Meta GGA Research Articles

Effects of London dispersion correction in density functional theory on the structures of organic molecules in the gas phase

A benchmark set of 25 rotational constants measured in the gas phase for nine molecules (termed ROT25) was compiled from available experimental data. The medium-sized molecules with 18-35 atoms cover common (bio)organic structure motifs including hydrogen bonding and flexible side chains. They were each considered in a single conformation. The experimental B0 values were back-corrected to reference equilibrium rotational constants (Be) by computation of the vibrational corrections ΔBvib. Various density functional theory (DFT) methods and Hartree-Fock with and without dispersion corrections as well as MP2 type methods and semi-empirical quantum chemical approaches are investigated. The ROT25 benchmark tests their ability to describe covalent bond lengths, longer inter-atomic distances, and the relative orientation of functional groups (intramolecular non-covalent interactions). In general, dispersion corrections to DFT and HF increase Be values (shrink molecular size) significantly by about 0.5-1.5% thereby in general improving agreement with the reference data. Regarding DFT methods, the overall accuracy of the optimized structures roughly follows the 'Jacobs ladder' classification scheme, i.e., it decreases in the series double-hybrid > (meta)hybrid > (meta)GGA > LDA. With B2PLYP-D3, SCS-MP2, B3LYP-D3/NL, or PW6B95-D3 methods and extended QZVP (def2-TZVP) AO basis sets, Be values, accurate to about 0.3-0.6 (0.5-1)% on average, can be computed routinely. The accuracy of B2PLYP-D3/QZVP with a mean deviation of only 3 MHz and a standard deviation of 0.24% is exceptional and we recommend this method when highly accurate structures are required or for problematic conformer assignments. The correlation effects for three inter-atomic distance regimes (covalent, medium-range, long) and the performance of minimal basis set (semi-empirical) methods are discussed.

C–N bond dissociation energies: An assessment of contemporary DFT methodologies

The assessment of the C–N bond dissociation energies is performed by using the various density functionals at 6-31+g(d,p) level. CBS-QB3 method was used to provide the theoretical benchmark values. The present results show that the three hybrid meta GGA functionals, BB1K, MPWB1K and M06 reproduce the experimental values well. M06-2X could normally overestimate the homolytic C–N bond dissociation energies. For the hybrid functionals, B3P86 and PBE1PBE can also behave almost as well as the above meta GGA functionals. Thus, they should be recommended as the most reliable method to estimate the energetic C–N bond dissociation energies.

Performance of Density Functional Theory for 3d Transition Metal-Containing Complexes: Utilization of the Correlation Consistent Basis Sets

The performance of 44 density functionals used in conjunction with the correlation consistent basis sets (cc-pVnZ where n = T and Q) has been assessed for the gas-phase enthalpies of formation at 298.15 K of 3d transition metal (TM) containing systems. Nineteen molecules were examined: ScS, VO, VO(2), Cr(CO)(6), MnS, MnCl(2), Mn(CO)(5)Cl, FeCl(3), Fe(CO)(5), CoH(CO)(4), NiCl(2), Ni(CO)(4), CuH, CuF, CuCl, ZnH, ZnO, ZnCl, and Zn(CH(3))(2). Of the functionals examined, the functionals that resulted in the smallest mean absolute deviation (MAD, in parentheses, kcal mol(-1)) from experiment were B97-1 (6.9), PBE1KCIS (8.1), TPSS1KCIS (9.6), B97-2 (9.7), and B98 (10.7). All five of these functionals include some degree of Hartree-Fock (HF) exchange. The impact of increasing the basis set from cc-pVTZ to cc-pVQZ was found to be slight for the generalized gradient approximation (GGA) and meta-GGA (MGGA) functionals studied, indicating basis set saturation at the triple-zeta level. By contrast, for most of the generalized gradient exchange (GGE), hybrid GGA (HGGA), and hybrid meta-GGA (HMGGA) functionals considered, improvements in the average MAD of 2-3 kcal mol(-1) were seen upon progressing to a quadruple-zeta level basis set. Overall, it was found that the functionals that include Hartree-Fock exchange performed best overall, but those with greater than 40% HF exchange exhibit significantly poor performance for the prediction of enthalpies of formation for 3d TM complexes. Carbonyl-containing complexes, a mainstay in organometallic TM chemistry, are demonstrated to be exceedingly difficult to describe accurately with all but 2 of the 44 functionals considered. The most accurate functional, for both CO-containing and CO-free compounds, is B97-1/cc-pVQZ, which is shown to be capable of yielding results within 1 kcal mol(-1) of high-level ab initio composite methodologies.

Can the hybrid meta GGA and DFT‐D methods describe the stacking interactions in conjugated polymers?

Newly developed hybrid meta density functionals and density functionals augmented by a classical London dispersion term have been systematically applied for the description of stacking energy and intermolecular distance of thiophene dimer and substituted thiophene dimer. The performance of the various approaches is compared with the benchmark ab-initio calculations done with CCSD(T) (Tsuzuki et al., JACS 2002, 124, 12200). Our results indicate that, contrary to the previous DFT methods which are not reliable, the new generation of DFT performs better the stacking interactions. These functionals, and especially those with an empirical correction, are suitable for general application in conducting polymers and, in particular, the modeling of solid state in which the overlap of Pi-Pi interactions between the conjugated chains is important.

Stacking and Solvent Effects on the Electronic and Optical Properties of Gold and Mercury Acetylide Aggregations: A Theoretical Study

The effects of various packing styles, solvents, and substituents on the electronic structures of gold(I) and mercury(II) acetylides are investigated by using the density functional theory (DFT) and the time-dependent density functional theory (TDDFT). In comparison with the second-order Moeller−Plesset (MP2) and coupled-cluster (CCSD(T)) results, most of the hybrid GGA and hybrid meta GGA (among the studied 36 DFT functionals) can give reasonable predictions on binding energies in a dimer. A series of packing aggregates extended along intermolecular Au···Au and π−π (between aryl ligands) contacting directions are employed to illustrate the stacking dependence of the low-lying vertical excitation energies. The lowest excitation energy undergoes little change from the Au···Au linked dimer to higher oligomers. A polarized continuum model (PCM) study is carried out on a series of substituted gold and mercury acetylide derivatives in several solutions. The lowest vertical excitation energies exhibit a blue sh...

Nonempirical Construction of Current-Density Functionals from Conventional Density-Functional Approximations

Density-functional approximations for the exchange-correlation energy Exc[n] of a many-electron ground state are highly developed and widely useful. When a paramagnetic current jp(r) is present, Vignale and Rasolt have extended the Kohn-Sham theorems and presented an additive correction valid to second order in the gauge-invariant vorticity nu=Delta x (jp/n):Exc[n, jp]=Exc[n, jp=0] + DeltaE(VR)(xc)[n, nu]. Apart from spin-polarization effects, their correction is unambiguous for a generalized gradient approximation (GGA). But for a meta-GGA (MGGA), one needs to know how to go back from the orbital kinetic energy density tau([n, jp];r) to tau([n,0];r); we show how to do this here. Numerical tests on the degeneracies for open-shell atoms show that current-density corrections reduce the error of GGA from 2 to 1 kcal/mol, and of MGGA from 5 to 2 kcal/mol.

New Effective Core Method (Effective Core Potential and Valence Basis Set) for Al Clusters and Nanoparticles and Heteronuclear Al-Containing Molecules.

In previous work we have shown that the PBE0 hybrid density functional method with the MG3 all-electron basis set is an accurate method for calculating the atomization energies of small aluminum clusters (Al2-Al7). However, the MG3 basis set is very expensive for molecules much larger than Al13; therefore, we have developed a new effective core potential (ECP) method for aluminum to reduce the cost of obtaining accurate results for nanoparticles. Our method involves a hybrid of the Stuttgart semiempirical effective core potential and the compact effective potential (CEP) potential, and it uses a newly optimized polarized valence triple-ζ basis set. The combination of the new ECP and the new polarized valence triple-ζ basis set for Al is called the Minnesota effective core (MEC) method for Al. The method was optimized with a training set of atomization energies and geometries for AlH, AlC, AlO, AlCCH, Al2H, Al2C, Al2O, and Al3 and atomization energies of three Al13 structures, and we tested it on six test sets composed of 20 atomization energies for systems as large as Al13. We also present an improved all-electron polarized triple split basis set for oxygen, called 6-311+G(d*,p). For the test sets, the mean unsigned error (MUE) of the new method with respect to PBE0/MG3 is 0.06 eV for atomization energies and 0.007 Å for bond lengths, which constitutes a very significant improvement over the quality of the results that can be obtained with effective core potentials and valence basis sets in the literature (of the eight methods in the literature, the best previous method had average errors of 0.63 eV and 0.036 Å). We have also tested the MEC method with a variety of hybrid density functional theory, hybrid meta density functional theory, and pure GGA and meta GGA functionals and found that the average MUE, relative to each functional with all-electron basis sets, is 0.04 eV for atomization energies and 0.009 Å for bond lengths for the new effective core method and 0.16-0.20 eV and 0.013-0.033 Å for effective core potential and valence basis sets in the literature.

On the geometric structure of the (0 0 0 1) hematite surface

A theoretical study of the surface structural relaxation of the (0 0 0 1) hematite is presented which explores the influence of the size of a slab model, the number of relaxed surface layers and various computational approaches, all of them based on density functional theory (DFT). Four different slab models including 9, 12, 15, and 18 layers were analyzed. In each model, sequences from 1 to 7 layers were relaxed while keeping the bottom layers fixed to mimic the constraints imposed by the bulk. In the geometry optimization procedure, four different DFT approximation levels were employed, namely, the non-selfconsistent Harris functional, the local spin-density approximation, LSDA, the PW91 or BP meta GGA functionals and the hybrid B3LYP method. It was found that the relaxation predicted for up to four layers is independent of the slab thickness. Except for the Harris functional, all methods and models predict consistent values for the relaxation of the innermost layers. It is concluded that the Harris functional can be used to explore the adequacy of a given model but not to provide an accurate enough structure of the relaxed hematite (0 0 0 1) surface.

Two-dimensional limit of exchange-correlation energy functional approximations

We investigate the behavior of three-dimensional (3D) exchange-correlation energy functional approximations of density-functional theory in anisotropic systems with two-dimensional (2D) character. Using two simple models, the quasi-2D electron gas and two-electron quantum dot, we show a fundamental limitation of the local density approximation (LDA) and its semilocal extensions, generalized gradient approximation (GGA) and meta-GGA (MGGA), the most widely used forms of which are worse than the LDA in the strong 2D limit. The origin of these shortcomings is in the inability of the local (LDA) and semilocal (GGA/MGGA) approximations to describe systems with 2D character in which the nature of the exchange-correlation hole is very nonlocal. Nonlocal functionals provide an alternative approach, and explicitly the average density approximation is shown to be remarkably accurate for the quasi-2D electron gas system. Our study is not only relevant for understanding of the functionals but also practical applications to semiconductor quantum structures and materials such as graphite and metal surfaces. We also comment on the implication of our findings to the practical device simulations based on the (semi)local density-functional method.