Constrained Density Functional Theory Research Articles

Highly Accurate and Robust Constraint-Based Orbital-Optimized Core Excitations.

We adapt our recently developed constraint-based orbital-optimized excited-state method (COOX) for the computation of core excitations. COOX is a constrained density functional theory (cDFT) approach based on excitation amplitudes from linear-response time-dependent DFT (LR-TDDFT), and has been shown to provide accurate excitation energies and excited-state properties for valence excitations within a spin-restricted formalism. To extend COOX to core-excited states, we introduce a spin-unrestricted variant which allows us to obtain orbital-optimized core excitations with a single constraint. Using a triplet purification scheme in combination with the constrained unrestricted Hartree-Fock formalism, scalar-relativistic zero-order regular approximation corrections, and a semiempirical treatment of spin-orbit coupling, COOX is shown to produce highly accurate results for K- and L-edge excitations of second- and third-period atoms with subelectronvolt errors despite being based on LR-TDDFT, for which core excitations pose a well-known challenge. L- and M-edge excitations of heavier atoms up to uranium are also computationally feasible and numerically stable, but may require more advanced treatment of relativistic effects. Furthermore, COOX is shown to perform on par with or better than the popular ΔSCF approach while exhibiting more robust convergence, highlighting it as a promising tool for inexpensive and accurate simulations of X-ray absorption spectra.

Light-Induced Polaronic Crystals in Single-Layer Transition Metal Dichalcogenides.

Light-induced ordered states can emerge in materials after irradiation with ultrafast laser pulses. However, their prediction is challenging because the inverted band occupation confounds our chemical intuition. Hence, we use a recently developed constrained density functional perturbation theory approach to systematically screen single-layer transition metal dichalcogenides (TMDs) for light-induced ordered states. We demonstrate that all examined single-layer TMDs reveal similar light-induced charge orderings. The corresponding reconstructions are periodic arrangements of polarons (polaronic crystals), characterized by triangular metal clusters and having no equivalent at equilibrium conditions. The polarons are accompanied by localized midgap states in the electronic band structure, detectable by experimental methods. We assess the selenides as the most promising candidates for potential photoexcitation experiments because they transition at low critical fluences, have low transition barriers, and maintain an open band gap under photoexcitation. Our work paves the way for innovative material design approaches targeting light-induced phases.

A Constraint-Based Orbital-Optimized Excited State Method (COOX).

In this work, we present a novel method to directly calculate targeted electronic excited states within a self-consistent field calculation based on constrained density functional theory (cDFT). The constraint is constructed from the static occupied-occupied and virtual-virtual parts of the excited state difference density from (simplified) linear-response time-dependent density functional theory calculations (LR-TDDFT). Our new method shows a stable convergence behavior, provides an accurate excited state density adhering to the Aufbau principle, and can be solved within a restricted SCF for singlet excitations to avoid spin contamination. This also allows the straightforward application of post-SCF electron-correlation methods like MP2 or direct RPA methods. We present the details of our constraint-based orbital-optimized excited state method (COOX) and compare it to similar schemes. The accuracy of excitation energies will be analyzed for a benchmark of systems, while the quality of the resulting excited state densities is investigated by evaluating excited state nuclear forces and excited state structure optimizations. We also investigate the performance of the proposed COOX method for long-range charge transfer excitations and conical intersections with the ground-state.

Electronic structure, absorption spectra and oxidation dynamics in polyynes and dicyanopolyynes.

The advent of femtosecond to attosecond experimental tools has made now possible to study such ultrafast carrier dynamics, e.g., the spatial and temporal charge density evolution, after an initial oxidation or reduction in molecules, candidates for atomic wires like polyynes and dicyanopolyynes. Here, we study the electronic structure and hole transfer in symmetric molecules containing carbon, nitrogen and hydrogen, the first members in the series of polyynic carbynes and dicyanopolyynes, using methods based on density functional theory (DFT): constrained DFT (CDFT), time-dependent DFT (TDDFT) and real-time TDDFT (RT-TDDFT), with Löwdin population analysis, comparing many levels of theory and obtaining convergence of the results. For the same purposes, we develop a tight binding (TB) variant using all valence orbitals of all atoms. This TB variant is applied here in linear molecules, but it is also adequate for electronic structure, charge transfer and charge transport of non-linear molecules and clusters of molecules. We calculate the electronic structure, the time-dependent dipole moment and the probabilities of finding the hole at each site, their mean over time values, the mean transfer rates from the oxidation site to other sites and the frequency content (using charge as well as dipole moment oscillations). We take into account zero-point motion. The initial conditions for RT-TDDFT are obtained by CDFT. For TB, we explore different initial conditions: we place the hole at a particular orbital or distribute it among a number of orbitals; it is also possible to include phase differences between orbitals. Finally, we compare with available experimental data.

First-Principles Nonadiabatic Dynamics of Molecules at Metal Surfaces withVibrationally Coupled Electron Transfer.

Accurate description of nonadiabatic dynamics of molecules at metal surfaces involving electron transfer has been a long-standing challenge for theory. Here, we tackle this problem by first constructing high-dimensional neural network diabatic potentials including state crossings determined by constrained density functional theory, then applying mixed quantum-classical surface hopping simulations to evolve coupled electron-nuclear motion. Our approach accurately describes the nonadiabatic effects in CO scattering from Au(111) without empirical parameters and yields results agreeing well with experiments under various conditions for this benchmark system. We find that both adiabatic and nonadiabatic energy loss channels have important contributions to the vibrational relaxation of highly vibrationally excited CO(v_{i}=17), whereas relaxation of low vibrationally excited states of CO(v_{i}=2) is weak and dominated by nonadiabatic energy loss. The presented approach paves the way for accurate first-principles simulations of electron transfer mediated nonadiabatic dynamics at metal surfaces.

First-Order Rhombohedral-to-Cubic Phase Transition in Photoexcited GeTe.

Photoexcited GeTe undergoes a nonthermal phase transition from a rhombohedral to a rocksalt crystalline phase. The microscopic mechanism and the nature of the transition are unclear. By using constrained density functional perturbation theory and by accounting for quantum anharmonicity within the stochastic self-consistent harmonic approximation, we show that the nonthermal phase transition is strongly first order and does not involve phonon softening, at odds with the thermal one. The transition is driven by the closure of the single particle gap in the photoexcited rhombohedral phase. Finally, we show that ultrafast x-ray diffraction data are consistent with a coexistence of the two phases, as expected in a first order transition. Our results are relevant for the understanding of phase transitions and bonding in phase change materials.

Analytical Model for the Molecular Ionization Energy in an External Electric Field.

A model for the molecular ionization energy in an applied electric field is presented on the basis of a perturbation expansion in the electric field. The leading term arises from the Frenkel approach, which is the same for all molecules normally used in the Poole-Frenkel model for conductivity in an electric field. For a set of test molecules, the quality of the results is comparable to that of previous results using constrained density functional theory. We conclude that the Frenkel term is dominant and sufficient at relatively low fields and that the dipole and polarizability terms, the leading terms dependent on the properties of the individual molecule, make a significant contribution only at high fields and for relatively large molecules. Because the presented model is analytical, quantum chemical calculations are avoided for a variety of electric field strengths and molecular orientations, and the model can therefore be applied directly in coarse-grained models for electronic processes in dielectric condensed phases.

Exploring the Reactivity of Donor-Acceptor Systems through a Combined Conceptual and Constrained DFT Approach.

In the context of the conceptual density functional theory (cDFT) and based on the computational efficiency of the constrained DFT (CDFT), we demonstrate that chemical reactivity can be governed by the difference between the local interacting chemical potentials of the reactants (referred as Edual), in agreement with Sanderson's equalization principle. In a proof-of-concept study, we investigated illustrative examples involving typical non-covalent donor-acceptor systems and reactive systems are provided. For the selected systems, our approach reveals significant mimicking between Edual and the DFT-computed intermolecular interaction energy profiles. We further evaluate the influence of the Coulomb and exchange-correlation contributions in Edual. These latter results suggest that numerous potential energy surfaces of clusters can be explored using a Sanderson-like model only based on classical interactions between molecular orbitals domains. To conclude, this study achieved a deeper understanding of the principles of cDFT and assessed, in a wider context, its efficiency in predicting the chemical reactivity.

Exploring charge hopping transport in amorphous HfO2: An approach combing ab initio methods and model Hamiltonian

Charge hopping transport is typically modeled by Marcus theory with the coupling strengths and activation energies extracted from the constrained density functional theory. However, such a method may not be a practical route for amorphous materials due to the tremendous amount of hopping paths, therefore computationally unreachable. This work presents a general approach combining the ab initio method and model Hamiltonian, yielding similar results to constrained density functional theory. Such an approach is computationally efficient, allowing us to consider all 23 220 hopping paths between oxygen vacancies in our demonstrated amorphous hafnium dioxide model containing 324 atoms. Based on these hopping rates, charge mobility in amorphous hafnium dioxide is investigated as a function of oxygen vacancies concentration. It is found that a minimum oxygen vacancies concentration of 0.7×1021 cm−3 is required to enable the connectivity of the charge hopping network.

The Role of Water Molecules on Polaron Behavior at Rutile (110) Surface: A Constrained Density Functional Theory Study.

Understanding the behavior of a polaron in contact with water is of significant importance for many photocatalytic applications. We investigated the influence of water on the localization and transport properties of polarons at the rutile (110) surface by constrained density functional theory. An excess electron at a dry surface favors the formation of a small polaron at the subsurface Ti site, with a preferred transport direction along the [001] axis. As the surface is covered by water, the preferred spatial localization of the polarons is moved from the subsurface to the surface. When the water coverage exceeds half a monolayer, the preferred direction of polaron hopping is changed to the [110] direction toward the surface. This characteristic behavior is related to the Ti3d-orbital occupations and crystal field splitting induced by different distorted structures under water coverage. Our work describes the reduced sites that might eventually play a role in photocatalysis for rutile (110) surfaces in a water environment.

Donor-acceptor pairs in wide-bandgap semiconductors for quantum technology applications

We propose a quantum science platform utilizing the dipole-dipole coupling between donor-acceptor pairs (DAPs) in wide bandgap semiconductors to realize optically controllable, long-range interactions between defects in the solid state. We carry out calculations based on density functional theory (DFT) to investigate the electronic structure and interactions of DAPs formed by various substitutional point-defects in diamond and silicon carbide (SiC). We determine the most stable charge states and evaluate zero phonon lines using constrained DFT and compare our results with those of simple donor-acceptor pair (DAP) models. We show that polarization differences between ground and excited states lead to unusually large electric dipole moments for several DAPs in diamond and SiC. We predict photoluminescence spectra for selected substitutional atoms and show that while B-N pairs in diamond are challenging to control due to their large electron-phonon coupling, DAPs in SiC, especially Al-N pairs, are suitable candidates to realize long-range optically controllable interactions.

Cation-induced changes in the inner- and outer-sphere mechanisms of electrocatalytic CO2 reduction

The underlying mechanism of cation effects on CO2RR remains debated. Herein, we study cation effects by simulating both outer-sphere electron transfer (OS-ET) and inner-sphere electron transfer (IS-ET) pathways during CO2RR via constrained density functional theory molecular dynamics (cDFT-MD) and slow-growth DFT-MD (SG-DFT-MD), respectively. Our results show without any cations, only OS-ET is feasible with a barrier of 1.21 eV. In the presence of K+ (Li+), OS-ET shows a very high barrier of 2.93 eV (4.15 eV) thus being prohibited. However, cations promote CO2 activation through IS-ET with the barrier of only 0.61 eV (K+) and 0.91 eV (Li+), generating the key intermediate (adsorbed CO{}_{2}^{delta -}). Without cations, CO2-to-CO{}_{2}^{delta -}(ads) conversion cannot proceed. Our findings reveal cation effects arise from short-range Coulomb interactions with reaction intermediates. These results disclose that cations modulate the inner- and outer-sphere pathways of CO2RR, offering substantial insights on the cation specificity in the initial CO2RR steps.

Simulating Electron Transfer Reactions in Solution: Radical-Polar Crossover.

Single-electron transfer (SET) promotes a wide variety of interesting chemical transformations, but modeling of SET requires a careful treatment of electronic and solvent effects to give meaningful insight. Therefore, a combined constrained density functional theory and molecular mechanics (CDFT/MM) tool is introduced specifically for SET-initiated reactions. Mechanisms for two radical-polar crossover reactions involving the organic electron donors tetrakis(dimethylamino)ethylene (TDAE) and tetrathiafulvalene (TTF) were studied with the new tool. An unexpected tertiary radical intermediate within the TDAE system was identified, relationships between kinetics and substitution in the TTF system were explained, and the impact of the solvent environments on the TDAE and TTF reactions were examined. The results highlight the need for including solvent dynamics when quantifying SET kinetics and thermodynamics, as a free energy difference of >20 kcal/mol was observed. Overall, the new method informs mechanistic analysis of SET-initiated reactions and therefore is envisioned to be useful for studying reactions in the condensed phase.

First-principles study of luminescence and electronic properties of Ce-doped Y2SiO5.

The transition of energy from the 4f to the 5d state is a fundamental element driving various applications, such as phosphors and optoelectronic devices. The positioning of the 4f ground states and the 5d excited states significantly influences this energy shift. In our research, we delve into the placement of these states utilizing a hybrid density functional theory (DFT) combined with spin-orbit coupling (SOC) via the supercell method. Additionally, we scrutinize the transition energy, applying the constrained density functional theory (cDFT) approach in conjunction with the ΔSCF method. Our study illustrates that the synergy of cDFT and SOC generates a discrepancy of about 2% for Ce1 and 4% for Ce2 when comparing the calculated results to experimental data. Moreover, We have determined the positions of the 4f ground states to be 2.73eV above the Valence Band Maximum (VBM) for Ce1 and 2.70eV for Ce2. We also note a tight correlation between the 5d levels identified in the experimental data and the theoretical outcomes derived from wave function calculations at the CASPT2 accuracy level.

Light-Induced Nonthermal Phase Transition to the Topological Crystalline Insulator State in SnSe.

Femtosecond pulses have been used to reveal hidden broken symmetry states and induce transitions to metastable states. However, these states are mostly transient and disappear after laser removal. Photoinduced phase transitions toward crystalline metastable states with a change of topological order are rare and difficult to predict and realize experimentally. Here, by using constrained density functional perturbation theory and accounting for light-induced quantum anharmonicity, we show that ultrafast lasers can permanently transform the topologically trivial orthorhombic structure of SnSe into the topological crystalline insulating rocksalt phase via a first-order nonthermal phase transition. We describe the reaction path and evaluate the critical fluence and possible decay channels after photoexcitation. Our simulations of the photoexcited structural and vibrational properties are in excellent agreement with recent pump-probe data in the intermediate fluence regime below the transition with an error on the curvature of the quantum free energy of the photoexcited state that is smaller than 2%.

Correcting charge distribution in reduced Li-molecule pair for computational screening of battery solvents.

Li-molecule pair is a widely used model for the simulation of reduction in Li-ion batteries. We demonstrate that this model provides incorrect results for some solvents. When an electron is added to the Li-molecule pair, it may go to the lithium-ion and neutralize it. Instead, we suggest placing this additional electron on the molecule using constrained density functional theory (CDFT). This approach resembles electron behaviour in the condensed phase and reproduces the physics of the reduction. We demonstrate that suggested in this work approach provides improved agreement with experimental data. Suggested CDFT-based method is fast, reliable and may be used in computational screening of solvents. We demonstrate the practical application of the method by benchmarking it on a set of 30 molecules from the electrolyte solvent database.

Exploring energy landscapes of charge multipoles using constrained density functional theory

Exploring energy landscapes of charge multipoles using constrained density functional theory

Constrained Nuclear-Electronic Orbital Density Functional Theory with a Dielectric Continuum Solvent Model.

Solvent effects are crucial for simulating chemical and biological processes in solutions. The continuum solvation model is widely used for incorporating solvent effects with different levels of theoretical descriptions of solutes. For solutes and solutions containing hydrogen atoms, nuclear quantum effects can also be nonnegligible for reliable simulations. In this work, we couple our recently developed constrained nuclear-electronic orbital density functional theory with a dielectric continuum solvation model to cover nuclear quantum effects and solvent effects simultaneously. This approach is applied to the formate ion, where an anomalous solvatochromic shift in C-H stretch frequency was reported in experiments. By using this new approach to account for nuclear quantum effects and solvent effects, we show that the vibrational frequency of the C-H stretch and the solvatochromic shift are accurately described.

Cluster model of C12 in the density functional theory framework

We employ the constrained density functional theory to investigate cluster phenomena for the $^{12}\mathrm{C}$ nucleus. The proton and neutron densities are generated from the placement of three $^{4}\mathrm{He}$ nuclei ($\ensuremath{\alpha}$ particles) geometrically. These densities are then used in a density constrained Hartree-Fock calculation that produces an antisymmetrized state with the same densities through energy minimization. In the calculations no a priori analytic form for the single-particle states is assumed and the full energy density functional is utilized. The geometrical scan of the energy landscape provides the ground state of $^{12}\mathrm{C}$ as an equilateral triangular configuration of three $\ensuremath{\alpha}\mathrm{s}$ with molecular bond like structures. The use of the nucleon localization function provides further insight to these configurations. One can conclude that these configurations are a hybrid between a pure mean-field and a pure $\ensuremath{\alpha}$ particle condensate. This development could facilitate density functional theory based fusion calculations with a more realistic $^{12}\mathrm{C}$ ground state.

Creation and repair of luminescence defects in hexagonal boron nitride by irradiation and annealing for optical neutron detection

Hexagonal boron nitride (hBN) is promising for applications in neutron detection and quantum sensing. Here we created spin-dependent luminescence defects in hBN using 50 keV helium ion beam. The irradiated hBN flakes with a dose around 2 × 1014–1 × 1015/cm2 have the maximum photoluminescence (PL) intensity. The PL spectra are in the range of 700–1000 nm with a peak around 818 nm at 297 K after irradiation with a dose of less than 2 × 1014/cm2, which can be eliminated by high temperature annealing at 1097 K due to defects repair according to Raman spectra. However, the PL peaks exhibit a redshift from 818 nm to 830 nm when the irradiation dose is no less than 1 × 1015/cm2. Combining with constrained density functional theory calculations, it is found that high dose irradiation can cause local lattice swelling and further induce the redshift of PL spectra by 12 nm/0.33% strain. Furthermore, we proposal a novel optical neutron detection method by recording the intensity and position of PL signal of luminescence defects induced by neutron-10B nuclear reaction daughter particles. This work would be helpful to create luminescence defects in hBN for quantum sensing, and develop a novel neutron detector.