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The dissociation energy of BiI derived from potential energy curves
J Quant Spectrosc gadml Trans/erVol 27, No 2, pp 207-21~,19~2 Printed in GreatBritain
0022-4073t821020207~)2~300/0 © 1982PergamonPressLid
NOTE T H E D I S S O C I A T I O N E N E R G Y OF BiI D E R I V E D FROM P O T E N T I A L E N E R G Y C U R V E S P. SAMBASIVARAOt and T V. RAMAKRISHNARAO$ Spectroscopic Laboratories, Physics Department, S V U A Post-Graduate Centre. Anantapur-515003, Indm
(Received 13 May 1981)
Abstract--The potential energy curve for the ground state of Bd has been constructed by the methods of Lakshman and Ran and of Jarmam The dissociation energy IS est,mated to be 1.949_+ 0 009 eV from fitting the three-parameter L.pplncott potential function The value recommended by Gaydon ~s 25-+1 0eV INTRODUCTION
Potential energy curves are useful in computing the dis~ociatmn energy of a diatomlc molecule. In the present study, we have estimated the dtssociation energy (Do) of BiI from potential energy curves for the ground state Required molecular constants have been taken from Huber and Herzberg.' POTENTIAL E N E R G Y C U R V E
The method of Lakshman and Rap2 is an improved form of the RKR method3 in whtch [ and g terms are written in a simplified form. Because the method of Lakshman and Rap has been described before, ~ only the results of the analysis are given in Table 1 The turning points for the vibrational motion obtained from Jarmain's method4 are also shown in Table 1 DISSOCIATION
ENERGY
Accurate evaluation of the dissociation energy from curve fitting requires a good emptrlcal potential function The three-parameter Lippmcott potential function s has been shown to reproduce well RKRV curves over a wide range of energies and for a number of diatom~c molecules ~ Table 1 Turning points of the ground state potential energy curve of BII and calculated energies obtained from the Llppincott function for D, = 15800 cm -I Im~shmm & b o ' s
•
g (e= - 1 )
0
81.87
I 2 ] 4 5
245.17 407.87 569.94 731.33 892.04
6 7
1052.02 1211,24
m~l~o~
Jart~In's method
rmz(~) rmx(~) rmn(~) rmax(2) Umn(em-1) 2.75108 2.71689 2.69450
2,85324 2.89409 2.92337
2.67648 2.66147 2.64836 2.65664 2.62601
2.94789 2.96963 2.98947 3.00794 3.02533
Umax(em-1
2.75108 2.71689 2.69430 2.67648 2.66147
2.85324 2.89409 2.92335 2,94783 2,96960
245.75 4O8.35 569.94 730.62
408.66 570.63 731.88
2.64836 2.63665 2.62604
2.98930 5.00768 3.02498
890.11 1048.57 1205.77
892.24 1051.64 1210.14
82.13
82.14 245.76
The turning points of the ground state of Bd obtained m the present study have been used in the Lippincott function for a particular value of De The observed energy values of U have then been compared with calculated energy values (Urn,,, U~.~x) This procedure was repeated for different values of De. The value (15,800 cm-') for which the best fit obtains is taken to be the dissociation energy of the molecule. tAIso at Physics Department. J N Technological University. College of Engineering. Anantapur-515002, India :~Also at' lnstltut des Sciences Exactes, Unlverslte de Constantine. Constantine, Algeria 207
P SAMBASIVAelal.
208
Table2 Average percentagedevlationsforselected Devalues De
(cm -I )
Average devlatlon (%)
14800
15300
15800
16300
16800
6.04
2.95
0.18
3.38
6.55
RESULTS AND DISUSSION
The turning points obtained for eight vibrational levels of the ground state of BII are shown in Table 1, together with calculated energies obtained from the Lippmcott function for D, = 15,800 cm '. The average percentage deviations for other selected De values are given in Table 2 A "best" fit of calculated energies is achieved for De -- 1.959 eV, when the average percentage deviation is only 0.18 Thus, D~--1959-+0009eV; the value derived from the lowest vibrational level is Do= 1949_+0009eV The value recommended by Gaydon 9 is Do = 2.5 _+1.0 eV Acknowledgement--The authors wish to express their thanks to Profs S V J Lakshman and S V Subrahmanyam for their interest m the present work REFERENCES 1_ K P Huber and G herzberg, MolecularSpectra and Molecular Structure IV Constants of Dtatomic Molecules, p 98. Van Nostrand Reinhold, New York (1979) 2_ S V J. Lakshman and T V Ramaknshna Rao, J Phys B4, 269 (1971) A G L Rees, Proc Phys Soc 59, 998 (1947) 4 W R Jarmam, Can J Phys 38, 217 (1960) 5. D_ Steele and E R Llpplncott, J Chem Phys 35, 2065 (1%1) 6. B P Asthana, V S. Kushawaha and K P R Nalr, Acta Phystca Polomca A42, 739 (1972) 7. K P R Nalr, Ram B Slngh, and D K Ral, J Chem Phys 43, 3570 (1%5) 8 T. V Ramaknshna Rao and S V J Lakshman, Curr Sc~ 40, 316 (1971) 9 A G Gaydon, Dissociation Energies and Spectra of Dlatomtc Molecules, p 265 Chapman & Hall, London (1%8)
0022-4073t821020207~)2~300/0 © 1982PergamonPressLid
NOTE T H E D I S S O C I A T I O N E N E R G Y OF BiI D E R I V E D FROM P O T E N T I A L E N E R G Y C U R V E S P. SAMBASIVARAOt and T V. RAMAKRISHNARAO$ Spectroscopic Laboratories, Physics Department, S V U A Post-Graduate Centre. Anantapur-515003, Indm
(Received 13 May 1981)
Abstract--The potential energy curve for the ground state of Bd has been constructed by the methods of Lakshman and Ran and of Jarmam The dissociation energy IS est,mated to be 1.949_+ 0 009 eV from fitting the three-parameter L.pplncott potential function The value recommended by Gaydon ~s 25-+1 0eV INTRODUCTION
Potential energy curves are useful in computing the dis~ociatmn energy of a diatomlc molecule. In the present study, we have estimated the dtssociation energy (Do) of BiI from potential energy curves for the ground state Required molecular constants have been taken from Huber and Herzberg.' POTENTIAL E N E R G Y C U R V E
The method of Lakshman and Rap2 is an improved form of the RKR method3 in whtch [ and g terms are written in a simplified form. Because the method of Lakshman and Rap has been described before, ~ only the results of the analysis are given in Table 1 The turning points for the vibrational motion obtained from Jarmain's method4 are also shown in Table 1 DISSOCIATION
ENERGY
Accurate evaluation of the dissociation energy from curve fitting requires a good emptrlcal potential function The three-parameter Lippmcott potential function s has been shown to reproduce well RKRV curves over a wide range of energies and for a number of diatom~c molecules ~ Table 1 Turning points of the ground state potential energy curve of BII and calculated energies obtained from the Llppincott function for D, = 15800 cm -I Im~shmm & b o ' s
•
g (e= - 1 )
0
81.87
I 2 ] 4 5
245.17 407.87 569.94 731.33 892.04
6 7
1052.02 1211,24
m~l~o~
Jart~In's method
rmz(~) rmx(~) rmn(~) rmax(2) Umn(em-1) 2.75108 2.71689 2.69450
2,85324 2.89409 2.92337
2.67648 2.66147 2.64836 2.65664 2.62601
2.94789 2.96963 2.98947 3.00794 3.02533
Umax(em-1
2.75108 2.71689 2.69430 2.67648 2.66147
2.85324 2.89409 2.92335 2,94783 2,96960
245.75 4O8.35 569.94 730.62
408.66 570.63 731.88
2.64836 2.63665 2.62604
2.98930 5.00768 3.02498
890.11 1048.57 1205.77
892.24 1051.64 1210.14
82.13
82.14 245.76
The turning points of the ground state of Bd obtained m the present study have been used in the Lippincott function for a particular value of De The observed energy values of U have then been compared with calculated energy values (Urn,,, U~.~x) This procedure was repeated for different values of De. The value (15,800 cm-') for which the best fit obtains is taken to be the dissociation energy of the molecule. tAIso at Physics Department. J N Technological University. College of Engineering. Anantapur-515002, India :~Also at' lnstltut des Sciences Exactes, Unlverslte de Constantine. Constantine, Algeria 207
P SAMBASIVAelal.
208
Table2 Average percentagedevlationsforselected Devalues De
(cm -I )
Average devlatlon (%)
14800
15300
15800
16300
16800
6.04
2.95
0.18
3.38
6.55
RESULTS AND DISUSSION
The turning points obtained for eight vibrational levels of the ground state of BII are shown in Table 1, together with calculated energies obtained from the Lippmcott function for D, = 15,800 cm '. The average percentage deviations for other selected De values are given in Table 2 A "best" fit of calculated energies is achieved for De -- 1.959 eV, when the average percentage deviation is only 0.18 Thus, D~--1959-+0009eV; the value derived from the lowest vibrational level is Do= 1949_+0009eV The value recommended by Gaydon 9 is Do = 2.5 _+1.0 eV Acknowledgement--The authors wish to express their thanks to Profs S V J Lakshman and S V Subrahmanyam for their interest m the present work REFERENCES 1_ K P Huber and G herzberg, MolecularSpectra and Molecular Structure IV Constants of Dtatomic Molecules, p 98. Van Nostrand Reinhold, New York (1979) 2_ S V J. Lakshman and T V Ramaknshna Rao, J Phys B4, 269 (1971) A G L Rees, Proc Phys Soc 59, 998 (1947) 4 W R Jarmam, Can J Phys 38, 217 (1960) 5. D_ Steele and E R Llpplncott, J Chem Phys 35, 2065 (1%1) 6. B P Asthana, V S. Kushawaha and K P R Nalr, Acta Phystca Polomca A42, 739 (1972) 7. K P R Nalr, Ram B Slngh, and D K Ral, J Chem Phys 43, 3570 (1%5) 8 T. V Ramaknshna Rao and S V J Lakshman, Curr Sc~ 40, 316 (1971) 9 A G Gaydon, Dissociation Energies and Spectra of Dlatomtc Molecules, p 265 Chapman & Hall, London (1%8)