Ab initio calculations on the ground and low-lying excited states of InI

MOLECULAR PHYSICS, 1OCTOBER 23, VOL. 11, NO. 19, 2963 2968 Ab initio calculations on the ground and low-lying excited states of InI WENLI ZOU, MEIRONG LIN*, XINZHENG YANG and BAOZHENG ZHANG Institute of Modern Optics, Opto-electronic Information Science and Technology Laboratory, EMC, Nankai University, Tianjin 371, PR China (Received 4 March 23; revised version accepted 9 July 23 Potential energy curves (PECs of the ground and the low-lying excited states of the InI molecule are computed using the internally contracted multireference singles and doubles configuration interaction with the Davidson correction (ic-mr-cisd þ Q method based on the relativistic effective core potentials (RECPs. The spectroscopic constants are obtained, including the excitation energy (T e, the equilibrium bond distance (R e, the dipole moment (m e and the vibrational constants (! e and! e e. Finally, we predict the transition dipole moments, the radiative lifetimes, and the Franck Condon factors for the transitions of A 3 þ X 1 þ þ and B3 1 X 1 þ þ. The results reveal that A3 þ and B 3 1 are long-lived states with the lifetimes being of the order of microseconds. 1. Introduction The indium monohalides have been attracting interest in their unique physical and chemical properties for a long time. They play important roles in the development of new semiconductor devices in high-frequency and optoelectronic applications. In chemical vapour deposition techniques such as the Effer process [1], indium monohalides act as gas-phase transporters of semiconductor materials [2, 3]. There are many experimental studies on the low-lying electronic states of indium monohalides, which extend and deepen our comprehension of the properties of the electronic states of these molecules. These molecules have been of great value for searching laser media and semiconductors. Wehrli and Miescher [4 7] carried out the early experimental spectroscopic studies on InI, the two bands of A 3 þ X 1 þ and B 3 1 X 1 þ being observed. Moreover, they found a C 1 state at about 31 5 cm 1 as well. Thereafter, Barrett and Mandel [8] measured the spectroscopic constants of the ground state using microwave technology, and Barrow [9] got the dissociation energy (D e of InI. All of these early experimental data are summarized in [1] in detail. After this, Vempati and Jones [11 13] obtained the newest spectroscopic constants by analysing the rotational structure of the A XandB X bands, and researched the D e and the potential energy curves (PECs of the X, A and B states experimentally. Using these experimental results, Bharate et al. [14] computed the *Author for correspondence. e-mail: linzh@nankai.edu.cn Rydberg Klein Rees (RKR curves of the X and A states. In a more recent experimental study on InI, King et al. [15] observed the absorption spectra and laserinduced fluorescence (LIF spectra of the A X, B X and C X bands, and studied the D e of the ground state. The theoretical works on InI have focused mainly on its ionization energy [16] and spectroscopic constants of the ground state [17, 18]. However, there seems to be no theoretical concern about its low-lying excited states. The main goal of the present paper is to study the PECs, obtain the spectroscopic constants and predict the transition properties of the low-lying electronic states of InI. 2. Computational details After complete active space self-consistent-field (CASSCF calculations, we compute the energies of the electronic states for a series of given bond lengths using the internally contracted multireference singles and doubles configuration interaction (ic-mr-cisd [19 21] with the Davidson correction ( þ Q [22, 23]. Both steps are carried out in C 2v point group symmetry. The PECs are obtained by connecting the calculated points with the aid of the avoided crossing rule between electron states of the same C 1 v point group symmetry. The spectroscopic constants, including the excitation energy (T e, the equilibrium bond length (R e, the vibrational constants (! e and! e e, the dipole moment (m e and the dissociation energy (D e, are obtained. Molecular Physics ISSN 26 8976 print/issn 1362 328 online # 23 Taylor & Francis Ltd http://www.tandf.co.uk/journals DOI: 1.18/26897311614246

2964 W. Zou et al. We employ the relativistic effective core potentials (RECPs with the spin orbit coupling of Metz et al. [24, 25], which include the outer 21 electrons for the indium atom and the outer seven electrons for the iodine atom in the valence space, respectively, and the valence Gaussian basis sets of (12s12p9d/[6s6p4d] [24] and (6s6p1d/[3s3p1d] [26] are used for In and I, respectively. As active space, nine molecular orbitals are selected which are in correspondence with the In 5s5p6s and I 5s5p shells. The outermost 5s 2 5p 1 electrons of In and 5s 2 5p 5 electrons of I are placed in the active space, and the 1 electrons in the 4d shells of In are used for some core valence correlations, while the rest of the electrons are frozen. That is to say, there are 2 electrons altogether used in the correlation energy calculations. All the computations are performed using the MOLPRO 22 software package [27]. The spectroscopic constants are evaluated by using Le Roy s LEVEL program [28]. All the computations are performed on a PC LINUX computer with a Pentium IV 2. GHz CPU. 3. Results and discussion 3.1. Potential energy curves and spectroscopic constants of low-lying -S states Table 1 shows the dissociation relationships for the possible low-lying -S electronic states of InI. The computed PECs are plotted in figure 1. It can be seen that only the ground state, the 3 state, and four Rydberg states are bound, whereas the others are repulsive. The fitted spectroscopic constants of the six bound states are summarized in table 2. The ground state X 1 þ is characterized mainly by the closed-shell configuration 1s 2 2s 2 1p 4 3s 2. The calculated! e is 174.2 cm 1, which is in good agreement with the experimental figure of 176.86 cm 1 [12]; whereas the calculated R e is.51 A larger than the experimental value of 2.754 A [12]. The calculated D e is 3.54 ev, a little higher than the experimental figure of 3.44 ev [1]. There are two states of 3 and 1 arising from the dominant configuration of 1s 2 2s 2 1p 4 3s 1 2p 1. Experimentally, only two components of the 3 (namely A 3 þ and B 3 1 are observed, lying at 24 42.91 and 25 5.6 cm 1 [12], respectively. The computed excitation energy is 24 527.4 cm 1, being closer to the energy of the A 3 þ state. Compared with the experimental values! e ¼ 158.5 cm 1 and R e ¼ 2.71 A of the A 3 þ state, the computed! e ¼ 165.84 cm 1 matches well, whereas the theoretical R e of 2.751 A is a bit larger. The 1 is the proverbial C state. However, no potential well is obtained. Four Rydberg states of 1 ðiiiþ, 3 þ ðiiiþ, 1 þ ðiiiþ and 1 ðiiiþ are also obtained, lying at 44 968.9, 55 69.64, 56 48. and 56 88.64 cm 1, respectively. None of these Rydberg states has been observed experimentally. 3.2. Potential energy curves and spectroscopic constants of low-lying states Table 3 shows the dissociation limits for the possible low-lying states and the corresponding energy separations. Compared with table 1, the dissociation limit In( 2 P þ I( 2 P splits into four asymptotes, namely 2 P 1/2 þ 2 P 3/2, 2 P 3/2 þ 2 P 3/2, 2 P 1/2 þ 2 P 1/2 and 2 P 3/2 þ 2 P 1/2, while In( 2 S þ I( 2 P splits into 2 S 1/2 þ 2 P 3/2 and 2 S 1/2 þ 2 P 1/2. Altogether there are 31 states correlating with these six asymptotes. The calculated atomic energy splittings of 191 ( 2 P 3/2 2 P 1/2 of In and 72 cm 1 ( 2 P 1/2 2 P 3/2 of I are in agreement with the Table 1. Atomic state (In þ I 2 P þ 2 P (6s 2 S þ 2 P 3 C 1 Π 3 Π 1 Σ 1 Σ (ΙΙΙ 1 3 1 Π(ΙΙΙ (ΙΙΙ 3 Π(ΙΙΙ 1 Σ (ΙΙ 3 Π(ΙΙ (ΙΙ Χ 1 Σ 1 Π(ΙΙ In( 2 P I( 2 P In( 2 S I( 2 P Figure 1. Potential energy curves for the low-lying -S states of the InI molecule: singlet ( and triplet (- - -. Table 2. Dissociation relationships of some low-lying -S states of InI. -S state 1 þ (2, 3 þ (2, 1, 3, 1 (2, 3 (2, 1, 3 1 þ, 3 þ, 1, 3 Spectroscopic constants of low-lying -S states of InI. State T e (cm 1 R e (Å! e (cm 1! e e (cm 1 X 1 þ. 2.85 174.2.39 3 24 527.4 2.751 165.84.547 3 (III 44 968.9 3.277 171.1 2.434 3 þ (III 55 69.64 3.384 98.28 1.769 1 þ (III 56 48. 2.748 169.41 1.81 1 (III 56 88.64 3.111 12.87 1.772

Ground and low-lying excited states of InI 2965 Table 3. Dissociation relationships of some low-lying states of InI. Energy (cm 1 Atomic state (In þ I state Theory Expt. [29] 2 P 1/2 þ 2 P 3/2 2, 1, 1, þ, 2 P 3/2 þ 2 P 3/2 3, 2, 2, 1, 1, 1, 191 2213 þ, þ,, 2 P 1/2 þ 2 P 1/2 1, þ, 72 763 2 P 3/2 þ 2 P 1/2 2, 1, 1, þ, 8912 9816 (6s 2 S 1/2 þ 2 P 3/2 2, 1, 1, þ, 3 527 24 373 (6s 2 S 1/2 þ 2 P 1/2 1, þ, 37 529 31 976 splitting of 3 527 cm 1 ( 2 S 1/2 2 P 1/2 of In seems much larger than the experimental value of 24 373 cm 1 [29]. We have plotted the PECs of seven states of ¼ þ in figure 2, while the other seven states with ¼ are given in figure 3. Eleven states with ¼ 1 are shown in figure 4, and the PECs of five states of ¼ 2 and one state of ¼ 3 symmetries are drawn in figure 5. The spectroscopic constants and the dominant compositions of a few low-lying states are reported in table 4. For the closed-shell ground state X þ that is mainly composed of X 1 þ, the spin orbit effect can be ignored. The R e and! e with spin orbit correction are close to the above -S results, while the D e is 3.37 ev, showing a little improvement. 3 Figure 2. A 3 Π Χ 1 Σ I( 2 P 1/2 I( 2 P 3/2 I( 2 P 1/2 I( 2 P 1/2 I( 2 P 3/2 I( 2 P 3/2 Ω= Potential energy curves of InI: low-lying ¼ þ states. In( 2 S 1/2 I( 2 P 1/2 I( 2 P 3/2 I( 2 P 1/2 I( 2 P 1/2 3 C 1 Π 1 In( 2 P B 3 3/2 I( 2 P 3/2 Π 1 I( 2 P 3/2 Χ 1 Σ Ω=1 Figure 4. Potential energy curves of InI: low-lying ¼ 1 states (ground þ state curve is shown by the dashed line. observed values of 2213 and 763 cm 1 [29], whereas the I( 2 P 1/2 I( 2 P 3/2 I( 2 P 3/2 3 I( 2 P 1/2 I( 2 P 1/2 I( 2 P 3/2 I( 2 P 3/2 3 I( 2 P 1/2 I( 2 P 3/2 I( 2 P 3/2 Χ 1 Σ Ω= - Figure 3. Potential energy curves of InI: low-lying ¼ states (ground þ state curve is shown by the dashed line. Χ 1 Σ Ω=2 Ω=3 Figure 5. Potential energy curves of InI: low-lying ¼ 2 and 3 states (ground þ state curve is shown by the dashed line.

2966 W. Zou et al. Table 4. Spectroscopic constants of low-lying states of InI. State T e (cm 1 R e (Å! e (cm 1! e e (cm 1 m e (Debye Dominant -S states at the corresponding R e X 1 þ þ. 2.87 172.54.29 3.33 X1 þ (99.4, 3 (.4, 1 þ (II(.1 (. (2.754 (176.86 (.33 3 2 415.73 2.77 151.6.675 1.53 3 (97.5, 3 þ (1.4, 1 (1., 3 þ (II(.1 A 3 þ 24 183.28 2.763 156.86.72 1.64 (24 42.91 (2.71 (158.5 (1.59 B 3 1 24 85.85 2.777 146.93.656 1.49 (25 5.6 (2.729 (146.36 (2.2 3 2 25 768.28 2.78 146.76.559 1.49 C 1 1 31 15.32 (31 5 1.52 3 ðiiiþ 43 782.2 3.286 154.5 1.82 2.85 3 þðiiiþ 43 978.33 3.278 159.75 1.921 2.36 3 1 (III 44 576.11 3.282 159.95 2.62 2.86 3 2 (III 45 497.55 3.28 157.11 1.385 2.89 3 (97.9, 3 (1.3, 1 þ (II(.4, 1 þ (.3 3 (96.4, 3 (1.7, C 1 (1., 3 þ (.5, 3 (.3 3 (97.5, 3 (1.3, 1 (1.1 C 1 (52.4, 3 þ (38.7, 3 (5.7, 3 (2.5, 3 (.5, 1 (II(.2 3 (III(98.5, 1 (.8, 3 þ (.6 3 (III(93.8, 3 (II(4.6, 3 (.9, 1 þ (II(.4, 3 (.2, 1 þ (.1 3 (III(98.5, 3 (.6, 3 (.5, 3 þ (.3 3 (III(98.6, 3 (.7, 1 (.7 3 þ ðiiiþ 55 132.3 3.385 13.4.898 4.1 3 þ (III(99.7, 3 (II(.2, 3 (III(.1 3 þ 1 ðiiiþ 55 75.4 3.378 88.3 2.443 3.74 3 þ (III(94.4, 1 (III(5.4, 3 (II(.1, 1 (II(.1 1 þ þðiiiþ 56 585.38 2.749 157.78.768 1.25 1 þ (III(99.9 1 1 (III 56 744.95 3.94 125.17 3.289.8 1 (III(58.9, 3 þ (III(4.8, 1 (II(.1, 3 (III(.1 Figures in parentheses are experimental values from references [12] (for the X, A and B states and [4] (for the C state. Moreover, we computed the electric dipole moment as 3.33 Debye. The four components of, þ, 1 and 2 are mainly composed of the first excited state of 3, and their energies increase in the order as, þ, 1 and 2 near their equilibrium bond lengths. Experimentally, only the two states A þ and B1 have been found with the energy separation of 647.69 cm 1 [12], which is in good agreement with our result of 622.57 cm 1. Furthermore, the computed splittings of þ and 1 2 are 167.55 and 962.43 cm 1, respectively. For the A and B states, the calculated excitation energies and frequencies match well with the observed values, whereas the R e values are.5 A larger. As can be seen in figure 5, there is an avoided crossing between the 3 2 state and a mixed ¼ 2 state (55.2% 3 and 41.% 1 at about 3.3 A, which is similar to that of the TlCl molecule [3]. When R > 3.3 A, the dominant composition of the first ¼ 2 state will not be 3, whereas the 3 2 state will be the second ¼ 2 state which dissociates to 2 P 3/2 þ 2 P 3/2. Relative to the deep potential well components of the X 1 þ and 3 states, the C 1 1 state has a shallow potential well. Wehrli and Miescher [4] obtained its energy of about 31 5 cm 1, and King et al. [15] also observed the continuous absorption band of C 1 X 1 þ in the region of 315 35 nm. However, there is no potential well obtained in our calculations. So, only the vertical excitation energy of the C 1 1 state is computed at the experimental R e of the ground state. Table 4 gives the energy of 31 15.32 cm 1, which matches the experimental value. It may be noted that in figure 1 there is a 3 þ state crossing with the C 1 state at about 2.9 A, and both the former and the latter have an ¼ 1 component. As a result of the avoided crossing rule between two ¼ 1 states and the mixture of them, the PEC shape of the C state will obviously be changed. By examining the compositions, it is found that C 1 1 has a strong mixture with the 3 þ 1 state. Similar to the first excited state 3, the Rydberg state 3 ðiiiþ splits into four components in the increasing energy order of, þ, 1 and 2. Also, the 3 þ ðiiiþ state splits into and 1. The transitions from these to the ground state have not been observed experimentally, hence their degrees of agreement are not known. 3.3. Transition properties The dipole transitions from A 3 þ and B 3 1 to X 1 þ are allowed, and figure 6 shows the computed þ transition moments as a function of the bond distance. The radiative lifetimes of the A and B states for given vibrational levels which can be evaluated from the

Ground and low-lying excited states of InI 2967 Table 5. Computed radiative lifetimes of two transitions at different vibrational levels. Radiative lifetimes (ms Transitions v ¼ v ¼ 1 v ¼ 2 v ¼ 3 A 3 þ X 1 þ þ.961.94.922.95 B 3 1 X 1 þ þ 1.171 1.174 1.179 1.185 Table 6. Calculated Franck Condon factors between the excited and the ground state of InI. ¼ 1 2 3 4 5 6 A 3 þ X 1 þ þ ¼.776.175.4.8.1.. 1.216.466.214.79.2.4.1 2.8.341.31.199.17.32.9 3..17.419.213.165.125.43 B 3 1 X 1 þ þ ¼.898.81.18.2... 1.11.752.99.4.6.1. 2..161.678.87.62.9.3 3.1.3.187.647.64.83.1 Transition moment (a.u..4.35.3.25.2.15.1.5. Figure 6. A 3 Π Χ 1 Σ B 3 Π 1 Χ 1 Σ 2.4 2.6 2.8 3. 3.2 3.4 Calculated transition moments for the A 3 þ X 1 þ þ and B3 1 X 1 þ þ transitions. dipole transition moments are given in table 5. It can be seen that the lifetimes of both states are of the order of microseconds. Finally, the predicted Franck Condon factors for the A 3 þ X 1 þ þ and B 3 1 X 1 þ þ transitions are shown in table 6, whereas there are no experimental data at present. Acknowledgement This work is supported by the National Natural Science Foundation of China (Project No. 698781. References [1] EFFER, D., 1965, J. Electrochem. Soc., 112, 12. [2] DONNELLY, V. M., and KARLICEK, R. F., 1982, J. appl. Phys., 53, 6399. [3] KARLICEK, R. F., HAMMARLUND, B., and GINOCCHIO, J., 1986, J. appl. Phys., 6, 794. [4] WEHRLI, M., and MIESCHER, E., 1933, Helv. Phys. Acta, 6, 457. [5] WEHRLI, M., and MIESCHER, E., 1934, Helv. Phys. Acta, 7, 298. [6] WEHRLI, M., 1934, Helv. Phys. Acta, 7, 611. [7] WEHRLI, M., 1936, Helv. Phys. Acta, 9, 587. [8] BARRETT, A. H., and MANDEL, M., 1958, Phys. Rev., 19, 1572. [9] BARROW, R. F., 196, Trans. Faraday Soc., 56, 952. [1] HUBER, K. P., and HERZBERG, G., 1979, Molecular Spectra and Molecular Structure, Vol. IV, Constants of Diatomic Molecules (New York: Van Nostrand- Reinhold. [11] VEMPATI, S. N., and JONES, W. E., 1986, J. molec. Spectrosc., 12, 441. [12] VEMPATI, S. N., and JONES, W. E., 1987, J. molec. Spectrosc., 122, 19. [13] VEMPATI, S. N., and JONES, W. E., 1988, J. molec. Spectrosc., 127, 232. [14] BHARATE, N. S., BHARTIYA, J. B., and BEHERE, S. H., 1994, Indian J. Phys. B, 68, 79. [15] KING, K. K., HERRING, C. M., and EDEN, J. G., 1999, J. chem. Phys., 111, 931. [16] ROSEN, A., and ELLIS, D. E., 1975, J. chem. Phys., 62, 339. [17] DOBBS, K. D., and HEHRE, W. J., 1986, J. comput. Chem., 7, 359. [18] MARTIN, J. M. L., and SUNDERMANN, A., 21, J. chem. Phys., 114, 348.

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