An ab initio study of antimony dicarbide (C2Sb)

Chemical Physics Letters 565 (2013) 28–34

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An ab initio study of antimony dicarbide (C2Sb) Milan Z. Milovanovic´, Stanka V. Jerosimic´ ⇑ Faculty of Physical Chemistry, University of Belgrade, Studentski trg 12, P.O. Box 47, PAK 105305, 11158 Belgrade, Serbia

a r t i c l e

i n f o

Article history: Received 17 December 2012 In final form 19 February 2013 Available online 27 February 2013

a b s t r a c t Antimony dicarbide was investigated employing coupled cluster and multiconfigurational methods. The relativistic effects were taken into account by using pseudopotentials for the Sb atom; additional corrections due to all-electron correlations and spin–orbit effects were also included. C2Sb is found to be quasilinear in the ground 2A00 [X 2P] state with a very small barrier to linearity (0.07 kJ mol1); T-shaped cyclic C2v (2B2) geometry was found just about 2.9 kJ mol1 higher in energy. A molecular orbital analysis, spin– orbit constants, dissociation energies of C2Sb (X 2P), and the low-lying excited valence-type electronic states are reported. Ó 2013 Elsevier B.V. All rights reserved.

1. Introduction The present study was initiated by theoretical studies of dicarbides C2P [1] and C2As [2,3]. The results strongly supported the analysis of experimental data by the Clouthier’ group [4] and offered reliable predictions for experimental searches of heretofore unobserved electronic states, for instance, the 12R and 12R+ electronic states of C2P. Furthermore, the interpretation of the experimentally observed spectra of C2As performed by Wei et al. [5] was confirmed as well. Dicarbides have received much attention due to their importance in the field of astrochemistry, their role in advanced functional materials, and their relevance in structural chemistry. In particular, transition-metal dicarbides have been studied as their structures and reactivities are quite important in many areas of chemistry, such as catalysis, combustion, and materials; just to mention the theoretical studies of C2Sc [6], C2Ti [7,8], C2Fe [9,10], C2Co [11,12], C2Y [13], C2La [14], and C2U [15]. Since the much studied silicon dicarbide was found to be cyclic in its ground state [16,17], many of dicarbides have also been predicted to have cyclic ground states, especially dicarbides with electropositive atoms, for instance – the first row transition metal dicarbides [18]. Furthermore, competition between linear, L-shaped (bent molecule), and T-shaped (cyclic) geometries exist in the second-row main group dicarbides – Largo et al. [19] reported that dicarbides with Na, Mg, Al and Si have cyclic ground states, and those with P, S and Cl – a linear structure. Similar competition was found by Rayón et al. [20] in the third-row main group dicarbides – K, Ca and Ga dicarbides prefer T-shape ground states, whereas As [21], Se, and Br dicarbides prefer linear or quasi-linear ground states. In the case of germanium dicarbide a very flat potential energy surface (PES)

⇑ Corresponding author. Fax: +381 11 2187133. E-mail address: [email protected] (S.V. Jerosimic´). 0009-2614/$ - see front matter Ó 2013 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.cplett.2013.02.047

was found and an L-shape structure was reported to be the ground state [22]. Herein, a detailed ab initio investigation of the ground and lowlying excited electronic states of C2Sb is reported. To the best of our knowledge, there are neither theoretical nor experimental data on this molecule in the gas phase or plasma. The subject of the present Letter seems to be important, especially due to the findings that this molecule has a very flat potential curve that would well influence its spectroscopy. In particular, having an unusually largeamplitude bending mode with a very low frequency (43 cm1), it is not so spectroscopically tractable (for the influence of the flat potential energy on the spectroscopy of T-shaped dicarbides, see e.g., a comparison of the C2Al and C2Si spectra [23]).

2. Computational details The calculations were realized using the open-shell coupled cluster RCCSD(T) method as a single reference [24,25], the stateaverage full-valence complete active space self-consistent field (SA-FVCASSCF) [26,27], and the internally contracted multi-reference configuration interaction approach (MRCISD) with quasidegenerate Davidson corrections, i.e., the MRCI(Q) method, developed by Werner and Knowles [28,29] and implemented in MOLPRO [30], which employs a CASSCF reference. The CASSCF active space used as a reference for the MRCI(Q) calculations was constructed including 13 electrons in 12 orbitals (full valence). A smaller active space, i.e., CAS(9,8), was also used. Different basis sets were employed, but a basis set that is a combination of the aug-cc-pVTZ basis set for the carbon atom [31] and the Stuttgart/Cologne group scalar-relativistic effective core potential ECP28MDF in conjunction with aug-cc-pVTZ basis set for antimony, i.e., aug-cc-pVTZ-PP [32,33] was primarily chosen for the presentation of the results. This pseudopotential was adjusted to reliably reproduce atomic valence-energy spectra;

M.Z. Milovanovic´, S.V. Jerosimic´ / Chemical Physics Letters 565 (2013) 28–34

static relativistic effects were included. Moreover, ECP28MDF with a spin–orbit part (in conjunction with the aug-cc-pVTZ and aug-ccpVQZ valence basis sets) for antimony [34] were used to predict the values for the spin–orbit constants. Different trials with larger valence basis sets showed no significant differences, in other words, the quality of the chosen one-electron space matched the quality of the employed N-electron models. Wavefunctions were restricted regarding space and spin symmetry. The calculations were performed within C2v (a subgroup of the C1v point group) and Cs framework for linear nuclear arrangements, the Cs group for planar geometries and within the C2v and Cs groups for the T-shaped C2–Sb geometry. Regarding the choice of the molecule fixed axes, we adopted the following convention: the z axis was chosen to coincide with the principal axis a, which has the smallest moment of inertia Iaa (Iaa < Ibb < Icc) all the way from linearity to the isosceles triangle geometry; next, the y axis was the b axis, and the x was placed on the c axis. Consequently, at linearity the z axis was the vertical C1 axis (or C2 axis in the C2v subgroup), while the x and y axes were normal to it. Next, at planar bent geometries, the symmetry plane was the y, z plane, and the x axis was normal to the molecular plane, with A00 symmetry. Finally, when a molecule becomes a symmetrical triangle, i.e., at C2v geometry, the z axis (C2) had A1 symmetry, the x axis B1 and the y axis B2 symmetry. Hence, the A0 irreducible representation correlates with A1 and B2, and A00 with A2 and B1 (the same would have been if we had used the usual choice of the axes for the Cs group). Geometrical optimizations were performed at the RCCSD(T)/ aug-cc-pVTZ(C), aug-cc-pVTZ-PP(Sb) level. For the most relevant species, MRCI optimizations were also performed; excited electronic states were optimized with the CAS(13,12)-MRCI and CAS(9,8)-MRCI methods at linear nuclear arrangements in the same basis set. The full valence MRCI(Q)/aug-cc-pVTZ optimization within the framework of the Cs group has not been performed due to high computational costs. Optimizations performed using the CCSD(T) and MRCI methods employed numerical gradient calculations [35]. For harmonic vibrational frequencies and normal modes, the Hessians were numerically approximated using central differences [36]. The potential energy surface was refined by means of single-point calculations at the full-valence MRCI(Q) level. Account was taken of valence-only correlation effects (at both the RCCSD(T) and MRCI(Q) levels); however, RCCSD(T) calculations with correlations of both core and valence electrons were additionally performed in the core-valence correlation consistent basis set cc-pwCVTZ for the carbon atoms [37] and the relatively new ccpwCVTZ-PP basis set for antimony [38]. All calculations were realized using the MOLPRO 2010.1 program package [30].

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in the range between q = 0° (the linear C–C–Sb nuclear arrangement) and q = 108° (C2v geometry of the isosceles triangle) and are plotted in Figure 1. As can be seen, the predicted equilibrium nuclear geometry of the ground state is not strictly linear, but a bent-structure (known as the ‘L-shaped geometry’; in the present case it is not really Lshaped, so it is rather labeled as the ‘bent geometry’) with re(CC) = 1.297 Å, re(CSb) = 1.971 Å and qe = 37.2° at the RCCSD(T) level, which is by only 71 cm1 lower in energy than the ground state in the linear nuclear arrangement. The global minimum obtained at the CAS(13,12)-MRCI/aug-cc-pVDZ(C), aug-cc-pVDZPP(Sb) level was at re(CC) = 1.320 Å, re(CSb) = 1.990 Å, and qe = 31.5°, confirming the bent-structure as the global minimum. The one-dimensional cuts (Figure 1) of the potential energy surfaces obtained at the RCCSD(T), MRCI and MRCI(Q) levels of theory are very similar to one another, especially bearing in mind that the plotted energies are in cm1. Equilibrium nuclear geometries and harmonic frequencies of several stationary structures of C2Sb are presented in Table 1. In addition, their RCCSD(T)-optimized geometries are shown in Figure 2. The results of the calculations show that there are four most relevant geometries in the ground state potential energy surface: the global minimum – bent geometry (b), the real minimum at C2v geometry (T-shaped geometry) (t), the real minimum at linear CSbC, and transition state at linear geometry CCSb (l), according to one imaginary (bending) frequency. As can be seen from Table 1, the three stationary points (l, b and t) lie energetically very close to each other; the barrier to linearity is very small, only 0.25– 0.85 kJ mol1 (21–71 cm1). If this value is compared with the value of zero-point vibrational energy (about 15 kJ mol1), it could be concluded that the molecule is quasi-linear. On the average, it has linear geometry and most probably the X 2P state would be observed in experiments. Indeed, even the lowest vibrational frequency level lies above the barrier to linearity. Given that the structural isomer, linear CSbC, lies energetically at about 470–480 kJ mol1 above the global minimum of C2Sb (see Table 1), this isomer was not investigated in detail; instead attention was directed to the three geometries (l, b and t). The T-shaped structure (t) has energy of about 2.2–7.7 kJ mol1 above the global minimum. The barrier to the C2v structure is around 17 kJ mol1 [MRCI(Q)]. The 12A’ state correlates with the 12B2 state at C2v geometry and the 12A’’ with the 12B1. The ground state of the isomer (t) is 12B2. The first excited state is 12B1 with geometry re(CC) = 1.275 [1.276] Å, re(CSb) = 2.133 [2.138] Å,

3. Results and discussion 3.1. The ground electronic state 2A00 [X 2P] 3.1.1. The most relevant geometries The bending potential energy curve of the ground 2A00 [X 2P] electronic state of C2Sb was computed using the single-reference RHF-RCCSD(T) and the multi-reference full-valence MRCI(Q) methods, in the aug-cc-pVTZ(C), aug-cc-pVTZ-PP(Sb) basis set. The 2P electronic state of the linear nuclear arrangement splits upon bending into two components, 2A0 and 2A00 . The internuclear distances were optimized along the bending angle q, defined as the supplement of the C–C–Sb bond angle (q = 180°–hCCSb), for each of the states 2A0 and 2A00 using the RCCSD(T)/ aug-cc-pVTZ(C), aug-cc-pVTZ-PP(Sb) level. The optimized nuclear geometries were then used for single-point full-valence MRCI(Q) calculations along q. Electronic energies as a function of the angle q were computed

Figure 1. Potential energy minimum path of the ground electronic state of C2Sb vs. bending angle q (=180°–hCCSb) calculated at the RCCSD(T) (solid lines), the MRCI (dashed lines) and the MRCI(Q) (dotted lines) levels in the combined basis set that consists of aug-cc-pVTZ for carbon and aug-cc-pVTZ-PP for antimony. The internuclear distances were relaxed at each angle for both states.

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Table 1 Equilibrium geometries (defined by re(CC), re(CSb) and hCCSb, see Figure 2), harmonic frequencies, zero point vibrational energies (ZPVE), electronic energies and relative energies DE (with respect to the bent structure) in the ground state of C2Sb, calculated using the RCCSD(T), full valence-MRCI and MRCI(Q) methods in the aug-cc-pVTZ(C), aug-cc-pVTZPP(Sb) basis set. The ground state geometry and energy of the isomer CSbC is also presented. Full-valence MRCI optimization was performed within the framework of the C2v group (l and t geometries), and in Cs symmetry, the MRCI(Q) energy was calculated at the RCCSD(T) geometries. Additionally, the results of RCCSD(T)/cc-pwCVTZ(C), cc-pwCVTZPP(Sb) calculations that included all electron-correlations are presented.d For ZPVE the imaginary frequencies were ignored. Linear geometry C2Sb (l) (X 2P) re(CC)/Å re(CSb)/Å hCCSb/deg x1/cm1 x2/cm1 x3/cm1 ZPVE/kJ mol1 Energy/hartree

DE/cm1 a b c d

a

b

d

1.298 1.302 1.294 1.964a 1.966b 1.935d 180.0 1766a 1777d (a1) 547a 558d (a1) 60ia, 151a 27id, 174d (b1) 14.738a 15.007d 315.273215a 315.250779b 315.274989c 316.077481d E(2P) – E(2A’’) = 71a, 21b, 45c, 6d

Bent geometry C2Sb (b) (12A’’) a

d

1.297 1.293 1.971a 1.938d 142.8a 156.7d 1740a 1765d (a0 ) 621a 590d (a0 ) 86a 43d (a0 ) 14.635a 14.082d 315.273537a 315.250876b 315.275192c 316.077507d 0

T-shaped geometry C2Sb (t) (12B2) a

b

d

1.320 1.320 1.315 2.139a 2.135b 2.108d 72.0a 72.6b71.8d 1550a 1557d (a1) 541a 549d (a1) 200a 227d (b2) 13.703a 13.957d 315.272679a 315.247942b 315.273455c 316.076408d E(2B2) – E(2A’’) = 188a, 645b, 382c 241d

Linear CSbC (2Pg) – 2.039, 2.039a2.040, 2.040b 179.9a 180.0b 659a 626a 77a 8.152a 315.090015a 315.068906b 315.096031c 40 278a, 39 938b, 39 323c

RHF-RCCSD(T)/aug-cc-pVTZ(C), aug-cc-pVTZ-PP(Sb). CAS(13,12)-MRCI/aug-cc-pVTZ(C), aug-cc-pVTZ-PP(Sb). CAS(13,12)-MRCI(Q)/aug-cc-pVTZ(C), aug-cc-pVTZ-PP(Sb). (+core corr.)RHF-RCCSD(T)/cc-pwCVTZ(C), cc-pwCVTZ-PP(Sb).

Figure 2. The most relevant C2Sb geometries studied in this work. The presented equilibrium distances (in Å) and angles (in degrees) were calculated at the RCCSD(T)/aug-cc-pVTZ(C), aug-cc-pVTZ-PP(Sb) level.

qe = 107.4 [107.4] deg, calculated employing the MRCI [RCCSD(T)] method. The energy difference between the ground 12B2 and the first excited 12B1 state is 29.20 kJ mol1 according to the RCCSD(T) method, and 31.68 kJ mol1 according to the MRCI(Q) method. Unlike C2Ge that also has a very flat PES of the ground state [22], the T-shaped geometry of C2Sb was found to be a true minimum at every level of theory. A bent C2Sb stationary point (b) was found at every level of theory. The bent equilibrium geometry has similar C–C and C–Sb bond distances to those in the linear structure. On the other hand, the bond angle hCCSb in the bent geometry is dependent on the theoretical model employed; the values lie between 140° and 160°. The potential energy surface is extremely flat, and only several kJ mol1 is enough to invert the Sb atom with respect to the C–C bond. According to RHF-RCCSD(T) calculations, the linear structure (l) has an imaginary harmonic vibrational frequency for the degenerate bending mode (60i cm1). Employing the RHF-UCCSD(T) level of theory, a value of 59i was obtained. It appears that the linear C2Sb is a transition state that connects two bent geometries. The results of the present calculations showed that antimony dicarbide has a very flat potential surface. Isomerization to the Tshaped geometry is easily achievable, and at this geometry, the asymmetric stretching vibration was found to be only about 200 cm1. 3.1.2. The highest level RCCSD(T) results The combination of cc-pwCVTZ basis set for carbon and ccpwCVTZ-PP for antimony, documented in Section 2, was used with

the RCCSD(T) method that included correlations of all electrons. This is the best single-reference method used in the present study that includes these two effects, namely, the core-valence correlation through the use of the cc-pwCVTZ basis sets, and, more significant, correlation of all electrons invoked in RCCSD(T) method [30]. Geometry optimizations and frequency calculations at the three stationary points (l, b and t) were conducted. The results are included in Table 1. As noted above, the RCCSD(T)/aug-cc-pVTZ(-PP) level predicts an imaginary harmonic frequency of 60i for the bending mode of the linear geometry. Inclusion of core-correlations produces a smaller imaginary value of 27i. This value generally confirms the earlier prediction that the linear geometry is a transition state; however, the likelihood that the linear geometry really is a transition state decreases. In addition, the frequency of the bending mode (x3) at the global minimum has an even smaller value of 43 cm1. Regarding energetics of three stationary structures, the relative energy of the T-shaped geometry is 2.88 kJ mol1, similar to the value obtained by the valence-correlated RCCSD(T) of 2.25 kJ mol1. However, the relative energy of the linear geometry is 0.07 kJ mol1, which is smaller by 0.18 kJ mol1 relative to the RCCSD(T)/aug-cc-pVTZ(-PP) method. This ’destabilization’ of the bent geometry with respect to the linear geometry suggests that the employment of higher level ab initio calculations (e.g., all-electron relativistic calculations) may change the nature of the stationary point at linearity, and change the prediction of quasilinearity. This could put antimony dicarbide together with the two isovalent analogues C2P and C2As, which were found to be linear in their ground states. The frequencies at the T-shaped geometry confirm the presence of a real minimum at this geometry.

3.1.3. Molecular orbitals The electronic configuration of the ground state (X 2P) at the MRCI optimized distances for the linear nuclear arrangement, can be expressed according to the CAS(13,12) natural orbitals: [core] 12r1.99 13r1.98 14r1.97 15r1.96 6p3.72 7p1.2 8p0.12 16r0.04 17r0.02, with the occupation numbers as superscripts. The major configuration is as follows: [core] 12r2 13r2 14r2 15r2 6p4 7p1 (X 2P). There are 12 valence orbitals occupied by 13 electrons in the C2v and Cs symmetry groups; the 12 valence orbitals are 14a1 – 19a1, 6b1 – 8b1, 6b2 – 8b2 and 19a0 – 27a0 , 8a00 – 10a00 . The 6p orbital

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Figure 3. The energy of natural orbitals in the ground state along the angle q calculated within the framework of the C1v, CS and C2v point groups using the full-valence CASSCF method in the aug-cc-pVTZ(-PP) basis set. The solid lines correspond to a0 orbitals and the dashed lines to a00 orbitals.

Table 2 Dissociation energy (De) of C2Sb in its ground X 2P state, calculated at three levels of theory: RHF-RCCSD(T), CAS(13,12)-MRCI and CAS(13,12)-MRCI(Q) in the aug-cc-pVTZ(C), aug-cc-pVTZ-PP(Sb) basis set. De + ZPVE is dissociation energy with zero-point energy correction, BSSE is the basis set superposition error. Final values (Decorr + SO) take into account ZPVE, BSSE, and SO splitting. The values of zero point vibrational energies for C2Sb, C2 and SbC are 14.635, 9.731 and 4.957 kJ mol1, respectively [CCSD(T) results]. Channels

De (kJ mol1)

De + ZPVE (kJ mol1)

BSSE (kJ mol1)

Decorr (kJ mol1)

Decorr + SO (kJ mol1)

C2Sb (X 2P) ? C2 (3Pu) + Sb (4S)

361.5a 325.7b 353.8c 623.2a 587.1b 609.8c

356.5a 320.8b 348.9c 613.5a 577.4b 600.2c

4.2a 3.7b 3.8c 7.5a 6.8b 7.2c

352.4a 317.1b 345.1c 606.0a 570.6b 593.0c

363.0a 327.7b 355.7c 616.6a 581.2b 603.6c

C2Sb (X 2P) ? SbC (2R+) + C (3P)

a b c

RHF-RCCSD(T)/aug-cc-pVTZ(C), aug-cc-pVTZ-PP(Sb). CAS(13,12)-MRCI/aug-cc-pVTZ(C), aug-cc-pVTZ-PP(Sb). CAS(13,12)-MRCI(Q)/aug-cc-pVTZ(C), aug-cc-pVTZ-PP(Sb).

(6b1 and 6b2; 23a0 and 8a00 ) is C–C–Sb bonding, the 7p (7b1 and 7b2; 24a0 and 9a00 ) (HOMO) is of the C–C bonding and C–Sb antibonding type and the 8p orbital (8b1 and 8b2; 25a0 and 10a00 ) is C–C and C– Sb antibonding. At the global minimum (Cs symmetry), the electronic configuration according to the full-valence CASSCF natural orbitals is: [core] (19a0 )1.99 (20a0 )1.98 (21a0 )1.96 (22a0 )1.95 (8a00 )1.92 (23a0 )1.83 (9a00 )1.02 (24a0 )0.16 (25a0 )0.06 (10a00 )0.07 (26a0 )0.04 (27a0 )0.02. In order to explain in a qualitative manner the change in the ground state potential energy and the change in symmetry upon bending from linear to cyclic geometry, the calculated orbital energies vs. angle q are plotted in Figure 3. This (Walsh-like) diagram was constructed with the valence natural orbitals obtained from SA-FVCASSCF calculations, whereby the two ground state configurations (A0 and A00 ) were averaged (with equal weights). The highest occupied molecular orbital (HOMO) at linearity is the 7p (7b1 and 7b2 degenerate orbitals in the C2v subgroup), which splits into 24a0 and 9a00 upon bending. According to the qualitative rule that a molecule will adopt a structure that best provides the most stability for its HOMO, the orbitals 24a0 and 9a00 (which are HOMO for the A0 and A00 state, respectively) are responsible for the atypical crossing of the A0 and A00 states at about q = 80 deg. Indeed, observing only these two orbitals (right-hand part of Figure 3), 24a0 becomes more stable than 9a00 at angles above 80°. Regarding the atomic composition, at linear nuclear arrangement, they consist of py (24a0 ) and px (9a00 ) atomic orbitals of antimony and carbons; they are degenerate, lying in two perpendicular planes. On bending, the energies of 9a00 and 24a0 rose in a similar way. The 24a0 molecular orbital, lying in the yz-molecular plane, becomes more stable at about q = 80°; primarily it consists of py orbitals, but there is also some contribution of the pz orbitals of

the terminal carbon and pz orbitals of antimony, which overlap. Additionally, the s atomic orbitals from carbon atoms that also participate in 24a0 become close enough to overlap and the overall effect is an energy decrease of 24a0 . On the other hand, 9a00 is normal to the molecular plane and has no additional overlapping between atomic orbitals on bending. However, the energy trend of the HOMO cannot explain, not even qualitatively, the predicted quasi-linearity and flat potential curve. 3.1.4. Spin–orbit constant The spin–orbit constant, SO, of C2Sb was calculated assuming that its value would be high due to the presence of antimony. The spin–orbit eigenstates were obtained by diagonalizing Hel + HSO in the basis of eigenfunctions of Hel in the linear geometry [39]. In the state-average CASSCF method, the 12B1 and 12B2 states (which correlate with the X 2P state) were averaged with the same weights, using then this reference function to obtain the MRCI wavefunction. With the pseudopotential ECP28MDF, which has a spin–orbit relativistic part, in combination with the valence augcc-pVTZ and aug-cc-pVQZ basis sets, values of 1799 and 1805 cm1, respectively, were obtained. In comparison, the value was 141 cm1 for C2P [1] and 728 cm1 for C2As [2,3]. The experimentally observed value for the spin–orbit splitting of the first excited state 2 D0 (splitting between the 2 D05=2 and 2 D03=2 ) of the neutral antimony atom was 1342 cm1 and the splitting of the terms 2 P03=2 and 2 P 01=2 of the second excited state 2P0 was 2069 cm1 [40]. In the ground state of Sb (4 S03=2 ), there is no splitting (these three states arise from the electronic configuration ...5s2 5p3 of antimony). Carbon has a small SO constant, e.g., in the ground state 3P, the splitting between J = 1 and J = 0 terms is 16.4 cm1 [40]; similar value

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Table 3 The vertical spectrum of the low-lying doublet and quartet excited electronic states of C2Sb calculated by the SA-FVCASSCF(13,12) and SA-FVCAS(13,12)-MRCI(Q) method in the combined aug-cc-pVTZ(C) and aug-cc-pVTZ-PP(Sb) basis set, at the linear equilibrium geometry of the ground X 2P state [re(CC) = 1.3016 Å, re(CSb) = 1.9662 Å], and the lowest quartet state 14R [re(CC) = 1.2365 Å, re(CSb) = 2.0646 Å], optimized by the MRCI procedure within the framework of the C2v subgroup. All doublet and quartet states are averaged in the SA-CAS procedure. The x, y and z transition matrix elements and oscillator strengths (f-values) from the ground state (and the lowest quartet state) are also presented (the nuclear framework lies in the z axis). The doublet–quartet splitting gap is 4702 cm1. State

Doublets X 2P 1 2R 1 2D 2 2P 1 2R+ 1 2U ... Quartets 1 4R 1 4P 2 4R 3 4R ... a b c

DE (cm1)

Transition moments (a.u.)



j 12 P yjij j 12 P xjij

f-values

j 12 P zjij 1.7154a 1.7154a 0.0000

Relaxed distances at linear geometry rCC (Å)

rCSb (Å)

E (cm1)

Dipole moments (a.u.)

1.302b 1.296c 1.231b 1.227c 1.241b 1.235c 1.312b 1.304c 1.245b 1.236c 1.314b 1.304c

1.966b 1.952c 2.109b 2.109c 2.066b 2.065c 2.119b 2.104c 2.054b 2.048c 2.134b 2.129c

315.274536b 315.270319c 315.239868b 315.237378c 315.220197b 315.217801c 315.210681b 315.208735c 315.196387b 315.193079c 315.195092b 315.192039c

1.9641b 1.8999c 0.5470b 0.5542c 0.4165b 0.4365c 1.6522b 1.6273c 0.3545b 0.3313c 1.5238b 1.5610c

0a 0b 7920a 10 434b 12 859a 13 378b 16 366a 15 873b 16 975a 18 401b 20 486a 19 332b

0.0000

0.0000

0.2544a

0.2544a

0.1607a 0.1607a 0.0000

0.1607a 0.1607a 0.0000

0.1865a

0.1865a

0.1937a 0.1937a 0.0000

0.0000

0.0000

0.0000

0.0016 0.0021 0.0020 0.0021 0.0019 0.0018 0.0018 0.0019 0

0a 0b 10 654a 7661b 31 497a 33 102a

0.0000

0.0000

0.3689a

0

1.236c

2.065c

315.248897c

0.4879c

0.1719a

0.1719a

0.0000

1.302c

2.137c

315.222540c

1.6046c

0.0000 0.0000

0.0000 0.0000

0.0144a 0.7400a

0.0019 0.0014 0.0000 0.0551

– –

– –

– –

– –

0.0000

0

CAS(13,12)/aug-cc-pVTZ(C), aug-cc-pVTZ-PP(Sb). CAS(13,12)-MRCI(Q)/aug-cc-pVTZ(C), aug-cc-pVTZ-PP(Sb). CAS(9,8)-MRCI(Q)/aug-cc-pVTZ(C), aug-cc-pVTZ-PP(Sb).

of 15.25 cm1 is found for the splitting of the 3Pu,1 and 3Pu,2 terms of C2 [41]. The theoretically predicted value of 1805 cm1 for the ground state of C2Sb obtained in this study is predominantly the consequence of relativistic effects of the core-electrons of antimony. In order to check the sensitivity of this result to variation of the bond angle, computations of SO constants at the bent equilibrium geometries optimized with RCCSD(T) were performed. The splitting between the A0 and A00 states is increased due to spin–orbit interaction by 1460 cm1 at (+core corr.)RCCSD(T)/cc-pwCVTZ(PP) equilibrium geometry and by 1109 cm1 at RCCSD(T)/aug-ccpVTZ(-PP) equilibrium geometry. Consequently, the SO constant has lower values at bent geometries. Additionally, the SO constants for the 12D and 22P degenerate states were found to be 13 and 737 cm1, respectively, obtained with the combined ECP28MDF and aug-cc-pVTZ basis sets.

3.1.5. Dissociation energy It was also of interest to calculate the dissociation energy (De) of C2Sb in the ground state, in order to gain some information about the thermodynamic stability of this species. The dissociation energy (De) of the channels C2Sb (X 2P) ? C2 (3Pu) + Sb (4S) and C2Sb (X 2P) ? SbC(2R+) + C(3P) were calculated [RCCSD(T)/augcc-pVTZ(C),aug-cc-pVTZ-PP(Sb) level] to be 363 and 617 kJ mol1, respectively (see Table 2). More reliable data were obtained from the corresponding MRCI(Q) calculations, namely, values of 356 and 604 kJ mol1. Thus, the RCCSD(T) calculations predict higher values by about 2%. It should be mentioned that the electronic configuration of the ground state X 2P of C2Sb correlates with the ground state 4S of Sb and the first triplet state 3Pu of the C2 molecule, and not with the ground state of C2, 1Rg+; however, the stability of the molecule with respect to the ground states of Sb and C2 [C2 (1Rg+) + Sb (4S)] is 354.3 kJ mol1 [MRCI(Q)], which is very close to the value of 356 kJ mol1. In the second dissociation channel C2Sb ? SbC + C, the state X 2P correlates with the ground state dissociation limit. In comparison, the computed De values of the

dissociation of the isovalent analogue arsenic dicarbide in its ground electronic state [C2As(X 2P) ? C2(3Pu) + As(4S)] was 433 kJ mol1 [21] and for C2P, the calculated value was 470 kJ mol1 [19]. These are all relatively high values for De. The dissociation energies calculated herein were corrected by taking into account zero-point vibrational energies (ZPVE) of the molecules, the basis set superposition error (BSSE) calculated by using the counterpoise method [42], and the SO splitting of C2Sb (X 2 P), C2 (3Pu), and C (3P). BSSE lowered the De by about 1.2%; ZPVE lowered the De by about 1.5%. 3.2. Low-lying excited valence-type electronic states The excitation energies of the low-lying doublet and quartet valence-type electronic states, at relaxed linear geometries of the ground doublet and quartet states, respectively, were computed by means of the SA-CASSCF and the MRCI(Q) methods, with a view to assist future spectral assignments of the absorption or laser-induced fluorescence spectra of C2Sb, when they become available. The vertical energies obtained using the SA-FVCAS wavefunctions, the SAFVCAS wavefunctions for MRCI calculations, and MRCI(Q) results, in the aug-cc-pVTZ basis set for carbon and aug-cc-pVTZ-PP set for antimony, are presented in Table 3. Some MRCI energy values are missing due to convergence problems. The states are labeled by the symmetry species of the C1v group. All calculations of the excited states were calculated within the framework of C2v point group symmetry, as a subgroup of the C1v group. The values of transition matrix elements and oscillator strengths of transitions from the ground state (and the lowest quartet state) are given. To avoid possible confusion, the absolute values for the transition moment matrix elements computed for all components of spatially degenerate electronic states are explicitly given. An inspection of Table 3 showed that the transition from the ground state to the 2D species is the most probable, but the oscillator strengths of transitions from the ground to the 12R, 22P, and 12R+ states have almost the same values.

M.Z. Milovanovic´, S.V. Jerosimic´ / Chemical Physics Letters 565 (2013) 28–34

Figure 4. The low-lying doublet electronic states of C2Sb calculated within the framework of the CS symmetry group using the state-average full-valence CASSCF procedure in the aug-cc pVTZ(-PP) basis set, at equilibrium geometries of the ground state. Zero energy corresponds to the minimum of the ground 2A00 [2P] state. Solid lines: A’ states; dashed-lines: A’’ states.

When an electron is promoted from the 15r to the 7p orbital, the electronic configuration becomes ... 6p4 15r1 7p2 8p0, i.e., a p  p configuration, from which results R+, R and D states; the energy order of the doublet excited states is: 12R, 12D and 12R+. This configuration is also the configuration of the lowest quartet state, 14R that lies under 12R. The next excitation is 6p ? 7p, resulting in the electronic configuration ... 15r2 6p3 7p2 8p0; from the direct product p  p  p, the states P  P  P  U result. In the SA-CAS calculations of doublets, it was decided to average the ground X 2P, and the 12R, 12D, 22P, 12R+, 12U, and 32P states. The internuclear distances of several low-lying excited states were optimized using the SA-CAS(13,12)-MRCI and SA-CAS(9,8)MRCI procedures, and the results are also summarized in Table 3. To obtain the active space for CAS(9,8), the 12r, 13r, 16r and 17r orbitals were discarded. The equilibrium geometry of the first excited doublet, 12R, was predicted to be re(CC) = 1.231 Å, re(CSb) = 2.109 Å (the C–C bond is stronger and the Sb–C weaker than in the ground state). For the energy difference between the minima of the potential energy surfaces of the 12D and X 2P states, a value of 11 926 cm1 was obtained. The adiabatic excitation energies of the 12R, 22P and 12R+ states were found to be 7609, 14 015 and 17 152 cm1, respectively. The quartet states were optimized with CAS(9,8)-MRCI wavefunctions. The equilibrium geometry of the lowest 14R state is re(CC) = 1.236 Å, re(CSb) = 2.065 Å. The energy gap between the linear equilibrium structures of the ground doublet and quartet state is 4702 cm1. The potential energy curves of the low-lying doublet excited electronic states, calculated at the SA-FVCAS(13,12)/aug-ccpVTZ(-PP) level at geometries of the ground state, along the bending angle q, are presented in Figure 4. All states were included with equal weight. The splitting of the adiabatic potentials gradually decreases from P to U electronic state. The shape of these curves is qualitative due to the use of the ground state equilibrium geometries (the vertical spectrum). 4. Conclusions

the global minimum at bent geometry and is shown to be a true minimum with a predicted barrier for isomerization of around 17–20 kJ mol1. The linear CSbC is about 470 kJ mol1 less stable than the linear CCSb. Core-valence corrections and inclusion of all-electron correlations at the RCCSD(T)/cc-pwCVTZ(C), ccpwCVTZ-PP(Sb) level were found to stabilize the linear geometry over the bent structure, but the nature of the three stationary points did not change. Although all of the calculations placed the linear geometry above the bent geometry, we are of the opinion that due to extremely flat nature of the ground state potential energy surface and the small energy difference of the three stationary points (l, b and t), a definitive conclusion about the energetics of these three geometries will be achieved only after highly precise experimental work on this species would be conducted. Owing to the findings that the barrier towards linearity is only about 0.07 kJ mol1, which is about 200 times smaller than the zero-point correction, and that the bending frequency is found to be a high amplitude frequency with the value of only 43 cm1, it was concluded that the linear X 2P species should be detected in experiments as the ground state of antimony dicarbide. The calculated dissociation energies of antimony dicarbide are relatively high. The spin–orbit constant for the ground state was predicted to be 1805 cm1. The electronic spectrum X 2P – 12D should be observed with the origin at approximately 11 900 cm1. The transitions to the 12R, 22P and 12R+ state should be sufficiently intense to be observed. It is hoped that this investigation will be of importance for future experimental and theoretical investigation of this species.

Acknowledgments The authors thank the Ministry of Education, Science and Technological Development of the Republic of Serbia for their financial support (Contract No. 172040).

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The goal of this study was to predict the geometry and electronic structure of the ground state and electronic spectra of C2Sb. It was found that antimony dicarbide is quasi-linear in its ground state. The linear structure (X 2P) was found to be a transition state between two very shallow wells at bent geometries. The cyclic T-shaped isomer, the 2B2 species, lies only 2.9 kJ mol1 above

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