonian formalism and a 6D vibrational calculation procedure is described and implemented, designed for the exploration of vibrational motion in ammonia (and any XH₃ molecule). The 6D potential energy surface of ammonia was modelled in simple analytical form (including the inversion potential) at the planar, totally symmetric (D_3h) reference configuration. Using the described method (which is an adaptation of the formalism, previously developed and applied to benzene), 6D calculations were carried out on the vibrational level system of ammonia ¹⁴NH₃, at the lower levels of vibrational excitation. On the basis of the satisfactory agreement between the calculated and the experimentally measured vibrational frequencies, the values of some important harmonic and anharmonic force constants, characterizing the ammonia PES were determined.     

Boson description of collective states: (II). Description of odd vibrational nuclei

By addition of the so-called ideal quasiparticle to the boson space one can represent the odd fermion states in that product space. In such a way one finds various representations of the fermion operators in terms of the boson operators and ideal quasiparticles. From these boson expansions of the fermion operators a finite one is selected by considering non-unitary transformations. Thus, the direct generalization, of the Dyson representation for even systems is given for the case of odd systems. The Hamiltonian can be divided into three parts: the boson term which describes the vibrational motion of the even core, the unperturbed motion of the quasiparticle, and the interaction between the quasiparticle and the bosons. This interaction consists of two terms, one of which agrees with the term used by Kisslinger and Sorensen ²), which is usually called the dynamical interaction, and the additional term is due to the antisymmetrization between the extra particle and the even core. The latter term can be identified as kinematical interaction which is responsible for the anomalous coupling states. For example, it is demonstrated that this term produces qualitatively the same splitting of the one-phonon multiplet as was obtained by Kuriyama et al. ³) for the j-shell. Furthermore, it is shown for the more complicated case of ¹¹⁷Sn that the effect of this additional interaction between phonons and quasiparticle is important when many shells to the states in the odd nucleus are taken into account.     

Optical absorption of s2-configuration ions in alkali halide crystals—IV: Line shape of the C band in Sn2+-doped crystals

The line shape of the C band in the alkali halide phosphors KBr:Sn²⁺, RbBr:Sn²⁺, and RbCl:Sn²⁺ has been measured as a function of temperature between about 15 K and room temperature. In contrast to earlier measurements on In⁺-doped phosphors, the C band shows a well-marked triplet structure over the whole temperature range. This triplet structure cannot be accounted for solely in terms of the dynamical Jahn-Teller effect without assuming a very large temperature-dependence for the coupling constant to vibrational modes of trigonal symmetry. The temperature-dependence both of the second moment of the line shape and of the separation between the components of the C band, suggests that there is a contribution to the splitting of the C state from a lowering in the symmetry of the static crystal field and a model which includes such a static splitting in addition to the dynamical Jahn-Teller effect provides a good representation of the experimental line shapes.     

Ab initio calculations on the spectroscopic constants, vibrational levels and classical turning points for the 21∏u state of dimer 7Li2

The accurate dissociation energy and harmonic frequency for the highly excited 2^1Пu state of dimer ^7Li2 have been calculated using a symmetry-adapted-cluster configuration-interaction method in complete active space. The calculated results are in excellent agreement with experimental measurements. The potential energy curves at numerous basis sets for this state are obtained over a wide internuclear separation range from about 2.4a0 to 37.0a0. And the conclusion is gained that the basis set 6-311＋＋G（d,p） is a most suitable one. The calculated spectroscopic constants De, Re, ωe, ωeχe, ae and Be at 6-311＋＋G（d,p） are 0.9670 eV, 0.3125 nm, 238.6 cm^-1, 1.3705 cm^-1, 0.0039 cm^-1 and 0.4921 cm^-1, respectively. The vibrational levels are calculated by solving the radial SchrSdinger equation of nuclear motion. A total of 53 vibrational levels are found and reported for the first time. The classical turning points have been computed. Comparing with the measurements, in which only the first nine vibrational levels have been obtained so far, the present calculations are very encouraging. A careful comparison of the present results of the parameters De and We with those obtained from previous theories clearly shows that the present calculations are much closer to the measurements than previous theoretical results, thus representing an improvement on the accuracy of the ab initio calculations of the potentials for this state.     

Wavelet analysis and Arnold web picture for detecting energy transfer in a Hamiltonian dynamical system

Our motivation is to understand how, in chemical reactions, the reaction coordinate effectively gains dynamical energy from the other degrees of freedom (i.e., bath coordinates) avoiding thermalization of the redistributed energy. In such a system, the phase space structure should be not homogeneous; i.e., the system is never ergodic. In this study, we introduce a way to capture the inhomogeneity of the phase space and to monitor energy transfers among their partial degrees of freedom in nonergodic systems using wavelet analysis and a picture of the Arnold web. First, we examine several simple energy transfer processes, i.e., a motion on a resonance line, between resonance lines, and around a resonance junction in a simple three-degree-of-freedom (DOF) system and show how the elemental processes of the intramolecular vibrational energy redistribution (IVR) are detected by our tools. We especially note that the structure of the higher order resonance of the system can be detected by wavelet analysis and motion in the action space. Next, we analyze a reaction process in a simple Hamiltonian system of 3 DOF with a double-well potential, i.e., a system with a transition state of the center-saddle-center type, and detect energy transfers in the reactive process. The aim of the study is to propose a way to characterize the inhomogeneity of the phase space, e.g., the reactive doorway, which leads to controllability of the chemical reaction by light, i.e., control of the reaction by selectively preparing an initial state in the reactive doorway by optical excitation.     

Tunneling energy levels of an off-center impurity of the hydroxyl ion in NaCl crystal

Fine structures of the vibrational spectrum of OH^– in NaCl have been investigated by their dependence on the OH^– concentration, temperature and uniaxial stress. The absorption bands of A and C at 3651. 2 and 3655.2 cm-1 are ascribed to the tunneling motion of the off-center impurity of OH^–. The stress splitting factor of the tunneling levels has been estimated to be B(S11–S12)=0.96±0.10 cm-1/10⁸ dyn cm-2 in the ground state and it is about 1.4 times larger in the vibrational excited state.     

Theory of sparse random matrices and vibrational spectra of amorphous solids

The random matrix theory has been used for analyzing vibrational spectra of amorphous solids. The random dynamical matrix M = AA ^T with nonnegative eigenvalues ɛ = ω² has been investigated. The matrix A is an arbitrary square (N-by-N) real sparse random matrix with n nonzero elements in each row, mean values 〈A _ij 〉 = 0, and finite variance 〈A _ij ²〉 = V ². It has been demonstrated that the density of vibrational states g(ω) of this matrix at N, n ≫ 1 is described by the Wigner quarter-circle law with the radius independent of N. For n ≪ N, this representation of the dynamical matrix M = AA ^T makes it possible in a number of cases to adequately describe the interaction of atoms in amorphous solids. The statistics of levels (eigenfrequencies) of the matrix M is adequately described by the Wigner surmise formula and indicates the repulsion of vibrational terms. The participation ratio of the vibrational modes is approximately equal to 0.2–0.3 almost over the entire range of frequencies. The conclusions are in qualitative and, frequently, quantitative agreement with the results of numerical calculations performed by molecular dynamics methods for real amorphous systems.