Non-local Exchange-correlation Functionals Research Articles

Taming Negative Ion Resonances Using Nonlocal Exchange-Correlation Functionals.

The characterization of negative ion resonances poses a fundamental challenge to density functional methods due to the unbound nature of resonances. To overcome this challenge, we propose one-particle nonlocal exchange-correlation (xc) potentials combining the exact-exchange (EXX) and the random phase approximation (RPA) correlation potentials. The negative ion resonances are identified by perturbing the real Hermitian nonlocal xc potentials using complex absorbing local potentials. Our studies show that the nonlocal EXX+RPA potential significantly enhances the description of positions and widths of negative ion resonance states compared to potentials that exclude dynamic polarization in RPA or include only EXX. The use of low-scaling algorithms simplifies the computation of the RPA potential, thereby providing a practical solution for resonance-state characterization within the density functional framework. A theoretical framework and the underlying assumptions required for combining real Hermitian nonlocal xc potentials with complex local potentials are discussed.

Superconductivity in transition metal carbides, TaC and HfC: A density functional theory study with local, semilocal, and nonlocal exchange–correlation functionals

We studied electronic, dynamical, and superconducting properties of TaC and HfC using local, semilocal, and nonlocal exchange–correlation functionals in the density functional theory. It turns out that there is a slight shift of Fermi energy and the corresponding density of states with different functionals. However, the phonon frequencies of, especially, the optical modes for both TaC and HfC shift by moderately larger values. The most important differences are observed for the electron–phonon interactions where the electron–phonon coupling constant, λ≈0.9, calculated using the nonlocal correlation functionals, vdW-DF2 and vdW-DF3 for TaC, are in the closest agreement with the experimental results. Although the Kohn anomalies and Fermi surface nesting are critical for the electron–phonon coupling, a significant contribution to λ, for TaC, comes from the regions of the Brillouin zone where the matrix elements have a predominant role. Moreover, the optical modes give 20%–23% of λ for TaC and 50%–57% for HfC.

Note: Reproducibility of potential energy surfaces of organic/metal interfaces on the example of PTCDA on Ag(111).

We recently published a benchmark study of common local, semi-local, and non-local exchange correlation functionals in combination with various van der Waals (vdW) corrections, where we investigated the reproducibility of the potential energy surface of perylenetetracarboxylic dianhydride on Ag(111). This Note presents an additional benchmark of the recently developed non-local many body dispersion (MBD-NL) vdW correction, coupled with the Perdew-Burke-Ernzerhof (PBE) functional. We find that this computation method shows similar performance as the established approaches. Notably, it yields very similar results as PBE + MBD.

EQE 2.0: Subsystem DFT beyond GGA functionals

By adopting a divide-and-conquer strategy, subsystem-DFT (sDFT) can dramatically reduce the computational cost of large-scale electronic structure calculations. The key ingredients of sDFT are the nonadditive kinetic energy and exchange-correlation functionals which dominate it's accuracy. Even though, available semilocal nonadditive functionals find a broad range of applications, their accuracy is somewhat limited especially for those systems where achieving balance between exchange-correlation interactions on one side and nonadditive kinetic energy on the other is crucial. In eQE 2.0, we improve dramatically the accuracy of sDFT simulations by (1) implementing nonlocal nonadditive kinetic energy functionals based on the LMGP family of functionals; (2) adapting Quantum ESPRESSO's implementation of rVV10 and vdW-DF nonlocal exchange-correlation functionals to be employed in sDFT simulations; (3) implementing “deorbitalized” meta GGA functionals (e.g., SCAN-L). We carefully assess the performance of the newly implemented tools on the S22-5 test set. eQE 2.0 delivers excellent interaction energies compared to conventional Kohn-Sham DFT and CCSD(T). The improved performance does not come at a loss of computational efficiency. We show that eQE 2.0 with nonlocal nonadditive functionals retains the same linear scaling behavior achieved previously in eQE 1.0 with semilocal nonadditive functionals. Program summaryProgram title: eQECPC Library link to program files:https://doi.org/10.17632/g55n9xmnt2.1Developer's repository link:https://gitlab.com/Pavanello/eqeLicensing provisions: GPLv2Programming language: Fortran 90External routines/libraries: BLACS, MPINature of problem: Solving the electronic structure of molecules and materials with subsystem density functional theorySolution method: This version of eQE uses subsystem Density-Functional Theory (DFT) to compute the electronic structure of molecules and materials. Subsystem DFT is a divide-and-conquer version of DFT that can be massively parallelized and is linear scaling in work and data. However, it requires the use of density functionals for kinetic and exchange-correlation energies. eQE can now employ nonlocal functionals as well as meta-GGA functionals for these energy terms.Additional comments: Url of stable release http://eqe.rutgers.edu

Kinetic and Exchange Energy Densities near the Nucleus

We investigate the behavior of the kinetic and the exchange energy densities near the nuclear cusp of atomic systems. Considering hydrogenic orbitals, we derive analytical expressions near the nucleus, for single shells, as well as in the semiclassical limit of large non-relativistic neutral atoms. We show that a model based on the helium iso-electronic series is very accurate, as also confirmed by numerical calculations on real atoms up to two thousands electrons. Based on this model, we propose non-local density-dependent ingredients that are suitable for the description of the kinetic and exchange energy densities in the region close to the nucleus. These non-local ingredients are invariant under the uniform scaling of the density, and they can be used in the construction of non-local exchange-correlation and kinetic functionals.

Crystal structure optimisation using an auxiliary equation of state.

Standard procedures for local crystal-structure optimisation involve numerous energy and force calculations. It is common to calculate an energy-volume curve, fitting an equation of state around the equilibrium cell volume. This is a computationally intensive process, in particular, for low-symmetry crystal structures where each isochoric optimisation involves energy minimisation over many degrees of freedom. Such procedures can be prohibitive for non-local exchange-correlation functionals or other "beyond" density functional theory electronic structure techniques, particularly where analytical gradients are not available. We present a simple approach for efficient optimisation of crystal structures based on a known equation of state. The equilibrium volume can be predicted from one single-point calculation and refined with successive calculations if required. The approach is validated for PbS, PbTe, ZnS, and ZnTe using nine density functionals and applied to the quaternary semiconductor Cu2ZnSnS4 and the magnetic metal-organic framework HKUST-1.

Dispersion effects inSiO2polymorphs: Anab initiostudy

The effect of electronic dispersion over a wide variety of SiO2 polymorphs (faujasite, ferrierite, α-cristobalite, α-quartz, coesite, and stishovite) is investigated using state-of-the-art density functional theory. Different functionals and dispersion correction schemes are compared, ranging from the local density approximation to fully nonlocal exchange-correlation functionals. It is shown that both empirical dispersion corrections and fully nonlocal functionals improve the energetics and give correct volumetric data. However, the correct volume results come from error cancellation between an overestimation of the Si-O distance and an underestimation of the Si-O-Si angle. Quantum Monte Carlo is used to compute the quartz-cristobalite energy difference within an accuracy of 0.2 kCal/mol per SiO2 unit. This demonstrates the feasability of achieving subchemical accuracy on extended systems, and confirms the validity of the Slater-Jastrow ansatz for describing SiO2 polymorphs.

Nuclear Quantum Effects and Nonlocal Exchange-Correlation Functionals Applied to Liquid Hydrogen at High Pressure

Using first-principles molecular dynamics, we study the influence of nuclear quantum effects (NQEs) and nonlocal exchange-correlation density functionals (DFs) near molecular dissociation in liquid hydrogen. NQEs strongly influence intramolecular properties, such as bond stability, and are thus an essential part of the dissociation process. Moreover, by including DFs that account for either the self-interaction error or dispersion interactions, we find a much better description of molecular dissociation and metallization than previous studies based on classical protons and/or local or semilocal DFs. We obtain excellent agreement with experimentally measured optical properties along Hugoniot curves for precompressed states, and while we still find a first-order liquid-liquid transition at low temperatures, transition pressures are increased by more than 100GPa.

Hydrogen migration on the C60 fullerene

We investigate the migration barriers, transition states, and optimum migration paths of hydrogen on the C60 fullerene using the ab initio density functional theory. Calculated energy barriers tend to be higher for non-local exchange-correlation functionals. We find that the migration between adsorption sites with the same energy has high migration barriers, and thus the initial stages of the H nucleation requires desorption–adsorption cycles. The migration barrier is reduced near another H adsorbate. The migration may be involved more in the later stages of the regio-selective hydrogenation of C60. We find that the migration barriers are reduced by the presence of hydrogen sources, and the hydrogenating agents in the environment are required in order to reach the regio-selective hydrogenation of the C60 fullerene.

Trans-1,2-Dicyano-cyclopropane and other cyano-cyclopropane derivatives

In this work we present the experimental vibrational absorption (VA), vibrational circular dichroism (VCD) and Raman spectra for (+)-trans-1(S),2(S)-dicyanocyclopropane and its dideuterio derivative, trans-1(S),2(S)-dicyano-1(S),2(S)-dideuteriocyclopropane, along with VA, VCD, Raman and Raman optical activity (ROA) spectral simulations. Here we investigate the applicability of various local and non-local exchange-correlation (XC) functionals, hybrids and meta-hybrids to reproduce the vibrational spectra of this strained ring system, which also bears two cyano groups. At the highest level of theory, B3PW91/ aug-cc-pVTZ, we also investigated the trans-, cis- and gem-dicyanocyclopropane (trans-, cis-, and gem-DCCP), cyanocyclopropane (CCP) and the parent molecule cyclopropane (CP). In doing so we have investigated the electronic effects (coupling) between the cyano groups and the cyclopropane ring. In addition to providing an interpretation of the experimentally observed vibrational spectra for these molecules, this work also provides benchmark calculations for other methods, especially semi-empirical based wave function and density functional theory (DFT) based methods, such as SCC-DFTB and PM6. For the semi-empirical DFT based methods to be used for 3-membered ring systems, one ought to document their reliability for systems which were not used in the parameterization. The small 3- and 4-membered ring systems are good test systems because they contain non-standard bonding, which may be difficult to determine accurately with the approximations used in the SCC-DFTB and other semi-empirical methods. Like molecular mechanics force fields, semi-empirical methods, based on DFT and wave function quantum mechanics (WFQM), must be benchmarked against high level ab initio and DFT calculations and experimental data. In addition to bonding, the changes in the electric dipole moment, magnetic dipole moment, electric dipole-electric dipole polarizability, electric dipole-magnetic dipole polarizability and electric dipole-electric quadrupole polarizability with respect to nuclear displacement and nuclear velocity can be determined by the VA, VCD, Raman and ROA intensities. Hence it is important that the semi-empirical based DFT and wave function methods not only be parameterized to determine energies, gradients and Hessians, but also the electric and magnetic moments and their derivatives that determine the electronic and magnetic properties of these molecules and their interactions with matter and radiation. This will allow biochemists, biophysicists, molecular biologists, and physical biologists to use experimental and theoretical VA, VCD, Raman and ROA spectroscopies to probe biophysical and biochemical function and processes at the molecular level.

On the performance of local, semilocal, and nonlocal exchange-correlation functionals on transition metal molecules

The lowest singlet-triplet transition (X (1)Sigma+-(3)Sigma+) of AgI has been used to study systematically the performance of local [local density approximation (LDA)], semilocal [generalized gradient approximation (GGA)], and nonlocal (semiempiric hybrid and meta)-type exchange-correlation functionals on a transition metal molecule where dynamic electronic correlation effects are essential. Previous benchmark ab initio calculations showed that the triplet ground state possesses a shallow well in the Franck-Condon region before becoming repulsive at longer internuclear distance [A. Ramirez-Solis, J. Chem. Phys. 118, 104 (2003)]. Several density functional theory (DFT) descriptions are compared with the benchmark complete active space self-consistent-field+averaged coupled pair functional results, using the same relativistic effective core potentials and optimized Gaussian basis sets. A rather unreliable performance of exchange-correlation functionals was found when ascending the various rungs in DFT Jacob's ladder for this complex molecule. While some of the simpler (LDA and GGA) functionals correctly predict the presence of a short-distance maximum for the (3)Sigma+ state, more sophisticated hybrid and meta-functionals lead to totally repulsive or oscillating curves for the ground triplet state. A thorough discussion addressing the local versus nonlocal character of the exchange and correlation effects on the triplet potential curve is presented. The author concludes that any new efforts directed at producing more accurate exchange-correlation functionals must take into account the more complex electronic structure arising in transition metal molecules, whether these efforts follow the dominant pragmatic semiempiric trend or the more philosophically correct nonempiric pathway to develop better exchange-correlation functionals; only then will the Kohn-Sham version of DFT make the necessary improvements to correctly describe the electronic structure of complex transition metal systems.

DFT studies using supercells and projector‐augmented waves for structure, energetics, and dynamics of glycine, alanine, and cysteine

A large variety of gas phase conformations of the amino acids glycine, alanine, and cysteine is studied by numerically efficient semi-local gradient-corrected density functional theory calculations using a projector-augmented wave scheme and periodic boundary conditions. Equilibrium geometries, conformational energies, dipole moments, vibrational modes, and IR optical spectra are calculated from first principles. A comparison of our results with values obtained from quantum-chemistry methods with localized basis sets and nonlocal exchange-correlation functionals as well as with experimental data is made. For conformations containing strong intramolecular hydrogen bonds deviations in their energetic ordering occur, which are traced back to different treatments of spatial nonlocality in the exchange-correlation functional. However, even for these structures, the comparison of calculated and measured vibrational frequencies shows satisfying agreement.

A density functional theory analysis of Raman and IR spectra of 2-adamantanone

The vibrational force fields for cage-like molecules 2-adamantanone (2-A) and adamantane (A) were calculated by employing density functional theory (DFT) using 6-31G(d,p) basis set with two non-local exchange-correlation functionals BLYP (Becke–Lee–Young–Parr) and the Becke's three-parameter compound functional B3LYP. DFT infrared intensities and the Raman scattering activities were also calculated to simulate the vibrational spectra. The analysis of the two chosen models show that they are comparable in predicting geometry, vibrational frequencies, IR and Raman intensities. The agreement between the predicted and observed IR and Raman spectra is not satisfactory in the region 1500–1200 cm −1 for either of them. The overestimation of the computed intensity connected to the motion of methylene hydrogen atoms is ascribed to the systematic shortcoming of the computational theory. The approach to assignment of the vibrational spectra that combines the comparison of not only calculated and observed frequencies but also of IR and Raman intensities is tested on A and applied to reassignment of the normal modes of 2-A. The scale factors for the force constants of the CO group were derived. The scaled BLYP and B3LYP force fields reproduced the experimental frequencies of 2-A with an average error of 12 and 10 cm −1, respectively. The error in reproducing the experimental frequencies of A is 13 cm −1 (BLYP).

Accurate density functionals: Approaches using the adiabatic-connection fluctuation-dissipation theorem

Fully nonlocal exchange-correlation functionals derived from the adiabatic-connection fluctuation-dissipation theorem can go beyond local or gradient corrected functionals and include the van der Waals interaction. We implement three functionals of this class, in a pseudopotential plane-wave framework, (1) using the random-phase approximation (RPA), (2) adding to the RPA short-range correlations $(\mathrm{RPA}+),$ and (3) including density fluctuations through an exchange kernel. We find the binding energy of the ${\mathrm{H}}_{2}$ and ${\mathrm{Be}}_{2}$ molecules described, by all three functionals, within 0.1 eV accuracy.

Theoretical Study of Hydrogen Adsorption and Diffusion on TiN(100) Surface

TiN bulk and surface energy and hydrogen atom adsorption at three different sites have been studied using density functional theory (DFT) with local and non-local exchange–correlation functionals. Calculations of surface energies confirm the experimental findings that the (100) surface has the lowest and the (111) surface the highest surface energy, respectively. Adsorption of H on top of Ti atom is more favorable by 1.7 kcal/mol than on top of N atom and is in agreement with plane-wave calculations and experimental results available in the literature. We also discuss the surface diffusion scenario of H on the (100) surface of TiN.

Vibrational spectroscopic and quantum chemical studies of the trioxatriangulenium carbocation

Raman and infrared (IR) spectra of the stable carbocation trioxatriangulenium (TOTA) are reported. In a theoretical effort, ab initio and density function theory (DFT) methods are used to determine the vibrational spectra and the optimized geometry of TOTA. The theoretical results are compared with the experimentally obtained spectra and with the previously reported X-ray crystal structure. It is concluded that DFT calculations based on the non-local exchange-correlation functionals (UB-LYP) yields the most accurate description of the vibrational spectra and the geometry of TOTA. As a result of the calculations, it appears that the positive charge in the TOTA carbocation is substantially delocalized.

Density Functional Theory Study of the Hydrogen-Bonded Pyridine−H2O Complex: A Comparison with RHF and MP2 Methods and with Experimental Data

As a test for the applicability of the density functional theory (DFT) to hydrogen-bonded systems, various local and nonlocal exchange correlation functionals have been used to calculate the equilibrium structure and the harmonic vibrational frequencies of the pyridine−water complex. We also performed restricted Hartree−Fock (RHF) and Moller−Plesset (MP2) calculations for comparison. Three different basis sets (6-31G**, 6-31++G**, and 6-311++G(2d, 2p) 6d)) were used in the study. The best agreement between the DFT computed and the experimental rotational constants for monomeric pyridine were obtained with the B3-PW91 and B3-LYP functionals. For the vibrational frequencies of the H-bonded complex, the experimental data from matrix FT-IR spectrometry as well as the results obtained from the ab initio methods were best reproduced with the DFT method with the nonlocal exchange and correlation functionals. The hybrid approaches, which mix HF and Slater exchange, are particularly effective in these types of calculations.

Ab initio molecular study of hydrogen peroxide.: Application of density functional methods

A systematic study of the abilities of a broad family of density functional methods and basis sets has been carried out on hydrogen peroxide. Calculations have been performed using different basis sets from 3-21G to 6-311+G(3d, 2p). Various local and non-local exchange, exchange-correlation and hybrid functionals have been applied in order to study the structure, energetic and vibrational properties of hydrogen peroxide. Comparison with experimental data and also with results from ab initio methods (HF and correlated levels) shows a good performance of non-local density functional methods for the description of the hydrogen peroxide geometry, especially the torsion angle τ, when we use basis sets of sufficient quality (at the least basis sets with a polarization function on oxygen). Different density functionals have been used in order to study cis and trans rotational transition states, using 6-31G(2d,p) and 6-31+G(2d,p) basis sets. The calculated torsional barriers and zero-point vibrational energies (ZPEs) are in very good agreement with experimental values.

Density functional study on the structures and vibrational spectra of the radical anion and cation of biphenyl

Density functional theory using the 6–31G ∗ basis set and two non-local exchange-correlation functionals (B-YLP and B3-LYP) has been applied to the calculations of the structures and vibrational spectra of the radical anion and cation, of biphenyl. The B3-LYP dihedral angles between the two phenyl rings are 5.8 ° and 19.5 ° for the radical anion and cation respectively. Upon ionization, structural changes occur in the direction from benzenoid to quinoid. The unsealed vibrational frequencies calculated at the B-YLP/6–31G ∗ level are mostly in agreement with the frequencies in the Raman spectra of the radical anion and cation of the normal and perdeuterated species reported in the literature. The calculations predict that both the radical anion and cation give rise to a very strong infrared band, and that this band arises from a mode in which the benzenoid-to-quinoid deformation occurs out of phase in the two phenyl rings.

Hydrogen-bonding in glycine and malonaldehyde: Performance of the Lap1 correlation functional

The conformational equilibrium of gaseous glycine presents a severe challenge to quantum chemistry and, in particular, to density functional theory (DFT), due to the presence of internal hydrogen bonds. We present new DFT results for the structure and the energetics of glycine and malonaldehyde, using the recently developed nonlocal exchange-correlation functionals BLap1 and PLap1. A comparative analysis is made with the results of the generalized-gradient-approximation (GGA) schemes Becke–Perdew (BP86) and Becke–Lee–Yang–Parr (BLYP), the hybrid Hartree–Fock (HF)-DFT methods B3PW91 and B3LYP, with post-HF methods, and with the available experimental data. Our BLap1/TZVP and PLap1/TZVP values for the energy margin between the two lowest conformers of glycine (0.84 and 1.05 kcal/mol, respectively) are within the experimental error bars (1.0±0.5 kcal/mol). MP2 underestimates this energy difference by about 0.5 kcal/mol, BLYP and the hybrid methods are off by about 0.9 kcal/mol. The optimized geometry of malonaldehyde is improved with the Lap1 functionals, compared to the GGA results reported previously. Improvement over the GGA is also achieved for the energy barrier for the internal proton transfer in malonaldehyde. Recent high quality post-HF (G2) calculations of Barone and Adamo1 yield 4.4 kcal/mol. The best GGA (PP86) value of 2.1 kcal/mol is seriously underestimated. The best B3LYP estimate is 3.0 kcal/mol.1 Our BLap1/TZVP (3.28 kcal/mol) and PLap1/TZVP (4.56 kcal/mol) values are in the correct energy range, the latter being, in fact, very close to the G2 estimate.