Chemical Physics Letters 478 (2009) 115–119

Contents lists available at ScienceDirect

Chemical Physics Letters

journal homepage: www.elsevier .com/ locate /cplet t

Thermochemistry for silicic acid formation reaction: Prediction of newreaction pathway

Bhaskar Mondal, Deepanwita Ghosh, Abhijit K. Das *

Department of Spectroscopy, Indian Association for the Cultivation of Science, Jadavpur, Kolkata 700032, India

a r t i c l e i n f o

Article history:Received 18 May 2009In final form 18 July 2009Available online 23 July 2009

0009-2614/$ - see front matter � 2009 Elsevier B.V. Adoi:10.1016/j.cplett.2009.07.063

* Corresponding author. Fax: +91 33 2473 2805.E-mail address: spakd@iacs.res.in (A.K. Das).

a b s t r a c t

Reaction between SiO2 and water has been studied extensively using ab initio methods. The mechanismfor formation of metasilicic acid SiO(OH)2 and orthosilicic acid Si(OH)4 has been explored and a new path-way for formation of Si(OH)4 is predicted. Heats of reaction (DrH

�298) and heats of formation (Df H�298) at

298 K for the related reactions and species calculated at two different theoretical levels G3B3 andG3MP2B3 agree well with the literature values. It is found that when SiO2 reacts simultaneously withtwo water molecules, the thermodynamic as well as kinetic feasibility of the process is much greater thanthat when SiO2 reacts with one molecule of water.

� 2009 Elsevier B.V. All rights reserved.

1. Introduction

Silicon-based ceramics are promising candidate for structuralmaterials of heat engines. The long-term stability of these materi-als to environmental degradation depends on the formation andretention of a protective SiO2 layer. It is well known that SiO2 formsstable volatile hydroxides in the presence of water vapor at ele-vated temperatures. Combustion conditions, which characteristi-cally are at high velocities, contain significant water vaporpressures, and high temperatures tend to promote continuous for-mation of these hydroxides with resulting material degradation.For the degradation of silicon-based ceramics to be predicted,accurate thermodynamic data on the formation of silicic hydrox-ides are needed. The transport of silica in steam atmosphere is gov-erned by some vapor species like metasilicic acid SiO(OH)2,orthosilicic acid Si(OH)4 and their mixed dimer SiO(OH)6 [1]. Rea-sonable chemical processes involving silica and water can be rep-resented by the following reactions:

SiO2 ðquartzÞ þH2O ðgasÞ ! SiOðOHÞ2 ðgasÞSiO2 ðquartzÞ þ 2H2O ðgasÞ ! SiðOHÞ4 ðgasÞ2SiO2 ðquartzÞ þ 3H2O ðgasÞ ! Si2OðOHÞ6 ðgasÞ

The thermodynamics of gaseous silicon hydroxides and the effectson the volatility of silica in the presence of steam are of interestin the analysis of geologic phenomena, and also in assessing thedurability of silica catalyst supports for use in natural gas combus-tion. In the work of Hildenbrand and Lau, a brief thermochemicalstudy of the silica-steam reaction was made by mass spectrometry[2,3]. Theoretical and experimental characterization of the thermo-

ll rights reserved.

chemical properties of Si–O–H systems can also be found in litera-ture [4,5]. Zhou et al. made a density functional approach inaddition to matrix isolation infrared spectroscopy, to characterizethe reaction between SiO2 and water [6]. But as far as our knowl-edge goes there is no theoretical work on the thermochemistryfor the silica (SiO2)–water reaction. Our objective of this Letter isto study the mechanism and thermochemistry for the underlyingsilicon dioxide–water reaction process. Besides, it is important toexplore the kinetic aspects of the silicic acid formation reaction.We have used high level theories and composite ab initio methodsto explain the silicon dioxide–water reaction. Although SiO2 canform complexes like SiO2�(H2O)n, where n = 1, 2, 3, 4, etc. in pres-ence of water vapor, but in this letter we concentrated only onthe mechanism of silicic acid formation reaction. So, the complexesof SiO2 with one and two molecules of water are considered here. Infuture the reaction processes of SiO2 with water will be investigatedthoroughly taking into account all possible stable SiO2�(H2O)n com-plexes as reactant states.

2. Computational details

All ab initio molecular orbital theory calculations have been car-ried out using GAUSSIAN 03 suite of quantum chemistry program [7].The equilibrium geometries of the species involved are obtained atthe level of second order Møller-Plesset perturbation (MP2) theory[8] with 6-311+G(d,p) basis set. The connecting first order saddlepoints i.e. the transition states between the equilibrium geometriesare obtained using synchronous transit-guided quasi-Newton(STQN) method. Normal mode analysis has been carried out atthe same level of theory for equilibrium as well as transition stategeometries and characterized as minima (no imaginary frequency)or as a transition state (one imaginary frequency). A parallel intrin-sic reaction co-ordinate calculation (IRC) has been performed with

Table 2Relative energies (kcal/mol) of various species in the SiO2 + H2O reaction calculated atdifferent theoretical levels.

Species CCSD(T)/6-311G(d,p)//MP2/6-311+G(d,p)

G3B3 G3MP2B3

SiO2 + H2O 0.00 0.00 0.00SiO2�H2O �19.30 �22.04 �19.90TS1 �11.60 �14.12 �11.68SiO(OH)2 �63.44 �68.06 �65.62SiO(OH)2 + H2O 0.00 0.00 0.00SiO(OH)2�H2O �18.61 �17.91 �16.40TS2 �15.45 �15.15 �13.30Si(OH)4 �67.74 �67.45 �65.91SiO2 + 2H2O 0.00 0.00 0.00SiO2�2H2O �36.20 �40.45 �36.65TS10 �32.70 �36.18 �32.10SiO(OH)2�H2O �82.06 �85.97 �82.02TS2 �78.90 �83.21 �78.91Si(OH)4 �131.20 �135.50 �131.53

116 B. Mondal et al. / Chemical Physics Letters 478 (2009) 115–119

all the transitions states to confirm whether these connect to theright minima or not. The higher-order correlation energy correc-tion to the MP2 energies are obtained at the single point usingCCSD(T)/6-311G(d,p) method [9] with the zero point energies(ZPE) calculated at MP2/6-311+G(d,p) level. For the calculation ofthermochemical parameters accurately, two methods from G3family, namely G3B3 and G3MP2B3 are used. These methods aredesigned to predict highly accurate energies based on the geome-tries obtained from computationally cheaper method and the stepsinvolved in these methods can be found elsewhere [10]. All the rel-ative energies in Table 2 have been corrected for zero-point vibra-tional energies (ZPVE). The relative energies predicted from G3B3level of theory are used to draw the potential energy surfaces(PES) of the mechanisms studied here. The standard heat of forma-tion at 298 K (Df H

�298) is calculated using the general formula given

below,

Df H�298ðSiO2 � H2OÞ ¼ Df H

�298ðSiO2Þ þ Df H�298ðH2OÞ þ DrH

�298

The standard enthalpies of formation for SiO2 Df H�298 [SiO2, g] =

�66.9 ± 4 kcal/mol and for H2O Df H�298 [H2O, g] = �57.08

± 0.01 kcal/mol have been taken from the experimental values ofHildenbrand and Lau [2] and Chase et al. [11], respectively.

3. Results and discussions

3.1. Potential energy surface and reaction mechanism

3.1.1. Reactions of SiO2 with H2OTo verify the accuracy of the theoretical methods used in this

calculation, we have studied all reaction steps using two differentmethodologies, namely B3LYP/6-311++G(d,p) and MP2/6-311+G(d,p). The mechanism for stepwise addition of water toSiO2 has been studied first and then addition of two water mole-cules is studied. To avoid a large number of data, the B3LYP ener-gies are skipped in Table 1. The MP2 geometrical parameters alongwith B3LYP geometries are shown in Fig. 1. All the relative energiesare calculated with respect to the reactants SiO2 + H2O.

SiO2 has a linear structure and the Si–O bond length is 1.526 Å.The association reaction of SiO2 with H2O can form a planar molec-ular complex SiO2�H2O as shown in Fig. 1. In the complex the line-arity of the O–Si–O part breaks and the bond angle \OSiO iscalculated to be 159.7� and both the Si–O bonds are elongated by0.006 Å. The SiO2�H2O complex lies 22.04 kcal/mol below the reac-tants at the G3B3 level. The predicted values are 19.30 kcal/moland 19.9 kcal/mol by CCSD(T)/6-311G(d,p) and G3MP2B3 methods,respectively. The B3LYP value of Zhou et al. was 19.4 kcal/mol [6].The G3B3 enthalpy for the complex is 23.31 kcal/mol lower thanthe reactants. The initial association of water to SiO2 is a barrier-

Table 1Absolute energies (a. u.) of the species at three different theoretical levels.

Species Symmetry CCSD(T)/6-3

SiO2 (1Rþg ) C1v �439.17910

H2O (1A1) C2v �76.25448SiO2 + H2O – �515.43358SiO2�H2O (1A1) C2v �515.46435TS1 (1A) C1 �515.45204SiO(OH)2 (1A1) C2v �515.53469SiO(OH)2 + H2O – �591.78917SiO(OH)2�H2O (1A) C1 �591.81884TS2 (1A) C1 �591.81380Si(OH)4 (1A) S4 �591.89713SiO2 + 2H2O – �591.68807SiO2�2H2O (1A) C1 �591.74577TS10 (1A) C1 �591.74016

a CCSD(T)/6-311G(d,p) energies are corrected with ZPE taken from MP2/6-311+G(d,p)

free process and this observation agrees with the experimentalfindings of Zhou et al. where the SiO(OH)2 absorptions increasedon annealing.

The rearrangement of the SiO2�H2O complex to SiO(OH)2 re-quires a reactant-like transition state TS1 of energy 7.92 kcal/molabove the complex and 14.12 kcal/mol below the reactants calcu-lated at G3B3 level of theory. These values are 8.21 and11.68 kcal/mol, respectively at G3MP2B3 level of theory. The lowactivation barrier of the rearrangement process suggests that theSiO2�H2O complex is very short-lived, rapidly rearranging to formthe SiO(OH)2 molecule. In TS1 the transition vector is dominatedby the motion of the hydrogen which is in between two oxygenatoms and the distances are 1.425 Å and 1.127 Å from the two oxy-gen atoms, respectively. The transition state is non-planar wherethe third Si–O distance is shortened by 0.4 Å with respect to thatof SiO2�H2O complex. The formation of the SiO(OH)2 is highly exo-thermic and the net exothermicity of the process is about68.0 kcal/mol at G3B3 level of theory. This value is close to theB3LYP value 61.1 kcal/mol reported by Zhou et al. The SiO(OH)2

molecule was subjected to several theoretical studies [12,13] andobserved in solid argon matrix via silane and oxygen atom reac-tions [14]. SiO(OH)2 has a planar structure with C2v symmetry hav-ing triangular Si–O–O moiety as shown in Fig. 1.

A further association of the SiO(OH)2 with another molecule ofwater yields Si(OH)4. The resulting complex of the initial associa-tion of SiO(OH)2 and water is stable over the reactants SiO(OH)2 + -H2O by 17.91 kcal/mol at G3B3 level of theory. The formation ofSiO(OH)2�H2O complex is also barrier-free. The complexSiO(OH)2�H2O rearranges to Si(OH)4 through a transition state

11G(d,p)a G3B3 G3MP2B3

3 �439.753169 �439.393578

4 �76.383726 �76.3456457 �516.136895 �515.7392230 �516.172016 �515.7709444 �516.159403 �515.7578482 �516.245352 �515.8437936 �592.629078 �592.1894382 �592.657626 �592.2155806 �592.653229 �592.2106259 �592.736570 �592.2944791 �592.520621 �592.0848680 �592.585086 �592.1432735 �592.578283 �592.136030

calculation.

O

H H0.959

103.5

0.961

105.0 O Si O1.5261.516

Si O

O

O

H

H

1.532

1.943

0.964159.7 113.0

159.3 114.2

1.526

1.930

0.966

Si

O

O

O

H

H

121.2

125.9

83.81.524

1.571

1.127

1.425

0.965

1.839

0.966

1.134

1.436

1.5681.518

1.831121.4

84.0

128.0

H2O SiO2 SiO2·H2O TS1

O Si

O

O

H

H

1.530

1.626

0.961

115.4

102.9

1.524

1.627

116.9

103.4

0.962

O

Si

OO

H

H

O

H

H

1.539

1.6511.633

1.986

0.958

0.967

102.8

0.9671.9931.537

1.6411.652

0.960

103.2

Si

O

O O

O

H H

H

H1.637

1.6291.578

1.873

0.9590.964

0.959

1.110

1.455104.3

125.7

83.9

104.3

125.5

83.8 0.960

1.631

1.638

0.960

1.878

0.965

1.119

1.459

1.577

SiO(OH)2 SiO(OH)2·H2O TS2

SiO

O

O

O

H

H

H

H

106.4

116.9

1.644

0.958

118.4

106.3

0.960

1.646 OSi

O

HO

H

O

H

H

1.5401.981

0.966

151.7

0.968

1.981 1.538

151.9

O

Si

O

O

O

H

H

H

H

1.943

1.876

0.9641.4461.110

1.533 0.967

83.3

148.2

118.5

109.5

0.9691.945

1.530

1.875

0.966

1.123 1.446

119.4

83.2

148.0

111.1

Si(OH)4 SiO2·2H2O TS1'

Fig. 1. Optimized geometries at the MP2/6-311+G(d,p) (B3LYP/6-311++G(d,p) values are shown in italics) level of the species involved in SiO2 + H2O reaction.

-70

-60

-50

-40

-30

-20

-10

0

10

SiO(OH)

TS1

SiO .H O

SiO + H O

(-68.05)

(-14.12)

(-22.04)

(0.0)

Rel

ativ

e E

ner

gy

(kca

l/mo

l)

Reaction Progress

Fig. 2. Reaction of SiO2 with H2O at the G3B3 theory level.

B. Mondal et al. / Chemical Physics Letters 478 (2009) 115–119 117

TS2 having an activation barrier of 2.75 kcal/mol calculated atG3B3 level. The corresponding G3MP2B3 value is 3.11 kcal/mol.The Si(OH)4 is surrounded by four –OH groups arranged tetrahe-drally with each Si–O bond having bond distance 1.644 Å as shownin Fig. 1. According to our MP2 calculations, the Si(OH)4 has S4

symmetry which is in good agreement with the previous theoret-ical study [15]. The G3B3 potential energy surfaces (PES) for theabove stepwise reaction mechanisms are shown in Figs. 2 and 3.

3.1.2. Reaction of SiO2 with 2H2OIn this section we describe in detail the mechanism of direct

two water addition reaction to SiO2 and the resulting formationof Si(OH)4. The direct association of two molecules of water withSiO2 via a barrier-free process stabilizes the system by about40.0 kcal/mol with respect to the reactants SiO2 + 2H2O. This sta-bilization is almost double than the association of one moleculeof water with SiO2. The complex formed has a non-planar structurewith \OSiO = 151.7�. Both the –OH2 moiety are datively bonded tothe Si-atom with a distance of 1.981 Å. The complex SiO(OH)2�H2Odiscussed earlier, is stable over the SiO2�2H2O by 45.5 kcal/mol andhence the later can easily convert to the former through a transi-tion state TS10. The activation barrier for this conversion is calcu-lated to be 4.25 kcal/mol (G3B3 value) which is very small andthus favors the conversion rapidly. The TS10 has a non-planar struc-ture where one water molecule is datively bonded to the Si-atom.A distance between the Si-moiety and the water molecule is main-tained as 1.943 Å. The final conversion of the complexSiO(OH)2�H2O to the Si(OH)4 follows the same pathway discussedabove with a activation barrier of about 2.75 kcal/mol. The alterna-tive route for Si(OH)4 formation via two water complex is pre-dicted to be thermodynamically more favorable due to largethermodynamic feasibility of initial complex formation. At thisjuncture it is important to investigate the kinetic feasibility ofthe two pathways leading to Si(OH)4. The SiO2�H2O complex pro-ceeds through an activation barrier of 7.91 kcal/mol (G3B3 value)for further reaction to form Si(OH)2 which leads to Si(OH)4 viaSi(OH)2�H2O formation, whereas the SiO2�2H2O complex proceeds

-70

-60

-50

-40

-30

-20

-10

0

10

Si(OH)

TS2

SiO(OH) + H O

SiO(OH) .H O

(-67.45)

(-15.16)(-17.91)

(0.0)

Rel

ativ

e E

ner

gy

(kca

l/mo

l)

Reaction Progress

Fig. 3. Reaction of SiO(OH)2 with H2O at the G3B3 theory level.

-140

-120

-100

-80

-60

-40

-20

0

20

Si(OH)

TS2SiO(OH) .H O

TS1'SiO .2H O

SiO + 2H O

(-135.50)

(-83.21)(-85.97)

(-36.2)(-40.45)

(0.0)

Rel

ativ

e E

ner

gy

Reaction Progress

Fig. 4. Reaction of SiO2 with 2H2O at the G3B3 theory level.

118 B. Mondal et al. / Chemical Physics Letters 478 (2009) 115–119

through a relatively lower activation barrier of 4.25 kcal/mol(G3B3 value). The barrier height of a reaction controls the rate ofthe reaction; lower barrier assists a reaction to occur fast. So, fromkinetic point of view, Si(OH)4 forms more rapidly from a two-watercomplex than from a one-water complex. Thus the formation ofSi(OH)4 through the second route is thermodynamically as well

Table 3Heats of reaction (DrH�298) and heats of formation (Df H�298) of species at 298 K predicted a

Species DrH

G3B

SiO2 + H2O reactionSiO2�H2O SiO2 + H2O ? SiO2�H2O (R1) �2TS1 SiO2�H2O ? TS1SiO(OH)2 TS1 ? SiO(OH)2 �5SiO(OH)2�H2O SiO(OH)2 + H2O ? SiO(OH)2�H2O (R2) �1TS2 SiO(OH)2�H2O ? TS2Si(OH)4 TS2 ? Si(OH)4 �5

SiO2 + 2H2O reactionSiO2�2H2O SiO2 + 2H2O ? SiO2�2H2O (R3) �4TS10 SiO2�2H2O ? TS10

SiO(OH)2�H2O TS10 ? SiO(OH)2�H2O �4TS2 SiO(OH)2�H2O ? TS2Si(OH)4 TS2 ? Si(OH)4 �5

as kinetically more favorable. A G3B3 PES for the Si(OH)4 formationin two different pathways is shown in the Figs. 3 and 4.

3.2. Heats of formation

The predicted heats of formation at 298 K of the species in-volved in the reaction including the transition states are presentedin Table 3. Heats of formation are estimated using the energies ob-tained from G3B3 and G3MP2B3 calculations and the calculatedvalues are found consistent for the two different methods selectedhere. As the G3B3 values are close to the existing literature values,the G3B3 values are used for further discussions. The heats of for-mation of SiO2�H2O and SiO2�2H2O are determined by combiningthe computed heat of reaction (DrH

�298) from the reactions R1 and

R3, respectively (refer to Table 3) with the experimental Df H�298

(298 K) values for SiO2 (�66.9 kcal/mol) and H2O (�57.80 kcal/mol). Using these heats of formation values, the heats of formationof the other species are calculated on the basis of the reactionslisted in Table 3. The heats of reaction calculated at G3B3 levelare �23.31 kcal/mol and �42.43 kcal/mol, respectively for thereactions R1 and R3. The predicted heats of formation Df H�298

(298 K) of the SiO2�H2O is �147.98 kcal/mol and that of SiO2�2H2Ois �224.80 kcal/mol. The predicted heats of formation at G3B3 le-vel for TS1, SiO(OH)2�H2O, TS2 and TS10 are �140.47, �270.62,�268.45 and �221.25 kcal/mol, respectively. These values aresummarized in Table 3 and there are no theoretical and experi-mental results available for comparison. Using reactions R1, R2and R3, the heats of formation of SiO(OH)2 and Si(OH)4 are calcu-lated. The Df H�298 (298 K) value for SiO(OH)2 is �194.14 kcal/molat G3B3 level of theory. This value is very much close to theBAC-MP4(SDTQ) value �192.3 ± 6.2 of Allendorf et al. [4]. Theexperimental heat of formation �213.4 ± 4 kcal/mol of SiO(OH)2

determined by Hildenbrand et al. is also comparable with theG3B3 values. The Df H

�298 (298 K) value �320.32 kcal/mol for

Si(OH)4 calculated by G3B3 method is in very good agreement withthe BAC-MP4(SDTQ) value �320.8 ± 3.3 kcal/mol of Allendorf et al.The experimental heats of formation of Si(OH)4 predicted by Kriko-rian [16] and Hildenbrand and Lau [2] were �327 kcal/mol and�297 kcal/mol, respectively. The G3MP2B3 heats of formation val-ues are listed in Table 3 along with the G3B3 values. Form theabove analysis on heats of formation it is clear that our calculatedG3B3 values are very much close to the existing theoretical andexperimental values.

4. Conclusions

The reaction mechanisms for the reaction between SiO2 andH2O have been investigated in detail by ab initio MP2, G3B3 and

t the G3B3 and G3MP2B3 level of theory are given in kcal/mol.

�298 Df H�298

3 G3MP2B3 G3B3 G3MP2B2

3.31 �21.17 �147.98 �145.857.52 7.81 �140.47 �138.033.67 �53.67 �194.14 �191.718.69 �17.17 �270.62 �266.672.17 2.51 �268.45 �264.151.86 �52.19 �320.32 �316.34

2.34 �38.54 �224.80 �221.003.55 3.82 �221.25 �217.179.36 �49.50 �270.62 �266.662.17 2.51 �268.45 �264.151.86 �52.19 �320.32 �316.34

B. Mondal et al. / Chemical Physics Letters 478 (2009) 115–119 119

G3MP2B3 methods. When SiO2 reacts with one H2O molecule infirst step to form SiO(OH)2 and then with another H2O moleculein second step to form Si(OH)4, the reaction possesses an initialSiO2–H2O complex of thermal stability about 22.04 kcal/mol withrespect to the reactants SiO2 + H2O. We find that if SiO2 reacts withtwo molecules of H2O simultaneously the initial complex possessesa thermal stability of 40.45 kcal/mol with respect to the reactantsSiO2 + 2H2O. The SiO2�H2O proceeds through a relatively higherbarrier than SiO2�2H2O for Si(OH)4 formation. Therefore, formationof Si(OH)4 through the simultaneous reaction of SiO2 with twowater molecules is thermodynamically as well as kinetically morefavorable. Our calculated enthalpy change for these reactionsDrH

�298, �23.31 and �42.34 kcal/mol also supports the above con-

clusion. Based on the G3B3 and G3MP2B3 energies we have calcu-lated the enthalpies of formation Df H

�298 at 298 K for the species

involved in the new reaction pathway. Enthalpies of formation at298 K for metasilicic (SiO(OH)2) and orthosilicic (Si(OH)4) havebeen calculated to be �194.14 kcal/mol and �320.32 kcal/mol,respectively. These values are in very good agreement with theexisting theoretical and experimental values.

Acknowledgements

B. Mondal is grateful to the Council of Scientific and IndustrialResearch (CSIR), Govt. of India for providing him Junior Research

Fellowship (JRF). Thanks are due to the reviewer for his construc-tive comments to improve the manuscript.

References

[1] E.L. Brady, J. Phys. Chem. 57 (1953) 706.[2] D.L. Hildenbrand, K.H. Lau, J. Chem. Phys. 101 (1994) 6076.[3] D.L. Hildenbrand, K.H. Lau, J. Chem. Phys. 108 (1998) 6535.[4] M.K. Allendorf, C.F. Melius, P. Ho, M.R. Zachariah, J. Phys. Chem. 99 (1995)

15285.[5] N.S. Jacobson, E.J. Opila, D.L. Myers, E.H. Copland, J. Chem. Thermodyn. 37

(2005) 1130.[6] M. Zhou, L. Zhang, H. Lu, L. Shao, M. Chen, J. Mol. Struct. 605 (2002)

149.[7] M.J. Frisch et al., GAUSSIAN 03, Revision B. 04, Gaussian Inc, Pittsburgh,

PA, 2003.[8] M.J. Frisch et al., Chem. Phys. Lett. 153 (1988) 503.[9] J.A. Pople, M. Head-Gordon, K. Raghavachari, J. Chem. Phys. 87 (1987)

5968.[10] A.G. Baboul, L.A. Curtiss, P.C. Redfern, K. Raghavachari, J. Chem. Phys. 110

(1999) 7650.[11] M.W. Chase, C.A. Davies, J.R. Downey, D.J. Frurip, R.A. McDonald, A.N. Syverud,

JANAF Thermochemical Tables, third edn., J. Phys. Chem. Ref. Data. 14(Suppl.)(1985) 1.

[12] J.M.L. Martin, J. Phys. Chem. A 102 (1998) 1394.[13] D.A. Dixon, J.L. Gole, Chem. Phys. Lett. 125 (1986) 179.[14] R. Withnall, L. Andrews, J. Phys. Chem. 89 (1985) 3261.[15] G.V. Gibbs, P. D’Arco, M.B. Boisen Jr, J. Phys. Chem. 91 (1987) 5347.[16] O.H. Krikorian, in: Symposium on Engineering with Nuclear Explosives, vol. 5,

14–16 January 1970, Las Vegas, NV, 1970, p. 215.