TDDFT-B3LYP

Table 14 CASSCF/CASPT2 and TDDFT/B3LYP excitation energies (eV), oscillator strengths / (in parentheses), and assignments of the low-lying electronic transitions of [Ru(SnH3)(CH3)(CO)2(Me-DAB)] and [Ru(Cl)(CH3)(CO)2(Me-DAB)] [2, 191] ...

The first investigation into the excited states of ZnPc based on first-principles methods is the TDDFT/SAOP study by Ricciardi et al [135], where the UV-vis and the vacuum ultraviolet region of the electronic spectrum of ZnPc are described in detail. Subsequently, Nguyen and Pachter, in the context of a TDDFT/B3LYP study of the electronic spectroscopy of the zinc tetrapyrrole series [140], ZnP, ZnPz, ZnTBP, and ZnPc, came to a somewhat different interpretation of the Uv-vis spectrum of this phthalocyanine. 

Table TDDFT(B3LYP) calculated excitation energies (eV) for oligo(cyclopentadiene)s, oligo(pyrrole)s, oligo(phosphole)s (Ph) ollgo(thlophene)s (Th)n, and the corresponding polymers (DFT HOMO-LUMO gaps in parentheses)...

Figure 3.3. Comparison of calculated and experimental excitation energies corresponding to OPA (top) and TPA (bottom) of molecules experimentally investigated [131, 132, 287]. Calculations were done at the TDDFT/B3LYP level using three different optimized geometry sets (B3LYP, HF/planar, and HF/nonplanar). From Ref. [236] with permission of the American Chemical Society.

Figure 46 (-)-Chimonantine 119 experimental CD spectrum in cyclohexane and two calculated in the velocity and length formalism. The TDDFT/B3LYP/6-31G calculated spectra were obtained as Boltzmann average upon the total six conformers taking into account the 40 lowest energy transitions and assuming a Gaussian distribution with (7i = 0.15eV. Redrawn from E. Giorgio K. Tanaka L. Verotta K. Nakanishi N. Berova C. Rosini, Chirality 2007, 19, 434-445.

Figure 4.1 Important features of ground- and excited-state PESs for ethylene photodynamics and demonstration of the inadequacy of TDDFT and CIS methods for this problem, (a) Sq and PESs for ethylene in the pyramidalization and torsion coordinates (defined in the inset) that dominate the photodynamics. This surface was calculated using multireference perturbation theory — CAS(2/2) PT2. The global minimum on Si occurs at twisted and pyramidalized geometries. (b-d) A quantitative comparison of the Si PES obtained with CAS(2/2) PT2, TDDFT/B3LYP, and CIS, respectively. All calculations use the 6-3IG basis set. The TDDFT and CIS calculations are performed in a spin-unrestricted formalism. Contour values are given in eV, and in all cases the energies are referenced to the Sq equilibrium geometry at the corresponding level of theory. Only the multireference calculation captures the Si minimum correctly.

Table 14.12 Excitation distribution and CT numbers (in %) for the lowest singlet nn transition in phenyl-pentafulvene at CIS/PPP, FCI/PPP and TDDFT/B3LYP levels...

Table 3 Comparison of Calculated [TDDFT-B3LYP/TZV(d,p)] and Experimental 0-0 Excitation Energies (in eV) for the Lowest Singlet States (nn ) of Unsaturated Systems...

This behavior of the DF is also observed in molecular applications. Vertical singlet excitation energies from CASPT2 % TDDFT-B3LYP, and... 

The naphthalene molecule, which is used as an example here, has a lowest triplet state of Bxu symmetry and n n (La) character. The dipole allowed transitions that are polarized in the plane of the molecule thus belong to transitions to Ag and B g excited states. The results of the unrestricted TDDFT-B3LYP treatment are shown in comparison with the experimental spectrum in Figure 18. 

To account for this fact, the TDDFT-B3LYP calculations of the spectra have been carried out with a TZV(2df) basis set augmented with diffuse functions at the sulfur atoms as well as at the neighboring carbon atoms and a TZV(d,p) basis set for the remaining atoms. The B3LYP/TZV(d,p) ground-state geometry has been used for these calculations. The theoretical spectrum has been blue shifted by 0.39 eV to match the experimental band A. 

Figure 19 Comparison of the experimental and computed [TDDFT-B3LYP/aug-TZV(2df)] UV and CD spectra for 2,3-(5,5)-dithiadecalin. The theoretical spectra have been blue-shifted by 0.39 eV.

Hexahelicene is one of the most widely studied molecules in theoretical CD spectroscopy (see, e.g.. Refs. 47 and 136 and references cited therein). The system is rather large [120 valence electrons, 590 basis functions with a TZV(d,p) AO basis] and IJ-IO excited states are necessary to describe the experimental spectrum entirely. This example is presented here to show that correlated ab initio treatments are also applicable for such cases. The simplified coupled-cluster model CC2 together with the RI approximation is used and compared to the standard TDDFT-B3LYP approach. 

Figure 20 Comparison of the experimental and computed [TZV(d,p) AO basis, B3LYP optimized geometry] CD spectrafor ( M)-[6]helicene. The theoretical spectra have been shifted by 0.20 (B3LYP) and —0.22 eV (CC2), respectively. The filled circles/triangles indicate the two lowest states with small intensity obtained by CC2/TDDFT-B3LYP. The vertical lines correspond to results from the CC2 method.

Figure 22 Comparison of the computed [TDDFT-B3LYP/TZV(d,p)] and experimental UV spectra for the state of anthracene. The 0-0 transition energy is set to zero.

All calculations were performed at the (TD)DFT-B3LYP/TZV(d,p) level employing Cih symmetry. In contrast to the experimental data, the TDDFT calculation yields an Si state with B symmetry (AE = = 4.05 eV) and the 2Ag state as the second one (AE = 4.89 eV). This error can be traced to the systematic underestimation of excitation energies for ionic states with TDDFT-B3LYP. Because of the adiabatic approximation used in the... 

Figure 25 Ground and first excited-state potential energy curves [TDDFT-B3LYP/ TZV(d,p)] along the pyramidalization coordinate of formaldehyde. For comparison, the dashed line shows the harmonic potential.

Table 8 Computed TDDFT(B3LYP)/6-3 IG excitation energies (eV) and oscillator strengths for the four lowest excited states of the most stable dimers of D102 and D149. The corresponding shifts of the lowest excited state (eV) with respect to the reference monomers are listed in the last ...

Optimum structures. While the nuclear positions are defined by the reference framework and remain fixed during the optimization, TB-LCAP optimization of the objective function with respect to the participation coefficients identifies local minima on the alchemical potential hypersurface. The participation coefficients corresponding to the alchemical minimum are then rounded off to yield a chemically representable candidate. The geometry of the candidate structure is then optimized in a DFT/B3LYP gas phase calculation, yielding the optimum structure. Subsequently, the TDDFT/B3LYP photoabsorption... 

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