Hartree-Fock Research Articles

Excited states from GW/BSE and Hartree-Fock theory: Effects of polarizability and transition type on accuracy of excited state energies.

GW and Bethe-Salpeter equation (BSE) methods are used to calculate energies of excited states of organic molecules in the Quest-3 database [Loos et al., J. Chem. Theory Comput. 16, 1711 (2020)]. The self-energy in the GW approximation is conventionally calculated using the RPA polarizability. Inclusion of a screened electron-hole interaction in the polarizability was recently shown to improve predictions of experimental ionization energies in organic molecules [C. H. Patterson, J. Chem. Theory Comput. 20, 7479 (2024)]. Self-energies from RPA or screened time-dependent Hartree-Fock (TDHF) polarizabilities in the GW/BSE method are used to calculate 141 singlet excited states in Quest-3. Theoretical best estimate excited state energies from the CC3 coupled cluster method and aug-cc-pVTZ basis sets are used to benchmark GW/BSE and CIS calculations using the same molecular geometries and basis sets. Differences between GW/BSE or CIS excited state energies and best estimate values show that there are systematic variations in the accuracies of excited state energies classified as ππ*, nπ*, πR (Rydberg), or nR character. The origin of these variations is the accuracy of self-energies of states of nonbonding vs π bonding character. In particular, N or O lone pair states require large self-energy corrections owing to strong orbital relaxation in the localized hole state, while π states have smaller corrections. Self-energies from a screened TDHF vs RPA polarizability are typically over(under)estimated for nonbonding states, leading to under(over)estimation of energies of excited states of nπ* or nR character.

Thermal quasiparticle theory.

The widely used thermal Hartree-Fock (HF) theory is generalized to include the effect of electron correlation while maintaining its quasi-independent-particle framework. An electron-correlated internal energy (or grand potential) is postulated in consultation with the second-order finite-temperature many-body perturbation theory (MBPT), which then dictates the corresponding thermal orbital (quasiparticle) energies in such a way that all fundamental thermodynamic relations are obeyed. The associated density matrix is of a one-electron type, whose diagonal elements take the form of the Fermi-Dirac distribution functions, when the grand potential is minimized. The formulas for the entropy and chemical potential are unchanged from those of Fermi-Dirac or thermal HF theory. The theory thus stipulates a finite-temperature extension of the second-order Dyson self-energy of one-particle many-body Green's function theory and can be viewed as a second-order, diagonal, frequency-independent, thermal inverse Dyson equation. At low temperatures, the theory approaches finite-temperature MBPT of the same order, but it may outperform the latter at intermediate temperatures by including additional electron-correlation effects through orbital energies. A physical meaning of these thermal orbital energies is proposed (encompassing that of thermal HF orbital energies, which has been elusive) as a finite-temperature version of Janak's theorem.

Thermal mean-field theories.

Several closely related abinitio thermal mean-field theories for fermions, both well-established and new ones, are compared with one another at the formalism level and numerically. The theories considered are Fermi-Dirac theory; thermal Hartree-Fock (HF) theory; two modifications of the thermal single-determinant approximation of Kaplan and Argyres, Ann. Phys. 92, 1-24 (1975); and the first-order finite-temperature many-body perturbation theory based on a zero-temperature or thermal HF reference. Thermal full-configuration-interaction theory is used as the benchmark.

Mixing of isoscalar and isovector characteristics in the low-energy dipole mode

We investigated isospin splitting in low-energy dipole (LED) states of spherical nuclei such as 40Ca, 90Zr, 132Sn, 208Pb, and several N=50 isotones using self-consistent Hartree–Fock plus random phase approximation calculations. Our analysis of isovector dipole (IVD) and isoscalar dipole (ISD) strengths, along with transition densities, reveals a clear energy-dependent relationship between IS and IV modes in 40Ca and 90Zr. For 208Pb and 132Sn, LED states show mixed IS + IV characteristics due to different neutron and proton shell structures. In N=50 isotones, E1 modes exhibit varying IS and IV properties with smooth transitions as neutron excess increases. Our results suggest that compressional ISD strengths could provide valuable insights into the slope parameter of the nuclear equation of state. The observed dependence on nuclear shell structures and neutron–proton correlations highlights the need for precise measurements and further research in nuclear physics.

Crystal Structure, Spectroscopic Analysis, and Nonlinear Optical Properties of Terphenyl‐Based Compound for Optoelectronic Applications

AbstractMulti‐aryl compounds, with conjugated backbones having electron donor and acceptor groups, are widely recognized for their significant nonlinearity. In this context, a new terphenyl compound, ethyl‐4″‐chloro‐5′‐hydroxy‐[1,1′:3′,1″‐terphenyl]‐4′‐carboxylate (EHCMT), has been synthesized for potential use as an optoelectronic material. Single crystal X‐ray diffraction (XRD) analysis of EHCMT revealed a triclinic system with the centrosymmetric space group , providing most accurate description for its crystal structure. The structure of compound was further elucidated through FTIR, NMR (1H, 13C & 2D‐HSQC), and UV–Visible spectroscopic techniques. Hirshfeld surface analysis was employed to examine the magnitude and significance of individual intermolecular interactions in the crystalline arrangement. The third‐order nonlinear optical (NLO) properties were investigated using the Z‐scan technique in a solution phase at 532 nm. The study revealed significant results, namely, nonlinear refraction value of −1.165 × 10−9 cm2 W−1, nonlinear absorption coefficient value of 13.4 × 10−5 cm W−1, and third‐order nonlinear susceptibility value of 0.50 × 10−7 esu. The structural parameters of experimental results were validated by comparing the same with quantum chemical calculations using hybrid functional, namely, Hartree–Fock ‐ Density functional theory (HF–DFT).

Scalable learning of potentials to predict time-dependent Hartree–Fock dynamics

We propose a framework to learn the time-dependent Hartree–Fock (TDHF) inter-electronic potential of a molecule from its electron density dynamics. Although the entire TDHF Hamiltonian, including the inter-electronic potential, can be computed from first principles, we use this problem as a testbed to develop strategies that can be applied to learn a priori unknown terms that arise in other methods/approaches to quantum dynamics, e.g., emerging problems such as learning exchange–correlation potentials for time-dependent density functional theory. We develop, train, and test three models of the TDHF inter-electronic potential, each parameterized by a four-index tensor of size up to 60 × 60 × 60 × 60. Two of the models preserve Hermitian symmetry, while one model preserves an eight-fold permutation symmetry that implies Hermitian symmetry. Across seven different molecular systems, we find that accounting for the deeper eight-fold symmetry leads to the best-performing model across three metrics: training efficiency, test set predictive power, and direct comparison of true and learned inter-electronic potentials. All three models, when trained on ensembles of field-free trajectories, generate accurate electron dynamics predictions even in a field-on regime that lies outside the training set. To enable our models to scale to large molecular systems, we derive expressions for Jacobian-vector products that enable iterative, matrix-free training.

High-precision measurements of the atomic mass and electron-capture decay Q value of 95Tc

A direct measurement of the ground-state-to-ground-state electron-capture decay Q value of 95Tc has been performed utilizing the double Penning trap mass spectrometer JYFLTRAP. The Q value was determined to be 1695.92(13) keV by taking advantage of the high resolving power of the phase-imaging ion-cyclotron-resonance technique to resolve the low-lying isomeric state of 95Tc (excitation energy of 38.910(40) keV) from the ground state. The mass excess of 95Tc was measured to be −86015.95(18) keV/c2, exhibiting a precision of about 28 times higher and in agreement with the value from the newest Atomic Mass Evaluation (AME2020). Combined with the nuclear energy-level data for the decay-daughter 95Mo, two potential ultra-low Q-value transitions are identified for future long-term neutrino-mass determination experiments. The atomic self-consistent many-electron Dirac–Hartree–Fock–Slater method and the nuclear shell model have been used to predict the partial half-lives and energy-release distributions for the two transitions. The dominant correction terms related to those processes are considered, including the exchange and overlap corrections, and the shake-up and shake-off effects. The normalized distribution of the released energy in the electron-capture decay of 95Tc to excited states of 95Mo is compared to that of 163Ho currently being used for electron-neutrino-mass determination.

Acceleration of self-consistent field iteration for Kohn–Sham density functional theory

Acceleration of self-consistent field iteration for Kohn–Sham density functional theory

Laser-induced epoxide ring opening on graphene oxide leading to C–O single bonds: An ab initio prediction

The dynamics of the epoxide in graphene oxide under laser irradiation were investigated based on the frameworks of time-dependent density functional theory and molecular dynamics within the Ehrenfest approximation. Two combinations of the laser wavelength (λ) and full width at half-maximum (FWHM) were examined: λ=266 nm with FWHM=100 fs and λ=810 nm with FWHM=35 fs. Upon tuning the laser fluence to just below the threshold for oxygen desorption, epoxide ring opening to form a carbon–oxygen (C–O) single bond was observed. Further simulations revealed that the laser-generated C–O bonds were inert in the presence of water molecules. Conventional static density functional theory calculations and complete-active-space self-consistent field calculations indicated that the C–O bonds were (meta)stable in the electronically excited and negatively charged states. Finally, the feasibility of experimentally observing the C–O bond was considered.

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

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

Dissecting neurofilament tail sequence-phosphorylation-structure relationships with multicomponent reconstituted protein brushes

Neurofilaments (NFs) are multisubunit, bottlebrush-shaped intermediate filaments abundant in the axonal cytoskeleton. Each NF subunit contains a long intrinsically disordered tail domain, which protrudes from the NF core to form a "brush" surrounding each NF. Precisely how the tails' variable charge patterns and repetitive phosphorylation sites mediate their conformation within the brush remains an open question in axonal biology. We address this problem by grafting recombinant NF tail protein constructs NF-Light, -Medium, and -Heavy (NFL, NFM, and NFH) to surfaces, yielding protein brushes of defined stoichiometry that can be phosphorylated in vitro. Atomic force microscopy measurements reveal that brush height depends on composition monotonically but not always linearly for binary NFL:NFM or NFL:NFH systems, and that NFM-based brushes are highly extended, while brushes incorporating the much larger NFH are surprisingly compact even after multisite phosphorylation. Complementary self-consistent field theory (SCFT) predicts multilayer brush morphologies for NFM and phosphorylated NFH brushes. Further experiments and SCFT analysis with designed mutants reveal that N-terminal negative charges in the NFH tail repel phosphorylated residues to generate the multilayer morphology, while the C-terminal charge-neutral region contributes to multilayer brush morphology but not total brush height. Charge-shuffled NFM variants show that charge segregation promotes brush collapse near physiological ionic strengths. Collectively, this study supports a role for NFM in establishing a dynamic range for NF brush conformation, lending insight into previous in vitro and in vivo findings. More broadly, this work establishes a platform for dissecting contributions of disordered protein sequence to conformation at interfaces.

Radiative decay rates for magnetic dipole (M1) and electric quadrupole (E2) transitions between low-lying levels within the 4f3 ground configuration of Pr III

Abstract A new set of theoretical radiative decay rates characterizing forbidden transitions in doubly charged praseodymium (Pr III) is reported in the present paper. More precisely, transition probabilities were computed for all magnetic dipole (M1) and electric quadrupole (E2) lines involving the lowest energy levels of the 4f$^3$ ground configuration located below 20000 cm$^{-1}$ since the levels above this limit are preferentially depopulated by allowed electric dipole (E1) transitions. The calculations were carried out using different computational strategies based firstly on the pseudo-relativistic Hartree-Fock (HFR) method and secondly on the fully relativistic Multiconfiguration Dirac-Hartree-Fock (MCDHF) method. The comparison between the results obtained by these independent approaches makes it possible to estimate their reliability. Comparisons with the few previously published data were also made. In addition, some astrophysical implications were deduced from the new atomic parameters computed in the present work, such as the possible presence of [Pr III] lines in the infrared spectra recorded by the {\it James Webb Space Telescope} ($JWST$) in the context of the investigation of kilonovae in their nebular phase, i.e. several days after neutron star mergers.

Calculated ionization energies, orbital eigenvalues (HOMO), and related QSAR descriptors of organic molecules: a set of 61 experimental values enables elimination of systematic errors and provides realistic error estimates.

Ionization energies (IEs) of organic compounds come in different forms-adiabatic, vertical, as electrode potentials, or as orbital eigenvalues via Koopmans' theorem. They have been linked to the reactivity towards electrophiles and have been used to quantitatively describe electron transfer processes. The de novo prediction of IEs is only meaningful when an estimate of the prediction's uncertainty is included. Pulsed-field ionization (PFI) experiments have quantified adiabatic IEs with unprecedented precision. In this work, a new set of PFI-derived IEs is compiled from the literature as a benchmark for prediction methods. This set includes many common functional groups, a size range from diatomics to two aromatic rings, and IEs between 7 and 14 eV. The first-principles CCSD(T)/CBS protocol presently used reproduces these values within 0.05 eV. For adiabatic IEs and vertical IEs/orbital eigenvalues predicted using approximate density functional theory (DFT), linear regression models are proposed, so that IEs calculated using different methods can be directly compared on a physical scale. This elimination of systematic errors improves the error statistics and allows the performance of predicted IEs to be evaluated if used in quantitative structure-property or -activity relationships, as the latter implicitly correct a descriptor's bias. Owing to the structural scope of the test set, the minimum and maximum deviations from experiment should correspond to those expected for common organic molecules. Deviations from reference values found for orbital eigenvalues but also for IEs calculated explicitly with HF or semi-empirical MO methods were as large as 0.5 eV to 2.0 eV. Such large errors could also propagate into quantitative structure-property models, as shown in illustrative examples of oxidation rate constants in solution.

DFT-SCRF Calculations of Nitrogen Isotopic Reduced Partition Function Ratios for Amino Acids in Aqueous Solution at pH 7.4.

Using the self-consistent reaction field (SCRF) method, the nitrogen isotopic reduction partition function ratio (RPFR), a fundamental physical quantity for theoretical consideration of equilibrium isotope effects, was evaluated by density functional theory (DFT) for 20 proteinogenic and two related amino acids under physiological conditions at pH 7.4. At this pH value, all amino acids were of the zwitterion-type form with α-NH3+ and α-COO- groups, regardless of the net charge of -1 (monoanion), 0 (zwitterion), or +1 (monocation). The largest RPFR value by far was for proline (Pro). This is due to the fact that the nitrogen atom of Pro has two C-N bonds and two N-H bonds, whereas the α-nitrogen atoms of other amino acids form one C-N bond and three N-H bonds. There was a clear correlation between the RPFR value of α-nitrogen and the distance of the N-H covalent bond of the hydrogen atom involved in the formation of the intramolecular hydrogen bond (HB); the stronger the intramolecular HB, the lower the RPFR value of α-nitrogen. It was suggested that equilibrium isotope effects were partially responsible for the nitrogen isotope fractionation in the enzymatic glutamic acid/aspartic acid transamination and in ammonia assimilation during the formation of glutamine from glutamic acid.

Two-molecule theory of polyethylene liquids.

Two-molecule theory refers to a class of microscopic, self-consistent field theories for the radial distribution function in classical molecular liquids. The version examined here can be considered as one of the very few formally derived closures to the reference interaction site model (RISM) equation. The theory is applied to polyethylene liquids, computing their equilibrium structural and thermodynamic properties at melt densities. The equation for the radial distribution function, which is represented as an average over the accessible states of two molecules in an external field that mimics the effects of the other molecules in the liquid, is computed by Monte Carlo simulation along with the intramolecular structure function. An improved direct sampling algorithm is utilized to speed the equilibration. Polyethylene chains of 24 and 66 united atom CH2 units are studied. The results are compared to full, many-chain molecular dynamics (MD) simulations and self-consistent polymer-RISM (PRISM) theory with the atomic Percus-Yevick (PY) closure under the same conditions. It is shown that the two-molecule theory produces results that are close to those of MD and is thus able to overcome defects of PRISM-PY theory and predict more accurate liquid structure at both short and long ranges. Predictions for the equation of state are also discussed.

Importance of Electron Correlation on the Geometry and Electronic Structure of [2Fe-2S] Systems: A Benchmark Study of the [Fe2S2(SCH3)4]2-,3-,4-, [Fe2S2(SCys)4]2-, [Fe2S2(S-p-tol)4]2-, and [Fe2S2(S-o-xyl)4]2- Complexes.

Iron-sulfur clusters are crucial for biological electron transport and catalysis. Obtaining accurate geometries, energetics, manifolds of their excited electronic states, and reduction energies is important to understand their role in these processes. Using a [2Fe-2S] model complex with FeII and FeIII oxidation states, which leads to different charges, i.e., [Fe2S2(SMe)4]2-,3-,4-, we benchmarked a variety of computational methodologies ranging from density functional theory (DFT) to post-Hartree-Fock methods, including complete active space self-consistent field (CASSCF), multireference configuration interaction, the second-order N-electron valence state perturbation theory (NEVPT2), and the linearized integrand approximation of adiabatic connection (AC0) approaches. Additionally, we studied three experimentally well-characterized complexes, [Fe2S2(SCys)4]2-, [Fe2S2(S-o-tol)4]2-, and [Fe2S2(S-o-xyl)4]2-, via DFT methods. We conclude that the dynamic electron correlation is important for accurately predicting the geometry of these complexes. Broken symmetry (BS) DFT correctly predicts experimental geometries of low-spin multiplicity, while CASSCF does not. However, BS-DFT significantly overestimates the difference between the low- and high-spin electronic states for a given oxidation state. At the same time, CASSCF underestimates it but provides relative energies closer to the reference NEVPT2 results. Finally, AC0 provides energetics of NEVPT2 quality with the additional advantage of being able to use large CASSCF sizes. NEVPT2 gives the best estimates of the FeIII/FeIII → FeII/FeIII (4.27 eV) and FeII/FIII → FeII/FII (7.72 eV) reduction energies. The results provide insight into the electronic structure of these complexes and assist in the understanding of their physical properties.

Hartree-Fock approximation for non-Coulomb interactions in three and two-dimensional systems

We analyzed the Hartree-Fock approximation for an electron system. The interaction between particles is modeled by a non-Coulombian potential. We analyzed both the three-dimensional and two-dimensional systems. We obtained accurate analytical results for the particle energy, the particle velocity, the ground state energy of the system as well as the momentum dependent density of states. The previous classical results for the Coulombian case were reobtained as particular cases.

Effect of Oriented External Electric Field in Altering Magnetic Exchange and Magnetic Anisotropy in Lanthanide-Radical Complexes.

Magnetic exchange coupling (J) is one of the important spin Hamiltonian parameters that control the magnetic characteristics of single-molecule magnets (SMMs). While numerous chemical methodologies have been proposed to modify ligands and control the J value, and magneto-structural correlations have been developed accordingly, altering this parameter through non-chemical means remains a challenging task. This study explores the impact of an Oriented-External Electric Field (OEEF) on over twenty lanthanide-radical complexes using Density Functional Theory (DFT) and ab initio Complete Active Space Self-Consistent Field (CASSCF) methods. Five complexes - [{(Me3Si)2N]2Gd(THF)}2(μ-η2:η2-N2)] (1), [Gd(Hbpz3)2(dtbsq)] (2), [Gd(hfac)3(IM-2py)] (3), [Gd(hfac)3(NITBzImH)] (4), and [Gd(hfac)3{2Py-NO}(H2O)] (5) - were selected for detailed analysis, revealing significant OEEF effects on magnetic exchange interactions and structural parameters. Various parameters such as bond distances, bond angles, and torsional angles were examined as a function of OEEF to establish guiding principles for molecule selection. In complexes 1, 2, and 3, OEEF influenced torsional angles and altered exchange interactions. Complex 4 demonstrated enhanced ferromagnetic coupling under OEEF, reaching a maximum J value of +5.3 cm-1. Complex 5 reveals switching the sign of JGd-rad exchange interaction from antiferromagnetic to ferromagnetic under OEEF, highlighting the potential of electric fields in designing materials with tuneable magnetic properties. These findings offer valuable insights for future research and applications in advanced materials and molecular electronics.

Global Uniform in N Estimates for Solutions of a System of Hartree–Fock–Bogoliubov Type in the Case $$\beta <1$$

Global Uniform in N Estimates for Solutions of a System of Hartree–Fock–Bogoliubov Type in the Case $$\beta <1$$

Non-Equilibrium Quantum Brain Dynamics: Water Coupled with Phonons and Photons.

We investigate Quantum Electrodynamics (QED) of water coupled with sound and light, namely Quantum Brain Dynamics (QBD) of water, phonons and photons. We provide phonon degrees of freedom as additional quanta in the framework of QBD in this paper. We begin with the Lagrangian density QED with non-relativistic charged bosons, photons and phonons, and derive time-evolution equations of coherent fields and Kadanoff-Baym (KB) equations for incoherent particles. We next show an acoustic super-radiance solution in our model. We also introduce a kinetic entropy current in KB equations in 1st order approximation in the gradient expansion and show the H-theorem for self-energy in Hartree-Fock approximation. We finally derive conserved number density of charged bosons and conserved energy density in spatially homogeneous system.