Quasi-Periodic and Fractal Polymers: Energy Structure and Carrier Transfer

Mantela, Marilena; Lambropoulos, Konstantinos; Theodorakou, M.; Simserides, Constantinos

doi:10.3390/ma12132177

Cited by 12 publications

(21 citation statements)

References 93 publications

(149 reference statements)

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“…The time scale of the bp twist Equation ( 5) is completely determined by the characteristic frequency ω ϕ , whereas the radial Equation ( 6) involves three different characteristic frequencies, namely, ω ϕ , ω ϕS,n,n±1 (related to twist-stacking coupling), and ω ϕSH (fully coupling twist, stacking, and stretching interactions). The set of coupled Equations ( 5) and ( 6) describes the dynamics of general dsDNA molecules, with two kinds of bps arranged either periodically or aperiodically [32][33][34][35][36], and their mathematical structure clearly shows the correlated nature of next-neighboring bps dynamics. Thus, it is most convenient to zoom our perspective and consider the dynamics of consecutive triplets of bps, known as codon units in genomics.…”

Section: General Expressionsmentioning

confidence: 99%

Synchronized Oscillations in Double-Helix B-DNA Molecules with Mirror-Symmetric Codons

Maciá

2021

Symmetry

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A fully analytical treatment of the base-pair and codon dynamics in double-stranded DNA molecules is introduced, by means of a realistic treatment that considers different mass values for G, A, T, and C nucleotides and takes into account the intrinsic three-dimensional, helicoidal geometry of DNA in terms of a Hamitonian in cylindrical coordinates. Within the framework of the Peyrard–Dauxois–Bishop model, we consider the coupling between stretching and stacking radial oscillations as well as the twisting motion of each base pair around the helix axis. By comparing the linearized dynamical equations for the angular and radial variables corresponding to the bp local scale with those of the longer triplet codon scale, we report an underlying hierarchical symmetry. The existence of synchronized collective oscillations of the base-pairs and their related codon triplet units are disclosed from the study of their coupled dynamical equations. The possible biological role of these correlated, long-range oscillation effects in double standed DNA molecules containing mirror-symmetric codons of the form XXX, XX’X, X’XX’, YXY, and XYX is discussed in terms of the dynamical equations solutions and their related dispersion relations.

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Section: General Expressionsmentioning

confidence: 99%

Synchronized Oscillations in Double-Helix B-DNA Molecules with Mirror-Symmetric Codons

Maciá

2021

Symmetry

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“…In this case, the site label dependence involves all the

terms. The set of coupled Equations ( 19 ) and ( 21 ) describes the dynamics of general dsDNA molecules, where two kinds of bps can be arranged either periodically or aperiodically [ 21 , 46 , 47 , 48 , 49 ].…”

Section: Dynamical Equations Of Motionmentioning

confidence: 99%

Base-Pairs’ Correlated Oscillation Effects on the Charge Transfer in Double-Helix B-DNA Molecules

Maciá

2020

Materials

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By introducing a suitable renormalization process, the charge carrier and phonon dynamics of a double-stranded helical DNA molecule are expressed in terms of an effective Hamiltonian describing a linear chain, where the renormalized transfer integrals explicitly depend on the relative orientations of the Watson–Crick base pairs, and the renormalized on-site energies are related to the electronic parameters of consecutive base pairs along the helix axis, as well as to the low-frequency phonons’ dispersion relation. The existence of synchronized collective oscillations enhancing the π-π orbital overlapping among different base pairs is disclosed from the study of the obtained analytical dynamical equations. The role of these phonon-correlated, long-range oscillation effects on the charge transfer properties of double-stranded DNA homopolymers is discussed in terms of the resulting band structure.

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“…In TBI,

and

. Details and discussions of various aspects of the TBI wire model can be found elsewhere [ 5 , 33 , 34 , 35 , 36 , 37 ]. In TBImod,

and

.…”

Section: Tight-binding Wire Model Variantsmentioning

confidence: 99%

Hole Transfer in Open Carbynes

2020

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We investigate hole transfer in open carbynes, i.e., carbon atomic nanowires, using Real-Time Time-Dependent Density Functional Theory (RT-TDDFT). The nanowire is made of N carbon atoms. We use the functional B3LYP and the basis sets 3-21G, 6-31G*, cc-pVDZ, cc-pVTZ, cc-pVQZ. We also utilize a few Tight-Binding (TB) wire models, a very simple model with all sites equivalent and transfer integrals given by the Harrison ppπ expression (TBI) as well as a model with modified initial and final sites (TBImod) to take into account the presence of one or two or three hydrogen atoms at the edge sites. To achieve similar site occupations in cumulenes with those obtained by converged RT-TDDFT, TBImod is sufficient. However, to achieve similar frequency content of charge and dipole moment oscillations and similar coherent transfer rates, the TBImod transfer integrals have to be multiplied by a factor of four (TBImodt4times). An explanation for this is given. Full geometry optimization at the B3LYP/6-31G* level of theory shows that in cumulenes bond length alternation (BLA) is not strictly zero and is not constant, although it is symmetrical relative to the molecule center. BLA in cumulenic cases is much smaller than in polyynic cases, so, although not strictly, the separation to cumulenes and polyynes, approximately, holds. Vibrational analysis confirms that for N even all cumulenes with coplanar methylene end groups are stable, for N odd all cumulenes with perpendicular methylene end groups are stable, and the number of hydrogen atoms at the end groups is clearly seen in all cumulenic and polyynic cases. We calculate and discuss the Density Functional Theory (DFT) ground state energy of neutral molecules, the CDFT (Constrained DFT) “ground state energy” of molecules with a hole at one end group, energy spectra, density of states, energy gap, charge and dipole moment oscillations, mean over time probabilities to find the hole at each site, coherent transfer rates, and frequency content, in general. We also compare RT-TDDFT with TB results.

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Quasi-Periodic and Fractal Polymers: Energy Structure and Carrier Transfer

Cited by 12 publications

References 93 publications

Synchronized Oscillations in Double-Helix B-DNA Molecules with Mirror-Symmetric Codons

Synchronized Oscillations in Double-Helix B-DNA Molecules with Mirror-Symmetric Codons

Base-Pairs’ Correlated Oscillation Effects on the Charge Transfer in Double-Helix B-DNA Molecules

Hole Transfer in Open Carbynes

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