Abstract: Although the simulation of quantum chemistry is one of the most anticipated applications of quantum computing, the scaling of known upper bounds on the complexity of these algorithms is daunting. Prior work has bounded errors due to discretization of the time evolution (known as ``Trotterization'') in terms of the norm of the error operator and analyzed scaling with respect to the number of spin orbitals. However, we find that these error bounds can be loose by up to 16 orders of magnitude for some molecules. Furthermore, numerical results for small systems fail to reveal any clear correlation between ground-state error and number of spin orbitals. We instead argue that chemical properties, such as the maximum nuclear charge in a molecule and the filling fraction of orbitals, can be decisive for determining the cost of a quantum simulation. Our analysis motivates several strategies to use classical processing to further reduce the required Trotter step size and estimate the necessary number of steps, without requiring additional quantum resources. Finally, we demonstrate improved methods for state preparation techniques which are asymptotically superior to proposals in the simulation literature.

Abstract: In transition-metal oxides, the ability to control which atomic orbitals are occupied by electrons could be used to develop materials with new functionalities.

Abstract: The calculation of absolute total cross sections requires accurate wave functions of the photoelectron and of the initial and final states of the system. The essential information contained in the latter two can be condensed into a Dyson orbital. We employ correlated Dyson orbitals and test approximate treatments of the photoelectron wave function, that is, plane and Coulomb waves, by comparing computed and experimental photoionization and photodetachment spectra. We find that in anions, a plane wave treatment of the photoelectron provides a good description of photodetachment spectra. For photoionization of neutral atoms or molecules with one heavy atom, the photoelectron wave function must be treated as a Coulomb wave to account for the interaction of the photoelectron with the +1 charge of the ionized core. For larger molecules, the best agreement with experiment is often achieved by using a Coulomb wave with a partial (effective) charge smaller than unity. This likely derives from the fact that the effective charge at the centroid of the Dyson orbital, which serves as the origin of the spherical wave expansion, is smaller than the total charge of a polyatomic cation. The results suggest that accurate molecular photoionization cross sections can be computed with a modified central potential model that accounts for the nonspherical charge distribution of the core by adjusting the charge in the center of the expansion.

Abstract: On the basis of first-principles calculations, we have systematically studied the adsorption and diffusion of Li ions on monolayer MnO2 and compared with other transition metal dichalcogenides (TMDs) and transition metal dioxides (TMOs). Monolayer MnO2 shows a relatively high Li adsorption energy of 4.37 eV and low Li diffusion barrier of 0.148 eV. The electronic analysis indicates that the electron transferred from Li to the empty orbital of the O atom and there is some orbital coupling between the s orbital of the Li atom and the pz orbital of the O atom in MnO2. Due to Li adsorption on both sides of the MnO2 layer, the theoretical Li storage capacity reaches as high as 616 mAh/g. Our results demonstrated that, compared to other two-dimensional (2D) nanomaterials, monolayer or few-layer MnO2 exhibits excellent performance on Li storage capacity and diffusion rate and is believed to be a promising electrode material for high-capacity Li ion batteries.

Abstract: The electronic structure and optical properties of hexagonal armchair and zigzag-edged graphene quantum dots (GQDs) are investigated within the framework of many-body perturbation theory. Many-body effects are significant due to quantum confinement and reduced screening. The quasi-particle corrections and exciton binding energies can be several eV, much larger than those of other carbon allotropes with higher dimensionality. All the GQDs show similar absorption spectra when electron–hole interaction is included, with a prominent peak emerging below the absorption onset of the noninteracting spectrum. This peak is contributed by a pair of double-degenerate excited states originating from the transitions between degenerate frontier orbitals. The spin singlet–triplet splitting is closely related to the electron–hole overlap, which can be approximately measured by the overlap between frontier orbitals involved in the optical transitions. The strong many-body effects in GQDs should be of great importance in op...

Abstract: The development and first applications of a new periodic energy decomposition analysis (pEDA) scheme for extended systems based on the Kohn-Sham approach to density functional theory are described. The pEDA decomposes the bonding energy between two fragments (e.g., the adsorption energy of a molecule on a surface) into several well-defined terms: preparation, electrostatic, Pauli repulsion, and orbital relaxation energies. This is complemented by consideration of dispersion interactions via a pairwise scheme. One major extension toward a previous implementation [Philipsen and Baerends, J. Phys. Chem. B 110, 12470 (2006)] lies in the separate discussion of electrostatic and Pauli and the addition of a dispersion term. The pEDA presented here for an implementation based on atomic orbitals can handle restricted and unrestricted fragments for 0D to 3D systems considering periodic boundary conditions with and without the determination of fragment occupations. For the latter case, reciprocal space sampling is enabled. The new method gives comparable results to established schemes for molecular systems and shows good convergence with respect to the basis set (TZ2P), the integration accuracy, and k-space sampling. Four typical bonding scenarios for surface-adsorbate complexes were chosen to highlight the performance of the method representing insulating (CO on MgO(001)), metallic (H2 on M(001), M = Pd, Cu), and semiconducting (CO and C2H2 on Si(001)) substrates. These examples cover diverse substrates as well as bonding scenarios ranging from weakly interacting to covalent (shared electron and donor acceptor) bonding. The results presented lend confidence that the pEDA will be a powerful tool for the analysis of surface-adsorbate bonding in the future, enabling the transfer of concepts like ionic and covalent bonding, donor-acceptor interaction, steric repulsion, and others to extended systems.

Abstract: We introduce a simple and general scheme to derive from wavefuntion analysis the most appropriate atomic/fragment electron configurations in a molecular system, from which oxidation states can be inferred. The method can be applied for any level of theory for which the first-order density matrix is available, and unlike others, it is not restricted to transition metal complexes. The method relies on the so-called spin-resolved effective atomic orbitals which for the present purpose is extended here to deal with molecular fragments/ligands. We describe in detail the most important points of the new scheme, in particular the hierarchical fragment approach devised for practical applications. A number of transition metal complexes with different formal oxidation states and spin states and a set of organic and inorganic compounds are provided as illustrative examples of the new scheme. Challenging systems such as transition state structures are also tackled on equal footing.

Abstract: Electron occupation of orbitals in two-dimensional (2D) layered materials controls the magnitude and anisotropy of the interatomic electron transfer and exerts a key influence on the chemical bonding modes of 2D layered lattices. Therefore, their orbital occupations are believed to be responsible for massive variations of the physical and chemical properties from electrocatalysis and energy storage, to charge density waves, superconductivity, spin–orbit coupling, and valleytronics. Especially in nanoscale structures such as nanoribbons, nanoplates, and nanoflakes, 2D layered materials provide opportunities to exploit new quantum phenomena.In this Account, we report our recent progress in the rational design and chemical, electrochemical, and electrical modulations of the physical and chemical properties of layered nanomaterials via modification of the electron occupation in their electronic structures. Here, we start with the growth and fabrication of a group of layered chalcogenides with varied orbital o...

Abstract: An implementation of coupled-cluster (CC) theory to treat atoms and molecules in finite magnetic fields is presented. The main challenges for the implementation stem from the magnetic-field dependence in the Hamiltonian, or, more precisely, the appearance of the angular momentum operator, due to which the wave function becomes complex and which introduces a gauge-origin dependence. For this reason, an implementation of a complex CC code is required together with the use of gauge-including atomic orbitals to ensure gauge-origin independence. Results of coupled-cluster singles–doubles–perturbative-triples (CCSD(T)) calculations are presented for atoms and molecules with a focus on the dependence of correlation and binding energies on the magnetic field.

Abstract: An electrostatic model based on the effective-point-charge approach is proposed to predict the quantized axis of rare-earth ions, even in low symmetry. The effective charges of coordination atoms create an electrostatic potential interacting with the aspherical 4f electron cloud of the rare-earth ion. The quantized axis can be determined by minimizing the electrostatic energy. The effective charge displacements must be considered according to the nature of the coordination bond, which can be calculated by the atomic orbital wavefunctions for the σ- and π-bonds, respectively. Using our model, the experimentally determined magnetic easy axis of some complexes with Tb3+, Dy3+ and Er3+ can be very well reproduced.

Abstract: Orbital degree of freedom plays a fundamental role in understanding the unconventional properties in solid state materials. Experimental progress in quantum atomic gases has demonstrated that high orbitals in optical lattices can be used to construct quantum emulators of exotic models beyond natural crystals, where novel many-body states such as complex Bose-Einstein condensation and topological semimetals emerge. A brief introduction of orbital degree of freedom in optical lattices is given and a summary of exotic orbital models and resulting many-body phases is provided. Experimental consequences of the novel phases are also discussed.

Abstract: Complete active space self-consistent field (CASSCF) wavefunctions and an orbital entanglement analysis obtained from a density-matrix renormalisation group (DMRG) calculation are used to understand the electronic structure, and, in particular, the Ru–NO bond of a Ru nitrosyl complex. Based on the configurations and orbital occupation numbers obtained for the CASSCF wavefunction and on the orbital entropy measurements evaluated for the DMRG wavefunction, we unravel electron correlation effects in the Ru coordination sphere of the complex. It is shown that Ru–NO π bonds show static and dynamic correlation, while other Ru–ligand bonds feature predominantly dynamic correlation. The presence of static correlation requires the use of multiconfigurational methods to describe the Ru–NO bond. Subsequently, the CASSCF wavefunction is analysed in terms of configuration state functions based on localised orbitals. The analysis of the wavefunctions in the electronic singlet ground state and the first triplet state provides a picture of the Ru–NO moiety beyond the standard representation based on formal oxidation states. A distinct description of the Ru and NO fragments is advocated. The electron configuration of Ru is an equally weighted superposition of RuII and RuIII configurations, with the RuIII configuration originating from charge donation mostly from Cl ligands. However, and contrary to what is typically assumed, the electronic configuration of the NO ligand is best described as electroneutral.

Abstract: Electronic and topological behaviors of Sb(111) monolayers decorated with H and certain magnetic atoms are investigated by using ab initio methods. The drastic exchange field induced by the magnetic atoms, together with strong spin–orbit coupling (SOC) of Sb atoms, generates one new category of valley polarized topological insulators, called quantum spin-quantum anomalous Hall (QSQAH) insulators in the monolayer, with a band gap up to 53 meV. The strong SOC is closely related to Sb px and py orbitals, instead of pz orbitals in usual two-dimensional (2D) materials. Topological transitions from quantum anomalous Hall states to QSQAH states and then to time-reversal-symmetry-broken quantum spin Hall states are achieved by tuning the SOC strength. The behind mechanism is revealed. Our work is helpful for future valleytronic and spintronic applications in 2D materials.

Abstract: Despite recent advances, systematic quantitative treatment of the electron correlation problem in extended systems remains a formidable task. Systematically improvable Green's function methods capable of quantitatively describing weak and at least qualitatively strong correlations appear promising candidates for computational treatment of periodic systems. We present a periodic implementation of temperature-dependent self-consistent 2nd-order Green's function method (GF2), where the self-energy is evaluated in the basis of atomic orbitals. Evaluating the real-space self-energy in atomic orbitals and solving the Dyson equation in $\mathbf{k}$-space are the key components of a computationally feasible algorithm. We apply this technique to the 1D hydrogen lattice - a prototypical crystalline system with a realistic Hamiltonian. By analyzing the behavior of the spectral functions, natural occupations, and self-energies, we claim that GF2 is able to recover metallic, band insulating, and at least qualitatively Mott regimes. We observe that the iterative nature of GF2 is essential to the emergence of the metallic and Mott phases.

Abstract: The exact formulation of multi-configuration density-functional theory is discussed in this work. As an alternative to range-separated methods, where electron correlation effects are split in the coordinate space, the combination of configuration interaction methods with orbital occupation functionals is explored at the formal level through the separation of correlation effects in the orbital space. When applied to model Hamiltonians, this approach leads to an exact site-occupation embedding theory (SOET). An adiabatic connection expression is derived for the complementary bath functional and a comparison with density matrix embedding theory is made. Illustrative results are given for the simple two-site Hubbard model. SOET is then applied to a quantum chemical Hamiltonian, thus leading to an exact complete active space site-occupation functional theory (CASSOFT) where active electrons are correlated explicitly within the CAS and the remaining contributions to the correlation energy are described with an ...

Abstract: 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.

Abstract: We introduce a novel and efficient explicitly correlated implementation of second-order perturbation theory for solids. The required three-electron integrals are computed directly using a plane wave basis set. We parametrize the employed correlation factors using results previously obtained for a finite uniform electron gas simulation cell. We demonstrate for a range of solids that basis set converged correlation energies, equilibrium volumes, and bulk moduli can be obtained efficiently in this theory using a few ten orbitals per atom. To stretch the capabilities of this novel method we compute the Schottky defect formation energy in MgO, studying systems with 54 atoms in the supercell. We verify the accuracy of the calculated formation energies using the more accurate coupled cluster singles and doubles theory. Furthermore, we discuss other potential applications for the derived and implemented expressions such as an occupied orbital only correlation energy functional.

Abstract: We present a gauge-invariant implementation of the four-component Dirac-Hartree-Fock method for simulating the electronic structure of heavy element complexes in magnetic fields. The additional cost associated with the magnetic field is shown to be only 10-13% of that at zero field. The Dirac-Hartree-Fock wave function is constructed from gauge-including atomic orbitals. The so-called restricted magnetic balance is used to generate 2-spinor basis functions for the small component. The molecular integrals for the Coulomb and Gaunt interactions are computed using density fitting. Our efficient, parallel implementation allows for simulating the electronic structure of molecules containing more than 100 atoms with a few heavy elements under magnetic fields.

Abstract: We present two improvements to the tight-binding approximation of time-dependent density functional theory (TD-DFTB): Firstly, we add an exact Hartree-Fock exchange term, which is switched on at large distances, to the ground state Hamiltonian and similarly to the coupling matrix that enters the linear response equations for the calculation excited electronic states. We show that the excitation energies of charge transfer states are improved relative to the standard approach without the long-range correction by testing the method on a set of molecules from the database in J. Chem. Phys. (2008),128,044118. that are known to exhibit problematic charge transfer states. The degree of spatial overlap between occupied and virtual orbitals indicates where TD-DFTB and lc-TD-DFTB can be expected to produce large errors. Secondly, we improve the calculation of oscillator strengths. The transition dipoles are obtained from Slater Koster files for the dipole matrix elements between valence orbitals. In particular excitations localized on a single atom, which appear dark when using Mulliken transition charges, in this way acquire a more realistic oscillator strength. These extensions pave the way for using long-range corrected TD-DFTB (lc-TD-DFTB) to describe the electronic structure of large chromophoric polymers, where uncorrected TD-DFTB fails to describe the high degree of conjugation and produces spurious low-lying charge transfer states.

Abstract: First-principles calculations were performed to investigate the electronic structure of two-dimensional (2-D) Ge, Sn, and Pb without and with the presence of an external electric field in combination with spin-orbit coupling. Tight-binding calculations based on four orbitals per atom and an effective single orbital are presented to match with the results obtained from first-principles calculations. In particular, the electronic band structure and the band splitting are investigated with both models. Moreover, the simple $k\cdot p$ model is also considered in order to understand the band splitting in the presence of an external electric field and spin-orbit coupling. A large splitting is obtained, which is expected to be useful for spintronic devices. The fair agreement between the first-principle, $k\cdot p$ model, and tight-binding approaches leads to a table of parameters for future tight-binding studies on hexagonal 2-D nanostructures. By using the tight binding parameters, the transport properties of typical 0-D triangular quantum dots between two semi-infinite electrodes in the presence of spin-orbit coupling are addressed.

Abstract: A novel algorithm for performing configuration interaction (CI) calculations using non-orthogonal orbitals is introduced. In the new algorithm, the explicit calculation of the Hamiltonian matrix is replaced by the direct evaluation of the Hamiltonian matrix times a vector, which allows expressing the CI-vector in a bi-orthonormal basis, thereby drastically reducing the computational complexity. A new non-orthogonal orbital optimization method that employs exponential mappings is also described. To allow non-orthogonal transformations of the orbitals, the standard exponential mapping using anti-symmetric operators is supplemented with an exponential mapping based on a symmetric operator in the active orbital space. Expressions are obtained for the orbital gradient and Hessian, which involve the calculation of at most two-body density matrices, thereby avoiding the time-consuming calculation of the three- and four-body density matrices of the previous approaches. An approach that completely avoids the calcu...

Abstract: First-principles calculations were performed to investigate the electronic structure of two-dimensional (2-D) Ge, Sn, and Pb without and with the presence of an external electric field in combination with spin–orbit coupling. Tight-binding calculations based on four orbitals per atom and an effective single orbital are presented to match with the results obtained from first-principles calculations. In particular, the electronic band structure and the band splitting are investigated with both models. Moreover, the simple k·p model is also considered in order to understand the band splitting in the presence of an external electric field and spin–orbit coupling. A large splitting is obtained, which is expected to be useful for spintronic devices. The fair agreement between the first-principle, k· p model, and tight-binding approaches leads to a table of parameters for future tight-binding studies on hexagonal 2-D nanostructures. By using the tight binding parameters, the transport properties of typical 0-D t...

Abstract: Density functional theory (DFT) calculations at the B3LYP/6-31G* level are performed to investigate the adsorption properties and quantum molecular descriptors of H2S adsorbed on the external surface of (6,0) single-walled aluminum phosphide nanotube (AlPNT). The vibrational frequencies and physical properties such as dipole moment, chemical potential, chemical hardness and chemical electrophilicity of all studied configurations have been systematically explored. Also, the interaction of H2S gas and AlPNT on the basis of five reactivity descriptors such as the overall stabilization energy (∆E SE(AB)), the individual energy change of the acceptor (∆E A(B)), the individual energy change of donor (∆E B(A)), the global electrophilicity difference of AlPNT and H2S gas (∆w) and charge transfer (∆N) has been explained. All adsorptions are electronically harmless processes and venial impacts on the energy gap of the AlP nanotube. The natural bond orbital calculations are done to derive natural atomic orbital occupancies. The H2S molecule physisorbed on the surface of pristine AlP nanotube with adsorption energy of about −20 kJ/mol. The AIM theory has been also used to examine the properties of the bond critical points: their electron densities and Laplacians. The adsorption energy of H2S molecule is not so large to hinder the recovery of the AlPNT, and therefore, the sensor will possess short recovery times. Electronic structures of pristine AlPNT and adsorbed H2S gas AlPNT models are examined by DFT calculations of chemical shielding (CS) parameters of 27Al and 31P atoms. The isotropic and anisotropic CS parameters are divided into layers based on the detection of similar electronic environments by the atomic sites of each layer.

Abstract: We present two improvements to the tight-binding approximation of time-dependent density functional theory (TD-DFTB): First, we add an exact Hartree-Fock exchange term, which is switched on at large distances, to the ground state Hamiltonian and similarly to the coupling matrix that enters the linear response equations for the calculation of excited electronic states. We show that the excitation energies of charge transfer states are improved relative to the standard approach without the long-range correction by testing the method on a set of molecules from the database in Peach et al. [J. Chem. Phys. 128, 044118 (2008)] which are known to exhibit problematic charge transfer states. The degree of spatial overlap between occupied and virtual orbitals indicates where TD-DFTB and long-range corrected TD-DFTB (lc-TD-DFTB) can be expected to produce large errors. Second, we improve the calculation of oscillator strengths. The transition dipoles are obtained from Slater Koster files for the dipole matrix elements between valence orbitals. In particular, excitations localized on a single atom, which appear dark when using Mulliken transition charges, acquire a more realistic oscillator strength in this way. These extensions pave the way for using lc-TD-DFTB to describe the electronic structure of large chromophoric polymers, where uncorrected TD-DFTB fails to describe the high degree of conjugation and produces spurious low-lying charge transfer states.

Abstract: The relative energies and occupancies of valence orbital states can dramatically influence collective electronic and magnetic phenomena in correlated transition metal oxide systems. We review the current state of research on the modification and control of these orbital properties in rare-earth nickelates, especially LaNiO3, a model degenerate d orbital system where significant recent progress has been made. Theoretical and experimental results on thin films and heterostructures are described, including the influence of electronic correlation effects. We highlight the latest approaches to achieving non-degenerate bands and discuss the outlook and applicability of this body of knowledge to other correlated metal oxide systems.

Abstract: High-harmonic radiation emitted from molecules in a strong laser field contains information on molecular structure and dynamics. When multiple molecular orbitals participate in high-harmonic generation, resolving the contribution of each orbital is crucial for understanding molecular dynamics and for extending high-harmonic spectroscopy to more complicated molecules. We show that two-dimensional high-harmonic spectroscopy can resolve high-harmonic radiation emitted from the two highest-occupied molecular orbitals, HOMO and HOMO-1, of aligned molecules. By the application of an orthogonally polarized two-color laser field that consists of the fundamental and its second-harmonic fields to aligned ${\mathrm{CO}}_{2}$ molecules, the characteristics attributed to the two orbitals are found to be separately imprinted in odd and even harmonics. Two-dimensional high-harmonic spectroscopy may open a new route to investigate ultrafast molecular dynamics during chemical processes.

Abstract: The quantum mechanical states of electrons in atoms and molecules are distinct orbitals, which are fundamental for our understanding of atoms, molecules and solids. Electronic orbitals determine a wide range of basic atomic properties, allowing also for the explanation of many chemical processes. Here, we propose a novel technique to optically image the shape of electron orbitals of neutral atoms using electron–phonon coupling in a Bose–Einstein condensate. To validate our model we carefully analyze the impact of a single Rydberg electron onto a condensate and compare the results to experimental data. Our scheme requires only well-established experimental techniques that are readily available and allows for the direct capture of textbook-like spatial images of single electronic orbitals in a single shot experiment.