B3LYP, density functional theory

Density functional theory (B3LYP) has been used to investigate the mechanism of the cis-trans isomerization in Ir(H)2(CO)(C6H3 CH2P(H2) 2).300 The preferred mechanism involves two consecutive trigonal twists in which the complex passes through a distorted octahedral intermediate, as shown in reaction Scheme 19. 

Because of the presence of two azide groups in positions adjacent to the ring nitrogen atoms in compound 13a, valence bond isomerization can result in formation of 6-azido-7-methyltetrazolo[l,5-A pyridazine 14a, 6-azido-8-methyltetrazolo[l,5-A pyridazine 15a, and the bis-tetrazole compound 16a. Calculations have been carried out by using hybrid density functional theory (B3LYP/6-311+G(d,p)) and complete basis set treatments (CBS-4M). All calculations revealed that the 8-methyl derivative 15a is the most stable isomer. Similar studies on the triazide derivative 13b, however, indicated that in this case the equilibrium is shifted to the 7-methyl form 14b. All these conclusions proved to be in entire agreement with the experimental findings (see Section 11.18.3.2.). 

Figure 5. Normal modes for vibration of tetrahedral [Cr04] (chromate). There are four distinct vibrational frequencies, including one doubly-degenerate vibration (E symmetry) and two triply-degenerate vibrations (F2 symmetry), for a total of nine vibrational modes. Arrows show the characteristic motions of each atom during vibration, and the length of each arrow is proportional to the magnitude of atomic motion. Only F2 modes involve motion of the central chromium atom, and as a result their vibrational frequencies are affected by Cr-isotope substitution. The normal modes shown here were calculated with an ab initio quantum mechanical model, using hybrid Hartree-Fock/Density Functional Theory (B3LYP) and the 6-31G(d) basis set—other ab initio and empirical force-field models give very similar results.

Figure 11.31 Conformational equilibria of pyridine-2,6-dicarboxamides, as calculated using density functional theory (B3LYP/6-311-L G //B3LYP/6-31G ), favors a syn-syn conformation.

A second variation of Gaussian-3 (G3) theory uses geometries and zero-point energies from B3LYP density functional theory [B3LYP/6-31G(d)] instead of geometries from second-order perturbation theory [MP2/6-31G(d)] and zero-point energies from Hartree-Fock theory [HF/6-31G(d)].98 This varia-... 

Nucleophilic vinylic substitutions of 4//-pyran-4-onc and 2,6-dimethyl-4//-pyran-4-one with a hydroxide ion in aqueous solution were calculated by the density functional theory (B3LYP) and ab initio (MP2) methods using the 6-31+G(d) and 6-31G (d) basis sets. The aqueous solution was modelled by a supermolecular approach, where 11 water molecules were involved in the reaction system. The calculations confirmed a different addition-elimination mechanism of the reaction compared with that in the gas phase or non-polar solution. Addition of OH- at the C(2) vinylic carbon of the pyranone ring with an activation barrier of 10-11 kcalmol-1 (B3LYP) has been identified as the rate-determining step, in good quantitative and qualitative agreement with experimental kinetics. Solvent effects increase the activation barrier of the addition step and, conversely, decrease the barrier of the elimination step.138... 

Figure 2.60. Potential energy surface in eV along two co-ordinates for two hydrogen atoms near a nickel surface distance between hydrogen atoms d and height z of the centre of mass of the two H atoms over the (1,1,1) surface of the Ni-layer below the top layer. The quantum chemical calculation uses the density functional theory B3LYP and a set of basis functions called SV (see section 3.2). The energy scale has an arbitrarily chosen origin (Sorensen, 2004f).

Figure 3.8. Molecular orbitals for the oxygen atom, with indication of their quantum numbers (main, orbital angular momentum and projection along axis of quantisation). Shown is the oxygen nucleus and the electron density (where it has fallen to 0.0004 it is identical for each pair of two spin projections), but with two different shades used for positive and negative parts of the wavefunction. The calculation uses density functional theory (B3LYP) and a Gaussian basis of 9 functions formed out of 19 primitive Gaussian functions (see text for further discussion). The first four orbitals (on the left) are filled in the ground state, while the remaining ones are imoccupied.

Figure 3.10. Potential energy surface of two water molecules over an Ni surface, as a function of height over the surface (z measured from the second layer of Ni atoms) and 2e, the distance between the oxygen atoms. The quantum chemical calculation of the potential energies employs Hartree-Fock for the two layers of 24 Ni atoms and density functional theory (B3LYP) for the rest, the set of basis function called SV (cf. section 3.2). Ihe position of the water molecules for one set of parameter values is shown in the insert. The zero of the energy scale is chosen arbitrarily (Sorensen, 2004b).

Theoretical calculations by Siegbahn and Crabtree [4] found the barrier for the reaction via the [PP (R)(H)] intermediate to be a little lower in energy compared with a one-step mechanism, while a study by Hill and Puddephatt favors type interactions [5]. The most recent theoretical study was conducted by Hush and co-workers using density functional theory (B3LYP functional) calculations with double-f to polarized double- basis sets [6]. They also studied solvation effects by a dielectric continuum method. 

More recently, gas phase ab initio (HF/6-31G, HF/6-31+G, MP2/6-31+G, MP3/6-31+G ) and density functional theory (B3LYP/6-31G, B3LYP/ 6-31+G ) calculations have been carried out on methyl a-D-arabinofuranose [116]. A protocol developed by Serianni and coworkers [117,118], was used to construct the 10 possible envelope forms by fixing four atoms in a plane then, upon minimization, the other parameters (bond lengths, bond angles, etc.) were optimized. 

Two levels of theory are commonly used in the design of the nickel-based catalysts shown in Figure 11 Density Functional Theory (B3LYP functional used with effective core potentials for Ni and 6-3IG for everything else in the complex) and molecular mechanics (both the UFF (4) and reaction force field, RFF (85,86) are used) (87). All these methods are complementary, and the experiments are guided from the results of several calculations using different molecular modeling techniques. 

Ab initio (HF, MP2, and MP4) (99JCS(P2)801) and SCF + MBTP(2) methods (90JPC7406) also predict the predominance of the thiol tautomer in the gas phase however, the relative stability of the thiol tautomer is overestimated by 1 kcal/mol and 6.5 kcal/mol, respectively. Similarly, calculations using large (TZV2P) basis sets and electron correlation at the QCISD(T) level overestimate the thiol stability by 3.6 kcal/mol (93JCS(P2)861). In contrast, the density functional theory (B3LYP)... 

Macrocycles 90 (X = (CH2)6 Y = (CH2) n — 4—6) containing aminopyrimidine and uracil moiety have been studied by IR and UV spectroscopy and calculated by ab initio MO (HF/6-31G, MP2/6-31G ) and density functional theory (B3LYP/ 6-31G ). The results showed that the aminopyrimidine fragment exists exclusively in the amino form both in the solid state and in solution (04JST(707)1). 

A density functional theory (B3LYP/6-311 - -G ), ab initio (HF/3-21G ) and semi-empirical (PM3) study of intrinsic basicities, protonation energies or protonation enthalpies of phosphazene bases has been reported. The study shows that the organic superbases can reach the basicity level of the strongest inorganic superbases, such as alkali metal... 

Despotovic, I., Kovacevic, B. and Maksic, Z.B. (2007) Pyridine and j-triazine as building blocks of nonionic organic superbases - density functional theory B3LYP study. New Journal of Chemistry, 31, 447 57. 

In the present chapter, we test the use of the common Density Functional Theory (B3LYP/6-311G(d,p) by comparing enthalpy results obtained for the unsaturated oxy-... 

Bordwell et al. [321] have developed a relationship between the bond dissociation energies (BDEs), oxidation potentials, and the pK s of weak acids. Chandra, Nam, and Nguyen [324] have used density functional theory (B3LYP/6-311-H-G ) to determine the BDEs and proton affinities (PAs) of a number of substituted thiophenols and their anions. Greater PA values are expected to correspond to lower acidities. 

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