Unrestricted Hartree-Fock Calculations Research Articles

Quantum Chemical Studies on Possible Molecular Devices Based on Electric Field-Induced Intramolecular Charge Transfer.

We report quantum chemical studies on possible molecular devices working based on electric field-induced intramolecular charge transfer (EFIMCT). In the case of donor-acceptor (DA)-type molecular systems, intramolecular charge transfer (IMCT) can be induced by applying the external electric field to molecular systems along the charge transport direction, providing a possible switching mechanism which does not depend upon the electron-phonon coupling effect and is different from the negative differential resistance mechanism observed in the well-known NO2-substituted phenylene ethynylene oligomers. When the EFIMCT proceeds, the molecular systems have strong static electron correlation effects, where the standard nonequilibrium Green's function-density functional theory (DFT) approach cannot be applied to the molecular junction. As a first step toward practical switching devices, we do quantum chemical studies on the EFIMCT in such molecular systems as an isolated molecule, instead of using the electrode-junction-electrode open quantum system model. A prototype molecule P1 is designed as a tentative candidate molecule where the EFIMCT can proceed. The complete active space self-consistent field (CASSCF) molecular orbital calculations on P1 indicate that the EFIMCT can proceed at the external electric field intensity of 0.003 au, corresponding to about 2.25 V bias voltage. This calculated result strongly suggests that the development of this type of switching devices working at practically low bias voltage is feasible if the molecular system is properly designed. Broken symmetry unrestricted Hartree-Fock and spin-polarized Kohn-Sham DFT calculations also qualitatively reproduce the CASSCF results on P1, to some extent, indicating that these approaches can be employed for rough estimations on the EFIMCT such as the first screening of a large quantity of candidate molecules for this type of molecular devices. The possibility of molecular memory devices based on the EFIMCT is also discussed by analyzing the ground and excited potential energy surface model. Remaining challenges to develop practical molecular devices are discussed.

Itinerant ferromagnetism in SU(N)-symmetric fermi gases at finite temperature: first order phase transitions and time-reversal symmetry

At temperatures well below the Fermi temperature T F , the coupling of magnetic fluctuations to particle-hole excitations in a two-component Fermi gas leads to non-analytic corrections in the renormalized free energy and makes the transition to itinerant ferromagnetism first order. On the other hand, despite that larger symmetry often introduces larger degeneracies in the low-lying states, here we show that for a Fermi gas with SU(N > 2)-symmetry in three space dimensions the ferromagnetic phase transition is first order in agreement with the predictions of Landau’s mean-field theory in its minimal formulation, which contains a cubic term in the free-energy (Cazalilla et al 2009 New J. Phys. 11 103033). By performing unrestricted Hartree–Fock calculations for an SU(N > 2)-symmetric Fermi gas with short range interactions, we find the order parameter undergoes a finite jump across the transition. In addition, for SU(N > 2) we do not observe any tri-critical point up to temperatures , for which the thermal smearing of the Fermi surface and thermal fluctuations are substantial. Going beyond mean-field theory, we find that the coupling of magnetic fluctuations to particle-hole excitations makes the transition more abrupt and further enhances the tendency of the gas to become fully polarized for smaller values of N and the gas parameter . In our study, we also clarify the role of time reversal symmetry in the microscopic Hamiltonian and obtain the temperature dependence of Tan’s contact. For the latter, the presence of the tri-critical point for N = 2 leads to a more pronounced temperature dependence around the transition than for SU(N > 2)-symmetric gases. Although the results are obtained for a microscopic model relevant to ultracold atomic gases, they may also apply to models of solid state systems with SU(N > 2) symmetry provided Coulomb interactions are sufficiently well screened.

Non-coplanar magnetism, topological density wave order and emergent symmetry at half-integer filling of moiré Chern bands

Twisted double- and mono-bilayer graphene are graphene-based moiré materials hosting strongly correlated fermions in a gate-tunable conduction band with a topologically non-trivial character. Using unbiased exact diagonalization complemented by unrestricted Hartree-Fock calculations, we find that the strong electron-electron interactions lead to a non-coplanar magnetic state, which has the same symmetries as the tetrahedral antiferromagnet on the triangular lattice and can be thought of as a skyrmion lattice commensurate with the moiré scale, competing with a set of ferromagnetic, topological charge density waves featuring an approximate emergent O(3) symmetry, “rotating” the different charge density wave states into each other. Direct comparison with exact diagonalization reveals that the ordered phases are accurately described within the unrestricted Hartree-Fock approximation. Exhibiting a finite charge gap and Chern number |C|=1, the formation of charge density wave order which is intimately connected to a skyrmion lattice phase is consistent with recent experiments on these systems.

Magnetic and charge instabilities in vanadium-based topological kagome metals

Vanadium-based topological kagome metals ${\mathrm{AV}}_{3}{\mathrm{Sb}}_{5}$ ($A=\mathrm{K}$, Rb, Cs) have drawn great attention recently due to the discoveries of charge order, nematic phase, time-reversal symmetry breaking, and superconductivity. In this work, we study the Fermi-surface instabilities of topological kagome metals ${\mathrm{AV}}_{3}{\mathrm{Sb}}_{5}$ ($A=\mathrm{K}$, Rb, Cs) in all the charge-orbital-spin channels based on first principles calculations, and provide a first principles theory for the current-loop state in this class of materials. After comprehensive analysis of the interaction-renormalized generalized susceptibility tensor combined with unrestricted Hartree-Fock calculations, we find that the leading instability modes at the Fermi surface are three spin magnetic modes at $\mathrm{\ensuremath{\Gamma}}$ point, giving rise to ferromagnetism within the kagome plane with small magnetization on the V atoms. We further show that counter-propagating current loops within the kagome plane can be generated due to the interplay between spin magnetism and spin-orbit coupling, and the current pattern is consistent with recent muon spin spectroscopy measurements. Moreover, some other puzzling experiments in this system such as the giant anomalous Hall effect and nematicity can also be explained from our results.

Correlated Insulators, Density Wave States, and Their Nonlinear Optical Response in Magic-Angle Twisted Bilayer Graphene.

The correlated insulator (CI) states and the recently discovered density wave (DW) states in magic-angle twisted bilayer graphene (TBG) have stimulated intense research interest. However, to date, the nature of these "featureless" correlated states with zero Chern numbers are still elusive and lack a characteristic experimental signature. Thus, an experimental probe to identify the characters of these featureless CI and DW states is urgently needed. In this Letter, we theoretically study the correlated insulators and density wave states at different integer and fractional fillings of the flat bands in magic-angle TBG based on extended unrestricted Hartree-Fock calculations including the Coulomb screening effects from the remote bands. We further investigate the nonlinear optical response of the various correlated states and find that the nonlinear optical conductivities can be used to identify the nature of these CI and DW states at most of the fillings. Therefore, we propose that a nonlinear optical response can serve as a promising experimental probe for unveiling the nature of the CI and DW states observed in magic-angle TBG.

Efficient Method for Prediction of Metastable or Ground Multipolar Ordered States and Its Application in Monolayer α-RuX_{3} (X=Cl, I).

Exotic high-rank multipolar order parameters have been found to be unexpectedly active in more and more correlated materials in recent years. Such multipoles are usually dubbed "hidden orders" since they are insensitive to common experimental probes. Theoretically, it is also difficult to predict multipolar orders via abinitio calculations in real materials. Here, we present an efficient method to predict possible multipoles in materials based on linear response theory under random phase approximation. Using this method, we successfully predict two pure metastable magnetic octupolar states in monolayer α-RuCl_{3}, which is confirmed by self-consistent unrestricted Hartree-Fock calculations. We then demonstrate that these octupolar states can be stabilized in monolayer α-RuI_{3}, one of which becomes the octupolar ground state. Furthermore, we also predict a fingerprint of an orthogonal magnetization pattern produced by the octupole moment that can be easily detected by experiment. The method and the example presented in this Letter serve as a guide for searching multipolar order parameters in other correlated materials.

Path-integral Monte Carlo study of electronic states in quantum dots in an external magnetic field

We explore the correlated electron states in harmonically confined few-electron quantum dots in an external magnetic field by the path-integral Monte Carlo method for a wide range of the field and the Coulomb interaction strength. Using the phase structure of a preceding unrestricted Hartree-Fock calculation for phase fixing, we find a rich variety of correlated states, often completely different from the prediction of mean-field theory. These are finite temperature results, but sometimes the correlations saturate with decreasing temperature, providing insight into the ground-state properties.

Quantum chemistry with Coulomb Sturmians: Construction and convergence of Coulomb Sturmian basis sets at the Hartree-Fock level

The first discussion of basis sets consisting of exponentially decaying Coulomb Sturmian functions for modelling electronic structures is presented. The proposed basis set construction selects Coulomb Sturmian functions using separate upper limits to their principle, angular momentum and magnetic quantum numbers. Their common Coulomb Sturmian exponent is taken as a fourth parameter. The convergence properties of such basis sets are investigated for second and third row atoms at the Hartree-Fock level. Thereby important relations between the values of the basis set parameters and the physical properties of the electronic structure are recognised. For example, an unusually large limit for the angular momentum quantum number in unrestricted Hartree-Fock calculations can be linked to the breaking of spherical symmetry in such cases. Furthermore, a connection between the optimal, i.e. minimum-energy, Coulomb Sturmian exponent and the average Slater exponents values obtained by Clementi and Raimondi (E. Clementi and D. L. Raimondi, J. Chem. Phys. 38, 2686 (1963)) is made. These features of Coulomb Sturmian basis sets emphasise their ability to correctly reproduce the physical features of Hartree-Fock wave functions.

TDHF Investigations of the U+U Quasifission Process

The use of actinide collisions have been suggested as a way to produce neutron rich isotopes of high Z nuclei. The collision dynamics of these reactions can be studied using unrestricted time-dependent Hartree-Fock (TDHF) calculations. Here, we report on the recent studies of quasifission for the $^{238}$U+$^{238}$U system.

Localization of holes near charged defects in orbitally degenerate, doped Mott insulators

We study the role of charged defects, disorder and electron-electron (e-e) interactions in a multiband model for t2g electrons in vanadium perovskites R1−xCaxVO3 (R = La,…,Y). By means of unrestricted Hartree-Fock calculations, we find that the atomic multiplet structure persists up to 50% Ca doping. Using the inverse participation number, we explore the degree of localization and its doping dependence for all electronic states. The observation of strongly localized wave functions is consistent with our conjecture that doped holes form spin-orbital polarons that are strongly bound to the charged Ca2+ defects. Interestingly, the long-range e-e interactions lead to a discontinuity in the wave function size across the chemical potential, where the electron removal states are more localized than the addition states.

Bayesian Approach to Effective Model of NiGa2S4 Triangular Lattice with Boltzmann Factor

We propose a method for inducting the Boltzmann factor to extract effective classical spin Hamiltonians from mean-field-type electronic structural calculations by means of the Bayesian inference. This method enables us to compare electronic structural calculations with experiments according to the classical model at a finite temperature. Application of this method to the unrestricted Hartree–Fock calculations for NiGa2S4 led to the estimation that the superexchange interaction between the nearest neighbor sites is ferromagnetic at low temperature, which is consistent with magnetic experiment results. This supports the theory that competition between the antiferromagnetic third neighbor interaction and ferromagnetic nearest neighbor interaction may lead to the quantum spin liquid in NiGa2S4.

Polyradical Character of Triangular Non-Kekulé Structures, Zethrenes, p-Quinodimethane-Linked Bisphenalenyl, and the Clar Goblet in Comparison: An Extended Multireference Study.

In this work, two different classes of polyaromatic hydrocarbon (PAH) systems have been investigated in order to characterize the amount of polyradical character and to localize the specific regions of chemical reactivity: (a) the non-Kekulé triangular structures phenalenyl, triangulene and a π-extended triangulene system with high-spin ground state and (b) PAHs based on zethrenes, p-quinodimethane-linked bisphenalenyl, and the Clar goblet containing varying polyradical character in their singlet ground state. The first class of structures already have open-shell character because of their high-spin ground state, which follows from the bonding pattern, whereas for the second class the open-shell character is generated either because of the competition between the closed-shell quinoid Kekulé and the open-shell singlet biradical resonance structures or the topology of the π-electron arrangement of the non-Kekulé form. High-level ab initio calculations based on multireference theory have been carried out to compute singlet–triplet splitting for the above-listed compounds and to provide insight into their chemical reactivity based on the polyradical character by means of unpaired densities. Unrestricted density functional theory and Hartree–Fock calculations have been performed for comparison also in order to obtain better insight into their applicability to these types of complicated radical systems.

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.

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.

Sign reversal of the Hall response in a crystalline superconductor

We consider the Hall conductivity due to the motion of a vortex in a lattice-model of a clean superconductor, using a combination of general arguments, unrestricted Hartree-Fock calculations, and exact diagonalization. In the weak coupling limit, $k_F \xi \gg 1$, the sign of the Hall response of the superconducting state is the same as that of the normal (non-superconducting) state. For intermediate and strong coupling, however, ($k_F \xi \sim 1$) we find that the sign of the Hall response in the superconducting state can be opposite to that of the normal state. In addition, we find that the sign reversal of the Hall response is correlated with a discontinuous change in the density profile at the vortex core. Implications for experiments in the cuprate superconductors are discussed.

Model Selection of NiGa2S4 Triangular Lattice by Bayesian Inference

We propose a novel method for extracting effective classical spin Hamiltonians from mean-field type electronic structural calculations by means of the Bayesian inference. We apply the method for a NiS2 triangular lattice in NiGa2S4, where the ground state is a spin disordered state. Starting from unrestricted Hartree–Fock calculations for the spin configurations of 16 Ni sites, we estimated that not only the strongest superexchange interaction between the third nearest neighbor-sites but also those between the nearest and the second nearest neighbor-sites should be considered for the effective classical spin Hamiltonian for NiGa2S4.

非制限ハートリーフォック(UHF)計算に対する最適ダンピングアルゴリズムの開発

We have developed a couple of optimal damping algorithms (ODAs) for unrestricted Hartree-Fock (UHF) calculations of open-shell molecular systems. A series of equations were derived for both concurrent and alternate constructions of alpha- and beta-Fock matrices in the integral-direct self-consistent-field (SCF) procedure. Several test calculations were performed to check the convergence behaviors. It was shown that the concurrent algorithm provides better performance than does the alternate one.

Impact of Local Lattice Disorder on Spin and Orbital Orders in Ca2-xSrxRuO4

We have studied relationship between local lattice disorder, Ru 4$d$ spin-orbit interaction, and global spin/orbital orders of Ca$_{2-x}$Sr$_x$RuO$_4$ in the Sr-rich and Ca-rich regions of its phase diagram by using unrestricted Hartree-Fock calculation on a $8\times8$ RuO$_4$ lattice model. The calculations show that the local elongation of RuO$_6$ octahedron in an antiferromagnetic insulator Ca$_2$RuO$_4$ induces local orbital change with making the Mott gap narrower. On the other hand, local compression of RuO$_6$ octahedron in a paramagnetic metal Sr$_2$RuO$_4$ induces global antiferromagnetic or ferromagnetic states. This result is consistent with a recent systematic $\mu$SR study by Carlo {\it et al.} which has revealed the static antiferromagnetic order at low temperature in the Sr-rich region.

Spin–Charge–Orbital Ordering in Hollandite-Type Manganites Studied by Model Hartree–Fock Calculation

We have studied spin–charge–orbital orderings in a Mn3+/Mn4+ mixed valence state on a hollandite-type lattice using unrestricted Hartree–Fock calculation on a multi-band Mn \(3d\)–O \(2p\) lattice model. The calculations show that all the Mn3+–Mn4+, Mn3+–Mn3+, and Mn4+–Mn4+ superexchange interactions are ferromagnetic and play important roles to stabilize the charge and orbital ordering patterns. The most stable charge and orbital ordering pattern is consistent with the \(1\times 1\times 1\) orthorhombic or monoclinic structure of K1.6Mn8O16.

Impact of Mn–O–O–Mn superexchange pathways in a honeycomb lattice Mn oxide with small charge-transfer energy

We investigated the electronic structure of layered Mn oxide Bi3Mn4O12(NO3) with a Mn honeycomb lattice by x-ray absorption spectroscopy and model calculations. The valence of Mn was determined to be 4+ with a small charge-transfer energy of ∼ 1eV. The values of (J1, J2, J3, Jc, Jc1, and Jc2) obtained by unrestricted Hartree–Fock calculations on Mn 3d–O 2p lattice models show that intra-layer second and third neighbor superexchange interactions J2 and J3 as well as inter-layer superexchange interactions Jc, Jc1, and Jc2 are enhanced due to Mn–O–O–Mn pathways, which are activated by the smallness of charge-transfer energy. The present analysis indicates that the ferromagnetic Jc1 and antiferromagnetic Jc2 are responsible to the antiferromagnetic inter-layer coupling and that the intra-layer exchange interactions with the ferromagnetic J2 and antiferromagnetic J3 have no frustration effect.