Bending Vibrational Levels in the Electronic Spectra of Small Radicals

The role played by bending vibrations in the spectroscopy of small carbon‐containing radicals is illustrated by the patterns and effects shown by C₃, CCH, and C₃Ar. Because of the large change in the bending frequency between the ¹Σ⁺_g and ¹Π_u states of C₃, the ¹Π_u state provides one of the best known examples of the coupling of electronic and vibrational motion in linear molecules (the Renner–Teller effect). The ²Σ⁺ and ²Π states of CCH provide a classic instance of vibronic coupling between two close‐lying electronic states, which leads very rapidly to a chaotic pattern of mixed‐state vibrational energy levels, which can only be understood by extensive high‐quality ab initio calculations. C₃Ar is an approximately T‐shaped molecule with no less than four large‐amplitude vibrations. Its state provides a beautiful example of what happens to the angular momentum of a Π state of C₃ when the symmetry is lowered by complex formation.     

Synthesis and Structures of d10–d10 M2(μ‐dppm)2 Complexes with Sensitive Metal–Metal Distances in Response to the Binding of Sigma Donors

Diphosphine‐bridged dicopper(I) acetate complexes [Cu₂(μ‐dppm)₂(μ‐OAc)]X ( 2 X; X^? = , ) and [Cu₂(μ‐dppm)₂(μ‐OAc)(MeCN)]X ( 4 X) were prepared and the structures of 2 (PF₆ ) and 4 (PF₆ ) determined by X‐ray crystallography. The ground‐state geometries of [Cu₂(μ‐dppm)₂(μ‐OAc)]⁺ and [Cu₂(μ‐dppm)₂(μ‐OAc)(L)]⁺ (L = py, MeCN, THF, acetone, MeOH) were also obtained using density functional theory (DFT). The increased Cu – Cu distances found experimentally and theoretically by comparing the structures of cation [Cu₂(μ‐dppm)₂(μ‐OAc)]⁺ and its derivatives [Cu₂(μ‐dppm)₂(μ‐OAc)(L)]⁺ reflect the binding of various sigma donors (L). When using [Cu₂(μ‐dppm)₂(μ‐OAc)]⁺ as a structure sensor, the electron‐donating strength of a sigma donor can be quantitatively expressed as a DFT‐calculated Cu – Cu distance with the relative strength in the order py > MeCN > THF > acetone > MeOH, as determined.     

Green's Function and Eigenvalue Representation of Time Lag for Absorptive Permeation Across a Heterogeneous Membrane

The time‐lag problem is treated for absorptive penetration across a heterogeneous membrane, where both the diffusivity D (x ) and the partition coefficient K (x ) depend on the coordinate x (0 ≦ x ≦ h ), with 0 and h being the coordinates of the upstream and downstream faces, respectively. A new concept of time‐lag distribution is introduced, and the first (time) moment and the second (time) moment over this distribution are also difined and treated in the Lapalce domain in conjuction with the Green's function G (x ,y ), and eigenvalues associated with the time‐independent diffusion equation subject to the absorbing boundary condition at both ends of the membrane. Our central results include and , where λ _i is the i th eigenvalue of the aforementioned diffusion equation. The merits of these new resprentations and comparison with the treatments of Frisch or Eyring are also discussed.     

The Trifluoromethyl Anion: Evidence for [K(crypt‐222)]+

[K(crypt‐222)]⁺ ( 1 ) and [K(crypt‐222)]⁺ ( 3 ) are isostructural, displaying nearly identical unit cell parameters. The two structures are similar to the extent that the previously reported [K(crypt‐222)]⁺ model can be refined against the new data for [K(crypt‐222)]⁺ , with extra electron density being observed from the fourth fluorine atom of the . In agreement with experimental observations, theoretical calculations suggest that deprotonated [K(crypt‐222)]⁺ is highly unstable even at as low as 195 K. The previously considered 1:1 CHF ₃ clathrate of deprotonated [K(crypt‐222)]⁺ (crystallographically indistinguishable from 1 ) is ruled out on the basis of all available data.     

Toward a Better Determination of Infrared Molar Absorptivities and Dimer Formation Constants in Self‐association Through Hydrogen Bonding: 3‐Ethyl‐2‐methyl‐3‐pentanol in Tetrachloroethylene as an Example

The monomer–dimer self‐association of the dilute 3‐ethyl‐2‐methyl‐3‐pentanol in tetrachloroethylene in the very dilute state was studied by infrared spectroscopy at several temperatures. The solute was deliberately chosen so that higher oligomers were suppressed by the steric hindrance arising from bulky groups on both sides of hydroxyl group. Two linear utility equations were derived to treat, respectively, the integrated absorbance of the monomer band, A _m, and of the dimer band, A _d, as functions of the initially prepared solute concentration, [B ]₀. The respective molar absorptivities were obtained by fitting these equations to the data. Unlike previous methods, the dimerization constant (K ) can be obtained from either A _m or A _d. Any discrepancy between these two values of K serves as a measure of the quality of the data. The values of K at different temperatures were employed to calculate the standard enthalpy and entropy of dimerization by using a van't Hoff plot. The dimer is predominantly in the cyclic form where both hydroxyl protons are hydrogen‐bonded. This is inferred from the following observations: (1) the spectrum displays only two bands between 3300 and 3750 cm⁻¹; (2) the constancy of as a function of [B ]₀ ; and (3) the linearity of both plots [B ]₀/A _m vs. A _m , and [B ]₀/A _d vs. .     

Synthesis,structural analysis,spectral investigations,and DFT calculations of 1‐(3‐amino‐4‐thia‐1,2‐diazaspiro[4.11]hexadec‐2‐en‐1‐yl)ethan‐1‐one

1‐(3‐amino‐4‐thia‐1,2‐diazaspiro[4.11]hexadec‐2‐en‐1‐yl)ethan‐1‐one was synthesized and experimentally characterized by using FT‐IR, ¹H NMR, ¹³C NMR, and UV–Vis spectroscopy. The structure of the compound was confirmed by single‐crystal X‐ray diffraction. In the crystal structure, the molecules are linked by pairs of N‐H⋯N hydrogen bonds, forming centrosymmetric dimers with the graph‐set motif. The water molecule also plays an important role in the stabilization of the crystal structure, bridging the dimers to form a two‐dimensional supramolecular network. The molecular geometry, frontier molecular orbitals, vibrational frequencies, electronic properties, and molecular electrostatic potential were calculated using density functional theory (DFT) with the B3LYP/6‐311G(d,p) basis set. Geometric parameters, vibrational assignments, and electronic properties such as calculated energies, excitation energies, and oscillator strengths were compared with the experimental data, and it was seen that the theoretical results support the experimental parameters.     

Ruthenium(II) complexes bearing pyridine‐based tridentate and bidentate ligands: catalytic activity for transfer hydrogenation of aryl ketones

Ru(II) complexes of the general formula [RuCl₂(′′)(L)] (1: ′N = N_b, L = MeOH; 2: ′N = N_b, L = CH₃CN; 3: ′N = N_d, L = CH₃CN; 4: ′N = N_p, L = CH₃CN), [Ru(p‐cymene)(_a–b)Cl]Cl (5a: N N_a = 2,2′‐bipyridine; 5b: N N_b = 4,4′‐dimethyl–2,2′‐bipyridine), [Ru(′′)(_a–b)Cl]Cl (6a: ′N = N_b, _a = 2,2′‐bipyridine; 6b: ′N = N_b, _b = 4,4′‐dimethyl‐2,2′‐bipyridine; 7a: ′N = N_d, _a = 2,2′‐bipyridine; 7b: ′N = N_d, _b = 4,4′‐dimethyl‐2,2′‐bipyridine; 8a: ′N = N_p, _a = 2,2′‐bipyridine; 8b: ′N = N_p, _b = 4,4′‐dimethyl‐2,2′‐bipyridine) and [Ru(′′)(_a)Cl]BF₄ (9a: ′N = N_b; _a = 2,2′‐bipyridine) were synthesized from the corresponding [RuCl₂(p‐cymene)]₂ dimer, ′′ and _a–b ligands. The compounds were characterized by elemental analysis, IR and NMR. Complex 9a was studied by X‐ray diffraction, confirming its cationic‐mononuclear [RuCl(_bb)(_a)]⁺ nature. The synthesized Ru(II) complexes (1–8) were employed as catalysts for the transfer hydrogenation of ketones to secondary alcohols in the presence of KOH using 2‐propanol as a hydrogen source at 82°C. The rates of the transfer hydrogenation reactions strongly depended on the type of and ancillary ligands. Copyright © 2012 John Wiley & Sons, Ltd.     

Spin–orbit effects on magnetically induced current densities in the () clusters

This study reports the spin–orbit effects on the aromaticity of the , , , , , and anionic clusters via the magnetically induced current‐density method. All‐electron density functional theory (DFT) calculations were carried out using the four‐component Dirac‐Coulomb (DC) hamiltonian, including scalar and spin–orbit relativistic effects. The magnetic index of aromaticity was calculated by numerical integration over the current flow between two atoms in the pentagonal ring. These values were compared to the spin‐free values (spin–orbit coupling switched off), in order to assess the spin–orbit effect on aromaticity. It was found that in the heavy anions, and , there is a significant influence of the spin–orbit coupling. © 2018 Wiley Periodicals, Inc.     

One‐range Addition Theorems for Complete Sets of Modified Exponential Type Orbitals and Noninteger n Slater Functions in Standard Convention

Using the L ‐generalized Laguerre polynomials L ‐GLPs) and φ ‐generalized exponential type orbitals φ ‐GETOs) introduced by the author in standard convention, the one‐ and two‐center onerange addition theorems are established for the complete sets of Ψ^(α*) ‐modified exponential type orbitals (Ψ^(α*) ‐METOs) and noninteger n χ‐Slater type orbitals (χ‐NISTOs), where p_l* = 2l + 2 ‐ α* and α* is the integer (α* = α, ?∞ < α ≤2) or noninteger (α* ≠ α, ?∞ < α* < 3) self‐frictional quantum number. It should be noted that the origin of the L ‐GLPs, φ ‐GETOs and Ψ^(α*) ‐METOs, therefore, of the one‐range addition theorems presented in this work is the Lorentz damping or self‐frictional field produced by the particle itself.     

Theoretical prediction of the optical rotation of chiral molecules in ordered media: A computational study of (Ra)‐1,3‐dimethylallene, (2R)‐2‐methyloxirane,and (2R)‐N‐methyloxaziridine

A theoretical procedure has been developed and implemented to calculate the optical rotation of chiral molecules in ordered phase via origin‐independent diagonal components , of the optical activity tensor and origin‐independent components , for , of the mixed electric dipole‐electric quadrupole polarizability. Origin independence was achieved by referring these tensors to the principal axis system of the electric dipole dynamic polarizability at the same laser frequency ω. The approach has been applied, allowing for alternative quantum mechanical methods based on different gauges, to estimate near Hartree–Fock values for three chiral molecules, (2R)‐N‐methyloxaziridine C₂NOH₅, (2R)‐2‐methyloxirane (also referred to as propylene oxide) C₃OH₆, and ( )‐1,3‐dimethylallene C₅H₈, at two frequencies. The theoretical predictions can be useful for an attempt at measuring correspondent experimental values in crystal phase. © 2015 Wiley Periodicals, Inc.     

(Rg = He ∼ Rn,n = 1–4): In quest of the potential trapping ability of the aromatic ring

A new series of divalent boron‐rare gas cations (Rg = He ∼ Rn, n = 1–4) have been predicted theoretically at the B3LYP, MP2, and CCSD(T) levels to present the structures, stability, charge distributions, bond natures, and aromaticity. The Rg B bond energies are quite large for heavy rare gases and increase with the size of the Rg atom. Because of steric hindrance new Rg atoms introduced to the B₄ ring will weaken the Rg B bond. Thus in the Rg B bond has the largest binding energy 90–100 kcal/mol. p‐ has a slightly shorter Rg B bond length and a larger bond energy than o‐ . NBO and AIM analyses indicate that for the heavy Rg atoms Ar ∼ Rn the B Rg bonds have character of typical covalent bonds. The energy decomposition analysis shows that the σ‐donation from rare gases to the boron ring is the major contribution to the Rg B bonding. Adaptive natural density partitioning and nuclear‐independent chemical shift analyses suggest that both and have obvious aromaticity.     

Full–dimensional quantum molecular dynamics calculations of the rovibrationally mediated X → 2 transition of nitrous oxide

A full dimensional time‐dependent quantum wavepacket approach is used to study the photodissociation dynamics of nitrous oxide for the X → 2 bound–bound transition based on new highly accurate potential energy and transition dipole moment surfaces. The computed 2 absorption spectra at room temperature are characterized by sharp vibrational structures that contribute slightly to the diffuse vibrational structures around the maximum peak at 180 nm of the first ultraviolet absorption band (from the contribution of 2 , 1 , and 2 states) of N₂O. Transitions from different initial rovibrational states reveal that the sharp structures arise mainly from N₂? O bending vibrations, whereas, at higher temperatures, the N₂? O and N? NO stretching vibrations are responsible for enhancing the intensity of the structures. At absorption wavelengths 166 nm and 179 nm, vibrational quantum state distributions of N₂ product fragments decrease monotonically with increasing vibrational quantum number v = 0, 1, 2. At 166 nm, rotational quantum state distributions of N₂ at fixed v = 0 and v = 1 display multimodal profiles with maximum peaks at j = 77 and j = 75, respectively, whereas, the distributions at the 179 nm absorption wavelength display bimodal profiles with maximum peaks at j = 73 and j = 71, respectively. Accordingly, the presence of rotationally hot N₂ from previous experimental and theoretical works in the first band strongly implies a significant influence of the 2 state in determining the final dissociation pathway of N₂ + O. © 2016 Wiley Periodicals, Inc.     

Exploring possible reaction pathways for the o‐atom transfer reactions to unsaturated substrates catalyzed by a [Ni‐NO2] ↔ [Ni‐NO] redox couple using DFT methods

The (nitro)(N‐methyldithiocarbamato)(trimethylphospane)nickel(II), [Ni(NO₂)(S₂CNHMe)(PMe₃)] complex catalyses efficiently the O‐atom transfer reactions to CO and acetylene. Energetically feasible sequence of elementary steps involved in the catalytic cycle of the air oxidation of CO and acetylene are proposed promoted by the Ni(NO₂)(S₂CNHMe)(PMe₃)] ↔ Ni(NO₂)(S₂CNHMe)(PMe₃) redox couple using DFT methods both in vacuum and dichloromethane solutions. The catalytic air oxidation of HC≡CH involves formation of a five‐member metallacycle intermediate, via a [3 + 2] cyclo‐addition reaction of HC≡CH to the Ni‐N = O moiety of the Ni(NO₂)(S₂CNHMe)(PMe₃)] complex, followed by a β H‐atom migration toward the C_α carbon atom of the coordinated acetylene and release of the oxidation product (ketene). The geometric and energetic reaction profile for the reversible [Ni( ‐NO₂)(S₂CNHMe)(PMe₃)] [Ni( ‐ONO)(S₂CNHMe)(PMe₃)] linkage isomerization has also been modeled by DFT calculations. © 2017 Wiley Periodicals, Inc.     

Carbon–sulfur chains: A high‐resolution infrared and quantum‐chemical study of C3S and SC7S

In the course of a 5 μm high‐resolution infrared study of laser ablation products from carbon–sulfur targets, the ν₁ vibrational mode region of linear C₃S has been studied continuously from 2046 to 2065 cm^?1. Besides the prominent vibrational fundamental, the region was found to feature the , and even hot bands, the latter two of which were observed for the first time. Owing to the high signal‐to‐noise ratio obtained, the ν₁ mode of S could also be observed in natural abundance for the first time at high spectral resolution in the infrared. At 2061 cm^?1, hidden inside the branch of the C₃S ν₁ fundamental mode, a weak new band is observed which exhibits very tight line spacing and stems from a heavy both carbon and sulfur containing carrier. On the basis of high‐level quantum‐chemical calculations of selected carbon–sulfur chains and other carbon‐rich cumulenes, this feature is attributed to the ν₅ vibrational fundamental of linear SC₇S, which stands for the first gas‐phase spectroscopic detection of this long cumulenic chain.     

Transition‐Metal‐Free Synthesis of 1,3‐Butadiene‐Containing π‐Conjugated Polymers

This work describes the synthesis of π‐conjugated polymers possessing arylene and 1,3‐butadiene alternating units in the main chain by the reaction of α,β‐unsaturated ester/nitrile containing γ‐H with aromatic/heteroaromatic aldehyde compound. By using 4‐(4‐formylphenyl)‐2‐butylene acid ethyl ester as a model monomer, the different polymerization conditions, including catalyst, catalyst amount, and solvent, are optimized. The polymerization of 4‐(4‐formylphenyl)‐2‐butylene acid ethyl ester is carried out by refluxing in ethanol for 72 h with 1,8‐diazabicyclo[5.4.0]undec‐7‐ene (DBU) as a catalyst to give a 1,3‐butadiene‐containing π‐conjugated polymer, poly(phenylene‐1,3‐butadiene), in 84.3% yield with and / (PDI) estimated as 6172 and 1.65, respectively. Based on this new methodology, a series of π‐conjugated polymers containing 1,3‐butadiene units with different substituents are obtained in high yields. A possible mechanism is proposed for the polymerization through a six‐membered ring transition state and then a 1,5‐H shift intermediate.

     

Rate Constants for the Gas‐Phase Reactions of Ozone and Nitrate Radicals with the Sesquiterpenes: Valencene and Farnesol

Sesquiterpenes are constituents of a variety of essential oils that are used in flavorings, perfumes, personal care, and cleaning products. Two sesquiterpenes that are commonly used as indoor fragrances are valencene and farnesol. Knowing the reaction rate constants of these chemicals with ozone (O₃) and nitrate radical () is an important factor in determining their fate indoors. In this study, the bimolecular rate constants of , , , and were measured using the relative rate technique at 297 ± 3 K and 1 atm total pressure. Using the rate constants reported here and measured/modeled indoor concentrations of O₃ and (20 ppb and 1 ppt, respectively), pseudo–first‐order‐rate lifetimes , , , and were determined.     

Mechanochemical Synthesis of 3d Transition‐Metal–1,2,4‐Triazole Complexes as Precursors for Microwave‐Assisted and Thermal Conversion to Coordination Polymers with a High Influence on the Dielectric Properties

The complexes [MCl₂(TzH)₄] (M=Mn ( 1 ), Fe ( 2 ); TzH=1,2,4‐1H‐triazole) and [ZnCl₂(TzH)₂] ( 3 ) have been obtained by mechanochemical reactions of the corresponding divalent metal chloride and 1,2,4‐1H‐triazole. They were successfully used as precursors for the formation of coordination polymers either by a microwave‐assisted reaction or by thermal conversion. For manganese, the conversion directly yielded [MnCl₂TzH] ( 4 ), whereas for the iron‐containing precursor, [FeCl₂TzH] ( 6 ), was formed via the intermediate coordination polymer [FeCl(TzH)₂]Cl ( 5 ). For cobalt, the isotypic polymer [CoCl(TzH)₂]Cl ( 7 ) was obtained, but exclusively by a microwave‐induced reaction directly from CoCl₂. The crystal structures were resolved from single crystals and powders. The dielectric properties were determined and revealed large differences in permittivity between the precursor complexes and the rigid chain‐like coordination polymers. Whereas the monomeric complexes exhibit very different dielectric behaviour, depending on the transition metal, from “low‐k” to “high‐k” with the permittivity ranging from 4.3 to >100 for frequencies of up to 1000 Hz, the coordination polymers and complexes with strong intermolecular interactions are all close to “low‐k” materials with very low dielectric constants up to 50 °C. Therefore, the conversion procedures can be used to deliberately influence the dielectric properties from complex to polymer and for different 3d transition‐metal ions.     

Structure,stability, and nature of bonding in carbon monoxide bound complexes (E = group 14 element; X = H,F, Cl,Br, I)

A density functional theory study is performed to predict the structures and stability of carbon monoxide (CO) bound (E = C, Si, Ge, Sn, Pb; X = H, F, Cl, Br, I) complexes. The possibility of bonding through both C‐ and O‐sides of CO is considered. Thermochemical analysis reveals that all the dissociation processes producing CO and are endothermic in nature whereas most of the dissociation reactions are endergonic in nature at room temperature. The nature of bonding in E? C/O bonds is analyzed via Wiberg bond index, natural population analysis, electron density, and energy decomposition analyses in conjunction with natural orbitals for chemical valence scheme. In comparison to C? O stretching frequency ( ) in free CO, while a red shift is noted in O‐side binding, the C‐side binding results in a blue shift in . The relative change in values in CO bound complexes on changing either E or X is scrutinized and possible explanation is provided in terms of polarization in the σ‐ and π‐orbitals and the relative strength of C→E or O→E σ‐donation and E→C or E→O π‐back‐donation. © 2016 Wiley Periodicals, Inc.     

Insights into the Kramers’ flux‐over‐population rate for chemical reactions in liquid phases through the matrix transport equation

Kramers’ equation models a chemical reaction as a Brownian particle diffusing over a potential barrier under the influence of medium viscosity. In the case of high viscosity, the equation reduces to a simpler Smoluchowski equation. In this report, we have contrived an equivalent matrix‐transport equation that relates the ordered pair (activity, flux) of the output (activated complex) to that of the input (reactant). With an initial condition of the Dirac delta type placed at the location of the reactant, and a reflecting boundary condition set on the reactant state, and an absorbing boundary condition on the activated complex state, we are able to prove the equality relation between the mean first passage time, , for the diffusion and the inverse of the rate constant, k^?1, for the reaction counterpart. We have also derived , where λ_i is the ith eigenvalue of the Smoluchowski differential operator stipulated with the above‐mentioned boundary conditions. We have also deduced that, in the long time limit, the number of particles remaining inside the diffusion domain decays exponentially with a relaxation time just the same as the concentration of the reactant does for a first‐order reaction system.     

Catalytic and Atom‐Economic C −C Bond Formation: Alkyl Tantalum Ureates for Hydroaminoalkylation

Atom‐economic and regioselective C ?C bond formation has been achieved by rapid C?H alkylation of unprotected secondary arylamines with unactivated alkenes. The combination of Ta(CH₂SiMe₃)₃Cl₂, and a ureate N,O‐chelating‐ligand salt gives catalytic systems prepared in situ that can realize high yields of β‐alkylated aniline derivatives from either terminal or internal alkene substrates. These new catalyst systems realize C?H alkylation in as little as one hour and for the first time a 1:1 stoichiometry of alkene and amine substrates results in high yielding syntheses of isolated amine products by simple filtration and concentration.