Inclusion Of Exact Exchange Research Articles

Orbital-Optimized Versus Time-Dependent Density Functional Calculations of Intramolecular Charge Transfer Excited States.

The performance of time-independent, orbital-optimized calculations of excited states is assessed with respect to charge transfer excitations in organic molecules in comparison to the linear-response time-dependent density functional theory (TD-DFT) approach. A direct optimization method to converge on saddle points of the electronic energy surface is used to carry out calculations with the local density approximation (LDA) and the generalized gradient approximation (GGA) functionals PBE and BLYP for a set of 27 excitations in 15 molecules. The time-independent approach is fully variational and provides a relaxed excited state electron density from which the extent of charge transfer is quantified. The TD-DFT calculations are generally found to provide larger charge transfer distances compared to the orbital-optimized calculations, even when including orbital relaxation effects with the Z-vector method. While the error on the excitation energy relative to theoretical best estimates is found to increase with the extent of charge transfer up to ca. -2 eV for TD-DFT, no correlation is observed for the orbital-optimized approach. The orbital-optimized calculations with the LDA and the GGA functionals provide a mean absolute error of ∼0.7 eV, outperforming TD-DFT with both local and global hybrid functionals for excitations with a long-range charge transfer character. Orbital-optimized calculations with the global hybrid functional B3LYP and the range-separated hybrid functional CAM-B3LYP on a selection of states with short- and long-range charge transfer indicate that inclusion of exact exchange has a small effect on the charge transfer distance, while it significantly improves the excitation energy, with the best-performing functional CAM-B3LYP providing an absolute error typically around 0.15 eV.

Multiconfigurational short-range density functional theory for nuclear magnetic resonance shielding constants with gauge-including atomic orbitals.

In this paper, we present the theory and implementation of nuclear magnetic resonance shielding constants with gauge-including atomic orbitals for the hybrid multiconfigurational short-range density functional theory model. As a special case, this implementation also includes Hartree-Fock srDFT (HF-srDFT). Choosing a complete-active space (CAS) wave function as the multiconfigurational parameterization of the wave function, we investigate how well CAS-srDFT reproduces experimental trends of nuclear shielding constants compared to DFT and complete active space self-consistent field (CASSCF). Calculations on the nucleobases adenine and thymine show that CAS-srDFT performs on average the best of the tested methods, much better than CASSCF but only marginally better than HF-srDFT. The performance, compared to regular DFT, is similar when functionals containing exact exchange are used. We generally find that the inclusion of exact exchange is important for an accurate description of the shielding constants. In cases where no exact exchange is included, we observe that the HF- and CAS-srDFT often outperform regular DFT. For calculations on transition metal nuclei in organometallic compounds with significant static correlation, the CAS-srDFT method again outperforms CASSCF compared to experimental shielding constants, and the change from HF-srDFT is substantial. In conclusion, the static correlation posed by the metal complexes seems to be captured by CAS-srDFT, which is promising since this type of correlation is not well described by regular DFT.

Excited-State Properties for Extended Systems: Efficient Hybrid Density Functional Methods.

Time-dependent density functional theory has become state-of-the-art for describing photophysical and photochemical processes in extended materials because of its affordable cost. The inclusion of exact exchange was shown to be essential for the correct description of the long-range asymptotics of electronic interactions and thus a well-balanced description of valence, Rydberg, and charge-transfer excitations. Several approaches for an efficient treatment of exact exchange have been established for the ground state, while implementations for excited-state properties are rare. Furthermore, the high computational costs required for excited-state properties in comparison to ground-state computations often hinder large-scale applications on periodic systems with hybrid functional accuracy. We therefore propose two approximate schemes for improving computational efficiency for the treatment of exact exchange. Within the auxiliary density matrix method (ADMM), exact exchange is estimated using a relatively small auxiliary basis and the introduced basis set incompleteness error is compensated by an exchange density functional correction term. Benchmark results for a test set of 35 molecules demonstrate that the mean absolute error introduced by ADMM is smaller than 0.3 pm for excited-state bond lengths and in the range of 0.02-0.04 eV for vertical excitation, adiabatic excitation, and fluorescence energies. Computational timings for a series of covalent-organic frameworks demonstrate that a speed-up of at least 1 order of magnitude can be achieved for excited-state geometry optimizations in comparison to conventional hybrid functionals. The second method is to use a semiempirical tight binding approximation for both Coulomb and exchange contributions to the excited-state kernel. This simplified Tamm-Dancoff approximation (sTDA) achieves an accuracy comparable to approximated hybrid density functional theory when referring to highly accurate coupled-cluster reference data. We find that excited-state bond lengths deviate by 1.1 pm on average and mean absolute errors in vertical excitation, adiabatic excitation, and fluorescence energies are in the range of 0.2-0.5 eV. In comparison to ADMM-approximated hybrid functional theory, sTDA accelerates the computation of broad-band excitation spectra by 1 order of magnitude, suggesting its potential use for large-scale screening purposes.

The binding of atomic hydrogen on graphene from density functional theory and diffusion Monte Carlo calculations.

In this work, density functional theory (DFT) and diffusion Monte Carlo (DMC) methods are used to calculate the binding energy of a H atom chemisorbed on the graphene surface. The DMC value of the binding energy is about 16% smaller in magnitude than the Perdew-Burke-Ernzerhof (PBE) result. The inclusion of exact exchange through the use of the Heyd-Scuseria-Ernzerhof functional brings the DFT value of the binding energy closer in line with the DMC result. It is also found that there are significant differences in the charge distributions determined using PBE and DMC approaches.

Assessing the Accuracy of the SCAN Functional for Water through a Many-Body Analysis of the Adiabatic Connection Formula.

We present a systematic analysis of the accuracy of a series of SCANα functionals for water, with varying fractions (α) of exact exchange, which are constructed through the adiabatic connection formula. Our results indicate that all SCANα functionals exhibit substantial errors in the representation of the water 2-body energies. Importantly, the inclusion of exact exchange is found to have opposite effects on the ability of the SCANα functionals to describe the interaction energies of water clusters with 2-dimensional and 3-dimensional hydrogen-bonding arrangements. These errors are found to directly affect the ability of the SCANα functionals to describe the structure of liquid water at ambient conditions, which is investigated using explicit many-body models (MB-SCANα) derived from the corresponding SCANα data. In particular, it is found that all MB-SCANα models predict a more compact first hydration shell, which results in a denser liquid with a more ice-like structure. These apparent opposite trends can be explained by the inability of the SCANα functionals to provide a balanced description of the water 2B and 3B energies at the fundamental level. The analyses presented in this study provide new insights that can guide future developments of improved exchange-correlation functionals for aqueous systems.

Electronic structure of TiSe2 from a quasi-self-consistent G0W0 approach

In a previous work, it was shown that the inclusion of exact exchange is essential for a first-principles description of both the electronic and the vibrational properties of $\mathrm{Ti}{\mathrm{Se}}_{2}$, M. Hellgren et al. [Phys. Rev. Lett. 119, 176401 (2017)]. The $GW$ approximation provides a parameter-free description of screened exchange but is usually employed perturbatively (${G}_{0}{W}_{0}$), making results more or less dependent on the starting point. In this work, we develop a quasi-self-consistent extension of ${G}_{0}{W}_{0}$ based on the random phase approximation (RPA) and the optimized effective potential of hybrid density functional theory. This approach generates an optimal ${G}_{0}{W}_{0}$ starting point and a hybrid exchange parameter consistent with the RPA. While self-consistency plays a minor role for systems such as Ar, BN, and ScN, it is shown to be crucial for $\mathrm{Ti}{\mathrm{S}}_{2}$ and $\mathrm{Ti}{\mathrm{Se}}_{2}$. We find the high-temperature phase of $\mathrm{Ti}{\mathrm{Se}}_{2}$ to be a semimetal with a band structure in good agreement with experiment. Furthermore, the optimized hybrid functional agrees well with our previous estimate and therefore accurately reproduces the low-temperature charge-density-wave phase.

On the influence of exact exchange on transition metal superatoms.

The electronic structure of A7C (A = Hg, Pd, V, Cr, Mn, Fe, Ni, Cu; C = 0, ±1, ±2) clusters has been determined using density functional theory methods. The A7C (A = Hg, Pd, Cr, Cu; C = 0, ±1, ±2) clusters all conform to the existing superatomic model, with a sufficiently stabilised local structure to prevent perturbation upon the introduction of exact exchange to the exchange correlation functional. For the A7C (A = Mn, Fe, Ni; C = 0, ±1, ±2) clusters the incorporation of exact exchange separates the atomic s- and d-electrons, leading to a net increase in the number of superatomic electrons. Conversely the incorporation of exact exchange into the exchange correlation functional decreases the number of superatomic electrons for the V7C (C = 0, ±1, ±2) clusters, owing to the radial extension of the d-orbitals influencing their ability to contribute into superatomic shells.

Hybrid-DFT Modeling of Lattice and Surface Vacancies in MnO

We have investigated the properties of defects in MnO bulk and at (100) surfaces, as used in catalytic applications, using hybrid-level density functional theory (i.e., inclusion of exact exchange within the exchange-correlation evaluation) in a hybrid QM/MM embedded-cluster approach. Initially, we calculate the formation energy for bulk Mn and O vacancies, comparing charged-defect compensation with charge carriers at the Fermi Level (ϵf) and through Schottky defect formation. Oxygen vacancies were also investigated at the (100) surface, where the vacancy formation energy is very similar to the bulk. Defect levels associated with the most stable vacancies are calculated using the ΔSCF method: all are positioned mid band gap, with surface environments failing to alter strongly the overall nature of the defect relative to bulk. Chemical activity of the (100) MnO surface was considered through the adsorption of a probe CO2 molecule, which is considered the initial step in the transformation of CO2 into hydro...

A hybrid density functional study of optical and electronic properties of Al\\Ga-codoped ZnO

The energetic, electronic structures and optical properties of Al-, Ga-doped and Al\\Ga-codoped ZnO systems with the concentration x = y = 3.125% have been investigated using first-principles calculations. The results show that the Al\\Ga-codoped ZnO can be easily prepared at O-rich condition with higher stability than that of Al- and Ga-doped ZnO. Furthermore, the incorporation of Al and Ga into ZnO present a good optical and electronic property with significant improvement for the ZnO co-doped compared to monodoped and pure ZnO. While, the absorbance of Al\\Ga-codoped ZnO becomes lower that the case of pure ZnO in the UV region. The calculations using HSE06 functional underline the impact that inclusion of exact exchange has on the electronic and optical properties.

Electronic and spin–orbit properties of the kagome MOF family M3(1,2,5,6,9, 10-triphenylenehexathiol)2 (M = Ni, Pt, Cu and Au)

We investigate, through first-principles calculations, the electronic band structure—including the spin–orbit coupling—of single-layer M3(THT)2 metal-organic frameworks, where M = Ni, Pt, Cu and Au, and THT is the 1,2,5,6,9,10-triphenylenehexathiol molecule. This MOF family contains, in its electronic structure, spin–orbit gaps that could allow their use in quantum spin Hall effect devices. We find that the partial inclusion of exact exchange in the calculations (beyond a semi-local exchange-correlation level) leads to quantitative, and even qualitative, modifications of the electronic structure of Ni3(THT)2 and Pt3(THT)2 relative to calculations at semi-local exchange-correlation level: upon inclusion of exact exchange, the predicted fundamental band gap of these semiconductor materials increases to more than twice, and the predicted spin–orbit gaps change by as much as 44%. Even the qualitative description of the valence bands of these materials changes upon inclusion of exact exchange. We also find that the magnitudes of the spin–orbit gaps are not monotonic with the atomic number of the metal atom.

Local structure analysis in ab initio liquid water

Within the framework of density functional theory, the inclusion of exact exchange and non-local van der Waals/dispersion (vdW) interactions is crucial for predicting a microscopic structure of ambient liquid water that quantitatively agrees with experiment. In this work, we have used the local structure index (LSI) order parameter to analyse the local structure in such highly accurate ab initio liquid water. At ambient conditions, the LSI probability distribution, P(I ), was unimodal with most water molecules characterised by more disordered high-density-like local environments. With thermal excitations removed, the resultant bimodal P(I ) in the inherent potential energy surface (IPES) exhibited a 3:1 ratio between high-density- and low-density-like molecules, with the latter forming small connected clusters amid the predominant population. By considering the spatial correlations and hydrogen bond network topologies among water molecules with the same LSI identities, we demonstrate that the signatures of the experimentally observed low- and high-density amorphous phases of ice are present in the IPES of ambient liquid water. Analysis of the LSI autocorrelation function uncovered a persistence time of ∼ 4 ps – a finding consistent with the fact that natural thermal fluctuations are responsible for transitions between these distinct yet transient local aqueous environments in ambient liquid water.

A density functional theory investigation of the electronic structure and spin moments of magnetite

We present the results of density functional theory (DFT) calculations on magnetite, Fe3O4, which has been recently considered as electrode in the emerging field of organic spintronics. Given the nature of the potential applications, we evaluated the magnetite room-temperature cubic phase in terms of structural, electronic, and magnetic properties. We considered GGA (PBE), GGA + U (PBE + U), and range-separated hybrid (HSE06 and HSE(15%)) functionals. Calculations using HSE06 and HSE(15%) functionals underline the impact that inclusion of exact exchange has on the electronic structure. While the modulation of the band gap with exact exchange has been seen in numerous situations, the dramatic change in the valence band nature and states near the Fermi level has major implications for even a qualitative interpretation of the DFT results. We find that HSE06 leads to highly localized states below the Fermi level while HSE(15%) and PBE + U result in delocalized states around the Fermi level. The significant differences in local magnetic moments and atomic charges indicate that describing room-temperature bulk materials, surfaces and interfaces may require different functionals than their low-temperature counterparts.

Ab initio parameterisation of the 14 band k·p Hamiltonian: Zincblende study

Despite continued and rapid progress in high performance computing, atomistic level device modelling is still largely out of reach, necessitating the use of quantum mechanical continuum methods, including k·p perturbation theory. The effective use of such methods requires reliable parameterisation, often obtained from experiment and ab initio calculations. A major limitation of this, the systematic tendency of ab initio density functional theory to underestimate semiconducting material energy band gaps and related properties, can be greatly improved upon by the inclusion of exact exchange, calculated within the Hartree-Fock formalism. We demonstrate that the 14 band k·p Hamiltonian can be effectively parameterised using this method, at greatly reduced cost in comparison to GW methods.

Simulated Photoemission Spectra of Hydroxylated MgO(100) at Elevated Temperatures

Density functional theory has been used to investigate photoemission O1s core-level shifts (CLS) of hydroxylated MgO(100). Rapid proton exchange at elevated temperatures (300 K) yields broad features in the simulated photoemission signal, in good agreement with experimental observations. The results provide further evidence that the stable structure of hydroxylated MgO(100) consists of a partly dissociated water monolayer. Analysis of the CLS for adsorbed hydroxyl groups at different coverage reveals a pronounced effect on hydrogen bonding to neighboring H2O molecules. The inclusion of exact exchange by use of the hybrid PBE0 functional leads to quantitatively similar results as the gradient corrected PBE functional.

Influence of Triplet Instabilities in TDDFT.

Singlet and triplet vertical excitation energies from time-dependent density functional theory (TDDFT) can be affected in different ways by the inclusion of exact exchange in hybrid or Coulomb-attenuated/range-separated exchange-correlation functionals; in particular, triplet excitation energies can become significantly too low. To investigate these issues, the explicit dependence of excitation energies on exact exchange is quantified for four representative molecules, paying attention to the effect of constant, short-range, and long-range contributions. A stability analysis is used to verify that the problematic TDDFT triplet excitations can be understood in terms of the ground state triplet instability problem, and it is proposed that a Hartree-Fock stability analysis should be used to identify triplet excitations for which the presence of exact exchange in the TDDFT functional is undesirable. The use of the Tamm-Dancoff approximation (TDA) significantly improves the problematic triplet excitation energies, recovering the correct state ordering in benzoquinone; it also affects the corresponding singlet states, recovering the correct state ordering in naphthalene. The impressive performance of the TDA is maintained for a wide range of molecules across representative functionals.

Application of Hybrid Functionals to the Modeling of NO Adsorption on Cu−SAPO-34 and Co−SAPO-34: A Periodic DFT Study

The structural and chemical properties of Cu- and Co-exchanged silicoaluminophosphates with a chabazite-type structure (SAPO-34) and the adsorption of NO molecules on the extraframework cations have been studied using periodic density functional (DFT) calculations using both convential gradient-corrected exchange-correlation functionals and hybrid functionals mixing exact (i.e., Hartree−Fock) and DFT exchange. To assess the importance of the cation-support interaction, comparative studies of NO adsorption on isolated metal atoms and ions have been performed. We find that whereas the geometrical properties for stoichiometric aluminophosphate (ALPO-34) and protonated silicoaluminophosphate (H−SAPO-34) calculated using both types of functionals are essentially on par, the hybrid functionals predict much wider energy gaps in better agreement with experiment. Significant differences arise for the coordination of extraframework cations in the metal-exchanged silicoaluminophosphates (Cu−SAPO-34 and Co−SAPO-34) and, in particular, for the electronic eigenstates of the cations. The different metal−framework coordination and the differences in the electronic properties lead to markedly different predictions of the chemical reactivities: hybrid functionals predict a weaker binding of molecular adsorbates such as NO. The reduction of the adsorption energy is more pronounced for the magnetic Cu(II) and Co(II) cations than for the nonmagnetic Cu(I) cation. This is a consequence of a much larger exchange splitting of the d states of the cation and also of an enhanced ligand-field splitting due to the binding to the framework. The occupied d states of the transition-metal cations are shifted to larger binding energies, and the empty d states are located in the upper part of the energy gap. Hybrid functionals tend to overestimate the N−O stretching frequency even for the isolated molecule and for gas-phase nitrosyls, whereas conventional functionals predict eigenvalues that are too low. This tendency is also reflected in the vibrational spectra of the Cu(Co)−NO adsorption complexes, whereas the adsorption-induced frequency shifts predicted by both types of functionals are in reasonable agreement with experiment. Significant differences are found in the prediction of the spin states of the adsorption complexes. Altogether, we conclude that conventional gradient-corrected DFT functionals describe these complex materials with good accuracy, whereas the inclusion of exact exchange in the hybrid functionals does not lead to improved performance for the metal-exchanged systems.

Selenium chemistry with DFT: molecular structures and 77Se NMR shielding constants

Optimized geometries of fourteen selenium-containing molecules are determined using density functional theory, with the KT3, HCTH and OLYP generalized gradient approximations and the B3LYP and B97-2 hybrid functionals. Bond length quality can be summarized as B97-2 > KT3 > B3LYP > HCTH > OLYP. For a subset of seven molecules, the same functionals are used to determine isotropic and anisotropic shielding constants. The shielding quality can be summarized as KT3 > B97-2 > HCTH ≈ OLYP > B3LYP. The study supports earlier observations that, by DFT standards, KT3 can simultaneously provide good quality geometries and shielding constants, without the inclusion of exact exchange. The study also highlights the relatively poor results from the widely-used B3LYP functional.

Practical failures from the inclusion of exact exchange: how much exact exchange is appropriate?

The influence of exact exchange incorporated into exchange—correlation functionals on the predictions of relative energies, structures, electronic states, and vibrational spectra is examined numerically. Failures of widely used hybrid exchange—correlation functionals due to either the physical unacceptability of including exact exchange or an unbalanced mixing of exact exchange are considered. One set of examples involves tetraatomic chalcogen clusters and charge transfer complexes between diatomic chalcogens and diatomic oxygen. Poor energetic predictions from Hartree-Fock rule against the inclusion of exact exchange into the exchange—correlation functionals for these systems with significant left—right electron correlation effects. The energies of the conformers of [10]annulene are considered from an unusual viewpoint, namely, the empirical adjustment of the admixture of exact exchange to match the predictions of very high level theoretical methods. For this annulene with insignificant left-right electron correlation effects, a greater (50%) percentage of exact exchange should be included. The relationship of symmetry breaking to the inclusion of exact exchange is examined for seven linear radicals, OXO (X = B, Al, Ga, In, TI). AIOS, and OAIS. exchange—correlation functionals generate symmetry adapted solutions at the expense of an unusual ordering of the Kohn-Sham orbitals, which can cause uncharacteristic electronic states, incorrect vibrational spectra, and poorer predictions of energetics. These effects are greater when exact exchange is included. In all the examples considered, the appropriate focus for a detailed discussion of molecular properties involves consideration of the effects of exact exchange.

Inclusion of exact exchange for self-interaction corrected H 3 density functional potential energy surface

The effect of the inclusion of the exact exchange into self-interaction corrected generalized gradient approximation density functional theory (GGA-DFT) for the simplest hydrogen abstraction reaction, H + H2 → H3 → H2 + H, is presented using a triple-zeta augmented 6-311++G(d,3pd) basis set. The introduction of the self-interaction correction has a considerably larger effect on molecular geometry and vibrational frequencies than the inclusion of the exact exchange. We investigate the influence of the self-interaction error on the shape of the potential energy surface around the transition state of the hydrogen abstraction reaction. The decomposition of the self-interaction error into correlation and exchange parts shows that the exchange self-interaction error is the main component of the energy barrier error. The best agreements with the experimental barrier height were achieved by self-interaction corrected B3LYP, B-LYP and B3PW functionals with errors of 1.5, 2.9 and 3.0 kcal/mol, respectively.