Seite - 94 - in Charge Transport in DNA - Insights from Simulations

AParametrizedModel toSimulateCT inDNA Table7.2: Obtainedwavenumbers for thefluctuationof IPdue to internaldynamicsof thenucleobases adenine andguanine anddue to environmental dynamics Adenine Guanine Environment 1866.7,1860.0,1823.3, 1900.0,1883.3,1833.3, 883.3,796.7,733.3,620.0,450.0, obtained 1790.0,1770.0,1756.7, 1810.0,1783.3,1756.7, 376.7,323.3,220.0,176.7,132.7, wavenumbers 1653.3,1583.3,1540.0, 1670.0,1630.0,1560.0, 103.3,61.7,41.7,30.0,20.7, [cm−1] 1380.0,1310.0,1246.7, 1433.3,1376.7,1243.3, 14.7,9.7,8.7,4.7,4.0, 1126.7,1076.7,943.3, 1156.7,1076.7,1026.7, 3.0,1.6,0.7,0.3, IP(t)=∑ n An ·cos ( t ·2π Tn ) +E0 (7.5) Tn is theperiodandAn is the correspondingamplitudeof theoscillation. While theTn are obtainedwith the Fourier transformation, the An have to be ob- tained fromotherdata. Theamplitudeshave tobefitted to reproduce thestandard deviations of the IP inMD simulations accurately. To this end, additional simu- lations of 20 ns with the IP calculated every 2 ps were performed to obtain the statistics of the IP time series. Two types of simulationswereperformed toobtain different amplitudes for the internal andexternalfluctuations. Toobtain theamplitudesof the internalfluctuations, simulationswithnoQM/MM coupling were performed. This way, the IP will fluctuate only as a result of the internalmodes of vibration of thenucleobases. Table 7.3 (left) shows the statistics of the IPof adeninenucleobases inapolyAsequence,whennoQM/MMcoupling is applied. Now, the sumof cosine functionswas set up including only the internal fluctua- tionswiththecorrespondingperiods. Thesumofcosinefunctionswasthenshifted bya constantE0 to yield the samemeanvalues as obtained fromMDsimulations. And, the amplitudes An were chosen in a way that an overall magnitude of the fluctuations is achieved,whichmatches the value obtained fromMDsimulations withoutQM/MMcoupling, i.e. 0.1 eV. To obtain the amplitudes for the environmental fluctuations, simulations with QM/MM coupling were performed. Again, the obtained time series of IP were analyzed formeanvalues and standarddeviations. Themeanvalues showed that 94