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** A simple example---the quantum mechanical basis for macroscopic rate equations **

Simple Basis Set for Molecular Wavefunctions Containing First- and Second-Row Atoms E. Clementi... [Pg.159]

A systematic approach to the crystal chemistry of borides is possible on the simple basis of atom size considerations, as well as the tendency of B to form covalent skeletons. [Pg.123]

The catalysis afforded by the La3 + system for the transesterifications of paraoxon in ethanol and methanol is quite spectacular relative to the background reactions that are assumed to be promoted by the lyoxide. The reaction rate constant of ethoxide with paraoxon in ethanol at 5.1 x 10-3 dm3 mol-1 s-133 is roughly a factor of two lower than the rate constant of methoxide with paraoxon in methanol (1.1 x 10 2dm3mol 1 s-1).17a However a solution 2mmoldm-3 in total [La3 + ], which contains 1 mmol dm-3 of Lal+, has a maximum rate constant of 7 x 10-4s-1 for decomposition of 1 in ethanol at pH of 7.3, and accelerates the rate of ethanolysis of paraoxon by a factor of 4.4 x 10n-fold relative to the ethoxide reaction at the same pH.34 By way of comparison, the acceleration afforded by a 1 mmol dm-3 solution of the La + dimer catalyzing the methanolysis of 1 at the maximal pH of 8.3 (kobs = 0.0175 s 1) is 109-fold greater than its background methoxide reaction. On this simple basis La2+ in ethanol appears to be catalytically superior to La2+ in methanol, but this stems almost exclusively from the pH values... [Pg.282]

Animals that encounter some individuals more often than others theoretically have the ability to segregate conspecifics into categories of familiar and unfamiliar, although the extent to which they do so is likely to vary according to capacity and necessity. This simple basis of assessment is likely to influence a range of... [Pg.277]

Example 1. Dissociation of H O by symmetric stretch Reference calculations are first performed at equilibrium geometry, using a simple basis of contracted gaussian functions [8]. The molecule is then dissociated by symmetric stretch, energies being calculated at bond length intervals of AR = Q.2Re up to i = 6.0J e (where dissociation is effectively complete). [Pg.26]

Roetti, C., and Clementi, E. (1974). Simple basis sets for molecular wavefiinctions containing atoms from Z=2 to Z 54. J. Chem. Phys. 60, 4725-4729. [Pg.399]

Although atoms are not mentioned in the brief prospectus, chemical atomism is the basis of Daltons New System, in which the third chapter clearly tends to place the whole science of Chemistry upon a new, and more simple basis. It is interesting that the new atomic chemistry does not occur in Daltons book until the third chapter, which occupies less than ten percent of Part I. Chapter One is chiefly focused on heat and gases, and Chapter Two on the three states of matter. As we have already seen, the third chapter presents his method for determining the relative weights of the atoms, with the promise that from... [Pg.254]

Wahl et al.15 suggest an analytic procedure similar to analytic Hartree-Fock methods whereby each molecular orbital is expanded as a linear combination of some simple basis functions over which all the one- and two-electron integrals can be efficiently calculated. We have... [Pg.237]

All the calculations of F2 are carried out with a simple basis set of double-zeta polarization type, the standard 6-31G(d) basis set, and are performed at a fixed interatomic distance of 1.44 A, which is approximately the optimized distance for a full Cl calculation in this basis set. Only the

Conclusion. There are still uncertainties in the final inter-pretation of mixing and chemical reaction at the molecular level. The IEM model seems to provide a simple basis for representing interaction between particles, even by molecular diffusion. The problem is to decide what is hidden behind the micromixing time tm Corrsin s time constant ts (32) A diffusion constant based on Kolmogorov microscale (113, 114) Further research should be developed in the following directions ... [Pg.182]

We choose to work in the simple basis set q, A J, Mj) where A is the component of electronic angular momentum along the intemuclear axis rj represents all relevant unspecified quantum numbers, including the vibrational quantum number. We use J, which is appropriate for molecules, rather than N there is no distinction between J and N for molecules in singlet states. The matrix elements of (8.277) in this basis are given by... [Pg.465]

On a simple basis of polarity, it would be expected that simple sugars would be more soluble in such polar solvents as alcohols than they actually are. It would appear, from work conducted by Moye... [Pg.86]

Let us now work out the representation of a point group for a very simple basis. We will choose just the changes, Ar, and Ar2, of the two N-H bond lengths of the diimide molecule, N2H2 (4-1). [Pg.184]

Since a representation—reducible or irreducible—is a set of matrices corresponding to all symmetry operations of a group, the representation can be described by the set of characters of all these matrices. For the simple basis of A/t and Ar2 used before for the HNNH molecule in the C2h point group, the representation consisted of four 2x2 matrices ... [Pg.190]

The diimide molecule (4-1) is our example again, and the basis is the two N-H bond length changes (see Figure 4-7). It is easy to generate the matrices corresponding to each operation using such a simple basis however, even this may not be necessary. As mentioned before, instead of the representations themselves, we can work with their characters. For this particular case the characters of the representation have already been determined ... [Pg.204]

This experiment directly demonstrates that when electricity is passed through a fused salt, there is a movement of the salt as a whole. In other words, the mass center of the liquid electrolyte moves. Now, the ions also are drifting with certain mobilities, i.e., velocities under unit field. But velocities with respect to what One must define a coordinate system, or frame ofreference, in relation to which the velocities (distances traversed in unit time) are reckoned. Though the laws of physics are independent of the choice of the coordinate system—the principle of relativity—all coordinate systems are not equally convenient. In fused salt it has been found convenient to use the mass center of the moving liquid electrolyte as the frame ofreference, even though this choice, while providing a simple basis for computations, suffers from difficulties. [Pg.670]

Equations 4 and 5 provide a simple basis for defining the energy differences between two electronic states. Thus, the dominant contribution to /iVmax in solution should... [Pg.319]

Exact calculations of the potential energy surfaces for complex molecular systems are impossible to carry out from a practical point of view. Such calculations involve the solution of the electronic Schrodinger equation for the system including electron correlation effects and full geometry optimization. However, an estimate of the 8 A lq> value can be obtained in a different way. One can carry out an ab initio calculation in the Hartree-Fock (HF) approximation by using a simple basis set, e.g., (7s, 3p/3s), contracted to a minimal basis set, STO-3G, or 3-21G, etc., with full geom-... [Pg.91]

The basis sets used are the simple basis sets without polarization fimctions... [Pg.257]

** A simple example---the quantum mechanical basis for macroscopic rate equations **

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