B3LYP/6-31G level

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). 

Table 3.21. Formal n moieties, NRT bond orders of associated atoms, and conjugative stabilization energies for molecules 17-24 in Fig. 3.40 (B3LYP/6-311++G //B3LYP/6-31G level)...

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.

Fig. 15 Predicted cooperative effects on activation energies (in kcal/mol) at the B3LYP/ 6-31G level for model enediynes ( push and pull denote through-space repulsive (steric) and attractive (H-bonding) interactions of ort/zo-substituents with in-plane 71-orbitals of an adjacent acetylene moeity).

Fig. 19 The reaction energy profiles for thermal (on the left) and radical-anionic (on the right) C1-C6 and C1-C5 cyclizations of the parent enediyne computed at the B3LYP/ 6-31G level.

The hydrogen abstraction from alkoxyamidyl 102 has been modeled at B3LYP/ 6-31G level by the reaction of methyl radical (R = CH3 ), with methoxy-formamidyl 102e giving 103e and methane. Energies are presented in Table 13. 

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). 

In this case, single point energies on HF/3-21G geometries were evaluated at the B3LYP/6-31G level, a density functional theory method. 

Figure L Optimized 1,5-p-H-bridged secondary cyclodecyl cation 10, showing bond distance (A) and bond angle (degree) at the B3LYP/6-31G level... 

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. 

Figure 4. The l, 6-p-H-bridged stereoisomers (17 and 18) formed from 2-heptyl cation showing bond distance and bond angles at the B3LYP/6-31G level... 

Figure 6. Optimized primary-secondary I-5-p-H-bridged structure 19 at the B3LYP/6-31G level. Notice the long and very weakly bridgedp-H bond.

Figure 14. The transition-states for H2 loss in the cis- and trans- secondaryprimary-1, 6-p-H-bridged 3-octyl cations 26 and 27 showing some of the key geometric parameters at the B3LYP/6-31G level.

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...

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