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This paper presents the first implementation of a coupling between advanced wavefunction theories and molecular density functional theory (MDFT). This method enables the modeling of solvent effect into quantum mechanical (QM) calculations by incorporating an electrostatic potential generated by solvent charges into the electronic Hamiltonian. Solvent charges are deduced from the spatially and angularly dependent solvent particle density. Such a density is obtained through the minimization of the functional associated with the molecular mechanics (MM) Hamiltonian describing the interaction between the fluid particles. The introduced QM/MDFT framework belongs to QM/MM family of methods, but its originality lies in the use of MDFT as the MM solver, offering two main advantages. First, its functional formulation makes it competitive with respect to sampling-based molecular mechanics. Second, it preserves a molecular-level description lost in macroscopic continuum approaches. The excited state properties of water and formaldehyde molecules solvated into water have been computed at the selected configuration interaction (SCI) level. The excitation energies and dipole moments have been compared with experimental data and previous theoretical work. A key finding is that using the Hartree–Fock method to describe the solute allows for predicting the solvent charge around the ground state with sufficient precision for the subsequent SCI calculations of excited states. This significantly reduces the computational cost of the described procedure, paving the way for the study of more complex molecules. [ABSTRACT FROM AUTHOR]

We investigate the performance of time-dependent density functional theory (TDDFT) for reproducing high-level reference x-ray absorption spectra of liquid water and water clusters. For this, we apply the integrated absolute difference (IAD) metric, previously used for x-ray emission spectra of liquid water [T. Fransson and L. G. M. Pettersson, J. Chem. Theory Comput. 19, 7333–7342 (2023)], in order to investigate which exchange–correlation (xc) functionals yield TDDFT spectra in best agreement to reference, as well as to investigate the suitability of IAD for x-ray absorption spectroscopy spectrum calculations. Considering highly asymmetric and symmetric six-molecule clusters, it is seen that long-range corrected xc-functionals are required to yield good agreement with the reference coupled cluster (CC) and algebraic-diagrammatic construction spectra, with 100% asymptotic Hartree–Fock exchange resulting in the lowest IADs. The xc-functionals with best agreement to reference have been adopted for larger water clusters, yielding results in line with recently published CC theory, but which still show some discrepancies in the relative intensity of the features compared to experiment. [ABSTRACT FROM AUTHOR]

Simulations of condensed matter systems at the hybrid density functional theory level pose significant computational challenges. The elevated costs arise from the non-local nature of the Hartree–Fock exchange (HFX) in conjunction with the necessity to approach the thermodynamic limit. In this work, we address these issues with the development of a new efficient method for the calculation of HFX in periodic systems, employing k-point sampling. We rely on a local atom-specific resolution-of-the-identity scheme, the use of atom-centered Gaussian type orbitals, and the truncation of the Coulomb interaction to limit computational complexity. Our real-space approach exhibits a scaling that is, at worst, linear with the number of k-points. Issues related to basis set diffuseness are effectively addressed through the auxiliary density matrix method. We report the implementation in the CP2K software package, as well as accuracy and performance benchmarks. This method demonstrates excellent agreement with equivalent Γ-point supercell calculations in terms of relative energies and nuclear gradients. Good strong and weak scaling performances, as well as graphics processing unit (GPU) acceleration, make this implementation a promising candidate for high-performance computing. [ABSTRACT FROM AUTHOR]

Kohn–Sham density functional theory has been the most popular method in electronic structure calculations. To fulfill the increasing accuracy requirements, new approximate functionals are needed to address key issues in existing approximations. It is well known that nonlocal components are crucial. Current nonlocal functionals mostly require orbital dependence such as in Hartree–Fock exchange and many-body perturbation correlation energy, which, however, leads to higher computational costs. Deviating from this pathway, we describe functional nonlocality in a new approach. By partitioning the total density to atom-centered local densities, a many-body expansion is proposed. This many-body expansion can be truncated at one-body contributions, if a base functional is used and an energy correction is approximated. The contribution from each atom-centered local density is a single finite-range nonlocal functional that is universal for all atoms. We then use machine learning to develop this universal atom-centered functional. Parameters in this functional are determined by fitting to data that are produced by high-level theories. Extensive tests on several different test sets, which include reaction energies, reaction barrier heights, and non-covalent interaction energies, show that the new functional, with only the density as the basic variable, can produce results comparable to the best-performing double-hybrid functionals, (for example, for the thermochemistry test set selected from the GMTKN55 database, BLYP based machine learning functional gives a weighted total mean absolute deviations of 3.33 kcal/mol, while DSD-BLYP-D3(BJ) gives 3.28 kcal/mol) with a lower computational cost. This opens a new pathway to nonlocal functional development and applications. [ABSTRACT FROM AUTHOR]

We investigate two limits in open-shell diradical systems: O3, in which the interesting orbitals are in close proximity to one another, and (C21H13)2, where there is a significant spatial separation between the two orbitals. In accord with earlier calculations, we find that standard density-functional approximations do not predict the open-shell character for the former case but uniformly predict the open-shell character for the latter case. We trace the qualitatively incorrect behavior in O3 predicted by these standard density functional approximations to self-interaction error and use the Fermi–Löwdin-orbital-self-interaction-corrected formalism to determine accurate triplet, closed-shell singlet, and open-shell broken-spin-symmetry electronic configurations. Analysis of the resulting many-electron overlap matrices allows us to unambiguously show that the broken-spin-symmetry configurations do not participate in the representation of the Ms = 0 triplet states and allows us to reliably extract the singlet–triplet splitting in O3 by analyzing the energy as a function of Fermi-orbital-descriptor permutations. The results of these analyses predict the percentage of open-shell character in O3, which agrees well with conventional wavefunction-based methods. While these techniques are expected to be required in cases near the Coulson–Fischer point, we find that they will be less necessary in diradical systems with well-separated electrons, such as (C21H13)2. Results based on energies from self-interaction-corrected generalized gradient, local density, and Hartree–Fock approximations and experimental results are in generally good agreement for O3. These results help form the basis for deriving extended Heisenberg-like Hamiltonians that are needed for descriptions of molecular magnets when there are competing low-energy electronic configurations. [ABSTRACT FROM AUTHOR]

The regularized and restored semi-local meta-generalized gradient approximation (meta-GGA) exchange–correlation functional r2SCAN [Furness et al., J. Phys. Chem. Lett. 11, 8208–8215 (2020)] is used to create adiabatic-connection-derived global double-hybrid functionals employing spin-opposite-scaled MP2. The 0-DH, CIDH, QIDH, and 0–2 type double-hybrid functionals are assessed as a starting point for further modification. Variants with 50% and 69% Hartree–Fock exchange (HFX) are empirically optimized (Pr2SCAN50 and Pr2SCAN69), and the effect of MP2-regularization (κPr2SCAN50) and range-separated HFX (ωPr2SCAN50) is evaluated. All optimized functionals are combined with the state-of-the-art London dispersion corrections D4 and NL. The resulting functionals are assessed comprehensively for their performance on main-group and metal-organic thermochemistry on 90 different benchmark sets containing 25 800 data points. These include the extensive GMTKN55 database, additional sets for main-group chemistry, and multiple sets for transition-metal complexes, including the ROST61, the MOR41, and the MOBH35 sets. As the main target of this study is the development of a broadly applicable, robust functional with low empiricism, special focus is put on variants with moderate amounts of HFX (50%), which are compared to the so far successful PWPB95-D4 (50% HFX, 20% MP2 correlation) functional. The overall best variant, ωPr2SCAN50-D4, performs well on main-group and metal-organic thermochemistry, followed by Pr2SCAN69-D4 that offers a slight edge for metal-organic thermochemistry and by the low HFX global double-hybrid Pr2SCAN50-D4 that performs robustly across all tested sets. All four optimized functionals, Pr2SCAN69-D4, Pr2SCAN50-D4, κPr2SCAN50-D4, and ωPr2SCAN50-D4, outperform the PWPB95-D4 functional. [ABSTRACT FROM AUTHOR]

Separating the Coulomb potential into short-range and long-range components enables the use of different electron repulsion integral algorithms for each component. The short-range part can be efficiently computed using the analytical algorithm due to the locality in both the Gaussian-type orbital basis and the short-range Coulomb potentials. The integrals for the long-range Coulomb potential can be approximated with the density fitting method. A very small auxiliary basis is sufficient for the density fitting method to accurately approximate the long-range integrals. This feature significantly reduces the computational efforts associated with the N4 scaling in density fitting algorithms. For large molecules, the range separation and long-range density fitting method outperforms the conventional analytical integral evaluation scheme employed in Hartree–Fock calculations and provides more than twice the overall performance. In addition, this method offers a higher accuracy compared to conventional density fitting methods. The error in the Hartree–Fock energy can be easily reduced to 0.1 μEh per atom or smaller. [ABSTRACT FROM AUTHOR]

Recent measurements of the third harmonic scattering responses of molecules have given a new impetus for computing molecular second hyperpolarizabilities (γ) and for deducing structure–property relationships. This paper has employed a variety of wavefunction and density functional theory methods to evaluate the second hyperpolarizability of the p-nitroaniline prototypical push-pull π-conjugated molecule, addressing also numerical aspects, such as the selection of an integration grid and the impact of the order of differentiation vs the achievable accuracy by using the Romberg quadrature. The reliability of the different methods has been assessed by comparison to reference Coupled-Cluster Singles and Doubles with perturbative treatment of the Triples results. On the one hand, among wavefunction methods, the MP2 scheme offers the best accuracy/cost ratio for computing the static γ. On the other hand, using density functional theory, γ remains a challenging property to compute because all conventional, global hybrid or range-separated hybrid, exchange–correlation functionals underestimate static γ values by at least 15%. Even tuning the range-separating parameter to minimize the delocalization errors does not enable to improve the γ values. Nevertheless, the original double-hybrid B2-PLYP functional, which benefits from 27% of PT2 correlation and 53% Hartree–Fock exchange, provides accurate estimates of static γ values. Unfortunately, the best performing exchange–correlation functionals for γ are not necessarily reliable for the first hyperpolarizability, β, and vice versa. In fact, the β of p-nitroaniline (pNA) could be predicted, with a good accuracy, with several hybrid exchange–correlation functionals (including by tuning the range-separating parameter), but these systematically underestimate γ. As for γ, the MP2 wavefunction method remains the best compromise to evaluate the first hyperpolarizability of pNA at low computational cost. [ABSTRACT FROM AUTHOR]

The calculation of two-electron repulsion integrals (ERIs) is a crucial aspect of Hartree–Fock calculations. In computing the ERIs of varying angular momentum, both the central processing unit (CPU) and the graphics processing unit (GPU) have their respective advantages. To accelerate the ERI evaluation and Fock matrix generation, a hybrid CPU/GPU method has been proposed to maximize the computational power of both CPU and GPU while overlapping the CPU and GPU computations. This method employs a task queue where each task corresponds to ERIs with the same angular momentum. The queue begins with ERIs of low angular momentum, which are computationally efficient on GPUs, and ends with ERIs of high angular momentum, which are better suited for CPU computation. CPUs and GPUs dynamically grab and complete tasks from the start and end of the queue using OpenMP dynamic scheduling until all tasks are finished. The hybrid CPU/GPU computation offers the advantage of enabling calculations with arbitrary angular momentum. Test calculations showed that the hybrid CPU/GPU algorithm is more efficient than "GPU-only" when using a single GPU. However, as more GPUs are involved, the advantage diminishes or disappears. The scaling exponents of the hybrid method were slightly higher than "GPU-only," but the pre-exponent factor was significantly lower, making the hybrid method more effective overall. [ABSTRACT FROM AUTHOR]

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Copyright of Baghdad Science Journal is the property of Republic of Iraq Ministry of Higher Education & Scientific Research (MOHESR) and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

A numerical algorithm based on the probabilistic path integral approach for solving Schrödinger equation has been devised to treat molecular systems without Born–Oppenheimer approximation in the nonrelativistic limit at zero temperature as an alternative to conventional variational and perturbation methods. Using high-quality variational trial functions and path integral method based on generalized Feynman–Kac method, we have been able to calculate the non-Born–Oppenheimer energy for hydrogen molecule for the X 1 Σ g 1 state and hydrogen molecular ion. Combining these values and the value for ionization potential for atomic hydrogen, the dissociation energy and ionization potential for hydrogen molecules have been determined to be 36 113.672(3) cm − 1 and 124 446.066(10) cm − 1 , respectively. Our results favorably compare with other theoretical and experimental results and thus show the promise of being a nonperturbative alternative for testing fundamental physical theories. [ABSTRACT FROM AUTHOR]

Context: The study of platinum (Pt) clusters and nanoparticles is essential due to their extensive range of potential technological applications, particularly in catalysis. The electronic properties that yield optimal catalytic performance at the nanoscale are significantly influenced by the size and structure of Pt clusters. This research aimed to identify the lowest-energy conformers for Pt 18 , Pt 19 , and Pt 20 species using Density Functional Theory (DFT). We discovered new low-symmetry conformers for Pt 19 and Pt 20 , which are 3.0 and 1.0 kcal/mol more stable, respectively, than previously reported structures. Our study highlights the importance of using density functional approximations that incorporate moderate levels of exact Hartree-Fock exchange, alongside basis sets of at least quadruple-zeta quality. The resulting structures are asymmetric with varying active sites, as evidenced by sigma hole analysis on the electrostatic potential surface. This suggests a potential correlation between electronic structure and catalytic properties, warranting further investigation. Methods: An equivariant graph neural network interatomic potential (NequIP) within the Atomic Simulation Environment suite (ASE) was used to provide initial geometries of the aggregates under study. DFT calculations were performed with the ORCA 5 package, using functional approximations that included Generalized Gradient Approximation (PBE), meta-GGA (TPSS, M06-L), hybrid (PBE0, PBEh), meta-GGA hybrid (TPSSh), and range-separated hybrid (ω B97x) functionals. Def2-TZVP and Def2-QZVP as well as members of the cc-pwCVXZ-PP family to check basis set convergence were used. QTAIM calculations were performed using the AIMAll suite. Structures were visualized with the AVOGADRO code. [ABSTRACT FROM AUTHOR]

A two-component contour deformation (CD) based GW method that employs frequency sampling to drastically reduce the computational effort when assessing quasiparticle states far away from the Fermi level is outlined. Compared to the canonical CD-GW method, computational scaling is reduced by an order of magnitude without sacrificing accuracy. This allows for an efficient calculation of core ionization energies. The improved computational efficiency is used to provide benchmarks for core ionized states, comparing the performance of 15 density functional approximations as Kohn–Sham starting points for GW calculations on a set of 65 core ionization energies of 32 small molecules. Contrary to valence states, GW calculations on core states prefer functionals with only a moderate amount of Hartree–Fock exchange. Moreover, modern ab initio local hybrid functionals are also shown to provide excellent generalized Kohn–Sham references for core GW calculations. Furthermore, the core–valence separated Bethe–Salpeter equation (CVS-BSE) is outlined. CVS-BSE is a convenient tool to probe core excited states. The latter is tested on a set of 40 core excitations of eight small inorganic molecules. Results from the CVS-BSE method for excitation energies and the corresponding absorption cross sections are found to be in excellent agreement with those of reference damped response BSE calculations. [ABSTRACT FROM AUTHOR]

Spin crossover (SCO) complexes, which exhibit changes in spin state in response to external stimuli, have applications in molecular electronics and are challenging materials for computational design. We curate a dataset of 95 Fe(II) SCO complexes (SCO-95) from the Cambridge Structural Database that have available low- and high-temperature crystal structures and, in most cases, confirmed experimental spin transition temperatures (T1/2). We study these complexes using density functional theory (DFT) with 30 functionals spanning across multiple rungs of "Jacob's ladder" to understand the effect of exchange–correlation functional on electronic and Gibbs free energies associated with spin crossover. We specifically assess the effect of varying the Hartree–Fock exchange fraction (aHF) in structures and properties within the B3LYP family of functionals. We identify three best-performing functionals, a modified version of B3LYP (aHF = 0.10), M06-L, and TPSSh, that accurately predict SCO behavior for the majority of the complexes. While M06-L performs well, MN15-L, a more recently developed Minnesota functional, fails to predict SCO behavior for all complexes, which could be the result of differences in datasets used for parametrization of M06-L and MN15-L and also the increased number of parameters for MN15-L. Contrary to observations from prior studies, double-hybrids with higher aHF values are found to strongly stabilize high-spin states and therefore exhibit poor performance in predicting SCO behavior. Computationally predicted T1/2 values are consistent among the three functionals but show limited correlation to experimentally reported T1/2 values. These failures are attributed to the lack of crystal packing effects and counter-anions in the DFT calculations that would be needed to account for phenomena such as hysteresis and two-step SCO behavior. The SCO-95 set thus presents opportunities for method development, both in terms of increasing model complexity and method fidelity. [ABSTRACT FROM AUTHOR]

We consider a one-dimensional effective quantum electrodynamics (QED) model of the relativistic hydrogen-like atom using delta-potential interactions. We discuss the general exact theory and the Hartree–Fock approximation. The present one-dimensional effective QED model shares the essential physical feature of the three-dimensional theory: the nuclear charge polarizes the vacuum state (creation of electron–positron pairs), which results in a QED Lamb-type shift of the bound-state energy. Yet, this 1D effective QED model eliminates some of the most serious technical difficulties of the three-dimensional theory coming from renormalization. We show how to calculate the vacuum-polarization density at zeroth order in the two-particle interaction and the QED Lamb-type shift of the bound-state energy at first order in the two-particle interaction. The present work may be considered a step toward the development of a quantum-chemistry effective QED theory of atoms and molecules. [ABSTRACT FROM AUTHOR]

The recently reported Grassmann interpolation (G-Int) method [J. A. Tan and K. U. Lao, J. Chem. Phys. 158, 051101 (2023)] has been extended to spin-unrestricted open-shell systems. In contrast to closed-shell systems, where G-Int has to be performed only once since the α and β density matrices are the same, spin-unrestricted open-shell systems require G-Int to be performed twice—one for the α spin and another for the β spin density matrix. In this work, we tested the performance of G-Int to the carbon monoxide radical cation CO●+ and nickelocene complex, which have the doublet and triple ground states, respectively. We found that the Frobenius norm errors associated with the interpolations for the α and β spin density matrices are comparable for a given molecular geometry. These G-Int density matrices, when used as an initial guess for a self-consistent field (SCF) calculation, outperform the conventional SCF guess schemes, such as the superposition of atomic densities, purified superposition of atomic densities, core Hamiltonian, and generalized Wolfsberg–Helmholtz approximation. Depending on the desired accuracy, these G-Int density matrices can be used to directly evaluate the SCF energy without performing SCF iterations. In addition, the spin-unrestricted G-Int density matrices have been used for the first time to directly calculate the atomic charges using the Mulliken and ChElPG population analysis. [ABSTRACT FROM AUTHOR]

In a combined mean-field and semiclassical regime, we consider the time evolution of N fermions interacting through singular pair interaction potentials of the form j, which includes the Coulomb and gravitational interactions. We prove that the many-body dynamics of mixed states are well approximated by solutions of the Hartree-Fock and Vlasov equations in terms of Schatten norms. The errors in these approximations are expressed in terms of the expected number of particles, N, and the Planck constant, h. For cases where a 2 .0;1=2/, we obtain local-in-time results when N1=2 \ h ≤ N1=3. Notably, this leads to the derivation of the Vlasov equation with singular potentials. For cases where a ∈ [1/2, 1], our results hold only within a small time scale or require an N-dependent cut-off. A fundamental ingredient in our analysis is the propagation of regularity for solutions to the Hartree-Fock equation uniformly in the Planck constant, which holds for a ∈ (0, 1]. [ABSTRACT FROM AUTHOR]

The development of novel double-hybrid density functionals offers new levels of accuracy and is leading to fresh insights into the fundamental properties of matter. Hartree–Fock exact exchange and correlated wave function methods, such as second-order Møller–Plesset (MP2) and direct random phase approximation (dRPA), are usually required to build such functionals. Their high computational cost is a concern, and their application to large and periodic systems is, therefore, limited. In this work, low-scaling methods for Hartree–Fock exchange (HFX), SOS-MP2, and direct RPA energy gradients are developed and implemented in the CP2K software package. The use of the resolution-of-the-identity approximation with a short range metric and atom-centered basis functions leads to sparsity, allowing for sparse tensor contractions to take place. These operations are efficiently performed with the newly developed Distributed Block-sparse Tensors (DBT) and Distributed Block-sparse Matrices (DBM) libraries, which scale to hundreds of graphics processing unit (GPU) nodes. The resulting methods, resolution-of-the-identity (RI)-HFX, SOS-MP2, and dRPA, were benchmarked on large supercomputers. They exhibit favorable sub-cubic scaling with system size, good strong scaling performance, and GPU acceleration up to a factor of 3. These developments will allow for double-hybrid level calculations of large and periodic condensed phase systems to take place on a more regular basis. [ABSTRACT FROM AUTHOR]

The rigorous quantum mechanical description of the collective interaction of many molecules with the radiation field is usually considered numerically intractable, and approximation schemes must be employed. Standard spectroscopy usually contains some levels of perturbation theory, but under strong coupling conditions, other approximations are used. A common approximation is the 1-exciton model in which processes involving weak excitations are described using a basis comprising the ground state and singly excited states of the molecule cavity-mode system. In another frequently used approximation in numerical investigations, the electromagnetic field is described classically, and the quantum molecular subsystem is treated in the mean-field Hartree approximation with its wavefunction assumed to be a product of single molecules' wavefunctions. The former disregards states that take long time to populate and is, therefore, essentially a short time approximation. The latter is not limited in this way, but by its nature, disregards some intermolecular and molecule-field correlations. In this work, we directly compare results obtained from these approximations when applied to several prototype problems involving the optical response of molecules-in-optical cavities systems. In particular, we show that our recent model investigation [J. Chem. Phys. 157, 114108 (2022)] of the interplay between the electronic strong coupling and molecular nuclear dynamics using the truncated 1-exciton approximation agrees very well with the semiclassical mean-field calculation. [ABSTRACT FROM AUTHOR]

This study is an overview of the atomic data and opacity computations performed by the Atomic Physics and Astrophysics Unit of Mons University in the context of kilonova emission following neutron star mergers, in both the photospheric and nebular phases. In this work, as a sample case, we focus on a specific lanthanide ion, namely Er III. As far as the LTE photospheric phase of the kilonova ejecta is concerned, we present our calculations using both a theoretical method (the pseudo-relativistic Hartree-Fock method, HFR) and a statistical approach (the Resolved Transition Array approach, RTA) to obtain the atomic data required to estimate the Er III expansion opacity for typical conditions expected in kilonova ejecta one day after the merger. In order to draw the limitations of both of our strategies, the results obtained using the latter are compared, and a calibration procedure of the HFR atomic data in this context is also discussed. Concerning the kilonova ejecta nebular phase, atomic parameters that characterize forbidden lines in Er III are calculated using HFR as well as another computational approach, namely the Multiconfiguration Dirac–Hartree–Fock (MCDHF) method. The potential detection of such lines in late-phase kilonova spectra is then discussed. [ABSTRACT FROM AUTHOR]

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 = [ − 1 N + − 1 Z ] / 2 is introduced to distinguish even–even, odd–odd and odd-A nuclei; and the so-called Casten factor P ≡ v p v n v p + v n 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. [ABSTRACT FROM AUTHOR]

We present on shell-scheme for the 2PI formalism with a particular focus on the renormalized equations of motion. We first revisit the so-called Hartree approximation where we give the counterterms for both the broken and unbroken phases. Moreover, we give explicit formulas for the renormalized three- and four-point functions in the broken phase. We then turn to the sunset approximation, with only scalars and then including fermions. We give explicit formulas for the wave function and mass counterterms. Moreover, we show that, in particular, the two-point functions can be obtained numerically in a fast converging scheme even for large couplings of order one. [ABSTRACT FROM AUTHOR]

In this paper, we study the L²-critical Hartree equation with harmonic potential which arises in quantum theory of large system of nonrelativistic bosonic atoms and molecules. Firstly, by using the variational characteristic of the nonlinear elliptic equation and the Hamilton conservations, we get the sharp threshold for global existence and blow-up of the Cauchy problem. Then, in terms of a change of variables, we first find the relation between the Hartree equation with and without harmonic potential. Furthermore, we prove the upper bound of blow-up rate in R³ as well as the mass concentration of blow-up solution for the Hartree equation with harmonic potential in RN. [ABSTRACT FROM AUTHOR]

Photoplethysmography (PPG) is widely utilized in wearable healthcare devices due to its convenient measurement capabilities. However, the unrestricted behavior of users often introduces artifacts into the PPG signal. As a result, signal processing and quality assessment play a crucial role in ensuring that the information contained in the signal can be effectively acquired and analyzed. Traditionally, researchers have discussed signal quality and processing algorithms separately, with individual algorithms developed to address specific artifacts. In this paper, we propose a quality-aware signal processing mechanism that evaluates incoming PPG signals using the signal quality index (SQI) and selects the appropriate processing method based on the SQI. Unlike conventional processing approaches, our proposed mechanism recommends processing algorithms based on the quality of each signal, offering an alternative option for designing signal processing flows. Furthermore, our mechanism achieves a favorable trade-off between accuracy and energy consumption, which are the key considerations in long-term heart rate monitoring. [ABSTRACT FROM AUTHOR]

We theoretically study biexcitons and quadrons in quantum dots with parabolic confinement and give a complete comparison between the two excitations. The calculation of quadron and biexciton binding energies as functions of electron-to-hole confinement potentials and mass ratios, using the unrestricted Hartree–Fock method, shows the essential differences between biexcitons and quadrons. The crossover between the negative and positive binding energies is indicated. The effect of an external magnetic field on the quadron and biexciton binding energies has also been investigated. In addition, the crossover between anti-binding and binding of both excited quadron and biexciton states in a certain range of the electron-to-hole oscillator length ratios has been found. [ABSTRACT FROM AUTHOR]

The energies, structures, and vibrational frequencies of [Sb(H2O)n]3+, n = 0–9, 18 have been calculated at the Hartree–Fock and second-order Møller–Plesset levels of theory using the CEP, LANL2, and SDD effective core potentials in combination with their associated basis sets, or with the 6-31G* and 6-31+G* basis sets. The metal–oxygen distances and totally symmetric stretching frequency of the aqua ions were compared with each other and with related crystal structure measurements where available. [ABSTRACT FROM AUTHOR]

Complexes containing a transition metal atom with a 3d4–3d7 electron configuration typically have two low-lying, high-spin (HS) and low-spin (LS) states. The adiabatic energy difference between these states, known as the spin-crossover energy, is small enough to pose a challenge even for electronic structure methods that are well known for their accuracy and reliability. In this work, we analyze the quality of electronic structure approximations for spin-crossover energies of iron complexes with four different ligands by comparing energies from self-consistent and post-self-consistent calculations for methods based on the random phase approximation and the Fermi–Löwdin self-interaction correction. Considering that Hartree–Fock densities were found by Song et al., J. Chem. Theory Comput. 14, 2304 (2018), to eliminate the density error to a large extent, and that the Hartree–Fock method and the Perdew–Zunger-type self-interaction correction share some physics, we compare the densities obtained with these methods to learn their resemblance. We find that evaluating non-empirical exchange-correlation energy functionals on the corresponding self-interaction-corrected densities can mitigate the strong density errors and improves the accuracy of the adiabatic energy differences between HS and LS states. [ABSTRACT FROM AUTHOR]

For reproducing the carbon K-edge x-ray absorption spectra of liquid alcohols, inner-shell quantum chemical calculations based on the Hartree–Fock method were performed with the snapshots of the liquid structures obtained by molecular dynamics simulations. The C K-edge inner-shell spectrum of liquid ethanol (EtOH) was obtained by the summation of one thousand calculated spectra of EtOH molecules including neighbor EtOH molecules within the CH2–CH2 distance of 6 Å. For the C K-edge inner-shell spectrum of liquid methanol (MeOH), we have calculated one thousand spectra of MeOH molecules including neighbor MeOH molecules within the CH3–CH3 distance of 6 Å. The calculated C K-edge inner-shell spectra of liquid alcohols well reproduced the spectral shapes of the experimentally obtained x-ray absorption spectra and the spectral changes from gas to liquid phases. [ABSTRACT FROM AUTHOR]

We present analytic gradients for local density fitting Hartree–Fock (HF) and hybrid Kohn–Sham (KS) density functional methods. Due to the non-variational nature of the local fitting algorithm, the method of Lagrange multipliers is used to avoid the solution of the coupled perturbed HF and KS equations. We propose efficient algorithms for the solution of the arising Z-vector equations and the gradient calculation that preserve the third-order scaling and low memory requirement of the original local fitting algorithm. In order to demonstrate the speed and accuracy of our implementation, gradient calculations and geometry optimizations are presented for various molecular systems. Our results show that significant speedups can be achieved compared to conventional density fitting calculations without sacrificing accuracy. [ABSTRACT FROM AUTHOR]

We consider the calculations of photoionization spectra and core resonances of open-shell systems using range-separated time-dependent density-functional theory. Specifically, we use the time-dependent range-separated hybrid (TDRSH) scheme, combining a long-range Hartree–Fock exchange potential and kernel with a short-range potential and kernel from a local density-functional approximation, and the time-dependent locally range-separated hybrid (TDLRSH) scheme, which uses a local range-separation parameter. To efficiently perform the calculations, we formulate a spin-unrestricted linear-response Sternheimer approach in a non-orthogonal B-spline basis set using appropriate frequency-dependent boundary conditions. We illustrate this approach on the Li atom, which suggests that TDRSH and TDLRSH are adequate simple methods for estimating the single-electron photoionization spectra of open-shell systems. [ABSTRACT FROM AUTHOR]

The Jordan–Wigner transformation establishes a duality between su(2) and fermionic algebras. We present qualitative arguments and numerical evidence that when mapping spins to fermions, the transformation makes strong correlation weaker, as demonstrated by the Hartree–Fock approximation to the transformed Hamiltonian. This result can be rationalized in terms of rank reduction of spin shift terms when transformed to fermions. Conversely, the mapping of fermions to qubits makes strong correlation stronger, complicating its solution when one uses qubit-based correlators. The presence of string operators poses challenges to the implementation of quantum chemistry methods on classical computers, but these can be dealt with using established techniques of low computational cost. Our proof of principle results for XXZ and J1-J2 Heisenberg (in 1D and 2D) indicates that the JW transformed fermionic Hamiltonian has reduced complexity in key regions of their phase diagrams and provides a better starting point for addressing challenging spin problems. [ABSTRACT FROM AUTHOR]

Sun et al. [J. Chem. Phys. 144, 191101 (2016)] suggested that common density-functional approximations (DFAs) should exhibit large energy errors for excited states as a necessary consequence of orbital nodality. Motivated by self-interaction corrected density-functional calculations on many-electron systems, we continue their study with the exactly solvable 1s, 2p, and 3d states of 36 hydrogenic one-electron ions (H–Kr35+) and demonstrate with self-consistent calculations that state-of-the-art DFAs indeed exhibit large errors for the 2p and 3d excited states. We consider 56 functionals at the local density approximation (LDA), generalized gradient approximation (GGA) as well as meta-GGA levels, and several hybrid functionals such as the recently proposed machine-learned DM21 local hybrid functional. The best non-hybrid functional for the 1s ground state is revTPSS. As predicted by Sun et al., the 2p and 3d excited states are more difficult for DFAs, and LDA functionals turn out to yield the most systematic accuracy for these states among non-hybrid functionals. The best performance for the three states overall is observed with the BHandH global hybrid GGA functional, which contains 50% Hartree–Fock exchange and 50% LDA exchange. The performance of DM21 is found to be inconsistent, yielding good accuracy for some states and systems and poor accuracy for others. Based on these results, we recommend including a variety of one-electron cations in future training of machine-learned density functionals. [ABSTRACT FROM AUTHOR]

One-electron ionization processes X → X i + in orbitally degenerate systems, such as atoms with the open-shell configuration pN, can be divided into two groups. The first group involves the processes that are allowed in photoelectron spectra. The processes of this group in atoms obey the familiar selection rules (SRs) formulated within the Russell–Saunders L, S coupling. All other ionization processes, for which SRs are not obeyed, belong to the second group. Here, we analyze the validity of Koopmans' theorem (KT) for the processes of the second group forbidden by SRs. We show that the general formulation of KT in the Hartree–Fock method [Plakhutin, J. Chem. Phys. 148, 094101 (2018)] is implicitly based on the assumption that a X → X i + process is allowed by SRs, and this presents a limitation of KT. To overcome the latter, we develop an extension of KT that enables estimating the energies of SR-forbidden processes. We prove that the variational condition underlying KT gives different results for SR-allowed and SR-forbidden processes. For the former processes, this condition gives the familiar KT relationship Ii = −ɛi, while for SR-forbidden processes, the respective relationship between Ii and ɛi takes a more complex form. The practical applicability of the extension of KT is verified by applying it to the totality of ionization processes in the valence 2s and 2p shells of atoms C, N, and O in their ground and excited states, which involves a total of 29 SR-allowed and 34 SR-forbidden processes. For all of these processes, we compare KT estimates of ionization energies (IEs) with the relevant experimental data. For comparison, we also present the respective estimates of IEs derived with a ΔSCF approach. Particular attention is paid to the analysis of the validity of KT in the specific cases of violation of Hund's rules for cation states. [ABSTRACT FROM AUTHOR]

Partial charges are a central concept in general chemistry and chemical biology, yet dozens of different computational definitions exist. In prior work [Cho et al., ChemPhysChem21, 688‐696 (2020)], we showed that these can be reduced to at most three 'principal components of ionicity'. The present study addressed the dependence of computed partial charges q on 1‐particle basis set and (for WFT methods) n‐particle correlation treatment or (for DFT methods) exchange‐correlation functional, for several representative partial charge definitions such as QTAIM, Hirshfeld, Hirshfeld‐I, HLY (electrostatic), NPA, and GAPT. Our findings show that semi‐empirical double hybrids can closely approach the CCSD(T) 'gold standard' for this property. In fact, owing to an error compensation in MP2, CCSD partial charges are further away from CCSD(T) than is MP2. The nonlocal correlation is important, especially when there is a substantial amount of nonlocal exchange. Employing range separation proves to be "mostly" not advantageous, while global hybrids perform optimally for 20%–30% Hartree‐Fock exchange across all charge types. Basis set convergence analysis shows that an augmented triple‐zeta heavy‐aug‐cc‐pV(T+d)Z basis set or a partially augmented jun‐cc‐pV(T+d)Z basis set is sufficient for Hirshfeld, Hirshfeld‐I, HLY, and GAPT charges. In contrast, QTAIM and NPA display slower basis set convergence. It is noteworthy that for both NPA and QTAIM, HF exhibits markedly slower basis set convergence than the correlation components of MP2 and CCSD. Triples corrections in CCSD(T), denoted as CCSD(T)‐CCSD, exhibit even faster basis set convergence. [ABSTRACT FROM AUTHOR]

Structural, electronic, and vibrational properties of phosphates LiCdPO4, NaCdPO4, RbCdPO4, CsCdPO4 are studied by density functional theory and Hartree–Fock methods using the CRYSTAL17 code in the LCAO basis set with gradient PBE, PBEsol and hybrid PBE0, PBEsol0 functionals. It is shown that the crystal structures contain infinite zigzag chains consisting of [CdO6] octahedra and [PO4] tetrahedra inside which there are alkali metal atoms. By the Gaussian broadening of normal long-wave modes IR absorption and Raman spectra are calculated. Differences in the number of spectral bands, their polarization and intensities are related to different symmetry space groups of the crystals. [ABSTRACT FROM AUTHOR]

The asymmetric Hubbard dimer is a model that allows for explicit expressions of the Hartree–Fock (HF) and Kohn–Sham (KS) states as analytical functions of the external potential, Δv, and of the interaction strength, U. We use this unique circumstance to establish a rigorous comparison between the individual contributions to the correlation energies stemming from the two theories in the {U, Δv} parameter space. Within this analysis of the Hubbard dimer, we observe a change in the sign of the HF kinetic correlation energy, compare the indirect repulsion energies, and derive an expression for the "traditional" correlation energy, i.e., the one that corrects the HF estimate, in a pure site-occupation function theory spirit [Eq. (45)]. Next, we test the performances of the Liu–Burke and the Seidl–Perdew–Levy functionals, which model the correlation energy based on its weak- and strong-interaction limit expansions and can be used for both the traditional and the KS correlation energies. Our results show that, in the Hubbard dimer setting, they typically work better for the HF reference, despite having been originally devised for KS. These conclusions are somewhat in line with prior assessments of these functionals on various chemical datasets. However, the Hubbard dimer model allows us to show the extent of the error that may occur in using the strong-interaction ingredient for the KS reference in place of the one for the HF reference, as has been carried out in most of the prior assessments. [ABSTRACT FROM AUTHOR]

We investigate the moiré band structures and the strong correlation effects in twisted bilayer MoTe2 for a wide range of twist angles, employing a combination of various techniques. Using large-scale first-principles calculations, we pinpoint realistic continuum modeling parameters, subsequently deriving the maximally localized Wannier functions for the top three moiré bands. Simplifying our model with reasonable assumptions, we obtain a minimal two-band model, encompassing Coulomb repulsion, correlated hopping, and spin exchange. Our minimal interaction models pave the way for further exploration of the rich many-body physics in twisted MoTe2. Furthermore, we explore the phase diagrams of the system through Hartree-Fock approximation and exact diagonalization (ED). Our two-band ED analysis underscores significant band-mixing effects in this system, which enlarge the optimal twist angle for fractional quantum anomalous Hall states. [ABSTRACT FROM AUTHOR]

We investigate the moiré band structures and the strong correlation effects in twisted bilayer MoTe2 for a wide range of twist angles, employing a combination of various techniques. Using large-scale first-principles calculations, we pinpoint realistic continuum modeling parameters, subsequently deriving the maximally localized Wannier functions for the top three moiré bands. Simplifying our model with reasonable assumptions, we obtain a minimal two-band model, encompassing Coulomb repulsion, correlated hopping, and spin exchange. Our minimal interaction models pave the way for further exploration of the rich many-body physics in twisted MoTe2. Furthermore, we explore the phase diagrams of the system through Hartree-Fock approximation and exact diagonalization (ED). Our two-band ED analysis underscores significant band-mixing effects in this system, which enlarge the optimal twist angle for fractional quantum anomalous Hall states. [ABSTRACT FROM AUTHOR]

The unrestricted Hartree‐Fock method is extended to correlation calculation within the density‐matrix functional theory. The method is derived from an entropic cumulant functional for the correlation energy. The eigenvalue equations for the spin‐orbitals are modified by the orbital occupation numbers. The Euler equation for the occupation numbers results in the Fermi‐Dirac distribution, which is very efficient to update as soon as the orbital eigenvalue equations are solved. The method is demonstrated on the ground state of O2. [ABSTRACT FROM AUTHOR]

This work is a development and extension of the previous one (DOI: 10.1039/d3cp00882g). Here, H‐dimers of acridine (acridine orange—AO and proflavine—PF), thiazine (methylene blue—MB and thionine—TH), and oxazine (brilliant cresyl blue—BCB and Nile blue—NB) dyes were modeled using hybrid functionals with a large proportion of exact Hartree–Fock exchange and long‐range correction. It turned out that nine functionals (LC‐ωHPBE, M06HF, M052X, M062X, M08HX, M11, MN15, SOGGA11X, and ωB97XD) reliably stabilize these molecular aggregates in both the ground and excited states. In addition, these functionals ensure that the conditions for transition moments (M(dimer) ≈ 2$$ \sqrt{2} $$M(monomer) from strong coupling theory for H‐aggregates) and absorption maxima (λmax(dimer) < λmax(monomer) from Kasha exciton theory) are met. The S2 excited state stabilizes the H‐dimers more strongly than the ground state, while the S1 state stabilizes even more than S2. This is due to the large overlap between the corresponding molecular orbitals (LUMO > HOMO−1 > HOMO). When calculating the vibronic absorption spectra, the best agreement with the experiment for AO2, PF2, and NB2 showed the M08HX functional, and M11—for MB2 and BCB2. For dye monomers, these functionals gave the worst agreement, and MN15 demonstrated the closest similarity to the experiment. Vibronic absorption spectra for AO2, MB2, BCB2, and NB2 were calculated for the first time. The exciton splitting is calculated, which for MB2 is in good agreement with the experimental value. [ABSTRACT FROM AUTHOR]

In the present work one biphenyl benzoate cored liquid crystal was characterized using geometrical optimization and electro-optic study. Geometry of the molecule was optimized using Hartree-Fock method with 3-21G basis. The simulated value of molecular length and dipole moment was reported. The Infrared (IR) spectra were also simulated and analyzed. The energy gap between highest occupied molecular orbit (HOMO) and lowest unoccupied molecular orbit (LUMO) was calculated. The phase transition temperatures and phase sequences were identified by observing the topological defects in the optical textures at different temperatures under polarizing microscope. It exhibited ferroelectric smectics C* (SmC*) phase for a wide range of temperature and then directly melted into isotropic phase. The optical tilt angle of the compound was measured in SmC* phase and was fitted with mean field model to explore the nature of phase transition. The applicability of the compound for display applications were judged based on the parameters measured. [ABSTRACT FROM AUTHOR]

1,3-thiazines were synthesised using Schiff base and 3-mercaptopropanoic acid and characterised. Using the Gaussian 09W program, the current investigation utilised the Hartree-Fock approximation (HF) to compute diverse molecular characteristics, comprising optimisation, hardness, EHOMO, ELUMO, and energy gap, for a collection of synthesised molecules. [ABSTRACT FROM AUTHOR]

Our recent work on multiple locations of boron atoms in the exohedral and endohedral C60 fullerene, [1], carried out within the Hartree-Fock method with the second order Møller-Plesset perturbation theory MP2 (HF-MP2), prompted recently a comment from Xu and Hou, [2], who have performed several density functional theory (DFT) calculations using DFT functionals of different complexity. In three out of five cases considered in our work, DFT calculations give the same ground state confirmations whereas in two cases optimal configurations have turned out to be different. However, depending on the choice of the exchange-correlation functional, the geometry optimization within DFT can also result in different ground state confirmations. The energy balance between nearest confirmations in these molecular complexes is subtle, and various methods can give different ground state structures. We therefore argue that the presented DFT calculations are not benchmark, and their results should be compared with ours (HF-MP2) on equal ground. We also present additional HF geometry optimizations with the 6-31G* basis set, which confirm the ground state confirmations obtained at the HF/6-31G level. [ABSTRACT FROM AUTHOR]

The present investigation focuses on the geometrical optimized parameters, IR and raman activity based on vibrational frequencies, and global reactivity descriptors of mesogens namely; para-azoxyanisole (PAA), ethyl para-azoxybenzoate (EPAB) and non-mesogen biphenyl-4-carboxylic acid (BCA) molecules via the Density functional theory (DFT) and Hartree–Fock (HF) technique accompanied with 6–31++G (d, p) basis set. The wavenumbers/frequencies obtained for utmost of the vibrational modes are in the predicted range but with minimal error. Reactivity of these molecules based on the molecular properties viz., HOMO, LUMO energies, ionization potential, electro negativity, chemical potential, electron affinity, chemical hardness, and softness has also been focused. The DFT method considers all different electronic interactions thereby give accurate results as compared to Hartree–Fock method. The azoxy bond plays an important role in chemical bond formation in liquid crystals, chemical intermediates, process control, and pharmaceuticals etc. Further, the estimated band gap values indicate the understanding of fine tuning mechanism for exploring the possible industrial applications. [ABSTRACT FROM AUTHOR]