2.10 One-electron transition density matrix
2.10.4 Participation ratio of NTOs (PR NTO )
PRNTO is defined as PRNTO=(P
i
λi)2/P
i
λ2i,162,166 where λi is the weight of the tran- sition between two states. PRNTO provides the number of natural transition orbitals (NTO) participating to produce an excited state. NTO itself is obtained by a singular value decomposition of the 1-TDM.
Excited-state properties of pyridine-thiophene oligomers:
DFT vs RI-ADC(2)
Monomer
UV spectra
Excited State properties
Pentamer (helical) CD spectra
Charge-transfer states TD-DFT vs ADC(2)
Figure: DFT vs ADC(2) for oligomers of pyridine-thiophene.
In this chapter, performances of various DFT functionals to reproduce the absorp- tion and CD spectra of pyridine-thiophene oligomers are examined. Starting from a linear system like monomer, calculations are carried out at ADC(2) and DFT levels till a helical system like pentamer is formed. Analysis of excited-state properties shows that the state ordering patterns or results regarding natural transition orbitals from these DFT functionals sometimes differ from the ADC(2) results. A part of the content of this chapter is published in J. Phys. Chem. A,2021, 125, 1, 115-125.
3.1 Introduction
Over the last few decades, DFT based methods have been widely used in chemistry, bi- ology and materials science. In contrast to the electron-correlated wave function based methods, DFT methods are able to handle large-sized systems due to their low compu- tational cost. The method has been very successful while predicting ground state struc- tures and properties. In materials science, modeling of organic layers in OLEDs, organic photovoltaics (OPVs) and organic field-effect transistors (OFETs), DFT has been the preferred method producing qualitatively correct ground state results. However, DFT has its limitations because of the use of approximate exchange-correlation functionals, although the theory itself is exact. In addition to DFT, linear-response TD-DFT149,167 is the most widely used single-reference method till date for studying excited states.
But computations for the properties of excited states using standard TD-DFT has not been as successful as DFT. Description of closely-lying excited states168,169 or excited states arising out of multiple excitations169–173 are problems for TD-DFT as it relies on single-determinant expression of ground state wave function. In addition, charge-transfer excited states are also not properly described using TD-DFT methods.174–180 Further, failure of standard DFT functionals to describe excited states of extendedπ-conjugated systems has also been highlighted.181–188 To address these issues, a large number of functionals, including so-called range-separated functionals have been developed in re- cent times and the usual strategy has been to benchmark the TD-DFT results against either experimental results or results from wave function based methods such as the second-order coupled-cluster (CC2),189 the second/third order algebraic diagrammatic construction (ADC(2)/ADC(3)),152–154,190 symmetry-adapted-cluster configuration in- teraction (SAC-CI)191–193 or if possible, from multi-configurational methods such as complete active space self-consistent field (CASSCF)120,121 methods.
Our group has been interested in studying co-oligomers based on six- membered
only being helical without having any asymmetric carbons. Helical polymers are im- portant because of potential applications in materials used for chiral recognition, liquid crystals and optical materials.196–199Noncovalent interactions such asπ-π and hydrogen bonding interactions help in stabilizing these type of systems. In recent times, synthetic helical polymers based on furan, thiophene etc. have garnered a lot of attention.39,200,201 In earlier studies,194,195our group reported interaction energies, absorption spectra, and CD spectra of oligomers based on furan, thiophene, pyrrole, phenyl and pyridine. All those studies were carried out at DFT (and TD-DFT) level of theory. It was observed that stability increases with increase in the size of helix. In addition, it was also found that for major electronic transitions, molecular orbitals (MO) other than the frontier or- bitals contribute significantly. To take the studies further, in the present article, we aim to assess the accuracy of TD-DFT results taking into account various functionals against the ADC(2) results. For the purpose, we have taken into account the pyridine-thiophene (PT)oligomers. We have considered oligomers up to pentamers only. It is notable that monomer and polymers of (PT) have already been synthesized and spectroscopically characterized.202–207,207–210In particular,π-donating andπ-accepting capabilities of five- membered and six-membered rings, respectively, in these type of systems have been of much interest and a lot of work has been carried out. ADC(2) calculations for oligomers larger than pentamers (containing ten rings in our case) are time-consuming and since a pentamer is already in a helix conformation, we start from linear structures and proceed till a helix is formed. In Sec. 3.2, computational details are described. This is followed by results and discussion section in which we present a comparison of the absorption and CD spectra results obtained using various DFT functionals with the ADC(2) re- sults. Later in the section, we provide a quantitative comparison of the excited state properties by computing few excited state descriptors. Next, we have carried out a brief discussion over emission properties of (PT)3-(PT)5. In the last section, we provide a summary and conclude.
(a) (b)
(c)
(d) (e)
Figure 3.1: Optimized structures of(PT) oligomers: (a)-(e) show monomer to pen- tamer structures. These structures are obtained at RI-MP2/def2-SVP level. The gray,
white, yellow and blue colours indicate C, H, S and N atoms, respectively.