An approach to thermodynamics

Suggestions are given for a new method of teaching thermodynamics starting from a minimum knowledge of quantum mechanics. For didactical reasons much reference is made to systems having only two energy levels in order to minimise difficulties in understanding the concepts of equilibrium and non-equilibrium.     

A perturbation approach to finite difference methods

A perturbation theoretic approach to finite difference methods for the calculation of eigenvalues is shown to permit an increase in the accuracy of the calculations and also to make possible the calculation of expectation values along with the eigenvalues. An application of the virial theorem can then boost the order of accuracy of any given finite difference method. Integrated probabilities and point values of the normalized wavefunction can be found without any use of quadratures. Illustrative examples are given involving the Schrodinger equation for simple polynomial potentials.     

A chemical systems approach to evolution

A novel approach to the evolution of organisms is given. It asserts that biological evolution was consequential upon geochemical, environment, change and was inevitable not accidental.     

A novel approach to 4-benzylisoouinolines

The reaction of quinone methides with 3.4-dihydroisoquinoline or isoquinoline leads to benzylisoquinoline derivatives. NMR and ms investigations as well as chemical degradation prove that benzylation takes place at C-4 of the isoquinoline nucleus. Spectroscopic data are given for all new compounds.     

Superoperator approach to propagator approximations

The superoperator formalism for matrix propagators is reviewed, with special attention to the validity of superoperator resolution of the identity. The equation of motion for the particle-hole propagator is discussed. Decoupling procedures based on inner projections and partitioning are examined showing the desirability of self-consistent approximations. The conditions under which a state can be a vacuum for a given linear manifold of operators are analyzed.     

A quantitative approach to optical resolution

Significant statistical relationships have been found between the parameters characterizing the results and circumstances of the resolutions of seventeen phenylglycine derivatives. The successful predictions given for the results of six independent resolutions prove the utility of these relationships.     

Molecular spinors from the quasi-relativistic pseudopotential approach

A quasi-relativistic (two-component) pseudopotential SCF method is presented. Kramers symmetry is imposed on the Fock operator. A matrix formulation using a basis of non-relativistic real atomic spin orbitals is given. The molecular spinors obtained have maximum similarity to conventional real molecular orbitals.     

A new approach to angular momentum constraints in bimolecular reactions

The well-known analysis of angular momentum constraints for diatomic systems in terms of a bond potential containing a J-dependent centrifugal part is here extended to larger systems. The new procedure is based on the identification of the minimal kinetic energy associated with a given spatial configuration and J value. Alternatively, for a given total energy E and spatial configuration the maximum J value can be identified. Constant J_max curves have been obtained by a Monte Carlo sampling scheme for a model of the KNaCl system at several different total internal energies. Particular attention is given to the estimation of J-dependent reaction thresholds.     

A field theoretical approach to calculate electronic Born-Oppenheimer coupling terms

In this paper we suggest to consider the spatial distribution of the Born-Oppenheimer nonadiabatic coupling terms as fields which are created by sources, located at degeneracy points, and which can be derived using the ordinary mathematical tools of field theory. It is shown that the curl-divergence equations as formed within a given Hilbert space [M. Baer, Chem. Phys. Lett. 35, 112 (1975)] can be converted into a set of inhomogeneous coupled Poisson equations which are solved for a given set of boundary conditions. The method is applied to the three-state Hilbert subspace of the H(3) system. The numerical results are compared with ab initio calculations for which a very encouraging fit is found.     

On the generalized approach to the structure count

A generalized approach to the structure count of n-radical-m-cation systems based on the properties of the acyclic polynomial is presented. The mathematical proof for the expression relating the structure count to the coefficients of the acyclic polynomial is given. The connection between the structure count of biradical structures and the number of Dewar structures is discussed and tested on some examples.     

A decision theory approach to fitness for purpose in analytical measurement

The choice of an analytical procedure and the determination of an appropriate sampling strategy are here treated as a decision theory problem in which sampling and analytical costs are balanced against possible end-user losses due to measurement error. Measurement error is taken here to include both sampling and analytical variances, but systematic errors are not considered. The theory is developed in detail for the case exemplified by a simple accept or reject decision following an analytical measurement on a batch of material, and useful approximate formulae are given for this case. Two worked examples are given, one involving a batch production process and the other a land reclamation site.     

The integrated multivariate approach in materials science

The combination and application of different multivariate statistical methods for glass synthesis and glass technology is demonstrated for the design of new photochromic materials. Factor analysis and cluster analysis are used to provide a multivariate view of the experimental data, for data preprocessing and for extraction of interactions of variables. The partial least-squares method finds a new application for optimization of synthetic and technical parameters in a search for glasses with optimal combinations of properties given by points in the common latent-variables space.     

Extended thermodynamic approach to ion interaction chromatography: a thorough comparison with the electrostatic approach,and further quantitative validation

Based on a simple, chromatography-based analogy, a quantitatively exact explanation for the strong additional band broadening induced by the presence of the side-walls in flow channels with a large aspect-ratio rectangular cross-section is given and validated for two different flow types: pressure-driven and shear-driven flow.     

Calibration — A multidimensional approach

Analytical calibration, in its entirety, comprises both qualitative and quantitative analysis and has to be considered, therefore, from a multidimensional point of view. The relationships must be characterised between the presence of certain analytes and typical signal patterns (e.g. at certain wavelengths) on the one hand and between the amount of given analytes and signal intensities on the other. It is useful to take a three dimensional model as the basis for the classical quantitative analysis and calibration. The relationships between the signal intensity and the true concentration of reference materials used for calibration and the concentration to be estimated in real analytical samples spread a three dimensional function whose corresponding two dimensional projections represent the common calibration function, the analytical evaluation function and the recovery function, which is important for validation (testing the accuracy). Under certain conditions the three dimensional model can be simplified to the common two dimensional one. Multivariate calibration relates to multidimensionality in analytical problems and data sets in principle. Multicomponent analysis and multisignal evaluation are characterized and illustrated by special applications.     

An integrated approach to knowledge-driven structure-based virtual screening

In many practical applications of structure-based virtual screening (VS) ligands are already known. This circumstance requires that the obtained hits need to satisfy initial made expectations i.e., they have to fulfill a predefined binding pattern and/or lie within a predefined physico-chemical property range. Based on the RApid Index-based Screening Engine (RAISE) approach, we introduce cRAISE—a user-controllable structure-based VS method. It efficiently realizes pharmacophore-guided protein-ligand docking to assess the library content but thereby concentrates only on molecules that have a chance to fulfill the given binding pattern. In order to focus only on hits satisfying given molecular properties, library profiles can be utilized to simultaneously filter compounds. cRAISE was evaluated on a range of strict to rather relaxed hypotheses with respect to its capability to guide binding-mode predictions and VS runs. The results reveal insights into a guided VS process. If a pharmacophore model is chosen appropriately, a binding mode below 2 Å is successfully reproduced for 85 % of well-prepared structures, enrichment is increased up to median AUC of 73 %, and the selectivity of the screening process is significantly enhanced leading up to seven times accelerated runtimes. In general, cRAISE supports a versatile structure-based VS approach allowing to assess hypotheses about putative ligands on a large scale.     

Graphical unitary group approach to spin–spin interaction

A detailed exposition of spin–spin operator matrix elements is presented in the context of the graphical unitary group approach (GUGA ) to atomic and molecular physics and quantum chemistry. A compendium of subgraph types and formulae is given. Aspects of computer implementation within the structure of the Columbus CI programs is discussed.     

Theoretical approach to reactions of polyatomic molecules

A scheme for systematic reduction of the theoretical treatment of elementary reactions involving polyatomic molecules is described; it consists of (1) limitation to the energetically relevant regions of the nuclear configuration space (the reaction path and its near environs) and (2) restriction to the dynamically relevant subspace of the nuclear configuration space (the active modes). Starting from a generalized reaction path Hamiltonian of Nauts and Chapuisat allowing for the use of arbitrary curvilinear coordinates and several large-amplitude modes, the realization of the above-sketched scheme is discussed. A compilation of recent work along these lines, mostly based on the simplified Miller-Handy-Adams reaction path Hamiltonian, is given with particular emphasis on applications of a statistical adiabatic model.