Self-consistent Mean-field Theory Research Articles

Side-chain conformational space analysis (SCSA): A multi conformation-based QSAR approach for modeling and prediction of protein–peptide binding affinities

In this article, the concept of multi conformation-based quantitative structure-activity relationship (MCB-QSAR) is proposed, and based upon that, we describe a new approach called the side-chain conformational space analysis (SCSA) to model and predict protein-peptide binding affinities. In SCSA, multi-conformations (rather than traditional single-conformation) have received much attention, and the statistical average information on multi-conformations of side chains is determined using self-consistent mean field theory based upon side chain rotamer library. Thereby, enthalpy contributions (including electrostatic, steric, hydrophobic interaction and hydrogen bond) and conformational entropy effects to the binding are investigated in terms of occurrence probability of residue rotamers. Then, SCSA was applied into the dataset of 419 HLA-A 0201 binding peptides, and nonbonding contributions of each position in peptide ligands are well determined. For the peptides, the hydrogen bond and electrostatic interactions of the two ends are essential to the binding specificity, van der Waals and hydrophobic interactions of all the positions ensure strong binding affinity, and the loss of conformational entropy at anchor positions partially counteracts other favorable nonbonding effects.

Screening of Magnetic Moments in PuAm Alloy: Local Density Approximation and Dynamical Mean Field Theory Study

The puzzling absence of Pu magnetic moments in a PuAm environment is explored using the self-consistent dynamical mean field theory calculations in combination with the local density approximation. We argue that delta-Pu-Am alloys provide an ideal testbed for investigating the screening of moments from the single impurity limit to the dense limit. Several important effects can be studied: volume expansion, shift of the bare Pu on-site f energy level, and the reduction of the hybridization cloud resulting from the collective character of the Kondo effect in the Anderson lattice. These effects compensate each other and result in a coherence scale, which is independent of alloy composition, and is around 800 K.

Kπ=8−isomers andKπ=2−octupole vibrations inN=150shell-stabilized isotones

Isomers have been populated in {sup 246}Cm and {sup 252}No with quantum numbers K{sup {pi}}=8{sup -}, which decay through K{sup {pi}}=2{sup -} rotational bands built on octupole vibrational states. For N=150 isotones with (even) atomic number Z=94-102, the K{sup {pi}}=8{sup -} and 2{sup -} states have remarkably stable energies, indicating neutron excitations. An exception is a singular minimum in the 2{sup -} energy at Z=98, due to the additional role of proton configurations. The nearly constant energies, in isotones spanning an 18% increase in Coulomb energy near the Coulomb limit, provide a test for theory. The two-quasiparticle K{sup {pi}}=8{sup -} energies are described with single-particle energies given by the Woods-Saxon potential and the K{sup {pi}}=2{sup -} vibrational energies by quasiparticle random-phase approximation calculations. Ramifications for self-consistent mean-field theory are discussed.

Phase Behavior of Gradient Copolymers

A multiblock model is developed for the study of the phase behavior of gradient copolymers. The model is able to describe gradient copolymer chains with arbitrary composition profiles. The validity of the multiblock model of gradient copolymers is established by good agreement between RPA (random phase approximation) results for a continuous composition distribution and a multiblock model. The phase behavior of gradient copolymers is examined using self-consistent mean-field theory (SCMFT) for multiblock copolymers. Phase diagrams of gradient copolymer melts with different gradient profiles are constructed by solving the SCMFT equations. It is discovered that the phase behavior depends sensitively on the gradient profiles. In particular, new triple points are observed, and the stability region of phases with curved interfaces shrinks as the gradient profile becomes smooth. For linear gradient copolymers, the lamellar phase is predicted to be the only stable ordered phase.

Effective shell model Hamiltonians from density functional theory: Quadrupolar and pairing correlations

We describe a procedure for mapping a self-consistent mean-field theory (also known as density functional theory) onto a shell-model Hamiltonian that includes quadrupole-quadrupole and monopole pairing interactions in a truncated space. We test our method in the deformed $N=Z \mathit{sd}$-shell nuclei $^{20}\mathrm{Ne}$, $^{24}\mathrm{Mg}$, and $^{36}\mathrm{Ar}$, starting from the Hartree-Fock plus Bardeen-Cooper-Schrieffer (BCS) approximation of the universal $\mathit{sd}$ shell-model interaction. A similar method is then followed using the SLy4 Skyrme energy density functional in the particle-hole channel plus a zero-range density-dependent force in the pairing channel. Based on the ground-state solution of this density functional theory at the Hartree-Fock plus BCS level, an effective shell-model Hamiltonian is constructed. We apply this mapped Hamiltonian to extract quadrupolar and pairing correlation energies beyond the mean-field approximation. The rescaling of the mass quadrupole operator in the truncated shell-model space is found to be almost independent of the coupling strength used in the pairing channel of the underlying mean-field theory.

Adsorption of star polymers studied by a new numerical mean field theory

We present a systematic theoretical investigation of star-like polymers of various architectures near adsorbing surface, using a new numerical self-consistent mean field theory. The comparison of the experimentally reported adsorption profiles with the predictions of our method shows excellent agreement. The study of the structural properties of the formed brushes indicates that as the number of branches is increased the number of adsorbed polymers is significantly reduced. Mixtures of different kinds of star polymers show interesting behaviors as the more branched polymers try to develop in the outer region of brush. We also estimate the forces obtained when curved surfaces come close as a function of the distance between the surfaces.

Specific Features of Defect Structure and Dynamics in the Cylinder Phase of Block Copolymers

We present a systematic study of defects in thin films of cylinder-forming block copolymers upon long-term thermal or solvent annealing. In particular, we consider in detail the peculiarities of both classical and specific topological defects, and conclude that there is a strong "defect structure-chain mobility" relationship in block copolymers. In the systems studied, representative defect configurations provide connectivity of the minority phase in the form of dislocations with a closed cylinder end or classical disclinations with incorporated alternative, nonbulk structures with planar symmetry. In solvent-annealed films with enhanced chain mobility, the neck defects (bridges between parallel cylinders) were observed. This type of nonsingular defect has not been identified in block copolymer systems before. We argue that topological arguments and 2D defect representation, sufficient for lamellar systems, are not sufficient to determine the stability and mobility of defects in the cylindrical phase. In-situ scanning force microscopy measurements are compared with the simulations based on the dynamic self-consistent mean field theory. The close match between experimental measurements and simulation results suggests that the lateral defect motion is diffusion-driven. In addition, 3D simulations demonstrated that the bottom (wetting) layer is only weakly involved into the structure ordering at the free surface. Finally, the morphological evolution is considered with the focus on the motion and interaction of the representative defect configurations.

Diffusion and coupled fluxes in concentrated alloys under irradiation: a self-consistent mean-field approach

When an alloy is irradiated, atomic transport can occur through the two types of defects which are created: vacancies and interstitials. Recent developments of the self-consistent mean field (SCMF) kinetic theory could treat within the same formalism diffusion due to vacancies and interstitials in a multi-component alloy. It starts from a microscopic model of the atomic transport via vacancies and interstitials and yields the fluxes with a complete Onsager matrix of the phenomenological coefficients. The jump frequencies depend on the local environment through a ‘broken bond model’ such that the large range of frequencies involved in concentrated alloys is produced by a small number of thermodynamic and kinetic parameters. Kinetic correlations are accounted for through a set of time-dependent effective interactions within a non-equilibrium distribution function of the system. The different approximations of the SCMF theory recover most of the previous diffusion models. Recent improvements of the theory were to extend the multi-frequency approach usually restricted to dilute alloys to diffusion in concentrated alloys with jump frequencies depending on local concentrations and to generalize the formalism first developed for the vacancy diffusion mechanism to the more complex diffusion mechanism of the interstitial in the dumbbell configuration. To cite this article: M. Nastar, C. R. Physique 9 (2008).

Self-consistent slave rotor mean-field theory for strongly correlated systems

Building on the work by Florens and Georges [Phys. Rev. B 70, 035114 (2004)], we formulate and study a self-consistent slave rotor mean-field theory for strongly correlated systems. This approach views the electron, in the strong correlation regime, as a composite of a neutral spinon and a charged rotor field. We solve the coupled spinon-rotor model self-consistently using a cluster mean-field theory for the rotors and various Ans\atze for the spinon ground state. We illustrate this approach with a number of examples relevant to ongoing experiments in strongly correlated electronic systems such as (i) the phase diagram of the isotropic triangular lattice organic Mott insulators, (ii) quasiparticle excitations and tunneling asymmetry in the weakly doped cuprate superconductors, and (iii) the cyclotron mass of carriers in commensurate spin-density wave and U(1) staggered flux (or $d$-density wave) normal states of the underdoped cuprates. We compare the estimated cyclotron mass with results from recent quantum oscillation experiments on ortho-II $\mathrm{Y}{\mathrm{Ba}}_{2}{\mathrm{Cu}}_{3}{\mathrm{O}}_{6.5}$ by Doiron-Leyraud et al. [Nature (London) 447, 565 (2007)] which appear to find Fermi pockets in the magnetic field induced normal state. We comment on the relation of this normal ground state to Fermi arcs seen in photoemission experiments above ${T}_{c}$. This slave rotor mean-field theory can be generalized to study inhomogeneous states and strongly interacting models relevant to ultracold atoms in optical lattices.

The thermodynamics of micelles in surfactant solution: Lattice mean field theory

The lattice self-consistent mean field theory is applied to study the thermodynamics of micelles in surfactant solution. The model surfactants used are H 4 T 4 and H 2 T 4. The formation of spherical micelles is considered. The effect of the head length on the thermodynamic stability of the micellar solution is examined. The critical micelle concentration is studied at different lengths of head, fractional charge, solvent quality, and univalent salt concentration. A lower critical micelle concentration is associated with a larger aggregation number, while the smallest micelles are found at the lowest univalent salt concentration.

Split interstitials in an interacting bcc alloy. II. Transport coefficients

The transport coefficients are derived in a concentrated interacting body centered cubic alloy for diffusion with the dumbbell mechanism. We use the self-consistent mean field theory in both point and pair approximations on the basis of the first paper of the series, and present two independent approximations (first and second shell approximations) for the calculation of the corresponding correlation coefficients. Correlation coefficients and uncorrelated transport coefficients obtained by those approximations are compared with Monte Carlo simulations for different sets of interactions. In the specific case of a strong clustering tendency and/or strong dumbbell-atom interactions, good agreement with Monte Carlo simulations requires a statistical pair approximation for the uncorrelated transport coefficients and a second shell approximation for the correlation coefficients.

Force spectrum of a few chains grafted on an AFM tip: Comparison of the experiment to a self-consistent mean field theory simulation

A simulation model based on self-consistent mean field theory (SCMFT) has been developed to inspect the approaching process of the polymer chain grafted AFM tip to a substrate. The effects of various controlling parameters, such as grafting position, chain number, chain length, as well as solvent- and substrate-chain interactions, on the force curve were investigated. Real force spectroscopy of AFM tips modified by poly(ethylene glycol) (PEG) chains interacting with the fresh mica has been recorded, and several typical types of the force curves that correspond to the different states of the grafting chain were assorted. The simulations fit the experimental results well, providing a strong support to the model.

Nonequilibrium Green’s function method for thermal transport in junctions

We present a detailed treatment of the nonequilibrium Green's function method for thermal transport due to atomic vibrations in nanostructures. Some of the key equations, such as self-energy and conductance with nonlinear effect, are derived. A self-consistent mean-field theory is proposed. Computational procedures are discussed. The method is applied to a number of systems including one-dimensional chains, a benzene ring junction, and carbon nanotubes. Mean-field calculations of the Fermi-Pasta-Ulam model are compared with classical molecular dynamics simulations using a generalized Langevin heat bath. We find that nonlinearity suppresses thermal transport even at moderately high temperatures.

Microphase separation and molecular conformation of AB2 miktoarm star copolymers by dissipative particle dynamics

We simulate the microphase separation behavior and analyze the molecular conformation of AB2 miktoarm star copolymers via dissipative particle dynamics (DPD). The phase diagram is constructed by varying the composition and interaction parameter. Through a mapping of the interaction parameter for a finite chain length, we find that the phase diagram via DPD is in near quantitative agreement with that predicted by the self-consistent mean-field (SCMF) theory. However, when the B composition is small, AB2 is not able to form the ordered microstructure as easily as SCMF has predicted. Instead, only a tube-like phase is formed. This aggregated micelle-like phase via DPD, which is ignored in the SCMF study, has been frequently observed in experiments. In the analysis of the radius of gyration (Rg), when the interaction parameter increases, the Rg values of each A and B arm remain relatively unchanged; while the overall radius of gyration of AB2 significantly increases. Furthermore, the angle between A and B arms shows an increasing trend while the angle between B and B arms shows a decreasing behavior with the interaction parameter. These results reveal that in order to reduce the contacts between A and B, the A and B arms tend to separate from each other, and the two B arms are squeezed onto the same side.

The nature of phase transitions of symmetric diblock copolymer melts under confinement

The effects of confinement, both the structure frustration and the surface field, on phase transitions of symmetric diblock copolymer melts are investigated within several theoretical methods on the mean-field level. Confinements are applied by restricting polymer chains in the finite spaces of slabs. The surface can be neutral or preferential depending on the strength of the surface field. Within the one-dimensional self-consistent mean-field theory, for the neutral surface case, an oscillative behavior is observed for the size dependence of the order–disorder transition (ODT) point ( χN) t due to the structure frustration. The spinodal ( χN) s for this corresponding confined system is also calculated using the Gaussian fluctuation theory and the Landau–Brazovskii theory, and ( χN) s coincides exactly with ( χN) t. On the other hand, the surface effect plays the role to decrease ( χN) t due to the surface-induced spatial oscillation for the preferential surface case. In all confined systems considered, the ODT for symmetric diblock copolymer melts is a continuous second-order phase transition in the present mean-field calculation.

Exploration of Pseudospin Symmetry in the Resonant States

Taking 120Sn as an example, we discuss the pseudospin symmetryin the single proton resonant states by examining the energies,widths and the wavefunctions. The information of the single protonresonant states in spherical nuclei are extracted from an analyticcontinuation in the coupling constant method within the framework ofthe self-consistent relativistic mean field theory under therelativistic boundary condition. We find small energy splitting ina pair of pseudospin partners in the resonant states. The lowercomponents of the Dirac wavefunctions of a pseudospin doublet agreewell in the region where nuclear potential dominates. It is concludedthat the pseudospin symmetry is also well conserved for the resonantstates in realistic nuclei.

Theory of the in-plane anisotropy of magnetic excitations in YBa 2Cu 3O 6+ y

A pronounced xy-anisotropy was observed in recent neutron scattering experiments for magnetic excitations in untwinned YBa 2Cu 3O 6+ y (YBCO). The small anisotropy of the bare band structure due to the orthorhombic crystal symmetry seems to be enhanced by correlation effects. A natural possibility is that the system is close to a Pomeranchuk instability associated with a d-wave Fermi surface deformation (dFSD). We investigate this possibility in the bilayer t– J model within a self-consistent slave-boson mean-field theory. We show that the dFSD correlations drive a pronounced xy-anisotropy of magnetic excitations at low doping and at relatively high temperatures, providing a scenario for the observed xy-anisotropy in optimally doped as well as underdoped YBCO, including the pseudogap phase.

Domain Size Control in Self-Assembling Rod−Coil Block Copolymer and Homopolymer Blends

The addition of homopolymers to a self-assembling rod−coil block copolymer is demonstrated to be a flexible route toward domain size control. Molecular weight matched rod-like homopolymers interdigitate with the rod-blocks within their respective lamellae. As a result of the interdigitation, the coil blocks must rearrange to occupy more interfacial area resulting in an unprecedented decrease in domain spacing with increasing rod homopolymers. Conversely coil homopolymers were locally solubilized within the coil microdomain resulting in an increase of domain spacing with increasing coil homopolymers. The mechanisms of homopolymers solubilization are in qualitative agreement with predictions made by self-consistent mean-field theory (SCFT) calculations.

Relativistic wave functions for single-proton resonant states

With the relativistic boundary condition, single-proton resonant states in spherical nuclei are studied by an analytic continuation in the coupling constant (ACCC) method within the framework of the self-consistent relativistic mean-field (RMF) theory. In this scheme, we investigate the wave functions for l≠ 0 proton resonant states close to the continuum threshold in the stable nuclide 120Sn for the first time. Some hints for pseudospin symmetry in the resonant states of nuclei are mentioned as well.

Lateral Organization in Lipid-Cholesterol Mixed Bilayers

Interactions between lipid and cholesterol molecules in membranes play an important role in the structural and functional properties of cell membranes. Although structural properties of lipid-cholesterol mixtures have been extensively studied, an understanding of the role of cholesterol in the lateral organization of bilayers has been elusive. In this article, we propose a simple yet powerful model, based on self-consistent mean-field theory and molecular dynamics simulations, for lipid bilayers containing cholesterol. Properties predicted by our model are shown to be in excellent agreement with experimental data. Our model predicts that cholesterol induces structural changes in the bilayer through the formation of regions of ordered lipids surrounding each cholesterol molecule. We find that the “smooth” and “rough” sides of cholesterol play crucial roles in formation and distribution of the ordered regions. Our model is predictive in that input parameters are obtained from independent atomistic molecular dynamics simulations. The model and method are general enough to describe other heterogeneous lipid bilayers, including lipid rafts.