Time evolution with a regular or irregular spectrum, revisited

The remarks of Davis et al. on an earlier paper by Brumer and Shapiro are addressed. Computations in these two papers. It is argued, are consistent and complimentary, providing insight into possible types of quantum dynamics in regular and irregular conservative hamiltonian systems.     

The perfect revival time of localized wave packet consisting of superposition of bound states with an arbitrary energy spectrum

A study is made of the long-term evolution of the wave packet, which is initially well localized in a one-dimensional confined potential. The wave packet consists of a linear superposition of bound states with an arbitrary energy spectrum. An exact analytical expression is derived, which predicts all revival times in any time scale. The perfect revival time is also calculated. The Pöschl–Teller oscillator has been considered as a simple example.     

Intramolecular vibrational dynamics in S1 p-fluorotoluene. I. Direct observation of doorway states

Picosecond time-resolved photoelectron spectroscopy is used to investigate intramolecular vibrational redistribution (IVR) following excitation of S(1) 18a(1) in p-fluorotoluene (pFT) at an internal energy of 845 cm(-1), where ν(18a) is a ring bending vibrational mode. Characteristic oscillations with periods of 8 ps and 5 ps are observed in the photoelectron signal and attributed to coupling between the initially excited zero-order bright state and two doorway states. Values for the coupling coefficients connecting these three vibrational states have been determined. In addition, an exponential change in photoelectron signal with a lifetime of 17 ps is attributed to weaker couplings with a bath of dark states that play a more significant role during the latter stages of IVR. A tier model has been used to assign the most strongly coupled doorway state to S(1) 17a(1) 6a(2)('), where ν(17a) is a CH out-of-plane vibrational mode and 6a(2)(') is a methyl torsional level. This assignment signifies that a torsion-vibration coupling mechanism mediates the observed dynamics, thus demonstrating the important role played by the methyl torsional mode in accelerating IVR.     

Moment expansion approach to the time dynamics of genetic evolution

We use moment expansion methods to analyze the time dynamics for genetic evolution under selection, mutation, and reproduction. We consider a N-allele diploid genotype reproducing randomly in a fitness landscape with either one or two maxima, and mutation is assumed to occur such that any allele can mutate into any other type. We find that the moment expansion works well, where a small number of moments can capture the general behavior toward equilibrium. Our methods allow a systematic way to capture the time dynamics of the evolutionary process efficiently using a small number of coupled equations.     

Post-transition state dynamics for propene ozonolysis: Intramolecular and unimolecular dynamics of molozonide

A direct chemical dynamics simulation, at the B3LYP6-31G(d) level of theory, was used to study the post-transition state intramolecular and unimolecular dynamics for the O3 + propene reaction. Comparisons of B3LYP6-31G(d) with CCSD(T)/cc-pVTZ and other levels of theory show that the former gives accurate structures and energies for the reaction's stationary points. The direct dynamics simulations are initiated at the anti and syn O3 + propene transition states (TSs) and the TS symmetries are preserved in forming the molozonide intermediates. Anti<-->syn molozonide isomerization has a very low barrier of 2-3 kcalmol and its Rice-Ramsperger-Kassel-Marcus (RRKM) lifetime is 0.3 ps. However, the trajectory isomerization is slower and it is unclear whether this anti<-->syn equilibration is complete when the trajectories are terminated at 1.6 ps. The syn (anti) molozonides dissociate to CH3CHO + H2COO and H2CO + syn (anti) CH3CHOO. The kinetics for the latter reactions are in overall good agreement with RRKM theory, but there is a symmetry preserving non-RRKM dynamical constraint for the former. Dissociation of anti molozonide to CH3CHO + H2COO is enhanced and suppressed, respectively, for the trajectory ensembles initiated at the anti and syn O3 + propene TSs. The dissociation of syn molozonide to CH3CHO + H2COO may also be enhanced for trajectories initiated at the syn O3 + propene TS. At the time the trajectories are terminated at 1.6 ps, the ratio of the trajectory and RRKM values of the CH3CHO + H2COO product yield is 1.6 if the symmetries of the initiation and dissociation TSs are the same and 0.6 if their symmetries are different. There are coherences in the intramolecular energy flow, which depend on molozonide's symmetry (i.e., anti or syn). This symmetry related dynamics is not completely understood, but it is clearly related to the non-RRKM dynamics for anti<-->syn isomerization and anti molozonide dissociation to CH3CHO + H2COO. Correlations are found between the stretching motions of molozonide, indicative of nonchaotic and non-RRKM dynamics. The non-RRKM dynamics of molozonide dissociation partitions vibration energy to H2COO that is larger than statistical partitioning. Though the direct dynamics simulations are classical, better agreement is obtained using quantum instead of classical harmonic RRKM theory. This may result from the neglect of anharmonicity in the RRKM calculations, the non-RRKM dynamics of the classical trajectories, or a combination of these two effects. The trajectories suggest that the equilibrium syn/anti molozonide ratio is approximately 1.1-1.2 times larger than that predicted by the harmonic densities of state, indicating an anharmonic correction.     

Intramolecular interactions in the triplet excited states of benzophenone-thymine dyads

Time-resolved and product studies on the synthesized dyads 1 and 2 have provided evidence that the benzophenone-to-thymine orientation strongly influences intramolecular photophysical and photochemical processes. The prevailing reaction mechanism has been established as a Paterno-Büchi cycloaddition to give oxetanes 3-6; however, the ability of benzophenone to achieve a formal hydrogen abstraction from the methyl group of thymidine has also been evidenced by the formation of photoproducts 7 and 8. These processes have been observed only in the case of the cisoid dyad 1. Adiabatic photochemical cycloreversion of the oxetane ring is achieved upon direct photolysis to give the starting dyad 1 in its excited triplet state. The photobiological implications of the above results are discussed with respect to benzophenone-photosensitized damage of thymidine.     

A priori resolution of the intermediate spectra in the bacteriorhodopsin photocycle: the time evolution of the L spectrum revealed

Resolution of the spectra of the intermediates in the photocycle of wild-type bacteriorhodopsin (BR) was achieved by singular value decomposition with exponential-fit-assisted self-modeling (SVD-EFASM) treatment of multichannel difference spectra measured at 5 degrees C during the course of the photocycle. New is the finding that two spectrally distinct L intermediates, L(1) and L(2), form sequentially. Our conclusion is that the photocycle is more complex than most published schemes. The dissection of the spectrally different L forms eliminates stoichiometric discrepancies usually appearing as systematically varying total intermediate concentrations before the onset of BR recovery. In addition, our analysis reveals that the red tails in the spectra of K and L(1) are more substantial than those of L(2) and BR. We suggest that these subtle differences in the shapes of the spectra reflect torsional and/or environmental differences in the retinyl chromophore.     

Molecular dynamics simulation of Matrix Metalloproteinase 2: fluctuations and time evolution of recognition pockets

We report a molecular dynamics simulation study of a zinc-protease--gelatinase A or MMP2--which is a major target for drug design, being involved in tumor metastasis and other degenerative diseases. Two structures have been employed as starting conditions, one based on the crystal of multi-domain proMMP2, the other consisting of the catalytic domain only. The overall fold of the two models is maintained over the 1260 ps trajectory, enabling us to analyze correlations of fluctuations among domains, and to observe the presence of correlations within the catalytic domain in the multi-domain enzyme only, hence due to the presence of hemopexin and fibronectin domains. In the multi-domain protein, two cavities are conserved over the trajectory, one of them pointing to a key region, a crevice surrounding the catalytic zinc. The other one is localized across the three domains of the MMP2 metalloproteinase. These areas are partially covered by the propeptide in the crystal structure of proMMP2. We propose a model of MMP2-collagen interaction that involves both identified cavities and takes into account the inter/intra domain cross-correlations.     

Twist dynamics of 9-(N-carbazolyl)-anthracene: effects of Intramolecular Vibrational Redistribution and non-adiabatic transitions in coupled bright and dark states

The twist dynamics of 9-(N-carbazolyl)-anthracene (C9A) in the electronically excited bright and dark states S ₁ and S _X is investigated theoretically. Effects of Intramolecular Vibrational Redistribution (IVR) as well as the diabatic transition S ₁ → S _X are taken into account. Based on a model hamiltonian and IVR-rates, which have been derived earlier from laser induced fluorescence spectra and life times observed by Monte et al. [1], the Liouville-von Neumann equation is integrated with a dissipative Liouvillian in Lindblad form. The resulting time dependent density matrix yields nearly coherent twist dynamics of this rather large molecule, at least on a timescale of several ps. The corresponding pump-probe spectra are predicted following the approach proposed by Manz et al. [2].     

Intramolecular vibrational redistribution in Ne-Br2: the signature of intermediate resonances in the excitation spectrum

Quantum-mechanical simulations of the Ne-Br(2)(B,v') excitation spectra produced after vibrational predissociation in the v'=20-35 range are reported. The aim is to investigate the signature in the excitation spectra of intermediate resonances lying in the lower v相似文献   

Intramolecular basis set superposition error effects on the planarity of benzene and other aromatic molecules: a solution to the problem

Recently, the surprising result that ab initio calculations on benzene and other planar arenes at correlated MP2, MP3, configuration interaction with singles and doubles (CISD), and coupled cluster with singles and doubles levels of theory using standard Pople's basis sets yield nonplanar minima has been reported. The planar optimized structures turn out to be transition states presenting one or more large imaginary frequencies, whereas single-determinant-based methods lead to the expected planar minima and no imaginary frequencies. It has been suggested that such anomalous behavior can be originated by two-electron basis set incompleteness error. In this work, we show that the reported pitfalls can be interpreted in terms of intramolecular basis set superposition error (BSSE) effects, mostly between the C-H moieties constituting the arenes. We have carried out counterpoise-corrected optimizations and frequency calculations at the Hartree-Fock, B3LYP, MP2, and CISD levels of theory with several basis sets for a number of arenes. In all cases, correcting for intramolecular BSSE fixes the anomalous behavior of the correlated methods, whereas no significant differences are observed in the single-determinant case. Consequently, all systems studied are planar at all levels of theory. The effect of different intramolecular fragment definitions and the particular case of charged species, namely, cyclopentadienyl and indenyl anions, respectively, are also discussed.     

Apparent relaxation‐time spectrum cutoff in dilute polymer solutions: An effect of solvent dynamics

The apparent short time cutoff of the relaxation‐time spectrum at surprisingly long times for polymers in solution is a well known but not yet understood observation. To elucidate its origins we revisit viscoelastic and oscillatory flow birefringence data for solutions and melts of two linear polymers (polystyrene and polyisoprene) and present new measurements of oscillatory flow birefringence of the latter. Previous measurements have suggested that the “flexibility” of both polymers in solution is smaller than in the melt on the basis of the breadth of the relaxation‐time spectrum of the solution as compared with that of the melt. Our new measurements have explored a higher effective frequency range than was previously possible. This has allowed us to observe the effect of the rotational relaxation time of the solvent on the dynamics of the solution at high frequencies. To obtain the polymer global motion contribution, one now needs to subtract from the solution properties a frequency‐dependent complex solvating environment contribution. We show that the decrease in apparent “flexibility” for solutions arises from the presence of a solvent that exhibits a rotational relaxation time and thus simple viscoelastic behavior somewhat near the frequency window of the experiment. Although recent predictions of a model for a chain in a solvent with a single relaxation time are in qualitative agreement with our results, our data suggest that the solution results may reflect the influence of solvent on the development of the “entropic spring” forces at short times. © 2001 John Wiley & Sons, Inc. J Polym Sci Part B: Polym Phys 39: 2860–2873, 2001     

The irregular energy spectrum of the Hénon-Heiles system

The properties of the quantal energy spectrum of the Hénon-Heiles system, as obtained by Pomphrey and by Pullen and Edmonds, apparently conflict with those obtained by Noid, Koszkowski, Tabor and Marcus, and by Weissman and Jortner. We discuss this and conclude that the classical transition from regular to irregular motion corresponds to the onset of avoided crossings in the quantal spectrum with high second differences of the energy eigenvalues as a function of pertubation parameter.     

Intramolecular charge-transfer dynamics in covalently linked perylene-dimethylaniline and cyanoperylene-dimethylaniline

The excited-state dynamics of covalently linked electron donor-acceptor systems consisting of N, N-dimethylaniline (DMA) as electron donor and either perylene (Pe) or cyanoperylene (CNPe) as acceptor has been investigated in a large variety of solvents, including a room-temperature ionic liquid, by using femtosecond time-resolved fluorescence and absorption spectroscopy. The negligibly small solvent dependence of the absorption spectrum of both compounds and the strong solvatochromism of the fluorescence are interpreted by a model where optical excitation results in the population of a locally excited state (LES) and emission takes place from a charge-separated state (CSS). This interpretation is supported by the fluorescence up-conversion and the transient absorption measurements that reveal substantial spectral dynamics in polar solvents only, occurring on time scales going from a few hundreds of femtoseconds in acetonitrile to several tens of picoseconds in the ionic liquid. The early transient absorption spectra are similar to those found in nonpolar solvents and are ascribed to the LES absorption. The late spectra due to CSS absorption show bands that are red-shifted relative to those of the radical anion of the acceptor moiety by an amount that depends on solvent polarity, pointing to partial charge separation. Global analysis of the time-resolved data indicates that the charge separation dynamics in PeDMA is essentially solvent controlled, whereas that in CNPeDMA is faster than diffusive solvation, this difference being accounted for by a larger driving force for charge separation in the latter. On the other hand, the CSS lifetime of PeDMA is of the order of a few nanoseconds independently of the solvent, whereas that of CNPeDMA decreases with increasing solvent polarity from a few nanoseconds to a few hundreds of picoseconds. Comparison of these results with previously published data on the fluorescence quenching of Pe and CNPe in pure DMA shows that the charge separation and the ensuing charge recombination occur on similar time scales independently of whether these processes are intra- or intermolecular.     

Calculation of the infrared spectrum and density of the vibrational states of an SiO2 melt by molecular dynamics

The density of the vibrational states of an SiO₂ melt under various PT conditions, the distributions of the Si-O-Si and O-Si-O angles in it, and its IR absorption spectra have been calculated by molecular dynamics with the use of a pairwise additive Born-Mayer potential. A comparison with the experimental data reveals that the ionic approximation selected is capable of basically reproducing the structural and spectroscopic properties of the melt, but the distributions of the bond angles are considerably broader than the experimentally determined distributions, and the absorption band caused by the stretching vibrations is not displayed in the calculated spectrum. The disparities indicated are apparently due to the isotropic nature of the potential of the interparticle interactions.V. I. Vernadskii Institute of Geochemistry and Analytical Chemistry, Academy of Sciences of the USSR, Moscow. Translated from Teoreticheskaya i Éksperimental'naya Khimiya, Vol. 27, No. 4, pp. 467–470, July–August, 1991. Original article submitted October 12, 1990.     

On the direct calculation of the time evolution of excited molecular states in the presence of nonadiabatic interactions

The possibility is explored of calculating the time evolution of a given initial molecular state, in the presence of sufficiently strong nonadiabatic interactions, with a fully quantum-mechanical approach. Two methods are presented. The first one is based on the determination of the molecular eigenstates, with expansion of the nuclear wavefunctions on a Hermite basis. The second method is based on the Padé 1,1 approximation of the time evolution operator and on a finite difference representation of the time-dependent nuclear wavefunctions. Both methods are applied to simple models of a diatomic molecule.     

Intramolecular vibrational redistribution in the vibrational predissociation dynamics of He-I2

The intramolecular vibrational redistribution (IVR) process is investigated in wave packet simulations of the vibrational predissociation dynamics of He-I(2)(B,upsilon') in the region of high upsilon' levels, upsilon' = 35-65. The simulations indicate that for upsilon' < or = 45 the dynamics is dominated by direct predissociation, whereas for higher upsilon' levels the onset of IVR appears and becomes increasingly important. The IVR process occurs via coupling of the initial state in the upsilon' manifold to intermediate long-lived resonances belonging to the lower upsilon < upsilon' vibrational manifolds. The IVR dynamics manifests itself in multiexponential behavior and oscillations in the time-dependent population curves associated with the He-I(2)(B,upsilon') initial state, the He-I(2)(B,upsilon < upsilon') intermediate complexes, and the final product states. The population curves corresponding to the upsilon'- 1 intermediate resonances located below the He + I(2)(B,upsilon'-1,j=0) dissociation limit are analyzed. It is found that initial population is transferred to all the intermediate resonance states considered, including those more separated in energy from the initial one. The results obtained for population transfer between the initial and the intermediate states can be explained by the intensity of the matrix elements coupling the initial and the intermediate resonances, in combination with the Rabi's formula for population exchange between two coupled states.