Self-consistent Field Model Research Articles

Polyelectrolyte brush in a cylindrical pore: A Poisson-Boltzmann theory.

The conformation of a polyelectrolyte (PE) brush grafted to the inner surface of a long cylindrical mesopore was described within analytical Poisson-Boltzmann strong stretching approximation. The internal structure of the PE brush, including brush thickness and radial density profile of monomer units, and radial distribution of electrostatic potential were analyzed as functions of the pore radius, degree of polymerization, and grafting density of the brush-forming PE chains as well as ionic strength of the solution. It is demonstrated that narrowing of the pore leads to a non-monotonous variation of the brush thickness, which passes through a maximum when the brush thickness becomes equal to the pore radius. Variation in the salt concentration triggers conformational transition that leads to the opening or closing of the hollow (PE-free) channel in the pore center that potentially allows controlling of the pore-selective permeability for charged nanocolloidal particles (e.g., globular proteins or viruses). The predictions of the analytical theory were validated by numerical calculations using the Scheutjens-Fleer self-consistent field modeling method. These theoretical findings may be used for the design of highly selective smart mesoporous membranes with PE brush-functionalized pores for, e.g., protein separation and purification.

Electric Field Gradient Calculations for Ice VIII and IX Using Polarizable Embedding: A Comparative Study on Classical Computers and Quantum Simulators.

We test the performance of the polarizable embedding variational quantum eigensolver self-consistent field (PE-VQE-SCF) model for computing electric field gradients with comparisons to conventional complete active space self-consistent-field (CASSCF) calculations and experimental results. We compute quadrupole coupling constants for ice VIII and ice IX. We find close agreement of the quantum-computing PE-VQE-SCF results with the results from the classical PE-CASSCF calculations and with experiment. Furthermore, we observe that the inclusion of the environment is crucial for obtaining results that match the experimental data. The calculations for ice VIII are within the experimental uncertainty for both CASSCF and VQE-SCF for oxygen and lie close to the experimental value for ice IX as well. With the VQE-SCF, which is based on an adaptive derivative-assembled problem-tailored (ADAPT) ansatz, we find that the inclusion of the environment and the size of the different basis sets do not directly affect the gate counts. However, by including an explicit environment, the wavefunction and therefore the optimization problem become more complicated, which usually results in the need to include more operators from the operator pool, thereby increasing the depth of the circuit.

Periodic cylindrical bilayers self-assembled from biblock polymers.

Amphiphilic polymers in aqueous solutions can self-assemble to form bilayer membranes, and their elastic properties can be captured using the well-known Helfrich model involving several elastic constants. In this paper, we employ the self-consistent field model to simulate sinusoidal bilayers self-assembled from diblock copolymers where an appropriate constraint term is introduced to stabilize periodic bilayers with prescribed amplitudes. Then, we devise several methods to extract the shape of these bilayers and examine the accuracy of the free energy predicted by the Helfrich model. Numerical results show that when the bilayer curvature is small, the Helfrich model predicts the excess free energy more accurately. However, when the curvature is large, the accuracy heavily depends on the method used to determine the shape of the bilayer. In addition, the dependence of free energy on interaction strength, constraint amplitude, and constraint period are systematically studied. Moreover, we have devised a method for attaining equilibrium states through the adjustment of constraints. Within the self-consistent field model, these equilibrium states manifest as distinct periodic cylindrical bilayers, which are consonant with the theoretical predictions formulated using the shape equations.

Deposition of uniform diamond films on three dimensional Si spheres by using faraday cage in MPCVD reactor

Deposition of a consistent diamond coating on intricate surfaces has historically posed a difficulty. This article presents the advancement in research on depositing a uniform diamond coating on three-dimensional (3D) silicon spheres, utilizing a faraday cage within a microwave plasma chemical vapor deposition (MPCVD) reactor. A self-consistent three-dimensional multi-physics field model has been established for simulating the microwave electric field and plasma inside a reactor with or without a faraday cage. Results indicate the cage effectively reduces the discharge at the top of the silicon sphere and improves uniformity of the distribution of the microwave electric field and plasma electron density on the sphere's surface. MPCVD trials have demonstrated that a powerful discharge takes place at the apex of the silicon sphere resulting in an excessive thermal gradient if the cage is not added. The apex of the silicon sphere is covered with a blend of diamond and graphite phases. Due to the excessive internal stress of the coating, approximately 50 % of the samples experience coating detachment. After the addition of the cage, the strong discharge is transferred to the top of the cage, effectively suppressing the microwave electric field and plasma inside the cage. Improved quality, reduced internal stress, and enhanced uniformity of the polycrystalline diamond coating are achievable on the silicon spheres within the cage. Moreover, this technique offers a novel approach to coat diamond on complex 3D geometries.

Theoretical studies on structural properties and decay modes of $$^{284-375}$$119 isotopes

Within the axially deformed relativistic mean field with $$\hbox {NL3}^*$$ parametrisation, the different bulk properties like binding energy, quadrupole deformation parameter, separation energies, density profile and shape co-existence for Z = 119 isotopic chain within the mass range 284 $$\le$$ A $$\le$$ 375 are computed. Further, a competition between possible decay modes such as α-decay, $$\beta$$ -decay and spontaneous fission (SF) of the isotopic chain of Z = 119 superheavy nuclei under study is systematically analysed within self-consistent relativistic mean field model and a close agreement is noticed among the calculations performed using various semi-empirical formulae and also with the estimations made by finite range droplet model (FRDM) wherever available. Our analysis confirmed that α–decay is restricted within the mass range 284 $$\le$$ A $$\le$$ 375 and thus being the dominant decay channel in this mass range and there is no possibility of $$\beta$$ –decay for the considered isotopic chain. In addition, we forecasted the α–decay chain of fission survival nuclides, i.e. $$^{284-296}119$$ and found as one α chain from $$^{284} 119$$ and $$^{296} 119$$ , $$2 \alpha$$ chains from $$^{285}119$$ and $$^{295} 119$$ consistently, $$3\alpha$$ chains from $$^{286} 119$$ and $$^{294} 119$$ consistently, $$4 \alpha$$ chains from $$^{287} 119$$ consistently, six consistent α chains from $$^{288-293} 119$$ . A comparative study of SF and α-decay half-live computed using the formula of Santhosh et al and Coulomb proximity potential model (CPPM), respectively, for the fission surviving isotopic chain reveals that isotopes $$^{288-293} 119$$ exhibit $$6\alpha$$ chains followed by SF, isotopes $$^{295,296} 119$$ exhibit $$4\alpha$$ chains followed by SF, and the rest of the nuclei show continuous α chains. This study has also established that the alpha half-life values computed using $$\hbox {Q}_\alpha$$ (RMF) agree with half-life values computed using experimental $$\hbox {Q}_\alpha$$ values within 1 order difference. Thus, such studies can be of great significance to the experimentalists in very near future for synthesizing the isotopes of Z = 119 superheavy nuclei.

Tracing chirality from molecular organization to triply-periodic network assemblies: Threading biaxial twist through block copolymer gyroids

Chirality transfer from the level of molecular structure up to mesoscopic lengthscales of supramolecular morphologies is a broad and persistent theme in self-assembled soft materials, from biological to synthetic matter. Here, we analyze the mechanism of chirality transfer in a prototypical self-assembly system, block copolymers (BCPs), in particular, its impact on one of the most complex and functionally vital phases: the cubic, triply-periodic, gyroid network. Motivated by recent experimental studies, we consider a self-consistent field model of ABC* triblock copolymers possessing an end-block of chiral chain chemistry and examine the interplay between chirality at the scale of networks in alternating double network phases and the patterns of segmental order within tubular network domains. We show that while segments in gyroids exhibit twist in both polar and nematic segmental order parameters, the magnitude of net nematic twist is generically much larger than polar twist, and more surprising, reverses handedness relative to the sense of polar order as well as the sense of dihedral twist of the network. Careful analysis of the intra-domain nematic order reveals that this unique chirality transfer mechanism relies on the strongly biaxial nature of segmental order in BCP networks and relates the biaxial twist to complex patterns of frame rotation of the principal directors in the intra-domain texture. Finally, we show that this mechanism of twist reversal leads to chirality selection of alternating gyroid networks in ABC* triblocks, in the limit of very weak chirality.

Toward more accurate adiabatic connection approach for multireference wavefunctions.

A multiconfigurational adiabatic connection (AC) formalism is an attractive approach to compute the dynamic correlation within the complete active space self-consistent field and density matrix renormalization group (DMRG) models. Practical realizations of AC have been based on two approximations: (i) fixing one- and two-electron reduced density matrices (1- and 2-RDMs) at the zero-coupling constant limit and (ii) extended random phase approximation (ERPA). This work investigates the effect of removing the "fixed-RDM" approximation in AC. The analysis is carried out for two electronic Hamiltonian partitionings: the group product function- and the Dyall Hamiltonians. Exact reference AC integrands are generated from the DMRG full configuration interaction solver. Two AC models are investigated, employing either exact 1- and 2-RDMs or their second-order expansions in the coupling constant in the ERPA equations. Calculations for model molecules indicate that lifting the fixed-RDM approximation is a viable way toward improving the accuracy of existing AC approximations.

Mimicking effects of cholesterol in lipid bilayer membranes by self-assembled amphiphilic block copolymers.

The effect of cholesterol on biological membranes is important in biochemistry. In this study, a polymer system is used to simulate the consequences of varying cholesterol content in membranes. The system consists of an AB-diblock copolymer, a hydrophilic homopolymer hA, and a hydrophobic rigid homopolymer C, corresponding to phospholipid, water, and cholesterol, respectively. The effect of the C-polymer content on the membrane is studied within the framework of a self-consistent field model. The results show that the liquid-crystal behavior of B and C has a great influence on the chemical potential of cholesterol in bilayer membranes. The effects of the interaction strength between components, characterized by the Flory-Huggins parameters and the Maier-Saupe parameter, were studied. Some consequences of adding a coil headgroup to the C-rod are presented. Results of our model are compared to experimental findings for cholesterol-containing lipid bilayer membranes.

Good Vibrations: Calculating Excited-State Frequencies Using Ground-State Self-Consistent Field Models.

The use of Δ-self-consistent field (SCF) approaches for studying excited electronic states has received a renewed interest in recent years. In this work, the use of this scheme for calculating excited-state vibrational frequencies is examined. Results from Δ-SCF calculations for a set of representative molecules are compared with those obtained using configuration interaction with single substitutions (CIS) and time-dependent density functional theory (TD-DFT) methods. The use of an approximate spin purification model is also considered for cases where the excited-state SCF solution is spin-contaminated. The results of this work demonstrate that an SCF-based description of an excited-state potential energy surface can be an accurate and cost-effective alternative to CIS and TD-DFT methods.

Localized Active Space-State Interaction: a Multireference Method for Chemical Insight.

Multireference electronic structure methods, like the complete active space (CAS) self-consistent field model, have long been used to characterize chemically interesting processes. Important work has been done in recent years to develop modifications having a lower computational cost than CAS, but typically these methods offer no more chemical insight than that from the CAS solution being approximated. In this paper, we present the localized active space-state interaction (LASSI) method that can be used not only to lower the intrinsic cost of the multireference calculation but also to improve interpretability. The localized active space (LAS) approach utilizes the local nature of the electron-electron correlation to express a composite wave function as an antisymmetrized product of unentangled wave functions in local active subspaces. LASSI then uses these LAS states as a basis from which to express complete molecular wave functions. This not only makes the molecular wave function more compact but also permits flexibility in choosing those states to be included in the basis. Such selective inclusion of states translates to the selective inclusion of specific types of interactions, thereby allowing a quantitative analysis of these interactions. We demonstrate the use of LASSI to study charge migration and spin-flip excitations in multireference organic molecules. We also compute the J coupling parameter for a bimetallic compound using various LAS bases to construct the Hamiltonian to provide insights into the coupling mechanism.

Реализация метода частиц на компьютере с графическими ускорителями

The effective variant of particle method algorithm for modeling surface generation, propagation and scattering of electrons in a self-consistent electromagnetic field is presented. An implementation of the algorithm on a hybrid cluster with graphic processor units (GPU) is worked out. Solutions to the problems of synchronization of recording results and data exchange are considered. The implementation is oriented on problems of electron emission and self-consistent electromagnetic field modeling in apparature blocks.

Using projection operators with maximum overlap methods to simplify challenging self-consistent field optimization.

Maximum overlap methods are effective tools for optimizing challenging ground- and excited-state wave functions using self-consistent field models such as Hartree-Fock and Kohn-Sham density functional theory. Nevertheless, such models have shown significant sensitivity to the user-defined initial guess of the target wave function. In this work, a projection operator framework is defined and used to provide a metric for non-aufbau orbital selection in maximum-overlap-methods. The resulting algorithms, termed the Projection-based Maximum Overlap Method (PMOM) and Projection-based Initial Maximum Overlap Method (PIMOM), are shown to perform exceptionally well when using simple user-defined target solutions based on occupied/virtual molecular orbital permutations. This work also presents a new metric that provides a simple and conceptually convenient measure of agreement between the desired target and the current or final SCF results during a calculation employing a maximum-overlap method.

Solvation of Potassium 5-Hydroxy Pentanoyl Trifluoroborate Salt in Aqueous Environment by Using FT-Raman and UV-Visible Spectra

The hydration process of potassium 5-hydroxypentanoyltrifluoroborate salt, K[C5H9BF3O2] and its 5-hydroxypentanoyltrifluoroborate [C5H9BF3O2]- anion have been studied by combining the experimental FT-Raman and ultraviolet-visible spectra in aqueous solution with hybrid B3LYP/6-311++G** calculations. Solvent effects have been considered with the self-consistent reaction field (SCRF) and solvation (SM) models. Here, the structures of [C5H9BF3O2].[H2O]n clusters of anion, with n from 1 to 5 implicit water molecules, were proposed in order to study the number of water molecules that could hydrate the anion. Calculations were performed in the gas phase and an aqueous solution to observe the effect of the medium on the dipole moment and volume values. Calculated solvation energies for all clusters were corrected by zero-point vibrational energy (ZPVE), non-electrostatic terms and by basis set superposition energy (BSSE). The dipole moment of salt in solution (10.19 D) suggests that the number of water molecules that could hydrate the anion vary between 3 and 4, in total agreement with the observed and predicted bands in the UV-Vis spectra for the salt and these two clusters in water between 180 and 400 nm. Comparisons among experimental and predicted Raman spectra show clearly the hydration effect because the bands attributed to OH, BF3 and C=O groups are shifted in solution, while, the predicted Raman spectra for all clusters in solution show strong changes in the intensities of many bands, in accordance with the corresponding experimental one. Evidently, the hydration occurs on the OH, BF3 and C=O groups.

On the unusual properties dielectric constant of the electric field of the free atmosphere

On the basis of experimental data vertical distribution electric field strength of the atmosphere, the applied problem of fitting constants in the model of the average self-consistent electric field is solved.The model is based on the nonlinear Poisson equation. Such an approach is not trivial because generally known in meteorology interpolation exponential function describing the empirical distribution of the electric field, space charge density and conductivity with a height not quite correctly reproduce a stable stratification of the electric field. Since aircraft measurements are carried out in a natural environment, the dielectric constant is lost, which leads to underestimated values of the electron-ion concentration.This is due to the fact that the potential in situ is screened and the Gauss theorem does not hold for it, and if it does, then for the radius of the Gaussian sphere it is less than the Debye screening radius. For a large Gaussian sphere, only the near-wall part of the electrometer is experimentally determined, and the shielded (inner) part does not contribute to the field flux through the surface by the dynamic screening of the electron. The magnitude of the screening of electrons in air is very large due to the dynamic polarizability of the medium and consists of two parts — the Debye and ion-plasma screening spheres. This, in turn, requires a redefinition of the dielectric constant for correct reproduction of field measurements. Thus, the verification of the dielectric constant was carried out on different experimental data, and its values lie within the same limits as the values obtained from the classical relations of Penn, Debye, and Landau.

Reversible multilayered vesicle-like structures with fluid hydrophobic and interpolyelectrolyte layers

Hydrophobic blocks of amphiphilic block copolymers often form glassy micellar cores at room temperature with a rigid structure that limits their applications as nanocapsules for targeted delivery. Nevertheless, we prepared and analyzed core/shell micelles with a soft core, formed by a self-assembled block copolymer consisting of a hydrophobic block and a polycation block, poly(lauryl acrylate)-block-poly(trimethyl-aminoethyl acrylate) (PLA-QPDMAEA), in aqueous solution. By light and small-angle neutron scattering, by transmission electron microscopy and by fluorescence spectroscopy, we showed that these core/shell micelles are spherical and cylindrical with a fluid-like PLA core and a positively charged outer shell and that they can encapsulate and release hydrophobic solutes. Moreover, after mixing these PLA-QPDMAEA core/shell micelles with another diblock copolymer, consisting of a hydrophilic block and a polyanion block, namely poly(ethylene oxide)-block-poly(methacrylic acid) (PEO-PMAA), we observed the formation of novel vesicle-like multicompartment structures containing both soft hydrophobic and interpolyelectrolyte (IPEC) layers. By combining small-angle neutron scattering with self-consistent field modeling, we confirmed the formation of these complex vesicle-like structures with a swollen PEO core, an IPEC inner layer, a PLA soft layer, an IPEC outer layer and a loose PEO corona. Thus, these multicompartment micelles with fluid and IPEC layers and a hydrophilic corona may be used as nanocapsules with several tunable properties, including the ability to control the thickness of each layer, the charge of the IPEC layers and the stability of the micelles, to deliver both hydrophobic and multivalent solutes.

Computer modeling of polymer stars in variable solvent conditions: a comparison of MD simulations, self-consistent field (SCF) modeling and novel hybrid Monte Carlo SCF approach.

Computer-aided modeling is a systematic approach to grasp the physics of macromolecules, but it remains essential to know when to trust the results and when not. For a polymer star, we consider three approaches: (i) Molecular Dynamics (MD) simulations and implementing a coarse-grained model, (ii) the self-consistent field approach based on a mean-field approximation and implementing the lattice model due to Scheutjens and Fleer (SF-SCF) and (iii) novel hybrid Monte Carlo self-consistent field (MC-SCF) method, which combines a coarse-grained model driven by a Monte Carlo method and a mean-field representation driven by SF-SCF. We compare the performance of these approaches under a wide range of solvent qualities. The MD approach is formally the most exact but suffers from reasonable convergence. The mean-field approach works similarly in all solvent qualities but is quantitatively least accurate. The MC-SCF hybrid allows us to combine the benefits of the simulation route and the effective performance of SCF. We consider the center-to-end distance Rce, the radius of gyration Rg2 of the star and the polymer density profiles φ(r) of polymer-segments in it. All three methods show a good qualitative agreement one to another. The MC-SCF method is in good agreement with the scaling predictions in the whole range of solvent quality values showing that it grasps the essential physics while remaining computationally in bounds.

Self-consistent field modeling of mesomorphic phase changes of monoolein and phospholipids in response to additives.

Mapping the topological phase behaviour of lipids in aqueous solution is time consuming and finding the ideal lipid system for a desired application is often a matter of trial and error. Modelling techniques that can accurately predict the mesomorphic phase behaviour of lipid systems are therefore of paramount importance. Here, the self-consistent field theory of Scheutjens and Fleer (SF-SCF) in which a lattice refinement has been implemented, is used to scrutinize how various additives modify the self-assembled phase behaviour of monoolein (MO) and 1,2-dioleoyl-phosphatidylcholine (DOPC) lipids in water. The mesomorphic behaviour is inferred from trends in the mechanical properties of equilibrium lipid bilayers with increasing additive content. More specifically, we focus on the Helfrich parameters, that is, the mean and Gaussian bending rigidities (κ and [small kappa, Greek, macron], respectively) supplemented with the spontaneous curvature of the monolayer (Jm0). We use previously established interaction parameters that position the unperturbed DOPC system in the lamellar Lα phase ([small kappa, Greek, macron] < 0, κ > 0 and Jm0 ≈ 0). Similar interaction parameters position the MO system firmly in a bicontinuous cubic phase ([small kappa, Greek, macron] > 0). In line with experimental data, a mixture of MO and DOPC tends to be in one of these two phases, depending on the mixing ratio. Moreover we find good correlations between predicted trends and experimental data concerning the phase changes of MO in response to a wide range of additives. These correlations give credibility to the use of SF-SCF modelling as a valuable tool to quickly explore the mesomorphic phase space of (phospho)lipid bilayer systems including additives.

Investigation of host-guest interactions between polyester dendrimers and ibuprofen using density functional theory (DFT)

Polyester dendrimers are mostly non-toxic and this advantage besides biodegradability gives them a great chance of success in the field of drug delivery. This study investigates electronic and structural characteristics of ibuprofen complexation with polyester G1 dendrimer using DFT calculations. Optimized structural geometries, interaction energies, NMR, NBO, and AIM analyses, revealed that the stability of G1:Ibu complex could be attributed to the intermolecular hydrogen bonds formed between the functional groups of polyester G1 dendrimer and ibuprofen molecule. All calculations were repeated using a self-consistent reaction field (SCRF) and polarizable continuum model (PCM) to consider implicit solvent effects and the outcomes were in line with gas phase calculations.

Self-Consistent Field Modeling of Pulling a Test-Chain away from or Pushing It into a Polymer Adsorption Layer.

We consider single chain force measurements to unravel characteristics of polymers at interfaces and to determine parameters that control adsorption or probe layer characteristics that are difficult to access otherwise. The idea is to have at the tip of an atomic force microscope (AFM), a probe chain and measure its behaviour near interfaces by pushing it to, or pulling it away from it. The self-consistent field modeling of this reveals that in the pulling mode—i.e., when the chain has an affinity for the surface—a typically inhomogeneous flower-like conformation forms with an adsorbed ’pancake’ and a stretched stem (tether) from the surface to the tip of the AFM. When about half the segments is in the tether it snaps loose in a first-order like fashion. The critical distance of the end-point from the surface and the critical force are experimentally accessible. Details of this transition depend on the surrounding of the test chain. Inversely, and this opens up many possibilities, the test chain reports about its surroundings. Our focus is on the classical case of homopolymers at interfaces. Pulling experiments may reveal the adsorption strength, the (average) chain length and/or the polymer concentration of the freely dispersed/adsorbed polymers. When the test-chain is non-adsorbing we envision that pushing this test-chain into the adsorption layer reports about various layer characteristics such as the layer thickness and (local) density. Moreover, when the test-chain has a length longer than the entanglement length, we can imagine that non-trivial dynamical properties of loops and tails may be scrutinised.

The structure of benzonitrile-water complex as unveiled by matrix isolation infrared spectroscopy: Is it linear or cyclic at low temperatures?

The hydrogen bonded interaction of benzonitrile (C6H5CN)-water (H2O) complexes have been studied experimentally using matrix isolation infrared spectroscopy to elucidate the structure(s) of the binary complexes produced at low temperatures. Computations performed at MP2 and B3LYP-D3 level of theory with aug-cc-pVDZ basis set predicted two complexes, of which global minimum complex A has a cyclic structure with the interactions occurring between ortho-hydrogen of C6H5CN and oxygen of H2O and the hydrogen of H2O with π-cloud of CN in C6H5CN. The linear acylic complex B, a local minimum is stabilized through a straight C-H⋯N interaction between nitrogen of C6H5CN and hydrogen of H2O and is present at a relative energy of ∼0.7 kcal/mol with respect to global minimum. While previous gas phase studies using a number of spectroscopic probes identify exclusively the cyclic global complex, our experiments performed under isolated conditions at low temperatures uniquely produced the acyclic linear C6H5CN-H2O complex, a local minimum in the potential energy surface. The CN stretching vibrational mode of C6H5CN was exploited as a unique marker to confirm the generation of local minimum. The effect of matrixes was simulated using Onsager self-consistent reaction field model and as a result, the linear complex (complex B) turned out to be energetically favored isomer under the influence of matrixes. The hydrogen bonding interaction in both the complexes was characterized using Atoms in Molecules, Natural Bond Orbital, Energy Decomposition and Non-Covalent Interaction analyses.