Constrained Density Functional Theory Research Articles

Electronic structure of rare-earth mononitrides: quasiatomic excitations and semiconducting bands

The electronic structure of the rare-earth mononitrides LnN (where Ln = rare-earth), which are promising materials for future spintronics applications, is difficult to resolve experimentally due to a strong influence of defects on their transport and optical properties. At the same time, LnN are challenging for theory, since wide semiconducting 2p and 5d bands need to be described simultaneously with strongly correlated 4f states. Here, we calculate the many-body spectral functions and optical gaps of a series of LnN (with Ln = Pr, Nd, Sm, Gd, Tb, Dy, Ho, Er) by a density-functional + dynamical mean-field theory (DFT + DMFT) approach treating the correlated Ln 4f shells within the quasi-atomic Hubbard-I approximation. The on-site Coulomb interaction in the 4f shell is evaluated by a constrained DFT + Hubbard-I approach. Furthermore, to improve the treatment of semiconducting bands in DFT + DMFT, we employ the modified Becke–Johnson semilocal exchange potential. Focusing on the paramagnetic high-temperature phase, we find that all investigated LnN are pd semiconductors with gap values ranging from 1.02 to 2.14 eV along the series. The pd band gap is direct for light Ln = La…Sm and becomes indirect for heavy rare-earths. Despite a pronounced evolution of the Ln 4f states along the series, empty 4f states are invariably found above the bottom of the 5d conduction band. The calculated spectra agree well with those available from x-ray photoemission, x-ray emission and x-ray absorption measurements.

Molecular Dynamics with Constrained Nuclear Electronic Orbital Density Functional Theory: Accurate Vibrational Spectra from Efficient Incorporation of Nuclear Quantum Effects.

Nuclear quantum effects play a crucial role in many chemical and biological systems involving hydrogen atoms yet are difficult to include in practical molecular simulations. In this paper, we combine our recently developed methods of constrained nuclear-electronic orbital density functional theory (cNEO-DFT) and constrained minimized energy surface molecular dynamics (CMES-MD) to create a new method for accurately and efficiently describing nuclear quantum effects in molecular simulations. By use of this new method, dubbed cNEO-MD, the vibrational spectra of a set of small molecules are calculated and compared with those from conventional ab initio molecular dynamics (AIMD) as well as from experiments. With the same formal scaling, cNEO-MD greatly outperforms AIMD in describing the vibrational modes with significant hydrogen motion characters, demonstrating the promise of cNEO-MD for simulating chemical and biological systems with significant nuclear quantum effects.

Possible existence of multiple wobbling modes in A≈60 nuclei

The nuclear multiple wobbling modes in $A\ensuremath{\approx}60$ mass region are explored by the adiabatic and configuration-fixed constrained covariant density functional theory for nickel isotopes for the first time. The potential-energy curves and deformation parameters $\ensuremath{\beta}$ and $\ensuremath{\gamma}$ of the ground and excited states of $^{57\text{--}62}\mathrm{Ni}$ are obtained to search for the possible wobbling candidates. It is shown that there are suitable triaxial deformations and high-$j$ particle(s) or hole(s) configurations in $^{57\text{--}62}\mathrm{Ni}$, which are beneficial to the appearance of wobbling motion, including the simple, longitudinal and transverse modes. Moreover, possible multiple wobbling motions based on different high-$j$ configurations might coexist in one single nucleus, which provides a promising basis for future experiments to find wobbling bands in the $A\ensuremath{\approx}60$ mass region. Finally, taking the nucleus $^{62}\mathrm{Ni}$ as an example, the experimental energy spectra, the angular momentum components, and the azimuthal plots are investigated by the combination of the covariant density functional theory and quantum particle rotor model. The transverse wobbling mode is suggested in this nucleus.

Light-Tunable Charge Density Wave Orders in MoTe2 and WTe2 Single Layers

By using constrained density functional theory modeling, we demonstrate that ultrafast optical pumping unveils hidden charge orders in group VI monolayer transition metal ditellurides. We show that irradiation of the insulating 2H phases stabilizes multiple transient charge density wave orders with light-tunable distortion, periodicity, electronic structure and bandgap. Moreover, optical pumping of the semimetallic 1T' phases generates a transient charge ordered metallic phase composed of 2D diamond clusters. For each transient phase we identify the critical fluence at which it is observed and the specific optical and Raman fingerprints to directly compare with future ultrafast pump-probe experiments. Our work demonstrates that it is possible to stabilize charge density waves even in insulating 2D transition metal dichalcogenides by ultrafast irradiation.

Using C-DFT to develop an e-ReaxFF force field for acetophenone radical anion.

Increased electricity usage over the past several decades has accelerated the need for efficient high-voltage power transmission with reliable insulating materials. Cross-linked polyethylene (XLPE) prepared via dicumyl peroxide (DCP) cross-linking has emerged as the insulator of choice for modern power cables. Although DCP cross-linking generates the desired XLPE product in high yield, other by-products are also produced. One such by-product, acetophenone, is particularly intriguing due to its aromaticity and positive electron affinity. In this work, constrained density functional theory (C-DFT) was utilized to develop an e-ReaxFF force field suitable for describing the acetophenone radical anion. Initial parameters were taken from the 2021 Akbarian e-ReaxFF force field, which was developed to describe XLPE chemistry. Then, C-DFT geometry optimizations were performed wherein an excess electron was constrained to each atom of acetophenone. The resulting C-DFT energy values for the various electronic positions were added to the e-ReaxFF training set. Next, an analogous set of structures was energy-minimized using e-ReaxFF, and equilibrium mixture compositions for the two methods were compared at multiple temperatures. Iterative fitting against C-DFT energy data was performed until satisfactory agreement was achieved. To test force field performance, molecular dynamics simulations were performed in e-ReaxFF and the resulting electronic distributions were qualitatively compared to unconstrained-DFT spin density data. By expanding our e-ReaxFF force field for XLPE, namely, adding the capability to describe acetophenone and its interactions with an excess electron, we move one step closer to a comprehensive molecular understanding of XLPE chemistry in a high-voltage power cable.

Charge transfer excitations and constrained density functional theory

Charge transfer excitations and constrained density functional theory

Beyond Conformational Control: Effects of Noncovalent Interactions on Molecular Electronic Properties of Conjugated Polymers.

Tuning the electronic properties of polymers is of great importance in designing highly efficient organic solar cells. Noncovalent intramolecular interactions have been often used for conformational control to enhance the planarity of polymers or molecules, which may reduce band gaps and promote charge transfer. However, it is not known if noncovalent interactions may alter the electronic properties of conjugated polymers through some mechanism other than the conformational control. Here, we studied the effects of various noncovalent interactions, including sulfur–nitrogen, sulfur–oxygen, sulfur–fluorine, oxygen–nitrogen, oxygen–fluorine, and nitrogen–fluorine, on the electronic properties of polymers with planar geometry using unconstrained and constrained density functional theory. We found that the sulfur–nitrogen intramolecular interaction may reduce the band gaps of polymers and enhance the charge transfer more obviously than other noncovalent interactions. Our findings are also consistent with the experimental data. For the first time, our study shows that the sulfur–nitrogen noncovalent interaction may further affect the electronic structure of coplanar conjugated polymers, which cannot be only explained by the enhancement of molecular planarity. Our work suggests a new mechanism to manipulate the electronic properties of polymers to design high-performance small-molecule-polymer and all-polymer solar cells.

Lattice dynamics of photoexcited insulators from constrained density-functional perturbation theory

We present a constrained density functional perturbation theory scheme for the calculation of structural and harmonic vibrational properties of insulators in the presence of an excited and thermalized electron-hole plasma. The method is ideal to tame ultrafast light induced structural transitions in the regime where the photocarriers thermalize faster than the lattice, the electron-hole recombination time is longer than the phonon period and the photocarrier concentration is large enough to be approximated by an electron-hole plasma. The complete derivation presented here includes total energy, forces and stress tensor, variable cell structural optimization, harmonic vibrational properties and the electron-phonon interaction. We discuss in detail the case of zone center optical phonons not conserving the number of electrons and inducing a Fermi shift in the photo-electron and hole distributions. We validate our implementation by comparing with finite differences in Te and VSe2. By calculating the evolution of the phonon spectrum of Te, Si and GaAs as a function of the fluence of the incoming laser light, we demonstrate that even at low fluences, corresponding to approximately 0.1 photocarriers per cell, the phonon spectrum is substantially modified with respect to the ground state one with new Kohn anomalies appearing and a substantial softening of zone center optical phonons. Our implementation can be efficiently used to detect reversible transient phases and irreversible structural transition induced by ultrafast light absorption.

Accurate and Transferable Reactive Molecular Dynamics Models from Constrained Density Functional Theory.

Chemical reactions constitute the central feature of many liquid, material, and biomolecular processes. Conventional molecular dynamics (MD) is inadequate for simulating chemical reactions given the fixed bonding topology of most force fields, while modeling chemical reactions using ab initio molecular dynamics is limited to shorter time and length scales given its high computational cost. As such, the multiscale reactive molecular dynamics method provides one promising alternative for simulating complex chemical systems at atomistic detail on a reactive potential energy surface. However, the parametrization of such models is a key barrier to their applicability and success. In this work, we present reactive MD models derived from constrained density functional theory that are both accurate and transferable. We illustrate the features of these models for proton dissociation reactions of amino acids in both aqueous and protein environments. Specifically, we present models for ionizable glutamate and lysine that predict accurate absolute pKa values in water as well as their significantly shifted pKa in staphylococcal nuclease (SNase) without any modification of the models. As one outcome of the new methodology, the simulations show that the deprotonation of ionizable residues in SNase can be closely coupled with side chain rotations, which is a concept likely generalizable to many other proteins. Furthermore, the present approach is not limited to only pKa prediction but can enable the fully atomistic simulation of many other reactive systems along with a determination of the key aspects of the reaction mechanisms.

Molecular Dynamics Simulations of Bimolecular Electron Transfer: the Distance-Dependent Electronic Coupling.

Understanding the distance dependence of the parameters underpinning Marcus theory is imperative when interpreting the results of experiments on electron transfer (ET). Unfortunately, most of these parameters are difficult or impossible to access directly with experiments, necessitating the use of computer simulations to model them. In this work, we use molecular dynamics simulations in conjunction with constrained density functional theory calculations to study the distance dependence of the electronic coupling matrix element, |HRP|, for bimolecular ET. Contrary to what is typically assumed for such intermolecular reactions, we find that the magnitude of |HRP| does not decay exponentially with the center-of-mass separation of the reactants, rCOM. The addition of other simple measures of donor/acceptor (D/A) orientation did not improve the correlation of |HRP| with rCOM. Using the minimum distance separation, rmin, of the reactants as the structural descriptor allowed the system to be partitioned into high-coupling/close-contact and low-coupling/non-contact regimes, but large fluctuations of |HRP| were still found for the close-contact reactant pairs. Despite the persistent large fluctuations of |HRP|, its mean value was found to decay piecewise exponentially with increasing rmin, which was attributed to significant changes in the average D/A pair structure. The results herein advise one to use caution when interpreting the experimental results derived from spherical reactant models of bimolecular ET.

Using Constrained Density Functional Theory to Track Proton Transfers and to Sample Their Associated Free Energy Surface.

Ab initio molecular dynamics (AIMD) and quantum mechanics/molecular mechanics (QM/MM) methods are powerful tools for studying proton solvation, transfer, and transport processes in various environments. However, due to the high computational cost of such methods, achieving sufficient sampling of rare events involving excess proton motion—especially when Grotthuss proton shuttling is involved—usually requires enhanced free energy sampling methods to obtain informative results. Moreover, an appropriate collective variable (CV) that describes the effective position of the net positive charge defect associated with an excess proton is essential both for tracking the trajectory of the defect and for the free energy sampling of the processes associated with the resulting proton transfer and transport. In this work, such a CV is derived from first principles using constrained density functional theory (CDFT). This CV is applicable to a broad array of proton transport and transfer processes as studied via AIMD and QM/MM simulations.

Photoluminescence spectra of point defects in semiconductors: Validation of first-principles calculations

Optically and magnetically active point defects in semiconductors are interesting platforms for the development of solid-state quantum technologies. Their optical properties are usually probed by measuring photoluminescence spectra, which provide information on excitation energies and on the interaction of electrons with lattice vibrations. We present a combined computational and experimental study of photoluminescence spectra of defects in diamond and SiC, aimed at assessing the validity of theoretical and numerical approximations used in first principles calculations, including the use of the Franck-Condon principle and the displaced harmonic oscillator approximation. We focus on prototypical examples of solid-state qubits, the divacancy centers in SiC and the nitrogen-vacancy in diamond, and we report computed photoluminescence spectra as a function of temperature that are in very good agreement with the measured ones. As expected we find that the use of hybrid functionals leads to more accurate results than semilocal functionals. Interestingly our calculations show that constrained density functional theory (CDFT) and time-dependent hybrid DFT perform equally well in describing the excited state potential energy surface of triplet states; our findings indicate that CDFT, a relatively cheap computational approach, is sufficiently accurate for the calculations of photoluminescence spectra of the defects studied here. Finally, we find that only by correcting for finite-size effects and extrapolating to the dilute limit, one can obtain a good agreement between theory and experiment. Our results provide a detailed validation protocol of first principles calculations of photoluminescence spectra, necessary both for the interpretation of experiments and for robust predictions of the electronic properties of point defects in semiconductors.

QCBED-DFT: experimentally constrained density functional theory

QCBED-DFT: experimentally constrained density functional theory

Evaluation of optical band gaps and dopant state energies in transition metal oxides using oxidation-state constrained density functional theory

We report the use of oxidation-state constrained density functional theory (OS-CDFT) to calculate the optical band gaps of transition metal oxides and dopant state energies of different doped anatase. OS-CDFT was used to control electron transfer from the valence band maximum of the transition metal system to the conduction band minimum or to the dopant state in order to calculate the band gap or the dopant state energies respectively. The calculation of the dopant state energies also allows identification of the transition responsible for the reduced band gap of the doped system in ambiguous cases. We applied this approach to the band gap calculation in TiO2 anatase and rutile, vanadium pentoxide (V2O5), chromium(III) oxide (Cr2O3), manganese(IV) oxide (MnO2), ferric oxide (Fe2O3), ferrous oxide (FeO) and cobalt(II) oxide (CoO). The dopant state energies calculations were carried out in the V-, Cr-, Mn-, and Fe-doped anatase.

Sensitivity of Intra- and Intermolecular Interactions of Benzo[h]quinoline from Car-Parrinello Molecular Dynamics and Electronic Structure Inspection.

The O-H...N and O-H...O hydrogen bonds were investigated in 10-hydroxybenzo[h]quinoline (HBQ) and benzo[h]quinoline-2-methylresorcinol complex in vacuo, solvent and crystalline phases. The chosen systems contain analogous donor and acceptor moieties but differently coupled (intra- versus intermolecularly). Car–Parrinello molecular dynamics (CPMD) was employed to shed light onto principle components of interactions responsible for the self-assembly. It was applied to study the dynamics of the hydrogen bonds and vibrational features as well as to provide initial geometries for incorporation of quantum effects and electronic structure studies. The vibrational features were revealed using Fourier transformation of the autocorrelation function of atomic velocity and by inclusion of nuclear quantum effects on the O-H stretching solving vibrational Schrödinger equation a posteriori. The potential of mean force (Pmf) was computed for the whole trajectory to derive the probability density distribution and for the O-H stretching mode from the proton vibrational eigenfunctions and eigenvalues incorporating statistical sampling and nuclear quantum effects. The electronic structure changes of the benzo[h]quinoline-2-methylresorcinol dimer and trimers were studied based on Constrained Density Functional Theory (CDFT) whereas the Electron Localization Function (ELF) method was applied for all systems. It was found that the bridged proton is localized on the donor side in both investigated systems in vacuo. The crystalline phase simulations indicated bridged proton-sharing and transfer events in HBQ. These effects are even more pronounced when nuclear quantization is taken into account, and the quantized Pmf allows the proton to sample the acceptor area more efficiently. The CDFT indicated the charge depletion at the bridged proton for the analyzed dimer and trimers in solvent. The ELF analysis showed the presence of the isolated proton (a signature of the strongest hydrogen bonds) only in some parts of the HBQ crystal simulation. The collected data underline the importance of the intramolecular coupling between the donor and acceptor moieties.

Efficient Free-energy Calculation of Proton Transfer by Constrained Density Functional Theory and Geometrically Restrained Molecular Dynamics Simulation

Recently, we proposed an MD simulation scheme for free-energy calculations of proton transfers that employs the constrained DFT method and the energy-gap coordinate. The present paper proposes to streamline the free-energy calculations by using adiabatic MD trajectories and umbrella sampling with geometric coordinates. The calculated free-energy profile reproduces the more accurate results by the free-energy perturbation.

Molecular Modes of Attosecond Charge Migration.

First-principles calculations are employed to elucidate the modes of attosecond charge migration (CM) in halogenated hydrocarbon chains. We use constrained density functional theory (DFT) to emulate the creation of a localized hole on the halogen and follow the subsequent dynamics via time-dependent DFT. We find low-frequency CM modes (∼1 eV) that propagate across the molecule and study their dependence on length, bond order, and halogenation. We observe that the CM speed (∼4 Å/fs) is largely independent of molecule length, but is lower for triple-bonded versus double-bonded molecules. Additionally, as the halogen mass increases, the hole travels in a more particlelike manner as it moves across the molecule. These heuristics will be useful in identifying molecules and optimal CM detection methods for future experiments, especially for halogenated hydrocarbons which are promising targets for ionization-triggered CM.

Fast, reversible mechanochromism of regioisomeric oxazine mechanophores: Developing in situ responsive force probes for polymeric materials

Summary To address hysteretic or irreversible mechanochromism found in most bond-scission-based mechanophores, we developed a new family of mechanophores based on the oxazine (OX) structural motif. Three OX regioisomers differing in their point of attachment to the indole ring show variable mechanochromic mechanoresponsiveness in a polydimethylsiloxane (PDMS) matrix. Constrained DFT simulations correlate the experimental findings to molecular scale events; two of the three regioisomers exhibit a force-activated rearrangement, while the third one is mechanochemically inactive. Most significantly, when compared with the spiropyran (SP) and the naphthopyran (NP), the OX mechanophores exhibit faster and reversible mechanochromism without any sign of fatigue. Such a rapid response to mechanical loads is rationalized by the difference between SP and OX scaffolds, given that the SP ring opening is accompanied by a trans-cis isomerization step. These fast-responsive mechanophores are anticipated to bring deeper understanding to a broad range of soft materials by in situ monitoring the local mechanics.

Drastic Modification of Lattice Thermal Conductivity in Thermoelectrics Induced by Electron–Hole Pairs

Low lattice thermal conductivity (κL) is desirable for advancing thermoelectric (TE) materials and devices. However, κL depends on many factors such as phonon scattering sources, electron-phonon interactions, etc. It remains not fully understood how κL is influenced by excited electron-hole (e-h) pairs ubiquitously present in thermoelectrics. To address this issue, the constrained density functional theory (CDFT) simulations are performed to investigate the phonon transport properties of two typical TE materials, Mg2Si and PbTe. Surprisingly, at high e-h concentrations of ∼1021 cm-3, the κL of Mg2Si is reduced significantly by ∼30% due to the softening phonon modes. In contrast, the κL of PbTe first decreases by ∼18% at a relatively low e-h concentration of 2.34 × 1020 cm-3, but it is enhanced by ∼3.4% as the carrier concentration increases to 7.02 × 1020 cm-3. The different behaviors of these two materials arise from the different distributions of excess electrons and holes under e-h excitation. The simulation results suggest that controlling e-h pairs may offer a promising approach to design high-performance TE devices.

Revealing Charge-Transfer Dynamics at Electrified Sulfur Cathodes Using Constrained Density Functional Theory.

To understand and control the behavior of electrochemical systems, including batteries and electrocatalysts, we seek molecular-level details of the charge transfer mechanisms at electrified interfaces. Recognizing some key limitations of standard equilibrium electronic structure methods to model materials and their interfaces, we propose applying charge constraints to effectively separate electronic and nuclear degrees of freedom, which are especially beneficial to the study of conversion electrodes, where electronic charge carriers are converted to much slower polarons within a material that is nonmetallic. We demonstrate the need for such an approach within the context of sulfur cathodes and the arrival of Li ions during discharge of a Li-S cell. The requirement that electronic degrees of freedom are arrested is justified by comparison with real-time evolution of the electronic structure. Long-lived metastable configurations provide plenty of time for nuclear dynamics and relaxation in response to the electrification of the interface, a process that would be completely missed without applying charge constraints. This approach will be vital to the study of dynamics at electrified interfaces which may be created deliberately, adding charge to the electrode, or spontaneously, due to finite temperature dynamics in the electrolyte.