Rotation In Ethane Research Articles

Excited State-Specific CASSCF Theory for the Torsion of Ethylene.

State-specific complete active space self-consistent field (SS-CASSCF) theory has emerged as a promising route to accurately predict electronically excited energy surfaces away from molecular equilibria. However, its accuracy and practicality for chemical systems of photochemical interest have yet to be fully determined. We investigate the performance of the SS-CASSCF theory for the low-lying ground and excited states in the double bond rotation of ethylene. We show that state-specific approximations with a minimal (2e,2o) active space provide comparable accuracy to state-averaged calculations with much larger active spaces, while optimizing the orbitals for each excited state significantly improves the spatial diffusivity of the wave function. However, the incorrect ordering of state-specific solutions causes excited state solutions to coalesce and disappear, creating unphysical discontinuities in the potential energy surface. Our findings highlight the theoretical challenges that must be overcome to realize practical applications of state-specific electronic structure theory for computational photochemistry.

Ethylene Polymerizations Catalyzed by Fluorinated "Sandwich" Diimine-Nickel and Palladium Complexes.

Nickel and palladium complexes bearing "sandwich" diimine ligands with perfluorinated aryl caps have been synthesized, characterized, and explored in ethylene polymerization reactions. The X-ray crystallographic analysis of the precatalysts 16 and 6b shows differences from their nonfluorinated analogues 17 and 19, with the perfluorinated aryl caps centered precisely over the nickel and palladium centers, which results in higher buried volumes of the metal centers relative to the nonfluorinated analogues. The sandwich diimine-palladium complexes 5a and 5b containing perfluorinated aryl caps polymerize ethylene in a controlled fashion with activities that are substantially increased compared with their nonfluorinated analogues. Migratory insertion rates in relevant methyl ethylene complexes agree with the activities exhibited in bulk polymerization experiments. DFT studies suggest that facility of ethylene rotation from its preferred orientation perpendicular to the Pd-alkyl bond into a parallel in-plane conformation contributes to the higher polymerization activity for 5b relative to 18a. For these palladium systems, polymer molecular weights can be controlled via hydrogen addition (hydrogenolysis), which is unusual for late-transition-metal-catalyzed olefin polymerizations with no catalyst deactivation occurring. Sandwich diimine-nickel complexes 6a and 6b with perfluorinated aryl caps show ethylene polymerization activities that are about half of those of classical tetraisopropyl-substituted catalyst 2 but again are more active than the analogous nonfluorinated sandwich complexes. Ethylene polymerizations exhibit living behavior, and branched ultrahigh-molecular-weight polyethylenes (UHMWPEs) with very low-molecular-weight distributions (less than 1.1) are obtained. The activated nickel catalysts are stable in the absence of monomer and show good long-term stability at 25 °C.

Universal Generalization of Density Functional Theory for Static Correlation.

A major challenge for density functional theory (DFT) is its failure to treat static correlation, yielding errors in predicted charges, band gaps, van der Waals forces, and reaction barriers. Here we combine one- and two-electron reduced density matrix (1- and 2-RDM) theories with DFT to obtain a universal O(N^{3}) generalization of DFT for static correlation. Using the lowest unitary invariant of the cumulant 2-RDM, we generate a 1-RDM functional theory that corrects the convexity of any DFT functional to capture static correlation in its fractional orbital occupations. Importantly, the unitary invariant yields a predictive theory by revealing the dependence of the correction's strength upon the trace of the two-electron repulsion matrix. We apply the theory to the barrier to rotation in ethylene, the relative energies of the benzynes, as well as an 11-molecule, dissociation benchmark. By inheriting the computational efficiency of DFT without sacrificing the treatment of static correlation, the theory opens new possibilities for the prediction and interpretation of significant quantum molecular effects and phenomena.

Anharmonic Correction to Free Energy Barriers from DFT-Based Molecular Dynamics Using Constrained Thermodynamic Integration.

For the calculation of anharmonic contributions to free energy barriers, constrained thermodynamic λ-path integration (λ-TI) from a harmonic reference force field to density functional theory is presented as an alternative to the established Blue Moon ensemble method (ξ-TI), in which free energy gradients along the reaction coordinate ξ are integrated. With good agreement in all cases, the λ-TI method is benchmarked against the ξ-TI method for several reactions, including the internal CH3 group rotation in ethane, a nucleophilic substitution of CH3Cl, a retro-Diels-Alder reaction, and a proton transfer in zeolite H-SSZ-13. An advantage of λ-TI is that one can use virtually any reference state to compute anharmonic contributions to reaction free energies or free energy barriers. This is particularly relevant for catalysis, where it is now possible to compute anharmonic corrections to the free energy of a transition state relative to any reference, for example, the most stable state of the active site and the reactants in the gas phase. This is in contrast to ξ-TI, where free energy barriers can only be computed relative to an initial state with all reactants coadsorbed. Finally, the Bennett acceptance ratio method combined with λ-TI is demonstrated to reduce the number of required integration grid points with tolerable accuracy, favoring thus λ-TI over ξ-TI in terms of computational efficiency.

Multireference Density Functional Theory for Describing Ground and Excited States with Renormalized Singles.

We applied renormalized singles (RS) in the multireference density functional theory (DFT) to calculate accurate energies of ground and excited states. The multireference DFT approach determines the total energy of the N-electron system as the sum of the (N - 2)-electron energy from a density functional approximation (DFA) and the two-electron addition energies from the particle-particle Tamm-Dancoff approximation (ppTDA), naturally including multireference description. The ppTDA@RS-DFA approach uses the RS Hamiltonian capturing all singles contributions in calculating two-electron addition energies, and its total energy is optimized with the optimized effective potential method. It significantly improves the original ppTDA@DFA. For ground states, ppTDA@RS-DFA properly describes dissociation curves tested and the double bond rotation of ethylene. For excited states, ppTDA@RS-DFA provides accurate excitation energies and largely eliminates the DFA dependence. ppTDA@RS-DFA thus provides an efficient multireference approach to systems with static correlation.

Precise Detection and Visualization of Cyclooxygenase-2 for Golgi Imaging by a Light-Up Aggregation-Induced Emission-Based Probe

Precise Detection and Visualization of Cyclooxygenase-2 for Golgi Imaging by a Light-Up Aggregation-Induced Emission-Based Probe

Rhodium and Iridium Complexes Bearing “Capping Arene” Ligands: Synthesis and Characterization

A series of olefin-coordinated RhI and IrI complexes bearing “capping arene” ligands (5-XFP and 6-XFP, see below) of the general formulas (FP)M(olefin)X, [(FP)M(olefin)2][M(olefin)2X2], and [(FP)M(olefin)2]BF4 (FP = “capping arene” ligands, X = halide or pseudohalide, olefin = ethylene, cyclooctene, (olefin)2 = (C2H4)2 or cyclooctadiene) were synthesized and characterized. Single-crystal X-ray diffraction studies revealed structural differences that are a function of the identity of the capping arene ligand and the metal. For 5-XFP ligands (5-XFP = 1,2-bis(N-7-azaindolyl)-benzene and derivatives with substituents on the arene moiety), the coordination to both Rh and Ir gives rise to complexes that are best described as 16-electron and square planar. For 6-XFP ligands (6-XFP = 8,8′-(1,2-phenylene)diquinoline and derivatives with substituents on the arene moiety), the structures of Rh and Ir complexes are better considered as 18-electron and trigonal bipyramidal due to an η2-C,C interaction between the metal center and the arene group of the capping arene ligand. Variable-temperature 1H NMR spectroscopy studies of ethylene rotation demonstrated that the Ir complexes possess higher activation barriers to rotation in comparison to Rh complexes and the 6-XFP complexes tend to give ethylene higher rotational barriers in comparison to 5-XFP complexes for complexes of the type (FP)Rh(η2-C2H4)Cl. DFT calculations are consistent with enhanced Rh to ethylene π-back-donation for Rh complexes ligated by the 6-XFP ligands in comparison to the 5-XFP ligands.

Finite-temperature-based time-dependent density-functional theory method for static electron correlation systems.

In this study, we developed a time-dependent density-functional theory (TDDFT) with a finite-temperature (FT) scheme, denoted as FT-TDDFT. We introduced the concept of fractional occupation numbers for random phase approximation equation and evaluated the excited-state electronic entropy terms with excited-state occupation number. The orbital occupation numbers for the excited state were evaluated from the change in the ground-state electron configuration with excitation and deexcitation coefficients. Furthermore, we extended the FT formulation to the time-dependent density-functional tight-binding (TDDFTB) method for larger systems, denoted as FT-TDDFTB. Numerical assessment for the FT-(TD)DFT method showed smooth potential curves for double-bond rotation of ethylene in both ground and excited states. Excited-state calculations based on the FT-TDDFTB method were applied to the uniform π-stacking columns composed of trioxotriangulene, possessing neutral radicals in strong correlation systems.

Spin-flip approach within time-dependent density functional tight-binding method: Theory and applications.

A spin-flip time-dependent density functional tight-binding (SF-TDDFTB) method is developed that describes target states as spin-flipping excitation from a high-spin reference state obtained by the spin-restricted open shell treatment. Furthermore, the SF-TDDFTB formulation is extended to long-range correction (LC), denoted as SF-TDLCDFTB. The LC technique corrects the overdelocalization of electron density in systems such as charge-transfer systems, which is typically found in conventional DFTB calculations as well as density functional theory calculations using pure functionals. The numerical assessment of the SF-TDDFTB method shows smooth potential curves for the bond dissociation of hydrogen fluoride and the double-bond rotation of ethylene and the double-cone shape of H3 as the simplest degenerate systems. In addition, numerical assessments of SF-TDDFTB and SF-TDLCDFTB for 39 S0 /S1 minimum energy conical intersection (MECI) structures are performed. The SF-TDDFTB and SF-TDLCDFTB methods drastically reduce the computational cost with accuracy for MECI structures compared with SF-TDDFT.

An investigation of ethylene rotational barriers for 5-coordinate d8 metal bis-ethylene complexes

The successful isolation and structural characterization of (CF3PCP)Ir(C2H4)2 is reported, which confirms a rare example of axial and equatorial ethylene coordination in a TBP coordination environment. DFT studies indicate a moderate barrier to ethylene rotation for the equatorial C2H4 group (ΔG‡=19.0kcalmol−1), and a negligible rotational barrier for the axial C2H4 (ΔG‡=1.2kcalmol−1). DFT analyses of ethylene rotational barriers for a series of known symmetrical (equatorial/equatorial) and asymmetric (equatorial/axial) bis ethylene Ir(I) complexes are consistent with previously reported experimental rotational barriers. In the case of the asymmetric systems ([9]aneS3)Ir(C2H4)2+ and (Tp)Ir(C2H4)2, a separate equatorial C2H4 rotational barrier is not observed due to facile conformational exchange of axial and equatorial ethylene coordination sites. Conformational exchange is not observed for (CF3PCP)Ir(C2H4)2.

Internal rotation barrier of the XH3[sbnd]YH3 (X, Y = C or Si) molecules. An energy decomposition analysis study

In this paper, the barriers of the internal rotation in ethane, methylsilane, and disilane are investigated by the generalized Kohn–Sham based energy decomposition analysis (GKS-EDA) scheme (P. Su, et al. J. Phys. Chem A 118 (2014) 2531). The rotation barriers and the inter-conversion energies from the three geometrical variation processes are decomposed into the electrostatic, exchange–repulsion, polarization, correlation and geometrical relaxation terms. It is concluded that the rotation barriers of the three molecules are all dominated by exchange–repulsion (Pauli repulsion). The geometry relaxation does not make a difference to the origin of the barrier.

Conformation of 2,2-dimethylpropane encapsulated in fullerenes

It is known that nano objects are capable of considerably affecting physicochemical characteristics of molecules encapsulated therein [1]. In particular, it has recently been shown that the potential energy minimum for internal rotation of ethane in a nanotube, in contrast to the free molecule, corresponds not to the staggered but to the eclipsed conformation [2]. The present communication reports on the conformational preference of 2,2-dimethylpropane (neopentane) molecule encapsulated in fullerenes C60 and C80 according to DFT PBE/3z calculations (PRIRODA software package [3]). An isolated 2,2-dimethylpropane molecule is characterized by an experimental barrier to restricted rotation of 4.3 kcal/mol, the staggered conformer being preferred [4]. The calculation data for free neopentane molecule also indicate relative preference of the staggered conformer, but the calculated ΔH value is lower by 0.5–1.3 kcal/mol than the experimental one (see table). The staggered conformer was also found to be more favorable for the system neopentane–fullerene C60, where the shortest distance from the neopentane hydrogen atoms to the fullerene sphere is 1.8–1.9 A, while the transition state is represented by the eclipsed structure. However, unlike free neopentane molecule, the calculated barrier to restricted rotation in the encapsulated molecule is three times higher, and the C–C bond in both conformers is considerably shorter. Correspondingly, the distance between the eclipsed hydrogen and carbon atoms also shortens. In the system neopentane–fullerene C80 where the internal fullerene cavity is larger, the distance between the neopentane hydrogen atoms and fullerene sphere is longer (2.1–2.2 A), and the potential barrier to restricted rotation increases to a lesser extent (by a factor of 2.2 to 2.4); also, the difference between the C–C and H · · · C distances in the free and encapsulated molecules becomes smaller (see table). The examined systems are characterized by an appreciable negative or positive charge on the encapsulated neopentane molecule both in the ground and in the transition states, though the entire fullerene–neoISSN 1070-4280, Russian Journal of Organic Chemistry, 2014, Vol. 50, No. 6, pp. 921–922. © Pleiades Publishing, Ltd., 2014. Original Russian Text © V.V. Kuznetsov, 2014, published in Zhurnal Organicheskoi Khimii, 2014, Vol. 50, No. 6, pp. 935–936.

Cyclobutadiene automerization and rotation of ethylene: energetics of the barriers by using spin-polarized wave functions.

Spin-projected spin polarized Møller-Plesset and spin polarized coupled clusters calculations have been made to estimate the cyclobutadiene automerization, the ethylene torsion barriers in their ground state, and the gap between the singlet and triplet states of ethylene. The results have been obtained optimizing the geometries at MP4 and/or CCSD levels, by an extensive Gaussian basis set. A comparative analysis with more complex calculations, up to MP5 and CCSDTQP, together with others from the literature, have also been made, showing the efficacy of using spin-polarized wave functions as a reference wave function for Møller-Plesset and coupled clusters calculations, in such problems.

Empirical Correction of Nondynamical Correlation Energy for Density Functionals

To provide an efficient means to address nondynamical correlation, an empirical correction for single and double hybrid density functionals has been formulated. The correction utilizes the highest doubly occupied, lowest unoccupied, and singly occupied generalized Kohn-Sham orbitals and, for potential energy curves, a few additional strongly correlated orbitals. Utilizing proposed nondynamical correlation corrections, hybrid BLYP predicted potential energy curves that fit well to those obtained by ab initio multireference methods for the torsional rotation of ethylene and the automerization of cyclobutadiene. The empirical nondynamical correlation corrections, calculated at the transition structures, also reduce the overall errors of B2K-PLYP for the DBH24 and BH76 barrier height data sets. The proposed empirical correction can efficiently enhance the utility of both single and double hybrid density functionals for chemical situations with moderate to significant nondynamical correlation.

Early Experiences with Computational Quantum Chemistry.

A description is given of the progress in computational quantum chemistry in the early 1960s, the time of the early mainframe computers. In particular, the first calculation of the barrier to internal rotation in ethane and the first molecular application of perturbed self-consistent-field equations are described with the accompanying developments, trials, and tribulations.

MS-Xα calculation of the barrier to internal rotation in ethylene

Calculations for ethylene using the multiple-scattering Xα method in the muffin-tin approximation are reported. Comparison of the calculated twisting potentials of both the singlet ground state and the first excited triplet with experimental values show about the same agreement as ab initio calculations including configuration interaction. In addition, the use of overlapping spheres is shown not to improve the Xα results.

Correlations between MO eigenvectors and enthalpies of formation for simple organic substances

Bondingness, originally used in a qualitative analysis of the barrier to rotation in ethane, has been used to model Δ f H° (g) for simple organic substances. The model is parameterised with a set of 345 molecules including alkanes, alkenes, alkynes, alcohols, ethers, aldehydes, ketones, carboxylic acids, esters, alkenoates, amines, amides, diazenes, nitriles, nitroalkanes, nitrates, thiols and benzenoids. The model is compared with a current empirical scheme as well as a comparison of variations of the model using different simple steric potentials. Using bondingness and the most approximate quantum chemical models a model can be formulated that is comparable with empirical group methods but requiring less parameters.

A Butane Analogue, 3-Hexyne, Is Eclipsed

In ethane the facts of a staggered equilibrium structure and a 2.9 kcal/mol torsional barrier are established.1 However, the origin of the barrier to internal rotation in ethane remains controversial. This debate centers around the relative importance of hyperconjugation vs steric/exchange interactions in determining the staggered structure and torsional barrier. A distinction between the competing models is that steric interactions primarily depend on the distance between interacting atoms, whereas hyperconjugation depends also on the symmetry (orientation) of the interacting orbitals. The orbital orientation distinction suggests another perspective on the barrier. The staggered gauche and trans conformers of butane are a corollary of the staggered ethane structure. 3-Hexyne (CH3CH2C⋮CCH2CH3) is butane elongated by a cylindrically symmetrical C⋮C spacer, which separates the ethyl groups. If hyperconjugation were the dominant interaction in this butane analogue, the equilibrium structure would be staggere...

The case for steric repulsion causing the staggered conformation of ethane.

The barrier to rotation in ethane (see picture) is considered a prototypical case of steric hindrance. This view has been recently contradicted, and hyperconjugation has been put forward as the right explanation. The authors argue that there is no reason to abandon the steric repulsion explanation, and discuss why different electronic structure analyses yield different views.

Synthesis and structural studies of perfluoroalkyl-rhodium and iridium(iii) compounds containing tris(pyrazolyl)borate ligands

Oxidative addition of perfluorobenzyl iodide to TpRh(C2H4)2 [Tp = tris(pyrazolyl)borate] affords TpRh(CF2C6F5)(C2H4)I, from which the ethylene ligand can be displaced by CO to afford TpRh(CF2C6F5)(CO)I. Similar reaction of perfluorobenzyl iodide with TpIr(CO)2 or Tp*M(CO)2 [Tp* = tris(3,5-dimethylpyrazolyl)borate; M = Rh, Ir] affords Tp*M(CF2C6F5)(CO)I. Displacement of CO from the carbonyl complexes using PMe3 is not clean and yields a mixture of compounds. However, displacement of ethylene from TpRh(CF2C6F5)(C2H4)I using PMe3 cleanly affords TpRh(CF2C6F5)(PMe3)I. Similar oxidative addition reactions of perfluoro-n-propyl iodide afford TpIr(C3F7)(CO)I, TpRh(C3F7)(CO)I, Tp*Rh(C3F7)(CO)I, Tp*Rh(C3F7)(PMe3)I, and TpM(C3F7)(C2H4)I [M = Rh, Ir]. While displacement of ethylene from TpRh(C3F7)(C2H4)I by PMe3, to give TpRh(C3F7)(PMe3)I is facile, the corresponding reaction of the iridium analogue affords the salt [TpM(C3F7)(C2H4)(PMe3)]+I−. Ethylene rotation barriers and Co stretching frequencies in these compounds are discussed. The molecular structures of TpIr(CF2C6F5)(CO)I, TpRh(CF2C6F5)(PMe3)I, and TpRh(C3F7)(PMe3)I have been determined, and are also discussed in detail.