Reaction Mechanism About Isomerization of Resin Acids and Synthesis of Acrylopimaric Acid Based on DFT Calculation

Acrylopimaric acid is considered one of the possible substitutes for petroleum-based polymeric monomers, which is an important industrial product. Resin acids were isomerized to form levopimaric acid(4), which reacted with acrylic acid to synthesize isomers of acrylopimaric acid. Density functional theory calculation was used to investigate the reaction mechanisms with seven reaction paths in five different solutions. The values of ΔG were sorted from highest to lowest by levopimaric acid(4), neoabietic acid(3), palustric acid(2), and bietic acid(1). From the perspective of dynamics, the energy barrier in the isomerization of palustric acid(2) to levopimaric acid(4) was the lowest, whereas the highest energy barrier was the isomerization of neoabietic acid(3) to levopimaric acid(4) in the same solution. The addition reaction of levopimaric acid(4) and acrylic acid(5) to acrylopimaric acid c(8) was the optimal reaction path dynamically. However, ΔG of acrylopimaric acid c(8) was higher than that of acrylopimaric acid d(9). In general, the rates of isomerization reactions for rosin resin acids and addition reaction for acrylopimaric acid in water were higher than those in other solvents. HOMO-LUMO and ESP were analyzed for 8 kinds of molecules. For acylpyimaric acid, the non-planar six-memed ring and the C-C double bonds were easily attacked by nucleophile, while the non-planar six-memed ring and the carboxyl group are easily reacted with electrophiles. The highest electrostatic potential of the eight molecules is located at H of the carboxyl group, while the highest electrostatic potential is located at C-O double bond of the carboxyl group.


INTRODUCTION
As a kind of renewable biomass resource, rosin is a crucial forest chemical product [1,2] . However, rosin as a natural resin is used directly, and its additional value needs to be further improved [3] . Rosin resin acids are tricyclic diterpenoid isomers with various components, of which the main component is abietic resin acid [4] . Levopimaric acid(4) with conjugated double bond structure can be formed continuously through the isomerization of abietic acid(1), palustric acid (2), and neoabietic acid(3) under heating condition (Scheme 1) [5] . Levopimaric acid(4) can react with acrylic acid through the Diels-Alder reaction to form isomers of acrylopimaric acid c (8) and acrylopimaric acid d (9) under microwave heat (Scheme 2) [6,7] . As an important modification product of rosin, its additional value is greatly improved. Given that its structure is similar to that of petroleum-based aromatic dicarboxylic acids, such as isophthalic acid and terephthalic acid, acrylopimaric acid is considered one of the possible substitutes for petroleum-based polymeric monomers [8,9] . The modification and application of acrylopimaric acid have been reported in the literature [10] . For example, acrylopimaric acid is prepared into surfactants, UV-curable coatings, polyurethane, epoxy resin, and polyester [11,12] . However, the mechanisms underlying the isomerization of levopimaric acid and the Diels-Alder addition reaction of acrylpimaric acid have not been studied in detail.
Quantum chemistry is one of the most reliable methods to study the mechanism of microscopic reactions [13] .
Quantum chemistry theory, density functional theory (DFT), and molecular dynamics play an important role in the study of organic reactions [14] . DFT has become a reliable and powerful tool for studying the kinetics, byproduct formation, and mechanism of organic reactions at the molecular level [15][16][17][18] . DFT was used to investigate the formation of acrylopimaric acid, and the effects of different solutions on the reaction were discussed. The isomerization of the four resin acids and the addition mechanism of acrylopimaric acid should be revealed to provide a theoretical basis for the large-scale synthesis of acrylopimaric acid, the selection of appropriate solvents, and the optimization of related process parameters.

DFT calculations
Theoretical calculation was performed using Gaussian 09 software [19] . Geometric optimization of the reactants, products, and transition state (TS) [20] structures was performed at the M062X/ 6-31G (d) level using the SMD [21] solvent model, and the temperature was set at 453 K. All reactants and products had no imaginary frequency, and the TS had only one virtual frequency. Intrinsic reaction coordinate analysis was performed at the same level to verify the relationship among reactants, TSs, and products [22] . M062X/def2TZVP was used to calculate the single point energy and obtain more precise results with the SMD solvent model. Gibbs free energies were corrected [23,24] .
According to the thermodynamic formula of TS theory (TST), the rate constant is calculated as follows [25,26] : , and

Reaction mechanism and reaction paths
The mechanism underlying the isomerization of acid resins is shown in Scheme 3, and the reaction of levopimaric acid with the addition of acrylic acid via four reaction paths is shown in Scheme 4. In all reactions, the structures of stationary points are shown in Fig. 1 and C18-C19 became single bonds, and the conjugated double bonds formed C16-C19 and C11-C18. Palustric acid (2) isomerized to levopimaric acid (4). H on C16 migrated to C20. Neoabietic acid(3) isomerized to levopimaric acid(4).
The C-C double bond of acrylic acid(5) gradually approached the C18-C19 single bond of levopimaric acid(4), and the six-membered ring of the conjugated double bond of levopimaric acid(4) became non-coplanar, forming a boat structure. The double bond between C18 and C19 became a single bond, and H was not migrated during this process. As a result of the different locations of the addition reaction between levopimaric acid(4) and acrylic acid (5)

Thermodynamics and kinetics of reactions in different solvents
From the perspective of thermodynamics, the isomerizations of bietic acid (1), palustric acid (2), and neoabietic acid(3) into levopimaric acid(4) exhibited an exothermic reaction ( Table 1). The values of ΔG were sorted from highest to lowest by levopimaric acid (4), neoabietic acid (3), palustric acid (2), and bietic acid(1). ΔG of levopimaric acid(4) was 19.25 KJ/mol in the solvent-free reaction and 18.22 KJ/mol in acetic acid, which was higher than the value of bietic acid (1). From the perspective of dynamics, the energy barrier in the isomerization of palustric acid (2) to levopimaric acid(4) was the lowest, whereas the highest energy barrier was the isomerization of neoabietic acid (3) to levopimaric acid (4) (4) indicates that the hydrogen transfer in the reaction is harsh. In the experiment, the reactants are usually heated by microwave to a high temperature of 453-523 K, with long reaction time of 1.5-10 h. The calculation is verified with the experimental results [6] .
From the perspective of thermodynamics, the Diels-Alder addition reaction of levopimaric acid(4) and acrylic acid(5) to acrylopimaric acid was exothermic ( Table 2). The ΔG value of acrylopimaric acid d(9) was the lowest, and the addition reaction of levopimaric acid(4) and acrylic acid(5) to acrylopimaric acid d(9) was the optimal reaction path thermodynamically. However, from the perspective of dynamics, the energy barrier in the addition reaction of levopimaric acid(4) and acrylic acid(5) to acrylopimaric acid c(8) was the lowest ( Table 3). The energy barrier of TS49 in the process of generating acrylopimaric acid d(9) was 13.99 KJ/mol higher than that of TS48, which was lower than that of TS46 and TS47. The addition reaction of levopimaric acid(4) and acrylic acid (5) to acrylopimaric acid c(8) was the optimal reaction path dynamically. The energy barriers generated by the addition of levopimaric acid(4) and acrylic acid(5) to acrylopimaric acid c(8) or acrylopimaric acid d (9) in aqueous solution were lower than those of other solvents.
The reaction rates k of isomerizations in order from fast to slow were palustric acid(2), abietic acid(1), and neoabietic acid(3) as shown in Table 4. The reaction rates k of the isomerizations of abietic acid(1) and neoabietic acid(3) in aqueous solution were faster than those of other solvents. However, the reaction rate k of the isomerization of palustric acid(2) to levopimaric acid(4) in DMSO solution was faster than that of other solvents. The reaction rates k of the addition reaction of levopimaric acid(4) and acrylic acid(5) to acrylopimaric acid in aqueous solution were faster than those of other solvents. However, the reaction rates k were lower in varying degrees in DMF solution and acetic acid solution. Therefore, water is a better solvent for the reactions than the other solvents.

HOMO-LUMO analysis
The energies of HOMO and LUMO are calculated to obtain an overall description of the reaction [27,28] . The gap between HOMO and LUMO is determined by the chemical reactivity, kinetic stability, and electronic properties of the molecule [29] . The HOMO of the molecule has a relatively loose bond to its electrons and has an electron donor property, whereas the LUMO has a strong affinity for electrons and has an electron acceptor property. I (-EHOMO) and As shown in figure 4, the active sites of the four isomeric resin acids were the C-C double bonds where the sixmember ring is located, and both C-C double bonds are easily attacked by both electrophiles and nucleophiles. For acylpyimaric acid, the non-planar six-memed ring (C53 and C55) and the C-C double bonds were easily attacked by nucleophile, while the non-planar six-memed ring (C9 and C15) and the carboxyl group (O1 and O2) are easily reacted with electrophiles. Given the similar structure of isomers, the greater the gap of HOMO-LUMO, the higher the chemical stability of the molecule. The gap of abietic acid(1) was 0.2111 eV higher than that of palustric acid(2), whereas the gap was 0.1859 eV higher than that of neoabietic acid(3) ( Table 5). Combined with the previous calculation of TS, neoabietic acid(3) was the easiest to be isomerized into levopimaric acid(4), followed by palustric acid(2); the isomerization rate of abietic acid (1)

ESP analysis
The ESP V(r) is generated by the nuclei and electrons of the molecule in the surrounding space and is defined as follows [30] : ZA is the nuclear charge at the RA distance of molecule A, and r(r') is the electron density. Multiwfn 3.4.7 software was used to analyze the vander surfaces of molecules [31] . The molecule was analyzed by ESP at the M062X/def2TZVP level. Based on the output file of Multiwfn program, the molecular surface ESP isosurface was rendered by VMD 1.9.3 program [32] .
ESP analysis of molecules is not related to reactivity, but it can provide theoretical basis for discussing molecular interactions. From Fig. 5, the red and blue grid surfaces are positive and negative potentials, respectively.
The yellow and green spheres represent extremely high and low points, respectively [33] . The areas are colored in white with potential close to zero. The highest electrostatic potential of the eight molecules is located at H of the carboxyl group, while the highest electrostatic potential is located at C-O double bond of the carboxyl group. The C-C double bond potentials of the four isomeric resinic acids are negative, and the C-C potentials of the allimaric acid are slightly positive. Regions with high electrostatic potential of molecules may interact with highly electronegative parts of other molecules, including solvent molecules.

CONCLUSION
Under the protection of nitrogen atmosphere, the resin acids were isomerized to form levopimaric acid(4).
Levopimaric acid(4) reacted with acrylic acid through the Diels-Alder reaction to synthesize isomers of acrylopimaric acid. The values of ΔG were sorted from highest to lowest by levopimaric acid(4), neoabietic acid (3), palustric acid (2), and bietic acid (1). The addition reaction of levopimaric acid(4) and acrylic acid(5) to acrylopimaric acid c(8) was the optimal reaction path dynamically. However, ΔG of acrylopimaric acid c(8) was higher than that of acrylopimaric acid d (9). It revealed the reason that levopimaric acid(4) can react with acrylic acid through the Diels-Alder reaction to form isomers of acrylopimaric acid c(8) and acrylopimaric acid d(9) under microwave heat [6] .
The reaction rates k in the addition reaction of levopimaric acid(4) and acrylic acid (5) to acrylopimaric acid in aqueous solution were faster than those of other solvents. Therefore, water is a better solvent for the reactions compared with the other solvents. The active sites of the four isomeric resin acids were the C-C double bonds where the six-member ring is located, and both C-C double bonds are easily attacked by both electrophiles and nucleophiles.
For acylpyimaric acid, the non-planar six-memed ring (C53 and C55) and the C-C double bonds were easily attacked by nucleophile, while the non-planar six-memed ring (C9 and C15) and the carboxyl group (O1 and O2) are easily reacted with electrophiles. The highest electrostatic potential of the eight molecules is located at H of the carboxyl group, while the highest electrostatic potential is located at C-O double bond of the carboxyl group. The C-C double bond potentials of the four isomeric resinic acids are negative, and the C-C potentials of the allimaric acid are slightly positive.