Density Functional Theory Approximation Research Articles

Ensemble Ground State of a Many-Electron System with Fractional Electron Number and Spin: Piecewise-Linearity and Flat-Plane Condition Generalized.

Description of many-electron systems with a fractional electron number (Ntot) and fractional spin (Mtot) is of great importance in physical chemistry, solid-state physics, and materials science. In this Letter, we provide an exact description of the zero-temperature ensemble ground state of a general, finite, many-electron system and characterize the dependence of the energy and the spin-densities on both Ntot and Mtot, when the total spin is at its equilibrium value. We generalize the piecewise-linearity principle and the flat-plane condition and determine which pure states contribute to the ground-state ensemble. We find a new derivative discontinuity, which manifests for spin variation at a constant Ntot, as a jump in the Kohn-Sham potential. We identify a previously unknown degeneracy of the ground state, such that the total energy and density are unique, but the spin-densities are not. Our findings serve as a basis for development of advanced approximations in density functional theory and other many-electron methods.

First-principles calculations to investigate structural, electronic, and elastic properties of Fe3SnC ternary alloy

In this paper, the structural, electronic, and elastic properties of Fe3SnC were calculated based on local density approximation (LDA) and generalized gradient approximation (GGA) in density functional theory (DFT). Compared with GGA, LDA underestimates lattice constants and overestimates binding energy and elastic constants. The calculated lattice constants are 3.76 Å (LDA) and 3.83 Å (GGA), respectively, and the latter is closer to the experimental values. With U correction in GGA and LDA, the magnetic properties of the system are shown in the band structure. The GGA calculation results are more accurate, and the calculated magnetic moment of Fe3SnC is 5.74μB. The band structure indicates that Fe3SnC is a metallic compound. The elastic constants show that Fe3SnC has a large elastic constant and bulk modulus, in which the C11 calculated by GGA is as high as 463.81GPa, and the Young's modulus is as high as 350.72GPa. This indicates that Fe3SnC is a potential cermet due to a strong deformation resistance. At the same time, with the minimum thermal conductivity of 1.65 W/mK calculated by the Cahill model.

AFLOW-CCE for the thermodynamics of ionic materials.

Accurate thermodynamic stability predictions enable data-driven computational materials design. Standard density functional theory (DFT) approximations have limited accuracy with average errors of a few hundred meV/atom for ionic materials, such as oxides and nitrides. Thus, insightful correction schemes as given by the coordination corrected enthalpies (CCE) method, based on an intuitive parametrization of DFT errors with respect to coordination numbers and cation oxidation states, present a simple, yet accurate solution to enable materials stability assessments. Here, we illustrate the computational capabilities of our AFLOW-CCE software by utilizing our previous results for oxides and introducing new results for nitrides. The implementation reduces the deviations between theory and experiment to the order of the room temperature thermal energy scale, i.e., ∼25 meV/atom. The automated corrections for both materials classes are freely available within the AFLOW ecosystem via the AFLOW-CCE module, requiring only structural inputs.

First-Principles Anharmonic Infrared and Raman Vibrational Spectra of Materials: Fermi Resonance in Dry Ice.

We introduce a computational tool for the quantum-mechanical simulation of anharmonic infrared and Raman vibrational spectra of materials. The approach, implemented in the CRYSTAL software, stems from Taylor's expansion of the potential energy surface (PES) on the basis of normal modes up to cubic and quartic terms. The PES can be sampled with four different numerical schemes at the level of density functional theory (DFT), with local, generalized-gradient, and hybrid density functional approximations. Anharmonic states are obtained by solving Shrödinger's nuclear equation with either the vibrational self-consistent field (VSCF) or vibrational configuration interaction (VCI) methods. Nuclear quantum effects (NQEs) are thus fully accounted for. Infrared intensities are computed numerically through a Berry phase approach or analytically through a coupled-perturbed (CP) approach. Raman intensities are computed analytically via the CP approach. A variety of anharmonic features of vibrational spectra of materials can be simulated, including band shifts, combination bands, overtones, resonances (first-order Fermi, second-order Darling-Dennison), and hot bands. We showcase the effectiveness of the approach on the description of a first-order Fermi resonance (FR) in CO2 dry ice: a challenging test-case given that the FR occurs in the Raman spectrum, requires NQEs, and involves two- and three-mode couplings. Fundamental mechanistic differences with respect to the well-known FR in molecular CO2 are addressed. This application represents the first quantum-mechanical, periodic description of FR in dry ice.

Bond length alternation of π-conjugated polymers predicted by the Fermi-Löwdin orbital self-interaction correction method.

π-conjugated polymers have been used in a wide range of practical applications, partly due to their unique properties that originate in the delocalization of electrons through the polymer backbone. The level of delocalization can be characterized by the induced bond length alternation (BLA), with shorter BLA connected with strong delocalization and vice versa. The accurate description of this structural parameter can be considered a benchmark for testing the capability of different electronic structure methods for self-interaction error (SIE) removal and electron correlation inclusion. Density functional theory (DFT), in its local or semi-local flavors, suffers from SIE and, thus, underestimates the BLA compared to self-interaction-free methods. In this work, we utilize the Fermi-Löwdin orbital self-interaction correction (FLOSIC) method for one-electron self-interaction removal to characterize the BLA of five oligomers with increasing length extrapolated to the polymeric limit. We compare the self-interaction-free BLA to several DFT approximations, Møller-Plesset second-order perturbation theory (MP2), and the BLA obtained with the domain based local pair natural orbital CCSD(T) [DLPNO-CCSD(T)] approximation. Our findings show that FLOSIC corrects for the small BLA given by (semi-)local DFT approximations, but it tends to overcorrect with respect to CAM-B3LYP, MP2, and DLPNO-CCSD(T).

Effect of Cu doping on the electronic structure, magnetic and optical properties of GaN/ZnS heterojunctions: a first-principles study

In this paper, the generalized gradient approximation method in density functional theory is adopted to calculate the GaN/ZnS heterojunction system with coexistence of Cu doping and point defects. The electronic structure, magnetic coupling mechanism and optical properties of each system are analyzed. It is shown by the research results that broader band gap width tuning (0.26–2.92 eV) can be achieved in the interface region of the Cu-doped GaN/ZnS heterojunction system. The magnetic sources of the system have two aspects, on the one hand, unpaired electrons are induced by cation vacancies to undergo spin polarization, thereby magnetic moments are contributed to the system, on the other hand, The GaN/ZnS heterojunction is induced by Cu doping to generate bound magnetic polarons, causing a magnetic phase transition in the system, and the total magnetic moment of the system is restricted by the concentration of bound magnetic polarons. In terms of optical properties, deep energy levels are introduced and hole-electron recombination centers are formed in the Cu-doped heterojunction system containing Ga vacancies. Compared with the non-magnetic heterojunction system, the magnetic heterojunction system exhibits a higher absorption intensity for visible light, and the redshift of its absorption spectrum is more pronounced. Furthermore, when the Cu-doped GaN/ZnS heterojunction system contains different vacancy defects, different conductive types can be achieved.

Adsorption and vibrational spectroscopy of CO on the surface of MgO from periodic local coupled-cluster theory.

The adsorption of CO on the surface of MgO has long been a model problem in surface chemistry. Here, we report periodic Gaussian-based calculations for this problem using second-order perturbation theory (MP2) and coupled-cluster theory with single and double excitations (CCSD) and perturbative triple excitations [CCSD(T)], with the latter two performed using a recently developed extension of the local natural orbital approximation to problems with periodic boundary conditions. The low cost of periodic local correlation calculations allows us to calculate the full CCSD(T) binding curve of CO approaching the surface of MgO (and thus the adsorption energy) and the two-dimensional potential energy surface (PES) as a function of the distance from the surface and the CO stretching coordinate. From the PES, we obtain the fundamental vibrational frequency of CO on MgO, whose shift from the gas phase value is a common experimental probe of surface adsorption. We find that CCSD(T) correctly predicts a positive frequency shift upon adsorption of +14.7 cm-1, in excellent agreement with the experimental shift of +14.3 cm-1. We use our CCSD(T) results to assess the accuracy of MP2, CCSD, and several density functional theory (DFT) approximations, including exchange correlation functionals and dispersion corrections. We find that MP2 and CCSD yield reasonable binding energies and frequency shifts, whereas many DFT calculations overestimate the magnitude of the adsorption energy by 5-15 kJ mol-1 and predict a negative frequency shift of about -20 cm-1, which we attribute to self-interaction-induced delocalization errors that are mildly ameliorated with hybrid functionals. Our findings highlight the accuracy and computational efficiency of the periodic local correlation for the simulation of surface chemistry with accurate wavefunction methods.

The p-block challenge: assessing quantum chemistry methods for inorganic heterocycle dimerizations.

The elements of the p-block of the periodic table are of high interest in various chemical and technical applications like frustrated Lewis-pairs (FLP) or opto-electronics. However, high-quality benchmark data to assess approximate density functional theory (DFT) for their theoretical description are sparse. In this work, we present a benchmark set of 604 dimerization energies of 302 "inorganic benzenes" composed of all non-carbon p-block elements of main groups III to VI up to polonium. This so-called IHD302 test set comprises two classes of structures formed by covalent bonding and by weaker donor-acceptor (WDA) interactions, respectively. Generating reliable reference data with ab initio methods is challenging due to large electron correlation contributions, core-valence correlation effects, and especially the slow basis set convergence. To compute reference values for these dimerization reactions, after thorough testing, we applied a computational protocol using state-of-the-art explicitly correlated local coupled cluster theory termed PNO-LCCSD(T)-F12/cc-VTZ-PP-F12(corr.). It includes a basis set correction at the PNO-LMP2-F12/aug-cc-pwCVTZ level. Based on these reference data, we assess 26 DFT methods in combination with three different dispersion corrections and the def2-QZVPP basis set, five composite DFT approaches, and five semi-empirical quantum mechanical methods. For the covalent dimerizations, the r2SCAN-D4 meta-GGA, the r2SCAN0-D4 and ωB97M-V hybrids, and the revDSD-PBEP86-D4 double-hybrid functional are found to be the best-performing methods among the evaluated functionals of the respective class. However, since def2 basis sets for the 4th period are not associated to relativistic pseudo-potentials, we obtained significant errors in the covalent dimerization energies (up to 6 kcal mol-1) for molecules containing p-block elements of the 4th period. Significant improvements were achieved for systems containing 4th row elements by using ECP10MDF pseudopotentials along with re-contracted aug-cc-pVQZ-PP-KS basis sets introduced in this work with the contraction coefficients taken from atomic DFT (PBE0) calculations. Overall, the IHD302 set represents a challenge to contemporary quantum chemical methods. This is due to a large number of spatially close p-element bonds which are underrepresented in other benchmark sets, and the partial covalent bonding character for the WDA interactions. The IHD302 set may be helpful to develop more robust and transferable approximate quantum chemical methods in the future.

Predicting spin states of iron porphyrins with DFT methods including crystal packing effects and thermodynamic corrections.

Accurate computational treatment of spin states for transition metal complexes, exemplified by iron porphyrins, lies at the heart of quantum bioinorganic chemistry, but at the same time represents a great challenge for approximate density functional theory (DFT) methods, which are predominantly used. Here, the accuracy of DFT methods for spin-state splittings in iron porphyrin is assessed by probing the ability to correctly predict the ground states for six FeIII or FeII complexes experimentally characterized in solid state. For each case, molecular and periodic DFT calculations are employed to quantify the effect of porphyrin side substituents and the crystal packing effect (CPE) on the spin-state splitting. It is proposed to partition the total CPE into additive components, the direct and structural one, the importance of which is shown to significantly vary from case to case. By knowing the substituent effect, the CPE, and the Gibbs free energy thermodynamic correction from calculations, one can employ the experimental ground-state information in order to derive a quantitative constraint on the electronic energy difference for a simplified (porphin) model of the experimentally characterized metalloporphyrin. The constraints derived in such a way-in the form of single or double inequalities-are used to assess the accuracy of dispersion-corrected DFT methods for 6 spin-state splittings of [FeIII(P)(2-MeIm)2]+, [FeIII(P)(2-MeIm)]+, [FeII(P)(THF)2] and [FeII(P)] models (where P is porphin, 2-MeIm is 2-methylimidazole, THF is tetrahydrofuran). These data constitute the new benchmark set of spin states for crystalline iron porphyrins (SSCIP6). The highest accuracy is obtained in the case of double-hybrid functionals (B2PLYP-D3, DSD-PBEB95-D3), whereas hybrid functionals, especially those with reduced admixture of the exact exchange (B3LYP*-D3, TPSSh-D3), are found to considerably overstabilize the intermediate spin state, leading to incorrect ground-state prediction in FeIII porphyrins. The present approach, which can be generalized to other transition metal complexes, is not only useful in method benchmarking, but also sheds light on the interpretations of experimental data for metalloporphyrins, which are important models to understand the electronic properties of heme proteins.

Performance of point charge embedding schemes for excited states in molecular organic crystals.

Modeling excited state processes in molecular crystals is relevant for several applications. A popular approach for studying excited state molecular crystals is to use cluster models embedded in point charges. In this paper, we compare the performance of several embedding models in predicting excited states and S1-S0 optical gaps for a set of crystals from the X23 molecular crystal database. The performance of atomic charges based on ground or excited states was examined for cluster models, Ewald embedding, and self-consistent approaches. We investigated the impact of various factors, such as the level of theory, basis sets, embedding models, and the level of localization of the excitation. We consider different levels of theory, including time-dependent density functional theory and Tamm-Dancoff approximation (TDA) (DFT functionals: ωB97X-D and PBE0), CC2, complete active space self-consistent field, and CASPT2. We also explore the impact of selection of the QM region, charge leakage, and level of theory for the description of different kinds of excited states. We implemented three schemes based on distance thresholds to overcome overpolarization and charge leakage in molecular crystals. Our findings are compared against experimental data, G0W0-BSE, periodic TDA, and optimally tuned screened range-separated functionals.

Doping effect on electronic and magnetic properties of Ag-doped single-walled (6,0) GaN nanotubes: First-principles study

The electronic and magnetic properties of GaN wurtzite, un-doped, and Ag-doped single-walled (6,0) chiral GaN nanotubes (SWGaNNT) were investigated using Density Functional Theory and Local Spin Density Approximation methods within Hubbard U semiempirical correction (DFT-LSDA + U). In a consecutive DFT-LSDA + U electronic structure simulation, the effects of defects on the nature and origin of ferromagnetism (FM) are studied for an Ag-doped SWGaNNT system. For the Ag-doped GaN nanotube configurations, the energy gap decreases with increasing concentration of impurity. The total energy calculations for doped systems show the stability of the ferromagnetic phase. In the case of the Ag-doping GaN NT system, the wide energy gap is decreasing and the total magnetic moment of this system is ∼2.0 μB. From first-principles calculations, an Ag-doped GaN nanosystem can be made into a magnetic ferromagnetic material, and it is an important candidate for spintronics device applications.

Probing Reactivity with External Forces: The Case of Nitroacetamides in Water.

Many computational methods have been applied to interpret and predict changes in reactivity by slight modifications of a given molecular scaffold. We describe a novel and simple method based on approximate density-functional theory of valence electrons that can be applied within a large high-performance computational infrastructure to probe such changes using a statistical sample of molecular configurations, including the solvent. All the used computational tools are fully open-source. Following our previous application, we are able to explain the high acidity of C-H bond at α position in nitro compounds when the amide linkage an ammonium group is inserted into the α substituent.

The Structural and Electronic Properties of the Ag5 Atomic Quantum Cluster Interacting with CO2, CH4, and H2O Molecules

Recent advancements in experimental approaches have made it possible to synthesize silver (Ag5) atomic quantum clusters (AQCs), which have shown a great potential in photocatalysis. This study employs the generalized gradient approximation (GGA) density functional theory (DFT) to explore the adsorption of CO2, CH4, and H2O molecules on the Ag5 AQC. Our investigations focus on the structural and electronic properties of the molecules in Ag5 AQC systems. This involves adsorption energy simulations, charge transfer, charge density difference, and the density of states for the modelled systems. Our simulations suggest that CH4 and H2O molecules exhibit higher adsorption energies on the Ag5 AQC compared to CO2 molecules. Remarkably, the presence of CH4 molecule leads to a significant deformation in the Ag5 AQC structure. The structure reforms from a bipyramidal to trapezoidal shape. This study also reveals that the Ag5 AQC donates electrons to CO2 and CH4 molecules, resulting in an oxidation state. In contrast, gaining charges from H2O molecules results in a reduced state. We believe the proposed predictions provide valuable insights for future experimental investigations of the interaction behaviour between carbon dioxide, methane, water molecules, and Ag5 sub-nanometre clusters.

Naphthalene derived Schiff base as a reversible fluorogenic chemosensor for aluminium ions detection

Schiff base (HNPD) was achieved by reacting 2-hydroxy-1-naphthaldehyde with N-phenyl-o-phenylenediamine in enthanol medium. The spectroscopic analyses were done to establish the formation of Schiff base apparently. Further, synthesized Schiff base conjugate was successfully used as a fluorogenic chemosensor to detect aluminium ions (Al3+) with high fluorescence amplification among the other interfering various metal ions. The limit of detection of 0.0248 × 10−6 M and a binding constant of 6.19 × 103 M−1 were obtained by the receptor HNPD for Al3+ detection. A high influence of intramolecular charge transfer kinetics was established to realize the selective responsiveness towards Al3+ ions. Density functional theory approximation formulated the band energy modulation and localization and delocalization of electron density for the HNPD and Al3+ complexation. The developed sensor ultimately inspected on the real soil and water samples and ascertained the practical ability of Al3+ ions detection of HNPD chemosensor.

The convexity condition of density-functional theory.

It has long been postulated that within density-functional theory (DFT), the total energy of a finite electronic system is convex with respect to electron count so that 2Ev[N0] ≤ Ev[N0 - 1] + Ev[N0 + 1]. Using the infinite-separation-limit technique, this Communication proves the convexity condition for any formulation of DFT that is (1) exact for all v-representable densities, (2) size-consistent, and (3) translationally invariant. An analogous result is also proven for one-body reduced density matrix functional theory. While there are known DFT formulations in which the ground state is not always accessible, indicating that convexity does not hold in such cases, this proof, nonetheless, confirms a stringent constraint on the exact exchange-correlation functional. We also provide sufficient conditions for convexity in approximate DFT, which could aid in the development of density-functional approximations. This result lifts a standing assumption in the proof of the piecewise linearity condition with respect to electron count, which has proven central to understanding the Kohn-Sham bandgap and the exchange-correlation derivative discontinuity of DFT.

Rational design of methane dissociation catalyst based on first principles

Based on the first principle, this paper uses the generalised gradient approximation density functional theory and slab model to investigate the dissociation of methane (CH4→CH3 + H) on the surfaces of Co group (Co, Rh, Ir) and Ni group (Ni, Pd, Pt), and investigate the influence of PtIr(100), PdRh(100) and PtPd(100) on methane decomposition. From the calculated activation energies of methane dissociation on single metal surfaces and alloy surfaces,we find that Pt and Ir are better catalysts for methane dissociation in the single metals studied. In addition, methane dissociation (CH4→CH3 + H) on PtIr(100) and PdRh(100) surfaces are easier than that on single metal surfaces(Co, Rh, Ir, Ni, Pd, Pt).

First-principles prediction of higher Curie temperature, metallic and half-metallic ferromagnetism in Zn1-x(Vx,Nix)O systems

The electronic and magnetic properties of Zn(V,Ni)O systems with 2.08 %, 4.16 %, 6.25 %, 8.3 %, and 12.5 % impurity concentrations were investigated based on ab initio simulations. The first-principles calculations were carried out using density functional theory and local spin density approximation by pseudopotential method. Analyzing the calculated density of states, the mechanism to stabilize the ferromagnetic phase in the 3d-metals doped ZnO systems is discussed. The analysis of the total density of states shows that the V-doped ZnO presents a metallic nature and Ni-doped ZnO exhibits a half-metallic character. First-principles calculations show that the stability of ferromagnetic or antiferromagnetic behaviors depends on impurity concentrations and impurity positions in related ZnO:V,Ni systems. Finally, we estimated and studied the Curie temperatures for V- and Ni-doped ZnO systems with different impurity concentrations. The Curie temperatures for VxZn1-xO and NixZn1-xO systems are higher than room temperature and these compounds are suitable ferromagnetic DMS materials for spintronic applications.

Introducing the embedded random phase approximation: H2 dissociative adsorption on Cu(111) as an exemplar

The random phase approximation (RPA) as a means of treating electron correlation recently has been shown to outperform standard density functional theory (DFT) approximations in a variety of cases. However, the computational cost of the RPA is substantially more than DFT, especially when aiming to study extended surfaces. Properly accounting for sufficient surface ensemble size, Brillouin zone sampling, and vacuum separation of periodic images in standard periodic-planewave-based DFT code raises the cost to achieve converged results. Here, we show that sub-system embedding schemes enable use of the RPA for modeling heterogeneous reactions at reduced computational cost. We explore two different embedded RPA (emb-RPA) approaches, periodic emb-RPA and cluster emb-RPA. We use the (experimentally and theoretically) well-studied H2 dissociative adsorption on Cu(111) as our exemplar, and first perform full periodic RPA calculations as a benchmark. The full RPA results match well the semi-empirical barrier fit to experimental observables and others derived from high-level computations, e.g., from recent embedded n-electron valence second order perturbation theory [Zhao et al., J. Chem. Theory Comput. 16(11), 7078–7088 (2020)] and quantum Monte Carlo [Doblhoff-Dier et al., J. Chem. Theory Comput. 13(7), 3208–3219 (2017)] simulations. Among the two emb-RPA approaches tested, the cluster emb-RPA accurately reproduces the energy profile (maximum error of 50 meV along the reaction pathway) while reducing the computational cost by approximately two orders of magnitude. We therefore expect that the embedded cluster approach will enable wider RPA implementation in heterogeneous catalysis.

Benchmark Data Set of Crystalline Organic Semiconductors.

This work reports a Benchmark Data set of Crystalline Organic Semiconductors to test calculations of the structural and electronic properties of these materials in the solid state. The data set contains 67 crystals consisting of mostly rigid molecules with a single dominant conformer, covering the majority of known structural types. The experimental crystal structure is available for the entire data set, whereas zero-temperature unit cell volume can be reliably estimated for a subset of 28 crystals. Using this subset, we benchmark r2SCAN-D3 and PBE-D3 density functionals. Then, for the entire data set, we benchmark approximate density functional theory (DFT) methods, including GFN1-xTB and DFTB3(3ob-3-1), with various dispersion corrections against r2SCAN-D3. Our results show that r2SCAN-D3 geometries are accurate within a few percent, which is comparable to the statistical uncertainty of experimental data at a fixed temperature, but the unit cell volume is systematically underestimated by 2% on average. The several times faster PBE-D3 provides an unbiased estimate of the volume for all systems except for molecules with highly polar bonds, for which the volume is substantially overestimated in correlation with the underestimation of atomic charges. Considered approximate DFT methods are orders of magnitude faster and provide qualitatively correct but overcompressed crystal structures unless the dispersion corrections are fitted by unit cell volume.

Synthesis, Spectroscopic and Nonlinear Optical Properties, and Antimicrobial Activity of Cu(II), Co(II), and Ni(II) Complexes: Experimental and Theoretical Studies.

Currently, we report the preparation of transition metal complexes Co(II), Ni(II), and Cu(II) of hydrazone Schiff base ligands, which are obtained by the condensation reaction of substituted salicylaldehyde and hydrazines. The synthesized hydrazone ligands and their metal complexes were characterized by spectroscopic methods such as Fourier transform infrared (FT-IR), UV-vis, nuclear magnetic resonance (1H NMR and C13 NMR), and mass spectrometry analyses. All of the quantum chemistry calculations were performed using DFT executed in the Gaussian 09 software package. The geometry was optimized by using the density functional theory (DFT) approximation at the B3LYP level with a basis set of 6-31G (d, p). There was excellent agreement between the FT-IR values obtained experimentally and those obtained theoretically for the test compounds. It is worth noting that none of the optimized geometries for any of the Schiff base and metal complexes had any eigenvalues that were negative, indicating that these geometries represent the true minimum feasible energy surfaces. We also analyzed the electrostatic potential of the molecule and NBO calculation at the same level of theory. Gauss View 6 was utilized for the file organization of the input data. Gauss View 6.0, Avogadro, and Chemcraft were used to determine the data. Additionally, synthesized compounds were screened for antimicrobial activity against Gram-negative bacteria (Salmonella typhi, Escherichia coli) and Gram-positive bacteria (Bacillus halodurans, Micrococcus luteus) and two fungal strains (Aspergillus flavus, Aspergillus niger). These research findings have established the potential of ligands and their metal complexes as antimicrobial agents. Additionally, the compounds demonstrated promising nonlinear optical (NLO) properties, with potential applications across a wide range of contemporary technologies.