Hartree-Fock Calculations Research Articles

Validity and limitations of the superexchange model for the magnetic properties ofSr2IrO4andBa2IrO4mediated by the strong spin-orbit coupling

Layered perovskites Sr2IrO4 and Ba2IrO4 are regarded as the key materials for understanding the properties of magnetic relativistic insulators, mediated by the strong spin-orbit (SO) coupling. One of the most fundamental issues is to which extent these properties can be described by the superexchange (SE) model, formulated in the limit of the large Coulomb repulsion. In the present work we address this issue by deriving the relevant models and extracting parameters of these models from the first-principles calculations. First, we construct the effective Hubbard-type model for the t2g bands, by recasting the problem in the language of Wannier orbitals. Then, we map the obtained electron model onto the pseudospin model by applying the theory of SE interactions. We discuss the microscopic origin of anisotropic SE interactions, inherent to the compass Heisenberg model, and the appearance of the antisymmetric Dzyaloshinskii-Moriya term, associated with the additional rotation of the IrO6 octahedra in Sr2IrO4. In order to evaluate the Neel temperature (TN), we employ the non-linear sigma model. While for Sr2IrO4 our value of TN agrees with the experimental one, for Ba2IrO4 it is overestimated by a factor two. We argue that this discrepancy is related to limitations of the SE model: while for more localized t2g states in Sr2IrO4 it works reasonably well, the higher-order terms, beyond the SE model, play a more important role in the more "itinerant" Ba2IrO4, giving rise to the new type of isotropic and anisotropic exchange interactions. This conclusion is supported by unrestricted Hartree-Fock calculations for the same electron model, where in the case of Ba2IrO4, already on the mean-field level, we were able to reproduce the experimentally observed magnetic ground state, while for Sr2IrO4 the main results are essentially the same as in the SE model.

Effects of relativity for atomization and isomerization energies of seaborgium carbonyl SgCO and seaborgium isocarbonyl SgOC: Relativity predicts SgOC to be more stable than SgCO

Our ab initio all-electron fully relativistic Dirac-Fock (DF) and nonrelativistic Hartree-Fock (NR) calculations for seaborgium isocarbonyl SgOC predict atomization energy (AE) of 13.04 and 11.05 eV, respectively. However, the corresponding DF and NR atomization energies for the seaborgium carbonyl SgCO are predicted as 12.75 and 12.45 eV, respectively. This is the first such result in Chemistry where an isocarbonyl (and especially for a system of superheavy element Sg) is predicted to be more stable at the DF level of theory than the corresponding carbonyl. The predicted energy for the formation of the carbonyl SgCO at the relativistic DF and NR levels of theory is -54.90 and -50.95 kJ /mol, whereas the corresponding energy of formation of the isocarbonyl SgOC is -64.44 and -18.64 kJ/mol, respectively. Ours are the first results of relativistic effects for isomerization and atomization energies of the superheavy seaborgium isocarbonyl SgOC and its isomer SgCO.The formation of isocarbonyl SgOC, should be favored over the carbonyl isomer SgCO in the first step of the reaction Sg+CO →SgOC.

Shell model and Hartree–Fock calculations for some exotic nuclei

Mass density distributions, the associated nuclear radii and elastic electron scattering form factors of light exotic nuclei, [Formula: see text]Li, [Formula: see text]Be, [Formula: see text]Be and 8B have been calculated using shell model (SM) and Hartree–Fock (HF) methods. We consider truncated spsdpf no core SM and WBP two-body effective interaction to give the SM wave functions. The single-particle matrix elements have been calculated with Skyrme-Hartree–Fock (SHF) potential with different parametrizations. It is shown that the calculated densities and form factors are in fine agreement with experimental data. This agreement can be interpreted as the adequacy of the HF mean-field approximation for exotic nuclei.

Modeling molecule-plasmon interactions using quantized radiation fields within time-dependent electronic structure theory.

We present a combined cavity quantum electrodynamics/ab initio electronic structure approach for simulating plasmon-molecule interactions in the time domain. The simple Jaynes-Cummings-type model Hamiltonian typically utilized in such simulations is replaced with one in which the molecular component of the coupled system is treated in a fully ab initio way, resulting in a computationally efficient description of general plasmon-molecule interactions. Mutual polarization effects are easily incorporated within a standard ground-state Hartree-Fock computation, and time-dependent simulations carry the same formal computational scaling as real-time time-dependent Hartree-Fock theory. As a proof of principle, we apply this generalized method to the emergence of a Fano-like resonance in coupled molecule-plasmon systems; this feature is quite sensitive to the nanoparticle-molecule separation and the orientation of the molecule relative to the polarization of the external electric field.

Three-dimensional hole transport in nickel oxide by alloying with MgO or ZnO

It has been shown previously that the movement of a hole in nickel oxide is confined to two dimensions, along a single ferromagnetic plane. Such confinement may hamper hole transport when NiO is used as a p-type transparent conductor in various solar energy conversion technologies. Here, we use the small polaron model, along with unrestricted Hartree-Fock and complete active space self-consistent field calculations to show that forming substitutional MxNi1−xO alloys with M = Mg or Zn reduces the barrier for movement of a hole away from the ferromagnetic plane to which it is confined. Such reduction occurs for hole transfer alongside one or two M ions that have been substituted for Ni ions. Furthermore, the Mg and Zn ions do not trap holes on O sites in their vicinity, and NiO's transparency is preserved upon forming the alloys. Thus, forming MxNi1−xO alloys with M = Mg or Zn may enhance NiO's potential as a p-type transparent conducting oxide, by disrupting the two-dimensional confinement of holes in pure NiO.

Fission dynamics within time-dependent Hartree-Fock: Deformation-induced fission

Background: Nuclear fission is a complex large-amplitude collective decay mode in heavy nuclei. Microscopic density functional studies of fission have previously concentrated on adiabatic approaches based on constrained static calculations ignoring dynamical excitations of the fissioning nucleus, and the daughter products. Purpose: To explore the ability of dynamic mean-field methods to describe fast fission processes beyond the fission barrier, using the nuclide $^{240}$Pu as an example. Methods: Time-dependent Hartree-Fock calculations based on the Skyrme interaction are used to calculate non-adiabatic fission paths, beginning from static constrained Hartree-Fock calculations. The properties of the dynamic states are interpreted in terms of the nature of their collective motion. Fission product properties are compared to data. Results: Parent nuclei constrained to begin dynamic evolution with a deformation less than the fission barrier exhibit giant-resonance-type behaviour. Those beginning just beyond the barrier explore large amplitude motion but do not fission, whereas those beginning beyond the two-fragment pathway crossing fission to final states which differ according to the exact initial deformation. Conclusions: Time-dependent Hartree-Fock is able to give a good qualitative and quantitative description of fast fission, provided one begins from a sufficiently deformed state.

Computational Study of some Double Headed Acyclo-C-Nucleosides

In the present paper we have a focus in a study of theoretical characterization of three double headed acyclo-C-nucleosides, which are a recent target of experimental studies. The structural and electronic properties of double headed acyclo-C-nucleosides, 1,4-bis (3-mercapto-1H-1,2,4-triazol-5-yl) butane-1,2,3,4-tetrol, 1,4-bis (4-amino-5-mercapto-4H-1,2,4-triazol-3-yl) butane-1,2,3,4-tetrol and 5,5'-(1,2,3,4-tetrahydroxybutane-1,4-diyl) bis (1,3,4-oxadiazole-2(3H)-thione), have been investigated theoretically by performing semi-empirical molecular orbital, ab initio Hartree-Fock (HF) and Density Functional Theory (DFT) calculations. Geometries of the three molecules are optimized at the level of Austin Model 1 (AM1). The electronic properties and relative energies of the molecules have been calculated by HF and DFT in the ground state.

Computational Study of some Double Headed Acyclo-C-Nucleosides

In the present paper we have a focus in a study of theoretical characterization of three double headed acyclo-C-nucleosides, which are a recent target of experimental studies. The structural and electronic properties of double headed acyclo-C-nucleosides, 1,4-bis (3-mercapto-1H-1,2,4-triazol-5-yl) butane-1,2,3,4-tetrol, 1,4-bis (4-amino-5-mercapto-4H-1,2,4-triazol-3-yl) butane-1,2,3,4-tetrol and 5,5'-(1,2,3,4-tetrahydroxybutane-1,4-diyl) bis (1,3,4-oxadiazole-2(3H)-thione), have been investigated theoretically by performing semi-empirical molecular orbital, ab initio Hartree-Fock (HF) and Density Functional Theory (DFT) calculations. Geometries of the three molecules are optimized at the level of Austin Model 1 (AM1). The electronic properties and relative energies of the molecules have been calculated by HF and DFT in the ground state.

Experimental and Theoretical Studies of the Vibrational and Electronic Properties of (2E)-2-[3-(1H-imidazol-1-yl)-1-phenyl-propylidene]-N-phenylhydrazinecarboxamide: An Anticonvulsant Agent

In the current investigation, the molecular structure of the anticonvulsant agent (2E)-2-[3-(1H-imidazol-1-yl)-1-phenylpropylidene]-N-phenylhydrazinecarboxamide ((2E)-HIPC) was theoretically modelled using ab initio Hartree-Fock (HF) and density functional theory (DFT/B3LYP) calculations. The Fourier transform (FT) infrared and FT-Raman spectra of (2E)-HIPC were also recorded, and the observed bands were assigned to the vibrational normal modes. The main functional groups were identified via vibrational analysis, and their absorption bands were assigned. A comparative analysis was performed for the computed and experimental results. Subtle differences were observed between the calculated and experimental UV-Vis spectra. Time-dependent density functional theory (TD-DFT) excitation energies were calculated for five excited electronic states. The calculations were applied to simulate the spectra of (2E)-HIPC, and these simulated spectra exhibited excellent agreement with the experimental spectra. The DFT/B3LYP/6-311++G(d,p) method, after scaling, exhibited better agreement with the experimental values than the results obtained by the HF method. The energy, oscillator strength, and wavelength computed by TD-DFT (IEFPCM) are consistent with the experimental results. The molecular electrostatic potential (MEP) and frontier molecular orbitals (HOMO-LUMO) were also determined to enable prediction of the structural changes and reactive sites. Mulliken population charges of the title molecule were also calculated in the gas phase. The NMR chemical shifts (13C and 1H) were calculated using the gauge-including atomic orbital method and the B3LYP/6-311++G(d,p) approach and were compared with the experimental values.

Twist-averaged boundary conditions for nuclear pasta Hartree-Fock calculations

Background: Nuclear pasta phases, present in the inner crust of neutron stars, are associated with nucleonic matter at sub-saturation densities arranged in regular shapes. Those complex phases, residing in a layer which is approximately 100 m thick, impact many features of neutron stars. Theoretical quantum-mechanical simulations of nuclear pasta are usually carried out in finite 3D boxes assuming periodic boundary conditions (PBC). The resulting solutions are affected by spurious finite-size effects. Purpose: In order to remove spurious finite-size effects, it is convenient to employ twist-averaged boundary conditions (TABC) used in condensed matter, nuclear matter, and lattice QCD applications. In this work, we study the effectiveness of TABC in the context of pasta phases simulations within nuclear density functional theory. Methods: We perform Skyrme-Hartree-Fock calculations in three dimensions by implementing Bloch boundary conditions. The TABC averages are obtained by means of Gauss-Legendre integration over twist angles. Results: We benchmark the TABC for a free nucleonic gas and apply it to simple cases such as the rod and slab phases, as well as to more elaborate P-surface and gyroidal phases. Conclusions: We demonstrate that by applying TABC reliable results can be obtained from calculations performed in relatively small volumes. By studying various contributions to the total energy, we gain insights into pasta phases in mid-density range.

Energy-Efficient Computational Chemistry: Comparison of x86 and ARM Systems.

The computational efficiency and energy-to-solution of several applications using the GAMESS quantum chemistry suite of codes is evaluated for 32-bit and 64-bit ARM-based computers, and compared to an x86 machine. The x86 system completes all benchmark computations more quickly than either ARM system and is the best choice to minimize time to solution. The ARM64 and ARM32 computational performances are similar to each other for Hartree-Fock and density functional theory energy calculations. However, for memory-intensive second-order perturbation theory energy and gradient computations the lower ARM32 read/write memory bandwidth results in computation times as much as 86% longer than on the ARM64 system. The ARM32 system is more energy efficient than the x86 and ARM64 CPUs for all benchmarked methods, while the ARM64 CPU is more energy efficient than the x86 CPU for some core counts and molecular sizes.

Extended Hartree-Fock study of the single-particle potential: The nuclear symmetry energy, nucleon effective mass, and folding model of the nucleon optical potential

The nucleon mean-field potential has been thoroughly investigated in an extended Hartree-Fock (HF) calculation of nuclear matter (NM) using the CDM3Y3 and CDM3Y6 density dependent versions of the M3Y interaction. The single-particle (SP) energies of nucleons in NM are determined according to the Hugenholtz--Van Hove theorem, which gives rise naturally to a rearrangement term (RT) of the SP potential at the Fermi momentum. Using the RT obtained exactly at the different NM densities and neutron-proton asymmetries, a consistent method is suggested to take into account effectively the momentum dependence of the RT of the SP potential within the standard HF scheme. To obtain a realistic momentum dependence of the nucleon optical potential (OP), the high-momentum part of the SP potential was accurately readjusted to reproduce the observed energy dependence of the nucleon OP over a wide range of energies. The impact of the RT and momentum dependence of the SP potential on the density dependence of the nuclear symmetry energy and nucleon effective mass has been studied in detail. The high-momentum tail of the SP potential was found to have a sizable effect on the slope of the symmetry energy and the neutron-proton effective mass splitting at supranuclear densities of the NM. Based on a local density approximation, the folding model of the nucleon OP of finite nuclei has been extended to take into account consistently the RT and momentum dependence of the nucleon OP in the same mean-field manner, and successfully applied to study the elastic neutron scattering on the lead target at the energies around the Fermi energy.

Accurate localized resolution of identity approach for linear-scaling hybrid density functionals and for many-body perturbation theory

A key component in calculations of exchange and correlation energies is the Coulomb operator, which requires the evaluation of two-electron integrals. For localized basis sets, these four-center integrals are most efficiently evaluated with the resolution of identity (RI) technique, which expands basis-function products in an auxiliary basis. In this work we show the practical applicability of a localized RI-variant (‘RI-LVL’), which expands products of basis functions only in the subset of those auxiliary basis functions which are located at the same atoms as the basis functions. We demonstrate the accuracy of RI-LVL for Hartree–Fock calculations, for the PBE0 hybrid density functional, as well as for RPA and MP2 perturbation theory. Molecular test sets used include the S22 set of weakly interacting molecules, the G3 test set, as well as the G2–1 and BH76 test sets, and heavy elements including titanium dioxide, copper and gold clusters. Our RI-LVL implementation paves the way for linear-scaling RI-based hybrid functional calculations for large systems and for all-electron many-body perturbation theory with significantly reduced computational and memory cost.

Molecular structure and vibrational and chemical shift assignments of (4R)-5-eno-4,7-epidioxy-3,7-O-methyl-1,2-O-(S)-trichloroethylidene-5,6,8-trideoxy-α-D-threo-1,4-furano-4,7-diulo-octose by DFT and ab initio HF calculations

Elemental analyses, single crystal X-ray diffraction method, and 1H and 13C NMR spectral techniques are used to synthesize and characterize the crystal structure of 4-diethylamino-2-{[4-(3-methyl-3-phenylcyclobutyl)- thiazol-2-yl]-hydrazonomethyl}-phenol. In order to calculate the molecular geometry along with vibrational frequencies and the gauge including atomic orbital (GIAO) 1H and 13C NMR chemical shift values of the title crystal structure in the ground state, the Hartree–Fock (HF) and density functional theory (DFT) methods with 6-311G(d,p) basis sets are utilized. The assignments of the vibrational frequencies are calculated with the help of the potential energy distribution (PED) analysis using the VEDA 4 software. Experimental data are used for comparison. The molecule contains C–H⋯O intra–inter–molecular interactions.

Shape evolution and collective dynamics of quasifission in the time-dependent Hartree-Fock approach

Background: At energies near the Coulomb barrier, capture reactions in heavy-ion collisions result either in fusion or in quasifission. The former produces a compound nucleus in statistical equilibrium, while the second leads to a reseparation of the fragments after partial mass equilibration without formation of a compound nucleus. Extracting the compound nucleus formation probability is crucial to predict superheavy-element formation cross-sections. It requires a good knowledge of the fragment angular distribution which itself depends on quantities such as moments of inertia and excitation energies which have so far been somewhat arbitrary for the quasifission contribution. Methods: We investigate the evolution of the nuclear density in time-dependent Hartree-Fock (TDHF) calculations leading to quasifission. Our main goal is to extract ingredients of the formula used in the analysis of experimental angular distributions. These include the moment-of-inertia and temperature. We study the dependence of these quantities on various initial conditions of the reaction process. Results: The evolution of the moment of inertia is clearly non-trivial and depends strongly on the characteristics of the collision. The temperature rises quickly when the kinetic energy is transformed into internal excitation. Then, it rises slowly during mass transfer. Conclusions: Fully microscopic theories are useful to predict the complex evolution of quantities required in macroscopic models of quasifission.

Uniform electron gases. III. Low-density gases on three-dimensional spheres.

By combining variational Monte Carlo (VMC) and complete-basis-set limit Hartree-Fock (HF) calculations, we have obtained near-exact correlation energies for low-density same-spin electrons on a three-dimensional sphere (3-sphere), i.e., the surface of a four-dimensional ball. In the VMC calculations, we compare the efficacies of two types of one-electron basis functions for these strongly correlated systems and analyze the energy convergence with respect to the quality of the Jastrow factor. The HF calculations employ spherical Gaussian functions (SGFs) which are the curved-space analogs of Cartesian Gaussian functions. At low densities, the electrons become relatively localized into Wigner crystals, and the natural SGF centers are found by solving the Thomson problem (i.e., the minimum-energy arrangement of n point charges) on the 3-sphere for various values of n. We have found 11 special values of n whose Thomson sites are equivalent. Three of these are the vertices of four-dimensional Platonic solids - the hyper-tetrahedron (n = 5), the hyper-octahedron (n = 8), and the 24-cell (n = 24) - and a fourth is a highly symmetric structure (n = 13) which has not previously been reported. By calculating the harmonic frequencies of the electrons around their equilibrium positions, we also find the first-order vibrational corrections to the Thomson energy.

Electric quadrupole and magnetic dipole moments of odd nuclei near the magic ones in a self-consistent approach

We present a model which describes the properties of odd-even nuclei with one nucleon more, or less, with respect to the magic number. In addition to the effects related to the unpaired nucleon, we consider those produced by the excitation of the closed shell core. By using a single particle basis generated with Hartree-Fock calculations, we describe the polarization of the doubly magic-core with Random Phase Approximation collective wave functions. In every step of the calculation, and for all the nuclei considered, we use the same finite-range nucleon-nucleon interaction. We apply our model to the evaluation of electric quadrupole and magnetic dipole moments of odd-even nuclei around oxygen, calcium, zirconium, tin and lead isotopes. Our Random Phase Approximation description of the polarization of the core improves the agreement with experimental data with respect to the predictions of the independent particle model. We compare our results with those obtained in first-order perturbation theory, with those produced by Hartree-Fock-Bogolioubov calculations and with those generated within the Landau-Migdal theory of finite Fermi systems. The results of our universal, self-consistent, and parameter free approach have the same quality of those obtained with phenomenological approaches where the various terms of the nucleon-nucleon interaction are adapted to reproduce some specific experimental data. A critical discussion on the validity of the model is presented.

Is It Possible To Obtain Coupled Cluster Quality Energies at near Density Functional Theory Cost? Domain-Based Local Pair Natural Orbital Coupled Cluster vs Modern Density Functional Theory.

The recently developed domain-based local pair natural orbital coupled cluster theory with single, double, and perturbative triple excitations (DLPNO-CCSD(T)) delivers results that are closely approaching those of the parent canonical coupled cluster method at a small fraction of the computational cost. A recent extended benchmark study established that, depending on the three main truncation thresholds, it is possible to approach the canonical CCSD(T) results within 1 kJ (default setting, TightPNO), 1 kcal/mol (default setting, NormalPNO), and 2-3 kcal (default setting, LoosePNO). Although thresholds for calculations with TightPNO are 2-4 times slower than those based on NormalPNO thresholds, they are still many orders of magnitude faster than canonical CCSD(T) calculations, even for small and medium sized molecules where there is little locality. The computational effort for the coupled cluster step scales nearly linearly with system size. Since, in many instances, the coupled cluster step in DLPNO-CCSD(T) is cheaper or at least not much more expensive than the preceding Hartree-Fock calculation, it is useful to compare the method against modern density functional theory (DFT), which requires an effort comparable to that of Hartree-Fock theory (at least if Hartree-Fock exchange is part of the functional definition). Double hybrid density functionals (DHDF's) even require a MP2-like step. The purpose of this article is to evaluate the cost vs accuracy ratio of DLPNO-CCSD(T) against modern DFT (including the PBE, B3LYP, M06-2X, B2PLYP, and B2GP-PLYP functionals and, where applicable, their van der Waals corrected counterparts). To eliminate any possible bias in favor of DLPNO-CCSD(T), we have chosen established benchmark sets that were specifically proposed for evaluating DFT functionals. It is demonstrated that DLPNO-CCSD(T) with any of the three default thresholds is more accurate than any of the DFT functionals. Furthermore, using the aug-cc-pVTZ basis set and the LoosePNO default settings, DLPNO-CCSD(T) is only about 1.2 times slower than B3LYP. With NormalPNO thresholds, DLPNO-CCSD(T) is about a factor of 2 slower than B3LYP and shows a mean absolute deviation of less than 1 kcal/mol to the reference values for the four different data sets used. Our conclusion is that coupled cluster energies can indeed be obtained at near DFT cost.

Examination of the stability of a rod-shaped structure inMg24

The stable existence of a six-$\alpha$ linear structure in highly excited states of $^{24}$Mg is studied based on a systematic Cranked Hartree-Fock calculation with various Skyrme-type interactions. Its stability is examined by allowing the transition of the cluster structure to the shell-model like structure. Especially, the six-$\alpha$ linear state is exposed to two major instabilities: the bending motion, which is the main path for the transition to low-lying states, and the spin-orbit interaction, which is the driving force to break the $\alpha$ clusters and enhance the independent motion of the nucleons. The linear structure with large angular momentum is obtained as a meta-stable stationary state.

Roothaan's approach to solve the Hartree-Fock equations for atoms confined by soft walls: Basis set with correct asymptotic behavior.

In this report, we use a new basis set for Hartree-Fock calculations related to many-electron atoms confined by soft walls. One- and two-electron integrals were programmed in a code based in parallel programming techniques. The results obtained with this proposal for hydrogen and helium atoms were contrasted with other proposals to study just one and two electron confined atoms, where we have reproduced or improved the results previously reported. Usually, an atom enclosed by hard walls has been used as a model to study confinement effects on orbital energies, the main conclusion reached by this model is that orbital energies always go up when the confinement radius is reduced. However, such an observation is not necessarily valid for atoms confined by penetrable walls. The main reason behind this result is that for atoms with large polarizability, like beryllium or potassium, external orbitals are delocalized when the confinement is imposed and consequently, the internal orbitals behave as if they were in an ionized atom. Naturally, the shell structure of these atoms is modified drastically when they are confined. The delocalization was an argument proposed for atoms confined by hard walls, but it was never verified. In this work, the confinement imposed by soft walls allows to analyze the delocalization concept in many-electron atoms.