Thermodynamic analysis and transition state study for pyrolysis of levoglucosan and glyceraldehyde through quantum simulation

Wu Shiliang Shen Dekui Gao Shanyun Zha Xiao Xiao Rui

(Key Laboratory of Energy Thermal Conversion and Control of Ministry of Education，Southeast University，Nanjing 210096，China)

W ith the increasing pressure of conventional energy supply and environmental deterioration，biomass has attracted more and more attention with regard to its outstanding characteristics such as widely distributed，environmentally friendly and renewable.Pyrolysis is one of the promising methods to produce bio-fuel of different types［1］.It is difficult to comprehensively understand the mechanism of biomass pyrolysis due to its complex constituents like cellulose，hemicellulose，lignin，extractives and a small amount of inorganics.Cellulose is the most abundant component in biomass，accounting for 40%to 60%of biomass in mass fraction［2］.As a result，the mechanism of cellulose decomposition will benefit the understanding of the whole biomass pyrolysis.

Levoglucosan is an important product from cellulose pyrolysis，possibly accounting for above 50% molar fraction in bio-oil［3］.Besides，levoglucosan is also an important reactant for the secondary reactions during cellulose pyrolysis［4-6］.It is confirmed that the products of levoglucosan pyrolysis are similar to those of cellulose pyrolysis［7］.Therefore，the investigation of the levoglucosan decomposition mechanism can help understand the pyrolysis of cellulose.Shafizadeh et al.［8］investigated the pyrolysis of levoglucosan by using isotopically labeled levoglucosan and proposed four possible reaction pathways for levoglucosan pyrolysis.In the first pathway，levoglucosan undergoes multi-step consecutive reactions to produce furfural after the ring of levoglucosan is opened.In the second pathway，levoglucosan directly forms a cyclic molecule with an oxygen ring，and then transforms into furfural.In the third pathway，levoglucosan isdecomposed into erythrose which is then cracked into pyruvaldehyde，butanedione，aldehyde，CO，etc.In the fourth pathway，levoglucosan decomposes into pentose，which is then cracked into pyruvaldehyde，glyoxal，aldehyde，CO，etc.These pathways are well-established for explaining the production of the relevant fragments and the possible kinetics for cellulose pyrolysis［9-11］.However，these pathways are still plausible and controversial for the formation of other important products during cellulose pyrolysis，since the transition states or intermediates of these chemical pathways are difficult to specify through experimental methods.

With regard to the above difficulties，theoretical analysis by quantum simulation may be the soundly acceptable method to explore the possible chemical pathways for pyrolysis of levoglucosan.The established reaction pathways are intensively discussed regarding the estimation of the free energy ΔGand the free enthalpy ΔH.The possible chemical pathways for glyceraldehyde，which is one of the important derivatives from levoglucosan pyrolysis and has a similar chemical structure as cellulose，will be proposed by means of the transition state theory.The assessment of the variation of distances between selected atoms and total potential energy surface is included，facilitating the understanding of the intrinsic kinetic process for glyceraldehyde pyrolysis.Another important objective of this work is to give a conceptual guidance in the application of quantum simulation in the area of pyrolysis of solid fuels.

1 Methods

1.1 Density function th eory

The basic theory of the density function was demonstrated by Hohenberg and Kohn in 1964［12］.The first Hohenberg-Kohn theory shows that all the properties of a system can be figured out with the electron density ρ(r)of the system.Because it is not easy to understand the wave function of a multi-electron system and it is difficult to solve the Schr?dinger equation of a multi-electron system，this theory avoids using the wave function and the Schr?dinger equation to compute the properties of the system.The second Hohenberg-Kohn theory shows that there is always a density function which connects the energy and the electron density distribution of the system.So the energy of a given system can be achieved if the density function of the system can be figured out.

Based on Ref.［13］，the B3LYP method is well-established to deal with quantum chemical problems in Gaussian 03［14］.It is reported that the B3LYP method has the smallest average absolute deviation between the calculated value and the experimental data for carbohydrate in different density function theory(DFT)methods［15］.

1.2 Thermodynamic analysis

By the chemical thermodynamic theory，Gibbs'free energy ΔGof a reaction is used to estimate whether the reaction will occur under the given conditions or not.The definition ofGis as follows:

whereHis the enthalpy of the molecular system;Tis the ambient temperature;andSis the entropy of the system.ΔGof the reaction is determined as

In quantum chemistry，the energy of a given system is usually calculated by solving the Schr?dinger equation.It is difficult to solve the Schr?dinger equation of a multielectron system，so the Born-Oppenheimer approximation is used to separate the electron motion from the nuclear motion.The electronic energy ε0can be obtained by adding nuclear repulsion energy to electron motion energy.

As for the nuclear motion，there are three kinds of nuclear motion:vibration，rotation，and translation.The energy of these three motions is usually dealt with the statistical thermodynamics.Once the partition function of each motion is given and the expression of thermodynamic parameters are derived from the partition function is obtained，the energy of the nuclear motion can be figured out.Combining electron motion with nuclear motion，the total energy，the entropy and the Gibbs free energy of the system are described as follows:

whereENis the energy of nuclear motion，kJ/mol;HNis the enthalpy of nuclear motion，kJ/mol;SNis the entropy of nuclear motion，kJ/(mol·K);kBis the Boltzmann constant，J/K.All the thermodynamic parametersET，HTandGTare calculated by Gaussian 03［14］at the B3LYP level with a standard 6-31G basis set.1.3 Transition state study

The transition state(TS)of a chemical reaction is a particular configuration along the reaction coordinate.It is defined as the state corresponding to the highest energy along this reaction coordinate.The transition state is also defined as an activated complex.The transition state structures can be determined by searching for the first-order saddle point on the potential energy surface.Such a saddle point is a point where there is a minimum in all dimensions.According to this characteristic，every transition state has but one imaginary frequency.

The B3LYP method is used to compute the energy of points along the reaction coordinate，and the Berry method is used to search for the first-order saddle point.After the transition state is found by the TS method，the frequency of the transition state is confirmed through the evidence of only one imaginary frequency.And the IRC method is also used to check the reaction pathway including reactant，transition state(s)and product.All the mentioned calculations are completed at the B3LYP level with a standard 6-31G basis set in Gaussian 03.

2 Results and Discussion

2.1 Reaction pathways for levoglucosan pyrolysis

Kawamoto et al.［5，8，16］did extensive experiments on pyrolysis of levoglucosan and found that the chemical components of products were very complicated.However，some of the main products were identified as aldehydes，ketones and organic acids.In detail，furfural，formaldehyde，pyruvaldehyde，glyceraldehyde，glycolal，glyxoal and aldehyde make up a large proportion of products from levoglucosan pyrolysis.It needs to be noted that those components also act as important precursors to produce small fragments through dehydration，decarbon-ylation or decarboxylation.That is why the formations of those prominent products from levoglucosan pyrolysis are of concern.

With regard to the above discussion and levoglucosan decomposition mechanism proposed by Shafizadeh，three chemical pathways resulting in the designated 7 products are designed in Fig.1.The three mechanisms share a parallel and competitive relationship during the pyrolysis of levoglucosan.

Fig.1 Three designated pathways of levoglucosan pyrolysis

2.2 Structural optimization of molecules

The optimization of the molecular structure is required before the quantum simulation.The most stable geometry structure of the given molecule is found during the structural optimization process.The geometry structures of reactants，transition states，intermediates and products are all optimized at the B3LYP level with a standard 6-31G basis set.The optimized molecular structure of levoglucosan is shown in Fig.2.Tab.1 shows the comparison of the bond length distributions of levoglucosan between the experimental data［17］and those after structural optimization.The difference between the calculated and experimental values is very tiny，confirming the acceptability of levoglucosan structural optimization.Although the experimental data for other molecules cannot be found at this point，structures of other involved molecules are considered to be reliable after optimization at the B3LYP level with a standard 6-31G basis set.

Fig.2 Molecular structure of levoglucosan

Tab.1 Comparison between calculated results and experimental data of levoglucosan pm

2.3 Assessment of established reaction pathways

The aim of thermodynamic analysis is to determine whether the reaction will occur within the temperature range of pyrolysis or not.Pictet et al.［18］reported that levoglucosan polymerizes at＞240℃.Kawamoto et al.［19］considered that effective pyrolysis of levoglucosan is above 300℃.Therefore，the thermodynamics parameters of pyrolysis reactions of levoglucosan are computed from 500 to 1 000 K.

Fig.3 Free energy ΔG of three pathways of levoglucosan pyrolysis within the temperature range from 500 to 1 000 K

Fig.4 Free enthalpy ΔH of three pathways of levoglucosan pyrolysis within the temperature range from 500 to 1 000 K

The results of ΔGand ΔHof three reaction pathways of levoglucosan pyrolysis are shown in Fig.3 and Fig.4.In Fig.3，ΔGof three pathways is always under zero and decreases with the increasing temperature within the pyrolysis temperature range.This implies that the products can be produced through the proposed chemical pathways according to the second law of thermodynamics.In Fig.4，ΔHof all pathways decreases with the increasing temperature.The chemical pathways are always above zero during the pyrolysis temperature range，indicating that all three reactions proposed are endothermic.It is consistent with Ball's result that cellulose polymerizes into coke is an exothermic reaction，but the decomposition of cellulose into volatile material is an endothermic reaction［20］.The absorption heat ΔHof pathway 2 is only half of those of pathway 1 and pathway 3，but the ΔGof the three pathways is the same.It is not sure that the formation of C3 molecules is favored during pyrolysis of levoglucosan.Shafizadeh's experimental work confirmed this result，showing that the amount of generated C3 molecules is higher than those of furfural and its derivatives.However，no significant difference between C3 molecules and C2 molecules is observed，which needs to be further specified.

2.4 Assessment of intermediates from levoglucosan pyrolysis

The above reaction pathways only concern reactants and products，while no intermediates are involved during the reactions.The existence of possible intermediates during the pyrolysis of levoglucosan will be estimated according to the thermodynamic method above mentioned.Tetrose is proposed as an important intermediate during levoglucosan pyrolysis［8，21］.Pyruvaldehyde，glyceraldehyde and butanedione can be generated from tetrose.As a result，a chemical pathway for levoglucosan decomposed to D-erythrose and glycolal as pathway 4 is designed in Fig.5.

Fig.5 Pathway 4 for levoglucosan decomposed to D-erythrose and glycol

As shown in Fig.6，ΔGof the reaction is always above zero，indicating that levoglucosan cannot be decomposed to D-erythrose through pathway 4 during the pyrolysis temperature range.Shafizadeh et al.［8，21］proposed that D-erythrose can pyrolysis into pyruvaldehyde and glyceraldehyde through decarbonylation，if butanedione is the product of both D-erythrose and levoglucosan.However，there is no direct evidence to prove the existence of D-erythrose.Hence，the speculation of D-erythrose as the intermediate from levoglucosan pyrolysis needs to be reconsidered，or other pathways should be specified.Li et al［6］concluded that levoglucosan cannot be pyrolysised into glycolal and D-erythrose at the same time through the observation of the yield of glycolal from levoglucosan pyrolysis.

Fig.6 Free enthalpy ΔH and free energy ΔG for pathway 4 of levoglucosan pyrolysis within the temperature range from 500 to 1 000 K

According to the pathways advanced by Shafizadeh et al.［8］，levoglucosan may undergo ring-open reaction during pyrolysis to produce a C6 straight-chain molecule as an intermediate.The straight-chain C6 molecule can be pyrolyzed into low molecular weight products，such as pyruvaldehyde and glyceraldehyde.The C6 intermediate is considered to be 4，5，6-trihydroxy-2-oxohexanal，while the detailed reaction pathway 5 is shown in Fig.7.ΔGof the reaction is always under zero，indicating that this reaction can occur spontaneously during the temperature range(see Fig.8).This confirms that 4，5，6-trihydroxy-2-oxohexanal may be the intermediates during levoglucosan pyrolysis.The reaction is slightly endothermic，since ΔHof the reaction is near zero.However，whether it is the intermediate of levoglucosan pyrolysis should be approved through experimental observation.

Fig.7 Pathway 5 for levoglucosan to 4，5，6-trihydroxy-2-oxohexanal

Fig.8 Free enthalpy ΔH and free energy ΔG for pathway 5 of levoglucosan pyrolysis within the temperature range from 500 to 1 000 K

2.5 Reaction pathways of glyceraldehydes pyrolysis

Since the intermediates or the transition states of levoglucosan pyrolysis are difficult to determine through the experiments，the transition state study is significant for proposing the possible chemical pathways for pyrolysis of macromolecules.Since glyceraldehyde gives a similar chemical structure as cellulose monomer(D-glucose:more than one—OH groups and one— ==HC O ending group)，the pyrolysis of glyceraldehydes is first studied through the transition state searching by quantum simulation.This also supplies a methodological guide for determining the pyrolysis of other relevant molecules.In Shafizadeh's reaction pathway of levoglucosan pyrolysis，glyceraldehyde is an important intermediate to produce pyruvaldehyde and other gases.Three possible pathways of glyceraldehyde decomposition are proposed.The optimized structures of reactants，transition states and the corresponding products in each pathway are shown in Fig.9.

Fig.9 Optimized structures of glyceraldehyde and three possible transition states for thermal cracking of glyceraldehyde(Red balls stands for O atoms，and grey for C，white for H)

In pathway A，glyceraldehyde is decomposed into malondialdehyde and water，and the transition state is TS1.The transition state TS1 is confirmed by only one imaginary frequency at-633.36i cm-1and the reaction pathway is checked by IRC.Thus，it is acceptable that TS1 is the transition state of the reaction that glyceraldehyde decomposes into malondialdehyde and water.Obvious differences between glyceraldehyde and TS1 are revealed(see Fig.9).Special attention should be paid to the distances between C2-O6，C3-O5，C3-H9，and O5-H11(see Fig.10(a)).The distances between C2-O6，C3-H9，and O5-H11 become longer and longer along the IRC pathway，but the distance between C3-O5 becomes shorter.It is of great interest that the distance between H and C or O changes slightly at the beginning and final stages of the process.But it gives a sharp increase during the middle stage of the IRC pathway.This indicates that the transition state is very unstable and the elongation of C2-O6 triggers the breakup of H11-O5 to generate water.It can be concluded that H11，H9，and the O6H12 group break away from glyceraldehyde and the single bond between C3-O5 tends to be a double bond.A structure like water is formed by the H11 and O6H12 group，while H9 is cleaved from glyceraldehyde and the bond between C3-O5 is stronger than a single bond but weaker than a double bond.

Fig.10 Variation of distance between the selected atoms in glyceraldehyde during the IRC process.(a)Reaction A;(b)Reaction B;(c)Reaction C

In pathway B，glyceraldehyde is decomposed into glycolal，carbon monoxide and hydrogen with the transition state as TS2 in Fig.9.The frequency of TS2 is confirmed with only one imaginary frequency at-883.95i cm .The variations of the bond lengths between C1-C2，C2-O6，O6-H12，and H12-H7 are plotted in Fig.10(b).The distances between C1-C2 and O6-H12 become longer and longer，while the distances between C2-O6 and H12-H7 are shorter along the IRC pathway.The carbonyl group is disrupted from glyceraldehyde in the transition state to form a structure like carbon monoxide and the two H atoms(H7 and H12).This gives the possible chemical pathway for glyceraldehyde decomposed to glycolal，carbon monoxide and hydrogen.

In pathway C，glyceraldehyde is decomposed into glycolal and formaldehyde with the transition state TS3 in Fig.9.The only one imaginary frequency of TS3 is determined to be-432.31i cm-1.The distance changes between C1-C2，C1-H12，C2-O6，and O6-H12 along the reaction pathway are shown in Fig.10(c).The distances between C1-C2 and O6-H12 become longer and those between C1-H12 and C2-O6 become shorter.The carbonyl group together with H7 is initially cleaved from glyceraldehydes.Then，the cleavage of H12 from the hydroxyl group favors the formation of designated formaldehyde.

The activation energies of these three proposed chemical pathways are determined.The potential energy surface and the activation energy of each pathway are shown in Fig.11.It is found that pathway B owns the minimum activation energy with ΔEof 59.15 kJ/mol，while ΔEfor pathway A is 64.61 kJ/mol and for pathway C it is 86.13 kJ/mol.This gives the hint that the decomposition of glyceraldehydes is in favor of pathway B and pathway C.Glyceraldehyde is decomposed preferably through the dehydration and decarbonylation to produce water，CO or formaldehyde.The reaction pathways proposed by Shafizadeh et al.［8］show that glyceraldehyde can produce pyruvaldehyde.However，it seems that no pathway for glyceraldehydes to produce pyruvaldehyde can be achieved through the quantum simulation.

Fig.11 Analysis of potential energy surface for the three proposed chemical pathways for the pyrolysis of glyceraldehyde

3 Conclusion

The three well-established chemical pathways for levoglucosan pyrolysis can occur spontaneously during the temperature range of pyrolysis(500 to 1 000 K).ΔGof each pathway is decreased with the increasing temperature，while all three chemical pathways are endothermic reactions when ΔHis above zero.

Thermodynamic analysis indicates that C4 molecules cannot be the intermediates from levoglucosan pyrolysis，since ΔGof the reaction with erythrose as the product is always above zero during the pyrolysis temperature range.But the reverse trend for hexoses can be obtained，confirming their production as the intermediates from levoglucosan pyrolysis.

Three possible chemical pathways of glyceraldehyde decomposition are proposed in quantum simulation.The variation of the bond length of molecules along the IRC pathway is analyzed and transition states of each chemical pathway are consequently figured out.Dehydration and decarbonylation are considered to be the preferable ways for glyceraldehyde decomposition.Meanwhile，no pathway for glyceraldehyde to produce pyruvaldehyde can be achieved through the quantum simulation.The quantum simulation is considered to be a useful method to figure out the transition states of the reactions，facilitating the understanding and control of biomass pyrolysis processes.

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