DFT/B3LYP calculations

Fig. 5.3 Variation of the li, 2s, 3s and contributions to the total electron density at the iron nucleus for a collection of iron complexes. Nonrelativistic B3LYP DFT calculations with the CP (PPP) basis set (taken from [19])...

TABLE 10.1 Typical Accuracy for B3LYP DFT Calculations on Small Molecule Test Sets"... 

Fig. 3 Electrostatic potential maps derived from B3LYP-DFT calculations for lumiflavin and ubiquinone in the respective oxidized (Fly and Qox) and radical anion forms (Flj-ad- and Qrad-)- Contour lines are at 60 kcal/mol intervals.

Of the two components, the major, a (70%), with more poorly resolved " N (of NO) hyperfine, is cited. B3LYP DFT calculation. 

Further studies by Garcia, Mayoral et al. [10b] also included DFT calculations for the BF3-catalyzed reaction of acrolein with butadiene and it was found that the B3LYP transition state also gave the [4+2] cycloadduct, as happens for the MP2 calculations. The calculated activation energy for lowest transition-state energy was between 7.3 and 11.2 kcal mol depending on the basis set used. These values compare well with the activation enthalpies experimentally determined for the reaction of butadiene with methyl acrylate catalyzed by AIGI3 [4 a, 10]. 

The ab initio methods used by most investigators include Hartree-Fock (FFF) and Density Functional Theory (DFT) [6, 7]. An ab initio method typically uses one of many basis sets for the solution of a particular problem. These basis sets are discussed in considerable detail in references [1] and [8]. DFT is based on the proof that the ground state electronic energy is determined completely by the electron density [9]. Thus, there is a direct relationship between electron density and the energy of a system. DFT calculations are extremely popular, as they provide reliable molecular structures and are considerably faster than FFF methods where correlation corrections (MP2) are included. Although intermolecular interactions in ion-pairs are dominated by dispersion interactions, DFT (B3LYP) theory lacks this term [10-14]. FFowever, DFT theory is quite successful in representing molecular structure, which is usually a primary concern. 

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... 

A calibration of the popular B3LYP and BP86 density functionals for the prediction of Fe isomer shifts from DFT calculations [16], using a large number of complexes with a wide range of iron oxidation states and a span of about 2 mm s for the isomer shifts, yielded a value for the calibration constant a = —0.3666 mm s a.u. (see Chap. 5). Note the negative sign, which indicates that a positive isomer shift of a certain compound relative to a reference material reveals a lower electron density at the nuclei in that compound as compared to nuclei in the reference material. 

Experimental and theoretical PVDOS for Fe(TPP)(NO) single-crystal and powder samples are shown in Fig. 5.17. The DFT calculations were performed, using the B3LYP and BP86 functionals. 

Fig. 5.17 Comparison of the experimental PVDOS determined from NIS measurements on Fe (TPP)(NO) (upper panel) with the PVDOS predicted on the basis of DFT calculations using the B3LYP (center panel) and BP86 (lower panel) functionals. Blue traces represent the PPVDOS Dp (v)for oriented crystals (see Appendix 2, Part III, 3 of CD-ROM), scaled by a factor of 3 for comparison with the total PVDOS Dpe(v)of unoriented polycrystalline powder (red traces). Since the X-ray beam direction k lies 6° from the porphyrin plane, modes involving Fe motion in the plane of the porphyrin are enhanced, and modes with Fe motion primarily normal to the plane are suppressed, in the scaled oriented crystal PVDOS relative to the powder PVDOS. In-plane Fe modes dominate the 200-500 cm range of the data, while Fe motion in modes observed at 74, 128, and 539 cm is predominantly out-of-plane. Crosshatching in the upper panel indicates the area attributable to acoustic modes. In the lower two panels, the Fe-NO bend/stretch modes predicted at 386 and 623 cm , have been artificially shifted to the observed 539 cm frequency to facilitate comparison with the experimental results. Predicted PVDOS are convolved with a 10 cm Gaussian (taken from [101])...

Fig. 9.40 NIS spectra of oxidized (filled circle) and reduced rubredoxin mutant Rm 2-4 (filled triangle) from Pyrococcus abyssi obtained at 25 K. The protein samples have been prepared with Fe concentrations of about 10 mM. Theoretically calculated NIS spectra based on DFT calculations (B3LYP/CEP-3IG) of 9, 21 and 49 atoms are shown below. The dotted lines represent calculated NIS spectra for the oxidized Fe S4 center and the dashed lines for the reduced Fe°S4 center. (Taken from [103])...

We now compare the PM3-D method with previous uncorrected DFT calculations on the S22 complexes [130], For the dispersion-bonded complexes the errors in the interaction distances for the PBE, B3LYP and TPSS functionals are reported to be 0.63, 1.16 and 0.69 A which are reduced to 0.17, 0.00 and 0.02 A when appropriate dispersive corrections are included. We see in Table 5-9 that the PM3-D method is capable of predicting the structures of dispersion-bonded complexes with greater accuracy than some uncorrected DFT functionals and with an accuracy comparable to that for the dispersion corrected PBE functional [130],... 

Poly(2,5-pyridyl) commonly know as poly(pyridine) has been the subject of considerable research effort as it luminesces in the blue region of the spectrum and may have uses in light emitting diodes (LEDs). Vaschetto and co-workers [103] reported a series of calculations on the molecule and its oligomers. The calculations included both the B3LYP and B3P88 density functions, Hartree-Fock calculations and a periodic solid-state DFT calculation using linear muffin tintype orbitals (LMTO). 

H20, CH3OH-. . H20, CN-. . HzO, HCC-. . H20, HCOCT. . H20. The DFT(B3LYP) and the DFT(BLYP) results were in a fair agreement with the MP2 results. The root mean square deviation of the DFT and the MP2 complexation enthalpies amounted to 0.7 and 1.1 kcal/mol, for B3LYP and BLYP, respectively. From the basis set dependence of the DFT results, it was concluded that the nonlocal DFT calculations require diffuse atomic functions. 

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