Pure Density Functional Theory Functionals Research Articles

What Is the Structure of the E4 Intermediate in Nitrogenase?

Nitrogenase is the only enzyme that can cleave the strong triple bond in N2. The active site contains a complicated MoFe7S9C cluster. It is believed that it needs to accept four protons and electrons, forming the E4 state, before it can bind N2. However, there is no consensus on the atomic structure of the E4 state. Experimental studies indicate that it should contain two hydride ions bridging two pairs of Fe ions, and it has been suggested that both hydride ions as well as the two protons bind on the same face of the cluster. On the other hand, density functional theory (DFT) studies have indicated that it is energetically more favorable with either three hydride ions or with a triply protonated carbide ion, depending on the DFT functional. We have performed a systematic combined quantum mechanical and molecular mechanical (QM/MM) study of possible E4 states with two bridging hydride ions. Our calculations suggest that the most favorable structure has hydride ions bridging the Fe2/6 and Fe3/7 ion pairs. In fact, such structures are 14 kJ/mol more stable than structures with three hydride ions, showing that pure DFT functionals give energetically most favorable structures in agreement with experiments. An important reason for this finding is that we have identified a new type of broken-symmetry state that involves only two Fe ions with minority spin, in contrast to the previously studied states with three Fe ions with minority spin. The energetically best structures have the two hydride ions on different faces of the FeMo cluster, whereas better agreement with ENDOR data is obtained if they are on the same face; such structures are only 6–22 kJ/mol less stable.

Structure of Electronically Reduced N-Donor Bidentate Ligands and Their Heteroleptic Four-Coordinate Zinc Complexes: A Survey of Density Functional Theory Results.

The role of Hartree-Fock exchange in describing the structural changes occurring upon reduction of bipyridine-based ligands and their complexes is investigated within the framework of density functional theory (DFT) calculations. A set of four free ligands in their neutral and radical anionic forms, and two of their zinc complexes in their dicationic and monocationic radical forms, is used to compare a large panel of pure, conventional, and long-range corrected hybrid DFT functionals; coupled cluster single and double calculations are used alongside experimental results as benchmarks. Particular attention has been devoted to the magnitude of the change, upon reduction, of the Δ-parameter, which measures the difference between the Cpy-Cpy and the C-N bond lengths in bipyridine ligand and is known to experimentally correlate with the charge of the ligands. Our results indicate that the structural changes significantly depend on the amount of exact exchange included in the functional. A progressive evolution is observed for the free ligands, whereas two distinct sets of results are obtained for the complexes. Functionals with a small degree of HF exchange, e.g., B3LYP, do not adequately describe geometric changes for the considered species, and, quite surprisingly, the same holds for the CC2 method. The best agreement to experimental and CCSD values is obtained with functionals that include a significant but not excessive part of exact exchange, e.g., CAM-B3LYP, M06-2X, and ωB97X-D. The calculated localization of the added electron after reduction, which depends on the self-interaction error, is used to rationalize these outcomes. Static correlation is also shown to play a role in the accurate description of the electronic structure.

Cryptophanes for Methane and Xenon Encapsulation: A Comparative Density Functional Theory Study of Binding Properties and NMR Chemical Shifts.

The host-guest chemistry of cryptophanes is an active research area because of its applications in sensor design, targeting small molecules and atoms in environmental and medical sciences. As such, the computational prediction of binding energies and nuclear magnetic resonance (NMR) properties of different cryptophane complexes are of interest to both theoreticians and experimentalists working in host-guest based sensor development. Herein we present a study of 10 known and some newly proposed cryptophanes using density functional theory (DFT) calculations. We benchmark the description of nonbonding interactions by different DFT functionals against spin-component-scaled, second-order Møller-Plesset theory (SCS-MP2) and predict novel host molecules with enhanced affinity toward methane and Xenon, two representative systems of high interest. We demonstrate the power and limitations of the different computational methods in describing the binding and NMR properties of these established and novel host systems. The results show the importance of including dispersion corrections in the DFT functionals. The overall analysis of the dispersion corrections indicated that results obtained from pure DFT functionals should be used cautiously when conclusions are drawn for molecular systems with considerable weak interactions. Proposed analogues of cryptophane-A, where the alkoxy bridges are replaced by alkyl chains, are predicted to display enhanced affinity toward both methane and Xenon.

Does the DFT Self-Interaction Error Affect Energies Calculated in Proteins with Large QM Systems?

We have examined how the self-interaction error in density-functional theory (DFT) calculations affects energies calculated on large systems (600-1000 atoms) involving several charged groups. We employ 18 different quantum mechanical (QM) methods, including Hartree-Fock, as well as pure, hybrid, and range-separated DFT methods. They are used to calculate reaction and activation energies for three different protein models in vacuum, in a point-charge surrounding, or with a continuum-solvent model. We show that pure DFT functionals give rise to a significant delocalization of the charges in charged groups in the protein, typically by ∼0.1 e, as evidenced from the Mulliken charges. This has a clear effect on how the surroundings affect calculated reaction and activation energies, indicating that these methods should be avoided for DFT calculations on large systems. Fortunately, methods such as CAM-B3LYP, BHLYP, and M06-2X give results that agree within a few kilojoules per mole, especially when the calculations are performed in a point-charge surrounding. Therefore, we recommend these methods to estimate the effect of the surroundings with large QM systems (but other QM methods may be used to study the intrinsic reaction and activation energies).

Use of Improved Orbitals for CCSD(T) Calculations for Predicting Heats of Formation of Group IV and Group VI Metal Oxide Monomers and Dimers and UCl6.

The prediction of the heats of formation of group IV and group VI metal oxide monomers and dimers with the coupled cluster CCSD(T) method has been improved by using Kohn-Sham density functional theory (DFT) and Brueckner orbitals for the initial wave function. The valence and core-valence contributions to the total atomization energies for the CrO3 monomer and dimer are predicted to be significantly larger than when using the Hartree-Fock (HF) orbitals. The predicted heat of formation of CrO3 with CCSD(T)/PW91 is consistent with previous calculations including high-order corrections beyond CCSD(T) and agrees well with the experiment. The improved heats of formation with the DFT and Brueckner orbitals are due to these orbitals being closer to the actual orbitals. Pure DFT functionals perform slightly better than the hybrid B3LYP functional due to the presence of exact exchange in the hybrid functional. Comparable heats of formation for TiO2 and the second- and the third-row group IV and group VI metal oxides are predicted well using either the DFT PW91 orbitals, Brueckner orbitals, or HF orbitals. The normalized clustering energies for the dimers are consistent with our previous work except for a larger value predicted for Cr2O6. The prediction of the reaction energy for UF6 + 3Cl2 → UCl6 + 3F2 was significantly improved with the use of DFT or Brueckner orbitals as compared to HF orbitals.

Bond Dissociation Energy of Halogen Oxides

Bond Dissociation Energy (BDE) of halogen oxides have been studied theoretically. Density Functional Theory (DFT) functionals have been performed on the 6-311+G (2df) level of basis set. For comparison, the results of composite method G3B3 and available experimental data are used. In general both pure DFT functionals and hybrid methods predict excellent results for these energies. However, the hybrid method predictions are closer to experimental data than those of pure DFT functionals.

Benchmarking quantum chemical methods for the calculation of molecular dipole moments and polarizabilities.

The calculation of molecular electric moments, polarizabilities, and electrostatic potentials is a widespread application of quantum chemistry. Although a range of wave function and density functional theory (DFT) methods have been applied in these calculations, combined with a variety of basis sets, there has not been a comprehensive evaluation of how accurate these methods are. To benchmark the accuracy of these methods, the dipole moments and polarizabilities of a set of 46 molecules were calculated using a broad set of quantum chemical methods and basis sets. Wave function methods Hartree-Fock (HF), second-order Møller-Plesset (MP2), and coupled cluster-singles and doubles (CCSD) were evaluated, along with the PBE, TPSS, TPSSh, PBE0, B3LYP, M06, and B2PLYP DFT functionals. The cc-pVDZ, cc-pVTZ, aug-cc-pVDZ, aug-cc-pVTZ, and Sadlej cc-pVTZ basis sets were tested. The aug-cc-pVDZ, Sadlej cc-pVTZ, and aug-cc-pVTZ basis sets all yield results with comparable accuracy, with the aug-cc-pVTZ calculations being the most accurate. CCSD, MP2, or hybrid DFT methods using the aug-cc-pVTZ basis set are all able to predict dipole moments with RMSD errors in the 0.12-0.13 D range and polarizabilities with RMSD errors in the 0.30-0.38 Å(3) range. Calculations using Hartree-Fock theory systematically overestimated dipole moments and underestimate polarizabilities. The pure DFT functionals included in this study (PBE and TPSS) slightly underestimate dipole moments and overestimate polarizability. Polarization anisotropy and implications for charge fitting are discussed.

An Investigation of the Accuracy of Different DFT Functionals on the Water Exchange Reaction in Hydrated Uranyl(VI) in the Ground State and the First Excited State.

We discuss the accuracy of density functional theory (DFT) in the gas phase for the water-exchange reactions in the uranyl(VI) aqua ion taking place both in the electronic ground state and in the first excited state (the luminescent (3)Δg state). The geometries of the reactant and intermediates have been optimized using DFT and the B3LYP functional, with a restricted closed-shell formalism for the electronic ground state and either an unrestricted open-shell formalism or the time-dependent DFT method for the (3)Δg state. The relative energies have been computed with wave-function-based methods such as Møller-Plesset second-order perturbation theory, or a minimal multireference perturbative calculation (minimal CASPT2); coupled-cluster method (CCSD(T)); DFT with B3LYP, BLYP, and BHLYP correlation and exchange functionals; and the hybrid DFT-multireference configuration interaction method. The results obtained with second-order perturbative methods are in excellent agreement with those obtained with the CCSD(T) method. However, DFT methods overestimate the energies of low coordination numbers, yielding to too high and too low reaction energies for the associative and dissociative reactions, respectively. Part of the errors appears to be associated with the amount of Hartree-Fock exchange used in the functional; for the dissociative intermediate in the ground state, the pure DFT functionals underestimate the reaction energy by 20 kJ/mol relative to wave-function-based methods, and when the amount of HF exchange is increased to 20% (B3LYP) and to 50% (BHLYP), the error is decreased to 13 and 4 kJ/mol, respectively.

Benchmark Calculations on the Electron Detachment Energies of MO3- and M2O6- (M = Cr, Mo, W)

Neutral and anionic molecules of the monomers and dimers of the group VIB transition metal oxides (MO3 and M2O6) were studied with density functional theory (DFT) and coupled cluster CCSD(T) theory. Franck-Condon simulations of the photoelectron spectra were carried out for the transition from the ground state of the anion to that of the neutral molecule. Molecular structures from the DFT and CCSD(T) methods are compared. Electron detachment energies reported in the literature were evaluated. The calculated adiabatic and vertical electron detachment energies (ADEs and VDEs) were compared with the experimental results. CCSD(T) gives results within 0.12 eV for the ADEs. CCSD(T) predicts VDEs that are in error by as much as 0.3 eV for M = Cr. DFT hybrid functionals were found to give poor results for the ADEs and VDEs for M = Cr due to the substantial amount of multireference character in the wavefunction, whereas the pure DFT functionals give superior results. For M = Mo and W, excellent agreement was found for both CCSD(T) and many DFT fucntionals. The BP86 functional yields the best overall results for the VDEs of all the metal oxide clusters considered. Heats of formation calculated at the CCSD(T) level extrapolated to the complete basis set limit are also in good agreement with available experimental data.

Assessment of time-dependent density functional schemes for computing the oscillator strengths of benzene, phenol, aniline, and fluorobenzene

In present study the relevance of using the time-dependent density functional theory (DFT) within the adiabatic approximation for computing oscillator strengths (f) is assessed using different LDA, GGA, and hybrid exchange-correlation (XC) functionals. In particular, we focus on the lowest-energy valence excitations, dominating the UV/visible absorption spectra and originating from benzenelike HOMO(pi)-->LUMO(pi(*)) transitions, of several aromatic molecules: benzene, phenol, aniline, and fluorobenzene. The TDDFT values are compared to both experimental results obtained from gas phase measurements and to results determined using several ab initio schemes: random phase approximation (RPA), configuration interaction single (CIS), and a series of linear response coupled-cluster calculations, CCS, CC2, and CCSD. In particular, the effect of the amount of Hartree-Fock (HF) exchange in the functional is highlighted, whereas a basis set investigation demonstrates the need of including diffuse functions. So, the hybrid XC functionals--and particularly BHandHLYP--provide f values in good agreement with the highly correlated CCSD scheme while these can be strongly underestimated using pure DFT functionals. These results also display systematic behaviors: (i) larger f and squares of the transition dipole moments (mid R:mumid R:(2)) are associated with larger excitation energies (DeltaE); (ii) these relationships present generally a linear character with R>0.9 in least-squares fit procedures; (iii) larger amounts of HF exchange in the XC functional lead to larger f, R:mumid R:(2), as well as DeltaE values; (iv) these increases in f, mid R:mumid R:(2), and DeltaE are related to increased HOMO-LUMO character; and (v) these relationships are, however, not universal since the linear regression parameters (the slopes and the intercepts at the origin) depend on the system under investigation as well as on the nature of the excited state.

Structure and ESR properties of self-trapped holes in pure silica from first-principles density functional calculations

The electronic structure and spectral properties of self-trapped holes (STH's) in $\mathrm{Si}{\mathrm{O}}_{2}$ are revisited using pure and hybrid density functional theory (DFT) approaches and cluster models. The structure and electron spin resonance (ESR) parameters [hyperfine coupling constants (hfcc's) and $g$ factors] have been determined for the two classical variants of STH's: ${\mathrm{STH}}_{1}$, consisting of a hole trapped at the $2p$ nonbonding orbital of an O atom bridging two Si atoms, and ${\mathrm{STH}}_{2}$, a metastable defect where the hole is delocalized over the $2p$ orbitals of two bridging O atoms. The computed ESR parameters fully support the experimental assignments based on the analysis of the ESR spectra. However, a nearly quantitative agreement between measured and computed hfcc's and $g$ factors is found only with a hybrid functional where 50% of the Hartree-Fock exchange is mixed in with the DFT exchange. Standard hybrid functionals, such as B3LYP, or pure DFT functionals, such as BLYP, fail completely in describing the two defects. According to these results, ${\mathrm{STH}}_{2}$ can form only in correspondence of specific O-Si-O angles of about 80\ifmmode^\circ\else\textdegree\fi{}--90\ifmmode^\circ\else\textdegree\fi{}, which classifies the defect center as a molecular polaron.

Density functional study of manganese dimer

AbstractChemical bonding and magnetic interaction of manganese dimer (Mn2) are still in controversy in experimental and theoretical studies. In this work, we examined various exchange correlation functionals of Kohn–Sham density functional theory (DFT), together with hybrid‐DFT, and Hartree–Fock plus DFT approaches on description of Mn2. We found that, in contrast to pure DFT functionals, the experimentally reported features of chemical bonding and antiferromagnetic interactions of Mn2 can be reproduced by employing the Hartree–Fock exchange terms. Thus, it is recommended to employ HF plus DFT, or hybrid DFT with large HF portion approach for the case that the direct interactions among manganese atoms play a major role to determine the electronic structure, such as manganese clusters. © 2007 Wiley Periodicals, Inc. Int J Quantum Chem, 2007

De novo prediction of the ground state structure of transition metal complexes using semiempirical and ab initio quantum mechanics. Coordination isomerism

The ground state coordination isomers for 30 different trigonal bipyramidal transition metal complexes have been predicted using different levels of quantum mechanics: semiempirical (PM3(tm)), ab initio (MP2//HF), pure (BPW91) and hybrid (B3PW91) density functional theory (DFT) methods. For species where these methods failed to reproduce crystallographic data, hybrid quantum mechanics/molecular mechanics (QM/MM) methods were used to study more exact experimental models. Literature deficiencies regarding ground state multiplicity of these species were supplemented by spin predictions using previously tested PM3(tm) methods. Geometry optimization calculations were performed for each possible coordination isomer. The predicted ground state minima provided by the different methods are compared to each other and with crystallographic data. Pure DFT functionals outperformed hybrid functionals and MP2//HF. The very rapid PM3(tm) parameterization method provided accurate predictions in comparison to other levels of theory. An integrated MM/PM3(tm)/DFT de novo scheme accurately reproduced crystallographic data for species where the individual methods failed.

Performance of the OPBE exchange-correlation functional

In a recent evaluation of density functional theory (DFT) functionals OPBE, which combines Handy's optimized exchange (OPTX) with the PBE correlation, was shown to correctly predict the spin states (singlet through sextet) of seven different iron complexes (2004, J. Phys. Chem. A, 108, 5479). The present study provides a further test of OPBE as well as that of the OPerdew and OLYP functionals, in which OPTX is combined with the Perdew and LYP correlations, respectively. These three are compared to other pure DFT functionals for their performance in calculating the atomization energies for the G2-set of up to 148 molecules, six reaction barriers of SN2 reactions, geometry optimizations of 19 small molecules and four metallocenes, and zero-point vibrational energies for 13 small molecules. OPBE performs exceptional well in all cases.

Efficient hybrid density functional calculations in solids: assessment of the Heyd-Scuseria-Ernzerhof screened Coulomb hybrid functional.

The present work introduces an efficient screening technique to take advantage of the fast spatial decay of the short range Hartree-Fock (HF) exchange used in the Heyd-Scuseria-Ernzerhof (HSE) screened Coulomb hybrid density functional. The screened HF exchange decay properties and screening efficiency are compared with traditional hybrid functional calculations on solids. The HSE functional is then assessed using 21 metallic, semiconducting, and insulating solids. The examined properties include lattice constants, bulk moduli, and band gaps. The results obtained with HSE exhibit significantly smaller errors than pure density functional theory (DFT) calculations. For structural properties, the errors produced by HSE are up to 50% smaller than the errors of the local density approximation, PBE, and TPSS functionals used for comparison. When predicting band gaps of semiconductors, we found smaller errors with HSE, resulting in a mean absolute error of 0.2 eV (1.3 eV error for all pure DFT functionals). In addition, we present timing results which show the computational time requirements of HSE to be only a factor of 2-4 higher than pure DFT functionals. These results make HSE an attractive choice for calculations of all types of solids.

Validation of Exchange−Correlation Functionals for Spin States of Iron Complexes

Spin state energies of iron complexes are important for biochemical applications such as the catalytic cycle of cytochrome P450. Due to the size of these systems and the presence of iron, accurate computational results can be obtained only with density functional theory (DFT). Validation of exchange-correlation (xc) DFT functionals for predicting the correct spin ground state of iron complexes is a rather unexplored area. In this contribution we report a systematic study on the performance of several xc functionals for seven iron complexes that are experimentally found to have either a low, intermediate, or high spin ground state. Standard xc functionals like LDA, BLYP, and PBE are found to disfavor high spin states, whereas hybrid and some meta-GGA functionals do provide the correct spin ground state for all molecules. Recently improved pure DFT functionals such as Handy's optimized exchange (OPTX) also perform well. The origin for the apparent performance of the DFT functionals has been addressed and seems to be related to the inclusion of fourth-order terms (s 4 ) of the dimensionless (or reduced) density gradient s in the exchange functional.

Static dipole polarizability and binding energy of sodium clusters Nan (n=1-10): A critical assessment of all-electron based post Hartree-Fock and density functional methods.

A systematic all electron post Hartree-Fock as well as density functional theory (DFT) based calculations for the polarizability and binding energy of sodium metal clusters have been performed and an in-depth analysis of the discrepancy between the experimental and theoretical results is presented. A systematic investigation for the assessment of different DFT exchange-correlation functionals in predicting the polarizability values has also been reported. All the pure DFT functionals have been found to considerably underestimate the calculated polarizability values as compared to the MP2 results. DFT calculations using the full Hartree-Fock exchange along with one-parameter progressive correlation functional have, however, been shown to yield results in good agreement with the MP2 and experimental results. The possible sources of error present in the experimental measurements as well as in the different theoretical methods have also been analyzed. One of the most important conclusions of the present study is that the effect of electron correlation plays a significant role in determining the polarizability of the clusters and the MP2 method can be considered to be one of the most reliable methods for their prediction. It has also been noted that the polarizability value of the lower member clusters (Na2 and Na4) calculated by highly sophisticated methods such as, CCSD and CCSD(T) are found to be very close to the corresponding MP2 values. The polarizability and the binding energy of the clusters are found to be inversely related to each other and their correlation is rationalized by invoking the minimum polarizability principle. A good linear correlation between the polarizability and volume of the cluster has also been found to exist.