Self-interaction artifacts on structural features of uranyl monohydroxide from Kohn�CSham calculations

Invoking a DFT?+?U approach, we explored self-interaction artifacts in results from Kohn?CSham (KS) density functional calculations on the geometry and the vibrational frequencies of uranyl monohydroxide and the corresponding tetra-aqua complex. Exchange?Ccorrelation functionals based on the local density approximation (LDA) and the generalized-gradient approximation (GGA) predict equilibrium geometries for [UO₂(OH)]⁺ that deviate from the results of hybrid DFT calculations and high-level wavefunction-based methods such as CCSD(T). LDA?+?U and GGA?+?U functionals with corrections for the insufficient localization of the U 5f shell yield better agreement, in particular for the angle U-O_h-H. At the LDA level, a linear coordination of the OH ligand results; with the +U correction, the angle U-O_h-H is reduced by ~35°, in good agreement with CCSD(T) results. At the GGA level, the bending angle is changed by ~20°. This relatively strong self-interaction artifact is traced back to a spurious ?? interaction between U 5f and O(p) orbitals which is less pronounced in the presence of further (aqua) ligands.     

Long-range and short-range Coulomb correlation effects as simulated by Hartree–Fock,local density approximation,and generalized gradient approximation exchange functionals

 Exchange functionals used in density functional theory (DFT) are generally considered to simulate long-range electron correlation effects. It is shown that these effects can be traced back to the self-interaction error (SIE) of approximate exchange functionals. An analysis of the SIE with the help of the exchange hole reveals that both short-range (dynamic) and long-range (nondynamic) electron correlation effects are simulated by DFT exchange where the local density approximation (LDA) accounts for stronger effects than the generalized gradient expansion (GGA). This is a result of the fact that the GGA exchange hole describes the exact exchange hole close to the reference electron more accurately than the LDA hole does. The LDA hole is more diffuse, thus leading to an underestimation of exchange and stronger SIE effects, where the magnitude of the SIE energy is primarily due to the contribution of the core orbitals. The GGA exchange hole is more compact, which leads to an exaggeration of exchange in the bond and the nonbonding region and negative SIE contributions. Partitioning of the SIE into intra-/interelectronic and individual orbital contributions makes it possible to test the performance of a given exchange functional in different regions of the molecule. It is shown that Hartree–Fock exchange always covers some long-range effects via interelectronic exchange while self-interaction-corrected DFT is lacking these effects. Received: 25 May 2002 / Accepted: 7 October 2002 / Published online: 21 January 2003 Correspondence to: E. Kraka e-mail: kraka@theoc.gn.se Acknowledgements. This work was supported financially by the Swedish Natural Science Research Council (NFR). Calculations were done on the supercomputers of Nationellt Superdatorcentrum (NSC), Link?ping, Sweden. The authors thank the NSC for a generous allotment of computer time.     

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.     

Modeling continuous changes in substituent electronegativity and chemical hardness using fictitious nuclear potentials

The performances of a family of recently developed generalized gradient approximation (GGA) functionals based on the Tognetti–Cortona–Adamo (TCA) family and making use of the gradient-regulated connection (GRAC) approach are here tested on an uncommon benchmark set for the prediction of transition state (TS) structures and energies of a series of four reactions involving an early transition metal (Zr, d ⁰). This benchmark test thus represents the first step in the organometallic world in which d ⁿ ions allowing complex phenomena such as spin crossover represent the higher level of complexity. The results obtained show that the performances of the GRAC-xxx functionals are comparable to those of global hybrid functionals both in the prediction of reaction barriers and of structural features of TSs. More complex functional forms (such as range-separated hybrids) in average enhance the energetic features, but not necessarily the overall accuracy on calculated structures. On the other hand, and as expected, purposely developed functionals for the prediction of chemical reactivity provide both structural and energetic features in good agreement with post-HF results. The present study, besides proving the good performances of GGA functionals of the GRAC-TCA family for the prediction of TS structural parameters and energetics of metal containing systems, also underlines the importance of the use of diversified benchmark sets to allow a fair evaluation of functionals performances.     

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.     

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.     

The Aqueous Ca2+ System,in Comparison with Zn2+, Fe3 +, and Al3 +: An Ab Initio Molecular Dynamics Study

Herein, we report on the structure and dynamics of the aqueous Ca²⁺ system studied by using ab initio molecular dynamics (AIMD) simulations. Our detailed study revealed the formation of well‐formed hydration shells with characteristics that were significantly different to those of bulk water. To facilitate a robust comparison with state‐of‐the‐art X‐ray absorption fine structure (XAFS) data, we employ a 1st principles MD‐XAFS procedure and directly compare simulated and experimental XAFS spectra. A comparison of the data for the aqueous Ca²⁺ system with those of the recently reported Zn²⁺, Fe³⁺, and Al³⁺ species showed that many of their structural characteristics correlated well with charge density on the cation. Some very important exceptions were found, which indicated a strong sensitivity of the solvent structure towards the cation′s valence electronic structure. Average dipole moments for the 2nd shell of all cations were suppressed relative to bulk water.     

Cytochrome P450 compound I in the plane wave pseudopotential framework: GGA electronic and geometric structure of thiolate‐ligated iron(IV)–oxo porphyrin

The cytochromes P450 constitute a ubiquitous family of metalloenzymes, catalyzing manifold reactions of biological and synthetic importance via a thiolate‐ligated iron‐oxo (IV) porphyrin radical species denoted compound I (Cpd I). Experimental investigations have implicated this intermediate in a broad spectrum of biophysically interesting phenomena, further augmenting the importance of a Cpd I model system. Ab initio molecular dynamics, including Car–Parrinello and path integral methods, conjoin electronic structure theory with finite temperature simulation, affording tools most valuable to approach such enzymes. These methods are typically driven by density functional theory (DFT) in a plane‐wave pseudopotential framework; however, existing studies of Cpd I have been restricted to localized Gaussian basis sets. The appropriate choice of density functional and pseudopotential for such simulations is accordingly not obvious. To remedy this situation, a systematic benchmarking of thiolate‐ligated Cpd I is performed using several generalized‐gradient approximation (GGA) functionals in the Martins–Troullier and Vanderbilt ultrasoft pseudopotential schemes. The resultant electronic and structural parameters are compared to localized–basis DFT calculations using GGA and hybrid density functionals. The merits and demerits of each scheme are presented in the context of reproducing existing experimental and theoretical results for Cpd I. © 2013 Wiley Periodicals, Inc.     

DFT study of the structural characteristics of the yttrium(3+) aqua ion

Density functional theory (DFT) using SVWN5, B3LYP, B3P86, O3LYP, B3PW91, B1LYP, B971, MPW1PW91, PBE1PBE, BHandH, and BHandHLYP density functionals was employed to study the structural characteristics of the Y(H₂O) ₈ ³⁺ yttrium aqua ion. The nonlocal hybrid GGA functionals show worse predictive ability in structural calculations of the Y(H₂O) ₈ ³⁺ aqua ion compared to the relatively simple combined functional BHandH and to the simplest SVWN5 functional in LSDA theory.     

Anthrone-spirolactam and quinoline hybrid based sensor for selective fluorescent detection of Fe3+ ions

The synthesis of a novel, and highly selective Fe³⁺ ion sensor based on anthrone-spirolactam and its quinoline hybrid ligand is reported. The designed ligand displayed selective detection of Fe³⁺ ions with enhanced fluorescence emission. The complexation of Fe³⁺ ion led to a red shift of 32 nm from 420 nm to 452 nm, and a several fold increase in intensity with fluorescent green emission. The complexation (detection) of Fe³⁺ ions with ligand resulted in chelation enhanced fluorescence and intramolecular charge transfer through the inhibition of C=N isomerization. This hybrid sensor shows high sensitivity and selectivity, spontaneous response, and works on a wide pH range a minimum detection limit of 6.83 × 10⁻⁸ M. Importantly, the sensor works through the fluorescence turn-on mechanism that overcomes the paramagnetic effect of Fe³⁺ ions. The binding mechanism between the ligand and the Fe³⁺ ions was established from the Job's plot method, optical studies, Fourier transfor infrared spectroscopy, NMR titration, fluorescence life-time studies, and density functional theory optimization. The sensor displayed excellent results in the quantification of Fe³⁺ ions from real water samples. Furthermore, due to its biocompatibility nature, fluorescent spotting of Fe³⁺ ions in live cells revealed its bioimaging applications.     

Performance of density functionals for modeling vapor liquid equilibria of CO2 and SO2

Vapor liquid equilibria (VLE) and condensed phase properties of carbon dioxide and sulfur dioxide are calculated using first principles Monte Carlo (FPMC) simulations to assess the performance of several density functionals, notably PBE‐D3, BLYP‐D3, PBE0‐D3, M062X‐D3, and rVV10. GGA functionals were used to compute complete vapor liquid coexistence curves (VLCCs) to estimate critical properties, while the hybrid and nonlocal van der Waals functionals were used only for computing density at a single state point due to the high computational cost. Our results show that the BLYP‐D3 functional performs well in predicting VLE properties for both molecules when compared with other functionals. In the liquid phase, pair correlation functions reveal that there is not a significant difference in the location of the peak for the first solvation shell while the peak heights are different for different functionals. Overall, the BLYP‐D3 functional is a good choice for modeling VLE of acidic gases with significant environmental implications such as CO₂ and SO₂. © 2017 Wiley Periodicals, Inc.     

A Monte Carlo simulation of free energy relationships for the electron transfer reaction between Fe+ and Fe2+ in water

A free energy barrier ΔF^≠ = 174.2 kJ/mol for the self-exchange electron transfer reaction model Fe⁺/Fe²⁺ in water has been calculated by combining Monte Carlo simulations and the statistical perturbation theory. We have shown that, even for those electron transfer reactions that present a very high free energy barrier of activation, the free energy curve behaves parabolically versus the reaction coordinate, which justifies the quadratic expression for the activation free energy done by Marcus.     

Simulating Nuclear subsystem rearrangement in the redox reaction between Fe2+ and Fe3+ ions

An approach that allows the numerical simulation of conformational rearrangements accompanying redox reactions in molecular systems is examined. The proposed method makes it possible on the basis of metadynamics to identify automatically the groups of atoms whose conformational motions give rise to changes in the redox properties of an investigated system. The method is used to simulate a classic model electron transfer reaction, i.e., the redox reaction between Fe²⁺ and Fe³⁺ ions in a solution. The effective activation energy of the reaction is reproduced quantitatively, and the reaction coordinate is determined. It is shown that this approach is promising for use in studying conformational changes that are associated with electron transport processes in complex molecular systems.     

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.     

Energies and Spin States of FeS0/−, FeS20/−, Fe2S20/−, Fe3S40/−, and Fe4S40/− Clusters

The structures and energies of the electronic ground states of the FeS^0/?, FeS₂^0/?, Fe₂S₂^0/?, Fe₃S₄^0/?, and Fe₄S₄^0/? neutral and anionic clusters have been computed systematically with nine computational methods in combination with seven basis sets. The computed adiabatic electronic affinities (AEA) have been compared with available experimental data. Most reasonable agreements between theory and experiment have been found for both hybrid B3LYP and B3PW91 functionals in conjugation with 6‐311+G* and QZVP basis sets. Detailed comparisons between the available experimental and computed AEA data at the B3LYP/6‐311+G* level identified the electronic ground state of ⁵Δ for FeS, ⁴Δ for FeS^?, ⁵B₂ for FeS₂, ⁶A₁ for FeS₂^?, ¹A₁ for Fe₂S₂, ⁸A′ for Fe₂S₂^?, ⁵A′′ for Fe₃S₄, ⁶A′′ for Fe₃S₄^?, ¹A₁ for Fe₄S₄, and ¹A₂ for Fe₄S₄^?. In addition, Fe₂S₂, Fe₃S₄, Fe₃S₄^?, Fe₄S₄, and Fe₄S₄^? are antiferromagnetic at the B3LYP/6‐311+G* level. The magnetic properties are discussed on the basis of natural bond orbital analysis.     

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