Constrained Density Functional Theory Research Articles

Nonadiabatic couplings from a variational excited state method based on constrained DFT.

Excited Costrained Density Functional Theory (XCDFT) [Ramos and Pavanello, J. Chem. Phys. 148, 144103 (2018)] is a variational excited state method that extends ground state DFT to the computation of low-lying excited states. It borrows much of the machinery of Constrained DFT (CDFT) with a crucial difference: the constraint imposes a population of one electron in the Hilbert space spanned by the virtuals of a reference ground state. In this work, we present theory and implementation for evaluating nonadiabatic coupling vectors (NACVs) between the first excited state computed with XCDFT and the ground state. Our NACVs are computed analytically using density functional perturbation theory with a formalism that is general enough that could be applied to CDFT diabatic states. We showcase the new method with pilot NACV calculations for the conical intersection in H3, the avoided crossing in selenoacrolein, and the NACV magnitudes in azobenzene. Despite complications from the nonorthogonality of the wavefunctions, XCDFT's energy surfaces and NACVs reproduce benchmark values and respect known sum rules within a reasonable degree. This shows that XCDFT is a viable method for nonadiabatic dynamics simulations.

Constrained density functional theory plus the Hubbard U correction approach for the electronic polaron mobility: A case study of TiO2

The formation and migration of polarons have important influences on physical and chemical properties of transition metal oxides. Density functional theory plus the Hubbard U correction (DFT+U) and constrained density functional theory (cDFT) are often used to obtain the transfer properties for small polarons. In this work we have implemented the cDFT plus the Hubbard U correction method in the projector augmented wave (PAW) framework, and applied it to study polaron transfer in the bulk phases of TiO2. We have confirmed that the parameter U can have significant impact on theoretical prediction of polaronic properties. It was found that using the Hubbard U calculated by the cDFT method with the same orbital projection as used in DFT+U, one can obtain theoretical prediction of polaronic properties of rutile and anatase phases of TiO2 in good agreement with experiment. This work indicates that the cDFT+U method with consistently evaluated U is a promising first-principles approach to polaronic properties of transition metal oxides without empirical input.

Synthesis and Photoluminescence Properties of Rare-Earth-Activated Sr3-xAxAlO4H (A = Ca, Ba; x = 0, 1): New Members of Aluminate Oxyhydrides.

A series of aluminate-based oxyhydrides, Sr3-xAxAlO4H (A = Ca, Ba; x = 0, 1), has been synthesized by high-temperature reaction of oxide and hydride precursors under a H2 atmosphere. Their crystal structures determined via X-ray and neutron powder diffraction are isostructural with tetragonal Sr3AlO4F (space group I4/mcm), consisting of (Sr1-x/3Ax/3)2H layers and isolated AlO4 tetrahedra. Rietveld refinement based on the diffraction patterns and bond-valence-sum analysis show that Ba preferentially occupies the 10-coordinated Sr1 sites, while Ca strongly prefers to occupy the 8-coordinated Sr2 sites. Luminescence owing to the 4f-5d transition of Eu2+ or Ce3+ was observed from Eu- and Ce-doped samples, Sr3-x-yAxByAlO4H (A = Ca, Ba; B = Eu, Ce; x = 0, 1, y = 0.02), under excitation of near-ultraviolet light. Compared with its fluoride analogue, Sr3AlO4H:Ce3+ shows red shifts of both the excitation and emission bands, which is consistent with the reported hydride-based phosphors and can be explained by the covalency of the hydride ligands. The observed luminescence spectra can be decomposed into two sets of sub-bands corresponding to Ce3+ centers occupying Sr1 and Sr2 sites with distinctly different Stokes shifts (1.27 and 0.54 eV, respectively), as suggested by the results of constrained density functional theory (cDFT). The cDFT results also suggest that the large shift for Ce3+ at Sr1 is induced by large distortion of the coordinated structure with shortening of the H-Ce bond in the excited state. The current findings expand the class of oxyhydride materials and show the potential of hydride-based phosphors for optical applications.

Facet Dependence of Photocatalytic Activity in Anatase TiO2: Combined Experimental and DFT Study

Abstract For enhancing the photocatalytic performance of anatase TiO2, proper control of the reactive facets and its molecular-level understanding are crucial. This experimental and theoretical study clarifies the facet dependence of the photocatalytic reaction at the anatase TiO2 surface. The 〈112〉-oriented anatase TiO2 layer is deposited on a Ru(0001) substrate at 360 °C by low-pressure chemical vapor deposition. The deposition rate is three times higher than that of the multi-orientation layer on the Pyrex glass. The photocatalytic activity induced by ultraviolet (UV) irradiation around 365 nm in methylene blue aqueous solutions is significantly high, and the rate constant is 6.1 × 10−1 min−1, which is two orders of magnitude greater than that on the multi-orientation TiO2. The density functional theory (DFT) calculations using the constrained DFT method and the hybrid functionals show that the (112) surface stabilizes the adsorbed water molecule most strongly. The photogenerated hole is stably trapped not at the bare surface but at the hydroxylated surface, especially at the hydroxyl group of the hydroxylated (112) and (001) surfaces. The experimental and theoretical findings consistently indicate the high photocatalytic activity at the anatase TiO2(112) surface.

Photochemical Ring Opening of Oxirane Modeled by Constrained Density Functional Theory.

A constrained density functional theory/classical trajectory surface hopping study of the photochemical dissociation of oxirane (CH2)2O is presented. The calculations confirm the Gomer–Noyes mechanism for the initial reaction and agree largely with experimental photolysis data including reaction yields. The calculated yields, however, depend both on temperature and its modeling. The timescales of the various reaction steps are well below 100 fs, similar to previous time-dependent density functional calculations. At variance with those, however, the present calculations obey Kasha’s rule, i.e., the photoreaction is initiated in the energetically lowest excited state.

Hole Transfer in Open Carbynes.

We investigate hole transfer in open carbynes, i.e., carbon atomic nanowires, using Real-Time Time-Dependent Density Functional Theory (RT-TDDFT). The nanowire is made of N carbon atoms. We use the functional B3LYP and the basis sets 3-21G, 6-31G*, cc-pVDZ, cc-pVTZ, cc-pVQZ. We also utilize a few Tight-Binding (TB) wire models, a very simple model with all sites equivalent and transfer integrals given by the Harrison expression (TBI) as well as a model with modified initial and final sites (TBImod) to take into account the presence of one or two or three hydrogen atoms at the edge sites. To achieve similar site occupations in cumulenes with those obtained by converged RT-TDDFT, TBImod is sufficient. However, to achieve similar frequency content of charge and dipole moment oscillations and similar coherent transfer rates, the TBImod transfer integrals have to be multiplied by a factor of four (TBImodt4times). An explanation for this is given. Full geometry optimization at the B3LYP/6-31G* level of theory shows that in cumulenes bond length alternation (BLA) is not strictly zero and is not constant, although it is symmetrical relative to the molecule center. BLA in cumulenic cases is much smaller than in polyynic cases, so, although not strictly, the separation to cumulenes and polyynes, approximately, holds. Vibrational analysis confirms that for N even all cumulenes with coplanar methylene end groups are stable, for N odd all cumulenes with perpendicular methylene end groups are stable, and the number of hydrogen atoms at the end groups is clearly seen in all cumulenic and polyynic cases. We calculate and discuss the Density Functional Theory (DFT) ground state energy of neutral molecules, the CDFT (Constrained DFT) “ground state energy” of molecules with a hole at one end group, energy spectra, density of states, energy gap, charge and dipole moment oscillations, mean over time probabilities to find the hole at each site, coherent transfer rates, and frequency content, in general. We also compare RT-TDDFT with TB results.

Exploring the effects of axial halogen substitutions of subphthalocyanine on the charge transfer nature in subPC/C60 solar cells

Boron subphthalocyanine chloride (Cl-subPC) and its derivatives have been extensively studied due to their unique structures and attractive optical performance in organic solar cells (OSCs). However, how axial halogen substitutions of Cl-subPC influence the delicate interfacial charge transfer (CT) is still an open question. In this work, by utilizing long range corrected and constrained density functional theory with polarizable continuum model, we have modelled X-subPC/C60 (X = F, Cl, Br) bi-molecular systems and studied the effect of axial halogen substitutions on CT and charge recombination (CR) rate constants (kCTs and kCRs) with Marcus theory. Fractional transfer charges and the effects of surrounding environment are obtained with high accuracy. The results indicate that cold and hot CTs play different roles to determine exciton dissociations, and the maximum kCTs in U configurations (C60 in the concave of subPC) are much larger than those in B configurations (C60 on the convex of subPC) due to better hybridizations between local excitation and CT states. Furthermore, the order of maximum kCTs in U/B configurations is Cl > F > Br / F > Br > Cl, respectively. Finally, the calculated lifetime (2.32 ps) of excitons in Cl-subPC/C60 B configurations matches with experiment (10 ps), and the much shorter lifetime of exciton in Cl-subPC/C60 U configuration implies that this molecular arrangement may not be dominant at the interface. The theoretical study here gives a deep insight about how halogen substitutions influence the CT nature in X-subPC/C60 OSCs.

Multiple chiral bands in $$^{137}$$Nd

Two new bands have been identified in \(^{137}\)Nd from a high-statistics JUROGAM II gamma-ray spectroscopy experiment. Constrained density functional theory and particle rotor model calculations are used to assign configurations and investigate the band properties, which are well described and understood. It is demonstrated that these two new bands can be interpreted as chiral partners of previously known three-quasiparticle positive- and negative-parity bands. The newly observed chiral doublet bands in \(^{137}\)Nd represent an important support to the existence of multiple chiral bands in nuclei. The present results constitute the missing stone in the series of Nd nuclei showing multiple chiral bands, which becomes the most extended sequence of odd–even and even-even nuclei presenting multiple chiral bands in the Segré chart.

Longitudinal spin fluctuations in bcc and liquid Fe at high temperature and pressure calculated with a supercell approach

Investigation of magnetic materials at realistic conditions with first-principles methods is a challenging task due to the interplay of vibrational and magnetic degrees of freedom. The most difficult contribution to include in simulations is represented by the longitudinal magnetic degrees of freedom (LSF) due to their inherent many-body nature; nonetheless, schemes that enable to take into account this effect on a semiclassical level have been proposed and employed in the investigation of magnetic systems. However, assessment of the effect of vibrations on LSF is lacking in the literature. For this reason, in this work we develop a supercell approach within the framework of constrained density functional theory to calculate self-consistently the size of local-environment-dependent magnetic moments in the paramagnetic, high-temperature state in presence of lattice vibrations and for liquid Fe in different conditions. First, we consider the case of bcc Fe at the Curie temperature and ambient pressure. Then, we perform a similar analysis on bcc Fe at Earth's inner core conditions, and we find that LSF stabilize non-zero moments which affect atomic forces and electronic density of states of the system. Finally, we employ the present scheme on liquid Fe at the melting point at ambient pressure, and at Earth's outer core conditions ($p \approx 200$ GPa, $T \approx 6000$ K). In both cases, we obtain local magnetic moments of sizes comparable to the solid-state counterparts.

Incorporating Electronic Information into Machine Learning Potential Energy Surfaces via Approaching the Ground-State Electronic Energy as a Function of Atom-Based Electronic Populations

Machine learning (ML) approximations to density functional theory (DFT) potential energy surfaces (PESs) are showing great promise for reducing the computational cost of accurate molecular simulations, but at present, they are not applicable to varying electronic states, and in particular, they are not well suited for molecular systems in which the local electronic structure is sensitive to the medium to long-range electronic environment. With this issue as the focal point, we present a new machine learning approach called "BpopNN" for obtaining efficient approximations to DFT PESs. Conceptually, the methodology is based on approaching the true DFT energy as a function of electron populations on atoms; in practice, this is realized with available density functionals and constrained DFT (CDFT). The new approach creates approximations to this function with neural networks. These approximations thereby incorporate electronic information naturally into a ML approach, and optimizing the model energy with respect to populations allows the electronic terms to self-consistently adapt to the environment, as in DFT. We confirm the effectiveness of this approach with a variety of calculations on LinHn clusters.

PyCDFT: A Python package for constrained density functional theory.

We present PyCDFT, a Python package to compute diabatic states using constrained density functional theory (CDFT). PyCDFT provides an object-oriented, customizable implementation of CDFT, and allows for both single-point self-consistent-field calculations and geometry optimizations. PyCDFT is designed to interface with existing density functional theory (DFT) codes to perform CDFT calculations where constraint potentials are added to the Kohn-Sham Hamiltonian. Here, we demonstrate the use of PyCDFT by performing calculations with a massively parallel first-principles molecular dynamics code, Qbox, and we benchmark its accuracy by computing the electronic coupling between diabatic states for a set of organic molecules. We show that PyCDFT yields results in agreement with existing implementations and is a robust and flexible package for performing CDFT calculations. The program is available at https://dx.doi.org/10.5281/zenodo.3821097.

Computational Analysis of Electron Transfer Kinetics for CO2 Reduction with Organic Photoredox Catalysts.

We present a fundamental description of the electron transfer (ET) step from substituted oligo(p-phenylene) (OPP) radical anions to CO2, with the larger goal of assessing the viability of underexplored, organic photoredox routes for utilization of anthropogenic CO2. This work varies the electrophilicity of para-substituents to OPP and probes the dependence of rate coefficients and interfragment interactions on the substituent Hammett parameter, σp, using constrained density functional theory (CDFT) and energy decomposition analysis (EDA). Large electronic couplings across substituents indicates an adiabatic electron transfer process for reactants at contact. As one might intuitively expect, free energy changes dominate trends in ET rate coefficients in most cases, and rates increase with substituent electron-donating ability. However, we observe an unexpected dip in rate coefficients for the most electron-donating groups, due to the combined impact of flattening free energies and a steep increase in reorganization energies. Our analysis shows that, with decreasing σp, flattening OPP LUMO levels lower the marginal increase in free energy. EDA reveals trends in electrostatics and charge transfer interactions between the catalyst and substrate fragments that influence free energy changes across substituents. Reorganization energies do not exhibit a direct dependence on σp and are largely similar across systems, with the exception of substituents containing lone pairs of electrons that exhibit significant deformation upon electron transfer. Our study therefore suggests that while a wide range of ET rates are observed, there is an upper limit to rate enhancements achievable by only tuning the substituent electrophilicity.

Neutral excitation density-functional theory: an efficient and variational first-principles method for simulating neutral excitations in molecules

We introduce neutral excitation density-functional theory (XDFT), a computationally light, generally applicable, first-principles technique for calculating neutral electronic excitations. The concept is to generalise constrained density functional theory to free it from any assumptions about the spatial confinement of electrons and holes, but to maintain all the advantages of a variational method. The task of calculating the lowest excited state of a given symmetry is thereby simplified to one of performing a simple, low-cost sequence of coupled DFT calculations. We demonstrate the efficacy of the method by calculating the lowest single-particle singlet and triplet excitation energies in the well-known Thiel molecular test set, with results which are in good agreement with linear-response time-dependent density functional theory (LR-TDDFT). Furthermore, we show that XDFT can successfully capture two-electron excitations, in principle, offering a flexible approach to target specific effects beyond state-of-the-art adiabatic-kernel LR-TDDFT. Overall the method makes optical gaps and electron-hole binding energies readily accessible at a computational cost and scaling comparable to that of standard density functional theory. Owing to its multiple qualities beneficial to high-throughput studies where the optical gap is of particular interest; namely broad applicability, low computational demand, and ease of implementation and automation, XDFT presents as a viable candidate for research within materials discovery and informatics frameworks.

Electron correlation effects and magneto-optical properties of yttrium iron garnet

The electronic structure, magnetic, optical and magneto-optical properties of yttrium iron garnet (YIG) were investigated by using first-principles calculations with Hubbard energy correction for the treatment of the strong electron correlation. The effective on-site Coulomb interaction parameters Ueff for YIG were determined from the constrained density functional theory within a linear response theory. Our results find a hybridization between the O-2p and Fe-3d orbitals. We also observe the crucial role of the electron correlation of the Fe-3d orbitals according to the magneto-optical properties of YIG.

Constrained dipole moment density functional theory for charge distributions in force fields for the study of molecular fluids

A new procedure, based on electronic structure calculations that only requires a dipole moment value for a given molecule as input and, from which the charges for all the atoms in it are uniquely determined, is developed and applied to the study of molecular fluids with classical dynamics. The dipole moment value considered for the isolated molecule is the one that reproduces the dielectric constant of its corresponding fluid. Following previous work, the Lennard-Jones parameters are determined to reproduce the liquid density and the surface tension at the liquid-vapor interface. The force field thus obtained leads to a reasonable description of several properties such as heats of vaporization, self-diffusion coefficients, shear viscosities, isothermal compressibilities, and volumetric expansion coefficients of pure substances.

Capturing multireference excited states by constrained-density-functional theory

The computation of excited electronic states with commonly employed (approximate) methods is challenging, typically yielding states of lower quality than the corresponding ground state for a higher computational cost. In this work, we present a mean field method that extends the previously proposed eXcited Constrained DFT (XCDFT) from single Slater determinants to ensemble 1-RDMs for computing low-lying excited states. The method still retains an associated computational complexity comparable to a semilocal DFT calculation while at the same time is capable of approaching states with multireference character. We benchmark the quality of this method on well-established test sets, finding good descriptions of the electronic structure of multireference states and maintaining an overall accuracy for the predicted excitation energies comparable to semilocal TDDFT.

Formation of Defects in Two-Dimensional MoS2 in the Transmission Electron Microscope at Electron Energies below the Knock-on Threshold: The Role of Electronic Excitations.

Production of defects under electron irradiation in a transmission electron microscope (TEM) due to inelastic effects has been reported for various materials, but the microscopic mechanism of damage development in periodic solids through this channel is not fully understood. We employ non-adiabatic Ehrenfest, along with constrained density functional theory molecular dynamics, and simulate defect production in two-dimensional MoS2 under electron beam. We show that when excitations are present in the electronic system, formation of vacancies through ballistic energy transfer is possible at electron energies which are much lower than the knock-on threshold for the ground state. We further carry out TEM experiments on single layers of MoS2 at electron voltages in the range of 20-80 kV and demonstrate that indeed there is an additional channel for defect production. The mechanism involving a combination of the knock-on damage and electronic excitations we propose is relevant to other bulk and nanostructured semiconducting materials.

Constrained nuclear-electronic orbital density functional theory: Energy surfaces with nuclear quantum effects

The nuclear-electronic orbital (NEO) framework enables the incorporation of nuclear quantum effects by treating both electrons and specific key nuclei quantum-mechanically. The conventional NEO method predicates on the controversial Born-Oppenheimer separation between classical and quantum nuclei, and its potential energy surface only depends on the coordinates of classical nuclei. In this paper, based on the fact that quantum nuclei are relatively localized, we develop the constrained nuclear-electronic orbital density functional theory (cNEO-DFT) by imposing a constraint on the expectation value of the quantum nuclear position. In this way, an extended NEO energy surface is obtained, which also depends on the quantum nuclear position. Compared to the potential energy surface obtained from conventional DFT, the extended NEO energy surface incorporates the nuclear quantum effects, which have notable impacts on the energy profile. Furthermore, cNEO-DFT can facilitate the location of NEO stationary states. It potentially can be used in geometry optimization, transition states search, and the calculation of reaction dynamics.

First principles density functional+U pseudopotential study on the electronic structure of layered perovskite LaSr3Fe3O10

The electronic, magnetic and crystal structures of layered perovskite oxide LaSr3Fe3O10 (LSFO) in the Ruddlesden-Popper structure were studied from first principles using the density functional theory (DFT)+U pseudopotential (PP) method and a self-consistent constrained DFT technique (Hamada and Ohno 2019 J. Phys.: Condens. Matter 31 065501). Using this technique, the magnetic structure of LSFO was determined to be antiferromagnetic and an effective Hubbard on-site interaction parameter for Fe 3d electrons, Ueff(Fe3d) = 6.08 eV was identified for LSFO. The DFT+U PP calculations of LSFO models using this Ueff(Fe3d) value reproduced the experimentally observed metallic characteristics and crystal structure of LSFO, demonstrating the correct determination of the Ueff(Fe3d) value of the large and complex LSFO material. The first-principles DFT+U calculation of large and complex strongly-correlated systems was enabled using the self-consistent constrained DFT technique.

Silver clusters tune up electronic properties of graphene nanoflakes: A comprehensive theoretical study

Graphene-silver composites show a synergic effect of both components with enhanced electronic, adsorption and catalytic properties. We present here the detailed theoretical study on geometric, thermodynamic and electronic properties of silver clusters Agn (n = 2–10) adsorbed on graphene nanoflakes as a model for silver-graphene composites. First, a benchmark study is performed on Agn…coronene complexes (n = 2, 4) by evaluating various functional against reported high level ab-initio method for the selection of best functional for further calculations. Then, density functional theory study at the best chosen level is performed to inquire how clustering of adsorbate attached with carbon surface can impact geometric, electronic and thermodynamic properties of silver-graphene composites. Furthermore, the interaction energies are corrected for dispersion and basis set superposition error in order to get more realistic estimate of interaction energies. In progression, we investigated the dependence of interaction energy upon cluster size and dimensionality. For Agn…coronene, the binding energies increase monotonically as the number of atoms in the cluster increases. However, for Agn…dodecabenzocoronene, the interaction energies show a sudden drop at Ag7…dodecabenzocoronene. The difference in behavior between Agn…dodecabenzocoronene and Agn…coronene for interaction energy is attributed to edge effect present in coronene. Furthermore, coplanar orientations of the silver clusters on polyaromatic hydrocarbons have higher interaction energies. The 2D-3D transition of the silver cluster is observed for Ag7…coronene. CDA analysis reveals that backdonation from dodecabenzocoronene to silver clusters is more dominant in Ag4–Ag7 whereas other clusters have dominant charge transfer to dodecabenzocoronene. Charge transfer analysis via constrained density functional theory (CDFT) reveals significant energy lowering from charge donor-acceptor interactions. Further energy decomposition analysis (EDA) using absolutely-localized molecular orbitals (ALMO) suggests that, while charge-transfer is important in these systems, the sum of electrostatics, Pauli repulsion, and London dispersion are far more significant as silver cluster size increases. NCI results also support the presence of van der Waals and electrostatic interactions. The hollow top is most favorite interaction sites compared to bridge top and head top binding sites over coronene lattice. The ionization potential, electron affinity, frontier molecular orbital analysis, chemical hardness, softness, chemical potential, and Fermi levels are deliberated to verify the stability and reactivity of most stable silver-graphene composites. The remarkable outcome of the current findings makes our silver-graphene composite as a potential applicant for high performance electronic and catalytic devices.