Number Of Electronic States Research Articles

Approximate Functionals for Multistate Density Functional Theory.

Recently Lu and Gao [J. Phys. Chem. Lett. 2022, 13 (33), 7762-7769] published a new, rigorous density functional theory for excited states and proved that the projection of the kinetic and electron-repulsion operators into the subspace of the lowest electronic states are a universal functional of the matrix density D(r). This is the first attempt to find an approximation to the multistate universal functional . It is shown that (i) does not explicitly depend on the number of electronic states and (ii) is an analytic matrix functional. The Thomas-Fermi-Dirac-von Weizsäcker model and the correlation energy of the homogeneous electron gas are turned into matrix functionals guided by two principles: that each matrix functional should transform properly under basis set transformations and that the ground state functional should be recovered for a single electronic state. Lieb-Oxford-like bounds on the average kinetic and electron-repulsion energies in the subspace are given. When evaluated on the numerically exact matrix density of LiF, this simple approximation reproduces the matrix elements of the electron-repulsion operator in the basis of the exact eigenstates accurately for all bond lengths. In particular the off-diagonal elements of the effective Hamiltonian that come from the interactions of different electronic states can be calculated with the same or better accuracy than the diagonal elements. Unsurprisingly, the largest error comes from the kinetic energy functional. More exact conditions that constrain the functional form of are needed to go beyond the local density approximation.

Nonadiabatic Molecular Dynamics in Momentum Space Beyond Harmonic Approximation: Hot Electron Relaxation in Photoexcited Black Phosphorus.

We simulated hot-electron relaxation in black phosphorus using the nonadiabatic molecular dynamics (NA-MD) approach with a non-Condon effect in momentum space beyond the harmonic approximation. By comparing simulations at the Γ point in a large supercell with those using a few k-points in a smaller supercell─while maintaining the same number of electronic states within the same energy range, we demonstrate that both setups yield remarkably consistent energy relaxation times, regardless of the initial state energy. This consistency arises from the complementary effects of supercell size in real space and the number of k-points in the reciprocal space. This finding confirms that simulations at a single k-point in large size supercells are an effective approximation for NA-MD with a non-Condon effect. This approach offers significant advantages for complex photophysics, such as intervalley scattering and indirect bandgap charge recombination, and is particularly suitable for large systems without the need for a harmonic approximation.

Structural and electronic properties of Ce‐doped Ti4O7 based on experiments and first‐principles calculations

AbstractA series of Ti4O7 powders with different Ce‐cation doping concentrations were successfully prepared through a new strategy combining the wet chemical method and hydrogen thermal reduction. It is shown that Ce, entering the lattice of Ti4O7 during the reduction process, only occurs in the form of Ce3+, and the solubility of Ce is equal to 8.93 at.%. Furthermore, the electrical conductivity of Ce‐doped Ti4O7 powders was tested for the first time and theoretically explained by the first‐principles calculations. It was revealed that Ce provides a negative effect on the electrical conductivity of Ti4O7 powders, which is due to the decrease in the number of electronic states near the Fermi energy level caused by the introduction of Ce.

A Dynamically Weighted Constrained Complete Active Space Ansatz for Constructing Multiple Potential Energy Surfaces within the Anderson-Holstein Model.

We derive and implement the necessary equations for solving a dynamically weighted, state-averaged constrained CASSCF(2,2) wave function describing a molecule on a metal surface, where we constrain the overlap between two active orbitals and the impurity atomic orbitals to be a finite number. We show that a partial constraint is far more robust than a full constraint. We further calculate the system-bath electronic couplings that arise because, near a metal, there is a continuum (rather than discrete) number of electronic states. This approach should be very useful for simulating heterogeneous electron transfer and electrochemical dynamics going forward.

Electronic structure of the ground and excited states of neutral and charged silicon hydrides, SiHx0/+/−, x = 1–4

The ground and excited electronic states of the titled species are investigated with multi-reference configuration interaction and diffuse basis sets. We found that in addition to the valence orbitals, the inclusion of the 4s, 4p, and especially 3d orbitals (although with minimal population) of silicon in the active space of the reference complete active space self-consistent field wavefunction are necessary for the proper convergence of the calculations. We also demonstrate that the aug-cc-pVTZ basis set provides quite accurate results compared to both larger basis sets and basis set limit results at a lower computational cost. The excited states involve excitations within the 3s and 3p orbitals of silicon (especially for the mono- and di-hydrides), followed by excitations from the Si-H bonding orbitals to either silicon valence or Rydberg (4s, 4p) orbitals. The number of electronic states per energy unit decrease as we add hydrogen atoms, and the first excited state of SiH4 is at 9.0 eV and leads to SiH3 + H. All species have stable ground state structures with all hydrogen atoms bound to silicon, except for SiH4+ and SiH4-. The former dissociates to SiH2+ + H2, while the latter loses an electron or can dissociate forming H2 as well.

Toward an Accurate Ab Initio Description of Low-Lying Singlet Excited States of Polyenes.

The low-lying excited states of carotenoids play a crucial role in many important biophysical processes such as photosynthesis. Most of these excited states are strongly correlated, which makes them both challenging for a qualitative ab initio description and an engaging model system for trying out emerging multireference methods. Among these methods, driven similarity renormalization group (DSRG) and its perturbative version (DSRG-MRPT2) are especially attractive in terms of both accuracy and moderate numerical complexity. In this paper, we applied density matrix renormalization group (DMRG) followed by DSRG-MRPT2 for the calculation of vertical and adiabatic excitation energies into the 2Ag-, 1Bu-, and 1Bu+ electronic states of polyenes containing from 8 to 13 conjugating double bonds acting as a model for natural carotenoids. It was shown that the DSRG flow parameter should be adjusted to ensure both the energy convergence with respect to it and the agreement with the experimental data. With the increased flow parameter, the proposed combination of methods provides a reasonable agreement with the experiment. The deviations of the adiabatic excitation energies are less than 1000 cm-1 for the 2Ag- and less than 3000 cm-1 for the excited states of the Bu symmetry, which in terms of accuracy significantly outperforms the N-electron valence state perturbation theory. At the same time, DSRG-MRPT2 is shown to be robust with respect to variation of quality of the DMRG reference wave function such as the orbital optimization or the number of electronic states in the averaging.

Thermodynamically Driven Surface Dedoping of Nb-Doped TiO2 for Stable Perovskite Solar Cells

In perovskite solar cells, the interfacial transfer of photogenerated electrons from the photoactive layers to TiO2 mesoporous layers is the key step that determines the power conversion efficiency and stability of the devices and is influenced by the contact condition. Although foreign element doping can facilitate the extraction of electrons from the perovskite layers, the increase in the number of electronic states on the surface of semiconductor scaffolds will undesirably aggravate the charge recombination. In this work, we manage to dedope the foreign element from the surface of Nb-doped TiO2 nanostructures via moderate temperature treatment. By doing this, the remaining lattice expansion of the dedoped surface can reduce the lattice mismatching between the anatase and the perovskite, therefore not only facilitating the electronic interaction but also alleviating the interfacial strain on temperature changes. Besides, the surface dedoping can also protect the cells from UV degradation by suppressing the survival of holes generated in the TiO2 skeleton.

Electronic Structure and Electronic Properties of PtSn4 Single Crystal

A topological semimetal PtSn4 single crystal is grown and the following properties are studied: its electrical resistivity in the temperature range from 4.2 to 300 K, galvanomagnetic properties at temperatures from 4.2 to 80 K and in magnetic fields of up to 100 kOe, and optical properties at room temperature. Theoretical calculations of the electronic structure are performed. It is shown that the residual resistivity is rather small: ρ0 = 0.47 μΩ cm, which is characteristic of a “good” metal. The ρ(T) dependence is of the metallic type, increasing monotonically with temperature. Analysis of the temperature dependences of the magnetoresistivity suggests that the Fermi surface of the PtSn4 compound may contain closed sheets. Studies of the Hall effect and the estimates made in the single-band model allowed us to conclude that the predominant type of current carriers are holes with concentration n = 6.8 × 1021 cm–3 and mobility μ ≈ 1950 cm2/(V s) at T = 4.2 K. It is shown that the optical properties of PtSn4 have features characteristic of “bad” metals. The calculation of the electronic structure of PtSn4 showed that, in general, this compound has a structure characteristic of metallic systems with a sufficiently large number of electronic states at the Fermi level, which is consistent with the experimental results on the electronic transport and optical properties of the PtSn4 single crystal.

Nonadiabatic Quantum Dynamics with Frozen-Width Gaussians.

We review techniques for simulating fully quantum nonadiabatic dynamics using the frozen-width moving Gaussian basis functions to represent the nuclear wave function. A choice of these basis functions is primarily motivated by the idea of the on-the-fly dynamics that will involve electronic structure calculations done locally in the vicinity of each Gaussian center and thus avoiding the "curse of dimensionality" appearing in large systems. For quantum dynamics involving multiple electronic states there are several aspects that need to be addressed. First, the choice of the electronic-state representation is one of most defining in terms of formulation of resulting equations of motion. We will discuss pros and cons of the standard adiabatic and diabatic representations as well as the relatively new moving crude adiabatic (MCA) representation. Second, if the number of electronic states can be fixed throughout the dynamics, the situation is different for the number of Gaussians needed for an accurate expansion of the total wave function. The latter increases its complexity along the course of the dynamics and a protocol extending the number of Gaussians is needed. We will consider two common approaches for the extension: (1) spawning and (2) cloning. Third, equations of motion for individual Gaussians can be chosen in different ways, implications for the energy conservation related to these ways will be discussed. Finally, to extend the success of moving basis approaches to quantum dynamics of open systems we will consider the Nonstochastic Open System Schrödinger Equation (NOSSE).

Spin Transport Investigations in Bilayer Graphene

We study the spin-based electron transport properties in bilayer graphene with half-metallic ferromagnetic (HMF) CrO2 electrodes. Out-of-plane bilayer graphene has been examined in this paper. A high magneto-resistance ratio (MR) of ∼99% is obtained in the bilayer structure for a potential range of 0 to 0.8 V, after which MR drops because of the increase in spin-up current in the anti-parallel configuration at 1.2 V. High spin filtration of ∼100% is obtained at all bias points. Transmission spectrum studies show that a large number of electronic states are present at the Fermi level in bilayer graphene, which would result in high current.

Effects of air annealing on DC characteristics of InAlN/GaN MOS high-electron-mobility transistors using atomic-layer-deposited Al2O3

We evaluated the DC characteristics of InAlN/GaN metal–oxide–semiconductor high-electron-mobility transistors (MOS-HEMTs) using atomic-layer-deposited (ALD-)Al2O3 by focusing on air annealing to control defect levels in Al2O3 and electronic states at the Al2O3/InAlN interface. We clarified that the transconductance linearity and subthreshold slope were improved by air annealing, indicating a reduction in the number of electronic states at the Al2O3/InAlN interface. Furthermore, the cathodoluminescence study demonstrated that the oxygen-related defects in ALD-Al2O3 were decreased by air annealing. Consequently, we could successfully reduce the threshold voltage shift of InAlN/GaN MOS-HEMTs by using air-annealed ALD-Al2O3.

The Ideal and Real Gas Heat Capacity of Potassium Atoms at High Temperatures

The ideal gas heat capacity, Cp, of cesium atoms is calculated to high temperatures using statistical mechanics. There are a large number of electronic states in the state sum that determines the partition function: 174 known levels for cesium atoms below the first ionization potential. Thus, at high temperatures, Cp becomes very large unless the number of contributing states is constrained. Two arguments are used to do this. First, at high temperatures, the increased size of the atoms constrains the sum (Bethe method). Second, the existence of interacting charged species at higher temperatures, which lowers the ionization potential, constrains the sum (ionization potential lowering method). If atoms constitute a real gas obeying the virial equation of state, the lowest non-ideal contribution to Cp depends on the second derivative of the second virial coefficient, B″(T), which depends on the interaction potential energy curves between two atoms. When two ground-state (2S) cesium atoms interact, they follow either of two potential energy curves. When a 2S cesium atom interacts with a cesium atom in the first electronically excited (2P) state, they follow any of eight potential energy curves. The values of B″(T) for the ten states are determined, then averaged, and used to calculate the lowest order non-ideal contribution to Cp.

Pressure induced structural instability of FeV intermetallic compound with B2 ordering

The structural, elastic, lattice dynamic, and electronic properties of intermetallic FeV with B2 ordering under hydrostatic pressure are extensively investigated by using the first-principles calculations within density functional theory. The calculated lattice constant, bulk modulus, magnetic moment, and number of electronic states at the Fermi level at P = 0GPa are in a good agreement with the previous calculated and experimental results. The elastic moduli show linearly increasing trends with pressure, except shear modulus which shows a linear softening trend. The transverse acoustic (TA) phonon mode propagating along the [110] direction polarized along the [11-0] direction decreases to be imaginary crossing the critical pressure ∼9.4 GPa, resulting in the structural instability of B2-FeV intermetallic. Comparing the phonon softening with the shear modulus softening, it is suggested that the soft phonon mode dominates the pressure-induced structural instability of B2-FeV. The electronic density of state (DOS) shows that a considerable increase in the number of electronic states at the Fermi level with increasing pressure, and this behavior is consistent with the phonon softening.

First-principles investigation of the structural, mechanical and electronic properties of the NbO-structured 3d, 4d and 5d transition metal nitrides

We have performed ab initio calculations on 29 nitride phases of transition metals from the 3d, 4d and 5d rows, in NbO structure. We calculated cohesive energy, lattice constant and elastic constants C11, C12 and C44, and derived mechanical moduli, related ratios and hardness. For five out of the ten 3d transition metal nitrides, namely, CrN, MnN, FeN, CoN and NiN, cohesive energy in this new structure is similar to that of the same composition in the rocksalt structure. The lattice constant and bulk modulus were found to be anti-correlated. We observed the correlation between the shear modulus (G), Pugh’s ratio (k) and derived Vickers hardness (HV). For identical metal element significant variations in the mechanical properties of nitrides are found between rocksalt and NbO structures. However for a fixed structure, 3d, 4d and 5d metal nitrides behave similarly. We computed Debye temperature and demonstrated its correlation with HV as proposed by Madelung, Einstein and Deus. The nitrides, CrN, MoN and WN in NbO structure show values of HV larger than 20GPa. We showed systematically that C44, G, k and HV are anti-correlated with the number of electronic states around EF, leading to a semi-quantitative link of nitride electronic structure to mechanical instability and hardness. The local density of states demonstrating systematic evolution of the electronic structure with the number of d electrons in the metal atoms was studied. Bader charge transfer from metal to nitrogen atom was analyzed throughout the 29 nitrides showing comparison with rocksalt structure and experimental electronegativity data.

Structural, mechanical and electronic properties of 3d transition metal nitrides in cubic zincblende, rocksalt and cesium chloride structures: a first-principles investigation

We report systematic results from ab initio calculations with density functional theory on three cubic structures, zincblende (zb), rocksalt (rs) and cesium chloride (cc), of the ten 3d transition metal nitrides. We computed lattice constants, elastic constants, their derived moduli and ratios that characterize mechanical properties. Experimental measurements exist in the literature of lattice constants for rs-ScN, rs-TiN and rs-VN and of elastic constants for rs-TiN and rs-VN, all of which are in good agreement with our computational results. Similarly, computed Vickers hardness (HV) values for rs-TiN and rs-VN are consistent with earlier experimental results. Several trends were observed in our rich data set of 30 compounds. All nitrides, except for zb-CrN, rs-MnN, rs-FeN, cc-ScN, cc-CrN, cc-NiN and cc-ZnN, were found to be mechanically stable. A clear correlation in the atomic density with the bulk modulus (B) was observed with maximum values of B around FeN, MnN and CrN. The shear modulus, Young’s modulus, HV and indicators of brittleness showed similar trends and all showed maxima for cc-VN. The calculated value of HV for cc-VN was about 30 GPa, while the next highest values were for rs-ScN and rs-TiN, about 24 GPa. A relation () between HV and Debye temperature (θD) was investigated and verified for each structure type. A tendency for anti-correlation of the elastic constant C44, which strongly influences stability and hardness, with the number of electronic states around the Fermi energy was observed.

Computation of magnetic circular dichroism by sum‐over‐states summations

Magnetic circular dichroism (MCD) spectroscopy has been established as a convenient method to study electronic structure, in particular for small symmetric organic molecules. Newer applications on more complex systems are additionally stimulated by the latest availability of precise quantum-chemical techniques for the spectral simulations. In this work, a sum over states (SOS) summation is reexamined as an alternative to the derivative techniques for the MCD modeling. Unlike in previous works, the excited electronic states are calculated by the time-dependent density functional theory (TDDFT). A gradient formulation of the MCD intensities is also proposed, less dependent on the origin choice than the standard expressions. The dependencies of the results on the basis set, number of electronic states, and coordinate origin are tested on model examples, including large symmetric molecules with degenerate electronic states. The results suggest that the SOS/TDDFT approach is a viable and accurate technique for spectral simulation. It may even considerably reduce the computational time, if compared with the traditional MCD computational procedures based on the response theory.

O + C2H4 potential energy surface: excited states and biradicals at the multireference level

The focus of this study is to understand the multiconfigurational nature of the biradical species involved in the early reaction paths of the oxygen plus ethylene PES. In previous work (J Phys Chem A 113, 12663, 2009), the lowest-lying O(3P) + C2H4 PES was extensively explored at the MCSCF, MRMP2, and MR-AQCC levels of theory. In the current work, ground and excited, triplet- and singlet-state reaction paths for the initial addition of oxygen to ethylene were found at the MCSCF and MRMP2 levels along with five singlet pathways near the ·CH2CH2O· biradical at the MCSCF, MRMP2, and CR-CC(2,3) levels. One of these five paths can lead to the CH2CO + H2 products from CH3CHO rather than from the ·CH2CH2O· biradical, and this pathway was investigated with a variety of CAS sizes. To provide further comparison between the MRMP2 and CR-CC(2,3) levels, MR-AQCC single-point energies and optimizations were performed for select geometries. After the initial exploration of this region of the surface, the lowest singlet–triplet surface crossings were explicitly determined at the MCSCF level. Additional MRMP2 calculations were performed to demonstrate the limitations of single-state perturbation theory in this biradical region of the PES, and SO-MCQDPT2 single-point energies using SA MCSCF were calculated on a grid of geometries around the primary surface crossing. In particular, these calculations were examined to determine a proper active space and a physically reasonable number of electronic states. The results of this examination show that at least four states must be considered to represent this very complex region of the PES.

A Compact Treatment of Singular Impurities Using the Artificial Friedel Resonance (FAIR) Technique

Building on the tools that Friedel introduced in the 1950s, an off-spring of the Friedel resonance is developed, which is called the FAIR approach for “Friedel Artificially Inserted Resonance”. In the FAIR approach, an arbitrary s-electron state $a_{0}^{\dagger}$ is cut out of the conduction band, and the remaining free electron Hamiltonian is orthogonalized, yielding an artificial Friedel resonance. In the presence of a real Friedel d-resonance state d †, one can find an optimal fair state $a_{0}^{\dagger}$ so that the exact n-electron ground state consists of two Slater states, one containing the d-electron and the other the fair state $a_{0}^{\dagger}$ . This separation according to the d-occupation is ideal for impurities with a Coulomb interaction between d-electrons. The wave function of the Friedel–Anderson (FA) impurity in the magnetic state and the singlet state are constructed with the FAIR method using two fair states $a_{0}^{\dagger}$ and $b_{0}^{\dagger}$ . The magnetic state consists of four, and the singlet state consists of eight Slater states. The latter is invariant with respect to the inversion of all spins. The FAIR ground state Ψ SS for the singlet state is composed of two magnetic states Ψ MS with opposite moments which are not orthogonal to each other. The degree of overlap determines the Kondo energy. Because of the compactness of the wave function, a number of properties can be calculated relatively quickly. Comparison with the best previous ground state energy and d-occupation by Gunnarson and Schoenhammer show excellent agreement. A number of physical properties are calculated; among them are (i) the Kondo cloud in a small magnetic field. Two components of polarization are observed (in linear response), an oscillating part and a nonoscillating part. (ii) The fidelity which represents the scalar product between the ground states of the symmetric FA-impurity and the symmetric Friedel impurity is calculated as a function of the number of electron states. (In the literature, this has the somewhat misleading name of fidelity.) This calculation does not show an Anderson orthogonality catastrophe, which indicates that the FA ground state has a phase shift of π/2 at the Fermi energy. (iii) The Friedel oscillations of the FA-impurity. Surprisingly, these oscillations are very similar to the Friedel oscillations of a very narrow Friedel resonance at the Fermi level. The amplitude A(r) is close to zero at short distances and saturates at two for large distances. The inversion point where A(r)=1 correlates with the characteristic energies of the impurities, the half-band width Γ for the Friedel impurity and the Kondo energy for the FA-impurity. This raises the fascinating question how these simple properties are hidden in the multielectron wave function.

Positive Vibrational Entropy of Chemical Ordering in FeV

Inelastic neutron scattering and nuclear resonant inelastic x-ray scattering were used to measure phonon spectra of FeV as a B2 ordered compound and as a bcc solid solution. The two data sets were combined to give an accurate phonon density of states, and the phonon partial densities of states for V and Fe atoms. Contrary to the behavior of ordering alloys studied to date, the phonons in the B2 ordered phase are softer than in the solid solution. Ordering increases the vibrational entropy by +0.22±0.03 kB/atom, which stabilizes the ordered phase to higher temperatures. First-principles calculations show that the number of electronic states at the Fermi level increases upon ordering, enhancing the screening between ions, and reducing the interatomic force constants. The effect of screening is larger at the V atomic sites than at the Fe atomic sites.

On the calculation of the magnetic structure of surfaces, near-surface layers, and interfaces of 3d metals

A microscopic approach to the calculation of the distribution of magnetic moments in the vicinity of surfaces, interfaces, and other spatially inhomogeneous 3d metal systems is proposed in the framework of model Hamiltonians for itinerant electrons. The method of Green’s functions in the configuration space is used. The equations for Green’s functions are solved by the recursion method. The poles of the Green’s functions of d electrons are numerically determined, and then, analytical expressions are derived for the density of states and the occupation numbers of electronic states. The magnetic moments in the vicinity of surfaces and interfaces with different orientations relative to crystallographic axes are calculated for ferromagnetic iron and antiferromagnetic chromium. The dependences of the magnitude of the magnetization on the distance to the surface for both metals proved to be very similar to each other, even though the densities of states and the types of their magnetic ordering are different. Compared to massive samples, the magnetic moments at Fe/Cr interfaces increase for chromium and decrease for iron, and the magnetization profile depends on the interface orientation. The results of the calculation make it possible to explain the experimental Mossbauer data for Cr/Sn and Fe/Cr/Sn multilayer systems.