Quantification of steric hindrance by geometric calculation, prediction of the reductive selectivity of ketones, and clarification of reaction mechanism

doi:10.21203/rs.3.rs-1715167/v1

Download PDF

Research Article

Quantification of steric hindrance by geometric calculation, prediction of the reductive selectivity of ketones, and clarification of reaction mechanism

https://doi.org/10.21203/rs.3.rs-1715167/v1

This work is licensed under a CC BY 4.0 License

Version 1

posted

You are reading this latest preprint version

Stereoisomers often have different physiological characteristics, and stereocontrol , which includes diastereoselective reduction of carbonyls, is important in the synthesis of pharmaceuticals and natural products. Here, we have developed a model that offers features that have been difficult to achieve simultaneously using conventional methods: reflective of the experimental values of selectivity, applicable to both chained and cyclic ketones, and can quantitatively predict diastereoreductive selectivity. The method, named Moving Sphere Model (MSM), predicts diastereoreductive selectivity by quantifying steric hindrance by the overlapping volume of ketone substrate atoms and a virtual sphere moving in both reaction directions. The reaction mechanism was predicted by examining how the consistency between the calculated selectivity by MSM and the experimental values of selectivity changes when the values of the radius r of the virtual sphere and reaction direction θ are changed. Thus, a reaction mechanism in which only hydride contributes to steric hindrance was inferred for the reduction of ketones by NaBH₄ in MeOH solvent. Meanwhile, for the reduction of ketones with NaBH₄ in ⁱPrOH solvent, a reaction mechanism in which the solvent introduced to the reducing agent also contributes to steric hindrance was inferred. The MSM enabled us to calculate the angle of nucleophilic attack to carbonyls based on experimental facts, to infer the reaction mechanism of the reduction of ketones with NaBH₄ in alcohol solvents, and to predict the reduction selectivity of ketones with NaBH₄ in MeOH solvents.

Ketone

hydride reduction

NaBH4

diastereoselectivity

steric hindrance

Stereoisomers express different physiological properties; thus, stereocontrol is important in the synthesis of natural products and pharmaceuticals. The search for stereoselective reaction conditions [1, 2] and the development of stereoselective reducing agents [3], which are similarly required in the reduction of carbonyls, could be efficiently performed by a model that explains reduction selectivity. Cram pioneered the qualitative explanation of diastereoreductive selectivity by ranking the bulk of substituents for carbonyl compounds with a chiral point at the α-position [4] ; Cram's method was further developed by Felkin et al. to incorporate stereoelectronic effects. Given the qualitative nature of the prediction of reductive selectivity by these methods, we attempted to quantitatively predict the diastereoreductive selectivity of ketones by quantifying steric hindrance in this study.

Quantification of steric hindrance has been addressed from three aspects: experimental, quantum chemical, and geometric calculations. Taft et al. defined the parameter Es for substituent bulkiness based on esterification and hydrolysis rates [5]. Es has been developed by Hancock et al. and Duboi et al. into E_s^c, which accounts for the effect of superconjugation [6], and Es', which is evaluated from a single reaction, [7], respectively Fujita et al. devised a method to express the E_s^c of a substituent represented by CR₁R₂R₃ by a linear combination of the E_s^c of R₁, R₂, and R₃, respectively [8]. Kirilyuk et al. quantified the steric hindrance of substituents around the nitroxide radical by measuring the half-life of the radical [9]. In the reduction of carbonyls, Wigfiel calculated the steric hindrance of the reaction for each substituent of cyclohexanone analogues and predicted the selectivity of diastereoreduction with NaBH₄ in ⁱPrOH solvent [10]. In addition, Sun et al. quantified the relationship between ring size and steric hindrance in cycloalkanes by the reduction rate of cycloalkyl phenyl ketones with NaBH₄ [11]. Murugan quantified the steric hindrance of cyclohexanone analogues by calculating constants for each substituent type and position [12]. These experimental methods are superior in that they reflect real systems; however, prediction is conducted based on experimental values of substrates with similar structures with minimal extrapolation.

We computationally calculated the activation enthalpies ${\Delta }{{H}_{1}}^{‡}$ and ${\Delta }{{H}_{2}}^{‡}$ of the reaction of radical addition to two olefins with different steric hindrance, respectively, and defined the difference in activation enthalpies as a dynamic parameter of steric hindrance (DPSH) and evaluate steric hindrance at the reaction point of radicals [13]. In the reduction of carbonyls, transition state calculations have been used to predict the selectivity of diastereoreduction with NaBH₄ in MeOH solvent [14]. While experimental methods can only be applied to real molecules, quantum chemical calculations can be performed on virtual molecules, whereas experimental methods can only be applied to real molecules. However, quantum chemical methods for determining transition states are difficult to apply uniformly to a large number of systems because the increase in the number of atoms to be considered often causes problems in ensuring the validity of the initial configuration and the convergence of the calculations.

Tolman et al. evaluated steric hindrance in phosphorus ligands of metal complexes using the Tolman cone angle, which is the angle at the top of the cone circumscribed to the ligand [15]. Hirota et al. assumed a light source in a molecule and developed a method to calculate the shadow area created when light emitted from the light source is blocked by the surrounding atoms [16]. Tomilin et al. considered a virtual sphere centered on the reaction point of a radical and calculated the number of atoms inside the sphere [17]. Cavallo et al. used the volume occupied by atoms in the sphere to evaluate steric hindrance [18]. We quantified the volume occupied by atoms in the sphere for steric hindrance of 70 different nitroxide radicals [19]. These geometric methods are superior to transition state calculations because they are computationally less expensive and are more extrapolative than experimental methods. However, these methods are difficult to interpret chemically because they do not consider specific reaction directions.

In this study, we attempted to predict the diastereoreductive selectivity of ketones by developing a model that quantifies the difference in steric hindrance based on the difference in the common volume of a virtual sphere and a substrate atom moving in both reaction directions (Moving Sphere Model, MSM). Despite the existence of kinetic approaches to quantifying steric hindrance in the reduction of carbonyls [20–23], diastereoselectivity, which is the reaction selectivity at the same reaction point in the same molecule as those in Cram's method [4], was used as the target system in this study. In contrast to the method for determining the reaction rate between substrates, the diastereoselectivity method, which reflected the reaction rate at the same reaction point, was considered to be more capable of eliminating electronic factors at the reaction point. To properly evaluate steric hindrance, we targeted substrates without heteroatoms and aromatic rings, which contribute to electrostatic effects and coordination to counter cations in the diastereoreductive selectivity of carbonyls [24]. Here, the variables of the model were optimized with experimental values so that the direction of the reductant reaction can be inferred based on experiments.

Creation of target systems and datasets

Two reaction systems were considered for the experimental conditions: NaBH₄ reduction in methanol solvent (NaBH₄/MeOH system) and NaBH₄ reduction in isopropanol solvent (NaBH₄/ⁱPrOH system). The substrate structure (SMARTS) in terms of diastereomeric ratio, diastereomeric ratio of the product (dr.), and experimental temperature were used for the data (SI).

Application of the sphere model

For each substrate structure information, 10 structures were generated by the Experimental-Torsion Distance Geometry(ETDG) method [25], and similar structures were eliminated using a threshold of 0.1 Å as the value of the root mean square error of each atom position. The optimized structure and energy H were subsequently obtained by MMFF94 [26]. Here, the OC-H bond distances (1.09927 Å for isopropoxide:[O-]C(C)C and 1.10064 Å for cyclohexoxide:[O-]C1CCCCCCC1) of the most stable conformations of the reaction intermediates obtained by the calculations under the conditions of the previous sentence were calculated. The sum V of the maximum overlapping volume of the substituent atom spheres and the virtual sphere of radius r moving in the part of the half line starting from the reaction point at an angle θ relative to the carbonyl atoms beyond 1.10 Å (OC-H bond distance of the reaction intermediate) was calculated (Figs. 1 and SI). The substituent atom sphere was defined as a sphere with Pauling's van der Waals radius [27] (C: 1.7 Å, H: 1.2 Å) for substrate atoms other than carbonyl and a total of four atoms at the α-position. Here, Brown described the reduction rate of carbonyl compounds in the NaBH₄/ⁱPrOH system using Eq. 3 [20].

$$\begin{array}{c}v=k\left[A\right]\left[B\right]\left(3\right)\end{array}$$

Given that the contributions of substrate concentration [A] and reductant concentration [B] to the reaction on both sides in the diastereoselective reduction can be considered equal, only the reaction rate constant k needs to be considered. The diastereomeric ratio (dr.) was calculated from the ratio of the relative reaction rate constants k (Eq. 2) for both sides calculated based on the Arrhenius-type equation weighted by the Boltzmann distribution (Eq. 3).

$$\begin{array}{c}k={{\Sigma }}_{\text{i}}\left[\text{exp}\left(-\frac{cV+H}{RT}\right)\right]\left(2\right)\end{array}$$

H is the energy of the conformation, $R$ is the gas constant($1.987 \text{c}\text{a}\text{l} \text{m}\text{o}{\text{l}}^{-1} {\text{K}}^{-1}$), T is the temperature of the system, and c is a constant.

$$\begin{array}{c}dr.=\frac{{k}_{up}}{{k}_{up}+{k}_{down}}\left(3\right)\end{array}$$

The subscript of k is the reaction surface.

Optimization of MSM and validation of predictability

Calculation 1

Selectivity values were calculated using a model with each variable value set to θ = 5°–170° (Δ = 5°) and r = 0.1–4.9Å (Δ = 0.1 Å) for each substrate (28 data for NaBH₄/MeOH system and 30 data for NaBH₄/ ⁱPrOH system). The variable c was optimized for each combination of θ and r (SI). The RMSE of the experimental values for the calculated values of selectivity was calculated, and its relationship with the combination of θ and r was illustrated.

Calculation 2

For each of the 28 data in the NaBH₄/MeOH system, predictability was tested by leave-one-out around the optimal solution of r and θ in Calculation 1. For each of the 28 data, the experimental value (expt.) was calculated relative to the predicted value (pred.).

Discussion of optimal values of r and θ

The relationship between r, θ, and root mean square error (RMSE) values is shown in Fig. 2, where the optimal solution exists at approximately θ = 85° and r = 0.8 Å for the NaBH₄/MeOH system. The nucleophilic angle of attack on the carbonyl was estimated to be the Bürgi–Dunitz angle (BD angle, 107°) by both crystallographic and quantum chemical calculations [28]. Considering the migration of substituents to the opposite plane as the reaction proceeds, the optimal θ = 90° for the NaBH₄/MeOH and 85° in the NaBH₄/MeOH system are considered reasonable for the BD angle.

In the NaBH₄/ⁱPrOH system, the RMSE is smaller than that of the peripheral region for a wide range of r, θ. Brown proposed a reaction mechanism in which a solvent is incorporated in the reduction of carbonyls with NaBH₄ in an alcohol solvent based on the fact that the reduction of carbonyls with NaBH₄ is enhanced by the addition of alcohol (Fig. 3) [21]. In the reaction mechanism proposed by Brown, different reductants with different numbers of introduced solvents are considered to produce the reaction. Among the alkoxides introduced into the reductants, the effect on r,θ is limited for bulky alkoxides such as methoxide; however, for isopropoxide, the r,θ of the reaction mechanism changes with the number of alkoxides introduced. Therefore, in the reaction with ⁱPrOH, which is larger than MeOH, multiple reductants with different bulk sizes were produced, resulting in multiple reduction reactions with different r and θ values. This reason explained why regions with smaller RMSE than the periphery were observed for a wide range of r and θ in the NaBH₄/ ⁱPrOH system.

Leave-one-out results

For each of the 28 NaBH₄/MeOH systems, predictability was tested using θ,r,c optimized by 27 data other than itself (leave-one-out). To optimize the system, c was optimized for all variable combinations θ = 50°–110 ° (Δ = 5°) and r = 0.4–1.5 Å (Δ = 0.1 Å) around the optimal solution of r,θ for the NaBH₄/MeOH system in Experiment 1 to obtain the pair of r,θ that gave the minimum value of the optimal RMSE. The predicted results of all leave-one-out evaluation data in the NaBH₄/MeOH system are shown in Fig. 4. This system contains a wide range of both cyclic and linear ketones but yields a result of RMSE = 15.9%.

Although generally good results were obtained, we discussed the outlier 4-substituted cyclohexanones (Ent. 17, Ent. 28, as seen in Fig. 5). The first effect is the topological bond distance from the reaction center. Considering the topological bond distances from the axial reaction point in 4-substituted cyclohexanones, the 3,5-axis hydrogen in cyclohexanone-substituted compounds is less mobile and more sterically hindered than the 2,6-axis hydrogen. The influence of bonding state on steric hindrance was also suggested in our previous study [19].The second effect is the superconjugation of the C-H σ orbital and the carbonyl π orbital at position 4. For cyclohexanone substituents, a model has been proposed in which the C-H σ orbital and the carbonyl π orbital at the 4-position in the boat configuration are spatially close to each other, resulting in superconjugation, and in which the carbonyl π* orbital extends toward the substituent R, thereby contributing to increased trans selectivity [29]. This model cannot consider the effects of bonding states or orbitals; therefore, the effect of the bonding state and orbital on 4-substituted cyclohexanones, which considerably affect the bonding state and orbital, is difficult to predict.

In this study, we developed an MSM that quantifies steric hindrance by geometric calculations. In MSM, the direction of the reductant can be inferred by optimizing the values of the variables r and θ based on experimental values. In the NaBH₄/MeOH system, MSM gave reasonable optimum θ values; quantification of the effects of bonding states and superconjugation, which were considered sources of error in the NaBH₄/MeOH system, provided better predictions. The r and θ values were not optimized to a single point in the NaBH₄/ⁱPrOH system presumably because of the steric hindrance of the alcohol solvent introduced into NaBH₄. We are currently investigating ways to obtain the large amount of experimental data necessary to describe complex conformations.

*Authors' contributions

All authors contributed to the project, and the main contributions were as follows: conceptualization, SD and HG; methodology, SD, and ; validation, SD; investigation, AK and SS; resources, SD; writing – original draft preparation, SD; writing – review and editing, and HG; visualization, AK and TF; supervision, HG; project administration, HG; funding acquisition, HG All authors have read and agreed to the published version of the manuscript.

*Competing Interests

The authors declare no competing interests.

*Availability of data and material

The electronic supplementary material is available.

*Code availability

Not applicable

*Funding

Herewith, the authors declare that no funds, grants, or other support were received during the preparation of this manuscript.

*Conflicts of interest/Competing interests

Not applicable

Fujisawa, T.; Kojima, E.; Itoh, T.; Sato, T. Diastereo- and Enantioselective Reduction of α,β-Diketodithiane with the Baker’s Yeast. Tetrahedron Letters 1985, 26 (49), 6089–6092. https://doi.org/10.1016/S0040-4039(00)95133-5.
Honma, M.; Nakada, M. Enantioselective Total Synthesis of (+)-Digitoxigenin. Tetrahedron Letters 2007, 48 (9), 1541–1544. https://doi.org/10.1016/j.tetlet.2007.01.024.
Tsurumaki, E.; Sung, J.; Kim, D.; Osuka, A. Subporphyrinato Boron(III) Hydrides. J Am Chem Soc 2015, 137 (3), 1056–1059. https://doi.org/10.1021/ja5126269.
Donald J. Cram, F. A. A. E. Studies in Stereochemistry. X. The Rule of ”Steric Control of Asymmetric Induction” in the Syntheses of Acyclic Systems. 1952, 74, 5828–5835.
Taft, R. W. Polar and Steric Substituent Constants for Aliphatic and ο-Benzoate Groups from Rates of Esterification and Hydrolysis of Esters. J Am Chem Soc 1952, 74 (12), 3120–3128. https://doi.org/10.1021/ja01132a049.
Hancock, C. K.; Meyers, E. A.; Yager, B. J. Quantitative Separation of Hyperconjugation Effects from Steric Substituent Constants. J Am Chem Soc 1961, 83 (20), 4211–4213. https://doi.org/10.1021/ja01481a027.
John Anthony MacPhee, Annick Panaye, J.-E. D. OPERATIONAL DEFINITION OF THE TAFT STERIC PARAMETER. AN HOMOGENEOUS SCALE FOR ALKYL GROUPS - EXPERIMENTAL EXTENSION TO HIGHLY HINDERED GROUPS. Tetrahedron Letters 1978, No. 35, 3293–3296.
Toshio Fujita, Chiyozo Takayama, and M. N. The Nature and Composition of Taft-Hancock Steric Constants. THE JOURNAL OF Organic Chemistry 1973, 38 (9), 1623–1630.
Kirilyuk, I. A.; Bobko, A. A.; Grigor’ev, I. A.; Khramtsov, V. v. Synthesis of the Tetraethyl Substituted PH-Sensitive Nitroxides of Imidazole Series with Enhanced Stability towards Reduction. Organic and Biomolecular Chemistry 2004, 2 (7), 1025–1030. https://doi.org/10.1039/b400252k.
Murugan, R. Quantitative Prediction of Stereochemistry in the Reduction of Cyclohexanones by Sodium Borohydride. Canadian Journal of Chemistry 1980, 58 (18), 1993–1995. https://doi.org/10.1139/v80-316.
Sun, S. F.; Neidig, P. R. The Effect of Ring Size on the Rate of Reaction of Cycloalkyl Phenyl Ketones with Sodium Borohydride. Journal of Organic Chemistry 1969, 34 (6), 1854–1856. https://doi.org/10.1021/jo01258a071.
Murugan, R. Quantitative Prediction of Stereochemistry in the Reduction of Cyclohexanones by Sodium Borohydride. Canadian Journal of Chemistry 1980, 58 (18), 1993–1995. https://doi.org/10.1139/v80-316.
Yamazaki, Y.; Naganuma, J.; Gotoh, H. A Theoretical, Dynamical Evaluation Method of the Steric Hindrance in Nitroxide Radicals Using Transition States of Model Reactions. Scientific Reports 2019, 9 (1), 1–11. https://doi.org/10.1038/s41598-019-56342-w.
Suzuki, Y.; Kaneno, D.; Tomoda, S. Theoretical Study on the Mechanism and Diastereoselectivity of NaBH 4 Reduction. Journal of Physical Chemistry A 2009, 113 (11), 2578–2583. https://doi.org/10.1021/jp809966u.
Tolman, C. A. Steric Effects of Phosphorus Ligands in Organometallic Chemistry and Homogeneous Catalysis. Chemical Reviews 1977, 77 (3), 313–348. https://doi.org/10.1021/cr60307a002.
Tamiki Komatsuzaki, K. S. M. H. A New Method for Evaluating the Steric Hindrance by Substituent. Tetrahedron Letters, 1989, 30 (25), 3309–3312.
Tomilin, O. B.; Tanaseichuk, B. S.; Boyarkina, O. V. Estimation of Steric Hindrances at the Dimerization of Free Organic Radicals. Russian Journal of Organic Chemistry 2016, 52 (11), 1576–1586. https://doi.org/10.1134/S1070428016110051.
Cavallo, L.; Correa, A.; Costabile, C.; Jacobsen, H. Steric and Electronic Effects in the Bonding of N-Heterocyclic Ligands to Transition Metals. Journal of Organometallic Chemistry 2005, 690 (24–25), 5407–5413. https://doi.org/10.1016/j.jorganchem.2005.07.012.
Naganuma, J.; Yamazaki, Y.; Gotoh, H. Evaluation Method of Steric Shielding Effect around Nitroxide Radical Reaction Center Based on Molecular Volume within a Virtual Ball. Structural Chemistry 2019, 30 (6), 2085–2092. https://doi.org/10.1007/s11224-019-01335-8.
Edward R. Garrett, D. A. L. The Kinetics of 20-Keto Reduction in Lla-Ace- Toxypregnane-3,20-Dione by Sodium Borohydride. JACS 1953, 75 (23), 6051.
Herbert C. Brown, Edward J. Mead, B. C. S. R. A Study of Solvents for Sodium Borohydride and the Effect of Solvent and the Metal Ion on Borohydride Reductions. 1955, 77 (23), 6209–6213.
Brown, H. C.; Wheeler, O. H.; Ichikawa, K. Chemical Effects of Steric Strains-XIII. Kinetics of the Reaction of Sodium Borohydride with Carbonyl Groups-a Convenient Tool for Investigating the Reactivities of Aldehydes and Ketones. Tetrahedron 1957, 1 (3), 214–220. https://doi.org/10.1016/0040-4020(57)88041-7.
Ichikawa, H. C. B. and K. The Effect of Ring Size on the Rate of Reaction of the Cyclanones with Sodium Borohydride. Tetrahedron 1957, 1 (3), 221–230.
Chérest, M.; Felkin, H.; Prudent, N. Torsional Strain Involving Partial Bonds. The Stereochemistry of the Lithium Aluminium Hydride Reduction of Some Simple Open-Chain Ketones. Tetrahedron Letters 1968, 9 (18), 2199–2204. https://doi.org/10.1016/S0040-4039(00)89719-1.
Riniker, S.; Landrum, G. A. Better Informed Distance Geometry: Using What We Know to Improve Conformation Generation. Journal of Chemical Information and Modeling 2015, 55 (12), 2562–2574. https://doi.org/10.1021/acs.jcim.5b00654.
Halgren, T. a. Merck Molecular Force Field. J. Comput. Chem. 1996, 17 (5–6), 490–519.
Batsanov, S. S. Van Der Waals Radii of Elements. Inorganic Materials 2001, 37 (9), 871–885. https://doi.org/10.1023/A:1011625728803.
Bürgi, H. ‐B. Stereochemistry of Reaction Paths as Determined from Crystal Structure Data—A Relationship between Structure and Energy. Angewandte Chemie International Edition in English 1975, 14 (7), 460–473. https://doi.org/10.1002/anie.197504601.
Uchiyama, F. Stereoselectivity and Vertical Polarity Hypothesis for Carbonyl Addition Theoretical Hypothesis : 2019, 1–5.

No competing interests reported.

Download PDF

Version 1

posted

You are reading this latest preprint version

Quantification of steric hindrance by geometric calculation, prediction of the reductive selectivity of ketones, and clarification of reaction mechanism

Status:

Version 1

Abstract

Figures

Introduction

Experimental

Creation of target systems and datasets

Application of the sphere model

Optimization of MSM and validation of predictability

Calculation 1

Calculation 2

Results And Discussion

Discussion of optimal values of r and θ

Leave-one-out results

Conclusion

Declarations

References

Additional Declarations

Supplementary Files

Status:

Version 1