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Kazuo Takatsuka

Publications and source records attributed to Kazuo Takatsuka.

15 recordsLinked to original sources
PubMed2006

Time-resolved photoelectron spectroscopy of proton transfer in the ground state of chloromalonaldehyde: wave-packet dynamics on effective potential surfaces of reduced dimensionality.

We report on a simple but widely useful method for obtaining time-independent potential surfaces of reduced dimensionality wherein the coupling between reaction and substrate modes is embedded by averaging over an ensemble of classical trajectories. While these classically averaged potentials with their reduced dimensionality should be useful whenever a separation between reaction and substrate modes is meaningful, their use brings about significant simplification in studies of time-resolved photoelectron spectra in polyatomic systems where full-dimensional studies of skeletal and photoelectron dynamics can be prohibitive. Here we report on the use of these effective potentials in the studies of dump-probe photoelectron spectra of intramolecular proton transfer in chloromalonaldehyde. In these applications the effective potentials should provide a more realistic description of proton-substrate couplings than the sudden or adiabatic approximations commonly employed in studies of proton transfer. The resulting time-dependent photoelectron signals, obtained here assuming a constant value of the photoelectron matrix element for ionization of the wave packet, are seen to track the proton transfer.

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PubMed2006

On the validity range of the Born-Oppenheimer approximation: a semiclassical study for all-particle quantization of three-body Coulomb systems.

The validity range of the Born-Oppenheimer (BO) approximation is studied with respect to the variation of the mass (m) of negatively charged particle by substituting an electron (e) with muon (mu) and antiproton (p) in hydrogen molecule cation. With the use of semiclassical quantization applied to these (ppe), (ppmu), and (ppp) under a constrained geometry, we estimate the energy difference of the non-BO vibronic ground state from the BO counterpart. It is found that the error in the BO approximation scales to the power of 3/2 to the mass of negative particles, that is, m(1.5). The origin of this clear-cut relation is analyzed based on the original perturbation theory due to Born and Oppenheimer, with which we show that the fifth order term proportional to m(5/4) is zero and thereby the first correction to the BO approximation should arise from the sixth order term that is proportional to m(6/4). Therefore, the validity range of the Born-Oppenheimer approximation is wider than that often mistakenly claimed to be proportional to m(1/4).

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PubMed2006

Non-Born-Oppenheimer path in anti-Hermitian dynamics for nonadiabatic transitions.

A serious difficulty in the semiclassical Ehrenfest theory for nonadiabatic transitions is that a path passing across the avoided crossing is forced to run on a potential averaged over comprising adiabatic potential surfaces that commit the avoided crossing. Therefore once a path passes through the crossing region, it immediately becomes incompatible with the standard view of "classical trajectory" running on an adiabatic surface. This casts a fundamental question to the theoretical structure of chemical dynamics. In this paper, we propose a non-Born-Oppenheimer path that is generated by an anti-Hermitian Hamiltonian, whose complex-valued eigenenergies can cross in their real parts and avoid crossing in the imaginary parts in the vicinity of the nonadiabatic transition region. We discuss the properties of this non-Born-Oppenheimer path and thereby show its compatibility with the Born-Oppenheimer classical trajectories. This theory not only allows the geometrical branching of the paths but gives the nonadiabatic transition amplitudes and quantum phases along the generated paths.

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PubMed2005

Very fast tunneling in the early stage of reaction dynamics.

The difference between quantum and classical survival probabilities for molecular dissociation dynamics in the time domain, which arises mainly from quantum mechanical tunneling, has interesting characteristics that are not noticed through the counterpart in energy domain. It is shown that the early stage undergoes a fast tunneling, while the later stage is characterized with a long-lasting slow tunneling. The mechanism of this behavior is analyzed in terms of a quasi-semiclassical theory featuring the geometrical distribution of the so-called tunneling points. In particular, the role of dynamical tunneling is discussed as a phenomenon that typifies the time dependence of tunneling dynamics. It is predicted that these tunneling characteristics will be reflected in the isotope effect and should be experimentally observable.

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PubMed2005

Nonadiabatic chemical dynamics in an intense laser field: electronic wave packet coupled with classical nuclear motions.

Dynamics of molecules in an intense laser field is studied in terms of the quantum electronic wave packet coupled with classical nuclear motions. The equations of motion are derived taking a proper account of molecular interactions with the vector potential of a classical electromagnetic field, along with the nonadiabatic interaction due to the breakdown of the Born-Oppenheimer approximation. With the aid of electronic structure calculations, the present method enables us to track, in an ab initio manner, the dynamics of polyatomic molecules in an intense field. Preliminary calculations are carried out for the vibrational state of LiF and a collision of Li+F under an intense laser pulse, which are limited to the domain of no ionization.

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PubMed2005

Dynamic charge fluctuation of endohedral fullerene with coencapsulated Be atom and H2.

As one of the typical examples of characteristic reaction field generated in inclusion (enclosure) compounds, the dynamics of an endohedral metallofullerene, (Be+nH2)@C60(n=1,2), is studied with Be atom serving as a test probe. A very large dynamical and thermal fluctuation of electronic state of Be has been found, which is surprising since the highest occupied molecular orbital-lowest unoccupied molecular orbital gap of Be is so wide that such a large fluctuation in a low temperature is never expected. This finding demonstrates one of the special features of endohedral reaction field offered by the fullerene. The physical origin of this phenomenon is analyzed.

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PubMed2005

Extended quantization condition for constructive and destructive interferences and trajectories dominating molecular vibrational eigenstates.

The role of destructive quantum interference in semiclassical quantization of molecular vibrational states is studied. This aspect is crucial for correct quantization, since failure in the appropriate treatment of destructive interference quite often results in many spurious peaks and broad background to hide the true peaks. We first study the time-Fourier transform of the autocorrelation function without performing summation over the trajectories. The resultant quantity, the prespectrum which is a function of individual classical trajectories, provides a clear view about how destructive interference among the trajectories should function. It turns out that the prespectrum is oscillatory but never a random noise. On the contrary, it bears a systematic and regular structure, which is sometimes characterized in terms of very sharp and high peaks in the energy space of the sampled classical trajectories. We have found an extended quantization condition that is responsible for generating these peaks in the prespectrum, which we call the prior quantization condition. Integration of the prespectrum over the trajectory space is supposed to give "zero" (practically a small value of the order of the Planck constant) at a noneigenvalue energy, which is actually a materialization of the destructive interference. Besides, certain finite peaks in the prespectrum survive after the integration to form the true spikes (eigenvalues) in the final spectrum, if they satisfy an additional resonance condition. For these resonance components, the prior quantization condition is reduced to the Einstein-Brillouin-Keller quantization condition. Based on these analyses, we propose a rather conventional filtering technique to efficiently handle tedious computation for destructive interference, and numerically verify that it works well even for multidimensional chaotic systems. This filtering technique is further utilized to extract a few trajectories that dominate an eigenstate of molecular vibration.

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PubMed2005

Symmetry-adapted correlation function for semiclassical quantization.

We study a very simple method to incorporate quantum-mechanical symmetries, including the permutational symmetry on an equal footing with spatial symmetries, into the semiclassical calculation of correlation functions. This method is applied to the calculation of energy spectra to verify its validity by reproducing quantum energy levels for systems of bosons (symmetrized) and fermions (antisymmetrized). The mechanism of how the phase-space structure of classical dynamics is linked with the relevant quantum symmetry is discussed.

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PubMed2005

Quantum fluctuation of electronic wave-packet dynamics coupled with classical nuclear motions.

An ab initio electronic wave-packet dynamics coupled with the simultaneous classical dynamics of nuclear motions in a molecule is studied. We first survey the dynamical equations of motion for the individual components. Reflecting the nonadiabatic dynamics that electrons can respond to nuclear motions only with a finite speed, the equations of motion for nuclei include a force arising from the kinematic (nuclear momentum) coupling from electron cloud. To materialize these quantum effects in the actual ab initio calculations, we study practical implementation of relevant electronic matrix elements that are related to the derivatives with respect to the nuclear coordinates. Applications of the present scheme are performed in terms of the configuration state functions (CSF) using the canonical molecular orbitals as basis functions without transformation to particular diabatic basis. In the CSF representation, the nonadiabatic interaction due to the kinematic coupling is anticipated to be rather small, and instead it should be well taken into account through the off-diagonal elements of the electronic Hamiltonian matrix. Therefore it is expected that the nonadiabatic dynamics based on this CSF basis neglecting the kinematic coupling may work. To verify this anticipation and to quantify the actual effects of the kinematic coupling, we compare the dynamics with and without the kinematic-coupling terms using the same CSF set. Applications up to the fifth electronically excited states in a nonadiabatic collision between H(2) and B(+) shows that the overall behaviors of these two calculations are surprisingly similar to each other in an average sense except for a fast fluctuation reflecting the electronic time scale. However, at the same time, qualitative differences in the collision events are sometimes observed. Therefore it turns out after all that the kinematic-coupling terms cannot be neglected in the CSF-basis representation. The present applications also demonstrate that the nonadiabatic electronic wave-packet dynamics within ab initio quantum chemical calculation is feasible.

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PubMed2005

Dynamical and statistical effects of the intrinsic curvature of internal space of molecules.

The Hamilton dynamics of a molecule in a translationally and/or rotationally symmetric field is kept rigorously constrained in its phase space. The relevant dynamical laws should therefore be extracted from these constrained motions. An internal space that is induced by a projection of such a limited phase space onto configuration space is an intrinsically curved space even for a system of zero total angular momentum. In this paper we discuss the general effects of this curvedness on dynamics and structures of molecules in such a manner that is invariant with respect to the selection of coordinates. It is shown that the regular coordinate originally defined by Riemann is particularly useful to expose the curvature correction to the dynamics and statistical properties of molecules. These effects are significant both qualitatively and quantitatively and are studied in two aspects. One is the direct effect on dynamics: A trajectory receives a Lorentz-like force from the curved space as though it was placed in a magnetic field. The well-known problem of the trapping phenomenon at the transition state is analyzed from this point of view. By showing that the trapping force is explicitly described in terms of the curvature of the internal space, we clarify that the physical origin of the trapped motion is indeed originated from the curvature of the internal space and hence is not dependent of the selection of coordinate system. The other aspect is the effect of phase space volume arising from the curvedness: We formulate a general expression of the curvature correction of the classical density of states and extract its physical significance in the molecular geometry along with reaction rate in terms of the scalar curvature and volume loss (gain) due to the curvature. The transition state theory is reformulated from this point of view and it is applied to the structural transition of linear chain molecules in the so-called dihedral angle model. It is shown that the curvature effect becomes large roughly linearly with the size of molecule.

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PubMed2004

Kinematic effects associated with molecular frames in structural isomerization dynamics of clusters.

Kinematic effects associated with movements of molecular frames, which specify instantaneous orientation of molecules, is investigated in structural isomerization dynamics of a triatomic cluster whose total angular momentum is zero. The principal-axis frame is employed to introduce the so-called principal-axis hyperspherical coordinates, with which the mechanism of structural isomerization dynamics of the cluster is systematically analyzed. A force called "democratic centrifugal force" is extracted from the associated kinematics. This force arises from an intrinsic non-Euclidean metric in the internal space and has an effect of distorting the triatomic cluster to a collapsed shape and of trapping the system around collinear transition states. The latter effect is particularly important in that the kinematics effectively makes a basin at the saddle (transition state) on the potential surface. Based on this framework, we study the effect of the gauge field associated with the Eckart frame in internal space, which has not been carefully examined in the conventional reaction rate theories. Numerical comparison between the dynamics with and without the gauge field has revealed that this field has an effect to suppress the rate of isomerization reaction to a considerable amount. Thus a theory neglecting this effect will significantly overestimate the rate of isomerization. We show the physical origin of this suppressing effect.

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PubMed2004

Time-dependent probability of quantum tunneling in terms of the quasisemiclassical method.

In view of the rapid progress in experiments of the tunneling dynamics in the time domain, we develop a quasisemiclassical method that is aimed at a study of the proton-transfer dynamics in a large system such as tropolone and its interesting derivatives, to which not only full quantum mechanics, but even a standard semiclassical theory is never easy to apply. In our very tractable method for multidimensional systems, the tunneling paths are generated in terms of the generalized classical mechanics, but the quantum phases arising from the action integral, the Maslov index, and the semicalssical amplitude factor as well in the semiclassical kernels are entirely neglected. This approach is called the quasisemiclassical method. One of the technical issues involved in the general semiclassical scheme is how to locate points from which a tunneling path emanates. Hence the studies of such tunneling points and the quasisemiclassical method should be examined collectively. We test several ways of determining the tunneling point, including those already proposed in the literature and a newly proposed one. It is shown numerically that the quasisemiclassical method with an appropriate choice of tunneling points reproduces the full quantum mechanical tunneling probability reasonably well. This case study indicates that the present conventional approach is promising to the study of large systems. The role of tunneling points in the initial process of tunneling is also discussed.

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PubMed2003

Pump-probe photoionization study of the passage and bifurcation of a quantum wave packet across an avoided crossing.

The application of femtosecond pump-probe photoelectron spectroscopy to directly observe vibrational wave packets passing through an avoided crossing is investigated using quantum wave packet dynamics calculations. Transfer of the vibrational wave packet between diabatic electronic surfaces, bifurcation of the wave packet, and wave packet construction via nonadiabatic mixing are shown to be observable as time-dependent splittings of peaks in the photoelectron spectra.

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PubMed2002

Quantum chaos induced by nonadiabatic coupling in wave-packet dynamics.

The effect of nonadiabatic coupling due to breakdown of the Born-Oppenheimer approximation on chaos is investigated. A couple of measures (indicators) that detect the extent of chaos in wave-packet dynamics on coupled potential functions are devised. Using them, we show that chaos is indeed induced by a nonadiabatic coupling in individual time-dependent wave-packet dynamics. This chaos is genuinely of quantum nature, since it arises from bifurcation and merging of a wave packet at the quasicrossing region of two coupled potential functions.

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