Density Computations

Optimize the structure of acetyl radical using the 6-31G(d) basis set at the HF, MP2, B3LYP and QCISD levels of theory. We chose to perform an Opt Freq calculation at the Flartree-Fock level in order to produce initial force constants for the later optimizations (retrieved from the checkpoint file via OptsReadFC). Compare the predicted spin polarizations (listed as part of the population analysis output) for the carbon and oxygen atoms for the various methods to one another and to the experimental values of 0.7 for the C2 carbon atom and 0.2 for the oxygen atom. Note that for the MP2 and QCISD calculations you will need to include the keyword Density=Current in the job s route section, which specifies that the population analysis be performed using the electron density computed by the current theoretical method (the default is to use the Hartree-Fock density). 

In order to save computation time, set up the second and subsequent jobs to extract the electron density from the checkpoint file by using the Geom=Checlcpoint and Densiiy=(Checkpoint/AP2) keywords in the route section. You will also need to include Den iiy=MP2 for the first job, which specifies that the population analysis should be performed using the electron density computed at the MP2 level (the default is to use the Hartree-Fock density). 

Ultraviolet coatings for excimer lasers. These lasers are likely to play a large role in lithography of very high density computer chips,... 

Iversen et al, in their study of crystalline beryllium [32], were the first to make use of NUP distributions calculated by superposition of thermally-smeared spherical atoms. More recently, a superposition of thermally-smeared spherical atoms was used as NUP in model studies on noise-free structure factor amplitudes for crystalline silicon and beryllium by de Vries et al. [38]. The artefacts present in the densities computed with a uniform prior-prejudice distributions have been shown to disappear upon introduction of the NUP. No quantitative measure of the residual errors were given. 

Electron Density Computation. The average2 electron density of a material or of a specific phase within a material,... 

Figure 36. The scaled distributions of mean, P(H/Y ) (a), and Gaussian, P(K/Y]2) (b), curvatures scaled with the inteface area density, computed at several time intervals of the spindal decomposition of a symmetric blend. There is no scaling at the late times because the amplitude of the thermal undulations does not depend on the average growth of the domains, and therefore the scaled curvature distributions functions broaden with rescaled time.

The alkali iodide isomeric shifts (13) number of iodine ion p holes calculated rupole resonance data (25) the sum of overlap integrals (11) the fractional iodine ion density computed from the isomeric shift data. Equation 7, and 8. 

Interest in spectral hole burning comes from its potential application as high density computer memory. An external electric field can be used to shift the spectral holes so as to obtain an even larger number of detectable holes than with the excitation wavelength alone. 

In point-charge simulation this electronic rearrangement is of no immediate consequence except for the assumption of a reduced interatomic distance, which is the parameter needed to calculate increased dissociation energies. However, in Heitler-London calculation it is necessary to compensate for the modified valence density, as was done for heteronuclear interactions. The closer approach between the nuclei, and the consequent increase in calculated dissociation energy, is assumed to result from screening of the nuclear repulsion by the excess valence density. Computationally this assumption is convenient and effective. 

Several numerical tests and detailed comparisons of MEDLA electron densities to electron densities computed by traditional ab initio SCF technique using 3-21G and 6-31G basis sets have shown [67,71] that the MEDLA results are invariably of better quality than the standard 3-21G ab initio results, and the MEDLA results are virtually indistinguishable from the standard ab initio 6-31G basis set results obtained with the traditional Hartree-Fock method. 

Whereas density functional theory guaranties that for the ground electronic state of molecules the electron density determines the energy, the actual construction of such energy functions from first principles is a problem of considerable complexity. The electron densities computed by the MEDLA method suggest various approximations to the molecular energy of large systems. 

Matrix Assembler (ADMA) method [18-21] generates a macromolecular density matrix P((p(K)) that can be used for the computation of a variety of molecular properties besides ab initio quality macromolecular electron densities. In electron density computations the accuracy of the ADMA macromolecular density matrix P(cp(K)) corresponds to that of a MEDLA result of an infinite resolution numerical grid. 

FIGURE 1 The fuzzy body of the electron density of a bovine insulin molecule is represented by three molecular isodensity contour surfaces (MlDCOs), for the density thresholds of 0.1, 0.01, and 0.001 a.u. (atomic unit), respectively, as computed using the MEDLA method. Bovine insulin was among the proteins selected for the first ab initio quality electron density computations for macromolecules. ... 

Figure 4a. Continuous underway measurements of temperature salinity, dissolved O2 and pH. Density, computed from temperature and salinity, also is shown. Calibration data are shown with a symbol. Numbers at the top of the figure refer to CTD station numbers and the stippled areas show the...

A Local Density Computational Method based on the Adjustable... 

The antioxidant efficiency of phenolic acids, as determined by the accelerated autooxidation of methyl linoleate and scavenging of the free radical 2,2-diphenyl-1-picrylhydrazyl (141) ° methods, was found to be inversely proportional to the maximal detector response potential in the voltammetric determination of these compounds. No similar correlation was found for the flavonoids . A good correlation was found between the O—H bond dissociation energy of a phenolic compound and its effectiveness as antioxidant, expressed as the rate constant of free radical scavenging . The bond dissociation energy of the phenol O—H bond was estimated by a three-dimensional quantitative structme-activity relationship method incorporating electron densities computed using the Austin Method 1 (AMI) followed by correlation of the... 

L. F. Pacios, CHECKDEN a computer program to generate ID, 2D and 3D grids of functions dependent on the molecular ab initio electron density, Comput. Biol. Chem. 27, 197-209 (2003). 

Here C is the gas phase (uncoupled) flux autocorrelation function, Zbath is the bath partition function, J(co) is the bath spectral density (computed as described above from a classical molecular dynamics computation), Bi and B2 are combinations of trigonometric functions of the frequency a> and the inverse barrier frequency, and Anally ... 

Application of this methodology to this model of horse liver alcohol dehydrogenase yields the results shown in Fig. 9.4. In fact we do see strong numerical evidence for the presence of a promoting vibration - intense peaks in the spectral density for the reaction coordinate are greatly reduced at a point between the reactant and product wells. This is defined as a point of minimal coupling. As we have described, the restraint on the hydride does not impact the spectral density computation. This computation measures the forces on the reaction coordinate, not those... 

P15.24 (a) The first figure displays spin densities computed by molecular modeling software (ab initio, density... 

The simplest model consists of a benzylic species in which the benzylic carbon simulates an electron donor if it provides two electrons and an acceptor if it has none. Hence for the electron donor example, the system has eight electrons for the electron-withdrawing-group example, the system has six electrons. The densities computed in 1963 for the benzylic species molecular orbitals are shown in Scheme 1.9. 

The geometry of the n-n triplet (43T n-n ) was twisted around the enone double bond. To determine the nature of this structural change, we resorted to our delta-density computations applied to triplets 43T(n-Ji ) and 43T(jt-ji ) as well as inspection of the electronic population of the two species (note Table 8.11 and Table 8.12 for our CASSCF-NBO analysis). 

The delta-density computations showed a heavy loss of the electron density from the n (i.e., Py) orbital of the planar triplet 43T(n-Jt ) as well as from the carbonyl 71-bond. This is then identified as having an n-71 configuration (column 2... 

Table 8.11 Delta-Density Computation for the Two Triphenyl Enone 43T Triplets...

A. E. Bergles, N. Bakhru, and J. W. Shires, Cooling of High-Power-Density Computer Components, EPL Rep. 70712-60, Massachusetts Institute of Technology, Cambridge, MA, 1968. 

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