6.3 Linear absorption of Pheo and P 16 next to a MNP
6.3.2 Linear absorption for a large number of molecules coupled to the MNP . 109
In experimental measurements the proportion between the number of MNPs and the number of molecules in general is not 1 : 1. In most cases the number of molecules exceeds the number of MNPs by a factor of Nmol/NMNP [33], with the respective numbers of molecules Nmoland the number of MNPs NMNP.
In terms of the above introduced methodology that treats the molecules in atomic detail and the MNP parametrically, linear absorption experiments with systems including a single MNP coupling to hundreds of molecules may be simulated in two ways. On the one hand, the TDSE can be solved for the whole system, including the excitonic coupling between each Pheo and the MNP and including the excitonic coupling between neighboring Pheos on the MNP surface (each Pheo may be represented by another part of the MD data). On the other hand, the coupling between neighboring molecules may be neglected; it has to be assumed that the MNP couples to each molecule, regardless of the presence of the other molecules. However, in what follows, this approximation is made. The number of Pheos on the MNP surface is chosen to be 10000. On the one hand, this is the number that was utilized in recent experiments [33] (with another porphyrin - tetraphenylporphyrin). On the other hand, 10000 is exactly the number of Pheos that cover the surface of the MNP (using a diameter of 1 nm for Pheo). The number of P16molecules that cover an MNP with a radius of 30 nm was calculated to be 930 (using a diameter of 4 nm for P16).
The linear absorption curves for the MNP covered with Pheo, on the one hand, and P16, on the other hand, is shown in Fig. 6.3. The results look very similar for both molecules. Concern-ing the calculated amplification of the Pheo and P16 linear absorption due to the presence of
Figure 6.4: Qy and Qx band linear absorption for the Pheo-MNP system in ethanol. Full black line:
Qy linear absorption band calculated for a single Pheo. Full red line: Qxlinear absorption band. The respective dashed lines show the differences between the Pheo-MNP Qyand Qxband linear absorption lineshapes and the linear absorption lineshape of the MNP.
the MNP and the fact that the number of Pheos within 930 P16molecules is 14880, the result is reasonable.
6.3.3 Linear absorption of the Qxband
Utilizing the theory that was discussed in Sec. 3.6.1, additionally to the Qyband, the Qxband for Pheo next to an MNP is calculated. Since the Qxband is in resonance with the MNP absorption, the amplification of the absorption signal is expected to be larger than for the Qy band. In Fig. 6.4 the differences between the respective Pheo-MNP Qyand Qx band linear absorption lineshapes and the linear absorption lineshape of the MNP are shown. For the Qx band, the peak is overlayed by a deep dip. In Fig. 6.5 the Qyand Qxband linear absorption for an MNP that is covered with 10000 Pheos is shown. As in the foregoing section, the interaction between the Pheos was neglected. It can be seen that the dip at the Qxband position is overlayed by the MNP absorption. In respective experiments, the MNP absorption is additionally affected by scattering effects [33]. Thus, Fig. 6.5 shows that the treatment of the Qxband can be neglected for this system, even though the Qxband is resonant with the MNP absorption.
6.3 Linear absorption of Pheo and P16next to a MNP
Figure 6.5:Qyand Qxband linear absorption for a MNP covered with Pheo molecules in ethanol. Black line: linear absorption of the MNP. Red line: Qy linear absorption of 10000 Pheos on the surface of a MNP. Green line: combined Qxand Qyband linear absorption of 10000 Pheos on the surface of an MNP.
7 Screening in supramolecular complexes
7.1 Introduction
It was explained in the chapters 3 and 4 how to derive optical properties of a CC in solution from classical MD simulations. The key to those computations was the calculation of the energy gap functionUmeg(t)of chromophorem(cf. Sec. 4.3).
However, even if the energy gap functionsUmeg(t)can be calcuted in good approximation, the quality of the CC description depends strongly on the quality of the transition couplings Jmn between two chromophores m and n (Sec. 4.3.2). As discussed earlier in Sec. 4.3.2, the transition density of a chromophore can be translated to respective transition partial charges {qtri }={qi(ge)}. As explained in Sec. 3.3.3, the transition partial charges have to be normalized to an experimental value of the transition dipole moment [32]. Then Eq. 3.49 can be utilized to compute the coupling energy Jmnbetween two chromophoresmandn.
However, this formula neglects the screening of partial charges via the surrounding medium.
The two chromophores m and n interact not only with themselves, but with all the other molecules around. This electrostatic coupling to the other molecules effectively changes the coupling between the chromophoresmandn. The couplingJmnis screened.
There exist mainly two approaches to compute the screening within large chromophore com-plexes in solution. The method that will be utilized within this thesis was proposed by the group of Renger and computes the transition density of a chromophore without taking the specific conformation of the surrounding medium into account [34, 35]. The effective poten-tial of the respective transition parpoten-tial charges is computed by solving the Poisson equation.
Other approaches of the group that compute the transition densities, taking the surrounding medium into account, can be found in [174, 175, 176]. A more sophisticated but also much more computationally expensive ansatz has been pursued in the group of Menucci. In their ansatz, the conformation of each solvent and protein molecule near the chromophore contributes to the screening, which is obtained by DFT computations of the electronic coupling between two chromophores, involving solvent and protein molecules [23, 177, 178].
The following chapter refers to the work of the Renger group. The computation is much more practicable. It can be utilized to compute the screening for a lot of chromophore pairs with different distance and mutual orientation. This data will be utilized to find a fitting procedure that includes not only the distance dependence (as utilized for example in [28, 29]), but also the conformational dependence of the screening between two chromophores (cf. [179]).