Standard Exchange-correlation Functionals Research Articles

Localization versus delocalization of d-states within the hbox {Ni}_{{2}}MnGa Heusler alloy

We present calculations based on density-functional theory with improved exchange-correlation approaches to investigate the electronic structure of hbox {Ni}_2MnGa magnetic shape memory alloy prototype. We study the effects of hybrid functionals as well as a Hubbard-like correction parameter U on the structural, electronic and magnetic properties of the alloy. We show that the previously successful application of U on Mn should be extended by including U on Ni to describe the d localized electrons more accurately and in better agreement with experiments. The bonding interactions within this intermetallic alloy are analysed including the role of non-transition metal. We found that the strongest and most stabilizing bond is formed between the Ga–Ni pairs due to the delocalized s–s and p–s orbital hybridization. Our findings suggest that minimization of the over-delocalization error introduced by standard semi-local exchange-correlation functionals leads to a better description of the hbox {Ni}_2MnGa alloy. Furthermore we propose that the experimental total magnetic moment of Ni–Mn–Ga alloys could be increased after carefully selected heat treatment procedures.

Accurate Electronic Properties and Intercalation Voltages of Olivine-Type Li-Ion Cathode Materials from Extended Hubbard Functionals

The design of novel cathode materials for Li-ion batteries would greatly benefit from accurate first-principles predictions of structural, electronic, and magnetic properties as well as intercalation voltages in compounds containing transition-metal elements. For such systems, density-functional theory (DFT) with standard (semi-)local exchange-correlation functionals is of limited use as it often fails due to strong self-interaction errors that are especially relevant in the partially filled $d$ shells. Here, we perform a detailed comparative study of the phospho-olivine cathode materials Li$_x$MnPO$_4$, Li$_x$FePO$_4$, and the mixed transition metal Li$_x$Mn$_{1/2}$Fe$_{1/2}$PO$_4$ ($x=0, 1/4, 1/2, 3/4, 1$) using four electronic-structure methods: DFT, DFT+$U$, DFT+$U$+$V$, and HSE06. We show that DFT+$U$+$V$, with onsite $U$ and intersite $V$ Hubbard parameters determined from first principles and self-consistently with respect to the structural parameters by means of density-functional perturbation theory (linear response), provides the most accurate description of the electronic structure of these challenging compounds. In particular, we demonstrate that DFT+$U$+$V$ displays very clearly "digital" changes in oxidation states of the transition-metal ions in all compounds, including the mixed-valence phases occurring at intermediate Li concentrations, leading to voltages in remarkable agreement with experiments. We show that the inclusion of intersite Hubbard interactions is essential for the accurate prediction of thermodynamic quantities, balancing the drive for localization induced by the onsite $U$ with intersite $V$ orbital hybridizations.

Electronic structure of pristine and Ni-substituted LaFeO3 from near edge x-ray absorption fine structure experiments and first-principles simulations

We present a joint theoretical and experimental study of the oxygen $K$-edge spectra for LaFeO$_3$ and homovalent Ni-substituted LaFeO$_3$ (LaFe$_{0.75}$Ni$_{0.25}$O$_3$), using first-principles simulations based on density-functional theory with extended Hubbard functionals and x-ray absorption near edge structure (XANES) measurements. Ground-state and excited-state XANES calculations employ Hubbard on-site $U$ and inter-site $V$ parameters determined from first principles and the Lanczos recursive method to obtain absorption cross sections, which allows for a reliable description of XANES spectra in transition-metal compounds in a very broad energy range, with an accuracy comparable to that of hybrid functionals but at a substantially lower cost. We show that standard gradient-corrected exchange-correlation functionals fail in capturing accurately the electronic properties of both materials. In particular, for LaFe$_{0.75}$Ni$_{0.25}$O$_3$ they do not reproduce its semiconducting behaviour and provide a poor description of the pre-edge features at the O $K$ edge. The inclusion of Hubbard interactions leads to a drastic improvement, accounting for the semiconducting ground state of LaFe$_{0.75}$Ni$_{0.25}$O$_3$ and for a good agreement between calculated and measured XANES spectra. We show that the partial substitution of Fe for Ni affects the conduction-band bottom by generating a strongly hybridized O($2p$)-Ni($3d$) minority-spin empty electronic state. The present work, based on a consistent correction of self-interaction errors, outlines the crucial role of extended Hubbard functionals to describe the electronic structure of complex transition-metal oxides such as LaFeO$_3$ and LaFe$_{0.75}$Ni$_{0.25}$O$_3$ and paves the way to future studies on similar systems.

Performance of the standard exchange-correlation functionals in predicting melting properties fully from first principles: Application to Al and magnetic Ni

We apply the efficient two-optimized references thermodynamic integration using Langevin dynamics method [Phys. Rev. B 96, 224202 (2017)] to calculate highly accurate melting properties of Al and magnetic Ni from first principles. For Ni we carefully investigate the impact of magnetism on the liquid and solid free energies including longitudinal spin fluctuations and the reverse influence of atomic vibrations on magnetic properties. We show that magnetic fluctuations are effectively canceling out for both phases and are thus not altering the predicted melting temperature. For both elements, the generalized gradient approximation (GGA) and the local-density approximation (LDA) are used for the exchange-correlation functional revealing a reliable ab initio confidence interval capturing the respective experimental melting point, enthalpy of fusion, and entropy of fusion.

Improving the predictive quality of time-dependent density functional theory calculations of the X-ray emission spectroscopy of organic molecules.

The simulation of X-ray emission spectra of organic molecules using time-dependent density functional theory (TDDFT) is explored. TDDFT calculations using standard hybrid exchange-correlation functionals in conjunction with large basis sets can predict accurate X-ray emission spectra provided an energy shift is applied to align the spectra with experiment. The relaxation of the orbitals in the intermediate state is an important factor, and neglect of this relaxation leads to considerably poorer predicted spectra. A short-range corrected functional is found to give emission energies that required a relatively small energy shift to align with experiment. However, increasing the amount of Hartree-Fock exchange in this functional to remove the need for any energy shift led to a deterioration in the quality of the calculated spectral profile. To predict accurate spectra without reference to experimental measurements, we use the CAM-B3LYP functional with the energy scale determined with reference to a Δself-consistent field calculation for the highest energy emission transition.

Plane-Wave Implementation and Performance of à-la-Carte Coulomb-Attenuated Exchange-Correlation Functionals for Predicting Optical Excitation Energies in Some Notorious Cases.

Linear-response time-dependent density functional theory (LR-TD-DFT) has become a valuable tool in the calculation of excited states of molecules of various sizes. However, standard generalized-gradient approximation and hybrid exchange-correlation (xc) functionals often fail to correctly predict charge-transfer (CT) excitations with low orbital overlap, thus limiting the scope of the method. The Coulomb-attenuation method (CAM) in the form of the CAM-B3LYP functional has been shown to reliably remedy this problem in many CT systems, making accurate predictions possible. However, in spite of a rather consistent performance across different orbital overlap regimes, some pitfalls remain. Here, we present a fully flexible and adaptable implementation of the CAM for Γ-point calculations within the plane-wave pseudopotential molecular dynamics package CPMD and explore how customized xc functionals can improve the optical spectra of some notorious cases. We find that results obtained using plane waves agree well with those from all-electron calculations employing atom-centered bases, and that it is possible to construct a new Coulomb-attenuated xc functional based on simple considerations. We show that such a functional is able to outperform CAM-B3LYP in some cases, while retaining similar accuracy in systems where CAM-B3LYP performs well.

Calculation of linear and nonlinear optical properties of azobenzene derivatives with Kohn-Sham and coupled-cluster methods.

Linear polarizabilities (α) and second hyperpolarizabilities (γ) of unsubstituted azobenzenes and 'push-pull' azobenzene derivatives are investigated using Kohn-Sham theory (KST) and coupled-cluster (CC) approaches. Various standard exchange-correlation functionals as well as a non-empirically 'tuned' long-range corrected (LC) functional with range-separated exchange are used in the KST calculations. When compared to correlated ab initio calculations and measurements, the tuned functional gives accurate low-energy excitation energies, especially for charge transfer (CT) transitions, and performs well for α. Basis set and solvent effects are also studied. In contrast to expectations, but in agreement with a prior study of π-conjugated systems that do not have low-energy CT excitations, the improvements of the CT excitation energies for the push-pull π-chromophores due to tuning do not go along with clear improvements of γ toward the CC reference data, likely due to the importance of the dynamic electron correlation for this property.

The effect of basis set and exchange-correlation functional on time-dependent density functional theory calculations within the Tamm-Dancoff approximation of the x-ray emission spectroscopy of transition metal complexes.

The simulation of X-ray emission spectra of transition metal complexes with time-dependent density functional theory (TDDFT) is investigated. X-ray emission spectra can be computed within TDDFT in conjunction with the Tamm-Dancoff approximation by using a reference determinant with a vacancy in the relevant core orbital, and these calculations can be performed using the frozen orbital approximation or with the relaxation of the orbitals of the intermediate core-ionised state included. Both standard exchange-correlation functionals and functionals specifically designed for X-ray emission spectroscopy are studied, and it is shown that the computed spectral band profiles are sensitive to the exchange-correlation functional used. The computed intensities of the spectral bands can be rationalised by considering the metal p orbital character of the valence molecular orbitals. To compute X-ray emission spectra with the correct energy scale allowing a direct comparison with experiment requires the relaxation of the core-ionised state to be included and the use of specifically designed functionals with increased amounts of Hartree-Fock exchange in conjunction with high quality basis sets. A range-corrected functional with increased Hartree-Fock exchange in the short range provides transition energies close to experiment and spectral band profiles that have a similar accuracy to those from standard functionals.

Accurate Ionization Potentials and Electron Affinities of Acceptor Molecules II: Non-Empirically Tuned Long-Range Corrected Hybrid Functionals

The performance of non-empirically tuned long-range corrected hybrid functionals for the prediction of vertical ionization potentials (IPs) and electron affinities (EAs) is assessed for a set of 24 organic acceptor molecules. Basis set-extrapolated coupled cluster singles, doubles, and perturbative triples [CCSD(T)] calculations serve as a reference for this study. Compared to standard exchange-correlation functionals, tuned long-range corrected hybrid functionals produce highly reliable results for vertical IPs and EAs, yielding mean absolute errors on par with computationally more demanding GW calculations. In particular, it is demonstrated that long-range corrected hybrid functionals serve as ideal starting points for non-self-consistent GW calculations.

Enhancing photocatalytic properties of rutile TiO2 by codoping with N and metals – Ab initio study

Substitutional N to O and M to Ti (M = Pt, V, Sb) codoped rutile TiO2 was investigated using density functional theory (DFT) based calculations with both standard and hybrid exchange-correlation functionals. The band gaps calculated using generalized gradient approximation (GGA) exhibited narrowing compared to the pure rutile TiO2 in all the investigated cases. In contrast, the results obtained with hybrid exchange-correlation functional showed that there was no band gap narrowing, but doping induced localized states within the band gap just above the valence band, as well as below the conduction band for Pt doped TiO2. The presence of broad intermediate states (IS) in the band gap could enhance visible light absorption through a two step optical transition from the valence to the conduction band via the IS and at the same time lower recombination of the photogenerated charges.

Toward the complete range separation of non-hybrid exchange-correlation functional.

In this study, we use a very simple scheme to achieve range separation of a total exchange-correlation functional. We have utilized this methodology to combine a short-range pure density functional theory (DFT) functional with a corresponding long-range pure DFT, leading to a "Range-separated eXchange-Correlation" (RXC) scheme. By examining the performance of a range of standard exchange-correlation functionals for prototypical short- and long-range properties, we have chosen B-LYP as the short-range functional and PBE-B95 as the long-range counterpart. The results of our testing using a more diverse range of data sets show that, for properties that we deem to be short-range in nature, the performance of this prescribed RXC-DFT protocol does resemble that of B-LYP in most cases, and vice versa. Thus, this RXC-DFT protocol already provides meaningful numerical results. Furthermore, we envisage that the general RXC scheme can be easily implemented in computational chemistry software packages. This study paves a way for further refinement of such a range-separation technique for the development of better performing DFT procedures.

Does DFT-SAPT method provide spectroscopic accuracy?

Ground state potential energy curves for homonuclear and heteronuclear dimers consisting of noble gas atoms from He to Kr were calculated within the symmetry adapted perturbation theory based on the density functional theory (DFT-SAPT). These potentials together with spectroscopic data derived from them were compared to previous high-precision coupled cluster with singles and doubles including the connected triples theory calculations (or better if available) as well as to experimental data used as the benchmark. The impact of midbond functions on DFT-SAPT results was tested to study the convergence of the interaction energies. It was shown that, for most of the complexes, DFT-SAPT potential calculated at the complete basis set (CBS) limit is lower than the corresponding benchmark potential in the region near its minimum and hence, spectroscopic accuracy cannot be achieved. The influence of the residual term δ(HF) on the interaction energy was also studied. As a result, we have found that this term improves the agreement with the benchmark in the repulsive region for the dimers considered, but leads to even larger overestimation of potential depth De. Although the standard hybrid exchange-correlation (xc) functionals with asymptotic correction within the second order DFT-SAPT do not provide the spectroscopic accuracy at the CBS limit, it is possible to adjust empirically basis sets yielding highly accurate results.

Ab Initio Calculations of Band Gaps and Absolute Band Positions of Polymorphs of RbPbI3 and CsPbI3: Implications for Main-Group Halide Perovskite Photovoltaics

Lead halide perovskites have attracted great interest because of rapid improvements in the efficiency of photovoltaics based on these materials. To predict new related functional materials, a good understanding of the correlations between crystal chemistry, electronic structure, and optoelectronic properties is required. Describing the electronic structure of these materials using density functional theory provides a choice of exchange-correlation functionals, including hybrid functionals, and inclusion of spin-orbit coupling, which is critical for the correct description of band gap and absolute band positions (ionization energy). Here, various computational schemes that employ different choices of exchange-correlation and hybrid functionals, and include or exclude spin-orbit coupling were implemented to examine these effects. Using PbI2 as an initial structural model, it is found that standard exchange correlation functionals (PBE) in conjunction with spin-orbit coupling suffice to locate ionization ene...

Quantum Chemical Calculations of X-ray Emission Spectroscopy.

The calculation of X-ray emission spectroscopy with equation of motion coupled cluster theory (EOM-CCSD), time-dependent density functional theory (TDDFT), and resolution of the identity single excitation configuration interaction with second-order perturbation theory (RI-CIS(D)) is studied. These methods can be applied to calculate X-ray emission transitions by using a reference determinant with a core-hole, and they provide a convenient approach to compute the X-ray emission spectroscopy of large systems since all of the required states can be obtained within a single calculation, removing the need to perform a separate calculation for each state. For all of the methods, basis sets with the inclusion of additional basis functions to describe core orbitals are necessary, particularly when studying transitions involving the 1s orbitals of heavier nuclei. EOM-CCSD predicts accurate transition energies when compared with experiment; however, its application to larger systems is restricted by its computational cost and difficulty in converging the CCSD equations for a core-hole reference determinant, which become increasing problematic as the size of the system studied increases. While RI-CIS(D) gives accurate transition energies for small molecules containing first row nuclei, its application to larger systems is limited by the CIS states providing a poor zeroth-order reference for perturbation theory which leads to very large errors in the computed transition energies for some states. TDDFT with standard exchange-correlation functionals predicts transition energies that are much larger than experiment. Optimization of a hybrid and short-range corrected functional to predict the X-ray emission transitions results in much closer agreement with EOM-CCSD. The most accurate exchange-correlation functional identified is a modified B3LYP hybrid functional with 66% Hartree-Fock exchange, denoted B(66)LYP, which predicts X-ray emission spectra for a range of molecules including fluorobenzene, nitrobenzene, acetone, dimethyl sulfoxide, and CF3Cl in good agreement with experiment.

Experimental and theoretical electronic structure of quinacridone

The energy positions of frontier orbitals in organic electronic materials are often studied experimentally by (inverse) photoemission spectroscopy and theoretically within density functional theory. However, standard exchange-correlation functionals often result in too small fundamental gaps, may lead to wrong orbital energy ordering, and do not capture polarization-induced gap renormalization. Here, we examine these issues and a strategy for overcoming them by studying the gas phase and bulk electronic structure of the organic molecule quinacridone (5Q), a promising material with many interesting properties for organic devices. Experimentally, we perform angle-resolved photoemission spectroscopy (ARUPS) on thin films of the crystalline $\beta$-phase of 5Q. Theoretically, we employ an optimally-tuned range-separated hybrid functional (OT-RSH) within density functional theory. For the gas phase molecule, our OT-RSH result for the ionization potential (IP) represents a substantial improvement over the semi-local PBE and the PBE0 hybrid functional results, producing an IP in quantitative agreement with experiment. For the bulk crystal, we take into account the correct screening in the bulk, using the recently developed OT-SRSH approach, while retaining the optimally-tuned parameters for the range-separation and the short-range Fock exchange. This leads to a band gap narrowing due to polarization effects and results in a valence band spectrum in excellent agreement with experimental ARUPS data, with respect to both peak positions and heights. Finally, full-frequency $G_0W_0$ results based on a hybrid functional starting point are shown to agree with the OT-SRSH approach, improving substantially on the PBE-starting point.

Direct calculation of exciton binding energies with time-dependent density-functional theory

Excitons are electron-hole pairs appearing below the band gap in insulators and semiconductors. They are vital to photovoltaics, but are hard to obtain with time-dependent density-functional theory (TDDFT), since most standard exchange-correlation (xc) functionals lack the proper long-range behavior. Furthermore, optical spectra of bulk solids calculated with TDDFT often lack the required resolution to distinguish discrete, weakly bound excitons from the continuum. We adapt the Casida equation formalism for molecular excitations to periodic solids, which allows us to obtain exciton binding energies directly. We calculate exciton binding energies for both small- and large-gap semiconductors and insulators, study the recently proposed bootstrap xc kernel [S. Sharma et al., Phys. Rev. Lett. 107, 186401 (2011)], and extend the formalism to triplet excitons.

Charging of Gold Atoms on Doped MgO and CaO: Identifying the Key Parameters by DFT Calculations

The use of transition metals (TM) as dopants is a versatile way to change the properties of oxides. One example is the possibility to induce charge transfer from the TM to species adsorbed on the oxide surface. In the case of wide-gap alkaline-earth oxides, such as MgO and CaO, the charge transfer is determined by the respective position of the energy levels of the impurity and the adsorbate and resides in the capability of the TM to be stabilized in various oxidation states. The structural and electronic properties of Cr- and Mo-doped MgO and CaO are investigated by density functional theory (DFT) calculations. Because of limitations of DFT in the description of band gaps and energy levels alignment, we compare the results obtained with standard GGA, GGA+U, and hybrid exchange-correlation functionals. The ability of the impurity ion to transfer one electron to the adsorbed species is considered for the case of electronegative Au adatoms. The study of the thermodynamic stability of the TM ions in combination with the formation of cation vacancies shows that Mo impurities are stable in the oxide lattice as Mo3+ or Mo4+ but can assume also higher oxidation states and are therefore able to transfer electrons to adsorbed gold. Conversely, Cr impurities are stabilized as Cr3+ and the high cost of further oxidation results in the absence of charge transfer to gold on both Cr-doped MgO and Cr-doped CaO.

Combined Theoretical and Experimental Investigation of CO Adsorption on Coordinatively Unsaturated Sites in CuBTC MOF

The adsorption of CO in metal-organic framework CuBTC material is investigated by a combination of theoretical and experimental approaches. The adsorption enthalpy of CO on CuBTC determined experimentally to be -29 kJ mol(-1) at the zero-coverage limit is in very good agreement with the adsorption enthalpy calculated at the combined DFT-ab initio level with the periodic model. Calculations show that polycarbonyl complexes cannot be formed on regular coordinatively unsaturated sites in CuBTC. Experimental IR spectra of the CO probe molecule adsorbed in CuBTC are interpreted based on calculated CO stretching frequencies. Calculations show that long-range interactions are insignificant for the CO/CuBTC system and that this system can be accurately modeled with just a Cu(2)(HCOO)(4) cluster model of the paddle wheel. The reliability of various methods for the description of CO interaction with the Cu(2+) site in CuBTC is discussed based on the experimental results and accurate coupled-cluster calculations. It is shown that standard exchange-correlation functionals do not provide a reliable description of CO interaction with coordinatively unsaturated Cu(2+) sites in CuBTC.

Van der Waals density functional study of energetic, structural, and vibrational properties of small water clusters and iceIh

We present results for a density functional theory study of small water clusters and hexagonal ice Ih, using the van der Waals density functional (vdW-DF). In particular, we examine energetic, structural, and vibrational properties of these systems. Our results exhibit excellent agreement with both experiment and quantum-chemistry calculations and show a systematic and consistent improvement over standard exchange-correlation functionals---making vdW-DF a promising candidate for resolving longstanding difficulties with density functional theory in describing water. In addition, by comparing our vdW-DF results with quantum-chemistry calculations and other standard exchange-correlation functionals, we shed light on the question of why standard functionals often fail to describe these systems accurately.

Relativistic four-component calculations of Buckingham birefringence using London atomic orbitals

We present the first relativistic study of the electric-field-gradient induced birefringence (Buckingham birefringence), with application to the series of molecules CX2 (X = O, S, Se, Te). A recently developed atomic-orbital-driven scheme for the calculation of time-dependent molecular properties using one-, two- and four-component relativistic wave functions (Bast et al. in Chem Phys 356:177, 2009) is extended to first-order frequency-dependent magnetic-field perturbations, using London atomic orbitals to ensure gauge-origin independent results and to improve basis-set convergence. Calculations are presented at the Hartree–Fock and Kohn–Sham levels of theory and results for CO2 and CS2 are compared with previous high-level coupled-cluster calculations. Except for the heaviest member of the series, relativistic effects are small—in particular for the temperature-independent contribution to the birefringence. By contrast, the effects of electron correlation are significant. However, the reliability of standard exchange-correlation functionals in describing Buckingham birefringence remains unclear based on the comparison with high-level coupled-cluster singles-and-doubles calculations.