Theoretical Studies of Properties and Reactions Involving Mercury

Jul 16, 2009 - ... continuous emission measurement of flue gas from laboratory-scale coal combustion. J. Liu , Q. Falcoz , D. Gauthier , G. Flamant , ...
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Energy Fuels 2010, 24, 117–122 Published on Web 07/16/2009

: DOI:10.1021/ef9005143

Theoretical Studies of Properties and Reactions Involving Mercury Species Present in Combustion Flue Gases† Jing Liu,* Wenqi Qu, Jinzhou Yuan, Shouchun Wang, Jianrong Qiu, and Chuguang Zheng State Key Laboratory of Coal Combustion, Huazhong University of Science and Technology, Wuhan 430074, China Received May 23, 2009. Revised Manuscript Received June 21, 2009

The thermochemical properties of mercury species present in combustion flue gases were studied using quantum mechanical methods combined with effective core potentials (ECP) basis sets. At various levels of theory, the calculated geometries, vibrational frequencies of the species, and the reaction enthalpies were compared with experimental data in order to validate the quantum mechanical method and basis set combination. The results show that the QCISD/RCEP28DVZ combination provides the most accurate results and the B3PW91/RCEP28DVZ and B3LYP/ECP28MWB combinations also perform well. On the basis of the evaluation of theoretical methods and basis sets of quantum chemistry, theoretical exploration on the mercury reaction mechanism in flue gas was conducted on the level of atoms and molecules. The properties of stable minimums were validated by vibration frequencies analysis. The activation energies were calculated by thermal energy calibration (including zero point energy calibration). The reaction rate constants in the temperature range of 298-1500 K were calculated from the transition state theory.

harder to reduce than oxidized mercury emissions. Fortunately, elemental mercury can react with oxidizing species in the flue gas and can be transformed into an oxidized form that can be captured more easily. But the mechanisms by which these reactions occur are still not clear. To develop an effective control technology for removing mercury from flue gas, knowledge of the detailed chemistry and kinetics of reactions is very important.6 However, little kinetics data is currently available for reactions involving mercury. Some models7-10 have been used to predict mercury speciation in flue gases, and their accuracy is essential for developing more-effective control strategies for preventing mercury’s release into the atmosphere. The model developed by Widmer et al.7 was developed from the chlorine chemistry of Senkin11 and a general combustion chemistry mechanism adapted from the work of Glarborg et al.12 The preexponential factor was taken from corresponding reactions of lead presented by Cosic and Fontijn.13 The substituting one species for another, even if they are electronically similar, leads to gross inaccuracies for kinetic estimations.14 Therefore, the model work of Widmer et al. should be questioned.15

1. Introduction Mercury is one of the most toxic elements known to mankind and the environment. Coal combustion is one of the primary sources of anthropogenic release of mercury. When coal combusts, mercury is volatilized and escapes from the smokestacks. Once in the atmosphere, elemental mercury is relatively inert with a residence time on the order of one year, classifying it as a global pollutant.1 The emission of mercury by coal-fired power plants has become an important environmental concern. On March 15, 2005, the U.S. Environmental Protection Agency (EPA) issued the Clean Air Mercury Rule establishing a target of 70% reduction in mercury emissions from coal-fired power plants by the year 2018.2 The speciation of mercury during combustion is of particular importance for the development of control technologies. The two main forms of mercury (oxidized and elemental mercury) behave differently.3,4 The oxidized mercury is soluble in aqueous solutions and has a tendency to associate with particulate matter. Therefore, oxidized mercury is easily captured in pollution-control equipment such as a flue gas desulfurization (FGD) system. On the contrary, elemental mercury is highly volatile and insoluble and does not adsorb readily on most solid substrates, with capture rates between 10 and 80%.5 Therefore, elemental mercury emissions are

(6) Liu, J.; Abanades, S.; Gauthier, D.; Flamant, G.; Zheng, C.; Lu, J. Environ. Sci. Technol. 2005, 39 (23), 9331–9336. (7) Widmer, N. C.; West, J.; Cole, J. A. 93 Annual Meeting, Air & Waste Management Association, Salt Lake City, UT, June 18-22, 2000; AWMA: Pittsburgh, PA, 2000. (8) Niksa, S.; Helble, J. J.; Fujiwara, N. Environ. Sci. Technol. 2001, 35, 3701–3706. (9) Senior, C. L.; Sarofim, A. F.; Zeng, T.; Helble, J. J.; MamaniPaco, R. Fuel Proc. Tech. 2000, 63, 197–213. (10) Krishnakumar, B.; Helble, J. J. Environ. Sci. Technol. 2007, 41, 7870–7875. (11) Sentan, S. M. Survey of Rate Coefficients in the C-H-Cl-O System. Gas-Phase Combustion Chemistry. Gardiner W. C., Jr., Ed., Springer Verlag: New York, 2000, pp 389-487. (12) Glarborg, P.; Miller, J. A.; Kee, R. J. Combust. Flame 1986, 65, 177–202. (13) Cosic, B.; Fontijn, A. J. Phys. Chem. 2000, 23, 5517–5524. (14) Sliger, R. N.; Kramlich, J. C.; Marinov, N. M. Fuel Process. Technol. 2000, 65-66, 423–438. (15) Wilcox, J.; Blowers, P. Environ. Chem. 2004, 1, 166–171.

† Presented at the 2009 Sino-Australian Symposium on Advanced Coal and Biomass Utilisation Technologies. *To whom correspondence should be addressed. Telephone: þ86 027 87545526. Fax: þ86 027 87545526. E-mail: [email protected]. (1) Slemr, F.; Schuster, G.; Seiler, W. J. Atmos. Chem. 1985, 3, 407– 434. (2) U.S. Environmental Protection Agency. Mercury; URI: http:// www.epa.gov/mercury. (3) Panta, Y. M.; Liu, J.; Cheney, M. A.; Joo, S. W.; Qian, S. J. Colloid Interface Sci. 2009, 333, 485–490. (4) Cheney, M. A.; Keil, D.; Qian, S. J. Colloid Interface Sci. 2008, 320, 369–375. (5) Ghorishi, S. B. J. Air Waste Manage. 1998, 48, 1191–1198.

r 2009 American Chemical Society

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Quantum mechanical methods are capable of estimating reaction rates and kinetic parameters for mercury reactions. However, little computational studies have been done so far to understand mercury reactions using quantum chemistry.14-20 Wilcox et al.15 have estimated the computational levels of theory, but the B3PW91 method of density functional theory was not considered and the vibriational frequencies were not compared. Other researchers14 have not verified the accuracy of the computational levels of theory, and the previous kinetics parameters can be updated by using more reliable computational levels of theory. In this paper, a series of basis sets along with various quantum mechanical methods are compared to determine which level of theory would be most accurate for the reactions of mercury. We provide accurate geometries, vibrational frequencies of the species, and the reaction enthalpies to compare with the high quality experimental data from the National Institute of Standards and Technology (NIST) database.21 Comparisons between each calculation are given along with a discussion of the better performance of a quantum mechanical method and basis set combination. Then, the reaction rate constants were calculated to enrich the database in this field. Not only Hg/Cl interactions, but also Hg/O interactions were explored, since HgO production may be important for coals with low Cl content.22 This possibility is also furthered by equilibrium analyses, which indicate the presence of trace amounts of HgO at higher temperatures.23

using an optimizing process based upon the energy-overlap functional. Energy-optimized (5s5p)/[2s2p] Gaussian type double-B quality sp and triple-B quality d functions were used, with the triple-B d functions essential for describing the orbital shape changes that exist with d occupancy. ECP28MWB uses the relativistic pseudopotential of the Stuttgart group25 for mercury, with the respective energy-optimized (4s2p)/[3s2p] and (4s5p)/[2s3p] Gaussian-type orbital (GTO) valence bases optimized using multiconfiguration Dirac-Fock (MCDF) calculations. LANL2DZ and SDD are the built-in Gaussian basis sets. Therefore they have been readily used by other researchers to perform the quantum mechanical calculations.14,16,18 In addition, the complete basis set 6-311þþG (3df, 3pd) was used for nonmetal elements (Cl, O, H, N). This extended Pople basis set includes both diffuse and polarization functions. 2.2. Choice of Theoretical Methods. Theoretical methods can be divided into two categories: ab initio methods based on the molecular orbital (MO) approach and density functional methods. To determine the most accurate level of theory, four methods were evaluated: QCISD (quadratic configuration interaction with single and double excitations), MP2 (second order Møller-Plesset perturbation theory), B3PW91 (Becke’s three-parameter hybrid exchange functional with the correlation functional of Perdew and Wang), and B3LYP (Becke’s three-parameter hybrid functional and the Lee-Yang-Parr correlation). QCISD and MP2 are ab initio methods, while B3PW91 and B3LYP are density functional theory (DFT) methods. B3LYP and B3PW91 are hybrid methods of Hartree-Fock exchange with density functional exchange-correlation. PW91 includes the generalized gradient approximation functional. These methods are typical and are used widely. The QCISD method uses summation techniques to add certain terms in the MP expansion to infinite order, thus alleviating the problem of convergence. These approaches are also size-consistent, which means that the method scales correctly with the number of particles in the system. Møller-Plesset (MP) perturbation theory is the next step in sophistication, taking the HF wave function and energy as the zeroth order components and applying the standard ansatz of Rayleigh-Schrodinger (RS) perturbation theory.19 B3PW91 and B3LYP are the most popular density functional theories provided by Gaussian. 2.3. Reaction Mechanism Computation. Theoretical exploration on mercury reaction mechanism in flue gas was conducted on the level of atoms and molecules. The geometry optimizations of reactant, transition state, intermediate, and product were made at the validated theoretical method and basis set combination. Transition states were identified by the presence of a single imaginary frequency, and the intrinsic reaction coordinate was followed if there was any ambiguity about the nature of the transition state. The activation energies were calculated by thermal energy calibration (including zero-point energy calibration). Calculations were carried out using the Gaussian 98 software.26 Kinetic parameters were evaluated at different temperatures (298, 600, 1000, and 1500 K) by the transition state theory (see eq 1)27

2. Computational Methods 2.1. Choice of Basis Sets. Mercury is difficult to study because it has 80 electrons, which makes the quantum mechanical calculations computationally intensive. The use of relativistic effective core potentials is necessary to make the calculations tractable while obtaining accurate theoretical rate constants.17 Basis sets incorporating relativistic effects for the inner electrons were explored through the use of small core relativistic effective core potentials (ECP) for mercury. Four ECP basis sets were considered for mercury: RCEP28DVZ,24 ECP28MWB,25 LANL2DZ, and SDD. The RCEP28DVZ and ECP28MWB basis sets are the most recently available in the literature for mercury. Reference 15 showed that both RCEP28DVZ and ECP28MWB basis sets when used in conjunction with the density functional method B3LYP provide both accurate geometries and heats of reaction, but the important density functional method B3PW91 was not studied. RCEP28DVZ uses a relativistic compact effective potential of the Stevens et al. group,24 which replaces 28 of mercury’s atomic core electrons, derived from numerical Dirac-Fock wave functions, (16) Zheng, C. G.; Liu, J.; Liu, Z. H.; Xu, M. H.; Liu, Y. H. Fuel 2005, 84, 1215–1220. (17) Wilcox, J.; Robles, J.; Marsden, D.; Blowers, P. Environ. Sci. Technol. 2003, 37, 4199–4204. (18) Xu, M.; Qiao, Y.; Zheng, C.; Li, L.; Liu, J. Combust. Flame 2003, 132, 208–218. (19) Wilcox, J.; Marsden, D. C. J.; Blowers, P. Fuel Process. Technol. 2004, 85, 391–400. (20) Xu, M.; Qiao, Y.; Liu, J.; Zheng, C. Powder Technol. 2008, 180, 157–163. (21) Malcolm W. Chase. NIST-JANAF Thermochemical Tables; NIST: Washington DC, U.S., 1998. (22) Senior, C. L.; Helble, J. J.; Sarofim, A. F. Proceedings of the A&WMA International Specialty Conference on Mercury in the Environment, Minneapolis, MN, September 1999; pp 128-139. (23) Edwards, J. R.; Srivastava, R. K.; Kilgroe, J. D. J. Air Waste Manage. 2001, 51, 869–877. (24) Stevens, W. J.; Krauss, M. Can. J. Chem. 1992, 70, 612–630. (25) Martin, J. M. L.; Sundermann, A. J. Chem. Phys. 2001, 114 (8), 3408–3420.

(26) Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Scuseria, G. E.; Robb, M. A.; Cheeseman, J. R.; Zakrzewski, V. G.; Montgomery, J. A., Jr.; Stratmann, R. E.; Burant, J. C.; Dapprich, S.; Millam, J. M.; Daniels, A. D.; Kudin, K. N.; Strain, M. C.; Farkas, O.; Tomasi, J.; Barone, V.; Cossi, M.; Cammi, R.; Mennucci, B.; Pomelli, C.; Adamo, C.; Clifford, S.; Ochterski, J.; Petersson, G. A.; Ayala, P. Y.; Cui, Q.; Morokuma, K.; Malick, D. K.; Rabuck, A. D.; Raghavachari, K.; Foresman, J. B.; Cioslowski, J.; Ortiz, J. V.; Stefanov, B. B.; Liu, G.; Liashenko, A.; Piskorz, P.; Komaromi, I.; Gomperts, R.; Martin, R. L.; Fox, D. J.; Keith, T.; Al-Laham, M. A.; Peng, C. Y.; Nanayakkara, A.; Gonzalez, C.; Challacombe, M.; Gill, P. M. W.; Johnson, B. G.; Chen, W.; Wong, M. W.; Andres, J. L.; Head-Gordon, M.; Replogle, E. S.; Pople, J. A. Gaussian 98, revision A.11; Gaussian, Inc.: Pittsburgh, PA, 1998. (27) Eyring, H. J. Chem. Phys. 1935, 3, 107–111.

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Table 1. Calculated and Experimental Bond Lengths (in A˚) and Bond Angles (in deg) level of theory QCISD QCISD B3PW91 B3PW91 B3LYP B3LYP B3LYP MP2 bond length/ a a a a a a species bond angel experimental RCEP28DVZ ECP28MWB RCEP28DVZ ECP28MWB RCEP28DVZ ECP28MWB LANL2DZ SDD HgCl r(HgCl) 2.23 HgO r(HgO) 1.84 2.31 HgCl2 r(HgCl) θ(ClHgCl) 180 HCl r(HCl) 1.2746 r(ClCl) 1.9879 Cl2 HOCl r(HO) 0.96 r(OCl) 1.689 θ(HOCl) 102.5 OH r(OH) 0.9706 r(OO) 1.2074 O2 1.1282 N2O r(NN) r(NO) 1.1842 θ(NNO) 180 r(NN) 1.0876 N2 r(OO) 1.278 O3 θ(OOO) 116.8 ClO r(ClO) 1.5697 average absolute error a

2.4121 1.9414 2.3003 180 1.2739 1.9973 0.9616 1.687 103.6 0.9684 1.1993 1.1212 1.1863 180 1.0975 1.2478 117.9 1.5777 0.0250

2.4084 1.9538 2.3112 180 1.2739 1.9973 0.9616 1.687 103.6 0.9684 1.1993 1.1212 1.1863 180 1.0975 1.2478 117.9 1.5777 0.0250

2.4515 1.9293 2.2974 180 1.2788 1.9892 0.9648 1.6849 103.6 0.9722 1.1967 1.1208 1.1765 180 1.091 1.243 118.4 1.5637 0.0275

2.4308 1.9288 2.3007 180 1.2788 1.9892 0.9648 1.6849 103.6 0.9722 1.1967 1.1208 1.1765 180 1.091 1.243 118.4 1.5637 0.0259

2.4898 1.9499 2.3195 180 1.2808 2.0105 0.9662 1.6993 103.6 0.974 1.2031 1.1211 1.1822 180 1.0912 1.2514 118.3 1.5758 0.0319

2.4648 1.9474 2.3211 180 1.2808 2.0105 0.9662 1.6993 103.6 0.974 1.2031 1.1211 1.1822 180 1.0912 1.2514 118.3 1.5758 0.0302

2.5602 2.0247 2.3924 180 1.2808 2.0105 0.9662 1.6993 103.6 0.974 1.2031 1.1211 1.1822 180 1.0912 1.2514 118.3 1.5758 0.0465

2.4706 1.9077 2.3489 180 1.3144 2.2455 0.9968 1.8559 103.5 0.9973 1.3557 1.2358 1.2359 180 1.1754 1.3631 115.2 1.6886 0.0985

6-311þþG(3df,3pd) basis set used for atoms other than mercury.

Table 2. Calculated and Experimental Vibrational Frequencies (in cm-1) level of theory

species

QCISD QCISD B3PW91 B3PW91 B3LYP B3LYP B3LYP MP2 experia a a a a a mental RCEP28DVZ ECP28MWB RCEP28DVZ ECP28MWB RCEP28DVZ ECP28MWB LANL2DZ SDD

vibrational mode

sym. stretch asym. stretch bend HgCl stretch HgO stretch average absolute error

HgCl2

a

360 413 70 290.94 680

340.8 394 97.6 290.7 579.9 16.5

338.8 389.0 89.0 297.9 582.4 17.8

329.1 385.1 94.3 262.9 573.0 37.3

329.0 382.7 85.1 276.8 585.5 27.8

318.6 374.5 92.7 244.3 539.3 22.6

319.3 373.1 84.4 260.9 554.6 31.3

291.0 344.8 67.0 233.6 518.1 49.4

333.2 398.7 87.1 280.8 673.2 17.1

6-311þþG(3df,3pd) basis set used for atoms other than mercury.

modified with the tunneling correction factor given by eq 2,28 so that the final rate constant value was given by eq 3.   kB T QTS -Ea ð1Þ exp kTST ¼ RT h QA QB

kT ¼ 1þ

   1 hνim c 2 24 kB T

k ¼k

TST

kT

ð2Þ

HgþClO ¼ HgOþCl

ð3Þ

HgþCl2 þM ¼ HgCl2 þM

ð4Þ

HgþN2 O ¼ HgOþN2

ð5Þ

HgþO3 ¼ HgOþO2

ð6Þ

HgOþHCl ¼ HgClþOH

ð7Þ

HgOþHOCl ¼ HgClþHO2

ð8Þ

HgþNO ¼ HgOþN

ð9Þ

ð3Þ

Here, kB is the Boltzmann constant; QTS is the partial function of transition state; QA and QB are the partial functions of reactants, respectively; Ea is the activation energy; Q is the multiplier of transitional (Qtrans), rotational (Qrot), vibrational (Qvib) and electronic (Qelec) partial function, which has the relationship as Qtotal=QtransQrotQvibQelec; kT accounts for the tunneling correction; h is Planck’s constant; νimrepresents the single imaginary frequency value of the transition structure; and c is light velocity. The reactions listed below may take place in the flue gases of coal combustion and were studied in this paper: HgþHCl ¼ HgClþH

ð1Þ

HgþHOCl ¼ HgClþOH

ð2Þ

3. Results and Discussion 3.1. Validation of Accuracy of Calculation Results. In general, the quantum mechanical method and basis set should be examined carefully in terms of their accuracy relative to experimental data. Because of the lack of experimental rate constant data available for mercury reactions, validation of the method and basis set combination must be explored through the comparison of theoretical geometries, vibrational frequencies, and heats of reaction to experiment.

(28) Wigner, E. J. Phys. Chem. B 1932, 19, 203–207.

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Table 3. Reaction Enthalpies of Mercury Reactions (in kcal mol-1) level of theory

reaction

QCISD QCISD B3PW91 B3PW91 B3LYP B3LYP B3LYP MP2 experia a a a a a mental RCEP28DVZ ECP28MWB RCEP28DVZ ECP28MWB RCEP28DVZ ECP28MWB LANL2DZ SDD

Hg þ HCl = HgCl þ H 78.25 Hg þ HOCl = HgCl þ OH 31.20 HgCl þ HCl = HgCl2 þ H 20.45 HgCl þ Cl2 = HgCl2 þ Cl -24.72 Hg þ Cl = HgCl -24.91 33.07 Hg þ Cl2 = HgCl þ Cl -49.63 Hg þ Cl2 = HgCl2 -82.71 HgCl þ Cl = HgCl2 HgCl þ HOCl = HgCl2 þ -26.59 OH Hg þ 2HCl = HgCl2 þ H2 -5.51 average absolute error a

74.29 21.61 21.99 -29.73 -26.51 22.57 -56.24 -78.81 -30.70

67.15 14.47 18.07 -33.65 -33.65 15.43 -67.30 -82.73 -34.61

76.78 29.04 25.72 -18.74 -25.99 32.32 -44.74 -77.06 -22.02

68.60 20.86 19.69 -24.77 -34.18 24.14 -58.95 -83.09 -28.05

79.01 29.65 28.87 -18.34 -23.33 31.80 -41.67 -73.46 -20.48

71.62 22.27 22.59 -24.62 -30.71 24.41 -55.33 -79.74 -26.76

74.38 25.02 33.44 -13.77 -27.96 27.17 -41.73 -68.90 -15.92

54.48 14.50 3.60 -45.64 -15.73 5.24 -61.37 -66.61 -36.38

-6.81 4.81

-17.87 10.36

0.71 3.80

-13.50 5.81

3.16 5.20

-10.51 4.61

3.09 8.39

-26.85 17.42

6-311þþG(3df,3pd) basis set used for atoms other than mercury.

3.1.1. Equilibrium Geometry Comparison. Table 1 provides a list of computed geometries at each level of theory considered and experimental data, which were obtained from the NIST database,21 showing the QCISD/RCEP28DVZ combination and QCISD/ECP28MWB combination to be the most accurate with an average absolute error of 0.025 A˚. B3PW91/ECP28MWB, B3PW91/RCEP28DVZ, and B3LYP/ ECP28MWB also give good results with the average absolute bond distance errors of less than 0.03 A˚. MP2/SDD combination shows a large error with 0.0985 A˚. 3.1.2. Vibrational Frequency Comparison. The accurate prediction of the vibrational frequencies of the species in a system also closely predicts the energy of the system, which is important for the calculation of thermodynamic and kinetic properties. Table 2 presents computed vibrational frequencies along with experimental values from the NIST database.21 When compared with experiment, the QCISD/ RCEP28DVZ combination is the most accurate level of theory, showing an average absolute error of 16.5 wave numbers. In addition, QCISD/ECP28MWB, MP2/SDD, B3LYP/ECP28MWB, and B3PW91/ECP28MWB also provide predictions closest to experiment with the average absolute error about 20 wave numbers. B3LYP/LANL2DZ shows a large error with 49.4 wave numbers. 3.1.3. Reaction Enthalpies. Table 3 present the reaction enthalpies data for a selection of gas phase reactions involving mercury. It includes both the total energy change calculated for each reaction and the deviation of that value from the experimentally determined reaction enthalpies. A general comparison of the experimental data to the theoretical reveals that the B3PW91/RCEP28DVZ combination is the most accurate with an average absolute error of 3.80 kcal/mol. B3LYP/ECP28MWB and QCISD/RCEP28DVZ perform also well with an average absolute error of less than 4.81 kcal/mol. MP2/SDD combination shows a large error with 17.42 kcal/mol. Overall, from the comparison of theoretical results with the experimental data, the optimized quantum mechanical method can be used to accurately predict geometries, vibrational frequencies of the species, and the reaction enthalpies. The more sophisticated basis sets and more rigorous mathematical methods produced the greatest degree of accuracy with regard to the available experimental data. The QCISD/RCEP28DVZ combination leads to the most accurate results. Also, the B3PW91/RCEP28DVZ combination and the B3LYP/ECP28MWB combination provide

reasonably accurate results for these systems. These combinations of method and basis set should not be neglected. In fact, B3PW91 and B3LYP require significantly less computational time than QCISD, so they can be used in some larger systems. The basis sets of RCEP28DVZ and ECP28MWB give low errors for all computational methods that have been examined. A cursory examination of the performance of the RECP’s reveals that the RCEP28DVZ basis set proves to be more accurate than the ECP28MWB. It may be that the basis functions in the RCEP28DVZ basis set are simply better at representing the electrons in the mercury atom than those in the ECP28MWB basis set. It improves the calculation results by appointing different basis set for metal atom and nonmetal atoms. 3.2. Reaction Mechanisms. With the above validation of these computational method and basis set combinations, the QCISD/RCEP28DVZ was performed to study the reaction mechanisms of Hg/Cl and Hg/O interactions. Note that in several instances, the single point energy calculation performed at the designated level of theory utilized the optimized geometry of a less computationally expensive level due to a lack of computational resources. The calculated geometry configurations of transition states (TS) and intermediates (M) are shown in Figure 1. Reactions 1, 3, 4, 5, 6, and 9 are direct reaction with one transition state, and there is no intermediate formed. For reaction 2, Hg þ HOCl=HgCl þ OH, Hg reacts with HOCl to form the stable intermediate M2 without activation energy, and then M2 breaks down into HgCl and free radical OH via the transition state TS2. The process is Hg þ HOCl f M2 f TS2 f HgCl þ OH. During the reaction process, the distance between Hg and Cl reduces from 3.3997 to 2.4519 A˚ and the Hg-Cl bond is formed. At the same time, the distance between Cl and O changes from 1.8655 to 2.6542 A˚, namely, the bond lengthens and cleaves in the end. The changes of geometric configurations about intermediate and transition state can clearly describe the process of the reaction. For reaction 7, HgO þ HCl=HgCl þ OH, there are two transition states (TS7 and TS70 ). The first step is HgO þ HCl f M7 f TS7 f M70 , the second step is M70 f TS70 f HgCl þ OH. During the reaction process, the distance between Hg and O increases gradually (1.8906 f 1.9127 f 2.0111 f 3.2738 A˚), and the distance between Hg and Cl reduces gradually. The changes of bond distance indicate the breaking of the Hg-O bond and the forming of the Hg-Cl bond. 120

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Figure 1. Geometrical parameters for transition states (TS) and intermediates (M). Bond lengths (in A˚) and bond angles (in deg). Table 4. Imaginary Frequencies of the Transition States (cm-1) transition state TS1 TS2 TS3 TS4 TS5

imaginary frequency

transition state

imaginary frequency

-601.4 -257.1 -504.9 -78.3 -410.2

TS6 TS7 TS70 TS8 TS9

-486.8 -54.8 -179.2 -254.8 -53.8

which indicated intermediates were the stationary points of potential surface. There was only one imaginary vibration frequency of every transition state, and the imaginary frequencies are listed in Table 4. The intrinsic reaction coordinate was followed if there was any ambiguity about the nature of the transition state. From the above analyses and geometric configurations of the various stationary points, we could describe the reaction microcosmic mechanisms theoretically. The activation energies were calculated by thermal energy calibration (including zero-point energy calibration). Kinetic parameters were evaluated in different temperature (298, 600, 1000, and 1500 K) by the transition state theory. Finally, the rate expressions calculated for the reactions involving mercury in the standard Arrhenius form, k = A exp(-Ea/RT), are shown in Table 5 in the temperature range of 298-1500 K.

At the same time, the O-H bond forms during the forming of M70 . The rate of the M70 f TS70 f HgCl þ OH step is the slowest step in the mechanism and is rate determining. For reaction 8, HgO þ HOCl=HgCl þ HO2, the process is similar with reaction 2, HgO þ HOCl f M8 f TS8 f HgCl þ HO2. During the reaction process, the distance between Hg and O increases gradually (1.9077 f 2.0382 f 2.6655 A˚). At the same time, the distance between O and O reduces gradually (1.5837 f 1.3928 f 1.3859 A˚). The changes of bond distance indicate the forming of the Hg-O bond and the breaking of the O-O bond. Vibration frequency analyses were used to verify intermediates and transition states. The results showed that all the vibration frequencies of intermediates were positive numbers,

4. Conclustions The use of quantum mechanical method and basis set combinations have been validated through a comparison of theoretically determined geometries, frequencies, and reaction enthalpies to experimental values found in the literature. 121

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Table 5. Kinetic Parameters (T = 298-1500 K, P = 1 atm) No. 1 2 3 4 5 6 7 8 9

reaction

A (cm3 mol-1 s-1)

Ea (kcal mol-1)

Hg þ HCl = HgCl þ H Hg þ HOCl = HgCl þ OH Hg þ ClO = HgO þ Cl Hg þ Cl2 þ M = HgCl2 þ M Hg þ N2O = HgO þ N2 Hg þ O3 = HgO þ O2 HgO þ HCl = HgCl þ OH HgO þ HOCl = HgCl þ HO2 Hg þ NO = HgO þ N

1.69  1014 1.14  1014 1.81  1012 1.04  1014 7.35  1014 1.44  1014 2.36  1013 1.75  1011 1.32  1013

89.06 14.88 50.60 39.49 43.94 32.31 78.39 57.17 161.36

Results show that the QCISD/RCEP28DVZ combination leads to the most accurate results. Also, the B3PW91/ RCEP28DVZ combination and the B3LYP/ECP28MWB combination provide reasonably accurate results for these systems. The B3PW91 method of density functional theory is within acceptable errors for predicting geometries compared to the larger and more expensive calculation method. On the basis of the evaluation of theoretical methods and basis sets of quantum chemistry, theoretical exploration on mercury oxidation reaction mechanism in flue gas was conducted on the level of atoms and molecules. The activation energies were calculated by thermal energy calibration (including zero-point energy calibration). The reaction rate constants in the temperature range of 298-1500 K were calculated from the transition state theory.

rate expression (cm3 mol-1 s-1) k = 1.69  1014e-44821/T k = 1.14  1014e-7490/T k = 1.81  1012e-25465/T k = 1.04  1014e-19872/T k = 7.35  1014e-22110/T k = 1.44  1014e-16258/T k = 3.32  1013e-39451/T k = 2.54  1011e-28772/T k = 1.32  1013e-81205/T

There are no experimental kinetic data available to compare to the theory due to the difficulty of measurement. This stresses the need for quantum mechanical modeling in this area. This work discovers in nature the formation of different species of mercury and the reaction mechanisms of mercury with other elements during coal combustion. The rate expressions can be incorporated into the development of kinetic models of predicting the mercury speciation under a variety of process conditions. It provides a foundation for finding economic and effective method of mercury control. Acknowledgment. This work was supported by National Natural Science Foundation of China (50606013, 20877030), 973 Program of China (2006CB200304) and National Science Foundation for Distinguished Young Scholars (50525619).

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