Hemoglobin Bohr effects: atomic origin of the histidine residue contributions.

The Bohr effect in hemoglobin, which refers to the dependence of the oxygen affinity on the pH, plays an important role in its cooperativity and physiological function. The dominant contribution to the Bohr effect arises from the difference in the pKa values of His residues of the unliganded (deoxy) and liganded (carbonmonoxy) structures. Using recent high resolution structures, the residue pKa values corresponding to the two structures are calculated. The method is based on determining the electrostatic interactions between residues in the protein, relative to those of the residue in solution, by use of the linearized finite difference Poisson-Boltzmann equation and Monte Carlo sampling of protonation states. Given that good agreement is obtained with the available experimental values for the contribution of His residues in HbA to the Bohr effect, the calculated results are used to determine the atomic origin of the pKa shift between deoxy and carbonmonoxy HbA. The contributions to the pKa shift calculated by means of the linear response approximation show that the salt bridge involving His146 plays an important role in the alkaline Bohr effect, as suggested by Perutz but that other interactions are significant as well. A corresponding analysis is made for the contribution of His143 to the acid Bohr effect for which there is no proposed explanation. The method used is summarized and the program by which it is implemented is described in the Appendix .

Lagrangian formulation with dissipation of Born-Oppenheimer molecular dynamics using the density-functional tight-binding method.

An important element determining the time requirements of Born-Oppenheimer molecular dynamics (BOMD) is the convergence rate of the self-consistent solution of Roothaan equations (SCF). We show here that improved convergence and dynamics stability can be achieved by use of a Lagrangian formalism of BOMD with dissipation (DXL-BOMD). In the DXL-BOMD algorithm, an auxiliary electronic variable (e.g., the electron density or Fock matrix) is propagated and a dissipative force is added in the propagation to maintain the stability of the dynamics. Implementation of the approach in the self-consistent charge density functional tight-binding method makes possible simulations that are several hundred picoseconds in lengths, in contrast to earlier DFT-based BOMD calculations, which have been limited to tens of picoseconds or less. The increase in the simulation time results in a more meaningful evaluation of the DXL-BOMD method. A comparison is made of the number of iterations (and time) required for convergence of the SCF with DXL-BOMD and a standard method (starting with a zero charge guess for all atoms at each step), which gives accurate propagation with reasonable SCF convergence criteria. From tests using NVE simulations of C(2)F(4) and 20 neutral amino acid molecules in the gas phase, it is found that DXL-BOMD can improve SCF convergence by up to a factor of two over the standard method. Corresponding results are obtained in simulations of 32 water molecules in a periodic box. Linear response theory is used to analyze the relationship between the energy drift and the correlation of geometry propagation errors.

Extended Lagrangian Born-Oppenheimer molecular dynamics with dissipation.

Stability and dissipation in the propagation of the electronic degrees of freedom in time-reversible extended Lagrangian Born-Oppenheimer molecular dynamics [Niklasson et al., Phys. Rev. Lett. 97, 123001 (2006); Phys. Rev. Lett. 100, 123004 (2008)] are analyzed. Because of the time-reversible propagation the dynamics of the extended electronic degrees of freedom is lossless with no dissipation of numerical errors. For long simulation times under "noisy" conditions, numerical errors may therefore accumulate to large fluctuations. We solve this problem by including a dissipative external electronic force that removes noise while keeping the energy stable. The approach corresponds to a Langevin-like dynamics for the electronic degrees of freedom with internal numerical error fluctuations and external, approximately energy conserving, dissipative forces. By tuning the dissipation to balance the numerical fluctuations the external perturbation can be kept to a minimum.

Quantum chemical molecular dynamics study of "shrinking" of hot giant fullerenes.

We present a detailed analysis of size-down trajectories of the "Shrinking Hot Giant" road of fullerene formation, revealed before by our quantum chemical molecular dynamics simulations. It is found that shrinkage of giant fullerenes occurs in two stages, fall-off and pop-out stage, respectively, and that it is an irreversible process occurring naturally at high temperatures. The driving force behind the energetically unfavorable C2 evaporation is the increase in entropy and pi-conjugation stabilization of the increasingly more spherical fullerene cages. A comparison of the theoretical results with existing experimental data shows the importance of annealing for the synthesis of smaller (C60, C70) fullerenes.

The C60 formation puzzle "solved": QM/MD simulations reveal the shrinking hot giant road of the dynamic fullerene self-assembly mechanism.

The dynamic self-assembly mechanism of fullerene molecules is an irreversible process emerging naturally under the nonequilibrium conditions of hot carbon vapor and is a consequence of the interplay between the dynamics and chemistry of polyyne chains, pi-conjugation and corresponding stabilization, and the dynamics of hot giant fullerene cages. In this feature article we briefly present an overview of experimental findings and past attempts to explain fullerene formation and show in detail how our recent quantum chemical molecular dynamics simulations of the dynamics of carbon vapor far from thermodynamic equilibrium have assisted in the discovery of the combined size-up/size-down "shrinking hot giant" road that leads to the formation of buckminsterfullerene C60, C70, and larger fullerenes. This formation mechanism is the first reported case of order created out of chaos where a distinct covalent bond network of an entire molecule is spontaneously self-assembled to a highly symmetric structure and fully explains the fullerene formation process consistently with all available experimental observations a priori. Experimental evidence suggests that it applies universally to all fullerene formation processes irrespective of the carbon source.

Density functional study of the roles of chemical composition of di-transition-metal-substituted gamma-Keggin polyoxometalate anions.

The roles of chemical composition (X, M and M(FW)) of di-transition-metal-substituted gamma-Keggin polytungstates and polymolybdates, [(X(n)(+)O(4))M(2)(OH)(2)(M(FW))(10)O(32)]((8-n)-), on the geometry, electronic structure, and magnetic properties of these species have been investigated at the density functional level. It was shown that the change of the heteroatom X via Al(III)-Si(IV)-P(V)-S(VI) slightly stabilizes the broken-symmetry (BS) state over the high-spin (HS) state, increases the antiferromagnetic coupling constant, J, of these species, and lowers the energies of their highest-occupied molecular orbitals (HOMOs) and lowest-unoccupied molecular orbitals (LUMOs). The change of the redox-active center M from Mn to Fe slightly increases the M-(XO(4)) interaction, J-coupling constant, and energy gap between the HS and BS states. Meanwhile, the LUMOs are stabilized, indicating the stronger oxidant character of [(X(n)(+)O(4))M(2)(OH)(2)W(10)O(32)]((8-n)-) for M = Fe than Mn. It was shown that the change of addenda atom M(FW) from W to Mo makes (a) the geometry of Keggin "cage" slightly smaller, (b) the interaction of redox-active centers (Fe) with the central XO(4)-unit slightly stronger, and (c) the J-coupling constant, as well as the energy gap DeltaE(BS-HS), slightly larger.

Fe/C interactions during SWNT growth with C2 feedstock molecules: A quantum chemical molecular dynamics study.

We are presenting the first quantum chemical molecular dynamics (QM/MD) model simulations for iron catalyzed single-walled carbon nanotube (SWNT) growth based on the density functional tight binding (DFTB) quantum chemical potential. As model systems, open-ended (10,10) armchair tube fragments were selected with 0, 10, and 20 Fe atoms attached in 1,4-positions on the open rims, and ensembles of randomly oriented C2 molecules were included to simulate carbon plasma feedstock molecules. Isokinetic trajectories at 1500 K to 3000 K show that divalent Fe increases the number of coordination partners with carbon and/or Fe, depending on the Fe concentration. Fe/C interactions weaken the tube sidewall due to electron transfer from Fe into antibonding carbon orbitals, and C2 addition occurs mainly in an Fe-C2-Fe bridge addition mechanism, while growth of polyyne chains characteristic for high-temperature carbon systems is suppressed in the presence of Fe on the rims of the growing SWNT. Our findings are the first quantum chemical evidence for the importance of intermetallic interactions during SWNT growth.

Time-Dependent Density Functional Tight Binding: New Formulation and Benchmark of Excited States.

A new formulation of time-dependent density functional tight binding (TD-DFTB) is reported in this paper. It is derived from the application of the linear response theory to the ground state DFTB Hamiltonian, without the introduction of additional parameters for the description of the excited states. The method is validated for several sets of organic compounds, against the best theoretical estimates from the literature, density functional theory, semiempirical methods, and experimental data. The comparison shows that TD-DFTB gives reliable results both for singlet and triplet excitation energies. In addition, the application of TD-DFTB to open-shell systems shows promising results.

Parameter Calibration of Transition-Metal Elements for the Spin-Polarized Self-Consistent-Charge Density-Functional Tight-Binding (DFTB) Method: Sc, Ti, Fe, Co, and Ni.

Recently developed parameters for five first-row transition-metal elements (M = Sc, Ti, Fe, Co, and Ni) in combination with H, C, N, and O as well as the same metal (M-M) for the spin-polarized self-consistent-charge density-functional tight-binding (DFTB) method have been calibrated. To test their performance a couple sets of compounds have been selected to represent a variety of interactions and bonding schemes that occur frequently in transition-metal containing systems. The results show that the DFTB method with the present parameters in most cases reproduces structural properties very well, but the bond energies and the relative energies of different spin states only qualitatively compared to the B3LYP/SDD+6-31G(d) density functional (DFT) results. An application to the ONIOM(DFT:DFTB) indicates that DFTB works well as the low level method for the ONIOM calculation.

Origin of the linear relationship between CH2/NH/O-SWNT reaction energies and sidewall curvature: armchair nanotubes.

The origin of the linear relationship between the reaction energy of the CH2/NH/O exo and endo additions to armchair (n, n) single-walled carbon nanotubes (SWNTs) and the inverse tube diameter (1/d) measuring sidewall curvature was elucidated using density functional theory and density functional tight binding methods for finite-size SWNT models with n = 3, 4, ..., 13. A nearly perfect linear relationship between DeltaE and 1/d all through exohedral (positive curvature) and endohedral (negative curvature) additions is due to cancellation between the quadratic contributions of the SWNT deformation energy and the interaction energy (INT) between the deformed SWNT and CH2/NH/O adducts. Energy decomposition analysis shows that the quadratic contributions in electrostatic, exchange, and orbital terms mostly cancel each other, making INT weakly quadratic, and that the linear 1/d dependence of INT, and therefore of DeltaE, is a reflection of the 1/d dependence of the back-donative orbital interaction of b1 symmetry from the occupied CH2/NH/O p pi orbital to the vacant C=C pi* LUMO of the SWNT. We also discuss the origin of the two isomers (open and three-membered ring) of the exohedral addition product and explain the behavior of their associated minima on the C-C potential energy surfaces with changing d.

Theory and experiment agree: single-walled carbon nanotube caps grow catalyst-free with chirality preference on a SiC surface.

High-temperature quantum chemical molecular dynamics simulations have been performed on model systems of thin SiC crystal surfaces with two graphene sheets placed on top of either C or Si face. In agreement with experiment, we find that (a) the C-face-attached graphene layer warps readily to form small diameter, stable nanocaps, suitable for further perpendicular growth of nanotubes, (b) the Si-face-attached graphene sheet does not readily wrap and forms more volatile Si-graphene bonds, and (c) C face nanocaps appear to anneal to dome-shape structures with zigzag chirality.

Modeling carbon nanostructures with the self-consistent charge density-functional tight-binding method: vibrational spectra and electronic structure of C(28), C(60), and C(70).

The self-consistent charge density-functional tight-binding (SCC-DFTB) method is employed for studying various molecular properties of small fullerenes: C(28), C(60), and C(70). The computed bond distances, vibrational infrared and Raman spectra, vibrational densities of states, and electronic densities of states are compared with experiment (where available) and density-functional theory (DFT) calculations using various basis sets. The presented DFT benchmark calculations using the correlation-consistent polarized valence triple zeta basis set are at present the most extensive calculations on harmonic frequencies of these species. Possible limitations of the SCC-DFTB method for the prediction of molecular vibrational and optical properties are discussed. The presented results suggest that SCC-DFTB is a computationally feasible and reliable method for predicting vibrational and electronic properties of such carbon nanostructures comparable in accuracy with small to medium size basis set DFT calculations at the computational cost of standard semiempirical methods.

Towards formation of buckminsterfullerene C60 in quantum chemical molecular dynamics.

We present follow-up studies on the formation mechanism of fullerene molecules from random ensembles of C2 molecules using quantum chemical molecular dynamics. Two possible roadmaps are investigated as to how buckminsterfullerene C60 and higher fullerenes could be formed. In a "size-up" scenario, fullerenes of the cage size of C72-C96 were found to form directly from high concentrations of C2 molecules at 2000 K with periodic supply of batches of additional C2's. In a "size-down" approach, smaller fullerenes are sometimes formed by losing carbon fragments in "fall-off" or "pop-out" annealing processes under prolonged heating of giant fullerenes, which were self-assembled at initial stages from C2's with lower concentrations. Both roadmaps are found to provide explanations for the appearance of C60 and larger fullerenes in combustion and carbon arc experiments.