Kazuo Takatsuka

We propose a new vairational principle for scattering theory which extends the Schwinger variational principle beyond the static-exchange approximation and to inelastic scattering. Application of this formulation to the scattering of electrons by hydrogen atoms at energies below ${k}^{2}=0.64$ demonstrates the rapid convergence of the phase shift with respect to the number of basis functions for both the open- and closed-channel orbitals. Furthermore, we show that the convergence of the phase sh

We discuss a multichannel formulation of the Schwinger and a related variational principle (of one order higher than the Schwinger principle) in a form suitable for application to the scattering of low-energy electrons by both linear and nonlinear molecules. The theory includes the effects of polarization straightforwardly and should be particularly useful for obtaining electronically inelastic cross sections. An expansion of the trial scattering wave function in a discrete basis is possible. Wi

Chemical theory and its application to dynamical electrons in molecules under intense electromagnetic fields is explored, in which we take an explicit account of nuclear nonadiabatic (kinematic) interactions along with simultaneous coupling with intense optical interactions. All the electronic wavefunctions studied here are necessarily time-dependent, and thereby beyond stationary state quantum chemistry based on the Born-Oppenheimer framework. As a general and tractable alternative framework wi

Classical trajectory study of nuclear motion on the Born-Oppenheimer potential energy surfaces is now one of the standard methods of chemical dynamics. In particular, this approach is inevitable in the studies of large molecular systems. However, as soon as more than a single potential energy surface is involved due to nonadiabatic coupling, such a naive application of classical mechanics loses its theoretical foundation. This is a classic and fundamental issue in the foundation of chemistry. To

We propose a variational method for scattering in which the functional is of a fractional form as for the Schwinger variational principle. However, our functional does not involve the Green's function, but the Hamiltonian and the potential function. This method shows features of both the Schwinger-type variational principles and the Kohn-type standard variational principles. As a result, our method can derive distinct advantages from both of these approaches. The resultant $K$ matrix is symmetri

We have previously shown how femtosecond angle- and energy-resolved photoelectron spectroscopy can be used to monitor quantum wavepacket bifurcation at an avoided crossing or conical intersection and also how a symmetry-allowed conical intersection can be effectively morphed into an avoided crossing by photo-induced symmetry breaking. The latter result suggests that varying the parameters of a laser to modify a conical intersection might control the rate of passage of wavepackets through such re

This Letter presents the first application of the Schwinger variational principle for multichannel scattering. Results are presented for an exactly soluble two-channel model problem. The accuracy and convergence of the Schwinger variational principle are shown to be extremely good and superior to those of other variational methods.

We establish the correct mathematical relationship between the Schwinger and Kohn variational principles for scattering theory and show that the Schwinger principle is one rank higher than the Kohn principle. If the same trial scattering wave function is used in these two principles, the Schwinger method should hence give superior results. Application of the Schwinger and Kohn variational principles to scattering by a simple model potential gives results which clearly illustrate this relationshi

The spin-optimized SCF general-spin–orbital (SO–SCF–GSO) method, which has previously been proposed by us, is applied to the 2 2S and 2 2P states of a lithium atom. The energies obtained are −7.448522 and −7.381053 hartree, respectively, which account for as much as 99.7% (2 2S) and and 97.7% (2 2P) of the radial limits of electron correlation. However, the Fermi contact terms calculated [2.750 (2 2S) and −0.1953 (2 2P)] are not necessarily improvements over the values obtained by hitherto-known

A new method to calculate eigenfunctions and eigenvalues in a given energy range is proposed, which can therefore be applied to highly excited states of electronic and/or vibrational states of a molecule. The spectral components of a wave packet that lie outside the energy range are projected out through the time evolution; that is, the packet is screened onto the energy range. If the range includes only a single root, the corresponding eigenfunction is screened first, and the eigenvalue follows