Bioinorganic chemistry modeled with the TPSSh density functional

In this work, the TPSSh density functional has been benchmarked against a test set of experimental structures and bond energies for 80 transition-metal-containing diatomics. It is found that the TPSSh functional gives structures of the same quality as other commonly used hybrid and nonhybrid functionals such as B3LYP and BP86. TPSSh gives a slope of 0.99 upon linear fitting to experimental bond energies, whereas B3LYP and BP86, representing 20% and 0% exact exchange, respectively, give linear fits with slopes of 0.91 and 1.07. Thus, TPSSh eliminates the large systematic component of the error in other functionals, reducing rms errors from 46-57 to 34 kJ/mol. The nonhybrid version of the functional, TPSS, gives a slope of 1.08, similar to BP86, implying that using 10% exact exchange is the main reason for the success of TPSSh. Typical bioinorganic reactions were then investigated, including spin inversion and electron affinity in iron-sulfur clusters, and breaking or formation of bonds in iron proteins and cobalamins. The results show that differences in reaction energies due to exact exchange can be much larger than the usually cited approximately 20 kJ/mol, sometimes exceeding 100 kJ/mol. The TPSSh functional provides energies approximately halfway between nonhybrids BP86 and TPSS, and 20% exact exchange hybrid B3LYP: Thus, a linear correlation between the amount of exact exchange and the numeric value of the reaction energy is observed in all these cases. For these reasons, TPSSh stands out as a most promising density functional for use and further development within the field of bioinorganic chemistry.     

Understanding the Effect of the Exchange-Correlation Functionals on Methane and Ethane Formation over Ruthenium Catalysts

Density functional theory (DFT) has been established as a powerful research tool for heterogeneous catalysis research in obtaining key thermodynamic and/or kinetic parameters like adsorption energies, enthalpies of reaction, activation barriers, and rate constants. Understanding of density functional exchange-correlation approximations is essential to reveal the mechanism and performance of a catalyst. In the present work, we reported the influence of six exchange-correlation density functionals, including PBE, RPBE, BEEF+vdW, optB86b+vdW, SCAN, and SCAN+rVV10, on the adsorption energies, reaction energies and activation barriers of carbon hydrogenation and carbon-carbon couplings during the formation of methane and ethane over Ru(0001) and Ru(1011) surfaces. We found the calculated reaction energies are strongly dependent on exchange-correlation density functionals due to the difference in coordination number between reactants and products on surfaces. The deviation of the calculated elementary reaction energies can be accumulated to a large value for chemical reaction involving multiple steps and vary considerably with different exchange-correlation density functionals calculations. The different exchange-correlation density functionals are found to influence considerably the selectivity of Ru(0001) surface for methane, ethylene, and ethane formation determined by the adsorption energies of intermediates involved. However, the influence on the barriers of the elementary surface reactions and the structural sensitivity of Ru(0001) and Ru(1011) are modest. Our work highlights the limitation of exchange-correlation density functionals on computational catalysis and the importance of choosing a proper exchange-correlation density functional in correctly evaluating the activity and selectivity of a catalyst.     

Comparison of one‐parameter and linearly scaled one‐parameter double‐hybrid density functionals for noncovalent interactions

We have compared the performances of the one‐parameter and linearly scaled one‐parameter double‐hybrid density functionals (1DH‐DFs and LS1DH‐DFs) for noncovalent interactions. The only one parameter related to the Hartree–Fock (HF) exchange for each of the tested 1DH‐DFs and LS1DH‐DFs has been fitted with the well‐designed S66 database. The obtained DHDFs are dubbed as 1DH‐PBE‐NC, LS1DH‐PBE‐NC, 1DH‐TPSS‐NC, LS1DH‐TPSS‐NC, 1DH‐PWB95‐NC, and LS1DH‐PWB95‐NC, where “NC” denotes noncovalent interactions. With a specific combination of exchange and correlation functionals, the dependent parameters related to the nonlocal second‐order perturbative energies are nearly identical for the 1DH and LS1DH models. According to our benchmark computations against the S66, S22B, NCCE31, ADIM6, and L7 databases, we suggest that the 1DH‐PWB95‐NC and LS1DH‐PWB95‐NC functionals are much more suitable for evaluating noncovalent interaction energies. Unlike the versatile DHDFs with dispersion corrections for general purpose, our optimized 1DH‐DFs and LS1DH‐DFs only aim at noncovalent interactions. © 2016 Wiley Periodicals, Inc.     

Determining the role of the underlying orbital‐dependence of PBE0‐DH and PBE‐QIDH double‐hybrid density functionals

We study the orbital‐dependence of three (parameter‐free) double‐hybrid density functionals, namely the PBE0‐DH, the PBE‐QIDH models, and the SOS1‐PBE‐QIDH spin‐opposite‐scaled variant of the latter. To do it, we feed all their energy terms with different sets of orbitals obtained previously from self‐consistent density functional theory calculations using several exchange‐correlation functionals (e.g., PBE, PBE0, PBEH&H), or directly with HF‐PBE orbitals, to see their effect on selected datasets for atomization and reaction energies, the latter proned to marked self‐interaction errors. We find that the PBE‐QIDH double‐hybrid model shows a great consistency, as the best results are always obtained for the set of orbitals corresponding to its hybrid scheme, which prompts us to recommend this model without any other fitting or reparameterization. © 2017 Wiley Periodicals, Inc.     

Vibrational frequency scale factors for density functional theory and the polarization consistent basis sets

Calculated harmonic vibrational frequencies systematically deviate from experimental vibrational frequencies. The observed deviation can be corrected by applying a scale factor. Scale factors for: (i) harmonic vibrational frequencies [categorized into low (<1000 cm^?1) and high (>1000 cm^?1)], (ii) vibrational contributions to enthalpy and entropy, and (iii) zero‐point vibrational energies (ZPVEs) have been determined for widely used density functionals in combination with polarization consistent basis sets (pc‐n, n = 0,1,2,3,4). The density functionals include pure functionals (BP86, BPW91, BLYP, HCTH93, PBEPBE), hybrid functionals with Hartree‐Fock exchange (B3LYP, B3P86, B3PW91, PBE1PBE, mPW1K, BH&HLYP), hybrid meta functionals with the kinetic energy density gradient (M05, M06, M05‐2X, M06‐2X), a double hybrid functional with Møller‐Plesset correlation (B2GP‐PLYP), and a dispersion corrected functional (B97‐D). The experimental frequencies for calibration were from 41 organic molecules and the ZPVEs for comparison were from 24 small molecules (diatomics, triatomics). For this family of basis sets, the scale factors for each property are more dependent on the functional selection than on basis set level, and thus allow for a suggested scale factor for each density functional when employing polarization consistent basis sets (pc‐n, n = 1,2,3,4). A separate scale factor is recommended when the un‐polarized basis set, pc‐0, is used in combination with the density functionals. © 2012 Wiley Periodicals, Inc.     

On the applicability of density functional theory to manganese‐based complexes with catalytic activity toward water oxidation

The present contribution assesses the performance of several popular and accurate density functionals, namely B3LYP, BP86, M06, MN12L, mPWPW91, PBE0, and TPSSh toward manganese‐based coordination complexes. These compounds show promising properties toward application to catalytic water oxidation. Although manganese with N‐ and O‐biding ligands tends to give rise to high spin complexes, the results show that BP86, mPWPW91, and specially MN12L, tend to yield low‐spin complexes. The usage of these functionals for such compounds is, thus, discouraged. All the functionals considered deliver accurate geometries. The present results show, however, that B3LYP delivers geometries deviating from experimental values when compared to the other functionals of the set. M06, PBE0, and TPSSh deliver geometries of similar accuracy, PBE0 outstanding slightly with respect to the other two. © 2017 Wiley Periodicals, Inc.     

Long‐range corrected functionals satisfy Koopmans' theorem: Calculation of correlation and relaxation energies

In this article, we show that the long‐range‐corrected (LC) density functionals LC‐BOP and LCgau‐BOP reproduce frontier orbital energies and highest‐occupied molecular orbital (HOMO)—lowest‐unoccupied molecular orbital (LUMO) gaps better than other density functionals. The negative of HOMO and LUMO energies are compared with the vertical ionization potentials (IPs) and electron affinities, respectively, using CCSD(T)/6‐311++G(3df,3pd) for 113 molecules, and we found LC functionals to satisfy Koopmans' theorem. We also report that the frontier orbital energies and the HOMO‐LUMO gaps of LC‐BOP and LCgau‐BOP are better than those of recently proposed ωM05‐D (Lin et al., J. Chem. Phys. 2012, 136 , 154109). We express the exact IP in terms of orbital relaxation, and correlation energies and hence calculate the relaxation and correlation energies for the same set of molecules. It is found that the LC functionals, in general, includes more relaxation effect than Hartree–Fock and more correlation effect than the other density functionals without LC scheme. Finally, we scan μ parameter in LC scheme from 0.1 to 0.6 bohr^?1 for the above test set molecules with LC‐BOP functional and found our parameter value, 0.47 bohr^?1, is usefully applicable to our tested systems. © 2013 Wiley Periodicals, Inc.     

Numerical examination of performance of some exchange-correlation functionals for molecules containing heavy elements

The performance of 17 exchange-correlation functionals for molecules containing heavy elements are numerically examined through four-component relativistic density DFT calculations. The examined functionals show the similar accuracy as they do for the molecules containing light elements only except for bond lengths. LDA and OP86 produce good results for bond lengths and frequencies but bad bond energies. Different functionals do not show much different performance for bond energies except LDA. BP86 and GP86 produce results with average accuracy while LYP does not perform well. Although encouraging results are obtained with functional B97GGA-1, other heavily parameterized and meta-GGA functionals do not produce impressive results.     

Reaction energetics on long‐range corrected density functional theory: Diels–Alder reactions

The possibility of quantitative reaction analysis on the orbital energies of long‐range corrected density functional theory (LC‐DFT) is presented. First, we calculated the Diels–Alder reaction enthalpies that have been poorly given by conventional functionals including B3LYP functional. As a result, it is found that the long‐range correction drastically improves the reaction enthalpies. The barrier height energies were also computed for these reactions. Consequently, we found that dispersion correlation correction is also crucial to give accurate barrier height energies. It is, therefore, concluded that both long‐range exchange interactions and dispersion correlations are essentially required in conventional functionals to investigate Diels–Alder reactions quantitatively. After confirming that LC‐DFT accurately reproduces the orbital energies of the reactant and product molecules of the Diels–Alder reactions, the global hardness responses, the halves of highest occupied molecular orbital (HOMO)‐lowest unoccupied molecular orbital (LUMO) energy gaps, along the intrinsic reaction coordinates of two Diels–Alder reactions were computed. We noticed that LC‐DFT results satisfy the maximum hardness rule for overall reaction paths while conventional functionals violate this rule on the reaction pathways. Furthermore, our results also show that the HOMO‐LUMO gap variations are close to the reaction enthalpies for these Diels–Alder reactions. Based on these results, we foresee quantitative reaction analysis on the orbital energies. © 2012 Wiley Periodicals, Inc.     

Grid‐based density functional calculations of many‐electron systems

Exploratory variational pseudopotential density functional calculations are performed for the electronic properties of many‐electron systems in the 3D cartesian coordinate grid (CCG). The atom‐centered localized gaussian basis set, electronic density, and the two‐body potentials are set up in the 3D cubic box. The classical Hartree potential is calculated accurately and efficiently through a Fourier convolution technique. As a first step, simple local density functionals of homogeneous electron gas are used for the exchange‐correlation potential, while Hay‐Wadt‐type effective core potentials are employed to eliminate the core electrons. No auxiliary basis set is invoked. Preliminary illustrative calculations on total energies, individual energy components, eigenvalues, potential energy curves, ionization energies, and atomization energies of a set of 12 molecules show excellent agreement with the corresponding reference values of atom‐centered grid as well as the grid‐free calculation. Results for three atoms are also given. Combination of CCG and the convolution procedure used for classical Coulomb potential can provide reasonably accurate and reliable results for many‐electron systems. © 2007 Wiley Periodicals, Inc. Int J Quantum Chem, 2008     

Investigation of the use of density functionals in second‐ and third‐row transition metal dimer calculations

We explore the use of density functionals in calculating the equilibrium distances, dissociation energies, and harmonic vibrational frequencies of the homonuclear diatomics of the second‐row transition metals, platinum, and gold. The outermost s–d interconfigurational energies (ICEs) and the outermost s and d ionization potentials (IPs) were also calculated for the second‐ and third‐row transition metal atoms. Compared with the first‐row transition metal dimer calculations (J Chem Phys 2000, 112, 545–553), the binding energies calculated using the combination of the Becke 1988 exchange and the one‐parameter progressive correlation (BOP) functional and Becke's three‐parameter hybrid (B3LYP) functional are in better agreement with the experiment. However, the pure BOP functional still gives the deep and narrow dissociation potential wells for the electron configurations containing high‐angular‐momentum open‐shell orbitals. Analysis of the s–d ICEs and the s and d IPs suggests that the overestimation may be due to the insufficient long‐range interaction between the outermost s and d orbitals in the exchange functional. The hybrid B3LYP functional seems to partly solve this problem for many systems by the incorporation of the Hartree–Fock exchange integral. However, this still leads to an erroneous energy gap between the configurations of fairly different spin multiplicity, probably because of the unbalance of exchange and correlation contributions. © 2001 John Wiley & Sons, Inc. J Comput Chem 22: 1995–2009, 2001     

Electronic structures of 4d transition metal monoxides by density functional theory

Bond distances, dissociation energies, ionization potentials and electron affinities of 4d transition metal monoxides from YO to CdO and their positive and negative ions were studied by use of density functional methods B3LYP, BLYP, B3PW91, BPW91, B3P86, BP86, SVWN, MPW1PW91 and PBE1PBE. It was found that calculated properties are highly dependent on the functionals employed, especially for dissociation energy. For most neutral species, pure density functionals BLYP, BPW91 and BP86 have good performance in predicting dissociation energy than hybrid density functionals B3LYP, B3PW91 and B3P86. In addition, BLYP gives the largest bond distance compared with other density functional methods, while SVWN gives shortest bond distance, largest dissociation energy and electron affinity. For the ground state, the spin multiplicity of the charged species can be obtained by ± 1 of their corresponding neutral species.     

DFT Methods to Study the Reaction Mechanism of Iridium‐Catalyzed Hydrogenation of Olefins: Which Functional Should be Chosen?

To enable the selection of more accurate computational methods for the future theoretical exploration of the reaction mechanism of Ir‐catalyzed olefin hydrogenation, we compared high‐level ab initio coupled cluster and DFT calculations with a simplified model of Pfaltz's Ir/P,N‐type catalyst for all four previously proposed Ir^I/Ir^III and Ir^III/Ir^V mechanisms. Through the systematic assessment of the DFT performances, the DFT empirical dispersion correction (DFT‐D3) is found to be indispensable for improving the accuracy of relative energies between the Ir^I/Ir^III and Ir^III/Ir^V mechanisms. After including the DFT‐D3 correction, the three best performing density functionals (DFs) are B2‐PLYP, BP86, and TPSSh. In these recommended DFs, the computationally more expensive double‐hybrid functional B2‐PLYP‐D3 has a balanced and outstanding performance for calculations of the reaction barriers, reaction energies, and energy gaps between different mechanisms, whereas the less costly BP86‐D3 and TPSSh‐D3 methods have outstanding, but relatively less uniform performances.     

Analytical nuclear excited‐state gradients for the Tamm–Dancoff approximation using uncoupled frozen‐density embedding

We report the derivation and implementation of analytical nuclear gradients for excited states using time‐dependent density functional theory using the Tamm–Dancoff approximation combined with uncoupled frozen‐density embedding using density fitting. Explicit equations are presented and discussed. The implementation is able to treat singlet as well as triplet states and functionals using the local density approximation, the generalized gradient approximation, combinations with Hartree–Fock exchange (hybrids), and range‐separated functionals such as CAM‐B3LYP. The new method is benchmarked against supermolecule calculations in two case studies: The solvatochromic shift of the (vertical) fluorescence energy of 4‐aminophthalimide on solvation, and the first local excitation of the benzonitrile dimer. Whereas for the 4‐aminophthalimide–water complex deviations of about 0.2 eV are obtained to supermolecular calculations, for the benzonitrile dimer the maximum error for adiabatic excitation energies is below 0.01 eV due to a weak coupling of the subsystems. © 2017 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.     

The Heat of Formation of the Uranyl Dication: Theoretical Evaluation Based on Relativistic Density Functional Calculations

By using a set of model reactions, we estimated the heat of formation of gaseous UO₂²⁺ from quantum‐chemical reaction enthalpies and experimental heats of formation of reference species. For this purpose, we performed relativistic density functional calculations for the molecules UO₂²⁺, UO₂, UF₆, and UF₅. We used two gradient‐corrected exchange‐correlation functionals (revised Perdew–Burke–Ernzerhof (PBEN) and Becke–Perdew (BP)) and we accounted for spin‐orbit interaction in a self‐consistent fashion. Indeed, spin‐orbit interaction notably affects the energies of the model reactions, especially if compounds of U^IV are involved. Our resulting theoretical estimates for Δ_f (UO₂²⁺), 365±10 kcal mol^?1 (PBEN) and 370±12 kcal mol^?1 (BP), are in quantitative agreement with a recent experimental result, 364±15 kcal mol^?1. Agreement between the results of the two different exchange‐correlation functionals PBEN and BP supports the reliability of our approach. The procedure applied offers a general means to derive unknown enthalpies of formation of actinide species based on the available well‐established data for other compounds of the element in question.     

Standard grids for high‐precision integration of modern density functionals: SG‐2 and SG‐3

Density‐functional approximations developed in the past decade necessitate the use of quadrature grids that are far more dense than those required to integrate older generations of functionals. This category of difficult‐to‐integrate functionals includes meta‐generalized gradient approximations, which depend on orbital gradients and/or the Laplacian of the density, as well as functionals based on B97 and the popular “Minnesota” class of functionals, each of which contain complicated and/or oscillatory expressions for the exchange inhomogeneity factor. Following a strategy introduced previously by Gill and co‐workers to develop the relatively sparse “SG‐0” and “SG‐1” standard quadrature grids, we introduce two higher‐quality grids that we designate SG‐2 and SG‐3, obtained by systematically “pruning” medium‐ and high‐quality atom‐centered grids. The pruning procedure affords computational speedups approaching a factor of two for hybrid functionals applied to systems of atoms, without significant loss of accuracy. The grid dependence of several popular density functionals is characterized for various properties. © 2017 Wiley Periodicals, Inc.     

Benchmarking dispersion and geometrical counterpoise corrections for cost‐effective large‐scale DFT calculations of water adsorption on graphene

The physisorption of water on graphene is investigated with the hybrid density functional theory (DFT)‐functional B3LYP combined with empirical corrections, using moderate‐sized basis sets such as 6‐31G(d). This setup allows to model the interaction of water with graphene going beyond the quality of classical or semiclassical simulations, while still keeping the computational costs under control. Good agreement with respect to Coupled Cluster with singles and doubles excitations and perturbative triples (CCSD(T)) results is achieved for the adsorption of a single water molecule in a benchmark with two DFT‐functionals (Perdew/Burke/Ernzerhof (PBE), B3LYP) and Grimme's empirical dispersion and counterpoise corrections. We apply the same setting to graphene supported by epitaxial hexagonal boron nitride (h‐BN), leading to an increased interaction energy. To further demonstrate the achievement of the empirical corrections, we model, entirely from first principles, the electronic properties of graphene and graphene supported by h‐BN covered with different amounts of water (one, 10 water molecules per cell and full coverage). The effect of h‐BN on these properties turns out to be negligibly small, making it a good candidate for a substrate to grow graphene on. © 2014 Wiley Periodicals, Inc.