Theoretical study of Au/SAPO-11 catalyst and its potential use in thiophene HDS

Quantum chemistry calculations were carried out, using ONIOM2 methodology, in order to investigate the thiophene interaction with gold supported on silicoaluminophospates molecular sieves (Au/SAPO-11) catalysts. Two models were studied, one containing one Au atom per site, and the other with two Au atoms per site. Thiophene adsorption was found to be η¹ type. This adsorption presents a ΔH of ?13.2 and ?9.7 kcal/mol, for the models with one Au atom (Au/SAPO-11), and two Au atoms (Au₂/SAPO-11), respectively. The partial hydrogenation of the thiophene–Au/SAPO-11 and thiophene–Au₂/SAPO-11 complexes gives 2,5-dihydrothiophene (DHT), with a ΔH of ?23.0 and ?36.8 kcal/mol, respectively. 2-Butene production was found in both models with further hydrogenation. Likewise the direct butadiene elimination is achieved, but only with the separated Au dimer (ΔH = ?17.5 kcal/mol).     

An ONIOM and DFT study of water and ammonia adsorption on anatase TiO2 (001) cluster

Density functional theory (DFT) calculations at ONIOM DFT B3LYP/ 6‐31G**‐MD/UFF level are employed to study molecular and dissociative water and ammonia adsorption on anatase TiO₂ (001) surface represented by partially relaxed Ti₂₀O₃₅ ONIOM cluster. DFT calculations indicate that water molecule is dissociated on anatase TiO₂ (001) surface by a nonactivated process with an exothermic relative energy difference of 58.12 kcal/mol. Dissociation of ammonia molecule on the same surface is energetically more favorable than molecular adsorption of ammonia (?37.17 kcal/mol vs. ?23.28 kcal/mol). The vibration frequency values also are computed for the optimized geometries of adsorbed water and ammonia molecules on anatase TiO₂ (001) surface. The computed adsorption energy and vibration frequency values are comparable with the values reported in the literature. Finally, several thermodynamical properties (ΔH°, ΔS°, and ΔG°) are calculated for temperatures corresponding to the experimental studies. © 2010 Wiley Periodicals, Inc. Int J Quantum Chem, 2011     

Nanoceria Supported Gold Catalysts for CO Oxidation

Two types of CeO₂ nanocubes (average size of 5 and 20 nm, respectively) prepared via the hydrothermal process were selected to load gold species via a deposition‐precipitation (DP) method. Various measurements, including X‐ray diffraction (XRD), Raman spectra, high resolution transmission electron microscopy (HRTEM), in situ diffuse reflectance infrared Fourier transform spectroscopy (in situ DRIFTS), and temperature‐programmed reduction by hydrogen (H₂‐TPR), were applied to characterize the catalysts. It is found that the sample with ceria size of 20 nm (Au/CeO₂‐20) was covered by well dispersed both Au³⁺ and Au^δ+ (0 < δ < 1). For the other sample with ceria size of 5 nm (Au/CeO₂‐5), Au³⁺ is the dominant gold species. Au/CeO₂‐20 performed better catalytic activity for CO oxidation because of the strong CO adsorption of Au^δ+ in the catalysts. The catalytic activity of Au/CeO₂‐5 was improved due to the transformation of Au³⁺ to Au^δ+. Based on the CO oxidation and in situ DRIFTS results, Au^δ+ is likely to play a more important role in catalyzing CO oxidation reaction.     

Multiple CO Oxidation Promoted by Au2 Dimers in Au2TiO4− Cluster Anions

Time‐of‐flight mass spectrometry experiments demonstrated that laser ablation generated and mass selected Au₂TiO₄^? cluster anions can unexpectedly oxidize three CO molecules in an ion trap reactor. This is an improvement on the more commonly observed oxidation of at most two CO molecules by a doped cluster. Quantum chemistry calculations were performed to rationalize the reactions. The lowest energy isomer of Au₂TiO₄^? contains a superoxide unit, the participation of which in CO oxidation can be promoted by the Au₂ dimer. The Au₂ dimer functions as a rather flexible electron reservoir in each CO oxidation step in terms of the release and storage of electrons to drive the dissociation of superoxide to peroxide and then to lattice oxygen atoms, which can be removed by reaction with CO molecules. This gas‐phase study enriches our understanding toward the nature of reactive oxygen species involved in gold‐catalyzed oxidation reactions.     

Low‐Temperature Oxidation of Carbon Monoxide with Gold(III) Ions Supported on Titanium Oxide

Au/TiO₂ catalysts prepared by a deposition–precipitation process and used for CO oxidation without previous calcination exhibited high, largely temperature‐independent conversions at low temperatures, with apparent activation energies of about zero. Thermal treatments, such as He at 623 K, changed the conversion–temperature characteristics to the well‐known S‐shape, with activation energies slightly below 30 kJ mol^?1. Sample characterization by XAFS and electron microscopy and a low‐temperature IR study of CO adsorption and oxidation showed that CO can be oxidized by gas‐phase O₂ at 90 K already over the freeze‐dried catalyst in the initial state that contained Au exclusively in the +3 oxidation state. CO conversion after activation in the feed at 303 K is due to Au^III‐containing sites at low temperatures, while Au⁰ dominates conversion at higher temperatures. After thermal treatments, CO conversion in the whole investigated temperature range results from sites containing exclusively Au⁰.     

New insights on the Cd UPD on Au(111)

The Cd underpotential deposition (UPD) process on Au(111) was analyzed by means of combined electrochemical measurements and in situ scanning tunneling microscopy (STM). In the underpotential range 300?ΔE (mV) ?400, 2D Cd islands are formed on the fcc regions of the Au(111)‐(√3 × 22) reconstructed surface without lifting the reconstruction. At lower underpotentials, the 2D Cd islands grow and, simultaneously, new 2D islands nucleate and coalesce with the previous ones forming a complete condensed Cd monolayer (ML). STM images and long time polarization experiments performed at ΔE = 70 mV demonstrate the formation of an Au? Cd surface alloy. At ΔE = 10 mV, the formation of the complete Cd ML is accompanied by a significant Au? Cd surface alloying and the kinetic results reveal two different solid‐state diffusion processes. The first one, with a diffusion coefficient D₁ = 4 × 10^?17 cm² s^?1, could be ascribed to the mutual diffusion of Au and Cd atoms through a highly distorted (vacancy‐rich) Au? Cd alloy layer. The second and faster diffusion process (D₂ = 7 × 10^?16 cm² s^?1) is associated with the appearance of an additional peak in the anodic stripping curves and could be attributed to the formation of another Cd_zAu_x alloy phase. Copyright © 2008 John Wiley & Sons, Ltd.     

Supramolecular Binding Thermodynamics by Dispersion‐Corrected Density Functional Theory

The equilibrium association free enthalpies ΔG_a for typical supramolecular complexes in solution are calculated by ab initio quantum chemical methods. Ten neutral and three positively charged complexes with experimental ΔG_a values in the range 0 to ?21 kcal mol^?1 (on average ?6 kcal mol^?1) are investigated. The theoretical approach employs a (nondynamic) single‐structure model, but computes the various energy terms accurately without any special empirical adjustments. Dispersion corrected density functional theory (DFT‐D3) with extended basis sets (triple‐ζ and quadruple‐ζ quality) is used to determine structures and gas‐phase interaction energies (ΔE), the COSMO‐RS continuum solvation model (based on DFT data) provides solvation free enthalpies and the remaining ro‐vibrational enthalpic/entropic contributions are obtained from harmonic frequency calculations. Low‐lying vibrational modes are treated by a free‐rotor approximation. The accurate account of London dispersion interactions is mandatory with contributions in the range ?5 to ?60 kcal mol^?1 (up to 200 % of ΔE). Inclusion of three‐body dispersion effects improves the results considerably. A semilocal (TPSS) and a hybrid density functional (PW6B95) have been tested. Although the ΔG_a values result as a sum of individually large terms with opposite sign (ΔE vs. solvation and entropy change), the approach provides unprecedented accuracy for ΔG_a values with errors of only 2 kcal mol^?1 on average. Relative affinities for different guests inside the same host are always obtained correctly. The procedure is suggested as a predictive tool in supramolecular chemistry and can be applied routinely to semirigid systems with 300–400 atoms. The various contributions to binding and enthalpy–entropy compensations are discussed.     

Adsorption of small molecules on helical gold nanorods: A relativistic density functional study

We study the adsorption of a variety of small molecules on helical gold nanorods using relativistic density functional theory. We focus on Au₄₀ which consists of a central linear strand of five gold atoms with seven helical strands of five gold atoms on a coaxial tube. All molecules preferentially adsorb at a single low‐coordinated gold atom on the coaxial tube at an end of Au₄₀. In most cases, there is significant charge transfer (CT) between Au₄₀ and the adsorbate, for CO and NO₂, there is CT from the Au₄₀ to adsorbate while for all other molecules there is CT from the adsorbate to Au₄₀. Thus, Au₄₀‐adsorbate can be described as a donor–accepter complex and we use charge decomposition analysis to better understand the adsorption process. We determine the adsorption energy order to be C₅H₅N >NO₂ > CO > NH₃ > CH₂?CH₂ > CH₂?CH? CHO > NO > HC?CH > H₂S > SO₂ > HCN > CH₃OH > H₂C?O > O₂ > H₂O > CH₄ > N₂. We find that the Au? C, Au? N, Au? S, and Au? O bonds are surprisingly strong, with clear implications for reactivity enhancement of the adsorbate. The Au? H bond is relatively weak but, for interactions via an H atom that is bonded to a carbon atom (e.g., CH₄), we find that there is large charge polarization of the Au? H? C moiety and partial activation of the inert C? H bond. Although the Au? S and Au? O bonds are generally weaker than the Au? C and Au? N bonds, we find that adsorption of H₂S or H₂O causes greater distortion of Au₄₀ in the binding region. However, the degree of distortion is small and the helical structure is retained, demonstrating the stability of the helical Au₄₀ nanorod under perturbations. © 2014 Wiley Periodicals, Inc.     

Theoretical investigation on identical anionic halide‐exchange SN2 reaction processes on N‐haloammonium cation NH3X+ (X = F,Cl, Br,and I)

CCSD(T) calculations have been used for identically nucleophilic substitution reactions on N‐haloammonium cation, X^? + NH₃X⁺ (X = F, Cl, Br, and I), with comparison of classic anionic S_N2 reactions, X^? + CH₃X. The described S_N2 reactions are characterized to a double curve potential, and separated charged reactants proceed to form transition state through a stronger complexation and a charge neutralization process. For title reactions X^? + NH₃X⁺, charge distributions, geometries, energy barriers, and their correlations have been investigated. Central barriers ΔE for X^? + NH₃X⁺ are found to be lower and lie within a relatively narrow range, decreasing in the following order: Cl (21.1 kJ/mol) > F (19.7 kJ/mol) > Br (10.9 kJ/mol) > I (9.1 kJ/mol). The overall barriers ΔE relative to the reactants are negative for all halogens: ?626.0 kJ/mol (F), ?494.1 kJ/mol (Cl), ?484.9 kJ/mol (Br), and ?458.5 kJ/mol (I). Stability energies of the ion–ion complexes ΔE_comp decrease in the order F (645.6 kJ/mol) > Cl (515.2 kJ/mol) > Br (495.8 kJ/mol) > I (467.6 kJ/mol), and are found to correlate well with halogen Mulliken electronegativities (R² = 0.972) and proton affinity of halogen anions X^? (R² = 0.996). Based on polarizable continuum model, solvent effects have investigated, which indicates solvents, especially polar and protic solvents lower the complexation energy dramatically, due to dually solvated reactant ions, and even character of double well potential in reactions X^? + CH₃X has disappeared. © 2011 Wiley Periodicals, Inc. Int J Quantum Chem, 2011     

Novel Nanoporous Binary Au?Ru Electrocatalysts for Glucose Oxidation

In this work, we study the fabrication, structural characterization, and electrochemical activity of titanium‐supported binary Au? Ru catalysts for glucose oxidation. The catalysts including Au₉₉Ru₁, Au₉₅Ru₅, Au₉₃Ru₇ and Au₈₈Ru₁₂ were prepared by a hydrothermal method using formaldehyde as a reduction agent. The morphologies of the prepared Au? Ru catalyst structures are characterized by porous dendritic particles with roughened surfaces with nano‐sized flakes. Electrochemical catalytic activity of the binary Au? Ru catalysts towards glucose oxidation in alkaline solutions was investigated using cyclic voltammetry and chronoamperometry. All binary Au? Ru catalysts facilitate glucose oxidation at the lower potentials and deliver higher anodic oxidation currents compared to pure Au catalyst. Among them, the binary Au₉₅Ru₅ catalyst presents the most negative onset potential of ?0.872 V (vs. Ag/AgCl, 3 M KCl) for glucose oxidation in 0.1 M NaOH solution. For the Au₉₅Ru₅ catalyst, chronoamperometric data at the potential step of ?0.65 V (vs. Ag/AgCl,3 M KCl) exhibit a well linear dependence of the anodic oxidation current density on glucose concentration in the range of 0 to 15 mM glucose.     

Carbon Monoxide Oxidation by Polyoxometalate‐Supported Gold Nanoparticulate Catalysts: Activity,Stability, and Temperature‐ Dependent Activation Properties

Nanoparticulate gold supported on a Keggin‐type polyoxometalate (POM), Cs₄[α‐SiW₁₂O₄₀]?n H₂O, was prepared by the sol immobilization method. The size of the gold nanoparticles (NPs) was approximately 2 nm, which was almost the same as the size of the gold colloid precursor. Deposition of gold NPs smaller than 2 nm onto POM (Au/POM) was essential for a high catalytic activity for CO oxidation. The temperature for 50 % CO conversion was ?67 °C. The catalyst showed extremely high stability for at least one month at 0 °C with full conversion. The catalytic activity and the reaction mechanism drastically changed at temperatures higher than 40 °C, showing a unique behavior called a U‐shaped curve. It was revealed by IR measurement that Au^δ+ was a CO adsorption site and that adsorbed water promoted CO oxidation for the Au/POM catalyst. This is the first report on CO oxidation utilizing Au/POMs catalysts, and there is a potential for expansion to various gas‐phase reactions.     

N‐Heterocyclic Carbene Analogues of Thiele and Chichibabin Hydrocarbons

Stable N‐heterocyclic carbene analogues of Thiele and Chichibabin hydrocarbons, [(IPr)(C₆H₄)(IPr)] and [(IPr)(C₆H₄)₂(IPr)] ( 4 and 5 , respectively; IPr=C{N(2,6‐iPr₂C₆H₃)}₂CHCH), are reported. In a nickel‐catalyzed double carbenylation of 1,4‐Br₂C₆H₄ and 4,4′‐Br₂(C₆H₄)₂ with IPr ( 1 ), [(IPr)(C₆H₄)(IPr)](Br)₂ ( 2 ) and [(IPr)(C₆H₄)₂(IPr)](Br)₂ ( 3 ) were generated, which respectively afforded 4 and 5 as crystalline solids upon reduction with KC₈. Experimental and computational studies support the semiquinoidal nature of 5 with a small singlet?triplet energy gap ΔE_S?T of 10.7 kcal mol^?1, whereas 4 features more quinoidal character with a rather large ΔE_S?T of 25.6 kcal mol^?1. In view of the low ΔE_S?T, 4 and 5 may be described as biradicaloids. Moreover, 5 has considerable (41 %) diradical character.     

Co‐Adsorption of O2 and CO on Au2−: Infrared Photodissociation Spectroscopy and Theoretical Study of [Au2O2(CO)n]− (n=2–6)

The co‐adsorption of O₂ and CO on anionic sites of gold species is considered as a crucial step in the catalytic CO oxidation on gold catalysts. In this regard, the [Au₂O₂(CO)_n]^? (n=2–6) complexes were prepared by using a laser vaporization supersonic ion source and were studied by using infrared photodissociation spectroscopy in the gas phase. All the [Au₂O₂(CO)_n]^? (n=2–6) complexes were characterized to have a core structure involving one CO and one O₂ molecule co‐adsorbed on Au₂^? with the other CO molecules physically tagged around. The CO stretching frequency of the [Au₂O₂(CO)]^? core ion is observed around =2032–2042 cm^?1, which is about 200 cm^?1 higher than that in [Au₂(CO)₂]^?. This frequency difference and the analyses based on density functional calculations provide direct evidence for the synergy effect of the chemically adsorbed O₂ and CO. The low lying structures with carbonate group were not observed experimentally because of high formation barriers. The structures and the stability (i.e., the inertness in a sense) of the co‐adsorbed O₂ and CO on Au₂^? may have relevance to the elementary reaction steps on real gold catalysts.     

A mechanism of the 1,3‐dipolar cycloaddition between the hydrogen nitryl HNO2 and acetylene HCCH: The electron localization function study on evolution of the chemical bonds

The reaction between the simplest nitro compound HNO₂ (hydrogen nitryl) and acetylene HCCH ‐ formally proceeding via 1,3‐dipolar cycloaddition ‐ has been studied by means of the B3LYP, MPW1K and MP2 methods. The energy barrier of 20.74 ÷ 32.91 kcal/mol is similar to ΔE_a of the NNO + HCCH process but is essentially larger than computed for the reactions of HCCH with fulminic acid (HCNO) and NNCH₂. Whole process is exothermic with the reaction energy: ?10.87 ÷ ?17.94 kcal/mol. An evolution of the chemical bonding has been analyzed by means of the Bonding Evolution Theory (BET) at the B3LYP/6‐31+G(d) and B3LYP/cc‐pVTZ levels. Two approximations of the reaction path have been considered, namely: the IRC and pseudo‐reaction paths. The reaction requires five steps and seven catastrophes of the fold and cusp type. A different effect of first fold catastrophe has been noticed. At the B3LYP/6‐31+G(d) level one of two nonbonding V_i=1,2(N) attractors is annihilated (F), meanwhile at B3LYP/cc‐pVTZ new V(N) attractor is created (F^?). The chemical bonds are not formed/broken in TS. © 2010 Wiley Periodicals, Inc. Int J Quantum Chem, 2011     

CO Oxidation Promoted by the Gold Dimer in Au2VO3− and Au2VO4− Clusters

Investigations on the reactivity of atomic clusters have led to the identification of the elementary steps involved in catalytic CO oxidation, a prototypical reaction in heterogeneous catalysis. The atomic oxygen species O^.? and O^2? bonded to early‐transition‐metal oxide clusters have been shown to oxidize CO. This study reports that when an Au₂ dimer is incorporated within the cluster, the molecular oxygen species O₂^2? bonded to vanadium can be activated to oxidize CO under thermal collision conditions. The gold dimer was doped into Au₂VO₄^? cluster ions which then reacted with CO in an ion‐trap reactor to produce Au₂VO₃^? and then Au₂VO₂^?. The dynamic nature of gold in terms of electron storage and release promotes CO oxidation and O? O bond reduction. The oxidation of CO by atomic clusters in this study parallels similar behavior reported for the oxidation of CO by supported gold catalysts.     

Does enhanced oxygen activation always facilitate CO oxidation on gold clusters?

We investigate the catalytic activity of the subnanometer‐sized bimetallic Au₁₉Pt cluster for oxidation of CO via first‐principles density functional theory calculations. For this purpose we consider two structurally similar and energetically close homotops of the Au₁₉Pt cluster with the Pt atom occupying an edge (Td‐E) or a facet (Td‐S) site of a 20‐atom tetrahedron. Using these homotops as catalysts we calculate the complete reaction paths and the thermodynamic functions corresponding to the oxidation of CO to CO₂. It is found that the oxidation of CO on the Td‐S isomer occurs through a smaller reaction barrier (0.38 eV) as compared with that on the Td‐E isomer (0.70 eV), although the activation of O₂ on the latter is much higher than that on the former. Therefore, a clear conclusion is that a higher O₂ activation, which is generally believed to be the key factor for CO oxidation, solely cannot determine the catalytic efficiency of the Au‐Pt bimetallic clusters. In addition, we find a stronger CO adsorption on the Td‐E isomer (2.06 eV) as compared with that on the Td‐S isomer (1.68 eV). Although stronger CO adsorption on the Td‐E isomer leads to a higher O₂ activation; however, high value of CO adsorption energy deteriorates the catalytic activity of the Td‐E isomer towards the CO oxidation reaction. © 2015 Wiley Periodicals, Inc.     

Gold(I) and Gold(III) Trifluoromethyl Derivatives

Trifluoromethylation of AuCl₃ by using the Me₃SiCF₃/CsF system in THF and in the presence of [PPh₄]Br proceeds with partial reduction, yielding a mixture of [PPh₄][Au^I(CF₃)₂] ( 1′ ) and [PPh₄][Au^III(CF₃)₄] ( 2′ ) that can be adequately separated. An efficient method for the high‐yield synthesis of 1′ is also described. The molecular geometries of the homoleptic anions [Au^I(CF₃)₂]^? and [Au^III(CF₃)₄]^? in their salts 1′ and [NBu₄][Au^III(CF₃)₄] ( 2 ) have been established by X‐ray diffraction methods. Compound 1′ oxidatively adds halogens, X₂, furnishing [PPh₄][Au^III(CF₃)₂X₂] (X=Cl ( 3 ), Br ( 4 ), I ( 5 )), which are assigned a trans stereochemistry. Attempts to activate C? F bonds in the gold(III) derivative 2′ by reaction with Lewis acids under different conditions either failed or only gave complex mixtures. On the other hand, treatment of the gold(I) derivative 1′ with BF₃?OEt₂ under mild conditions cleanly afforded the carbonyl derivative [Au^I(CF₃)(CO)] ( 6 ), which can be isolated as an extremely moisture‐sensitive light yellow crystalline solid. In the solid state, each linear F₃C‐Au‐CO molecule weakly interacts with three symmetry‐related neighbors yielding an extended 3D network of aurophilic interactions (Au???Au=345.9(1) pm). The high $\tilde \nu $ _CO value (2194 cm^?1 in the solid state and 2180 cm^?1 in CH₂Cl₂ solution) denotes that CO is acting as a mainly σ‐donor ligand and confirms the role of the CF₃ group as an electron‐withdrawing ligand in organometallic chemistry. Compound 6 can be considered as a convenient synthon of the “Au^I(CF₃)” fragment, as it reacts with a number of neutral ligands L, giving rise to the corresponding [Au^I(CF₃)(L)] compounds (L=CNtBu ( 7 ), NCMe ( 8 ), py ( 9 ), tht ( 10 )).     

Reaction of H + ketene to formyl methyl and acetyl radicals and reverse dissociations

Thermochemical properties for reactants, intermediates, products, and transition states important in the ketene (CH₂?C?O) + H reaction system and unimolecular reactions of the stabilized formyl methyl (C·H₂CHO) and the acetyl radicals (CH₃C·O) were analyzed with density functional and ab initio calculations. Enthalpies of formation (ΔH_f°₂₉₈) were determined using isodesmic reaction analysis at the CBS‐QCI/APNO and the CBSQ levels. Entropies (S°₂₉₈) and heat capacities (C_p°(T)) were determined using geometric parameters and vibrational frequencies obtained at the HF/6‐311G(d,p) level of theory. Internal rotor contributions were included in the S and C_p(T) values. A hydrogen atom can add to the CH₂‐group of the ketene to form the acetyl radical, CH₃C·O (E_a = 2.49 in CBS‐QCI/APNO, units: kcal/mol). The acetyl radical can undergo β‐scission back to reactants, CH₂?C?O + H (E_a = 45.97), isomerize via hydrogen shift (E_a = 46.35) to form the slight higher energy, formyl methyl radical, C·H₂CHO, or decompose to CH₃ + CO (E_a = 17.33). The hydrogen atom also can add to the carbonyl group to form C·H₂CHO (E_a = 6.72). This formyl methyl radical can undergo β scission back to reactants, CH₂?C?O + H (E_a = 43.85), or isomerize via hydrogen shift (E_a = 40.00) to form the acetyl radical isomer, CH₃C·O, which can decompose to CH₃ + CO. Rate constants are estimated as function of pressure and temperature, using quantum Rice–Ramsperger–Kassel analysis for k(E) and the master equation for falloff. Important reaction products are CH₃ + CO via decomposition at both high and low temperatures. A transition state for direct abstraction of hydrogen atom on CH₂?C?O by H to form, ketenyl radical plus H₂ is identified with a barrier of 12.27, at the CBS‐QCI/APNO level. ΔH_f°₂₉₈ values are estimated for the following compounds at the CBS‐QCI/APNO level: CH₃C·O (?3.27), C·H₂CHO (3.08), CH₂?C?O (?11.89), HC·CO (41.98) (kcal/mol). © 2002 Wiley Periodicals, Inc. Int J Chem Kinet 35: 20–44, 2003     

Studies on the singlet and triplet states of unsaturated carbenes

Quantum chemical calculations and studies have been made on the different spin states of unsaturated carbenes X₂C?C: and X₂C?C?C: (X?H, Li, F). The geometries and relative stabilities of these carbenes with various groups X have been outlined. The ground states of unsaturated carbenes are all singlet. The energy splittings between the ground states and first excited states ΔE (¹A₁-³B₁) are generally within the value of 60 kcal/mol and change greatly with the electronegativities of groups X, but little with the sizes of the cumulidenes. The equilibrium conformations of ¹A₁ and ³B₁ are different.