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Potential energy curves and dissociation energies of diatomic fluorides and chlorides of gallium, indium and thallium
J. Quonr. Specmsc.
Rodiat.
Transfer. Vol. I I, pp. 1577-1581.
Pergamon
Press 1971. Printed
in Great
Britain
NOTE
POTENTIAL ENERGY CURVES AND DISSOCIATION ENERGIES OF DIATOMIC FLUORIDES AND CHLORIDES OF GALLIUM, INDIUM AND THALLIUM JAGADISHSINGH, K. P. R. NAIR and D. K. RAI Department
of Spectroscopy,
Banaras
Hindu
(Received 16 Nooember
University,
Varanasi-5,
India
1970)
Abstract-The dissociation energies of diatomic fluorides and chlorides of gallium, indium and thallium have been computed by fitting the electronegativity potential energy function to the experimental potential energy curves of these molecules. The dissociation energies obtained in this manner have been compared with earlier work. These values are then discussed with special reference to the binding in these molecules.
INTRODUCTION THE dissociation energy of group IIIA monohalides has been a subject of controversy.‘1-3’ Two general methods for estimating dissociation energies from thermochemical or spectroscopic data are usually employed. Of these, the spectroscopic method gives better results. The Birge-Sponer’4*5’ extrapolation is quite easy to perform and is fairly reliable for the determination of dissociation limits whenever a sufficiently large number of vibrational spacings is known. There are, however, several groups of molecules for which this method leads to surprisingly low values for the dissociation energy. The group IIIA monohalides are typical of this group and the estimated dissociation energy, using a Birge-Sponer extrapolation of the vibrational levels in the ground state, is only about 70 per cent of the true value”’ estimated by other methods. The low value has been attributed to the high degree of ionic binding in this group of molecule@ and the consequent breakdown of the Morse potential on which the Birge-Sponer method is based. An alternative procedure for estimating the dissociation energy is to compare the experimentally obtained potentialenergy curve(‘) with an empirical function depending on the dissociation energy.‘8-‘0) Previous work using the Lippincott function (3) has also yielded low estimates. The Lippincott function is based on a b-function model of binding and is essentially covalent in character. Recently, an empirical potential function depending explicitly on the electronegativities of the atoms involved has been suggested” I) and it was thought worthwhile to see if this function leads to an improvement in the accuracy of the estimate.
1577
1578
JAGADISH SINGH. K. P. R. NAIR and D. K.
COMPUTATIONAL
The electronegativity
potential
PROCEDURE
function
AND
RAI
DISCUSSION
is
where ‘/ = de/Dd12, and a and b are empirical parameters ; b is considered to be a universal constant (5 1.065)and a = 0.35 e”’ where e = (e,e2)“’ ; e, and e2 are the electronegativities of the two atoms; d is a constant which is related to the force constant by relation k, = d(e,e,D,)1i2r;‘. The function U(r) gives quite good agreement with the RKRV-curve and
TABLE 1. POTENTIAL ENERGY CURVESFOR THEGROUNDSTATES(X'Z+)OF GALLIUM, INDIUM AND THALLIUM MONOHALIDES Electronegativity function
RKR V Molecule
L’
GUF (D, = 6.2 eV)
Umin’Fm 1, (imax““’
‘mincA)
‘max(*)
311.0 928.0 1537.5 2142.2 2738.6 33284 3913.1 4492.7 5063.3
1.718 I.680 1.656 1.637 1.622 1.608 1.596 1.586 1.576
I.839 1.891 1.928 1.961 1.991 2.018 2044 2.069 2.093
303. I 886.1 1441.1 1991.4 2501.4 3040.8 3555.9 4022.7 4528.4
993.6 1648.7 23376 3038.8 3721.5 4422.2 5129.3 5835.3
8 9 10
266.7 794.0 1319.6 1839.2 2354.0 2863.1 3367.8 3866.0 4359.4 4848.8 5331.8
1.926 1.886 1.861 1.841 1.825 1.811 1.799 1.788 1.778 1.768 I.760
2.050 2.103 2.142 2.175 2.205 2.233 2.259 2.285 2.309 2.332 2.355
259.2 768.4 1244.1 1724.1 2174.1 2620.1 3040.1 3462.8 3874.8 4314.1 4688.7
269.4 832.4 1407.6 1983.7 2570.3 3162.8 3750.5 4369.7 4963.0 5553.2 6 159.9
0 I 2 3 4 5 6 7 8 9 10 11 12
238.1 709.2 1175.6 1643.9 2102.3 2557.3 301 I.0 3457.5 3894.8 4326.7 4757.6 5185.0 5610.3
2.024 1.983 1.957 1.937 1.920 1.906 1.893 1.881 1.870 1.861 1.852 1.844 1.836
2.152 2.206 2.245 2.279 2.309 2.338 2.364 2.391 2.416 2.439 2.463 2.485 2.507
228.9 685.8 1120.1 1541.3 1962.0 2353.3 2755.4 3162.3 3565.4 3918.3 4292.0 4641.6 5007.1
251.4 759.4 1265.0 1784.5 2296.8 2833.2 3344.4 3904.9 4444.5 4957.1 5507.7 6024.6 6549.8
[/(cm
0
I)
323.5
l?lF (D,, = 5.5 eV)
0
I 2 3 4 5 6
TlF (D, = 4.75 eV)
1)
1579
Potential energy curves and dissociation energies
TABLE
1. (continued)
Electronegativity function
RKRV Molecule
GaCl (D, = 3.7eV)
ItIC (D, = 4.5 eV)
TICI (D, = 3.75 eV)
V
rmaX(A) “min’Em~‘I
Urnax(Em~ ‘)
U(cm- ‘)
‘min’“’
0 1 2 3 4 5 6 7 8 9 10
182.2 545.1 906.8 1264.3 1619.4 1973.1 2324.5 2672.3 3018.4 3362.2 3703.6
2.147 2.104 2.075 2.052 2.032 2.015 1.999 1.985 1.971 1.959 1.947
2.274 2.323 2.359 2.389 2.415 2440 2.462 2.483 2.504 2.523 2.542
181.0 559.2 947.3 1344.1 1747.6 2154.6 2568.6 2988.9 3414.8 3845.2 4277.9
182.5 537.2 884.5 1227.9 1566.4 1903.0 2237.1 2568.7 2900.8 3226.0 3554.5
0 1 2 3 4 5 6 7 8 9 10 11 12
158.4 474.0 787.4 1098.5 1407.8 1714.8 2019.8 2323.3 2624.8 2923.9 3221.0 3516.2 3809.2
2.259 2.220 2.196 2.177 2.162 2.149 2.138 2.128 2.119 2.112 2.105 2.098 2.093
2.385 2.439 2.479 2.513 2.544 2.573 2.600 2.626 2.651 2.675 2.698 2.721 2.744
158.1 442.9 703.7 948.6 1180.5 1397.5 1605.1 1799.0 1984.5 2157.7 2323.6 2467.9 2630.0
157.3 503.5 864.4 1236.4 1614.8 1999.0 239@4 2783.1 3181.1 3582.7 3989.7 4396.1 4807.0
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14
143.4 429.8 710.9 990.0 1267.6 1542.6 1815.7 2085.7 2353.5 2619.1 2882.5 3143.7 3402.7 3659.5 3914.1
2.425 2.384 2.357 2.335 2.318 2.302 2.288 2.275 2.264 2.253 2.243 2.234 2.225 2.216 2.208
2.550 2.602 2.639 2.671 2.700 2.726 2.751 2.774 2.797 2.819 2.840 2.860 2.881 2.900 2.919
135.0 408.6 677.1 942.6 1206.1 1465.5 1722.0 1981.3 2235.7 2485.3 2737.1 2986.4 3231.9 3476.9 3718.4
150.7 452.8 758.8 1065.5 1376.2 1688.2 2002.0 2319.5 2635.3 2953.5 3274.2 3593.1 3914.6 4235.6 4557.7
estimates of dissociation energies obtained by this formula are quite reliable.(‘2-‘4) The estimated dissociation energies obtained by this method for boron and aluminium halides have been reported earlier ‘i3’and were found to be much too low. The calculations have now been extended to the other diatomic halides of the IIIA group of metals. The results of the calculations are shown in Table 1. The dissociation energies obtained for the gallium,
1580
JAGADISH SINGH, K. P. R. NAIR and
D. K. RAI
indium and thallium halides, except for GaCl, are in good agreement with the values reported earlier. Table 2 gives the values of the dissociation energies reported by different methods. TABLE 2. DIWCIATION ENERGIESOBTAINEDBY DIFFERENTMETHODSFOR THE FLUORIDESAND CHLORIDES OF GALLIUM, INDIUM AND THALLIUM (IN ev) l,, State
Molecule
Gaf IllF TlF GaCl InCi TlCl
Extrapolated
624 5.46 _ 4.71 - 4.90 4.43 3.83
Predissociation
I 5.58 I 4.98 4.65
* Herzberg also gives 3.7eV. vibrational levels.
but with
From wavelengths of maxima of photoionization
Highest observed vibrational level > 6.05 > 5.42 > 4.66 >4.88 >4.39
a poor
6.24 5.46 4.75 4.92 4.44 3.88 extrapolation
Present results
6.2 5.5 4.15 3.7* 4.5 3.75 of ground-state
It has been pointed out by Mulliken that the upper state of alkali hydride molecules have a predominantly atomic character for small values of r-rer whereas, at large values of r, the curve is nearly wholly ionic. The opposite is true for the ground state. To see if similar behaviour is observed for the IIIA group monohalides, the ionic function suggested by Hellman was applied to calculate the potential curve for these molecules. It was observed that the Hellman curve approaches the experimental curve for the ground state, even for low values of r, in the neighbourhood of re. For the excited states, on the other hand, the experimental curve meets the ionic curve only for large and small r-values.‘3’ This result may be taken as an indication that the ionic contribution to the binding at r - r, is large for the ground state but quite small for the excited states. The relative closeness of the Hellman curve and the true potential curves for the first excited state is more notable for the lighter molecules; for the heavier molecules, the ionic curve is closer to the ground state. These results indicate that the heavier molecules have more ionic character in their ground state than the lighter ones. Acknowledgement~The
authors
are thankful
to Professor
N. L.
SINGH
for his keen interest
in this work.
REFERENCES 1. 2. 3. 4. 5. 6. 7.
R. F. V. B. S. N. R. T. R. T.
BARROW, Trans. Faraday Sot. 56,952 (1960). GOHEL, Ind. J. Pure Appl. Phys. 7,376 (1969). THAKUR, R. B. SINGH and D. K. RAI, J. Sci. Ind. Res. (India) 27, 339 (1968). BARGEand H. SPONER, Phys. Rev. 28,259 (1926). BIRGE, Trans. Furadpy Sot. 25, 707 (1929). A. G. GAYDON, Dissociurion Energies (3rd Edn.), Chapman & Hall, London (1968). J. T. VANDERSLICE, E. A. MASON, W. G. MAISCH and E. R. LIPPINCOTT, J. molec. Spectrosc. 3, 17 (1959); 5,83 (1960).
Potential energy curves and dissociation energies 8. 9. 10. 11. 12. 13. 14.
D. STEELE, Spectrochim. Acra 19,411 (1963). R. B. SINGH and D. K. RAI, Can. J. Phys. 43,829 (1965). K. P. R. NAIR, R. B. SINGHand D. K. RAI, J. them. Phys. 43,357O (1965). S. SZ~KE and E. BAITZ, Can. J. Phys. 46,2563 (1968). J. SINGH.K. P. R. NAIR and D. K. RAI. J. Mol. Struct. 5.492 (1970). J. SINGH;K. P. R. NAIR and D. K. RAI. J. Mol. Struct. 6,‘328 (i970). J. SINGH,K. P. R. NAIR and D. K. RAI, Ind. J. Pure appl. Phys. 8,614 (1970).
1581
Rodiat.
Transfer. Vol. I I, pp. 1577-1581.
Pergamon
Press 1971. Printed
in Great
Britain
NOTE
POTENTIAL ENERGY CURVES AND DISSOCIATION ENERGIES OF DIATOMIC FLUORIDES AND CHLORIDES OF GALLIUM, INDIUM AND THALLIUM JAGADISHSINGH, K. P. R. NAIR and D. K. RAI Department
of Spectroscopy,
Banaras
Hindu
(Received 16 Nooember
University,
Varanasi-5,
India
1970)
Abstract-The dissociation energies of diatomic fluorides and chlorides of gallium, indium and thallium have been computed by fitting the electronegativity potential energy function to the experimental potential energy curves of these molecules. The dissociation energies obtained in this manner have been compared with earlier work. These values are then discussed with special reference to the binding in these molecules.
INTRODUCTION THE dissociation energy of group IIIA monohalides has been a subject of controversy.‘1-3’ Two general methods for estimating dissociation energies from thermochemical or spectroscopic data are usually employed. Of these, the spectroscopic method gives better results. The Birge-Sponer’4*5’ extrapolation is quite easy to perform and is fairly reliable for the determination of dissociation limits whenever a sufficiently large number of vibrational spacings is known. There are, however, several groups of molecules for which this method leads to surprisingly low values for the dissociation energy. The group IIIA monohalides are typical of this group and the estimated dissociation energy, using a Birge-Sponer extrapolation of the vibrational levels in the ground state, is only about 70 per cent of the true value”’ estimated by other methods. The low value has been attributed to the high degree of ionic binding in this group of molecule@ and the consequent breakdown of the Morse potential on which the Birge-Sponer method is based. An alternative procedure for estimating the dissociation energy is to compare the experimentally obtained potentialenergy curve(‘) with an empirical function depending on the dissociation energy.‘8-‘0) Previous work using the Lippincott function (3) has also yielded low estimates. The Lippincott function is based on a b-function model of binding and is essentially covalent in character. Recently, an empirical potential function depending explicitly on the electronegativities of the atoms involved has been suggested” I) and it was thought worthwhile to see if this function leads to an improvement in the accuracy of the estimate.
1577
1578
JAGADISH SINGH. K. P. R. NAIR and D. K.
COMPUTATIONAL
The electronegativity
potential
PROCEDURE
function
AND
RAI
DISCUSSION
is
where ‘/ = de/Dd12, and a and b are empirical parameters ; b is considered to be a universal constant (5 1.065)and a = 0.35 e”’ where e = (e,e2)“’ ; e, and e2 are the electronegativities of the two atoms; d is a constant which is related to the force constant by relation k, = d(e,e,D,)1i2r;‘. The function U(r) gives quite good agreement with the RKRV-curve and
TABLE 1. POTENTIAL ENERGY CURVESFOR THEGROUNDSTATES(X'Z+)OF GALLIUM, INDIUM AND THALLIUM MONOHALIDES Electronegativity function
RKR V Molecule
L’
GUF (D, = 6.2 eV)
Umin’Fm 1, (imax““’
‘mincA)
‘max(*)
311.0 928.0 1537.5 2142.2 2738.6 33284 3913.1 4492.7 5063.3
1.718 I.680 1.656 1.637 1.622 1.608 1.596 1.586 1.576
I.839 1.891 1.928 1.961 1.991 2.018 2044 2.069 2.093
303. I 886.1 1441.1 1991.4 2501.4 3040.8 3555.9 4022.7 4528.4
993.6 1648.7 23376 3038.8 3721.5 4422.2 5129.3 5835.3
8 9 10
266.7 794.0 1319.6 1839.2 2354.0 2863.1 3367.8 3866.0 4359.4 4848.8 5331.8
1.926 1.886 1.861 1.841 1.825 1.811 1.799 1.788 1.778 1.768 I.760
2.050 2.103 2.142 2.175 2.205 2.233 2.259 2.285 2.309 2.332 2.355
259.2 768.4 1244.1 1724.1 2174.1 2620.1 3040.1 3462.8 3874.8 4314.1 4688.7
269.4 832.4 1407.6 1983.7 2570.3 3162.8 3750.5 4369.7 4963.0 5553.2 6 159.9
0 I 2 3 4 5 6 7 8 9 10 11 12
238.1 709.2 1175.6 1643.9 2102.3 2557.3 301 I.0 3457.5 3894.8 4326.7 4757.6 5185.0 5610.3
2.024 1.983 1.957 1.937 1.920 1.906 1.893 1.881 1.870 1.861 1.852 1.844 1.836
2.152 2.206 2.245 2.279 2.309 2.338 2.364 2.391 2.416 2.439 2.463 2.485 2.507
228.9 685.8 1120.1 1541.3 1962.0 2353.3 2755.4 3162.3 3565.4 3918.3 4292.0 4641.6 5007.1
251.4 759.4 1265.0 1784.5 2296.8 2833.2 3344.4 3904.9 4444.5 4957.1 5507.7 6024.6 6549.8
[/(cm
0
I)
323.5
l?lF (D,, = 5.5 eV)
0
I 2 3 4 5 6
TlF (D, = 4.75 eV)
1)
1579
Potential energy curves and dissociation energies
TABLE
1. (continued)
Electronegativity function
RKRV Molecule
GaCl (D, = 3.7eV)
ItIC (D, = 4.5 eV)
TICI (D, = 3.75 eV)
V
rmaX(A) “min’Em~‘I
Urnax(Em~ ‘)
U(cm- ‘)
‘min’“’
0 1 2 3 4 5 6 7 8 9 10
182.2 545.1 906.8 1264.3 1619.4 1973.1 2324.5 2672.3 3018.4 3362.2 3703.6
2.147 2.104 2.075 2.052 2.032 2.015 1.999 1.985 1.971 1.959 1.947
2.274 2.323 2.359 2.389 2.415 2440 2.462 2.483 2.504 2.523 2.542
181.0 559.2 947.3 1344.1 1747.6 2154.6 2568.6 2988.9 3414.8 3845.2 4277.9
182.5 537.2 884.5 1227.9 1566.4 1903.0 2237.1 2568.7 2900.8 3226.0 3554.5
0 1 2 3 4 5 6 7 8 9 10 11 12
158.4 474.0 787.4 1098.5 1407.8 1714.8 2019.8 2323.3 2624.8 2923.9 3221.0 3516.2 3809.2
2.259 2.220 2.196 2.177 2.162 2.149 2.138 2.128 2.119 2.112 2.105 2.098 2.093
2.385 2.439 2.479 2.513 2.544 2.573 2.600 2.626 2.651 2.675 2.698 2.721 2.744
158.1 442.9 703.7 948.6 1180.5 1397.5 1605.1 1799.0 1984.5 2157.7 2323.6 2467.9 2630.0
157.3 503.5 864.4 1236.4 1614.8 1999.0 239@4 2783.1 3181.1 3582.7 3989.7 4396.1 4807.0
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14
143.4 429.8 710.9 990.0 1267.6 1542.6 1815.7 2085.7 2353.5 2619.1 2882.5 3143.7 3402.7 3659.5 3914.1
2.425 2.384 2.357 2.335 2.318 2.302 2.288 2.275 2.264 2.253 2.243 2.234 2.225 2.216 2.208
2.550 2.602 2.639 2.671 2.700 2.726 2.751 2.774 2.797 2.819 2.840 2.860 2.881 2.900 2.919
135.0 408.6 677.1 942.6 1206.1 1465.5 1722.0 1981.3 2235.7 2485.3 2737.1 2986.4 3231.9 3476.9 3718.4
150.7 452.8 758.8 1065.5 1376.2 1688.2 2002.0 2319.5 2635.3 2953.5 3274.2 3593.1 3914.6 4235.6 4557.7
estimates of dissociation energies obtained by this formula are quite reliable.(‘2-‘4) The estimated dissociation energies obtained by this method for boron and aluminium halides have been reported earlier ‘i3’and were found to be much too low. The calculations have now been extended to the other diatomic halides of the IIIA group of metals. The results of the calculations are shown in Table 1. The dissociation energies obtained for the gallium,
1580
JAGADISH SINGH, K. P. R. NAIR and
D. K. RAI
indium and thallium halides, except for GaCl, are in good agreement with the values reported earlier. Table 2 gives the values of the dissociation energies reported by different methods. TABLE 2. DIWCIATION ENERGIESOBTAINEDBY DIFFERENTMETHODSFOR THE FLUORIDESAND CHLORIDES OF GALLIUM, INDIUM AND THALLIUM (IN ev) l,, State
Molecule
Gaf IllF TlF GaCl InCi TlCl
Extrapolated
624 5.46 _ 4.71 - 4.90 4.43 3.83
Predissociation
I 5.58 I 4.98 4.65
* Herzberg also gives 3.7eV. vibrational levels.
but with
From wavelengths of maxima of photoionization
Highest observed vibrational level > 6.05 > 5.42 > 4.66 >4.88 >4.39
a poor
6.24 5.46 4.75 4.92 4.44 3.88 extrapolation
Present results
6.2 5.5 4.15 3.7* 4.5 3.75 of ground-state
It has been pointed out by Mulliken that the upper state of alkali hydride molecules have a predominantly atomic character for small values of r-rer whereas, at large values of r, the curve is nearly wholly ionic. The opposite is true for the ground state. To see if similar behaviour is observed for the IIIA group monohalides, the ionic function suggested by Hellman was applied to calculate the potential curve for these molecules. It was observed that the Hellman curve approaches the experimental curve for the ground state, even for low values of r, in the neighbourhood of re. For the excited states, on the other hand, the experimental curve meets the ionic curve only for large and small r-values.‘3’ This result may be taken as an indication that the ionic contribution to the binding at r - r, is large for the ground state but quite small for the excited states. The relative closeness of the Hellman curve and the true potential curves for the first excited state is more notable for the lighter molecules; for the heavier molecules, the ionic curve is closer to the ground state. These results indicate that the heavier molecules have more ionic character in their ground state than the lighter ones. Acknowledgement~The
authors
are thankful
to Professor
N. L.
SINGH
for his keen interest
in this work.
REFERENCES 1. 2. 3. 4. 5. 6. 7.
R. F. V. B. S. N. R. T. R. T.
BARROW, Trans. Faraday Sot. 56,952 (1960). GOHEL, Ind. J. Pure Appl. Phys. 7,376 (1969). THAKUR, R. B. SINGH and D. K. RAI, J. Sci. Ind. Res. (India) 27, 339 (1968). BARGEand H. SPONER, Phys. Rev. 28,259 (1926). BIRGE, Trans. Furadpy Sot. 25, 707 (1929). A. G. GAYDON, Dissociurion Energies (3rd Edn.), Chapman & Hall, London (1968). J. T. VANDERSLICE, E. A. MASON, W. G. MAISCH and E. R. LIPPINCOTT, J. molec. Spectrosc. 3, 17 (1959); 5,83 (1960).
Potential energy curves and dissociation energies 8. 9. 10. 11. 12. 13. 14.
D. STEELE, Spectrochim. Acra 19,411 (1963). R. B. SINGH and D. K. RAI, Can. J. Phys. 43,829 (1965). K. P. R. NAIR, R. B. SINGHand D. K. RAI, J. them. Phys. 43,357O (1965). S. SZ~KE and E. BAITZ, Can. J. Phys. 46,2563 (1968). J. SINGH.K. P. R. NAIR and D. K. RAI. J. Mol. Struct. 5.492 (1970). J. SINGH;K. P. R. NAIR and D. K. RAI. J. Mol. Struct. 6,‘328 (i970). J. SINGH,K. P. R. NAIR and D. K. RAI, Ind. J. Pure appl. Phys. 8,614 (1970).
1581