Self-consistent Field Approach Research Articles

Modeling multiorbital effects in Sr2IrO4 under strain and a Zeeman field

We present a comprehensive study of a three-orbital lattice model suitable for the layered iridate Sr2IrO4. Our analysis includes various on-site interactions (including Hubbard and Hund's) as well as compressive strain, and a Zeeman magnetic field. We use a self-consistent mean field approach with multiple order parameters to characterize the resulting phases. While in some parameter regimes the compound is well described by an effective J=1/2 model, in other regimes the full multiorbital description is needed. As a function of the compressive strain, we uncover two quantum phase transitions: first a continuous metal-insulator transition, and subsequently a first order magnetic melting of the antiferromagnetic order. Crucially, bands of both J=1/2 and J=3/2 nature play important roles in these transitions. Our results qualitatively agree with experiments of Sr2IrO4 under strain induced by a substrate, and motivate the study of higher strains.

Symmetry-breaking-induced tipping to aging

The competing effect of heterogeneity and symmetry breaking coupling on the emerging dynamics in a system of N globally coupled Stuart-Landau oscillators is investigated. Increasing the heterogeneity, using the standard deviation of the Hopf bifurcation parameter, favors the macroscopic oscillatory state for low values of the symmetry breaking coupling and inhomogeneous steady state for larger values of the coupling. There is also a transition, tipping, to homogeneous steady state (aging state) from the macroscopic oscillatory state. The limiting factor in the diffusive coupling favors the macroscopic oscillatory state even in the presence of a large fraction of inactive oscillators in the network thereby increasing the robustness of the network. The globally coupled oscillators are reduced to a system of two evolution equations for the macroscopic order parameters, corresponding to the mean-field and the shape parameter, using the self-consistent field approach. The bifurcation diagrams obtained from the mean-field variables elucidate various bifurcation scenarios responsible for the dynamical transitions observed in N globally coupled Stuart-Landau oscillators. In particular, tipping to the aging state is found to occur via the Hopf and pitchfork bifurcations illustrating the phenomenon of bifurcation induced tipping. Analytical stability (critical) curves of these bifurcations, deduced from the mean-field variables, are found to fairly well agree with the simulation results.

Graphene on a hexagonal lattice substrate with on-site Hubbard interaction

We use the self-consistent mean field approach to study the dispersion relation of graphene on a substrate with hexagonal lattice structure, similar to that of graphene, taking into account on-site Hubbard interactions in the substrate sites. Different Hubbard interactions in the sublattices that constitute the substrate breaks the electron hole symmetry. The interaction between the substrate and the graphene sheet opens two gaps in the dispersion relation of graphene out of the Dirac K point. The position of the gaps depends on the ratio between the first neighbor interaction in graphene and the Hubbard on-site interaction in the substrate lattice.

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.

A diagonalization-free optimization algorithm for solving Kohn-Sham equations of closed-shell molecules.

A local optimization algorithm for solving the Kohn-Sham equations is presented. It is based on a direct minimization of the energy functional under the equality constraints representing the Grassmann Manifold. The algorithm does not require an eigendecomposition, which may be advantageous in large-scale computations. It is optimized to reduce the number of Kohn-Sham matrix evaluations to one per iteration to be competitive with standard self-consistent field (SCF) approach accelerated by direct inversion of the iterative subspace (DIIS). Numerical experiments include a comparison of the algorithm with DIIS. A high reliability of the algorithm is observed in configurations where SCF iterations fail to converge or find a wrong solution corresponding to a stationary point different from the global minimum. The local optimization algorithm itself does not guarantee that the found minimum is global. However, a randomization of the initial approximation shows a convergence to the right minimum in the vast majority of cases.

A Molecular Crystal Shows Multiple Correlated Magnetic and Ferroelectric Switchings

Simultaneous control of the magnetic and electric properties of materials is crucial for their application in next-generation memory and sensor devices. Herein, we report a single-crystal Co(II) co...

Self-Consistent Calculation of the Localized Orbital Scaling Correction for Correct Electron Densities and Energy-Level Alignments in Density Functional Theory.

The recently developed localized orbital scaling correction (LOSC) method shows the ability to systematically and size-consistently reduce the delocalization error existing in conventional density functional approximations (DFAs). However, the application of LOSC to DFAs was mainly through a post self-consistent field (SCF) manner, and few results from applying LOSC to DFAs in an SCF manner have been reported. The reason is that the originally proposed SCF approach to SCF-LOSC calculation uses an approximate Hamiltonian and encounters convergence problems easily in practice. In this work, we develop a new SCF approach with a correct Hamiltonian and achieve reliable SCF-LOSC calculations. We demonstrate the capability of the new SCF approach for SCF-LOSC to correctly describe the electron densities, total energies, and energy-level alignment for the molecular dissociation process, while conventional DFAs or LOSC-DFAs with post-SCF calculations show large errors. This work demonstrates that the new SCF approach for SCF-LOSC would be a promising method for studying problems for correct electron densities and energy-level alignments in large systems.

Dynamical robustness in a heterogeneous network of globally coupled nonlinear oscillators

Abstract Deterioration or failure of even a fraction of the microscopic constituents of a large class of networks leads to the loss of the macroscopic activity of the network as a whole. We deduce the evolution equation of two macroscopic order parameters from a globally coupled network of heterogeneous oscillators following the self-consistent field approach under the strong coupling limit. The macroscopic order parameter is used to classify the stable nontrivial steady state and the macroscopic oscillatory state of the network. We examine the dynamical robustness of the network by including a limiting factor that limits the degree of diffusion and a self-feedback factor in the network in addition to the heterogeneity of the network. The heterogeneity is introduced using the parameter specifying the distance from the Hopf bifurcation, which is drawn from a random statistical distribution. We also deduce the critical stability curves from the evolution equation of the macroscopic order parameters demarcating the stable nontrivial steady state and the macroscopic oscillatory state in the system parameter space. We show that a large heterogeneity and a large self-feedback factor facilitates the onset of the stable macroscopic oscillatory state by destabilizing the aging transition state, whereas limiting the degree of the diffusion favors the sustained macroscopic oscillation of the heterogeneous network.

Variational Density Functional Calculations of Excited States via Direct Optimization

The development of variational density functional theory approaches to excited electronic states is impeded by limitations of the commonly used self-consistent field (SCF) procedure. A method based on a direct optimization approach as well as the maximum overlap method is presented, and the performance is compared with previously proposed SCF strategies. Excited-state solutions correspond to saddle points of the energy as a function of the electronic degrees of freedom. The approach presented here makes use of a preconditioner determined with the help of the maximum overlap method to guide the convergence on a target nth-order saddle point. This method is found to be more robust and converge faster than previously proposed SCF approaches for a set of 89 excited states of molecules. A limited-memory formulation of the symmetric rank-one method for updating the inverse Hessian is found to give the best performance. A conical intersection for the carbon monoxide molecule is calculated without resorting to fractional occupation numbers. Calculations on the excited states of the hydrogen atom and a doubly excited state of the dihydrogen molecule using a self-interaction corrected functional are presented. For these systems, the self-interaction correction is found to improve the accuracy of density functional calculations of excited states.

The Reaction Path of Product Release in NO Detoxification at the Active Site of Truncated Hemoglobin N in MCSCF Approach

The Multi-Configurational Self-Consistent Field approach with the geometry optimization was applied to the calculation of electronic properties of active site of heme core of truncated hemoglobin N, with the inclusion of [ONOO] functional group and two water molecules. The localized molecular orbitals are employed as a starting set. Two subspaces of full interaction have been used by the construction of MCSCF wavefunction. The first one includes 3d orbitals of iron atom, and the second contains bonding and antibonding molecular orbitals of peroxynitrite with one unshared electronic pair of the O2 fragment. The reaction is characterized by two transition states; the products are nitrate anion and one unbound water molecule. There arise an evidence of NO2 and NO radicals as the reaction products.

Dynamic Self-Consistent Field Approach for Studying Kinetic Processes in Multiblock Copolymer Melts.

The self-consistent field theory is a popular and highly successful theoretical framework for studying equilibrium (co)polymer systems at the mesoscopic level. Dynamic density functionals allow one to use this framework for studying dynamical processes in the diffusive, non-inertial regime. The central quantity in these approaches is the mobility function, which describes the effect of chain connectivity on the nonlocal response of monomers to thermodynamic driving fields. In a recent study, one of us and coworkers have developed a method to systematically construct mobility functions from reference fine-grained simulations. Here we focus on melts of linear chains in the Rouse regime and show how the mobility functions can be calculated semi-analytically for multiblock copolymers with arbitrary sequences without resorting to simulations. In this context, an accurate approximate expression for the single-chain dynamic structure factor is derived. Several limiting regimes are discussed. Then we apply the resulting density functional theory to study ordering processes in a two-length scale block copolymer system after instantaneous quenches into the ordered phase. Different dynamical regimes in the ordering process are identified: at early times, the ordering on short scales dominates; at late times, the ordering on larger scales takes over. For large quench depths, the system does not necessarily relax into the true equilibrium state. Our density functional approach could be used for the computer-assisted design of quenching protocols in order to create novel nonequilibrium materials.

Relativistic correction scheme for core-level binding energies from GW.

We present a relativistic correction scheme to improve the accuracy of 1s core-level binding energies calculated from Green's function theory in the GW approximation, which does not add computational overhead. An element-specific corrective term is derived as the difference between the 1s eigenvalues obtained from the self-consistent solutions to the non- or scalar-relativistic Kohn-Sham equations and the four-component Dirac-Kohn-Sham equations for a free neutral atom. We examine the dependence of this corrective term on the molecular environment and the amount of exact exchange in hybrid exchange-correlation functionals. This corrective term is then added as a perturbation to the quasiparticle energies from partially self-consistent and single-shot GW calculations. We show that this element-specific relativistic correction, when applied to a previously reported benchmark set of 65 core-state excitations [D. Golze et al., J. Phys. Chem. Lett. 11, 1840-1847 (2020)], reduces the mean absolute error (MAE) with respect to the experiment from 0.55 eV to 0.30 eV and eliminates the species dependence of the MAE, which otherwise increases with the atomic number. The relativistic corrections also reduce the species dependence for the optimal amount of exact exchange in the hybrid functional used as a starting point for the single-shot G0W0 calculations. Our correction scheme can be transferred to other methods, which we demonstrate for the delta self-consistent field (ΔSCF) approach based on density functional theory.

Deposition of Synthetic and Bio-Based Polycations onto Negatively Charged Solid Surfaces: Effect of the Polymer Cationicity, Ionic Strength, and the Addition of an Anionic Surfactant

The deposition of layers of different polycations (synthetic or derived from natural, renewable resources) onto oppositely charged surfaces has been studied using ellipsometry and quartz crystal microbalance with dissipation monitoring (QCM-D). Information about the thickness of the deposited layers and their water content was ascertained. The adsorption of the different polycations onto negatively charged surfaces was found to be a complex process, which is influenced by the chemical nature of the polymer chains, ionic strength, polymer concentration and the addition of additives such as surfactants. The experimental picture shows a good agreement with theoretical calculations performed using the Self-Consistent Mean Field (SCF) approach. The results show that the electrostatically-driven deposition can be tuned by modifying the physico-chemical properties of the solutions and the chemical nature of the adsorbed polymer. This versatile approach is a big step forward in aiding the design of new polymers for many industrial applications and, in particular, the design of sustainable washing formulations for cosmetic applications.

Signatures of the Majorana spin in electrical transport through a Majorana nanowire

In this paper, we investigate the transport properties of spinful electrons tunnel coupled to a finite-length Majorana nanowire on one end which is further tunnel coupled to a quantum dot (QD) at the other end. Using a full counting statistics approach, we show that Andreev reflection can happen in two separate channels that can be associated with the two spin states of the tunneling electrons. In a low-energy model for the nanowire that is represented by two overlapping Majorana bound states (MBSs) localized at the ends of the wire, analytical formulas for conductance and noise reveal their crucial dependence on the spin-canting angle difference of the two MBSs in the absence of the QD if the spinful lead couples to both MBSs. We further investigate the influence of a finite temperature on the observation of the coupling to both MBSs. In the presence of the QD, the interference of different tunneling paths gives rise to Fano resonances and the symmetry of those provide decisive information about the coupling to both MBSs. We contrast the low-energy model with a tight-binding model of the Majorana nanowire and treat the Coulomb interaction on the QD with a self-consistent mean field approach. Using the scattering matrix approach, we thereby extend the transport results obtained in the low-energy model including also higher excited states in the nanowire.

Variational Localized Active Space Self-Consistent Field Method.

Fragmentation methods applied to multireference wave functions constitute a road toward the application of highly accurate ab initio wave function calculations to large molecules and solids. However, it is important for reproducibility and transferability that a fragmentation scheme be well defined with minimal dependence on initial orbital guesses or user-designed ad hoc fragmentation schemes. One way to improve this sort of robustness is to ensure that the energy obeys a variational principle; that is, the active orbitals and active space wave functions minimize the electronic energy in a certain ansatz for the molecular wave function. We extended the theory of the localized active space self-consistent field, LASSCF, method (JCTC 2019, 15, 972) to fully minimize the energy with respect to all orbital rotations, rendering it truly variational. The new method, called vLASSCF, substantially improves the robustness and reproducibility of the LAS wave function compared to LASSCF. We analyze the storage and operation cost scaling of vLASSCF compared to orbital optimization using a standard complete active space self-consistent field (CASSCF) approach, and we show results of vLASSCF calculations on some simple test systems. We show that vLASSCF is energetically equivalent to CASSCF in the limit of one active subspace and that vLASSCF significantly improves upon the reliability of LASSCF energy differences, allowing for more meaningful and subtle analysis of potential energy curves of dissociating molecules. We also show that all forms of LASSCF have a lower operation cost scaling than the orbital optimization part of CASSCF.

Nitrogen Isotopic Reduced Partition Function Ratios of Glycine and Serine in Water.

The nitrogen isotopic reduced partition function ratio (RPFR) of glycine (Gly) and serine (Ser) in water has been evaluated by a couple of methods. The experimental fact that those amino acids are present in the zwitterionic form in water has been best reproduced when trihydrated Gly and Ser molecules were treated by the discrete microsolvation method coupled with the self-consistent reaction field (SCRF) approach. The RPFR values of Gly and Ser in water at 25 °C are evaluated as 1.11152 and 1.11070, respectively, and the equilibrium constant of the nitrogen isotope exchange reaction between the two amino acids is calculated as 1.0007 ± 0.0008 at 25 °C. Equivalent results may be obtained by the SCRF method for non- and monohydrated molecules in the zwitterionic form.

The physics of microemulsions extracted from modeling balanced tensionless surfactant-loaded liquid–liquid interfaces

Microemulsions are explored using the self-consistent field approach. We consider a balanced model that features two solvents of similar size and a symmetric surfactant. Interaction parameter χ and surfactant concentration φs b complement the model definition. The phase diagram in χ-φs b coordinates is known to feature two lines of critical points, the Scott and Leibler lines. Only upon imposing a finite distance between the interfaces, we observe that the Scott line meets the Leibler line. We refer to this as a Lifshitz point (LP) for real systems. We add regions that are relevant for microemulsions to this phase diagram by considering the saturation line, which connects (χ, φs b)-points for which the interface becomes tensionless. Crossing this line implies a first-order phase transition as internal interfaces develop, characteristic for one-phase microemulsions. The saturation line ends at the so-called microemulsion point (MP). The MP is shown to connect with the LP by a line of MP-like critical points, found by searching for a "MP" while the distance between interfaces is fixed. A pair of binodal lines that envelop the three-phase (Winsor III) microemulsion region is shown to connect to the MP. The cohesiveness of the middle phase in Winsor III is related to non-monotonic, inverse DLVO-type interaction curves between the surfactant-loaded tensionless interfaces. The mean and Gaussian bending modulus, relevant for the shape fluctuations and the topology of interfaces, respectively, are evaluated along the saturation line. Near the MP, both rigidities are positive and vanish in a power-law fashion with coefficient unity at the MP. Overseeing these results proves that the MP has a pivoting role in the physics of microemulsions.

Does the Affinity of Cisplatin to B-Vitamins Impair the Therapeutic Effect in the Case of Patients with Lung Cancer-consuming Carrot or Beet Juice?

Cisplatin (CisPt) has a well-recognized anticancer activity by interacting with DNA and inducing programmed cell death. However, theoretical studies performed on the molecular level suggest that such nonspecific interactions can also take place with many competitive compounds, such as vitamins containing aromatic rings with lone-pair orbitals. This work is a theoretical study on the initial Pt-N7(N1) bond formation with vitamins from B group and their comparison with values characterizing native purines. Geometries of studied structures were optimized with an aid of Gaussian 09 using the B3LYP functional with the 6-31G** basis set. Atomic orbitals of platinum were represented by the lanl2dz basis. Solvation free energies were evaluated by a self-consistent reaction field (SCRF) approach. A dielectric constant of 78 for water was used in the PCM continuum model computations along with radii Bondii. The affinities of mono-aqua cis~[Pt(NH3)2Cl(H2O)]+ and di-aqua cis~ [Pt(NH3)2(H2O)2]2+ derivatives of Cisplatinum toward compounds belonging to the group of eight B vitamins were studied and compared to interactions with canonical purines. All the values of ΔGr unambiguously indicate that reactions with cisPt-diaqua are more preferable, but the comparison of ΔGr values obtained for compounds from vitamin B group and the ones characterizing complexes created by Guanine molecules indicates higher affinity of cisPt monomers toward purines. Based on the observations, the regular intake of vitamin-rich beetroot or carrot juices is strongly discouraged during anticancer therapy using CisPt drug. To confirm the results of the performed computational study, detailed clinical trials should be performed.

Predicting the Formation of Sulfur-Based Brønsted Acids from the Reactions of SOx with H2O and H2S.

We have performed an extensive computational investigation of the potential energy surfaces for the reactions of SOx (x = 2 or 3) with H2S and H2O in the gas phase and in aqueous solution at the CCSD(T)/CBS level of theory plus a self-consistent reaction field approach. Formation of a gas-phase H2SO4 from the hydrolysis of SO3 at lower temperatures requires the presence of additional water molecules. When additional waters are introduced, the barrier for H2SO4 formation is significantly reduced, and a barrierless transition occurs with only three excess waters as well as in aqueous solution. In a mixture of H2O, H2S, and SO3, formation of H2S2O3 has a lower barrier in the gas phase than does the formation of H2SO4. In aqueous solution, no barrier is predicted, and both are likely to be formed. Introduction of an additional water to the SO3 + H2S reaction results in a decrease in barrier height, nearly identical to the ∼18 kcal/mol catalytic effect of the first additional water in SO3 hydrolysis, with the barrier for H2S2O3 formation disappearing altogether in aqueous solution. Formation of H2SO3 by the way of SO2 hydrolysis is unlikely. Excess waters reduce the barrier for SO2 hydrolysis; however, the overall endothermicity is increased as waters are added. The formation of H2S2O2 from SO2 and H2S via an isostructural pathway to SO2 hydrolysis is unlikely, with additional water molecules resulting in a small increase in the overall endothermicity and a catalytic effect smaller than that observed for the SO3 reactions. The results of this work have implications pertaining to the formation of H2SO4, H2S2O3, H2SO3, and H2S2O2 in the atmospheres of Earth and Venus. These results also question the existence of H2S2O2 as an intermediate in the Claus process.

Quantum Mechanics/Extremely Localized Molecular Orbital Method: A Fully Quantum Mechanical Embedding Approach for Macromolecules.

The development of methods for the quantum mechanical study of macromolecules has always been an important challenge in theoretical chemistry. Nowadays, the techniques proposed in this context can be used to investigate very large systems and can be subdivided into two main categories: fragmentation and embedding strategies. In this paper, by modifying and improving the local self-consistent field approach originally proposed for quantum mechanics/molecular mechanics techniques, we introduce the new multiscale embedding quantum mechanics/extremely localized molecular orbital (QM/ELMO) method. The new strategy enables treatment of chemically relevant regions of large biological molecules through usual methods of quantum chemistry while describing the remaining parts of the systems by means of frozen extremely localized molecular orbitals transferred from properly constructed libraries. Test calculations have shown the correct functioning and the high reliability of the new approach, thus anticipating its possible applications to different fields of physical chemistry, such as rational drug design and structural refinements of proteins.