Performance of the M11-L density functional for bandgaps and lattice constants of unary and binary semiconductors

The recently developed SOGGA11 and M11-L density functionals have been tested for the prediction of bandgaps and lattice constants by comparing to databases containing 31 bandgaps and 34 lattice constants. To make a comparative assessment we also test several other density functionals against the same databases; in particular, we test the local spin density approximation, PBE, PBEsol, SOGGA, TPSS, revTPSS, and M06-L local density functionals and the HSE screened-exchange hybrid nonlocal density functional; and for a subset of 13 lattice constants we also compare the mean errors to those of the AM05 and WC local density functionals and the HISS and HSEsol nonlocal density functionals. The tests show that, of the ten functionals tested against all 65 data, the SOGGA, PBEsol, and HSE functionals are the most accurate for lattice constants, whereas the HSE, M11-L, and M06-L density functionals are the most accurate for bandgaps. However, the SOGGA11 density functional is the most accurate generalized gradient approximation for bandgaps.     

Evaluation of DFT methods for computing the interaction energies of homomolecular and heteromolecular dimers of monosubstituted benzene

We present density functional theory (DFT) interaction energies for the sandwich and T‐shaped conformers of substituted benzene dimers. The DFT functionals studied include TPSS, HCTH407, B3LYP, and X3LYP. We also include Hartree–Fock (HF) and second‐order Møller–Plesset perturbation theory calculations (MP2), as well as calculations using a new functional, P3LYP, which includes PBE and HF exchange and LYP correlation. Although DFT methods do not explicitly account for the dispersion interactions important in the benzene–dimer interactions, we find that our new method, P3LYP, as well as HCTH407 and TPSS, match MP2 and CCSD(T) calculations much better than the hybrid methods B3LYP and X3LYP methods do. © 2006 Wiley Periodicals, Inc. Int J Quantum Chem, 2006     

Dimers of boroglycine and methylamine boronic acid: a computational comparison of the relative importance of dative versus hydrogen bonding

Boronic acids are widely used in materials science, pharmacology, and the synthesis of biologically active compounds. In this Article, geometrical structures and relative energies of dimers of boroglycine, H2N-CH2-B(OH)2, and its constitutional isomer H3C-NH-B(OH)2, were computed using second-order M?ller-Plesset perturbation theory and density functional theory; Dunning-Woon correlation-consistent cc-pVDZ, aug-cc-pVDZ, cc-pVTZ, and aug-cc-pVTZ basis sets were employed for the MP2 calculations, and the Pople 6-311++G(d,p) basis set was employed for a majority of the DFT calculations. Effects of an aqueous environment were incorporated into the results using PCM and COSMO-RS methodology. The lowest-energy conformer of the H2N-CH2-B(OH)2 dimer was a six-membered ring structure (chair conformation; Ci symmetry) with two intermolecular B:N dative-bonds; it was 14.0 kcal/mol lower in energy at the MP2/aug-cc-pVDZ computational level than a conformer with the classic eight-centered ring structure (Ci symmetry) in which the boroglycine monomers are linked by a pair of H-O...H bonds. Compared to the results of MP2 calculations with correlation-consistent basis sets, DFT calculations using the PBE1PBE and TPSS functionals with the 6-311++G(d,p) basis set were significantly better at predicting relative conformational energies of the H2N-CH2-B(OH)2 and H3C-NH-B(OH)2 dimers than corresponding calculations using the BLYP, B3LYP, OLYP, and O3LYP functionals, particularly with respect to dative-bonded structures.     

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.     

A density functional study of chemical reactions

Density functional theory (DFT ) was used to study reactions involving small molecules. Relative energies of isomers and transition structures of diazene, formaldehyde, and methylenimine were determined using various DFT functionals and results were compared with MP 2 and MP 4 calculations. DFT reaction barriers were found to be consistently lower. For some reactions, such as OH + H₂→ H₂O + H, gradient-corrected functionals predict very low or nonexistent barriers. The hybrid Hartree–Fock–DFT adiabatic connection method (ACM ) often provides much better results in such cases. The performance of several density functionals, including ACM , was tested in calculations on over 100 atomization, hydrogenation, bond dissociation, and isodesmic reactions. The ACM functional provides consistently better geometries and reaction energetics than does any other functional studied. In cases where both HF and gradient-corrected DFT methods underestimate bond distances, the ACM geometries may be inferior to those predicted by gradient-corrected DFT methods. © 1995 John Wiley & Sons, Inc.     

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

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

On the mechanism of Re(I)-carboxylate bond cleavage by perchloric acid: a kinetic and spectroscopic study

We have studied the reaction between pz-CO(2)-Re(CO)(3)(bpy) and perchloric acid in acetonitrile by following the UV-vis and IR spectral changes in the reaction mixture. A fast equilibrium was found to be established between solvated protons, pz-CO(2)-Re(CO)(3)(bpy), and the protonated intermediate [pz-C(OH)O-Re(CO)(3)(bpy)](+) which finally yields pz-COOH and Re(CO)(3)(bpy)(CH(3)CN)(+) as reaction products. This intermediate has been characterized by UV-vis and IR spectroscopies and by DFT calculations. The fully optimized DFT/CPCM structures for pz-CO(2)-Re(CO)(3)(bpy) and [pz-C(OH)O-Re(CO)(3)(bpy)](+) were compared with the X-ray structure of pz-CO(2)-Re(CO)(3)(bpy). The structural parameters associated with the carboxyl group in the protonated intermediate are between those of pz-CO(2)-Re(CO)(3)(bpy) and pz-COOH. Multivariate curve resolution methods were employed to obtain the spectrum of the protonated intermediate and the concentration profiles from the full matrix of time-resolved UV-vis spectra. The proposed mechanism was numerically simulated by using Runge-Kutta methods. Model parameters were estimated by nonlinear regression fitting of the concentration profiles, yielding values of log(K) = 4.9 ± 0.3 and k = 0.16 ± 0.03 min(-1) for the formation equilibrium constant and the decay rate constant of the protonated intermediate, respectively.     

Intermolecular potentials of the silane dimer calculated with Hartree-Fock theory, Møller-Plesset perturbation theory, and density functional theory

We have calculated the intermolecular interaction potentials of the silane dimer at the D3d conformation using the Hartree-Fock (HF) self-consistent theory, the correlation-corrected second-order M?ller-Plesset (MP2) perturbation theory, and the density functional theory (DFT) with 108 functionals chosen from the combinations of 9 exchange and 12 correlation functionals. Single-point coupled cluster [CCSD(T)] calculations have also been carried out to calibrate the correlation effect. The HF calculations yield unbound potentials largely because of the exchange-repulsion interaction. In the MP2 calculations, the basis set effects on the repulsion exponent, the equilibrium bond length, the binding energy, and the asymptotic behavior of the calculated intermolecular potentials have been thoroughly studied. We have employed basis sets from the Slater type orbitals fitted with Gaussian functions (STO-nG, n = 3 approximately 6), Pople's medium size basis sets [up to 6-311++G(3df,3pd)], to Dunning's correlation consistent basis sets (cc-pVXZ and aug-cc-pVXZ, X = D, T, Q). With increasing basis size, the repulsion exponent and the equilibrium bond length converge at the 6-31G** basis set and the 6-311++G(3d,3p) basis set, respectively, while a large basis set (aug-cc-pVTZ) is required to converge the binding energy at a chemical accuracy ( approximately 0.05 kcal/mol). Up to the largest basis set used, the asymptotic dispersion coefficient has not converged to the expected C6 value from molecular polarizability calculations. We attribute the slow convergence partly to the inefficacy of using the MP2 calculations with Gaussian type functions to model the asymptotic behavior. Both the basis set superposition error (BSSE) corrected and uncorrected results are presented to emphasize the importance of including such corrections. Only the BSSE corrected results systematically converge to the expected potential curve with increasing basis size. The DFT calculations generate a wide range of interaction patterns, from purely unbound to strongly bound, underestimating or overestimating the binding energy. The binding energies calculated using the OPTXHCTH147, PBEVP86, PBEP86, PW91TPSS, PW91PBE, and PW91PW91 functionals and the equilibrium bond lengths calculated using the MPWHCTH93, TPSSHCTH, PBEVP86, PBEP86, PW91TPSS, PW91PBE, and PW91PW91 functionals are close to the MP2 results using the 6-311++G(3df,3pd) basis set. A correlation between the calculated DFT potentials and the exchange and correlation enhancement factors at the low-density region has been elucidated. The asymptotic behaviors of the DFT potentials are also analyzed.     

Generalized gradient approximation adjusted to transition metals properties: Key roles of exchange and local spin density

Perdew-Burke-Ernzerhof (PBE) and PBE adapted for solids (PBEsol) are exchange-correlation (xc) functionals widely used in density functional theory simulations. Their differences are the exchange, μ, and correlation, β, coefficients, causing PBEsol to lose the Local Spin Density (LSD) response. Here, the μ/β two-dimensional (2D) accuracy landscape is analyzed between PBE and PBEsol xc functional limits for 27 transition metal (TM) bulks, as well as for 81 TM surfaces. Several properties are analyzed, including the shortest interatomic distances, cohesive energies, and bulk moduli for TM bulks, and surface relaxation degree, surface energies, and work functions for TM surfaces. The exploration, comparing the accuracy degree with respect experimental values, reveals that the found xc minimum, called VV, being a PBE variant, represents an improvement of 5% in mean absolute percentage error terms, whereas this improvement reaches ~11% for VVsol, a xc resulting from the restoration of LSD response in PBEsol, and so regarded as its variant.     

Multiple structures and dynamics of [CpRu(CO)2]2 and [CpFe(CO)2]2 in solution revealed with two-dimensional infrared spectroscopy

Two-dimensional infrared (2DIR) spectroscopy is applied to both (Cp)(2)Fe(2)(CO)(4) and its ruthenium analog (Cp)(2)Ru(2)(CO)(4) in order to study the vibrational dynamics of these two systems. Combining the results of 2DIR spectroscopy and DFT calculations, the different structural forms of both the iron and the ruthenium complexes were characterized, furthering the previous assignment of the linear IR spectrum by determining the transition frequencies associated with the different isomeric forms. Monitoring the time-dependent amplitudes of the cross peaks enabled the observation of equilibrium energy transfer dynamics between different vibrational modes of the cis-B (Cp)(2)Fe(2)(CO)(4) and the gauche-NB (Cp)(2)Ru(2)(CO)(4) complexes. Treating the energy transfer as an equilibrium process, we extracted the rate constants associated with both the uphill and the downhill transfer of vibrational energy, finding that the difference in the rate constants of the two metal complexes maps to the difference in the energy gap between the two modes involved.     

Accurate Prediction of Au?P Bond Strengths by Density Functional Theory Methods

The recent development of Au‐catalyzed reactions has greatly enriched the methods of organic synthesis. The phosphine or phosphate‐coordinated Au complexes have shown high efficiency in catalyzing various C? C and C? H activations. In many of these reactions, the Au? P bond strength was found to play an important role in determining the catalytic efficiency. In the present study, the accuracy of different theoretical methods for prediction of Au? P strengths has been examined on basis of the experimental enthalpy changes between different ClAu(PR₃) and ClAu(THT) (THT=tetrahydrothiophene). By comparing the different DFT functionals (e.g. B3LYP, TPSS, M06), different basis sets (including the different effective core potentials on Au and the total electron basis sets on all other atoms), and different solution phase single point calculations, we found that the TPSS/(CPE‐121G+f:6‐311+G(d,p)(SMD)//TPSS/(CPE‐121G:6‐31G(d) ( M1 ) method gives the best correlations with the available experimental results. Meanwhile, the calculations with B3LYP//TPSS and M05//TPSS also give comparable calculation results. Finally, the specified method ( M1 ) is used to calculate the Au? P bond dissociation enthalpies and energies of different ClAu(PR₃)/ClAu(P(OR)₃) complexes. By accurately reproducing the available experimental results, we believe that the method ( M1 ) is reliable for the theoretical analysis of Au‐P systems.     

Accurate Structure and Bonding Description of the Transition Metal‐Disulfur Monoxide Complexes [(PMe3)2M(S2O)] (M = Ni,Pd, Pt): Grimme Dispersion Corrected DFT Study

Geometry and bonding energy analysis of M–S₂O bonds in the metal‐disulfur monoxide complexes [(PMe₃)₂M(S₂O)] of nickel, palladium, and platinum were investigated at DFT, DFT‐D3, and DFT‐D3(BJ) methods using three different functionals (BP86, PBE, and TPSS). The TPSS/DFT‐D3(BJ) yields better geometry, while the BP86 geometry is least accurate for studied complexes. The geometry of platinum complex optimized at TPSS/DFT‐D3(BJ) level is in excellent agreement with the available experimental values. The M–S bonds are shorter than the M–S(O) bonds. The Mayer bond orders suggest the presence of M–S and M–S(O) single bonds. Both the M–S and M–S(O) bond lengths vary with the density functionals as TPSS‐D3(BJ) < TPSS < PBE < BP86. The Hirshfeld charge distribution indicates that the overall charge flows from metal fragment to [S₂O]. The Ni–S₂O bond has greater degree of covalent character than the ionic. The contribution of dispersion interactions is large in computing accurate bond dissociation energies between the interacting fragments. The BDEs are largest for the functional TPSS and smallest for the functional BP86. The DFT‐D3 dispersion corrections to the BDEs between the metal fragments [(PMe₃)₂M] and ligand fragment [(S₂O)] for the TPSS functional are in the range 7.1–7.3 kcal · mol^–1, which are smaller than the corresponding DFT‐D3(BJ) dispersion corrections (9.4–10.6 kcal · mol^–1).     

Theoretical investigation of CO interaction with copper sites in zeolites: periodic DFT and hybrid quantum mechanical/interatomic potential function study

Periodic DFT and combined quantum mechanics/interatomic potential function (QM-pot) models were used to describe the interaction of CO with the Cu+ sites in FER. The CO stretching frequencies were calculated using omega(CO)(CCSD(T))/r(CO)(DFT) scaling method relating frequencies determined using a high-level quantum-chemical (coupled clusters) method for simple model carbonyls to CO bond lengths calculated using periodic DFT and QM-pot methods for the Cu+-zeolite system. Both periodic DFT and QM-pot models together with omega(CO)/r(CO) scaling describe the CO stretching dynamics with the "near spectroscopic accuracy", giving nu(CO) = 2156 cm(-1) in excellent agreement with experimental data. Calculations for various Cu+ sites in FER show that both types of Cu+ sites in FER (channel-wall sites and intersection sites) have the same CO stretching frequencies. Thus, the CO stretching frequencies are not site-specific in the CO/Cu+/FER system. The convergence of the results with respect to the model size was analyzed. When the same exchange-correlation functional is used the adsorption energies from periodic DFT and QM-pot are in good agreement (about 2 kcal/mol difference) but substantially larger than those of the experiment. The adsorption energy calculated with the B3LYP functional agrees with available experimental data. The overestimation of the adsorption energy in DFT calculations (periodic or QM-pot) is related to a red-shift of the CO stretching mode, both result from an underestimation of the HOMO(5sigma)-LUMO(2pi) gap of CO and the consequent overestimation of the Cu(+)(d)-CO(2pi*) back-donation. For the adsorption energy, this can be overcome by the use of hybrid B3LYP exchange-correlation functional. For the frequency calculations, the DFT problem can be overcome by the use of the omega(CO)(CCSD(T))/r(CO)(DFT) correlation.     

Benchmark study of DFT functionals for late-transition-metal reactions

The performance of a wide variety of DFT exchange-correlation functionals for a number of late-transition-metal reaction profiles has been considered. Benchmark ab-initio reference data for the prototype reactions Pd + H2, Pd + CH4, Pd + C2H6 (both C-C and C-H activation), and Pd + CH3Cl are presented, while ab-initio data of lesser quality were obtained for the catalytic hydrogenation of acetone and for the low-oxidation-state and high-oxidation-state mechanisms of the Heck reaction. "Kinetics" functionals such as mPW1K, PWB6K, BB1K, and BMK clearly perform more poorly for late-transition-metal reactions than for main-group reactions, as well as compared to general-purpose functionals. There is no single "best functional" for late-transition-metal reactions, but rather a cluster of several functionals (PBE0, B1B95, PW6B95, and TPSS25B95) that perform about equally well; if main-group thermochemical performance is additionally considered, then B1B95 and PW6B95 emerge as the best performers. TPSS25B95 and TPSS33B95 offer attractive performance compromises if weak interactions and main-group barrier heights, respectively, are also important. In the ab-initio calculations, basis set superposition errors (BSSE) can be greatly reduced by ensuring that the metal spd shell has sufficient radial flexibility in the high-exponent range. Optimal HF percentages in hybrid functionals depend on the class of systems considered, increasing from anions to neutrals to cations to main-group barrier heights; transition-metal barrier heights represent an intermediate situation. The use of meta-GGA correlation functionals appears to be quite beneficial.     

Binding energy curves from nonempirical density functionals. I. Covalent bonds in closed-shell and radical molecules

Binding or potential energy curves have been calculated for the ground-state diatomics H(2)(+), He(2)(+), LiH(+), H(2), N(2), and C(2), for the transition state H(3), and for the triplet first excited state of H(2) using the nonempirical density functionals from the first three rungs of a ladder of approximations: the local spin density (LSD) approximation, the Perdew-Burke-Ernzerhof (PBE) generalized gradient approximation (GGA), and the Tao-Perdew-Staroverov-Scuseria (TPSS) meta GGA. Good binding energy curves in agreement with coupled cluster or configuration interaction calculations are found from the PBE GGA and especially from the TPSS meta GGA. Expected exceptions are the symmetric radicals H(2)(+) and He(2)(+), where the functionals suffer from self-interaction error, and the exotically bonded C(2). Although the energy barrier for the reaction H(2) + H --> H + H(2) is better in PBE than in TPSS, the transition state H(3) is a more properly positioned and curved saddle point of the energy surface in TPSS. The triplet first excited state of H(2) obeys the Aufbau principle and thus is one of the exceptional excited states that are computable in principle from the ground-state functional. The PBE GGA and TPSS meta GGA are useful not only for chemical applications but also for the construction of higher-rung nonempirical functionals that can further improve the binding energy curves.     

Rozen's epoxidation reagent, CH3CN.HOF: a theoretical study of its structure, vibrational spectroscopy, and reaction mechanism

Rozen's epoxidation reagent, CH(3)CN.HOF, and a prototype epoxidation reaction employing it, have been subjected to an extensive ab initio and density functional study. Its anharmonic force field reveals a very strong red shift for the OH stretch and a strong blue shift for the HOF bend, in semiquantitative agreement with experiment. The very strong hydrogen bond (8.20 kcal/mol at the W1 level) not only serves to stabilize the reactant but also considerably lowers the barrier height for epoxidation of ethylene. Moreover, the reaction byproduct HF is found to act autocatalytically. The OH moiety acquires HO(+) character in the transition state. Our W1 benchmark data for the reaction profile allow the performance of various DFT functionals to be assessed. In general, "kinetics" functionals overestimate barrier heights, the BMK functional less so than the others. The B1B95 and TPSS33B95 meta-GGA functionals both perform very well, whereas general-purpose hybrid GGAs underestimate barrier heights. The simple PBE0 functional does reasonably well.     

A challenge for density functional theory: the XONO and XNO2 (X=F, Cl, and Br) molecules

The equilibrium geometries, harmonic frequencies, dipole moments, infrared intensities, and relative energies of the cis-XONO, trans-XONO, and XNO₂ (X=F, Cl, and Br) have been investigated using four functionals in common use in Kohn-Sham density functional theory (DFT) calculations. Two of the functionals include non-local or gradient correction terms, while the other two also incorporate some exact Hartree-Fock exchange and are labeled hybrid functionals. The quality of the results obtained from the functionals is determined by comparison to previously published high-level coupled-cluster calculations. The hybrid functionals perform better for prediction of the equilibrium geometries, where the two gradient corrected functionals yield qualitatively incorrect molecular structures for cis-FONO and cis-ClONO. None of the functionals perform well in predicting all six harmonic frequencies, showing that the correlation between equilibrium geometries and harmonic frequencies is not as strong for these DFT methods as it is for conventional wavefunction ab initio methods, such as coupled-cluster theory. Results from the various functionals generally come into better agreement with each other and also with the coupled-cluster results moving down the periodic table. Received: 12 February 1997 / Accepted: 25 March 1997     

Structure and properties of metal-exchanged zeolites studied using gradient-corrected and hybrid functionals. I. Structure and energetics

The structural and energetic properties of purely siliceous, proton-, and Cu- and Co-exchanged chabazite have been studied using periodic density-functional (DFT) calculations with both conventional gradient-corrected exchange-correlation functionals and hybrid functionals mixing exact (i.e., Hartree-Fock) and DFT exchange. Spin-polarized and fixed-moment calculations have been performed to determine the equilibrium and excited spin-configurations of the metal-exchanged chabazites. For the purely siliceous chabazite, hybrid functionals predict a slightly more accurate cell volume and lattice geometry. For isolated Al/Si substitution sites, gradient-corrected functionals predict that the lattice distortion induced by the substitution preserves the local tetrahedral symmetry, whereas hybrid functionals lead to a distorted Al coordination with two short and two long Al-O bonds. Hybrid functionals yield a stronger cation-framework binding that conventional functionals in metal-exchanged zeolites, they favor shorter cation-oxygen bonds and eventually also a higher coordination of the cation. Both types of functionals predict the same spin in the ground-state. The structural optimization of the excited spin-states shows that the formation of a high-spin configuration leads to a strong lattice relaxation and a weaker cation-framework bonding. For both Cu- and Co-exchanged chabazite, the prediction of a preferred location of the cation in a six-membered ring of the zeolite agrees with experiment, but the energy differences between possible cation locations and the lattice distortion induced by the Al/Si substitution and the bonding of the cation depends quite significantly on the choice of the functional. All functionals predict similar energy differences for excited spin states. Spin-excitations are shown to be accompanied by significant changes in the cation coordination, which are more pronounced with hybrid functionals. The consequences of electronic spectra and chemical reactivity are analyzed in the following papers.     

Dissociations of copper(II)-containing complexes of aromatic amino acids: radical cations of tryptophan, tyrosine, and phenylalanine

The dissociations of two types of copper(II)-containing complexes of tryptophan (Trp), tyrosine (Tyr), or phenylalanine (Phe) are described. The first type is the bis-amino acid complex, [Cu(II)(M)(2)].(2+), where M = Trp, Tyr, or Phe; the second [Cu(II)(4Cl-tpy)(M)].(2+), where 4Cl-tpy is the tridendate ligand 4'-chloro-2,2':6',2'-terpyridine. Dissociations of the Cu(ii) bis-amino acid complexes produce abundant radical cation of the amino acid, M.(+), and/or its secondary products. By contrast, dissociations of the 4Cl-tpy-bearing ternary complexes give abundant M.(+) only for Trp. Density functional theory (DFT) calculations show that for Tyr and Phe, amino-acid displacement reactions by H(2)O and CH(3)OH (giving [Cu(II)(4Cl-tpy)(H(2)O)].(2+) and [Cu(II)(4Cl-tpy)(CH(3)OH)].(2+)) are energetically more favorable than dissociative electron transfer (giving M.(+) and [Cu(I)(4Cl-tpy)](+)). The fragmentation pathway common to all these [Cu(II)(4Cl-tpy)(M)].(2+) ions is the loss of NH(3). DFT calculations show that the loss of NH(3) proceeds via a "phenonium-type" intermediate. Dissociative electron transfer in [Cu(II)(4Cl-tpy)(M-NH(3))].(2+) results in [M-NH(3)].(+). The [Phe-NH(3)] (+) ion dissociates facilely by eliminating CO(2) and giving a metastable phenonium-type ion that rearranges readily into the styrene radical cation.     

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.