Lattice potential energies of orthorhombic and cubic cyanides of the alkali metals Enthalpy of formation, ΔH°f(CN−)(g) and solvation, ΔH°solv(CN−)(g) of gaseous cyanide ion. Experimental determination of the enthalpy of solution of crystalline lithium cyanide, ΔH°soln(LiCN)(c), proton affinity of cyanide ion and electron affinity of CN. radical

j' .nor~ nuc] ( ' h i m . '977 \ o l 39 pp 2 3-220.

Pergamon Press.

Printed in Great Britain

LATTICE POTENTIAL ENERGIES OF ORTHORHOMBIC AND CUBIC CYANIDES OF THE ALKALI METALS E N T H A L P Y ()F F O R M A T I O N , AH}(CN )(g) A N D S O L V A T I O N , AH~oJv(CN)(g) O F G A S E O U S C Y A N I D E ION. E X P E R I M E N T A L D E T E R M I N A T I O N O F T H E ENTHALPY OF SOLUTION OF CRYSTALLINE LITHIUM CYANIDE. AHL,t,(LiCN)(c), P R O T O N A F F I N I T Y O F C Y A N I D E I O N A N D E L E C T R O N A F F I N I T Y O F CN" R A D I C A L H. D. B. JENKINS* and K. F. PRATT Department of MolecularSciences, University of Warwick, Coventry CV4 7AL, Warwickshire, England and T. C, WADDINGTON Department of Chemistry, University of Durham, South Road, Durham DH1 3LE, England

(Received 17 June 1976) Abstract--The lattice energies of the cubic and orthorhombic forms of the alkali metal cyanides are calculated: Up,,~(LiCN)o~,h.= 828 kJ mol ', Upot(NaCN)o~,o= 736 kJ mol--~, U~o,(NaCN)o.,b~= 729 kJ mot ~, U o , , t ( K C N ) o r t h . : : 669kj tool ', U,,,(KCNL,,~¢=664kJ tool '. U~o,(RbCNL.b~=638kJ tool ' and Uoo~(CsCNL°b~=601kJ tool '. Using these results we estimate AH~(CN )(g) = 36kJ tool ~, AH~o.~(CN )(g) - -329kJ mol ' the proton affinity of the gaseous CN ion to be -1438 kJ tool ', the dipole moment to be ~(CN ) = 1.62D and the electron affinity of the cyanide radical to be -380 or -399 kJ tool ' depending on the value of AH}(CN')(g) used.

INTRODUCTION The alkali metal cyanides are cubic at room temperature with the exception of LiCN, which is orthorhombic. The cubic forms of NaCN and KCN exhibit polymorphic transitions to orthorhombic structures at temperatures of 288.3 and 168.1 K respectively. Lattice energies have been determined mainly for the cubic crystals but recent studies by Ladd[1] and by Jenkins and Pratt[2] have considered the orthorhombic salts. The results of Sherman [3]. Yatsimrskii[4, 5], Waddington[6], Ladd and Lee[71, Morris[8] and Ladd[l] are given in Table 1, from which can be seen the wide divergence of results obtained, These results lead in turn to wide discrepancies in other thermodynamic parameters such as the enthalpy of formation of the gaseous cyanide ion, AH}(CN-)(g) and its enthalpy of solvation, AH°otv(CN-)(g) as can be seen in Table 2. The present work attempts to calculate the total lattice potential energies for all the alkali metal cyanides, to assign thermodynamic parameters for the CN ion and to consider the charge distribution in the ion. CALCULATIONS At room temperature NaCN and KCN have the cubic NaCI arrangement with free rotation of the CN ions and cell lengths, for NaCN a = 5.893,~, and for KCN a = 6.527 ,~, at lower temperatures this rotation cannot be maintained and the structures resort to orthorhombic symmetries [9]. Orthorhombic NaCN[9, 11, 12, 13] has a bimolecular unit cell with parameters a = 3.774 A, b = 4.719A and c = 5.64/~ and KCN[9, I l, 14-17] has a bimolecular unit cell with parameters a =4.24A, b = 5 . 1 4 A and c = 6.17 A. The orthorhombic LiCN [9, 10] has a tetramolecular cell with parameters a = 3.73 A,, b = 6.52 ~., c = 8.73 ,~. RbCN [9, 11] is a cubic cell with NaCI arrangement with

a = 6.82,~ and CsCN[9, 11] has the CsCI arrangement with a = 4.25 ,~. A distributed charge is chosen to reside on the atoms of the CN ion. A charge qc is placed on the carbon atom and a charge qN on the nitrogen such that:

qc + qN = - 1 .

(I)

(it The total lattice potential energies The "term by term" expression for the total lattice potential energy takes the form: Ut,o,(MCN) = U . + UsF.+ U. - U,

(21

where Uu is the Madelung component of the electrostatic energy and USE is the internal electrostatic energy of the CN- ions, Up is the dispersion energy and U~ is the repulsion energy. The calculation of Uelec, the combination of U~t and USE, proceeds for the orthorhombic salts as follows. The Madelung constants, M, and energies, UM, were calculated for each structure using the Bertaut method [ 19 I. The results take the form:

M= ~ c~iqN~

(3)

J:n

UM = ~ AiqN~

I'4)

i=o

where ai and Ai are the usual coefficients expressing the charge dependence, the values are cited in Table 3. For the self energies of the ions:

UsE -- ~a BiqNi i=1

213

(5)

cubic

cubic

cubic

KCN

RbCN

CsCN

1947

623

648

678

749

803

1956 1959

582

632

661

728

(c)

Waddington

(c) Born-Mayer Equation

644

6 74

699

774

(b)

Yatsimi~kii[5]

Equation

Yatsimkskii[4] (b)

(b) Yatsimlrskii

591

624

648

Ly~Cropic number determination.

orthorhombic

KCN

709

Born-Lande equation.

cubic

NaCN

(a)

(f)

orthorhombic

NaCN

1932

Sherman[3]

(a)

orthorhombic

LiCN

Lattice Energies, Upo t -I (kJ mol )

1960

6 74

745

(e)

Ladd/Lee[7]

(d) Term by Term

596

629

655

712

(d)

[6]

Table 1. The lattice energies of alkali metal cyanides (kJ mol-' 1961

1969 1975

1975

611

640

6 74

677

728

734

791

-

-

664

665

729

732

601

638

664

669

729

736

828

Ladd[l] Jenkins/Pratt[21Uhis work (e) (d) (d)

(e) Ladd and Lee Equation

665

741

Morrisl8] (f)

==

=

"2--

Lattice potential energies of orthorhombic and cubic cyanides of the alkali metals Table2. Enthalpy data for gaseous cyanide ion (kJ mol ') Source

Sherman 1932

AH~(CN-)(g)

[3]

AH~olv
Notes

23.1

average

[4i

53.8

average

Yatsim Lrskil [5] 1956

71.1

Waddington

29.9

average

28.0

average

Yatsim ~skii 1947

[6]

1959

Ladd and Lee [7] 1960

54.4

Morris [8] 1961

46.0

Ladd [i] 1969

44.3 ! 4

- 305

- 285 ± 4

Berkowitz, Chupka and Watter [31] 1969

68.5

Jenkins and Pratt [2] 1975

33

- 326

This work 1975

36

- 329

experimental

Table 3. Corn ~utational results for orthorhombic cyanides Parameter

M

LiCN

0.676302 O.881748 1.009264

0.629972 1.039965 1.O39965

O. 589937 i. 0;33728 I. 0133728

Lfl

1.1421

1.0476

1.0794

835.4 1379.2 1379.2

759.3 1330.5 1330.5

-1216.4

-1326.1

-1287.1

-1216.4

-1326.1

-1287.1

822.7 -143.8 11.3

835.5 53.0 53.0

759.3 43.4 43.4

UR+

0.5 14.9 107.4

0.4 12.6 83.8

0.7 3.8 88.9

UR

122.8

96.8

93.4

0.01

0.2

1.2

3.5

3.0

1.6

1.O

2.9

7.0

4.5

6.0

9.8

704.4

744.6 53.0

675. 7

53.0

43.4

B1

i kJ mol -] B2 Uelee c o I kJ mol ~] ~i 4-

kJ mol -I

uo4kJ

mol ~I UD UD+ UD

Upo t DO I kJ mol -I D 1 i

D2

822. 7 I072.6 1227.7

- 143.8

11.3

Notes

KCN

do ~I ~2

a0 UM A1 kJ mol ~] A2

USE

NaCN

43.4

based on C-N shortest distances = L

?.15

H. D. B. JENKINS et al.

216

where the BI coefficients express the self energy term charge dependence. In the orthorhombic case USE was calculated explicitly and the results are listed in Table 3. In the cubic phases, since the CN- ions are rotating, the rest of the lattice "sees" these ions as spheres of charge distribution and UM = Uo~o~. The electrostatic contribution, U,~o=is therefore calculated. The repulsion energies of the salts are calculated using the equations given

Upo~(NaCN)or~o= 736.4 kJ mol -l Upot(KCN)o~tho= 669.0 kJ mol-' Upo~(NaCN)cubi¢= 728.8 kJ tool -1 Upot(KCN)c,bic= 663.8 kJ mol-l Upo,(RbCN)o.bic= 638.4 kJ mol -~ Upot(CsCN)c,bic= 600.9 kJ mol-~.

U=,~== ~ CqN'

(6)

i=0

in Ref. [2], which employ the Huggins and Mayer method[20]. The dispersion energies are calculated from the London[21] formula as given in Ref. [2]. The results for UR and Up are given in Tables 3 and 4. The total lattice potential energies are then calculated.

Upo~= ~ D~qN'.

(7)

i~0

On the basis of the charge distributions (qu =-0.81) calculated later we find the total lattice potential energies of the alkali metal cyanides to be: Upot(LiCN)o~,ho= 828.3 kJ mol-'

MCN(c)

,~E(MCN)+2RT

The results above are compared to our recent estimates (in the case of NaCN and KCN) and to other calculations in the literature in Table 1. (ii) Enthalpy o[ formation of CN- ion, AH~(CN-)(g) In order to carry out this study it was necessary to prepare a sample of LiCN and then measure AH°oz,(LiCN)(c) experimentally. The preparation and subsequent measurement are described in the Experimental Section of this paper. The results obtained were that AH~°oj,(LiCN)(c) = - 6 . 5 kJmo1-1. Combining the known values of AH~(Li+)(aq) = -278.4 kJ tool-' [22] and AH~(CN-)(aq) = 150.62 kJ tool-' [23] with the above result gives a value of AH~(LiCN)(c) = -121.3 kJ tool -~. Values for the sodium and potassium salts are available. From the cycle:

, M+(g) + CN-(g)

AH~(MCN)(c)

AH~(M+)(g) + AH~(CN-)(g) M(c) + C(c) + ~Nz(g)

AE(MCN) + 2RT = AH~(M+)(g) + AH~(CN-)(g) - AH~(MCN)(c).

(8)

Table 4. Computationalresults for cubic cyanides

Parameter

NaCN

L

UM = Uelec

MCN

~

UM/kJ mol -I

2.946

KCN

3.263

RbCN

3.41

CsCN

4.25

824.0

744.0

712.O

665.4

UR ++

O. 4

O. 7

O. 8

4.7

UR UR+ -

14.3 85.9

3.9 84.0

2.1 81.3

5.7 73. I

iOO. 5

88.6

84.2

83.4 6.9

kJ mol -I

!U R kJ mol -I

UR q-+ UD

UD

0.2

i.i

2.1

kJ tool-I

U D -UD + -

2.8

1.5

i,i

1.4

2.4

5.8

7.4

10.5

UD

5.4

8.4

10,6

18.9

Upo t

DO

728.8

663.8

638, 4

600, 9

kJ tools I

DI

0.0

0.0

O, 0

0.0

D2

0.O

0.0

0,0

0. O

217

I altice potential energies of orthorhombic and cubic cyanides of the alkali metals Simple thermodynamic arguments show that the total internal energy change, AE(MCN) + 2RT can be equated to the total lattice potential energy of the salt:

The curves (11) to (15) are plotted in Fig. 1. Table 5 gives details of the intersection points and values: ~H~(CN )(g) = 36.35 kJ tool '

AE(MCN)-- 2RT = Upo,(MCN)

(9)

(16)

AHt°(CN-)(9) vsq/v

and hence AH~tCN I(~o ) - U,,o,(M( N )(c) + AH~(MCN)(c) - AH}(M~)(g).

(10)

We use the known values AH~NaCN)(c,cubic)= -89.79 kJ tool ' AH}(NaCN)(c,orthorhombic) = -92.72 kJ tool '. AH~(KCN)(c,cubic) = -112.55 kJ tool '. AH}(KCN)(c,orthorhombic) = -113.81 kJ mol '[22, 24] and iH}(I.,i+)(g) = 687.16 kJ tool ', AH~(Na+)(g) = 609.84 kJ tool ', AH}(K+)(g) = 514.2 kJ tool '. From the data for Li(TN we find (in kJ tool ')

5O

~

CN

~ ~hombic

/

cV

IHT(('N )(~'i = - 1(!4.06- 143.80qN + 11.27q.~2 (11) from that for NatTN. for the cubic case we find: AH':(CN /!.e i = 29.19 kJ tool '

(12)

and for the orthorhomb~c salt

""orthorhombi@__l c

AH}(CN )(g) = 42 08 +53.02qN +53.02qu 2

(13)

for KCN. the orthorhombic case gives: AH~(CN K~,) = 4"L7 + 43.41qN + 43.41 qN:

(14)

05

and for the cubic case: AH~fCN )lg) = 37.06 kJ mol '.

qN Fig.I.

(15)

Table 5. Intersection points in Fig. 1. AH}(CN )(g) vs qN Point

AH~(CN-)(g)

qN

(kJ mol -I)

(proton units)

a b c d e f

29.19 29.19 38.33 37.06 37.06 37.06

-0.58 -0.87 -0.92 -0.57 - O. 92 -0.86

g

4.6.57

-0.97

Overall average

36.35

-0.81

Average of c and g

,12.45

-0.94

Intersection Points in Fisure 2.

Point

AH~ol.v(CN-)(g) (kJ tool-I)

a b c d

o AHsolv(CN

)(g) vs qN ~

qN (proton units)

-321.70 -321.70 -330.04 -330.17 -330.17 -330.17 -339.16

-0.58 -0.85 -0.91 -0.57 -0.91 -0.86 -0.96

C~erall Average

-329.02

-0,81

Average of c and g

--334.60

-0,94

e f g

iO

H. D. B. JENKINS et al.

218

qN = -0.81

(17)

are assigned. As has been noted in our earlier study [2], the symmetry of lattice potential energy curves for which

Upot=~ DiqNi=~ Diqci i =0

(18)

i =0

means that abscissae for intersection points to the right of qN = - 0 . 5 correspond to qN charges while abscissae for intersection points to the left of qN = -0.5 correspond to qc values and are related to the former abscissae by the required relationship:

qc + qN = -1.

(v) Proton a[finity of the CN- ion The proton affinity, AHI H+(g)+CN-(g)

an, ) HCN(g)

(19)

(iii) Enthalpy and solvation of CN- ion, AH%,~(CN-)(g) From the cycle: MCN(c)

(iv) Charge distribution in CN ion and dipole moment The value qN =-0.81, qc =-0.19 for the charge distribution of the CN- ion is in reasonable agreement with the results of Demnynck, Veillard and Vinot[26] (qN = -0.57), Hillier and Sanders [27] (qu = -0.59) and of our earlier study[2] (qN =-0.57). The calculated dipole moment on the basis of a charge distribution as obtained in this study is found to be 1.62D which lies between the values calculated recently by Bonaccorsi, Petrongolo, Scrocco and Tomasi[28, 29] (0.81D, 1.84D).

for the gaseous cyanide ion, has received some attention in the literature and values (after correction for the RT term) of - 1538 kJ mol-~ [28], -1554 kJ mol-~ [28],

aE(MCN)+2~T ' M+(g) + CN (g)

AH%,,(MCN)(c)

AH%,v(M+)(g) + AH~o,v(CN-)(g) ~M+(aq) + CN-(aq),

AHL,v(CN )(g) = AH%,,(MCN)(c)- Upot(MfN)(c) - aH°ot,(M+)(g).

Using the value AH%~.(LiCN)(c) = -6.5 kJ mol-' determined in this present study, together with the values AH%I.(NaCN)(c) = 1.26kJmo1-1 and AH%l,(KCN)(c) = 11.71 kJ mol -~ [22] and the solvation energies: AH%~,(Li+)(g) = -520.25 kJ mol -~, AH°o~v(Na+)(g) = -405.86 kJ mol-~, AH°o~v(K+)(g) = -321.93 kJ mol-~, taken from Halliwell and Nyberg [25] we obtain the equations below. From the orthorhombic salts, the data for LiCN gives: AH%,v(CN-)(g)

=

-190.65 + 143.80qN - 11.27q~

(20)

-1470 kJ mol-' [30] and -1434 kJ mol=' [2] have been assigned. Using the data[23] AH}(HCN)(g) = 135.1 kJ mol-' and AH~(H+)(g)= 1536.2kJmol -' we obtain from the present study, where AH~(CN-)(g) = 36.4 kJ tool-l, AH,

= -1438

kJ m o l - L

(28)

AHOv(cN-)(g) vs qN

(21)

LiCN

-310

for NaCN we have: AH%zv(CN-)(g) = -334.59 - 53.02qN - 53.02q~

(22)

and for KCN we have: AHs%lv(CN-)(g) = -340.81 - 43.41 qN - 43.41 q•

:u~c

NoCN

(23)

for the cubic data, for NaCN AH%I.(CN-)(g) = -321.70 kJ mo1-1

(24) -330

and for KCN AH%j,(CN-)(g) = -330.17 kJ mol-L

(25)

Curves (21)-(25) are plotted in Fig. 2. Table 5 gives details of the intersection points and values AH%~v(CN )(g) = -329.0 kJ mol-' qN = -0.81

(26) (27)

0

-0.5 q,v

are assigned.

Fig. 2.

-I.0

1,attice potential energies of orthorhombic and cubic cyanides of the alkali metals Ivi) Electron affinity of CN. radical The electron affinity of the CN- radical is given by the equation:

219

tatic charging of the particles was reduced by use of an Americium sample. (Found: C, 35.2. N, 42.9, Li, 20.3%, LiCN requires C, 36.4; N, 42.5; Li 21.1%). The enthalpy of solution was measured using the LKB 8700 Precision calorimeter system as manufactured by LKB Produckter A.B., S-I61 25 Bromina 1 Sweden, at Royal Holloway Col[ege, London, Several runs were made and it was a noteable trend that values for AH','o,,(LiCN)(c) as measured increased with time (-6.72 kJ mol ', -6.66 kJ mol ', -6.47 kJ mol ' and -6.21 kJ tool ') and we ascribed this trend to the fact that LiCN, being intensely hygroscopic, was picking up moisture even though

EA (CN') = AH}(CN )(g) - AH}(CN')(g) + ~RT. (29) Assuming our value for AH}(CN-)(g) and using the values for AH~CN')(g) as indicated we obtain the results in Table 6 which can be compared to the literature values given there.

Table 6. Electron affinity and enthalpy of formation of CN' radical E(CN" )

1932

Sherman [39]

3.0 eV

1932

Lederle [37]

4.0 eV a 3.0 eV a'c

1942

Rah~nowitch [41]

1947

Natsen, Robertson and Chouke[38]

7.0 eV a

1953

Prilchard [40]

3.6 eV

1959

Stein and Trieinin [42]

3.0 eV a'c

1959

Bak~ilina and Ionov [33]

3.7 eV a

1960

Herlon and Dibler [34]

1960-66

I~!naf Tables [32]

AH°(CN" ~(g) f

3.2 eV a 3.9 eV

422.5 kJ mol -I

1961

Brai~scombe [43]

> 3.0 eV a

1962

Bul(wicz and Padley [35]

1962

Bauer [361

1963

Napper and Page [35]

2.8 eV a'c

387.9 kJ mol -I

1969

Berkowitz, Chupka and Walter[31]

3.8 eV~ 4.2 eV

441.4 kJ mol -I

1975

J e n k i n s and P r a t t

4.2 eVb

441.4 kJ mo1-1

1975

This work

3.9 eVd 4. J eVe

422.5 kJ mol-i1 441.4 kd tool

3.0 eV a'c 523 kd mol -I

[2]

a.

Experimental values.

b.

Using present value for AH~(CN-)(g)

c.

Based on Napper and Page's value for AH~(CN')(g)[35I, which is based on

d.

Based on the AH~(CN')(g) value in reference [321.

e.

Based on the AH~(CN')(g) value in reference [231.

Co~trell's[44] value for AH~(CN-)!g).

EXPERIMENTAL

The preparation of crystalline lithium cyanide was adapted from that of Perret and Perrot[45]. Small lumps of lithium metal were cut under petroleum ether and transferred to a glass ampule terminating in a Rotaflo TF6/24 tap. After evacuation a slight excess of anhydrous hydrogen cyanide was condensed onto the metal at 77 K. The mixture was carefully warmed towards room temperature until the reaction became vigorous when it was stopped by recooling to 77 K The hydrogen was pumped away, further hydrogen cyanide added and the mixture again warmed towards room temperature. This process was repeated five times until a six-fold excess of hydrogen cyanide had been added. At this stage the reaction was not complete, but further reaction became very sluggish.t The excess hydrogen cyanide was distilled from the mixture by pumping on it through a trap cooled to 77 K for 12hr. The solid was transferred in a dry-box containing nitrogen dried with sodium-potassium alloy. The excess lithium metal was removed mechanically and the difficulty encountered with the transference of the very light powder due to the electros-

+This method produced a bulky white solid. If larger quantities of hydrogen cyanide are used to accelerate the reaction, higher temperatures and consequent polymerisation of the hydrogen cyanide occurs.

stringent precautions were taken at every stage to prevent this. An average value of -6.5 kJ tool ' was used for the present calculations. DISCUSSION The necessity of treating the CN ion as a spherical rotating charge in the cubic salts NaCN and KCN does not enable us to parameterise the cubic equations as charge dependent functions. Consequently values of the parameters in Table 5 derived from averages of the orthorhombic data (c and g) may be more reliable. The previous results[2] obtained from a consideration of the polymorphic modifications of NaCN and KCN and the known enthalpy of transition agree extremely well with those resulting from these studies. The thermodynamic data so derived (although somewhat at variance with the previous estimates (Table 2), particularly in the case of AH,%~v(CN )(g)) we believe represent reasonable estimates of the parameters involved. We also must bear in mind that even the more comprehensive of all the previous studies (probably those of Ladd and Lee[l] and Morris [8]) do not use equations which are directly applicable to complex ions. In order to seek further validation

220

H . D . B . JENKINS et al.

for the derived thermodynamic parameters for the gaseous C N - ion we shall attempt to calculate AH~(CN-)(g) and other parameters from a study of the NH4CN crystal, in addition to developing new approaches to the estimation of these quantities [46, 47].

Acknowledgements--Dr Peter Gates and Dr Arthur Finch are thanked for their kind hospitality to HDBJ and KFP at Royal Holloway College in September this year and for allowing the use of the L.K.B calorimeter for our purposes of measuring AH°o~,(LiCN)(c). Dr C. J. Ludman is thanked for his perseverance in preparing a pure sample of LiCN when many proposed preparative schemes proved unsatisfactory. The assistance of M. Stephens Esq. with the practical work is acknowledged.

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