Self-consistent Field Approach Research Articles

Self-Consistent Field Approach for the Variational Quantum Eigensolver: Orbital Optimization Goes Adaptive.

We present a self-consistent field (SCF) approach within the adaptive derivative-assembled problem-tailored ansatz variational quantum eigensolver (ADAPT-VQE) framework for efficient quantum simulations of chemical systems on near-term quantum computers. To this end, our ADAPT-VQE-SCF approach combines the idea of generating an ansatz with a small number of parameters, resulting in shallow-depth quantum circuits with a direct minimization of an energy expression that is correct to second order with respect to changes in the molecular orbital basis. Our numerical analysis, including calculations for the transition-metal complex ferrocene [Fe (C5H5)2], indicates that convergence in the self-consistent orbital optimization loop can be reached without a considerable increase in the number of two-qubit gates in the quantum circuit by comparison to a VQE optimization in the initial molecular orbital basis. Moreover, the orbital optimization can be carried out simultaneously within each iteration of the ADAPT-VQE cycle. ADAPT-VQE-SCF thus allows us to implement a routine analogous to the complete active space SCF, a cornerstone of state-of-the-art computational chemistry, in a hardware-efficient manner on near-term quantum computers. Hence, ADAPT-VQE-SCF paves the way toward a paradigm shift for quantitative quantum-chemistry simulations on quantum computers by requiring fewer qubits and opening up for the use of large and flexible atomic orbital basis sets in contrast to earlier methods that are predominantly based on the idea of full active spaces with minimal basis sets.

First-principles calculations to investigate the elastic, electronic, dynamical, and optical properties of cubic ZrCoAs half-Heusler semiconductor for photovoltaic applications

The electronic, mechanical, elastic, dynamical, and optical properties of the ZrCoAs half-Heusler compound have been systematically investigated using the plane wave self-consistent field approach with the Perdew-Burke-Erzerhof generalized gradient approximation (GGA-PBE) exchange-correlation functional. The study includes examinations with and without spin orbit coupling (SOC) effects. Results indicate a decrease in the Kohn-Sham band gap with the inclusion of SOC effects. Electronic bandgap formation was attributed to Co 3d, Zr 3d, and As 2p for the conduction band, and Co 3d and As 2p for the valence band without SOC effects. With SOC, Co 5d, Zr 8d, and As 3p dominated the conduction band, while Co 3d and As 3p dominated the valence band. The lattice constant showed a 0. 063% decrease with the SOC effects, which is better aligned with the experimental observations. ZrCoAs demonstrated ductility, mechanical stability, and dynamical stability. The optical properties were found to be excellent for photovoltaic applications, suggesting its potential in solar energy conversion technology. This study provides valuable information on ZrCoAs and presents opportunities for its use in solar cells, optoelectronic devices, and thermoelectric applications. The material's versatility and suitability for practical applications make it a promising candidate for further exploration in renewable energy research.

Dynamics of Nucleation in Solids: A Self-Consistent Phase Field Approach.

We derive a phase field method for computing rigorously the nucleation rate and the incubation time from the sole knowledge of the free energy of the system in the metastable regime. Our theoretical results are assessed against experimental data relative to demixing of an iron-chromium alloy. Our work clarifies the notions of nucleation rate and incubation time extensively used in classical nucleation theory (CNT) processes in solids. Our work thus emerges as an alternative to CNT but of more general applicability, and enables us to model the nucleation process across the whole range of condition encountered in first order phase transitions, an aspect in which CNT fails.

Role of octahedral tilting and rotation in [formula omitted]MnO3 ([formula omitted]=La-Ho) perovskites: An orbital scenario

The octahedral tilting and rotation, i.e. GdFeO3-type distortion, in perovskite RMnO3 (R=rare-earth), are investigated with respect to the Jahn–Teller distortion within the unified orbital scenario. The evolution of orbital ordering and magnetism with the rare-earth R ions in perovskite RMnO3 are examined with an effective Hamiltonian based on the competitive mechanism of the electron–electron and electron-lattice interactions by the cluster self-consistent field approach. It is clearly found that the GdFeO3-type distortion enhances the magnitude of the Jahn–Teller distortion and suppresses the ferromagnetic coupling in ab-plane due to the decreasing of the superexchange interaction with Mn–O–Mn bond angle deviating from 180°, which are in good agreement with the experiments. Both the structural and magnetic properties can be explained in an orbital perspective consistently. Furthermore, our model is able to capture the experimental trends including both Jahn–Teller distortion and magnetic coupling for RMnO3 considering the combined effects of the GdFeO3-type distortion. Our results not only shed new light on the interplay of various degrees of freedom, but also unveil the stabilization mechanism of the crystal structure in perovskites.

Cosmic voids and the kinetic analysis

We study structure formation in the late Universe within the Vlasov kinetic self-consistent field approach. Our work is principally focused on the use of the modified gravitational potential with a repulsive term of the cosmological constant, which is directly linked to observations that enable characterizations of the Hubble tension as the result of local and global flows. We formulate the criteria for the formation of the semi-periodic gravitating structures, along with the predictions of their quantitative scales associated with observable parameters. Our principal conclusion is that filament formation in the Local (late) Universe can proceed as a deterministic process that is distinct from the structures at larger scales that result from the essentially stochastic dynamics of density perturbations.

Symmetry breaking in core-valence double ionisation of allene

Conventional electron spectroscopy is an established one-electron-at-the-time method for revealing the electronic structure and dynamics of either valence or inner shell ionized systems. By combining an electron-electron coincidence technique with the use of soft X-radiation we have measured a double ionisation spectrum of the allene molecule in which one electron is removed from a C1s core orbital and one from a valence orbital, well beyond Siegbahns Electron-Spectroscopy-for-Chemical-Analysis method. This core-valence double ionisation spectrum shows the effect of symmetry breaking in an extraordinary way, when the core electron is ejected from one of the two outer carbon atoms. To explain the spectrum we present a new theoretical approach combining the benefits of a full self-consistent field approach with those of perturbation methods and multi-configurational techniques, thus establishing a powerful tool to reveal molecular orbital symmetry breaking on such an organic molecule, going beyond Löwdins standard definition of electron correlation.

Interpenetration and Friction of Brush-Coated Surfaces under External Load: Analytical Theory and SCF Calculations

We studied the compression and interpenetration properties of two opposing monodisperse polymer brushes under external load by analytical theory and by a numerical self-consistent field (SCF) approach. Analytical expressions are proposed for the brush density profiles in the interpenetration zone and verified by numerical SCF calculations. We quantify the interpenetration of two opposing brushes by the characteristic penetration length and by two integral parameters: the overlap integral, Γ, representing the number of interbush contacts, and the number of brush monomer units in the foreign half-space, Σ. The interpenetration parameters are studied in two conjugate ensembles as functions of the brush separation and of the external pressure. We propose a theoretical description of the solvent-mediated friction force in the low shearing rate regime on the basis of the Brinkman equation for two compressed brushes sliding against each other. We demonstrate that the total friction force which also includes direct brush–brush friction is expressed in terms of Γ and Σ. The SCF data for the interpenetration parameters Γ and Σ and hence for the total sliding friction force in the pressure ensemble collapse onto universal master curves when rescaled by the factor (N/σ)1/3 as suggested by the theory, where N is the chain length and σ is the surface grafting density. Finally, we define the kinetic friction coefficient as a function of the external pressure and analyze its universal rescaled behavior in the two limits of nondraining and free-draining brushes.

Analysis of the Ability of C6H5I to Phosphoresce.

The heavy atom effect is a widely utilized strategy to enhance the phosphorescence intensity of organic molecules. Among the preferred choices, heavy halogen atoms such as bromine (Br) or iodine (I) have gained popularity. However, the incorporation of these heavy atoms can introduce challenges due to the presence of unstable excited states that undergo dissociation upon excitation. This study focuses on investigating the excited states of the C6H5I molecule, with particular emphasis on the intricate interplay of spin-orbital coupling effects, employing multireference ab initio methodologies. The absence of phosphorescence in the C6H5I molecule is attributed to the efficient energy transfer to dissociative excited states and the near-zero spin-orbital coupling between stable triplet sub-levels and the ground singlet state. To gain insights into the explicit dynamics of the excited states, the research employed Ehrenfest dynamics driven by real-time time-dependent density functional theory (TDDFT). Furthermore, the study explored the complete active space compositions and various post-CASSCF (complete active space self-consistent field) approaches.

Quadripartite bond length rule applied to two prototypical aromatic and antiaromatic molecules

ContextIn 2000, a remarkably simple relationship was introduced, which connected the calculated geometries of isomolecular states of three different multiplicities. These encompass a ground single state, the first excited triplet state, as well as related radical anion and radical cation. The rule allows the prediction of the geometry of one of the species if the three remaining ones are known. Here, we verify the applicability of this bond length rule for two small planar cyclic organic molecules, i.e., benzene and cyclobutadiene, which stand as prototypical examples of, respectively, aromatic and antiaromatic systems. We see that the rule works fairly well to benzene, and it works independently for quinoid as well as for anti-quinoid minima, despite the fact that radical anion species poses challenges for correct theoretical description.MethodsTo obtain chosen electronic state equilibrium geometries, three types of computational approaches were utilized: fast and efficient density functional theory DFT, the coupled cluster method CC2, the complete active space self-consistent field (CASSCF) approach, and the most accurate but also resource-consuming perturbation theory with multireference wavefunction (CASPT2) with a default value and without IPEA-shift. Dunning and co-workers correlation-consistent basis sets (aug-)cc-pVXZ (X = D, T, Q) were employed. Gaussian 16 revision A.03, Turbomole 7.1, and Molcas 8.0 computational software were used.

Compression and interpenetration of adsorption-active brushes.

Compression and interpenetration of two opposing polymer brushes formed by end-grafted adsorption-active chains are studied by the numerical self-consistent field approach and by analytical theory. For sufficiently strong polymer-surface attraction, a fraction of chains in the adsorption-active brush condenses into a near-surface layer, while the remaining ones form the outer brush with reduced effective grafting density. Analysis shows that the normal pressure in adsorption-active brushes can be understood in terms of the effective grafting density concept although the pressure at small separations is affected by the presence of the dense adsorbed phase. We propose a simple theory modification that accounts for this effect. We also formulate a procedure for extracting the value of the effective grafting density directly from the pressure vs separation curves by inverting the equation of state. In contrast to the normal pressure, the interpenetration of the two opposing adsorption-active brushes demonstrates a much more intricate behavior. At weak to moderate compressions, the effective grafting density concept works well but fails spectacularly at small interbrush separations. We identify two interpenetration regimes for adsorption-active brushes: (i) at separations larger than the ideal Gaussian coil size N1/2, the overlap of the two brushes is concentrated in the mid-plane region, in the same way as in brushes grafted onto non-attractive surfaces; (ii) at separations less than N1/2, the brush overlap is strongly enhanced in the wall regions where the attractive interaction plays an important role both in generating the dense layer for the "proper" brush and in attracting the "foreign" chains.

Combining Time-Dependent Density Functional Theory and the ΔSCF Approach for Accurate Core-Electron Spectra.

Spectroscopies that probe electronic excitations from core levels into unoccupied orbitals, such as X-ray absorption spectroscopy and electron energy loss spectroscopy, are widely used to gain insight into the electronic and chemical structure of materials. To support the interpretation of experimental spectra, we assess the performance of a first-principles approach that combines linear-response time-dependent density (TDDFT) functional theory with the Δ self-consistent field (ΔSCF) approach. In particular, we first use TDDFT to calculate the core-level spectrum and then shift the spectrum such that the lowest excitation energy from TDDFT agrees with that from ΔSCF. We apply this method to several small molecules and find encouraging agreement between calculated and measured spectra.

Electromagnetically induced transparency and absorption cross-over with a four-level Rydberg system

Electromagnetically induced transparency (EIT) and absorption (EIA) are quantum coherence phenomena which result from the interference of excitation pathways. Combining these with Rydberg atoms have opened up many possibilities for various applications. We introduce a theoretical model to study Rydberg-EIT and Rydberg-EIA effects in cold Cs and Rb atomic ensembles in a four-level ladder type scheme taking into account van der Waals type interactions between the atoms. The proposed many-body method for analysis of such systems involves a self-consistent mean field approach and it produces results which display a very good agreement with recent experiments. Our calculations also successfully demonstrate experimentally observed EIT-EIA cross-over in the Rb case. Being able to simulate the interaction effects in such systems has significant importance, especially for controlling the optical response of these.

DLPGEN: Preparing Molecular Dynamics Simulations with Support for Polarizable Force Fields.

Preparing input files for molecular dynamics (MD) simulations can be a tedious task, particularly if different MD programs need to be used. Most simulation packages are accompanied by applications that handle this task, and, in some cases, software to perform interconversion between MD programs can be found. However, the conversion between different types of files is not always foolproof or the force field may not be fully supported, as quite often observed with polarization models. This work describes the program DLPGEN, which produces input files for the MD programs GROMACS, CHARMM, DL_POLY, and LAMMPS. The program can prepare polarizable force fields using a self-consistent field approach or with a dual thermostat-extended Lagrangian model. For GROMACS, a new polarization scheme suitable for the simulation of molecules containing more than one virtual particle is described. Results obtained for ethanol in the liquid state revealed that the system configurational energy, liquid density, and self-diffusion coefficient obtained with GROMACS are in good agreement with the data found with LAMMPS and CHARMM. In the case of DL_POLY, a problem with the Shells temperature control was found, suggesting that this program may not be suitable for the simulation of molecules containing multiple Drude particles.

Predicting the Mechanism and Products of CO2 Capture by Amines in the Presence of H2O

An extensive correlated molecular orbital theory study of the reactions of CO2 with a range of substituted amines and H2O in the gas phase and aqueous solution was performed at the G3(MP2) level with a self-consistent reaction field approach. The G3(MP2) calculations were benchmarked at the CCSD(T)/CBS level for NH3 reactions. A catalytic NH3 reduces the energy barrier more than a catalytic H2O for the formation of H2NCOOH and H2CO3. In aqueous solution, the barriers to form both H2NCOOH and H2CO3 are reduced, with HCO3- formation possible with one amine present and H2NCOO- formation possible only with two amines. Further reactions of H2NCOOH to form HNCO and urea via the Bazarov reaction have high barriers and are unlikely in both the gas phase and aqueous solution. Reaction coordinates for CH3NH2, CH3CH2NH2, (CH3)2NH, CH3CH2CH2NH2, (CH3)3N, and DMAP were also calculated. The barrier for proton transfer correlates with amine basicity for alkylammonium carbamate (ΔG‡aq < 15 kcal/mol) and alkylammonium bicarbonate (ΔG‡aq < 30 kcal/mol) formation. In aqueous solution, carbamic acids, carbamates, and bicarbonates can all form in small amounts with ammonium carbamates dominating for primary and secondary alkylamines. These results have implications for CO2 capture by amines in both the gas phase and aqueous solution as well as in the solid state, if enough water is present.

Diagonalization-free self-consistent field approach with localized molecular orbitals

Diagonalization-free self-consistent field approach with localized molecular orbitals

Methods and Models of Theoretical Calculation for Single-Molecule Magnets

Theoretical calculation plays an important role in the emerging field of single-molecule magnets (SMMs). It can not only explain experimental phenomena but also provide synthetic guidance. This review focuses on discussing the computational methods that have been used in this field in recent years. The most common and effective method is the complete active space self-consistent field (CASSCF) approach, which predicts mononuclear SMM property very well. For bi- and multi-nuclear SMMs, magnetic exchange needs to be considered, and the exchange coupling constants can be obtained by Monte Carlo (MC) simulation, ab initio calculation via the POLY_ANISO program and density functional theory combined with a broken-symmetry (DFT-BS) approach. Further application for these calculation methods to design high performance SMMs is also discussed.

Prediction of An(III)/Ln(III) Separation by 1,2,4-Triazinylpyridine Derivatives.

The effect of frustrated Lewis donors on metal selectivity between actinides and lanthanides was studied using a series of novel organic ligands. Structures and thermodynamic energies were predicted in the gas phase, in water, and in butanol using 9-coordinate, explicitly solvated (H2O) Eu, Gd, Am, and Cm in the +III oxidation state as reactants in the formation of complexes with 2-(6-[1,2,4]-triazin-3-yl-pyridin-2-yl)-1H-indole (Core 1), 3-[6-(2H-pyrazol-3-yl)pyridin-2-yl]-1,2,4-triazine (Core 2), and several derivatives. These complexations were studied using density functional theory (DFT) incorporating scalar relativistic effects on the actinides and lanthanides using a small core pseudopotential and corresponding basis set. A self-consistent reaction field approach was used to model the effect of water and butanol as solvents. Coordination preferences and metal selectivity are predicted for each ligand. Several ligands are predicted to have a high degree of selectivity, particularly when a low ionization potential in the ligand permits charge transfer to Eu(III), reducing it to Eu(II) and creating a half-filled f7 shell. Reasonable separation is predicted between Cm(III) and Gd(III) with Core 1 ligands, possibly due to ligand donor frustration. This separation is largely absent from Core 2 ligands, which are predicted to lose their frustration due to proton transfer from the 2N to the 3N position of the pyrazole component of the ligands via tautomerization.

Direct energy minimization based on exponential transformation in density functional calculations of finite and extended systems

The energy minimization involved in density functional calculations of electronic systems can be carried out using an exponential transformation that preserves the orthonormality of the orbitals. The energy of the system is then represented as a function of the elements of a skew-Hermitian matrix that can be optimized directly using unconstrained minimization methods. An implementation based on the limited memory Broyden-Fletcher-Goldfarb-Shanno approach with inexact line search and a preconditioner is presented and the performance compared with that of the commonly used self-consistent field approach. Results are presented for the G2 set of 148 molecules, liquid water configurations with up to 576 molecules and some insulating crystals. A general preconditioner is presented that is applicable to systems with fractional orbital occupation as is, for example, needed in the k-point sampling for periodic systems. This exponential transformation direct minimization approach is found to outperform the standard implementation of the self-consistent field approach in that all the calculations converge with the same set of parameter values and it requires less computational effort on average. The formulation of the exponential transformation and the gradients of the energy presented here are quite general and can be applied to energy functionals that are not unitary invariant such as self-interaction corrected functionals.

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.