Electronic structure and carrier transfer in B-DNA monomer polymers and dimer polymers: Stationary and time-dependent aspects of a wire model versus an extended ladder model

We employ two tight-binding (TB) approaches to systematically study the electronic structure and hole or electron transfer in B-DNA monomer polymers and dimer polymers made up of $N$ monomers (base pairs): (I) at the base-pair level, using the onsite energies of base pairs and the hopping integrals between successive base pairs, i.e., a wire model and (II) at the single-base level, using the onsite energies of the bases and the hopping integrals between neighboring bases, i.e., an extended ladder model since we also include diagonal hoppings. We solve a system of $M$ (matrix dimension) coupled equations [(I) $M=N$, (II) $M=2N]$ for the time-independent problem, and a system of $M$ coupled first order differential equations for the time-dependent problem. We perform a comparative study of stationary and time-dependent aspects of the two TB variants, using realistic sets of parameters. The studied properties include HOMO and LUMO eigenspectra, occupation probabilities, density of states and HOMO-LUMO gaps as well as mean over time probabilities to find the carrier at each site [(I) base pair or (II) base], Fourier spectra, which reflect the frequency content of charge transfer, and pure mean transfer rates from a certain site to another. The two TB approaches give coherent, complementary aspects of electronic properties and charge transfer in B-DNA monomer polymers and dimer polymers.

Figure 1

An example of type ${\alpha }^{\prime }$ polymers: LUMO (first row) and HOMO (second row) eigenspectra of poly(dA)-poly(dT), for wire model (TB I, first column) and extended ladder model (TB II, second column).

Figure 2

An example of type ${\beta }^{\prime }$ polymers: LUMO (first row) and HOMO (second row) eigenspectra of GCGC…, for wire model (TB I, first column) and extended ladder model (TB II, second column).

Figure 3

An example of type ${\gamma }^{\prime }$ polymers: LUMO (first row) and HOMO (second row) eigenspectra of TCTC…, for wire model (TB I, first column) and extended ladder model (TB II, second column).

Figure 4

DOS for an example of type ${\alpha }^{\prime }$ polymers, poly(dG)-poly(dC) ($N={10}^5$, HOMO), for the base-pair (TB I, top) and the single-base (TB II, bottom) approaches.

Figure 5

DOS for an example of type ${\beta }^{\prime }$ polymers, CGCG… ($N={10}^5$, LUMO), for the base-pair (TB I, top) and the single-base (TB II, bottom) approaches.

Figure 6

DOS for an example of type ${\gamma }^{\prime }$ polymers, CTCT… $\equiv$ AGAG… ($N={10}^5$, HOMO) for the base-pair (TB I, top) and the single-base (TB II, bottom) approaches.

Figure 7

HOMO-LUMO gaps of type ${\alpha }^{\prime }, {\beta }^{\prime }$, and ${\gamma }^{\prime }$ polymers, for the base-pair (TB I, blue dots) and the single-base (TB II, purple squares) approaches. The horizontal lines denote the HOMO-LUMO gaps of the two possible monomers.

Figure 8

Type ${\alpha }^{\prime }$ polymers. TB I and initial condition (extra carrier initially at the first base pair). Mean over time probabilities to find an extra hole (HOMO) or electron (LUMO) at each base pair. Here $N=12$.

Figure 9

Type ${\alpha }^{\prime }$ polymers. TB II and either initial condition 1 (left) or initial condition 2 (right), i.e., extra carrier initially at the first or the second base of the first base pair, respectively. Mean over time probabilities to find an extra hole (HOMO) or electron (LUMO) at each base. Here $N=12$.

Figure 10

Type ${\beta }^{\prime }$ polymers. TB I and initial condition (extra carrier initially at the first base pair). Mean over time probabilities to find an extra hole (HOMO) or electron (LUMO) at each base pair. $N$ even (here $N=12$, left) or $N$ odd (here $N=13$, right).

Figure 11

Type ${\beta }^{\prime }$ polymers. TB II and either initial condition 1 (left) or initial condition 2 (right), i.e., extra carrier initially at the first or the second base of the first base pair, respectively. Mean over time probabilities to find an extra hole (HOMO) or electron (LUMO) at each base. $N$ even (upper panels, here $N=12$) or $N$ odd (lower panels, here $N=13$).

Figure 12

Type ${\gamma }^{\prime }$ polymers. TB I and initial condition (extra carrier initially at the first base pair). Mean over time probabilities to find an extra hole (HOMO) or electron (LUMO) at each base pair. $N$ even (here $N=12$, left) or $N$ odd (here $N=13$, right).

Figure 13

Type ${\gamma }^{\prime }$ polymers. TB II and either initial condition 1 (left) or initial condition 2 (right), i.e., extra carrier initially at the first or the second base of the first base pair, respectively. Mean over time probabilities to find an extra hole (HOMO) or electron (LUMO) at each base. $N$ even (upper panels, here $N=12$) or $N$ odd (lower panels, here $N=13$).

Figure 14

Type ${\alpha }^{\prime }$ polymers, here poly(dA)-poly(dT), $N=20$. TB I and initial condition (extra carrier initially at the first base pair). Hole transfer Fourier spectra at the first and the last monomer.

Figure 15

Type ${\beta }^{\prime }$ polymers, here ATAT…, $N=14$. TB I and initial condition (extra carrier initially at the first base pair). Electron transfer Fourier spectra at the first and the last monomer.

Figure 16

Type ${\gamma }^{\prime }$ polymers, here TCTC…, $N=21$. TB I and initial condition (extra carrier initially at the first base pair). Hole transfer Fourier spectra at the first and the last monomer.

Figure 17

Type ${\alpha }^{\prime }$ polymers, here poly(dA)-poly(dT), $N=20$. TB II and either initial condition 1 (left) or initial condition 2 (right). Hole transfer Fourier spectra at the first and the last monomer.

Figure 18

Type ${\beta }^{\prime }$ polymers, here ATAT…, $N=14$. TB II and either initial condition 1 (left) or initial condition 2 (right). Electron transfer Fourier spectra at the first and the last monomer.

Figure 19

Type ${\gamma }^{\prime }$ polymers, here TCTC…, $N=21$. TB II and either initial condition 1 (left) or initial condition 2 (right). Hole transfer Fourier spectra at the first and the last monomer.

Figure 20

Type ${\alpha }^{\prime }$ polymers, here poly(dG)-poly(dC). Hole pure mean transfer rates (I) $k_{1,N}$ for TB I (left), and (II) $k_{1,2}, k_{2N-1,2N}, k_{1,2N-1}, k_{2,2N}, k_{1,2N}$, and $k_{2,2N-1}$ for TB II (right).

Figure 21

Type ${\beta }^{\prime }$ polymers, here is a case where, for $N$ even, the carrier is transferred at a large percentage to the last monomer but the transfer is very slow: electron pure mean transfer rates in ATAT…, either $k_{1,N}$ within TB I (left) or the largest transfer rates in TB II, i.e., $k_{1,2N-1}$ for $N$ odd, $k_{1,2N}$ for $N$ even, $k_{2,2N}$ for $N$ odd, $k_{2,2N-1}$ for $N$ even.

Figure 22

Type ${\gamma }^{\prime }$ polymers, here TCTC… . Hole pure mean transfer rates $k_{1,N}$ for TB I (left), and $k_{1,2N-1}, k_{2,2N}$ for TB II (right).

Figure 23

The decay length $\beta$ of the exponential fits $k=k_0{e}^{-\beta d}$, within TB II.

Figure 24

The decay length $\beta$ of the exponential fits, $k=A+k_0{e}^{-\beta d}$, within TB II.

Figure 25

The exponent $\eta$ of the power-law fits $k=k_0^{\prime }{N}^{-\eta }$, within TB II.

Figure 26

The correlation coefficients of the exponential fit $k=k_0{e}^{-\beta d}$, within TB II.

Figure 27

The correlation coefficients of the exponential fit $k=A+k_0{e}^{-\beta d}$, within TB II.

Figure 28

The correlation coefficients of the power-law fit $k=k_0^{\prime }{N}^{-\eta }$, within TB II.