It is proved analytically that a one-dimensional half-filled polymer chain is subject to two coupled spontaneous conformational relaxations, the well-known Peierls bond length alternation and a uniform bond contraction. These two coupled relaxations work cooperatively against the lattice elastic energy penalty so that all bonds alternate and contract less than the case when these two relaxations are independent. When the fully relaxed neutral chain is taken as reference, creating self-localized charge carriers upon doping results in spontaneous bond contraction within the self-localized domain where the undimerization is enforced. Numeric results based on the Su-Schrieffer-Heeger and extended Peierls-Hubbard models and ab initio calculations resolve a long-lasting puzzle observed by x-ray scatterings concerning of the initial zero slope and accompanied sharp knee in the strain response of trans-polyacetylene to the Na + dopant concentration. The demonstrated doping-induced polymer chain length variation mechanism has implications for ultrafast artificial muscle designs.A one-dimensional ͑1D͒ equally spaced metallic polymer chain of one electron per ionic site is unstable with respect to the spontaneous relaxation via optical phonons with the double Fermi wave vector, resulting in a dimerized insulating polymer chain. This is the Peierls instability, originally derived using the free-electron energy dispersion relation. 1 A more rigorous proof was given by Kennedy and Lieb 2 stating that such a dimerization is exact without additional symmetry breakdown, at least for the Su-Schrieffer-Heeger ͑SSH͒ type of Hamiltonians 3 in which the nearest-neighbor electron hopping integrals vary linearly with the distance. This work points to the existence of a ubiquitously coupled twin of the Peierls distortion, with validations from previously unresolved puzzling x-ray scattering data on Na + doped trans-polyacetylene. [4][5][6][7][8][9] Without loss of generality, 10 we follow Kennedy and Lieb 2 to focus on the SSH Hamiltonian. It is well recognized that the SSH Hamiltonian is subject to a spontaneous contraction. Explicitly, Su proposed a constant tension of 4␣ / to compensate such a undesired global contraction. 11 Later, Stafstrom and Chao 12 suggested a 2% correction to Su's term and attributed such a difference to the discrete energy spectrum of using a finite system. Vos et al. expressed the contraction as a function of the electron-phonon coupling coefficient for the perfectly dimerized case and obtained the sound speeds of acoustic and optical modes. 13 Nevertheless, we note that the chain length variation in the above mentioned arguments is independent of the polymer charge state; namely, if the neutral dimerized chain is taken as reference, no further chain length variations would be expected upon charge injections. In addition, Bishop et al. 14 observed local contractions at the soliton center via adiabatic exciton dynamics and attributed such local contractions to the coupling between moving solitons and acoustic ...

A generic history-penalized metabasin escape algorithm that contains no predetermined parameters is presented in this work. The spatial location and volume of imposed penalty functions in the configurational space are determined in self-learning processes as the 3N-dimensional potential energy surface is sampled. The computational efficiency is demonstrated using a binary Lennard-Jones liquid supercooled below the glass transition temperature, which shows an O(10(3)) reduction in the quadratic scaling coefficient of the overall computational cost as compared to the previous algorithm implementation. Furthermore, the metabasin sizes of supercooled liquids are obtained as a natural consequence of determining the self-learned penalty function width distributions. In the case of a bulk binary Lennard-Jones liquid at a fixed density of 1.2, typical metabasins are found to contain about 148 particles while having a correlation length of 3.09 when the system temperature drops below the glass transition temperature.

A generic class of Hamiltonians based on the Su-Schrieffer-Heeger ͑SSH͒ model is introduced to address the material-specific properties of conducting polymers beyond polyacetylene. Two physical parameters are incorporated into the original SSH model Hamiltonian, one being the scaling parameter ␥ accounts for the modified electron-phonon coupling strength of aromatic rings and the other parameter representing the attractive cores of heterogeneous atoms, such as NH, S, and O. Their values are uniquely determined by two independent measurements, such as the experimental band gap of bulk polypyrrole ͑PPy͒ and the dimerization amplitude of pyrrole monomer computed by ab initio coupled cluster methods as chosen in this work. With the optimized values of ͕␥ = 1.46, = 4.27 eV͖, the adapted SSH ͑aSSH͒ Hamiltonian accurately reproduces the band gaps, molecular geometries, quasiparticle energies and wave functions, order parameters, discretized phonons around nonlinear polarons, and infrared and Raman spectra of both neutral and p-doped PPy chains of all lengths. It is expected that the generic formalism of the aSSH Hamiltonian, equipped with their corresponding ͕␥ , ͖ values, would be applicable to other conducting polymers, such as polythiophene, polyfuran, poly-͑p-phenylene-vinylene͒, polyaniline, and their functional derivatives.

Dimensionality reduction methods have been widely used to study the free energy landscapes and low-free energy pathways of molecular systems. It was shown that the non-linear dimensionality-reduction methods gave better embedding results than the linear methods, such as principal component analysis, in some simple systems. In this study, we have evaluated several non linear methods, locally linear embedding, Isomap, and diffusion maps, as well as principal component analysis from the equilibrium folding/unfolding trajectory of the second β–hairpin of the B1 domain of streptococcal protein G. The CHARMM parm19 polar hydrogen potential function was used. A series of criteria which reflects different aspects of the embedding qualities were employed in the evaluation. Our results show that principal component analysis is not worse than the non-linear ones on this complex system. There is no clear winner in all aspects of the evaluation. Each dimensionality-reduction method has its limitations in a certain aspect. We emphasize that a fair, informative assessment of an embedding result requires a combination of multiple evaluation criteria rather than any single one. Caution should be used when dimensionality-reduction methods are employed, especially when only a few of top embedding dimensions are used to describe the free energy landscape.

Two transferable physical parameters are incorporated into the Su-Schrieffer-Heeger Hamiltonian to model conducting polymers beyond polyacetylene: the parameter γ scales the electron-phonon coupling strength in aromatic rings and the other parameter ε specifies the heterogeneous core charges. This generic Hamiltonian predicts the fundamental band gaps of polythiophene, polypyrrole, polyfuran, poly-(p-phenylene), poly-(p-phenylene vinylene), and polyacenes, and their oligomers of all lengths, with an accuracy exceeding time-dependent density functional theory. Its computational costs for moderate-length polymer chains are more than eight orders of magnitude lower than first-principles approaches.