Accurate spectroscopic calculations of the 17 Λ–S and 59 Ω states of the AsP molecule including the spin–orbit coupling effect

Spectrochimica Acta Part A: Molecular and Biomolecular Spectroscopy 135 (2015) 736–746

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Accurate spectroscopic calculations of the 17 K–S and 59 X states of the AsP molecule including the spin–orbit coupling effect Deheng Shi ⇑, Qionglan Liu, Shuai Wang, Jinfeng Sun, Zunlue Zhu College of Physics and Electronic Engineering, Henan Normal University, Xinxiang 453007, China

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

 Convergence is observed with respect

to the basis set.  Effect of core–valence correlation and

relativistic corrections on PECs is evaluated.  PECs of 17 K–S and 59 X states are extrapolated to the CBS limit.  Spectroscopic parameters of 11 K–S and 32 X bound states are obtained.  SO coupling effect on the spectroscopic parameters is discussed.

a r t i c l e

i n f o

Article history: Received 13 May 2014 Received in revised form 14 July 2014 Accepted 23 July 2014 Available online 1 August 2014 Keywords: Spectroscopic parameter Potential energy curve Spin–orbit coupling effect Relativistic correction Core–valence correlation correction

a b s t r a c t The potential energy curves (PECs) of 59 X states generated from the 17 K–S states (X1R+, a3R+, 15R+, b3D, c3P, 15P, 25R+, 23D, 23P, 33R+, A1P, 23R+, 35R+, 17R+, 15D, 25D, and 25P) of AsP molecule are studied for the first time for internuclear separations from about 0.10 to 1.10 nm. All the K–S states are contributed to the first three dissociation channels of AsP molecule except for the A1P. The 23R+, 35R+, 17R+, 15D, 25D, and 25P are found to be the repulsive states. The a3R+, 15P, b3D, 17R+, 15D, 25D, and 25P are found to be the inverted states. Each of the 33R+, c3P, 23P, 15P, and 15R+ states has one potential barrier. The PECs are calculated by the CASSCF method, which is followed by the internally contracted MRCI approach with Davidson correction. Core–valence correlation and scalar relativistic corrections are included. The convergent behavior of present calculations is discussed with respect to the basis set and level of theory. The spin–orbit coupling effect is accounted for. All these PECs are extrapolated to the complete basis set limit. The spectroscopic parameters are evaluated for the bound states involved, and are compared with available measurements. Excellent agreement has been found between the present results and the measurements. It shows that the spectroscopic parameters reported in this paper can be expected to be reliably predicted ones. The conclusion is gained that the effect of spin–orbit coupling on the spectroscopic parameters is not obvious for all the K–S bound states except for few ones such as 15R+ and c3P. Ó 2014 Elsevier B.V. All rights reserved.

Introduction

⇑ Corresponding author. Tel.: +86 373 3328876. E-mail address: [email protected] (D. Shi). http://dx.doi.org/10.1016/j.saa.2014.07.065 1386-1425/Ó 2014 Elsevier B.V. All rights reserved.

The AsP is an important semiconductor material, which has been extensively employed in various semiconductor devices. The accurate spectroscopic knowledge of AsP molecule is very

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crucial in the applications, in particular when it is used as the lightemitting material. However, little spectroscopic knowledge has been known about the molecule. Up to now, the spectroscopic information about the molecule, as is available, is all derived from the only measurements [1–6] and calculations [7–10]. Furthermore, accurate spectroscopic parameters of this molecule are available only for few K–S states and only for few X states. For this reason, this paper will in detail study the potential energy curves (PECs) of AsP molecule so that some spectroscopic knowledge can be extended. Historically, in 1969, Yee and Jones [1] observed the emission spectrum of AsP molecule. They [1] found 12 red-degraded bands in the region 296–322 nm, and assigned them to the transitions A1P–X1R+. In 1970, Harding et al. [2] made the rotational analysis of the five most intense spectrum bands, which were attributed to the A1P–X1R+ transitions of the AsP molecule. In 1974, Gingerich et al. [3] determined the ground-state dissociation energy of this molecule to be 4.4474 ± 0.1304 eV by a mass spectrometric technique. In 1979, Huber and Herzberg [11] summarized some accurate spectroscopic parameters of the molecule prior to 1979. In 1982, Rajamanickam et al. [12] obtained the dissociation energy of 4.46 ± 0.15 eV for the X1R+ state from the RKR-estimated PEC. In 1986, Rasanen et al. [4] prepared the AsP in a neon matrix and performed the laser induced fluorescence (LIF) spectroscopy measurements. They [4] evaluated a number of spectroscopic parameters and molecular constants for the X1R+ and A1P K–S states and for the a3R+0, c3P0+, and b3D1 X states. In 1995, Wood and Johnson [5] determined the internuclear equilibrium separation to be about 0.19 ± 0.04 nm for the X1R+ state at high temperature by molecular beam flux measurements. In 2006, Leung et al. [6] prepared the AsP using the reaction of PH3 gas at a concentration of 0.3% by volume in argon, and measured some rotational transitions for the X1R+ and A1P states. They [6] evaluated a number of spectroscopic parameters and molecular constants of the X1R+ and A1P states. Summarizing the measurements [1–6], we have found the following. The spectroscopic results are determined only for the X1R+ and A1P K–S states and only for the a3R+0, c3P0+, and b3D1 X states. No spectroscopic measurements of any other states were performed in the past several decades. Even for these states, the available spectroscopic knowledge [1–6] is still very limited. For this reason, to understand accurately the spectroscopic properties of AsP molecule, some theoretical work should be done even for these K–S and X states, for which some measurements [1–6] can be available. Theoretically, in 1992, Toscano and Russo [7] made the first ab initio study on the spectroscopic properties of AsP molecule. They [7] calculated the PECs of six K–S states by the LCGTO-MP-LSD method. In 1991, Martin and Sundermann [8] made the benchmark calculations for many molecules including the AsP using the correlation-consistent valence basis sets with the Stuttgart– Dresden–Bonn relativistic effective core potentials. In 2007, Zhang et al. [9] calculated the PECs of nine K–S states by the multireference configuration interaction (MRCI) approach with the augcc-PVQZ (AVQZ) basis set. In 2012, Liu et al. [10] reported the ground-state PEC of the molecule, which was calculated by the internally contracted MRCI (icMRCI) approach with the correlation-consistent basis sets. Some spectroscopic parameters were evaluated [7–10]. However, no core–valence correlation and scalar relativistic corrections were included in the work [9,10]. To this day, only four groups of spectroscopic calculations [7–10] can be found. Summarizing these spectroscopic results, we find the following. (1) These four groups of spectroscopic calculations are focused only on several K–S states. And more importantly, only few spectroscopic results achieve high quality. (2) No spin–orbit (SO) coupling effect has been evaluated for any X states, though

the SO coupling effect can bring about some important influences on the spectroscopic properties, in particular for Te and xe. The aim of this work is to extend the spectroscopic knowledge of AsP molecule. Firstly, we will determine the spectroscopic properties of a large number of K–S states since the accurate spectroscopic parameters can be gained only for few electronic states up to now. For this reason, extensive ab initio calculations on the PECs will be performed over a wide internuclear separation. In order to determine the spectroscopic parameters of AsP molecule as accurately as possible, core–valence correlation and scalar relativistic corrections are included into the present calculations because these two corrections have important effect on the accurate prediction of spectroscopic properties. Secondly, the effect of SO coupling on the PECs will be introduced into the calculations since no PECs have been calculated for any X states up to now. In the next section, we will briefly describe the methodology used in this paper. In Section ‘Results and discussion’, the PECs of the 17 K–S states [X1R+ (11R+), 13R+ (a3R+), 15R+, 13D (b3D), 13P (c3P), 15P, 25R+, 23D, 23P, 33R+, 11P (A1P), 23R+, 35R+, 17R+, 15D, 25D, and 25P] are calculated for internuclear separations from 0.10 to 1.10 nm. The PECs of the 59 X states generated from all the K–S states are studied for the first time over the same internuclear separation. The PECs are calculated using the complete active space self-consistent field (CASSCF) method, which is followed by the icMRCI approach [13,14] with Davidson correction (icMRCI+Q) [15,16]. The SO coupling effect is accounted for. The effect of core–valence correlation and scalar relativistic corrections on the PECs is included. All the PECs are extrapolated to the complete basis set (CBS) limit. The spectroscopic parameters are evaluated for all the states involved. The spectroscopic parameters are compared with those available in the literature. Concluding remarks are given in Section ‘Conclusions’. Methodology To find out the dissociation channels of the electronic states involved here, we first deduce all the electronic states resulting from the lowest five dissociation channels of the AsP molecule. These states in combination with their corresponding dissociation channels are collected in Table 1 [17]. As seen in Table 1, four states are attributed to the first dissociation channel. Six states are attributed to the second dissociation channel. Six states are attributed to the third dissociation channel. Four states are attributed to the fourth dissociation channel. And thirty states are attributed to the fifth dissociation channel. Altogether, the 50 states are generated from the first five

Table 1 Dissociation relationships of the 50 K–S states generated from the first five dissociation channels of AsP molecule. Molecular states

X1R+, 13R+, 15R+, 17R+ 23R+, 25R+, 13P, 15P, 13D, 15D 33R+, 35R+, 23P, 25P, 23D, 25D 13R, 33P, 15R, 35P 21R+, 31R+, 41R+, 43R+, 53R+, 63R+, 11R, 21R, 23R, 33R, 11P, 21P, 31P, 41P, 43P, 53P, 63P, 73P, 11D, 21D, 31D, 33D, 43D, 53D, 11U, 21U, 13U, 23U, 11C, 13C

States of separate atoms

As(4Su) + P(4Su) As(2Du) + P(4Su) As(4Su) + P(2Du) As(4Su) + P(2Pu) As(2Du) + P(2Du)

Relative energy (cm1) This work

Exp. [17]

0.0 10646.59 11485.28 18853.52 22403.74

0.0 10753.55 11378.63 18735.36 22132.18

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dissociation channels of the molecule. For the sake of length limitation, here we only study all the 16 states generated from the first three dissociation channels. The A1P state generated from the fifth dissociation channel is also included in the present work since some measurements [1,2,4] can be found for this state. With these measurements [1,2,4], we can make some comparisons between theory and experiment. Here, all the PECs are calculated by the CASSCF method, which is followed by the icMRCI approach. The CASSCF is employed as the reference wavefunction for the icMRCI calculations in this work. For the PEC calculations, the icMRCI theory has proven particularly successful. A number of high-quality spectroscopic calculations have been made for a variety of diatomic molecules [18–24]. In this work, the basis set used to calculate all the PECs is the aug-cc-pV5Z (AV5Z) set [25,26]. All the PECs are calculated with the MOLPRO 2010.1 program package [27]. In the calculations, the orbitals are optimized by the CASSCF approach. The state-averaged technique is used in the CASSCF calculations. In the CASSCF and subsequent icMRCI calculations, eight molecular orbitals (MOs) are put into the active space, including 4a1, 2b1, and 2b2 symmetry MOs, which correspond to the 10– 13r, 5p, and 6p MOs in the molecule. Five valence electrons in the 4s4p orbitals of As atom and five valence electrons in the 3s3p orbitals of P atom are placed into the active space, which consists of full valence space. That is, ten valence electrons in the AsP molecule are distributed into the eight outmost valence MOs (10– 13r, 5p, and 6p) in the calculations. The energy ordering of these outmost valence MOs is 10r11r5p12r6p13r. As a result, this active space can be referred to as CAS (10, 8). The 38 inner electrons are put into the 19 closed-shell orbitals (10a1, 4b1, 4b2, and 1a2), which correspond to the 1–9r, 1–4p, and 1d MOs in the molecule. In the calculations, the number of external orbitals amounts to 368, including 151a1, 85b1, 85b2, and 47a2 symmetry MOs. In summary, the 27 MOs (14a1, 6b1, 6b2, and 1a2) are used to calculate all the PECs. When we use these MOs to calculate the present PECs, we find that all the PECs are smooth over the present internuclear separation range, and each PEC is convergent. To determine accurately all the PECs, the point spacing interval used here is 0.02 nm for each state, except near the equilibrium position where the point spacing is 0.002 nm. Here, a smaller step is adopted near the equilibrium separation of each state so that the properties of each PEC can be displayed more clearly. The obtained PEC of each K–S or X state is convergent. It means that the two atomic fragments, As and P, are completely separated at 1.10 nm. The convergence of each PEC clarifies that the dissociation energy can be determined by the difference between the total energy of the AsP molecule at the equilibrium position (which is obtained by fitting) and the total energy of the molecule on the same PEC at 1.10 nm, or is obtained by the difference between the total energy of the AsP molecule at the equilibrium position and the total energy of the molecule on the same PEC at the highest barrier when the energy at the highest barrier is higher than that at the dissociation limit. In this work, core–valence correlation correction is included with a cc-pCVTZ basis set [24,28], and its contribution is denoted as CV. Scalar relativistic correction is taken into account by the third-order Douglas-Kroll Hamiltonian (DKH3) approximation at the level of a cc-pVTZ basis set [29] by both taking and not taking into account the scalar relativistic effect, and its contribution is denoted as DK. It should be pointed out that the core–valence correlation and scalar relativistic corrections are calculated at the level of icMRCI theory, and are applied across the entire PEC of each state. Two successive correlation-consistent basis sets, AVQZ and AV5Z [25,26], are used for two-point basis set extrapolation. The extrapolation formula is written as [30]

ref a ref DEref ; X ¼ E1 þ A X

ð1Þ

corr b DEcorr ¼ Ecorr X : X 1 þA

ð2Þ

DEref X

DEcorr X

Here, and are the Hartree–Fock and correlation energies, respectively, obtained by the aug-cc-pVXZ (AVXZ) basis set. corr DEref are the Hartree–Fock and correlation energies, 1 and DE1 respectively, obtained by the aug-cc-pV1Z (AV1Z) basis set. And the extrapolation parameters a and b are taken as 3.4 and 2.4 for the present Hartree–Fock and correlation energies [30], respectively. From the PECs obtained, the spectroscopic parameters are evaluated. To determine accurately the spectroscopic parameters, all the PECs are fitted to an analytical form by cubic splines so that the corresponding rovibrational Schrödinger equation is conveniently solved. In this paper, we solve the rovibrational Schrödinger equation with Numerov’s method [31]. That is, the rovibrational constants are first determined in a direct forward manner from the analytic potential by solving the rovibrational Schrödinger equation, and then the spectroscopic parameters are evaluated by fitting the first ten vibrational levels whenever available. Results and discussion Using the approach outlined in Section ‘Methodology’, we have calculated the PECs of 17 K–S states and 59 X states for internuclear separations from about 0.1 to 1.10 nm. At the same time, we have included the core–valence correlation and scalar relativistic corrections into the present PEC calculations. We have found that the 23R+, 35R+, 17R+, 15D, 25D, and 25P are the repulsive states. Here, for convenience of discussion, the valence configurations of 11 bound states as determined from the icMRCI wavefunctions around the equilibrium positions are collected in Table 2. For comparison with available measurements [17], we have also calculated the energy separations between each higher dissociation channel and the lowest one, and tabulated them in Table 1. As seen in Table 1, the present energy separations agree well with their respective measurements [17]. It should be pointed out that the energy separations collected in Table 2 are obtained by the icMRCI+Q/Q5+CV+DK calculations. Now we study the multireference characterizations of these states. According to Table 2, only the 25R+ state has obvious multireference characterizations near the internuclear equilibrium position when we ignore the spin orientation of electrons. The main valence configurations of this state can be essentially represented by 10r211r25p212r26p213r0, 10r211r25p312r16p113r1, and 10r211r25p112r16p313r1. The a3R+, b3D, 23D, 25R+, and 33R+ states have the multireference characterizations around the equilibrium positions when the spin orientation of electrons is taken into account. As clearly seen in Table 2, only the spin orientation of electrons in the 5p orbital is different for each main valence configuration of the a3R+ and b3D states. Only the spin orientation of electrons in the 5p and 6p orbitals is different for each main valence configuration of 23D and 33R+ states. The X1R+, c3P, 15R+, A1P, 15P, and 23P states can be essentially represented by only one dominant valence configuration near the equilibrium positions, whether the spin orientation of electrons is taken into account or not. From these configurations, we can easily find out how the electronic transition occurs from one state to another. High-quality ab initio calculations must be convergent with respect to the basis set and level of theory. Otherwise, the spectroscopic results obtained make little sense due to low accuracy. On the one hand, for the present work, few measurements are available and few calculations can be found in the literature. Therefore, we cannot make the extensive comparison between the

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D. Shi et al. / Spectrochimica Acta Part A: Molecular and Biomolecular Spectroscopy 135 (2015) 736–746 Table 2 Valence configurations of 11 bound states of the AsP near the equilibrium positions. State 1

Valence configurations around the equilibrium positions ...10rab11rab5pabab12rab6p013r0 (0.80)a . . .10rab11rab5paab12rab6pa13r0 (0.40) . . .10rab11rab5pa12rab6paba13r0 (0.03) . . .10rab11rab5paab12rab6pa13r0 (0.42) . . .10rab11rab5pabab12ra6pa13r0 (0.81) ...10rab11rab5paa12rab6paa13r0 (0.86) ...10rab11rab5pabab12ra6pb13r0 (0.79) . . .10rab11rab5pab12rab6pbb13r0 (0.57) . . .10rab11rab5paba12ra6paa13r0 (0.86) . . .10rab11rab5pabab12ra6pa13r0 (0.76) . . .10rab11rab5paa12rab6paa13r0 (0.24) ...10rab11rab5paba12ra6pa13ra (0.20) . . .10rab11rab5pa12ra6paab13ra (0.12) . . .10rab11rab5paa12rab6pba13r0 (0.34) . . .10rab11rab5pab12rab6pbb13r0 (0.11) . . .10rab11rab5paba12ra6pa13rb (0.07)

+

X R a3R+

b3D c3P 15R+ A1P 23D 15P 23P 25R+

33R+

a

. . .10rab11rab5pab12rab6pab13r0 (0.04) . . .10rab11rab5paba12rab6pa13r0 (0.40) . . .10rab11rab5pa12rab6paab13r0 (0.03) . . .10rab11rab5paba12rab6pa13r0 (0.42) . . .10rab11rab5pab12ra6paab13r0 (0.03) . . .10rab11rab5pab12ra6pbab13r0 (0.03) . . .10rab11rab5paa12rab6pab13r0 (0.29) . . .10rab11rab5pab12ra6paab13r0 (0.06) . . .10rab11rab5paab12ra6pa13ra (0.20) . . .10rab11rab5pa12ra6paba13ra (0.12) . . .10rab11rab5paa12rab6pab13r0 (0.23) . . .10rab11rab5paab12ra6pa13rb (0.07)

Values in parentheses are the coefficients squared of CSF associated with the electronic configuration.

present results and the measurements; on the other hand, to verify the rationality of spectroscopic parameters and to estimate the resident errors behind the calculations, we must discuss the convergence of present calculations with respect to the basis set and level of theory. Due to length limitation, in Table 3, we only collect the spectroscopic parameters of the two states calculated by the icMRCI and icMRCI+Q methods with the aug-cc-pVTZ (AVTZ), AVQZ, and AV5Z basis sets and the extrapolation to the CBS limit using the AVQZ and AV5Z basis sets. It should be pointed out that the two states used for the present discussion are optionally selected. From Table 3, we can clearly see that Te of the two states converge toward the CBS limit. For the A1P state, the basis sets from the AVTZ to the AVQZ and from the AVQZ to the AV5Z raise Te by 97.9 and 87.8 cm1 at the icMRCI, and raise Te by 105.8 and 98.3 cm1 at the icMRCI+Q level of theory, respectively. It reminds us that Te of the A1P state may quickly converge with respect to the basis set. It has been proved by the extrapolation to the CBS limit. When we extrapolate the AVXZ to the AV1Z basis set, Te of the A1P state are raised by 110.1 and 125.4 cm1 for the icMRCI and icMRCI+Q calculations, respectively. Such result proves that the present calculations of A1P state have excellent convergent behavior with respect to the basis set. For the c3P state, similarly, when we extrapolate the AVXZ to the AV1Z basis set, Te of the c3P state are raised by 131.9 and 143.6 cm1 for the icMRCI and icMRCI+Q calculations, respectively. As a conclusion, we think that the Te of the A1P and c3P states is convergent with respect to the basis set at the present level of theory. Similar to the Te, the same procedure is done for the Re. As seen in Table 3, when we extrapolate the AVXZ to the AV1Z basis set, Re of the A1P state are shortened by only 0.00030 and 0.00034 nm, and Re of the c3P state are shortened by 0.00028 and 0.00032 nm

for the icMRCI and icMRCI+Q calculations, respectively. That is, the present Re results are convergent with respect to the basis set at the present level of theory. Having studied the xe of the two states, we find that the convergence also exists with respect to the basis set. In addition to the above two states, we have studied the convergent behavior with respect to the basis set and level of theory for other nine bound states of AsP molecule. Similar conclusion can be gained. In conclusion, we think that the present calculations are convergent with respect to the basis set and present level of theory. Consequently, we use the PECs obtained by the icMRCI+Q method and the extrapolation to the CBS limit for the following spectroscopic calculations. Spectroscopic parameters of the 11 K–S bound states To show clearly the relationships of all the PECs, here we depict them in Figs. 1 and 2. Careful calculations have clarified that the 33R+, c3P, 23P, 15P, and 15R+ states possess the potential barriers. As seen in Figs. 1 and 2, only the barrier of the 33R+ state is obvious. The barriers of the c3P, 23P, 15P, and 15R+ states are very small. Using the PECs determined by the icMRCI+Q/Q5+CV+DK calculations, we have evaluated the spectroscopic parameters of all the bound states by the theoretical method outlined in Section ‘Methodology’. For convenience of discussion, we divide the present 11 bound states into two categories. One is the X1R+ and A1P, which are the states with the experimental spectroscopic parameters [1–6,11] and RKR results [12]. The other is the a3R+, b3D, c3P, 15R+, 23D, 15P, 23P, 25R+, and 33R+, which are the states without the measurements so far. We collect the spectroscopic

Table 3 Convergence of spectroscopic parameters with respect to the basis set and level of theory for the A1P and c3P states. icMRCI

icMRCI+Q

Te (cm1)

Re (nm)

xe (cm1)

xexe (cm1)

Te (cm1)

Re (nm)

xe (cm1)

xexe (cm1)

A1P AVTZ AVQZ AV5Z Q5

32403.7 32501.6 32589.4 32699.5

0.21342 0.21253 0.21231 0.21201

464.48 471.67 473.71 475.34

2.36 2.78 2.89 2.09

31765.2 31871.0 31969.3 32094.7

0.21351 0.21254 0.21230 0.21196

460.71 468.63 470.71 473.66

2.00 2.06 2.06 2.06

c3P AVTZ AVQZ AV5Z Q5

26408.1 26596.4 26699.8 26831.7

0.21163 0.21079 0.21057 0.21029

478.28 485.22 487.29 489.79

3.04 2.98 3.10 2.93

25788.1 25992.8 26104.5 26248.1

0.21149 0.21057 0.21034 0.21002

477.94 486.07 488.16 490.49

2.39 2.35 2.35 2.00

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D. Shi et al. / Spectrochimica Acta Part A: Molecular and Biomolecular Spectroscopy 135 (2015) 736–746

Potential energy /Hartree

8

9

As(2Du) + P(2Du)

-2600.70

As(4Su) + P(2Du) As(2Du) + P(4Su)

7 6

-2600.76

As(4Su) + P(4Su)

5 4

-2600.82

3

-2600.88

2 1

-2600.94

0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

Internuclear separation /nm Fig. 1. PECs of 9 K–S states of AsP molecule 1 – X1R+; 2 – a3R+; 3 – c3P; 4 – A1P; 5 – 23D; 6 – 15P; 7 – 33R+; 8 – 25R+; 9 – 35R+.

Potential energy /Hartree

67 -2600.72

8

As(4Su) + P(2Du) As(2Du) + P(4Su)

5 4

-2600.76

3

As(4Su) + P(4Su)

-2600.80 2 -2600.84

1 0.2 0.3

0.4

0.5

0.6 0.7 0.8 0.9 1.0

Internuclear separation /nm Fig. 2. PECs of 8 K–S states of AsP molecule 1 – b3D; 2 – 15R+; 3 – 17R+; 4 – 23P; 5 – 23R+; 6 – 25P; 7 – 15D; 8 – 25D.

results the of X1R+ and A1P states in Table 4, and tabulate the spectroscopic parameters of the a3R+, b3D, c3P, 15R+, 23D, 15P, 23P, 25R+, and 33R+ states in Table 5.

X1R+ and A1P states As pointed out above, some measurements [1–6,11] and RKR data [12] are available for the X1R+ and A1P states. Due to the length limitation, here we only tabulate the selected measurements [3,6,11] and RKR data [12] in Table 4 for convenience of comparison.

As tabulated in Table 2, the dominant valence configurations of the X1R+ and A1P states can be represented by 10rab11rab 5pabab12rab6p013r0 and 10rab11rab5pabab12ra6pb13r0 near the equilibrium positions, respectively. Therefore, the electronic transition between the X1R+ and the A1P state can be regarded as arising from the 12r ? 6p electron promotion. As seen in the literature, only the transitions between X1R+ and A1P state have extensively been observed. As seen in Table 4, the present theoretical prediction of energy separation between the X1R+ and the A1P state is 32285.4 cm1, which agrees favorably with the measurements of 32417.05 cm1 [11]. The difference between them is only 131.7 cm1. Four groups of calculations [7–10] have reported the spectroscopic parameters of AsP molecule so far. By comparison, we find that few spectroscopic parameters are closer to the measurements [3,11] and RKR results [12] than the present ones. For example, for the X1R+ state, no other Re and De [7–10] are closer to the measurements [3,11] and RKR data [12] than the present ones. Only the theoretical xe available in Refs. [7,8] are closer to the measurements [11] than the present one. For the A1P state, no other Te and xe are closer to the measurements [11] than the present ones. As for the Re, only the result obtained by Toscano and Russo [7] is superior to the present one in quality when compared with the measurements [11]. On the whole, the present results are slightly closer to the experimental ones [11] than those obtained by Zhang et al. [9]. By comparison between the present calculations and those [7,8], we find that these studies [7,8] dismissed some important corrections such as core–valence correlation correction and Davidson correction. Thus, the present spectroscopic results should be more reliable than those available in Refs. [7,8]. For the X1R+ state, the present xe of 601.54 cm1 is in fair agreement with the measurements of 604.02 cm1 [11], and their difference is only 2.48 cm1 (0.41%). The present Re of 0.20121 nm agrees well with the measurements of 0.1999 nm [11], and their difference is also only 0.00131 nm (0.66%). As for the De, we think that the result obtained by Gingerich et al. [3] should be more reliable than that by Leung et al. [6], since the latter was determined at a concentration of 0.3% by volume in argon. Obviously, the present De of 4.3614 eV is closer to the measurements [3] and RKR data [12] than any other theoretical ones [7,10]. However, the present xexe of 3.83 cm1 is in very poor agreement with the measurements of 2.04 cm1 [6] and 1.98 cm1 [11]. For the A1P state, the present xe is 471.80 cm1, which deviates from the measurements of 475.52 cm1 [11] only by 3.72 cm1 (0.78%). The present Re is determined to be 0.21154 nm, which deviates from the measurements of 0.2100 nm [11] only by 0.00154 nm (0.73%). Different from the

Table 4 Comparison of the spectroscopic parameters obtained by the icMRCI+Q/Q5+CV+DK calculations with available experimental and theoretical results for the X1R+ and A1P states. Te (cm1)

De (eV)

Re (nm)

xe (cm1)

xexe(cm1)

102 xeye(cm1)

Be (cm1)

104 ae(cm1)

X R Exp. [3] Exp. [6]a Exp. [11] RKR [12] Theor. [7]b Theor. [8] Theor. [9] Theor. [10]

0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0

4.3614 4.4474 ± 0.1304 5.9616 – 4.46 ± 0.15 5.79 – – 4.2823

0.20121

601.54

3.83

30.60

0.18999

7.09

0.19995 0.1999

627 604.02

2.04 1.98

– –

0.19265 0.1925

8.0 8.0

0.19849 0.20194 0.2023 0.20194

603 604.1 594.9 598.60

1.895 1.984

0.6442 –

0.1878 0.18862

7.82 7.49

A1P Exp. [11] Theor. [7]b Theor. [9]

32319.4 32417.05 28545 32624

3.0892 – 5.72 –

0.21154 0.2100 0.20908 0.2124

471.80 475.52 503 470.9

2.08 2.12

4.88 –

0.17190 0.1744

9.14 9.0

1.873

0.2498

0.1704

8.86

1

a b

+

Results obtained at a concentration of 0.3% by volume in Ar. LCGTO-MP-LSD.

741

D. Shi et al. / Spectrochimica Acta Part A: Molecular and Biomolecular Spectroscopy 135 (2015) 736–746

Table 5 Comparison of spectroscopic parameters of AsP molecule obtained by the icMRCI+Q/Q5+CV+DK calculations with other theoretical results for the a3R+, b3D, c3P, 15R+, 23D, 15P, 23P, 25R+, and 33R+ states.

3

+

a R Theor. Theor. 3 b D Theor. Theor. c3P Theor. Theor. 5 + 1 R Theor. 23D 15P Theor. 23P 5 + 2 R 33R+ a

[7]a [9] [7]a [9] [7]a [9] [9]

[9]

Te (cm1)

De (eV)

Re (nm)

xe (cm1)

xexe (cm1)

102 xeye (cm1)

Be (cm1)

104 ae (cm1)

16182.5 19621 16219 21485.5 23989 22105 26534.5 24189 26668 27133.4 26749 34597.5 37440.4 37240 43186.9 44149.5 49465.8

2.3790 3.36 – 3.0092 4.53 – 2.4776 4.51 – 1.0682 – 1.4461 1.1149 – 0.4796 0.2169 0.5011

0.22058 0.21220 0.2221 0.21888 0.21331 0.2201 0.20967 0.20860 0.21066 0.24682 0.2481 0.24661 0.23553 0.2366 0.23769 0.32688 0.25038

436.91 476 427.6 457.72 519 452.4 487.44 544 486.5 315.20 305.5 320.48 323.88 311.0 294.19 160.15 424.02

1.89

1.06

0.15811

7.90

1.898 1.54

0.02924 1.23

0.1558 0.16056

8.24 7.21

1.618 1.90

0.3081 4.58

0.1588 0.17498

7.54 8.76

2.117 1.40 0.919 1.27 2.25 2.002 2.99 0.89 15.22

0.1602 7.48 7.84 1.25 5.53 1.352 16.50 16.88 176.62

0.1733 0.12629 0.125 0.12648 0.13866 0.1374 0.13617 0.07209 0.12234

9.13 7.23 9.05 6.96 9.61 9.74 12.87 3.79 31.22

Results obtained by the LCGTO-MP-LSD approach.

X1R+, the present xexe of 2.08 cm1 for the A1P state compares well with the measurements of 2.12 cm1 [11]. On the whole, such comparison indicates that the present spectroscopic results should achieve high quality. We think that the reasons for achieving such high-quality spectroscopic parameters may be several aspects. Two main reasons are as follows. One is that the core–valence correlation and scalar relativistic corrections are included into the calculations. The other is that the residual errors behind the basis sets are eliminated by the extrapolation to the CBS limit. a3R+, b3D, c3P, 15R+, 23D, 15P, 23P, 25R+, and 33R+ states No experimental results can be available in the literature for these states. And only two groups of calculations [7,9] were performed in the past several decades. We collect the present spectroscopic parameters determined by the icMRCI+Q/Q5+CV+DK calculations together with the only theoretical ones [7,9] in Table 5 for convenience of discussion. Of the nine states, the 33R+ possesses relatively high potential barrier near 0.27575 nm. The well depth is 4041.64 cm1, and the barrier height is 7379.21 cm1. As seen in Fig. 1, the energy of this well at its equilibrium position is obviously larger than that at its dissociation limit. Calculations have determined that this well possesses 11 vibrational states, which vibrational levels are 171.66, 489.99, 806.78, 1170.15, 1549.22, 1894.55, 2248.92, 2624.88, 3066.24, 3498.56, and 3913.45 cm1 for t = 0–10, respectively. To some extent, this state can be observed in an experiment, though it may be unstable. We expect that some experiments will be done in the near future so that some results proposed here can be validated. The detailed PECs have shown that each of the c3P, 23P, 15P, and 15R+ states only possesses a small barrier. The barrier heights are 498.20, 601.79, 109.33, and 196.78 cm1, and the barrier positions are at 0.35142, 0.34427, 0.39068, and 0.36535 nm for the c3P, 23P, 15P, and 15R+ states, respectively. As shown in Figs. 1 and 2, the wells of these states are very deep, and the energies of these wells at their respective equilibrium positions are obviously smaller than those at their respective dissociation limits. In addition, calculations have obtained that each of these four states possesses more than ten vibrational states. For example, the 23P state possesses the 21 vibrational states, which vibrational levels are 146.33, 434.00, 714.21, 987.01, 1251.74, 1507.84, 1754.79, 1992.01, 2219.36, 2438.37, 2657.61, 2883.82, 3100.46, 3271.14, 3421.81, 3541.46, 3620.50, 3665.52, 3713.41, 3765.66, and 3823.24 cm1 for t = 0–20, respectively. From this point, we think that these four states should be stable and are not difficult to be

observed in an experiment. In addition, as seen in Table 5, the magnitudes of present Te, Re, and xe can be comparable with those determined by Zhang et al. [9]. As pointed out above, the two groups of results are both close to the measurements [11]. The 25R+ state possesses the shallowest well. Even for such a shallow well, it still possesses the 12 vibrational states, which vibrational levels are 79.83, 237.65, 392.19, 543.38, 691.20, 835.75, 977.04, 1115.07, 1250.11, 1382.18, 1511.07, and 1636.50 cm1 for t = 0–11, respectively. Therefore, this state is also stable and is not difficult to be observed in an experiment. Spectroscopic parameters of the 32 X bound states With the SO coupling effect included, the first dissociation channel of the molecule does not split. Its second and third dissociation channels split into four dissociation asymptotes. And its fifth dissociation channel splits into four dissociation asymptotes, of which only the As(2D3/2) + P(2D3/2) is involved here. Table 6 collects the dissociation relationships of all the possible X states generated from the six dissociation asymptotes. In the present work, the SO coupling effect is accounted for by the state interaction method with the Breit-Pauli Hamiltonian. The calculations are performed at the level of icMRCI theory with the all-electron aug-cc-pCVTZ (ACVTZ) basis set. From that, the PECs of 59 X states involved here are obtained. It should be pointed out that all the SO coupling calculations are made across the entire PEC of each X state. The all-electron ACVTZ basis set with the Breit-Pauli Hamiltonian and the all-electron ACVTZ basis set with no Breit-Pauli Hamiltonian are used to calculate the SO coupling contribution. The difference between the two energies generates the SO coupling energy. Adding the SO coupling splitting energies to the icMRCI+Q/Q5+CV+DK results, we obtain the final PEC of each X state. We have calculated the energy separation relative to the lowest dissociation channel for each higher dissociation asymptote, and collected these results in Table 6. For convenience of discussion, Table 6 also tabulates the experimental energy separation [17] between each of the higher dissociation asymptotes and the lowest one. As seen in Table 6, ten X states (X1R+0+, a3R+1, a3R+0, 15R+2, 15R+1, 5 + 1 R0+, 17R+3, 17R+2, 17R+1, and 17R+0) belong to the lowest dissociation channel, As(4S3/2) + P(4S3/2). Ten X states (25R+2, 25R+1, 25R+0+, 23R+0, 23R+1, c3P0+, c3P0, 15P3, 15P2, and 15P1) are attributed to the As(2D3/2) + P(4S3/2) dissociation channel. Fourteen X states (b3D3, b3D2, b3D1, 15P0+, 15P0, 15P1, c3P2, c3P1, 15D4, 15D3, 15D2, 15D1, 15D0+, and 15D0) correlate to the As(2D5/2) + P(4S3/2)

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D. Shi et al. / Spectrochimica Acta Part A: Molecular and Biomolecular Spectroscopy 135 (2015) 736–746

Table 6 Dissociation relationships of possible X states obtained by the icMRCI+Q/Q5+CV+DK+SO calculations.

X states

As(4S3/2) + P(4S3/2) As(2D3/2) + P(4S3/2) As(2D5/2) + P(4S3/2) As(4S3/2) + P(2D3/2) As(4S3/2) + P(2D5/2) As(2D3/2) + P(2D3/2)

3, 3, 4, 3, 4, 3,

2 2 3 2 3 2

(2), (2), (2), (2), (2), (2),

Relative energy (cm1)

1 1 2 1 2 1

(3), (3), (3), (3), (3), (3),

0+ (2), 0 (2) 0+ (2), 0 (2) 1 (3), 0+ (2), 0 (2) , 1 0+ (2), 0 (2) 1 (3), 0+ (2), 0 (2), 1 0+ (2), 0 (2)

dissociation channel. Ten X states (35R+2, 35R+1, 35R+0+, 23D3, 23D2, 23D1, 33R+1, 33R+0, 23P0+, and 23P0) belong to the As(4S3/2) + P(2D3/2) dissociation channel. Fourteen X states (25P3, 25P2, 25P1, 25P0+, 25P0, 25P1, 23P2, 23P1, 25D4, 25D3, 25D2, 25D1, 25D0+, and 25D0) correlate to the As(4S3/2) + P(2D5/2) dissociation channel. In addition, ten X states correlate to the As(2D3/2) + P(2D3/2) dissociation asymptote, for which only the A1P1 state is studied in this paper due to the length limitation. Here, the PECs of 59 X states are depicted in Figs. 3–8 and their respective dissociation asymptotes are labeled in the same figure. As seen in Fig. 4, the PECs of 35R+0+ and 25D0+ states are almost overlapped together. As seen in Fig. 6, the PECs of 35R+1 and 25D4 states are also almost superposed. Due to the length limitation, here we do not depict each of them in a separate figure. Altogether, there are 32 X bound states among the 59 X states involved here. Using the PECs obtained by the icMRCI+Q/ Q5+CV+DK+SO calculations, we have evaluated the spectroscopic parameters (Te, Re, xe, and De) of these X bound states by the method given in Section ‘Methodology’. These spectroscopic

This work

Exp. [17]

0.0 10270.7 10849.4 11235.3 11516.2 22275.0

0.0 10592.5 10914.6 11361.7 11376.5 21954.2

13 12 11 5

-2600.676

Potential energy /Hartree

States of separate atom

10

-2600.728

9 8

-2600.780

7

-2600.832

3

6

As(4D3/2) + P(4D3/2) As(4S3/2) + P(4D5/2) As(4S3/2) + P(4D3/2) As(4D5/2) + P(4S3/2) As(2D3/2) + P(4S3/2) As(4S3/2) + P(4S3/2)

4 2 1

-2600.884

0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

Internuclear separation /nm Fig. 5. PECs of 13 X states of AsP molecule for X = 1 1 – a3R+1; 2 – b3D1; 3 – 15R+1; 4 – c3P1; 5 – A1P1; 6 – 17R+1; 7 – 23D1; 8 – 15P1; 9 – 23P1; 10 – 23R+1; 11 – 25P1; 12 – 15D1; 13 – 25D1.

10

-2600.64

9

-2600.70

6 -2600.76

5

-2600.82

3 2

7 8

As(4S3/2) + P(4D5/2) As(4S3/2) + P(4D3/2) As(4D5/2) + P(4S3/2) As(4D3/2) + P(4S3/2)

4

As(4S3/2) + P(4S3/2)

1

-2600.88

0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

Internuclear separation /nm Fig. 3. PECs of 10 X states of AsP molecule for X = 0 1 – a3R+0; 2 – c3P0; 3 – 15P0; 4 – 17R+0; 5 – 23P0; 6 – 23R+0; 7 – 33R+0; 8 – 25P0; 9 – 15D0; 10 – 25D0.

Potential energy /Hartree

910 -2600.70 6 5 4

-2600.76

8 7

3 -2600.82

As(4S3/2) + P(4D5/2) As(4S3/2) + P(4D3/2) As(4D5/2) + P(4S3/2) As(4D3/2) + P(4S3/2) As(4S3/2) + P(4S3/2)

2

-2600.88 -2600.94

1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

Internuclear separation /nm

Fig. 4. PECs of 10 X states of AsP molecule for X = 0+ 1 – X1R+0+; 2 – c3P0+; 3 – 15R+0+; 4 – 15P0+; 23P0+; 6 – 25R+0+; 7 – 15P0+; 8 – 15D0+; 9 – 35R+0+; 10 – 25D0+.

-2600.67

Potential energy /Hartree

Potential energy /Hartree

567

-2600.70 -2600.73

4 3 2

-2600.76 1 -2600.79

As(4S3/2) + P(2D5/2) As(4S3/2) + P(2D3/2) As(2D5/2) + P(4S3/2) As(2D3/2) + P(4S3/2)

0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

Internuclear separation /nm Fig. 6. PECs of 7 X states of AsP molecule for X = 1, 1 and 4 1 – 15P1; 2 – 25R+1; 3 – 25P1; 4 – 33R+1; 5 – 15D4; 6 – 35R+1; 7 – 25D4.

parameters are collected in Tables 7–9 together with available measurements [4]. At the same time, the state compositions of each X state near the equilibrium position are also tabulated in Tables 7–9. It should be pointed out that the 23R+, 35R+, 17R+, 15D, 25D, and 25P are still the repulsive states with the SO coupling effect included. Of these six repulsive states, the 17R+, 15D, 25D, and 25P states are found to be inverted. We divide the present 32 X bound states into three categories according to their symmetries for convenience of discussion. The first group is the eleven X states generated from the X1R+, a3R+, 15R+, 25R+, and 33R+ states. The second group is the fifteen X states generated from the c3P, A1P, 15P, and 23P states. And the last group is the six X states generated from the b3D and 23D states. Eleven X states generated from the X1R+, a3R+, 15R+, 25R+, and 33R+ states Table 7 tabulates the spectroscopic parameters of eleven X states generated from the X1R+, a3R+, 15R+, 25R+, and 33R+ states.

D. Shi et al. / Spectrochimica Acta Part A: Molecular and Biomolecular Spectroscopy 135 (2015) 736–746

1112

Potential energy /Hartree

9

10

-2600.72

As(4S3/2) + P(2D5/2) As(4S3/2) + P(2D3/2)

8 6

-2600.76

As(2D5/2) + P(4S3/2) As(2D3/2) + P(4S3/2)

5

7

4

-2600.80

As(4S3/2) + P(4S3/2)

3 -2600.84

2 1 0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

Internuclear separation /nm Fig. 7. PECs of 12 X states of AsP molecule for X = 2 1 – b3D2; 2 – c3P2; 3 – 15R+2; 4 – 23D2; 5 – 15P2; 6 – 23P2; 7 – 17R+2; 8 – 25P2; 9 – 25R+2; 10 – 15D2; 11 – 35R+2; 12 – 25D2.

6

Potential energy /Hartree

-2600.70

7

-2600.73 4

5

3

As(2D5/2) + P(4S3/2) As(2D3/2) + P(4S3/2)

2

As(4S3/2) + P(4S3/2)

-2600.76 -2600.79

As(4S3/2) + P(2D5/2) As(4S3/2) + P(2D3/2)

-2600.82 -2600.85

1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

Internuclear separation /nm

Fig. 8. PECs of 7 X states of AsP molecule for X = 3 1 – b3D3; 2 – 23D3; 3 – 15P3; 4 – 17R+3; 5 – 25P3; 6 – 15D3; 7 – 25D3.

Meanwhile, Table 7 also collects the dominant K–S state compositions of each X state near the equilibriums position for convenience of discussion. The dominant state composition of the X1R+0+ X component is almost pure near the equilibrium position. As shown in Tables 4 and 7, Re is the same for the X1R+ and X1R+0+ states. The differences of xe and De between the X1R+ and X1R+0+ states are only 0.06 cm1 and 0.0002 eV, respectively. Thus, the effect of SO coupling on the Re, xe, and De is small. For the a3R+ state, Te of the a3R+1 component is smaller than, and Te of the a3R+0 is larger than that of the a3R+ state. Thus, the a3R+ is an inverted state. Similar to the X1R+0+, the dominant state compositions of a3R+1 and a3R+0 components are also

743

almost pure. As a result, the effect of SO coupling on the Re, xe, and De is still small. In detail, the energy splitting in the a3R+ state is only 38.6 cm1, and the largest deviations of Re, xe, and De from those of the a3R+ state are only 0.00002 nm, 0.33 cm1, and 0.007 eV, respectively. For the a3R+0 state, Te obtained by Rasanen et al. [4] is 16417.6 cm1, which is larger than the present one by 224.4 cm1. Here, we should notice that the measurements [4] were made in the solid Ne matrix, not in the gas phase. Similar to the a3R+ state, the dominant state compositions of the 33R+1 and 33R+0 components also almost keep pure. As a result, the energy splitting in the 33R+ state is only 15.2 cm1, and the differences of the Re, xe, and De between the 33R+1 and the 33R+0 state are only 0.00012 nm, 0.29 cm1, and 0.0048 eV, respectively. Thus, the effect of SO coupling on the spectroscopic parameters of the 33R+ state is tiny. The 15R+ is a regular state. The dominant K–S state compositions of 15R+0+ and 15R+1 components slightly mix with the 23D state, whereas those of the 15R+2 state are almost pure around the equilibrium positions. The energy separation between the 15R+0+ and the 15R+1 state is 195.6 cm1, and the energy separation between the 15R+1 and the 15R+2 state is 79.4 cm1. Thus, the effect of SO coupling on the energy splitting in the 15R+ state is obvious. The deviations of Re, xe, and De from those of the 15R+ state are 0.00002 nm, 0.70 cm1, and 0.0074 eV for the 15R+0+; the deviations of Re, xe, and De from those of the 15R+ state are 0.00005 nm, 0.26 cm1, and 0.0205 eV for the 15R+1; and the deviations of Re, xe, and De from those of the 15R+ state are 0.00075 nm, 2.19 cm1, and 0.0164 eV for the 15R+2 state, respectively. On the whole, the effect of SO coupling on the Re, xe, and De is small. As for the 25R+ state, the dominant K–S state compositions of each X component slightly mix with the c3P and 15P states near the equilibrium positions. The energy separations between the two neighboring X states from the 25R+0+ to the 25R+2 are 6.8 and 19.2 cm1, which are very small when compared with those of the 15R+ and a3R+ states. In addition, the differences of Re between the two neighboring X states from the 25R+0+ to the 25R+2 are only 0.00030 and 0.00041 nm, and the differences of xe between the two neighboring X states from the 25R+0+ to the 25R+2 are also only 1.16 and 0.97 cm1. According to these, we think that the effect of SO coupling on the spectroscopic parameters of 25R+ state is tiny. In conclusion, (1) only the a3R+ is an inverted state with the SO coupling effect taken into account; (2) the effect of SO coupling on the spectroscopic parameters of the X1R+, a3R+, 25R+, and 33R+ states is small, whereas the effect on the energy splitting in the 15R+ state is pronounced. Fifteen X states generated from the c3P, A1P, 15P, and 23P states Table 8 collects the spectroscopic parameters of fifteen X states generated from the c3P, A1P, 15P, and 23P states, and also tabulates the dominant K–S state compositions of each X state

Table 7 Spectroscopic parameters determined by the icMRCI+Q/Q5+CV+DK+SO calculations for the 11 X states generated from the X1R+, a3R+, 15R+, 25R+, and 33R+ states.

1

+ 0+ + 1 + 0

X R a3R a3R Exp. [4] 15R+0+ 15R+1 15R+2 25R+0+ 25R+1 25R+2 33R+0 33R+1 a

Te (cm1)

Re (nm)

xe (cm1)

De (eV)

Dominant K–S state compositions near the Re (%)

0.0 16154.6 16193.2 16417.6a 26938.6 27134.2 27213.6 44143.9 44150.7 44169.9 49454.3 49469.5

0.20121 0.22056 0.22057 – 0.24680 0.24677 0.24757 0.32563 0.32593 0.32634 0.24934 0.24946

601.48 437.24 436.94 439.7a 315.90 314.94 313.01 160.98 159.82 160.79 424.02 424.31

4.3616 2.3860 2.3812

X1R+ (99.9) a3R+ (99.54), 15P (0.4) a3R+ (99.9)

1.0756 1.0887 1.0846 0.2223 0.2222 0.2179 0.4988 0.5036

15R+ 15R+ 15R+ 25R+ 25R+ 25R+ 33R+ 33R+

Results obtained in the solid Ne matrix.

(96.91), 23D (3.00) (97.68), 23D (2.24) (99.96) (98.28), c3P (0.97), 15P (0.69) (98.28), c3P (0.97), 15P (0.69) (97.9), c3P (1.36), 15P (0.64) (99.33), 23R+ (0.53), 25P (0.10) (99.44), 25P (0.46)

744

D. Shi et al. / Spectrochimica Acta Part A: Molecular and Biomolecular Spectroscopy 135 (2015) 736–746

Table 8 Spectroscopic parameters determined by the icMRCI+Q/Q5+CV+DK+SO calculations for the 15 X states generated from the c3P, A1P, 15P, and 23P states.

3

c P0 c3P0+ Exp. [4] c3P1 c3P2 A1P1 15P3 15P2 15P1 15P0+ 15P0 15P1 23P0 23P0+ 23P1 23P2 a

Te (cm1)

Re (nm)

xe (cm1)

De (eV)

Dominant K–S state compositions near the Re (%)

26141.8 26187.5 25969.0a 26486.6 26815.0 32380.3 37206.2 37318.9 37336.9 37461.9 37595.6 37623.7 43185.1 43185.6 43233.6 43245.9

0.21101 0.21021

486.65 487.58

2.5273 2.5223

c3P (99.68), b3D (0.28) c3P (99.88)

0.21208 0.21198 0.21155 0.23500 0.23548 0.23528 0.23550 0.23562 0.23563 0.23783 0.23783 0.23781 0.23755

488.45 485.57 472.05 327.29 326.55 323.56 323.06 324.55 324.74 289.65 289.60 291.04 294.78

2.4901 2.4478 3.0853 1.1406 1.1270 1.1248 1.1114 1.0979 1.0944 0.4815 0.4814 0.4784 0.4769

c3P (94.32), 23D (5.04), b3D (0.34), 11D (0.25) c3P (99.88) A1P (99.45), c3P (0.36), 23D (0.10) 15P (99.65), 23D (0.22) 15P (99.52), 23P (0.28), c3P (0.11) 15P (99.11), 23P (0.36), 23D (0.27), c3P (0.16) 15P (99.28), 23P (0.32), 23D (0.22), c3P (0.12). 15P (99.52), 23P (0.28) 15P (99.65), 23D (0.22) 23P (99.66), 15P (0.32) 23P (99.64), 15P (0.32) 23P (99.49), 15P (0.38) 23P (99.66), 15P (0.28)

Result obtained in the solid Ne matrix.

Table 9 Spectroscopic parameters determined by the icMRCI+Q/Q5+CV+DK+SO calculations for the 6 X states generated from the b3D and 23D states.

3

b D3 b3D2 b3D1 Exp. [4] 23D1 23D2 23D3 a

Te (cm1)

Re (nm)

xe (cm1)

De (eV)

Dominant K–S state compositions near the Re (%)

21472.1 21476.2 21497.3 21714.1a 34500.8 34608.3 34638.4

0.21889 0.21889 0.21887 – 0.24753 0.24736 0.24709

457.51 457.52 457.44 461.2a 319.37 320.89 319.24

3.0138 3.0138 3.0107

b3D (99.76), c3P (0.14) b3D (99.80), c3P (0.16) b3D (99.77), c3P (0.14)

1.4606 1.4473 1.4446

23D (99.18), 15P (0.79) 23D (99.31), 15P (0.6) 23D (99.18), 15P (0.77)

Results obtained in the solid Ne matrix.

near the equilibrium positions. As seen in Table 8, the main K–S state composition of A1P1 component is almost pure near the equilibrium position, and the effect of SO coupling on its spectroscopic parameters is tiny. The c3P is a regular state. As seen in Table 8, between the two neighboring X states from the c3P0 to the c3P2, the energy separations are 45.7, 299.1, and 328.4 cm1; the differences of Re are 0.0008, 0.00187, and 0.0002 nm; the differences of xe are 0.93, 0.87, and 2.88 cm1; and the differences of De are 0.005, 0.0322, and 0.0423 eV, respectively. According to these, we think that the effect of SO coupling on the Re and xe is small, but the effect of SO coupling on the energy separation and De is large. As tabulated in Table 8, the present Te of c3P0+ state is 26187.5 cm1, which is larger than the measurements [4] of 25969.0 cm1 by 218.5 cm1. As pointed out above, such measurements [4] were made still in the solid Ne matrix, not in the gas phase. So, the present difference between theory and experiment [4] is easily understood. Now we discuss the effect of SO coupling on the spectroscopic parameters of 15P state. As seen in Tables 5 and 8, Te of the 15P3, 15P2, and 15P1 X states are smaller than, but Te of the 15P0+, 15P0, and 15P1 states are larger than that of the 15P state. According to this, the 15P is an inverted state. The dominant K–S state composition of each X state keeps almost pure near the equilibrium positions. On the whole, the effect of SO coupling on the spectroscopic parameters of 15P state is not obvious. Only the energy separations between the two neighboring X states are slightly large. The 23P is a regular K–S state. Similar to the X components generated from other P states, the dominant K–S state composition of each X state yielded from the 23P state is also almost pure. To our surprise, the energy separation between the 23P0 and the 23P0+ state is only 0.5 cm1, and the energy separation between the 23P0+ and the 23P1, and between the 23P1 and the 23P2 state are also only 48.0 and 12.3 cm1, which are very tiny. As clearly

shown in Table 8, the effect of SO coupling on the Re and xe is not obvious for the 23P state. As a conclusion, (1) only the 15P is the inverted state; (2) on the whole, the effect of SO coupling on the spectroscopic parameters of the c3P, A1P, 15P, and 23P states are not obvious except for the energy splitting and dissociation energy of the c3P state. Six X states generated from the b3D and 23D states Table 9 collects the spectroscopic parameters of six X states generated from the b3D and 23D states. Similar to Tables 7 and 8, we still tabulate the dominant K–S state compositions of each X state around the equilibrium positions in Table 9 for convenience of discussion. Obviously, the K–S state compositions of each X component generated from the b3D and 23D K–S states keep almost pure near the equilibrium positions. Similar to the a3R+ and 15P, the b3D is also an inverted state. Because the dominant K–S state compositions of each X component are almost pure around the equilibrium positions, the effect of SO coupling on the spectroscopic parameters is small. It can be clearly seen by comparison of the Re and xe collected in Tables 5 and 9. The energy separation between the b3D3 and b3D2 states is only 4.1 cm1, and the energy separation between the b3D2 and b3D1 states is only 21.1 cm1, which are very small when compared with those of the c3P and 15R+ states. In addition, Te of the b3D1 state is 21497.3 cm1, which compares well with the measurements [4] of 21714.1 cm1 obtained in the solid Ne matrix. The differences of xe between the two neighboring X states from the b3D3 to the b3D1 are 0.01 and 0.08 cm1, and the largest deviation of xe of these X components from that of b3D state is 0.28 cm1. To some extent, we can say that the effect of SO coupling on the xe is very tiny. The present xe of b3D1 state is 457.44 cm1, which is in good accord with the measurements [4] of 461.2 cm1 obtained in the solid Ne matrix. The discussion demonstrates that the present calculations are accurate. In

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Table 11 Radiative lifetimes of the transitions from the a3R+1, c3P1, and A1P1 X states to the X1R+0+ X state for several low vibrational states. Transitions

3

a +1–X1 c3 1–X1 A1 1–X1

R P P

Fig. 9. TDM versus internuclear separation for the A1P1–X1R+0+, a3R+1–X1R+0+ and c3P1–X1R+0+ transitions.

addition, the largest deviation of Re from the b3D state is only 0.00001 nm for the b3D3, b3D2, and b3D1 states. On the whole, the effect of SO coupling on the Te, Re, and xe of the b3D state is very small. Different from the b3D, the 23D is a regular state. The energy separation between the 23D1 and the 23D2 state is 107.5 cm1, but the energy separation between the 23D2 and the 23D3 state is only 30.1 cm1. Compared with that of the b3D state, the effect of SO coupling on the energy splitting in the 23D state is relatively large. The difference of Re between the two neighboring X states is 0.00027 nm, and the largest deviation of the Re from that of the 23D state is 0.00092 nm, which is not large. Similarly, the conclusion can be gained that the effect of SO coupling on the xe is not obvious on the whole. In conclusion, (1) the b3D is an inverted state with the SO coupling effect included; and (2) the effect of SO coupling on the spectroscopic parameters of b3D and 23D states is not large on the whole. Transition properties For the sake of length limitation, here we briefly study the spectroscopic transition properties of three transitions, a3R+1–X1R+0+, c3P1–X1R+0+, and A1P1–X1R+0+. For this reason, we calculate the transition dipole moments (TDMs) versus internuclear separation

+ 0+ + 0+ + 0+

R R R

Radiative lifetimes (ls)

t0 = 0

t0 = 1

t0 = 2

t0 = 3

t0 = 4

1480 4120 8.56

1460 4080 8.64

1450 4130 8.73

1480 4200 8.75

1560 4230 8.80

for the three transitions, and depict these results in Fig. 9. It should be pointed out that the TDMs shown in Fig. 9 are obtained by the Breit-Pauli Hamiltonian with the all-electron ACVTZ basis set at the icMRCI level of theory. From Fig. 7, we can clearly see that the largest TDMs of the a3R+1–X1R+0+ and c3P1–X1R+0+ transitions are less than 0.015 a.u. over a small internuclear separation range near the equilibrium position, which is consistent with the fact that the singlet–triplet transitions are forbidden. We employ the following formula [32] to calculate the radiative lifetime for a given vibrational t0

st0 ¼ ðAt0 Þ1 ¼ ¼

64p

4 ja 0

3h g0  2P 3 g 00  e  TDMj t0 qt0 ;t00 ðDEt0 ;t00 Þ

4:936  105 g0  ; 2P 3 g 00 jTDMj t0 qt0 ;t00 ðDEt0 ;t00 Þ

ð3Þ

where qt0 , t00 denotes the Franck–Condon factor. TDM is the averaged TDM in atomic unit. g0 and g00 are the degeneracy of upper and lower states, respectively. The energy separation DEv0 , v00 is in cm1 and the radiative lifetime sv0 is in s. Using the PECs determined by the icMRCI+Q/Q5+CV+DK+SO calculations, with the help of LEVEL Program [33], we have evaluated the Frank–Condon factors at different vibrational levels for the a3R+1–X1R+0+, c3P1–X1R+0+, and A1P1–X1R+0+ transitions. For the lowest five vibrational levels of the transitions selected here, we have also evaluated their radiative lifetimes. For convenience of discussion, we collect these results in Tables 10 and 11, respectively. On the one hand, as demonstrated in Table 10, for the a3R+1–X1R+0+ transition, only the transition for the t0 from 3-3 is very strong. Other transitions, such as 0-3, 0-4, 0-5, 0-6, 0-7, 1-2, 1-3, 2-2, 3-1, and 4-1 are weak, whereas the rest transitions collected in Table 10 are very weak since their Frank–Condon factors are very small. As collected in Table 11, the radiative lifetimes of the 0-0, 1-1, 2-2, 3-3, and 4-4 transitions are very long. Similar to the a3R+1–X1R+0+

Table 10 Frank–Condon factors for the a3R+1–X1R+0+, c3P1–X1R+0+, and A1P1–X1R+0+ transitions of the AsP molecule.

3

a R

+ 1 1–X

R

t00 = 0

t00 = 1

t00 = 2

t00 = 3

t00 = 4

t00 = 5

t00 = 6

t00 = 7

t00 = 8

0.0019 0.0103 0.0289 0.0563 0.0861

0.0137 0.0519 0.0978 0.1197 0.1031

0.0466 0.1142 0.1221 0.0641 0.0090

0.1019 0.1381 0.0530 0.8780 0.0335

0.1597 0.0880 0.0000 0.0000 0.0696

0.1904 0.0168 0.0446 0.0507 0.0085

0.1795 0.0052 0.0924 0.0002 0.0242

0.1376 0.0608 0.0576 0.0744 0.0671

0.0876 0.1231 0.0043 0.0143 0.0214

0.2355 0.3688 0.2294 0.1057 0.0413

0.3483 0.0410 0.0680 0.1884 0.1777

0.2530 0.0760 0.1541 0.0051 0.0603

0.1181 0.2312 0.0000 0.1236 0.0727

0.0371 0.1858 0.1325 0.0048 0.0436

0.0072 0.0762 0.2182 0.0304 0.1140

0.0007 0.0180 0.1361 0.1797 0.0011

0.0000 0.0025 0.0475 0.1856 0.0933

0.0000 0.0003 0.0111 0.0935 0.1857

0.1531 0.2705 0.2545 0.1689 0.0891

0.2970 0.1178 0.0003 0.0830 0.1583

0.2786 0.0031 0.1443 0.0833 0.0002

0.1677 0.1305 0.0734 0.0221 0.1153

0.0723 0.2104 0.0055 0.1263 0.0107

0.0237 0.1576 0.1201 0.0284 0.0697

0.0061 0.0754 0.1823 0.0247 0.0906

0.0013 0.0260 0.1317 0.1364 0.0016

0.0002 0.0069 0.0061 0.1621 0.0613

+ 0+

t0 = 0 t0 = 1 t0 = 2 t0 = 3 t0 = 4 c3P1–X1R+0+

t0 = 0 t0 = 1 t0 = 2 t0 = 3 t0 = 4 A1P1–X1R+0+

t0 = 0 t0 = 1 t0 = 2 t0 = 3 t0 = 4

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transition, only few transitions for the c3P1–X1R+0+ and A1P1–X1R+0+ are strong, though the A1P1–X1R+0+ transition is not forbidden.

Conclusions In this paper, the PECs of 17 K–S and 59 X states have been studied for internuclear separations from about 0.1 to 1.10 nm using the CASSCF method, which is followed by the icMRCI and icMRCI+Q approaches. Of these 17 K–S states, the X1R+, a3R+, 15R+, and 17R+ states correlate to the first dissociation channel. The 23R+, 25R+, c3P, 15P, b3D, and 15D state correlate to the second dissociation channel. The 33R+, 35R+, 23P, 25P, 23D, and 25D states correlate to the third dissociation channel. Only the A1D state correlates to the fifth dissociation channel of AsP molecule. In addition, the 23R+, 35R+, 17R+, 15D, 25D, and 25P are found to be the repulsive states, and the a3R+, 15P, b3D, 17R+, 15D, 25D, and 25P are found to be the inverted states. The SO coupling effect is accounted for by the Breit-Pauli Hamiltonian with the all-electron ACVTZ basis set. To obtain more reliable results, the effect of core–valence correlation and scalar relativistic corrections on the PECs is included. Core–valence correlation correction is calculated by the cc-pCVTZ basis set. Scalar relativistic corrections are incorporated by the DKH3 approximation at the level of a cc-pVTZ basis set. The spectroscopic parameters of 11 K–S and 32 X bound states have been calculated, and compared in detail with those available in the literature. Excellent agreement has been found between the present results and the measurements. On the whole, the effect of SO coupling on the spectroscopic parameters is not obvious except for few states such as 15R+ and c3P. The analyses show that the spectroscopic properties of the 11 K–S states and 32 X states reported in this paper can be expected to be reliably predicted ones, and can be used as good references for the future laboratory research and theoretical work. Acknowledgments This work was sponsored by the National Natural Science Foundation of China under Grant No. 11274097, the Program for Science and Technology of Henan Province in China under Grant No. 122300410303 and the Natural Science Foundation of Education Bureau of Henan Province in China under Grant No. 2010B140013.

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