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Theoretical study of the MgSH radical
Journal of Molecular Structure (Theochem) 634 (2003) 299–304 www.elsevier.com/locate/theochem
Theoretical study of the MgSH radical A. Zaidia,*, S. Lahmara, Z. Ben Lakhdara, P. Rosmusb, J.P. Flamentc a
Laboratoire de Spectroscopie Atomique et Mole´culaire et Applications, Faculte´ des Sciences de Tunis, Tunis, Tunisia b Laboratoire de Chimie The´orique, Universite´ de Marne La Valle´e, Champs sur Marne, France c Laboratoire de Physique des Lasers, Atomes et Mole´cules, Universite´ de Lille I, Lille, France Received 25 April 2003; accepted 12 May 2003
Abstract Ab initio RCCSD(T) and MRCI calculations have been carried out for the ground and excited electronic states of MgSH. For the X2A0 state a quartic force field has been generated using the RCCSD(T) approach and spectroscopic constants for MgSH and MgSD have been obtained from standard second order perturbation theory. The bent equilibrium geometry is found to be in a reasonably good agreement with previous empirical values. The anharmonic fundamental wavenumbers (in cm21) are calculated to be 408 (MgS stretch), 470 (bending) and 2572 (SH stretch) for MgSH, whereas the lowest frequency in MgSD at 330 corresponds to the bending, the MgS stretch is calculated to lie at 421 and the SD stretch at 1867 (all values are in cm21). For the low-lying doublet and quartet excited states the Mg· · ·SH and MgS· · ·H colinear paths to dissociation asymptotes are calculated and several regions of conical intersections are located. It is found that the first two 2P lead to bent/bent Renner– Teller pairs, but their 2A0 components form a conical intersection for an apex angle around 1408. Hence all four resulting electronic components are rovibronically coupled. As in other alkaline-earth monohydrosulfide the future experimental electronic spectra between the ground and A, B and C doublet states, calculated to lie at 23000– 26000 cm21, could provide additional information about this radical. q 2003 Elsevier B.V. All rights reserved. Keywords: MgSH; RCCSD(T); Ground state; Spectroscopic constants
1. Introduction The pure rotational spectrum of MgSH (X2A0 ) was observed using milimeter-wave absorption spectroscopy in the 280 –365 GHz region and ab initio geometry optimization calculations at MP2 level of theory were performed in order to help in the search for the millimeter-wave spectrum [1]. An equilibrium * Corresponding author. Tel.: þ 216-7174-6551; fax: þ 2169865-5216. E-mail address: [email protected] (A. Zaidi).
geometry was extracted by applying the S-reduced Hamiltonian. Due to the absence of b-type transitions and spectra of the deuterated molecule it was necessary to fix the S – H bond distance to the ab initio value and only approximate r0 structure was deduced. To date, neither vibrational transitions nor information about the electronically excited states of this species have been known. The isovalent alkaline earth monohydrosulfides CaSH and SrSH were the subject of several experimental and theoretical works [2 –7]. An early computational study of the electronic states of CaSH
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[2] was found to be useful in the interpretation of the laser-induced fluorescence spectra of CaSH and SrSH from three electronically excited doublet states [3]. Later the A2A0 and B2A00 states of CaSH were investigated with higher resolution [4,5]. Accurate molecular constants obtained from rotational data were reported for CaSH in Ref. [6] and SrSH in Ref. [7]. The strongly bent structures of MgSH, CaSH and SrSH are suggestive of a significant contribution of covalent character to the ionic bond [2 –7]. Alkalineearth monohydroxides CaOH, SrOH and BaOH have linear ground states, the MgOH is quasi –linear. The aim of the present study was to calculate the quartic force field of the X2A0 electronic ground state to obtain rotational and vibrational molecular constants from second order perturbation theory. For low lying electronically excited doublet and quartet states their vertical excitation energies and their dissociation paths were investigated and several conical intersections, including one in the electronic ground state, were located.
2. Electronic structure calculations The standard correlation consistent generally contracted spdf subset of the cc-pVQZ (basis AÞ and ccpV5Z (basis BÞ basis sets of Dunning [8] for Mg and S atoms were used. For the hydrogen atom the functions of the basis A were employed. The state averaged full valence CASSCF [9,10] followed by internally contracted MRCI [11], available in the MOLPRO program suite [12], were used to calculate the excitation energies and the dissociation paths of low lying doublet and quartet states of MgSH, whereas near the equilibrium three-dimensional potential energy surface (PES) of the X2A0 state was generated by the RCCSD(T) method [13] using basis B: The equilibrium geometries of the ground state were calculated by MRCI and RCCSD(T) using both basis sets. In the state averaged full valence CASSCF computations all doublets and quartets resulting from the first four dissociation asymptotes Mg þ SH had equal weights. For the MgS þ H dissociation paths all quartet and doublet states of the seven lowest asymptotes were averaged together. In the cut of the PES’s along the bending coordinate only the three
lowest 2A0 and two 2A00 states were calculated simultaneously. In all cases the resulting CASSCF wavefunctions were used as reference wavefunctions for the internally contracted MRCI computations, the reference was selected according to a threshold of 0.05 of the CASSCF coefficient in the corresponding CI expansion. In the RCCSD(T) and in the MRCI calculations only all valence electrons were correlated, the core-valence correlation was neglected.
3. Dissociation paths Mg· · ·SH and MgS· · ·H and electronically excited states In Fig. 1 the MRCI colinear dissociation paths of all doublet and quartet states ð3x2 S; 2x2 P; 2 D; 2S2, 4 þ 4 S , P, 4D, 4S2) correlating with the four lowest asymptotes are displayed. The bent X2A0 state becomes at linearity the lowest 2Sþ state. The MRCI vertical energy difference from the bent minimum (Section 4) to linearity has been calculated to be 5680 cm21. The electronic ground state dissociates diabatically to the second asymptote. The PES crosses around RMgS ¼ 5:5 bohr the lowest 2 P state and in bent structures both 2A0 form an avoided crossing leading to a vibronic coupling between both states. As follows from Fig. 1, in colinear structures most of the electronically excited states are repulsive. For MgS distances longer than about 6 bohr the quartet and doublet states lie very close together and strong spin – orbit coupling will mix the doublet and quartet states and also other angular momenta coupling effects will complicate a detailed understanding of the long range interactions of Mg and SH. The second 2P state and the 2Sþ state correlating with the ionic asymptote are the only excited states among those treated with local minima in linear structures. The diabatic path of the second 2P state is very complex due to crossings with several other states of the same spin multiplicity but also with several quartet states. In CaSH and SrSH three electronically excited doublet states were observed experimentally [3 – 5] and it was assumed that they could correlate with doubly degenerate P states. We have, therefore, calculated the one-dimensional cuts of the two lowest 2P states of MgSH along the bending coordinate in order to find similar bound – bound
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Fig. 1. MRCI (basis A) colinear cuts of the PES’s along the Mg· · ·S dissociation path with RSH ¼ 2:53 bohr: At 4.5 bohr the order of the states is: 2 þ 2 S , P, 4Sþ, 4D, 4S2, 2Sþ, 4P and 2Sþ.
electronic transitions also in the MgSH radical. The results are shown in Fig. 2 together with the PES cut of the electronic ground state. The lower 2P state forms first a bent/linear Renner –Teller pair, but its 2A0 component possesses an avoided
crossing with the component of the same symmetry correlating with the second 2P state. The two Renner – Teller systems are vibronically coupled. In the Franck –Condon region of the bent electronic ground state one 2A0 and two 2A00 excited state also
Fig. 2. MRCI (basis A) cuts of the electronic ground state and the two lowest 2P states along the bending coordinate with bond lengths fixed at their ground state equilibrium distances (Table 2).
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Table 1 MRCI and MRCI þ Q vertical transition energies of MgSH (in cm21, basis AÞ State
MRCI
MRCI þ Q
X2A0 A 2A0 B 2A00 C 2A00 D 2A0 a 4A00 E 2 A0 F 2A00 b 4 A0 c 4A0 d 4A00 e 4A00
0.0 22926 23865 26077 31889 36646 37016 37480 37769 43214 43911 45838
0.0 23027 24838 26261 32822 38049 37297 38850 39160 44509 44698 47092
The total energies at the equilibrium geometries (Table 2) of the X2A0 state were calculated to be: 2598.008105 a.u. (MRCI) and 2598.030543 a.u. (MRCI þ Q).
have their minima. In Table 1 the MRCI and MRCI þ Davidson correction vertical excitation energies are given. The three lowest excited states lie between about 23000 –26000 cm21. The electronic transitions in CaSH were detected [3] around 15000 –16000 cm21 in SrSH [3] around 14000– 15000 cm21 and it was suggested that the electronic excitations occur in the orbitals strongly
located on the metal atom which is in accord with the calculated blue shift for MgSH. In Fig. 3 the dissociation paths MgS· · ·H for colinear structures are displayed. The ground state and the two lowest 2P states have local minima along this dissociation path. The second 2P state forms another avoided crossing with a higher state of the same symmetry. Several other electronically excited states possess local minima along this coordinate. It is interesting to note that the isomer HMgS has a 2P electronic ground state [14] minimum lying 7934.6 cm21(RCCSD(T), basis B) above the MgSH minimum. For the H migration path these cuts provide the basis for the understanding of the intramolecular dynamics in this radical. Other alkaline-earth monohydrosulfide might also have secondary P minima on the ground state potentials. 4. Electronic ground state X2A0 of MgSH and MgSD The three-dimensional PES of the electronic ground state has been mapped by RCCSD(T) and full valence MRCI methods using the atomic orbital basis A and B: The computations were done for 78 geometries in the following range: 3.8 # RMgS
Fig. 3. MRCI (basis A) colinear cuts of the PES’s along the MgS· · ·H dissociation path with RMgS ¼ 4:38 bohr:
A. Zaidi et al. / Journal of Molecular Structure (Theochem) 634 (2003) 299–304 Table 2 MRCI and RCCSD(T) equilibrium geometries of the electronic ground state of MgSH and comparison with previous theoretical and experimental results (distances in bohr and apex angle in degree) Method
RMgS
RSH
Q
MRCI/basis A MRCI/basis B RCCSD(T)/basis A RCCSD(T)/basis B MP2a Exp.a RCCSD(T)/basis Bb
4.4038 4.3840 4.4024 4.4016 4.4100 4.3780 4.405
2.5330 2.5305 2.5348 2.5381 2.5312 2.5312 2.530
91.4 91.5 92.0 91.2 91.1 87.5 89.7
a
Ref. [1]. Calculated from the A0 ; B0 and C0 constants given in the footnote of Table 3. b
# 5.4 bohr, 2:0 # RSH # 3.4 bohr and 608 , Q # 1358: The energies were fitted to sextic polynomial expansions in displacement coordinates by the SURFIT program [15]. The expansions were then transformed to quartic force fields in internal and dimensionless normal coordinates. The calculated equilibrium geometries are compared with experimental and MP2 geometries reported previously [1] in Table 2. The experimental values represent an approximate r0 structure with RSH distance fixed to calculated MP2 ReSH distance. Our values are the calculated r e structures. Whereas the SH distance varies only slightly with the methods and basis sets used, the equilibrium angle is larger by about 48 than the empirical estimate. The cc-pV5Z (basis B) MgS distance is more accurate than the MP2 value though this distance will be shortened by the core-valence electron correlation neglected in the present work. In Table 3 only the set of spectroscopic constants calculated with basis B and RCCSD(T) method from the quartic force field in dimensionless normal coordinates is presented. The corresponding quartic force field in internal coordinates is given in Table 4. The full set of a constants allowed us to calculate the r0 rotational constants which are given in the footnote of Table 3 for MgSH. The r0 geometry calculated from our re geometry is compared with the experimental estimate in Table 2. The agreement is quite satisfactory considering the fact that the neglected core-valence correlation will shorten the MgS bond length and influence also the bond angle. The first
303
Table 3 RCCSD(T) (basis B) and experimental spectroscopic constants of MgSH and MgSD (rotational constants in MHz, all other constants in cm21) MgSH Ae b Be Ce DK aA1 aB1 aC1 aA2 aB2 aC2 aA3 aB3 aC3 v1 v2 v3 x11 x22 x33 x12 x13 x23 n1 n2 n3
287189.7 6701.1 6548.3 15.6 20.29466 0.00113 0.00122 20.35998 20.00048 0.00004 0.29665 20.00011 0.00004 411.56 479.24 2674.88 21.36 22.86 248.72 1.95 22.04 28.91 408.8 470.0 2572.4
Exp.a
MgSD
289001.8 6799.6 6629.6 15.1
148342.6 6606.6 6324.9 4.402 20.13100 20.00080 0.00004 20.01931 0.00136 0.00127 0.11174 20.00015 0.00005 333.87 426.38 1920.34 0.55 21.92 225.13 22.80 25.74 0.28 330.7 421.3 1867.3
a
Ref. [1]. The RCCSD(T) r0 rotational constants are: A0 ¼ 288580:84; B0 ¼ 6692:6; C0 ¼ 6528:8 (in MHz); the masses used in the evaluations of the rotational constants were: 23.985040 (Mg), 31.972070 (S), 1.007825 (H) and 2.014 (D). b
order centrifugal distortion constant DK is calculated in good agreement with the empirical estimate. Apart from the diagonal SH stretch x33 value the other anharmonic constants are relatively small. The harmonic modes for the MgS stretch and MgSH(D) bending are strongly influenced by isotope substitution. For MgSH the v1 in Table 3 corresponds to MgS stretch and v2 to the bending, for MgSD the MgS stretch corresponds to v2 and the MgSD bending becomes the lowest vibrational mode (Table 3). The normal bending mode of both isotopomers includes also strong changes of the MgS distance. The MgS stretch is calculated to lie higher in MgSD than in MgSH by about 15 cm21. The corresponding anharmonic fundamental vibrational wave numbers for
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Table 4 RCCSD(T) (basis B) quartic force field of the X2A0 state of MgSH in internal coordinates f11 f22 f33 f12 f13 f23 f111 f222 f333 f112 f122 f113 f223 f123 f133 f233 f1111 f2222 f3333 f1112 f1222 f1122 f1113 f2223 f1123 f1223 f1133 f2233 f1233 f1333 f2333
1.4230 4.1197 0.2286 0.0092 0.0110 0.0895 25.5650 221.8100 20.1756 20.0160 20.0231 0.0211 0.0296 20.0769 0.1015 20.1201 19.2809 101.5902 0.1750 20.0830 20.1667 0.1671 20.1907 20.3668 20.0734 20.0181 20.5802 20.3692 20.0001 0.6271 20.0491
The indicies correspond to RMgS RSH and Q; all values are in ˚ 2n; factorials are excluded. aJA
both isotopomers are given as well. The zero point energy for MgSH is calculated to be 1767.4 cm21. The IR region of higher overtones and combination levels will exhibit anharmonic resonances and vibronic coupling due to the conical intersection between the electronic ground state and the first 2P state.
5. Conclusion Ab initio MRCI calculation for the ground and excited states of MgSH have been used to obtain information about the electronically excited states and their dissociation. For the ground state the RCCSD(T)
anharmonic vibrational frequencies for the fundamentals for both H/D isotopomers have been evaluated. It is found that the ground state dissociates via a conical intersection to the ground states of Mg and SH. Several other conical intersections and coupling regions between the electronically excited quartets and doublets were located. The minimum of the HMgS isomer is calculated to lie 7934 cm21 above the minimum of MgSH [14].
Acknowledgements This work has been supported by cooperation between Laboratoire de physique des lasers, atomes et mole´cules, Universite´ de Lille 1, France, Laboratoire de chimie the´orique, Universite´ Marne la Valle´e, France and Laboratoire de spectroscopie atomique et mole´culaire et applications, Faculte´ des sciences, Tunis. A.Z. thanks N. Jaidane and G. Chambaud for stimulating discussions and J.M. Robbe for his help with the calculations.
References [1] A. Taleb-Bendiab, D. Chomiak, Chem. Phys. Lett. 334 (2001) 195. [2] J.V. Ortiz, Chem. Phys. Lett. 169 (1990) 116. [3] W.T.L. Fernando, R.S. Ram, L.C. O’Brien, P.F. Bernath, J. Phys. Chem. 95 (1991) 2665. [4] C.N. Jarman, P.F. Bernath, J. Chem. Phys. 98 (1993) 6697. [5] C.T. Scurlock, T. Henderson, S. Bosely, K.Y. Jung, T.C. Steimle, J. Chem. Phys. 100 (1994) 5481. [6] A. Taleb-Bendhiab, F. Scappini, T. Amano, J.K.G. Watson, J. Chem. Phys. 104 (1996) 7431. [7] D.T. Halfen, A.J. Apponi, J.M. Thompsen, L.M. Ziurys, J. Chem. Phys. 115 (2001) 11131. [8] T.H. Dunning Jr., J. Chem. Phys. 90 (1989) 1007. [9] H.-J. Werner, P.J. Knowles, J. Chem. Phys. 89 (1988) 5803. [10] P.J. Knowles, H.-J. Werner, J. Chem. Phys. 145 (1988) 514. [11] P.J. Knowles, J. Hampel, H.-J. Werner, J. Chem. Phys. 99 (1993) 5219. [12] MOLPRO is a package of ab initio programs written by H.J.Werner, P.J. Knowles. Further information can be obtained from http://www.tc.bham.ac.uk/molpro/ [13] J.D. Watts, J. Gauss, R.J. Bartlett, J. Chem. Phys. 98 (1993) 8718. [14] A. Zaidi, S. Lahmar, Z. Ben Lakhdar, P. Rosmus, J.P. Flament, in preparation. [15] J. Senekowitsch, PhD Thesis, University of Frankfurt, 1988.
Theoretical study of the MgSH radical A. Zaidia,*, S. Lahmara, Z. Ben Lakhdara, P. Rosmusb, J.P. Flamentc a
Laboratoire de Spectroscopie Atomique et Mole´culaire et Applications, Faculte´ des Sciences de Tunis, Tunis, Tunisia b Laboratoire de Chimie The´orique, Universite´ de Marne La Valle´e, Champs sur Marne, France c Laboratoire de Physique des Lasers, Atomes et Mole´cules, Universite´ de Lille I, Lille, France Received 25 April 2003; accepted 12 May 2003
Abstract Ab initio RCCSD(T) and MRCI calculations have been carried out for the ground and excited electronic states of MgSH. For the X2A0 state a quartic force field has been generated using the RCCSD(T) approach and spectroscopic constants for MgSH and MgSD have been obtained from standard second order perturbation theory. The bent equilibrium geometry is found to be in a reasonably good agreement with previous empirical values. The anharmonic fundamental wavenumbers (in cm21) are calculated to be 408 (MgS stretch), 470 (bending) and 2572 (SH stretch) for MgSH, whereas the lowest frequency in MgSD at 330 corresponds to the bending, the MgS stretch is calculated to lie at 421 and the SD stretch at 1867 (all values are in cm21). For the low-lying doublet and quartet excited states the Mg· · ·SH and MgS· · ·H colinear paths to dissociation asymptotes are calculated and several regions of conical intersections are located. It is found that the first two 2P lead to bent/bent Renner– Teller pairs, but their 2A0 components form a conical intersection for an apex angle around 1408. Hence all four resulting electronic components are rovibronically coupled. As in other alkaline-earth monohydrosulfide the future experimental electronic spectra between the ground and A, B and C doublet states, calculated to lie at 23000– 26000 cm21, could provide additional information about this radical. q 2003 Elsevier B.V. All rights reserved. Keywords: MgSH; RCCSD(T); Ground state; Spectroscopic constants
1. Introduction The pure rotational spectrum of MgSH (X2A0 ) was observed using milimeter-wave absorption spectroscopy in the 280 –365 GHz region and ab initio geometry optimization calculations at MP2 level of theory were performed in order to help in the search for the millimeter-wave spectrum [1]. An equilibrium * Corresponding author. Tel.: þ 216-7174-6551; fax: þ 2169865-5216. E-mail address: [email protected] (A. Zaidi).
geometry was extracted by applying the S-reduced Hamiltonian. Due to the absence of b-type transitions and spectra of the deuterated molecule it was necessary to fix the S – H bond distance to the ab initio value and only approximate r0 structure was deduced. To date, neither vibrational transitions nor information about the electronically excited states of this species have been known. The isovalent alkaline earth monohydrosulfides CaSH and SrSH were the subject of several experimental and theoretical works [2 –7]. An early computational study of the electronic states of CaSH
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[2] was found to be useful in the interpretation of the laser-induced fluorescence spectra of CaSH and SrSH from three electronically excited doublet states [3]. Later the A2A0 and B2A00 states of CaSH were investigated with higher resolution [4,5]. Accurate molecular constants obtained from rotational data were reported for CaSH in Ref. [6] and SrSH in Ref. [7]. The strongly bent structures of MgSH, CaSH and SrSH are suggestive of a significant contribution of covalent character to the ionic bond [2 –7]. Alkalineearth monohydroxides CaOH, SrOH and BaOH have linear ground states, the MgOH is quasi –linear. The aim of the present study was to calculate the quartic force field of the X2A0 electronic ground state to obtain rotational and vibrational molecular constants from second order perturbation theory. For low lying electronically excited doublet and quartet states their vertical excitation energies and their dissociation paths were investigated and several conical intersections, including one in the electronic ground state, were located.
2. Electronic structure calculations The standard correlation consistent generally contracted spdf subset of the cc-pVQZ (basis AÞ and ccpV5Z (basis BÞ basis sets of Dunning [8] for Mg and S atoms were used. For the hydrogen atom the functions of the basis A were employed. The state averaged full valence CASSCF [9,10] followed by internally contracted MRCI [11], available in the MOLPRO program suite [12], were used to calculate the excitation energies and the dissociation paths of low lying doublet and quartet states of MgSH, whereas near the equilibrium three-dimensional potential energy surface (PES) of the X2A0 state was generated by the RCCSD(T) method [13] using basis B: The equilibrium geometries of the ground state were calculated by MRCI and RCCSD(T) using both basis sets. In the state averaged full valence CASSCF computations all doublets and quartets resulting from the first four dissociation asymptotes Mg þ SH had equal weights. For the MgS þ H dissociation paths all quartet and doublet states of the seven lowest asymptotes were averaged together. In the cut of the PES’s along the bending coordinate only the three
lowest 2A0 and two 2A00 states were calculated simultaneously. In all cases the resulting CASSCF wavefunctions were used as reference wavefunctions for the internally contracted MRCI computations, the reference was selected according to a threshold of 0.05 of the CASSCF coefficient in the corresponding CI expansion. In the RCCSD(T) and in the MRCI calculations only all valence electrons were correlated, the core-valence correlation was neglected.
3. Dissociation paths Mg· · ·SH and MgS· · ·H and electronically excited states In Fig. 1 the MRCI colinear dissociation paths of all doublet and quartet states ð3x2 S; 2x2 P; 2 D; 2S2, 4 þ 4 S , P, 4D, 4S2) correlating with the four lowest asymptotes are displayed. The bent X2A0 state becomes at linearity the lowest 2Sþ state. The MRCI vertical energy difference from the bent minimum (Section 4) to linearity has been calculated to be 5680 cm21. The electronic ground state dissociates diabatically to the second asymptote. The PES crosses around RMgS ¼ 5:5 bohr the lowest 2 P state and in bent structures both 2A0 form an avoided crossing leading to a vibronic coupling between both states. As follows from Fig. 1, in colinear structures most of the electronically excited states are repulsive. For MgS distances longer than about 6 bohr the quartet and doublet states lie very close together and strong spin – orbit coupling will mix the doublet and quartet states and also other angular momenta coupling effects will complicate a detailed understanding of the long range interactions of Mg and SH. The second 2P state and the 2Sþ state correlating with the ionic asymptote are the only excited states among those treated with local minima in linear structures. The diabatic path of the second 2P state is very complex due to crossings with several other states of the same spin multiplicity but also with several quartet states. In CaSH and SrSH three electronically excited doublet states were observed experimentally [3 – 5] and it was assumed that they could correlate with doubly degenerate P states. We have, therefore, calculated the one-dimensional cuts of the two lowest 2P states of MgSH along the bending coordinate in order to find similar bound – bound
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301
Fig. 1. MRCI (basis A) colinear cuts of the PES’s along the Mg· · ·S dissociation path with RSH ¼ 2:53 bohr: At 4.5 bohr the order of the states is: 2 þ 2 S , P, 4Sþ, 4D, 4S2, 2Sþ, 4P and 2Sþ.
electronic transitions also in the MgSH radical. The results are shown in Fig. 2 together with the PES cut of the electronic ground state. The lower 2P state forms first a bent/linear Renner –Teller pair, but its 2A0 component possesses an avoided
crossing with the component of the same symmetry correlating with the second 2P state. The two Renner – Teller systems are vibronically coupled. In the Franck –Condon region of the bent electronic ground state one 2A0 and two 2A00 excited state also
Fig. 2. MRCI (basis A) cuts of the electronic ground state and the two lowest 2P states along the bending coordinate with bond lengths fixed at their ground state equilibrium distances (Table 2).
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Table 1 MRCI and MRCI þ Q vertical transition energies of MgSH (in cm21, basis AÞ State
MRCI
MRCI þ Q
X2A0 A 2A0 B 2A00 C 2A00 D 2A0 a 4A00 E 2 A0 F 2A00 b 4 A0 c 4A0 d 4A00 e 4A00
0.0 22926 23865 26077 31889 36646 37016 37480 37769 43214 43911 45838
0.0 23027 24838 26261 32822 38049 37297 38850 39160 44509 44698 47092
The total energies at the equilibrium geometries (Table 2) of the X2A0 state were calculated to be: 2598.008105 a.u. (MRCI) and 2598.030543 a.u. (MRCI þ Q).
have their minima. In Table 1 the MRCI and MRCI þ Davidson correction vertical excitation energies are given. The three lowest excited states lie between about 23000 –26000 cm21. The electronic transitions in CaSH were detected [3] around 15000 –16000 cm21 in SrSH [3] around 14000– 15000 cm21 and it was suggested that the electronic excitations occur in the orbitals strongly
located on the metal atom which is in accord with the calculated blue shift for MgSH. In Fig. 3 the dissociation paths MgS· · ·H for colinear structures are displayed. The ground state and the two lowest 2P states have local minima along this dissociation path. The second 2P state forms another avoided crossing with a higher state of the same symmetry. Several other electronically excited states possess local minima along this coordinate. It is interesting to note that the isomer HMgS has a 2P electronic ground state [14] minimum lying 7934.6 cm21(RCCSD(T), basis B) above the MgSH minimum. For the H migration path these cuts provide the basis for the understanding of the intramolecular dynamics in this radical. Other alkaline-earth monohydrosulfide might also have secondary P minima on the ground state potentials. 4. Electronic ground state X2A0 of MgSH and MgSD The three-dimensional PES of the electronic ground state has been mapped by RCCSD(T) and full valence MRCI methods using the atomic orbital basis A and B: The computations were done for 78 geometries in the following range: 3.8 # RMgS
Fig. 3. MRCI (basis A) colinear cuts of the PES’s along the MgS· · ·H dissociation path with RMgS ¼ 4:38 bohr:
A. Zaidi et al. / Journal of Molecular Structure (Theochem) 634 (2003) 299–304 Table 2 MRCI and RCCSD(T) equilibrium geometries of the electronic ground state of MgSH and comparison with previous theoretical and experimental results (distances in bohr and apex angle in degree) Method
RMgS
RSH
Q
MRCI/basis A MRCI/basis B RCCSD(T)/basis A RCCSD(T)/basis B MP2a Exp.a RCCSD(T)/basis Bb
4.4038 4.3840 4.4024 4.4016 4.4100 4.3780 4.405
2.5330 2.5305 2.5348 2.5381 2.5312 2.5312 2.530
91.4 91.5 92.0 91.2 91.1 87.5 89.7
a
Ref. [1]. Calculated from the A0 ; B0 and C0 constants given in the footnote of Table 3. b
# 5.4 bohr, 2:0 # RSH # 3.4 bohr and 608 , Q # 1358: The energies were fitted to sextic polynomial expansions in displacement coordinates by the SURFIT program [15]. The expansions were then transformed to quartic force fields in internal and dimensionless normal coordinates. The calculated equilibrium geometries are compared with experimental and MP2 geometries reported previously [1] in Table 2. The experimental values represent an approximate r0 structure with RSH distance fixed to calculated MP2 ReSH distance. Our values are the calculated r e structures. Whereas the SH distance varies only slightly with the methods and basis sets used, the equilibrium angle is larger by about 48 than the empirical estimate. The cc-pV5Z (basis B) MgS distance is more accurate than the MP2 value though this distance will be shortened by the core-valence electron correlation neglected in the present work. In Table 3 only the set of spectroscopic constants calculated with basis B and RCCSD(T) method from the quartic force field in dimensionless normal coordinates is presented. The corresponding quartic force field in internal coordinates is given in Table 4. The full set of a constants allowed us to calculate the r0 rotational constants which are given in the footnote of Table 3 for MgSH. The r0 geometry calculated from our re geometry is compared with the experimental estimate in Table 2. The agreement is quite satisfactory considering the fact that the neglected core-valence correlation will shorten the MgS bond length and influence also the bond angle. The first
303
Table 3 RCCSD(T) (basis B) and experimental spectroscopic constants of MgSH and MgSD (rotational constants in MHz, all other constants in cm21) MgSH Ae b Be Ce DK aA1 aB1 aC1 aA2 aB2 aC2 aA3 aB3 aC3 v1 v2 v3 x11 x22 x33 x12 x13 x23 n1 n2 n3
287189.7 6701.1 6548.3 15.6 20.29466 0.00113 0.00122 20.35998 20.00048 0.00004 0.29665 20.00011 0.00004 411.56 479.24 2674.88 21.36 22.86 248.72 1.95 22.04 28.91 408.8 470.0 2572.4
Exp.a
MgSD
289001.8 6799.6 6629.6 15.1
148342.6 6606.6 6324.9 4.402 20.13100 20.00080 0.00004 20.01931 0.00136 0.00127 0.11174 20.00015 0.00005 333.87 426.38 1920.34 0.55 21.92 225.13 22.80 25.74 0.28 330.7 421.3 1867.3
a
Ref. [1]. The RCCSD(T) r0 rotational constants are: A0 ¼ 288580:84; B0 ¼ 6692:6; C0 ¼ 6528:8 (in MHz); the masses used in the evaluations of the rotational constants were: 23.985040 (Mg), 31.972070 (S), 1.007825 (H) and 2.014 (D). b
order centrifugal distortion constant DK is calculated in good agreement with the empirical estimate. Apart from the diagonal SH stretch x33 value the other anharmonic constants are relatively small. The harmonic modes for the MgS stretch and MgSH(D) bending are strongly influenced by isotope substitution. For MgSH the v1 in Table 3 corresponds to MgS stretch and v2 to the bending, for MgSD the MgS stretch corresponds to v2 and the MgSD bending becomes the lowest vibrational mode (Table 3). The normal bending mode of both isotopomers includes also strong changes of the MgS distance. The MgS stretch is calculated to lie higher in MgSD than in MgSH by about 15 cm21. The corresponding anharmonic fundamental vibrational wave numbers for
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Table 4 RCCSD(T) (basis B) quartic force field of the X2A0 state of MgSH in internal coordinates f11 f22 f33 f12 f13 f23 f111 f222 f333 f112 f122 f113 f223 f123 f133 f233 f1111 f2222 f3333 f1112 f1222 f1122 f1113 f2223 f1123 f1223 f1133 f2233 f1233 f1333 f2333
1.4230 4.1197 0.2286 0.0092 0.0110 0.0895 25.5650 221.8100 20.1756 20.0160 20.0231 0.0211 0.0296 20.0769 0.1015 20.1201 19.2809 101.5902 0.1750 20.0830 20.1667 0.1671 20.1907 20.3668 20.0734 20.0181 20.5802 20.3692 20.0001 0.6271 20.0491
The indicies correspond to RMgS RSH and Q; all values are in ˚ 2n; factorials are excluded. aJA
both isotopomers are given as well. The zero point energy for MgSH is calculated to be 1767.4 cm21. The IR region of higher overtones and combination levels will exhibit anharmonic resonances and vibronic coupling due to the conical intersection between the electronic ground state and the first 2P state.
5. Conclusion Ab initio MRCI calculation for the ground and excited states of MgSH have been used to obtain information about the electronically excited states and their dissociation. For the ground state the RCCSD(T)
anharmonic vibrational frequencies for the fundamentals for both H/D isotopomers have been evaluated. It is found that the ground state dissociates via a conical intersection to the ground states of Mg and SH. Several other conical intersections and coupling regions between the electronically excited quartets and doublets were located. The minimum of the HMgS isomer is calculated to lie 7934 cm21 above the minimum of MgSH [14].
Acknowledgements This work has been supported by cooperation between Laboratoire de physique des lasers, atomes et mole´cules, Universite´ de Lille 1, France, Laboratoire de chimie the´orique, Universite´ Marne la Valle´e, France and Laboratoire de spectroscopie atomique et mole´culaire et applications, Faculte´ des sciences, Tunis. A.Z. thanks N. Jaidane and G. Chambaud for stimulating discussions and J.M. Robbe for his help with the calculations.
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