Excited States of SnSi: A Configuration Interaction Study - The Journal

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J. Phys. Chem. A 2010, 114, 7248–7256

Excited States of SnSi: A Configuration Interaction Study Susmita Chakrabarti and Kalyan Kumar Das* Department of Chemistry, Physical Chemistry Section, JadaVpur UniVersity, Kolkata 700 032, India ReceiVed: April 12, 2010; ReVised Manuscript ReceiVed: June 1, 2010

Electronic structure and spectroscopic properties of the ground and low-lying excited states of SnSi within 4 eV have been investigated by using a multireference singles and doubles configuration interaction (MRDCI) method that includes relativistic effective core potentials. Potential energy curves of a number of Λ-S states of singlet, triplet, and quintet spin multiplicities are constructed. Spectroscopic parameters (Te, re, ωe, De, and µe) of 27 bound Λ-S states are reported. The ground state of SnSi belongs to the X3Σ- symmetry with an estimated dissociation energy (De) of 2.49 eV. However, with the inclusion of the spin-orbit coupling, De reduces to 2.11 eV. Spectroscopic properties of at least 36 Ω states are determined. Transition probabilities of several singlet-singlet and triplet-triplet transitions are calculated. Partial radiative lifetimes of some of these transitions are estimated. A number of weak Ω-Ω transitions with partial radiative lifetimes of the order of milliseconds or more is also predicted here. 1. Introduction Elements of group IV have interesting electronic properties and important practical applications. There are large number of studies relating the structure and energetics of small molecules containing group IV elements. Silicides are technologically important because of their potential uses in semiconductor and optoelectronics industries.1–6 The low electrical resistivity of silicides in combination with higher thermal stability, electromigration resistance, and excellent diffusion barrier characteristics make it a viable alternative in microelectronic applications.7 The epitaxially grown alloy systems SnxSi1-x are predicted to have direct and tunable energy gaps for Sn composition exceeding some critical concentration.8,9 Although the lightest representative of the group IV diatomic silicides, GeSi, has been the subject of many experimental and theoretical investigations,10–19 much less is known about the heavier isovalent systems such as SnSi and PbSi. The first theoretical investigation on SnSi was carried out by Andzelm et al.12 using LCGTO-MP-LSD methodology. These authors predicted the ground state of SnSi as 3Σ- followed by 3Π and 1 + Σ low-lying excited states. They also reported spectroscopic constants of these states. The infrared absorption spectra of SnSi and GeSi molecules were observed by Li et al.14 for frequencies up to 3000 cm-1 in argon matrices at 4 K. The vibrational frequency of SnSi in solid argon was specified as 360 ( 1 cm-1. The transition to the low-lying electronic state, 3Π r X 3Σwas also observed as a vibrational progression. Recently, Ciccioli et al.20 reported the optimized molecular parameters, such as bond distance, harmonic vibrational frequency, transition energy, and dissociation energy of the ground state of SnSi at the CCSD level of theory with the aug-cc-pVTZ-pp basis set for Sn and the aug-cc-pVTZ basis set for Si. In this paper, we report high-level calculations to investigate spectroscopic properties of low-lying electronic states of SnSi by using MRDCI methodology, taking into account of the relativistic effects through the effective core potentials. Effects of spin-orbit coupling on the electronic spectrum of SnSi are * To whom correspondence should be addressed. E-mail: kkdas@chemistry. jdvu.ac.in, [email protected].

studied. Other properties, such as transition probabilities of dipole allowed and spin-forbidden transitions, radiative lifetimes, and dipole moments of the ground and some of the excited states, are also calculated and compared with the available data. 2. Computational Details The full-core average relativistic effective potentials (AREP) of Sn are taken from LaJohn et al.21 The 5s25p2 electrons of the atom are kept in the valence space, and the remaining inner electrons are described by AREP. Likewise, the 1s22s2 2p6 core electrons of the Si atom are replaced by the AREP of Pacios and Christiansen.22 The 3s3p4d primitive Gaussian basis functions of Sn, taken from LaJohn et al.,21 are augmented with a number of diffuse and polarization functions. Here we have added two s functions (ζs ) 0.0638 and 0.0251 a0-2), two p functions (ζp ) 0.0568 and 0.0202 a0-2), a set of d functions (ζd ) 0.0425 a0-2), and a set of f functions (ζf ) 0.1093 a0-2). The first two d functions are contracted with coefficients 0.333845 and 0.474286. The final contracted basis set for Sn is [5s5p4d1f]. The 4s4p primitive Gaussian functions of Pacios and Christiansen22 for Si are augmented with three s functions (ζs ) 0.04525, 0.02715, and 0.0163 a0-2), two p functions (ζp ) 0.06911 and 0.02499 a0-2), five d functions (ζd ) 4.04168, 1.46155, 0.52852, 0.19112, and 0.06911 a0-2), and two f functions (ζf ) 0.19112 and 0.06911 a0-2) from Matos et al.23 The first two sets of d functions are contracted using the contraction coefficients of 0.054268 and 0.06973. Similarly, the two f functions are contracted using the contraction coefficients of 0.29301 and 0.536102. So, the contracted basis set for Si used in the present MRDCI calculations is [7s6p4d1f]. In the initial step, self-consistent-field (SCF) calculations are carried out for the 3Σ- state of the SnSi molecule with 8 active electrons at different internuclear distances ranging from 3.0 to 20.0 a0. We have kept Sn at the origin and Si along the +z axis, and the C2V subgroup has been used for the molecular calculation. The symmetry adapted optimized SCF-MOs are subsequently used as one electron basis for the generation of configurations in the CI calculation. The MRDCI method of Buenker and co-workers24–29 with perturbative correction and energy extrapolation technique is used throughout. The table-

10.1021/jp103259y  2010 American Chemical Society Published on Web 06/15/2010

Excited States of SnSi CI algorithm30 has been employed to handle the open-shell configurations, which appear because of the excitation process. The direct CI version31 of the code has been used for computing energies and wave functions. All the relativistic effects except the spin-orbit term are incorporated in the calculation of Λ-S states through AREP. A set of reference configurations is chosen for the low-lying states of a given spin and spatial symmetry. A maximum of eight roots are optimized for 1A1, 1A2, 3A1, 3A2, and 3B1/3B2 symmetries of the molecule. On single and double excitations from these references, a large number of configurations with a maximum of the order of six million is generated. However, using a configuration-selection threshold, T ) 0.5 µhartree, the number of selected configurations is kept below 200 000. Sums of the square of coefficients of the reference configurations are always above 0.90. The energy extrapolation method24–26 is used to estimate energies at zero threshold. The neglect of the higher order excitations is partly taken care by the Davidson correction.32–34 Spectroscopic properties of the Λ-S states of SnSi are calculated from the estimated CI energies and wave functions. The spin-orbit CI calculations are carried out by allowing all the spin components of the low-lying Λ-S states to interact. The spin-orbit operators,21,22 compatible with AREP of both Sn and Si, are used for this purpose. The spin independent CI wave functions are multiplied with appropriate spin functions, 2 double group representation. The which transform as C2V diagonals of the spin included Hamiltonian matrix consist of energies of the Λ-S CI calculations, whereas the off-diagonals are calculated by using the spin-orbit operators and Λ-S CI wave functions. The Ω states of the molecule belong to the A1, 2 double group. Energies A2, and B1/B2 representations of C2V and wave functions are obtained from the diagonalization of the spin-orbit CI blocks whose dimensions are 46, 43, and 44 for A1, A2, and B1/B2, respectively. Using MRDCI energies, potential energy curves of both spin independent and spin included states of SnSi are constructed. These curves are fitted into polynomials and the corresponding one-dimensional nuclear Schro¨dinger equations are then solved by the Numerov-Cooley method35 to obtain vibrational energies and wave functions for the bound states of the molecule. Transition dipole moments for the pair of vibrational functions in a particular transition are subsequently calculated. Einstein spontaneous emission coefficients, transition probabilities, and hence the radiative lifetimes at different vibrational levels are also estimated. 3. Spectroscopic Properties of Λ-S States Ground states of both Sn and Si atoms belong to the 3Pg symmetry.36 Eighteen Λ-S states of singlet, triplet, and quintet spin multiplicities correlate with the lowest dissociation limit of SnSi. The second and third dissociation limits of SnSi are nearly degenerate. Both the limits correlate with the excited triplets of Σ+, Σ-(2), Π(3), ∆(2), and Φ symmetries of the molecule. The first excited states (1Dg) of both the atoms combine to generate 14 Λ-S singlets. The computed relative energies of the second and fourth asymptotes are 5950 and 13 400 cm-1, respectively, which compare well with the observed values. As SnSi is isoelectronic with Ge2, the electronic spectra of these two molecules are expected to be similar. Potential energy curves of 34 Λ-S states of SnSi dissociating into the lowest few limits are drawn in Figures 1a-c for triplet, singlet, and quintet spin multiplicities, respectively. Spectroscopic param-

J. Phys. Chem. A, Vol. 114, No. 26, 2010 7249 eters (Te, re, ωe, De, and µe) of 27 bound states within 34 000 cm-1 are tabulated in Table 1. The ground state of SnSi belongs to X3Σ- with a dominant configuration, σ12σ22π12. The σ1 MO is antibonding, whereas σ2 is strongly bonding comprising s and pz AOs of Sn and Si. The π1 MO is also strongly bonding combination of the px/y orbitals of the two atoms. The MRDCI estimated re of the ground state is about 0.02 Å longer than the previously reported values,12,20 whereas its vibrational frequency is comparable. The vibrational frequency determined from the infrared absorption spectrum14 of the SnSi molecule in argon matrices at 4 K is about 360 cm-1. The ground-state dissociation energy of SnSi obtained from the MRDCI calculation without spin-orbit coupling is 2.49 eV, which is much smaller than the value reported from the local spin density calculation.12 Although no experimental D00 is available, Ciccioli et al.20 predicted a dissociation energy of 2.43 eV for SnSi, which agrees well with the present value. The first excited state of SnSi is assigned as A3Π in accordance with other group IV heterodiatomic molecule. It lies only 790 cm-1 above the ground state. The transition energy and vibrational frequency of the 3Π state predicted from the local spin density calculations of Andzelm et al.12 are 810 and 378 cm-1, respectively. Li et al.14 observed a transition, 3Π r X 3Σ- as a vibrational progression from which Te was reported to be 1628.9 cm-1 with a vibrational frequency of 413.8 cm-1. The equilibrium bond length of the A 3Π state calculated in the present study is 2.443 Å with a vibrational frequency of 352 cm-1. However, Andzelm et al.12 reported a shorter bond length. The Sn-Si bond in the A 3Π state is at least 0.094 Å shorter than the ground-state bond. The larger stability of the bond in the low-lying 3Π state is quite common for this type of intragroup IV molecules and is attributed to the increased delocalization of the π1 MO. The lowest three singlets, a1∆, c1Π, and b1Σ+ are located in the range 3500-4800 cm-1. The a1∆ state originates from the same configuration as the ground state. The c1Π state has a much shorter bond length (re ) 2.448 Å) with a transition energy of 4740 cm-1. The nature of the potential energy curve and the composition of the c1Π state are comparable with those of its triplet counterpart, A3Π. The transition energy of b1Σ+ obtained in the present study is smaller than that in the previous calculation12 by about 550 cm-1, and other spectroscopic constants of the state also differ largely. Besides σ12σ22π12 (dominant), there is a significant contribution of the closed shell configuration, σ12π14 in the composition of the b1Σ+ state in the Franck-Condon region. This is due to a strong interaction with its higher root denoted as d1Σ+. Although not prominently displayed in the potential energy curves, the CI wave functions in the range 4-5 a0 confirm that there is an avoided crossing around 4.6 a0. As a result, the adiabatic curve of d1Σ+ has a comparatively larger ωe and shorter re. At the potential minimum of the d1Σ+ state, the closed shell configuration, σ21π41 dominates over σ12σ22π12. Between the lowest two 1Σ+ states there exists a strongly bound 5Π state with a potential minimum at 2.712 Å. The computed transition energy of 5Π is 7873 cm-1 and the state arises due to a σ2 f π*2 excitation. The spin components of 5Π may interact with those of the other low-lying states. Next three close-lying states, 1Σ-, 3∆, and 3Σ+ are dominated by the σ21σ22π1π*2 configuration. They have similar spectroscopic constants with longer bond lengths and smaller vibrational frequencies than the ground-state values. Two spectroscopically important states, denoted as B3Π and C3Π arise mainly due to the σ2 f π*2 excitation. Transitions from these states to X3Σand A3Π in the energy range 12 000-16 000 cm-1 are expected

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Figure 1. Potential energy curves of low-lying Λ-S states of SnSi for (a) triplet, (b) singlet, and (c) quintet spin multiplicities.

to carry sufficient intensities. The B3Π state dissociates into the ground-state fragments, while C3Π converges with the first excited state of Sn. The lower root has a shorter bond length, but their ωe values are comparable. The 21Π state has a very shallow potential energy curve, which holds only a few vibrational levels. The lowest 3Φ and 1Φ states of SnSi originate from σ12σ2π12π*2 with transition energies of 16 892 and 21 079 cm-1, respectively. The binding energy of 1Φ is about 1.5 times larger than that of its triplet counterpart. The 23Σ+ state is characterized by the σ12π13π*2 configuration. The dissociation energy of the state is estimated to be only 0.35 eV. It has a

relatively shorter equilibrium bond length due to the interaction with its lower root, 3Σ+(σ12σ22π1π*2 ). The second root of 3Σ- is dominated by the configuration arising out of a π1 f π*2 excitation. The 23Σ--X3Σ- transition may take place around 19 000 cm-1. The 23Σ- state has a much longer bond length with ωe ) 218 cm-1, which reduces Franck-Condon overlap factor for this transition. The excited 3Π states, namely 43Π and 53Π correlate with Sn(1Dg) + Si(3Pg). The potential minimum of 43Π is predicted to be at 2.803 Å having a transition energy of 22 080 cm-1. The configuration, which arises out of a σ2 f π*2 excitation,

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TABLE 1: Spectroscopic Constants of Low-Lying Λ-S States of SnSi Te (cm-1)

state 3 -

XΣ

0

A3Π 790 810a 1 a ∆ 3568 c1Π 4740 b1Σ+ 4780; 5322a 5 Π 7873 d1Σ+ 9107 1 Σ 11 187 3 ∆ 12 505 3 + Σ 12 802 B3Π 12 939 C3Π 15 907 3 Φ 16 892 23Σ+ 17 780 23Σ- 19 023 1 Φ 21 079 43Π 22 080 23∆ 23 510 21∆ 24 180 21Σ- 26 759 31Π 26 978 33Σ- 28 066 41Π 30 023 51Π 31 530 33Σ+ 32 262 25Σ- 33 475 a

re (Å)

ωe (cm-1)

2.537 344 2.519a; 2.514c 339a; 360b; 353c 2.443 352 2.372a 378a 2.592 324 2.448 337 2.570; 2.435a 254; 308a 2.712 245 2.466 400 2.934 216 2.935 216 2.944 185 2.717 254 2.742 240 2.738 251 2.728 219 2.952 218 2.770 248 2.803 209 2.681 208 2.903 226 2.622 235 2.881 169 2.670 220 3.245 155 3.286 153 2.318 496 2.536 390

De (eV)

µe (D)

2.49 3.39a; 2.43c

1.00

2.42 3.29a 2.04 1.90 1.89; 2.70a 1.51 1.36 1.10 0.94 0.90 0.88 1.25 1.00 0.35 0.87 1.53 0.49 0.31 1.15 0.66 0.80

0.97

0.43 0.24

0.81 0.97 0.79 1.02 0.91 0.51 0.51 0.48 0.79 1.00 1.00 0.61 1.60 1.22 0.94 0.89 2.11 1.35 1.27 1.32 0.33 0.33 1.09 0.23

Reference 12. b Reference 14. c Reference 20.

Figure 2. Dipole moment curves of some low-lying Λ-S states of SnSi.

TABLE 2: Relative Energies of the Ω States in the Dissociation Limit atomic states

3

dominates in the 4 Π state at equilibrium. The potential energy curve of the fifth root of 3Π shows a couple of avoided crossings. At 6.4 a0, an avoided crossing occurs between the curves of 43Π and 53Π states. The computed transition energy of the 23∆ state is 23 510 cm-1 at the equilibrium bond length of 2.681 Å. The excited 21∆ state lying close to 23∆, has a multiconfiguration character with a much longer bond length of 2.903 Å. Unlike 23∆, the singlet state dissociates into Sn(1Dg) + Si(1Dg) with a dissociation energy of 1.15 eV. Two closely spaced states, 21Σ- and 31Π are predicted in the energy range 26 500-27 000 cm-1. The Sn-Si bond in the 31Π state is at least 0.25 Å longer than the bond in 21Σ-, while the vibrational frequency is smaller by 65 cm-1. The third root of 3Σ- has a shallow potential minimum at 2.67 Å holding only 2-3 vibrational levels mainly due to an avoided crossing with its higher root. However, the state may become important from the spectroscopic point of view as its lowest vibrational level may undergo strong radiative transition to the ground state. The 33Σ+ state has a steep potential minimum followed by a barrier of 0.33 eV at the bond length of 5 a0. Among the excited quintets, only 25Σ- is bound, whereas 5 + 5 Σ , Σ , and 25Π states are repulsive dissociating into the lowest limit. The other two excited states, 25Σ+ and 5∆, predissociate into the same limit with a very small barrier. The 25Σ- state has a Rydberg character with a much shorter bond length (re ) 2.536 Å) and larger vibrational frequency of 390 cm-1. An avoided crossing of the state with its lower repulsive root is noted at 4.5 a0 (Figure 1c). The computed dipole moments (µe) of all the low-lying states of SnSi at the corresponding re are given in Table 1. Dipole moment curves of some of the low-lying states are given in Figure 2. The ground-state dipole moment of the molecule is about 1.0 D with a Sn+ Si- polarity. Most of the excited states

Ω state +

0 0-, 1 0+, 1, 2 0-, 1 0+(2), 0-, 1(2), 2 0+, 0-(2), 1(3), 2(2), 3 0+, 1, 2 0+, 0-(2), 1(3), 2(2), 3 0+(3), 0-(2), 1(4), 2(3), 3(2), 4 a

Sn + Si 3

P0 P0 3 P0 3 P1 3 P1 3 P1 3 P2 3 P2 3 P2 3

+ + + + + + + + +

3

P0 P1 3 P2 3 P0 3 P1 3 P2 3 P0 3 P1 3 P2 3

relative energy/cm-1 expt.

a

0 77 223 1692 1769 1915 3428 3505 3651

calc. 0 70 257 1721 1786 1945 3459 3544 3683

Reference 36.

have dipole moments are around one Debye with the same sense of polarity as that of the ground state. The lower dipole moment of the molecule is supported by the small electronegativity difference between of Sn and Si. The Sn-Si bond is, therefore, mostly covalent in nature in the ground as well as other lowlying states of the SnSi molecule. 4. Effects of Spin-Obit Coupling Due to spin-orbit coupling the lowest dissociation limit, Sn(3Pg) + Si(3Pg) splits into nine asymptotes which correlate with 50 Ω states of 0+, 0-, 1, 2, 3, and 4 symmetries. In the spin-orbit calculation, all the low-lying Λ-S states correlating with the lowest two dissociation limits are included. The overall spin-orbit splitting among the components of the 3P state of Sn is more than 3400 cm-1, whereas for Si it is only 223 cm-1. Relative energies of these asymptotes and their correlation with Ω states are shown in Table 2. The agreement between the computed and observed values36 is found to be very good. Figures 3a-d show the potential energy curves of the low-lying

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Figure 3. Potential energy curves of low-lying Ω states of SnSi for (a) Ω ) 0+; (b) Ω ) 0-; (c) Ω ) 1, 3; and (d) Ω ) 2, 4.

Ω states of SnSi, and Table 3 displays the fitted spectroscopic constants of 36 Ω states and their compositions at re. The zerofield-splitting in the ground state (X3Σ-) of SnSi is computed to be 115 cm-1. As a result of the spin-orbit mixing mainly with the components of A3Π, the equilibrium bond lengths of X3Σ0-+ and X3Σ1- are shortened by about 0.013 and 0.022 Å, respectively, whereas the ωe values of their adiabatic curves are decreased to some extent. The contribution of the components of A3Π in both X3Σ0-+ and X3Σ1- states is about 20%. The first excited state splits in an inverted order and the largest spin-orbit splitting is estimated to be 1476 cm-1. The A3Π1 and A3Π0+ components mix strongly with the

corresponding component of the ground state. Thus, spectroscopic parameters of these two components change to a large extent. The spin-orbit mixing in the next three singlets, a1∆2, c1Π1, and b1Σ0++, is small, and their transition energies increase only by 600-800 cm-1. The overall spin-orbit splitting among the components of 5Π is 1440 cm-1 with the 5Π-1 state lying lowest. Several avoided crossings are noted in the potential energy curves of Ω ) 1 states. The diabatic curves of 5Π-1 and 5Π1 states are fitted to calculate their spectroscopic constants, which do not deviate much from the spin-orbit coupling excluded data. In the potential energy curve of d1Σ0++, two sharp avoided crossings, one with the



TABLE 3: Spectroscopic Constants of Low-Lying Ω States of SnSi state

Te (cm-1)

re (Å)

ωe (cm-1)

composition of Λ-S state (% contribution at re)

X3Σ0-+ X3Σ 1 A 3Π 2 A 3Π 1 A3Π0A 3Π 0+ a1∆2 c1Π1 b1Σ0++ 5 Π-1 5 Π0 5 Π0 + 5 Π1 5 Π2 5 Π3 d1Σ0++ 1 -Σ0 3 ∆1 3 ∆2 3 + Σ1 3 +Σ0 B 3Π 2 3 ∆3 B 3Π 1 B 3 Π 0+ B3Π0C 3 Π 0C3Π0+ 23Σ0+C 3Π 1 C3Π2 3 Φ2 2 3 Σ+ 1

0 115 414 1512 1628 1890 4224 5443 5582 7774 8096 8206 8516 8837 9214 10 028 11 188 11 810 12 878 13 455 13 777 14 001 14 063 14 110 14 292 14 699 16 524 16 609 17 672 16 714 17 723 17 936 18 234 18 400 18 628 19 334

2.524 2.515 2.445 2.482 2.446 2.474 2.584 2.453 2.562 2.718 2.712 2.712 2.711 2.711 2.714 2.469 2.934 2.921 2.919 2.940 2.899 2.767 2.930 2.779 2.734 2.813 2.746 2.753 2.789 2.780 2.760 2.758 2.752 2.783 2.758 2.753

308 300 347 377 349 367 333 335 263 239 246 245 236 246 240 394 192 194 205 168 149 293 200 288 230 253 208 206 175 185 192 228 211 183 227 225

X3Σ-(81), A3Π(15), b1Σ+(2), 5Π(2) X3Σ-(74), A3Π(23), c1Π(2) A3Π(97), a1∆(3) A3Π(69), X3Σ-(30) A3Π(99) A3Π(72), X3Σ-(24), d1Σ+(3) a1∆(94), A3Π(5) c1Π(98), A3Π(1) b1Σ+(95), X3Σ-(4) 5 Π(96), X3Σ-(2) 5 Π(97), A3Π(2) 5 Π(96), X3Σ-(2) 5 Π(95), A3Π(2) 5 Π(97), A3Π(1), B3Π(1) 5 Π(99) d1Σ+(96), A3Π(3) 1 Σ (78), 3Σ+(2), B3Π(2) 3 ∆(99) 3 ∆(95), 5Π(2), a1∆(1) 3 + Σ (96), B3Π(2) 3 + Σ (95) B3Π(89), 3∆(8), a1∆(1) 3 ∆(96), 5Π(2) B3Π(84), 3Σ+(12), 5Π(1) B3Π(95), C3Π(2) B3Π(53), 3Σ+(25), b1Σ+(16), 23Σ+(3), C3Π(2) C3Π(92), 23Σ+(7) C3Π(97), B3Π(2) 23Σ+(88), C3Π(6), B3Π(4) C3Π(63), 21Π(34) C3Π(96), 5Σ+(2) 3 Φ(97), 3∆(1) 23Σ+(53), 21Π(31), C3Π(13), B3Π(2) 21Π(43), 23Σ+(31), C3Π(22) 3 Φ(98) 3 Φ(100)

1(XI) 3 Φ3 3 Φ4

curve of 5Π0+ around 4.65 a0 and the other with that of B3Π0+ at 5.6 a0 exist. Spectroscopic properties of 1Σ0-- remain almost unchanged. The spin-components of the 3∆ state split in a regular order with a largest splitting of 2253 cm-1. The 3∆1, 3Σ1+, and B3Π1 states undergo several avoided crossings in the bond length region 4.6-5.2 a0(Figure 3c). The spin-orbit splitting of the B3Π state in the inverted order is predicted to be about 700 cm-1. Except for B3Π0+, the spin contamination is substantially large. As a result of many curve crossings, the fitted spectroscopic constants of these components change considerably. The two spin components of the lowest 3Σ+ state are separated by 322 cm-1, and their re and ωe do not change much. The 3Σ0+state is predicted to have shorter re and smaller ωe than the other component. The excited C3Π and 3Φ states split in a regular order and the computed transition energies of their spin components lie in the energy range 16 500-19 500 cm-1. The largest spin-orbit splitting among the components of 3Φ is 1400 cm-1, and the states are found to be not much spin contaminated with others. On the other hand, the 0- and 1 components of 23Σ+ are strongly coupled in the Franck-Condon region with the nearby components. So, their spectroscopic parameters change significantly due to the spin contamination. The eleventh root of Ω ) 1 symmetry is composed of three dominant states, namely 21Π, 23Σ+, and C3Π, and its transition energy is predicted to be 18 400 cm-1. 5. Radiative Transitions and their Lifetimes Transition moments of some important dipole-allowed transitions in SnSi are computed from the MRDCI wave functions.

Electronic transitions from the excited triplets and singlets to their respective ground and low-lying states below 15 000 cm-1 are considered in the present study. The computed partial radiative lifetimes at the lowest three vibrational levels for transitions involving triplets and singlets are reported in Table 4 and 5, respectively. The A3Π-X3Σ- transition is very weak, which is reflected in the longer lifetime of the A3Π state. Transition moments for B3Π-A3Π in the Franck-Condon region are about 0.5 ea0, whereas for the B3Π-X3Σ- transition, these are negligibly small. The partial radiative lifetime for the B-A transition is predicted to be 3.04 µs. Transition probabilities of five transitions from the C3Π state are not very large. A strong transition, C3Π-X3Σ- is expected to take place around 16 000 cm-1. The total radiative lifetime of the C3Π state at V′ ) 0 is about 0.64 µs. Of five dipole-allowed transitions from the excited 43Π to the low-lying states, the 43Π-A3Π transition is the strongest with a partial lifetime in the lowest vibrational level of the order of a microsecond. Other transitions are much weaker due to their smaller transition moment values. Transition moments of three transitions from 23Σ+ to the lower states are calculated. Of these, the 23Σ+-A3Π transition is predicted to have the highest transition probability. Similarly, three symmetry allowed transitions are predicted from the 23∆ state and the estimated total lifetime of 23∆ is about 21 µs at V′ ) 0. Transition moments of 23Σ--X3Σ- and 33Σ--X3Σtransitions are found to be considerably large, making them highly probable. Their transition moment curves (Figure 4) show maxima in the bond length region 4.0-5.0 a0. The estimated radiative lifetimes for the 23Σ--X3Σ- transition at the lowest three vibrational levels are in the range 170-190 ns, whereas

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TABLE 4: Radiative Lifetime(s) of Some Excited Triplet States of SnSia total lifetime of the upper state

partial lifetime transition

V′ ) 0

V′ ) 1

V′ ) 2

V′ ) 0

A3Π-X3ΣB3Π-X3ΣB3Π-A3Π C3Π-X3ΣC3Π-A3Π C3Π-B3Π C3Π-3∆ C3Π-3Σ+ 23Σ+-A3Π 23Σ+-B3Π 23Σ+-3Σ+ 23Σ--X3Σ23Σ--A3Π 23Σ--B3Π 43Π-X3Σ43Π-A3Π 43Π-B3Π 43Π-3∆ 43Π-3Σ+ 23∆-A3Π 23∆-B3Π 23∆-3∆ 33Σ--X3Σ33Σ--A3Π 33Σ--B3Π

1.16(-1) 1.24(-2) 3.04(-6) 6.79(-5) 1.17(-3) 3.19(-2) 3.22(-2) 2.88(-3) 5.08(-5) 2.18(-4) 3.88(-2) 1.89(-7) 1.29(-3) 7.87(-6) 3.57(-4) 1.04(-6) 9.95(-5) 8.96(-3) 3.56(-3) 2.12(-5) 3.69(-3) 4.56(-3) 8.47(-8) 2.35(-5) 1.82(-5)

2.56(-2) 1.07(-2) 3.12(-6) 6.92(-5) 4.43(-4) 2.47(-2) 2.58(-2) 2.55(-3) 5.47(-5) 2.37(-4) 3.41(-2) 1.74(-7) 1.47(-3) 7.36(-6) 3.37(-4) 1.06(-6) 8.21(-5) 7.89(-3) 2.95(-3) 2.00(-5) 2.80(-3) 3.69(-3) 6.84(-8) 2.26(-5) 1.67(-5)

1.43(-2) 9.35(-3) 3.22(-6) 7.07(-5) 2.65(-4) 2.06(-2) 2.33(-2) 2.26(-2) 5.87(-5) 2.64(-4) 3.19(-2) 1.71(-7) 1.65(-3) 6.87(-6) 3.18(-4) 1.09(-6) 6.82(-5) 7.25(-3) 2.57(-3) 1.97(-5) 2.40(-3) 3.11(-3) 6.43(-8) 2.05(-5) 1.52(-6)

τ (A3Π) ) 1.16(-1) τ (B3Π) ) 3.04(-6)

a

τ(C3Π) ) 6.39(-5)

τ (23Σ+) ) 4.16(-5) τ (23Σ-) ) 1.85(-7) τ (43Π) ) 1.03(-6)

τ (23∆) ) 2.10(-5) τ (33Σ-) ) 8.40(-8) Figure 4. Transition dipole moment curves of some low-lying triplet-triplet and singlet-singlet transitions.

Values in parentheses are powers to the base 10.

TABLE 5: Radiative Lifetime(s) of Some Excited Singlet States of SnSia total lifetime of the upper state

partial lifetime transition

V′ ) 0

V′ ) 1

V′ ) 2

V′ ) 0

c1Π-a1∆ d1Σ+-b1Σ+ 21Π-a1∆ 21Π-c1Π 21Π-d1Σ+ 21Π-1Σ1 Φ-a1∆ 21∆-a1∆ 21∆-c1Π 21Σ--c1Π 21 Σ - - 1 Σ 31Π-a1∆ 31Π-c1Π 31Π-d1Σ+ 31Π-1Σ-

1.21(-3) 1.62(-3) 1.21(-2) 1.42(-3) 2.11(-3) 1.61(-3) 1.16(-4) 1.53(-7) 3.02(-3) 1.81(-3) 2.11(-3) 2.02(-2) 1.42(-4) 3.28(-3) 2.19(-6)

1.12(-3) 1.47(-3) 1.12(-2) 1.21(-3) 1.89(-3) 1.49(-3) 1.22(-4) 1.41(-7) 2.87(-3) 1.59(-3) 1.82(-3) 1.98(-2) 1.20(-4) 3.11(-3) 1.75(-6)

1.02(-3) 1.29(-3) 1.02(-2) 1.17(-3) 1.77(-3) 1.22(-3) 1.47(-4) 1.31(-7) 2.63(-3) 1.42(-3) 1.52(-3) 1.57(-2) 1.01(-4) 2.78(-3) 1.52(-6)

τ (c1Π) ) 1.21(-3) τ (d1Σ+) ) 1.62(-3) τ (21Π) ) 5.35(-4)

a

τ (1Φ) ) 1.16(-4) τ (21∆) ) 1.53(-7) τ (21Σ-) ) 9.74(-4) τ (31Π) ) 2.15(-6)

Values in parentheses are power to base 10.

for 33Σ--X3Σ- these are in between 60 and 90 ns. Thus, the 33Σ--X3Σ- transition is considered to be the strongest one predicted for SnSi. A much larger Franck-Condon overlap factor as well as larger energy separation make the transition stronger. The 33Σ--A3Π transition has also stronger probability than 23Σ--A3Π, which has a smaller Franck-Condon overlap factor due to much longer bond length of the upper state compared to the lower one. The radiative lifetimes for 23Σ--B3Π and 33Σ--B3Π at V′ ) 0 are in the microsecond order. However, the total radiative lifetimes of 23Σ- and 33Σat the lowest vibrational level are 185 and 84 ns, respectively. Transition probabilities of some singlet-singlet transitions in SnSi are also calculated. The computed partial and total

radiative lifetimes of the excited singlet states are reported in Table 5. The transition moment for c1Π-a1∆ monotonically decreases to zero at longer bond distances and is found to be fairly weak due to a very small energy gap and low Franck-Condon overlap factor. The partial radiative lifetime for the d1Σ+-b1Σ+ transition is of the order of a millisecond. All four transitions from the 21Π state are predicted to be weak with their lifetimes of the order of milliseconds or more. Of four possible transitions from 31Π, the 31Π-1Σ- transition has the largest transition probability with a lifetime of 2.2 µs at V′ ) 0. The strongest singlet-singlet transition which may be observed in SnSi at 20 600 cm-1 is due to 21∆-a1∆. The computed transition moments in the Frack-Condon region for this transition are in the range 0.6-0.8 ea0. The partial lifetime of the 21∆ state at V′ ) 0 is about 150 ns. The second transition, 21∆-c1Π, is much weaker due to smaller transition dipole moments. Two more transitions such as 21Σ--c1Π and 21Σ--1Σ- have longer lifetimes. As the spin-orbit interaction makes some changes in the potential energy curves of the excited states of SnSi, we have calculated transition probabilities of some of the Ω-Ω transitions. Most of these transitions are weak with partial lifetimes of the order of milliseconds or more (Table 6). Among the 3 3 0+-0+ transitions, B3Π0+-X3Σ0+ and C Π0+-X Σ0+ are somewhat stronger. The computed partial lifetimes for transitions from the excited 0+ states to the X3Σ1- components are larger than half a millisecond. Transitions from A3Π0+ and A3Π1 components to the ground-state components are very weak. The present calculations show that the radiative lifetimes of the spinforbidden transitions, d1Σ0++-X3Σ0-+ and d1Σ0++-X3Σ1-, are 4.2 and 3.8 ms, respectively. 6. Summary Ab initio based MRDCI calculations, which include relativistic effective core potentials of both Sn and Si atoms, are carried



TABLE 6: Radiative Lifetime(s) of Some of the Low-Lying Ω States of SnSia partial lifetime transition

V′ ) 0

V′ ) 1

V′ ) 2

A Π0+-X3Σ0-+ b1Σ0++-X3Σ0-+ 5 Π0+-X3Σ0-+ d1Σ0++-X3Σ0-+ B3Π0+-X3Σ0-+ C3Π0+-X3Σ0-+ A3Π1-X3Σ0-+ C1Π1-X3Σ0-+ 5 Π-1-X3Σ0-+ 5 Π1-X3Σ0-+ C3Π1-X3Σ0-+ 3 23Σ+ 1 -X Σ0+ 1(XI)-X3Σ0-+ A3Π1-X3Σ1 C1Π1-X3Σ1 5 3 Π-1-X Σ1 5 Π1-X3Σ1 C3Π1-X3Σ1 3 23Σ+ 1 -X Σ1 1(XI)-X3Σ1 A3Π0+-X3Σ1 b1Σ0++-X3Σ1 5 Π0+-X3Σ1 d1Σ0++-X3Σ1 B3Π0+-X3Σ1 3 3 C Π0+-X Σ1

3.90 5.87(-2) 4.61(-3) 4.16(-3) 5.86(-4) 1.49(-5) 2.11 7.11(-2) 5.87(-2) 3.11(-2) 3.92(-3) 2.11(-3) 2.88(-3) 5.52 7.62(-2) 6.12(-2) 5.12(-2) 4.97(-3) 4.33(-4) 4.11(-4) 3.11 4.12(-2) 4.87(-3) 3.81(-3) 4.82(-4) 4.11(-4)

4.31 4.90(-2) 4.23(-3) 3.97(-3) 5.16(-4) 1.22(-5) 1.87 6.91(-2) 5.11(-2) 2.87(-2) 3.81(-3) 1.81(-3) 1.87(-3) 5.10 6.79(-2) 6.01(-2) 4.79(-2) 4.26(-3) 3.57(-4) 3.97(-4) 2.87 4.01(-2) 4.39(-3) 2.88(-3) 3.99(-4) 3.87(-4)

5.62 4.37(-2) 3.99(-3) 3.86(-3) 4.89(-4) 1.02(-5) 1.41 5.87(-2) 5.01(-2) 2.19(-2) 3.57(-3) 1.70(-3) 1.09(-3) 4.99 6.21(-2) 5.67(-2) 4.10(-2) 4.01(-3) 3.21(-4) 3.88(-4) 1.98 3.87(-2) 4.11(-3) 2.12(-3) 3.98(-4) 3.12(-4)

3

a

Values in parentheses are power to base 10.

out for studying the spectroscopic properties of the diatomic tin silicide molecule in the ground and low-lying electronic states. Potential energy curves of 34 Λ-S states of the molecule are constructed from the MRDCI energies. Spectroscopic constants (Te, re, ωe, De, and µe) of 27 bound states within 4 eV are calculated. The ground state of SnSi is mainly characterized by σ12σ22π12 (85%) at re. The MRDCI estimated re of the ground state is somewhat higher than the previously reported values,12,20 but its ωe agrees well. The vibrational frequency is also supported by the experimental data from the infrared spectra14 of the molecule in rare gas matrices at 4 K. The ground-state dissociation energy of SnSi obtained from the MRDCI calculations without any spin-orbit coupling is 2.49 eV, which is comparable with the values reported in other calculations. However, the spin-orbit corrected dissociation energy of the molecule is reduced to 2.11 eV. The first excited state A3Π is only 790 cm-1 away from the ground state. The lowest three strongly bound singlets, namely, a1∆, c1Π, and b1Σ+, lie between 3500 and 4800 cm-1. The lowest 5Π state is located 7873 cm-1 above the ground state. The nearly degenerate states, 3∆ and 3 + Σ , originate from a π1 f π*2 excitation, while two important Π states, designated as B and C, exist in the range 12 900-15 900 cm-1. The lowest quintet state, 5Π is strongly bound. Except 25Σ-, most of the low-lying quintets are repulsive. The 33Σand 33Σ+ states are found to be predissociating after crossing a small barrier. The dipole moments of SnSi in different lowlying states are small, as expected from the electronegativity differences of the two atoms. The ground-state dipole moment is only 1.0 D with a Sn+Si- polarity. The overall spin-orbit splitting of the lowest dissociation limit of SnSi is estimated to be 3683 cm-1. Spectroscopic constants of many low-lying states change due to several avoided crossings. The zero-field-splitting of SnSi is calculated to be 115 cm-1. The spin components of the first excited 3Π

state split in an inverted order with an overall splitting of 1476 cm-1. The largest spin-orbit splitting of 2253 cm-1 has been reported for the 3∆ state. Of all the triplet-triplet symmetry allowed transitions, 23Σ--X3Σ- and 33Σ--X3Σ- have the highest transition probabilities. The computed partial lifetimes for the 23Σ--X3Σ- transition at the lowest three vibrational levels (V′ ) 0-2) are in the range 170-190 ns, whereas for 33Σ--X3Σ- these are 64-85 ns. The strongest singlet-singlet transition, which should be observed at 20 600 cm-1, is predicted to be 21∆-a1∆. The radiative lifetime of 21∆-a1∆ at V′ ) 0 is about 150 ns. All the spin-forbidden transitions are fairly weak and their computed lifetimes are of the order of millisecond or more. Acknowledgment. The authors thank Professor Dr. R. J. Buenker, Bergische Universita¨t, Wuppertal, Germany for the permission to use the CI codes. The financial support received from the Centre for Advanced Studies (CAS) program of the Department of Chemistry is gratefully acknowledged. S.C. thanks the CSIR, Government of India for providing the senior research fellowship. References and Notes (1) Yuen, M. J. Appl. Opt. 1982, 21, 136. (2) Lu, Z. Y.; Wang, C. Z.; Ho, K. M. Phys. ReV. B 2000, 61, 2329. (3) Jutzik, M.; Berroth, M. In Properties of Silicon Germanium and Si:Carbon; Kasper, E., Lyutovich, K., Eds.; EMIS Data Review Series No. 24 (INSPEC/IEE); London, 2000; p 342. (4) De Salvador, D.; Petrovich, M.; Berti, M.; Romanato, F.; Napolitani, E.; Drigo, A.; Stangl, J.; Zerlauth, S.; Muhlberger, M.; Schaffler, F.; Bauer, G.; Kelires, P. C. Phys. ReV. B 2000, 61, 13005. (5) Venezuela, P.; Dalpian, G. M.; da Silva Antonio, J. R.; Fazzio, A. Phys. ReV. B 2001, 64, 193202. (6) Shim, I.; Baba, M. S.; Gingerich, K. A. Chem. Phys. 2002, 277, 9. (7) Murarka, S. P. Silicides for VLSI Applications; Academic Press: New York, 1983. (8) Soref, R. A.; Perry, C. H. J. Appl. Phys. 1991, 69, 539. (9) Atwater, H. A.; He, G.; Saipetch, K. Mater. Res. Soc. Symp. Proc. 1995, 355, 123. (10) Drowart, J.; DeMaria, G.; Boerboom, A. J. H.; Inghram, M. G. J. Chem. Phys. 1959, 30, 308. (11) Huber, K. P.; Herzberg, G. Constants of Diatomic Molecules. In Molecular Spectra and Molecular Structure; Van Nostrand Reinhold, Princeton, NJ, 1979; Vol. 4. (12) Andzelm, J.; Russo, N.; Salahub, D. R. J. Chem. Phys. 1987, 87, 6562. (13) Sefyani, F. L.; Schamps, J.; Delaval, J. M. J. Mol. Spectrosc. 1993, 162, 269. (14) Li, S.; Van Zee, R. J.; Weltner, W. Chem. Phys. Lett. 1994, 229, 531. (15) Li, S.-D.; Zhao, Z.-G.; Zhao, X.-F.; Wu, H.-S.; Jin, Z.-H. Phys. ReV. B 2001, 64, 195312. (16) Sari, L.; Yamaguchi, Y.; Schaefer III, H. F. J. Chem. Phys. 2003, 119, 8266. (17) Ueno, L. T.; Marim, L. R.; Dal Pino, A., Jr.; Machado, F. B. C. Int. J. Quantum Chem. 2006, 106, 2677. (18) Wielgus, P.; Roszak, S.; Majumdar, D.; Saloni, J.; Leszczynski, J. J. Chem. Phys. 2008, 128, 144305. (19) Chakrabarti, S.; Das, K. K. J. Mol. Spectrosc. 2008, 252, 160. (20) Ciccioli, A.; Gigli, G.; Meloni, G.; Testani, E. J. Chem. Phys. 2007, 127, 054303. (21) LaJohn, L. A.; Christiansen, P. A.; Ross, R. B.; Atastroo, T.; Ermler, W. C. J. Chem. Phys. 1987, 87, 2812. (22) Pacios, L. F.; Christiansen, P. A. J. Chem. Phys. 1985, 82, 2664. (23) Matos, J. M. O.; Kello¨, V.; Roos, B. O.; Sadlej, A. J. J. Chem. Phys. 1988, 89, 423. (24) Buenker, R. J.; Peyerimhoff, S. D. Theo. Chim. Acta 1974, 35, 33. (25) Buenker, R. J.; Peyerimhoff, S. D. Theo. Chim. Acta 1975, 39, 217. (26) Buenker, R. J. Int. J. Quantum Chem. 1986, 29, 435. (27) Buenker, R. J. In Proceedings of the Workshop on Quantum Chemistry and Molecular Physics; Burton, P., Ed.; University Wollongong: Wollongong, Australia, 1980. (28) Buenker, R. J. Current Aspects of Quantum Chemistry. In Studies in Physical and Theoretical Chemistry; Carbo, R., Ed.; Elsevier: Amsterdam, 1982; Vol. 21. (29) Buenker, R. J.; Peyerimhoff, S. D.; Butscher, W. Mol. Phys. 1978, 35, 771.

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JP103259Y

Excited States of SnSi: A Configuration Interaction Study - The Journal

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