Successive partitioning technique and Feenberg perturbation theory

Successive partitioning technique, when based on a modified bordering method for solving a system of linear equations and a relation for the inverse of a partitioned matrix leads to Feenberg's perturbation theory. This sheds light on the properties of the expansion, its bracketing properties and the nature of the “counting operators” used sometimes in this connection.     

Adaptive density partitioning technique in the auxiliary plane wave method

We have developed the adaptive density partitioning technique (ADPT) in the auxiliary plane wave method, in which a part of the density is expanded to plane waves, for the fast evaluation of Coulomb matrix. Our partitioning is based on the error estimations and allows us to control the accuracy and efficiency. Moreover, we can drastically reduce the core Gaussian products that are left in Gaussian representation (its analytical integrals is the bottleneck in this method). For the taxol molecule with 6-31G** basis, the core Gaussian products accounted only for 5% in submicrohartree error.     

Level crossings and branch points studied by the multidimensional partitioning technique

The possibility of level crossings is discussed from a general multidimensional partitioning viewpoint. By extending the traditional motion of a self-adjoint Hamiltonian to a self-adjoint analytic family of operators, it is found that level intersections that appear fall into two mutually exclusive categories: the conventional diagonal one corresponding to Jordan blocks of order m = 1, and the nondiagonal one with m ≥ 2. Consequences with respect to some recent examples, such as Longuet-Higgins “sign-reversing loop” construction and the ¹II near degeneracy in SiO, are discussed and examined.     

Intramolecular energy transfer dynamics in 24-mode pyrazine by partitioning technique: A time-dependent approach

We investigate the intramolecular energy transfer dynamics of the S(2) excited electronic state of pyrazine due to radiationless transitions to energetically lower-lying singlet electronic states using a new time-dependent method. The femtosecond decay of S(2) to the S(1) excited state and the picosecond decay of S(2) to the ground electronic state S(0) are studied within an efficient methodology for computing the intramolecular dynamics in multidimensional configurational spaces. Our method is based on partitioning the full configuration space into the (small) subspace of interest Q and the rest, the subspace P. The exact equations of motion for the states in Q, under the influence of P, are derived in the time domain in form of a system of integrodifferential equations. Their numerical solution is readily obtained when the Q space consists of just a few states. Otherwise, the integrodifferential equations for the states in Q are transformed into a (larger) system of ordinary differential equations, which can be solved by a single diagonalization of a general complex matrix. The former approach is applied to study the pyrazine picosecond S(2)→S(0) dynamics and the latter is applied to the study of the ultrafast pyrazine S(2)→S(1) decay dynamics.     

A comment on SCF energy partitioning schemes

Starting from the symmetry groupG × SU(2) for the special case of negligible spin-orbit coupling, a general character formula is derived for them-tuplet representation, which is realized in the space of state functions ofn-electron systems in fields with symmetryG. Apart from the characters of the initial representation for the single electron space function, the formula only contains the number of particlesn and the multiplicitym.

Herrn Professor Dr. Hermann Hartmann zu seinem 60. Geburtstag gewidmet.     

A note on atomic density

In atomic systems, electron density has a simple finite expansion in spherical harmonics times radial factors. The difficulties in the calculation of some radial factors are illustrated in the low‐lying states of the carbon atom. Single‐particle methods such as Hartree–Fock and approximate density functional theory cannot ensure the correct expansion of the density in spherical harmonics. Wave‐function methods are appropriate but, as some expansion terms are entirely due to correlation, these methods only will give correct results for high‐quality variational functions. Using full‐configuration integration (CI), all the terms predicted by the theory appear and are not negligible but the convergence of the term due to correlation toward its correct value is uncertain even for very large CI spaces. © 2012 Wiley Periodicals, Inc.     

A note on generalised time-lags

Derivations of an expression for the generalised outgoing ‘adsorption’ time-lag pertaining to transport through a slab membrane made by [Rutherford and Do, Review of time lag permeation technique as a method for characterisation of porous media and membranes, Adsorption 3 (1997) 283] and by [Ash et al., Sorption and surface flow in graphitized carbon membranes. II. Time-lag and blind pore character, Proc. Roy. Soc. London, Ser. A, 304 (1968) 407] are not in agreement. Causes for the discrepancy are identified. Two extensions of the generalised procedure are given with particular attention being paid to ΔL, the time-lag difference.     

A note on electro-optic effects

Tinoco's second-order electro-optic effect in isotropic fluids is discussed for the case of very high electric fields. The possibility of observing a linear electro-optic effect in oriented molecules of certain symmetry types is also analyzed.     

Analysis of the Valley-Ridge inflection points through the partitioning technique of the Hessian eigenvalue equation

The Valley-Ridge inflection (VRI) points are related to the branching of a reaction valley or reaction channel. These points are a special class of points of the potential energy surface (PES). They are also special points of the Valley-Ridge borderline of the PES. The nature of the VRI points and their differences with respect to the other points of the Valley-Ridge borderline is analyzed using the Löwdin’s partitioning technique applied to the eigenvalue equation of the Hessian matrix. Eigenvalues and eigenvectors of the Hessian are better imaginable than the former used adjoint matrix.     

A note on the neutrino theory of light

In this small note we ask several questions which are relevant to the construction of the self-consistent neutrino theory of light. The previous confusions in such attempts are explained in the more detailed publication.     

A note on the kinetics of suicide substrates

We determine the limit sets of a system modelling suicide substrate kinetics, and show that a result by Tatsunami et al. (Biochim Biophys Acta 662:226–235, 1981), derived under additional quasi-steady state assumptions, holds generally.     

A note on the equation of heat transfer

Liquids with properties βpv/c_p ⪡ 1 and p²vκ/c_pT ⪡ 1 are defined as “incompressible liquids”. The compression work in motion of incompressible liquid is negligibly small. The change in the internal energy of incompressible liquids with respect to the temperature is, however, proportional to c_p. Motions of perfect gases in open systems under appropriate conditions and in closed systems with no net heat addition (or removal) are prescribed by the energy equation with c_p as the appropriate specific heat. Otherwise, either no reduction is possible or both c_p and c_v may become the appropriate specific heats in the energy equation.