Hartree-Fock Research Articles

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.

Efficient and Robust Ab Initio Self-Consistent Field Acceleration Algorithm Based on a Semiempirical Model Hamiltonian.

A novel doubly iterative self-consistent field (SCF) approach using a semiempirical model Hamiltonian (denoted as the SMH algorithm) is proposed to accelerate the Hartree-Fock (HF) and density functional theory (DFT) calculations. This method first constructs the Fock matrix exactly in each SCF macroiteration, followed by a few SCF microiterations, where the Fock matrix is incrementally updated using an inexpensive semiempirical approximation. This leads to an improved wave function in each SCF macroiteration with minimal additional cost, and therefore a reduced number of exact Fock builds is required for SCF convergence. The SMH algorithm can be combined with conventional SCF convergence techniques such as level shifting, direct inversion in the iterative subspace (DIIS), and energy-DIIS (EDIIS). When integrated with DIIS, SMH enhances the convergence of simple organic molecules by approximately 10% compared to plain DIIS, with speedups of up to 60% for the more challenging transition metal systems compared to EDIIS + DIIS. Our results show that SMH is a reliable SCF accelerator that seldom deteriorates convergence and is highly robust.

Existence of slowly rotating bipolytropes with prolate cores

We report the existence of hydrostatic equilibrium states for a composite body made of two rigidly rotating, homogeneous layers bounded by spheroidal surfaces, where the core has a prolate shape. These new configurations require an oblate envelope that spins faster than the core. No solution with a prolate envelope is found. For some parameters, the prolate core can even be at rest. Numerical experiments based on the self-consistent field method support this result in the case of heterogeneous layers with polytropic equations of state. The possible cancellation of the first gravitational moment, $J_2$, is discussed.

Impact of correlations on nuclear binding energies

A strong effort will be dedicated in the coming years to extend the reach of ab initio nuclear-structure calculations to heavy doubly open-shell nuclei. In order to do so, the most efficient strategies to incorporate dominant many-body correlations at play in such nuclei must be identified. With this motivation in mind, the present work analyses the step-by-step inclusion of many-body correlations and their impact on binding energies of Calcium and Chromium isotopes. Employing an empirically-optimal Hamiltonian built from chiral effective field theory, binding energies along both isotopic chains are studied via a hierarchy of approximations based on polynomially-scaling expansion many-body methods. More specifically, calculations are performed based on (i) the spherical Hartree–Fock–Bogoliubov mean-field approximation plus correlations from second-order Bogoliubov many-body perturbation theory or Bogoliubov coupled cluster with singles and doubles on top of it, along with (ii) the axially-deformed Hartree–Fock–Bogoliubov mean-field approximation plus correlations from second-order Bogoliubov many-body perturbation theory built on it. The corresponding results are compared to experimental data and to those obtained via valence-space in-medium similarity renormalization group calculations at the normal-ordered two-body level that act as a reference in the present study. The spherical mean-field approximation is shown to display specific shortcomings in Ca isotopes that can be understood analytically and that are efficiently corrected via the consistent addition of low-order dynamical correlations on top of it. While the same setting cannot appropriately reproduce binding energies in doubly open-shell Cr isotopes, allowing the unperturbed mean-field state to break rotational symmetry permits to efficiently capture the static correlations responsible for the phenomenological differences observed between the two isotopic chains. Eventually, the present work demonstrates that polynomially-scaling expansion methods based on unperturbed states that possibly break (and restore) symmetries constitute an optimal route to extend ab initio calculations to heavy closed- and open-shell nuclei.

An Efficient RI-MP2 Algorithm for Distributed Many-GPU Architectures.

Second-order Møller-Plesset perturbation theory (MP2) using the Resolution of the Identity approximation (RI-MP2) is a widely used method for computing molecular energies beyond the Hartree-Fock mean-field approximation. However, its high computational cost and lack of efficient algorithms for modern supercomputing architectures limit its applicability to large molecules. In this paper, we present the first distributed-memory many-GPU RI-MP2 algorithm explicitly designed to utilize hundreds of GPU accelerators for every step of the computation. Our novel algorithm achieves near-peak performance on GPU-based supercomputers through the development of a distributed memory algorithm for forming RI-MP2 intermediate tensors with zero internode communication, except for a single asynchronous broadcast, and a distributed memory algorithm for the energy reduction step, capable of sustaining near-peak performance on clusters with several hundred GPUs. Comparative analysis shows our implementation outperforms state-of-the-art quantum chemistry software by over 3.5 times in speed while achieving an 8-fold reduction in computational power consumption. Benchmarking on the Perlmutter supercomputer, our algorithm achieves 11.8 PFLOP/s (83% of peak performance) performing and the RI-MP2 energy calculation on a 314-water cluster with 7850 primary and 30,144 auxiliary basis functions in 4 min on 180 nodes and 720 A100 GPUs. This performance represents a substantial improvement over traditional CPU-based methods, demonstrating significant time-to-solution and power consumption benefits of leveraging modern GPU-accelerated computing environments for quantum chemistry calculations.

Theoretical spin-orbit laser cooling for AlZn molecule.

A spin-orbit coupling electronic structure study of the AlZn molecule is conducted to investigate the molecular properties of the low-lying electronic states and their feasibility toward direct laser cooling. This study uses the complete active-space self-consistent field level of theory, followed by the multireference configuration interaction method with Davidson correction (+Q). The potential energy and dipole moment curves and the spectroscopic constants are computed for the low-lying doublet and quartet electronic states in the 2S+1Λ± and Ω(±) representations. The transition dipole moments, the Franck-Condon factors, the Einstein coefficient, the radiative lifetimes, the vibrational branching ratio, and the slowing distance are determined between the lowest spin-orbit bound electronic states. These results show that the molecule AlZn has a high potential for laser cooling through the X2Π1/2 → (2)2Π1/2 transition by utilizing four lasers at a wavelength in the ultraviolet region, reaching a sub-microkelvin temperature limit.

Molecular line lists for the singlet states in gaseous YN at high temperature

ABSTRACT Our aim in this study is to investigate the electronic structure of the gaseous YN molecule and provide an accurate molecular line list of spectroscopic transitions between the five lowest singlet states. The calculations were done by using large basis set for yttrium aug-cc-pVQZ-PP with relativistic effective core potentials at the spin-free level. We first used the method of complete active space self-consistent field, which was followed by the multireference singles and doubles configuration interaction. Potential energy curves and permanent and transition dipole moments were calculated at the internuclear distance range of 1.3–2.96 Å. For each state, we calculated the spectroscopic constants (Te, ωe, ωexe, ωeye, Be, αe, Re). The calculated values of the spectroscopic constants are in excellent agreement with the experimental constants available, with a relative difference of less than 5 cm−1. We further calculated the transition intensities of allowed transitions, and we provided the absorption spectra up to a temperature of 4000 K. The computed molecular line list contains 2.6 million transitions calculated between almost 18 186 vibro-rotational energy levels. It covers the frequency range between 0 and 30 000 cm−1. The effect of temperature on the spectra of hot YN was investigated with partition functions calculated between 298 and 4000 K. This study should help in identifying the singlet state spectrum of the hot YN molecule, which is possibly found in the atmospheres of cool stars and hot rocky super-Earths.

Importance of Orbital Invariance in Quantifying Electron-Hole Separation and Exciton Size.

A fundamental tenet of quantum mechanics is that properties should be independent of representation. In self-consistent field methods such as density functional theory, this manifests as a requirement that properties be invariant with respect to unitary transformations of the occupied molecular orbitals and (separately) the unoccupied molecular orbitals. Various ad hoc measures of excited-state charge separation that are commonly used to analyze time-dependent density-functional calculations violate this requirement, as they are based on incoherent averages of excitation amplitudes rather than expectation values involving coherent superpositions. As a result, these metrics afford markedly different values in various common representations, including canonical molecular orbitals, Boys-localized orbitals, and natural orbitals. Numerical values can be unstable with respect to basis-set expansion and may afford nonsensical results in the presence of extremely diffuse basis functions. In contrast, metrics based on well-defined expectation values are stable, representation-invariant, and physically interpretable. Use of natural transition orbitals improves the stability of the incoherent averages, but numerical values can only be interpreted as expectation value in the absence of superposition. To satisfy this condition, the particle and hole density matrices must each be dominated by a single eigenvector so that the transition density is well described by a single pair of natural transition orbitals. Counterexamples are readily found where this is not the case. Our results suggest that ad hoc charge-transfer diagnostics should be replaced by rigorous expectation values, which are no more expensive to compute.

Positron interactions with vinyl acetate from 0.1 eV to 5 keV

Abstract Scattering cross sections from positron impact on vinyl acetate are explored in the energy region 0.1~eV to a 5~keV, employing a cc-pVTZ basis set. The optimized molecular wavefunction of the target was obtained through a multi-center expansion of Gaussian-type orbitals in the Hartree-Fock self-consistent field framework. The elastic cross sections are computed using the single-centre-expansion formalism. Two distinct models were employed to address the long-range effects associated with the target's polar nature and yielded almost identical corrections. The Born-corrected elastic cross sections align more strongly with the existing experimental corrected data than the results reported from the independent-atom-model approximation. The differential and momentum transfer cross sections after applying Born-correction are also reported. The direct ionization cross sections are obtained using the binary-encounter-Bethe model for positrons. The cross sections obtained by summing elastic and ionization cross sections align closely with `forward angle corrected' experimental total cross sections across a significant energy range. The agreement significantly improves beyond 30 eV, suggesting that the omission of excitation and positronium formation cross sections becomes less significant. A brief analysis of the electron interaction with the target is also made.

Implementation of frozen density embedding in CP2K and OpenMolcas: CASSCF wavefunctions embedded in a Gaussian and plane wave DFT environment.

Most chemical processes happen at a local scale where only a subset of molecular orbitals is directly involved and only a subset of covalent bonds may be rearranged. To model such reactions, Density Functional Theory (DFT) is often inadequate, and the use of computationally more expensive correlated wavefunction (WF) methods is required for accurate results. Mixed-resolution approaches backed by quantum embedding theory have been used extensively to approach this imbalance. Based on the frozen density embedding freeze-and-thaw algorithm, we describe an approach to embed complete active space self-consistent field simulations run in the OpenMolcas code in a DFT environment calculated in CP2K without requiring any external tools. This makes it possible to study a local, active part of a chemical system in a larger and relatively static environment with a computational cost balanced between the accuracy of a WF method and the efficiency of DFT, which we test on environment-subsystem pairs. Finally, we apply the implementation to an oxygen molecule leaving an aluminum (111) surface and a ruthenium(IV) oxide (110) surface.

A deep equivariant neural network approach for efficient hybrid density functional calculations

Hybrid density functional calculations are essential for accurate description of electronic structure, yet their widespread use is restricted by the substantial computational cost. Here we develop DeepH-hybrid, a deep equivariant neural network method for learning the hybrid-functional Hamiltonian as a function of material structure, which circumvents the time-consuming self-consistent field iterations and enables the study of large-scale materials with hybrid-functional accuracy. Our extensive experiments demonstrate good reliability as well as effective transferability and efficiency of the method. As a notable application, DeepH-hybrid is applied to study large-supercell Moiré-twisted materials, offering the first case study on how the inclusion of exact exchange affects flat bands in magic-angle twisted bilayer graphene. The work generalizes deep-learning electronic structure methods to beyond conventional density functional theory, facilitating the development of deep-learning-based ab initio methods.

Semiclassical Nonadiabatic Molecular Dynamics Using Linearized Pair-Density Functional Theory.

Nonadiabatic molecular dynamics is an effective method for modeling nonradiative decay in electronically excited molecules. Its accuracy depends strongly on the quality of the potential energy surfaces, and its affordability for long direct-dynamic simulations with adequate ensemble averaging depends strongly on the cost of the required electronic structure calculations. Linearized pair-density functional theory (L-PDFT) is a recently developed post-self-consistent-field multireference method that can model potential energy surfaces with an accuracy similar to expensive multireference perturbation theories but at a computational cost similar to the underlying multiconfiguration self-consistent field method. Here, we integrate the SHARC dynamics and PySCF electronic structure code to utilize L-PDFT for electronically nonadiabatic calculations and use the combined programs to study the photoisomerization reaction of cis-azomethane. We show that L-PDFT is able to successfully simulate the photoisomerization without crashes, and it yields results similar to the more expensive extended multistate complete active space second-order perturbation theory. This shows that L-PDFT can model internal conversion, and it demonstrates its promise for broader photodynamics applications.

Collisional and radiative data for tellurium ions in kilonovae modelling and laboratory benchmarks

ABSTRACT Tellurium is a primary candidate for the identification of the 2.1 $\, \mu$m emission line in kilonovae (KNe) spectra AT2017gfo and GRB230307A. Despite this, there is currently an insufficient amount of atomic data available for this species. We calculate the required atomic structure and collisional data, particularly the data required for accurate non-local-thermodynamic-equilibrium (NLTE) modelling of the low temperatures and densities in KNe. We use a multiconfigurational Dirac–Hartree–Fock method to produce optimized one-electron orbitals for Te i-iii. As a result energy levels and Einstein A-coefficients for Te i-iii have been calculated. These orbitals are then employed within Dirac R-matrix collision calculations to provide electron-impact-excitation collision strengths that were subsequently averaged according to a thermal Maxwellian distribution. Subsequent tardis simulations using this new atomic data reveal no significant changes to the synthetic spectra due to the very minor contribution of Te at early epochs. NLTE simulations with the colradpy package reveal optically thin spectra consistent with the increasing prominence of the Te iii 2.1 $\, \mu$m line as the KNe ejecta cools. This is reinforced by the estimation of luminosities at nebular KNe conditions. New line ratios for both observation and laboratory benchmarks of the atomic data are proposed.

No more gap-shifting: Stochastic many-body-theory based TDHF for accurate theory of polymethine cyanine dyes.

We introduce an individually fitted screened-exchange interaction for the time-dependent Hartree-Fock (TDHF) method and show that it resolves the missing binding energies in polymethine organic dye molecules compared to time-dependent density functional theory (TDDFT). The interaction kernel, which can be thought of as a dielectric function, is generated by stochastic fitting to the screened-Coulomb interaction of many-body perturbation theory (MBPT), specific to each system. We test our method on the flavylium and indocyanine green dye families with a modifiable length of the polymethine bridge, leading to excitations ranging from visible to short-wave infrared. Our approach validates earlier observations on the importance of inclusion of medium range exchange for the exciton binding energy. Our resulting method, TDHF@vW, also achieves a mean absolute error on a par with MBPT at a computational cost on a par with local-functional TDDFT.

An Efficient Algorithm for Constrained CASSCF(1,2) and CASSCF(3,2) Simulations as Relevant to Electron and Hole Transfer Problems.

We propose an efficient algorithm for the recently published electron/hole-transfer Dynamical-weighted State-averaged Constrained CASSCF (eDSC/hDSC) method studying charge transfer states and D1-D0 crossings for systems with odd numbers of electrons. By separating the constrained minimization problem into an unconstrained self-consistent-field (SCF) problem and a constrained nonself-consistent-field (nSCF) problem, as well as accelerating the direct inversion in the iterative subspace (DIIS) technique to solve the SCF problem, the overall computational cost is reduced by a factor of 8-20 compared with directly using sequential quadratic programming (SQP). This approach should be applicable for other constrained minimization problems, and in the immediate future, once gradients are available, the present eDSC/hDSC algorithm should allow for speedy nonadiabatic dynamics simulations.

Improved Gaussian basis sets for norm-conserving 4f-in-core pseudopotentials of trivalent lanthanides (Ln = Ce-Lu).

The first-principles quantum chemical computations often scale as Nk (N = basis sets; k = 1-4 for linear scaling, Hartree-Fock or density functional theory methods), which makes the development of accurate pseudopotentials and efficient basis sets necessary ingredients in modeling of heavy elements such as lanthanides and actinides. Recently, we have developed 4f-in-core norm-conserving pseudopotentials and associated basis sets for the trivalent lanthanides [Lu et al., J. Chem. Theory Comput. 19, 82-96 (2023)]. In the present paper, we present a unified approach to optimize high-quality Gaussian basis sets for modeling and simulations of condensed-phase systems. The newly generated basis sets not only capture the low total energy and fairly reasonable condition number of overlap matrix of lanthanide-containing systems, but also exhibit good transferability and reproducibility. These advantages ensure the accuracy of the basis sets while avoiding linear dependency concern of atom-centered basis sets. The performance of the basis sets is further illustrated in lanthanide molecular and condensed-phase systems by using Gaussian-plane wave density functional approach of CP2K. These new basis sets can be of particular interest to model structurally complicated lanthanide molecules, clusters, solutions, and solid systems.

Quantified asymptotic analysis for the relativistic quantum mechanical system with electromagnetic fields

We study the asymptotic analysis of a relativistic quantum mechanical system interacting with self-consistent electromagnetic fields, with a specific focus on the Maxwell–Klein–Gordon (MKG) system. Firstly, we show that the MKG system is globally well-posed under the Coulomb gauge condition, even in the presence of self-interacting potential. Furthermore, to derive the asymptotic analysis, we consider the non-relativistic and semi-classical regime simultaneously, introducing a single scaling parameter that serves to parameterize both the speed of light and the Planck constant. As the scaling parameter approaches zero, we obtain rigorous and quantified estimates on the asymptotic convergence of the electrostatic MKG system toward the classical Euler–Poisson system. Our analytical framework relies on the modulated energy estimate.

Design of N-doped C60-σ-B-doped C60 photodetector based on resonant tunneling diode using DFT and NEGF method.

Photodetectors utilizing donor/acceptor (D/A) molecules have the capacity to detect light through molecular interactions between a donor and an acceptor molecule. These devices leverage electronic or optical changes within molecules when exposed to light, resulting in observable modifications. The unique properties of photodetectors with D/A molecules make them valuable tools in various fields, including molecular electronics. This paper presents the modeling and simulation of a single-molecule photodetector based on a D/A molecule configuration. The acceptor molecule used is N-doped C60 fullerene, while the donor molecule is B-doped C60 fullerene. Initially, simulations were conducted at zero bias voltage to determine the energy and states of the bipartite molecule. Subsequently, the system's Hamiltonian was computed based on these results. The self-consistent field method (SCF) and optical self-energy coefficients were employed for modeling. Finally, the current-voltage curve of the device was derived for various input light frequencies. The simulation and modeling results demonstrated that the device exhibited negative differential resistances at bias voltages of 0.33 V, 1.58 V, and - 0.93 V, depending on the input light frequency. Furthermore, the designed device demonstrated the ability to detect and absorb waves with different frequencies. The number of current peaks in the current-voltage curve varied with by altering the number of optical modes. The computational work was conducted using the software package of Atomistix ToolKit (ATK-2018.06) and MATLAB code. The calculations were based on the density functional theory (DFT) approach and the self-consistent field method, specifically the non-equilibrium Green function (NEGF). The exchange correlation function was investigated using the generalized gradient approximation (GGA) proposed by Perdew, Burke, and Ernzerhof (PBE). For the calculations, we employed the double-ζ plus polarization (DZP) basis set. Initially, the structures of N doped-C60-σ-B-doped-C60 molecule underwent optimization using the DFT approach implemented in the ATK package. This optimization process allowed us to extract the parameters of the molecule. Subsequently, we utilized the NEGF formalism in MATLAB software to model and simulate photodetector based on the optimized molecule. We calculated important features of the photodetector, such as photocurrent, and compared the performance of the photodetector using photons with energies of 2 and 3 eV.

General relativistic self-gravitating equilibrium discs around rotating neutron stars

ABSTRACT In modelling a relativistic disc around a compact object, the self-gravity of the disc is often neglected while it needs to be incorporated for more accurate descriptions in several circumstances. Extending the Komatsu–Eriguchi–Hachisu self-consistent field method, we present numerical models of a rapidly rotating neutron star with a self-gravitating disc in stationary equilibrium. In particular, our approach allows us to obtain numerical solutions involving a massive disc with the rest mass $\mathcal {O}(10^{-1})-\mathcal {O}(10^0)\, \mathrm{ M}_\odot$ closely attached to a rotating neutron star, given that the disc is mainly supported by the relativistic electron degeneracy pressure. We also assess the impact of self-gravity on the internal structure of the disc and the neutron star. These axisymmetric, stationary solutions can be employed for simulations involving the neutron star–disc system in the context of high-energy transients and gravitational-wave emissions.

Improving Predictions of Spin-Crossover Complex Properties through DFT Calculations with a Local Hybrid Functional.

We conducted a study on the performance of the local hybrid exchange-correlation functional PBE0r for a set of 95 experimentally characterized iron spin-crossover (SCO) complexes [Vennelakanti, V.; J. Chem. Phys. 2023, 159, 024120]. The PBE0r functional is a variant of PBE0 where the exchange correction is restricted to on-site terms formulated on the basis of local orbitals. We determine the free parameters of the PBE0r functional against the experimental data and other hybrid functionals. With a Hartree-Fock (HF) exchange factor of 4%, the PBE0r functional accurately reproduces the electronic and free-energy trends predicted in prior DFT studies for these 95 complexes by using the B3LYP functional. Larger values of HF exchange stabilize high-spin states. The PBE0r-predicted bond lengths tend to exceed the experimental bond lengths, although bond lengths are less sensitive to HF exchange than in global hybrids. The predicted SCO transition temperatures T1/2 from PBE0r correlate moderately with the experimental transition temperatures, showing a slight improvement compared to the previous modB3LYP-predicted T1/2. This study suggests that the PBE0r functional is computationally cost-effective and offers the possibility of simulating larger complexes with accuracy comparable to global hybrid functionals, provided the HF-exchange parameter is carefully optimized.