[en] A revision of the method of molecular parameter scaling is made. Detailed discussion on the scaling of the nuclear and electron charges, the nuclear and electron masses and the real and complex scaling of the coordinates is performed. (A.C.A.S.)

[en] In this course, scattering theory and chemical reactions are presented including scattering of one particle by a potential, n-particle systems, colinear triatomic molecules and the study of reactive scattering for 3-dimensional triatomic systems. (A.C.A.S.)

[en] The modified Born-Oppenheimer equation arising from Berry's phase is studied extensively in two physical systems. One is the spin-1/2 neutral particle in the spherically symmetric magnetic field, the other is the electron in the cylindrically symmetric magnetic field. The results show the significant topological effects in simple quantum systems. (author)

[en] In our previous paper [B. T. Sutcliffe and R. G. Woolley, J. Chem. Phys. 137, 22A544 (2012)] we argued that the Born-Oppenheimer approximation could not be based on an exact transformation of the molecular Schrödinger equation. In this Comment we suggest that the fundamental reason for the approximate nature of the Born-Oppenheimer model is the lack of a complete set of functions for the electronic space, and the need to describe the continuous spectrum using spectral projection

No abstract available

[en] We deal with the application of the nuclear Born–Oppenheimer (NBO) method to the study of nuclear collective motion. In particular, we look at the description of nuclear rotations and vibrations. The collective operators are specified within the NBO method only to the extent of identifying the type of collective degrees of freedom we intend to describe; the operators are then determined from the dynamics of the system. To separate the collective degrees of freedom into rotational and vibrational terms, we transform the collective tensor operator from the lab fixed frame of reference to the frame defined by the principal axes of the system; this transformation diagonalizes the tensor operator. We derive a general expression for the NBO mean energy and show that it contains internal, collective and coupling terms. Then, we specify the approximations that need to be made in order to establish a connection between Bohr's collective model and the NBO method. We show that Bohr's collective Hamiltonian can be recovered from the NBO Hamiltonian only after adopting some rather crude approximations. In addition, we try to understand, in light of the NBO approach, why Bohr's collective model gives the wrong inertial parameters. We show that this is due to two major reasons: the ad hoc selection of the collective degrees of freedom within the context of Bohr's collective model and the unwarranted neglect of several important terms from the Hamiltonian. (author)

[en] Consider a Hamiltonian system that consists of a slow subsystem S and a fast subsystem F. The autonomous dynamics of S is driven by an effective Hamiltonian, but its thermodynamics is unexpected. We show that a well-defined thermodynamic arrow of time (second law) emerges for S whenever there is a well-defined causal arrow from S to F and the back-action is negligible. This is because the back-action of F on S is described by a non-globally Hamiltonian Born–Oppenheimer term that violates the Liouville theorem, and makes the second law inapplicable to S. If S and F are mixing, under the causal arrow condition they are described by microcanonical distributions P(S) and P(S|F). Their structure supports a causal inference principle proposed recently in machine learning

[en] Our purpose is to point out the basic inadequancy of the existing theory of positron annihilation in metals (PAM). The latter, indeed, neglects the presence of the screening cloud moving the positron and influencing its Hamiltonian. Its importance is shown by positron effective mass measurements contradicting any theory of PAM but agreeing with the point of view of this paper. While trying to find the one-positron wave function, the Born-Oppenheimer approach is shown to be of some help. It suggests a one-positron Hamiltonian in which three effects neglected up to now must be taken into account: the internal energy of the positron-screening cloud system, the lattice potential of the screening cloud, The influence of the screening cloud on the kinetic part of the positron Hamiltonian. (author)

[en] Corrections to the Born-Oppenheimer approximation were investigated for a number of diatomic hydrides and deuterides in order to obtain information about electronic isotope effects on the gas phase isotopic exchange reaction. The results of some of these calculations are reported

[en] We consider the use of quasi-diabatic bases to improve upon the Born-Oppenheimer approximation in molecular systems. In a nonrigorous, but still suggestive, manner, it is shown that, when the quasi-diabatic approximation is a good one, the use of 'frozen' electronic states will often be equally good, or nearly so.