Alexander Alijah and Geoffrey Duxbury, "Effects of orbital angular momentum in PH2 and PD2:Renner–Teller and spin–orbit coupling," J. Opt. Soc. Am. B 11, 208-218 (1994)
The vibrational and K-type rotational levels of the
and Ã2A1 states of PH2 have been fitted by least squares to give a pair of Born–Oppenheimer potential curves for the combining electronic states. The effects of the orbital angular-momentum coupling between these states, which are derived from a common 2Π state of linear PH2, have been considered in detail. The effects are manifest in both the behavior of the vibronic origins and the effective vibronic spin–orbit coupling constants. We have also calculated the rotational constants for a range of vibronic states of PH2. Analogous rotational constants, band origins, and spin–orbit coupling constants of PD2 have been calculated by use of the potential curves derived from the fit to PH2. The agreement between the calculated origins and those measured experimentally is quite satisfactory. The vibronic dependence of the relative transition moments and of the fluorescence lifetimes have also been calculated for both PH2 and PD2.
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These correspond to ν2bent = −1/2 bond lengths of 1.427 and 1.407 Å, respectively for the
and Ã2A1 states.
Ref. 1.
Optimum value.
For gK from H2S+.
Adjusted to give the correct variation of Λ(ρ) for PD2.
From H2S+ fit, Ref. 22.
Table 2
Observed and Calculated Vibronic Levels and Rotational and Spin–Orbit Coupling Constants of the Ã2A1 State of PH2 (cm−1)a
The observed values are taken from Ref. 1.
This parameter was called ɛ by BDD1; the present notation is from Jungen and Merer.21
Calculated after final diagonalization.
Table 3
Observed and Calculated Vibronic Levels and Rotational and Spin–Orbit Coupling Constants of the Ã2A1 State of PD2 (cm−1)a
The calculated values are 103 times the squared matrix elements of sin(ρ/2). The qualitative estimates of the intensities are from Refs. 4 and 7. Parentheses indicate that the assignment may be incorrect.4
Calculated values are with K = 0.
Estimated emission intensities from Ref. 4.
Estimated from the number of absorption lines seen per band by Berthou et al.7
Table 6
Calculated and Observed Intensity Factors for the
Transition of PD2a
The calculated values are 103 times the squared matrix elements of sin(ρ/2). The qualitative estimates of the intensities are from Refs. 4 and 8. Parentheses indicate that the assignment may be incorrect.
Estimated emission intensities from Ref. 4.
Estimated from the number of absorption lines seen per band by Vervloet and Berthou et al.8
Table 7
Observed and Calculated Fluorescence Lifetimes (μs) of the Ã2A1 State of PH2
Calculated with |μe0|2 = 0.14e2a02, this corresponds to a transition moment at the equilibrium ground-state geometry of |μeeq|2 = 0.068e2a02. This is much smaller than that of SiH2, which is |μeeq|2 = 0.30e2a02.18
Observed lifetimes taken from Ref. 10.
Table 8
Calculated Fluorescence Lifetimes (μs) of the Ã2A1 State of PD2a
υ2′
K
0
1
2
3
0
5.14
5.12
5.06
4.96
1
4.07
4.05
4.00
3.93
2
3.39
3.37
3.33
3.26
3
2.92
2.91
2.87
2.81
4
2.59
2.58
2.54
2.47
5
2.35
2.33
2.29
2.23
6
2.16
2.16
2.12
2.05
7
2.03
2.05
2.02
1.93
8
1.92
2.03
2.00
1.88
9
1.83
2.23
2.12
1.94
10
1.72
3.27
2.64
2.27
11
1.57
1.79
2.02
2.23
Calculated with |μe0|2 = 0.14e2a02, this corresponds to a transition moment at the equilibrium ground-state geometry of |μeeq|2 = 0.068e2a02. This is much smaller than that of SiH2, which is |μeeq|2 = 0.30e2a02.18
Table 9
Calculated Mean Vibronic Origins Tυ,K and Doublet Splittings AυSO(cm−1) for Low- and High-Angular-Momentum Levels of the
, state of PH2a
Ka
υ2
Tυ,K
∊(AυSO)
Ka
υ2
Tυ,K
∊(AυSO)
Variation with Ka for υ2″ = 0
Variation with Ka for υ2″ = 1
0
0
0
0
0
1
1103.87
0
1
0
9.14
−0.29
1
1
1113.34
−0.32
2
0
36.54
−0.58
2
1
1141.74
−0.63
3
0
82.14
−0.86
3
1
1188.98
−0.94
4
0
145.85
−1.15
4
1
1254.97
−1.25
5
0
227.55
−1.43
5
1
1339.53
−1.56
6
0
327.08
−1.70
6
1
1442.47
−1.84
7
0
444.25
−1.96
7
1
1563.56
−2.14
8
0
578.84
−2.23
8
1
1702.53
−2.41
20
0
3450.82
−4.75
20
1
4644.18
−5.02
25
0
5251.31
−5.45
25
1
6473.51
−5.66
30
0
7352.08
−5.97
30
1
8595.59
−6.13
35
0
9714.24
−6.31
35
1
10972.71
−6.43
40
0
12305.48
−6.50
40
1
13570.07
−6.50
Variation with Ka for υ2″ = 2
Variation with Ka for υ2″ = 3
0
2
2196.51
0
0
3
3278.10
0
1
2
2206.35
−0.35
1
3
3288.35
−0.39
2
2
2235.86
−0.69
2
3
3319.09
−0.76
3
2
2284.93
−1.03
3
3
3370.19
−1.13
4
2
2353.43
−1.37
4
3
3441.48
−1.51
5
2
2441.16
−1.69
5
3
3532.69
−1.86
6
2
2547.85
−2.02
6
3
3643.51
−2.20
7
2
2673.24
−2.32
7
3
3773.61
−2.54
8
2
2816.99
−2.62
8
3
3922.56
−2.85
20
2
5832.10
−5.24
20
3
7014.83
−5.51
25
2
7689.50
−5.88
25
3
8900.36
−6.09
30
2
9833.31
−6.28
30
3
11065.12
−6.44
35
2
12224.06
−6.51
35
3
13647.93
−6.61
40
2
14825.40
−6.56
40
3
16070.78
−6.58
The calculations were made with ASO = 198 cm−1 and gK = 1.4 cm−1.
Tables (9)
Table 1
Parameters Used to Calculate the Banding Levels of the
, and Ã2A1 states of PH2
These correspond to ν2bent = −1/2 bond lengths of 1.427 and 1.407 Å, respectively for the
and Ã2A1 states.
Ref. 1.
Optimum value.
For gK from H2S+.
Adjusted to give the correct variation of Λ(ρ) for PD2.
From H2S+ fit, Ref. 22.
Table 2
Observed and Calculated Vibronic Levels and Rotational and Spin–Orbit Coupling Constants of the Ã2A1 State of PH2 (cm−1)a
The observed values are taken from Ref. 1.
This parameter was called ɛ by BDD1; the present notation is from Jungen and Merer.21
Calculated after final diagonalization.
Table 3
Observed and Calculated Vibronic Levels and Rotational and Spin–Orbit Coupling Constants of the Ã2A1 State of PD2 (cm−1)a
The calculated values are 103 times the squared matrix elements of sin(ρ/2). The qualitative estimates of the intensities are from Refs. 4 and 7. Parentheses indicate that the assignment may be incorrect.4
Calculated values are with K = 0.
Estimated emission intensities from Ref. 4.
Estimated from the number of absorption lines seen per band by Berthou et al.7
Table 6
Calculated and Observed Intensity Factors for the
Transition of PD2a
The calculated values are 103 times the squared matrix elements of sin(ρ/2). The qualitative estimates of the intensities are from Refs. 4 and 8. Parentheses indicate that the assignment may be incorrect.
Estimated emission intensities from Ref. 4.
Estimated from the number of absorption lines seen per band by Vervloet and Berthou et al.8
Table 7
Observed and Calculated Fluorescence Lifetimes (μs) of the Ã2A1 State of PH2
Calculated with |μe0|2 = 0.14e2a02, this corresponds to a transition moment at the equilibrium ground-state geometry of |μeeq|2 = 0.068e2a02. This is much smaller than that of SiH2, which is |μeeq|2 = 0.30e2a02.18
Observed lifetimes taken from Ref. 10.
Table 8
Calculated Fluorescence Lifetimes (μs) of the Ã2A1 State of PD2a
υ2′
K
0
1
2
3
0
5.14
5.12
5.06
4.96
1
4.07
4.05
4.00
3.93
2
3.39
3.37
3.33
3.26
3
2.92
2.91
2.87
2.81
4
2.59
2.58
2.54
2.47
5
2.35
2.33
2.29
2.23
6
2.16
2.16
2.12
2.05
7
2.03
2.05
2.02
1.93
8
1.92
2.03
2.00
1.88
9
1.83
2.23
2.12
1.94
10
1.72
3.27
2.64
2.27
11
1.57
1.79
2.02
2.23
Calculated with |μe0|2 = 0.14e2a02, this corresponds to a transition moment at the equilibrium ground-state geometry of |μeeq|2 = 0.068e2a02. This is much smaller than that of SiH2, which is |μeeq|2 = 0.30e2a02.18
Table 9
Calculated Mean Vibronic Origins Tυ,K and Doublet Splittings AυSO(cm−1) for Low- and High-Angular-Momentum Levels of the
, state of PH2a
Ka
υ2
Tυ,K
∊(AυSO)
Ka
υ2
Tυ,K
∊(AυSO)
Variation with Ka for υ2″ = 0
Variation with Ka for υ2″ = 1
0
0
0
0
0
1
1103.87
0
1
0
9.14
−0.29
1
1
1113.34
−0.32
2
0
36.54
−0.58
2
1
1141.74
−0.63
3
0
82.14
−0.86
3
1
1188.98
−0.94
4
0
145.85
−1.15
4
1
1254.97
−1.25
5
0
227.55
−1.43
5
1
1339.53
−1.56
6
0
327.08
−1.70
6
1
1442.47
−1.84
7
0
444.25
−1.96
7
1
1563.56
−2.14
8
0
578.84
−2.23
8
1
1702.53
−2.41
20
0
3450.82
−4.75
20
1
4644.18
−5.02
25
0
5251.31
−5.45
25
1
6473.51
−5.66
30
0
7352.08
−5.97
30
1
8595.59
−6.13
35
0
9714.24
−6.31
35
1
10972.71
−6.43
40
0
12305.48
−6.50
40
1
13570.07
−6.50
Variation with Ka for υ2″ = 2
Variation with Ka for υ2″ = 3
0
2
2196.51
0
0
3
3278.10
0
1
2
2206.35
−0.35
1
3
3288.35
−0.39
2
2
2235.86
−0.69
2
3
3319.09
−0.76
3
2
2284.93
−1.03
3
3
3370.19
−1.13
4
2
2353.43
−1.37
4
3
3441.48
−1.51
5
2
2441.16
−1.69
5
3
3532.69
−1.86
6
2
2547.85
−2.02
6
3
3643.51
−2.20
7
2
2673.24
−2.32
7
3
3773.61
−2.54
8
2
2816.99
−2.62
8
3
3922.56
−2.85
20
2
5832.10
−5.24
20
3
7014.83
−5.51
25
2
7689.50
−5.88
25
3
8900.36
−6.09
30
2
9833.31
−6.28
30
3
11065.12
−6.44
35
2
12224.06
−6.51
35
3
13647.93
−6.61
40
2
14825.40
−6.56
40
3
16070.78
−6.58
The calculations were made with ASO = 198 cm−1 and gK = 1.4 cm−1.
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