Assessing the performance of density functional theory for the dynamic polarizabilities of amino acids: Treatment of correlation and role of exact exchange

The theoretical determination of electric response properties of the biological systems is a field where the application of density functional theory (DFT) appears to be quite promising. In this work, the performance of 41 density functional methods is evaluated in predicting dynamic polarizabilities of an experimental benchmark set of 20 proteinogenic amino acids. The behavior of a large number of density functionals, including various types of the local spin density approximation (LSDA), generalized gradient approximation (GGA), meta‐GGA (m‐GGA), hybrid‐GGA (h‐GGA), hybrid meta‐GGA (hm‐GGA), and range‐separated hybrid‐GGA (rsh‐GGA), has been assessed for the purpose. Analyzing the results of our DFT benchmarking, we found that these computationally economical methods show very diverse predictive capability and a careful selection of DFT functionals is very important in the polarizability calculations. Considering the role of exchange, correlation, dispersion and long‐range corrections, it turned out that in the LSDA class, SVWN3 gives better results than SPL and SVWN5 toward the reference values. Of the GGA methods, OPBE outperforms all other functionals. The M06‐L is the best method of m‐GGA class. The B3LYP and TPSSh are the best functionals of h‐GGA and hm‐GGA lineages, respectively. Finally, CAM‐B3LYP is the best method of rsh‐GGA functionals that predicts the most accurate polarizability for amino acids by a large margin with respect to others. Overall, the best performing functionals turn out to be hm‐GGAs TPSSh, TPSS1KCIS, M05, tau‐HCTHhyb, and h‐GGA B3LYP. Hopefully, the results of this investigation might provide the useful guidance to propose a new exchange‐correlation functional for calculating the optical properties of biomolecular materials. © 2013 Wiley Periodicals, Inc.     

Spin‐component‐scaled double hybrids: An extensive search for the best fifth‐rung functionals blending DFT and perturbation theory

Following up on an earlier preliminary communication (Kozuch and Martin, Phys. Chem. Chem. Phys. 2011, 13 , 20104), we report here in detail on an extensive search for the most accurate spin‐component‐scaled double hybrid functionals [of which conventional double hybrids (DHs) are a special case]. Such fifth‐rung functionals approach the performance of composite ab initio methods such as G3 theory at a fraction of their computational cost, and with analytical derivatives available. In this article, we provide a critical analysis of the variables and components that maximize the accuracy of DHs. These include the selection of the exchange and correlation functionals, the coefficients of each component [density functional theory (DFT), exact exchange, and perturbative correlation in both the same spin and opposite spin terms], and the addition of an ad‐hoc dispersion correction; we have termed these parametrizations “DSD‐DFT” (Dispersion corrected, Spin‐component scaled, Double‐hybrid DFT). Somewhat surprisingly, the quality of DSD‐DFT is only mildly dependent on the underlying DFT exchange and correlation components, with even DSD‐LDA yielding respectable performance. Simple, nonempirical GGAs appear to work best, whereas meta‐GGAs offer no advantage (with the notable exception of B95c). The best correlation components appear to be, in that order, B95c, P86, and PBEc, while essentially any good GGA exchange yields nearly identical results. On further validation with a wider variety of thermochemical, weak interaction, kinetic, and spectroscopic benchmarks, we find that the best functionals are, roughly in that order, DSD‐PBEhB95, DSD‐PBEP86, DSD‐PBEPW91, and DSD‐PBEPBE. In addition, DSD‐PBEP86 and DSD‐PBEPBE can be used without source code modifications in a wider variety of electronic structure codes. Sample job decks for several commonly used such codes are supplied as electronic Supporting Information. Copyright © 2013 Wiley Periodicals, Inc.     

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. © 2015 Wiley Periodicals, Inc.     

Broken symmetry density functional study of a mixed‐valence unsymmetrical dinuclear iron complex

Density functional theory (DFT) calculations with different exchange‐correlation functionals were performed for a mixed valence Fe(II)/Fe(III) binuclear complex with μ‐methoxo and two μ‐carboxylate bridging ligands, (1) with geometry optimizations being performed for all possible spin multiplicities (M_S = 2, 4, 6, 8, and 10). Within the exchange‐correlation functionals studied, only the hybrid GGA functionals B3P and B3LYP and also the pure GGA functional RPBE, predicts the geometry with high spin (S = 9/2) to be more stable than the geometry with low spin state (S = 1/2) by 20 kcal/mol, in agreement with the experimental findings. These functionals also predict the same stability order for the different spin states, being M_S = 10>8>6>2>4. The meta‐GGA functionals TPSS and TPSSh and also the pure GGA functionals BLYP and BP86 predict different stability orders. The computed average EPR g‐tensor, g_av, of 2.03, at the B3LYP level, is in good agreement with the experimental findings. Heisenberg exchange coupling constants, J, were calculated within the broken‐symmetry formalism, at the B3LYP level, showing that the two iron centers are antiferromagnetic coupling, with a very weak coupling constant of about ?7 cm^?1, in good agreement with the experimental value. Additionally, the effect of using different multiplicities of the reference geometries on the computed J value is discussed. © 2009 Wiley Periodicals, Inc. Int J Quantum Chem, 2010     

How reliable is DFT in predicting relative energies of polycyclic aromatic hydrocarbon isomers? comparison of functionals from different rungs of jacob's ladder

Density functional theory (DFT) is the only quantum‐chemical avenue for calculating thermochemical/kinetic properties of large polycyclic aromatic hydrocarbons (PAHs) such as graphene nanoflakes. Using CCSD(T)/CBS PAH isomerization energies, we find that all generalized gradient approximation (GGA) and meta GGA DFT functionals have severe difficulties in describing isomerization energies in PAHs. The poor performance of these functionals is demonstrated by the following root‐mean‐square deviations (RMSDs) obtained for a database of C₁₄H₁₀ and C₁₈H₁₂ isomerization energies. The RMSDs for the GGAs range between 6.0 (BP86‐D3) and 23.0 (SOGGA11) and for the meta GGAs they range between 3.5 (MN12‐L) and 11.9 (τ‐HCTH) kJ mol⁻¹. These functionals (including the dispersion‐corrected methods) systematically and significantly underestimate the isomerization energies. A consequence of this behavior is that they all predict that chrysene (rather than triphenylene) is the most stable C₁₈H₁₂ isomer. A general improvement in performance is observed along the rungs of Jacob's Ladder; however, only a handful of functionals from rung four give good performance for PAH isomerization energies. These include functionals with high percentages (40–50%) of exact Hartree–Fock exchange such as the hybrid GGA SOGGA11‐X (RMSD = 1.7 kJ mol⁻¹) and the hybrid‐meta GGA BMK (RMSD = 1.3 kJ mol⁻¹). Alternatively, the inclusion of lower percentages (20–30%) of exact exchange in conjunction with an empirical dispersion correction results in good performance. For example, the hybrid GGA PBE0‐D3 attains an RMSD of 1.5 kJ mol⁻¹, and the hybrid‐meta GGAs PW6B95‐D3 and B1B95‐D3 result in RMSDs below 1 kJ mol⁻¹. © 2016 Wiley Periodicals, Inc.     

Comparison of DFT methods for molecular orbital eigenvalue calculations

We report how closely the Kohn-Sham highest occupied molecular orbital (HOMO) and lowest unoccupied molecular orbital (LUMO) eigenvalues of 11 density functional theory (DFT) functionals, respectively, correspond to the negative ionization potentials (-IPs) and electron affinities (EAs) of a test set of molecules. We also report how accurately the HOMO-LUMO gaps of these methods predict the lowest excitation energies using both time-independent and time-dependent DFT (TD-DFT). The 11 DFT functionals include the local spin density approximation (LSDA), five generalized gradient approximation (GGA) functionals, three hybrid GGA functionals, one hybrid functional, and one hybrid meta GGA functional. We find that the HOMO eigenvalues predicted by KMLYP, BH&HLYP, B3LYP, PW91, PBE, and BLYP predict the -IPs with average absolute errors of 0.73, 1.48, 3.10, 4.27, 4.33, and 4.41 eV, respectively. The LUMOs of all functionals fail to accurately predict the EAs. Although the GGA functionals inaccurately predict both the HOMO and LUMO eigenvalues, they predict the HOMO-LUMO gap relatively accurately (approximately 0.73 eV). On the other hand, the LUMO eigenvalues of the hybrid functionals fail to predict the EA to the extent that they include HF exchange, although increasing HF exchange improves the correspondence between the HOMO eigenvalue and -IP so that the HOMO-LUMO gaps are inaccurately predicted by hybrid DFT functionals. We find that TD-DFT with all functionals accurately predicts the HOMO-LUMO gaps. A linear correlation between the calculated HOMO eigenvalue and the experimental -IP and calculated HOMO-LUMO gap and experimental lowest excitation energy enables us to derive a simple correction formula.     

Analysis of the performance of DFT functionals in the study of light emission by oxyluciferin analogs

Firefly bioluminescence has attracted much attention from the research community due to its most intriguing multicolor bioluminescence. Computational studies have been fundamental to the clarification of this phenomenon. However, no clear demonstration of the accuracy of the theoretical methods used in this field of research has been provided. In this work, we have used luciferin and dehydroluciferin in water as a model for the calculation of the emission wavelength of oxyluciferin and analogs. This model was used in a density functional theory (DFT) benchmarking in which 24 functionals were tested. A non‐negligible “case to case” dependence was observed. However in general, the better classes of the DFT functionals are generalized gradient approximation (GGA) and meta GGA. The generalized gradient exchange functional TPSSVWN5, the hybrid‐meta GGA functional mPWKCIS, and the hybrid GGA functional MPWLYP1M also present good results. For the contrary, the popular hybrid GGA functionals present a worse performance. © 2012 Wiley Periodicals, Inc.     

On the DFT Ground State of Crystalline Bromine and Iodine

We report on an erroneous ground state within common density functional theory (DFT) methods for the solid elements bromine and iodine. Phonon computations at the GGA level for both molecular crystals yield imaginary vibrational modes, erroneously indicating dynamic instability—that fact alone could easily pass as a computational artefact, but these imaginary modes lead to energetically more favorable and dynamically stable structures, made up of infinite monoatomic chains. In contrast, meta‐GGA and hybrid functionals yield the correct energetic order for bromine, while for iodine, most global hybrids do not improve the GGA result significantly. The qualitatively correct answer, in both cases, is given by the long‐range corrected hybrid LC‐ωPBE, the Minnesota functionals M06L and M06, and by periodic Hartree–Fock and MP2 theory. This poor performance of economic DFT functionals should be kept in mind, for example, during global structure optimizations of systems with significant contributions from halogen bonds.     

Correlation functional in screened‐exchange density functional theory procedures

In the present study, we have explored several prospects for the further development of screened‐exchange density functional theory (SX‐DFT) procedures. Using the performance of HSE06 as our measure, we find that the use of alternative correlation functionals (as oppose to PBEc in HSE06) also yields adequate results for a diverse set of thermochemical properties. We have further examined the performance of new SX‐DFT procedures (termed HSEB‐type methods) that comprise the HSEx exchange and a (near‐optimal) reparametrized B97c (c _OS,0 = c _SS,0 = 1, c _OS,1 = −1.5, c _OS,2 = −0.644, c _SS,1 = −0.5, and c _SS,2 = 1.10) correlation functionals. The different variants of HSEB all perform comparably to or slightly better than the original HSE‐type procedures. These results, together with our fundamental analysis of correlation functionals, point toward various directions for advancing SX‐DFT methods. © 2017 Wiley Periodicals, Inc.     

Electronic ground states of iron porphyrin and of the first species in the catalytic reaction cycle of cytochrome P450s

Electronic structures of iron(II) and iron(III) porphyrins are studied with density functional theory (DFT) using the GGA exchange functional OPTX in combination with the correlation functional PBE (OPBE) and with the correlation functional Perdew (OPerdew) together with a triple zeta-type basis set. These functionals, known for accurately predicting the spin ground state of iron complexes, are evaluated against other functionals for their performance in calculating relative energies for the various electronic states of both the iron porphyrins. The calculated energy orderings are triplet < quintet < singlet for the iron(II) porphyrin and quartet < sextet < doublet for the iron(III) porphyrin cation. Complexation by a thiolate ion (SH-) changes the preferred ground state for both species to high spin. This thiolate complex is used as a mimic for the cytochrome P450s active site to model the first step of the catalytic cycle of this enzyme. This first step is believed to concern the removal of an axial oxygen donating ligand from the hexacoordinated aqua-thiolate-porphyrin-iron(III) resting state. The DFT results suggest that this is not a free water molecule, because of its repulsive nature, but that it has instead hydroxy anion character. These calculations are in line with the experimentally observed change in the spin state from low to high spin upon this removal of the axial hydroxo ligand by binding of the substrate in the heme pocket of cytochrome P450.     

Energy landscapes of nucleophilic substitution reactions: a comparison of density functional theory and coupled cluster methods

We have carried out a detailed evaluation of the performance of all classes of density functional theory (DFT) for describing the potential energy surface (PES) of a wide range of nucleophilic substitution (SN2) reactions involving, amongst others, nucleophilic attack at carbon, nitrogen, silicon, and sulfur. In particular, we investigate the ability of the local density approximation (LDA), generalized gradient approximation (GGA), meta-GGA as well as hybrid DFT to reproduce high-level coupled cluster (CCSD(T)) benchmarks that are close to the basis set limit. The most accurate GGA, meta-GGA, and hybrid functionals yield mean absolute deviations of about 2 kcal/mol relative to the coupled cluster data, for reactant complexation, central barriers, overall barriers as well as reaction energies. For the three nonlocal DFT classes, the best functionals are found to be OPBE (GGA), OLAP3 (meta-GGA), and mPBE0KCIS (hybrid DFT). The popular B3LYP functional is not bad but performs significantly worse than the best GGA functionals. Furthermore, we have compared the geometries from several density functionals with the reference CCSD(T) data. The same GGA functionals that perform best for the energies (OPBE, OLYP), also perform best for the geometries with average absolute deviations in bond lengths of 0.06 A and 0.6 degrees, even better than the best meta-GGA and hybrid functionals. In view of the reduced computational effort of GGAs with respect to meta-GGAs and hybrid functionals, let alone coupled cluster, we recommend the use of accurate GGAs such as OPBE or OLYP for the study of SN2 reactions.     

Role of nonlocal exchange in molecular crystals: The case of two proton‐ordered phases of ice

We present a periodic density functional theory investigation of twoproton‐ordered phases of ice. Their equilibrium lattice parameters,relative stabilities, formation energies, and densities of states havebeen evaluated. Nine exchange‐correlation functionals, representativeof the generalized gradient approximation (GGA), global hybrids,range‐separated hybrids, meta‐GGA, and hybrid meta‐GGA families havebeen taken into account, considering two oxygen basis sets. Althoughthe hydrogen‐bond network of ice is well reproduced at the B3LYP,M06‐L, or LC‐ wPBE levels, formation energies are only correctlyevaluated with the two former functionals. Band gaps on the other handare only quantitatively reproduced at the B3LYP level. These resultsindicate that this last functional, a de facto reference formolecular calculations, gives in average the most accurate results forthe considered ice properties. © 2011 Wiley Periodicals, Inc. J Comput Chem, 2011     

Is the uniform electron gas limit important for small Ag clusters? Assessment of different density functionals for Ag(n) (n < or = 4)

Twenty-three density functional theory (DFT) methods, including the second- and the third-generation functionals, are tested in conjunction with two basis sets (LANL2DZ and SDD) for studying the properties of neutral and ionic silver clusters. We find that DFT methods incorporating the uniform electron gas limit in the correlation functional, namely, those with Perdew's correlation functionals (PW91, PBE, P86, and TPSS), Becke's B95, and the Van Voorhis-Scuseria functional VSXC, generally perform better than the other group of functionals, e.g., those incorporating the LYP correlation functional and variations of the B97 functional. Strikingly, these two groups of functionals can produce qualitatively different results for the Ag3 and Ag4 clusters. The energetic properties and vibrational frequencies of Ag(n) are also evaluated by the different functionals. The present study shows that the choice of DFT methods for heavy metals may be critical. It is found that the exact-exchange-incorporated PBE functional (PBE1PBE) is among the best for predicting the range of properties.     

Which density functional is close to CCSD accuracy to describe geometry and interaction energy of small noncovalent dimers? A benchmark study using Gaussian09

A benchmark study on all possible density functional theory (DFT) methods in Gaussian09 is done to locate functionals that agree well with CCSD/aug‐cc‐pVTZ geometry and Ave‐CCSD(T)/(Q‐T) interaction energy (E_int) for small non‐covalently interacting molecular dimers in “dispersion‐dominated” (class 1), “dipole‐induced dipole” (class 2), and “dipole‐dipole” (class 3) classes. A DFT method is recommended acceptable if the geometry showed close agreement to CCSD result (RMSD < 0.045) and E_int was within 80–120% accuracy. Among 382 tested functionals, 1–46% gave good geometry, 13–44% gave good E_int, while 1–33% satisfied geometry and energy criteria. Further screening to locate the best performing functionals for all the three classes was made by counting the acceptable values of energy and geometry given by each functionals. The meta‐generalized gradient approximation (GGA) functional M06L was the best performer with total 14 hits; seven acceptable energies and seven acceptable geometries. This was the only functional “recommended” for at least two dimers in each class. The functionals M05, B2PLYPD, B971, mPW2PLYPD, PBEB95, and CAM‐B3LYP gave 11 hits while PBEhB95, PW91B95, Wb97x, BRxVP86, BRxP86, HSE2PBE, HSEh1PBE, PBE1PBE, PBEh1PBE, and PW91TPSS gave 10 hits. Among these, M05, B971, mPW2PLYPD, Wb97x, and PW91TPSS were among the “recommended” list of at least one dimer from each class. Long‐range correction (LC) of Hirao and coworkers to exchange‐correlation functionals showed massive improvement in geometry and E_int. The best performing LC‐functionals were LC‐G96KCIS and LC‐PKZBPKZB. Our results predict that M06L is the most trustworthy DFT method in Gaussian09 to study small non‐covalently interacting systems. © 2013 Wiley Periodicals, Inc.     

Density, structure, and dynamics of water: the effect of van der Waals interactions

It is known that ab initio molecular dynamics (AIMD) simulations of liquid water at ambient conditions, based on the generalized gradient approximation (GGA) to density functional theory (DFT), with commonly used functionals fail to produce structural and diffusive properties in reasonable agreement with experiment. This is true for canonical, constant temperature simulations where the density of the liquid is fixed to the experimental density. The equilibrium density, at ambient conditions, of DFT water has recently been shown by Schmidt et al. [J. Phys. Chem. B, 113, 11959 (2009)] to be underestimated by different GGA functionals for exchange and correlation, and corrected by the addition of interatomic pair potentials to describe van der Waals (vdW) interactions. In this contribution we present a DFT-AIMD study of liquid water using several GGA functionals as well as the van der Waals density functional (vdW-DF) of Dion et al. [Phys. Rev. Lett. 92, 246401 (2004)]. As expected, we find that the density of water is grossly underestimated by GGA functionals. When a vdW-DF is used, the density improves drastically and the experimental diffusivity is reproduced without the need of thermal corrections. We analyze the origin of the density differences between all the functionals. We show that the vdW-DF increases the population of non-H-bonded interstitial sites, at distances between the first and second coordination shells. However, it excessively weakens the H-bond network, collapsing the second coordination shell. This structural problem is partially associated to the choice of GGA exchange in the vdW-DF. We show that a different choice for the exchange functional is enough to achieve an overall improvement both in structure and diffusivity.