The performance of density‐functional/Hartree–Fock hybrid methods: Cationic transition‐metal methyl complexes MCH+3 (M=Sc–Cu,La,Hf–Au)

Rydberg electron stabilizes the charge localized state of the diamine cation

A previous controversial discussion regarding the interpretation of Rydberg spectra of gaseous dimethylpiperazine (DMP) as showing the co-existence of a localized and delocalized mixed-valent DMP+ radical cation is revisited. Here we show by high-level quantum-chemical calculations that an apparent barrier separating localized and delocalized DMP+ minima in previous multi-reference configuration-interaction (MRCI) calculations and in some other previous computations were due to unphysical curve crossings of the reference wave functions. These discontinuities on the surface are removed in state-averaged MRCI calculations and with some other, orthogonal high-level approaches, which do not provide a barrier and thus no localized minimum. We then proceed to show that in the actually observed Rydberg state of neutral DMP the 3s-type Rydberg electron binds more strongly to a localized positive charge distribution, generating a localized DMP* Rydberg-state minimum, which is absent for the DMP+ cation. This work presents a case where interactions of a Rydberg electron with the underlying cationic core alter molecular structure in a fundamental way.

Spin-State Splittings in 3d Transition-Metal Complexes Revisited: Benchmarking Approximate Methods for Adiabatic Spin-State Energy Differences in Fe(II) Complexes

The CASPT2+δMRCI composite approach reported in a companion paper has been extended and used to provide high-quality reference data for a series of adiabatic spin gaps (defined as ΔE = E_quintet - E_singlet) of [Fe^IIL₆]²⁺ complexes (L = CNH, CO, NCH, NH₃, H₂O), either at nonrelativistic level or including scalar relativistic effects. These highly accurate data have been used to evaluate the performance of various more approximate methods. Coupled-cluster theory with singles, doubles, and perturbative triples, CCSD(T), is found to agree well with the new reference data for Werner-type complexes but exhibits larger underestimates by up to 70 kJ/mol for the π-acceptor ligands, due to appreciable static correlation in the low-spin states of these systems. Widely used domain-based local CCSD(T) calculations, DLPNO-CCSD(T), are shown to depend very sensitively on the cutoff values used to construct the localized domains, and standard values are not sufficient. A large number of density functional approximations have been evaluated against the new reference data. The B2PLYP double hybrid gives the smallest deviations, but several functionals from different rungs of the usual ladder hierarchy give mean absolute deviations below 20 kJ/mol. This includes the B97-D semilocal functional, the PBE0* global hybrid with 15% exact-exchange admixture, as well as the local hybrids LH07s-SVWN and LH07t-SVWN. Several further functionals achieve mean absolute errors below 30 kJ/mol (M06L-D4, SSB-D, B97-1-D4, LC-ωPBE-D4, LH12ct-SsirPW92-D4, LH12ct-SsifPW92-D4, LH14t-calPBE-D4, LHJ-HFcal-D4, and several further double hybrids) and thereby also still overall outperform CCSD(T) or uncorrected CASPT2. While exact-exchange admixture is a crucial factor in favoring high-spin states, the present evaluations confirm that other aspects can be important as well. A number of the better-performing functionals underestimate the spin gaps for the π-acceptor ligands but overestimate them for L = NH₃, H₂O. In contrast to a previous suggestion, non-self-consistent density functional theory (DFT) computations on top of Hartree-Fock orbitals are not a promising path to produce accurate spin gaps in such complexes.

Spectroscopic Identification of the Carbyne Hydride Structure of the Dehydrogenation Product of Methane Activation by Osmium Cations

The present work explores the structures of species formed by dehydrogenation of methane (CH₄) and perdeuterated methane (CD₄) by the 5d transition metal cation osmium (Os⁺). Using infrared multiple photon dissociation (IRMPD) action spectroscopy and density functional theory (DFT), the structures of the [Os,C,2H]⁺ and [Os,C,2D]⁺ products are explored. This study complements previous work on the related species formed by dehydrogenation of methane by four other 5d transition metal cations (M⁺ = Ta⁺, W⁺, Ir⁺, and Pt⁺). Osmium cations are formed in a laser ablation source, react with methane pulsed into a reaction channel downstream, and the resulting products spectroscopically characterized through photofragmentation using the Free-Electron Laser for IntraCavity Experiments (FELICE) in the 300-1800 cm^-1 range. Photofragmentation was monitored by the loss of H₂/D₂. Comparison of the experimental spectra and DFT calculated spectra leads to identification of the ground state carbyne hydride, HOsCH⁺ (²A') as the species formed, as previously postulated theoretically. Further, a full description of the systematic spectroscopic shifts observed for deuterium labeling of these complexes, some of the smallest systems to be studied using IRMPD action spectroscopy, is achieved. A full rotational contour analysis explains the observed linewidths as well as the observation of doublet structures in several bands, consistent with previous observations for HIrCH⁺ (²A'). Graphical Abstract ᅟ.

Noncollinear Two-Component Quasirelativistic Description of Spin Interactions in Exchange-Coupled Systems. Mapping Generalized Broken-Symmetry States to Effective Spin Hamiltonians

We provide a consistent mapping of noncollinear two-component quasirelativistic DFT energies with appropriate orientations of localized spinor quantization axes for multinuclear exchange-coupled transition-metal complexes onto an uncoupled anisotropic effective spin Hamiltonian. This provides access to the full exchange interaction tensor between the centers of spin-coupled systems in a consistent way. The proposed methodology may be best viewed as a generalized broken-symmetry density functional theory approach (gBS-DFT). While the calculations provided are limited to trinuclear systems ([M₃O(OOCH)₆(H₂O)₃]⁺, where M = Cr(III), Mn(III), Fe(III)) with C₃ symmetry, the method provides a general framework that is extendable to arbitrary systems. It offers an alternative to previous approaches to single-ion zero-field splittings, and it provides access to the less often examined antisymmetric Dzyaloshinskii-Moriya exchange interaction. Spin-orbit coupling is included self-consistently. This will be of particular importance for complexes involving 4d or 5d transition metal centers or possibly also for f-block elements, where a perturbational treatment of spin-orbit coupling may not be valid anymore. While a comparison with experimental data was indirect due to simplifications in the chosen model structures, the agreement obtained indicates the essential soundness of the presented approach.

Activation of H2 by Gadolinium Cation (Gd+): Bond Energy of GdH+ and Mechanistic Insights from Guided Ion Beam and Theoretical Studies

The energy-dependent reactions of the lanthanide gadolinium cation (Gd⁺) with H₂, D₂, and HD are investigated using guided ion beam tandem mass spectrometry. From analysis of the resulting endothermic product ion cross sections, the 0 K bond dissociation energy for GdH⁺ is measured to be 2.18 ± 0.07 eV. Theoretical calculations on GdH⁺ are performed for comparison with the experimental thermochemistry and generally appear to overestimate the experimental GdH⁺ bond dissociation energy. The branching ratio of the products in the HD reaction suggests that Gd⁺ reacts primarily via a statistical insertion mechanism to form the hydride product ion with contributions from direct mechanisms. Relaxed potential energy surfaces for GdH₂⁺ are computed and are consistent with the availability of both statistical and direct reaction pathways. The reactivity and hydride bond energy for Gd⁺ is compared with previous results for the group three metal cations, Sc⁺ and Y⁺, and the lanthanides, La⁺ and Lu⁺, and periodic trends are discussed.

Theoretical study of novel complexed structures for methoxy derivatives of scytonemin: potential biomarkers in iron-rich stressed environments

Scytonemin is a cyanobacterial sheath pigment with potent UV (UVA, UVB, and UVC) absorbing properties. Di- and tetramethoxy derivatives of scytonemin have also been found and described in the literature. The importance of these biomolecules is their photoprotective function, which is one of the major survival strategies adopted by extremophiles in environmentally stressed conditions. Also, iron compounds [particularly iron(III) oxides] offer an additional UV-protecting facility to subsurface endolithic biological colonization; hence, banded iron formations (accompanied by zones of depletion of iron) in rock matrices have attracted attention with special interest in the method of transportation of iron compounds through the rock. Di- and tetramethoxyscytonemin and their iron(III) complexes have been modeled and studied computationally by using density functional theory calculations at the level of B3LYP/6-31G** methodology. We propose new structures that could feature in survival strategy and facilitate the movement of iron through the rock especially for iron-rich stressed terrestrial environments exemplified by the Río Tinto system with the added potential of subsurface Mars exploration. This study represents a continuation of our previous work on scytonemin. The calculated Raman spectra of the proposed iron complexes are compared with those of their parent compounds and discussed in relation to structural changes effected in the parent ligand upon complexation. This information leads to new insights to be gained by experimental Raman spectroscopists and the characterization of spectroscopic biosignatures for the database being compiled for the remote Raman analytical interrogation of the martian surface and subsurface being proposed for the ESA ExoMars mission planned for launch in 2018.

Dioxygen reactivity of new bispidine-copper complexes

The reactivity of copper complexes of three different second-generation bispidine-based ligands (bispidine = 3,7-diazabicyclo[3.3.1]nonane; mono- and bis-tetradentate; exclusively tertiary amine donors) with dioxygen [(reversible) binding of dioxygen by copper(I)] is reported. The UV-vis, electrospray ionization mass spectrometry, electron paramagnetic resonance, and vibrational spectra (resonance Raman) of the dioxygen adducts indicate that, depending on the ligand and reaction conditions, several different species (mono- and dinuclear, superoxo, peroxo, and hydroperoxo), partially in equilibrium with each other, are formed. Minor changes in the ligand structure and/or experimental conditions (solvent, temperature, relative concentrations) allow switching between the different forms. With one of the ligands, an end-on peroxodicopper(II) complex and a mononuclear hydroperoxocopper(II) complex could be characterized. With another ligand, reversible dioxygen binding was observed, leading to a metastable superoxocopper(II) complex. The amount of dioxygen involved in the reversible binding to Cu(I) was determined quantitatively. The mechanism of dioxygen binding as well as the preference of each of the three ligands for a particular dioxygen adduct is discussed on the basis of a computational (density functional theory) analysis.

Iron-scytonemin complexes: DFT calculations on new UV protectants for terrestrial cyanobacteria and astrobiological implications

Cyanobacterial colonies produce the radiation-protectant biomolecule scytonemin as part of their response strategy for survival in environmentally stressed conditions in hot and cold deserts. These colonies frequently use sandstone rocks as host matrices for subsurface colonization, which is accompanied by a zone of depletion of iron and transportation of iron compounds to the mineral surface. It is suggested that an iron-scytonemin complex could feature in this survival strategy and facilitate the movement of iron through the rock. Calculations were carried out on several hypothetical iron-scytonemin complexes to evaluate the most stable structure energetically and examine the effect of the complexation of the biomolecule upon the electronic absorption characteristics of the radiation-protectant species. The implications for extraterrestrial planetary detection and analytical monitoring of an iron-scytonemin complex are assessed.

Theoretical study of the vibrational spectra of the hydrogen-bonded systems between pyridine-3-carboxamide (nicotinamide) and DMSO

The vibrational characteristics (vibrational frequencies and infrared intensities) for the hydrogen-bonded systems of nicotinamide (NA(Z) and NA(E)) with dimethyl sulfoxide (DMSO) have been predicted using ab initio SCF/6-31G(d,p) and DFT (BLYP/6-311++G(d,p)) calculations. The changes in the vibrational characteristics from free monomers to a complex have been calculated. The ab initio and BLYP calculations show that the complexation between nicotinamide (NA(Z) and NA(E)) and DMSO leads to large red shifts of the stretching vibrations for the hydrogen-bonded N-H bonds of nicotinamide and very strong increase in their IR intensity. The results from the BLYP/6-311++G(d,p) calculations show that the predicted red shifts of the nu(s)(NH) and nu(as)(NH) vibrations for the complex NA(E)-DMSO (1:2) (Deltanu(as)(NH)=-186 cm(-1) and Deltanu(s)(NH)=-198 cm(-1)) are in better agreement with the experimentally measured. The magnitudes of the wavenumber shifts are indicative of strong NH...O hydrogen-bonded interactions in both complexes. The calculations predict an increase of the IR intensity of nu(s)(NH) and nu(as)(NH) vibrations in the complexes up to 14 times. Having in mind that in more cases the predicted changes in the vibrational characteristics for the complexes studied are very near, it could be concluded that both conformers of nicotinamide, Z-conformer and E-conformer, are present in the solution forming the hydrogen-bonded complexes with DMSO.

Density functional localized orbital corrections for transition metals

This paper describes the development of the B3LYP localized orbital correction model which improves the accuracy of the B3LYP thermochemical predictions for compounds containing transition metals. The development of this model employs a large data set containing 36 experimental atomic energies and 71 bond dissociation energies. B3LYP calculations were carried out on these systems with different basis sets. Based on an electronic structure analysis and physical arguments, we built a set of 10 parameters to correct atomic data and a set of 21 parameters to correct bond dissociation energies. Using the results from our biggest basis set, the model was shown to reduce the mean absolute deviation from 7.7 to 0.4 kcalmol for the atomic data and from 5.3 to 1.7 kcalmol for the bond dissociation energies. The model was also tested using a second basis set and was shown to give relatively accurate results too. The model was also able to predict an outlier in the experimental data that was further investigated with high level coupled-cluster calculations.

Energetics and mechanisms of C-H bond activation by a doubly charged metal ion: guided ion beam and theoretical studies of Ta2+ + CH4

A guided ion beam tandem mass spectrometer is used to study the kinetic-energy dependence of doubly charged atomic tantalum cations (Ta(2+)) reacting with CH4 and CD4. As for the analogous singly charged system, the dehydrogenation reaction to form TaCH2(2+) + H2 is exothermic. The charge-transfer reaction to form Ta(+) + CH4(+) and the charge-separation reaction to form TaH(+) + CH3(+) are also observed at low energies in exothermic processes, as is a secondary reaction of TaCH2(2+) to form TaCH3(+) + CH3(+). At higher energies, other doubly charged products, TaC(2+) and TaCH3(2+), are observed, although no formation of TaH(2+) was observed. Modeling of the endothermic cross sections provides 0 K bond dissociation energies (in electronvolts) of D0(Ta(2+)-C) = 5.42 +/- 0.19 and D0(Ta(2+)-CH3) = 3.40 +/- 0.16. These experimental bond energies are in poor agreement with density functional calculations at the B3LYP/HW+/6-311++G(3df,3p) level of theory. However, the Ta(2+)-C bond energy is in good agreement with calculations at the QCISD(T) level of theory, and the Ta(2+)-CH3 bond energy is in good agreement with density functional calculations at the BHLYP level of theory. Theoretical calculations reveal the geometric and electronic structures of all product ions and are used to map the potential energy surface, which describes the mechanism of the reaction and key intermediates. Both experimental and theoretical results suggest that TaH(+), TaCH2(2+), and TaCH3(2+) are formed through a H-Ta(2+)-CH3 intermediate.

Structure and vibrational spectrum of the hydrogen-bonded system between 4-tert-butylphenol and N-bases: Ab initio and DFT studies

The structural and vibrational characteristics of the hydrogen-bonded system between 1,5,7-triazabicyclo [4.4.0] dec-5-ene (TBD) and 4-tert-butylphenol have been investigated employing ab initio and DFT calculations at different basis sets. The calculations show that the optimized structure of the studied system is cyclic. The corrected values of the dissociation energy for the hydrogen-bonded complex have been calculated in order to estimate its stability. The influence of the hydrogen bonding on the properties of the monomers (TBD and 4-tert-butylphenol) has been investigated. The hydrogen bonding between TBD and 4-tert-butylphenol leads to changes in the structural (bond lengths and angles) and vibrational (vibrational frequencies and infrared intensities) characteristics of the monomers. It was established that the TBD molecule is considerably deformed upon hydrogen bonding, while the deformation of the 4-t-BuPhOH is smaller. In agreement with the experiment, the calculations show that the stretching O-H vibration from 4-tert-butylphenol is shifted to lower frequency upon hydrogen bonding. The predicted frequency shift Deltanu(O-H) (-338cm(-1)) is in very good agreement with the experimentally observed (-351cm(-1)). In the same time the IR intensity of the nu(O-H) increases dramatically in the hydrogen-bonded system.

Theoretical study of the structures and vibrational spectra of the hydrogen-bonded systems of 4-cyanophenol with N-bases

The structural and vibrational features of the hydrogen bonded complexes of 1,5,7-triazabicyclo [4.4.0] dec-5-ene (TBD) with one and two 4-CNPhOH molecules have been studied extensively by ab initio SCF/6-31G(d,p) and BLYP calculations with various basis sets: 6-31G(d,p), 6-31+G(d,p) and 6-31++G(d,p). Full geometry optimization was made for the complexes studied. The nature of the hydrogen bonding and the influence of the hydrogen bonding on the structural and vibrational characteristics of the monomers have been investigated. The corrected values of the dissociation energy for the hydrogen-bonded complexes have been calculated in order to estimate their stability. The calculated values of the dissociation energy per phenol molecule indicate that the complex: TBD: 4-CNPhOH (1:1) is more stable than the complex: TBD: 4-CNPhOH (1:2). The changes in the structural and vibrational characteristics upon hydrogen bonding depend on the strength of the hydrogen bonds. In agreement with the experiment, the calculations show that the complexation between TBD and 4-CNPhOH leads to considerably changes in the vibrational characteristics of the stretching O-H vibration. The vibrational frequency of the O-H stretching vibration is shifted to lower wave numbers upon hydrogen bonding. The predicted frequency shifts Deltanu(O-H) for the complexes--TBD: 4-CNPhOH (1:1) and TBD: 4-CNPhOH (1:2) are in the range from -190 cm(-1) to -586 cm(-1). In the same time the IR intensity of the O-H stretching vibration increases dramatically in the hydrogen-bonded complexes.

Activation of CH4 by gas-phase Mo+, and the thermochemistry of Mo-ligand complexes

The kinetic-energy dependence of the reactions of Mo(+) ((6)S) with methane has been studied using guided ion beam mass spectrometry. No exothermic reactions are observed in this system, as also found previously, but efficient dehydrogenation occurs at slightly elevated energies. At higher energies, MoH(+) dominates the product spectrum and MoC(+), MoCH(+), and MoCH(3)(+) are also observed. Modeling of the endothermic reaction cross sections yields the 0 K bond dissociation energies (in eV) of D(0)(Mo(+)-C) = 4.55 +/- 0.19, D(0)(Mo(+)-CH) = 5.32 +/- 0.14, D(0)(Mo(+)-CH(2)) = 3.57 +/- 0.10, and D(0)(Mo(+)-CH(3)) = 1.57 +/- 0.09. The results for Mo(+) are compared with those for the first- and third-row transition-metal congeners, Cr(+) and W(+), and the differences in behavior and mechanism are discussed. Theoretical results are used to elucidate the geometric and electronic structures of all product ions as well as the complete potential-energy surface for reaction. The efficiency of the coupling between the sextet and quartet spin surfaces is also quantified.

Guided-ion beam and theoretical study of the potential energy surface for activation of methane by W+

A guided-ion beam tandem mass spectrometer is used to study the reactions, W(+) + CH(4) (CD(4)) and [W,C,2H](+) + H(2) (D(2)), to probe the [W,C,4H](+) potential energy surface. The reaction W(+) + CH(4) produces [W,C,2H](+) in the only low-energy process. The analogous reaction in the CD(4) system exhibits a cross section with strong differences at the lowest energies caused by zero-point energy differences, demonstrating that this reaction is slightly exothermic for CH(4) and slightly endothermic for CD(4). The [W,C,2H](+) product ion reacts further at thermal energies with CH(4) to produce W(CH(2))(x)(+) (x = 2-4). At higher energies, the W(+) + CH(4) reaction forms WH(+) as the dominant ionic product with smaller amounts of WCH(3)(+), WCH(+), and WC(+) also formed. The energy dependent cross sections for endothermic formation of the various products are analyzed and allow the determination of D(0)(W(+)-CH(3)) approximately 2.31 +/- 0.10 eV, D(0)(W(+)-CH(2)) = 4.74 +/- 0.03 eV, D(0)(W(+)-CH) = 6.01 +/- 0.28 eV, and D(0)(W(+)-C) = 4.96 +/- 0.22 eV. We also examine the reverse reaction, [W,C,2H](+) + H(2) (D(2)) --> W(+) + CH(4) (CH(2)D(2)). Combining the cross sections for the forward and reverse processes yields an equilibrium constant from which D(0)(W(+)-CH(2)) = 4.72 +/- 0.04 eV is derived. Theoretical calculations performed at the B3LYP/HW+/6-311++G(3df,3p) level yield thermochemistry in reasonable agreement with experiment. These calculations help identify the structures and electronic states of the species involved and characterize the potential energy surface for the [W,C,4H](+) system.

Activation of methane by gold cations: guided ion beam and theoretical studies

The potential energy surface for activation of methane by the third-row transition metal cation, Au+, is studied experimentally by examining the kinetic energy dependence of this reaction using guided ion beam tandem mass spectrometry. A flow tube ion source produces Au+ primarily in its 1S0 (5d10) electronic ground state level but with some 3D (and perhaps higher lying) excited states that can be completely removed by a suitable quenching gas (N2O). Au+ (1S0) reacts with methane by endothermic dehydrogenation to form AuCH2+ as well as C-H bond cleavage to yield AuH+ and AuCH3+. The kinetic energy dependences of the cross sections for these endothermic reactions are analyzed to give 0 K bond dissociation energies (in eV) of D0(Au+ - CH2) = 3.70 +/- 0.07 and D0(Au+ -CH3) = 2.17 +/- 0.24. Ab initio calculations at the B3LYPHW + /6-311++G(3df,3p) level performed here show good agreement with the experimental bond energies and previous theoretical values available. Theory also provides the electronic structures of the product species as well as intermediates and transition states along the reactive potential energy surface. Surprisingly, the dehydrogenation reaction does not appear to involve an oxidative addition mechanism. We also compare this third-row transition metal system with the first-row and second-row congeners, Cu+ and Ag+. Differences in thermochemistry can be explained by the lanthanide contraction and relativistic effects that alter the relative size of the valence s and d orbitals.

Theoretical study of the changes in the vibrational characteristics arising from the hydrogen bonding between Vitamin C (L-ascorbic acid) and H2O

The vibrational characteristics (vibrational frequencies, infrared intensities and Raman activities) for the hydrogen-bonded system of Vitamin C (L-ascorbic acid) with five water molecules have been predicted using ab initio SCF/6-31G(d,p) calculations and DFT (BLYP) calculations with 6-31G(d,p) and 6-31++G(d,p) basis sets. The changes in the vibrational characteristics from free monomers to a complex have been calculated. The ab initio and BLYP calculations show that the complexation between Vitamin C and five water molecules leads to large red shifts of the stretching vibrations for the monomer bonds involved in the hydrogen bonding and very strong increase in their IR intensity. The predicted frequency shifts for the stretching vibrations from Vitamin C taking part in the hydrogen bonding are up to -508 cm(-1). The magnitude of the wavenumber shifts is indicative of relatively strong OH...H hydrogen-bonded interactions. In the same time the IR intensity and Raman activity of these vibrations increase upon complexation. The IR intensity increases dramatically (up to 12 times) and Raman activity increases up to three times. The ab initio and BLYP calculations show, that the symmetric OH vibrations of water molecules are more sensitive to the complexation. The hydrogen bonding leads to very large red shifts of these vibrations and very strong increase in their IR intensity. The asymmetric OH stretching vibrations of water, free from hydrogen bonding are less sensitive to the complexation than the hydrogen-bonded symmetric OH stretching vibrations. The increases of the IR intensities for these vibrations are lower and red shifts are negligible.

Density Functionals for Inorganometallic and Organometallic Chemistry

We present a database of 21 bond dissociation energies for breaking metal-ligand bonds. The molecules in the metal-ligand bond energy database are AgH, CoH, CoO+, CoOH+, CrCH3+, CuOH2+, FeH, Fe(CO)5, FeO, FeS, LiCl, LiO, MgO, MnCH3NiCH2+, Ni(CO)4, RhC, VCO+, VO, and VS. We have also created databases of metal-ligand bond lengths and atomic ionization potentials. The molecules used for bond lengths are AgH, BeO, CoH, CoO+, FeH, FeO, FeS, LiCl, LiO, MgO, RhC, VO, and VS and the ionization potentials are for the following atoms: C, Co, Cr, Cu, Ni, O, and V. The data were chosen based on their diversity and expected reliability, and they are used along with three previously developed databases (transition metal dimer bond energies and bond lengths and main-group molecular atomization energies) for assessing the accuracy of several kinds of density functionals. In particular, we report tests for 42 previously defined functionals: 2 local spin density approximation (LSDA) functionals, 14 generalized gradient approximation (GGA) methods, 13 hybrid GGA methods, 7 meta GGA methods, and 8 hybrid meta GGA methods. In addition to these functionals, we also examine the effectiveness of scaling the correlation energy by testing 13 functionals with scaled or no gradient-corrected correlation energy, and we find that functionals of this kind are more accurate for metal-metal and metal-ligand bonds than any of the functionals already in the literature. We also present a readjusted GGA and a hybrid GGA with parameters adjusted for metals. When we consider these 57 functionals for metal-ligand and metal-metal bond energies simultaneously with main-group atomization energies, atomic ionization potentials, and bond lengths we find that the most accurate functional is G96LYP, followed closely by MPWLYP1M (new in this article), XLYP, BLYP, and MOHLYP (also new in this article). Four of these five functionals have no Hartree-Fock exchange, and the other has only 5%. As a byproduct of this work we introduce a convenient diagnostic, called the B1 diagnostic, for ascertaining the multireference character in a bond.

Guided Ion Beam and Theoretical Study of the Reactions of Ir+ with H2, D2, and HD

We present the kinetic energy dependence of reactions of the late third-row transition metal cation Ir(+) with H(2), D(2), and HD measured using a guided ion beam tandem mass spectrometer. A flow tube ion source produces Ir(+) ions in its electronic ground state term and primarily in the ground spin-orbit level. Corresponding state-specific reaction cross sections are obtained. The kinetic energy dependence of the cross sections for forming IrH(+) and IrD(+) are analyzed to give a 0 K bond dissociation energy of D(0)(Ir(+)-H) = 3.12 +/- 0.06 eV. Ab initio calculations at the B3LYP/HW+/6-311+G(3p), BHLYP/HW+/6-311+G(3p), and QCISD(T)/HW+/6-311+G(3p) levels performed here show reasonable agreement with the experimental bond energies and with the previous theoretical values available. Theory also provides the electronic structures of these species and the reactive potential energy surfaces. We also compare this third-row transition metal system with those of the first-row and second-row congeners Co(+) and Rh(+). We find that Ir(+) has a stronger M(+)-H bond, which can be explained by the lanthanide contraction and relativistic effects that alter the relative size of the valence s and d orbitals. Results from reactions with HD provide insight into the reaction mechanisms and indicate that Ir(+) reacts largely via an insertion mechanism, in contrast with the lighter group 9 metal ions Co(+) and Rh(+) which react via direct mechanisms.

Benchmarking approximate density functional theory. I.s/d excitation energies in 3d transition metal cations

The performance of a number of different implementations of density functional theory (DFT) for predicting the s/d interconfigurational energies of the 3d transition metal cations is investigated. Systematic comparisons of computed results with experimental data indicate that gradient corrected correlation functionals, like the LYP GGA, efficiently correct the flaws of the LDA, but reveal shortcomings in the treatment of exchange by currently available GGAs. The admixture of exact exchange in hybrid functionals eventually leads to largely reduced errors. Several basis sets available for the 3d elements are tested in combination with the B3LYP functional. Finally, the influence of variations of the admixture of exact exchange is systematically tested. The results reveal that computed s/d excitation energies obtained for the individual ions depend in markedly different ways on the amount of exact exchange admixture and that there is no single optimal and transferable exchange parameter to create a hybrid functional that yields improved results for all ions alike. Several of the recently devised functionals perform as good as or slightly better than the B3LYP functional in the present study. But given the fact that the B3LYP functional has been identified as the most successful DFT method in an overwhelming number of systematic investigations in very many areas of chemical research, there is no persuasive motivation to recommend its replacement by one of the other functionals, as much less is known about their robustness.

Probes of spin conservation in heavy metal reactions: Experimental and theoretical studies of the reactions of Re[sup +] with H[sub 2], D[sub 2], and HD

A guided ion beam tandem mass spectrometer is used to examine the kinetic energy dependence of reactions of the third-row transition metal cation, Re(+), with molecular hydrogen and its isotopologues. A flow tube ion source produces Re(+) in its (7)S(3) electronic ground state. Reaction with H(2), D(2), and HD forms Re H(+)(Re D(+)) in endothermic processes. Modeling of the endothermic reaction cross sections yields the 0 K bond dissociation energy of D(0)(Re(+)-H)=2.29+/-0.07 eV (221+/-6 kJ/mol). The experimental thermochemistry is consistent with ab initio calculations, performed here and in the literature. Theory also provides the electronic structures of these species and is used to examine the reactive potential energy surfaces. Results from reactions with HD provide insight into the reaction mechanisms and indicate that the late metal ion, Re(+), reacts largely via a statistical mechanism. This is consistent with the potential energy surfaces which locate a stable Re H(2) (+)((5)B(2)) complex. Results for this third-row transition metal system are compared with the first-row congener (Mn(+)) and found to have much higher reactivity towards dihydrogen and stronger M(+)-H bonds. These differences can be attributed to efficient coupling among surfaces of different spin along with lanthanide contraction and relativistic effects.

Theoretical studies on structures and reactivities of organocuprate(I) and organocopper(III) species

Systematic evaluation of method and basis set on the structure and energetics of organocuprate(I) and organocopper(III) species has been carried out. Various structures of organocuprate(I) and organocuprate(III) complexes were optimized with the HF, MP2, and B3LYP methods, and compared with the structures determined by X-ray crystallography (i.e., Me(2)Cu(I)(-), (CF(3))(4)Cu(III)(-)). Both the MP2 and B3LYP methods reasonably reproduce the X-ray structures while the HF method does not. Using larger basis set and incorporating the relativistic effects for Cu afford the best results. In the studies on the energetics of a Libond;Cu cluster model (Me(2)CuLi. LiCl) and Me(3)Cu model with the MP2, MP3, MP4DQ, MP4SDQ, CCSD(T), and B3LYP methods, the B3LYP method gives energetics similar to those obtained with the CCSD(T) method with much less cost, and hence, is judged to be the best practical method. The studies have shown that B3LYP method with the basis set incorporating the relativistic effective core potentials for Cu and the 6-31G* basis set for the rest is the theoretical method that is the most cost-effective for the studies of the structure and energetics of organocuprate(I) and organocopper(III) species.

Assessment of the OLYP and O3LYP density functionals for first-row transition metals

We have investigated the performance of the OLYP and O3LYP density functionals for predicting atomic excitation energies and ionization potentials, and bond dissociation energies, geometries, and vibrational frequencies for selected first-row transition metal compounds, including hydrides (MH) and singly charged methylene and methyl cations. The OLYP and O3LYP functionals are similar to the well-known BLYP and B3LYP functionals, respectively, but use a new optimized exchange functional (OPTX) developed by Handy and Cohen (Mol Phys 2001, 99, 403) in place of the standard B88 exchange. A previous study by us on organic reactions (J Chem Phys 2002, 117, 1331) indicated that both OLYP and O3LYP gave results for heats of reaction and barrier heights that were overall superior to those using the popular B3LYP functional. For transition metals, however, although OLYP is overall superior to BLYP for molecular calculations, it is inferior to B3LYP. O3LYP provides results for molecules of about the same quality as B3LYP. For atomic excitation and 4s ionization energies, unless relativistic effects are included, OLYP and O3LYP are clearly worse than both BLYP and B3LYP. There is thus no real incentive to use either OLYP or O3LYP in place of B3LYP for calculations involving first-row transition metals.