Spectrochimica Acta Part A: Molecular and Biomolecular Spectroscopy 142 (2015) 1–7
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Ab initio study on the low-lying excited states of gas-phase PH+ cation including spin–orbit coupling Xia Li a, Xiaomei Zhang b,c, Bing Yan b,c,⇑ a
Hospital Affiliated of Changchun University of Chinese Medicine, Changchun 130021, China Institute of Atomic and Molecular Physics, Jilin University, Changchun 130012, China c Jilin Provincial Key Laboratory of Applied Atomic and Molecular Spectroscopy (Jilin University), Changchun 130012, China b
h i g h l i g h t s
g r a p h i c a l a b s t r a c t +
The excited states of PH have been
The PECs of K–S states of the PH+.
studied by high-level MRCI wavefunctions. + The SOC effect on PH is accounted for via state interaction method. The SO matrix elements reveal the strong interactions of the K–S states. The transition properties are evaluated and in good agreement with measurement.
a r t i c l e
i n f o
Article history: Received 18 October 2014 Received in revised form 18 January 2015 Accepted 28 January 2015 Available online 7 February 2015 Keywords: MRCI+Q Potential energy curve (PEC) Spectroscopic constants PH+
a b s t r a c t Ab initio calculations have been performed on the low-lying excited and ground states of PH+. The potential energy curves (PECs) of the K–S states were calculated with multi-reference configuration interaction (MRCI) method along with the basis sets at 5-n level. In order to improve the PECs, the Davidson(+Q) correction and the Scalar relativistic effect are included. The corresponding spectroscopic constants were determined and good agreements with the available measurement were found. The interactions of the A2D–4P and 12R+–4P by the spin–orbit coupling (SOC) effect were well described by the spin–orbit matrix elements. The SOC effect makes the original 8 K–S states split into 15 X states. The X = 1/2 state generated from the X2P state is confirmed to the ground X state. And the SOC splitting for the X2P is calculated to be 294 cm1. The SOC effect has large effect on the PECs of the A2D and 12R+ states, leading to much more shallow potential wells as well as potential barriers. The analysis of the wavefunction for the X states shows that the strong spin–orbit interaction exists near the crossing points of the PECs for the K–S states. The transition dipole moments (TDMs) of transitions A2D–X2P and 12R–X2P are evaluated with the MRCI wavefunction. Based on the TDMs along with the calculated Franck–Condon factors, the radiative lifetimes for the selected vibrational levels of A2D and 12R states are predicted at the microseconds (ls). Good agreement with the measurement shows that the lowest vibrational level for A2D state is almost uninfluenced by the perturbation via the SOC effect. Ó 2015 Elsevier B.V. All rights reserved.
⇑ Corresponding author at: Institute of Atomic and Molecular Physics, Jilin University, Changchun 130012, China. E-mail address:
[email protected] (B. Yan). http://dx.doi.org/10.1016/j.saa.2015.01.070 1386-1425/Ó 2015 Elsevier B.V. All rights reserved.
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X. Li et al. / Spectrochimica Acta Part A: Molecular and Biomolecular Spectroscopy 142 (2015) 1–7
Introduction Gas-phase small diatomic phosphides are of considerable interest in the field of the astrophysical chemistry that are concerned with the chemical composition and chemical process of cosmic materials. Although neutral diatomic phosphides such as CP and PN have been detected in the intermundium space [1,2], most of the cations which may also be abundant in the interstellar space, have not been observed. Accurate prediction of spectroscopic properties of the electronic states is conducive to the interstellar detection of these phosphide cations. The present work aims at the low-lying electronic states of the lightest phosphide cations, PH+. Previous experimental studies focused on the spectrum of the first transition-allowed excited state, A2D. The pioneering experimental work was performed by Narasimham [3], in which the A2D–X2P transition of PH+ molecule was observed. Huber and Herzberg [4] summarized the spectroscopic constants of the X2P and A2D states. Edwards et al. [5] observed the 1–2 band and part of the 0–1 band of the A2D–X2P transition of the PH+ molecular ion. Theoretically, Bruna et al. [6] calculated the potential energy curves (PECs) of the electronic states of PH+ with the multi-reference configuration interaction (MRCI) method. The spectroscopic constants of the X2P, a4R, and A2D were reported. Elander et al. [7] investigated the radiative lifetimes and predissociation rates of A2D state experimentally and theoretically. Recently, Li et al. [8] employed SO-MCQDPT method to study the PH+ cation, and spectroscopic constants of the X states X2P1/2, 2P3/2, A2D3/2, and A2D5/2 were calculated. So far, the information of the low-lying electronic states and their spectroscopic properties is quite limited, especially for excited electronic states. In addition, it is well known that spin–orbit coupling (SOC) effect may bring the great change to the shapes of the PECs for diatomic molecules via the interaction between the different electronic states that have the common X components [9]. The SOC effect on PH+ is only investigated for the ground state X2P and the first excited state A2D in the SO-MCQDPT calculations reported by Li et al. [8]. In this paper, we performed a comprehensive study on the ground as well as the low-lying excited states of PH+ with the high-level relativistic multireference configuration interaction with Davidson correction (MRCI+Q). The PECs of the 8 K–S states associated with three dissociation limits of PH+, as well as those of 15 X states generated from the K–S states after considering the SOC effect, were obtained. Based on the PECs, the spectroscopic constants for the bound states were obtained, most of which have
Fig. 1. The PECs of K–S states of the PH+.
not been reported previously. The interaction between different electronic states via the SOC effect, and the transition properties were also analyzed in detail. The calculation presented here will provide more accurate results for the interstellar detection of the PH+.
Calculation method The whole ab initio calculations on the electronic structure of PH+ cation were performed via the quantum chemistry MOLPRO 2010.1 program package [10]. The spectroscopic constants were determined with the aid of the LEVEL 8.0 program [11]. The single-point energy calculations were carried out to obtain the potential energy curves (PECs), where the contracted Gaussiantype all-electron augmented correlation consistent basis sets augcc-pwCV5Z-DK [12] are selected for atoms P and aug-cc-pV5Z-DK [13] for H in the calculations. In order to obtain the high-level PECs of PH+, the potential energies at a set of bond lengths are calculated by adopting the following three steps: first, the restricted Hartree–Fock (RHF) method is selected to produce the single-configuration wavefunction of the ground state. Then, the multi-configuration wavefunction is calculated with the state-averaged complete active space self-consistent field (SA-CASSCF) method [14,15]. Finally, the internally contracted multi-reference configuration interaction (MRCI) approach [16,17] is employed to launch the correlation energy calculation and achieve the accurate energies based on the acquired optimized reference wavefunction in the SA-CASSCF calculation. At the same time, the calculation is extended to include the relativistic effect in order to improve the level of the PECs, where the one-electron integral second-order Douglas–Kroll integrals is used to evaluate the relativistic effect [18]. Adding the Davidson correction (+Q) balances the size-consistency error of MRCI method. The potential energy curves (PECs) of these 8 K–S electronic states are drawn with the help of the avoided crossing rule of the same symmetry. Because of the limit of the MOLPRO program, C2m point group symmetry, the subgroup of the C1m point group, is adopted in the calculation of electronic structures, which holds A1/B1/B2/A2 irreducible representations. For PH+, 3a1, 1b1 and 1b2, symmetry molecular orbitals (MOs) are determined as the active space, which correspond to the atoms P 3s3p and H 1s shells. The outermost 3s23p2 electrons of P+ and 1s1 electrons of H are placed in the active space. 8 electrons of 2s2p shell of P are placed in the closed shell. These orbitals are doubly occupied in all reference configuration state functions, and correlated via single and double excitations. The rest of the inner electrons for 1s orbital of P were kept in frozen-core orbitals. That is, there are total 13 electrons of PH+ used in the calculation of electronic correlation energy. The spin–orbit coupling (SOC) effect is taken into consideration via the state interaction approach with the Breit–Pauli Hamiltonian operator (HBP) and the mean-field one-electron Fock operator after the MRCI calculation [19]. The off-diagonal spin–orbit matrix elements are calculated with the MRCI wavefunctions, while the diagonal spin–orbit matrix elements are from the energies of the MRCI+Q calculation. The energies of the X states are obtained by the diagonalization spin–orbit matrix. After considering the SOC effect, the 8 K–S electronic states split into 15 X electronic states. The PECs of the X states are plotted with the aid of the avoided crossing rule for the electronic states of the same symmetry. Based on the PECs of the K–S and X electronic states, the spectroscopic constants, including equilibrium internuclear distance Re, excitation energy Te, vibrational constants xe and xeve, balanced rotation constant Be, are determined by numerical solution of the one-dimensional nuclear Schrödinger equation. The dissociation
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X. Li et al. / Spectrochimica Acta Part A: Molecular and Biomolecular Spectroscopy 142 (2015) 1–7
energy De is obtained by subtracting the molecular energy at Re from the energy at a large separation. The TDMs of the transitions A2D–X2P and 12R–X2P are also calculated and the Franck–Condon factors are evaluated by the LEVEL8.0 program. Finally, the radiative lifetimes of the transitions A2D–X2P and 12R–X2P are calculated. Results and discussion The PECs and spectroscopic constants of the K–S state The 8 K–S states of the PH+ have been calculated at the level of relativistic MRCI+Q method, which are related to the dissociation limits P+(3Pg) + H(2Sg), P+(1Dg) + H(2Sg), and P+(1Sg) + H(2Sg), respectively. The potential energy curves (PECs) of the ground and excited states are drawn in Fig. 1. The calculating step length was set at 0.05 Å for R = 0.7–3.5 Å and 0.1 Å for R = 3.5–8.0 Å in calculations of the single point energy of these electronic states. Among the calculated states, only the 22P and the 14P states are repulsive over the internuclear distance, while the remaining six K–S states are all bound states. The spectroscopic constants of the bound states are obtained by solving the corresponding nuclear Schrödinger equations. The spectroscopic constants as well as the dominated electronic configurations at Re of each state are presented in Table 1. Also listed in the table are the calculated and experimental results reported in the previous literatures. Experimental results are only available for the ground state X2P and the excited state A2D. The ground state X2P of the PH+, mainly characterized by the electronic configuration 4r25r26r02pa, is a bound state with a deep potential well. The depth of the potential well for the X2P state is calculated to be 3.53 eV (D0 = 3.376 eV), which is in good agreement with the experimental measurements [3–5]. In contrast with the valence-isoelectronic molecular system, the De value of PH+ is much smaller than that of NH+ (4.66 eV) [21], while much close to that of CH(3.64 eV)[22]. The excited state A2D also could be observed easily in experiment with respect to the potential-well depth of 1.277 eV. The spectroscopic constants (Re, xe, xeve, and Be) of X2P and A2D states obtained in our MRCI+Q
calculations are in good agreement with other theoretical results [6,7] and the latest experimental measurements [5]. It must be mentioned that the excited state A2D has also attracted much attention, because of the PECs’ intersection with the repulsive state 14P. The crossings between PECs may lead to the strong coupling. The related details will be discussed latter. The excitation energy Te of the first quartet state a4R is calculated to be 13998 cm1. This is unlike the case in the valence-isoelectronic NH+. The X2P and a4R states are nearly degenerate for the NH+, and the adiabatic excitation energy is only 509 cm1 [23]. While for the case of CH, the energy separation between a4R and ground state is prominently larger than that of NH+, and the a4R state of PH+ and CH show more similarity. In addition, the depth (3.66 eV [21]) of the potential well for NH+ is much deeper than that (1.79 eV) for PH+. Surprisingly, hitherto, no experimental studies and only one theoretical study about the a4R state for PH+ are available in the literature. The resulting Re, xe, xeve, and Be values in our MRCI+Q calculation are consistent with those reported in the previous study [6]. The spectroscopic results of the remaining three bound K–S states, 12R, 12R+, and 22R+ have never been studied experimentally or theoretically. Our MRCI+Q calculations indicate that all of them are weakly bound states, with dissociation energies of 0.490, 0.222, and 0.287 eV, for the 12R, 12R+, and 22R+ states, respectively. The bonds of these states in CH and NH+ are also found weaker. The electronic states of PH+ give consistent energy order with NH+ [24], while for CH, the energy order for A2D and 12R states differs from that of NH+ and PH+. The spectroscopic constants obtained in the present calculation could be of great value for performing further experimental studies on these states of the PH+. As shown in Fig. 2, the PEC of the A2D (at v0 = 0 and 4) crosses with those of the bound 12R and repulsive 14P states. By contrast, the PEC of the 12R+ only crosses with that of repulsive 14P at v0 = 1. Under the influence of the SOC effect, the PECs’ crossing may lead to the disturbance and even the predissociation between the K–S states. The interaction could be well described by the corresponding spin–orbit matrix elements. Therefore, the absolute R-dependent SO matrix elements of the systems A2D14P and
Table 1 The spectroscopic constants of the K–S states.
K–S state
Te (cm1)
Re (Å)
xe (cm1)
xexe (cm1)
Be (cm1)
De (eV)
Main configurations (%) at Re
X2P Expt. Expt. Expt. Theor. Theor. a4R Theor.
0 0a 0b 0c 0d 0e 13,998
2412.79
44.38
4r25r26r02pa(93.0)
– 41.67c 47.2d 46.86e 58.12 56d 44.57
1.790
4r25ra6r02paa(93.2)
24,476
2290.60b 2382.75c 2354d 2424.82e 1832.51 1781d 823.68
8.5369 8.5051a 8.3851b 8.508c 8.509d 8.597e 7.8819 7.7803d 5.3735
3.525 3.06 ± 0.25a 63.36 (D0)b 3.369c 3.41d
2
1.4226 1.4251a 1.4352b 1.4247c 1.424d 1.4205e 1.4816 1.4899d 1.7914
0.490
A2D Expt. Expt. Theor. Theor. 12R+ 22R+
26,322 26,221a 26221.1c
1.5454 1.5726a 1.5492c 1.5465d 1.5402e 1.6058 2.2346
1512.20 1398.76a 1534.6c 1458d 1539.1e 850.48 669.69
55.44 – 68.8c 60d 69.77e 100.61 48.76
7.2028 6.9833a 7.19635c 7.2224d 7.1979e 6.9618 3.4771
1.277 0.967 ± 0.247a 1.251 (D0)c
4r25ra6r02pab(89.44) 4r25r06ra2pab(2.17) 4ra5rb6ra2pab(1.48) 4r25ra6r02pab(92.31)
R
a b c d e
Ref. Ref. Ref. Ref. Ref.
[3]. [4]. [5]. [6]. [7].
34,837 47,161
1.10 (D0)e 0.222 0.287
4r25ra6r02pab(91.93) 4r25r26ra2p0(39.76) 4r25ra6r02pab(26.23) 4r25ra6r22p0(24.62)
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X. Li et al. / Spectrochimica Acta Part A: Molecular and Biomolecular Spectroscopy 142 (2015) 1–7
12R+14P are calculated over R = 0.9–6.0 Å, and the results are presented in Fig. 3. The 12R and A2D states are non-interacting in this case, because they have no common X component. As shown in Fig. 3, the system A2D–14P hold large SO matrix element about 110 cm1 at the crossing point of the PECs. In contrast, the numerical value of the system 12R+–14P is about 40 cm1. Hence, for the A2D and 12R+ states, the predissociation pathways provided by the 14P could be open after the influence of the SOC effect. Nevertheless, in the strength, the former are much stronger than the latter.
The PECs and spectroscopic constants of the X state
of the X states are plotted in Fig. 4, which are correlated with the five dissociation limits, respectively. The detailed dissociation relationships are summarized in Table 2. The calculated energy intervals of P+(3P1)–P+(3P0), P+(3P2)–P+(3P1), P+(1D2)–P+(3P2), and P+(1S0)–P+(1D2) are 164, 304, 8541, and 12844 cm1, in a good agreement with the observed values 165, 304, 8413, and 12694 cm1, respectively. The spectroscopic constants obtained from the PECs of the bound X states are listed in Table 3, along with the main K–S components at Re. The K–S state X2P splits into two X states: X = 1/2 and 3/2, which almost completely consist of the X2P at Re. Between them, the 1/2 state is energetically lowest and hence is the ground X state. The X-state spectroscopic constants differ little
In this section, the detailed MRCI+Q calculations including SOC effect for the PECs of the electronic states of PH+ were presented. The SOC effect causes the strong interaction among the K–S states. At the intersections of PECs, under the influence of the SOC effect, the K–S electronic states may suffer from the disturbance from the other electronic states, and would split into different X states. The SOC effect makes the 8 K–S states of the PH+ split into 15 X states including eight states of X = 1/2, five states of X = 3/2, and two states of X = 5/2. According to the avoided crossing rule, the PECs
Fig. 2. The PECs’ crossing region of the K–S states.
Fig. 4. The PECs of the X states (a) X = 1/2 (b) X = 3/2 and 5/2.
Table 2 The dissociation relationships of the X states.
Fig. 3. The absolute R-dependent SO matrix elements of A2D–14P and 12R+–14P systems.
a
K–S state
Atomic state
Energy
X1/2 (1)3/2, (2)1/2, (3)1/2 (1)5/2, (2)3/2, (3)3/2, (4)1/2, (5)1/2, (6)1/2 (2)5/2, (4)3/2, (5)3/2, (7)1/2, (8)1/2, (9)1/2 (10)1/2
P+(3P0) + H(2S1/2) P+(3P1) + H(2S1/2) P+(3P2) + H(2S1/2)
0 164 468
0a 164.90a 469.12a
P+(1D2) + H(2S1/2)
9009
8882.31a
P+(1S0) + H(2S1/2)
21,853
21575.63a
Ref. [20].
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X. Li et al. / Spectrochimica Acta Part A: Molecular and Biomolecular Spectroscopy 142 (2015) 1–7 Table 3 The spectroscopic constants of the X state.
a b
X state
Te/cm1
Re/Å
xe/cm1
X1/2 Expt. Theor. (1)3/2 Theor. (2)1/2 (2)3/2 (3)1/2 (3)3/2 Theor. (1)5/2 Theor. (4)1/2 (4)3/2 (2)5/2
0 0a 0b 294 258.25b 14,144 14,148 24,621 26,470 25941.66b 26,722 26253.78b 34,991 32,667 32,855
1.4226 1.4247a 1.4b 1.4226 1.4b 1.4817 1.4816 1.7915 1.5454 1.550b 1.5507 0.1550b 1.6059 2.3787 2.3722
2412.23 2382.75a 2536.10b 2413.43 2534.65b 1833.04 1828.82 808.68 1532.55 1607.68b 1572.23 1539.76b 1090.38 (DG1/2) 1368.98 1422.56
xexe/cm1 44.35 41.67a 52.35b 44.46 52.3299b 58.22 57.65 40.23 62.81 60.3172b 73.15 65.4715b – 125.59 138.50
Be/cm1
De/eV
Main K–S components (%) at Re
8.5365 8.508a 8.8117b 8.5372 8.8117b 7.8818 7.8823 5.3737 7.2028 7.1888b 7.2110 7.1888b 6.2515 (B0) 3.0951 3.1086
3.504 3.369a 3.357b 3.487 3.361b 1.775 1.770 0.509 0.718 1.25b 0.712 1.162b – 0.510 0.486
X2P (100)
X2P (100) a4R (99.98) a4R (99.99) 2 R (100.0) A2D (100.0) A2D (100.0) 2
R+ (100.0) P (99.2) 4 P (72.5), A2D (27.5) 4
Ref. [5]. Ref. [8].
Fig. 5. The K–S components of the wavefunctions for the (3)3/2, (4)3/2, (1)5/2, and (2)5/2 states.
from those of the ground K–S state. In addition, the SOC splitting of X2P is calculated to be 294 cm1, which is in excellent agreement with measured values [4], 295.9 cm1 and 296.2 cm1 for v = 0 and 1 vibrational levels, respectively. All the above calculations indicate that the SOC effect has little effect on the ground X2P state except the SOC splitting of X2P at Re. Turning to the other theoretical work, large difference
could be found with Li’s results [8], in which the smaller 6311+g basis set was employed. The a4R state splits into X = 1/2 and 3/2 states with the energy separation of 3 cm1. In contrast, the interval of the A2D state is calculated to be 252 cm1; this value strongly differs from early experimental value, 1 cm1. Further investigations on A2D state should be carried out. The vibrational constants xe changes greatly after
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X. Li et al. / Spectrochimica Acta Part A: Molecular and Biomolecular Spectroscopy 142 (2015) 1–7 Table 5 The radiative lifetimes of the transitions A2D–X2P and 2R–X2P. Radiative lifetime (ls)
Transition
2
2
R –X P A2D–X2P
Theor. Expt. a
Fig. 6. The transition dipole moments of the transitions the A2D–X2P, and 12R– X2P.
the consideration of the SOC effect, with the difference of 20 and 60 cm1 for (3)3/2 and (1)5/2 states, respectively. The (4)1/2 holds a very shallow potential well, and only two vibrational levels could be found. Both the (4)3/2 and (2)5/2 states have large Re and xeve, showing obvious mix of the different K–S states for the two X states. As mentioned above, the PEC of the A2D state crosses with that of the 14P state. And the 2D and 14P states have the common X components of 3/2 and 5/2. The rearranged PECs of the X states are greatly different from original ones of the K–S states according to the adiabatic avoided crossing rule between the electronic states of the same symmetry. As shown in Fig. 4, the avoided crossings lead to the more shallow potential well as well as the potential barrier around the longer internuclear distance of 2.37 Å, which is presented in the states X = (3)3/2 and (1)5/2 states. The dissociation energies of (3)3/2 and (1)5/2 states are calculated to be 0.718 and 0.712 eV, which are much smaller than the dissociation energy 1.277 eV of A2D state. In contrast with the results of Li et al., the dissociation energies De = 1.25 and 1.162 eV are much closer to our results of A2D state. This is because the multi-state interaction is accounted for in our SOC calculation, while only the interaction between A1 and A2 components of A2D in C2v symmetry was considered in Li’s calculation [8]. In addition, the avoided crossings also exhibit the strong coupling among the K–S states A2D and 14P. In order to illustrate present the qualitative description of the coupling around the crossing between the A2D and 14P, Rdependent weights of the K–S components for four adjacent states i.e. (3)3/2, (4)3/2, (1)5/2 and (2)5/2 are depicted in Fig. 5. For the wavefunction of the (3)3/2 state, the K–S components switch suddenly between the A2D and 14P states at the crossing point. At large internuclear distance towards dissociation limit, not only
v0 = 0
1
2
1.043 1.505 1.37a 1.5 ± 0.2a
1.104 1.718 1.56a
1.965 1.72a
Ref. [7].
14P state but also the a4R and 12P play important role in the compositions of wavefunction. Unlike the (3)3/2 state, for the (4)3/2 state, the 22P state is also the important components at short R and dissociation limit because of the crossing with the 14P state in the high-energy region (in the small R region) and A2D at dissociation limit. Two X = 5/2 states are purely from the splitting of the K–S states A2D and 14P in our present calculation. Therefore, only the mutual couplings between the A2D and 14P states are found in the wavefunctions of the two X = 5/2 states. In contrast, for the X states that have higher energies, most of them are formed by the mixture of different K–S components, but they are essentially repulsive over R. The analysis of the transition properties In Fig. 6, the curves of the absolute transition dipole moments (TDMs) for the transitions from the A2D and 12R states to the ground state X2P are depicted as the function of the internuclear distance from 1.7 Å to 3.7 Å. Both of the transitions have large TDMs in the Franck–Condon region. By contrast, the former transition 12R–X2P is somewhat larger than that of the A2D–X2P. However, the TDMs of both transitions decrease quickly with the increasing R. The Franck–Condon factors of transitions A2D–X2P and 12R–X2P are evaluated with the aid of the LEVEL program, and the results are tabulated in Table 4. Based on the calculated TDMs, the radiative lifetimes of the selected vibrational level v’ has been computed by the following formula [25,26]: 3h sm’ ¼ ðAm’ Þ1 ¼ 64p4 ja eTDMj2 P 0
q ðDEm’;m’’ Þ m’’ m’;m’’
3
5
4:93610 ¼ jTDMj2 P q ðD E m’’ m’;m’’
m’;m’’ Þ
3
where qm0 ,m0 0 is the Franck–Condon factor; TDM is the averaged transition dipole moment in atomic unit; the energy separation DEm0 ,m0 0 is in cm1; sm0 is in second. The results of the radiative lifetimes are at the level of microsecond (ls) and presented in Table 5. For the higher vibrational levels v’ > 7 that have not been observed in experiment, they tend to suffer from the strong disturbance from the 14P state by the SOC effect, and the corresponding lifetimes will become short. However, our calculated radiative lifetime (1.505 ls)
Table 4 The Franck–Condon factors of the transitions A2D–X2P and 2R–X2P. v0 0 = 0 2
A v0 v0 v0
1
2
3
4
5
6
7
8
9
10
11
12
13
0.30512 0.07998 0.25515
0.09281 0.30890 0.01669
0.01916 0.22119 0.11985
0.00283 0.08087 0.26131
0.00030 0.01841 0.17513
0.00002 0.00275 0.06177
0.00000 0.00027 0.01313
0.00000 0.00002 0.00173
0.00000 0.00000 0.00013
0.00000 0.00000 0.00001
0.00000 0.00000 0.00000
0.00000 0.00000 0.00000
0.00000 0.00000 0.00000
0.12662 0.14552
0.20298 0.09316
0.22310 0.01137
0.18509 0.01655
0.12049 0.10163
0.06251 0.17238
0.02600 0.17079
0.00861 0.11692
0.00223 0.05841
0.00044 0.02146
0.00006 0.00564
0.00000 0.00098
0.00000 0.00009
2
D–X P =0 0.57977 =1 0.28761 =2 0.09511 2 R –X2P v0 = 0 0.04187 v0 = 1 0.08508
X. Li et al. / Spectrochimica Acta Part A: Molecular and Biomolecular Spectroscopy 142 (2015) 1–7
of v0 = 0 of the transition A2D–X2P is in good agreement with the experimental measurement (1.5 ± 0.2 ls)[7], which shows that the lowest 3 vibrational levels are almost uninfluenced by perturbation of 14P via the SOC effect. Conclusions The 8 K–S states of PH+ have been studied by the relativistic MRCI+Q method. The potential energy curve (PECs) and the corresponding spectroscopic constants of the K–S states are obtained. The calculated spectroscopic constants are in good agreements with the available experimental results. The calculated spin–orbit matrix elements indicate the strong interaction between the 2D and 14P states. The SOC effect is considered for the PH+ and the 8 K–S states split into 15 X states. The X2P state splits into two X states: X = 1/2 and X = 3/2 states, of which, the X = 1/2 state is the lowest and confirmed to be the ground X state. The spectroscopic results indicate that the SOC effect has little effect on the ground state X2P. The analysis of the wavefunctions for the X states shows the strong coupling between the A2D and 14P states at their crossing region. However, for A2D and 12R states, this effect leads to more shallow potential wells as well as the potential barriers. In addition, the transition dipole moments of the A2D– X2P and 12R–X2P are calculated as the function of internuclear distance. Both of the transitions have large TDM values in the Franck–Condon region. In combination with the Franck–Condon factors, the radiative lifetimes of the lowest three vibrational levels of these two transitions are evaluated at the microsecond (ls) level. The lifetime (v 0 = 0) of A2D is calculated to be in good agreement with the experimental value because the lowest three vibrational levels are unaffected by the disturbance of the 14P via the SOC effect.
7
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