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We investigate the existence of ground states for a class of Schrödinger equations with both a standard power nonlinearity and delta nonlinearity concentrated at finite vertices of the periodic metric graphs G. Using variational methods, if α > 0 and the standard nonlinearity power is L 2 − subcritical, we establish the existence of ground states for every mass and every periodic graph. If α < 0 and the standard nonlinearity power is L 2 − critical, we show that two types of topological structures on G will prevent the existence of ground states. Furthermore, for graphs that do not satisfy these two types of topological structures, ground states exist when the given mass belongs to an appropriate range and the parameter | α | is small enough. [ABSTRACT FROM AUTHOR]

The purpose of this paper is three-fold. First, we establish singular Trudinger–Moser inequalities with less restrictive constraint: (0.1) sup u ∈ H 1 ( R 2 ) , ∫ R 2 (| ∇ u | 2 + V (x) u 2 ) d x ≤ 1 ∫ R 2 e 4 π 1 − β 2 u 2 − 1 | x | β d x < + ∞ , where 0 < β < 2 , V (x) ≥ 0 and may vanish on an open set in R 2 . Second, we consider the existence of ground states to the following Schrödinger equations with critical exponential growth in R 2 : (0.2) − Δ u + γ u = f (u) | x | β , where the nonlinearity f has the critical exponential growth. In order to overcome the lack of compactness, we develop a method which is based on the threshold of the least energy, an embedding theorem introduced in (C. Zhang and L. Chen, "Concentration-compactness principle of singular Trudinger-Moser inequalities in R n and n -Laplace equations," Adv. Nonlinear Stud., vol. 18, no. 3, pp. 567–585, 2018) and the Nehari manifold to get the existence of ground states. Furthermore, as an application of inequality (0.1), we also prove the existence of ground states to the following equations involving degenerate potentials in R 2 : (0.3) − Δ u + V (x) u = f (u) | x | β . [ABSTRACT FROM AUTHOR]

We investigate the source of error in the Thomas–Fermi–von Weizsäcker (TFW) density functional relative to Kohn–Sham density functional theory (DFT). In particular, through numerical studies on a range of materials, for a variety of crystal structures subject to strain and atomic displacements, we find that while the ground state electron density in TFW orbital-free DFT is close to the Kohn–Sham density, the corresponding energy deviates significantly from the Kohn–Sham value. We show that these differences are a consequence of the poor representation of the linear response within the TFW approximation for the electronic kinetic energy, confirming conjectures in the literature. In so doing, we find that the energy computed from a non-self-consistent Kohn–Sham calculation using the TFW electronic ground state density is in very good agreement with that obtained from the fully self-consistent Kohn–Sham solution. [ABSTRACT FROM AUTHOR]

The excited state properties of thionated 5‐fluorouridine (2′,3′,5′‐tri‐O‐acetyl‐5‐fluoro‐4‐thiouridine; ta5F4TUrd), synthesized with Lawesson's reagent, have been intensively investigated with nanosecond transient absorption spectroscopy, time‐resolved thermal lensing, near‐infrared emission, and quantum chemical calculation. The intrinsic triplet lifetime of ta5F4TUrd was determined to be 4.2±0.7 μs in acetonitrile, and the formation quantum yield of the excited triplet state was as large as 0.79±0.01. The quenching rate constants of the triplet ta5F4TUrd by the dissolved oxygen molecule and by the self‐quenching process were found to be nearly equal to the diffusion‐controlled rate of acetonitrile. The quantum yield of the singlet molecular oxygen produced through energy transfer between the triplet ta5F4TUrd and the dissolved oxygen, ΦΔ, was successfully determined to be 0.61±0.02 under the oxygen‐saturated condition. From the oxygen concentration dependence of the ΦΔ value, the fraction of triplet ta5F4TUrd quenched by dissolved oxygen which gives rise to the 1O2* formation, SΔ, was successfully obtained to be 0.78±0.01, which was the largest among the thionucleobases and the thionucleosides reported so far. This could be due to the lower energy and/or the ππ* character of the triplet state. [ABSTRACT FROM AUTHOR]

The excited state properties of thionated 5‐fluorouridine (2′,3′,5′‐tri‐O‐acetyl‐5‐fluoro‐4‐thiouridine; ta5F4TUrd), synthesized with Lawesson's reagent, have been intensively investigated with nanosecond transient absorption spectroscopy, time‐resolved thermal lensing, near‐infrared emission, and quantum chemical calculation. The intrinsic triplet lifetime of ta5F4TUrd was determined to be 4.2±0.7 μs in acetonitrile, and the formation quantum yield of the excited triplet state was as large as 0.79±0.01. The quenching rate constants of the triplet ta5F4TUrd by the dissolved oxygen molecule and by the self‐quenching process were found to be nearly equal to the diffusion‐controlled rate of acetonitrile. The quantum yield of the singlet molecular oxygen produced through energy transfer between the triplet ta5F4TUrd and the dissolved oxygen, ΦΔ, was successfully determined to be 0.61±0.02 under the oxygen‐saturated condition. From the oxygen concentration dependence of the ΦΔ value, the fraction of triplet ta5F4TUrd quenched by dissolved oxygen which gives rise to the 1O2* formation, SΔ, was successfully obtained to be 0.78±0.01, which was the largest among the thionucleobases and the thionucleosides reported so far. This could be due to the lower energy and/or the ππ* character of the triplet state. [ABSTRACT FROM AUTHOR]

The contemporary paper refers back to the instability of linear in GeX2 (X=F, Cl & Br) molecules because of the vibronic coupling effect. Optimization and the following frequency calculations in those molecules found out that every one of those molecules were unstable in high symmetry linear (with D∞h symmetry) geometry and their systems have been bent to lower C2v symmetry geometry. On this work, we've used, TD-DFT (B3LYP/6-31G (d) calculations to gain the strength curves of the ground and excited in the bending directions Q (πu) of compounds 1-3. The vibronic coupling interaction between 1∑g+ ground and the first 1∑u excited states in the Q (∑u) direction via (1∑g+ + 1πu) ⊗ πu PJTE problem was the reason for the symmetry breaking phenomenon. Additionally, changing atoms with different elements together with the electronegative exchange and the degree of overlap at once have an effect on the pattern of molecular orbitals. The NBO calculations were carried out to define a stability measure through the stabilization energy, E2 parameter. According to the consequences received from the vibronic principle of PJT, the bent shape of those analogs is the result of LP(3) X → LP*(2)Ge1 electron delocalization .The PJT stabilization strength decreases from compound 1 to compound three. Moreover, by the decrease of the energy gaps between reference states (Δ) the primary force constant of the ground state in the Q (πu) direction (K0) could decrease from compound 1 to compound 3. [ABSTRACT FROM AUTHOR]

A path integral ground state approach has been used to estimate the ground-state energy and structural properties of hydrogen fluoride molecules pinned to a one-dimensional lattice. In the simulations, the molecules are assumed to be rigid, and only the continuous rotational degrees of freedom are considered. The constituents of a many-body system interact through the dipole-dipole interaction because the molecules have a permanent dipole moment. The workability of our approach has been demonstrated by estimating the ground-state energy, order parameter and nearest neighbour correlation for the systems of 2 and 3 HF molecules using quantum Monte Carlo simulations based on the path integral ground state methodology. The results agree satisfactorily with those obtained from exact Hamiltonian matrix diagonalisation. In addition, the effect of neighbours on the ground state properties has been investigated for larger systems. The converged ground-state energy per neighbour as a function of inter-nuclear separation is considered to be the equation of state for the system. The chemical potential of the rotor chains also supports the convergence test. [ABSTRACT FROM AUTHOR]

Stochastic density functional theory (sDFT) is becoming a valuable tool for studying ground-state properties of extended materials. The computational complexity of describing the Kohn–Sham orbitals is replaced by introducing a set of random (stochastic) orbitals leading to linear and often sub-linear scaling of certain ground-state observables at the account of introducing a statistical error. Schemes to reduce the noise are essential, for example, for determining the structure using the forces obtained from sDFT. Recently, we have introduced two embedding schemes to mitigate the statistical fluctuations in the electron density and resultant forces on the nuclei. Both techniques were based on fragmenting the system either in real space or slicing the occupied space into energy windows, allowing for a significant reduction in the statistical fluctuations. For chemical accuracy, further reduction of the noise is required, which could be achieved by increasing the number of stochastic orbitals. However, the convergence is relatively slow as the statistical error scales as 1 / N χ according to the central limit theorem, where Nχ is the number of random orbitals. In this paper, we combined the embedding schemes mentioned above and introduced a new approach that builds on overlapped fragments and energy windows. The new approach significantly lowers the noise for ground-state properties, such as the electron density, total energy, and forces on the nuclei, as demonstrated for a G-center in bulk silicon. [ABSTRACT FROM AUTHOR]

The nuclear–electronic orbital (NEO) framework provides a practical approach for directly incorporating nuclear quantum effects and non-Born–Oppenheimer effects of specified nuclei, typically protons, into quantum chemistry calculations. Multicomponent wave function based methods, such as NEO coupled cluster singles and doubles, and multicomponent density functional theory (DFT), such as NEO-DFT, require the appropriate selection of electronic and nuclear basis sets. Although a wide array of electronic basis sets are available, systematically developed nuclear basis sets that balance accuracy and efficiency have been lacking. Herein, a series of nuclear basis sets are developed and shown to be accurate and efficient for describing both ground and excited state properties of multicomponent systems in which electrons and specified protons are treated quantum mechanically. Three series of Gaussian-type nuclear basis sets, denoted PB4, PB5, and PB6, are developed with varying levels of angular momentum. A machine-learning optimization procedure relying on the Gaussian process regression method is utilized to accelerate the optimization process. The basis sets are validated in terms of predictions of ground state energies, proton densities, proton affinities, and proton vibrational excitation energies, allowing the user to select the desired balance between accuracy and efficiency for the properties of interest. These nuclear basis sets will enhance the tractability of NEO methods for applications to a wide range of chemical systems. [ABSTRACT FROM AUTHOR]

In this study, we developed a time-dependent density-functional theory (TDDFT) with a finite-temperature (FT) scheme, denoted as FT-TDDFT. We introduced the concept of fractional occupation numbers for random phase approximation equation and evaluated the excited-state electronic entropy terms with excited-state occupation number. The orbital occupation numbers for the excited state were evaluated from the change in the ground-state electron configuration with excitation and deexcitation coefficients. Furthermore, we extended the FT formulation to the time-dependent density-functional tight-binding (TDDFTB) method for larger systems, denoted as FT-TDDFTB. Numerical assessment for the FT-(TD)DFT method showed smooth potential curves for double-bond rotation of ethylene in both ground and excited states. Excited-state calculations based on the FT-TDDFTB method were applied to the uniform π-stacking columns composed of trioxotriangulene, possessing neutral radicals in strong correlation systems. [ABSTRACT FROM AUTHOR]

The BDF (Beijing Density Functional) program package is in the first place a platform for theoretical and methodological developments, standing out particularly in relativistic quantum chemical methods for chemistry and physics of atoms, molecules, and periodic solids containing heavy elements. These include the whole spectrum of relativistic Hamiltonians and their combinations with density functional theory for the electronic structure of ground states as well as time-dependent and static density functional linear response theories for electronically excited states and electric/magnetic properties. However, not to be confused by its name, BDF nowadays comprises also of standard and novel wave function-based correlation methods for the ground and excited states of strongly correlated systems of electrons [e.g., multireference configuration interaction, static–dynamic–static configuration interaction, static–dynamic–static second-order perturbation theory, n-electron valence second-order perturbation theory, iterative configuration interaction (iCI), iCI with selection plus PT2, and equation-of-motion coupled-cluster]. Additional features of BDF include a maximum occupation method for finding excited states of Hartree–Fock/Kohn–Sham (HF/KS) equations, a very efficient localization of HF/KS and complete active space self-consistent field orbitals, and a unique solver for exterior and interior roots of large matrix eigenvalue problems. [ABSTRACT FROM AUTHOR]

The third-order non-Dyson algebraic-diagrammatic construction approach to the electron propagator [IP-ADC(3)] is extended using the intermediate state representation (ISR) formalism, allowing the wave functions and properties of molecular states with detached electron to be studied. The second-order ISR equations [ISR(2)] for the one-particle (transition) density matrix have been derived and implemented in the Q-CHEM program. The approach is completely general and enables evaluation of arbitrary one-particle operators and interpretation of electron detachment processes in terms of density-based quantities. The IP-ADC(3)/ISR(2) equations were implemented for Ŝ z -adapted intermediate states, allowing open-shell molecules to be studied using unrestricted Hartree-Fock references. As a first test for computations of ground state properties, dipole moments of various closed- and open-shell molecules have been computed by means of electron detachment from the corresponding anions. The results are in good agreement with experimental data. The potential of IP-ADC(3)/ISR(2) for the interpretation of photoelectron spectra is demonstrated for the galvinoxyl free radical. [ABSTRACT FROM AUTHOR]

The two-state lasing conditions at room temperature in InAs/InP quantum dot (QD) lasers under a continuous wave electrical bias current are studied. It is found that excited state (ES) lasing is promoted by moderately decreasing spacer thickness and increasing dot-size dispersion in a QD stack, and the physical origins are due to the increased bottleneck effect and inhomogeneous broadening. Moreover, it is proved theoretically that ground state (GS) lasing with high inhomogeneous broadening may result in high phase and intensity noise at a high bias current. Therefore, an appropriate spacer thickness together with appropriate inhomogeneous broadening is critical to the GS and/or ES lasing, which helps an optimal design of laser geometry. [ABSTRACT FROM AUTHOR]

In this paper, our major concern is the existence of normalized solutions for a Choquard equation with a L 2 -subcritical growth. As a result, we prove that the normalized solutions and ground state solutions are equivalent by constructing Pohozaev sequence and combining the principle of compactness concentration. [ABSTRACT FROM AUTHOR]

Linear scaling density functional theory is important for understanding electronic structure properties of nanometer scale systems. Recently developed stochastic density functional theory can achieve linear or even sublinear scaling for various electronic properties without relying on the sparsity of the density matrix. The basic idea relies on projecting stochastic orbitals onto the occupied space by expanding the Fermi-Dirac operator and repeating this for Nχ stochastic orbitals. Often, a large number of stochastic orbitals are required to reduce the statistical fluctuations (which scale as N χ − 1 / 2 ) below a tolerable threshold. In this work, we introduce a new stochastic density functional theory that can efficiently reduce the statistical fluctuations for certain observable and can also be integrated with an embedded fragmentation scheme. The approach is based on dividing the occupied space into energy windows and projecting the stochastic orbitals with a single expansion onto all windows simultaneously. This allows for a significant reduction of the noise as illustrated for bulk silicon with a large supercell. We also provide theoretical analysis to rationalize why the noise can be reduced only for a certain class of ground state properties, such as the forces and electron density. [ABSTRACT FROM AUTHOR]

Calculating charge transfer (CT) excitation energies with high accuracy and low computational cost is a challenging task. Kohn-Sham density functional theory (KS-DFT), due to its efficiency and accuracy, has achieved great success in describing ground state problems. To extend to excited state problems, our group recently demonstrated an approach with good numerical results to calculate low-lying and Rydberg excitation energies of an N-electron system from a ground state KS or generalized KS calculations of an (N − 1)-electron system via its orbital energies. In the present work, we explore further the same methodology to describe CT excitations. Numerical results from this work show that performance of conventional density functional approximations (DFAs) is not as good for CT excitations as for other excitations due to the delocalization error. Applying localized orbital scaling correction (LOSC) to conventional DFAs, a recently developed method in our group to effectively reduce the delocalization error, can improve the results. Overall, the performance of this methodology is better than time dependent DFT (TDDFT) with conventional DFAs. In addition, it shows that results from LOSC-DFAs in this method reach similar accuracy to other methods, such as ΔSCF, G0W0 with Bethe-Salpeter equations, particle-particle random phase approximation, and even high-level wavefunction methods like CC2. Our analysis shows that the correct 1/R trend for CT excitation can be captured from LOSC-DFA calculations, stressing that the application of DFAs with the minimal delocalization error is essential within this methodology. This work provides an efficient way to calculate CT excitation energies from ground state DFT. [ABSTRACT FROM AUTHOR]

The electronic and magnetic properties of a material can be altered by strain engineering. We elucidate the strain dependence of electronic and magnetic properties in α - RuCl 3 monolayer by varying the biaxial in-plane tensile strain from 1% to 8%. The magnetic ground state of the α - RuCl 3 monolayer evolves from antiferromagnetic zigzag (AFM-ZZ) configuration to ferromagnetic (FM) under a biaxial in-plane tensile strain higher than 2%. In a strain-free state, the FM configuration has a direct bandgap of 0.54 eV, and the AFM-ZZ configuration has an indirect bandgap of 0.73 eV. The energy bandgap of the α - RuCl 3 monolayer undergoes a change by the variation of the tensile strain. Furthermore, a detailed Monte Carlo simulation has been implemented to investigate the magnetic properties of the considered system for varying values of tensile strain. Temperature dependencies of the thermodynamic quantities of interest as functions of strains display strong evidence supporting the first-principles calculations within density functional theory. Our Monte Carlo findings also suggest that the Curie temperature of the α - RuCl 3 monolayer tends to get higher up to 20.11 K with a tensile strain 8%, which means that applying a strain leads to getting a more stable FM ground state. In addition, we find that magnetocrystalline anisotropy in the α - RuCl 3 monolayer can be controlled by the applied strain. [ABSTRACT FROM AUTHOR]

Ground state, structural, and magnetic phase transitions of strained BiVO3 were investigated using the first-principles calculation based on the self-interaction corrected local density approximation + U functional. The calculated total energy indicated that the ground state structure for BiVO3 was a monoclinic P21/a phase and ferromagnetic ordering is predicted to be the magnetic ground state. Furthermore, it was found that BiVO3 are metastable compounds under strain effects, where several structural phase transitions were predicted from the monoclinic P 21 / a phase to the orthorhombic P b n m phase (at compressive volumetric strain) and to monoclinic C m and C c phases (at expansive volumetric strain). Furthermore, calculations on electronic band structure and density of states for the monoclinic P21/a phase and the monoclinic C c phase of BiVO3 with ferromagnetic ordering were conducted. The calculated band structure predicted a small energy gap with a direct energy bandgap of 0.456 eV and an indirect energy gap of 0.466 eV. Interestingly, the obtained results revealed that the BiVO3 calculated density of states exhibited Mott-Hubbard insulator type. Therefore, the ground state monoclinic C c phase of strained BiVO3 with ferromagnetic ordering is suggested as a new candidate for multiferroic materials at room temperature and a visible light driven photocatalytic/photovoltaic effect. The obtained results in this study could provide valuable theoretical information on BiVO3 under strain effects, which could open new opportunities for future research and technological applications. [ABSTRACT FROM AUTHOR]

We explore the effects of correlation on the ground-state energies and on photoionization dynamics in atomic Be and Ne. We apply the time-dependent restricted-active-space self-consistent-field method for several excitation schemes and active orbital spaces with and without a dynamic core to address the effects systematically at different levels of approximation. For the ground-state many-electron wave functions, we compare the correlation energies with entropic measures of entanglement. A larger magnitude of the correlation energy does not always correspond to a larger value of the considered entanglement measures. To evaluate the impact of correlation in a process involving continua, we consider photoionization by attosecond pulses. The photoelectron spectra may be significantly affected by including a dynamical core. [ABSTRACT FROM AUTHOR]

We report a quantum Monte Carlo study, on a very simple but nevertheless very instructive model system of four hydrogen atoms, recently proposed in Gasperich et al. [J. Chem. Phys. 147, 074106 (2017)]. We find that the Jastrow correlated Antisymmetrized Geminal Power (JAGP) is able to recover most of the correlation energy even when the geometry is symmetric and the hydrogens lie on the edges of a perfect square. Under such conditions, the diradical character of the molecule ground state prevents a single determinant Ansatz to achieve an acceptable accuracy, whereas the JAGP performs very well for all geometries. Remarkably, this is obtained with a similar computational effort. Moreover, we find that the Jastrow factor is fundamental in promoting the correct resonances among several configurations in the JAGP, which cannot show up in the pure Antisymmetrized Geminal Power (AGP). We also show the extremely fast convergence of this approach in the extension of the basis set. Remarkably, only the simultaneous optimization of the Jastrow and the AGP part of our variational Ansatz is able to recover an almost perfect nodal surface, yielding therefore state of the art energies, almost converged in the complete basis set limit, when the so called diffusion Monte Carlo is applied. [ABSTRACT FROM AUTHOR]

Ground state, structural, and magnetic phase transitions of strained BiVO3 were investigated using the first-principles calculation based on the self-interaction corrected local density approximation + U functional. The calculated total energy indicated that the ground state structure for BiVO3 was a monoclinic P21/a phase and ferromagnetic ordering is predicted to be the magnetic ground state. Furthermore, it was found that BiVO3 are metastable compounds under strain effects, where several structural phase transitions were predicted from the monoclinic P 21 / a phase to the orthorhombic P b n m phase (at compressive volumetric strain) and to monoclinic C m and C c phases (at expansive volumetric strain). Furthermore, calculations on electronic band structure and density of states for the monoclinic P21/a phase and the monoclinic C c phase of BiVO3 with ferromagnetic ordering were conducted. The calculated band structure predicted a small energy gap with a direct energy bandgap of 0.456 eV and an indirect energy gap of 0.466 eV. Interestingly, the obtained results revealed that the BiVO3 calculated density of states exhibited Mott-Hubbard insulator type. Therefore, the ground state monoclinic C c phase of strained BiVO3 with ferromagnetic ordering is suggested as a new candidate for multiferroic materials at room temperature and a visible light driven photocatalytic/photovoltaic effect. The obtained results in this study could provide valuable theoretical information on BiVO3 under strain effects, which could open new opportunities for future research and technological applications. [ABSTRACT FROM AUTHOR]

Employment of exact numerical quadratures in the evaluation of matrix elements involving highly accurate wavefunctions of helium (and its isoelectronic congeners) generated with the help of the regularized Krylov sequences of Nakatsuji results in an efficient algorithm for the calculation of natural orbitals and the corresponding natural amplitudes {λnl}. The results of such calculations are presented for the total of 600 natural orbitals pertaining to the ground state of the helium atom. The benchmark-quality values of {λnl} computed for 1 ≤ n ≤ 100 and 0 ≤ l ≤ 5 reveal gross inaccuracies in the previously published data. In particular, the dependence of λnl on n is found to follow very closely a simple power-scaling law λ n l ≈ − A l (n + B l ) − 4 with Al that, contrary to previous claims, varies only weakly with l. Even more importantly, the numerical trends observed in the present calculations strongly suggest that in the case of the ground state of the helium atom, the only positive-valued natural amplitude is that pertaining to the strongly occupied orbital, i.e., λ10. The relevance of this finding to the existence of unoccupied natural orbitals pertaining to the ground state wavefunction of the H2 molecule is discussed. [ABSTRACT FROM AUTHOR]

We demonstrate that the Swift-Hohenberg functional, which is used to describe patterning observed in out of equilibrium systems such as diblock copolymers, Rayleigh-Benard convection, and thin film magnetic garnets, can be applied to radiation-induced patterns that occur in non-miscible alloys. By comparing ground states obtained from the minimization of this functional and a 2D numerical simulation performed on an irradiated AgCu material, which is the archetype of a non-miscible alloy, we show that the Swift-Hohenberg functional provides all possible patterns generated under irradiation and the solubility limits of radiation-induced precipitates in these patterns. To rationalize the formation of these radiation-induced patterns, we propose a generic "pseudophase diagram" that relies not only on the irradiation flux and temperature but also on the overall composition of the alloy. Tuning this overall composition offers the opportunity to tailor new materials with various micro-structures overcoming the limitation of the equilibrium phase diagram. [ABSTRACT FROM AUTHOR]

Wavefunctions for large electron numbers N are plagued by the Exponential Wall Problem (EWP), i.e., an exponential increase in the dimensions of Hilbert space with N. Therefore, they lose their meaning for macroscopic systems, a point stressed, in particular, by Kohn. The EWP has to be resolved in order to provide a solid basis for wavefunction based electronic structure calculations of macroscopic systems, e.g., solids. The origin of the EWP is the multiplicative property of wavefunctions when independent subsystems are considered. Therefore, it can only be avoided when wavefunctions are formulated so that they are additive instead, in particular, when matrix elements involving them are calculated. We describe how this is done for the ground state of a macroscopic electron system. Going over from a multiplicative to an additive quantity requires taking a logarithm. Here it implies going over from Hilbert space to the operator- or Liouville space with a metric based on cumulants. The operators which define the ground-state wavefunction generate fluctuations from a mean-field state. The latter does not suffer from an EWP and therefore may serve as a vacuum state. The fluctuations have to be connected like the ones caused by pair interactions in a classical gas when the free energy is calculated (Meyer's cluster expansion). This fixes the metric in Liouville space. The scheme presented here provides a solid basis for electronic structure calculations for the ground state of solids. In fact, its applicability has already been proven. We discuss also matrix product states, which have been applied to one-dimensional systems with results of high precision. Although these states are formulated in Hilbert space, they are processed by using operators in Liouville space. We show that they fit into the general formalism described above. [ABSTRACT FROM AUTHOR]

We present a comprehensive discussion of the so-called asymmetric Wigner bilayer system, where mobile point charges, all of the same sign, are immersed into the space left between two parallel, homogeneously charged plates (with possibly different charge densities). At vanishing temperatures, the particles are expelled from the slab interior; they necessarily stick to one of the two plates and form there ordered sublattices. Using complementary tools (analytic and numerical), we study systematically the self-assembly of the point charges into ordered ground state configurations as the inter-layer separation and the asymmetry in the charge densities are varied. The overwhelming plethora of emerging Wigner bilayer ground states can be understood in terms of the competition of two strategies of the system: net charge neutrality on each of the plates on the one hand and particles' self-organization into commensurate sublattices on the other hand. The emerging structures range from simple, highly commensurate (and thus very stable) lattices (such as staggered structures, built up by simple motives) to structures with a complicated internal structure. The combined application of our two approaches (whose results agree within remarkable accuracy) allows us to study on a quantitative level phenomena such as over- and underpopulation of the plates by the mobile particles, the nature of phase transitions between the emerging phases (which pertain to two different universality classes), and the physical laws that govern the long-range behaviour of the forces acting between the plates. Extensive, complementary Monte Carlo simulations in the canonical ensemble, which have been carried out at small, but finite temperatures along selected, well-defined pathways in parameter space confirm the analytical and numerical predictions within high accuracy. The simple setup of the Wigner bilayer system offers an attractive possibility to study and to control complex scenarios and strategies of colloidal self-assembly, via the variation of two system parameters. [ABSTRACT FROM AUTHOR]

The free-complement (FC) theory for solving the Schrödinger equation (SE) was applied to calculate the potential energy curves of the ground and excited states of the hydrogen molecule (H2) with the 1Σg+, 1Σu+, 3Σg+, 3Σu+, 1Πg, 1Πu, 3Πg, 3Πu, 1Δg, 1Δu, 3Δg, 3Δu, 1Φg, 1Φu, 3Φg, and 3Φu symmetries (in total, 54 states). The initial functions of the FC theory were formulated based on the atomic states of the hydrogen atom and its positive and negative ions at the dissociation limits. The local Schrödinger equation (LSE) method, which is a simple sampling-type integral-free methodology, was employed instead of the ordinary variational method and highly accurate results were obtained stably and smoothly along the potential energy curves. Thus, with the FC-LSE method, we succeeded to perform the comprehensive studies of the H2 molecule from the ground to excited states belonging up to higher angular momentum symmetries and from equilibriums to dissociation limits with almost satisfying spectroscopic accuracy, i.e., 10−6 hartree order around 1 cm−1, as absolute solutions of the SE by moderately small calculations. [ABSTRACT FROM AUTHOR]

We proposed a methodology that allows to maximize the population transfer from a high vibrational state of the a3Σ+ triplet state to the vibrational ground state of the X1Σ+ singlet state though the optimization of one pump and one dump laser pulses. The pump pulse is optimized using a fitness function, heuristically improved, that includes the effect of the spin-orbit coupling of the KRb [b-A]-scheme. The dump pulse is optimized to maximize the population transfer to the ground state. We performed a comparison with the case in which the pump and dump pulses are optimized to maximize the population transfer to the ground state employing a genetic algorithm with a single fitness function. The heuristic approach turned out to be 70% more efficient than a quantum optimal control optimization employing a single fitness function. The method proposed provides simple pulses that have an experimental realm. [ABSTRACT FROM AUTHOR]

The accuracy and efficiency of ab initio Quantum Monte Carlo (QMC) algorithms benefit greatly from compact variational trial wave functions that accurately reproduce ground state properties of a system. We investigate the possibility of using multi-Slater-Jastrow trial wave functions with non-orthogonal determinants by optimizing identical single particle orbitals independently in separate determinants. As a test case, we compute variational and fixed-node diffusion Monte Carlo (FN-DMC) energies of a C2 molecule. For a given multi-determinant expansion, we find that this non-orthogonal orbital optimization results in a consistent improvement in the variational energy and the FN-DMC energy on the order of a few tenths of an eV. In some cases, fewer non-orthogonal determinants are required compared to orthogonal ones in order to achieve similar accuracy in FN-DMC. Our calculations indicate that trial wave functions with non-orthogonal determinants can improve computed energies in a QMC calculation when compared to their orthogonal counterparts. [ABSTRACT FROM AUTHOR]

The potential energy curves (PECs) of the ground and excited states that correlate in the atomic limit with Ar([Ne]3s23p6,1S), Ar([Ne]3s23p54s1, 3P, 1P), and Ar([Ne]3s23p54p1, 3D, 3P, 3S, 1D, 1P, 1S) are calculated at the multireference configuration interaction (MRCI+Q) theoretical level with extrapolations to the complete basis set limit using all-electron correlation consistent triple-, quadruple-, and quintuple-zeta basis sets. Scalar relativistic corrections are calculated using second-order Douglas-Kroll-Hess Hamiltonian with the corresponding basis sets contracted for scalar relativistic Hamiltonians. For these calculations, the 3s orbitals of the Ar atom are not included in the active space but are correlated through single and double excitations. Spin-orbit eigenstates are computed by diagonalizing the Breit-Pauli matrix between internal configurations with no electrons in external orbitals and added to the scalar relativistic results. A total of 32 molecular PECs are computed with spin-orbit contributions, which correlate with 1s1, 1s5−2, and 2p10−1 atomic Ar energies in Paschen notation. Important features of the PECs and system crossings are discussed. [ABSTRACT FROM AUTHOR]

The boron rotor B 13 + 11 consists of a tri-atomic inner "wheel" that may rotate in its pseudo-rotating ten-atomic outer "bearing"—this concerted motion is called "contorsion." B 13 + 11 in its ground state has zero contorsional angular momentum. Starting from this initial state, it is a challenge to ignite contorsion by a laser pulse. We discover, however, that this is impossible, i.e., one cannot design any laser pulse that induces a transition from the ground to excited states with non-zero contorsional angular momentum. The reason is that the ground state is characterized by a specific combination of irreducible representations (IRREPs) of its contorsional and nuclear spin wavefunctions. Laser pulses conserve these IRREPs because hypothetical changes of the IRREPs would require nuclear spin flips that cannot be realized during the interaction with the laser pulse. We show that all excited target states of B 13 + 11 with non-zero contorsional angular momentum have different IRREPs that are inaccessible by laser pulses. Conservation of nuclear spins thus prohibits laser-induced transitions from the non-rotating ground to rotating target states. We discover various additional constraints imposed by conservation of nuclear spins, e.g., laser pulses can change clockwise to counter-clockwise contorsions or vice versa, but they cannot stop them. The results are derived in the frame of a simple model. [ABSTRACT FROM AUTHOR]

The ground-state structure of monolayers and nanoplatelets of SnS with a thickness from two to five monolayers is calculated from first principles. It is shown that nanoobjects with only an odd number of monolayers are ferroelectric. The ferroelectric, piezoelectric, and elastic properties of these polar structures are calculated. The appearance of polarization in these nanoobjects is explained by an uncompensated polarization that exists in an antiferroelectric structure of bulk SnS. The mechanism of ferroelectricity, in which the ferroelectric distortion is associated with short-range ordering of lone pairs, can be regarded as a way of creating ferroelectrics with high Curie temperature. [ABSTRACT FROM AUTHOR]

The stable low energy states of the HPS and DPS molecules have been studied through multi-reference ab initio methods in conjunction with large atomic basis sets. Stable states for these species have been examined up to 7 eV above the ground state minimum. We found six stable electronic states that are mostly mono-configurational. These states may be involved in the photodynamics and photodissociation of this molecule. In particular, the 2 1A′ state presents two minima on the potential energy surface, one of them close to linear configuration. This state may be populated after the absorption of a visible photon from the ground state and gives rise to large amplitude motions that may eventually induce isomerization to electronically excited HSP. Moreover, we characterized these states spectroscopically to facilitate the assignment of the vibronic spectra of the HPS and DPS species. For these low-energy states, we thus computed vertical and adiabatic excitation energies, and for the stable ones, a full set of spectroscopic constants including harmonic frequencies and anharmonic vibrational, rotational, and centrifugal distortion constants. The calculated potential energy surfaces for these states have been used in a variational procedure to deduce the pattern of vibrational levels up to 4000 cm−1 above the corresponding vibrationless level. Our data may serve for the assignment of the IR and Vis spectra of HPS and DPS. [ABSTRACT FROM AUTHOR]

We report photodetachment and resonant photoelectron-imaging studies of cryogenically cooled phenoxide (C6H5O−) and thiophenoxide (C6H5S−) anions. In a previous study [H. T. Liu et al. Angew. Chem., Int. Ed. 52, 8976 (2013)], a dipole-bound excited state was observed for C6H5O− at 97 cm−1 below the detachment threshold. Eight resonant photoelectron spectra were obtained via excitations to eight vibrational levels of the dipole-bound state (DBS) followed by autodetachment. Here we present a complete photodetachment spectrum of C6H5O− covering a spectral range 2600 cm−1 above the detachment threshold and revealing nine additional vibrational resonances of the DBS. We also report the first observation of a dipole-bound excited state for C6H5S−, 39 cm−1 below its detachment threshold of 18 982 cm−1. Photodetachment spectroscopy covering a spectral range 1500 cm−1 above the threshold reveals twelve vibrational resonances for the DBS of C6H5S−. By tuning the detachment laser to the vibrational resonances in the DBS of C6H5O− and C6H5S−, we obtain highly non-Franck-Condon resonant photoelectron spectra, as a result of mode-selectivity and the Δv = −1 propensity rule for vibrational autodetachment. Five new fundamental vibrational frequencies are obtained for the ground state of the C6H5O (X2B1) radical. Intramolecular inelastic scattering is observed in some of the resonant photoelectron spectra, leading to the excitation of the Franck-Condon-inactive lowest-frequency bending mode (ν20) of C6H5O. The first excited state of C6H5O (A2B2) is observed to be 0.953 eV above the ground state. Twelve resonant photoelectron spectra are obtained for C6H5S−, allowing the measurements of seven fundamental vibrational frequencies of the C6H5S radical, whereas the non-resonant photoelectron spectrum exhibits only a single Franck-Condon active mode. The current study again demonstrates that the combination of photodetachment spectroscopy and resonant photoelectron spectroscopy is a powerful technique to obtain vibrational information about polar radical species. [ABSTRACT FROM AUTHOR]

In this paper, we consider a class of critical Schrödinger-Bopp-Podolsky system. By virtue of the Nehari manifold and variational methods, we study the existence, nonexistence and asymptotic behavior of ground state solutions for this problem. [ABSTRACT FROM AUTHOR]

In the present paper we study a class of Schrödinger-Poisson equations { − Δ u + V (x) u + ϕ u = a (x) | u | p − 1 u , x ∈ R 3 − Δ ϕ = u 2 , x ∈ R 3 , (1) where V (x) and a (x) are of different forms on the half space, i.e. V (x) = V 1 (x) , a (x) = a 1 (x) for x 1 > 0 and V (x) = V 2 (x) , a (x) = a 2 (x) for x 1 < 0 , where V 1 , V 2 , a 1 and a 2 are periodic in each coordinate direction. By using a concentration compactness discussion, we establish the existence of surface gap soliton ground state of (1) for p ∈ [ 3 , 5). We also give a Mountain-Pass type ground state of (1) for p ∈ (3 , 5). [ABSTRACT FROM AUTHOR]

The Hohenberg–Kohn (HK) theorem for interacting electrons is a cornerstone of modern electronic structure calculations. For a general quantum system, a HK‐type Hamiltonian in the form of Ĥhk{gi}=Ĥint+∑igiÔi$\hat {H}_{\rm hk}\lbrace g_i\rbrace =\hat {H}_{\rm int}+\sum_i g_i \hat O_i$ can always be defined, by grouping those terms with fixed or preknown coefficients into an internal part of the Hamiltonian Ĥint$\hat {H}_{\rm int}$, and factorizing the remaining as the superposition of a set of Hermitian operators {Ôi}$\lbrace\hat {O}_i\rbrace$. It is asked whether the HK theorem can be extended to such a general setting, so that the ground‐state expectation values of {Ôi}$\lbrace\hat {O}_i\rbrace$ as the generalized density can in principle be used as the fundamental variables determining all the properties of the system. It is shown that the question can be addressed by the invertibility of generalized density correlation matrix (GDCM) defined with respect to the {Ôi}$\lbrace\hat {O}_i\rbrace$ operators. This criterion is applied to several representative examples, including the quantum Ising dimer, frustration‐free systems, N‐level quantum systems and a fermionic Hubbard chain. It is suggested that for a finite‐size system, finding an invertible GDCM under one single {gi}$\lbrace g_i\rbrace$ configuration is typically sufficient to establish the generic extensibility of the HK theorem in the entire parameter space. [ABSTRACT FROM AUTHOR]

The free-complement chemical-formula theory (FC-CFT) for solving the Schrödinger equation (SE) was applied to the first-row atoms and several small molecules, limiting only to the ground state of a spin symmetry. Highly accurate results, satisfying chemical accuracy (kcal/mol accuracy for the absolute total energy), were obtained for all the cases. The local Schrö dinger equation (LSE) method was applied for obtaining the solutions accurately and stably. For adapting the sampling method to quantum mechanical calculations, we developed a combined method of local sampling and Metropolis sampling. We also reported the method that leads the calculations to the accurate energies and wave functions as definite converged results with minimum ambiguities. We have also examined the possibility of the stationarity principle in the sampling method: it certainly works, though more extensive applications are necessary. From the high accuracy and the constant stability of the results, the present methodology seems to provide a useful tool for solving the SE of atoms and molecules. [ABSTRACT FROM AUTHOR]

The properties of the bound states of two quantum waveguides coupled via the window of the width s in their common boundary are calculated under the assumption that the transverse electric field E is applied to the structure. It is shown that the increase in the electric intensity brings closer to each other fundamental propagation thresholds of the opening and the arms. As a result, the ground state, which in the absence of the field exists at any nonzero s, exhibits the energy E0 decrease for the growing E and in the high-field regime E0 stays practically the same regardless of the size of the connecting region. It is predicted that the critical window widths s c r n , n = 1 , 2 , … , at which new excited localized orbitals emerge, strongly depend on the transverse voltage; in particular, the field leads to the increase in s c r n , and, for quite strong electric intensities, the critical width unrestrictedly diverges. This remarkable feature of the electric-field-induced switching of the bound states can be checked, for example, by the change of the optical properties of the structure when the gate voltage is applied; namely, both the oscillator strength and absorption spectrum exhibit a conspicuous maximum on their E dependence and turn to zero when the electric intensity reaches its critical value. Comparative analysis of the two-dimensional (2D) and 3D geometries reveals their qualitative similarity and quantitative differences. [ABSTRACT FROM AUTHOR]

We theoretically investigate the energy of the ground state exciton confined to two-dimensional (2D) monolayers with circular shape. Within an effective mass approach employing a nonlocal screening effect on the Coulomb potential energy, we demonstrate how the exciton energy is correlated with the radius of the circle, electron-hole reduced mass, and 2D susceptibility. In addition, we show that a dead layer around the circle edge, into which the electron-hole pair cannot penetrate, is necessary for understanding the energy shift recently observed in monolayer WSe2 quantum dots. [ABSTRACT FROM AUTHOR]

Quantum Monte Carlo (QMC) is a stochastic method that has been particularly successful for ground-state electronic structure calculations but mostly unexplored for the computation of excited-state energies. Here, we show that within a Jastrow-free QMC protocol relying on a deterministic and systematic construction of nodal surfaces using selected configuration interaction (sCI) expansions, one is able to obtain accurate excitation energies at the fixed-node diffusion Monte Carlo (FN-DMC) level. This evidences that the fixed-node errors in the ground and excited states obtained with sCI wave functions cancel out to a large extent. Our procedure is tested on two small organic molecules (water and formaldehyde) for which we report all-electron FN-DMC calculations. For both the singlet and triplet manifolds, accurate vertical excitation energies are obtained with relatively compact multideterminant expansions built with small (typically double-ζ) basis sets. [ABSTRACT FROM AUTHOR]

This manuscript introduces a methodology (within the Born-Oppenheimer picture) to compute electronic ground-state properties of molecules and solids/surfaces with fractionally occupied components. Given a user-defined division of the molecule into subsystems, our theory uses an auxiliary global Hamiltonian that is defined as the sum of subsystem Hamiltonians, plus the spatial integral of a second-quantized local operator that allows the electrons to be transferred between subsystems. This electron transfer operator depends on a local potential that can be determined using density functional approximations and/or other techniques such as machine learning. The present framework employs superpositions of tensor-product wave functions, which can satisfy size consistency and avoid spurious fractional charges at large bond distances. The electronic population of each subsystem is in general a positive real number and is obtained from wave-function amplitudes, which are calculated by means of ground-state matrix diagonalization (or matrix propagation in the time-dependent case). Our method can provide pathways to explore charge-transfer effects in environments where dividing the molecule into subsystems is convenient and to develop computationally affordable electronic structure algorithms. [ABSTRACT FROM AUTHOR]

Selected resonance states of the deuterated formyl radical in the electronic ground state X ̃ 2 A ′ are computed using our recently introduced dynamically pruned discrete variable representation [H. R. Larsson, B. Hartke, and D. J. Tannor, J. Chem. Phys. 145, 204108 (2016)]. Their decay and asymptotic distributions are analyzed and, for selected resonances, compared to experimental results obtained by a combination of stimulated emission pumping and velocity-map imaging of the product D atoms. The theoretical results show good agreement with the experimental kinetic energy distributions. The intramolecular vibrational energy redistribution is analyzed and compared with previous results from an effective polyad Hamiltonian. Specifically, we analyzed the part of the wavefunction that remains in the interaction region during the decay. The results from the polyad Hamiltonian could mainly be confirmed. The C=O stretch quantum number is typically conserved, while the D—C=O bend quantum number decreases. Differences are due to strong anharmonic coupling such that all resonances have major contributions from several zero-order states. For some of the resonances, the coupling is so strong that no further zero-order states appear during the dynamics in the interaction region, even after propagating for 300 ps. [ABSTRACT FROM AUTHOR]

The suppression of Raman scattering is of high interest for the achievement of sub-diffraction-limited resolution in Raman scattering spectroscopy and microscopy. We present density matrix calculations of the suppression of spontaneous Raman scattering via ground state depletion in a level system based on the molecule tris(bipyridine)ruthenium(ii). This particular molecule has been earlier used for an experimental demonstration of the suppression of spontaneous Raman scattering, allowing us to successfully verify the validity of our numerical calculations by a comparison to the experimental results. We investigate the required level of detail of the molecule model as well as the influence of certain molecule and pulse parameters on the Raman scattering suppression. It was found that pulses with a duration longer than the lifetime of the electronic states allow for a high suppression of the Raman scattering. Pulses shorter than the coherence lifetime between the ground state and electronic states lead to a similarly high suppression but also accomplish the suppression with more than one order of magnitude lower pulse energy fluence. Additionally, using a laser wavelength that is in resonance with one of the electronic transitions of the sample should allow suppressing the Raman scattering with four to six orders of magnitude lower pulse energy fluence. [ABSTRACT FROM AUTHOR]

A new approach for preventing zero-point energy (ZPE) violation in quasi-classical trajectory (QCT) simulations is presented and applied to H2CO “roaming” reactions. Zero-point energy may be problematic in roaming reactions because they occur at or near bond dissociation thresholds and these channels may be incorrectly open or closed depending on if, or how, ZPE has been treated. Here we run QCT simulations on a “ZPE-corrected” potential energy surface defined as the sum of the molecular potential energy surface (PES) and the global harmonic ZPE surface. Five different harmonic ZPE estimates are examined with four, on average, giving values within 4 kJ/mol—chemical accuracy—for H2CO. The local harmonic ZPE, at arbitrary molecular configurations, is subsequently defined in terms of “projected” Cartesian coordinates and a global ZPE “surface” is constructed using Shepard interpolation. This, combined with a second-order modified Shepard interpolated PES, V, allows us to construct a proof-of-concept ZPE-corrected PES for H2CO, Veff, at no additional computational cost to the PES itself. Both V and Veff are used to model product state distributions from the H + HCO → H2 + CO abstraction reaction, which are shown to reproduce the literature roaming product state distributions. Our ZPE-corrected PES allows all trajectories to be analysed, whereas, in previous simulations, a significant proportion was discarded because of ZPE violation. We find ZPE has little effect on product rotational distributions, validating previous QCT simulations. Running trajectories on V, however, shifts the product kinetic energy release to higher energy than on Veff and classical simulations of kinetic energy release should therefore be viewed with caution. [ABSTRACT FROM AUTHOR]

For a perturbed quantum system initially in the ground state, the coefficient ck(t) of excited state k in the time-dependent wave function separates into adiabatic and nonadiabatic terms. The adiabatic term ak(t) accounts for the adjustment of the original ground state to form the new ground state of the instantaneous Hamiltonian H(t), by incorporating excited states of the unperturbed Hamiltonian H0 without transitions; ak(t) follows the adiabatic theorem of Born and Fock. The nonadiabatic term bk(t) describes excitation into another quantum state k; bk(t) is obtained as an integral containing the time derivative of the perturbation. The true transition probability is given by bk(t) 2, as first stated by Landau and Lifshitz. In this work, we contrast bk(t) 2 and ck(t) 2. The latter is the norm-square of the entire excited-state coefficient which is used for the transition probability within Fermi’s golden rule. Calculations are performed for a perturbing pulse consisting of a cosine or sine wave in a Gaussian envelope. When the transition frequency ωk0 is on resonance with the frequency ω of the cosine wave, bk(t) 2 and ck(t) 2 rise almost monotonically to the same final value; the two are intertwined, but they are out of phase with each other. Off resonance (when ωk0 ≠ ω), bk(t) 2 and ck(t) 2 differ significantly during the pulse. They oscillate out of phase and reach different maxima but then fall off to equal final values after the pulse has ended, when ak(t) ≡ 0. If ωk0 < ω, bk(t) 2 generally exceeds ck(t) 2, while the opposite is true when ωk0 > ω. While the transition probability is rising, the midpoints between successive maxima and minima fit Gaussian functions of the form a exp[−b(t − d)2]. To our knowledge, this is the first analysis of nonadiabatic transition probabilities during a perturbing pulse. [ABSTRACT FROM AUTHOR]