Nakamura Theory Research Articles

Seeking double personality: Nakamura Kokyō's work in abnormal psychology in early 20th-century Japan.

This paper examines Nakamura Kokyō's study of a woman with a split personality who lived in his home as a maid from 1917 until her death in 1940. She was his indispensable muse and assistant in his efforts to promote abnormal psychology and psychotherapy. This paper first explores the central position of multiple personality in Nakamura's theory of the subconscious, which was largely based on the model of dissociation. It then examines how it became a central issue in Nakamura's disputes with religions including the element of spirit possession, which invoked Western psychical research to modernize their doctrines. While both were concerned with the subconscious and alterations in personality, Nakamura's psychological view was distinguished from those spiritual understandings by his emphasis on individual memories, particularly those that were traumatic, and hysteria. The remaining sections of the paper will examine Nakamura's views on memory and hysteria, which conflicted with both the academic mainstream and the established cultural beliefs. This conflict may partly explain the limited success of Nakamura's academic and social campaigns.

Chiral conversion and periodical decay in bridged-azobenzene photoisomerization: an ab initio on-the-fly nonadiabatic dynamics simulation

On-the-fly trajectory surface hopping dynamics simulations on the cis ↔ trans photoisomerization mechanisms of bridged-azobenzene upon S1 excitation at the CASSCF level.

Photochemical dynamics simulations for trans–cis photoisomerizations of azobenzene and bridged azobenzene

Surface hopping dynamics simulations based on the Zhu–Nakamura theory were performed to investigate the trans–cis photoisomerization mechanisms of azobenzene and bridged azobenzene excited to S1 state. In geometry optimization, both for the two compounds, two minimum-energy conical intersections between the ground state and the lowest excited state are located. Two conical intersections are confirmed to be decay funnels in the trans–cis photoisomerization processes in azobenzene but only one plays important parts in the photoisomerization of bridged azobenzene. Due to the smaller slope of potential energy surface in the S1 state, the lifetime of the S1 state of azobenzene in our work is much longer than that of bridged azobenzene. We show that the torsion around the central NN bond is the preferred reaction mechanism in the isomerization of two molecules. Rotation around the central NN bond and twisting of phenyl rings around their NC bonds allows the molecule to move to a minimum-energy conical intersection, after which surface hopping from S1 to S0 occurs. In the ground state, further rotation occurs around the NN bond and two NC bonds until the azo moiety and phenyl rings complete their isomerization. The additional CH2CH2 bridge in bridged azobenzene starts to rotate toward the cis form after the azo moiety and two phenyl rings complete their reorientation. The bridge structure in bridged azobenzene makes the rotation of the azo moiety faster and the torsion of two phenyl rings slower.

中村敏雄の学校体育論における理論的出発点に関する一考察

中村敏雄の学校体育論における理論的出発点に関する一考察

QM/MM Trajectory Surface Hopping Approach to Photoisomerization of Rhodopsin and Isorhodopsin: The Origin of Faster and More Efficient Isomerization for Rhodopsin

The photoinduced cis-trans isomerization dynamics of rhodopsin and isorhodopsin are studied using a newly developed hybrid QM/MM trajectory surface hopping MD scheme based on the Zhu-Nakamura theory for nonadiabatic transitions. Rhodopsin and isorhodopsin have 11-cis and 9-cis forms of retinal as chromophore and the two proteins are isomerized to bathorhodopsin enclosing the all-trans form. The simulation reproduced faster and more efficient isomerization in rhodopsin than in isorhodopsin. In the excited state, rhodopsin shows a straightforward dynamics, whereas isorhodopsin dynamics is rather complicated and in a back-and-forth manner. The latter complicated dynamics would be mainly due to a narrow space near the active dihedral angle ═C8-C9═C10-C11═ (ϕ9) created by Thr 118 and Tyr 268 in opsin. Rhodopsin gives bathorhodopsin only while isorhodopsin yields a byproduct. The rigorous selectivity in rhodopsin would be another reason why rhodopsin is selected biologically. Comparison with our previous opsin-free investigations reveals that opsin tends to confine the twist of the active dihedral to only one direction and funnels transitions into the vicinity of minimum energy conical intersections (MECI). The twist-confinement totally blocks simultaneous twisting of ϕ9 and ϕ11 (═C10-C11═C12-C13═) and enhances the quantum yields. The opposite rotation of ϕ9 and ϕ11 ("wring-a-wet-towel" motion) takes place upon photoexcitation, which also does without opsin. The wring-a-wet-towel motion is dynamically enhanced in comparison with the one expected from locations of the MECI. The present simulation reveals that the Weiss-Warshel model for cis-trans photoisomerization is not applicable for rhodopsin because the branching ratio after transition is crucial.

The three-dimensional nonadiabatic dynamics calculation of DH2+ and HD2+ systems by using the trajectory surface hopping method based on the Zhu–Nakamura theory

A theoretical investigation on the nonadiabatic processes of the full three-dimensional D(+)+H(2) and H(+)+D(2) reaction systems has been performed by using trajectory surface hopping (TSH) method based on the Zhu-Nakamura (ZN) theory. This ZN-TSH method refers to not only classically allowed hops but also classically forbidden hops. The potential energy surface constructed by Kamisaka et al. is employed in the calculation. A new iterative method is proposed to yield the two-dimensional seam surface from the topography of the adiabatic potential surfaces, in which the inconvenience of directly solving the first-order partial differential equation is avoided. The cross sections of these two systems are calculated for three competing channels of the reactive charge transfer, the nonreactive charge transfer, and the reactive noncharge transfer, for ground rovibrational state of H(2) or D(2). Also, this study provides reaction probabilities of these three processes for the total angular momentum J=0 and ground initial vibrational state of H(2) or D(2). The calculated results from ZN-TSH method are in good agreement with the exact quantum calculations and the experimental measurements.

A numerical comparison of theories of violent relaxation

Using N-body simulations with a large set of massless test particles we compare the predictions of two theories of violent relaxation, the well known Lynden-Bell theory and the more recent theory by Nakamura. We derive ``weaken'' versions of both theories in which we use the whole equilibrium coarse-grained distribution function as a constraint instead of the total energy constraint. We use these weaken theories to construct expressions for the conditional probability $K_i(\tau)$ that a test particle initially at the phase-space coordinate $\tau$ would end-up in the $i$'th macro-cell at equilibrium. We show that the logarithm of the ratio $R_{ij}(\tau) \equiv K_i(\tau)/K_j(\tau)$ is directly proportional to the initial phase-space density $f_0(\tau)$ for the Lynden-Bell theory and inversely proportional to $f_0(\tau)$ for the Nakamura theory. We then measure $R_{ij}(\tau)$ using a set of N-body simulations of a system undergoing a gravitational collapse to check the validity of the two theories of violent relaxation. We find that both theories are at odds with the numerical results, qualitatively and quantitatively.

SEMICLASSICAL FROZEN GAUSSIAN PROPAGATION METHOD FOR ELECTRONICALLY NONADIABATIC CHEMICAL DYNAMICS: MØLLER OPERATOR FORMULATION AND INCORPORATION OF THE ZHU-NAKAMURA THEORY

The title theory is developed by combining the Herman–Kluk semiclassical theory for adiabatic propagation on single potential energy surface and the Zhu–Nakamura theory for nonadiabatic transition. A fairly simple expression for the propagator based on classical trajectories is derived using the Møller operator formulation of scattering theory. The theory takes into account almost all quantum effects that occur during nonadiabatic transition, especially at low energies and is expected to be applicable to general chemical dynamics of high dimensions. Application to a two-dimensional model system shows that the theory works well for the propagation duration of several molecular vibrational periods and wide wave packet energy range.

Laser control of electronic transitions of wave packet by using quadratically chirped pulses

An effective scheme is proposed for the laser control of wave packet dynamics. It is demonstrated that by using specially designed quadratically chirped pulses, fast and nearly complete excitation of wave packet can be achieved without significant distortion of its shape. The parameters of the laser pulse can be estimated analytically from the Zhu-Nakamura theory of nonadiabatic transition. If the wave packet is not too narrow or not too broad, then the scheme is expected to be utilizable for multidimensional systems. The scheme is applicable to various processes such as simple electronic excitation, pump-dump, and selective bond breaking, and it is actually numerically demonstrated to work well by taking diatomic and triatomic molecules (LiH, NaK, H(2)O) as examples.

Evaluation of canonical and microcanonical nonadiabatic reaction rate constants by using the Zhu–Nakamura formulas

We consider a problem of calculating both thermal and microcanonical rate constants for nonadiabatic chemical reactions. Instead of using the conventional transition state theory, we use a generalized seam surface and introduce a concept of a coordinate dependent effective nonadiabatic transition probability based on the Zhu-Nakamura theory which can treat the nonadiabatic tunneling properly. The present approach can be combined with Monte Carlo method so as to be applicable to chemical reactions in complicated systems. The method is demonstrated to work well in wide energy and temperature range. Numerical tests also show that it is very essential for accurate evaluation of the thermal rate constant to use the generalized seam surface and take into account the nonadiabatic tunneling effect.

Semiclassical theory of electronically nonadiabatic chemical dynamics: incorporation of the Zhu-Nakamura theory into the frozen Gaussian propagation method.

The title theory is developed by combining the Herman-Kluk semiclassical theory for adiabatic propagation on single potential-energy surface and the semiclassical Zhu-Nakamura theory for nonadiabatic transition. The formulation with use of natural mathematical principles leads to a quite simple expression for the propagator based on classical trajectories and simple formulas are derived for overall adiabatic and nonadiabatic processes. The theory is applied to electronically nonadiabatic photodissociation processes: a one-dimensional problem of H2+ in a cw (continuous wave) laser field and a two-dimensional model problem of H2O in a cw laser field. The theory is found to work well for the propagation duration of several molecular vibrational periods and wide energy range. Although the formulation is made for the case of laser induced nonadiabatic processes, it is straightforwardly applicable to ordinary electronically nonadiabatic chemical dynamics.

New implementation of the trajectory surface hopping method with use of the Zhu–Nakamura theory. II. Application to the charge transfer processes in the 3D DH2+ system

The newly implemented trajectory surface hopping (TSH) method for the collinear system with use of the Zhu–Nakamura semiclassical theory of nonadiabatic transition [C. Zhu, K. Nobusada, and H. Nakamura, J. Chem. Phys. 115, 3031 (2001)] is extended to treat 3D nonadiabatic reactions. Since the avoided crossing seam becomes a two-dimensional surface in the 3D system, the nonadiabatic transition region and the possibility of classically forbidden hops are enlarged very much in comparison with those in the collinear case. As a result, the contribution of the classically forbidden hops is quite a bit enhanced in the 3D system. Conservation of total angular momentum J is taken into account by slightly rotating the direction of momentum during the hop in the classically forbidden case. The method is tested by applying to the charge transfer processes in the 3D DH2+ system for J=0. Numerical results clearly demonstrate that the new TSH method works very well at all energies and for all initial vibrational states considered compared to the old TSH method based on the Landau–Zener formula. The significant discrepancy between the two TSH methods survives even at high collision energy and high vibrational states in contrast to the collinear case, indicating the importance of the classically forbidden hops in 3D systems. The new TSH method is considered to be a very promising method to deal with high dimensional nonadiabatic dynamics. It should also be noted that the new TSH method does not require any knowledge of nonadiabatic coupling and is based only on adiabatic potentials.

Significant improvement of the trajectory surface hopping method by the Zhu–Nakamura theory

By taking the three-dimensional D++H2 reaction system, the trajectory surface hopping method based on the Zhu–Nakamura theory is demonstrated to work much better than the old one and to be very promising to treat high-dimensional electronically nonadiabatic processes. The difference between the new and old survives even at high initial vibrational states and high energies.

New implementation of the trajectory surface hopping method with use of the Zhu–Nakamura theory

A new implementation of the trajectory surface hopping (TSH) method is proposed to treat multidimensional nonadiabatic dynamics by incorporating the analytical Zhu–Nakamura semiclassical theory of nonadiabatic transition. The problem of classically forbidden hops in the TSH method can now be solved and dealt with just as easily as the classically allowed hops by introducing nonvertical hopping techniques. This is made possible, because the theory can treat both classically allowed and forbidden hops accurately in a unified way. The Zhu–Nakamura theory also enables us to predetermine important regions of potential energy surface before carrying out any dynamics calculations, and thus to save a lot of computational efforts. The charge transfer processes in the collinear H3+ system are studied numerically to test the new TSH method. Comparing the new and old versions of TSH with exact quantum calculations, the new method shows much better agreement with the exact calculations. It also works well when all trasitions are classically forbidden and the old method fails completely.

Shapes of Moving Domain Boundary Affected by Edge Dislocation in Ferroelectric Crystal of Triglycine Sulfate

Shapes of moving 180°-wall affected by stresses due to a dislocation were obtained for TGS crystals from calculations based on Nakamura's theory of domain growth. Anisotropic sidewise velocity, v , of wall motion under the stress T was determined on the assumption that v depended on T through the wall energy density σ; the T dependence of σ was derived from the Zhirnov-type continuum theory. An edge component, rather than a screw component, of a dislocation which is parallel to the ferroelectric axis affects the value of σ. Under a low field the wall is caught in the dislocation, while under a high field it easily passes through the dislocation. The results are in qualitative agreement with experimental observations.

Shapes of Growing Domains in Ferroelectric Triglycine Sulfate and Triglycine Selenate

In TGS and TGSe, shapes of the domains growing under electric field have been investigated on the basis of Nakamura's theory which offers the envelope constructed from elementary plane waves of growth. In the formula v = v ∞ exp (-δ/ E ) for the normal velocity v of sidewise wall motion under electric field E , the activation field δ has been assumed to be proportional to 3/2 powers of wall-energy density of σ'. The values of v in the various directions have been calculated with σ' obtained from the Zhirnov-type continuum theory. The domain shapes and their dependence on the applied field have been determined with the calculated values of v . The results satisfactorily explain the experimentally observed lenticular and elliptical shapes in TGS and the restricted lenticular, lenticular and elliptical shapes in TGSe. It has been shown that there exist critical fields for the classification of these kinds of shape.

Position-Dependent Superconductivity

A discussion is given of several methods used in generalizing the Bardeen-- Cooper-- Schrieffer theory of superconductivity to problems where position dependence plays a key role. It is pointed out that the method in most common use (that of Gorkov) is inappropriate for discussing the rather long-range effects on each other (extending over distances of about 10/sup -5/ cm) of two metals in contact. A method appropriate for describing such effects is obtained by generalizing the Nakamura theory of position-independent superconductivity. This method leads to results qualitatively similar to those obtained previously by Parmenter using heuristic arguments. The various methods of treating position- dependent superconductivity are all different limiting forms of a very general form of theory due to Blatt, or, in an equivalent but particle-nonconserving form, due to Bogoliubov and Valatin. The saddle-point method of summing cluster expansions, used in both the Blatt and Nakamura theories, is shown to be mathematically justified, in contrast to the situation with most condensed systems. (auth)

Antiferromagnetism of CuF2·2H2O

The perpendicular and parallel magnetic susceptibilities have been calculated for Cu${\mathrm{F}}_{2}$\ifmmode\cdot\else\textperiodcentered\fi{}2${\mathrm{H}}_{2}$O on the basis of Nakamura's theory. The computed values of molar susceptibility for the same compound have been compared with the recent measurements of Bozorth and Nielsen and are found to be in good agreement.