Diabatic

Abstract: The situation considered is that of a zonally symmetric model of the middle atmosphere subject to a given quasi-steady zonal force F, conceived to be the result of irreversible angular momentum transfer due to the upward propagation and breaking of Rossby and gravity waves together with any other dissipative eddy effects that may be relevant. The model's diabatic heating is assumed to have the qualitative character of a relaxation toward some radiatively determined temperature field. To the extent that the force F may be regarded as given, and the extratropical angular momentum distribution is realistic, the extratropical diabatic mass flow across a given isentropic surface may be regarded as controlled exclusively by the F distribution above that surface (implying control by the eddy dissipation above that surface and not, for instance, by the frequency of tropopause folding below). This “downward control” principle expresses a critical part of the dynamical chain of cause and effect governin...

Abstract: On the basis of recent data for the roughness Reynolds number of the sea surface, and using the Owen-Thomson theory on the transfers of heat and mass between a rough surface and the flow above it, the bulk transfer coefficients of the sea surface have been estimated. For a reference height of 10 m, the neutral-lapse transfer coefficient for water vapor is larger by only a few percent than that for sensible heat. When the wind speed at the 10-m height is u10>3 m s−1, the coefficient for sensible heat CH is larger by about 10% than that for momentum CD. For u10<5 m s−1, however, the value of CD exceeds the value of CH, and for u10=15 m s−1 it is shown that CH≈0.8CD. It may be also proposed that 103CD=1.11 to 1.70, 103CE=1.18 to 1.30, and 103CH=1.15 to 1.26 for a range of u10=4 to 20 m s−1. A plot of diabatic transfer coefficients versus wind speed is obtained by using a parameter of the sea-air temperature difference. For practical purposes, the coefficients are approximated by empirical formulae.

Abstract: The equations of the general Born-Oppenheimer separation into electronic and heavy-particle coordinates are re-examined, and the coupled equations that result for the heavy-particle motion are expressed in a particularly simple form. This is accomplished by introducing a generalized matrix operator for the effective momentum associated with the heavy particles; the matrix portion of this operator represents a coupling of the nuclear momentum with the electronic motion. The commutator between the momentum and potential matrices is a force matrix, which provides an alternative means of evaluating the momentum matrix. The momentum coupling has both radial and angular parts; the angular momentum coupling agrees with Thorson's expression. In the usual adiabatic molecular representation, the potential energy matrix is diagonalized, and all the coupling is thrown into the radial and angular momentum matrices. For collision problems it is often more important to diagonalize the radial momentum matrix, putting the radial off-diagonal coupling into the potential matrix; this generates a family of diabatic representations, the most important of which dissociates to unique separated atom states. This standard diabatic representations has the properties called for by Lichten, is uniquely defined even with the inclusion of configuration interaction, and leads immediately to the Landau-Zener-Stueckelberg limiting case under appropriate conditions.

Abstract: We show how the presence of a conical intersection in the adiabatic potential energy hypersurface can be handled by including a new vector potential in the nuclear‐motion Schrodinger equation. We show how permutational symmetry of the total wave function with respect to interchange of nuclei can be enforced in the Born–Oppenheimer approximation both in the absence and the presence of conical intersections. The treatment of nuclear‐motion wave functions in the presence of conical intersections and the treatment of nuclear‐interchange symmetry in general both require careful consideration of the phases of the electronic and nuclear‐motion wave functions, and this is discussed in detail.

Abstract: A strictly diabatic electronic basis is defined as one for which all components of the nuclear momentum coupling vanish. We examine the possibility that such a basis may exist, and we find that, in general, it does not. The only important exception is for diatomic states of the same symmetry. We also consider some conditions for the definition of an approximately diabatic electronic basis. For molecular systems with three or more nuclei, one can obtain useful approximate diabatic basis sets if the transverse (solenoidal) part of the coupling is negligible; this may occur, for example, if the part of the coupling due to the internuclear‐distance dependence of the configurational wave functions is negligible as compared to that due to the internuclear‐distance dependence of the configurational coefficients. We derive a criterion showing that such approximations may be useful and accurate if the role of the coupling is important over regions of sufficiently small linear dimensions.