B3LYP/6-31G level calculations

Theoretical calculations on the cycloaddition reactions of a range of 1,3-dipoles to ethene in the gas phase have been carried out (85) with optimization of the structures of these precursor complexes and the transition states for the reactions at the B3LYP/6-31G level. Calculated vibration frequencies for the orientation complexes revealed that they are true minima on the potential energy surface. The dipole-alkene bond lengths in the complexes were found to be about twice that in the final products and binding was relatively weak with energies <2 kcal mol . Calculations on the cycloaddition reactions of nitrilium and diazonium betaines to ethene indicate that the former have smaller activation energies and are more exothermic. 

Su and Chu <1999CPL(308)283> have also carried out B3LYP/6-31G level calculations for 1,3-diazetidine, especially for carbene generation from this heterocycle. The carbene generated from 1,3-diazetidine is a 4k electron system. The relative energies of carbene 21 are summarized. 

They reported that the DFT calculations of 114 at the B3LYP/6-31G level showed that the ji-HOMO lobes at the a-position are slightly greater for the syn-n-face than for the anti face. The deformation is well consistent with the prediction by the orbital mixing rule. However, the situation becomes the reverse for the Jt-LUMO lobes, which are slightly greater at the anti than the syn-n-face. They concluded that the iyn-Jt-facial selectivity of the normal-electron-demand Diels-Alder reactions... 

The efficiency of the methods outlined above has been tested by calculating the intermolecular Coulomb energies and forces for a series of water boxes (64,128,256, 512 and 1024) under periodic boundary conditions [15, 62], The electron density of each monomer is expanded on five sites (atomic positions and bond mid-points) using two standard ABSs, A2 and PI.These sets were used to fit QM density of a single water molecule obtained at the B3LYP/6-31G level. We have previously shown that the A1 fitted density has an 8% RMS force error with respect to the corresponding ab initio results. In the case of PI, this error is reduced to around 2% [15, 16], Table 6-1 shows the results for the 5 water boxes using both ABSs (Table 6-7). 

Murphy et al. [34,45] have parameterized and extensively tested a QM/MM approach utilizing the frozen orbital method at the HF/6-31G and B3LYP/6-31G levels for amino acid side chains. They parameterized the van der Waals parameters of the QM atoms and molecular mechanical bond, angle and torsion angle parameters (Eq. 3, Hqm/mm (bonded int.)) acting across the covalent QM/MM boundary. High-level QM calculations were used as a reference in the parameterization and the molecular mechanical calculations were performed with the OPLS-AA force... 

Fig. 4 The crossings of in-plane and out-of-plane frontier MOs in the radical-anionic Bergman and C1-C5 cyclizations, respectively calculated at the B3LYP/6-31G level. Adapted from reference26.

Fig. 13 The steric assistance mechanism for the ortho-effect. Energy profile for the para-isomer is given in dotted lines whereas data for ort/zo-isomer are shown in solid lines. Calculations were performed at the BLYP/6-31G (in bold) and B3LYP/6-31G levels. P stands for products, R stands for reactants. Adapted from reference49.

This mechanism has recently been probed by carrying out density functional theory calculations at the B3LYP/6-31G level of theory [73]. Addition of an ester to titanacydo-propane 12 was found to be fast, exothermic, and irreversible, while the cyclopropaneforming step was concluded to occur directly from 13 to 14, to be rate-determining, and to determine the experimentally observed cis diastereoselectivity (see below). 

There are three possible secondary heptyl cations, 2-heptyl, 3-heptyl and 4-heptyl. Calculation at the B3LYP/6-31G level shows that the 3-heptyl cation is about lkcal/mol more stable than either the 2- or 4- heptyl cation. The 2-heptyl cation can in principle form a 1-5-p-H-bridged structure with a methyl group at each termini (isomeric structures 15 and 16) or a 1,6-p-H-bridge with a primary carbon at one end (isomeric structures 17 and 18), as shown in the following diagrams ... 

Calculations at the B3LYP/6-31G level on structures 15 to 19 shows that the cis- 1,5-p-H-bridged structure 16 is the global minimum. This result is similar to that found in a recent computational study by Siehl (26). In Table 1, the relative energies of 15 to 19 are compared, where the c/s-l,5-p-H-bridged structure 16 is set as an arbitrary zero reference point for these energy comparisons. 

Numerous studies concerning the structure and dynamics of the CH5+ have been reported (5-7, 16, 18, 67-74). Figure 2 shows the Bom-Oppenheimer molecular dynamics (BOMD) calculations for CHS+, calculated at B3LYP/6-31G level. The structures (a) and (b) correspond to snapshots from the dynamics. Figure 2 (c) shows the superimposed structures from the dynamics, indicating the high fluxionality of CH5+. 

Scheme 9.31 Cyclic transition states for the (M)-l, 2-butadienylzinc additions to acetaldehyde calculated at the B3LYP/6-31G level of theory.

Fig. 5 A proposed mechanism for enhanced emission (or AIEE) in solid-state organic dye nanoparticles. The dye considered here is trans-biphenylethylene (CN-MBE) compound. The geometry is optimized by the density functional theory (DFT) calculation at the B3LYP/6-31G level. Molecular distortion such as twisting and/or subsequent planarization causes prevention of radiationless processes along with specific aggregation such as the /-aggregate in the nanoparticles...

The mass resolved lcR2PI spectrum of the bare chiral chromophore Cr = (R)-(+)-l-phenyl-1-propanol, shows three intense signals at 37577 (A), 37618 (B), and 37624 cm (C) in the electronic Sj — Sq band origin region. A similar triplet falls at 38106, 38148, and 38155 cm . This pattern is common to substituted arenes and is interpreted as due to three stable conformers. Quantum chemical calculations at the RF1F/3-21G and B3LYP/6-31G levels of theory confirm this hypothesis. 

Density functional theory calculations (B3LYP/6-31G level) have provided an explanation for the stereodivergent outcome of the Staudinger reaction between acyl chlorides and imines to form 2-azetidinones (/3-lactams). When ketene is formed prior to cycloaddition, preferential or exclusive formation of ct5-j6-lactam (50) is predicted. If, however, the imine reacts directly with the acid chloride, the step that determines the stereochemical outcome is an intramolecular 5n2 displacement, and preferential or exclusive formation of trans isomer (51) is predicted. These predictions agree well with the experimental evidence regarding the stereochemical outcome for various reactants and reaction conditions. 

A theoretical study of the reactivity of prototype ketene CH2=C=0 with several radicals including HsSi has been reported. Scheme 5.11 shows that three adducts are possible with the corresponding energy barriers for their formation calculated at B3LYP/6-31G level of theory [75]. However, all the levels of theory used in this study predicted that silyl radical prefers to add to the carbon terminus of ketene. 

Scheme 48). From there, neutralization leads to the free triazenes 312,314, and 315 with insignificant losses (<1%) [99-100]. The compounds 315 are almost isoenergetic with their tautomers as formed by 1,3-H shift to the other N atom according to DTF calculations at the B3LYP/6-31G level [100]. The precautions during grinding should be followed for safety reasons ... 

In summary, transition structures with dioxirane and dimethyldioxirane are unsymmet-rical at the MP2/6-31G level, but are symmetrical at the QCISD/6-31G and B3LYP/6-31G levels. The transition states for oxidation of ethylene by carbonyl oxides do not suffer from the same difficulties as those for dioxirane and peroxyforaiic acid. Even at the MP2/6-31G level, they are symmetrical (Figure 17). The barriers at the MP2 and MP4 levels are similar and solvent has relatively little effect. The calculated barriers agree well with experiment . In a similar fashion, the oxidation of ethylene by peroxyformic acid has been studied at the MP2/6-31G, MP4/6-31G, QCISD/6-31G and CCSD(T)/6-31G and B3LYP levels of theory. The MP2/6-31G level of theory calculations lead to an unsymmetrical transition structure for peracid epoxidation that, as noted above, is an artifact of the method. However, QCISD/6-31G and B3LYP/6-31G calculations both result in symmetrical transition structures with essentially equal C—O bonds. 

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