Stationary Polarons in Discrete Molecular Chains Dragan Toprek, [a] Zoran Ivic ´,* [b] Darko Kapor, [c] and Sreten Lekic ´ [d] Properties of the large acoustic polarons in discrete molecular chains have been investigated within the adiabatic approximation. It turns out that practically all the polaron features are determined by the single parameter-coupling constant which represents the ratio between the small polaron binding energy and the electron bandwidth. Three different types of stationary solutions were found corresponding to weak, intermediate, and strong coupling limits, respectively. In the weak coupling regime, that is, for the values of coupling constant exceeding the limit of the applicability of continuum approximation but lower than the critical one (g C ), we observe symmetric bond-centered solution corresponding to the polaron positioned in the middle between the adjacent lattice sites. When coupling constant overgrows, this critical value transition toward the site-centered state occurs. It takes place continuously through the intermediate asymmetric state whose position gradually approaches lattice site as coupling constant increases. One of the main consequences of the lat- tice discreteness is the emergence of the periodic potential, Peierls-Nabarro potential relief, through which polarons have to pass to transfer along the chain. The conditions for the po- laron propagation are formulated in terms of the threshold ve- locity. V C 2012 Wiley Periodicals, Inc. DOI: 10.1002/qua.24353 Introduction During the last 30 years, it has been widely speculated that the processes of the long-distance charge and energy transfer in quasi-one-dimensional (Q1D) substances, such as biological macromolecules (a–helix or DNA for example) [1–9] and organic linear-chain conductors (organic salts such as TTF-TCQN and conjugated polymers from the polyacetylene family), [10–14] may be facilitated by the large polaron mechanism. The basic idea behind the whole concept is that the energy losses of an excess quasiparticle (electron, hole, exciton, vibron,…) in the 1D media may be prevented by its (self)-trapping in the long- range potential well created by the induced local distortion of surrounding crystal lattice. So-formed complex object, the po- laron, may coherently propagate along the molecular chain in a soliton form with minimal energy dissipation preserving its shape and velocity for a long time. Such physical picture fully relies on the adiabatic theory and holds under the condition that system parameters fit into the adiabatic-strong coupling limit: that is, when electron band- width and so-called small polaron binding energy both highly exceed maximal phonon energy. [15,16] ‘ Adibaticity ’ provides that electron subsystem is fast as compared with lattice dynamics and enables theoretical treatment of phonons within the quasi- classical approximation. Strong coupling condition ensures po- laron stability y . Detailed analytical studies, [2,3,17] and recent, fully quantum-mechanical, numerical investigations [18,19] performed within the Holstein’s molecular crystal model, [20] had confirmed the validity of such an approach. Under these conditions, polaron dynamics may be described by the system of coupled difference-differential equations for the quasiparticle (electron, exciton,…) wave function and mo- lecular displacements. Their exact analytical solutions are still unknown. However, if the electron–phonon interaction is not too strong, polaron radius is large as compared to the lattice constant and its properties may be examined within the con- tinuum approximation. Thus, passing to continuum limit, assuming the travelling wave form of the solutions for the mo- lecular displacement, and keeping only the particular part, the aforementioned system of equations may be reduced to a nonlinear Schr€ odinger equation (NSE). [1,11,12,21,22,23] It is exactly integrable and possesses the well-known soliton solutions and the above physical picture immediately emerges. Such an idealized concept enables the analysis of the vari- ous aspects of polaron dynamics in the pretty restricted area of system parameter space as, on the increasing of the cou- pling strength, polaron radius gradually shrinks so that the continuum approximation becomes inapplicable. Despite of that, the validity of soliton concept is maintained even in the intrinsically discrete systems, however, discreteness may lead to completely new features in the static and dynamic proper- ties of polaron. In particular, the aforementioned system of [a] D. Toprek Laboratory for Nuclear and Plasma Physics–011, ‘Vincˇa’ Institute of Nuclear Sciences, University of Belgrade, P.O. BOX 522, 11001, Belgrade, Serbia [b] Z.Ivic´ Laboratory for Theoretical and Condensed Matter Physics–020, ‘Vincˇa’ Institute of Nuclear Sciences, University of Belgrade, P.O. BOX 522, 11001, Belgrade, Serbia E-mail: zivic@vinca.rs [c] D. Kapor Department of Physics, Faculty of Science, University of Novi Sad, Trg Dositeja Obradovic´a 4, 21000 Novi Sad, Serbia [d] S.Lekic´ Department of Physics, Faculty of Science, University of Banja Luka, Ulica Dr Mladena Stojanovic´a 2, 78 000 Banja Luka, Bosnia and Herzegovina Contract grant sponsor: Serbian Ministry of Education and Science; contract grant numbers: III–45010, OI–171009, OI–171023, OI–171018. V C 2012 Wiley Periodicals, Inc. y In the next section, these conditions will be formulated more precisely. 1522 International Journal of Quantum Chemistry 2013, 113, 1522–1533 WWW.CHEMISTRYVIEWS.ORG FULL PAPER WWW.Q-CHEM.ORG