Effective Molarities Values Research Articles

ChemInform Abstract: Supramolecular Control of Reactivity and Catalysis — Effective Molarities of Recognition‐Mediated Bimolecular Reactions

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Supramolecular Control of Reactivity and Catalysis – Effective Molarities of Recognition‐Mediated Bimolecular Reactions

AbstractReactivity data relating to bimolecular reactions of compounds featuring complementary recognition sites are critically surveyed and discussed in terms of effective molarity (EM) as an absolute measure of the efficiency of the intracomplex reactions. Comparison of experimentally determined EM values with idealized values estimated for strain‐free cyclizations on the basis of the number of internal rotors in the linker allowed quantification of the penalties of imperfect design in terms of entropy and strain.

Measurement of supramolecular effective molarities for intramolecular H-bonds in zinc porphyrin–imidazole complexes

The association constants for formation of 1 : 1 complexes between five different imidazole ligands and eight different porphyrins have been measured by UV/vis titration experiments in two different solvents, toluene and 1,1,2,2-tetrachloroethane (TCE). Ligands equipped with H-bond acceptors (ester or amide) and porphyrins equipped with H-bond donors (phenol) can make H-bonds in addition to the zinc-nitrogen coordination interaction. The free energy contributions of these H-bonds to the overall stabilities of the complexes were determined using chemical double mutant cycles. Amide-phenol H-bonds contribute up to 5 kJ mol(-1) to the free energy change on complexation, and ester-phenol H-bonds contribute up to 3 kJ mol(-1). Porphyrin-ligand combinations with poor geometric complementarity do not make detectable H-bonding interactions. Effective molarities (EM) for the formation of H-bonds in the complexes were estimated by comparing the equilibrium constants for formation of the intramolecular interaction with the corresponding intermolecular interaction: the values are between 3 mM and 200 mM, which is comparable to previous results obtained for porphyrin-pyridine complexes. The values of EM measured for flexible and rigid ligand systems are comparable. This suggests that there is a trade off between restriction of conformational mobility in the flexible ligands and geometric strain in the rigid ligands, which results in similar binding affinities.

Relationship between Chemical Structure and Supramolecular Effective Molarity for Formation of Intramolecular H-Bonds

Effective molarity (EM) is a key parameter that determines the efficiency of a range of supramolecular phenomena from the folding of macromolecules to multivalent ligand binding. Coordination complexes formed between zinc porphyrins equipped H-bond donor sites and pyridine ligands equipped with H-bond acceptor sites have allowed systematic quantification of EM values for the formation of intramolecular H-bonds in 240 different systems. The results provide insights into the relationship of EM to supramolecular architecture, H-bond strength, and solvent. Previous studies on ligands equipped with phosphonate diester and ether H-bond acceptors were inconclusive, but the experiments described here on ligands equipped with phosphine oxide, amide, and ester H-bond acceptors resolve these ambiguities. Chemical double-mutant cycles were used to dissect the thermodynamic contributions of individual H-bond interactions to the overall stabilities of the complexes and hence determine the values of EM, which fall in the range 1-1000 mM. Solvent has little effect on EM, and the values measured in toluene and 1,1,2,2-tetrachloroethane are similar. For H-bond acceptors that have similar geometries but different H-bond strengths (amide and ester), the values of EM are very similar. For H-bond acceptors that have different geometries but similar H-bond strengths (amide and phosphonate diester), there is little correlation between the values of EM. These results imply that supramolecular EMs are independent of solvent and intrinsic H-bond strength but depend on supramolecular architecture and geometric complementarity.

Computationally-designed phenylephrine prodrugs – a model for enhancing bioavailability

DFT calculations at B3LYP 6-31G (d,p) for intramolecular proton transfer in a number of Kirby's enzyme models demonstrated that the driving force for the proton transfer efficiency is the distance between the two reactive centres (rGM) and the attack angle (α); and the rate of the reaction is linearly correlated with rGM2 and sin (180°- α). Based on these results three phenylephrine prodrugs were designed to provide phenylephrine with higher bioavailability than their parent drug. Using the experimental t1/2 (the time needed for the conversion of 50% of the reactants to products) and EM (effective molarity) values for these processes the t1/2 values for the conversion of the three prodrugs to the parent drug, phenylephrine were calculated. The calculated t1/2 values for ProD 1 and ProD 2 were very high (145 days and several years, respectively) whereas that of ProD 3 was found to be about 35 hours. Therefore, the intra-conversion rates of the phenylephrine prodrugs to phenylephrine can be programmed according to the nature of the prodrug linker.

Quantification of the Effect of Conformational Restriction on Supramolecular Effective Molarities

The association constants for a family of 96 closely related zinc porphyrin-pyridine ligand complexes have been measured in two different solvents, toluene and 1,1,2,2-tetrachloroethane (TCE). The zinc porphyrin receptors are equipped with phenol side arms, which can form intramolecular H-bonds with ester or amide side arms on the pyridine ligands. These association constants were used to construct 64 chemical double mutant cycles, which measure the free energy contributions of intramolecular H-bonding interactions to the overall stability of the complexes. Measurement of association constants for the corresponding intermolecular H-bonding interactions allowed determination of the effective molarities (EM) for the intramolecular interactions. Comparison of ligands that feature amide H-bond acceptors and ester H-bonds at identical sites on the ligand framework show that the values of EM are practically identical. Similarly, the values of EM are practically identical in toluene and in TCE. However, comparison of two ligand series that differ by one degree of torsional freedom shows that the values of EM for the flexible ligands are an order of magnitude lower than for the corresponding rigid ligands. This observation holds for a range of different supramolecular architectures with different degrees of receptor-ligand complementarity and suggests that in general the cost of freezing a rotor in supramolecular complexes is of the order of 5 kJ/mol.

Influence of the Solvent and Metal Center on Supramolecular Chirality Induction with Bisporphyrin Tweezer Receptors. Strong Metal Modulation of Effective Molarity Values

We describe the synthesis of a bisporphyrin tweezer receptor 1·H(4) and its metalation with Zn(II) and Rh(III) cations. We report the thermodynamic characterization of the supramolecular chirality induction process that takes place when the metalated bisporphyrin receptors coordinate to enantiopure 1,2-diaminocyclohexane in two different solvents, toluene and dichloromethane. We also performed a thorough study of several simpler systems that were used as models for the thermodynamic characterization of the more complex bisporphyrin systems. The initial complexation of the chiral diamine with the bisporphyrins produces a 1:1 sandwich complex that opens up to yield a simple 1:2 complex in the presence of excess diamine. The CD spectra associated with the 1:1 and 1:2 complexes of both metalloporphyrins, 1·Zn(2) and 1·Rh(2), display bisignate Cotton effects when the chirogenesis process is studied in toluene solutions. On the contrary, in dichloromethane solutions, only 1·Zn(2) yields CD-active 1:1 and 1:2 complexes, while the 1:2 complex of 1·Rh(2) is CD-silent. In both solvents, porphyrin 1·Zn(2) features a stoichiometrically controlled chirality inversion process, which is the sign of the Cotton effect of the 1:1 complex is opposite to that of the 1:2 complex. In contrast, porphyrin 1·Rh(2) affords 1:1 and 1:2 complexes in toluene solutions with the same sign for their CD couplets. Interestingly, in both solvents, the signs of the CD couplets associated with the 1:1 sandwich complexes of 1·Zn(2) and 1·Rh(2) are opposite. The amplitudes of the CD couplets are higher for 1·Zn(2) than for 1·Rh(2). This observation is in agreement with 1·Rh(2) having a smaller extinction coefficient than 1·Zn(2). We performed DFT-based calculations and assigned molecular structures to the 1:1 and 1:2 complexes that explain the observed signs for their CD couplets. Unexpectedly, the quantification of the thermodynamic stability of the two metallobisporphyrin/diamine 1:1 sandwich complexes revealed the existence of interplay between effective molarity values (EM) and the strength of the intermolecular interaction (K(m); N···Zn or N···Rh) used in their assembly. The EM for the N···Rh(III) intramolecular interaction is 3 orders of magnitude smaller than that for the N···Zn(II) interaction, both of which are embedded in the same scaffold of the 1·M(2) bisporphyrin receptor.

Solvent effects on chelate cooperativity

High-throughput UV/Vis absorption titrations have been used to characterise the properties of 120 different zinc porphyrin–pyridine complexes that contain between zero and four additional intramolecular H-bond interactions. Chemical double mutant cycles were used to measure the free energy contribution of each H-bond in each complex and hence determine the effective molarities (EM) for the intramolecular interactions. The experiments have been carried out in 1,1,2,2-tetrachloroethane (TCE) and previously in toluene. For an ester-phenol H-bond, the strength of the intermolecular H-bond does not change with solvent, and the values of EM for formation of intramolecular interactions are also solvent-independent. Intermolecular phosphonate diester–phenol H-bonds are one order of magnitude stronger than ester–phenol H-bonds in TCE and two orders of magnitude stronger in toluene. However, the differences in intermolecular interaction strength are not fully expressed in the intramolecular interactions. Thus the values of EM measured in TCE are up an order of magnitude larger than the values measured for the same complexes in toluene. This suggests that there may be some internal compensation in cooperative recognition interfaces, where stronger interactions lead to more organised structures reducing the value of EM. There is also evidence of structure specific effects due to differences in the details of the solvation shells of the complexes.

Steric desolvation enhances the effective molarities of intramolecular H-bonding interactions

Free energy contributions due to intramolecular phosphonate diester-phenol H-bonds have been measured for 20 different supramolecular architectures in cyclohexanone solution. High throughput UV/Vis titrations were used in combination with chemical double mutant cycles to dissect out the contributions of different functional group interactions to the stabilities of over 100 different zinc porphyrin-pyridine ligand complexes. These complexes have previously been characterised in toluene and in 1,1,2,2-tetrachloroethane (TCE) solution. Intramolecular ester-phenol H-bonds that were measured in these less polar solvents are too weak to be detected in cyclohexanone, which is a more competitive solvent. The stability of the intermolecular phosphonate diester-phenol H-bond in cyclohexanone is an order of magnitude lower than in TCE and two orders of magnitude lower than in toluene. As a consequence, only seven of the twenty intramolecular phosphonate diester-phenol interactions that were previously measured in toluene and TCE could be detected in cyclohexanone. The effective molarities (EM) for these intramolecular interactions are different in all three solvents. Determination of the EM accounts for solvent effects on the strengths of the individual H-bonding interactions and the zinc porphyrin-pyridine coordination bond, so the variation in EM with solvent implies that differences in the solvation shells make significant contributions to the overall stabilities of the complexes. The results suggest that steric effects lead to desolvation of bulky polar ligands. This increases the EM values measured in TCE, because ligands that fail to replace the strong interactions made with this solvent are unusually weakly bound compared with ligands that make intramolecular H-bonds.

Computer-assisted design for atenolol prodrugs for the use in aqueous formulations

Based on stability studies on the drugs atenolol and propranolol and some of their derivatives it is believed that increasing the lipophilicity of the drug will lead to an increase in the stability of its aqueous solutions and will provide a prodrug system with the potential for releasing atenolol in a controlled manner. Using DFT theoretical calculations we have calculated an intramolecular acid catalyzed hydrolysis in nine maleamic (4-amino-4-oxo-2butenoic) acids (Kirby's N-alkylmaleamic acids), 1-9. The DFT calculations confirmed that the acid-catalyzed hydrolysis mechanism in these systems involves: (1) a proton transfer from the hydroxyl of the carboxyl group to the adjacent amide carbonyl carbon, (2) an approach of the carboxylate anion toward the protonated amide carbonyl carbon to form a tetrahedral intermediate; and (3) a collapse of the tetrahedral intermediate into products. Furthermore, DFT calculations in different media revealed that the reaction rate-limiting step depends on the reaction medium. In aqueous medium the rate-limiting step is the collapse of the tetrahedral intermediate whereas in the gas phase the formation of the tetrahedral intermediate is the rate-limiting step. Furthermore, the calculations establish that the acid-catalyzed hydrolysis efficiency is largely sensitive to the pattern of substitution on the carbon-carbon double bond. Based on the experimental t(1/2) (the time needed for the conversion of 50% of the reactants to products) and EM (effective molarity) values for processes 1-9 we have calculated the t(1/2) values for the conversion of the two prodrugs to the parental drug, atenolol. The calculated t(1/2) values for ProD 1-2 are predicted to be 65.3 hours and 11.8 minutes, respectively. Thus, the rate by which atenolol prodrug undergoes cleavage to release atenolol can be determined according to the nature of the linker of the prodrug (Kirby's N-alkylmaleamic acids 1-9).

Computer-assisted design for paracetamol masking bitter taste prodrugs

It is believed that the bitter taste of paracetamol, a pain killer drug, is due to its hydroxyl group. Hence, it is expected that blocking the hydroxy group with a suitable linker could inhibit the interaction of paracetamol with its bitter taste receptor/s and hence masking its bitterness. Using DFT theoretical calculations we calculated proton transfers in ten different Kirby's enzyme models, 1-10. The calculation results revealed that the reaction rate is linearly correlated with the distance between the two reactive centers (r(GM)) and the angle of the hydrogen bonding (α) formed along the reaction pathway. Based on these results three novel tasteless paracetamol prodrugs were designed and the thermodynamic and kinetic parameters for their proton transfers were calculated. Based on the experimental t(1/2) (the time needed for the conversion of 50% of the reactants to products) and EM (effective molarity) values for processes 1-10 we have calculated the t(1/2) values for the conversion of the three prodrugs to the parental drug, paracetamol. The calculated t(1/2) values for ProD 1-3 were found to be 21.3 hours, 4.7 hours and 8 minutes, respectively. Thus, the rate by which the paracetamol prodrug undergoes cleavage to release paracetamol can be determined according to the nature of the linker of the prodrug (Kirby's enzyme model 1-10). Further, blocking the phenolic hydroxyl group by a linker moiety is believed to hinder the paracetamol bitterness.

The role of proximity orientation in intramolecular proton transfer reactions

Using Becke three-parameter hybrid functional combined with the Lee, Yang, and Parr correlation functional, denoted B3LYP, at 6-31G (d,p) level 21 intramolecular proton transfer reactions were computed. The DFT calculation results revealed that the reaction rate (activation energy) is strongly dependent on the distance between the two reacting centers ( r GM in the ground state and r TS in the transition state), and the hydrogen bonding angle ( α GM) between them. Strong correlations were obtained between the activation energy, Δ G ‡, values on one hand and r GM, r TS and α GM on the other hand. Correlation of calculated effective molarities (EM) with experimental EM values for certain intramolecular proton transfers demonstrates the strength of the DFT methods to predict reaction rate based on calculated geometrical parameters.

Analyzing the efficiency of proton transfer to carbon in Kirby’s enzyme model—a computational approach

A mechanistic study using ab initio and DFT calculation methods on the intramolecular ring-closing of enol ethers 1Z, 1E, and 2 (Kirby’s enzyme models for aldolase and isomerase) has revealed that proton transfer is the rate determining step and involves two stages: re-organization of the global minimum structure (having the lowest enthalpic energy and a relatively long distance between the two reactive centers, r) to a more organized ground state conformation (having the smallest r distance among all the conformations), and a second stage by which the proton is transferred from the organized state to the corresponding transition state. The energy needed for the first stage to occur is dependent on the rotation barrier for the proton to be in proximity to the C C double bond carbon (proximity effects), whereas, that needed for the second step is largely affected by the strain energies of the reactant and the corresponding product. In addition, it was found that the oxocarbocation intermediate involved in the proton transfer is unstable and undergoes ring-closing to the corresponding product with zero activation energy. Further, the calculated DFT effective molarities (EM) for 1Z, 1E, and 2 were found to correlate strongly with experimental EM values.

The effective molarity (EM) – A computational approach

The effective molarity (EM) for 12 intramolecular S N2 processes involving the formation of substituted aziridines and substituted epoxides were computed using ab initio and DFT calculation methods. Strong correlation was found between the calculated effective molarity and the experimentally determined values. This result could open a door for obtaining EM values for intramolecular processes that are difficult to be experimentally provided. Furthermore, the calculation results reveal that the driving forces for ring-closing reactions in the two different systems are proximity orientation of the nucleophile to the electrophile and the ground strain energies of the products and the reactants.

DABCO-Induced Self-Assembly of a Trisporphyrin Double-Decker Cage: Thermodynamic Characterization and Guest Recognition

This paper describes the thermodynamic characterization of the self-assembly of a Zn trisporphyrin induced by coordination with 1,4-diazabicyclo[2.2.2]octane (DABCO) to form a stable 2:3 double-decker molecular coordination cage that recognizes benzene-1,3,5-tricarboxamides. The self-assembly process has been studied using UV-vis and (1)H NMR spectroscopy and quantitatively characterized in terms of a single stability constant that describes the strength of the individual coordination interactions and two effective molarities (EM) that describe the additional stability imparted by intramolecular cyclization. The EM values of the two consecutive cyclic intramolecular interactions are very similar. At micromolar concentrations, the formation of the fully assembled coordination cage is highly favored over the formation of intermediate species stabilized by fewer interactions, and so self-assembly is an all-or-nothing process. In contrast, at millimolar concentrations, the relative stability of intermediate species increases, leading to a stepwise self-assembly process, and a 2:2 intermediate can be clearly identified using (1)H NMR spectroscopy. The molecular recognition of benzene-1,3,5-tricarboxamides by the cage was investigated using (1)H NMR spectroscopy. The tricarboxamides bind inside the central cavity of the cage complex, and isothermal titration calorimetry (ITC) allowed the quantification of the stoichiometry and binding affinities.

Physical basis of self-assembly. Part 2. A theoretical and experimental study of the self-assembly of a zinc meso-pyridyl porphyrin

A previously reported theoretical treatment for self-assembly macrocyclisations occurring under thermodynamic control has been tested experimentally. The fundamental quantities on which the treatment is based are the effective molarity (EM) of the self-assembling cyclic n-mer and the equilibrium constant for the intermolecular model reaction between monofunctional reactants (Kinter). Provided that estimates of EM and Kinter are available, this treatment can be used to predict not only whether the self-assembly process is more or less favoured, but also the distribution of all the species present in solution. Since Kinter values are approximately known from the literature, we have proposed a method, based on molecular modelling techniques, to estimate the EM. The method has been applied to the self-assembly of Zn(PyP3P), where PyP3P is 5-(4-pyridyl)-10,15,20-triphenylporphyrinato dianion. An EM greater than 0.1 mol L−1 has been estimated for its cyclotetramerisation by PM3 calculations, suggesting that self-assembly should be favoured in solvents like toluene and chloroform. Self-assembly of Zn(PyP3P) has been studied in these solvents by UV/visible spectroscopy. The data are consistent with the formation of the cyclotetramer, and at variance with the model of linear polymerisation. The experimental values of the EM were little affected by the nature of the solvent (EM values were 20 mol L−1 in toluene and 15 mol L−1 in chloroform), indicating that the solvent affects the process of self-assembly mainly through the value of Kinter.

Kinetic treatment of irreversible cyclooligomerization of bifunctional chains and its relevance to the synthesis of many-membered rings

The reaction of a bifunctional reactant A-B under batchwise conditions to give macrocycles has been simulated by numerical integration of the proper system of differential rate equations. This was set up considering all the possible processes of concurrent cyclization and polymerization up to a polymerization degree of 12. In order to obtain meaningful yield data for the cyclooligomers, realistic sets of effective molarities (EM) have been considered. The results show how the yields of the various cyclooligomers vary as a function of the initial monomer concentration and provide useful guidelines to achieve maximum selectivity in the synthesis of a given ring. It is clearly shown that the yield of any cyclooligomer is a function of the whole set of EM values. This observation is the basis of a procedure here developed to evaluate EM data from experimental yields of cyclooligomers. Merits and limitations of more simplified kinetic schemes, which had been previously suggested, are discussed in light of the present results. © 1988 American Chemical Society.