Limulus polyphemus hemocyanin: 10 A cryo-EM structure, sequence analysis, molecular modelling and rigid-body fitting reveal the interfaces between the eight hexamers.

The blue copper protein hemocyanin from the horseshoe crab Limulus polyphemus is among the largest respiratory proteins found in nature (3.5 MDa) and exhibits a highly cooperative oxygen binding. Its 48 subunits are arranged as eight hexamers (1x6mers) that form the native 8x6mer in a nested hierarchy of 2x6mers and 4x6mers. This quaternary structure is established by eight subunit types (termed I, IIA, II, IIIA, IIIB, IV, V, and VI), of which only type II has been sequenced. Crystal structures of the 1x6mer are available, but for the 8x6mer only a 40 A 3D reconstruction exists. Consequently, the structural parameters of the 8x6mer are not firmly established, and the molecular interfaces between the eight hexamers are still to be defined. This, however, is crucial for understanding how allosteric transitions are mediated between the different levels of hierarchy. Here, we show the 10 A structure (FSC(1/2-bit) criterion) of the oxygenated 8x6mer from cryo-electron microscopy (cryo-EM) and single-particle analysis. Moreover, we show its molecular model as obtained by DNA sequencing of subunits II, IIIA, IV and VI, and molecular modelling and rigid-body fitting of all subunit types. Remarkably, the latter enabled us to improve the resolution of the cryo-EM structure from 11 A to the final 10 A. The 10 A structure allows firm assessment of various structural parameters of the 8x6mer, the 4x6mer and the 2x6mer, and reveals a total of 46 inter-hexamer bridges. These group as 11 types of interface: four at the 2x6mer level (II-II, II-IV, V-VI, IV-VI), three form the 4x6mer (V-V, V-VI, VI-IIIB/IV/V), and four are required to assemble the 8x6mer (IIIA-IIIA, IIIA-IIIB, II-IV, IV-IV). The molecular model shows the amino acid residues involved, and reveals that several of the interfaces are intriguingly histidine-rich and likely to transfer allosteric signals between the different levels of the nested hierarchy.

Importance of short-range versus long-range Hartree-Fock exchange for the performance of hybrid density functionals.

We consider a general class of hybrid density functionals with decomposition of the exchange component into short-range and long-range parts. The admixture of Hartree-Fock (HF) exchange is controlled by three parameters: short-range mixing, long-range mixing, and range separation. We study how the variation of these parameters affects the accuracy of hybrid functionals for thermochemistry and kinetics. For the density functional component of the hybrids, we test three nonempirical approximations: local spin-density approximation, generalized gradient approximation (GGA), and meta-GGA. We find a great degree of flexibility in choosing the mixing parameters in range-separated hybrids. For the studied properties, short-range and long-range HF exchange seem to have a similar effect on the errors. One may choose to treat the long-range portion of the exchange by HF to recover the correct asymptotic behavior of the exchange potential and improve the description of density tail regions. If this asymptote is not important, as in solids, one may use screened hybrids, where long-range HF exchange is excluded. Screened hybrids retain most of the benefits of global hybrids but significantly reduce the computational cost in extended systems.

Energy band gaps and lattice parameters evaluated with the Heyd-Scuseria-Ernzerhof screened hybrid functional.

This work assesses the Heyd-Scuseria-Ernzerhof (HSE) screened Coulomb hybrid density functional for the prediction of lattice constants and band gaps using a set of 40 simple and binary semiconductors. An extensive analysis of both basis set and relativistic effects is given. Results are compared with established pure density functionals. For lattice constants, HSE outperforms local spin-density approximation (LSDA) with a mean absolute error (MAE) of 0.037 A for HSE vs 0.047 A for LSDA. For this specific test set, all pure functionals tested produce MAEs for band gaps of 1.0-1.3 eV, consistent with the very well-known fact that pure functionals severely underestimate this property. On the other hand, HSE yields a MAE smaller than 0.3 eV. Importantly, HSE correctly predicts semiconducting behavior in systems where pure functionals erroneously predict a metal, such as, for instance, Ge. The short-range nature of the exchange integrals involved in HSE calculations makes their computation notably faster than regular hybrid functionals. The current results, paired with earlier work, suggest that HSE is a fast and accurate alternative to established density functionals, especially for solid state calculations.

Density functional theory study of optical transitions in semiconducting single-walled carbon nanotubes.

We present a density functional theory study of optical transitions in semiconducting single-walled carbon nanotubes. We utilize recently developed exchange-correlation functionals in a set of 21 tubes that includes large and chiral nanotubes. The novel TPSSh meta-generalized gradient approximation hybrid functional accurately reproduces optical excitations with mean absolute errors of 0.024 and 0.065 eV for first and second transitions, respectively. We also report predictions for higher order optical transitions.

Assessment and validation of a screened Coulomb hybrid density functional.

This paper presents a revised and improved version of the Heyd-Scuseria-Ernzerhof screened Coulomb hybrid functional. The performance of this functional is assessed on a variety of molecules for the prediction of enthalpies of formation, geometries, and vibrational frequencies, yielding results as good as or better than the successful PBE0 hybrid functional. Results for ionization potentials and electron affinities are of slightly lower quality but are still acceptable. The comprehensive test results presented here validate our assumption that the screened, short-range Hartree-Fock (HF) exchange exhibits all physically relevant properties of the full HF exchange. Thus, hybrids can be constructed which neglect the computationally demanding long-range part of HF exchange while still retaining the superior accuracy of hybrid functionals, compared to pure density functionals.

Efficient hybrid density functional calculations in solids: assessment of the Heyd-Scuseria-Ernzerhof screened Coulomb hybrid functional.

The present work introduces an efficient screening technique to take advantage of the fast spatial decay of the short range Hartree-Fock (HF) exchange used in the Heyd-Scuseria-Ernzerhof (HSE) screened Coulomb hybrid density functional. The screened HF exchange decay properties and screening efficiency are compared with traditional hybrid functional calculations on solids. The HSE functional is then assessed using 21 metallic, semiconducting, and insulating solids. The examined properties include lattice constants, bulk moduli, and band gaps. The results obtained with HSE exhibit significantly smaller errors than pure density functional theory (DFT) calculations. For structural properties, the errors produced by HSE are up to 50% smaller than the errors of the local density approximation, PBE, and TPSS functionals used for comparison. When predicting band gaps of semiconductors, we found smaller errors with HSE, resulting in a mean absolute error of 0.2 eV (1.3 eV error for all pure DFT functionals). In addition, we present timing results which show the computational time requirements of HSE to be only a factor of 2-4 higher than pure DFT functionals. These results make HSE an attractive choice for calculations of all types of solids.

Interaction of atomic hydrogen with single-walled carbon nanotubes: a density functional theory study.

We have studied the interaction of atomic hydrogen with (5,5) and (10,0) single-walled carbon nanotubes (SWNT) using density functional theory. These calculations use Gaussian orbitals and periodic boundary conditions. We compare results from the local spin density approximation, generalized gradient approximation (GGA), and hybrid density functionals. We have first kept the SWNT geometric structure fixed while a single H atom approaches the tube on top of a carbon atom. In that case, a weakly bound state with binding energies from -0.8 to -0.4 eV was found. Full geometry relaxation leads to a strong SWNT deformation, weakening the nearest C-C bonds and increasing the binding energy by about 1 eV. Full hydrogen coverage of the (5,5) SWNT converts this metallic nanotube into an insulator with a band gap of 3.4 eV for the GGA functional and 4.8 eV for the hybrid functional. Hybrid functionals perform similar to pure density functional theory functionals for the calculation of binding energies while band gaps critically depend on the functional choice.