Quantum chemical study of 5,5-dimethyl-1,3-dioxane isomerization to 2,2-dimethyl-3-methoxypropanal, - the general reaction scheme

The results of quantum chemical simulation by B3PW91 method in the 6-31G(d,p) basis for formation of 2,2-dimethyl-3-methoxypropanal from 5,5- dimethyl- 1,3- dioxane in the presence of proton are given. The proposed reaction scheme involves protonation of the parent molecule - formation of the oxonium ion, breaking of C-0 bond with receipt of alkoxycarbenium ion, rearrangement of the alkoxycarbenium ion by two successive 1,3-displacement or 1,5 displacement of positive charge, deprotonation of the oxycarbenium ion with formation of the reaction product. Data on the structure and energy characteristics of molecular products, ions, and transition states are obtained not only for the states characterized minimum Gibbs energy (G298, δG298, δG# 298), but also for possible conformers and transitions between them. Based on the calculations, an energy diagram is drawn up in accordance with the general reaction scheme. Comparison of the estimated activation barriers (δG# 298) for implementation of the reaction in two stages (1,3-migrations) and one-stage 1,5-migration showed that they are comparable in size, the difference is about 2 kcal/mol. Since conversion of 5,5- dimethyl- 1,3- dioxane to 2,2-dimethyl-3-methoxypropanal is an endothermal reaction with heat absorption of 3.4 kcal/mol, it can be assumed that in real conditions transformation of ions as per the reaction coordinate will include both two-stage and one-stage conversion of alkoxycarbenium ion to the oxycarbenium ion.


Introduction
Some examples of isomerization of 1,3-dioxanes in the presence of acid catalysts are known [1,2]. 1,3-Dioxanes with substituents at C(4) form tetrahydropyranols, which are easily transformed into dihydropyrans [3]. Presence of substituents at C(5) provides for isomerization of 3-methoxypropanal. Rearrangement occurs at an elevated temperature in the presence of pumice or silica gel, which have the properties of weak acids [4][5][6].
It should be noted that there is no experimental data on the possibility of rearranging in liquid phase 5,5-disubstituted 1,3-dioxanes into the corresponding alkoxypropanals in the liquid phase. On the other hand, it is known that acyclic acetals are converted to alkoxycarbenium ions as a result of the carbenium center displacement [7][8][9].
. The study of the behavior of 1,3-dioxanes that do not contain substituents at C(2) in superacid media showed that the first stage of the reaction includes formation of cyclic oxonium ion, which  [10]. The structure of these ions [11,12] suggests the possibility of the reaction center displacement to form a new alkoxycarbenium ion.
Quantum chemical calculations of non-substituted, 2-methyl-, 5-methyl-and 2,5-dimethyl-1,3dioxanes indicate this possibility, since the activation energy of the limiting stage is 21.7-33.1 kcal/mol [13]. On the other hand, it has been experimentally shown that in the presence of zeolites, the reaction products formation is associated with ion hydrogenation, isomerization, splitting, and their combinations. 3-Methoxypropanols are present in small quantities among the reaction products (at temperatures of 400-440 0 C) [14]. It is possible that the relatively high temperatures and mobility of the hydrogen atom at C(5) are the reasons for low selectivity of the transformations directions.

Materials and methods
The calculations were performed using the PC GAMESS FireFly 8.2.0 software [13].
The geometry of molecules, transition states and all possible ion conformations is optimized using the density functional method [16] (B3PW91/6-31+G(d,p)). This method is applicable for calculating the states with closed and open shells and conveys well the geometric parameters of 1,3-dioxanes [17]. Identification of stationary points on PPE surface was carried out by the Hessian analysis. The Gibbs energy (G 298 ) values at a temperature of 298.15 K are determined.

Results
Transition of 5,5-dimethyl-1,3-dioxane (1) to 2,2-dimethyl-3-methoxypropanal (2) involves several stages: protonation of molecule 1 to form oxonium ion 3; dissociation of the C─O bond in the oxonium ion, which leads to formation of alkoxycarbenium ion 4; migration of the carbenium center in ion 4, which can proceed in two directions -either two successive 1,3-migrations (formation of ion 5 and its transition to ion 6), or formation of ion 6 in one stage, i.e. 1,5-migration of the positive charge.
Deprotonation of ion 6 leads to the reaction product -molecule 2 (figure 1). Ions 3 formed by protonation of molecule 1 are structurally as chair and twist conformations with axial or equatorial orientation of the bond OH + . In addition, it is possible to assume the possibility of implementation of other conformations of ion 3. However, it is known that such ions have high energies [18][19][20][21], so the ion in boat-like conformations have not yet been analyzed.
Analysis of energy transitions between ions 3 indicates the possibility of all isomers, activation barriers are 6.8-13.6 kcal/mol (table 1). The difference in the energy of the formed 3 ions is 4.3 kcal/mol, and the transition states of TS3 are about 6.8 kcal/mol. It can be assumed that when the reaction is implemented in real conditions, the formation of all 3 ions is possible.
Transformation of oxonium ions 3 to alkoxycarbenium ions 4 involves the С─О bond rupture. This reaction stage proceeds with heat absorption, the thermal effect is about 10 kcal/mol, and the energy of transition states equals from 8.2 to 29.3 kcal/mol (table 1). , the energy of ion 3 in the chair-like conformation with the axial orientation of the proton is assumed (G 298 = -242432.7 kcal/mol) as the initial (zero) level Analysis of the geometric characteristics of ions 4 shows that their formation is associated with different spatial locations of СН 3 ─СНО + and ─CH 2 OH fragments due to their rotation C(4) ─C(5) and C(5) ─C(6), as well as fragments of CH 2 O + and OH due to rotation around bonds O(1) ─C (6)  Transition between groups of 5 and 6 ions is possible through transition states TS5-6 with penetration of the barrier from 6.7 to 19.6 kcal/mol, the endothermal effect reaches 8.1 kcal/mol.
The transformation of ions 4 → 5 → 6 represents two successive rearrangements leading to 1,3displacements of the carbenium center. An alternative option of ion 6 formation consists in direct isomerization of ion 4 to ion 6, i.e. 1.5-rearrangement. Calculation of energy parameters of the rearrangement shows that its implementation occurs through barriers of 18.8 kcal/mol, which correspond to two transition states (table 1) Comparison of activation energies during the transition of ion 4 to ion 6 in two stages (4 → 5 → 6) or in one stage (4 → 6) shows that the direct transformation of ion 4 to ion 6 occurs with lower energy costs. However, the difference in the energies of two and one-stage transitions is not great, it is only 2.2 kcal/mol. In this regard, it can be assumed that in real conditions the isomerization of 5,5dimethyl-1,3-dioxane to 2,2-dimethyl-3-methoxypropanal can occur with implementation of the ion rearrangement mechanism both in two or in one stage.