Hartree-Fock Research Articles

Distinguishing homolytic vs heterolytic bond dissociation of phenylsulfonium cations with localized active space methods

Modeling chemical reactions with quantum chemical methods is challenging when the electronic structure varies significantly throughout the reaction and when electronic excited states are involved. Multireference methods, such as complete active space self-consistent field (CASSCF), can handle these multiconfigurational situations. However, even if the size of the needed active space is affordable, in many cases, the active space does not change consistently from reactant to product, causing discontinuities in the potential energy surface. The localized active space SCF (LASSCF) is a cheaper alternative to CASSCF for strongly correlated systems with weakly correlated fragments. The method is used for the first time to study a chemical reaction, namely the bond dissociation of a mono-, di-, and triphenylsulfonium cation. LASSCF calculations generate smooth potential energy scans more easily than the corresponding, more computationally expensive CASSCF calculations while predicting similar bond dissociation energies. Our calculations suggest a homolytic bond cleavage for di- and triphenylsulfonium and a heterolytic pathway for monophenylsulfonium.

An Adaptive High-Order Surface Finite Element Method for Polymeric Self-Consistent Field Theory on General Curved Surfaces

An Adaptive High-Order Surface Finite Element Method for Polymeric Self-Consistent Field Theory on General Curved Surfaces

Systematic study of capture thresholds with time dependent Hartree-Fock theory

Systematic study of capture thresholds with time dependent Hartree-Fock theory

Effect of Additive (1-Butyl-1-methyl Pyrrolidinium Tetrafluoroborate) on Volumetric, Acoustic and Conductance Properties of Binary Aqueous Solutions of Benzylamine at T = (288.15, 298.15, 308.15, 318.15) K

Effect of additive, 1-butyl-1-methyl pyrrolidinium tetrafluoroborate [BmPyrr+][BF4–] on the volumetric, acoustic and conductance properties of binary aqueous solution of benzylamine has been analyzed at equidistant temperature range using different techniques. Using density and speed of sound data, volumetric and acoustic parameters like apparent and partial molar volumes (Vφ and Vφ0), apparent and partial molar isentropic compressions (Kφ,S and K0φ,S), partial molar volume of transfer and partial molar isentropic compression of transfer (ΔVφ0 and ΔK0φ,S) have been calculated. Conductance parameters like molar conductance (Λm), limiting molar conductance (Λ°m) and activation energy are also calculated using conductance data. All these parameters were used to analyze various types of interactions present in the system. Furthermore, density functional theory (DFT) calculations were conducted for comprehensive understanding of structural variations of ion pairs affecting their physical properties. The hydrogen bond formation in the mixture components was examined by using IR spectrum. Both DFT and Hartee-Fock (HF) methods were used to analyze the results. In addition, the DFT/B3LYP-D3 calculations were also carried out to gather data on the molecular geometry, interactions and other molecular characteristics of the ionic liquid under study.

Deformed Shell Model Applications to Weak Interaction Processes

The deformed shell model (DSM), based on Hartree–Fock intrinsic states with angular momentum projection and band mixing, has been found to be quite successful in describing many spectroscopic properties of nuclei in the A = 60–100 region. More importantly, DSM has been used recently with good success in calculating nuclear structure factors, which are needed for a variety of weak interaction processes. In this article, in addition to giving an overview of this, we discuss the applications of DSM to obtain cross-sections for coherent and incoherent neutrino nucleus scattering on 96,98,100Mo targets and also for obtaining two neutrino double beta decay nuclear transition matrix elements for 100Mo.

Assessing the viability of hydrogen-based perovskites for optoelectronic and thermoelectric applications via first principle modeling.

In this study, we delve into the physical characteristics of six hydride perovskites of ABH3-type materials (CsCaH3, CsSrH3, KMgH3, LiBaH3, NaBeH3, and RbCaH3). Our investigation primarily focuses on assessing their structural stability by determining the enthalpy of formation and examining the dispersion of phonons. Using band structure calculations, we discern the characteristics of semiconductors, observing a direct bandgap in all four perovskites except NaBeH3 and KMgH3, which exhibit indirect gaps. Among these, NaBeH3 possesses the narrowest gap at 1.91 eV, while the widest gap is observed in the perovskite RbCaH3, measuring 4.56 eV. Furthermore, we conduct a thorough analysis of their optical properties, including parameters such as the real and imaginary dielectric function, absorption coefficient, and refractive index within an energy range of 0 to 14 eV. The results of our study are highly encouraging, suggesting that these materials hold significant promise for utilization in photovoltaic cells. This is primarily attributed to their remarkable ability to absorb light across both the ultraviolet (UV) and visible spectra. Additionally, we conducted an assessment of the thermoelectric properties of the six perovskite materials. RbMgH3 exhibits a maximum Seebeck coefficient (Smax) of 1.5 mV/K, whereas KMgH3 achieves a figure of merit reaching unity. These findings present promising opportunities for utilizing these compounds in thermoelectric devices. In this study, all self-consistent field (SCF) calculations were performed using density functional theory (DFT), employing the FP-LAPW + lo method as implemented in the Wien2k code. The Perdew-Burke-Ernzerhof (PBE) generalized gradient approximation, the modified Becke-Johnson (mBJ) methods, and the HSE06 hybrid functional were employed to characterize the exchange-correlation interactions. Thermoelectric parameters were extracted using the BoltzTraP software.

How Does HF-DFT Achieve Chemical Accuracy for Water Clusters?

Bolstered by recent calculations of exact functional-driven errors (FEs) and density-driven errors (DEs) of semilocal density functionals in the water dimer binding energy [Kanungo, B. J. Phys. Chem. Lett. 2024, 15, 323-328], we investigate approximate FEs and DEs in neutral water clusters containing up to 20 monomers, charged water clusters, and alkali- and halide-water clusters. Our proxy for the exact density is r2SCAN 50, a 50% global hybrid of exact exchange with r2SCAN, which may be less correct than r2SCAN for the compact water monomer but importantly more correct for long-range electron transfers in the noncompact water clusters. We show that SCAN makes substantially larger FEs for neutral water clusters than r2SCAN, while both make essentially the same DEs. Unlike the case for barrier heights, these FEs are small in a relative sense and become large in an absolute sense only due to an increase in cluster size. SCAN@HF, short for SCAN evaluated on the Hartree-Fock (HF) density, produces a cancellation of errors that makes it chemically accurate for predicting the absolute binding energies of water clusters. Likewise, adding a long-range dispersion correction to r2SCAN@HF, as in the composite method HF-r2SCAN-DC4, makes its FE more negative than in r2SCAN@HF, permitting a near-perfect cancellation of FE and DE. r2SCAN by itself (and even more so, r2SCAN evaluated on the r2SCAN 50 density), is almost perfect for the energy differences between water hexamers, and thus probably also for liquid water away from the boiling point. Thus, the accuracy of composite methods like SCAN@HF and HF-r2SCAN-DC4 is not due to the HF density being closer to the exact density, but to a compensation of errors from its greater degree of localization. We also give an argument for the approximate reliability of this unconventional error cancellation for diverse molecular properties. Finally, we confirm this unconventional error cancellation for the SCAN description of the water trimer via Kohn-Sham inversion of the CCSD(T) density.

Theoretical exploration of atomic structure calculation of sodium atom confined in the fullerene cage: a primer investigation for EIT applications

Alterations in the electronic structural properties of a sodium atom confined inside a fullerene cage are investigated in this manuscript; the engineered atom is explored to suit for the quantum technique applications. A Gaussian annular square well (GASW) model has been used to mimic the fullerene environment. Electronic properties such as energy levels, probabilities, the lifetime of the levels, etc, have been studied for various confinement depths of GASW using the multi-configuration Dirac Hartree–Fock technique. The wavelengths of the D lines of the sodium atom have been shifted from the typical yellow to the blue and then to the ultraviolet region upon confinement. Using the range-shifted blue D lines of the engineered atom, a typical Λ-type electromagnetically induced transparency configuration is proposed. Furthermore, we have shown the explicit dependency of relevant atomic parameters on the confinement depth, which showcases the tunability to suit the engineered atoms for various applications; for instance, increasing the confinement depth increases the lifetime of 3D5/2 and 3D3/2 states significantly from the typical lifetime value, which has potential applications in quantum technologies.

Relativistic Brueckner–Hartree–Fock Calculations for Cold and Hot Neutron Stars

This study investigates the properties of symmetric and asymmetric nuclear matter using the relativistic Brueckner–Hartree–Fock formalism, examining both zero and finite temperatures up to 70 MeV. Employing the full Dirac space, we incorporate three Bonn potentials (A, B, and C), which account for meson masses, coupling strengths, cutoff parameters, and form factors. The calculated properties of asymmetric nuclear matter form the basis for constructing equation-of-state (EOS) models tailored for neutron stars. These models, in turn, enable the computation of bulk properties for nonrotating, uniformly rotating, and differentially rotating neutron stars. Notably, the EOS models studied in this paper are sufficiently versatile to accommodate the mass of the most massive neutron star ever detected, PSR J0952–0607, estimated to be 2.35 ± 0.17 M ⊙. Furthermore, they yield masses and radii for PSR J0030+451 that align with the confidence intervals established for this pulsar.

Nondipolar photoelectron angular distributions from fixed-in-space N2 molecules

We investigate experimentally and theoretically the N 1s photoionization of fixed-in-space N2 molecules at a photon energy of 880 eV. In our experiment, we employed circularly polarized synchrotron radiation for the photoionization and coincident electron and fragment-ion detection using cold target recoil ion momentum spectroscopy. The accompanying angle-resolved calculations were carried out by the multichannel single-center method and code within the frozen-core Hartree–Fock approximation. The computed emission distributions exhibit two distinct features along the molecular axis, which are the results of a superposition of the direct and nearest-neighbor scattering amplitudes for the photoemission from two nitrogen atoms. In the electric-dipole approximation, these peaks are symmetric with respect to both nitrogen atoms. Including nondipole (retardation) effects in the calculations results in a simultaneous increase and decrease of the scattering peaks towards the nitrogen atoms pointing in the forward and backward directions along the light propagation, respectively. These theoretical findings are in agreement with our experimental findings.

Comparative study of kilonova opacities for three elements of the sixth period (hafnium, osmium, and gold) from new atomic structure calculations in Hf I–IV, Os I–IV, and Au I–IV

Aims. It is now well established that a large amount of heavy (trans-iron) elements are produced during neutron star (NS) mergers. These elements can be detected in the spectra of the kilonova emitted from the post-merger ejected materials. Due to the high level densities that characterize the complex configurations belonging to heavy elements, thus giving rise to millions of absorption lines, the kilonova ejecta opacity is of significant importance. The elements that contribute the most to the latter are those with an unfilled nd subshell belonging to the fifth and the sixth rows of the periodic table, and those with an unfilled nf subshell belonging to the lanthanide and actinide groups. The aim of the present work is to make a new contribution to this field by performing large-scale atomic structure calculations in three specific sixth-row 5d elements, namely hafnium, osmium, and gold, in the first four charge stages (I–IV), and by computing the corresponding opacities, while focusing on the importance of the atomic models used. Methods. The pseudo-relativistic Hartree–Fock (HFR) method, including extended sets of interacting configurations, was used for the atomic structure and radiative parameter calculations, while the expansion formalism was used to estimate the opacities. Results. Theoretical energy levels, wavelengths, and oscillator strengths were computed for millions of spectral lines in Hf I–IV, Os I–IV, and Au I–IV ions, the reliability of these parameters being assessed through detailed comparisons with previously published experimental and theoretical results. The newly obtained atomic data were then used to calculate expansion opacities for typical kilonova conditions expected one day after the NS merger; these are a density of ρ = 10−13 g cm−3 and temperatures ranging from T = 5000 K to T = 15 000 K. Some agreements and differences were found when comparing our results with available data, highlighting the importance of using sufficiently complete atomic models for the determination of opacities.

Predicting compatibilized polymer blend toughness.

Polymer blends can yield superior materials by merging the unique properties of their components. However, these mixtures often phase separate, leading to brittleness. While compatibilizers can toughen these blends, their vast design space makes optimization difficult. Here, we develop a model to predict the toughness of compatibilized glassy polymer mixtures. This theory reveals that compatibilizers increase blend toughness by creating molecular bridges that stitch the interface together. We validate this theory by directly comparing its predictions to extensive molecular dynamics simulations in which we vary polymer incompatibility, chain stiffness, compatibilizer areal density, and blockiness of copolymer compatibilizers. We then parameterize the model using self-consistent field theory and confirm its ability to make predictions for practical applications through comparison with simulations and experiments. These results suggest that the theory can optimize compatibilizer design for industrial glassy polymer blends in silico while providing microscopic insight, allowing for the development of next-generation mixtures.

Prediction of the 1st excitation energy of odd–odd nuclei with the Bayesian neural network approach

A Bayesian neural network (BNN) is developed to predict the 1st excitation energy of odd–odd nuclei. Aside from the proton number and neutron number, we introduce two empirical physical quantities into the input layer. δ=[−1N+−1Z]/2 is introduced to distinguish even–even, odd–odd and odd-A nuclei; and the so-called Casten factor P≡vpvnvp+vn is introduced to stand for collectivity. The BNN is trained with an experimental dataset of the 1st excitation energy for 434 odd–odd, 649 even–even and 1050 odd-A nuclei. After training, the BNN predicts the 1st excitation energy of odd–odd nuclei with a rms of 0.21 MeV. Examples of Dy, Gd, Eu and Cs isotopes are also shown. The BNN results show moderate predictive ability, in comparison with results from the projected Hartree–Fock method.

Investigating the Electronic Properties and Stability of Rh3 Clusters on Rutile TiO2 for Potential Photocatalytic Applications.

Addressing the pressing needs for alternatives to fossil fuel-based energy sources, this research explores the intricate interplay between Rhodium (Rh3) clusters and titanium dioxide (TiO2) to improve photocatalytic water splitting for the generation of eco-friendly hydrogen. This research applies the density functional theory (DFT) coupled with the Hartree-Fock theory to meticulously examine the structural and electronic structures of Rh3 clusters on TiO2 (110) interfaces. Considering the photocatalytic capabilities of TiO2 and its inherent limitations in harnessing visible light, the potential for metals such as Rh3 clusters to act as co-catalysts is assessed. The results show that triangular Rh3 clusters demonstrate remarkable stability and efficacy in charge transfer when integrated into rutile TiO2 (110), undergoing oxidation in optimal adsorption conditions and altering the electronic structures of TiO2. The subsequent analysis of TiO2 surfaces exhibiting defects indicates that Rh3 clusters elevate the energy necessary for the formation of an oxygen vacancy, thereby enhancing the stability of the metal oxide. Additionally, the combination of Rh3-cluster adsorption and oxygen-vacancy formation generates polaronic and localized states, crucial for enhancing the photocatalytic activity of metal oxide in the visible light range. Through the DFT analysis, this study elucidates the importance of Rh3 clusters as co-catalysts in TiO2-based photocatalytic frameworks, paving the way for empirical testing and the fabrication of effective photocatalysts for hydrogen production. The elucidated impact on oxygen vacancy formation and electronic structures highlights the complex interplay between Rh3 clusters and TiO2 surfaces, providing insightful guidance for subsequent studies aimed at achieving clean and sustainable energy solutions.

Restricted Open-Shell Hartree-Fock Method for a General Configuration State Function Featuring Arbitrarily Complex Spin-Couplings.

In this work, we present a general spin restricted open-shell Hartree-Fock (ROHF) implementation that is able to generate self-consistent field (SCF) wave functions for an arbitrary configuration state function (CSF). These CSFs can contain an arbitrary number of unpaired electrons in arbitrary spin-couplings. The resulting method is named CSF-ROHF. We demonstrate that starting from the ROHF energy expression, for example, the one given by Edwards and Zerner, it is possible to obtain the values of the ROHF vector-coupling coefficients by setting up an open-shell for each group of consecutive parallel-coupled spins dictated by the unique spin-coupling pattern of any given CSF. To achieve this important and nontrivial goal, we employ the machinery of the iterative configuration expansion configuration interaction (ICE-CI) method, which is able to tackle general CI problems on the basis of spin-adapted CSFs. This development allows for the efficient generation of SCF spin-eigenfunctions for systems with complex spin-coupling patterns, such as polymetallic chains and metal clusters, while maintaining SCF scaling with system size (quadratic or less, depending on the specific algorithm and approximations chosen).

A dilute sodium hydroxide technique for radiolarian extraction from cherts

Radiolarians have been used to determine geological ages and have contributed markedly to our understanding of Earth’s history. Hydrofluoric acid (HF) has traditionally been used to extract radiolarian fossils from siliceous deposits (i.e., radiolarian cherts), but this acid is strictly regulated because of environmental and human health concerns. Here we report on the successful extraction of radiolarians from cherts using a low-concentration NaOH solution (1 mol/L NaOH) as an alternative to HF. The degree of chert dissolution in NaOH is strongly temperature-dependent and is limited at < 80 °C. However, even a 1 mol/L NaOH solution is sufficient to dissolve chert at 100 °C. Our new NaOH method yields better-preserved radiolarian fossils compared with the conventional HF method. The 1 mol/L NaOH solution is less hazardous, easier to handle, and has fewer effects on the environment and human health than HF. Therefore, this method can be widely used for research and teaching purposes in studies of radiolarian fossils, even in institutions where HF cannot be used owing to chemical restrictions.

Multimode Friedel oscillations in monolayer and bilayer graphene

This study systematically explores the influence of charged impurities on static screening in monolayer graphene and extends the investigation to AA-stacked and AB-stacked bilayer graphene (BLG). Applying the random phase approximation (RPA), monolayer graphene displays unique beating Friedel oscillations (FOs) in inter-valley and intra-valley channels. Shifting to BLG, the study emphasizes layer-specific responses on each layer by considering self-consistent field interactions between layers. It also explores the derived multimode FOs, elucidating distinctions from monolayer behavior. In AA-stacked BLG, distinct metallic screening behaviors are revealed, uncovering unique oscillatory patterns in induced charge density, providing insights into static Coulomb scattering effects between two Dirac cones. The exploration extends to AB-stacked BLG, unveiling layer-specific responses of parabolic bands in multimode FOs with increasing Fermi energy. This comprehensive investigation, integrating RPA considerations, significantly advances our understanding of layer-dependent static screening in the broader context of FOs in graphene, providing valuable contributions to the field of condensed matter physics.

Utilizing the Hartree-Fock Method to Analyze Carbon Dioxide Molecule

The determination of the ground state of the carbon dioxide molecule is conducted through matrix Hartree-Fock computations for a polyatomic molecule. Utilization of basis sets is implemented to achieve a precision that approaches the sub-μ Hartree of the CO&amp;lt;sub&amp;gt;2&amp;lt;/sub&amp;gt; molecule for the energy levels. Utilizing a 28s14p14d14f atom-centered and a 24sl0plld bond-centered Gaussian basis set, the upper limit for the Hartree-Fock ground state energy of CO&amp;lt;sub&amp;gt;2&amp;lt;/sub&amp;gt; at its practical picture has been calculated, yielding a value of -187.125408 Hartree. Utilizing our knowledge in diatomic molecules, we approximate the precision of this measurement to fall within 5-6 μ Hartree. The current computations offer a methodology to assess the precision of different basis sets frequently utilized in molecular self-consistent field investigations. These basis sets encompass STOJG, 4-31G, 6-31G, 6-31G(3d), 6-31IG, 6-311+G(3d0, D95, and D95V+(3d)), alongside cc-pVDZ, uug-cc-pVDZ, cc-pVTZ, and aug-cc-pVTZ, which have been proposed for the purpose of investigating electron correlation. We have recently performed calculations on the CO1 ground state at the nuclear geomevy employed in the presenl work using the basis sets proposed by Dunning and co-workers and designated cc-pVQZ. aupcc-pVQZ, cc-pVSZ and nupcc-pVSZ. The estimated basis set truncation emrs for these sets are 0.00371, 0.003 19, 0.00047 and 0.00039 Hartree respectively.

Multireference Ab Initio Calculations on Excited Electronic States of Carbazole-Based Organic Compounds for Thermally Activated Delayed Fluorescence.

The emerging technology of organic light-emitting diodes takes advantage of the thermally activated delayed fluorescence (TADF) mechanism for improved efficiency. Carbazole-based organic molecules are suitable for TADF emission because of charge transfer excitations between the electron-donor carbazole and an electron-acceptor unit. Computational design of new TADF molecules with the desired properties is challenging because charge-transfer excitations cannot be predicted accurately by time-dependent density functional theory. Four groups of carbazole-based donor-acceptor molecules have been studied using multireference ab initio methods to understand the nature of excited electronic states. The state-averaged complete active space self-consistent field (SA-CASSCF) and the N-electron valence state perturbation theory (NEVPT2) were used to calculate energies and oscillator strengths for multiple excited electronic states. The number of active electrons and orbitals and the number of excited states included in state-averaged CASSCF were selected such that the accuracy of ab initio predictions could be improved systematically. The procedure introduced here for the calculation of multiple excited electronic states of TADF candidates can be used to accelerate the computational search for efficient TADF materials.

Quantum chemical calculations of electron affinities of alkaline earth metal atoms (Ca, Sr, Ba, and Ra)

We performed high-level ab initio quantum chemical calculations, incorporating higher-order excitations, spin–orbit coupling (SOC), and the Gaunt interaction, to calculate the electron affinities (EAs) of alkaline earth (AE) metal atoms (Ca, Sr, Ba, and Ra), which are notably small. The coupled-cluster singles and doubles with perturbative triples [CCSD(T)] method is insufficient to accurately calculate the EAs of AE metal atoms. Higher-order excitations proved crucial, with the coupled-cluster singles, doubles, and triples with perturbative quadruples [CCSDT(2)Q] method effectively capturing dynamic electron correlation effects. The contributions of SOC (ΔESOs) to the EAs calculated using the multireference configuration interaction method with the Davidson correction, including SOC, positively enhance the EAs; however, these contributions are overestimated. The Dirac–Hartree–Fock (DHF)-CCSD(T) method addresses this overestimation and provides reasonable values for ΔESO (ΔESO−D). Employing additional sets of diffuse and core–valence correlation basis sets is critical for accurately calculating the EAs of AE metal atoms. The contributions of the Gaunt interaction (ΔEGaunt) to the EAs of AE metal atoms are negligible. Notably, the CCSDT(2)Q with the complete basis set limit + ΔESO−D + ΔEGaunt produced EA values for Ca, Sr, and Ba that closely aligned with experimental data and achieved accuracy exceeding the chemical accuracy. Based on our findings, the accurately proposed EA for Ra is 9.88 kJ/mol.