Minimum Energy Crossing Point Research Articles

Mechanism of O2 Activation by α-Ketoglutarate Dependent Oxygenases Revisited. A Quantum Chemical Study.

Four mechanisms previously proposed for dioxygen activation catalyzed by α-keto acid dependent oxygenases (α-KAO) were studied with dispersion-corrected DFT methods employing B3LYP and TPSSh functionals in combination with triple-ζ basis set (cc-pVTZ). The aim of this study was to revisit mechanisms suggested in the past decade and resolve remaining issues related to dioxygen activation. Mechanism A, which runs on the quintet potential energy surface (PES) and includes formation of an Fe(III)-superoxide radical anion complex, subsequent oxidative decarboxylation, and O-O bond cleavage, was found to be most likely. However, mechanism B taking place on the septet PES involves a rate limiting barrier comparable to the one found for mechanism A, and thus it cannot be excluded, though two other mechanisms (C and D) were ruled out. Mechanism C is a minor variation of mechanism A, whereas mechanism D proceeds through formation of a triplet Fe(IV)-alkyl peroxo bridged intermediate. The study covered also full optimization of relevant minimum energy crossing points (MECPs). The relative energy of critical intermediates was also studied with the CCSD(T) method in order to benchmark TPSSh and B3LYP functionals with respect to their credibility in predicting relative energies of septet and triplet spin states of the ternary enzyme-Fe-α-keto glutarate (α-KG)-O2 complex.

Mechanism of Synergistic Cu(II)/Cu(I)-Mediated Alkyne Coupling: Dinuclear 1,2-Reductive Elimination after Minimum Energy Crossing Point.

An in-depth theoretical study of synergistic Cu(II)/Cu(I)-mediated alkyne coupling was performed to reveal the detailed mechanism for C-C bond formation, which proceeded via an unusual dinuclear 1,2-reductive elimination. Because the reactant for dinuclear 1,2-reductive elimination was calculated to be triplet while the products were singlet, the minimum energy crossing point (MECP) was introduced to the Cu/TMEDA/alkyne system to clarify the spin crossing between triplet state and singlet state potential energy surfaces. Computational results suggest that C-H bond cleavage solely catalyzed by the Cu(I) cation is the rate-determining step of this reaction and Cu(II)-mediated dinuclear 1,2-reductive elimination after the MECP is a facile process. These conclusions are in good agreement with our previous experimental results.

Insights into the Spin-State Transitions in [Fe(tpy)2]2+: Importance of the Terpyridine Rocking Motion.

Iron(II) polypyridine complexes have the potential for numerous applications on a global scale, such as sensitizers, sensors, and molecular memory. The excited-state properties of these systems, particularly the intersystem crossing (ISC) rates, are sensitive to the choice of ligands and can be significantly altered depending on the coordination environment. We employ density functional theory and Smolyak's sparse grid interpolation algorithm to construct potential energy surfaces (PESs) for the photophysically relevant states ((1)A, (3,5)MC, and (1,3)MLCT) of the [Fe(tpy)2](2+) (tpy = 2,2':6',2"-terpyridine) complex, with the goal of obtaining a deeper understanding of the ground- and excited-state electronic structure of this system. The three dimensions that define our adiabatic PESs consist of equatorial and axial metal-ligand bond length distortions and a terpyridine ligand "rocking angle", which has not previously been investigated. The intersection crossing seams and minimum energy crossing points (MECPs) between surfaces are also determined. Overall, we find that the PESs of all electronic excited states investigated are characterized by low-energy valleys along the tpy rocking-angle coordinate. This results in the presence of large low-energy areas around the MECPs on the intersection seams of different electronic states and indicates that inclusion of this third coordinate is crucial for an adequate description of the PESs and surface crossing seams of the [Fe(tpy)2](2+) complex. Finally, we suggest that tuning the energetics of the tpy ligand rocking motion could provide a way to control the ISC process in this complex.

Spin Isomers and Ligand Isomerization in a Three-Coordinate Cobalt(I) Carbonyl Complex.

Hemilabile ligands, which have one donor that can reversibly bind to a metal, are widely used in transition-metal catalysts to create open coordination sites. This change in coordination at the metal can also cause spin-state changes. Here, we explore a cobalt(I) system that is poised on the brink of hemilability and of a spin-state change and can rapidly interconvert between different spin states with different structures ("spin isomers"). The new cobalt(I) monocarbonyl complex L(tBu)Co(CO) (2) is a singlet ((1)2) in the solid state, with an unprecedented diketiminate binding mode where one of the C═C double bonds of an aromatic ring completes a pseudo-square-planar coordination. Dissolving the compound gives a substantial population of the triplet ((3)2), which has exceptionally large uniaxial zero-field splitting due to strong spin-orbit coupling with a low-lying excited state. The interconversion of the two spin isomers is rapid, even at low temperature, and temperature-dependent NMR and electronic absorption spectroscopy studies show the energy differences quantitatively. Spectroscopically validated computations corroborate the presence of a low minimum-energy crossing point (MECP) between the two potential energy surfaces and elucidate the detailed pathway through which the β-diketiminate ligand "slips" between bidentate and arene-bound forms: rather than dissociation, the cobalt slides along the aromatic system in a pathway that balances strain energy and cobalt-ligand bonding. These results show that multiple spin states are easily accessible in this hemilabile system and map the thermodynamics and mechanism of the transition.

Study of the competitive mechanisms of cyclohexane dehydrogenation by gas-phase Ni2(+) cationic dimer: one-face dehydrogenation versus flip dehydrogenation.

The mechanism of cyclohexane dehydrogenation catalyzed by the cationic dimer Ni2 (+) has been investigated at the B3LYP level of density functional theory. The first dehydrogenation occurs readily (it is exothermic by 30kcal/mol), whereas the second and third dehydrogenations show weaker exothermicity than the first (23 and 21kcal/mol, respectively). These three hydrogenations corresponding to the total dehydrogenation of one face of cyclohexane mainly proceed in the doublet state due to the presence of significant minimum-energy crossing points (MECPs). In addition, because the elimination of non-negligible amounts of [H2,2D2] and [2H2,D2] in this reaction was also observed in a previous experiment, we calculated a flip mechanism which would yield results that agree with those experimental results. This flip process includes two MECPs, meaning that the reaction mainly proceeds along the doublet potential energy surface but finishes in the quartet state. The rate-limiting step ((2)IM9 → (2)TS9/10 → (2)IM10) of the flip process is endothermic by 3kcal/mol and the barrier to this step is 33kcal/mol. Our calculations indicate that one-face dehydrogenation is a more favorable channel than the flip one. We excluded the possibility that eliminations of [H2,2D2] or [D2,2H2] could proceed through a mechanism involving Ni2 (+) dissociation, or that [H-D] scrambling could occur through (2)TS11/13 ((4)TS12/15), due to the large amounts of energy required. In the dissociation of (2)IM19, (2)[(H2)Ni2(C6H6)](+), a molecule of hydrogen first dissociates, leaving a final product of (2)[Ni2(C6H6)](+). Neither C6H6 nor (H2)Ni2 (+) can easily dissociate from (2)IM19 due to π backdonation.

A theoretical view on CrO2+-mediated C–H bond activation in ethane

The gas-phase reaction of C–H bond activation in ethane by CrO2+ has been investigated using density functional theory (DFT) at the UB3LYP/6-311G(2d,p) level. Our results reveal that the activation process is actually a spin-forbidden reaction. The involved crossing point between the doublet and quartet potential energy surfaces (PES) has been discussed by two well-known methods, i.e., intrinsic reaction coordinate (IRC) approach for crossing point (CP) and Harvey’s algorithm for minimum energy crossing point (MECP). The obtained single (P1ISC=2.48×10−3) and double (P1ISC=4.95×10−3) passes estimated at MECP show that the intersystem crossing (ISC) occurs with a little probability. The C–H bond activation processes should proceed to be endothermic by 73.16kJ/mol on the doublet surface without any spin change.

High-resolution XPS and DFT investigations into Al-modified Phillips CrOx/SiO2 catalysts

In this work, the effects of Al-modification on Phillips catalysts were investigated by high-resolution X-ray photoelectron spectroscopy (XPS) and the performance in ethylene polymerization reactions. Density functional theory (DFT) method was used to achieve a deeper mechanistic understanding. The decreased Cr 2p binding energies (BE), related with an increase in electron density of chromium by Al-modification, have been confirmed by the DFT calculation. The ethylene polymerization activity over the Al-modified Phillips catalyst was increased. The molecular weight (MW) of polymer was decreased with the expansion of molecular weight distribution (MWD) to low MW side, which was in agreement with the decreased energy barrier difference between the chain transfer and chain propagation in DFT calculation. The initiation step undergoing a metallacycle reaction pathway was found through a spin crossover from the quintet energy surface via a minimum energy crossing point (MECP) to the triplet energy surface. Modeling results indicated that the promotion effect on polymerization activity from Al-modification for Phillips catalyst was mainly originated from the chain initiation reaction with lowered energy barrier for Al-modified Cr active sites. Improved environmental stress-crack resistance (ESCR) of polymer derived from the Al-modified catalyst could be expected from the less short chain branches (SCBs) distribution in the low MW side.

Computational studies on the radiative and nonradiative processes of luminescent N-heteroleptic platinum(II) complexes

Three N-heteroleptic Pt(II) complexes, [Pt(C^C)(O^O)] [O^O=acetylacetonate, C^C=1-phenyl-1,2,4-triazol-5-ylidene (1), C^C=4-phenyl-1,2,4-triazol-5-ylidene (2), C^C=2-phenylpyrazine (3)] have been investigated with density functional theory (DFT) and time-dependent density functional theory (TDDFT). The radiative decay rate constants of complexes 1–3 have been discussed with the oscillator strength (fn), the strength of spin–orbit coupling (SOC) interaction between the lowest energy triplet excited state (T1) and singlet excited states (Sn), and the energy gaps between E(T1) and E(Sn). To illustrate the nonradiative decay processes, the transition states between triplet metal-centered (3MC) and T1 states have been optimized and were verified with the calculations of vibrational frequencies and intrinsic reaction coordinate (IRC). In addition, the minimum energy crossing points (MECPs) between 3MC and ground states (S0) were optimized. At last, the potential energy curves relevant to the nonradiative decay pathways are simulated. The results show that complex 3 has the biggest photoluminescence quantum yield because the complex 3 has the biggest radiative decay rate constant and the smallest nonradiative decay rate constant in complexes 1–3.

A theoretical study of C–H bond of CH4 activation catalyzed by VO2+ in gas phase

The mechanism of C–H bond of CH4 activation catalyzed by VO2+(1A1/3A′) has been investigated by using density functional theory (DFT) at the CCSD/6-311G(2d,p)//B3LYP/6-311G(2d,p) level. According to our calculation results, the four channels have been well-established and the reactivity patterns on the singlet and triplet PESs are almost similar. And the reaction proceeds in three distinct manners yielding the [V(OCH2)++H2O] products, the [V(OH2)++CH2O] products, the [OV(OCH2)++H2] products and the [VO++CH3OH] products. Specially, the crossing points (CPs) between the different PESs have been located by means of the intrinsic reaction coordinate (IRC) approach used by Yoshizawa et al., and corresponding minimum energy crossing points (MECPs) that we obtained by the mathematical algorithm proposed by Harvey et al. has also been employed. In addition, the frontier molecular orbital interaction analysis about 1TS1, 3TS1, 1TS4 and 3TS4 are used to gain useful information about the C–H bond of CH4 activation by VO2+.

DFT study of the reaction of a two-coordinate iron(II) dialkyl complex with molecular oxygen.

DFT studies are reported of a monomeric iron dialkyl for which oxygen atom insertion into metal-methyl bonds occurs with O2: FeMe2 + O2 → Fe(OMe)2. Computation of the reaction coordinate implicates the intermediacy of Fe(III)-peroxo, Fe(VI)-dioxo, and Fe(IV)-oxo intermediates, connected by O2 oxidative addition and two methyl migration steps. Analysis of the reaction of O2 with d(6)-Fe(Me)2 indicates that oxy-insertion for this iron complex occurs with lower free energy barriers than competing homolytic/radical pathways, exploiting "spin-flip" processes via minimum energy crossing points (MECPs).

Nonadiabatic reaction mechanisms of the O(3P) with cyclopentene

The reaction mechanism of the ground state oxygen atom O(3P) with cyclopentene is investigated theoretically. The triplet and singlet potential energy surfaces are calculated at the CCSD(T)//MP2/6-311G(d,p) level and the minimum energy crossing points (MECPs) between the two surfaces are located by means of the Newton–Lagrange method, from which the complex nonadiabatic reaction pathways are revealed. Based on the theoretical results, the most probable reaction mechanism of O(3P) with c-C5H8 is described, which agrees with the experimental results nicely, including the condensed phase experiment. At the same time, the newly revealed reaction mechanism clarifies the previous controversial product distribution, and predicts the possible existence of the new enol product, cyclopentenol.

Theoretical investigation into the Co+ catalytic activity in the cycle reaction of N2O with C2H6 in the gas phase

The spin-forbidden mechanism of the reaction between N 2 O and C 2 H 6 catalyzed by Co + has been investigated using UB3LYP density functional theory. The Harvey method has been applied to optimize five minimum energy crossing points (MECP) on both triplet and quintet potential energy surfaces. Possible spin inversion processes are discussed by means of spin-orbit coupling calculations. According to the calculation of probability of electron hopping using the Landau-Zener formula, effective intersystem crossing may occur at each MECP. The energetic span model proposed by Kozuch has been applied to the catalytic cycles, and shows the turnover frequency reaches 3.35 × 10 –21 s –1 when Co + catalyzes the reaction to produce CH 3 CHO at 298K. The reaction of N 2 O and C 2 H 6 catalyzed by Co + is a typical two-state reaction. An energy span model has been applied to evaluate the catalytic performance of Co + .

Theoretical investigation for the cycle reaction of methane oxidation catalyzed by FeO<sup>+</sup> in the gas phase

The mechanism of the spin-forbidden reaction of CH4 with O2 catalyzed by FeO+ (6Σ+, 4Π+) on both quartet and sextet potential energy surfaces has been investigated at the B3LYP level of theory. Six competitive reaction pathways for the catalytic reaction and Path 6 are likely in competition with other pathways from energetic viewpoint. There are 6 crossing points in Path 6 and the crossing points 1 and 3 are very important. The minimum energy crossing points (MECP) of corresponding crossing points are optimized. The potential energy surfaces and the possible spin inversion processes are discussed by means of spin-orbit coupling (SOC) and probability of intersystem crossing (ISC) calculations. The SOC of MECP1 is 947.58 cm-1, and MECP3 is 1372.51 cm-1. The probability of ISC are 0.535 and 0.590 respectively. In order to understand the competitive reaction mechanism involving H atom transfer, the activation strain model was adopted for a simple analysis of the competitive reaction. The energetic span ( δE ) model coined by Kozuch is applied in this cycle. X TOF (degree of TOF control) of all of transition state and intermediate are calculated, and the turnover frequency (TOF)-determining transition state (TDTS) and TOF-determining intermediate (TDI) are confirmed. In this catalytic reaction, the TOF is 5.6716×10-42 s-1.

Hetero‐Wolff Rearrangement of an α‐Sulfinyl Carbene: Thermally Activated Intersystem Crossing of the Lowest Excited Triplet State of a Ground‐State Singlet Carbene

AbstractLaser flash photolysis (λexc = 266 nm) of α‐sulfinyl diazo compound 1b results in the formation of two transient phenomena. Transient absorption A (intense, λmax = 275 nm) shows jump‐and‐growth behaviour with a growth lifetime of τ = 2 μs. Transient absorption B (weak, λmax = 415 and 540 nm) decays with a lifetime of τ = 1.8 μs, which suggests that B decays into A. On the basis of a comparison with calculated UV/Vis spectra, transient absorption B is assigned to triplet carbene 37. DFT and CCSD(T) calculations indicate that carbene 7 should have a singlet (S) ground state with a singlet–triplet energy gap of ca. 11 kcal mol–1 in acetonitrile solution. The seemingly paradoxical observation of a triplet excited state of a ground‐state singlet carbene is rationalised in terms of the very different geometries of the singlet and triplet carbene; the most prominent difference lies in the pyramidalisation at the sulfoxide sulfur atom. For the singlet carbene 17, the O–S–C:–C(=O) dihedral angle is calculated to be 172.8°, whereas it is –80.0° for the triplet carbene 37. Therefore, for efficient intersystem crossing (ISC) to occur, the triplet carbene must significantly change its geometry. A triplet–singlet minimum energy crossing point (MECP) was located with an O–S–C:–C(=O) dihedral angle of –141.3°. On the basis of the energy of this MECP (15.2 kcal mol–1 above the S carbene in CH3CN) and on the ISC rate constant of diphenyl carbene taken as preexponential factor, a rate for the ISC of 37 is estimated that matches the experimental value within one order of magnitude.

The reliability of DFT methods to predict electronic structures and minimum energy crossing point for [FeIVO](OH)2 models: A comparison study with MCQDPT method

In order to test the reliability of DFT methods for calculating electronic structures of [Fe(IV)O] system, detailed calculations of [Fe(IV)O](OH)2 models were performed for several low-energy states using multiconfiguration quasidegenerate perturbation theory (MCQDPT) as well as DFT-based methods. The minimum energy crossing points (MECP) of (5)A1/(5)B2 and (3)B2/(5)B2 were investigated based on Lagrange-Newton approach. The results show that M06 functional produce energy gaps close to those of MCQDPT results. Another topic in this article is that the electron configurations of [Fe(IV)O](OH)2 models strongly depend on the type of surface ligand used, and the two lowest states of these can facile transition each other by the MECP. The practicability of M06 method in locating the MECP is validated by the results of MCQDPT which demonstrate the two-state reactivity (TSR) can be studied with proper DFT method. These inspections provide the basis for further TSR study of larger [Fe(IV)O] system.

Mechanism and Enantioselectivity of Dirhodium-Catalyzed Intramolecular C–H Amination of Sulfamate

The mechanisms and enantioselectivities of the dirhodium (Rh2L4, L = formate, N-methylformamide, S-nap)-catalyzed intramolecular C-H aminations of 3-phenylpropylsulfamate ester have been investigated in detail with BPW91 density functional theory computations. The reactions catalyzed by the Rh2(II,II) catalysts start from the oxidation of the Rh2(II,II) dimer to a triplet mixed-valent Rh2(II,III)-nitrene radical, which should facilitate radical H-atom abstraction. However, in the Rh2(formate)4-promoted reaction, as a result of a minimum-energy crossing point (MECP) between the singlet and triplet profiles, a direct C-H bond insertion is postulated. The Rh2(N-methylformamide)4 reaction exhibits quite different mechanistic characteristics, taking place via a two-step process involving (i) intramolecular H-abstraction on the triplet profile to generate a diradical intermediate and (ii) C-N formation by intersystem crossing from the triplet state to the open-shell singlet state. The stepwise mechanism was found to hold also in the reaction of 3-phenylpropylsulfamate ester catalyzed by Rh2(S-nap)4. Furthermore, the diradical intermediate also constitutes the starting point for competition steps involving enantioselectivity, which is determined by the C-N formation open-shell singlet transition state. This mechanistic proposal is supported by the calculated enantiomeric excess (94.2% ee) with the absolute stereochemistry of the product as R, in good agreement with the experimental results (92.0% ee).

Photodissociation mechanisms of the CO22+ dication studied using multi-state multiconfiguration second-order perturbation theory

Employing the multi-state multiconfiguration second-order perturbation theory (MS-CASPT2) and complete active space self-consistent field (CASSCF) methods, the geometries, relative energies (T(v)') to the ground state (X(3)Σg(-)), adiabatic excited energies, and photodissociation mechanisms and corresponding kinetic energy releases for the lower-lying 14 electronic states of the CO2 (2+) ion are studied. The T(v)' values are calculated at the experimental geometry of the ground state CO2 molecule using MS-CASPT2 method and highly close to the latest threshold photoelectrons coincidence and time-of-flight photoelectron photoelectron coincidence spectrum observations. The O-loss dissociation potential energy curves (PECs) for these 14 states are drawn using MS-CASPT2 partial optimization method at C(∞v) symmetry with one C-O bond length ranging from 1.05 to 8.0 Å. Those 14 states are confirmed to be correlated to the lowest four dissociation limits [CO(+)(X(2)Σ(+)) + O(+)((4)S(u)), CO(+)(A(2)Π) + O(+)((4)S(u)), CO(+)(X(2)Σ(+)) + O(+)((2)D(u)), and CO(+)(X(2)Σ(+)) + O(+)((2)P(u))] by analyzing Coulomb interaction energies, charges, spin densities, and bond lengths for the geometries at the C-O bond length of 8.0 Å. On the basis of these 14 MS-CASPT2 PECs, several state/state pairs are selected to optimize the minimum energy crossing points (MECPs) at the CASSCF level. And then the CASSCF spin-orbit couplings and CASPT2 state/state energies are calculated at these located MECPs. Based on all of the computational results, the photodissociation mechanisms of CO2(2+) are proposed. The relationships between the present theoretical studies and the previous experiments are discussed.

The performance of density functional approximations for the structures and relative energies of minimum energy crossing points

The structural parameters and relative energies of the minimum-energy crossing points (MECPs) of eight small molecules are calculated using five different representative density functional theory approximations as well as MP2, MP4, and CCSD(T) as a reference. Compared to high-level wavefunction methods, the main structural features of the MECPs of the systems included in this Letter are reproduced reasonably well by density functional approximations, in agreement with previous works. Our results show that when high-level wavefunction methods are computationally prohibitive, density functional approximations offer a good alternative for locating and characterizing the MECP in spin-forbidden chemical reactions.

Theoretical Views on Activation of Methane Catalyzed by Hf2+and Oxidation of CO (x1Σ+) by N2O (x1Σ+) Catalyzed by HfO2+and TaO2+

The mechanisms of activation of CH4 catalyzed by (1/3)Hf(2+) and oxidation of CO by N2O catalyzed by (1/3)HfO(2+) or (2/4)TaO(2+) have been investigated using the B3LYP level of theory. For the activation of methane, the TSR (two-state reactivity) mechanism has been certified through the spin-orbit coupling (SOC) calculation and the Landau-Zener-type model. In the vicinity of the minimum energy crossing point (MECP), SOC equals 900.23 cm(-1) and the probability of intersystem crossing is approximately 0.62. Spin inversion makes the activation barrier decline from 1.63 to 0.57 eV. NBO analysis demonstrates that empty 6s and 5d orbitals of the Hf atom play the major role for the activation of C-H bonds. Finally, CH4 dehydrogenates to produce Hf-CH2(2+). For oxidation of CO by N2O catalyzed by HfO(2+) or TaO(2+), the covalent bonds between transition metal atoms and the oxygen atom restrict the freedom of valence electrons. Therefore, they are all SSR (single-state reactivity). The oxygen atom is directly extracted during the course of oxygen transfer, and its microscopic essence has been discussed. The detailed kinetic information of two catalytic cycles has been calculated by referencing the "energetic span (δE)" model. Finally, TOF(HfO(2+))/TOF(TaO(2+)) = 2.7 at 298.15 K, which has a good consistency with the experimental result.

Understanding the reactivity bottleneck in the spin-forbidden reaction FeO+ + H2 → Fe+ + H2O

New coupled cluster theory calculations, including extrapolation to the complete basis set limit, are reported for key species on the [Fe,O,H2]+ potential energy surfaces. Test calculations including Bruecker orbital methods suggest that the single-reference coupled-cluster approach is reliable for this system. The minimum energy crossing point (MECP) between the sextet and quartet states has been found to lie close in energy and structure to the quartet reactant complex 4FeO+H2. Non-adiabatic transition state theory is used to calculate the rate constant for hydrogen oxidation, and is found to agree reasonably well with experiment, considering the remaining uncertainties in the ab initio energies and the kinetic modelling. The isotope effects are reproduced fairly well also. The transition state theory calculations suggest that the bottleneck to reaction is an adiabatic quartet transition state for insertion of FeO+ into the HH bond. Spin state change at the MECP is calculated to be considerably faster, even allowing for errors in the relative energies.