Inner correlation

HyperChem supports MP2 (second order Mpller-Plesset) correlation energy calculationsusing afe mi/io methods with anyavailable basis set. In order to save main memory and disk space, the HyperChem MP2 electron correlation calculation normally uses a so called frozen-core approximation, i.e. the inner shell (core) orbitals are omitted. A setting in CHEM.INI allows excitations from the core orbitals to be included if necessary (melted core). Only the single point calculation is available for this option. 

Correlations for Convective Heat Transfer. In the design or sizing of a heat exchanger, the heat-transfer coefficients on the inner and outer walls of the tube and the friction coefficient in the tube must be calculated. Summaries of the various correlations for convective heat-transfer coefficients for internal and external flows are given in Tables 3 and 4, respectively, in terms of the Nusselt number. In addition, the friction coefficient is given for the deterrnination of the pumping requirement. 

The minimum velocity requited to maintain fully developed turbulent flow, assumed to occur at Reynolds number (R ) of 8000, is inside a 16-mm inner diameter tube. The physical property contribution to the heat-transfer coefficient inside and outside the tubes are based on the following correlations (39) ... 

Values of A and B for the base component are back-calculated for each stage in the outer loop from a suitable iC-value correlation (e.g. the SRK equation, which is also used to compute the iC values of the other components on each of the other stages so that values of Ot) can be computed). The values of A, B, and Ot are passed from the outer loop to the inner loop, where they are used to formulate the phase equihb-ria equation ... 

The equivalence of the inner NH protons (Sm = - 2.35) as well as correlation signals with the pyrrolic carbons only (5c = 143.8, 141.6, 139.8 and 136.7) provide evidence for the diaza[18]-annulene tautomer 4a. Two separate NT/ proton signals and cross signals with the a-carbon atoms (5c = 159.3) of the triazole ring are expected, in contrast, for the tetraaza[18]annulene tautomer 4b. 

In standard quantum-mechanical molecular structure calculations, we normally work with a set of nuclear-centred atomic orbitals Xi< Xi CTOs are a good choice for the if only because of the ease of integral evaluation. Procedures such as HF-LCAO then express the molecular electronic wavefunction in terms of these basis functions and at first sight the resulting HF-LCAO orbitals are delocalized over regions of molecules. It is often thought desirable to have a simple ab initio method that can correlate with chemical concepts such as bonds, lone pairs and inner shells. A theorem due to Fock (1930) enables one to transform the HF-LCAOs into localized orbitals that often have the desired spatial properties. 

We hear a lot these days about the relationships between saturated fats, cholesterol, and heart disease. What are the facts It s well established that a diet rich in saturated animal fats often leads to an increase in blood serum cholesterol, particularly in sedentary, overweight people. Conversely, a diet-lower in saturated fats and higher in polyunsaturated fats leads to a lower serum cholesterol level. Studies have shown that a serum cholesterol level greater than 240 mg/dL (a desirable value is <200 mg/dL) is correlated with an increased incidence of coronary artery disease, in which cholesterol deposits build up on the inner walls of coronary arteries, blocking the flow of blood to the heart muscles. 

In the preliminary discussions in the 1929 paper (Eq. 11), Hylleraas also discussed some lower approximations and pointed out the importance of a configuration where there exist one "inner electron and one "outer electron. In modern terminology, this corresponds to a splitting of the closed shell (Is)2 into an open shell (Is, Is), or to the use of "different orbitals for different electrons. Hylleraas reported the good result E = —2.8754 at.u. for such a configuration, but pointed also out that a "correlated wave function of the form... 

Complexation of Pu is discussed in terms of the relative stabilities of different oxidation states and the "effective" ionic charge of Pu0 and Pu02+2. An equation is proposed for calculating stability constants of Pu complexes and its correlation with experimental values demonstrated. The competition between inner v outer sphere complexation as affected by the oxidation state of Pu and the pKa of the ligand is reviewed. Two examples of uses of specific complexing agents for Pu indicate a useful direction for future studies. 

Carpenter and Colburn have put forward a simple correlation of their results for condensation at varying vapour velocities on the inner surface of a vertical tube which takes the form ... 

In rat liver mitochondria, in state 4, the AP was estimated to be about 220 mV, with the membrane potential representing about 90% of this (Nicholls, 1974 Appendix 3). Similar values have been reported for human and rat skeletal muscle mitochondria in state 4 (Stumpf et al., 1982). The control of the rate of electron transport is not only determined by the availability of ADP, but also of Pj oxidizable substrates, and oxygen. There is evidence for futile cycling of protons in intact normal rat hepatocytes (Brand et al., 1993). Recently, Porter and Brand (1993) found a correlation between the proton permeability of the inner membrane of liver mitochondria and body size in animals from the mouse (20 g) to horses (150 kg) with a decrease in permeability with increasing weight of several-fold at a constant... 

This correlation was obtained as a result of extensive measurements with shake flasks of volume = 100-2000 ml and corresponding inner diameter dg= 6.1-16 cm, a filled volume ofVL= (0.04-0.2)V, and eccentricity of shaking machine of 25 and 50 mm. 

In the segments strong immunological deposition was found throughout the tissue. Again the results indicate a slight correlation of cell size and the amount of acetyl esterase. In the small cells in the periphery of the juice vesicles, acetyl esterase is clearly intracellular (Fig 3 D,E), whereas the acetyl esterase was found on the cell walls of the large inner juice cells. This... 

Here is the soft and normally attractive part of the pair potential. This simple bilinear form of functional lacks correlation effects except that which is introduced by the truncation of the integral at the onset of the inner hard part of the potential. We are then using an extended form of the mean field approximation as did van der Waals in his original... 

The IR bands in a number of nickel complexes of triaryl formazans have been assigned by Arnold and Schiele.415 A similar assignment of the electronic bands has been carried out.414 LCAO-MO calculations correlate well with these assignments417 and have been extended to include both inner ligand transitions as well as charge transfer bands and d—d transitions.418 EPR spectra have been used to study the nature of bonding in copper complexes of heterocyclic-containing formazans.419 Metal formazan complexes have also been studied by electrochemistry.283,398 420-422... 

As in ethyne (Figure 2) this is probably due to electron-electron correlations in the inner valence region. 

Equation (5b), in Table VII, established by Lin et al. (L9) for coaxial flow in annuli with k = 0.5, was originally taken by them to be a striking confirmation of the theoretically derived correlation, Eq. (27), with 0=1. The latter condition, however, corresponds only to the limiting case of Eq. (27), at /c->0, that is, mass transfer to the wall of an outer cylinder, without an inner cylinder present. On these grounds, and because of other experimental conditions, the correlation of Lin et al. (L9) was criticized by Friend and Metzner (F9), who calculated that the constant in Eq. (5b) of... 

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