Time dependent DFT

To use direct dynamics for the study of non-adiabatic systems it is necessary to be able to efficiently and accurately calculate electronic wave functions for excited states. In recent years, density functional theory (DFT) has been gaining ground over traditional Hartree-Fock based SCF calculations for the treatment of the ground state of large molecules. Recent advances mean that so-called time-dependent DFT methods are now also being applied to excited states. Even so, at present, the best general methods for the treatment of the photochemistry of polyatomic organic molecules are MCSCF methods, of which the CASSCF method is particularly powerful. 

Figure 9-2. Performance of various functionals in the framework of time-dependent DFT for excitation energies...

We only consider static response properties in this chapter, which arise from fixed external field. Their dynamic counterparts describe the response to an oscillating electric field of electromagnetic radiation and are of great importance in the context of non-linear optics. As an entry point to the treatment of frequency-dependent electric response properties in the domain of time-dependent DFT we recommend the studies by van Gisbergen, Snijders, and Baerends, 1998a and 1998b. 

In this chapter we will focus on one particular, recently developed DFT-based approach, namely on first-principles (Car-Parri-nello) molecular dynamics (CP-MD) [9] and its latest advancements into a mixed quantum mechanical/molecular mechanical (QM/MM) scheme [10-12] in combination with the calculation of various response properties [13-18] within DFT perturbation theory (DFTPT) and time-dependent DFT theory (TDDFT) [19]. 

The UV Vis spectrum of 34 features a broad band centered at 363 nm, E— 17,400mol cm . As indicated by a time-dependent DFT calculation, electronic excitations from the Highest Occupied Molecular Orbital (HOMO), HOMO-1 and HOMO-2 to the LUMO are the major contributors to this broad band. 

Currently the time dependent DFT methods are becoming popular among the workers in the area of molecular modelling of TMCs. A comprehensive review of this area is recently given by renown workers in this field [116]. From this review one can clearly see [117] that the equations used for the density evolution in time are formally equivalent to those known in the time dependent Hartree-Fock (TDHF) theory [118-120] or in its equivalent - the random phase approximation (RPA) both well known for more than three quarters of a century (more recent references can be found in [36,121,122]). This allows to use the analysis performed for one of these equivalent theories to understand the features of others. 

Analytical gradients and Hessians are available for CASSCF, and it is expected that this technology will be extended to the MR-CI and MP2 methods soon. Further, by virtue of the multireference approach, a balanced description of ground and excited states is achieved. Unfortunately, unlike black boxes such as first-order response methods (e.g., time-dependent DFT), CAS-based methods require considerable skill and experience to use effectively. In the last section of this chapter, we will present some case studies that serve to illustrate the main conceptual issues related to computation of excited state potential surfaces. The reader who is contemplating performing computations is urged to study some of the cited papers to appreciate the practical issues. 

Scandola and coworkers have explored in detail the consequences of the asymmetry of the coordination environment. On the basis of results from time-dependent DFT calculations, it is concluded that for a series of complexes including Ir(tdppy)(tterpy)+ and Ir(tdppy)(Brpterpy)—wherein the Ir(III) center is coordinated by 2,6-diphenylpyridine (dppy) and terpy fragments—the lowest-lying states can display a unique directional character, of dppy -> terpy nature (LLCT). Table 12 collects spectroscopic and electrochemical properties for these complexes that feature intense CT absorption in the visible and emission in the red region, A.em = 690 nm for Ir(tdppy)(Brpterpy) [95,96]. 

Finally, the time-dependent DFT calculations agreed with the experimental results, showing that the transition responsible for the luminescent behavior is that from an antibonding occupied orbital, mainly centered in the gold interacting atoms with a contribution from the heterometals, to a bonding virtual orbital located between the gold and the silver (or copper) centers. 

Table 7.9 UV spectra (as transition energies in eV) of acetone, acetaldehyde, and formaldehyde, calculated by time-dependent DFT, using Gaussian 98 [78]. The results of using MP2/6-311+G [110] and (calculations by the author) AMI geometries are compared both sets of calculations are single-point B3P86/6-311++G. For each molecule only 6 transitions, all singlets, are shown. The number of positive and negative deviations from experiment and the mean absolute errors are given...

A time-dependent DFT method was utilized for calculating the electronic transition energies of a series of 5-aryl-NH-tetrazoles in solution, and the calculated absorption bands were compared with experimental data <2003CPH65>. However, Sadlej-Sosnowska et al. compared the theoretically calculated spectra of 2//-tautomcrs with the spectra measured in solutions where the prevalence of l //-tautomers was well known. 

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