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Potential energy curves for the C2∑+u and X2∑+g states of N+2
J. Quant.
Spcc~rosc.
Radiar.
Trans~r.
Vol.6.pp.211-213. PergamonPress Ltd., 1966. Printed inGreatBritam
NOTE
POTENTIAL
ENERGY
CURVES FOR THE STATES OF N2+
C2C,+ AND
X2x,+
K. C. JOSHI* Wentworth Institute, Boston, Mass., USA (Receioed 18 October 1965) Abstract-The Morse and RKR potential energy curves for C*Zl and X*Z: states of N: molecule have been calculated by using the C and X state vibrational constants obtained by the author (JOSHI( The agreement
between the Morse and RKR values is very good for the X-state but for C-state there is some difference between the two values.
system of N: bands can be excited by different methods (HOPFIELD”); and KooNTz(~); SETLOW( MIESCHER and BAER(~); BAER and MIESCHER(@; TAKAMINE, SUGA and TANAKA(‘) ; WILKINSON@) ; TANAKA(~) ; CARROLL(’ O) and TANAKA, NAMIOKA JLTRSA~“)). If a condensed discharge is passed through pure nitrogen, very weak bands of low vibrational quantum numbers are observed. If nitrogen is mixed with helium, the bands having U’2 3 are obtained. If neon is used instead of helium, bands with v’ < 3 are also obtained along with those having higher v’ values. A detailed investigation of this type of selective excitation has been carried out (JOSHI(~ On examining AG vs. v curve of the C-state, it is found that the curve is not very smooth. Some vibrational perturbation has been reported in the C-state (WATSON and KOONTZ(~). WILKINSON@) and CARROLL (lo) The amount of vibrational perturbation is, however, &all and is 38.2, 19.8 and 7.2 cm- ’ for c’ = 0, 1 and 2 respectively. Along with the vibrational perturbation, there is some rotational perturbation in the C-state (WILKINSON(*) and CARROLL(")). The vibrational constants for this state were, therefore, derived by taking the bands with v‘ higher than 2. Both 14N2 and “N, were used to confirm the analysis. A summary of the vibrational constants has been given in Table 1. THE C2C:-X2C,f
WATSON
TABLE 1. VIBRATIONAL CONSTANTS (in cm-‘)
Constant
C-state calculated from l4N2+ ‘5,;
FOR THE C AND A'-STATES
X-state calculated from ‘4N: ‘5,;
2099.84 2099.62 2206.24 14.740 14,191 16.166 -0.0143 -0.1415 -0.0154 - 0.00972 - 0.00 162 -0.00155 Average v,(C - X) = 64 558.63
2204.44 15.870 -0.0431 - 0~00068
* Present address: Optics Division, National Physical Laboratory, New Delhi, India 211
K. C. JO~HI
212
The constants listed in column for “N,f are those derived from “N: combining them with suitable ratios of reduced masses. Using the above constants, the Morse and RKR (WEISSMAN, VANDERSLICE and BATTINO”‘)) energies have been calculated. It has been assumed that there is no vibrational perturbation in the C-state. Also for the Morse curve of this state, because of the fact that the dissociation energy is not known, it has been assumed that N(2Do)+N+(3P) are the dissociation products. Consequently the dissociation energy (D,) used is 26 162 cm-‘. The calculated potential energies (?;,) at various internuclear distances (r) have been listed in Tables 2 and 3 for the X and (‘ states respectively. TABLE
V
2. POTENTIAL ENERGY CURVESFOR X-STATE
K,(cm-‘)
RKR method rlllax
-t 0
1
2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
- 1099.5 0 2174.8 4317.0 6426.4 8502.8 10545.8 12555.0 14530.7 16470.6 18377.6 20249.7 22086.5 23887.6 25652.4 27380.5 29071.6 30725.1
1.116A I.166 1.207 I.237 1,263 1.287 1.310 1.331 1,352 1.372 1.392 I.411 I.43 1 1,450 1.470 1.489 I.508 I.528
Morse method
rrn,n
rma.
rmin
1.116A I.072 I.043 I.025 1.011 0.999 0.989 0,980 0,972 0.965 0.958 0.952 0.946 0.941 0,936 0.93 1 0.926 0.922
1.116/i I.166 I.207 I.237 I.263 1.288 I.310 I.332 I.353 I.373 1,393 I.413 1,433 I.452 I.472 I.491 I.510 I.530
1.116A I.072 I.043 I.025 I.011 0.999 0,989 0.980 O-972 O-965 0,958 0.952 0,947 0.942 0.937 0.932 0.928 0.924
TABLE 3. POTENTIAL ENERGY CIJRVESFOR C-STATE ~__
V
T”(cm- ’ )
0 1 2 3 4 5 6 7 8 9 10
63463.9 64510.1 66684.9 68827.1 70936.6 73012.9 75055.9 77065.1 79040.8 80980.7 82887-7 84759.8
-f
RKR method
1.260A I.309 I.348 1.377 I.401 1.423 1444 1.465 I.484 I.504 I.523 1.543
I .260/i 1.213 I.181 1.159 1,142 I.128 I.1 16 I.105 1.095 1.086 1.077 I.070
Morse method
1.260/i I.313 I.361 I ,400 I.437 1.474 l-512 l-552 I.595 1,644 I-700 I 768
1,260A I.216 I-189 1.172 I.159 I.149 I.140 I.132 I.126 I.120 I.1 14 I.109
Potential
energy
curves for the C*Z:
and X2X:
states of Nl
213
Acknowledgements-The author would like to express his thanks to Dr. Y. TANAKA of the U.S. Air Force Cambridge Research Laboratories for suggesting the problem and for constant encouragement during the work. He wishes to thank Prof. J. T. VANDERSLICEand S. WEISSMANof the University of Maryland for making available their RKR potential energy curve programme; he also thanks Mr. N. J. GROSSBARD of the U.S. Air Force Cambridge Research Laboratories for processing the calculations of RKR potential energy curves. This work was done at the U.S. Air Force Cambridge Research Laboratories. Bedford. Mass. under Contract No. AF 19 (6X)-246.
REFERENCES I. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12.
K. C. JOSHI, Proc. Phys. Sot. [To be published in Vol. 87, (1966)]. J. J. HOPFIELD. Phys. Rev. 36, 789 (1930). W. W. WATSON and P. G. KOONTZ, Phys. Rer. 46, 32 (1934). R. B. SETLOW, Phys. Rev. 74, 153 (1948). E. MIESCHER and P. BAER, Noture, Lond. 169, %I (1952). P. BAER and E. MIFSCHER, Helc Phys. Acta. 26, 91 (1953). T. TAKAMINE, T. SUGA and Y. TANAKA, Inst. Phys. Chem. Res. (T&v), 36, 437 (1939). P. G. WILKINSON, Can. J. Php. 34, 250 (1956). Y. TANAKA, J. Chem. PhJv. 21, 1402 (1953). P. K. CARROLL, Can. J. Phys. 37, 880 (1959). Y. TANAKA, T. NAMIOKA and A. S. JURSA, Cwz. J. Phrs. 39, 1138 t 1961). S. WEISSMAN. J. T. VANDERSLICEand R. BATTINO, J. Chem. Plz~s. 39, 2226 (1963)
Spcc~rosc.
Radiar.
Trans~r.
Vol.6.pp.211-213. PergamonPress Ltd., 1966. Printed inGreatBritam
NOTE
POTENTIAL
ENERGY
CURVES FOR THE STATES OF N2+
C2C,+ AND
X2x,+
K. C. JOSHI* Wentworth Institute, Boston, Mass., USA (Receioed 18 October 1965) Abstract-The Morse and RKR potential energy curves for C*Zl and X*Z: states of N: molecule have been calculated by using the C and X state vibrational constants obtained by the author (JOSHI( The agreement
between the Morse and RKR values is very good for the X-state but for C-state there is some difference between the two values.
system of N: bands can be excited by different methods (HOPFIELD”); and KooNTz(~); SETLOW( MIESCHER and BAER(~); BAER and MIESCHER(@; TAKAMINE, SUGA and TANAKA(‘) ; WILKINSON@) ; TANAKA(~) ; CARROLL(’ O) and TANAKA, NAMIOKA JLTRSA~“)). If a condensed discharge is passed through pure nitrogen, very weak bands of low vibrational quantum numbers are observed. If nitrogen is mixed with helium, the bands having U’2 3 are obtained. If neon is used instead of helium, bands with v’ < 3 are also obtained along with those having higher v’ values. A detailed investigation of this type of selective excitation has been carried out (JOSHI(~ On examining AG vs. v curve of the C-state, it is found that the curve is not very smooth. Some vibrational perturbation has been reported in the C-state (WATSON and KOONTZ(~). WILKINSON@) and CARROLL (lo) The amount of vibrational perturbation is, however, &all and is 38.2, 19.8 and 7.2 cm- ’ for c’ = 0, 1 and 2 respectively. Along with the vibrational perturbation, there is some rotational perturbation in the C-state (WILKINSON(*) and CARROLL(")). The vibrational constants for this state were, therefore, derived by taking the bands with v‘ higher than 2. Both 14N2 and “N, were used to confirm the analysis. A summary of the vibrational constants has been given in Table 1. THE C2C:-X2C,f
WATSON
TABLE 1. VIBRATIONAL CONSTANTS (in cm-‘)
Constant
C-state calculated from l4N2+ ‘5,;
FOR THE C AND A'-STATES
X-state calculated from ‘4N: ‘5,;
2099.84 2099.62 2206.24 14.740 14,191 16.166 -0.0143 -0.1415 -0.0154 - 0.00972 - 0.00 162 -0.00155 Average v,(C - X) = 64 558.63
2204.44 15.870 -0.0431 - 0~00068
* Present address: Optics Division, National Physical Laboratory, New Delhi, India 211
K. C. JO~HI
212
The constants listed in column for “N,f are those derived from “N: combining them with suitable ratios of reduced masses. Using the above constants, the Morse and RKR (WEISSMAN, VANDERSLICE and BATTINO”‘)) energies have been calculated. It has been assumed that there is no vibrational perturbation in the C-state. Also for the Morse curve of this state, because of the fact that the dissociation energy is not known, it has been assumed that N(2Do)+N+(3P) are the dissociation products. Consequently the dissociation energy (D,) used is 26 162 cm-‘. The calculated potential energies (?;,) at various internuclear distances (r) have been listed in Tables 2 and 3 for the X and (‘ states respectively. TABLE
V
2. POTENTIAL ENERGY CURVESFOR X-STATE
K,(cm-‘)
RKR method rlllax
-t 0
1
2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
- 1099.5 0 2174.8 4317.0 6426.4 8502.8 10545.8 12555.0 14530.7 16470.6 18377.6 20249.7 22086.5 23887.6 25652.4 27380.5 29071.6 30725.1
1.116A I.166 1.207 I.237 1,263 1.287 1.310 1.331 1,352 1.372 1.392 I.411 I.43 1 1,450 1.470 1.489 I.508 I.528
Morse method
rrn,n
rma.
rmin
1.116A I.072 I.043 I.025 1.011 0.999 0.989 0,980 0,972 0.965 0.958 0.952 0.946 0.941 0,936 0.93 1 0.926 0.922
1.116/i I.166 I.207 I.237 I.263 1.288 I.310 I.332 I.353 I.373 1,393 I.413 1,433 I.452 I.472 I.491 I.510 I.530
1.116A I.072 I.043 I.025 I.011 0.999 0,989 0.980 O-972 O-965 0,958 0.952 0,947 0.942 0.937 0.932 0.928 0.924
TABLE 3. POTENTIAL ENERGY CIJRVESFOR C-STATE ~__
V
T”(cm- ’ )
0 1 2 3 4 5 6 7 8 9 10
63463.9 64510.1 66684.9 68827.1 70936.6 73012.9 75055.9 77065.1 79040.8 80980.7 82887-7 84759.8
-f
RKR method
1.260A I.309 I.348 1.377 I.401 1.423 1444 1.465 I.484 I.504 I.523 1.543
I .260/i 1.213 I.181 1.159 1,142 I.128 I.1 16 I.105 1.095 1.086 1.077 I.070
Morse method
1.260/i I.313 I.361 I ,400 I.437 1.474 l-512 l-552 I.595 1,644 I-700 I 768
1,260A I.216 I-189 1.172 I.159 I.149 I.140 I.132 I.126 I.120 I.1 14 I.109
Potential
energy
curves for the C*Z:
and X2X:
states of Nl
213
Acknowledgements-The author would like to express his thanks to Dr. Y. TANAKA of the U.S. Air Force Cambridge Research Laboratories for suggesting the problem and for constant encouragement during the work. He wishes to thank Prof. J. T. VANDERSLICEand S. WEISSMANof the University of Maryland for making available their RKR potential energy curve programme; he also thanks Mr. N. J. GROSSBARD of the U.S. Air Force Cambridge Research Laboratories for processing the calculations of RKR potential energy curves. This work was done at the U.S. Air Force Cambridge Research Laboratories. Bedford. Mass. under Contract No. AF 19 (6X)-246.
REFERENCES I. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12.
K. C. JOSHI, Proc. Phys. Sot. [To be published in Vol. 87, (1966)]. J. J. HOPFIELD. Phys. Rev. 36, 789 (1930). W. W. WATSON and P. G. KOONTZ, Phys. Rer. 46, 32 (1934). R. B. SETLOW, Phys. Rev. 74, 153 (1948). E. MIESCHER and P. BAER, Noture, Lond. 169, %I (1952). P. BAER and E. MIFSCHER, Helc Phys. Acta. 26, 91 (1953). T. TAKAMINE, T. SUGA and Y. TANAKA, Inst. Phys. Chem. Res. (T&v), 36, 437 (1939). P. G. WILKINSON, Can. J. Php. 34, 250 (1956). Y. TANAKA, J. Chem. PhJv. 21, 1402 (1953). P. K. CARROLL, Can. J. Phys. 37, 880 (1959). Y. TANAKA, T. NAMIOKA and A. S. JURSA, Cwz. J. Phrs. 39, 1138 t 1961). S. WEISSMAN. J. T. VANDERSLICEand R. BATTINO, J. Chem. Plz~s. 39, 2226 (1963)