Theoretical investigations of candidate crystal structures for β-carbonic acid

Using multiple computational tools, we examine five candidate crystal structures for β-carbonic acid, a molecular crystal of environmental and astrophysical significance. These crystals comprise of hydrogen bonded molecules in either sheetlike or chainlike topologies. Gas phase quantum calculations, empirical force field based crystal structure search, and periodic density functional theory based calculations and finite temperature simulations of these crystals have been carried out. The infrared spectrum calculated from density functional theory based molecular dynamics simulations compares well with experimental data. Results suggest crystals with one-dimensional hydrogen bonding topologies (chainlike) to be more stable than those with two-dimensional (sheetlike) hydrogen bonding networks. We predict that these structures can be distinguished on the basis of their far infrared spectra.     

Theoretical study on decomposition of γ-halo allylalkoxide and β-halo acrylate ions

β, γ-Substituted γ-halo allylalkoxide ions decompose to form a halogen ion, formaldehyde, and an alkyne under mild conditions, for example at room temperature. The E isomer does not differ from the Z isomer in terms of activation energy. We attempted to shed light on the mechanism of the reaction by using ab initio molecular orbital calculations. The observed propensity was confirmed by the present calculation on model molecules, γ-chloro allylalkoxide ions. We conducted further calculations and compared the alkoxide results with a similar reaction of β-haloacrylate ions that release carbon dioxide instead of formaldehyde. This similar reaction needs heating as high as 150°C. The activation energy of the acrylate ions (36–39 kcal mol⁻¹) was calculated to be about 10 kcal mol⁻¹ higher than that of the alkoxide ions. The activation energy of the E acrylate ion is smaller by 0.8 kcal mol⁻¹ than that of the Z isomer at the MP2/6-31+G**//RHF/6-31+G* level of theory. This is consistent with experimental results. While the ready deprotonation from the carboxylic group does not activate the acrylate ion very much, the alkoxide ion is destabilized to a great degree in the process of anion formation. The difficulty in deprotonation that proceeds from the neutral molecule is seen in the difference in the activation energies for the decomposition of the corresponding anions. Therefore, the pK _a of a hydroxy or a carboxylic group plays the leading role in determining the magnitude of activation energies of allyl halides with a negatively charged fragment. Received: 2 July 1998 / Accepted: 9 September 1998 / Published online: 8 February 1999     

Theoretical Studies of β-Peptide Models

Recently, the β-peptides, which consist entirely of β-amino acids instead of α-amino acids, have received intensive attention because of their interesting secondary structures.^1-3 Depending upon side chain substitution pattern, β-sheets, 14-helices, and 12-helices all have been observed.¹ Due to great variety of substitution patterns,the easiness of formation of secondary structures with even 4-6 residues compared to about 15 for natural peptides,and ready formation of cyclic compounds that stack into tube structures,⁴ β-peptides have generated great excitement. In addition,β-amino acids also frequently occur in natural products, especially cyclic peptides. It has been found that β-amino acids have excellent stability toward proteases. Therefore, they have wide applications in drug development.⁶     

Theoretical calculations of β-lactam antibiotics

Summary We carried out a comprehensive theoretical study on the alkaline hydrolysis of the bicyclic system of penicillins (a four-member ring fused to a thiazolidine ring) on the basis of aB _AC2 mechanism. We assayed the MINDO/3, MNDO, and AM1 semi-empirical calculation methods in order to determine their suitability for studying -lactam rings.Both the geometric and the energetic results obtained for the different intermediate states were compared with literature values — chiefly those determined byab initio methods — with which they proved to be very consistent.The conformation of the carboxyl group at position 3 was found to be rather significant to the determination of the energy of the different reaction maxima and minima.     

Visible-light-promoted cc bond cleavage: photocatalytic generation of iminium ions and amino radicals

Photoscissors: Structurally variable and synthetically robust iminium ions and amino radicals species could be simultaneously generated by visible-light-promoted photoredox cleavage of the C?C bonds in simple vicinal diamine precursors under very mild reaction conditions.     

Synthesis and structural investigations of functionalizable hybrid β-hairpin

The solution and solid state conformations of a designed β-hairpin containing functionalizable α,β-unsaturated γ-amino acids at the antiparallel β-strands and a single step transformation to its saturated γ-peptide analogue are studied.     

Theoretical investigations on the thiol–thioester exchange steps of different thioesters

As the rate-determining step in native chemical ligation reactions, the thiol–thioester exchange step is important in determining the efficiency of the ligations of peptides. In the present study, systematic theoretical calculations were carried out on the relationships between the structure of different thioesters and the free energy barriers of the thiol–thioester exchange step. According to the calculation results, the thiol–thioester exchange step is disfavored by the steric hindrance around the carbonyl center, while the electronic effect(i.e. conjugation and hyper-conjugation effects) becomes important when the steric hindrance is insignificant.     

Theoretical insights into the catalytic mechanism of β-hexosaminidase

The enzyme (β-Hex) has a specific role in the degradation of a particular type of glycolipid, the GM2 ganglioside. This specificity is also manifested by its unusual mechanism of substrate-assisted catalysis, which is considered to be an alternative pathway for the breakage of glycosidic bonds. We have studied its catalytic mechanism using a small model of the enzyme: substrate Michaelis complex with DFT and MP2/MP3 methods. The results reflect the intrinsic chemical reactivity of the active site, decoupled from the long-range enzyme electrostatic field. The mechanism supports, and adds further atomic detail, on the earlier mechanistic suggestions based on experimental data. Moreover, we also have compared the geometry and full potential energy surface obtained with nine different exchange–correlation functionals. It was surprising that the B3LYP activation energies were lower than the ones from some of the hybrid meta functionals (known by their excellent performance on kinetics) by as much as 10 kcal/mol and lower than the MP2 energies by more than 12 kcal/mol. It is known that B3LYP underestimates barriers but underestimations of this extent are unusual and surprising. The effect of the theoretical method on the geometry, usually supposed to be less significant, had in some cases a relevant influence in the mechanism. Therefore, a more thoughtful choice should be made when choosing a methodology for geometry optimization.     

Calorimetric investigations of the hydrolytic degradation for a series of β-sultams

The hydrolytic degradation of four β-sultams was investigated using isothermal microcalorimetry to determine kinetic and enthalpic data. Firstly, all four compounds were analysed in the solid-state at 310 K, with a significant substituent-based stabilising/destabilising effect being observed. Secondly, the four compounds were analysed in the presence of pH 4 acetate buffer, at three temperatures (298, 310 and 323 K). Under these conditions, the substituent choice affected the rate of hydrolysis and the associated change in enthalpy for each compound. Based on the calorimetric data presented in this work, no change in reaction mechanism for the hydrolytic degradation was observed over the temperature range considered.     

Hyperaromatic stabilization of arenium ions: a remarkable cis stereoselectivity of nucleophilic trapping of β-hydroxyarenium ions by water

Cis- and trans-1,2-dihydrodiol isomers of benzene undergo acid-catalyzed dehydration to form phenol. In principle the isomeric substrates react through a common β-hydroxybenzenium (cyclohexadienyl) carbocation. Notwithstanding, the isomers show a large difference in reactivity, k(cis)/k(trans) = 4500. This difference is reduced to k(cis)/k(trans) = 440 and 50 for the 1,2-dihydrodiols of naphthalene and 9,10-dihydrodiols of phenanthrene, respectively, and to 6.9 for the dihydrodiols of the nonaromatic 7,8-double bond of acenaphthylene. Because the difference in stabilities of cis- and trans-dihydrodiols should be no more than 2-3-fold, these results imply a high cis stereoselectivity for nucleophilic trapping of a β-hydroxyarenium cation by water in the reverse of the carbocation-forming reaction. This is confirmed by studies of the 10-hydroxy-9-phenanthrenium ion generated from aqueous solvolyses of the trans-9,10-bromohydrin derivative of phenanthrene and the monotrichloroacetate ester of the phenanthrene cis-9,10-dihydrodiol. The cis stereoselectivity of forward and reverse reactions is explained by the formation (in the "forward" reaction) of different conformations of carbocation from cis- and trans-dihydrodiol reactants with respectively β-C-H and β-C-OH bonds in pseudoaxial positions with respect to the charge center of the carbocation optimal for hyperconjugation. Formation of different conformations is constrained by departure of the (protonated) OH leaving group from a pseudoaxial position. The difference in stability of the carbocations is suggested to stem (a) from the greater hyperconjugative ability of a C-H than a C-OH bond and (b) from enhanced conjugation arising from the stabilizing influence of an aromatic ring in the no-bond resonance structures representing the hyperconjugation (C(6)H(6)OH(+) ? C(6)H(5)OH H(+)). This is consistent with an earlier suggestion by Mulliken and a demonstration by Schleyer that the benzenium ion is subject to hyperconjugative aromatic stabilization. It is proposed that, in analogy with the terms homoconjugation and homoaromaticity, arenium ions should be considered as "hyperaromatic".     

Theoretical and crystallographic data investigations of noncovalent S···O interactions

Weak S···O bonding, a specific noncovalent interaction, plays crucial roles in fields as diverse as molecular recognition, crystal engineering, and biological systems. This article presents an ab initio investigation of a series of dimeric complexes formed between formaldehyde and several sulfur-containing molecules as electron accepters. The bond-length change, interaction energy, topological property of the electron density, and charge transfer of these S···O bonds have been systematically investigated. Moreover, a comprehensive search for nonbonded S···O interactions in proteins was also performed. It was found that the O atom shows a strong intrinsic tendency to approach S from the backside of the R–S bond (in the σ_s* direction); the S atom tends to approach the O atom either from the orientation of the lone pair of O (in the n_o direction) or from the vertical direction (in the π_o direction). Besides, the linearity of this interaction was further substantiated by the statistical study. As suggested by the results presented in this study, S···O contacts may control protein structures to some extent and the unique directional properties of S···O interactions could be applied in supermolecular assembly and biological design.     

Crystalline alignment of metal ions templated by β-chitin ester

The highly crystalline β-chitin from diatom Thalassiosira weissflogii was esterified via intercalation with succinic anhydride followed by simple heating, maintaining the original crystalline order. Due to the introduced free carboxyl groups, the chitin ester crystal showed ion exchange ability for metal cations in aq. solution. Heavy metal cations such as Pb²⁺ bound to the β-chitin succinate gave characteristic X-ray diffraction patterns, indicating regular alignment of metal ions. Such materials represent a new type of organometallic architecture, possibly leading to novel functionalities.     

Theoretical studies on the binding energy of β-sheet models

In this paper, B3LYP and MP2 methods are used to investigate the binding energy of seventeen antiparallel and parallel β-sheet models. The results indicate that the binding energy obtained from B3LYP calculations is weaker than that obtained from MP2 calculations but the relative binding energy yielded by B3LYP is almost the same as that by MP2. For the antiparallel β-sheets in which two N-H⋯O=C hydrogen bonds can form either a large hydrogen-bonded ring or a small hydrogen-bonded ring, the binding energy increases obviously when one large ring unit is added, whereas it only changes slightly when one small ring unit is added because of the secondary electrostatic repulsive interaction existing in the small ring unit which is estimated to be about 20 kJ/mol. For the parallel β-sheet models, the binding energy increases almost exactly linearly with the increase of the chain length.     

Theoretical study of spin-spin coupling constants in thecis-enol forms of β-dicarbonyl compounds

The values of the spin-spin coupling constant J(CH) of the bridging proton in the cis-enol forms of -dicarbonyl compounds have been calculated with consideration of the one-dimensional distribution functions of the proton. The results have been compared with the experimental data obtained in the present investigation. The dependence of the spin-spin coupling constants considered on the parameters of the potential of the intramolecular hydrogen bond has been discussed.Institute of Bioorganic Chemistry, Academy of Sciences of the Belorussian SSR, M. V. Lomonosov Moscow State University. Translated from Zhurnal Strukturnoi Khimii, Vol. 32, No. 2, pp. 84–87, March–April, 1991.     

Theoretical Study on the Inclusion Complex of β-Cyclodextrin and Nitrobenzene

Quantum chemical calculations were carried out to investigate the structures and properties for the inclusion complexes of nitrobenzene (NB) into β-cyclodextrin. Two low-energy conformations of β-cyclodextrin (A and B) in the gas phase were initially investigated by the PM3 and B3LYP/6-31+G(d,p) calculations, respectively. Three different orientations were considered in the inclusion process of A and B with NB to form 1:1 complexes. Potential energy scan by PM3 calculations indicated that the phenyl orientation Ab for conformation A and the equator orientation Bc for conformation B are more favorable in energy, respectively. We also considered the 2:1 inclusion complexes of host A or B with guest NB in the gas phase. PM3 calculation indicated that the host-guest interaction energies to form 1:1 complexes are more negative than those to form 2:1 NB/B complexes. Finally, we studied the solvent effect of NB/CD complex, and PM3 results show that the influence of water molecules on the inclusion process is very important. The driving forces for the inclusion process and the geometries of complexes were discussed in detail.     

Contribution of cation-π interactions in iminium catalysis

Ab initio calculations were carried out for a benzyl-substituted iminium cation derived from (E)-crotonaldehyde and a chiral imidazolidinone that was developed as an organocatalyst by MacMillan et al. At the MP2 level of theory it is predicted that the phenyl group is close to the iminium moiety in the most stable conformer, suggesting that the cation-π interaction contributes to the stabilization of this conformer. Energy decomposition analyses on model systems indicate that the electrostatic and polarization terms make significant contribution to the attractive interactions between the benzene ring and the iminium cation.     

The influence of simulation conditions in molecular dynamics investigations of model β-sheet peptides

The influence of simulation methods, cutoff based and particle mesh Ewald (PME) on the accuracy by which experimentally derived nuclear Overhauser effect (NOE) data are reproduced, has been investigated using 500-ns-long molecular dynamics simulations on a model -sheet peptide in explicit solvent. The structural and conformational features under the different conditions were evaluated in terms of flexibility, secondary structure content, hydrogen-bonding pattern and percent of native contacts as a function of time. It was found that the different simulation methods strongly influence the dynamics of the peptide, confirming previous observations based on ideal peptide models simulated for much shorter times. Moreover, the results of our simulations prove once more that it is necessary to reach extremely long time scales to obtain enough statistics to accurately reproduce experimental NOE restraints even in the case of the PME method, despite its tendency to the stabilization of conformations which are structurally closely related to the ones derived through experiment. Possible implications regarding the stabilization and folding mechanisms, together with their relationship to the experimental study of peptide models, are discussed.     

Theoretical study of β- and γ-cyclodextrin complexes with ferrocene-containing azoles

The interaction between cyclodextrins (β- and γ-CD) and ferrocenyl azoles (i.e., pyrazole ferrocenes (I, III–V) and benzimidazole ferrocenes (VI, VII)), along with 1-ferrocenylethanol (II), each in the form of (R)- and (S)-enantiomers, in forming inclusion complexes is studied for the first time using detailed quantum chemical calculations. Compounds are calculated in terms of the density functional theory (DFT), using the Becke–Lee–Yang–Parr (B3LYP) approach in the 6-31G* basis sets. For the considered CD complexes with enantiomers of I–VII, structures in which a guest partially enters a host cavity from the side of the heterocyclic substituent (pyrazole or benzimidazole) are found to be energetically advantageous. It is shown that for successful resolution of (R,S)-enantiomers on chiral phases containing cyclodextrins, we must consider the interaction between outer hydroxyl groups on the CD cone’s surface, in addition to the correspondence of geometric dimensions. The calculated data correlate well with the data from the chromatographic separation of guest enantiomers on cyclodextrin sorbents.     

Theoretical investigations into the enantiomeric and racemic forms of α-(trifluoromethyl)lactic acid

There are many different hypotheses on the origin of biomolecular homochirality. One possible scenario concerns the enantiomeric enrichment of a nearly racemic solid via self-disproportionation of enantiomers. In particular, in a recent paper Soloshonok and co-workers showed a first example of optical self-purification of α-(trifluoromethyl)lactic acid by sublimation [V. A. Soloshonok et al., J. Am. Chem. Soc. 2007, 129, 12112]. Here we present detailed theoretical studies of α-(trifluoromethyl)lactic acid in the solid state as well as in the gas-phase dimeric form. The calculations of energy differences between dimers show that in the solid state the enantiomeric pure compound is energetically preferred, while in the gas phase the equilibrium shifts towards the racemic mixture although thermodynamic corrections cannot be neglected, thus providing a detailed microscopic explanation for the enantio-purification process for the first time.     

Theoretical Study of the Inclusion Processes of Ibuprofen Enantiomers with Native and Modified β-CDs

PM3 calculations in vacuum were performedon the inclusion complexation of-cyclodextrin (-CD),heptakis-(2-O-methyl)--cyclodextrin(2-Me--CD) and heptakis-(6-O-methyl)--cyclodextrin(6-Me--CD) withibuprofen (IB) enantiomers. Inclusion processpathways are described and the most probablestructure of the 1:1 complex are sought througha potential energy scan. The energy differencesbetween the inclusion complexes and the hosts(native and modified CDs) by calculation show thatmodified CDs have much more interaction sites withIB and enhance van der Waals interaction andhydrophobic interaction between them, form morestable complexes than native CD does.Stabilization energies of S-IB complexes arehigher than that of R-IB complexes both for nativeand modified CDs.