We have theoretically investigated the intrinsic carrier mobility in semimetals with tilted Dirac cones under both longitudinal and transverse acoustic phonon scattering. An analytical formula for the carrier mobility was obtained. It shows that tilting significantly reduces the mobility. The theory was then applied to 8B-Pmmn borophene and borophane (fully hydrogenated borophene), both of which have tilted Dirac cones. The predicted carrier mobilities in 8B-Pmmn borophene at room temperature are 14.8 × 105 and 28.4 × 105 cm2 V−1 s−1 along the x and y directions, respectively, both of which are higher than that in graphene. For borophane, despite its superhigh Fermi velocity, the carrier mobility is lower than that in 8B-Pmmn owing to its smaller elastic constant under shear strain.

To extract protein dimension and energetics information from single-molecule fluorescence resonance energy transfer spectroscopy (smFRET) data, it is essential to establish the relationship between the distributions of the radius of gyration (Rg) and the end-to-end (donor-to-acceptor) distance (Ree). Here, we performed a coarse-grained molecular dynamics simulation to obtain a conformational ensemble of denatured proteins and intrinsically disordered proteins. For any disordered chain with fixed length, there is an excellent linear correlation between the average values of Rg and Ree under various solvent conditions, but the relationship deviates from the prediction of a Gaussian chain. A modified conversion formula was proposed to analyze smFRET data. The formula reduces the discrepancy between the results obtained from FRET and small-angle X-ray scattering (SAXS). The scaling law in a coil–globule transition process was examined where a significant finite-size effect was revealed, i.e., the scaling exponent may exceed the theoretical critical boundary [1/3, 3/5] and the prefactor changes notably during the transition. The Sanchez chain model was also tested and it was shown that the mean-field approximation works well for expanded chains.

We systematically studied the Raman spectra of graphyne (GY) and graphdiyne (GDY), analyzing their features under mechanical strain by group theory and first-principles calculations. The G bands in GY and GDY were softened compared with that in graphene, which provides a fingerprint useful in detecting their synthesis. We established a unified formulation to describe the effects of both uniaxial and shear strains, and combined this with calculated results to reveal the relationship underlying the changes in Raman evolution under various strains. Each doubly degenerate mode splits into two branches under strain, both of which are red-shifted with tensile uniaxial strain, but one is red-shifted and the other is blue-shifted under shear strain. The splitting under shear strain is double that under uniaxial strain.

Two-dimensional (2D) materials composed of sp and sp2 carbon atoms (e.g., graphyne and graphdiyne) show many interesting properties. These materials can be constructed through alkyne homocoupling; however, the occurrence of various side reactions increases the difficulty of their synthesis and structural characterization. Here, we investigate the thermodynamic properties and vibrational spectra of several aryl-alkynes. Both homocoupling and side reactions are found to occur spontaneously at room temperature in terms of thermodynamics. The calculated Raman spectra of the homocoupling products show regular changes with increasing polymerization degree. By rationalizing the vibrational modes of various oligomers, the Raman spectrum of a 2D sp–sp2 carbon sheet is predicted; it exhibits three sharp peaks at 2241, 1560, and 1444 cm−1. Although the target and byproducts display similar vibrational modes, a combination of Raman and infrared spectroscopies can be used to differentiate them. The theoretical results are then used to analyze the structure of a synthesized sample and provide useful information.

The influence of lattice symmetry on the existence of Dirac cones was investigated for two distinct systems: a general two-dimensional (2D) atomic crystal containing two atoms in each unit cell and a 2D electron gas (2DEG) under a periodic muffin-tin potential. A criterion was derived under a tight-binding approximation for the existence of Dirac cones in the atomic crystal. When the transfer hoppings are assumed to be single functions of the distance between atoms, it was shown that the probability of observing Dirac cones in the atomic crystal gradually decreases before being reduced to zero when the lattice changes from hexagonal to square. For a 2DEG with full square symmetry, a Dirac point exists at the Brillouin zone corners, where the energy dispersion is parabolic not linear. These results suggest that conventional Dirac fermions (such as those in graphene) are difficult to achieve in a square lattice with full symmetry (wallpaper group p4mm).

Various graphene quantum dots (GQDs) embedded in a hexagonal BN sheet were studied theoretically using the tight binding model. The effective mass was analyzed as a function of the distance between neighboring GQDs. It was found that the effective mass increases exponentially as the distance increases, indicating that the confined states of GQDs are well conserved in these hybrid systems. Further studies revealed that a ubiquitous gap of 0.3–3 eV exists, the size of which is mainly governed by the GQD's dimensions whereas it is insensitive to edge structures. These results show that GQDs in BN are promising candidates for optoelectronics.

Density functional theory (DFT) studies were performed to investigate the chlorination of graphene. Unlike hydrogenation and fluorination, where the adsorption of H and F is always by covalent C–H/C–F bonding, Cl atoms generate various states when single-sided graphene exposed. In the initial reaction stage, it forms Cl–graphene charge-transfer complex, where the C orbitals keep sp2 hybridization and the graphene is p-type doped. Further chlorination may form two adsorption configurations: one is covalent bonding Cl pairs, where the structure of the C atom is close to sp3 hybridization. With the Cl coverage increases, this configuration may further cluster into hexagonal rings, and the resulting coverage is less than 25%. The other configuration is nonbonding. This configuration is energy preferable, while Cl atoms will form Cl2 molecules and escaped. When both sides of the graphene are exposed, the most stable adsorption configuration is a homogeneous ordered pattern with a Cl coverage of 25% (C4Cl) rather than collective clusters. The electronic properties of various chlorinated forms were also obtained; these showed that it is possible to tune the graphene bandgap by chlorination in a range of 0–1.3 eV.

The electronic structures of BN-embedded graphene (BNG) were theoretically studied. A nonzero gap was found to exist in BNG regardless of the edge structures (zigzag/armchair) and the symmetries of the superlattice and BN quantum dots (QDs). The size of the gap is mainly determined by the width of the carbon wall between neighboring BN QDs. It is insensitive to the size of BN QDs, and thus obeys a universal scaling law. This significant and stable energy gap renders BNG as a promising way to control the electronic properties of graphene. The comparison with graphene antidot lattices and nanoribbons was also provided.

The electronic structure of graphene antidot lattices (GALs) with zigzag hole edges was studied with first-principles calculations. It was revealed that half of the possible GAL patterns were unintentionally missed in the usual construction models used in earlier studies. With the complete models, the bandgap of the GALs was sensitive to the width W of the wall between the neighboring holes. A nonzero bandgap was opened in hexagonal GALs with even W, while the bandgap remained closed in those with odd W. Similar alternating gap opening/closing with W was also demonstrated in rhombohedral GALs. Moreover, analytical solutions of single-walled GALs were derived based on a tight-binding model to determine the location of the Dirac points and the energy dispersion, which confirmed the unique effect in GALs.Keywords: antidot lattices; bandgap; electronic structure; first-principles calculations; graphene; tight-binding model

The mathematical basis of the hypothesis that type-2 topoisomerases recognize and act at specific DNA juxtapositions has been investigated by coarse-grained lattice polymer models, showing that selective segment passages at hooked juxtapositions can result in dramatic reductions in catenane and knot populations. The lattice modeling approach is here extended to account for the narrowing of variance of linking number (Lk) of DNA circles by type-2 topoisomerases. In general, the steady-state variance of Lk resulting from selective segment passages at a specific juxtaposition geometry j is inversely proportional to the average linking number, 〈Lk〉j, of circles with the given juxtaposition. Based on this formulation, we demonstrate that selective segment passages at hooked juxtapositions reduce the variance of Lk. The dependence of this effect on model DNA circle size is remarkably similar to that observed experimentally for type-2 topoisomerases, which appear to be less capable in narrowing Lk variance for small DNA circles than for larger DNA circles. This behavior is rationalized by a substantial cancellation of writhe in small circles with hook-like juxtapositions. During our simulations, we uncovered a twisted variation of the hooked juxtaposition that has an even more dramatic effect on Lk variance narrowing than the hooked juxtaposition. For an extended set of juxtapositions, we detected a significant correlation between the Lk narrowing potential and the logarithmic decatenating and unknotting potentials for a given juxtaposition, a trend reminiscent of scaling relations observed with experimental measurements on type-2 topoisomerases from a variety of organisms. The consistent agreement between theory and experiment argues for type-2 topoisomerase action at hooked or twisted–hooked DNA juxtapositions.

Intrinsically disordered proteins do not have stable secondary and/or tertiary structures but still function. More than 50 prediction methods have been developed and inherent relationships may be expected to exist among them. To investigate this, we conducted molecular simulations and algorithmic analyses on a minimal coarse-grained polypeptide model and discovered a common basis for the charge-hydropathy plot and packing-density algorithms that was verified by correlation analysis. The correlation analysis approach was applied to realistic datasets, which revealed correlations among some physical-chemical properties (charge-hydropathy plot, packing density, pairwise energy). The correlations indicated that these biophysical methods find a projected direction to discriminate ordered and disordered proteins. The optimized projection was determined and the ultimate accuracy limit of the existing algorithms is discussed.

βαβ structural motifs are commonly used building blocks in protein structures containing parallel β-sheets. However, to our knowledge, no stand-alone βαβ structure has been observed in nature to date. Recently, for the first time that we know of, a small protein with an independent βαβ structure (DS119) was successfully designed in our laboratory. To understand the folding mechanism of DS119, in the study described here, we carried out all-atom molecular dynamics and coarse-grained simulations to investigate its folding pathways and energy landscape. From all-atom simulations, we successfully observed the folding event and got a stable folded structure with a minimal root mean-square deviation of 2.6 Å with respect to the NMR structure. The folding process can be described as a fast collapse phase followed by rapid formation of the central helix, and then slow formation of a parallel β-sheet. By using a native-centric Gō-like model, the cooperativity of the system was characterized in terms of the calorimetric criterion, sigmoidal transitions, conformation distribution shifts, and free-energy profiles. DS119 was found to be an incipient downhill folder that folds more cooperatively than a downhill folder, but less cooperatively than a two-state folder. This may reflect the balance between the two structural elements of DS119: the rapidly formed α-helix and the slowly formed parallel β-sheet. Folding times estimated from both the all-atom simulations and the coarse-grained model were at microsecond level, making DS119 another fast folder. Compared to fast folders reported previously, DS119 is, to the best of our knowledge, the first that exhibits a parallel β-sheet.

Intrinsically disordered proteins (IDPs) are recognized to play important roles in many biological functions such as transcription and translation regulation, cellular signal transduction, protein phosphorylation, and molecular assemblies. The coupling of folding with binding through a “fly-casting” mechanism has been proposed to account for the fast binding kinetics of IDPs. In this article, experimental data from the literature were collated to verify the kinetic advantages of IDPs, while molecular simulations were performed to clarify the origin of the kinetic advantages. The phosphorylated KID–kinase-inducible domain interacting domain (KIX) complex was used as an example in the simulations. By modifying a coarse-grained model with a native-centric Gō-like potential, we were able to continuously tune the degree of disorder of the phosphorylated KID domain and thus investigate the intrinsic role of chain flexibility in binding kinetics. The simulations show that the “fly-casting” effect is not only due to the greater capture radii of IDPs. The coupling of folding with binding of IDPs leads to a significant reduction in binding free-energy barrier. Such a reduction accelerates the binding process. Although the greater capture radius has been regarded as the main factor in promoting the binding rate of IDPs, we found that this parameter will also lead to the slower translational diffusion of IDPs when compared with ordered proteins. As a result, the capture rate of IDPs was found to be slower than that of ordered proteins. The main origin of the faster binding for IDPs are the fewer encounter times required before the formation of the final binding complex. The roles of the interchain native contacts fraction (Qb) and the mass–center distance (ΔR) as reaction coordinates are also discussed.

The influence of lattice symmetry on the existence of Dirac cones was investigated for two distinct systems: a general two-dimensional (2D) atomic crystal containing two atoms in each unit cell and a 2D electron gas (2DEG) under a periodic muffin-tin potential. A criterion was derived under a tight-binding approximation for the existence of Dirac cones in the atomic crystal. When the transfer hoppings are assumed to be single functions of the distance between atoms, it was shown that the probability of observing Dirac cones in the atomic crystal gradually decreases before being reduced to zero when the lattice changes from hexagonal to square. For a 2DEG with full square symmetry, a Dirac point exists at the Brillouin zone corners, where the energy dispersion is parabolic not linear. These results suggest that conventional Dirac fermions (such as those in graphene) are difficult to achieve in a square lattice with full symmetry (wallpaper group p4mm).

Various graphene quantum dots (GQDs) embedded in a hexagonal BN sheet were studied theoretically using the tight binding model. The effective mass was analyzed as a function of the distance between neighboring GQDs. It was found that the effective mass increases exponentially as the distance increases, indicating that the confined states of GQDs are well conserved in these hybrid systems. Further studies revealed that a ubiquitous gap of 0.3–3 eV exists, the size of which is mainly governed by the GQD's dimensions whereas it is insensitive to edge structures. These results show that GQDs in BN are promising candidates for optoelectronics.

Two-dimensional (2D) materials composed of sp and sp2 carbon atoms (e.g., graphyne and graphdiyne) show many interesting properties. These materials can be constructed through alkyne homocoupling; however, the occurrence of various side reactions increases the difficulty of their synthesis and structural characterization. Here, we investigate the thermodynamic properties and vibrational spectra of several aryl-alkynes. Both homocoupling and side reactions are found to occur spontaneously at room temperature in terms of thermodynamics. The calculated Raman spectra of the homocoupling products show regular changes with increasing polymerization degree. By rationalizing the vibrational modes of various oligomers, the Raman spectrum of a 2D sp–sp2 carbon sheet is predicted; it exhibits three sharp peaks at 2241, 1560, and 1444 cm−1. Although the target and byproducts display similar vibrational modes, a combination of Raman and infrared spectroscopies can be used to differentiate them. The theoretical results are then used to analyze the structure of a synthesized sample and provide useful information.