Ab Initio Methods for the Calculation of Excited States

The configuration interaction (Cl) procedure is one of the commonly used methods for determination of electronically excited states [30]. Starting from a finite set l/j of orthonormal one-electron basis functions (which can be either Hartree-Fock (HF) or canonical multiconfigurational self-consistent field (MCSCF) orbitals) [30], a subset of all possible antisymmetrized products have to be constructed  

The linear response methods offer a viable alternative to the Cl procedure [38]. A time-dependent (TD) perturbation theory (e.g. involving an oscillating electric field), combined with the SCF or MCSCF method is referred to as the TD-SCF (or random phase approximation, RPA) or the TD-MCSCF (or multiconfigurational linear response, MCLR), respectively. Let us consider the time development of the dipole moment (z-component for simplicity)  

The first term on the right-hand side is the permanent dipole moment and the second one is the first-order change of the dipole moment  

The Fourier component of the first-order perturbed time-dependent wave function is called the linear response function  

Both transition energies and oscillator strengths are needed for determination of optically allowed absorption spectra. In the multi-configuration version of the linear response theory (MCLR) one constructs an approximation to the exact linear response function by exposing the optimized (MC) SCF wavefunction 0 to a time-dependent perturbation. In this case the time-dependent wave function assumes the form 

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Dreuw A, Head-Gordon M (2005) Single-reference ab initio methods for the calculation of excited states of large molecules. Chem Rev 105 4009 1037... 

A. Dreuw and M. Head-Gordon, Chem. Rev., 105,4009-4037 (2005). Single-Reference ab Initio Methods for the Calculation of Excited States of Large Molecules. 

Needless to say, many extensions of the herein presented methods and different approaches are used to theoretically determine the electronic coupling. Conventional quantum chemistry ranging from fundamental ab initio methods to sophisticated semi-empirical approaches for the calculation of excited state properties is a useful tool to evaluate molecular-wire properties. 

Having these severe approximations in mind, SCC-DFTB performs surprisingly well for many systems of interest, as discussed above. However, it has a lower overall accuracy than DFT or post HF methods. Therefore, applying it to new classes of systems should be only done after careful examination of its performance. This can be done e.g. by conducting reference calculations on smaller model systems with DFT or ab initio methods. A second source of errors is related to some intrinsic problems with the GGA functionals also used in popular DFT methods (SCC-DFTB uses the PBE functional), which are inherited in SCC-DFTB. This concerns the well known GGA problems in describing van der Waals interactions [32], extended conjugate n systems [45,46] or charge transfer excited states [47, 48],... 

The properties of oligomers of thiophene at the ground and excited states have been investigated by semi-empirical and ab initio methods. Semi-empirical calculations for the ground state of thiophene involve the QCFF/PI -f CISD method, while ab initio calculations are carried out at the HF/6-31G and the CASSF/3-21G" levels and also at the SCF and the averaged coupled-pair functional (ACPF) levels, with (basis set I) and without (basis set II) the sulfur 3d-orbitals. 

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