The conformations, equilibrium structures, hydrogen bonds, and non-covalent interactions involved in the mechanisms of tautomerization, condensations, and C-sulfenylation and O-sulfenylation of 2,4-pentanedione by sulfur hydride hydroxide (hydrogen thioperoxide, oxadisulfane, H–SOH) have been studied using BD(T), CCSD(T), and QCISD(T) with the cc-pVTZ basis set and using B3LYP, B3PW91, CAM-B3LYP, PBE1PBE, PBEh1PBE, LC-ωPBE, M06-2X, and ωB97XD with the 6-311+G(d,p) basis set. All levels of theory predict the sulfenyl (H–SOH) tautomer of hydrogen thioperoxide to be lower in energy than the sulfinyl (H2S═O) tautomer. Four reasonable mechanisms were considered for the tautomerization of the sulfenyl tautomer of hydrogen thioperoxide to the sulfinyl tautomer: a cyclic three-membered water-free transition state (TS, CCSD(T) activation energy barrier E⧧ = 65.1 kcal/mol), a cyclic five-membered transition state with one water molecule (TSH2O, E⧧ = 31.1 kcal/mol), a cyclic seven-membered transition state with two water molecules (TS2H2O, E⧧ = 14.5 kcal/mol), and a cyclic nine-membered transition state with three water molecules (TS3H2O, E⧧ = 5.6 kcal/mol). The mechanisms involve hydrogen-bonded reactant complexes and hydrogen-bonded product complexes. The CCSD(T)-predicted energy barriers for the condensation of hydrogen thioperoxide to form thiosulfinic acid through transition states with zero, one, and two waters are E⧧ = 42.0, 18.3, and 0 kcal/mol, respectively. Mixed condensation reactions are predicted to afford organosulfur products and compounds containing sulfur–selenium bonds. Hydrogen thioperoxide is predicted to add to 2,4-pentanedione to form C-sulfenylated (sulfide, thioether) and O-sulfenylated (sulfenate ester) products. Similar mechanistic trends and reaction pathways are observed in the tautomerism, condensations, and C-sulfenylation and O-sulfenylation reactions of hydrogen thioperoxide. The water molecules set up proton relay networks (bridges) that reduce ring strain, generate favorable conformations for reactivity, lower energy barriers, and increase the numbers of stabilizing hydrogen bonds and nonbonding interactions.

Equilibrium and molecular structures, relative energies of conformers of gaseous cysteine (Cys, C, Cys-SH) and gaseous cysteine sulfenic acid (Cys-SOH), and the mechanisms of the reaction of Cys-SOH with 3-hydroxy-5,5-dimethyl-2-cyclohexen-1-one, the enol tautomer of 5,5-dimethyl-1,3-cyclohexadione (dimedone), have been studied using BD(T), CCSD(T), and QCISD(T) with the cc-pVTZ basis set and using MP2 and the density functionals B3LYP, B3PW91, PBE1PBE, PBEh1PBE, M062X, CAM-B3LYP, and WB97XD with the 6-311+G(d,p) basis set. The structures of the six lowest energy conformers of gaseous Cys-SOH are compared with the six lowest energy conformers of gaseous cysteine (Cys-SH). The relative stability of the six lowest energy conformers of Cys-SH and Cys-SOH are influenced by the interplay among many factors including dispersive effects, electronic effects, electrostatic interactions, hydrogen bonds, inductive effects, and noncovalent interactions. The mechanism of the addition of the lowest energy conformer of cysteine sulfenic acid (Cys-SOH) to dimedone may proceed through a six-membered ring transition state structure and through cyclic hydrogen-bonded transition state structures with one water molecule (8-membered ring), with two water molecules (10-membered ring), and with three water molecules (12-membered ring). Inclusion of one and two water molecules in the transition state structures lowers the activation barrier, whereas inclusion of a third water molecule raises the activation barrier.

Structural features of hydrogen thioperoxide (oxadisulfane, H–S–O–H) and of alkanesulfenic acids (R–S–O–H; R = CH3, CH2CH3, CH2CH2CH3, CH(CH3)2, C(CH3)3, CF3, CCl3) and the mechanisms of their dehydrative cyclocondensation to the respective sulfinothioic acid (H–(S═O)–S–H) and alkyl alkanethiosulfinates (R–(S═O)–S–R) have been studied using coupled cluster theory with single and double and perturbative triple excitations [CCSD(T)] and quadratic configuration interaction with single and double and perturbative triple excitations [QCISD(T)] with the cc-pVDZ basis set and also using second-order Møller-Plesset perturbation theory (MP2) and the hybrid density functionals B3LYP, B3PW91, and PBE1PBE with the 6-311+G(d,p) basis set. The concerted cyclodehydration mechanisms include cyclic five-center transition states with relatively long distance sulfur–sulfur bonding interactions. Attractive and repulsive nonbonding interactions are predicted in the sulfenic acids, transition states, and thiosulfinates. In the alkyl alkanethiosulfinates attractive cyclic C–H----O═S nonbonding interactions are predicted. CCSD(T) and QCISD(T) predict similar values for the relative energies and CCSD(T) predicts the barrier to the cyclocondensation of H–S–O–H to sulfinothioic acid (H–(S═O)–S–H) to be 41.8 kcal/mol, and barriers in the range of 37.5 to 39.6 kcal/mol are predicted for the condensation of alkanesulfenic acids to alkyl alkanethiosulfinates.

Electronic structures, partial atomic charges, singlet−triplet gaps (ΔEST), substituent effects, and mechanisms of 1,2-rearrangements of 1,3-oxazol-2-ylidene (5) and 4,5-dimethyl- (6), 4,5-difluoro- (7), 4,5-dichloro- (8), 4,5-dibromo- (9), and 3-methyl-1,3-oxazol-2-ylidene (10) to the corresponding 1,3-oxazoles have been studied using complete-basis-set methods (CBS-QB3, CBS-Q, CBS-4M), second-order Møller−Plesset perturbation method (MP2), hybrid density functionals (B3LYP, B3PW91), coupled-cluster theory with single and double excitations (CCSD) and CCSD plus perturbative triple excitations [CCSD(T)], and the quadratic configuration interaction method including single and double excitations (QCISD) and QCISD plus perturbative triple excitations [QCISD(T)]. The 6-311G(d,p), 6-31+G(d,p), 6-311+G(d,p), and correlation-consistent polarized valence double-ξ (cc-pVDZ) basis sets were employed. The carbenes have singlet ground states, and the CBS-QB3 and CBS-Q methods predict ΔEST values for 5−8 and 10 of 79.9, 79.8, 74.7, 77.0, and 82.0 kcal/mol, respectively. CCSD(T), QCISD(T), B3LYP, and B3PW91 predict smaller ΔEST values than CBS-QB3 and CBS-Q, with the hybrid density functionals predicting the smallest values. The concerted unimolecular exothermic out-of-plane 1,2-rearrangements of singlet 1,3-oxazol-2-ylidenes to their respective 1,3-oxazoles proceed via cyclic three-center transition states. The CBS-predicted barriers to the 1,2-rearrangements of singlet carbenes 5−9 to their respective 1,3-oxazoles are 41.4, 40.4, 37.8, 40.4, and 40.5 kcal/mol, respectively. During the 1,2-rearrangements of singlet 1,3-oxazol-2-ylidenes 5−9, there is a decrease in electron density at oxygen, N3 (the migration origin), and C5 and an increase in electron density at C2 (the migration terminus), C4, and the partially positive migrating hydrogen.

Second-order Møller–Plesset theory (MP2) and density functional theory (B3LYP) with the 6-311G(d,p) and 6-311+G(d,p) basis sets have been used to calculate the equilibrium geometries and relative energies of the chair, twist, and boat conformations of 4-chloro-4-silathiacyclohexane 1-oxide and 4,4-dichloro-4-silathiacyclohexane 1-oxide. The chair conformers of the axial sulfoxides are lower in energy than the chair conformers of the corresponding equatorial sulfoxides. MP2/6-311+G(d,p) predicted the chair conformer of axial trans-4-chloro-4-silathiacyclohexane 1-oxide (4a) to be 6.12, 0.44, and 0.45 kcal/mol, respectively, more stable than the corresponding 1,4-twist (4b), 2,5-twist (4c) and 1,4-boat (4d) conformers and 6.93 kcal/mol more stable than the 2,5-boat transition state ([4e]‡). Structures 4c and 4d are stabilized by intramolecular coordination of the sulfinyl oxygen with silicon that results in trigonal bipyramidal geometry at silicon. The 1,4-boat conformer (7d) of axial 4,4-dichloro-4-silathiacyclohexane 1-oxide is also stabilized by transannular coordination of the sulfinyl oxygen with silicon. The energy difference (Erel = 4.23 kcal/mol) between the chair conformer (7a) and 7d is larger than that between 4a and 4d. The relatively lower stability of the 1,4-boat conformer (7d) of axial 4,4-dichloro-4-silathiacyclohexane 1-oxide (7a) may be due to repulsive interactions of the axial halogen and sulfinyl oxygen atoms. The relative energies and structures of the conformers and transition states of cis- and trans-4-chloro-4-silathiacyclohexane 1-oxide and 4,4-dichloro-4-silathiacyclohexane 1-oxide are discussed in terms of hyperconjugative interactions, orbital interactions, nonbonded interactions, and intramolecular sulfinyl oxygen–silicon coordination.Boat and twist conformers of axial chlorosilathiacyclohexane 1-oxides were found to be minima and to be stabilized by transannular coordination of the sulfinyl oxygen with silicon that resulted in trigonal bipyramidal geometry at silicon.

Ab initio molecular orbital theory with the 6-31G(d), 6-31+G(d), 6-31G(d,p), and 6-31G(2d) basis sets has been used to calculate the geometry optimized structures and the relative energies (ΔE) of the rotamers of the chair conformers of 3-substituted equatorial tetrahydro-2H-thiopyran-1-oxides (tetrahydrothiopyran-1-oxides, thiacyclohexane-1-oxides, thiane-1-oxides; CH3, CF3, CHO, COCH3, CN, F, Cl, Br). The conformational free energies (ΔG°) and relative energies (ΔE) of the conformers and rotamers are discussed in terms of the repulsive nonbonded interactions in both conformers.

Ab initio theory and density functional theory (B3LYP) have been used to calculate the geometry optimized structures, configurational isomer energy differences (ΔE), and the configurational enthalpies (ΔH0), entropies (ΔS0), and free energies (ΔG0) of 4-alkyl equatorial tetrahydro-2H-thiopyran-1-oxides (tetrahydrothiopyran-1-oxides, thiacyclohexane-1-oxides, thiane-1-oxides (Me, Et, neo-Pent, i-Pr, tert-Bu) and 4-trimethylsilyl equatorial tetrahydro-2H-thiopyran-1-oxide. The calculated structural data indicate that repulsive steric interactions between the axial alkyl group and the ring atoms are the major contributors to the equatorial preference. The configurational isomer energy differences (ΔE), configurational enthalpies (ΔH0) and free energies (ΔG0) of the 4-alkyl equatorial tetrahydro-2H-thiopyran-1-oxides have been compared with the reported experimental conformational enthalpies (ΔH0) and free energies (ΔG0) of the corresponding alkylcyclohexanes and 4-alkyltetrahydro-2H-thiopyrans. The use of the configurational isomer energy differences (ΔE) and/or configurational free energies (ΔG0) of 4-alkyl equatorial tetrahydro-2H-thiopyran-1-oxides as possible models for assigning the difference in the steric requirements of an alkyl substituent in axial and equatorial positions is also discussed.

Ab initio Hartree–Fock and Density Functional Theory calculations were used to obtain the geometries and relative energies of the rotamers in the chair conformations of 2-alkyltetrahydro-2H-pyrans and 2-(trimethylsilyl)tetrahydro-2H-pyran. The MP2/6-31G*//6-31G* conformational energies (−ΔG°or A values, kcal/mol) of the 2-alkyltetrahydro-2H-pyrans (Me=3.18; Et=3.04; i-Pr=3.03; t-Bu=7.56; neo Pent=2.84) and 2-(trimethylsilyl)tetrahydro-2H-pyran (SiMe3=4.77) are larger than those calculated for the corresponding alkylcyclohexanes and 2-alkyltetrahydro-2H-thiopyrans (tetrahydrothiopyrans, thiacyclohexanes, thianes). Plots of the calculated conformational energies for the 2-substituted tetrahydro-2H-pyrans versus the calculated −ΔG° values for the corresponding alkylcyclohexanes (slope=1.34 and r=0.983) and for the corresponding 2-substituted tetrahydro-2H-thiopyrans (slope=2.01 and r=0.986) are linear.

Ab initio molecular orbital theory using the 3-21G(∗), 6-31G∗, 6-31G∗∗, 6-311G∗∗ basis sets, Møller-Plesset perturbation theory [MP2/3-21G(∗)//3-21G(∗), MP2/6-31G∗//6-31G∗, MP2/6-31G∗∗//6-31G∗∗, MP2/6-311G∗∗//6-311G∗∗], and density functional theory (pBP/DN∗∗) were used to calculate the geometries and energies of dihydrodioxins (3,4-dihydro-1,2-dioxin, 3,6-dihydro-1,2-dioxin, 4H-1,3-dioxin (1,3-diox-4-ene), and 2,3-dihydro-1,4-dioxin (1,4-dioxene). Frequency calculations show that the four dihydrodioxins exist in the half-chair conformation and that their boat conformers are transition states. Hyperconjugative orbital interactions (stereoelectronic effects) including , , are observed in 4H-1,3-dioxin. Ab initio (3-21G(∗), 6-31G∗) and MP2/6-31G∗//6-31G∗ calculations were used to obtain geometry optimized structures and conformational energies (−ΔG° or “A values”, kcal/mol) of the rotamers in the half-chair conformers of 2-alkyl-4H-1,3-dioxins and 2-trimethylsilyl-4H-1,3-dioxin [MP2/6-31G∗//6-31G∗: CH3(2.95), C2H5(2.89), iso-C3H7(2.97), tert-C4H9(7.34), neo-C5H11(2.16), Si(CH3)3(4.45)]. The calculated conformational energies of the 2-alkyl-4H-1,3-dioxins and 2-trimethylsilyl-4H-1,3-dioxin are larger than those calculated for the corresponding alkylcyclohexanes and 4-alkylcyclohexenes. Plots of the calculated conformational energies of the 2-alkyl-4H-1,3-dioxins and 2-trimethylsilyl-4H-1,3-dioxin versus the calculated −ΔG° values of the correspondingly substituted cyclohexanes (slope=1.320 and r=0.989) and 4-substituted cyclohexenes (slope=2.150 and r=0.968) are linear. Hyperconjugative orbital interactions are also observed in the 2-alkyl-4H-1,3-dioxins. The C(2)–Hax bond lengths are longer than the C(2)–Heq bond lengths and the C(2)–O(1) bond lengths are longer than the C(2)–O(3) bond lengths in 4H-1,3-dioxin and in the 2-substituted 4H-1,3-dioxins. The C(4)–O(3) bond lengths in the 4H-1,3-dioxins are generally 1.407 or 1.408 Å. In the 2-substituted 4H-1,3-dioxins, the O(1)–C(2)–O(1) bond angles vary from 110.4 to 112.8° and the C(2)–O(3)–C(4) and C(7)–C(2)–O(3) bond angles in the most stable axial conformer are larger that the corresponding angles in its most stable equatorial conformer.

Ab initio Hartree–Fock calculations using the 6-31G(d), 6-31G(2d), 6-31G(d,p), 6-311G(d,p), 6-31+G(d), and 6-311+G(d,p) basis sets, second-order Møller–Plesset perturbation theory (MP2) using the same basis sets, and density functional theory [SVWN/DN∗, SVWN/DN∗∗, pBP/DN∗, pBP/DN∗∗, BLYP/6–31G(d), B3BLYP/6–31G(d)] were used to calculate the geometry optimized structure of tetrahydro-2H-thiopyran (tetrahydrothiopyran, thiacyclohexane, thiane) and the conformational enthalpy (ΔH°), entropy (ΔS°), and free energy (ΔG°) of the chair conformers of methylcyclohexane and 2-methyl-, 3-methyl-, and 4-methyltetrahydro-2H-thiopyran. The DFT methods generally overestimate the conformational free energies (−ΔG°) while some of the MP2 methods give values closer to the experimental results. The MP2/6-311G(d,p) calculated value for 2-methyltetrahydro-2H-thiopyran is in excellent agreement with the experimentally reported value and the MP2/6-21G(2d) calculated value for 3-methyltetrahydro-2H-thiopyran is also in excellent agreement with the experimentally reported value. The equatorial preference of the methyl group is discussed in terms of the repulsive nonbonded interactions in the equatorial conformer, gauche butane (torsional) interactions in the axial conformer, and repulsive nonbonded interactions of the axial methyl group with the ring carbons and hydrogens.

Ab initio 6-31G∗ and 6-31G∗∗ basis sets and density functional theory (pBP/DN∗∗) were used to calculate the geometry of the chair conformer of tetrahydro-2H-thiopyran (tetrahydrothiopyran, thiacyclohexane, thiane). 6-31G∗ geometry optimization and MP2/6-31G∗//6-31G∗ single point energy methods were used to calculate the relative energies and conformational energies (−ΔG° or A values, kcal/mol) of 3-alkyltetrahydro-2H-thiopyrans (Me=1.56; Et=1.22; i-Pr=0.91; t-Bu=4.54; neo-Pent=1.06; SiMe3=2.01). The MP2/6-31G∗//6-31G∗ calculated conformational energies of the 3-alkylthiacyclohexanes are generally smaller than those for the corresponding alkylcyclohexanes and 4-alkylthiacyclohexanes, but are similar to those calculated for 2-alkylthiacyclohexanes. Plots of the calculated conformational energies of the 3-alkylthiacyclohexanes versus the calculated −ΔG° of the corresponding alkylcyclohexanes (slope=0.901 and r=0.997 for 6-31G∗ and slope=0.845 and r=0.994 for MP2/6-31G∗//6-31G∗), 2-alkylthiacyclohexanes (slope=1.273 and r=0.981 for 6-31G∗ and slope=1.273 and r=0.986 for MP2/6-31G∗//6-31G∗), and 4-alkylthiacyclohexanes (slope=0.888 and r=0.997 for 6-31G∗ and slope=0.839 and r=0.994 for MP2/6-31G∗//6-31G∗) are linear. Both carbon–sulfur bond lengths in the 3-alkylthiacyclohexanes are generally in the narrow range of 1.815 and 1.818 Å and the C(2)–Hax and C(6)–Hax bond lengths are slightly longer than the respective C(2)–Heq and C(6)–Heq bond lengths. The C–S–C bond angles vary from 97.1 to 99.0° and the C(2)–C(3)–C(7) and C(4)–C(3)–C(7) bond angles in the most stable axial conformer are larger that the corresponding angles in its most stable equatorial conformer.

Ab initio HF/6-31G∗ and MP2/6-31G∗//HF/6-31G∗ methods were used to calculate the relative energies of the rotamers in the chair conformations of 3-alkyltetrahydro-2H-pyrans (tetrahydropyrans, oxacyclohexanes, oxanes; CH3, C2H5, i-C3H7, t-C4H9, neo-C5H11) and 3-(trimethylsilyl)tetrahydro-2H-pyran; Si(CH3)3). The MP2/6-31G∗//HF/6-31G∗ conformational energies (−ΔG0 or A values, kcal/mol) of 3-alkyltetrahydro-2H-pyrans (CH3=0.97; C2H5=0.74; i-C3H7=0.59; t-C4H9=2.42; neo-C5H11=0.27; Si(CH3)3=0.86) are smaller than those calculated for alkylcyclohexanes and 2-alkyloxacyclohexanes. The carbon–oxygen bond lengths are in the narrow range of 1.399–1.403 Å with the C(2)–O(1) bond length essentially the same as the C(6)–O(1) bond length. The C(3)–H bond lengths range from 1.086 to 1.092 Å for the respective axial and equatorial conformers. The C(3)–C(7) bond length shows greater variability (1.528 to 1.640 Å) with the axial C(3)–C(7) bond generally ∽0.004 Å longer than the corresponding equatorial bond. The C(2)–O(1)–C(6) bond angles range from 112.9° to 114.2° and the C(3)–C(4)–C(5) angles vary from 110.7 to 114.6°. Plots of the calculated conformational energies for the 3-alkyloxacyclohexanes versus the calculated conformational energies for the corresponding alkylcyclohexanes are linear (slope=0.54 and r=0.992 for HF/6-31G∗ and slope=0.45 and r=0.977 for MP2/6-31G∗//HF/6-31G∗).