TDDFT calculations

Tables 11-6, 11-7, and 11-8 show calculated solvatochromic shifts for the nucle-obases. Solvation effects on uracil have been studied theoretically in the past using both explicit and implicit models [92, 94, 130, 149, 211-214] (see Table 11-6). Initial studies used clusters of uracil with a few water molecules. Marian et al. [130] calculated excited states of uracil and uracil-water clusters with two, four and six water molecules. Shukla and Lesczynski [122] studied uracil with three water molecules using CIS to calculate excitation energies. Improta et al. [213] used a cluster of four water molecules embedded into a PCM and TDDFT calculations to study the solvatochromic shifts on the absorption and emission of uracil and thymine. Zazza et al. [211] used the perturbed matrix method (PMM) in combination with TDDFT and CCSD to calculate the solvatochromic shifts. The shift for the Si state ranges between (+0.21) - (+0.54) eV and the shift for the S2 is calculated to be between (-0.07) - (-0.19) eV. Thymine shows very similar solvatochromic shifts as seen in Table 11-6 [92],...

In this section we have described the calculation of u (1) and 1) with TDDFT perturbed by a magnetic field. These quantities, in combination with u/0) and (0) obtained from an unperturbed TDDFT calculation, can be used with Eqs. (11, 17, 30, or 32) as appropriate to evaluate, respectively, Bj, Aj, Cj 1, or C/° 2 and thus an MCD spectrum using Eq. (33). We have explicitly avoided orbitally degenerate ground states and therefore cannot yet calculate classical C terms. This problem will be discussed in Section II.C.4 but before doing so, we will describe the calculation of MCD intensity from the imaginary part of the Verdet constant where the MCD intensity itself is calculated rather than parameters associated with the various MCD terms. 

If the most obvious reference state is problematic, as is the case if the ground state has orbital degeneracy, an alternative choice of reference can be useful provided a TDDFT calculation starting from the alternative reference can access all of the states of interest (including the problematic ground state). Given a reference density... 

The vectors corresponding to the zero eiegenvalues of the matrix (M-o l) are the eigenfunctions of the matrix M corresponding to eigenvalue u. These eigenfunctions will be available from the TDDFT calculation and can be projected out of the trial solution of the system of equations to improve convergence. 

The dipole strength parameter is straightforward to obtain in a TDDFT calculation. 

Similar information can be obtained from a TDDFT calculation of the MCD Bj or CjSO 2. In order to do so, rather than solving Eqs. (58) or (60) directly, the perturbed transition density can be expanded in the basis of eigenvectors of the appropriate matrix. For example, to solve Eq. (60) the eigenvectors of fl(0)are used... 

Therefore, a timing value less than 1.00 is faster than a Direct calculation and values greater than 1.00 are slower. The timing data includes the time required to perform the TDDFT calculation that is also required to produce the unperturbed transition densities and excitation energies as well as the time required to calculate the MCD parameters. 

As far as computational cost is concerned, the evaluation of the ground state magnetic moment is trivial and the TRICKS-TDDFT part is simply a normal TDDFT calculation of excitation energies but with an unusual choice of reference state orbital occupations. Preliminary results indicate that the accuracy of TRICKS-TDDFT excitation energies is similar or perhaps a little inferior to that of standard TDDFT calculations (88). 

Much like the porphyrin and TPP complexes, the observed MCD of the Q band of the TAP and Pc complexes is relatively straightforward to reproduce. TDDFT calculations find that this transition is dominated by the alu—>eg one-electron excitation (136,151-153) and the calculated Aj parameters are large and positive. 

Transition density vector from a TDDFT calculation with a nonhybrid functional. 

Re(dmpe)32+. Of interest is that both complexes make available extremely oxidizing excited states using a visible photon, since their absorption and emission energies are 528 nm (600 nm) for Re, and 590 nm (681 nm) for Tc, respectively. Unrestricted open shell TDDFT calculations confirm the nature of the transitions as LMCT and predict the proper relative energies of Re versus Tc. 

TDDFT calculations results were consistent with the band shapes of the optical spectra of the parent complexes and are shown in Fig. 14. The calculated optical transitions are shown as bars under the experimental spectra and consist of MLLCT, ligand-to-ligand charge transfer transitions (LLCT), intraligand n - tt transitions (IL), and metal-complex delocalized-charge transfer transitions (MCDCT). Triplet state energies were also calculated based on a3 MLLCT state and correlated with experimental emission spectral results [53]. 

A careful analysis, based on CASSCF/CASPT2 and TDDFT calculations, of the electronic spectrum of 7]5-CpMn(CO)3, a mono(cyclopentadienyl) complex which has been widely investigated for its photochemical reactivity, has been reported by Full et al [88]. The capability of TDDFT and highly correlated ab initio methods to describe MC and MLCT states of this organome-... 

For the M(P)2 series, a satisfactory description of the phosphorescence spectra and the triplet-triplet absorption spectra was also obtained by TDDFT calculations [136]. 

Undoubtedly, the most general conclusion to be drawn from this overview of recent TDDFT calculations on transition-metal complexes is that this technique, compared to other available theoretical methods, provides state-of-the-art results for excitation energies. We stress that in order for this to be a valid statement, there are two points that should receive due attention the applied functional, and the geometry of the system. 

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