Hartree-Fock Research Articles

Electron Binding Energies of Open-Shell Species from Diagonal Electron-Propagator Self-Energies with Unrestricted Hartree-Fock Spin-Orbitals.

For closed-shell molecules, valence electron binding energies may be calculated accurately and efficiently with ab initio electron-propagator methods that have surpassed their predecessors. Advantageous combinations of accuracy and efficiency range from cubically scaling methods with mean errors of 0.2 eV to quintically scaling methods with mean errors of 0.1 eV or less. The diagonal self-energy approximation in the canonical Hartree-Fock basis is responsible for the enhanced efficiency of several methods. This work examines the predictive capabilities of diagonal self-energy approximations when they are generalized to the canonical spin-orbital basis of unrestricted Hartree-Fock (UHF) theory. Experimental data on atomic electron binding energies and high-level, correlated calculations in a fixed basis for a set of open-shell molecules constitute standards of comparison. A review of the underlying theory and analysis of numerical errors lead to several recommendations for the calculation of electron binding energies: (1) In calculations that employ the diagonal self-energy approximation, Koopmans's identity for UHF must be qualitatively correct. (2) Closed-shell reference states are preferable to open-shell reference states in calculations of molecular ionization energies and electron affinities. (3) For molecular electron binding energies between doublets and triplets, calculations of electron detachment energies are more accurate and efficient than calculations of electron attachment energies. When these recommendations are followed, mean absolute errors increase by approximately 0.05 eV with respect to their counterparts obtained with closed-shell reference orbitals.

Optical Properties of Three‐Electron GaAs/AlxGa1−xAs QDs with Finite Confinement Potential

AbstractIn the case of finite confinement potential, the average energies and corresponding wave functions for the 1s2nl configurations, in which nl = 2s, 2p, 3d, and 4f, of three‐electron GaAs/AlxGa1−xAs quantum dot with and without impurity are computed by using a new variational approach which is a combination of Quantum Genetic Algorithm procedure and Hartree–Fock–Roothaan method. Using the calculated average energies and wave functions, a detailed investigation of the linear, third‐order nonlinear and total absorption coefficients (ACs) and the refractive index changes (RICs) for the quantum dot is performed, and the obtained results are presented as a function of dot radius and photon energies. The results show that the dot radius, the impurity charge, and the height of potential barrier have a strong influence on the average energies and absorption spectra of the system. As the potential barrier height increases, the peak positions of the ACs and RICs shift toward higher energy, and there is a significant increase in the amplitudes of the absorption spectra as the potential barrier height increases. In addition, the electron wave functions begin to enter the quantum well at smaller dot radii with increasing barrier height.

Ion Correlation-Driven Hysteretic Adhesion and Repulsion between Opposing Polyelectrolyte Brushes.

Polyelectrolyte (PE) brushes are widely used in biomaterials and nanotechnology to regulate the surface properties and interactions. Here, we apply the electrostatic correlation augmented self-consistent field theory to investigate the interactions between opposing PE brushes in a mixture of 1:1 and 3:1 salt solutions. Our theory predicts a hysteretic feature of the normal stress induced by strong ion correlations. In the presence of trivalent ions, the force profile is discontinuous: repulsive in the compression branch and adhesive in the separation branch. The molecular origin of the hysteretic force is the coexistence of two collapsed modes: two separated condensed layers on each surface in the compression and a single bundled condensed layer in the separation. With the systematic inclusion of ion correlations, our theory captures well the hysteretic force, adhesive separation, "jump-in" and "jump-out" features, and the "specific ion effect", all in good agreement with the reported experimental results.

Simulation of Vibrational Circular Dichroism Spectra Using Second-Order Møller-Plesset Perturbation Theory and Configuration Interaction Doubles.

We present the first single-reference calculations of the atomic axial tensors (AATs) with wave function-based methods including dynamic electron correlation effects using second-order Møller-Plesset perturbation theory (MP2) and configuration interaction doubles (CID). Our implementation involves computing the overlap of numerical derivatives of the correlated wave functions with respect to both nuclear displacement coordinates and the external magnetic field. Out test set included three small molecules, including the axially chiral hydrogen molecule dimer and (P)-hydrogen peroxide, and the achiral H2O. For our molecular test set, we observed deviations of the AATs for MP2 and CID from that of the Hartree-Fock (HF) method upward of 49%, varying with the choice of basis set. For (P)-hydrogen peroxide, electron correlation effects on the vibrational circular dichroism (VCD) rotatory strengths and corresponding spectra were particularly significant, with maximum deviations of the rotatory strengths of 62 and 49% for MP2 and CID, respectively, using our largest basis set. The inclusion of dynamic electron correlation to the computation of the AATs can have a significant impact on the resulting rotatory strengths and VCD spectra.

Effect of nonzero temperature to non-condensed fraction of a homogeneous dilute weakly interacting Bose gas

This study aims to investigate the effect of nonzero temperature to the non-condensed fraction of a homogeneous repulsive weakly interacting Bose gas in region of sufficiently low temperature. Within improved Hartree-Fock approximation, the Cornwall–Jackiw–Tomboulis effective action approach shows that the thermal fluctuations make the non-condensed fraction increase as a second and fourth-order power law of temperature. Indeed, the effect of non-infinite size of the trap is also integrated. The result is compared with experimental data.

Riemannian Newton Methods for Energy Minimization Problems of Kohn–Sham Type

This paper is devoted to the numerical solution of constrained energy minimization problems arising in computational physics and chemistry such as the Gross–Pitaevskii and Kohn–Sham models. In particular, we introduce Riemannian Newton methods on the infinite-dimensional Stiefel and Grassmann manifolds. We study the geometry of these two manifolds, its impact on the Newton algorithms, and present expressions of the Riemannian Hessians in the infinite-dimensional setting, which are suitable for variational spatial discretizations. A series of numerical experiments illustrates the performance of the methods and demonstrates their supremacy compared to other well-established schemes such as the self-consistent field iteration and gradient descent schemes.

A Polarizable QM/MM Model That Combines the State-Averaged CASSCF and AMOEBA Force Field for Photoreactions in Proteins.

This study presents the polarizable quantum mechanics/molecular mechanics (QM/MM) embedding of the state-averaged complete active space self-consistent field (SA-CASSCF) in the atomic multipole optimized energetics for biomolecular applications (AMOEBA) force field for the purpose of studying photoreactions in protein environments. We describe two extensions of our previous work that combine SA-CASSCF with AMOEBA water models, allowing it to be generalized to AMOEBA models for proteins and other macromolecules. First, we discuss how our QM/MM model accounts for the discrepancy between the direct and polarization electric fields that arises in the AMOEBA description of intramolecular polarization. A second improvement is the incorporation of link atom schemes to treat instances in which the QM/MM boundary goes through covalent bonds. A single-link atom scheme and double-link atom scheme are considered in this work, and we will discuss how electrostatic interaction, van der Waals interaction, and various kinds of valence terms are treated across the boundary. To test the accuracy of the link atom scheme, we will compare QM/MM with full QM calculations and study how the errors in ground state properties, excited state properties, and excitation energies change when tuning the parameters in the link atom scheme. We will also test the new SA-CASSCF/AMOEBA method on an elementary reaction step in NanoLuc, an artificial bioluminescence luciferase. We will show how the reaction mechanism is different when calculated in the gas phase, in polarizable continuum medium (PCM), versus in protein AMOEBA models.

The Block Copolymer Phase Behavior Database.

The Block Copolymer Database (BCDB) is a platform that allows users to search, submit, visualize, benchmark, and download experimental phase measurements and their associated characterization information for di- and multiblock copolymers. To the best of our knowledge, there is no widely accepted data model for publishing experimental and simulation data on block copolymer self-assembly. This proposed data schema with traceable information can accommodate any number of blocks and at the time of publication contains over 5400 block copolymer total melt phase measurements mined from the literature and manually curated and simulation data points of the phase diagram generated from self-consistent field theory that can rapidly be augmented. This database can be accessed via the Community Resource for Innovation in Polymer Technology (CRIPT) web application and the Materials Data Facility. The chemical structure of the polymer is encoded in BigSMILES, an extension of the Simplified Molecular-Input Line-Entry System (SMILES) into the macromolecular domain, and the user can search repeat units and functional groups using the SMARTS search syntax (SMILES Arbitrary Target Specification). The user can also query characterization and phase information using Structured Query Language (SQL) and download custom sets of block copolymer data to train machine learning models. Finally, a protocol is presented in which GPT-4, an AI-powered large language model, can be used to rapidly screen and identify block copolymer papers from the literature using only the abstract text and determine whether they have BCDB data, allowing the database to grow as the number of published papers on the World Wide Web increases. The F1 score for this model is 0.74. This platform is an important step in making polymer data more accessible to the broader community.

Exploiting the Correlation between the 1s, 2s, and 2p Energies for the Prediction of Core-Level Binding Energies of Si, P, S, and Cl species.

The binding energies (BEs) of the 1s, 2s, and 2p core electrons of third-period elements (Si, P, S, Cl) were calculated using Hartree-Fock (HF) and B3LYP, BH&HLYP, and LC-BOP ΔSCF, and the shifted KS ΔSCF methods. Linear relationships between two BEs were derived and compared with the Auger parameter. The derived lines are essentially parallel, with only the intercepts differing. The difference in intercepts is due to the lack of electron correlation effects in HF and the self-interaction errors (SIEs) of the functional. The slope is the slope of the linear relationship between the chemical shifts. The straight lines between the 2s and 2p BEs also coincided with the Auger parameter lines, which have a slope of 1 by definition and an intercept being the difference between the 2s and 2p BEs. The shifted KS ΔSCF scheme compensates for SIEs, yielding equations that are approximately invariant. The calculated average gaps for the 2s and 2p BEs are 51.21 eV for Si, 57.48 eV for P, 63.85 eV for S, and 70.48 eV for Cl. The straight lines representing the relationships between the BEs of the 1s and 2s and 1s and 2p electrons are also parallel to each other in ΔSCF and converge into a single line in the shifted ΔSCF scheme. However, these lines are steeper than the Auger parameter line. The derived relationships can be used to predict unknown BEs, which we have applied to many molecules. The results are highly accurate, with mean absolute errors (MAEs) of less than 0.2 eV compared to experimental values.

First-principle calculations of the electronic, vibrational, and thermodynamic properties of nitrogen-rich salt of 3,6-dinitramino-1,2,4,5-tetrazine [(NH4)2(DNAT)

Energy-containing materials such as explosives have attracted considerable interest recently. In the field of high-energy materials, tetrazine and its derivatives can largely meet the requirements of high nitrogen content and oxygen balance. Nitrogen-rich energetic salts are important research subjects. Nitrogen-rich salt of 3,6-dinitramino-1,2,4,5-tetrazine is a high-energy nitrogen-rich material, but there are few related studies. This paper systematically studies the crystal structure and electronic, vibrational, and thermodynamic properties of (NH4)2(DNAT). The lattice parameters of (NH4)2(DNAT) are observed to align well with the experimental values. The properties of electrons are analyzed by band structure and density of states (DOS). The phonon dispersion curves indicate that the compound is dynamically stable. The vibrational modes of bonds and chemical groups are described in detail, and the peaks in the Raman and infrared spectra are assigned to different vibration modes. Based on the vibration characteristics, thermodynamic properties such as enthalpy (H), Helmholtz free energy (F), entropy (S), Gibbs free energy (G), constant volume heat capacity (CV), and Debye temperature (Θ) are analyzed. This article can pave the way for subsequent work or provide data support to other researchers, promoting further research. In this study, we utilized the density functional theory (DFT) for our calculations. The exchange-correlation potential and van der Waals interactions were characterized based on the GGA-PBE + G function calculation. We obtained Brillouin zone integrals using Monkhorst-Pack k-point grids, with the k-point of the Brillouin zone set to a 2 × 2 × 2 grid. During the self-consistent field operation, we set the total energy convergence tolerance to 5 × 10-6eV per atom. The cut-off energy for the calculation was established at 830eV. Additionally, the states of H (1s1), C (2s2 2p2), N (2s2 2p3), and O (2s2 2p4) were treated as valence electrons in our study.

Geometric Optimization of Restricted-Open and Complete Active Space Self-Consistent Field Wave Functions.

We explore Riemannian optimization methods for Restricted-Open-shell Hartree-Fock (ROHF) and Complete Active Space Self-Consistent Field (CASSCF) methods. After showing that ROHF and CASSCF can be reformulated as optimization problems on so-called "flag manifolds", we review Riemannian optimization basics and their application to these specific problems. We compare these methods to traditional ones and find robust convergence properties without fine-tuning of numerical parameters. Our study suggests that Riemannian optimization is a valuable addition to orbital optimization for ROHF and CASSCF, warranting further investigation.

Nonlinear Charge Transport and Excitable Phenomena in Semiconductor Superlattices.

Semiconductor superlattices are periodic nanostructures consisting of epitaxially grown quantum wells and barriers. For thick barriers, the quantum wells are weakly coupled and the main transport mechanism is a sequential resonant tunneling of electrons between wells. We review quantum transport in these materials, and the rate equations for electron densities, currents, and the self-consistent electric potential or field. Depending on superlattice configuration, doping density, temperature, voltage bias, and other parameters, superlattices behave as excitable systems, and can respond to abrupt dc bias changes by large transients involving charge density waves before arriving at a stable stationary state. For other parameters, the superlattices may have self-sustained oscillations of the current through them. These oscillations are due to repeated triggering and recycling of charge density waves, and can be periodic in time, quasiperiodic, and chaotic. Modifying the superlattice configuration, it is possible to attain robust chaos due to wave dynamics. External noise of appropriate strength can generate time-periodic current oscillations when the superlattice is in a stable stationary state without noise, which is called the coherence resonance. In turn, these oscillations can resonate with a periodic signal in the presence of sufficient noise, thereby displaying a stochastic resonance. These properties can be exploited to design and build many devices. Here, we describe detectors of weak signals by using coherence and stochastic resonance and fast generators of true random sequences useful for safe communications and storage.

Combined Multireference-Multiscale Approach to the Description of Photosynthetic Reaction Centers.

A first-principles description of the primary photochemical processes that drive photosynthesis and sustain life on our planet remains one of the grand challenges of modern science. Recent research established that explicit incorporation of protein electrostatics in excited-state calculations of photosynthetic pigments, achieved for example with quantum-mechanics/molecular-mechanics (QM/MM) approaches, is essential for a meaningful description of the properties and function of pigment-protein complexes. Although time-dependent density functional theory has been used productively so far in QM/MM approaches for the study of such systems, this methodology has limitations. Here we pursue for the first time a QM/MM description of the reaction center in the principal enzyme of oxygenic photosynthesis, Photosystem II, using multireference wave function theory for the high-level QM region. We identify best practices and establish guidelines regarding the rational choice of active space and appropriate state-averaging for the efficient and reliable use of complete active space self-consistent field (CASSCF) and the N-electron valence state perturbation theory (NEVPT2) in the prediction of low-lying excited states of chlorophyll and pheophytin pigments. Given that the Gouterman orbitals are inadequate as a minimal active space, we define specific minimal and extended active spaces for the NEVPT2 description of electronic states that fall within the Q and B bands. Subsequently, we apply our multireference-QM/MM protocol to the description of all pigments in the reaction center of Photosystem II. The calculations reproduce the electrochromic shifts induced by the protein matrix and the ordering of site energies consistent with the identity of the primary donor (ChlD1) and the experimentally known asymmetric and directional electron transfer. The optimized protocol sets the stage for future multireference treatments of multiple pigments, and hence for multireference studies of charge separation, while it is transferable to the study of any photoactive embedded tetrapyrrole system.

Experimental molecular structures in the gas phase at the upper size limit: The case of Si6Tip6.

Currently, the largest (ramax = 19.9Å) and by far the most complicated (234 atoms, C1 symmetry, 696 independent geometrical parameters, and 27 261 interatomic terms) experimental molecular structure of a cage-type Si6Tip6 (Tip = 2,4,6-iPr3C6H2) isomer has been investigated in the gas phase by the electron diffraction method (Tav = 645K) supplemented with theoretical simulations. A detailed analysis of the current possibilities for experimentally investigating large molecular structures is performed. A series of density functional theory approximations and the role of dispersion interactions have been benchmarked using the obtained data. Based on the refined geometry of Si6Tip6, various quantum-chemical methods have been applied for the investigation of the electronic structure of its Si6 core. In particular, natural bond orbital, quantum theory of atoms in molecules, interacting quantum atoms, fractional occupation number weighted density, and complete active space self-consistent field (CASSCF) methods were utilized. The diradical character of the molecule has been assessed by the UHF and CASSCF approximations. The problem of bonding between the hemispheroidal silicon atoms has been investigated.

Long-range Corrected Density Functional Theory Including a Two-Gaussian Hartree-Fock Operator for High Accuracy Core-excitation Energy Calculations of Both the Second- and Third-Row Atoms (LC2gau-core-BOP).

In the previous work, LCgau-core-BOP, which includes the short-range interelectronic Gaussian attenuating Hartree-Fock (HF) exchange to the long-range HF exchange, showed high accuracy core-excitation energies from 1s orbitals of the second-row atoms (1s → π*, 1s → σ*, 1s → n*, and 1s → Rydberg), but underestimates the core-excitation energies from 1s orbitals of the third-row atoms. To improve this, we added one more Gaussian attenuating HF exchange to LCgau-core-BOP. We named it LC2gau-core-BOP, which achieves a mean absolute error (MAE) of 0.6 and 0.3 eV for core excitation energies of the second- and third-row atoms of the tested small molecules, respectively. We found that the inclusion of the short-range interelectronic HF exchange at a distance ranging from 0.2 to 0.6 a.u. contributes to the increase of performances on 1s orbital energy calculations of the second-row atoms, while the inclusion of more short-range interelectronic HF exchange at a distance ranging from 0 to 0.2 a.u. does to the increase of performance on 1s orbital energy calculations of the third-row atoms. It is notable that all of these improvements were accomplished using flexible Gaussian attenuating HF exchange inclusion. LC2gau-core-BOP shows deviations of less than 0.8 eV from experimental values for all of the core-excitation energies of the tested medium-size molecules consisting of thymine, oxazole, glycine, and dibenzothiophene sulfone. Moreover, by optimizing one parameter of the OP correlation functional, LC2gau-core-BOP provides atomization energies over the G3 test set with an accuracy comparable to that of B3LYP.

The Photophysics and Photochemistry of Phenylalanine, Tyrosine, and Tryptophan: A CASSCF/CASPT2 Study.

Among all amino acids, the three aromatic systems including phenylalanine, tyrosine, and tryptophan are known to manifest UV light absorption at the higher wavelengths. Their fluorescent properties are important for protein detection and determination of the spatial structure. Based on ab initio quantum chemical calculations, the absorption spectra in the 0-12 eV UV range of these aromatic amino acids were interpreted, and the photochemistry of the lowest-lying excited states was studied. For that, molecular ground-state geometries were determined using both the coupled-cluster single and double (CCSD) and complete active space self-consistent field (CASSCF) methods. The vertical electronic transition energies, associated oscillator strengths, and electric dipole moments of the lowest excited states were computed at the CASPT2//CASSCF level. The decay mechanisms of the lowest-energy excited states were investigated by performing minimum energy path (MEPs) computations. The results showed that the CCSD and CASSCF computations yielded similar structures. The lowest-energy S1 state in phenylalanine and tyrosine, and S1 and S2 in tryptophan are mainly described by the π → π* excitation localized in the aromatic ring. Upon light absorption, the main photoresponse of the molecules is driven by the benzene, phenol, and indole chromophoric units.

Multi-Level Protocol for Mechanistic Reaction Studies Using Semi-Local Fitted Potential Energy Surfaces.

In this work, we propose a multi-level protocol for routine theoretical studies of chemical reaction mechanisms. The initial reaction paths of our investigated systems are sampled using the Nudged Elastic Band (NEB) method driven by a cheap electronic structure method. Forces recalculated at the more accurate electronic structure theory for a set of points on the path are fitted with a machine learning technique (in our case symmetric gradient domain machine learning or sGDML) to produce a semi-local reactive potential energy surface (PES), embracing reactants, products and transition state (TS) regions. This approach has been successfully applied to a unimolecular (Bergman cyclization of enediyne) and a bimolecular (SN2 substitution) reaction. In particular, we demonstrate that with only 50 to 150 energy-force evaluations with the accurate reference methods (here complete-active-space self-consistent field, CASSCF, and coupled-cluster singles and doubles, CCSD) it is possible to construct a semi-local PES giving qualitative agreement for stationary-point geometries, intrinsic reaction coordinates and barriers. Furthermore, we find a qualitative agreement in vibrational frequencies and reaction rate coefficients. The key aspect of the method's performance is its multi-level nature, which not only saves computational effort but also allows extracting meaningful information along the reaction path, characterized by zero gradients in all but one direction. Agnostic to the nature of the TS and computationally economic, the protocol can be readily automated and routinely used for mechanistic reaction studies.

Matrix methods for opacity calculations

Atomic structure calculations are the first step in an opacity calculation. They provide the self-consistent electronic potential and electron wavefunctions that are needed to evaluate the Slater integrals and dipole matrix elements. In this paper, we show that simple matrix methods can be used to perform Hartree–Fock–Slater or LDA calculations on standard atomic structure grids, including relativistic corrections, yielding bound and continuum wavefunctions that can be used, in conjunction with statistical broadening techniques, to obtain realistic average-atom opacities.

First-principles investigation of lanthanides diffusion in HCP zirconium via vacancy-mediated transport

The diffusion of lanthanide fission products plays an important role in the growth of the fuel-cladding chemical interaction (FCCI) region in metallic fuels. The use of a Zr interdiffusion barrier may mitigate the transport of lanthanides from the fuel to the cladding, but the efficacy of such a liner is not yet known. In this paper, the stability and vacancy-mediated diffusion of La, Ce, Pr, and Nd in hexagonal close-packed (HCP) Zr is investigated via density functional theory (DFT) calculations and self-consistent mean field (SCMF) analysis. DFT is used to calculate the formation, binding, and migration energies of vacancies and vacancy-solute pairs. The DFT energetics are used in the KineCluE code to calculate the Onsager transport coefficients. La is found to be the fastest diffusing species in HCP Zr and experiences an almost isotropic diffusion behavior. The other three species (Ce, Pr, and Nd) demonstrate anisotropic diffusion where the diffusion in the basal planes is significantly faster than that along the c-axis. The calculated lanthanide diffusivities in HCP Zr are fitted to an Arrhenius relation and the activation energies and prefactors are reported for the first time. Furthermore, the vacancy drag and the segregation tendencies were analyzed using the calculated off-diagonal transport coefficients. According to our vacancy-mediated diffusion model, lanthanides are expected to be enriched at vacancy sinks at low temperatures, while at high temperatures, lanthanides are depleted at sinks and will preferably diffuse into the bulk. The enrichment/depletion transition temperature depends on the diffusion direction (basal or axial) and hence will be controlled by the grain texture and orientation.

Eliashberg Theory for Dynamical Screening in Bilayer Exciton Condensation.

We study the effect of dynamical screening of interactions on the transition temperatures (T_{c}) of exciton condensation in a symmetric bilayer of quadratically dispersing electrons and holes by solving the linearized Eliashberg equations for the anomalous interlayer Green's functions. We find that T_{c} is finite for the range of density and layer separations studied, decaying exponentially with interlayer separation. T_{c} is suppressed well below that predicted by a Hartree Fock mean field theory with unscreened Coulomb interaction, but is above the estimates from the statically screened Coulomb interaction. Furthermore, using a diagrammatic framework, we show that the system is always an exciton condensate at zero temperature but T_{c} is exponentially small for large interlayer separation.