Multireference configuration interaction study on the ground and excited electronic states of the AlO+ molecule

Computational and Theoretical Chemistry 1117 (2017) 258–265

Contents lists available at ScienceDirect

Computational and Theoretical Chemistry journal homepage: www.elsevier.com/locate/comptc

Multireference configuration interaction study on the ground and excited electronic states of the AlO+ molecule Peiyuan Yan, Xiang Yuan, Shuang Yin, Xiaoting Liu, Haifeng Xu ⇑, Bing Yan ⇑ Jilin Provincial Key Laboratory of Applied Atomic and Molecular Spectroscopy (Jilin University), Institute of Atomic and Molecular Physics, Jilin University, Changchun 130012, China

a r t i c l e

i n f o

Article history: Received 2 July 2017 Received in revised form 21 August 2017 Accepted 23 August 2017 Available online 30 August 2017 Keywords: AlO+ MRCI-F12 Potential energy curves Spectroscopic constant Transition property

a b s t r a c t High-level ab initio calculations on the electronic states of AlO+ cation have been performed with the explicitly correlated multi-reference configuration interaction (MRCI-F12) method. The potential energy curves (PECs) of 24 electronic states have been obtained, most of which are reported for the first time. From the computed PECs, the precise spectroscopic constants of the bound states are determined. Our calculations confirm that the ground state of AlO+ cation is the X1R+ state. The permanent dipole moments (PDMs) functions of the selected bound states are computed. The spin–orbit (SO) matrix elements between the electronic states involved in the crossing region of the PECs are calculated to analyze the predissociation mechanisms of the X1R+, A1P, and 21R+ states. Finally, the transition properties of four spin-allowed transitions are predicted, including the transition dipole moments (TDMs), FranckCondon Factors (FCFs), and the radiative lifetimes. This work should enhance our understanding on the electronic structure and spectroscopy of AlO+ cation. Ó 2017 Elsevier B.V. All rights reserved.

1. Introduction Since aluminium oxide (AlO) molecule has been detected in oxygen-rich giant stars [1,2] and VY Canis Majoris [3], and also exists in solar flames, it has become one of the research subjects in the astrophysics. Knowledge about the electronic structure, spectrum and dynamics of electronic excited states play a key role in understanding the chemical and physical processes involving the AlO molecule. During the past several decades, the low-lying electronic states of the neutral AlO have attracted considerable research interests, both in experimental spectroscopic measurements [4–9] and in ab initio calculations [10–14]. Despite the ability of AlO+ to be formed through reactions of Al+ with O2, O3, NO2, N2O, and CO2 [15,16], the experimental spectroscopic information is still deficient. Theoretically, the first study on AlO+ dates back to 1973 in work by Schamps [17], in which the spectroscopic constants of four low-lying electronic states were computed using the selfconsistent field (SCF) method. To date there exist a lack of consensus among different theoretical studies. Even the symmetry of the ground electronic state is still under debate. Using the complete active space self-consistent field (CASSCF) method, Marquez et al. [18] computed the potential energy curves (PECs) and the spectro-

⇑ Corresponding author. E-mail addresses: [email protected] (H. Xu), [email protected] (B. Yan). http://dx.doi.org/10.1016/j.comptc.2017.08.024 2210-271X/Ó 2017 Elsevier B.V. All rights reserved.

scopic constants of some low-lying states and concluded that the ground state of AlO+ is a3P state. However, using the multireference configuration interaction (MRCI) and the restrict coupled cluster singles and doubles with perturbative triples (RCCSD(T)) methods, Chambaud et al. [19] and Sghaier et al. [20] indicated that the ground state of AlO+ cation is a singlet 1R+ state. The spectroscopic constants of the first 1R+ and first 3P states were also given. Regarding high-lying electronic excited states that would be of crucial importance for understanding the photochemistry in the ultraviolet region, to the best of our knowledge, there is unfortunately neither experimental nor theoretical information available in the literatures. In addition, unlike its isovalent system, MgO, of which the predissociation dynamics of the first excited state has been investigated [21], the predissociation mechanism of the excited states of the AlO+ cation remains unknown, which serves as another motivation of present work. In the present work, we have performed a high-level ab initio study on the 24 electronic states associated with lowest four dissociation limits of the AlO+ cation, using the MRCI-F12 method. Based on these PECs, the spectroscopic constants of the bound states have been obtained, most of which are reported for the first time. We have calculated the spin-orbit (SO) coupling matrix elements, based on which the predissociation mechanisms of the AlO+ cation have been discussed. The transition properties including the transition dipole moments (TDMs), Franck-Condon Factors (FCFs), and the radiative lifetimes have been predicted. The present study

P. Yan et al. / Computational and Theoretical Chemistry 1117 (2017) 258–265

could enhance the knowledge on the structure, spectra and dynamics of electronic excited states of AlO+ cation. 2. Computational method In the present work, ab initio calculations on the electronic structures of the 27Al16O+ cation are performed with MOLPRO 2012 software package [22,23]. The spectroscopic constants are computed by solving the radial Schrödinger equation with the aid of the LEVEL program [24]. The correlation-consistent basis sets cc-pcvqz-f12 [25] for the Al atom and cc-pvqz-f12 [26] for the O atom are selected in our calculation. In order to obtain high-precision PECs of electronic states, the energies at a set of bond internuclear distances are calculated. The calculating step length is selected as 0.025 Å for R = 1.2–2 Å, 0.05 Å for R = 2–3.5 Å, and 0.5 Å for 3.5–5 Å. The detailed calculation process is as the following: Hartree-Fock calculation was firstly carried out to generate the single-configuration wavefunction of the ground state for the AlO+ cation; then, the singleconfiguration wavefunction was optimized to obtain the multiconfiguration molecular orbitals by using the complete active space self-consistent field (CASSCF) method [27,28]; finally, on the basis of the CASSCF wavefunction, the dynamic correlation energies were estimated by using the explicitly correlated multireference configuration interaction, that is MRCI-F12, method [29–31]. The MRCI-F12 method improves the computed precision and reduces the computed cost compared to MRCI. The Davidson correction (+Q) [32] is used to overcome the size-consistency error of the MRCI method. The PECs of these 24 K-S electronic states are drawn with the help of the avoided crossing rule of the same symmetry. The SOC effect is taken into consideration via the state interaction approach [33]. The off-diagonal SO matrix elements are calculated with the CASSCF wavefunctions. In the current calculation, the C2m point group that is the Abelian subgroup of the C1m point group is employed. And the corresponding relationships between the reducible representations of the two point group are R+ = A1, P = B1 + B2, D = A1 + A2, and R = A2, respectively. For the AlO+ cation, 4a1, 2b1, and 2b2 molecular orbitals (MOs) are selected as the active space to construct the wavefunctions of electronic states. The MOs in active space correspond to the atoms Al+ 3s3p shells and O 2s2p shells in CASSCF and MRCI-F12 calculations. The outermost 3s2 electrons of the Al+ cation and 2s22p4 electrons of the O atom are placed in the active space. The inner 2s22p6 electrons of Al+ are placed in the closed shell. That is, a total of 16 electrons of AlO+ are used in the calculation of electronic correlation energy. The rest of the inner electrons are kept in frozen-core orbitals but optimized in CASSCF procedure. From the calculated PECs, the adiabatic excitation energy Te, equilibrium internuclear distance Re, vibrational constants xe and xeve, and rotational constant Be are determined by solving the nuclear Schrödinger equation. The dissociation energy De is obtained by subtracting the molecular energy at Re from the energy at a large separation. The SO matrix elements are computed and used to analyze the predissociation mechanism of the AlO+ cation. The TDMs and the FCFs of the selected transitions are also determined. Furthermore, the radiative lifetimes of the transitions, based on the calculated TDMs and FCFs, are predicted in our work.

259

adiabatically relate to four dissociation limits of Al+(1Sg) + O(3Pg), Al+(1Sg) + O(1Dg), Al+(1Sg) + O(1Sg), and Al+(3Pu) + O(3Pg), as listed in Table 1. The calculated PECs are plotted in Fig. 1, for singlet states (Fig. 1(a)) and triplet/quintet states (Fig. 1(b)) respectively. From the PECs, the spectroscopic constants of the bound states have been determined. The results are listed in Table 2, along with the main electronic configuration state functions (CSFs) at equilibrium distance (Re). For comparison, previous theoretical results where available are also tabulated in the table. To date there is no information about the experimental spectroscopic constants available in the literature. Previous theoretical spectroscopic constants of AlO+ are focused on the lowest three electronic states. Our computed results of the ground X1R+ state are in good agreement with the recent theoretical results obtained by Sghaier et al. [20] with complete basis set (CBS) extrapolation at the MRCI-F12/ CBS and RCCSD(T)/CBS levels. Moreover, the spectroscopic constants for lowest few states of AlO+ with the MRCI-F12+Q method are also listed in the Table 2, demonstrating that the Davidson correction improves the accuracy of spectroscopic constants, especially for the De values of low-lying electroscopic constants. As shown in Fig. 1(a), in the singlet manifold, both the B1D and 1  2 R states are pure repulsive states, and the 31P state is a weakly bound state with a potential well only of 0.2163 eV. The other singlet states are all bound or quasi-bound electronic states. Among them, the ground state X1R+ and the first excited singlet state A1P have deep potential well of 2.9304 eV and 2.5972 eV, which can hold 32 and 41 vibrational levels, respectively. It is also noted from Fig. 1(a) that the 21R+ state exhibits double potential wells at R = 1.573 Å and 2.177 Å, respectively, which could be attributed to the avoided crossing with the above electronic state with same symmetry, 31R+ state. The avoided crossing leads to a potential barrier of the 31R+ state at R = 2.111 Å. In the triplet manifold, except for the b3R and 33R states which are the typically repulsive states over the internuclear distance, the other triplet states are the bound or quasi-bound states. For the quintet states, only the 15P state is al bound state with the potential well of 0.8977 eV. Our computed results indicate that the ground state of the AlO+ cation is X1R+ state, which is associated with the Al+(1Sg) + O(1Dg) dissociation limit. Through analyzing the MRCI wave function, it is found that the X1R+ state is mainly characterized by more than one electronic configuration including 5r26r27r08r02p43p0 (43.7%), 5r26ra7rb8r02p43p0 (31.3%), and 5r26r27r08r02p33pb (13.5%). This obviously indicates that the multi-configuration characteristic of the X1R+ state. From the X1R+ state, one-electron excitation 2p ? 7r could generate the lowest triplet state a3P and the first excited singlet state A1P. Both states are mainly dominated by the electronic configuration of 5r26r27r18r02p33p0 but correlated with two different dissociation limits Al+(1Sg) + O(3Pg) and Al+(1Sg) + O(1Dg), respectively. The a3P state lies only 292.4 cm1 above the ground state, and the calculated excitation energy Te value of the A1P state is 2636.2 cm1. There exhibits a high density of electronic states in the energy range of 30000–50000 cm1. In this energy region, a total of 18 excited states correlated with the highest dissociation limit investigated in the study (Al+(3Pu) + O (3Pg)) are found. It should be pointed out that only the 21R+ state corresponds to the third dissociation limit Al+(1Sg) + O(1Sg). Since Table 1 The dissociation relationships of the K-S states.

3. Results and discussion

Atomic state

K-S states

3.1. The PECs and spectroscopic constants of the electronic states

Al+(1 Sg) + O(3 Pg) Al+(1 Sg) + O(1Dg) Al+(1 Sg) + O(1 Sg) Al+(3Pu) + O(3Pu)

a3P, b3R X1R+, A1P, B1D 21R+ 21P, C1R, 21D, 21R, 31P, 31R+, 23P, 13D, 23R 33P, 33R, c3R+, 15P, 15R+, 15D, 15R, 25R, 25P

The PECs of a total of 24 electronic states of the AlO+ cation have been calculated with the MRCI-F12 method. These electronic states

260

P. Yan et al. / Computational and Theoretical Chemistry 1117 (2017) 258–265

Fig. 1. The PECs of the electronic states of AlO+ for (a) Singlet states. (b) Triplet and quintet states. The ground electronic state are also plotted in (b) (dashed line) for comparison.

the PEC of the 21R+ state exhibits a two-potential-well feature, the spectroscopic constants of each well have been determined and are listed in Table 2 as 21R+(1) and 21R+(2) respectively. The permanent dipole moments (PDMs) of the 8 bound states have been calculated as a function of bond distance in the range of 1.2–8 Å and the curves are plotted in Fig. 2. As shown in the Fig. 2, the PDM curves of these states are negative and leading to the asymptotic linear at large distance, which is corresponding to the dissociation limit of Al+ + O. 3.2. Interaction between the electronic states of the AlO+ cation Based on our calculation, furthermore we investigate the possible predissociation of low-lying electronic states of the AlO+ cation. As shown in Fig. 3, for the PECs of electronic states below 40000 cm1, the adjacent states X1R+ and A1P states exhibit PECs’ crossings with the repulsive b3R state at R = 1.974 (for X1R+) and 2.039 Å (for A1P), respectively. The crossing points are located between the classical points of m0 = 11 and 12 vibrational levels

for X1R+ state and m0 = 8 and 9 for A1P state. The SO matrix elements between the two states are calculated and are depicted in Fig. 4, which are determined to be 21.4 and 30.3 cm1 at the crossing point for X1R+-b3R and A1P-b3R respectively. The predissociation mechanism of the A1P state of MgO via the 13R state channel was studied by Maatouk et al. [21], and the corresponding SO matrix element between the two states is 24.5 cm1. As for the isovalent AlO+ system, similar order of magnitude for the SO matrix elements is found near the crossing points (Fig. 4). Therefore, we expect that the weak SO interactions exist between the X1R+, A1P states with the b3R state, and the predissociation is expected to be observed in further spectroscopic experiments. Turning to the higher excited state, the electronic structures are more complicated. For the 21R+ state, the double-well potential has been displayed due to avoided crossing with higher 31R+ state. Unexpectedly, the PEC of the 21R+ state also crosses with that of the repulsive b3R state. The crossing point is located at the bottom of potential well of the 21R+ state, and the corresponding SO matrix element of 21R+-b3R at the crossing point R = 1.571 Å is

261

P. Yan et al. / Computational and Theoretical Chemistry 1117 (2017) 258–265 Table 2 The spectroscopic constants of Ʌ-S state. State

method

Te/cm1

Re/Å

xe/cm1

xexe/cm1

Be/cm1

De/eV

Main CSFs at Re (%)

X R

MRCI-F12

0

1.603

1004.9

5.54

0.653

2.9304

5r26r27r08r02p43p0(43.7) 5r26ra7rb8r02p43p0(31.3) 5r26r27r08r02p33pb(13.5)

MRCI-F12+Q

0 0a

1.597 1.609a

6.393 4.8a

1.603c1/1.605c2 1.713

0.658 0.648a 0.638b 0.652c 0.565

3.1992

0c 292.4

1025.2 1014.5a 819b 1017.2c1/997.1c2 778.5

MRCI-F12+Q

531.8 623.1a

2636.2

799.9 803.9a 820b 805c 861.4

12.4 8.0a

MRCI-F12

1.717 1.727a 1.825d 1.723c 1.704

7c 5.68

0.568 0.563a 0.57b 0.565c 0.581

MRCI-F12+Q MRCI-F12

2691.3 2717.7a 12860.3

1.699 1.711a 1.602

879.7 869.9a 995.1

5.148 5.2a 3.97

0.582 0.573a 0.653

4.0085

MRCI-F12+Q

12886.9

1023.4 906.9d 1042.6

4.17

0.649

4.2939

12.27

0.676

1.1732

1

+

a3P

MRCI-F12

A1P

c3R+

5.5c 15.3

0.9333

1.1928

2.5972

2 R (1)

31264.8

21R+(2)

33359.8

2.177

501.6

2.74

0.354

0.3543

C1R

40243.8

1.936

421.5

8.65

0.447

0.5932

21P

34640.3

2.333

415.9

2.62

0.309

1.2872

21D

40146.6

1.957

423.4

8.69

0.438

0.6184

31R+

41813.4

1.868

1143.2

56.25

0.488

0.7020

31P

43389.1

2.612

170.9

3.51

0.246

0.2163

23P

28099.3

2.033

583.6

3.93

0.408

2.1002

33P

42256.5

2.266

271.5

5.63

0.327

0.3661

23R

41671.7

1.933

403.5

12.1

0.449

0.4184

13D

40207.3

1.861

496.1

13.24

0.484

0.6118

+

5r26r27ra8r02p33p0(82.7) 5r26r27r08ra2p33p0(4.95) 5r26r27ra8ra2pab3pb(2.8)

2.8666

1.607 1.665d 1.573

1

5r26r27ra8r02p33p0(84.21) 5r26r27r08ra2p33p0(2.84) 5r26r27ra8r02paa3pb(1.51)

5r26ra7ra8r02p43p0(82.5) 5r26ra7ra8r02p43p0(3.45) 5r26ra7r08ra2p43p0(2.67) 5r26ra7rb8r02p43p0(39.5) 5r26r27r08r02p33pb(34.9) 5r26r27r08r02p43p0(7.18) 5r26ra7r08rb2p43p0(5.13) 5r26r27r28r02p23p0(56.5) 5r26r27r08r02p33pb(13.4) 5r26r07r28r02p43p0(8.7) 5r26ra7ra8r02p33pb (3.3) 5r26ra7rb8r02p33p0(2.6) 5r26r27r08r02p33pb(33.6) 5r26r27r08r02p33pa(33.6) 5r26ra7rb8r02p33pb(10.9) 5r26ra7rb8r02p33pa(3.90) 5r26ra7rb8r02p33pb(3.90) 5r26ra7r28r02p33p0(48.8) 5r26r27ra8r02pab3pb(24.5) 5r26r27r08ra2p33p0(7.85) 5r26r27r08r02p33pb(33.13) 5r26r27r08r02p33pa(33.13) 5r26ra7ra8r02p33pb(11.66) 5r26ra7rb8r02p33pa(7.63) 5r26r07r28r02p33pa(3.40) 5r26r07r28r02p33pb(3.40) 5r26r27r28r02p23p0(45.5) 5r26r27r08r02p33pb(19.8) 5r26ra7rb8r02p43p0(15.7) 5r26r27ra8r02pab3pb(47.5) 5r26r27r0 8ra2p33p0(14.0) 5r26ra7r28r02pab3pb(7.33) 5r26ra7ra8rb2p33p0(6.53) 5r26r27ra8r02p33p0(62.0) 5r26r27r0 8ra2p33p0(6.85) 5r26r27ra8r02paa3pb(5.25) 5r26r27ra8r02pab3pa(9.22) 5r26r27ra8r02pab3pb(37.2) 5r26r27ra8r02paa3pb(19.6) 5r26r27r08ra2p33p0(7.45) 5r26ra7r28r02pab3pa(6.59) 5r26r27ra8r02pab3pa(4.95) 5r26r27r08r0p33pa(65.1) 5r26ra7ra8r02p33pb(6.26) 5r26ra7rb8r02p33pa(6.20) 5r26r27r28r02p33p0(5.16) 5r26ra7ra8r02p33pa(4.24) 5r26r27r08r02p33pa(79.8) 5r26ra7rb8r02p33pa(2.54) 5r26ra7ra8r02p43p0(2.49) 5r26r07r28r02p33pa(2.01) (continued on next page)

262

P. Yan et al. / Computational and Theoretical Chemistry 1117 (2017) 258–265

Table 2 (continued) Te/cm1

Re/Å

xe/cm1

xexe/cm1

Be/cm1

De/eV

Main CSFs at Re (%)

1 P

37794.1

2.163

354.6

4.12

0.359

0.8977

15R+

44837.8

2.879

64.8

3.511

0.203

0.0381

5r26r27ra8r02paa3pa(83.9) 5r26ra7r28r02paa3pa(9.85) 5r26ra7ra8r02p33pa(94.6)

State 5

a b c c1 c2 d

method

Reference[19]. Reference[15]. Reference [20]. using the RCCSD(T)/CBS method. using the MRCI-F12/CBS method. Reference[18].

Fig. 2. The calculated Permanent dipole moments of the K-S states as a function of the bond distance.

Fig. 3. The crossing regions of the PECs.

only 13.6 cm1. As shown in Fig. 4, the SO matrix element curve of 21R+-b3R changes abruptly at about 1.751 Å, which due to the avoided crossing occurs between the 21R+ and 31R+ states. The other excited states cross with the 21R+ state as well. The 23P state crosses with the 21R+ state at R = 1.725 Å and the corresponding

SO matrix element is determined to be 36.12 cm1, at the v = 2 and 3 vibrational levels of 21R+ state, which would be perturbed by the SO coupling (Fig. 4). The repulsive state B1D crosses with the 21R+ state, but will be free of SO coupling due to the selection rules of SOC. Our study strongly indicates that the low vibrational

P. Yan et al. / Computational and Theoretical Chemistry 1117 (2017) 258–265

263

Fig. 4. The spin-orbit matrix elements involving the X1R+, A1P, and 21R+ states. The crossing point between two state are also are also plotted.

states of the 21R+ state of AlO+ would be perturbed via spin-orbit coupling with the triplet electronic states. 3.3. Analysis of the transition properties The transition dipole moments (TDMs) of the several selected transitions to the ground X1R+ state and to the excited states are calculated as a function of the internuclear distance. The corresponding TDMs of the transitions including the A1P-X1R+, 21R+X1R+, 21R+-A1P, and c3R+-a3P, are depicted in Fig. 5. The FCFs of these transitions are also calculated with the aid of the LEVEL program and are depicted in Fig. 6. (The values of the FCFs are listed in the supplementary materials Table S1). Based on the calculated TDMs and the FCFs, we compute the radiative lifetimes of the transitions for the first time, the results of which are presented in Table 3. The radiative lifetime s of the selected vibrational level m’ for a given state is determined by the inverse of the total transition probability

s¼

X

A 0 00 m00 m m

1

ð1Þ

The Einstein coefficient Am0 m00 between vibrational levels m0 and m00 is evaluated by

~3 ðTDMÞ2 qm0 m00 Am0 m00 ¼ 2:026  106 m

ð2Þ

where m~ (in unit of cm1) is the energy difference between vibrational levels m0 and m00 , TDM (in atomic unit) is the average electronic transition dipole moment in the region of classical turning point, qm0 00 0 00 is the FCFs of the two vibrational levels m and m , and the radiam tive lifetime s is in unit of second. As shown in Fig. 5, the calculated TDM values of each of the studied transitions exhibit maxima in the Franck-Condon region and then reduces to zero with the increasing internuclear distance. For the A1P-X1R+ transition, the TDM curve decreases dramatically with the bond length and reduces to zero quicker than other transitions. The calculated radiative lifetime for A1P-X1R+ transition at

Fig. 5. The transitions dipole moments of the A1P-X1R+, 21R+-X1R+, 21R+-A1P, and c3R+-a3P transitions.

264

P. Yan et al. / Computational and Theoretical Chemistry 1117 (2017) 258–265

Fig. 6. FCFs of the A1P (v0 = 0)-X1R+, 21R+ (v0 = 0)-X1R+, 21R+ (v0 = 0)-A1P, and c3R+ (v0 = 0)-a3P transitions.

Table 3 The radiative lifetimes of the selected transitions of the AlO+. Transition

Radiative lifetime (ns)

m0 = 0 A P-X R 21R+-X1R+ 21R+-A1P c3R+-a3P 1

1

+

m0 = 1 6

1.522  10 19.2 30.9 0.304  106

0.738  10 19.1 29.6 0.277  106

v’ = 0 is as large as 1.522 ms and it decreases to 0.738 ms at v’ = 1. For the transitions involving the 21R+ state, one can see that the TDM curve has a bump along increasing the bond length due to the avoided crossing between 21R+ with 31R+ states at about Re = 1.849 Å. The calculated FCFs indicate that both transitions of A1P (v0 = 0) - X1R+ (v00 = 0) and 21R+ (v0 = 0) - X1R+ (v00 = 0) have short vibrational progress in absorption or emission spectrum (Fig. 6). The calculated FCF values of 21R+ (v0 = 0)-X1R+ (v00 = 0) peak at v0 = 0 and decrease quickly for the excited vibrational states, while those of A1P (v0 = 0) - X1R+ (v00 ) have apparent values only for the lowest vibrational states. Our study may shed more light on the vibrational spectra of electronic transitions of the AlO+ cation. 4. Conclusions In summary, the PECs of 24 electronic states for the AlO+ cation have been investigated by using the MRCI-F12 method. From the PECs, the spectroscopic constants of the bound states are obtained by solving the radial Schrödinger equation of nuclear motion, most of which are reported for the first time. Our results confirm that the ground state of AlO+ cation is the X1R+ state. The PDMs of some

m0 = 2

m0 = 3

19.0 29.7 0.265  106

18.9 30.1 0.238  106

6

bound states are negative and lead to the asymptotic linear at large distance, which correspond to the dissociation limit Al+ + O. We also compute the SO matrix elements to analyze the predissociation of the X1R+, A1P, and 21R+ states. The transition properties of four spin-allowed transitions are predicted, including the TDMs, FCFs, and the radiative lifetimes. The present would be valuable for future experimental studies on the structure and dynamics of electronic excited states of AlO+ cation. Acknowledgment This work was supported by National Natural Science Foundation of China (Grand Nos. 11574114, U1532138) and the Natural Science Foundation of Jilin Province, China (Grand No. 2015101003JC).

Appendix A. Supplementary material Supplementary data associated with this article can be found, in the online version, at http://dx.doi.org/10.1016/j.comptc.2017.08. 024.

P. Yan et al. / Computational and Theoretical Chemistry 1117 (2017) 258–265

References [1] P.W. Merrill, A.J. Deutsch, Absorption spectra of M-type mira variables, Astrophys. J. 136 (1962) 21–34. [2] D.P.K. Banerjee, W.P. Vaeeicatt, N.M. Ashok, Remarkable changes in the nearinfrared spectrum of the nova-like variable V4332 sagittarii, Astrophys. J. 598 (2003) L31–L34. [3] E.D. Tenenbaum, L.M. Ziurys, Millimeter detection of AlO (X2R+): metal oxide chemistry in the envelope of vy canis majoris, Astrophys. J. 694 (2009) L59– L63. [4] J.A. Coxon, S. Naxakis, Rotational analysis of the B2R+?X2R+ system of the aluminum monoxide radical, AlO, J. Mol. Spectrosc. 111 (1985) 102–113. [5] M.D. Saksena, G.S. Ghodgaonkar, M. Singh, The B2R+-X2R+ system of AlO, J. Phys. B 22 (1989) 1993–1996. [6] M. Singh, G.V. Zope, The B2R+-X2R+ transition of AlO, J. Phys. B 18 (1985) 1743–1745. [7] J.P. Towle, A. Marquez, O.L. Bourne, The C2P -X2R+ (0, 0) band in AlO, J. Mol. Spectrosc. 163 (1994) 300–308. [8] M. Singh, M.D. Saksena, C2Pr -X2R+ transition of AlO, Can. J. Phys. 31 (1983) 1347–1358. [9] M. Singh, M.D. Saksena, The D2R+-A2Pi and C2Pr- A2Pi transitions of AlO, Can. J. Phys. 63 (1985) 1162–1172. [10] J.K. Mcdonald, K.K. Innes, A low-lying excited electronic state of the AlO molecule and the ground-state dissociation energy, J. Mol. Spectrosc. 32 (1969) 501–510. [11] P.J. Dagdigian, Laser fluorescence study of AlO formed in the reaction Al + O2: Product state distribution, dissociation energy, and radiative lifetime, J. Chem. Phys. 62 (1975) 1824–1833. [12] B.H. Lengsfield, Ab initio dipole moment functions for the X2R+ and B2R+ states of AlO, J. Chem. Phys. 77 (1982) 6083–6089. [13] O. Launila, J. Jonsson, Spectroscopy of AlO: rotational analysis of the A2P-X2R+ transition in the 2-um region, J. Mol. Spectrosc. 168 (1994) 1–38. [14] N. Gilka, J. Tatchen, C.M. Marian, The g-tensor of AlO: principal problems and first approaches, Chem. Phys. 343 (2008) 258–269. [15] M.E. Weber, J.L. Elkind, P.B. Armentrout, Kinetic energy dependence of Al++O2?AlO++O, J. Chem. Phys. 84 (1986) 1521–1529. [16] D.E. Clemmer, M.E. Weber, Reactions of Al+(1S) with NO2, N2O, and CO2: thermochemistry of AlO and AlO+, J. Phys. Chem. 96 (1992) 10888–10893. [17] J. Schamps, The energy spectrum of aluminium monoxide, Chem. Phys. 2 (1973) 352–366.

265

[18] A. Marquez, M.J. Capitan, Spectroscopic properties and potential energy curves of some low-lying electronic states of AlO, AlO+, LaO. and LaO+: an ab initio CASSCF study, Int. J. Quantum Chem. 52 (1994) 1329–1338. [19] G. Chambaud, P. Rosums, M.L. Senent, P. Palmieri, Theoretical study of protonated aluminium oxide, Mol. Phys. 92 (1997) 399–408. [20] O. Sghaier, R. Linguerri, M.M.A. Mogren, J.S. Francisco, M. Hochlaf, spectroscopic constants of the X1R+ and 13P states of AlO+, Astrophys. J. 826 (2016) 163–175. [21] A. Maatouk, A.B. Houria, O. Yazidi, N. Jaidane, M. Hochlaf, Electronic states of MgO: spectroscopy, predissociation, and cold atomic Mg and O production, J. Chem. Phys. 133 (2010) 144302. [22] H.J. Werner, P.J. Knowles, G. Knizia, F.R. Manby, M. Schütz, P. Celani, T. Korona, R. Lindh, A. Mitrushenkov, G. Rauhut, MOLPRO, version 2010.1, a package of ab initio program. [23] H.J. Werner, P.J. Knowles, G. Knizia, F.R. Manby, M. Schütz, Molpro: a generalpurpose quantum chemistry program package, WIREs Comput. Mol. Sci. 2 (2012) 242–253. [24] R.J. LeRoy, LEVEL 8.0: a computer program for solving the radial Schrödinger equation for bound and quasibound levels, University of Waterloo Chemical Physics Research Report CP-663, 2007. [25] J.G. Hill, S. Mazumder, K.A. Peterson, Correlation consistent basis sets for molecular core-valence effects with explicitly correlated wave functions: the atoms B-Ne and Al-Ar, J. Chem. Phys. 132 (2010) 054108. [26] K.A. Peterson, T.B. Adler, Systematically convergent basis sets for explicitly correlated wavefunctions. The atoms H, He, B-Ne, and Al-Ar, J. Phys. Chem. 128 (2008) 084102–084112. [27] H.J. Werner, W. Meyer, A quadratically convergent multiconfiguration-selfconsistent field method with simultaneous optimization of orbitals and CI coefficients, J. Chem. Phys. 73 (1980) 2342–2356. [28] H.J. Werner, P.J. Knowles, A second order multiconfiguration SCF procedure with optimum convergence, J. Chem. Phys. 82 (1985) 5053–5063. [29] T. Shiozaki, G. Knizia, H.J. Werner, J. Chem. Phys. 134 (2011) 034113. [30] T. Shiozaki, H.J. Werner, Multireference explicitly correlated F12 theories, Mol. Phys. 111 (2013) 607–630. [31] T. Shiozaki, H.J. Werner, Explicitly correlated multireference configuration interaction: MRCI-F12, J. Chem. Phys. 134 (2011) 184104. [32] R.D. Stephen, R.D. Ernest, Configuration interaction calculation on the nitrogen molecule, Int. J. Quantum Chem. 14 (1978) 561–581. [33] A. Berning, M. Schweizer, H.J. Werner, P.J. Knowles, P. Palmieri, Spin-orbit matrix elements for internally contracted multireference configuration interaction wavefunctions, Mol. Phys. 98 (2000) 1823–1833.