Abstract

Line strengths of N2O and its rare isotopic derivatives have been measured in the 1120–1440-cm−1 spectral region. The spectra were obtained at low sample pressure and high resolution (0.0054 cm−1), and the data are analyzed to determine band strengths, rotationless dipole moment matrix elements, and F factor coefficients for the various bands. First-order nondegenerate perturbation theory was used to derive explicit expressions for the rotationless dipole moment matrix elements and F factor coefficients, and from this derivation, general expressions for the F factor are obtained: F = [1 + a1m + a2J′(J′ + 1) + a3J″(J″ + 1)]2 for Δl = 0, ±1 bands and F = (1 + a1m)2 · H for Δl = ±2, ±3 bands, where H is given to good approximation for |Δl| = 2 bands as H = [J′(J′ + 1)]2. These F factor expressions are applied in the analysis of the experimental data from which the vibrational band strength of the forbidden band 0220(e)–0000 was found to be (5.69 ± 0.26) × 10−8 cm−2/atm at 296 K. The theoretical results can also be applied to CO2 line strengths.

© 1984 Optical Society of America

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References

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  1. R. A. Toth, V. D. Gupta, J. W. Brault, “Line Positions and Strengths of HDO in the 2400–3300-cm−1 Region,” Appl. Opt. 21, 3337 (1982).
    [CrossRef] [PubMed]
  2. R. A. Toth, J. W. Brault, “Line Positions and Strengths in the (001), (110), and (030) Bands of HDO,” Appl. Opt. 22, 908 (1983).
    [CrossRef] [PubMed]
  3. L. R. Brown, J. S. Margolis, R. H. Norton, B. D. Stedry, “Computer Measurement of Line Strengths with Application to the Methane Spectrum, Appl. Spectrosc. 37, 287 (1983).
    [CrossRef]
  4. R. A. Toth, “Self-Broadened and N2 Broadened Linewidths of N2O,” J. Mol. Spectrosc. 40, 605 (1971).
    [CrossRef]
  5. J. S. Margolis, “Intensity and Half Width Measurements of the (00°2–00°0) Band of N2O,” J. Quant. Spectrosc. Radiat. Transfer 12, 751 (1972).
    [CrossRef]
  6. N. Lacome, A. Levy, “Line Strengths and Self-Broadened Linewidths of N2O in the 2-μm Region,” J. Mol. Spectrosc. 85, 205 (1981).
    [CrossRef]
  7. N. Lacome, C. Boulet, E. Arie, “Spectroscopic par Source Laser,” III. Intensitiés et Largeurs des Raies de la Transition 00°1–10°0 du Protoxyde d’Azote. Ecarts á la Forme de Lorentz,” Can. J. Phys. 51, 302 (1973).
    [CrossRef]
  8. L. S. Rothman, “AFGL Atmospheric Absorption Line Parameters Compilation: 1980 Version,” Appl. Opt. 20, 791 (1981).
    [CrossRef] [PubMed]
  9. L. S. Rothman et al., “AFGL Atmospheric Absorption Line Parameters Compilation: 1982 Edition,” Appl. Opt. 22, 2247 (1983).
    [CrossRef] [PubMed]
  10. G. Guelachvili, “Absolute N2O Wavenumbers Between 1118 and 1343 cm−1 by Fourier Transform Spectroscopy,” Can. J. Phys. 60, 1334 (1982).
    [CrossRef]
  11. C. Amiot, G. Guelachvili, “Extension of the 106 Samples Fourier Spectrometry to the Indium Antimonide Region: Vibration-Rotation Bands of 14N216O: 3.3–5.5μm Region,” J. Mol. Spectrosc. 59, 171 (1976).
    [CrossRef]
  12. C. Amiot, “Vibration-Rotation Bands of 14N15N16O–15N14N16O: 1.6–5.7μm Region,” J. Mol. Spectrosc. 59, 191 (1976).
    [CrossRef]
  13. C. Amiot, “Vibration-Rotation Bands of 15N216O–14N218N2O,” J. Mol. Spectrosc. 59, 380 (1976).
    [CrossRef]
  14. B. G. Whitford, K. J. Siemsen, H. D. Riccius, G. R. Hanes, “Absolute Frequency Measurements of N2O Laser Transitions,” Opt. Commun. 14, 70 (1975).
    [CrossRef]
  15. G. Guelachvili, “Experimental Doppler-Limited Spectra of the ν2 Bands of H216, H217O, H218O, and HDO by Fourier-Transform Spectroscopy: Secondary Wave-Number Standards Between 1066 and 2296 cm−1,” J. Opt. Soc. Am. 73, 137 (1983).
    [CrossRef]
  16. C. P. Rinsland, D. C. Benner, D. J. Richardson, R. A. Toth, “Absolute Intensity Measurements of the (111O)11 ← 00°O Band of 12C16O2 at 5.2 μm,” Appl. Opt. 22, 3805 (1983).
    [CrossRef] [PubMed]
  17. Y. Y. Kwan, “The Interacting States of An Asymmetric Top Molecule XY2 of Group C2V,” J. Mol. Spectrosc. 71, 260 (1978).
    [CrossRef]
  18. J. M. Flaud, C. Camy-Peyret, “Vibration-Rotation Intensities in H2O-Type Molecules Application to the 2ν2, ν1, and ν3 Bands of H216O,” J. Mol. Spectrosc. 55, 278 (1975).
    [CrossRef]
  19. H. D. Downing, B. J. Krohn, R. H. Hunt, “Coriolis Intensity Perturbations in π–∑ Bands of CO2,” J. Mol. Spectrosc. 55, 66 (1975).
    [CrossRef]
  20. R. A. Toth, “Line Strengths of N2O in the 2.9 Micron Region,” J. Mol. Spectrosc. 40, 588 (1971).
    [CrossRef]
  21. A. Baldacci, C. P. Rinsland, M. A. H. Smith, K. N. Rao, “Spectrum of 13C16O2 at 2.8 μm,” J. Mol. Spectrosc. 94, 351 (1982).
    [CrossRef]
  22. D. E. Burch, D. A. Gryvnak, J. D. Pembrook, “Infrared Absorption Bands of Nitrous Oxide,” final report to ARPA, monitored by AFGL under contract AFCRL-72-0387 (1972).
  23. R. H. Kagann, “Infrared Absorption Intensities for N2O,” J. Mol. Spectrosc. 95, 297 (1982).
    [CrossRef]

1983 (5)

1982 (4)

G. Guelachvili, “Absolute N2O Wavenumbers Between 1118 and 1343 cm−1 by Fourier Transform Spectroscopy,” Can. J. Phys. 60, 1334 (1982).
[CrossRef]

A. Baldacci, C. P. Rinsland, M. A. H. Smith, K. N. Rao, “Spectrum of 13C16O2 at 2.8 μm,” J. Mol. Spectrosc. 94, 351 (1982).
[CrossRef]

R. H. Kagann, “Infrared Absorption Intensities for N2O,” J. Mol. Spectrosc. 95, 297 (1982).
[CrossRef]

R. A. Toth, V. D. Gupta, J. W. Brault, “Line Positions and Strengths of HDO in the 2400–3300-cm−1 Region,” Appl. Opt. 21, 3337 (1982).
[CrossRef] [PubMed]

1981 (2)

L. S. Rothman, “AFGL Atmospheric Absorption Line Parameters Compilation: 1980 Version,” Appl. Opt. 20, 791 (1981).
[CrossRef] [PubMed]

N. Lacome, A. Levy, “Line Strengths and Self-Broadened Linewidths of N2O in the 2-μm Region,” J. Mol. Spectrosc. 85, 205 (1981).
[CrossRef]

1978 (1)

Y. Y. Kwan, “The Interacting States of An Asymmetric Top Molecule XY2 of Group C2V,” J. Mol. Spectrosc. 71, 260 (1978).
[CrossRef]

1976 (3)

C. Amiot, G. Guelachvili, “Extension of the 106 Samples Fourier Spectrometry to the Indium Antimonide Region: Vibration-Rotation Bands of 14N216O: 3.3–5.5μm Region,” J. Mol. Spectrosc. 59, 171 (1976).
[CrossRef]

C. Amiot, “Vibration-Rotation Bands of 14N15N16O–15N14N16O: 1.6–5.7μm Region,” J. Mol. Spectrosc. 59, 191 (1976).
[CrossRef]

C. Amiot, “Vibration-Rotation Bands of 15N216O–14N218N2O,” J. Mol. Spectrosc. 59, 380 (1976).
[CrossRef]

1975 (3)

B. G. Whitford, K. J. Siemsen, H. D. Riccius, G. R. Hanes, “Absolute Frequency Measurements of N2O Laser Transitions,” Opt. Commun. 14, 70 (1975).
[CrossRef]

J. M. Flaud, C. Camy-Peyret, “Vibration-Rotation Intensities in H2O-Type Molecules Application to the 2ν2, ν1, and ν3 Bands of H216O,” J. Mol. Spectrosc. 55, 278 (1975).
[CrossRef]

H. D. Downing, B. J. Krohn, R. H. Hunt, “Coriolis Intensity Perturbations in π–∑ Bands of CO2,” J. Mol. Spectrosc. 55, 66 (1975).
[CrossRef]

1973 (1)

N. Lacome, C. Boulet, E. Arie, “Spectroscopic par Source Laser,” III. Intensitiés et Largeurs des Raies de la Transition 00°1–10°0 du Protoxyde d’Azote. Ecarts á la Forme de Lorentz,” Can. J. Phys. 51, 302 (1973).
[CrossRef]

1972 (1)

J. S. Margolis, “Intensity and Half Width Measurements of the (00°2–00°0) Band of N2O,” J. Quant. Spectrosc. Radiat. Transfer 12, 751 (1972).
[CrossRef]

1971 (2)

R. A. Toth, “Self-Broadened and N2 Broadened Linewidths of N2O,” J. Mol. Spectrosc. 40, 605 (1971).
[CrossRef]

R. A. Toth, “Line Strengths of N2O in the 2.9 Micron Region,” J. Mol. Spectrosc. 40, 588 (1971).
[CrossRef]

Amiot, C.

C. Amiot, G. Guelachvili, “Extension of the 106 Samples Fourier Spectrometry to the Indium Antimonide Region: Vibration-Rotation Bands of 14N216O: 3.3–5.5μm Region,” J. Mol. Spectrosc. 59, 171 (1976).
[CrossRef]

C. Amiot, “Vibration-Rotation Bands of 14N15N16O–15N14N16O: 1.6–5.7μm Region,” J. Mol. Spectrosc. 59, 191 (1976).
[CrossRef]

C. Amiot, “Vibration-Rotation Bands of 15N216O–14N218N2O,” J. Mol. Spectrosc. 59, 380 (1976).
[CrossRef]

Arie, E.

N. Lacome, C. Boulet, E. Arie, “Spectroscopic par Source Laser,” III. Intensitiés et Largeurs des Raies de la Transition 00°1–10°0 du Protoxyde d’Azote. Ecarts á la Forme de Lorentz,” Can. J. Phys. 51, 302 (1973).
[CrossRef]

Baldacci, A.

A. Baldacci, C. P. Rinsland, M. A. H. Smith, K. N. Rao, “Spectrum of 13C16O2 at 2.8 μm,” J. Mol. Spectrosc. 94, 351 (1982).
[CrossRef]

Benner, D. C.

Boulet, C.

N. Lacome, C. Boulet, E. Arie, “Spectroscopic par Source Laser,” III. Intensitiés et Largeurs des Raies de la Transition 00°1–10°0 du Protoxyde d’Azote. Ecarts á la Forme de Lorentz,” Can. J. Phys. 51, 302 (1973).
[CrossRef]

Brault, J. W.

Brown, L. R.

Burch, D. E.

D. E. Burch, D. A. Gryvnak, J. D. Pembrook, “Infrared Absorption Bands of Nitrous Oxide,” final report to ARPA, monitored by AFGL under contract AFCRL-72-0387 (1972).

Camy-Peyret, C.

J. M. Flaud, C. Camy-Peyret, “Vibration-Rotation Intensities in H2O-Type Molecules Application to the 2ν2, ν1, and ν3 Bands of H216O,” J. Mol. Spectrosc. 55, 278 (1975).
[CrossRef]

Downing, H. D.

H. D. Downing, B. J. Krohn, R. H. Hunt, “Coriolis Intensity Perturbations in π–∑ Bands of CO2,” J. Mol. Spectrosc. 55, 66 (1975).
[CrossRef]

Flaud, J. M.

J. M. Flaud, C. Camy-Peyret, “Vibration-Rotation Intensities in H2O-Type Molecules Application to the 2ν2, ν1, and ν3 Bands of H216O,” J. Mol. Spectrosc. 55, 278 (1975).
[CrossRef]

Gryvnak, D. A.

D. E. Burch, D. A. Gryvnak, J. D. Pembrook, “Infrared Absorption Bands of Nitrous Oxide,” final report to ARPA, monitored by AFGL under contract AFCRL-72-0387 (1972).

Guelachvili, G.

G. Guelachvili, “Experimental Doppler-Limited Spectra of the ν2 Bands of H216, H217O, H218O, and HDO by Fourier-Transform Spectroscopy: Secondary Wave-Number Standards Between 1066 and 2296 cm−1,” J. Opt. Soc. Am. 73, 137 (1983).
[CrossRef]

G. Guelachvili, “Absolute N2O Wavenumbers Between 1118 and 1343 cm−1 by Fourier Transform Spectroscopy,” Can. J. Phys. 60, 1334 (1982).
[CrossRef]

C. Amiot, G. Guelachvili, “Extension of the 106 Samples Fourier Spectrometry to the Indium Antimonide Region: Vibration-Rotation Bands of 14N216O: 3.3–5.5μm Region,” J. Mol. Spectrosc. 59, 171 (1976).
[CrossRef]

Gupta, V. D.

Hanes, G. R.

B. G. Whitford, K. J. Siemsen, H. D. Riccius, G. R. Hanes, “Absolute Frequency Measurements of N2O Laser Transitions,” Opt. Commun. 14, 70 (1975).
[CrossRef]

Hunt, R. H.

H. D. Downing, B. J. Krohn, R. H. Hunt, “Coriolis Intensity Perturbations in π–∑ Bands of CO2,” J. Mol. Spectrosc. 55, 66 (1975).
[CrossRef]

Kagann, R. H.

R. H. Kagann, “Infrared Absorption Intensities for N2O,” J. Mol. Spectrosc. 95, 297 (1982).
[CrossRef]

Krohn, B. J.

H. D. Downing, B. J. Krohn, R. H. Hunt, “Coriolis Intensity Perturbations in π–∑ Bands of CO2,” J. Mol. Spectrosc. 55, 66 (1975).
[CrossRef]

Kwan, Y. Y.

Y. Y. Kwan, “The Interacting States of An Asymmetric Top Molecule XY2 of Group C2V,” J. Mol. Spectrosc. 71, 260 (1978).
[CrossRef]

Lacome, N.

N. Lacome, A. Levy, “Line Strengths and Self-Broadened Linewidths of N2O in the 2-μm Region,” J. Mol. Spectrosc. 85, 205 (1981).
[CrossRef]

N. Lacome, C. Boulet, E. Arie, “Spectroscopic par Source Laser,” III. Intensitiés et Largeurs des Raies de la Transition 00°1–10°0 du Protoxyde d’Azote. Ecarts á la Forme de Lorentz,” Can. J. Phys. 51, 302 (1973).
[CrossRef]

Levy, A.

N. Lacome, A. Levy, “Line Strengths and Self-Broadened Linewidths of N2O in the 2-μm Region,” J. Mol. Spectrosc. 85, 205 (1981).
[CrossRef]

Margolis, J. S.

L. R. Brown, J. S. Margolis, R. H. Norton, B. D. Stedry, “Computer Measurement of Line Strengths with Application to the Methane Spectrum, Appl. Spectrosc. 37, 287 (1983).
[CrossRef]

J. S. Margolis, “Intensity and Half Width Measurements of the (00°2–00°0) Band of N2O,” J. Quant. Spectrosc. Radiat. Transfer 12, 751 (1972).
[CrossRef]

Norton, R. H.

Pembrook, J. D.

D. E. Burch, D. A. Gryvnak, J. D. Pembrook, “Infrared Absorption Bands of Nitrous Oxide,” final report to ARPA, monitored by AFGL under contract AFCRL-72-0387 (1972).

Rao, K. N.

A. Baldacci, C. P. Rinsland, M. A. H. Smith, K. N. Rao, “Spectrum of 13C16O2 at 2.8 μm,” J. Mol. Spectrosc. 94, 351 (1982).
[CrossRef]

Riccius, H. D.

B. G. Whitford, K. J. Siemsen, H. D. Riccius, G. R. Hanes, “Absolute Frequency Measurements of N2O Laser Transitions,” Opt. Commun. 14, 70 (1975).
[CrossRef]

Richardson, D. J.

Rinsland, C. P.

Rothman, L. S.

Siemsen, K. J.

B. G. Whitford, K. J. Siemsen, H. D. Riccius, G. R. Hanes, “Absolute Frequency Measurements of N2O Laser Transitions,” Opt. Commun. 14, 70 (1975).
[CrossRef]

Smith, M. A. H.

A. Baldacci, C. P. Rinsland, M. A. H. Smith, K. N. Rao, “Spectrum of 13C16O2 at 2.8 μm,” J. Mol. Spectrosc. 94, 351 (1982).
[CrossRef]

Stedry, B. D.

Toth, R. A.

Whitford, B. G.

B. G. Whitford, K. J. Siemsen, H. D. Riccius, G. R. Hanes, “Absolute Frequency Measurements of N2O Laser Transitions,” Opt. Commun. 14, 70 (1975).
[CrossRef]

Appl. Opt. (5)

Appl. Spectrosc. (1)

Can. J. Phys. (2)

N. Lacome, C. Boulet, E. Arie, “Spectroscopic par Source Laser,” III. Intensitiés et Largeurs des Raies de la Transition 00°1–10°0 du Protoxyde d’Azote. Ecarts á la Forme de Lorentz,” Can. J. Phys. 51, 302 (1973).
[CrossRef]

G. Guelachvili, “Absolute N2O Wavenumbers Between 1118 and 1343 cm−1 by Fourier Transform Spectroscopy,” Can. J. Phys. 60, 1334 (1982).
[CrossRef]

J. Mol. Spectrosc. (11)

C. Amiot, G. Guelachvili, “Extension of the 106 Samples Fourier Spectrometry to the Indium Antimonide Region: Vibration-Rotation Bands of 14N216O: 3.3–5.5μm Region,” J. Mol. Spectrosc. 59, 171 (1976).
[CrossRef]

C. Amiot, “Vibration-Rotation Bands of 14N15N16O–15N14N16O: 1.6–5.7μm Region,” J. Mol. Spectrosc. 59, 191 (1976).
[CrossRef]

C. Amiot, “Vibration-Rotation Bands of 15N216O–14N218N2O,” J. Mol. Spectrosc. 59, 380 (1976).
[CrossRef]

Y. Y. Kwan, “The Interacting States of An Asymmetric Top Molecule XY2 of Group C2V,” J. Mol. Spectrosc. 71, 260 (1978).
[CrossRef]

J. M. Flaud, C. Camy-Peyret, “Vibration-Rotation Intensities in H2O-Type Molecules Application to the 2ν2, ν1, and ν3 Bands of H216O,” J. Mol. Spectrosc. 55, 278 (1975).
[CrossRef]

H. D. Downing, B. J. Krohn, R. H. Hunt, “Coriolis Intensity Perturbations in π–∑ Bands of CO2,” J. Mol. Spectrosc. 55, 66 (1975).
[CrossRef]

R. A. Toth, “Line Strengths of N2O in the 2.9 Micron Region,” J. Mol. Spectrosc. 40, 588 (1971).
[CrossRef]

A. Baldacci, C. P. Rinsland, M. A. H. Smith, K. N. Rao, “Spectrum of 13C16O2 at 2.8 μm,” J. Mol. Spectrosc. 94, 351 (1982).
[CrossRef]

R. A. Toth, “Self-Broadened and N2 Broadened Linewidths of N2O,” J. Mol. Spectrosc. 40, 605 (1971).
[CrossRef]

N. Lacome, A. Levy, “Line Strengths and Self-Broadened Linewidths of N2O in the 2-μm Region,” J. Mol. Spectrosc. 85, 205 (1981).
[CrossRef]

R. H. Kagann, “Infrared Absorption Intensities for N2O,” J. Mol. Spectrosc. 95, 297 (1982).
[CrossRef]

J. Opt. Soc. Am. (1)

J. Quant. Spectrosc. Radiat. Transfer (1)

J. S. Margolis, “Intensity and Half Width Measurements of the (00°2–00°0) Band of N2O,” J. Quant. Spectrosc. Radiat. Transfer 12, 751 (1972).
[CrossRef]

Opt. Commun. (1)

B. G. Whitford, K. J. Siemsen, H. D. Riccius, G. R. Hanes, “Absolute Frequency Measurements of N2O Laser Transitions,” Opt. Commun. 14, 70 (1975).
[CrossRef]

Other (1)

D. E. Burch, D. A. Gryvnak, J. D. Pembrook, “Infrared Absorption Bands of Nitrous Oxide,” final report to ARPA, monitored by AFGL under contract AFCRL-72-0387 (1972).

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Figures (1)

Fig. 1
Fig. 1

Slightly apodized observed spectra of N2O in the 1199–1220-cm−1 region. The spectral resolution was 0.005 cm−1, cell length 73.1 m, and gas sample pressure 1.00 Torr at 296 K. The location of the lines R24–R46 of the 0220(e)–0000 band are marked as well as the R35, R40, R45, and R50 lines of the 0200–0000 band.

Tables (5)

Tables Icon

Table I Isotopic Abundances, Vibrational (Qv), and Rotational(QR) Partition Functions of N2O at 296 K.

Tables Icon

Table II Vibrational Transitions V1V2 and Interacting States Which are Applicable for Evaluating the Rotationless Dipole Moment Matrix Element R12 and F Factor coefficients of N2O and CO2 Bands; Vibrational State Notation of N2O is used with K = |l| and ΔK = K2 − K1.

Tables Icon

Table III σ* Obtained from Least-Squares Fitting of the Measured N2O Line Strength Values to Various Forms of the F Factor.

Tables Icon

Table IV Band Strengths Sv, Rotationless Dipole Moment Matrix Elements |R|, and F Factor Coefficients of N2O; Sv in cm−1/atm at 296 K and |R| in Debye.

Tables Icon

Table V Observed Line Positions and Observed and Calculated* Line Strengths in the 0220(e)–0000 Band of N2O; Strengths in cm−2/atm at 296 K.

Equations (53)

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S = ( ν / ν 0 ) S v · P 2 · exp ( - E R / k T ) · [ 1 - exp ( - ν / k T ) ] · F / Q R ,
S v = 8 π 3 R 2 ν 0 3 h c · T · Q v exp ( - E v / k T ) ,
S v = 3.56 R 2 ν 0 exp ( - 1.4388 E v / T ) T · Q v .
F 1 = 1 , F 2 = 1 + a m , F 3 = ( 1 + ξ m ) 2 , F 4 = 1 + c m + d m 2 ,
F 5 = [ 1 + A 1 m + A 2 m 2 + A 3 m 3 + A 4 J ( J + 1 ) ] 2
S ( J , K , γ ) = 1 2 [ J , l > + ( - 1 ) γ J , - l > ] K 0 , S ( J , 0 , 0 ) = J , 0 > ,
A ° ( V n , J , K n , γ l ) = Ψ ν n · S ( J , K n , γ l ) , A ( V n , J , K n , γ l ) = n a n m A ° ( V m , J , K m , γ l n m ) V n 0 , J , K n , γ l > = A ° ( V n , J , K n , γ l ) V n , J , K n , γ l > = A ( V n , J , K n , γ l ) ,
γ = l for e levels , γ = l + 1 for f levels ,
W n m = V n , J , K n , γ l W V m , J , K m , γ l n m ,
W n m = h n m [ F 0 n m + F K n m K 2 + F j n m J ( J + 1 ) + δ K , 1 ( - 1 ) γ F x y n m 2 J ( J + 1 ) ] ,
W n m = Z K n h n m F x y n m G ( J , K n , ± ) ,
G ( J , K , ± ) = ½ [ ( J K - 1 ) ( J K ) ( J ± K + 1 ) ( J ± K + 2 ) ] 1 / 2 , Z K n = 2 if K n is 0 ( + sign ) or 2 ( - sign ) ; otherwise , Z k n = 1 ,
W n m = U K n g n m ½ [ ( J K n ) ( J K n + 1 ) ] 1 / 2 × [ ± C y n m + ( 2 K n ± 1 ) C x z n m ] ,
U K n = 2 if K n = 0 ( + sign ) or 1 ( - sign ) ; otherwise , U K n = 1 ,
S = X · V 1 , J , K , γ μ V 2 , J , K , γ 2 , R 12 · P 12 · f 12 = V 1 , J , K , γ μ V 2 , J , K , γ ,
r n m · p n m = V n , J , K , γ μ V m , J , K , γ ,
p n m = J , l ϕ z α J , l ,
P 12 = p 12 , Δ l = 0 , ± 1 , P 12 = p l m , m 2 , l - l = 2 , 3 , P 12 = p m 2 , m 1 , l - l = - 2 - 3.
a n m = a n m W n m d ( n , m ) with a n n = 1 ,
α n m = 1 , Δ l = 0 , ± 2 type interactions , α n m = - 1 , Δ l = ± 1 type interactions , d ( n , m ) = E n - E m = - d ( m , n ) .
F = [ 1 + a 1 m + a 2 J ( J + 1 ) + a 3 J ( J + 1 ) ] 2 , Δ K = 0 , ± 1 , F = ( 1 + a 1 m ) 2 · H , Δ K > 1 ,
H = [ ( J + K - 1 ) ( J + K ) ( J - K + 1 ) ( J - K + 2 ) ] , Δ K = 2 or 3 , H = [ ( J + K - 1 ) ( J + K ) ( J - K + 1 ) ( J - K + 2 ) ] , Δ K = - 2 or - 3 ,
K = l , Δ K = K - K .
K 6 = K 7 , P 12 = p 12 , K 6 - K 1 = Δ K 61 = ± 1 ,             Δ l = 0 bands , K 6 = K 1 and K 2 - K 1 = Δ K 21 = ± 1 ,             Δ l = ± 1 bands .
Δ l = 0 , R 12 = r 12 + r 13 ( F 0 23 + K 1 2 F K 23 ) d ( 2 , 3 ) + r 14 ( F 0 24 + K 1 2 K k 24 ) d ( 2 , 4 ) + r 25 ( F 0 15 + K 1 2 F K 15 ) d ( 1 , 5 ) + r 16 · Δ K 61 C y 26 2 · d ( 2 , 6 ) + r 17 · Δ K 61 C y 27 2 · d ( 2 , 7 ) ,
Δ l = ± 1 , R 12 = r 12 + μ 0 C y 12 2 d ( 2 , 1 ) + r 13 ( F 0 23 + F K 23 K 2 2 ) d ( 2 , 3 ) + r 14 ( F 0 24 + K 2 2 F K 24 ) d ( 2 , 4 ) + r 25 ( F 0 15 + K 1 2 F K 25 ) d ( 1 , 5 ) - r 16 · Δ K 21 · K 1 C y 26 2 d ( 2 , 6 ) - r 17 · Δ K 21 · K 1 C y 27 2 d ( 2 , 7 ) ,
Δ l = 0 , a 1 = 1 R 12 { 2 μ 0 d ( 2 , 1 ) [ F J 12 + δ K 1 , 1 ( - 1 ) γ F x y 12 2 ] + r 16 C y 26 2 · d ( 2 , 6 ) + r 17 C y 27 2 · d ( 2 , 7 ) } ,
Δ l = ± 1 , a 1 = 1 2 R 12 [ r 16 C y 26 ( γ ) d ( 2 , 6 ) + r 17 C y 27 ( γ ) d ( 2 , 7 ) } ,
Δ l = 0 , ± 1 , a 2 = 1 R 12 { r 13 d ( 2 , 3 ) [ F J 23 + δ K 2 , 1 ( - 1 ) γ F x y 23 2 ] + r 14 d ( 2 , 4 ) [ F J 24 + δ K 2 , 1 ( - 1 ) γ F x y 24 2 ] + ( Δ J - 1 ) · Δ K 61 2 K 1 [ r 16 C y 26 d ( 2 , 6 ) + r 17 C y 27 d ( 2 , 7 ) ] } ,
a 3 = r 25 R 12 · d ( 1 , 5 ) [ F J 15 + δ K 1 , 1 ( - 1 ) γ F x y 15 2 ] .
Δ K 21 = K 2 - K 1 = ± 2 , 3 , P 12 = p 13 , Δ K 21 = 2 , 3 , P 12 = p 52 Δ K 21 = - 2.
Δ K 21 = 2 , 3 ,             R 12 = 1 2 n ( R 13 F x y 23 d ( 2 , 3 ) + R 14 F x y 24 d ( 2 , 4 ) ) ,             n = ( K 2 - 1 ) / 2 ,
Δ K 21 = ± 2 ,             a 1 = 0 ,
Δ K 21 = 3 ,             a 1 = 1 2 n · R 12 { F x y 23 d ( 2 , 3 ) [ r 16 C y 36 d ( 3 , 6 ) + r 17 C y 37 d ( 3 , 7 ) ] + F x y 24 d ( 2 , 4 ) [ r 16 C y 46 d ( 4 , 6 ) + r 17 C y 47 d ( 4 , 7 ) ] }             n = ( K 2 + 1 ) / 2 ,
Δ K 21 = - 2 , R 12 = 1 2 n [ R 52 F x y 15 d ( 1 , 5 ) + R 5 a 2 F x y 15 a d ( 1 , 5 a ) ]             n = ( K 1 - 1 ) / 2.
S v ( V n V x ) S v ( V m V x ) 1 ,
x = 1 , m = 2 , Δ K = 0 , ± 1 , x = 1 , m = 3 , Δ K = 2 , 3 , x = 5 , m = 2 , Δ K = - 2 ,
ξ = m η 2 m R 1 m R 12 .
a 1 = m C y 2 m ( γ ) d ( 2 , m ) r 1 m R 12 ;
β = S { ( ν / ν 0 ) ( P 2 / Q R ) [ 1 - exp ( - ν / k T ) ] exp ( - E R / k T ) } - 1 .
β = S v · F .
F 6 = [ 1 + a 1 m + a 2 J ( J + 1 ) ] 2 .
σ = [ N ( S obs - S cal S obs ) 2 N ] 1 / 2 × 100.
σ ( F 2 ) σ ( F 3 ) , σ ( F 4 ) σ ( F 6 ) , σ ( F 3 ) > σ ( F 6 ) .
F 6 1 + 2 a 1 m + 2 a 2 J ( J + 1 ) .
F [ J ( J + 1 ) ] 2 , Δ K = 2 ,
| F 0 23 d ( 2 , 3 ) | = 0.342 + 0.191 - 0.171 r 12 = 0.111 D , r 13 = 0.064 D ,
116.771 cm - 1 > d ( 2 , 3 ) > 97.964 cm - 1 .
d ( 2 , 3 ) = { 4 ( E 2 - E ¯ 23 ) 2 1 + 4 [ F 0 23 / d ( 2 , 3 ) ] 2 } 1 / 2 ,
d ( 2 , 3 ) = 96.4 + 14.1 - 16.5 cm - 1 ,
| F 0 23 d ( 2 , 3 ) | = 0.79 + 1.34 - 0.57 r 12 = 0.07 D , r 13 = 0.08 D ,
131.199 cm - 1 > d ( 2 , 3 ) > 96.615 cm - 1 .
d ( 2 , 3 ) = 69.9 + 50.0 - 40.0 cm - 1 ,

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