Dynamics of benzene molecules situated in metal-organic frameworks

In this paper, we investigate the gyroscopic motion of a benzene molecule C₆H₆, which comprises an inner carbon ring and an outer hydrogen ring, and is suspended rigidly inside a metal-organic framework. The metal-organic framework provides a sterically unhindered environment and an electronic barrier for the benzene molecule. We model such gyroscopic motion from the inter-molecular interactions between the benzene ring and the metal-organic framework by both the Columbic force and the van der Waals force. We also capture additional molecular interactions, for example due to sterical compensations arising from the carboxylate ligands between the benzene molecule and the framework, by incorporating an extra empirical energy into the total molecular energy. To obtain a continuous approximation to the total energy of such a complicated atomic system, we assume that the atoms of the metal-organic framework can be smeared over the surface of a cylinder, while those for the benzene molecule are smeared over the contour line of the molecule. We then approximate the pairwise molecular energy between the molecules by performing line and surface integrals. We firstly investigate the freely suspended benzene molecule inside the framework and find that our theoretical results admit a two-fold flipping, with the possible maximum rotational frequency reaching the terahertz regime, and gigahertz frequencies at room temperature. We also show that the electrostatic interaction and the thermal energy dominate the gyroscopic motion of the benzene molecule, and we deduce that the extra energy term could possibly reduce the rotational frequency of the rigidly suspended benzene molecule from gigahertz to megahertz frequencies at room temperature, and even lower frequencies might be obtained when the strength of these interactions increases.     

双色双共振-多光子电离光谱研究小分子的碰撞诱导转动能量转移

用双色双共振多光子电离光谱方法测量了NO分子A~(2∑+)(v=0)态的转动能量转移, 得到了由R-F能量转移导致的转动可分辨的弛豫光谱, 计算了转动态-态转移速率常数。用以转移能量为基础的指数和幂指数能隙模型, 对碰撞弛豫态分布进行计算机模拟, 并从计算值与实验值的比较讨论了能隙模型存在的不足。用同法对I_2分子B∏(O_u~+)态的测量, 得到由转动能量转移导致的谱线展宽及交叠并作了分析。     

The rotation–vibration coupling equations for polyatomic molecules in internal coordinates

An exact vibration–rotation kinetic energy operator for polyatomic molecules has been obtained on the basis of Sutcliffe's method, in terms of curvilinear internal coordinates and rotational angular moment operators. This operator is derived from the kinetic energy operator in Cartesian coordinates by the successive transformations using the chain rule. This kinetic energy operator can be used not only for the system of any triatomic and tetraatomic molecules and common polyatomic molecules in chemistry, but also for the investigation of the collision problems between two molecules after some modifications. Finally, using this Hamiltonian, the rotation–vibration coupling equations of polyatomic molecules have been derived and discussed. © 1992 John Wiley & Sons, Inc.     

Angular intensity distribution of a molecular oxygen beam scattered from a graphite surface

The scattering of the oxygen molecule from a graphite surface has been studied using a molecular beam scattering technique. The angular intensity distributions of scattered oxygen molecules were measured at incident energies from 291 to 614 meV with surface temperatures from 150 to 500 K. Every observed distribution has a single peak at a larger final angle than the specular angle of 45° which indicates that the normal component of the translation energy of the oxygen molecule is lost by the collision with the graphite surface. The amount of the energy loss by the collision has been roughly estimated as about 30-41% based on the assumption of the tangential momentum conservation during the collision. The distributions have also been analyzed with two theoretical models, the hard cubes model and the smooth surface model. These results indicate that the scattering is dominated by a single collision event of the particle with a flat surface having a large effective mass. The derived effective mass of the graphite surface for the incoming oxygen is 9-12 times heavier than that of a single carbon atom, suggesting a large cooperative motion of the carbon atoms in the topmost graphene layer.     

Translational to rotational energy transfer in molecule-surface collisions

A theoretical approach that combines classical mechanics for treating translational and rotational degrees of freedom and quantum mechanics for describing the excitation of internal molecular modes is applied to the scattering of diatomic molecules from metal surfaces. Calculations are carried out for determining the extent of energy transfer to the rotational degrees of freedom of the projectile molecule. For the case of observed spectra of intensity versus final rotational energy, quantitative agreement with available experimental data for the scattering of NO and N(2) from close packed metal surfaces is obtained. It is shown that such measurements can be used to determine the average rotational energy of the incident molecular beam. Measurements of the exchange of energy between translational and rotational degrees of freedom upon collision are also described by calculations for these same systems.     

The role of angular momentum in collision-induced vibration-rotation relaxation in polyatomics

Vibrational relaxation of the 6(1) level of S(1)((1)B(2u)) benzene is analyzed using the angular momentum model of inelastic processes. Momentum-(rotational) angular momentum diagrams illustrate energetic and angular momentum constraints on the disposal of released energy and the effect of collision partner on resultant benzene rotational excitation. A kinematic "equivalent rotor" model is introduced that allows quantitative prediction of rotational distributions from inelastic collisions in polyatomic molecules. The method was tested by predicting K-state distributions in glyoxal-Ne as well as J-state distributions in rotationally inelastic acetylene-He collisions before being used to predict J and K distributions from vibrational relaxation of 6(1) benzene by H(2), D(2), and CH(4). Diagrammatic methods and calculations illustrate changes resulting from simultaneous collision partner excitation, a particularly effective mechanism in p-H(2) where some 70% of the available 6(1)-->0(0) energy may be disposed into 0-->2 rotation. These results support the explanation for branching ratios in 6(1)-->0(0) relaxation given by Waclawik and Lawrance and the absence of this pathway for monatomic partners. Collision-induced vibrational relaxation in molecules represents competition between the magnitude of the energy gap of a potential transition and the ability of the colliding species to generate the angular momentum (rotational and orbital) needed for the transition to proceed. Transition probability falls rapidly as DeltaJ increases and for a given molecule-collision partner pair will provide a limit to the gap that may be bridged. Energy constraints increase as collision partner mass increases, an effect that is amplified when J(i)>0. Large energy gaps are most effectively bridged using light collision partners. For efficient vibrational relaxation in polyatomics an additional requirement is that the molecular motion of the mode must be capable of generating molecular rotation on contact with the collision partner in order to meet the angular momentum requirements. We postulate that this may account for some of the striking propensities that characterize polyatomic energy transfer.     

Coupling of the overall molecular motion with the conformational transitions. II. The full rotational problem

The method proposed in the companion paper for analysing the coupling between overall and internal dynamics is applied to the study of the full rotational motion of a molecule with one internal degree of freedom. For systems characterized by a finite set of stable conformers determined by the minima of the intramolecular potential, a simplified time evolution operator of mixed type is derived, with the continuous diffusion equation and the generalized random walk operator representing the overall rotation and the internal dynamics, respectively. The dependence on the conformational state of the rotational diffusion tensor is one source of coupling between these two types of motion. Another source is represented by the recoil rotations acting on each subunit during a conformational transition. Both conformational-dependent rotational diffusion tensors and recoil rotations can be calculated from a model for the friction exerted by the solvent. Some applications of the theory are presented in relation to the butane molecule and the molecules having the structure of biphenyl, with particular emphasis on the calculation of the experimental observables in NMR and dielectric relaxation measurements.     

Giant Crystalline Molecular Rotors that Operate in the Solid State

Molecular motion in the solid state is typically precluded by the highly dense environment, and only molecules with a limited range of sizes show such dynamics. Here, we demonstrate the solid-state rotational motion of two giant molecules, i.e., triptycene and pentiptycene, by encapsulating a bulky N-heterocyclic carbene (NHC) Au(I) complex in the crystalline media. To date, triptycene is the largest molecule (surface area: 245 Ų; volume: 219 ų) for which rotation has been reported in the solid state, with the largest rotational diameter among reported solid-state molecular rotors (9.5 Å). However, the pentiptycene rotator that is the subject of this study (surface area: 392 Ų; volume: 361 ų; rotational diameter: 13.0 Å) surpasses this record. Single-crystal X-ray diffraction analyses of both the developed rotors revealed that these possess sufficient free volume around the rotator. The molecular motion in the solid state was confirmed using variable-temperature solid-state ²H spin-echo NMR studies. The triptycene rotor exhibited three-fold rotation, while temperature-dependent changes of the rotational angle were observed for the pentiptycene rotor.     

Energy transfer processes during the scattering of vibrationally excited no molecules from a graphite surface

Vibrationally excited NO molecules scattered from a cleaved graphite surface show rotational state populations and rotational accommodation identical to those of ground-state incoming molecules. The survival probability of the vibrational state is found to vary between 75 and 95%, depending on the surface temperature. Transfers of vibrational energy to both molecular rotation and translation are shown to be of only minor importance for the vibrational relaxation during the NO/graphite interaction.     

Internal dynamics features in the free jet rotational spectrum of the acetaldehyde-Kr molecular complex

The structure and the dynamics of internal motions in the complex formed between acetaldehyde and Kr are studied by free jet absorption microwave spectroscopy performed in the range 60-78 GHz. The fourfold structure of each rotational line is evidence of the vibration-rotation coupling between the overall rotation of the complex, a tunneling motion of the Kr atom between two equivalent positions and the internal rotation of the methyl group in the acetaldehyde moiety. The four sets of transitions could be fitted with a coupled Hamiltonian which allows for the Coriolis interaction obtaining the energy separation between the vibrational energy levels related to the tunneling motion, while the observed splittings due to the methyl group internal rotation were analyzed independently with an appropriate model. The potential energy barriers for the tunneling motion and the internal rotation of the methyl group have been calculated and the interaction of the rare gas atom with the acetaldehyde moiety is reflected in the change of the V(3) barrier to internal rotation in going from the molecule to the weakly bound complex.     

Study of internal ring rotation and molecular reorientation in the liquid crystal 5O.7 by deuterium N.M.R. spectroscopy

The spectral densities of motion were determined by deuterium N.M.R. relaxation measurements in the nematic, smectic A and smectic C phases of 4-n-pentyloxybenzylidene-d₁-4'-heptylaniline and 4-n-pentyloxybenzylidene-4'-heptylaniline-2,3,5,6-d₄. By examining two atomic sites on a 5O.7 molecule, we were able to gain information on the reorientation motion and internal rotation of the aniline ring. It was also found that director fluctuations make some contribution to the spectral density J₁ (ω). We use the superimposed rotations model to account for the internal ring motion and the small step rotational diffusion model for the molecular reorientation. The derived rotational diffusion constants for the spinning and tumbling motions appear to give physically plausible activation energies in the mesophases of 5O.7.     

Internal dynamics in complexes of water with organic molecules. Details of the internal motions in tert-butylalcohol-water

The peculiar propensity of water to have a high internal dynamic activity in its molecular complexes with organic molecules is described in this paper. Often, the corresponding large amplitude motions are reflected in the tunnelling splittings of the rotational transitions which, in turn, provide information for the determination of the potential energy surfaces and of the noncovalent interactions of water with a variety of atoms and/or functional groups. A classification of this kind of molecular complexes is given, also in relation to the tunnelling features of the rotational spectra. As a specific example, the rotational spectrum of tert-butylalcohol-water, investigated by Fourier transform microwave spectroscopy, is reported. Details are given of the large amplitude motions which take place in the adduct, the internal rotation of the hydroxyl group and the oscillations of the water molecule, by interpreting the experimental data with a flexible model.     

Nearest-neighbor nonparametric method for estimating the configurational entropy of complex molecules

A method for estimating the configurational (i.e., non-kinetic) part of the entropy of internal motion in complex molecules is introduced that does not assume any particular parametric form for the underlying probability density function. It is based on the nearest-neighbor (NN) distances of the points of a sample of internal molecular coordinates obtained by a computer simulation of a given molecule. As the method does not make any assumptions about the underlying potential energy function, it accounts fully for any anharmonicity of internal molecular motion. It provides an asymptotically unbiased and consistent estimate of the configurational part of the entropy of the internal degrees of freedom of the molecule. The NN method is illustrated by estimating the configurational entropy of internal rotation of capsaicin and two stereoisomers of tartaric acid, and by providing a much closer upper bound on the configurational entropy of internal rotation of a pentapeptide molecule than that obtained by the standard quasi-harmonic method. As a measure of dependence between any two internal molecular coordinates, a general coefficient of association based on the information-theoretic quantity of mutual information is proposed. Using NN estimates of this measure, statistical clustering procedures can be employed to group the coordinates into clusters of manageable dimensions and characterized by minimal dependence between coordinates belonging to different clusters.     

Lie algebraic approach to multiphoton excitation of diatomic molecules in intense laser fields

The quadratic anharmonic oscillator Lie algebraic model is used to study the multiphoton transition of the diatomic molecule placed in intense laser fields. The multiphoton excitation of vibration and vibration‐rotation of diatomic molecules in intense laser fields are discussed. In the pure vibration transition we calculate the transition probability versus the frequency of the laser fields for the CO molecule. We also investigate the roles of rotational motion in multiphoton processes and compare with pure vibration for the LiH molecule. The influences of the angular quantum number l and the molecular orientations in laser fields on the multiphoton processes are discussed. The averaged absorb energy changing with the laser field's frequency is calculated. ©1999 John Wiley & Sons, Inc. Int J Quant Chem 71: 201–207, 1999     

Dynamics of small,floppy molecules studied by high-resolution spectroscopic techniques

In molecular spectroscopy one of the common interests is how to transform the information obtained by high-resolution spectroscopic techniques into some reliable approximation of the potential energy surface of a particular molecule. Traditionally vibrational spectroscopy has been used. Rotational spectroscopy can only probe, at least at room temperature, molecular transitions arising from excited vibrational states up to approximately 1000 cm^?1. This corresponds roughly to 10% of a typical bond dissociation energy. However, floppy molecules which exhibit a large-amplitude, low-lying vibrational mode can be studied to a large extent by rotational spectroscopy in the microwave, millimeter and submillimeter wave range. Quasilinearity is a special form of large-amplitude motion, which complicates the observed molecular spectra substantially and which presents a real challenge to theoretical spectroscopists. In this lecture the highlights of quasilinear behavior of the molecules HCNO, OCCCO, HNCS and HNCO will be discussed. Another form of large amplitude motion is the inversion exhibited primarily by molecules derived from NH₃. Isocyanamide will be discussed and its special spectroscopic features will be shown. Cyanamide and isocyanamide are potential prebiotic molecules: cyanamide has been detected as a constituent in the interstellar medium. The analysis of the molecular dynamics of these molecules is shown to be necessary for understanding the frequencies and intensities of the observed spectra in the laboratory and in interstellar space.     

A molecular-beam study of the collision dynamics of methane and ethane upon a graphitic monolayer on Pt(111)

Utilizing a supersonic molecular-beam scattering technique, the angular intensity distributions of alkane molecules (CH4 and C2H6) have been measured, which are scattered from a chemically inert and highly oriented monolayer graphite (MG) on Pt(111). A MG which covers the Pt(111) surface with a full monolayer is found to induce a large energy loss of alkanes during collision with the surface by phonon creation due to the large mass ratio of an alkane molecule with respect to MG. Based on the classical cube model, only applicable to the molecules without internal mode excitation, the effective masses of MG of 76 (six atoms of carbon) and Pt(111) of 585 (three atoms of platinum) are determined from rare-gas atom scattering data. Despite the difference in the degree of freedom between CH4 and rare-gas atoms, CH4 scattering is found to be well described by the simple hard-cube model as a result of the high symmetry of the CH4 structure. With the recently developed ellipsoid-washboard model, an extension of the hard-cube model to include some internal mode excitation of impinging molecules in addition to the surface corrugation, it is found that unlike CH4 the cartwheel rotation mode of C2H6 is significantly excited during collision, while the helicopter mode excitation is negligible on a flat MG surface.     

Operations and Thermodynamics of an Artificial Rotary Molecular Motor in Solution

A general framework is provided that makes possible the estimation of time‐dependent properties of a stochastic system moving far from equilibrium. The process is investigated and discussed in general terms of nonequilibrium thermodynamics. The approach is simple and can be exploited to gain insight into the dynamics of any molecular‐level machine. As a case study, the dynamics of an artificial molecular rotary motor, similar to the inversion of a helix, which drives the motor from a metastable state to equilibrium, are examined. The energy path that the motor walks was obtained from the results of atomistic calculations. The motor undergoes unidirectional rotation and its entropy, internal energy, free energy, and net exerted force are given as a function of time, starting from the solution of Smoluchowski’s equation. The rather low value of the organization index, that is, the ratio of the work done by the particle against friction during the unidirectional motion per available free energy, reveals that the motion is mainly subject to randomness, and the amount of energy converted to heat due to the directional motion is very small.     

Measuring the extent and width of internal energy deposition in ion activation using nanocalorimetry

The recombination energies resulting from electron capture by a positive ion can be accurately measured using hydrated ion nanocalorimetry in which the internal energy deposition is obtained from the number of water molecules lost from the reduced cluster. The width of the product ion distribution in these experiments is predominantly attributable to the distribution of energy that partitions into the translational and rotational modes of the water molecules that are lost. These results are consistent with a singular value for the recombination energy. For large clusters, the width of the energy distribution is consistent with rapid energy partitioning into internal vibrational modes. For some smaller clusters with high recombination energies, the measured product ion distribution is narrower than that calculated with a statistical model. These results indicate that initial water molecule loss occurs on the time scale of, or faster than energy randomization. This could be due to inherently slow internal conversion or it could be due to a multi-step process, such as initial ion-electron pair formation followed by reduction of the ion in the cluster. These results provide additional evidence for the accuracy with which condensed phase thermochemical values can be deduced from gaseous nanocalorimetry experiments.     

Planar study of H2O+Cl<-->HO+HCl reactions

The first four dimensional (4D) quantum scattering calculations on the tetra-atomic H2O+Cl<-->HO+HCl reactions are reported. With respect to a full (6D) treatment, only the planar constraint and a fixed length for the HO spectator bond are imposed. This work explicitly accounts for the bending and local HO stretching vibrations in H2O, for the vibration of HCl and for the in-plane rotation of the H2O, HO and HCl molecules. The calculations are performed with the potential energy surface of Clary et al. and use a Born-Oppenheimer type separation between the motions of the light and the heavy nuclei. State-to-state cross sections are reported for a collision energy range 0-1.8 eV measured with respect to H2O+Cl. For the H2O+Cl reaction, present results agree with previous (3D) non planar calculations and confirm that excitation of the H2O stretching promotes more reactivity than excitation of the bending. New results are related to the rotation of the H2O molecule: the cross sections are maximal for planar rotational states corresponding to 10相似文献   

Application of the Monte Carlo method to modeling of kinetic processes with the participation of polyatomic molecules and clusters: 1. Kinetics of energy transfer during collisions of polyatomic molecules

The Monte Carlo method was used to model the collisional energy transfer for polyatomic molecules within the framework of the statistical theory of reactions. A model describing energy transfer through the formation of a statistical collisional complex was suggested. It was assumed that the total energy of the complex was randomized in the course of collisions and statistically distributed among the internal and translational degrees of freedom. The method was verified by comparing the equilibrium distribution functions for the vibrational, rotational, and total energies of the molecule. The mean energy portion and the root-mean-square energy portion transferred per collision, as functions of the total molecular energy, were determined. The relaxation parameters of the population distribution over energy after a sharp increase in the bath-gas temperature were calculated.