Hybridization extension

Meta-GGA functionals incorporate the Laplacian of the electron density and generally depend on the electron kinetic energy density. These features allow a systematic improvement of results for many quantum chemical calculations. We have used the exchange functional BR89 (Becke-Roussel 1989 represented in analytic form) [87,90] and the correlation functional B94 (Becke 1994) [90, 91]. Minnesota functionals tested are M05 [92], M05-2X [93], M06-L [94], M06-HF [95], M06 [96], M06-2X [96], and Ml 1 [97]. Another global hybrid studied is BMK [98]. A hybrid extension of the nonempirical exchange-correlation TPSS (Tao, Perdew, Staroverov, and Scuseria) [99] and functional TPSSh [100] is also examined. 

The PBEO functional is a hybrid extension of PBE and includes 25% exact exchange. 

In Chapter 1 we discussed hybridization extensively, including how distortions from normal bonding arrangements imply altered hybridizations. Shown below is the HOMO of fnms-cycloheptene (see Figure 2.16 for other views of this molecule). Focusing only on the it bond, discuss how the shape of this MO does or does not reflect the expected hybridization... 

The next step towards increasing the accuracy in estimating molecular properties is to use different contributions for atoms in different hybridi2ation states. This simple extension is sufficient to reproduce mean molecular polarizabilities to within 1-3 % of the experimental value. The estimation of mean molecular polarizabilities from atomic refractions has a long history, dating back to around 1911 [7], Miller and Sav-chik were the first to propose a method that considered atom hybridization in which each atom is characterized by its state of atomic hybridization [8]. They derived a formula for calculating these contributions on the basis of a theoretical interpretation of variational perturbation results and on the basis of molecular orbital theory. 

PM3/TM is an extension of the PM3 method to include d orbitals for use with transition metals. Unlike the case with many other semiempirical methods, PM3/TM s parameterization is based solely on reproducing geometries from X-ray diffraction results. Results with PM3/TM can be either reasonable or not depending on the coordination of the metal center. Certain transition metals tend to prefer a specific hybridization for which it works well. 

PM3/TM is an extension of the PM3 method to transition metals. Unlike the parameterization of PM3 for organics, PM3/TM has been parameterized only to reproduce geometries. This does, of course, require a reasonable description of energies, but the other criteria used for PM3 parameterization, such as dipole moments, are not included in the PM3/TM parameterization. PM3/TM tends to exhibit a dichotomy. It will compute reasonable geometries for some compounds and completely unreasonable geometries for other compounds. It seems to favor one coordination number or hybridization for some metals. 

This chapter provides brief descriptions of analyzer layouts for three hybrid instruments. More extensive treatments of sector/TOF (AutoSpec-TOF), liquid chromatography/TOF (LCT or LC/TOF with Z-spray), and quadrupole/TOF (Q/TOF), are provided in Chapters 23, 22, and 21, respectively. 

The application of these ideas to the mixing of low molecular weight liquids has been the object of extensive research. As a result of these investigations, the appropriate kind of hybridization of individual molecular properties in W12 is found to be the geometrical mean ... 

Lavender Oil Spike. Also known as spike oil, lavender oil spike is obtained by steam distillation of the flowering tops of l vandula latijolia Vik., which grows wild and is also cultivated throughout the Mediterranean region, with most production in Spain and France. There was a time when spike oil, particularly Spanish lavender oil [8016-78-2] found extensive use in soap perfumery however, with the introduction of the less expensive lavandin oil, a hybrid of tme lavender (L. angustifolid) and L. latijolia, utilization of spike oil in perfumery has been reduced appreciably. French spike oil, a more dehcate version, still finds considerable use in functional and industrial perfumery. A comparison of the volatiles of a commercial Spanish oil and a... 

Activated tertiary amines such as triethanolamine (TEA) and methyl diethanolamine (MDEA) have gained wide acceptance for CO2 removal. These materials require very low regeneration energy because of weak CO2 amine adduct formation, and do not form carbamates or other corrosive compounds (53). Hybrid CO2 removal systems, such as MDEA —sulfolane—water and DIPA—sulfolane—water, where DIPA is diisopropylamine, are aqueous alkaline solutions in a nonaqueous solvent, and are normally used in tandem with other systems for residual clean-up. Extensive data on the solubiUty of acid gases in amine solutions are available (55,56). 

Extension of the approach discussed above suggests several structural types which may be classified under this category, the main variable being the nature and hybridization of the electrophilic centers and the nature of the atoms joining these two centers. They may be conveniently divided into two groups ... 

The ally carbocation is an example of an intermediate whose structure has been extensively investigated by MO methods. The hybridization/resonance approach discussed earlier readily rationalizes some of the most prominent features of the allyl carbocation. The resonance structures suggest a significant stabilization and imply that the molecule would be planar in order to maximize the overlap of the n system. 

The VB and MO theories are both procedures for constructing approximations to the wavefunctions of electrons, but they construct these approximations in different ways. The language of valence-bond theory, in which the focus is on bonds between pairs of atoms, pervades the whole of organic chemistry, where chemists speak of o- and TT-bonds between particular pairs of atoms, hybridization, and resonance. However, molecular orbital theory, in which the focus is on electrons that spread throughout the nuclear framework and bind the entire collection of atoms together, has been developed far more extensively than valence-bond... 

The carhon-carbon double bond in alkenes is more reactive than carbon-carbon single bonds and gives alkenes their characteristic properties. As we saw in Section 3.4, a double bond consists of a a-bond and a 7r-bond. Each carbon atom in a double bond is sp2 hybridized and uses the three hybrid orbitals to form three cr-bonds. The unhvbridized p-orbitals on each carbon atom overlap each other and form a Tr-bond. As we saw in Section 3.7, the carbon-carbon 7r-bond is relatively weak because the overlap responsible for the formation of the 7r-bond is less extensive than that responsible for the formation of the a-bond and the enhanced electron density does not lie directly between the two nuclei. A consequence of this weakness is the reaction most characteristic of alkenes, the replacement of the 77-bond by two new a-bonds, which is discussed in Section 18.6. 

Although the s-p separation is nearly twice as large as the bond energy, there occurs extensive hybridization of the bond orbitals at the equilibrium intemuclear distance the bond orbitals are composed nearly equally of s and Pp, the ratio b/a being 0.92 (Fig. 8). This hybridization increases the bond energy by more than 100%, from 0.54 e. v. for a pure s bond (Fig. 7) to 1.19 e. v. The contribution of bond energy are of course smaller than they would be for zero s-p separation (b/a = 1.9 and D = 2.16 e. v. at r = 3.0 A.). It may be pointed out... 

The general qualitative agreement with experiment provides support for the theory that the potential barriers to internal rotation result from the interaction of adjacent hybrid bond orbitals with a small amount of / character. The magnitude of the potential barriers, about 4 per cent of the energy of the axial bond in case that there are three interacting bonds on each of the two atoms and proportionately less for a smaller number of bonds, is also reasonable. A detailed quantum-mechanical treatment of restricted rotation carried out along the lines sketched here should yield results that would permit a detailed test of the theory to be made in the meantime I believe that the above simple treatment and the extensive empirical support of the theory provide justification for it. 

The importance of one other type of reaction that metal ions undergo has been recognized and studied extensively in the past 40 years. This reaction is adsorption, in which metal ions bind to the surface of particulate matter and are thereby transported as part of a solid phase even though they do not form an identifiable precipitate. Conceptually, these reactions can be thought of as hybrids between complexation and precipitation reactions. Most studies of these reactions have used metal oxides or hydroxides as the solid (adsorbent) phase, and the... 

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