LDA method

Fig. 5. Calculated electronic structure by the LDA method of (a) an isolated Cuo molecule and (b) fee solid Cuo where the direct band gap at the X-point is 1.5 eV [60],...

The mean absolute deviations of LDA method are much larger (216.5 kcal/mol vs. 91.9 kcal/mol). The increase in the deviations is largest for the hydrocarbons and their substituted derivatives. For B3LYP, the mean absolute deviations increase from 2.92 kcal/mol (G2/97) to 9.64 kcal/mol (G3-3 subset) for the hydrocarbons, and from 2.22 kcal/mol (G2/97) to 7.15 kcal/mol (G3-3 subset) for substituted hydrocarbons. The B3LYP mean absolute deviation for the non-hydrogen species increases from 5.15 kcal/mol to 10.99 kcal/mol. An example of the increase in error with molecular size is evident from comparison of results for propane and n-octane. The B3LYP enthalpy deviates from experiment by -1.46 kcal/mol for propane and -14.04 kcal/mol for n-octane. The G3 deviations for these cases are only 0.33 kcal/mol and 0.88 kcal/mol, respectively. The error per bond in G3 theory is about 0.035 for both propane and n-octane, whereas for B3LYP it is 0.146 and 0.51 kcal/mol, respectively. 

Like the PLS-DA method, the LDA method is susceptible to overfitting through the use of too many LDs. Furthermore, as in PLS-DA, it assumes that the classes can be linearly separated in the classification space, and its performance suffers if this is not the case. 

Enolate 18 was prepared by two different methods either by deprotonation of the corresponding lactone 20 or 21 by LDA (method A) or by 1,4-addition of bis(methylthio)trimethylsilylmethyl-lithium as a nucleophile to the lactone 22 (method B)63,64... 

It is now common experimental practice to react ketones with lithium diisopropyl amide (LDA) in order to generate the enolate of the ketone. This methodology has largely replaced the older approach to enolates, which employed alkoxide bases to remove a proton alpha to the carbonyl group. Comparison of the equilibrium constants for these two acid-base reactions reveals why the LDA method is preferable. The use of the amide base leads to essentially complete conversion of die ketone to its enolate (Keq 1016). At equilibrium, there is virtually no... 

Recently, Quong et a/.10 studied (BH)i2 and (BH)32 besides small boron hydrides as the dual of fullerenes using LDA methods. They found that (BH)i2 is more stable than the (BH)32 cluster by 0.08 eV/BH. In our calculations the relative stability is the opposite. The (BH)32 sphere is more stable than the (BH)i2 sphere by 0.08 eV/BH and more stable than the (BH)2o sphere only by 0.005 eV/BH. However, the discrepancy between our results and those of Quong et al. needs further investigation. 

Benzothiazolyl anions were generated in situ (method B) or pre-formed with LDA (method A) for Pyr sulfones method A with n-butyllithium was used. High yields were obtained for some allyhc and propargylic sulfones. In general, relatively high stereochemical preferences were noted. 

The earliest class of DFT methods is known as local (electron) density approximation (LDA) methods in the case that the total electron density is decomposed into individual spin densities for +1 /2 and -1/2 spin we refer to these methods as local spin density approximation (LSDA) methods. In these methods the total molecular XC energy is evaluated by integration on a numerical grid of the electron density, and the energy is a function of only the specific value of the density at each point, hence the local density ... 

LDA methods have been employed to investigate solids in two types of approaches. If the solid has translational symmetry, as in a pure crystal, Bloch s theorem applies, which states that the one-electron wave function n at point (r + ft), where ft is a Bravais lattice vector, is equal to the wave function at point r times a phase factor ... 

The dispersion behavior of a and y for a few selected frequencies can be found in Tables 5 and 6 for nitrogen and benzene, respectively. We have selected the ESHG process for benzene and the THG processes for nitrogen to study the frequency dependence of y. The conclusions are consistent between the processes When the CCSD dispersion is taken as a reference value, we observe that the DFT methods provide satisfactory dispersion for the polarizability a. However, for the hyperpolarizability y there is a significant tendency to deviate from the CCSD dispersion curve. The only exception is the LB94/LDA method, where the deviation from the CCSD dispersion is found to be almost constant for the examined... 

Table 2 lists the An-X (X = centroid of Cot), An-C, C-C, C-H distances and the ZHCX of the Dg actinocenes obtained by using the scalar relativistic PW91 and LDA methods. These geometries are optimized for the high-spin electronic states with ie2gY (3c2a)y" ( = 0, 1,2, 3,4, 5 for An = Th-Am) configurations. 

QDA is identical to LDA, but this method is based on a quadratic classification curve instead of a straight line. The data must be normally distributed as for the LDA method. QDA is thus a linear parametric method. 

From Table 1 we see the deficiencies of the LDA method, since it underestimates both total and exchange energies. Such discrepancies are increased for small confinement radii. As we discussed in the introduction, the main difference between LDA and LDA-SIC is the self-interaction error, thus this spurious contribution is more important when the electrons are localized within small regions, as it has been pointed out before [21]. 

From the latter analytical expression, it is easily shown that the expression cannot be derived from the interaction of particles. On the other hand, the second term is discontinuous at densities corresponding to filled shells. As stated above, the potential of all the electrons in a crystalline solid changes discontinuously when another electron is added. This case is not predicted by the LDA method but it is predicted in the orbital-dependent forms. For an orbital functional, the kinetic energy is evaluated first ... 

Better results than with the LDA are obtained by an elaboration of the LDA in which electrons of a and spin in the uniform electron gas are assigned different spatial KS orbitals and from which different electron density functions and follow. This unrestricted LDA method (cf. UHF, section 5.2.3.6e) is called the local spin density approximation, LSDA, and has the advantages that it can handle systems with one or more unpaired electrons, like radicals, and systems in which electrons are becoming unpaired, such as molecules far from their equilibrium geometries even for ordinary molecules it appears to be more forgiving toward the use of (necessarily) inexact xcfunctionals [37], For species in which all the electrons are securely paired, the LSDA is equivalent to the LDA. Like and its functional derivative... 

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