A refined theoretical investigation of the hydrogen-electrode processes of an alkaline hydrogen-oxygen fuel cell

Journal of Molecular Structure (Theochem), 232 (1991) 225-238 Elsevier Science Publishers B.V., Amsterdam

225

A REFINED THEORETICAL INVESTIGATION OF THE HYDROGEN-ELECTRODE PROCESSES OF AN ALKALINE HYDROGEN-OXYGENFUELCELL

TING-HUA TANG”, I.G. CSIZMADIA”, L. PATAKIb, R.D. VENTERb and C.A. WARDb “Department of Chemistry, University of Toronto, Toronto, Ontario M5S IA1 (Canada) bDepartment of Mechanical Engineering, University of Toronto, Toronto, Ontario M5S IA1 (Canada) (Received 1 December 1990)

ABSTRACT Ab initio SCF MO calculations were carried out within the restricted Hartree-Fock (RHF) and restricted open-shell Hartree-Fock (ROHF) formalisms, for closed-shell and open-shell systems respectively, using a 6-31+ +G** basis set for the investigation of the 22 possible reaction mechanisms associated with the anodic process H2 -t2H+ + 2e- of the alkaline Hz-O2 fuel cell. Such hypothetical gaseous phase reactions might be used as a preliminary model for the understanding of the real electrochemical process.

INTRODUCTION

Theoretical studies on the various possible reaction mechanisms for the overall anonic process H, -+2H+ + 2e- of the Hz-O, alkaline fuel cell have been carried out previously at the 3-21 +G basis level [ 11. The analogous process for the Hz-O, acidic fuel cell has already been studied using the refined 6-31+ + G** basis set [ 2 1. The influence of correlation energy on some of the reactions at the MP4SDTQ/6-31G** level of theory has also been evaluated. In this particular case it appears that the 6-31+ + G” basis set at the HartreeFock (HF) level of theory is about as reliable as the calculations obtained at the MP4SDTQ/6-31G** level of theory. It seems that a more precise and in-depth study at a higher level of calculation of the Hz-O, alkaline fuel cell is also needed. In the present work we studied the hydrogen electrode of an Hz-O, fuel cell with an alkaline aqueous medium as electrolyte. The results of an ab initio study for the various possible reaction mechanisms for the overall anodic process H,-+2H+ + 2e- at the 6-31+ + G** level are reported herein. 0166-1280/91/$03.50

0 1991-

Elsevier Science Publishers B.V.

TABLE 1 The 22 possible reaction mechanisms for the overall process H, + 2HO- + 2H,0+4H,O Mechanism no.

Step no. Initial

1

+ 2e-

H,+2HO-

+2H,O

1

2

3

+H,O-+HO-+2H,O

+H,O+HO-+2Hz0+e-

+H,O++2H,O+HO-+2e+H,O; +2H,O+e-

+2H+2HO-

-i2Hz0- +2H,O +2H30+2HO-

2

+H40y +2H,O+e-

3 4 5 6

+2Hz0

7 8

+Hz++2HO-+2Hz0+e-

+H30+HO-+2Hz0+e-

+ 2H,O; +H30++2H,0+HO-+2e+ H,O, + 2H20 + 2e+H40~ +2H,O+e-

9

10 11 12 13 14 15 16 17 18 19 20 21 22

+2H30++2HO-+2e-. 2H40;

+H40+2HO-+HzO

+H40++2HO-+HzO+e-

+H502+HO-+HzO+e-

+H,Or+HO-+H20

+H30-

+2Hz0+HO-

-+H,Oz+HO-+H,O+e-

+H40++2HO-+HzO+e-

+H,Oz+HO-+HzO+e-

Mechanism no.

Step no. 4

5

6

1 2 3 4 6 6 7 8 9 10 11

-+4H,O+2e-+ + + + + + + + +

+HzO-+3Hz0+e+ H,Oz + 2H,O + 2e-

+ 2Hz0 - + 2Hz0 -+2H,02 + 2e+HzO-+3Hz0+e+ H,O* + 2H,O + 2e+H30+2H,0+HO-+e-

12 13 14 16 16

+H30+2H,0+HO-+e-

17 18 19 20 21 22

+H30+2Hz0+HO-+e-

-+H,O+2H,O+HO-+e-

Final

-+H30++2H,0+HO-+2e+H,O;+2H,O+e-+H30++2Hz0+HO-+2e+H,O,+2H,O+e+H30++2H,0+HO-+2e+H,O;+2H,O+e+H30++2Hz0+HO-+2e+H40;+2Hz0+e-

+H402+2H20+2e+H,O-+3H,O+2e+H,0z+2H,0+e+H,O-+3H,O+e-tH10z+2Hz0+2e-+H,O-+3H,O+e+ H,Oz + 2Hz0 + 2e+H*O-+3H,O+e-

+ + + + -b -+ + -i -+ + --t

228 TABLE 2 The 6-31+ + G” optimized geometries and related SCF energies of the species involved in the 22 possible mechanisms associated with the alkaline Hz-O2 fuel cell Molecule

Geometry”

H+

SCF energy (hartree ) 0.00000

HZ

R(H-H)

=1.0318

H20-

R(O-H) =0.9818 L (HOH) = 112.50

- 75.62422

H,O+

R(O-H)=0.9617 L (HOH) = 114.50 Csu

-76.31119

H,O+

R(O-H) =0.9760, R(O-H3) = 1.2608 L (H10H2) = 107.39, L (H30H4) =98.96 ~Dihedral= 102.39 C,,

- 76.68110

H

-0.59551

- 0.49880 - 1.13140

H2

R(H-H)=0.7330

OH

R(O-H) =0.9544

- 75.38941

H,G

R(O-H) =0.9432, L (HOH) = 107.09

-76.03131

H,G

R(O-H) cO.9848, L (HOH) =109.64 C,,

- 76.48478

H,G

R(O-H) = 1.0833 Td

- 76.88146

HO-

R(O-H) =0.9480

- 75.38419

H,O-

R(O-H)=0.9506

- 75.98973

H,O-

R(O-H1)=0.9912 C,, L (HOH) = 109.11

- 76.46573

H&zb H,Gzb H,Orb

- 152.07063 - 152.52759 - 152.04032

H,OF~

- 152.50191

“Bond lengths (R) in &ngstriims;bond angles in degrees. bOptimized geometrical parameters are shown in Fig. 1.

229

METHODS

The ab initio calculations for the possible theoretical mechanisms of the overall process Hz +2H+ + 2e- of the Hz-O, alkaline fuel cell were carried out within the restricted HF (RHF) and restricted open-shell HF (ROHF) formalism for closed-shell and open-shell systems respectively. All calculations were performed using the 6-31+ + G**basis set [ 31. The 6-31+ + G** basis set was derived from a standard split-valence basis set of 6-31G [ 41 type by adding a set of d orbitals as the polarization functions and a simple diffuse sp shell for heavy atoms as well as a set of p orbitals as the polarization functions and an extra diffuse s function for hydrogen. It was reported that the diffuse functions are more suitable for species with significant electron density far removed from nuclear centres and have significant effects on geometries and energies of anionic species [ 5 1. All computations were carried out on the CRAY XMP computer using the GAUSSIAN 90 program [ 61.

H4°2

H50 2

Fig. 1. Optimized geometries of H,02, H,O, level of theory.

, H502 and H50~ obtained at the HF/6-31+

+G”

TABLE 3 Total energies (hartree ) for the various reaction intermediates of the 22 possible mechanisms Mechanism no. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22

Step. no. Initial

1

2

3

- 303.96240

- 303.91254

-303.93159 -305.93159 -305.93159 - 304.04208 - 303.13794 - 303.73794 - 303.73794 - 303.93159 - 303.93159 - 303.93159 - 303.48079 -303.48079 - 303.48079 -303.91741 -303.91741 -303.91741 -303.91741 -303.91741 - 303.91741 - 303.48079 - 303.48079 - 303.48079

-303.75800 -304.10294 -304.10294

- 303.91259 - 303.91259 - 303.82860 - 303.82860 - 303.82~0 - 303.82860 - 303.42651 - 303.42651 - 303.42651 -303.42651 - 303.42651 - 303.42651 -303.68115 -303.68115 - 303.68115 -303.68115 -303.68115 - 303.68115 -303.68115 -303.68115 -303.68115

- 303:9076 - 304.0~64 - 304.08064 - 303.75800 - 304.10294 - 304.10294 - 303.94309 - 303.94309 - 303.94309 -303.91254 -303.91254 -303.91254 - 303.94309 - 303.94309 - 303.94309 - 303.943~ - 303.94309 - 303.94309

4 - 364:8366 -304.13325 --t

5

6

--t --f -_) --t -+

- 304~04208 -304.14126

--t

-a 3

- 304>8366 - 304.13325 -303.93159 -303.93159 -303.93159 - 303.93159 - 303.93159 -303.93159 -303.93159 -303.93159 - 303.93159 -303.93159 -303.93159 -303.93159

-+

-3037;5800 - 304.10294 -304.10294 - 303.75800 -304.10294 - 304.10294 - 303.75860 -304.10294 - 304.10294 - 303.75~ - 304.10294 - 304.10294

Final

-_, + -_, + -+ + + + -+ + -304.13325 - 304.06366 - 304T.3325 -304.06366 - 304T;3325 - 304.08366 - 304713325 - 304.06366

-304.12524

231

-303.4oc

-304.20 t

0

I

2

3

4

5

6

7

PATH NO. 4

-

w-303.60% & 2 s--303.60-

-304.20

-304.20-

t

i; 0

I 2

I 3

I 4

I 5

I 6

7

oL 2

3

4

5

6

7

Fig. 2. Schematic energy profiles for mechanisms l-4 of the possible reaction mechanisms associated with the anodic process of the Hz-O2 alkaline fuel cell. The initial state (H, + 2HO- + 2H,O) is represented by the lower broken line and the final state (4Hz0+ 2e-) is represented by the upper broken line in each case. The energy differences between adjacent steps are given in kJ mol-‘. On the horizontal axis, 0 stands for the initial states and the arabic numerals specify the consecutive intermediate states of the mechanism.

232

PATH NO. 5

/ , 1 I / L*

d-304.00-

b

c

-

t 427.54

1

-3w.20L tllllllll -304.20-

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I2

3

4

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6

01234567

7

-m3.40yl--zq

r------7

PATH NO. 13

-303.40-

1

t

,-304.00-

-30420-

-304’2L-2

Fig. 3. Schematic energy profiles for mechanisms 6-8

3

4

5

6

7

(see legend to Fig. 2 ) .

RESULTS AND DISCUSSION

There are a total of 22 possible reaction paths; these are listed in Table 1. These reaction mechanisms can be classified into four types according to the first step in the mechanism:

233

Nos. l-3:

H2+2HO-+2HzO+HsO-+HO-+2Hz0

(1)

Nos. 4-7:

Hz+2HO-+2H20+2H+2HO-+2Hz0

(2)

Nos. 8-13:

H,+2HO-+2H,O+H,+

(3)

Nos. 14-22:

Hz+2HO-+2HzO+H10+2HO-+HzO

I

I

I

I

I

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PATH

+2HO-+2H,O+e-

I

I

NO. 9

-

-303.40

(4)

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,

PATH

,

NO. IO -

-10917

-304.20-

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I 3

I 4

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, 7

I 2

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,

-3C!4.20-

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I -303.40

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-30140-

-

-304.20-

I 3

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I 4

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I 5

I

I 6

I

I

I 7

I

PATH

I

NO.

12 -

21.03

0

I I

I 2

I 3

I 4

Fig. 4. Schematic energy profiles for mechanisms B- 12 (see legend to Fig. 2).

I 5

I 6

-

I 7

234

In mechanism sets (1) and (4), the Hz molecule is associated with HO- and H20 respectively. In mechanism set (2), the Hz molecule is atomized. Mechanism set (3) involves the molecular ionization of the Hz molecule. The 6-31+ + G** optimized geometries and related self-consistent field (SCF) energies of the 18 species involved in the 22 above-mentioned possible mechanisms are illustrated in Table 2. Some of the geometries are quite dif-

PATH

NO. 13

14 I....

-304.20

I I

0

6

I 2

I

I

I 3

I

2

I 4

I 3

I 5

I 4

I

I 6

I

5

Fig. 5. Schematic energy profiles for mechanisms 13- 16 (see legend to Fig. 2 ) .

7

I

6

I

7

I

I

I

I

1

f

PATH

-303.40-

’

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NO. 17 -

-303.60-

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1

PATH

-30140-

NO. I8

-

21.03

_

-303.60-

G;

-3wm;: k

:, 1 . .._.__..,.,. .,.,,,,,,,........_..._........._...~....,..........

-~zo~

-304.20-

0

I2

3

4

5

6

7

lillIIll1

0

I2

1

3

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4

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5

,

0

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3

4

1

7

,

PATH

-303.40-

-3~~

6

,

NO. 20 -

-30420-

5

6

7

Fig. 6. Schematic energy profiles for mech~isms

tlllllll0

17-20

I2

3

4

5

6

7

(see legend to Fig. 2).

ferent from those found previously [ 1 ] using a substantiallysmallerbasis set. Consequently,the present optimized parametersshould be more reliable,because a larger basis set has been used, than the geometries reported in the previous study of the acidic H,-0, fuel cell [ 11. The geometriesof the last three speciesin Table 2, namelyH502,H, 0, and H50;, have not been reported in the literatureat this level of accuracy.These

TABLE 4 Comparison of the thermodynamic energy separation (dE =Efinal- Ebitti) for the acidic and alkaline hydrogen electrodes in an Hz-O2 fuel cell AE (kJ mol-‘)

Ref.

AE, alkaline (kJ mol-‘)

Ref.

+ 1500.8 + 1465.0

2 7

- 427.5 -331.2

This work 1

I

-x)340-

I

I

I

I

I

I

I

PATH NO. 21 -

-303.40

-

-304.20

-

0

I

I

I

I

,

I

PATH NO. 22 -

109.17

I I

I 2

I 3

I 4

I 5

I 6

I 7

Fig. 7. Schematic energy profiles for mechanisms 21 and 22 (see legend to Fig. 2).

species are depicted in Fig. 1 together with the water dimer H402. The total energies for the various reaction intermediates of the 22 possible reaction mechanisms are summarized in Table 3. The energy differences between adjacent steps for the 22 possible reaction mechanisms are depicted in Figs. 2-7. Comparing these figures with those published in the previous paper [l] it is clear that the present energy profiles are complete because it was possible to include the energy values of the four species given in Fig. 1. In the absence of transition state energies the thermodynamics of the individual steps are used as criteria for choosing the most favoured mechanism. In the previous paper [ 11, mechanism 4 which involves the atomization of H2 turned out to be the most favoured mechanism. The present study clearly indicates that mechanisms l-3 have favourable initial reaction energies in which H2 is associated with HO-, leading to H,O-. Subsequently, mechanism 1 involves an ion-pair formation ( H30+ and HO- ) in step no. 3 via an ionization

237

process and therefore it reaches an unfavourably high energy. For this reason mechanisms 2 and 3 remain the most favoured ones. In these mechanisms, until an electron has been ejected, the system is a closed electronic shell. After one electron has been ejected the system becomes an open electronic shell. Finally, after the ejection of the second electron the system becomes a closed shell again. For mechanism 2 the open-shell steps are 2,3 and 4 and for mechanism 3 the open-shell steps are 2 and 3. In these steps the correlation energy contribution might raise the energy levels to some degree. However, the change is expected to be relatively small so that mechanisms 2 and 3 remain the most favoured mechanisms. It is of some interest to compare the energetics of the reactions at the hydrogen electrode under acidic and alkaline media. In the former case the generated proton will form oxonium ions while in the latter case the generated proton will lead to the neutralization of HO-: Hz+2HzO+2H30++4H30++2e-

(5)

Hz +2Hz0+2HO-+4H20+2e-

(6)

Clearly the first of these (eqn. (5) ) is expected to be endothermic while the second is expected to be mildly exothermic due to the large difference in the proton affinities of Hz0 and HO-. These anticipated results are confirmed numerically by both the present and previous result [ 71 which are summarized in Table 4. ACKNOWLEDGEMENTS

The continued financial support of the Natural Sciences and Engineering Research Council (NSERC) of Canada is gratefully acknowledged. Thanks are also due to the Ontario Centre for Large Scale Computation (OSLSC ) for the CPU time on the CRAY X-MP/24 supercomputer, and to Energy, Mines and Resources, Canada, for their support through the Centre for Hydrogen and Electrochemical Studies at the University of Toronto.

REFERENCES L. Pataki, A. Mady, R.D. Venter, R.A. Poirier and I.G. Csizmadia, J. Mol. Struct. (Theochem), 110 (1984) 229. T.-H. Tang, I.G. Csizmadia, L. Pataki, R.D. Venter and C.A. Ward, J. Mol. Struct. (Theothem), 230 (1991) 313. T. Clark, J. Chandrasekhar, G.W. Spitznagel and P.v.R. Schleyer, J. Comput. Chem., 4 (1983) 294. W.J. Hehre, R. Ditchfield and J.A. Pople, J. Chem. Phys., 56 (1972) 2257. W.J. Hehre, L. Radom, P.v.R. Schleyer and J.A. Pople, Ab Initio Molecular Orbital Theory, Wiley, New York, 1986, p. 86.

6 M. Frisch, M. Head-Gordon, G.W. Trucks, J.B. Foresman, H.B. Schlegel, K. Raghavachari, M.A. Robb, J.S. Binkley, C. Gonzalez, D.J. Defrees, D.J. Fox, R.A. Whiteside, R. Seeger, C.F. Melius, J. Baker, R.L. Martin, L.R. Kahn, J.J.P. Stewart, S. Topiol and J.A. Pople, GAUSSIAN 90, Gaussian, Inc., Pittsburgh, PA, 1990. 7 L. Pat&i, A. Mady, R.D. Venter, R.A. Poirier, M.R. Peterson and I.G. Csizmadia, Chem. Phys. Lett., 109 (1984) 198.