Calculations B3LYP

The syn isomer can achieve a conjugated system with angles of up to 35° between adjacent p orbitals. The anti isomer is much more twisted. An X-ray crystal structure of the syn isomer shows C—C bond lengths between 1.368 and 1.418 A for the conjugated system (Fig. 9.3). ° The spectroscopic properties of the syn isomer are consistent with considering it to be a delocalized annulene. B3LYP calculations indicate that both the syn and anti structures are stabilized by delocalization, the syn (17.6kcal/mol) more so than the anti (8.1 kcal). ... 

The relative stability of the anions derived from cyclopropene and cyclopentadiene by deprotonation is just the reverse of the situation for the cations. Cyclopentadiene is one of the most acidic hydrocarbons known, with a of 16.0. The plCs of triphenylcyclo-propene and trimethylcyclopropene have been estimated as 50 and 62, respectively, from electrochemical cycles. The unsubstituted compound would be expected to fall somewhere in between and thus must be about 40 powers of 10 less acidic than cyclopentadiene. MP2/6-31(d,p) and B3LYP calculations indicate a small destabilization, relative to the cyclopropyl anion. Thus, the six-7c-electron cyclopentadienide ion is enormously stabilized relative to the four-7c-electron cyclopropenide ion, in agreement with the Hixckel rule. 

Seluflon Clearly, a hybrid functional is the best choice for this problem. We ran B3LYP calculations using the 6-31G(d), 6-31-i-G(d) and 6-311G(2d) basis sets. Here are the results ... 

As the formation of betaines from amide-stabilized ylides is known to be reversible (in contrast with aryl- or semistabilized ylides, which can exhibit irreversible anti betaine formation see Section 1.2.1.3), the enantiodifferentiating step cannot be the C-C bond-forming step. B3LYP calculations of the individual steps along the reaction pathway have shown that in this instance ring-closure has the highest barrier and is most likely to be the enantiodifferentiating step of the reaction (Scheme 1.16) [25]. 

Table 5.2 Contributions to the electron density at the iron nucleus in Fep4 unrestricted B3LYP calculations with the CP(PPP) basis set. Orbitals that electron density at the iron nucleus are printed in boldface...

Table 5.8 Contributions to the Fe hyperfine interaction in [Fe(0)(NH3)5] in the lowest 5=1 and 5 = 2 states from spin-polarized B3LYP calculations (in MHz) (from [60])...

Fig. 5.18 Four in-plane Fe modes, predicted on the basis of B3LYP calculations, contributing to the pair of experimental features at 312 and 333 cm in Fe(TPP)(NO). For ease of visualization, each arrow is 100(ot,/tofj,) longer than the zero-point vibrational amplitude of atom j. Color scheme as in Fig. 5.15 (taken from [101])...

Thus, the structure of a-lactones, as reflected in their observed TRIR spectra, is dependent both on substituents at the a-carbon and on solvent polarity, with electron-donating substituents and polar solvents favoring a zwitterionic ring-opened structure. B3LYP calculations using SCRF methods to account for solvent polarity are consistent with these experimental conclusions. 

Experimentally, two equivalents of the alkyne for one equivalent of the metal species are necessary to achieve reaction. One equivalent serves to abstract H2 from the starting materials, RuH(H2)XL2 or OsH3XL2, hence generating in situ the very reactive 14-electron compound MHXL2 (M = Ru, Os). It is assumed that the reaction starts from the 14-electron complex modeled as MHC1(PH3)2 (M = Ru, Os) and the acetylene is used as a model for phenyl acetylene. DFT (B3LYP) calculations were carried out to... 

B3LYP calculations as described in Section 2. b Structures optimized with a 6-31 G(d) basis for the main group elements. c Also alkylperoxo complexes. d Attack of Oa of the hydroperoxo (alkylperoxo) group.e Attack of OP of the hydroperoxo group. 

B3LYP calculations indicated that 2-adamantene (96) is 17.4kcalmor more stable than Ai-adamantylidene (97). The barrier to interconversion of (96) to (97) by [1,2]-H shift is 69.1 kcalmoP much higher than that for [1,2]-C migration... 

In the calculations of the energy of hydration of metal complexes in the inner coordination sphere, one must consider hydrogen bond formation between the first-shell water molecules and those in bulk water, which leads to chains of hydrogen-bonded water molecules. Such hydrogen-bonded chains of ethanol molecules attached to the central metal ion have been found as a result of DFT B3LYP calculations on ethanol adducts to nickel acetylacetonate, where the calculated energy of hydrogen bonds correlated well with experimental data [90]. 

In the case of thioanisole cation-radical, ESR spectroscopy (Alberti et al. 1984) and B3LYP calculations (Baciocchi and Gerini 2004) convincingly indicate that the planar conformation is by far the most stable. In the cation-radical, the thiomethyl group remains, in expectation, an electron-donating substituent. 

Deprotonation with the generation of the radical counterpart can be favorable as it is manifested by the low value. The dimethyl sulfide cation-radical in water is deprotonated in the following way [(CH3)2S] —> CH3SCH2 + H+. Accordingly, pA, value of [(CH3)2S] is 0.3 from B3LYP calculations and about 1.8 from experiments (Brunelle and Rank 2004). 

The hexafluoroantimonate salt of the terthiophene cation-radical in which terminal thiophene was completely surrounded by bicycle[2.2.2] octane units was studied by x-ray crystallography (Nishinaga et al. 2004). In the crystal lattice, the authors did not find only one isomer. They wrote about the dominant form, which was an x-trans-trans conformer. The central thiophene ring remains free, and only the terminal rings are fused with the bicycle[2.2.2] octane units—this cation-radical acquires a bent conformation. As B3LYP calculations show, the all-anti conformer is more stable than the all-syn counterpart by 5.35 kJ moY (Yamazaki et al. 2006). 

The theoretical study of complexation of silylalkenes and silylalkynes and their Ge- and C-analogs to metal cations by means of B3LYP calculations revealed a somewhat different picture. The gas-phase interaction of... 

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