Use of the chemical potential to improve energies from approximate wave functions

Summary An equation derived from density functional theory is used to improve energies calculated from approximate wave functions. The examples used are perturbed particle in a box and harmonic oscillators. The equation depends on the constancy of the chemical potential in these systems. The results are quite promising.     

Theoretical study of the reactivity of (CH3)2AlCH2I promoted cyclopropanation reactions

Density functional theory calculations are reported for the cyclopropanation reactions of (CH₃)₂AlCH₂I with ethylene for two reaction channels: methylene transfer and carbometalation. These computational results suggest that the methylene transfer process is favored and the competition from the carbometalation pathway is negligible.     

Density functional study of ethylene oxidation on an Ag(111) surface

The mechanism of ethylene epoxidation on Ag surfaces has been investigated using the density functional method and Ag _n clusters (n = 3 to 10) modeling the Ag(111) surface. The adsorption energy of O₂ to the Ag clusters was strongly dependent on the HOMO level of the cluster, and the clusters with higher HOMO levels afforded larger O₂ adsorption energies. The energetics was investigated for both the molecular and atomic oxygen epoxidation mechanisms. For the atomic oxygen mechanism, epoxidation was found to proceed without an activation energy, whereas a small amount of activation energy (about 5 kcal/mol) was calculated for the molecular oxygen mechanism. Received: 2 July 1998 / Accepted: 9 September 1998 / Published online: 8 February 1999     

The origin of the stereochemically active Pb(II) lone pair: DFT calculations on PbO and PbS

The concept of a chemically inert but stereochemically active 6s² lone pair is commonly associated with Pb(II). We have performed density functional theory calculations on PbO and PbS in both the rocksalt and litharge structures which show anion dependence of the stereochemically active lone pair. PbO is more stable in litharge while PbS is not, and adopts the symmetric rocksalt structure showing no lone pair activity. Analysis of the electron density, density of states and crystal orbital overlap populations shows that the asymmetric electron density formed by Pb(II) is a direct result of anion-cation interactions. The formation has a strong dependence on the electronic states of the anion and while oxygen has the states required for interaction with Pb 6s, sulphur does not. This explains for the first time why PbO forms distorted structures and possesses an asymmetric density and PbS forms symmetric structures with no lone pair activity. This analysis shows that distorted Pb(II) structures are not the result of chemically inert, sterically active lone pairs, but instead result from asymmetric electron densities that rely on direct electronic interaction with the coordinated anions.     

Oxygen anion (O−) and hydroxide anion (HO−) reactivity with a series of old and new refrigerants

The reactivity of a series of commonly used halogenated compounds (trihalomethanes, chlorofluorocarbon, hydrochlorofluorocarbon, fluorocarbons, and hydrofluoroolefin) with hydroxide and oxygen anion is studied in a compact Fourier transform ion cyclotron resonance. O⁻ is formed by dissociative electron attachment to N₂O and HO⁻ by a further ion‐molecule reaction with ammonia. Kinetic experiments are performed by increasing duration of introduction of the studied molecule at a constant pressure. Hydroxide anion reactions mainly proceed by proton transfer for all the acidic compounds. However, nucleophilic substitution is observed for chlorinated and brominated compounds. For fluorinated compounds, a specific elimination of a neutral fluorinated alkene is observed in our results in parallel with the proton transfer reaction. Oxygen anion reacts rapidly and extensively with all compounds. Main reaction channels result from nucleophilic substitution, proton transfer, and formal H₂⁺ transfer. We highlight the importance of transfer processes (atom or ion) in the intermediate ion‐neutral complex, explaining part of the observed reactivity and formed ions. In this paper, we present the first reactivity study of anions with HFO 1234yf. Finally, the potential of O⁻ and HO⁻ as chemical ionization reagents for trace analysis is discussed.     

Fluxional behavior of methyl-substituted tricarbonyl(tropone)iron complexes and their different reactivity

The compositions of regioisomeric mixtures of tricarbonyliron complexes of 2-methyltropone (1a,b), 3-methyltropone (2a,b) and 2,6-dimethyltropone (3a,b) are studied and compared with the results of ab initio computations. The structures, frontier orbitals, and population analysis are evaluated by means of density functional theory. The thermodynamic and kinetic parameters of regioisomerizations are determined using dynamic ¹H NMR technique. The influence of methyl-substituent(s) on the equilibrium ratio of regioisomers resulting from the haptotropic rearrangement is discussed. Significant differences in the reactivity of C-protonized methyl- and dimethyl-substituted tricarbonyl(tropone)iron complexes 4–6 in nucleophilic additions and corresponding O-trimethylsilylated complexes 7–9 in [3+2] cycloadditions are explained in terms of electronic and steric effects of the methyl group(s). Various hydroazulenone cycloadducts of tricarbonyl(η⁴-2,6-dimethyltropone)iron 3a,b have been prepared by stereoselective [3+2] cycloaddition with Fp-reagents 12–14 and characterized. Formerly proposed mechanism of [3+2] cycloaddition was approved.     

Convergence of the density functional one-centre expansion for the molecular continuum: N2 and (CH3)3N

A large-scale one-centre expansion with a radial B-spline basis set is implemented for bound and continuum states. A Kohn-Sham hamiltonian is employed with Hartree and exchange-correlation potentials calculated from the SCF electron density taken from a previous LCAO calculation. An inverse iteration method is used to obtain the continuum wavefunction, from which the cross section and asymmetry parameter are calculated. The convergence with respect to angular momentum and cut-off radius is analysed for N₂. The relevance of multipolar contributions even at large distances is shown and suggestions for further improvements are given. In order to show that the present method is suitable to treat systems of moderate size, the (CH₃)₃N molecule has also been calculated and the results are compared with experiment. Received: 19 May 1998 / Accepted: 20 August 1998 / Published online: 7 December 1998     

Density functional theory study of the mechanism for Ni(NHC)2 catalyzed dehydrogenation of ammonia-borane for chemical hydrogen storage

The mechanism for catalytic dehydrogenation of ammonia-borane (AB = H₃N-BH₃), a promising candidate for chemical hydrogen storage, by the Ni(NHC)₂ complexes was studied by using density functional theory at the non-empirical meta-GGA level, Tao-Perdew-Staroverov-Scuseria (TPSS) functional, with all-electron correlation-consistent polarized valence double-zeta (cc-pVDZ) basis set. The mechanism for both the first and the second H₂ release from AB was studied for the first time. Several unusual aspects of this catalytic mechanism were revealed through our calculations. First, the first H₂ release begins with proton transfer from nitrogen to the Ni bound carbene carbon, forming a new C-H bond, instead of the previously hypothesized direct B-H or N-H bond activation. Second, this new C-H bond is activated by the metal, transferring the H to Ni, then forming the H₂ molecule by transferring another H from B to Ni, rather than β-H transfer. Third, the second H₂ release from H₂N-BH₂ begins with the breaking of a 3-center, 2-electron Ni-H-B bridging structure with the assistance of the unsaturated carbene carbon atom to form a B-C bond. Fourth, a nearly rhombic N₂B₂H₆ structure is formed to help the regeneration of the catalyst Ni(NHC)₂. These reaction pathways explain the importance of NHC ligands in this catalytic process and yield lower energy barriers than those mechanisms that begin with N-H or B-H activations catalyzed by the metal atoms. The predicted reaction mechanism which features unexpected ligand participation points the way to finding new catalysts with higher efficiency, as partial unsaturation of the M-L bond may be essential for low energy H transfers.     

Myers–Saito and Schmittel cyclizations of enyne-(hetero)-1,2,3-trienes: A DFT study on the structure–reactivity relationship

The Myers–Saito (C²–C⁷) cyclization and the alternative Schmittel (C²–C⁶) cyclization of enyne-1,2,3-triene 1R and its hetero analogues 2R–5R were investigated by using pure density functional theory method (BPW91) in connection with the 6-311G(d, p) basis set. It has been shown that heteroatom-containing reactants lower significantly reaction barriers for both cyclization modes and reduce the difference between the barrier of the C²–C⁷ cyclization mode and that of the C²–C⁶ one. The Myers–Saito cyclization of 4R is associated with the smallest reaction barrier and the highest exothermicity. Whereas the Schmittel cyclization of 4R is exothermic, all the others are predicted to be endothermic.     

PdSi_n(n=1～15)团簇电子结构与光谱性质的理论研究

在卡里普索(CALYPSO)结构预测的基础上,采用密度泛函理论(DFT)B3LYP方法,优化得到PdSi_n(n=1~15)团簇的基态结构,对其电子性质、红外光谱和拉曼光谱进行了讨论.结果表明,PdSi_n(n=1~15)团簇的基态构型随n值的增大由平面结构向立体结构演化;当n≤4时,PdSi_n团簇的红外与拉曼活性在450~500 cm-1范围内表现较好,当n≥5时,PdSi_n团簇的红外与拉曼活性在50~500 cm~(-1)范围内表现较好.     

Density functional theory study on structural isomers and bonding of model complexes M(CO)5(BH3 · PH3) (M = Cr, Mo, W) and W(CO)5(BH3 · AH3) (A = N, P, As, Sb)

The influence of group 15 various substituents and effect of metal centers on metal-borane interactions and structural isomers of transition metal-borane complexes W(CO)₅(BH₃ · AH₃) and M(CO)₅(BH₃ · PH₃) (A = N, P, As, and Sb; M = Cr, Mo, and W), were investigated by pure density functional theory at BP86 level. The following results were observed: (a) the ground state is monodentate, η¹, with C₁ point group; (b) in all complexes, the η¹ isomer with C_S symmetry on potential energy surface is the transition state for oscillating borane; (c) the η² isomer is the transition state for the hydrogens interchange mechanism; (d) in W(CO)₅(BH₃ · AH₃), the degree of pyramidalization at boron, interaction energy as well as charge transfer between metal and boron moieties, energy barrier for interchanging hydrogens, and diffuseness of A increase along the series A = Sb < As < P < N; (e) in M(CO)₅(BH₃ · PH₃), interaction energy is ordered as M = W > Cr > Mo, while energy barrier for interchanging hydrogens decreases in the order of M = Cr > W > Mo.     

Understanding the stability, electronic and molecular structure of some copper(III) complexes containing alkyl and non alkyl ligands: Insights from DFT calculations

DFT calculations have been performed for some Cu(III)-alkyl complexes. Complexes 1-19 were optimized to the square planar (sq) geometry and observed no imaginary frequencies. Although formally copper adopts d⁸ configuration (Cu(III)) in all the complexes, the Natural Population Analysis (NPA) revealed that the copper actually in d¹⁰ (Cu(I)) configuration, Bond order calculation suggested that the Cu(III)-Et_trans bond gets more bond order in the presence of poor π-acidic co-ligand (probe ligand). Relatively smaller bond order was calculated for Cu(III)-Me_cis bond than Cu(III)-Et_trans bond and therefore Cu(III)-Et_trans bond is the strongest bond in all the complexes. Calculated less Chemical hardness (η) of complexes 1-19 suggested that all these complexes are less stable in nature. Energy Decomposition Analysis (EDA) revealed that the Cu(III)-Et_trans bond is relatively more stable than the Cu(III)-Me_cis and Cu(III)-L (L = co-ligand/probe ligand) bonds. And also the Cu(III)-alkyl (Cu(III)-Me_cis and Cu(III)-Et_trans) bond in complexes 1-17 is more of ionic in nature. However, Cu(III)-Et_trans bond is relatively more ionic than Cu(III)-Me_cis bond.     

(ClAlNH)n簇合物的结构与稳定性

用量子化学从头算方法（HF／6－31G）和密度泛函理论（DFT）的B3LYP方法,以6－31G标准基组加一个极化函数,对（ClAlNH)n(n=1-10)簇合物的几何构型,电子结构和红外光谱进行了优化,并讨论了聚合反应（ClAlNH)m→(ClAlNH)n的热力学效应,结果表明,（ClAlNH)n系列簇合物的基态稳定结构为Cs(n=1),D2h(n=2),D3h(n=3),Td(n=4),Cs(n=5),D3d(n=6),Cs(n=7),S4(n=8),D3h(n=9),C2h(n=10,n=2,4,6,8,10等偶数对应的（ClAlNH)n簇化合物的结构比n等于奇数量更稳定。     

Decomposition of alkyl hydroperoxide by a copper(I) complex: insights from density functional theory

The B3LYP theory and scaled hypersphere search method are utilized to explore pathways of (HO)₂PS₂Cu-mediated CH₃OOH decomposition, a model reaction of alkyl hydroperoxide with cuprous dialkyldithiophosphate [(RO)₂PS₂Cu]. It is found that the decomposition of CH₃OOH mediated by the copper(I) complex may lead to formaldehyde and water molecules via O-O bond heterolysis and subsequent intramolecular hydrogen transfer, with retainment of the copper(I) complex. The subsequent hydrogen transfer event and formation of water may add new understanding to the (RO)₂PS₂Cu-mediated decomposition process of alkyl hydroperoxide. The oxygen transfer from CH₃OOH to (HO)₂PS₂Cu moiety, as an O-O bond cleavage manner of CH₃OOH, is also found to occur.     

Study of the [Cr(H2O)5NO]2+ Complex via Density Functional Theory

On the basis of density functional theory, the spin ground state of chromium‐nitrosyl complex [Cr(H₂O)₅NO]²⁺ (S = 1/2) is studied via B3LYP hybrid method. Its vibrational frequencies, atomic charges, and spin densities are analyzed. The excitation energies are evaluated using the CIS method. Our calculated N‐O stretching frequency and excitation energies are in good agreement with the IR and UV‐vis data. The related Cr^I(H₂O)₆⁺, Cr^II(H₂O)₆²⁺, and Cr^III(H₂O)₆³⁺ complexes are employed as the reference compounds to determine the characteristics of the central Cr. Results indicate that the effective Cr oxidation state is close to Cr(I).     

A density functional theory study of the oxidative addition of methyl iodide to square planar [Rh(acac)(P(OPh)3)2] complex and simplified model systems

The transition state for the oxidative addition reaction [Rh(acac)(P(OPh)₃)₂] + CH₃I, as well as two simplified models viz. [Rh(acac)(P(OCH₃)₃)₂] and [Rh(acac)(P(OH)₃)₂], are calculated with the density functional theory (DFT) at the PW91/TZP level of theory. The full experimental model, as well as the simplified model systems, gives a good account of the experimental Rh-ligand bond lengths of both the rhodium(I) and rhodium(III) β-diketonatobis(triphenylphosphite) complexes. The relative stability of the four possible rhodium(III) reaction products is the same for all the models, with trans-[Rh(acac)(P(OPh)₃)₂(CH₃)(I)] (in agreement with experimental data) as the most stable reaction product. The best agreement between the theoretical and experimental activation parameters was obtained for the full experimental system.     

Mechanistic insight into the reactivity of oxotransferases by novel asymmetric dioxomolybdenum(VI) model complexes

The asymmetric molybdenum(VI) dioxo complexes of the bis(phenolate) ligands 1,4‐bis(2‐hydroxybenzyl)‐1,4‐diazepane, 1,4‐bis(2‐hydroxy‐4‐methylbenzyl)‐1,4‐diazepane, 1,4‐bis(2‐hydroxy‐3,5‐dimethylbenzyl)‐1,4‐diazepane, 1,4‐bis(2‐hydroxy‐3,5‐di‐tert‐butylbenzyl)‐1,4‐diazepane, 1,4‐bis(2‐hydroxy‐4‐flurobenzyl)‐1,4‐diazepane, and 1,4‐bis(2‐hydroxy‐4‐chlorobenzyl)‐1,4‐diazepane (H₂(L1)–H₂(L6), respectively) have been isolated and studied as functional models for molybdenum oxotransferase enzymes. These complexes have been characterized as asymmetric complexes of type [MoO₂(L)] 1–6 by using NMR spectroscopy, mass spectrometry, elemental analysis, and electrochemical methods. The molecular structures of [MoO₂(L)] 1–4 have been successfully determined by single‐crystal X‐ray diffraction analyses, which show them to exhibit a distorted octahedral coordination geometry around molybdenum(VI) in an asymmetrical cis‐β configuration. The Mo? O_oxo bond lengths differ only by ≈0.01 Å. Complexes 1 , 2 , 5 , and 6 exhibit two successive Mo^VI/Mo^V (E_1/2, ?1.141 to ?1.848 V) and Mo^V/Mo^IV (E_1/2, ?1.531 to ?2.114 V) redox processes. However, only the Mo^VI/Mo^V redox couple was observed for 3 and 4 , suggesting that the subsequent reduction of the molybdenum(V) species is difficult. Complexes 1 , 2 , 5 , and 6 elicit efficient catalytic oxygen‐atom transfer (OAT) from dimethylsulfoxide (DMSO) to PMe₃ at 65 °C at a significantly faster rate than the symmetric molybdenum(VI) complexes of the analogous linear bis(phenolate) ligands known so far to exhibit OAT reactions at a higher temperature (130 °C). However, complexes 3 and 4 fail to perform the OAT reaction from DMSO to PMe₃ at 65 °C. DFT/B3LYP calculations on the OAT mechanism reveal a strong trans effect.     

In-depth insight into the electronic and steric effects of phosphine ligands on the mechanism of the R-R reductive elimination from (PR3)2PdR2

The aim of this study was to investigate both the electronic and steric effects of the ancillary phosphine ligand L on the reductive elimination of Me-Me from a series of L₂PdMe₂ and LPdMe₂ complexes. Density functional theory was used to study these processes with the model ligands L = PMe₃, PH₃, PCl₃ and with the experimentally reported ligands L = PPh₃, PPh₂Me, PPhMe₂. For the model ligands we confirm that electron donation from L affects the barrier for reductive elimination from L₂PdMe₂ but not from LPdMe₂. In the former case the greater the electron donation or basicity of L, the greater the barrier and the later the transition state. This is because electron donation increases the σ^∗ antibonding between Pd and L in the transition structure. On the other hand, if L is a good π acceptor this stabilizes the occupied d_π orbital of Pd in the transition structure and lowers the barrier to reductive elimination. In the case of the reactions involving LPdMe₂ as the intermediate, it is the loss of the first L (L₂PdMe₂ → LPdMe₂ + L) which determines the differences in the barrier height. Greater electron donation leads to greater L-to-Pd σ donation and a stronger Pd-L bond, and thus a greater overall barrier. A comparison of these results with the reductive elimination of 1,3-butadiene from divinyl palladium complexes L₂PdR₂ shows that the barriers are lower in the vinyl case because of a mix of orbital factors. Our results show that there is a significant stabilizing interaction between the Pd d_π orbital and the vinyl-vinyl hybrid σ^∗/π^∗ orbitals in the reductive elimination transition structure. At the same time this Pd-R₂ orbital stabilization alleviates the potential antibonding interactions between Pd and L and makes the vinyl elimination much less susceptible to ancillary ligand effects. Energy-decomposition analyses have been used to elucidate the contributing factors to the activation energies for the reductive eliminations with the model phosphine ligands. These analyses have also been used to disentangle the electronic and steric effects involved in the larger ligand systems. The electronic effects of the experimentally reported ligands are found to be very similar to each other. On the other hand, steric effects lead to a destabilization of the reactant L₂PdMe₂ complexes but not the transition structures, which results in a decrease in the barriers to reductive elimination compared to the smaller phosphine ligands. These steric effects do not play a role in reductive elimination from LPdMe₂. These detailed analyses of the electronic and steric factors may be used to assist the design of systems which enhance or retard reductive elimination behaviour.     

PuX~ (X=H,O,N,C)的结构与势能函数

用密度泛函B3LYP方法对PuX＋(X=H,O,N,C)分子离子体系进行了理论研究.结果表明,这些分子离子的基态电子状态分别是X 7Σ－(PuH＋)、X 6Σ－(PuO＋)、X 5Σ＋(PuN＋)和X 8Σ－(PuC＋);势能函数为Murrell-Sorbie势函数.并得到了相应的几何性质、力学性质和光谱数据.     

Hydride abstraction of methylamine with Cu(S) in the gas phase: A density functional theory study

The gas-phase hydride abstraction of methylamine with Cu⁺(¹S) is theoretically investigated by using density functional theory. Geometries for all the stationary points involved are fully optimized at both the B3LYP/6-311++G(d,p) and B3LYP/6-311++G(3df,2p) levels and the reaction is analyzed in terms of the topology of potential energy surface. Approach of Cu⁺ towards methylamine could form either “classical” N or “nonclassical” η¹-methyl-H attached complex with the former being the global minimum. Both complexes are found to be key intermediates for the hydride abstraction, which could transfer into each other via two parallel routes, i.e., concerted metal movement and stepwise C-H activation-rearrangement. A charge-transfer process is detected for the “nonclassical” complex converting to a precursor species (CuH-NH₂CH₂⁺), which accounts for the final products by a nonreactive dissociation.