Density Functional BP86 Research Articles

Performance of DFT methods in the calculation of isotropic and dipolar contributions to 14N hyperfine coupling constants of nitroxide radicals.

In the present study, we tested the widely used density functionals BP86, PBE, OLYP, TPSS, M06-L, B3LYP, PBE0, mPW1PW, B97, BHandHLYP, TPSS0, M06, M06-2X, CAM-B3LYP, ωB97x, and B2PLYP with the cc-pCVQZ basis set in calculations on a set of 23 nitroxide radicals with well-resolved 14N anisotropic hyperfine coupling (HFC) constants. The results were compared with those obtained using the B3LYP/N07D and PBE/N07D methods. The convergence of the HFC values to the complete basis set limit is briefly discussed. The best results were obtained using the M06/COSMO method, with a mean absolute deviation (MAD) of 0.4G for the dipole-dipole contribution and MAD = 0.6G for the contact coupling contribution (as compared to 1.1G and 1.0G, respectively, for the B3LYP/N07D/COSMO method and 1.7G and 0.5G, respectively, for the B3LYP/N07D method). The majority of the functionals yielded satisfactory results for the dipole-dipole contribution, but only the M06 functional yielded similar errors for both the dipole-dipole and isotropic contributions. The RIJCOSX and RI approximations introduced errors equal to or smaller than 0.01G.

The nature of M-PNR2 bonds in the electrophilic phosphinidene complexes [(L)(CO)3M{PNR2}]+ (L = PMe3, PPh3; M = Co, Rh, Ir; R = Me, iPr): Structure, bonding and 31P NMR study

Theoretical insights into the structure and the nature of M-PNR2 bonding in the cationic electrophilic phosphinidene complexes [(L)(CO)3M{PNR2}]+ (M = Co, Rh, Ir; R = iPr, Me; L = PMe3, PPh3) have been investigated at DFT level with emphasis on the density functional BP86, PBE, PW91 and TPSS and dispersion interactions, DFT-D3(BJ). Dispersion corrected functional yields accurate geometries. The geometry optimized with PBE-D3(BJ) functional is in excellent agreement with the experimental geometry of structurally characterized cobalt phosphinidene complex [(PPh3)(CO)3Co{PNiPr2}]+ (IV). The effects of metal atom, trans-influence of phosphine ligands (PMe3, PPh3) and substituent at nitrogen atom of PNR2 ligand on the M-PNR2 bond distances and M-P-N bond angles have been studied. The lengthening of M-PNR2 bonds trans to PMe3 ligand than those trans to PPh3 are due greater trans-influence of the PMe3 ligand. The 31P NMR chemical shifts of phosphinidene and phosphine ligands phosphorus in the complexes I-XII have been calculated out at PBE-D3(BJ)/TZ2P/ZORA with scalar (SC) and spin orbit (SO) relativistic level of theory in solvent chloroform. The computed values of 31P NMR chemical shifts are within the range of experimental values. The Mulliken charge analysis shows that the overall charge flows from phosphinidene ligand to metal fragment. The energy decomposition analysis divulged that the contribution of the electrostatic interaction ΔEelstat in all studied complexes is larger (54.5%–61.3%) than the orbital interactions ΔEorb. The π-bonding contribution is much smaller than the σ-bonding (85.4%–87.0%).

Nature of the metal–ligand bond in some [(CO)4M ← BIIM(R)] {M = Cr, Mo, W; R = H, F, Cl, Br} complexes: A theoretical study

A theoretical study on the structure and nature of the M←N bond in some potential pharmacologically active complexes; [(CO)4M←BIIM(R)] {M=Cr, Mo and W, R=H, F, Cl and Br} with R(3,3 substitution), R(4,4 substitution), R(5,5 substitution) and R(3,3 4,4, 5,5 substitutions) was carried through density functional BP86 and ab initio MP2 methods using the def2-TZVPP basis set. The M←N bond was analyzed using NBO, AIM, EDA and ETS-NOCV to obtain the electrical charge and energy decomposition analysis (EDA). The results showed that [(CO)4W←BIIM(H)] and [(CO)4Cr←BIIM(F)] are related to the D form complex with the biggest and the smallest ΔEint, respectively. Additionally, the M←N bond interaction energies (ΔEint) increase in the group from top to bottom, from the lighter to the heavier elements (Cr<Mo<W). The EDA suggests that the [(CO)4M←BIIM(R)] attractive interactions come mainly from ΔEelstat, which provides ∼60% of ΔEint, while ∼40% comes from ΔEorb. The applicability of the ETS-NOCV scheme is demonstrated for the complexes and it is shown that the ΔEorb term arises mainly through [(CO)4M←BIIM(R)] σ-donation (in the range 54–61%) while a smaller part (∼27%) comes from [(CO)4M→BIIM(R)] π-back donation. The nature of the M←N bond in the complexes was also studied by AIM and NBO analyses. The data has confirmed that the M←N bond is partly covalent.

The nature of M–B and B–N bonding in iminoboryl complexes of rhodium and iridium cis,mer-[(L)3(Br)2M(B[tbnd]NSiMe3)] (L = PMe3, CO): Dispersion corrected DFT study

Dispersion corrected quantum-chemical calculations of iminoboryl complexes cis,mer-[(L)3(Br)2M(BNSiMe3)] (M = Rh, Ir; L = PMe3, CO) were studied with and without dispersion interactions using density functionals BP86, BLYP, PBE, PW91 and TPSS. The calculations of the 11B NMR chemical shifts were carried out at DFT-D3(BJ)/BP86/TZ2P/ZORA with scalar and spin orbit relativistic level of theory in solvent C6D6. The calculated geometrical parameters of the rhodium iminoboryl complex cis,mer-[(Me3P)3(Br)2Rh(BNSiMe3)] (Braunschweig et al., J. Am. Chem. Soc. 130 (2008) 7974–7983) are in good agreement with the available experimental values. The calculated M−B and B–N bond distances, Mayer bond orders and Pauling bond orders suggest that the M–B bond has more than single bond character and B–N bond has less than triple bond character. The calculated bond dissociation energies (BDEs) of the M−B bonds follow the order BLYP < BP86 < TPSS < PBE < PW91. The absolute value of orbital interactions is significantly larger than the electrostatic interactions. The 11B NMR shielding is larger for carbonyl complexes cis,mer-[(CO)3Br2M(BNSiMe3)] than the phosphine complexes cis,mer-[(PMe3)3Br2M(BNSiMe3)]. On going from rhodium to iridium in the complexes cis,mer-[(L)3(Br)2M(BNSiMe3)] (L = PMe3, CO), the 11B NMR chemical shift decreases. The calculation of 11B chemical shifts by means of the ZORA relativistic scalar yields reliable results.

Theoretical insights into M–SO bonds in transition metal-sulfur monoxide complexes [{N(SPMe2)2}2M(SO)] (M = Fe, Ru, Os): Assessment of density functionals and dispersion interactions

Geometry, electronic structure and bonding analysis of the sulfur monoxide complexes [{N(SPMe2)2}2M(SO)] (M=Fe, Ru, Os) have been investigated with the DFT, DFT-D3 and DFT-D3(BJ) methods using density functionals BP86, PW91, BLYP, PBE, revPBE, and TPSS. The BP86 and PBE optimized geometries of complex [{N(SPMe2)2}2Ru(SO)] are in good agreement with the reported experimental values. The Mayer and Gopinathan–Jug bond orders confirm the presence of M–SO and S–O multiple bond characters. Hirshfeld charge analysis shows transfer of electron density from metal fragments to antibonding π∗ orbital of SO ligand. Significant noncovalent interactions between metal fragment and SO ligand are observed in the studied sulfur monoxide complexes. Noncovalent M---O and S---SO interactions have been justified by molecular orbital analysis. The M–SO bond dissociation energies vary in the order Fe<Ru<Os and depends on the choice of density functionals. The BP86/D3(BJ) dispersion corrections add 38% to the bond dissociation energy of Fe–SO bond, while only 22% and 17% to Ru–SO and Os–SO bonds, respectively. The π-bonding contributions to the total M–SO bonds are relatively smaller (22.6–27.0%) than the σ-bonding contribution.

Structure and bonding analysis of intermediate model heme-imidazole and heme-thiolate enzymes complexed with formate, acetate and nitrate: A theoretical study

Structure and bonding analysis of the FeO bonds in the model heme-imidazole and heme-thiolate complexes [(por)Fe(Im)(R)] (R=HC(O)O−, 1FeIm, R=H3CC(O)O−, 2FeIm, R=NO3−, 3FeIm) and [(por)Fe(SMe))(R)]− (R=HC(O)O−, 4FeSMe, R=H3CC(O)O−, 5FeSMe, R=NO3−, 6FeSMe) were investigated at the DFT/TZP level of theory using density functionals BP86, PW91, PBE, TPSS and B3LYP. The FeO bond distances at BP86/TZP in the complexes [(por)Fe(Im)(R)] (1.858Å in 1FeIm, 1.868Å in 2FeIm and 1.919Å in 3FeIm) and [(por)Fe(SMe)(R)]− (1.955Å in 4FeSMe, 1.981Å in 5FeSMe and 1.991Å in 6FeSMe) are longer than those expected for a FeO single bond estimated on the basis of covalent radii predictions (FeO=1.79Å). The FeO bond distances in [(por)Fe(Im)(R)] 1FeIm–3FeIm are shorter than those in [(por)Fe(SMe)(R)]−4FeSMe–6FeSMe. The thiolate is more trans-directing ligand than the imidazole ligand. The results of optimized geometries, NPA charges, Wiberg bond indices, NHO analysis and BDEs clearly indicate that the formate, acetate and nitrate ligands bind more weakly in heme-thiolate complexes than in heme-imidazole complexes. The reaction intermediate of chloroperoxidase enzyme would be more reactive with organic substrates than the myeloperoxidase (MPO) enzyme. The quartet and the sextet spin states are less stable than the doublet spin state. The optimized bond distances are shortest for doublet spin state.

Effects of density functionals and dispersion interactions on geometries, bond energies and harmonic frequencies of E[tbnd]UX3 (E = N, P, CH; X = H, F, Cl)

Quantum-chemical calculations have been performed to evaluate the geometries, bonding nature and harmonic frequencies of the compounds [EUX3] at DFT, DFT-D3, DFT-D3(BJ) and DFT-dDSc levels using different density functionals BP86, BLYP, PBE, revPBE, PW91, TPSS and M06-L. The stretching frequency of UN bond in [NUF3] calculated with DFT/BLYP closely resembles with the experimental value. The performance of different density functionals for accurate UN vibrational frequencies follows the order BLYP>revPBE>BP86>PW91>TPSS>PBE>M06-L. The BLYP functional gives accurate value of the UE bond distances. The uranium atom in the studied compounds [EUX3] is positively charged. Upon going from [EUF3] to [EUCl3], the partial Hirshfeld charge on uranium atom decreases because of the lower electronegativity of chlorine compared to flourine. The Gopinathan–Jug bond order for UE bonds ranges from 2.90 to 3.29. The UE bond dissociation energies vary with different density functionals as M06-L<TPSS<BLYP<revPBE<BP86<PBE≈PW91. The orbital interactions ΔEorb, in all studied compounds [EUX3] are larger than the electrostatic interaction ΔEelstat, which means the UN bonds in these compound have greater degree of covalent character (in the range 63.8–77.2%). The UE σ-bonding interaction is the dominant bonding interaction in the nitride and methylidyne complexes while it is weaker in [PUX3]. The dispersion energy contributions to the total bond dissociation energies are rather small. Compared to the Grimme’s D3(BJ) corrections, the Corminboeuf’s dispersion corrections are larger with metaGGA functionals (TPSS, M06-L) while smaller with GGA functionals.

Targeting Intermediates of [FeFe]-Hydrogenase by CO and CN Vibrational Signatures

In this work, we employ density functional theory to assign vibrational signatures of [FeFe]-hydrogenase intermediates to molecular structures. For this purpose, we perform an exhaustive analysis of structures and harmonic vibrations of a series of CN and CO containing model clusters of the [FeFe]-hydrogenase enzyme active site considering also different charges, counterions, and solvents. The pure density functional BP86 in combination with a triple-ζ polarized basis set produce reliable molecular structures as well as harmonic vibrations. Calculated CN and CO stretching vibrations are analyzed separately. Scaled vibrational frequencies are then applied to assign intermediates in [FeFe]-hydrogenase's reaction cycle. The results nicely complement the previous studies of Darensbourg and Hall, and Zilberman et al. The infrared spectrum of the H(ox) form is in very good agreement with the calculated spectrum of the Fe(I)Fe(II) model complex featuring a free coordination site at the distal Fe atom, as well as, with the calculated spectra of the complexes in which H(2) or H(2)O are coordinated at this site. The spectrum of H(red) measured from Desulfovibrio desulfuricans is compatible with a mixture of a Fe(I)Fe(I) species with all terminal COs, and a Fe(I)Fe(I) species with protonated dtma ligand, while the spectrum of H(red) recently measured from Chlamydomonas reinhardtii is compatible with a mixture of a Fe(I)Fe(I) species with a bridged CO, and a Fe(II)Fe(II) species with a terminal hydride bound to the Fe atom.

A Study of the Interactions between I−/I3− Redox Mediators and Organometallic Sensitizing Dyes in Solar Cells

Specific interactions of the I−/I3− redox mediators with the reduced and oxidized dye, Ru(4,4′-dicarboxy-2,2′-bipyridyl)2(NCS)2, referred to as N3 or Ru(dcbpy)2(NCS)2, have been studied by means of density functional theory (DFT) with the focus on the charge transfer process involving {dye+ I−} adducts; computations had been performed with a series of density functionals (gradient-corrected density functional BP86, and the hybrid density functionals B3LYP, MPW1K, B3PW1K, and MPW1PW91). Different pathways leading to {dye+ I−} adducts have been studied. First, mechanistic insights into the interaction of I− with RuIII(dcbpy)2(NCS)2 via an SCN− ligand directly giving rise to RuII(dcbpy)2(NCS)2I⌉0 have been obtained with the distinctive S−I bonding. Second, the binding of I− to the N3 dye cation via I−−dcbpy interactions has been analyzed. We also report experimental and computational evidence that sheds light on the interaction of the redox mediator with bipyridyl moieties. Evidence for a charge transfer process in the presence of only one I− anion in the outer coordination sphere of the ruthenium center has been identified. Finally, geometries and electronic structures of plausible intermediates have been computationally analyzed based on an inner-sphere interaction between the metal center and the redox mediator, including a two-step regeneration reaction: RuIII(dcbpy)2(NCS)2⌉+ + I− → RuIII(dcbpy)2(NCS)I⌉+ + SCN−, followed by the interaction of a second I− with the intermediate RuIII(dcbpy)2(NCS)I⌉+ complex. Conclusive evidence of a charge-transfer process that gives rise to the regenerated RuII complex, where I− interacts with the intermediate RuIII(dcbpy)2(NCS)I⌉+ complex has been identified.

Theoretical Study on the Spin-State Energy Splittings and Local Spin in Cationic [Re]−Cn−[Re] Complexes

Total spin-state energy splittings are calculated for mono- and dications of the formula {[Re]-Cn-[Re]}z+ where [Re] = eta5-(C5Me5)Re(NO)(PPh3). Cn is an even-numbered carbon chain with n ranging from 4 to 20, and z is 1 or 2. These complexes are experimentally known, and their potential role as molecular electronic devices initiated this work. We have considered the different total spin states monocation/doublet, monocation/quartet, dication/singlet, and dication/triplet. Data obtained for two density functionals BP86 and B3LYP were compared to verify the internal consistency of the results. In both ionization states, the low-spin state is the ground state, but the spin-state splittings decrease as the chain gets longer. For the dications, the splitting reaches a nearly constant value of about 10 kJ/mol with BP86 and about 4 kJ/mol with B3LYP when there are at least 14 carbon atoms in the chain, whereas for the monocations, no constant value appears to be reached asymptotically, not even if 20 carbon atoms are in the chain. For monocations, the splittings range from 138 kJ/mol (n = 4) to 68 kJ/mol (n = 20) with BP86 and from 134 kJ/mol (n = 4) to 73 kJ/mol (n = 20) with B3LYP and are thus considerably higher than those of the dications. The spin-state splittings are qualitatively mirrored by the energy splitting between the highest-occupied molecular orbital with beta spin (HOMObeta) and the lowest-unoccupied molecular orbital with alpha spin (LUMOalpha) as obtained in the low-spin state. Furthermore, the HOMOalpha-LUMOalpha gaps decrease as the carbon chain lengthens. In addition, the local distribution of the ŝz expectation value is analyzed for the monocation/doublet, the monocation/quartet, and the dication/triplet state using a modified Löwdin partitioning scheme. In the monocation/doublet and the dication/triplet state, the electron spin is distributed mainly on the metal centers and slightly delocalized onto the carbon chain. In the monocation/quartet state for chain lengths of more than 8 carbon atoms, the electron spin is mainly localized on selected atoms of the chain and not on the metal centers. In all cases, the spin delocalization onto the chain increases as the chain gets longer.

Comparison between the geometric and electronic structures and reactivities of [FeNO]7 and [FeO2]8 complexes: a density functional theory study.

In a previous study, we analyzed the electronic structure of S = 3/2 [FeNO](7) model complexes [Brown et al. J. Am. Chem. Soc. 1995, 117, 715-732]. The combined spectroscopic data and SCF-X alpha-SW electronic structure calculations are best described in terms of Fe(III) (S = 5/2) antiferromagnetically coupled to NO(-) (S = 1). Many nitrosyl derivatives of non-heme iron enzymes have spectroscopic properties similar to those of these model complexes. These NO derivatives can serve as stable analogues of highly labile oxygen intermediates. It is thus essential to establish a reliable density functional theory (DFT) methodology for the geometry and energetics of [FeNO](7) complexes, based on detailed experimental data. This methodology can then be extended to the study of [FeO(2)](8) complexes, followed by investigations into the reaction mechanisms of non-heme iron enzymes. Here, we have used the model complex Fe(Me(3)TACN)(NO)(N(3))(2) as an experimental marker and determined that a pure density functional BP86 with 10% hybrid character and a mixed triple-zeta/double-zeta basis set lead to agreement between experimental and computational data. This methodology is then applied to optimize the hypothetical Fe(Me(3)TACN)(O(2))(N(3))(2) complex, where the NO moiety is replaced by O(2). The main geometric differences are an elongated Fe[bond]O(2) and a steeper Fe[bond]O[bond]O angle in the [FeO(2)](8) complex. The electronic structure of [FeO(2)](8) corresponds to Fe(III) (S = 5/2) antiferromagnetically coupled to O(2)(-) (S = 1/2), and, consistent with the extended bond length, the [FeO(2)](8) unit has only one Fe(III)-O(2)(-) bonding interaction, while the [FeNO](7) unit has both sigma and pi type Fe(III)-NO(-) bonds. This is in agreement with experiment as NO forms a more stable Fe(III)-NO(-) adduct relative to O(2)(-). Although NO is, in fact, harder to reduce, the resultant NO(-) species forms a more stable bond to Fe(III) relative to O(2)(-) due to the different bonding interactions.

Ligand influences on hydrogen migration in transition metal hydrido–carbyne complexes

Density Functional BP86 calculations are reported for the interconversion reactions of WH(CH)(CO)(PH 3) 3 and WH(CH)(CO) 2(PH 3) 2 to the corresponding five-coordinated carbene complexes W(CH 2)(CO)(PH 3) 3 and W(CH 2)(CO) 2(PH 3) 2, respectively. Transition states have been calculated to be 9.9 and 0.7 kcal mol −1 higher in energy than the carbynes. A comparison with the isoelectronic osmium system OsHCl 2(CMe)(PH 3) 2 with a transition state for interconversion 27.2 kcal mol −1 above the carbyne leads to the conclusion that additional π-acceptors competing with the carbyne or carbene ligand for back donation facilitate the interconversion reaction, whereas additional π-donors undergoing synergic push–pull interactions impede the interconversion reaction.