High-Resolution Study of the Three Lowest Infrared Bands of PHD2

Journal of Molecular Spectroscopy 214, 1–10 (2002) doi:10.1006/jmsp.2002.8563

High-Resolution Study of the Three Lowest Infrared Bands of PHD2 O. N. Ulenikov,∗ E. S. Bekhtereva,∗ O. L. Petrunina,∗ H. B¨urger,† and W. Jerzembeck† ∗ Laboratory of Molecular Spectroscopy, Physics Department, Tomsk State University, Tomsk, 634050, Russia, and Institute of Atmospheric Optics SB RAN, Tomsk, 634055, Russia; and †Anorganische Chemie, FB9, Universit¨at Gesamthochschule, D-42097 Wuppertal, Germany Received December 11, 2001; in revised form February 28, 2002

The high-resolution (2.3 × 10−3 cm−1 ) Fourier transform infrared spectrum of PHD2 was recorded for the first time and analyzed in the region of the three lowest bands belonging to the three bending fundamentals. Between 1100 and 1800 transitions were assigned to each of the ν3 , ν4 , and ν6 bands and 1267 upper energies were obtained thereof. These were fitted by 58 parameters, which reproduce the experimental upper energies with rms deviations of 1.3×10−4 cm−1 and 2.7×10−4 cm−1 for the J ≤ 17 C 2002 Elsevier Science (USA) and J ≥ 18 levels, respectively. 

Experimental details of the spectra that were used are given in Ref. (2). In brief, the resolution (1/maximum optical path difference) was 2.3 × 10−3 cm−1 , the 600–1160 cm−1 region was studied, and a cell of 28 cm length with pressures of 100 and 550 Pa employed. Calibration was with CO2 lines (14). Wavenumber precision of unblended, medium intensity lines is about 1 × 10−4 cm−1 . Two portions of the recorded spectra are shown in Figs. 1 and 2.

1. INTRODUCTION

The present contribution, which is a continuation of our recent studies of the mono- and dideuterated species of the phosphine molecule, Refs. (1, 2), is devoted to the high resolution spectra and their analysis of the three lowest-lying fundamental bands of PHD2 . Interest in the spectroscopy of the phosphine molecule and its isotopomers is caused both by their relevance for astrophysics (see, e.g., (3–5)), and by theoretical aspects, which follow from the fact that phosphine is a basic and one of the lightest polyatomic molecules. As a consequence, spectroscopic effects and peculiarities should be particularly pronounced in the spectra of phosphine species. Both PH3 and PD3 and the partially deuterated PH2 D species have been studied to some extent (see, e.g., (1, 2, 6–8) and references cited therein). As to PHD2 , this has been studied only in the microwave region (9–13), and recently in the far infrared regions (1). In this contribution we present the results of the first highresolution vibration–rotation study of the three lowest-lying fundamentals ν3 , ν4 , and ν6 . Infrared spectra in the 600–1160 cm−1 range of the PHD2 molecule have been recorded with the Bruker IFS 120HR interferometer at Wuppertal with a resolution of 0.0023 cm−1 . Experimental details are reported in Section 2, while Section 3 is devoted to the description of the Hamiltonian model used in the analysis. Assignments of the recorded transitions and the determination of the spectroscopic parameters are presented in Section 4.

3. THEORETICAL BACKGROUND

The PHD2 molecule is an asymmetric top, the value of the asymmetry parameter being κ = (2B − A − C)/(A − C) 0.174. Therefore the rotational Watson-type Hamiltonian in A reduction and Ir representation can be efficiently used for the description of its rotational–vibrational spectra, 

 1 i 1 i H = E + A − (B + C ) Jz2 + (B i + C i )J 2 2 2 ii

i

i

1 + (B i − C i )Jx2y − iK Jz4 − iJ K Jz2 J 2 − iJ J 4 2   − δ iK Jz2 , Jx2y + − 2δ iJ J 2 Jx2y + HKi Jz6 + HKi J Jz4 J 2  + H Ji K Jz2 J 4 + H Ji J 6 + Jx2y , h iK Jz4 + h iJ K J 2 Jz2  + h iJ J 4 + + L iK Jz8 + L iK K J Jz6 J 2 + L iK J Jz4 J 4  + L iK J J Jz2 J 6 + L iJ J 8 + Jx2y , l Ki Jz6 + l Ki J J 4 Jz2  + l iJ K J 2 Jz4 + l iJ J 6 + + · · · , [1]

2. EXPERIMENTAL DETAILS

The synthesis of a sample enriched to 60% PHD2 , 25% PH2 D, 10% PD3 , and 5% PH3 has been described (1). Moreover, a sample composed of 5% PH2 D, 10% PHD2 , and 85% PD3 was available for comparison and identification of lines belonging to other isotopomers of phosphine than PHD2 by means of relative intensities of lines.

where i = 3, 4, 6, and |3 = (001000), |4 = (000100), and |6 = (000001); Jx2y = Jx2 − Jy2 and J 2 = Jx2 + Jy2 + Jz2 . Since the PHD2 molecule has Cs symmetry, its three lowest vibrational bands, ν3 , ν4 , and ν6 , have A , A , and A symmetries, respectively. They are located close to each other, ν3 = 911.652 cm−1 , 1

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ULENIKOV ET AL. (a)

(b) z y

y

,

X

X H

x

,

z

X

x

D

H y

H H

(c)

,

H D

,

,

D H

z

,

x

FIG. 3. Orientation of the frame axes in the molecules PH3 , PHD2 and PH2 D: The frame axes are directed along the principal axes of inertia of the molecules (see text for details). FIG. 1. Portion of the ν4 band of PHD2 in the P-branch region, resolution 2.3 × 10−3 cm−1 . Assignments of the strongest lines are given. Both b-type and c-type transitions (in italics) are assigned.

ν4 = 766.887 cm−1 , and ν6 = 978.559 cm−1 (see Table 1), and, as a consequence, strongly interact with each other. The other vibrational fundamentals are located at ν1 = 2324.00 cm−1 , ν2 = 1886.08 cm−1 , and ν5 = 1892.76 cm−1 (15 ). They are far away from the three fundamentals discussed in the present study. Therefore, a Hamiltonian was used which has the following form: H v.−r. =



|i  j|H i j .

most convenient orientations of the coordinate axes in the PHD2 and PH2 D species are shown on Figs. 3b and 3c, respectively. It is evident that in the PH2 D molecule the axes y and z are located in the plane of symmetry. In the PHD2 molecule the axes x and y are located in the respective symmetry plane. This means that, contrary to the PH2 D molecule whose interaction operators have the form given in Eqs. [16]–[21] of Ref. (2), the resonance interaction operators for the PHD2 molecule should be taken in the following form. Interactions between the states (000100) and (001000), on the one hand, and the state (000001), on the other hand, should be described by the H i6 (i = 3, or 4) operators

[2]

H i6 = H 6i+ = HCi6x + HCi6y ,

i, j

The diagonal parts H ii have the form of Eq. [1]. With regard to the resonance interaction operators, we refer to the discussions in Refs. (1) and (2) concerning rotation of the molecular fixed coordinate axes when transformations are carried out from the “mother” PH3 molecule (see Fig. 3a) to the “daughter” molecules PHD2 or/and PH2 D. In accordance with (1, 2), the

[3]

where   HCi6x = (2Bζ x )i6 i Jx + C xi6K i Jx , Jz2 + + C xi6J i Jx J 2 + · · ·   i6 i6 2 + C yz [Jy , Jz ]+ + C yz K [J y , Jz ]+ , Jz +   i6 2 i6 2 2 + C yz J [J y , Jz ]+ J + · · · + C x x y i Jx , Jx − J y +    + C xi6x y K i Jx , Jx2 − Jy2 + , Jz2 +   + C xi6x y J i Jx , Jx2 − Jy2 + J 2 + · · · [4] and   HCi6y = (2Cζ y )i6 i Jy + C yi6K i Jy , Jz2 + + C yi6J i Jy J 2 + · · ·   + C xi6z [Jx , Jz ]+ + C xi6z K [Jx , Jz ]+ , Jz2 +   i6 2 2 + C xi6z J [Jx , Jz ]+ J 2 + · · · + C yx y i J y , Jx − J y +    i6 2 2 2 + C yx y K i J y , Jx − J y + , Jz +   2 i6 2 2 + C yx [5] y J i J y , Jx − J y + J + · · ·.

FIG. 2. Detail of the spectrum of PHD2 in the region of the ν3 and ν6 bands, resolution 2.3 × 10−3 cm−1 . Transitions of c-type belonging to the ν3 band are denoted in italics below the spectrum, those of the ν6 band above the spectrum. The latter comprise both a-type transitions and transitions of the fourth type (K a = 0, K c = 0) caused by resonance interactions. These are marked by asterisks.

In turn, the resonance interaction operator H 43 = H 34+ takes the form

 C 2002 Elsevier Science (USA)

H 43 = HF43 + HC43z ,

[6]

INFRARED BANDS OF PHD2

3

where HF43 = F 43 + FK43 Jz2 + FJ43 J 2 + FK43K Jz4 + · · ·

[7]

and HC43z = (2Aζ z )43 i Jz + C z43K i Jz3 + · · · + C z43J i Jz J 2 + C z43K K i Jz5   + · · · + C x43y [Jx , Jy ]+ + C x43y K [Jx , Jy ]+ , Jz2 +   + C x43y J [Jx , Jy ]+ J 2 + C x43y K K [Jx , Jy ]+ , Jz4 + +· · ·. [8]

4. ASSIGNMENT AND DISCUSSION

Since the (001000), (000100), and (000001) vibrational states have A , A , and A symmetries, respectively, the ν3 and ν4 bands should be associated with b- and c-type transitions while the ν6 band should reveal a-type transitions. In fact, both b- and ctype transitions were assigned in the ν3 and ν4 bands (see, for illustration, Figs. 1 and 2). The ν3 and ν6 bands are stronger than the ν4 band. On the other hand, the ν4 band is well separated from the overlapping ν3 /ν6 absorptions and, in spite of its smaller intensity, more lines belonging to ν4 could be assigned than for ν3 and ν6 . Assignments of transitions were made with the help of the ground state combination differences method. For this purpose the ground state parameters of PHD2 were taken from Ref. (1); for convenience they are reproduced in column 2 of Table 1. In result, we assigned 1460 (J max. = 22, K amax. = 20), 1770 (J max. = 22, K amax. = 19), and 1100 (J max. = 23, K amax. = 17) transitions to the ν3 , ν4 , and ν6 bands, respectively. Detailed statistical information concerning assignments and the studied states is gathered in Table 2. Accordingly the assigned transitions determine altogether 444, 435, and 388 upper state energies of the (001000), (000100), and (000001) vibrational states, respectively. The effective values of these upper state energies, which are the mean values obtained from several transitions reaching the same upper level, are presented in columns 2, 5, and 8 of Table 3. Columns 3, 6, and 9 of Table 3 give the experimental uncertainties  in units of 10−5 cm−1 . It is evident that the experimental uncertainties  have values of order (1–2) × 10−4 cm−1 for states with quantum number J ≤ 17 and begin to worsen for values J ≥ 18. This worsening is due to the decreasing strengths of the transitions as the value of the quantum number J increases and, as a consequence, the accuracy of the corresponding line positions gets worse. As was mentioned before, the three vibrational states (001000), (000100), and (000001) mutually perturb each other strongly. One particular feature of such perturbations is illustrated in Fig. 4, the bottom part of which shows the differences (J ) of the rovibrational energies E[JK a =J −1K c =1 ] and E[JK a =J −1K c =2 ] of the vibrational state (001000) versus the value of the quantum number J . Usually pairs of corre-

FIG. 4. Upper part (Fig. 4a): Dependence of the differences 1 (J ) = E[JK a =J −1K c =1 ] (001000)–E[JK a =J −6K c =6 ] (000001) and 2 (J ) = E[JK a = J −1K c =2 ] (001000)–E[JK a =J −6K c =7 ] (000001) on the value of quantum number J . Two reasons, namely the closeness to zero of 1 (16) and 2 (16), and the value of the ratio 2 (16)/1 (16) 4, cause, on the one hand, large shifts of both the [JK a =J −1K c =1 ] (001000) and [JK a =J −1K c =2 ] (001000) levels. On the other hand, the [JK a =J −1K c =1 ] (001000) level is considerably more shifted than the [JK a =J −1K c =2 ] (001000) level and the difference  of these shifts is illustrated in Fig. 4b (bottom part).

sponding states form clusters with equal energies. However, the presence of strong resonance interactions between the states [JK a =J −1K c =1 ] (001000) and [JK a =J −1K c =2 ] (001000), on the one hand, and the states [JK a =J −6K c =6 ] (000001) and [JK a =J −6K c =7 ] (000001), on the other hand, induce large splittings of the energy levels for the states [16151 ] (001000) and [16152 ] (001000). The top part of Fig. 4 illustrates that the curves representing the differences i (J ) (i = 1, 2) between the energies of the states [JK a =J −1K c =1 ] (001000) and [JK a =J −6K c =6 ] (000001) (1 ) and [JK a =J −1K c =2 ] (001000) and [JK a =J −6K c =7 ] (000001) (2 ) cross the i = 0 “zero” line close to the quantum number J = 16. Moreover, as can be seen from Table 3, the value

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ULENIKOV ET AL.

TABLE 1 Rotational and Centrifugal Distortion Parameters for Some Vibrational States of the PHD2 Molecule (in cm−1 )a Parameter

(000000)

(001000)

(000100)

(000001)

1

2

3

4

5

911.652101(34) 3.088432(572) 2.7443708(474) 2.166864(225) 0.98568(220) −0.4549697 0.371955(928) −0.29206(255) 0.124462(562) 0.27827 1.00554(336) −0.64788 0.189953 −0.09708 −0.29493(578) 0.088304 −2.070 2.737 −2.211 0.8163 −0.19426 −0.2961 0.0 0.0 −0.07629

766.887484(33) 3.194458(579) 2.75206948(998) 2.14730755(893) 0.991590(986) −0.38932(253) 0.365635(621) −0.36376(134) −0.1076684(325) 0.27827 0.97303 −0.64788 0.202415(992) −0.09708 −0.247351 0.101677(804) −2.070 2.737 −2.211 0.8163 −0.19426 −0.2961 0.0 0.0 −0.07629

978.558761(33) 3.13633668(992) 2.7072947(367) 2.164351(219) 1.07688(257) −0.56059(291) 0.40609(104) −0.38197(192) −0.103301(648) 0.27827 0.9532(113) −0.6387(110) 0.20051(121) −0.09708 −0.247351 −0.088304 −2.070 2.737 −2.211 0.8163 −0.19426 −0.2961 0.0 0.0 −0.07629

ν A B C  K × 104  J K × 104  J × 104 δ K × 104 δ J × 104 HK × 108 HK J × 108 H J K × 108 H J × 108 h K × 108 h J K × 108 h J × 108 L K × 1012 L K K J × 1012 L J K × 1012 L K J J × 1012 L J × 1012 l K × 1012 l K J × 1012 l J K × 1012 l J × 1012

3.132704199 2.732228719 2.162945246 0.9863227 −0.4549697 0.3728591 −0.3401298 0.10895370 0.27827 0.97303 −0.64788 0.189953 −0.09708 −0.247351 0.088304 −2.070 2.737 −2.211 0.8163 −0.19426 −0.2961 0.0 0.0 −0.07629

a Values in parentheses are the 1σ statistical confidence intervals. Parameters presented without confidence intervals were fixed to the values of corresponding parameters of the ground vibrational state.

1 (16) = 0.22105 cm−1 is small and about four times smaller than the corresponding value 2 (16) = 0.83335 cm−1 . In this case, the presence of the mentioned resonance interaction leads to a considerably larger shift of the [J = 16 K a =15K c =1 ] (001000) level to that of the [J = 16 K a =15K c =2 ] (001000) level. Another interesting consequence of the strong resonance interactions between the v6 = 1 level, on the one hand, and v3 = 1

and v4 = 1 levels, on the other hand, is the appearence of numerous transitions of the fourth type (J = 0, ±1; K a = 0; K c = 0) in the ν6 band. For illustration, some of these are shown in Fig. 2. Upper state energies obtained from the experimental transitions and gathered in columns 2, 5, and 8 of Table 3 were used in the fit procedure using the Hamiltonian [1]–[8]. As the

TABLE 2 Statistical Information on the Studied Bands of the PHD2 Molecule Band

Center/cm−1

J max

K amax

n tr a

Nl /Nl b

m 1 /m 1c

m 2 /m 2c

m 3 /m 3c

1

2

3

4

5

6

7

8

9

ν3 ν4 ν6

911.65210 766.88748 978.55876

22 22 23

20 19 17

1460 1770 1100

321/123 323/112 318/70

60.7/42.3 84.8/57.1 67.6/31.5

34.0/30.9 14.6/36.6 25.8/41.4

5.3/26.8 0.6/6.2 6.6/27.1

a

n tr is the number of assigned transitions. Nl and Nl are the numbers of obtained upper energies for the J ≤ 17 and J ≥ 18, respectively. c Here m = n /N × 100%, m  = n  /N  × 100% (i = 1, 2, 3); n , n , n and n  , n  , n  are the i i l 1 2 3 i i l 1 2 3 numbers of upper energies for which differences δ = E ex p − E calc satisfy the conditions δ ≤ 10 × −5 −1 −5 −1 −5 −1 −5 −1 10 cm , 10 × 10 cm < δ ≤ 25 × 10 cm , and δ > 25 × 10 cm ; values with “prime” and without “prime” correspond to the cases J ≥ 18 and J ≤ 17, respectively. b

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INFRARED BANDS OF PHD2

TABLE 3 Experimental Rovibrational Term Values for the (001000), (000100), and (000001) Vibrational States of the PHD2 Molecule (in cm−1 )a (001000)

(000100)

(000001)

(001000)

J Ka Kc

E



δ

E



δ

E



δ

1

2

3

4

5

6

7

8

9

10

771.75394 6 772.14733 7 772.72095 5 781.16173 5 781.30619 7 783.02656 5 784.20637 4 784.53061 2 794.83809 2 794.87431 2 798.17529 5 798.80350 5 800.04711 4 802.36953 3 802.50774 1 812.76520 3 812.77272 5 817.75717 3 817.98800 3 820.71269 3 822.24471 2 822.98873 3 826.68681 8 826.73552 1 834.96802 3 834.96942 1 841.54100 5 841.60472 3 846.90082 2 846.13086 3 848.89992 3 851.71011 3 852.06910 5 857.18711 3 857.20246 2 861.45397 22 861.45397 22 869.54251 3 869.55747 5 875.86174 3 876.14566 4 879.92205 6 881.68329 1 882.94143 3 887.27209 1 887.41669 3 893.87881 2 893.88340 1 892.22244 5 892.22244 5 901.80121 5 901.80442 5 909.73277 7 909.81586 3 915.57170 5

1 3 0 4 5 0 3 3 0 3 1 4 2 2 0 1 0 −2 1 −3 2 0 1 1 3 1 −4 −1 0 −3 −3 −1 −2 4 2 17 −9 0 −3 −4 −2 −6 0 −3 2 1 −1 2 0 −4 1 −1 −5 −4 −7

0 1 1 1 2 2 2 2 2 3 3 3 3 3 3 3 4 4 4 4 4 4 4 4 4 5 5 5 5 5 5 5 5 5 5 5 6 6 6 6 6 6 6 6 6 6 6 6 6 7 7 7 7 7 7 7

0 0 1 1 0 1 1 2 2 0 1 1 2 2 3 3 0 1 1 2 2 3 3 4 4 0 1 1 2 3 2 3 4 4 5 5 0 1 1 2 2 3 3 4 4 5 5 6 6 0 1 1 2 2 3 3

0 1 1 0 2 2 1 1 0 3 3 2 2 1 1 0 4 4 3 3 2 2 1 1 0 5 5 4 4 3 3 2 2 1 1 0 6 6 5 5 4 4 3 3 2 2 1 1 0 7 7 6 6 5 5 4

911.65192 916.44612 916.86951 917.55944 925.62634 925.76969 927.83663 929.10617 929.51597 938.88241 938.91501 942.85365 943.48737 945.02904 947.53401 947.72077 956.21769 956.22389 962.10857 962.31956 965.64529 967.21637 968.18929 972.20393 972.27446 977.67440 977.67546 985.37390 985.42617 991.57988 990.85664 994.11139 997.03463 997.53865 1003.14676 1003.17053 1003.27518 1003.27531 1012.70236 1012.71337 1020.15630 1020.39427 1025.05168 1026.75712 1028.44407 1033.01471 1033.23335 1040.37178 1040.37931 1033.03567 1033.03567 1044.15212 1044.15430 1053.41968 1053.48144 1060.40246

3 3 6 4 2 3 5 8 5 8 6 8 7 3 5 2 9 18 4 3 3 6 9 3 2 3 3 3 6 6 5 5 4 7 7 3 4 6 4 6 6 8 9 7 13 6 36 36 4 5 6 6 4

−18 −21 −15 −16 −12 −16 −14 −9 −3 −14 −12 −9 −4 −13 −3 −4 −15 −6 1 −7 −1 −2 5 1 4 −15 −13 −7 −7 0 4 5 7 6 12 12 −7 −11 −5 −1 0 2 6 7 10 11 11 17 22 −10 −13 7 −2 19 4 −6

978.55875 983.58762 983.96798 984.44319 993.39295 993.54806 994.97531 996.11594 996.36517 1007.73366 1007.77773 1010.54050 1011.19903 1012.18137 1014.41767 1014.51395 1026.56873 1026.57913 1030.81255 1031.08658 1033.28736 1034.85673 1035.39790 1038.92250 1038.95315 1049.90618 1049.90846 1055.55507 1055.64170 1060.26150 1059.38412 1061.78441 1064.60620 1064.84116 1069.65553 1069.66434 1077.73916 1077.73952 1084.74124 1084.76463 1090.10060 1090.47342 1093.46143 1095.38567 1096.26149 1100.51888 1100.60405 1106.62161 1106.62396 1110.05147 1110.05147 1118.39159 1118.39736 1125.21594 1125.34215 1130.06049

4 2 1 1 2 10 1 5 1 1 2 3 3 9 2 3 9 9 6 2 2 5 6 10 10 2 2 1 6 1 3 2 4 2

7 5 2 2 3 2 1 1 6 4 9 27 27 6 7 3 7 3

−1 −3 1 0 0 1 1 −1 0 1 1 0 2 0 −2 0 0 −2 2 4 6 0 −1 −2 −6 1 4 3 2 0 5 0 −2 −2 −5 −6 23 12 −3 2 1 2 −1 0 −3 −1 4 −11 −15 4 1 0 0 1 5 −1

J

Ka

Kc

1 7 7 7 7 7 7 7 7 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 10 10 10 10 10 10 10 10 10 10 10 10

4 4 4 3 5 3 5 2 6 2 6 1 7 1 7 0 0 8 1 8 1 7 2 7 2 6 3 6 3 5 4 5 4 4 5 4 5 3 6 3 6 2 7 2 7 1 8 1 8 0 0 9 1 9 1 8 2 8 2 7 3 7 3 6 4 6 4 5 5 5 5 4 6 4 6 3 7 3 7 2 8 2 8 1 9 1 9 0 0 10 1 10 1 9 2 9 2 8 3 8 3 7 4 7 4 6 5 6 5 5 6 5

(000100)

(000001)

E



δ

E



δ

E



δ

2

3

4

5

6

7

8

9

10

1061.14311 1064.78611 1067.93266 1068.88718 1075.20853 1075.29212 1083.87367 1083.87607 1066.96990 1066.96990 1079.75145 1079.75178 1090.73774 1090.75164 1099.71452 1099.95587 1105.99748 1107.72410 1110.26553 1115.18968 1115.64722 1123.64105 1123.67051 1133.63965 1133.63965 1105.09071 1105.09071 1119.51650 1119.51650 1132.17669 1132.17949 1142.96180 1143.02653 1151.42458 1152.14070 1156.99419 1160.21580 1161.75450 1168.59453 1168.78661 1178.31500 1178.32480 1189.65042 1189.65042 1147.40926 1147.40926 1163.46035 1163.46035 1177.76660 1177.76717 1190.25932 1190.27463 1200.71675 1200.94864 1208.40237 1210.07659

9 9 6 10 8 7

6 3 9 11 14 13 7 23 −16 −16 4 0 8 4 10 7 18 10 10 10 11 8 14 5 −17 −12 −12 0 −6 12 4 8 9 17 7 19 3 10 2 3 9 14 13 −5 −15 −15 4 3 6 7 8 1 23 8 12 4

916.42540 919.25925 922.42344 923.08296 928.97963 929.03125 936.75795 936.75927 927.27158 927.27158 938.32987 938.33053 947.79135 947.81258 955.41780 955.73422 960.60369 962.51081 964.37049 969.20612 969.49755 976.85529 976.87238 985.81400 985.81400 966.59831 966.59831 979.12946 979.12946 990.08655 990.09154 999.35040 999.44716 1006.43495 1007.33614 1011.07230 1014.49237 1015.52970 1022.09499 1022.20855 1030.90179 1030.90713 1041.03188 1041.03188 1010.19900 1010.19900 1024.19711 1024.19711 1036.63487 1036.63596 1047.44180 1047.46815 1056.35729 1056.69396 1062.68635 1064.68375

1131.12221 1133.21967 1136.55492 1136.96461 1142.63807 1142.66563 1149.81462 1149.81462 1146.82514 1146.82514 1156.50592 1156.50668 1164.72166 1164.75880 1171.18567 1171.64583 1175.43808 1177.67345 1178.92158 1183.85389 1184.01535 1190.98023 1190.98862 1199.22170 1199.22170 1188.04176 1188.04176 1199.06853 1199.06820 1208.64878 1208.65886 1216.63635 1216.80048 1222.49545 1223.72286 1226.42336 1230.22951 1230.84511 1237.33891 1237.39563 1245.54430 1245.54660 1254.82799 1254.82799 1233.68267 1233.68267 1246.06331 1246.06331 1257.00240 1257.00524 1266.42190 1266.47370 1273.98406 1274.52691 1279.13582 1281.65988

4 3 6 4 7 5

1 −4 −2 −1 −6 −4 16 −46 −6 −8 68 8 6 4 4 2 −4 3 −4 −2 1 −5 2 2 −14 −3 −4 10 −21 8 6 4 8 −3 1 −2 4 −3 2 4 0 −10 −7 −11 −17 −17 5 −2 −9 13 14 14 4 7 −9 11

13 13 2 3 7 6 7 7 7 6 7 7 8 13 7 6 6 15 15 13 13 12 4 7 7 8 9 3 10 9 12 7 12 7 12 12 16 16 10 10 10 8 9 4 10 9 15 10

4 0 5 −6 5 1 1 −2 6 1 6 −1 1 −2 3 0 4 −2 4 −3 2 −1 4 −1 4 −2 4 −3 6 −2 3 −1 4 −5 4 2 5 −4 3 0 4 1 3 −1 7 12 21 24 21 −12 2 2 2 2 14 2 14 −11 4 0 2 −2 9 −3 4 −3 6 −5 7 2 7 −9 4 1 5 −5 5 2 4 1 2 4 4 2 15 5 15 −5 10 −3 10 −3 11 0 11 −2 6 1 3 13 1 8 0 7 −1 6 −1 6 −9 4 1

8 8

8 5 5 8 5 7 7 8 7 6 6 29 29 20 20 37 37 6 7 10 9 6 10 10 6 5 6 10 3 10 10 10 10 17 17

12 8 10 6 10 15

a In Table 3,  is the experimental uncertainty of the energy value, equal to one standard deviation in units of 10−5 cm−1 ; δ is the difference E ex p. − E calc. , also in units of 10−5 cm−1 ;  is not quoted when the energy value was obtained from only one transition.

 C 2002 Elsevier Science (USA)

6

ULENIKOV ET AL.

TABLE 3—Continued (001000) J

Ka

Kc

1 10 10 10 10 10 10 10 10 10 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12

6 7 7 8 8 9 9 10 10 0 1 1 2 2 3 3 4 4 5 5 6 6 7 7 8 8 9 9 10 10 11 11 5 5 4 4 3 3 2 2 1 1 0 6 6 7 7 8 8 9 9 10 10 11 11 12

4 4 3 3 2 2 1 1 0 11 11 10 10 9 9 8 8 7 7 6 6 5 5 4 4 3 3 2 2 1 1 0 7 8 8 9 9 10 10 11 11 12 12 7 6 6 5 5 4 4 3 3 2 2 1 1

(000100)

(000001)

(001000)

E

 δ

E



δ

E

 δ

2

3

5

6

7

8

9

10

1283.31023 1288.88456 1289.14222 1297.03585 1297.05421 1306.32016 1306.32050 1316.61584 1316.61584 1283.73059 1283.73059 1297.47113 1297.47113 1309.77220 1309.77220 1320.58255 1320.59793 1329.72512 1329.92741 1336.59749 1337.98446 1341.30696 1345.56389 1346.41058 1353.70517 1353.80114 1362.94811 1362.95396 1373.29317 1373.29317 1384.56566 1384.56566 1398.39728 1389.81108 1389.74338 1379.13399 1379.12980 1366.94016 1366.94016 1353.27378 1353.27378 1338.16869 1338.16869 1399.02389 1404.45385 1407.26085 1409.33357 1415.53700 1415.90776 1424.72474 1424.75790 1435.06787 1435.06920 1446.44616 1446.44616 1458.65542

7 7 6 11 7

−9 6 4 18 4 9 −25 −13 −14 −17 −17 0 −2 34 −32 0 16 15 10 −6 6 −14 2 −10 16 6 4 16 11 −8 −2 −2 −5 8 9 4 8 −6 12 −4 −4 −13 −13 6 −3 1 −13 6 7 14 11 24 −15 7 2 −12

1213.59685 1218.70631 1219.50433 1228.18640 1228.25985 1239.21862 1239.22146 1251.88587 1251.88587 1193.93542 1193.93542 1211.59363 1211.59363 1227.52402 1227.52402 1241.67527 1241.67853 1253.92909 1253.99288 1263.84275 1264.51240 1270.64917 1273.83621 1276.08700 1283.27253 1283.63396 1293.97706 1294.00332 1306.33233 1306.33233 1320.32221 1320.32221 1323.08180 1311.20387 1311.18803 1297.24052 1297.23975 1281.46022 1281.46022 1263.92545 1263.92545 1244.67718 1244.67718 1323.29835 1332.16926 1333.74734 1338.35009 1343.50885 1344.75484 1353.96663 1354.11451 1365.95874 1365.96760 1379.63140 1379.63140 1394.93340

4

13 11 13 8 10 5 10 2 10 3 20 16 27 −9 27 3 27 −2 6 −12 6 −12 10 1 10 1 12 7 12 −3 17 9 6 −3 10 9 12 5 12 11 6 3 10 19 9 0 10 7 13 −7 5 3 13 −1 15 −3 22 37 22 −58 15 1 15 0 8 −2 8 7 13 4 2 −3 −10 18 3 18 4 9 1 9 1 6 −8 6 −8 11 −4 13 14 13 −18 29 14 27 0 12 −3 15 −13 15 −12 12 3 15 −5 14 3 14 −28 18 −11

1067.22201 1072.46315 1072.95490 1081.12478 1081.16546 1091.11016 1091.11182 1102.39529 1102.39529 1058.07000 1058.07000 1073.52885 1073.52885 1087.43790 1087.43823 1099.74689 1099.75345 1110.31979 1110.42669 1118.64319 1119.57083 1124.26219 1127.86761 1129.35460 1136.49823 1136.70324 1146.30547 1146.31928 1157.46588 1157.46588 1169.88547 1169.88547 1178.59892 1168.44321 1168.41245 1156.28616 1156.28453 1142.49293 1142.49293 1127.12029 1127.12029 1110.20704 1110.20704 1178.94928 1186.08177 1188.13485 1191.41532 1196.98670 1197.73220 1206.64354 1206.72175 1217.63087 1217.63537 1229.95008 1229.95008 1243.48138

6 −5 7 3 6 0 9 0 10 −1 4 2 2 6 12 −8 12 −11 12 −2 12 −2 13 −6 13 −6 −6 2 7 0 12 −13 10 −2 9 −1 10 −6 5 3 8 −6 18 −11 10 1 9 2 6 2 9 −1 5 6 6 25 16 −22 18 −5 18 −6 8 1 8 5 5 2 12 0 13 0 10 −11 10 −6 13 1 13 1 16 −3 16 −3 8 −3 3 0 3 −1 3 −1 10 −2 5 1 3 −1 6 5 8 1 7 5 9 4 9 −10 17 −16

23 23 18 18 11 11 70 70 22 15 14 9 7 9 9 5 11 2 10 9 15 19 19 33 33 22 14 11 42 10 10 10 14 14 17 17 11 25 11 11 10 15 11 9 15 8 7 7 19

J

Ka

Kc

1 12 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14

12 0 1 1 2 2 3 3 4 4 5 5 6 6 7 7 8 8 9 9 10 10 11 11 12 12 13 13 0 1 1 2 2 3 3 4 4 5 5 6 6 7 7 8 8 9 9 10 10 11 11 12 12 13 13 14

 C 2002 Elsevier Science (USA)

0 13 13 12 12 11 11 10 10 9 9 8 8 7 7 6 6 5 5 4 4 3 3 2 2 1 1 0 14 14 13 13 12 12 11 11 10 10 9 9 8 8 7 7 6 6 5 5 4 4 3 3 2 2 1 1

(000100)

(000001)

E

 δ

E



δ

E

 δ

2

3

4

5

6

7

8

9 10

1394.93340 1299.64088 1299.64088 1320.46304 1320.46304 1339.58410 1339.58410 1356.96880 1356.96880 1372.56004 1372.56368 1386.23443 1386.29547 1397.56259 1398.17674 1405.64256 1408.71898 1411.79803 1419.17977 1419.78127 1430.81100 1430.86726 1444.11167 1444.11455 1459.08974 1459.08974 1475.69161 1475.69161 1358.83150 1358.83150 1381.21208 1381.21208 1401.90217 1401.90217 1420.87170 1420.87170 1438.07433 1438.07514 1453.42844 1453.44400 1466.71350 1466.91243 1477.18601 1478.64748 1484.41189 1489.51520 1491.31629 1500.91278 1501.17361 1513.82404 1513.80381 1528.41102 1528.41102 1544.67823 1544.67823 1562.56635

18 5 5 12 12 10 10 16 16 10 8 14 27 10 13 11 17 13 10 17 17 17 29 10 20 20 21 21 1 1 8 8 14 14 11 11

−11 −10 −10 0 0 13 12 7 −7 −4 −5 −4 6 −7 −12 25 −18 2 −5 −16 −12 −14 −7 −15 1 −9 −12 −14 1 1 8 7 10 10 12 10 3 4 −11 −20 −9 −14 1 −13 3 −27 −7 −21 −14 −9 −2 −32 15 22 −44 −17

1243.48138 1166.60562 1166.60562 1184.96617 1184.96617 1201.79514 1201.79514 1217.05731 1217.05771 1230.69342 1230.70182 1242.55364 1242.66879 1252.10484 1253.04857 1258.73168 1262.47569 1264.47452 1272.12556 1272.45355 1282.91665 1282.94464 1295.08611 1295.08755 1308.54300 1308.54300 1323.16084 1323.16084 1227.26079 1227.26079 1247.06142 1247.06142 1265.33892 1265.33892 1282.06208 1282.06208 1297.18322 1297.18535 1310.60876 1310.64355 1322.04727 1322.40885 1330.68562 1332.77672 1336.84712 1342.69601 1343.74472 1353.34041 1353.47176 1365.31454 1365.32398 1378.65135 1378.65193 1393.22191 1393.22191 1408.89902

1458.65542 1396.98097 1396.98097 1413.45386 1413.45386 1428.48904 1428.48904 1442.05522 1442.05667 1454.08813 1454.10933 1464.37708 1464.62024 1472.25847 1473.80923 1477.76119 1482.46750 1483.56268 1491.65396 1491.79849 1501.95132 1501.96227 1513.38007 1513.38007 1525.76009 1525.76009 1538.86192 1538.86192 1460.15253 1460.15253 1477.99442 1477.99442 1494.40088 1494.40088 1509.34435 1509.34435 1522.77596 1522.78216 1534.57509 1534.66055 1544.31133 1545.02842 1551.27293 1554.37231 1556.87545 1563.71292 1564.20892 1573.95499 1574.00724 1585.37786 1585.38114 1597.86695 1597.86695 1611.21400 1611.21400 1625.15977

19 −12 14 −19 14 −18 9 0 9 0 15 4 15 2 −6 25 12 11 13 11 12 5 11 9 15 −16 10 2 12 −19 8 1 6 −1 12 9 28 −2 14 1 10 8 21 24 21 −26 11 7 11 5 7 −10 7 −10 25 −21 25 −21 9 −14 9 −14 16 2 16 2 9 28 9 −1 26 17 16 3 37 −5 15 4 12 −9 12 −10 18 −12 13 −8 12 −13 10 0 7 3 12 8 10 14 14 −1 18 10 18 −4 24 −1 24 −1 5 −2

12 5 19 15 5 19 15 17 12 17 23 18 25 60 60 21 21 23

17 −16 18 −1 18 −1 16 −6 16 −6 14 1 14 0 7 0 21 2 7 0 6 9 7 9 8 8 6 −1 12 1 10 −8 8 3 10 13 5 4 8 −2 6 7 4 6 7 10 13 8 13 4 1 1 1 1 20 0 20 0 7 5 7 0 10 4 10 4 17 6 17 −3 11 12 10 9 13 5 11 11 5 7 10 6 2 −2 10 5 9 0 7 3 5 −5 15 13 6 2 6 6 3 −8 15 −17 −2 7 4 7 3 8 −6

7

INFRARED BANDS OF PHD2

TABLE 3—Continued (001000) J

Ka

Kc

1 14 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16

14 0 1 1 2 2 3 3 4 4 5 5 6 6 7 7 8 8 9 9 10 10 11 11 12 12 13 13 14 14 15 15 0 1 1 2 2 3 3 4 4 5 5 6 6 7 7 8 8 9 9 10 10 11 11 12

0 15 15 14 14 13 13 12 12 11 11 10 10 9 9 8 8 7 7 6 6 5 5 4 4 3 3 2 2 1 1 0 16 16 15 15 14 14 13 13 12 12 11 11 10 10 9 9 8 8 7 7 6 6 5 5

(000100)

(000001)

(001000)

E

 δ

E



δ

E

 δ

2

3

4

5

6

7

8

9

1562.56635 1422.25203 1422.25203 1446.17624 1446.17624 1468.41945 1468.41945 1488.95525 1488.95525 1507.74475 1507.74494 1524.72676 1524.73053 1539.77422 1539.83129 1552.47577 1553.03318 1561.84751 1564.76798 1568.77325 1576.22777 1577.14744 1588.74225 1588.84678 1602.93436 1602.92704 1618.82552 1618.82552 1636.36501 1636.36501 1655.52645 1655.52645 1489.90448 1489.90448 1515.35837 1515.35837 1539.13925 1539.13925 1561.22404 1561.22404 1581.57942 1581.57942 1600.15632 1600.15717 1616.86827 1616.88350 1631.49882 1631.68030 1643.32782 1644.66731 1651.64812 1656.62058 1659.07723 1668.93169 1669.35124 1682.67417

23 5 5 8 8 13 13 20 20 9 10 18 12 7 13 1 16 16 17 12 19 17 23 21

−27 −2 −2 −5 −5 7 7 12 11 −3 0 −12 −11 −2 −14 5 −21 3 −26 0 −21 −14 −6 −3 −8 −33 31 −25 3 −9 −30 −31 −8 −8 5 5 12 12 9 9 −12 −15 −15 −15 −14 −6 −15 −29 −5 −26 0 −17 −9 −2 30 16

1408.89902 1292.16729 1292.16729 1313.39994 1313.39994 1333.11822 1333.11822 1351.29336 1351.29336 1367.88481 1367.88524 1382.82431 1382.83425 1395.95006 1396.07293 1406.71388 1407.67117 1414.36608 1418.22135 1420.78178 1428.88888 1429.37129 1440.65613 1440.70541 1453.82259 1453.82574 1468.30509 1468.30509 1483.96271 1483.96271 1500.67020 1500.67020 1361.31951 1361.31951 1383.97588 1383.97588 1405.12652 1405.12652 1424.74483 1424.74483 1442.79470 1442.79470 1459.22160 1459.22422 1473.92216 1473.96087 1486.59222 1486.96525 1496.37942 1498.50350 1503.39463 1509.48876 1510.88333 1521.11976 1521.32117 1534.07416

33 33 27 27 25 25 11 11 8 8 16 16 19 19 39 39 9 12 22 5 12 19 20 18 19 18 15 10 20 27

8 −6 21 0 21 0 15 −3 15 −3 8 4 8 3 22 4 22 2 20 21 12 10 20 3 16 6 16 1 15 6 5 0 1 1 7 −4 15 −10 4 −14 20 6 11 −7 8 −4 5 −9 9 −3 7 −5 22 2 22 −11 5 −1 5 −2 1 −1 1 −1 22 −1 22 −1 19 −2 19 −2 20 −5 20 −5 20 −2 20 −2 17 9 17 −5 8 12 20 1 16 7 12 8 8 6 14 2 12 −1 3 4 −8 6 −2 13 −1 6 −15 8 −14 4 −5

1625.15977 1527.66905 1527.66905 1546.88011 1546.88011 1564.65792 1564.65792 1580.97904 1580.97904 1595.80181 1595.80405 1609.04760 1609.07590 1620.47370 1620.76201 1629.35397 1631.08205 1635.65756 1640.82857 1642.17995 1651.07796 1651.27835 1662.45148 1662.46923 1674.98873 1674.98939 1688.50877 1688.50877 1702.78558 1702.78558 1717.52184 1717.52184 1599.51698 1599.51698 1620.09552 1620.09552 1639.24504 1639.24504 1656.94304 1656.94304 1673.15350 1673.15350

1700.79174 1700.89796 1711.59850 1712.41684 1719.45732 1722.87148 1725.80031 1733.28825 1733.90843 1744.60961 1744.68424 1757.13613

10

5 −2 20 −23 20 −23 20 −9 20 −9 18 47 18 −49 18 9 18 5 −15 29 8 1 17 −3 8 −9 16 −14 11 −18 21 −8 13 −16 12 −9 16 −5 11 −4 8 3 9 16 5 8 25 11 −17 8 10 8 5 8 −2 8 −2 8 5 8 5 22 −15 22 −15 25 −10 25 −10 20 −3 20 −3 20 49 20 −47 35 18 35 −20

22 25 20 14 2 14 10 2 11 2 5 16

J

−27 −21 −19 2 −1 −29 18 −6 4 9 −4 16

Ka

Kc

1 16 16 16 16 16 16 16 16 16 17 17 17 17 17 17 17 17 17 17 17 17 17 17 17 17 17 17 17 17 17 17 17 17 17 17 17 17 17 17 17 17 17 17 17 18 18 18 18 18 18 18 18 18 18 18 18

12 13 13 14 14 15 15 16 16 0 1 1 2 2 3 3 4 4 5 5 6 6 7 7 8 8 9 9 10 10 11 11 12 12 13 13 14 14 15 15 16 16 17 17 0 1 1 2 2 3 3 4 4 5 5 6

 C 2002 Elsevier Science (USA)

4 4 3 3 2 2 1 1 0 17 17 16 16 15 15 14 14 13 13 12 12 11 11 10 10 9 9 8 8 7 7 6 6 5 5 4 4 3 3 2 2 1 1 0 18 18 17 17 16 16 15 15 14 14 13 13

(000100)

(000001)

E

 δ

E



δ

E

 δ

2

3

4

5

6

7

8

9 10

1682.71383 1698.15561 1698.15822 1715.32650 1715.32650 1734.12160 1734.12948 1754.53718 1754.53718 1561.78944 1561.78944 1588.75905 1588.75905 1614.06310 1614.06310 1637.68089 1637.68089 1659.58349 1659.58349 1679.72956 1679.72980 1698.05445 1698.05800 1714.42751 1714.48091 1728.45832 1728.96300 1739.12346 1741.86351 1746.87486 1754.30550 1755.62414 1767.67306

21

22 1 2 59 16 6 10 2 2 −7 −7 −10 −10 9 9 17 16 9 9 −11 −6 2 −20 −5 −17 −5 −16 6 −18 −2 2 −3 13

1534.09174 1548.42021 1548.42127 1564.02250 1564.02250 1580.73961 1580.73961 1598.44652 1598.44652 1434.71149 1434.71149 1458.78256 1458.78256 1481.35707 1481.35707 1502.40973 1502.40973 1521.90732 1521.90732 1539.80419 1539.80491 1556.02388 1556.03546 1570.39330 1570.52429 1582.35013 1583.32388 1591.03466 1594.99158 1598.14900 1606.67869 1607.34441 1619.42198 1619.50049 1633.58036 1633.58651 1649.08333 1649.08370 1665.77790 1665.77790 1683.52507 1683.52507 1702.19867 1702.19867 1512.33703 1512.33703 1537.81350 1537.81350 1561.80271 1561.80271 1584.28011 1584.28011 1605.21570 1605.21570 1624.56830 1624.56830

−10 −5 −1 −1 −5 −3 −3 1 1 −2 −2 −15 −15 −8 −8 12 11 3 0 31 29 4 1 10 22 −1 −10 −3 −8 7 −18 −14 −12 −9 −12 −5 −2 2 −2 −2 −5 −5 1 1 12 12 −7 −8 0 0 −2 −3 17 16 22 2

1757.14180 1770.76427 1770.76427 1785.28319 1785.28319 1800.45072 1800.45072 1815.91937 1815.91937 1675.68322 1675.68322 1697.62619 1697.62619 1718.14518 1718.14518 1737.21781 1737.21781 1754.81432 1754.81432

16 −3 9 13 9 −18 12 −17 12 −18 2 −5 2 −5 10 8 10 8 19 −9 19 −9 11 11 19 −4 19 −4 20 −4 20 4 22 64 22 −77

1785.33048 1785.36738 1797.87831 1798.22130 1807.74328 1809.67135 1814.85021 1820.51707 1822.12168 1831.84767 1832.10808 1844.32048 1844.34698 1857.99245 1857.99334 1872.68268 1872.68268 1888.16693 1888.16693

−56 −19 13 −30 −5 2 31 −16 12 −8 0 −2 7 57 −41 −6 −16 −28 −28

25 25 31 28

13 13 12 12 18 18 14 14 28 28

40 11 22 10 19 18 17 15 18 18

1782.69469 1782.70964

1817.87859 1817.87859 1837.90478 1837.90478 1872.68268 1859.56221 1637.90645 1637.90645 1666.37852 1666.37852 1693.19132 1693.19132 1718.32672 1718.32672 1741.75903 1741.75903 1763.45292 1763.45292

13 39

26 26 24 24 25 25

10 10 7 7 16 16 25 25 53 53

93 −6 19 17 −6 −3 3 3 −1 −1 3 3 18 17 17 17 2 −2

18 27 27 8 8

23 23 26 26 26 26 22 22 12 12

12 18 15 33 10 13 17 8 56 14 16 5 12 14 18 15 15

8 8 7 7 15 15 13 13 22 22 41 41

25

10 6 5 15

14 14 17 17

1920.32217 17 1920.32217 17 1756.15514 21 1 1756.15514 21 1 1779.45828 −35 1779.45828 −35

1821.78893 1821.78893 1840.76645 1840.76645 1858.23770 1858.23352

21 0 21 0 30 −63 30 51 10 −8 −13

8

ULENIKOV ET AL.

TABLE 3—Continued (001000) J

Ka

Kc

1 18 18 18 18 18 18 18 18 18 18 18 18 18 18 18 18 18 18 18 18 18 18 18 18 18 19 19 19 19 19 19 19 19 19 19 19 19 19 19 19 19 19 19 19 19 19 19 19 19 19 19 19 19 19 19 19 19 19 19 19 19 19 19

6 7 7 8 8 9 9 10 10 11 11 12 12 13 13 14 14 15 15 16 16 17 17 18 18 0 1 1 2 2 3 3 4 4 5 5 6 6 7 7 8 8 9 9 10 10 11 11 12 12 13 13 14 14 15 15 16 16 17 17 18 18 19

12 12 11 11 10 10 9 9 8 8 7 7 6 6 5 5 4 4 3 3 2 2 1 1 0 19 19 18 18 17 17 16 16 15 15 14 14 13 13 12 12 11 11 10 10 9 9 8 8 7 7 6 6 5 5 4 4 3 3 2 2 1 1

(000100)

(000001)

(001000)

E

 δ

E



δ

E

 δ

2

3

5

6

7

8

9

1783.35580 1783.35670 1801.38804 1801.40032 1817.30888 1817.47465 1830.45737 1831.68055 1839.90620 1844.70398 1847.90102 1857.90365 1858.53688 1872.46780 1872.53734 1888.78382 1888.79101 1906.80592 1906.80592 1926.45686 1926.45686 1947.68599 1947.68599 1970.56407 1970.56407 1718.25355 1718.25355 1748.21488 1748.21488 1776.52294 1776.52294 1803.16122 1803.16122 1828.10695 1828.10695 1851.32926 1851.32926 1872.78453 1872.78453 1892.40432 1892.40805 1910.05658 1910.10673 1925.37284 1925.83081 1937.31618

4

12 −8 11 −8 13 12 15 −3 19 −10 −6 8 12 8 −9 23 −3 17 −5 2 17 7 1 11 24 52 50 −7 51 39 55 43 124 43 8 23 −5 23 2 22 18 22 19 25 19 25 19 9 −3 9 −3 6 −13 6 −13 22 0 22 0 26 21 26 23 22 36 22 35 19 16 19 14 18 21 18 1 22 −10 21 −12 −46 20 14 0 12 −6 17 13

1945.94542 11 1953.28837 22 1955.07839

12 2 22

196.76017 21

39

2020.15170 16 2020.15862 2041.01015 3 2041.01015 3 2063.42592 9 2063.42592 9 2087.50160 16

30 7 12 18 5 5 38

1642.27708 1642.28030 1658.22971 1658.27280 1672.10930 1672.49631 1683.03035 1685.19266 1690.91802 1697.24402 1699.01652 1709.86609 1710.15352 1723.80059 1723.82967 1739.15315 1739.15510 1755.78585 1755.78585 1773.54397 1773.54397 1792.29023 1792.29023 1811.89578 1811.89578 1594.18910 1594.18910 1621.06125 1621.06125 1646.45550 1646.45550 1670.34842 1670.34842 1692.71139 1692.71139 1713.50779 1713.50779 1732.68602 1732.68678

7 −2 14 −18 15 −5 15 8 12 16 8 −13 4 −6 25 3 −8 4 −11 9 −17 7 −10 8 −6 6 −6 2 −6 18 4 18 14 21 21 7 13 7 13 −2 −2 8 8 8 8 13 −6 13 −6 21 −10 21 −10 19 −8 19 −8 11 −12 11 −12 18 −1 18 −6 21 1

1765.75215 1765.89248 1778.87909 1779.87672 1788.59217 1792.65579 1796.42859 1805.36736 1806.23951 1819.09128 1819.20672 1834.24278 1834.25311 1850.76625 1850.76689 1868.49973 1868.49973

20 −24 4 −4 12 −3 1 1 11 3 13 3 10 11 −1 4 0 15 −8 12 −13 5 7 11 3 7 8 10 7 28 26 28 26

1953.28851

10

1900.11230 −24 1901.04849 −45 1908.85413 11 1912.61844 −41 1915.95405 23 56 1924.12860 28 −34 1936.54910 1936.64888 1950.20343 1950.21233 1964.99736 1964.99736

1840.92045 1840.92045 1865.57902 1865.57902 1888.82549 1888.82549 1910.64126 1910.64126 1930.99494 1930.99494 1949.85253 1949.85253

16 8 20

7 7 16 11 53 36 53 −23

16 16 22 22

20 20

39 39

2078.12674 41 2078.12674 41 2094.85316 4 2094.85316 4

J

13 13 −5 −5 18 18 13 −2 19 19 42 −77

33 15 13 13

Ka

Kc

1 19 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 21 21 21 21 21 21 21 21 21 21 21 21 21 21 21 21 22 22 22 22 22 22 22 22 22 22 22 22 22 23 23 23 23

19 0 1 1 2 2 3 3 4 4 5 5 6 6 7 7 8 8 9 9 11 13 13 18 18 19 19 20 20 0 1 1 2 2 3 3 4 4 5 5 6 6 7 7 8 0 1 1 2 2 3 3 4 4 5 5 6 6 0 1 1 2

16

 C 2002 Elsevier Science (USA)

0 20 20 19 19 18 18 17 17 16 16 15 15 14 14 13 13 12 12 11 9 8 7 3 2 2 1 1 0 21 21 20 20 19 19 18 18 17 17 16 16 15 15 14 14 22 22 21 21 20 20 19 19 18 18 17 17 16 23 23 22 22

(000100)

(000001)

E

 δ

E



δ

E

 δ

2

3

4

5

6

7

8

9 10

2087.50160 1802.82827 1802.82827 1834.26618 1834.26618 1864.05585 1864.05585 1892.18266 1892.18266 1918.62596 1918.62596 1943.35928 1943.35928 1966.34425 1966.34425 1987.52650 1987.52739 2006.81457 2006.82831 2023.99883 2049.02323

16 27 27 7 7 10 10

38 −11 −11 −5 −5 −34 −34 27 28 23 38 40 40 16 9 −16 −12 −27 −49 −9 10

1953.28851 1680.26081 1680.26081 1708.51832 1708.51832 1735.30790 1735.30790 1760.60632 1760.60632 1784.38686 1784.38686 1806.61517 1806.61517 1827.24609 1827.24609 1846.21327 1846.21762

23 23 12 12 22 22

41 21 27

16 10 −11 10 −11 10 −8 10 −8 7 2 7 2 7 −8 7 −8 9 4 9 4 −10 −11 −37 −65 −35 8 −12

1929.96704 1929.96704 1955.97457 1955.97457 1980.57699 1980.57699 2003.75436 2003.75436 2025.48386 2025.48386 2045.72630 2045.72630

22 22 20 20

−4 −4 9 9 9 9 8 8 −2 −12 −12 −12 −14 −22

2023.28318 2023.28318 2050.63246 2050.63246 2076.58442 2076.58442 2101.12010 2101.12010 2124.21441 2124.21441

19 19 12 12 27 27

1865.03311 −19 1865.03311 −19 1896.02869 10 4 1896.02869 10 4 1925.57713 24 1925.57713 24 1953.65576 12 1953.65576 12 1980.23931 14 1980.23931 14

2120.85703 2120.85703 2149.54008 2149.54008 2176.83417 2176.83417

19 −4 19 −4 15 −14 15 −14 10 12 10 12

2222.67704 2222.67704 2252.68506 2252.68506

−28 −28 −33 −33

1919.44450 1919.83154 12 2161.51419 2161.51419 2185.08518 2185.08518 2210.32756 2210.32756 1891.62750 1891.62750 1924.52831 1924.52831 1955.78646 1955.78646 1985.38812 1985.38812 2013.31437 2013.31437

11 −25 11 −26 −62 −62 18 0 18 0 10 21 10 21 −37 −37 10 −6 10 −6 30 10 30 10 43 39 43 39

2064.03646 −2 2064.03646 −7 2086.75452 −14 2086.75452 −14 1984.64657 41 1984.64657 41 2018.99745 −69 2018.99745 −69 2051.71094 −19 2051.71094 −19 2082.77301 40 −8 2082.77301 40 −8 2112.16817 12 2112.16817 8 2139.87318 11 2139.87287 −30 2165.86068 27

1770.54479 1770.54479 1800.17702 1800.17702 1828.35130 1828.35130 1855.04522 1855.04522 1880.23251 1880.23251 1903.88175 1903.88175 1925.95223 1925.95223

21 21

15 15

14 14 −3 −3 9 9 8 −3 8 −3 −22 −34 7 −9

24 34

27 27

13 13 −3 −3 14 14 40 40 21 18

9

INFRARED BANDS OF PHD2

TABLE 4 Parameters of Resonance Interactions for the (000100), (001000), and (000001) Vibrational States of the PHD2 Molecule (in cm−1 )a Parameter

Value

Parameter

Value

Parameter

Value

Coriolis Type Interactions (2Cζ y )3−6 3−6 8 C yx y J × 10

−2.72677(263) −0.1670(391)

3 C x3−6 K × 10

(2Bζ x )3−6 8 C x3−6 x y K × 10

−0.70550(176) 5.546(260) 2.6587(261)

(2Bζ x )4−6 C y4−6 K C x4−6 zJ

0.77674(731)

3−6 × 105 C yx y

3−6 × 10 C yz

−0.34117(192)

3−6 4 C yz K × 10

3 C x4−6 J × 10

−0.10237(470)

4−6 × 10 C yz

C x4−6 z × 10

−0.17921(252)

4 C x4−6 z K × 10

3.4280(122)

3 C z4−3 K × 10

−2.59471(387)

3 C z4−3 J × 10

0.09361(825)

0.21450(630)

C x4−3 y

0.19539(156)

4 C x4−3 y J × 10

−0.04503(145)

4 FK4−3 K × 10

0.31780(153)

× 103

−0.2506(373)

× 104

−0.03097(137)

(2Aζ z )4−3 6 C z4−3 K K × 10 4−3 C x y K K × 107

× 10

−0.593(120) 0.063884(836) 0.18272(406) −0.00610(149)

0.25664(751) Fermi Type Interactions

FK4−3 a

× 10

−1.2207(365)

FJ4−3

× 10

0.05705(179)

See footnote to Table 1.

result of the fit over 1267 energies, the 58 parameters (33 parameters of the diagonal blocks and 25 belonging to the resonance interaction operators) were derived. These are presented in Tables 1 and 4 together with 1σ statistical confidence intervals for the obtained parameters. Parameters which are given without confidence intervals were fixed to the values of the respective parameters of the ground vibrational state (1). Comparing the corresponding parameters in the different columns of Table 1 confirms that all values are physically meaningful. In particular, the values of all rotational constants and centrifugal distortion parameters are similar to each other and correlate well with the corresponding values of the ground vibrational state. With regard to the resonance interaction parameters their values appear to be similarly meaningful. The reproductive power of the parameters obtained from the fit is another confirmation of their correctness. To illustrate this the parameters in columns 4, 7, and 10 of Table 3 give the values of the differences δ = E ex p − E calc in units of 10−5 cm−1 . The δ values are close to the corresponding experimental uncertainties. The accuracy of the reproduction of observation decreases expectedly with increasing quantum numbers J and K a . Statistical information on the reproduction of the experimental energies by the parameters obtained from the fit can be found in the three last columns of Table 2. The value of the rms deviation may be interesting, too. It is 1.3 × 10−4 cm−1 for the states with J ≤ 17, and 2.7 × 10−4 cm−1 for the states with J ≥ 18. 5. CONCLUSION

The infrared spectrum of phosphine containing ca. 60% PHD2 has been recorded in the region of the bending fundamentals ν3 , ν4 , and ν6 of PHD2 with a resolution of 2.3 × 10−3 cm−1 . The

analysis of the three interacting vibrational states has been performed employing the formerly determined ground state constants (1) by fitting altogether ca. 1300 energy levels to a total of 58 upper state parameters, of which 33 are diagonal parameters of a Watson-type Hamiltonian in A reduction and Ir representation, while 25 are Coriolis- and Fermi-type interaction parameters. The parameter set reproduces the states with J ≤ 17 with an rms of 1.3 × 10−4 cm−1 and those with 18 < J < 23 with an rms of 2.7 × 10−4 cm−1 . The energy level structure of the bending triad of PHD2 will be of value for forthcoming studies on more highly excited states of this molecule. ACKNOWLEDGMENTS Part of this work was supported by a grant of the Ministry of Education of the Russian Federation. H.B. thanks the Deutsche Forschungsgemeinschaft for financial support.

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ULENIKOV ET AL.

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