First-principles computation of the anharmonic vibrational spectra of sulfuryl halides SO2X2 (X = F, Cl, Br)

Chemical Physics 324 (2006) 359–366 www.elsevier.com/locate/chemphys

First-principles computation of the anharmonic vibrational spectra of sulfuryl halides SO2X2 (X = F, Cl, Br) Andrzej T. Kowal

*

Chemistry Department, Wrocław University of Technology, Wyb. St. Wyspian´skiego 27, 50-370 Wrocław, Poland Received 2 September 2005; accepted 31 October 2005 Available online 22 November 2005

Abstract Equilibrium geometries and anharmonic vibrational spectra of sulfuryl halides SO2X2 (X = F, Cl, Br) have been computed on MP2(frozen core) level of electronic structure theory in 6-31G(df) and effective core potential (ECP) Stevens–Basch–Krauss–Jasien–Cundari (SBKJC) SBKJC(3df) basis sets. Anharmonic spectra have been determined directly from MP2 potential energy surfaces using vibrational self-consistent field (VSCF) and correlation corrected vibrational self-consistent field (CC-VSCF) methods. Computed anharmonic corrections vary from 1.5 cm1 for low frequency d(O@S@O) and d(X–S–X) deformation modes to 12–20 cm1 for ma(S@O), ms(S@O), and ma(S–X) stretching modes. Wavenumbers of fundamental transitions of SO2F2 and SO2Cl2 calculated in SBKJC(3df) basis are within 2–12 cm1 of their experimental counterparts with RMSD of 7.7 and 7.3 cm1, respectively. Anharmonic spectra of SO2F2 and SO2Cl2 computed in 6-31G(df) basis are farther apart from experiment having RMSDs of 17.2 and 15.0 cm1. Overtone transitions with observable infrared intensity (above 0.5 km/mol) are attributable to 2m1(2ma(S@O)) and 2m2(2ms(S–F)) modes of sulfuryl fluoride or 2m2(2d(O@S@O)) mode of SO2Cl2 and SO2Br2.  2005 Elsevier B.V. All rights reserved. Keywords: Sulfuryl fluoride; Sulfuryl bromide; Sulfuryl chloride; Vibrational self-consistent field; MP2; Anharmonic; Effective core potential

1. Introduction Sulfuryl halides are tetrahedral-like asymmetric top molecules of C2v point group symmetry. Molecular structure of sulfuryl fluoride has been determined from gas phase electron diffraction (ED) [1] and subsequently from the rotational spectrum aided by high level ab initio calculations [2]. Density functional theory calculation using B3LYP, B1LYP and mPW1PW91 functionals with 6-311+G(3df) basis set provided vibrational spectrum of SO2F2 in the harmonic approximation [3], with rather ambiguous assignment of 544 cm1 transition to SF2 wagging vibration. Interpretation of the ground state rotational spectrum of SO2F2 [4] and its isotopic species [2] as well as of high-resolution FTIR spectrum of this molecule [5,6] definitely resolved ambiguities encountered in structural and spectro*

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scopic assignments. Sulfuryl chloride, SO2Cl2, the only second known member of the series, has been the subject of electron diffraction study [7], whereas its spectroscopic data are limited to low resolution gas phase infrared spectrum [8], and low temperature infrared and Raman spectra covering m3, m9, m7 triad near 400 cm1 [9]. Combined density functional theory-scaled quantum mechanical force field approach [9], employing B3PW91 functional with 631G(d) basis set, afforded harmonic approximation of the vibrational spectra of SO2F2, SO2Cl2, and SO2Br2 along with transition assignments based on potential energy distribution. Vibrational spectra calculated in the harmonic approximation within many electronic structure programs by means of ab initio or density functional methods are commonly used to assist spectral assignments. Computed transition energies usually overestimate experimental spectrum by as much as several hundred wavenumbers and require method/basis set dependent scaling in order to achieve agreement between computed and observed

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A.T. Kowal / Chemical Physics 324 (2006) 359–366

spectrum [10–12]. While the scaling factors are meant to account for incomplete description of electron correlation effects (including basis set) and complete neglect of anharmonicity, their origin remains purely empirical. Although sulfuryl halides can be viewed as rigid molecules and their vibrations are expected to be moderately anharmonic [6] it is of interest to provide consistent description of their spectra in the anharmonic approximation, including overtone and combination transitions. Anharmonic evaluation of SO2X2 (X = F, Cl, Br) spectra appears equally important because of opportunity to extend successful application of ECP in such calculation [13] to heavier atoms and fully exploit the benefits of fast computation of analytical second derivatives with ECP [14]. Such approach seems feasible since computational load associated with potential energy surface evaluation will remain constant within SO2X2 series due to ECP intrinsic properties. Vibrational self-consistent field (VSCF) method [15–20] and its correlation corrected enhancement (CCVSCF) [21–23], including degenerate perturbation theory implementation of the correlation correction [24], have been chosen to carry out this calculation. Direct evaluation of the potential energy surface required to perform the VSCF treatment on MP2 level of theory with medium sized basis set can be computationally expensive [25] and replacement of all-electron basis set by effective core potential/valence basis set combination greatly diminishes the computational burden [26] without significant deterioration of accuracy [27]. Typical errors resulting from such replacement are ˚ in bond lengths and a few wavenumwithin 0.005–0.010 A bers in harmonic frequencies [28]. Present work reports on direct VSCF and CC-VSCF computation of the anharmonic vibrational spectra of sulfuryl halides, SO2X2 (X = F, Cl, Br), on MP2 level of theory in 6-31G(df) and ECP SBKJC(3df) basis sets. Equilibrium geometries evaluated in effective core potential basis set are compared with those from high level ab initio calculations using core–core and core–valence correlation enhanced cc-pVnZ basis sets [2]. Anharmonic spectra and vibrational assignments are checked against available gas phase data and compared with the results of scaled quantum mechanical force field approach.

puted by numerical differentiation of analytically calculated energy gradients. Potential energy surfaces and dipole moment components were evaluated directly on MP2 level using 16 point grid (single mode) or 16 · 16 square grid (mode pair) across ½4  xi0:5 ; þ4  xi0:5  range (where xi is the harmonic frequency of ith normal mode) in the normal coordinate space (9360 points), in 631G(df) and SBKJC(3df) basis sets. System potential of the VSCF method has been approximated by the sum of single mode V diag ðQj Þ (diagonal) and mode pair coupling j V coup i;j ðQi ; Qj Þ terms and neglecting higher order interactions between normal modes (e.g., mode triples) [18] N N 1 X N X X V diag ðQj Þ þ V coup ðQi ; Qj Þ; V ðQ1 ; . . . ; QN Þ ¼ j ij j

i

j>i

where Qi denotes ith normal coordinate and N is the number of normal modes. Such 2-mode coupling representation of the potential has successfully been utilized in the description of highly anharmonic systems [34,35] and its application to moderately anharmonic vibrations [6] of sulfuryl halides is properly justified. Wavenumbers of the fundamental and overtone transitions were calculated in anharmonic approximation by direct VSCF method and its correlation corrected extension (CC-VSCF). Correlation correction was evaluated using second order perturbation theory (PT2-VSCF) [21], and virtual configuration interaction (VCI) of singly excited states (equivalent to CIS) followed by degenerate perturbation theory treatment (DPT2-VSCF) [24]. Wavenumbers of fundamentals calculated by PT2-VSCF and DPT2-VSCF methods were virtually identical. Intensities of fundamental and overtone transitions have been computed from MP2 dipole moment surfaces and VSCF wavefunctions of the corresponding states, Ii ¼

8p3 N a ð0Þ ðmÞ 2 xi jhWi ðQi Þj~ lðQi ÞjWi ðQi Þij ; 3hc

and wðmÞ denote VSCF wavefunctions of the where wð0Þ i i ground and the mth excited vibrational states of ith normal mode, xi is the CC-VSCF vibrational frequency of this mode, and the remaining symbols have their usual meaning [35]. 3. Results and discussion

2. Methods 3.1. Equilibrium geometry All ab initio calculations were performed using electronic structure program GAMESS [29]. Equilibrium geometry searches were completed on MP2(frozen core) level using 6-31G(df) and SBKJC(3df) [26,27,30] (SBKJC(3df) notation refers to SBKJC ECP and valence basis set augmented with three d-type and one f-type polarization functions) basis sets on all atoms under C2v symmetry constraints. The same calculation was repeated in large correlation-consistent polarized valence basis set of ccpVTZ type on O, F, Cl, Br atoms [31,33] and cc-pV(T+d)Z basis on sulfur [32,33], with all electrons correlated. Hessian matrices and harmonic vibrational spectra were com-

Experimental re geometry of sulfuryl fluoride derived from its rotational spectrum and combined ab initio CCSD(T)/cc-pVQZ+1 and MP2/cc-pwCVQZ calculation [2] is reproduced reasonably well in 6-31G(df), SBKJC(3df), and cc-pV(T+d)Z basis sets (Table 1). Equilibrium geometry computed on MP2/cc-pV(T+d)Z level differs by less than 0.2 pm in bond lengths and less than 0.2 in bond angles from that determined on the same level with fairly more complex cc-pwCVQZ basis set [2]. Overestimation of r(S@O) and r(S–F) bond lengths, attributable to core– core and core–valence correlation effects [2], decreases in

A.T. Kowal / Chemical Physics 324 (2006) 359–366

361

Table 1 Equilibrium geometry of sulfuryl halides computed at MP2 level in 6-31G(df), cc-pVTZc, and SBKJC(3df) basis sets SO2F2

SO2Cl2 a

Calcd.

r(S@O) [pm] r(S–X) [pm] \(O@S@O) [] \(X–S–X) [] \(O@S–X) [] l [D] A [GHz] B [GHz] C [GHz] a b c

Exptl.

6-31G(df)

cc-pVTZc

SBKJC(3df)

142.5 155.9 125.3 95.0 108.1 1.07 4.9797 4.9259 4.8773

140.5 153.9 125.2 95.4 108.1 1.06 5.1010 5.0519 5.0226

141.2 154.6 125.1 95.4 108.1 1.05 5.0555 5.0048 4.9744

140.1 153.2 124.9 95.5 108.6 – 5.1348 5.0731 5.0571

SO2Br2 b

Calcd.

Exptl.

6-31G(df)

cc-pVTZc

SBKJC(3df)

143.7 201.5 123.5 100.6 107.6 1.66 3.4298 2.3025 1.9127

141.7 201.1 123.6 100.1 107.7 1.65 3.4718 2.3365 1.9292

142.4 200.7 123.5 100.0 107.7 1.72 3.4572 2.3417 1.9345

141.7 201.1 123.5 100.3 108.0 – – – –

Calcd. 6-31G(df)

cc-pVTZc

SBKJC(3df)

144.1 219.9 123.3 101.1 107.6 1.88 2.5667 0.99741 0.84146

142.1 218.7 123.4 101.1 107.6 1.80 2.6134 1.0098 0.85139

142.8 220.5 123.4 101.0 107.6 1.81 2.5746 0.99504 0.83822

Interatomic distances and angles from [2], rotational constants from [6]. Ref. [7]. cc-pVTZ basis on O, F, Cl, and Br atoms and cc-pV(T+d)Z basis on sulfur.

the order 6-31G(df) > SBKJC(3df) > cc-pV(T+d)Z and amounts to 1.1 and 1.4 pm, respectively, in ECP basis whereas computed bond angles are independent of the basis set used and remain within 0.2 of the corresponding experimental values. Shortening of r(S@O) and r(S–F) distances of SO2F2 observed on going from 6-31G(df) to ECP basis (Table 1) can be attributed to the presence of additional d-type polarization functions in SBKJC(3df) basis as well as to the inclusion of core polarization effects in the pseudopotential itself [26,27]. Equilibrium geometry parameters of sulfuryl chloride calculated in ECP basis are also closer to the experimental structure derived from electron diffraction study [7] than those obtained in 6-31G(df) basis, but noticeably inferior to results of MP2/cc-pV(T+d)Z calculation. Interatomic distances of SO2Cl2 computed at MP2/ SBKJC(3df) level differ by 0.7 pm (r(S@O)) and 0.4 pm (r(S–Cl)) from the reported values [7], and bond angles are within 0.3 of those resulting from ED structure determination [7]. Inspection of the r(S@O), r(S–X) distances and \(O@S@O), \(X–S–X) bond angles computed in all three basis sets within SO2X2 (X = F, Cl, Br) series reveals that the trend observed in these geometry parameters is consistent with qualitative predictions [9] and follows that of experimental geometry [2,7]. The discrepancy between experimental and computed variation in \(O@S@O) angle in SO2F2 and SO2Cl2 reported recently [9] has been resolved upon re-determination of SO2F2 equilibrium geometry [2]. Projection of the accuracy of geometry parameters calculated on MP2/SBKJC(3df) level along the SO2X2 series onto sulfuryl bromide substantiates a presumption that equilibrium geometry of SO2Br2 on that level departs from the true geometry by less than 1%. 3.2. Vibrational spectra Harmonic approximation wavenumbers of SO2X2 (X = F, Cl, Br) halides computed on MP2(fc)/cc-pVTZ

and MP2(ae)/cc-pV(T+d)Z levels (Table 2) show striking regularity in overestimation of ma(S@O) and ms(S@O) modes, nearing 50 cm1 in the case of cc-pV(T+d)Z basis. Deformation modes of sulfuryl fluoride calculated in the latter basis are reasonably close to the experiment, but root mean square deviation (RMSD) of all modes exceeds 20 cm1. Harmonic spectrum of SO2Cl2 computed in ccpV(T+d)Z basis differs from that of SO2F2 in slightly worse description of all OSO deformation modes, in particular d(O–S–O) and qw(SO2) vibrations, and higher RMSD of 23.3 cm1. Intensity pattern of ma(S–X) and ms(S–X) transitions varies along SO2X2 series in accord with decreasing electronegativity of X atom, with the exception of sulfuryl chloride, showing negligible intensity of ms(S–Cl) mode. Wavenumbers of the fundamental transitions of sulfuryl fluoride computed in anharmonic approximation in SBKJC(3df) basis (Table 3) are significantly closer to the observed spectrum (RMSD = 9.0 and 7.7 cm1 for CCVSCF, and VSCF, respectively) than those resulting from VSCF calculation in 6-31G(df) basis (RMSD = 16.2 and 17.2 cm1 for CC-VSCF, and VSCF, respectively). Remarkably, harmonic approximation in SBKJC(3df) basis overvalues energies of ma(S@O) and ms(S@O) modes by 20 cm1 and correctly describes (within 5 cm1) those of the remaining fundamentals with RMSD of 7.7 cm1. Anharmonic corrections calculated in ECP basis shift the wavenumbers of ma(S@O) and ms(S@O) stretching modes to 2–4 cm1 apart from the observed spectrum and lower the energy of ma(S–F), ms(S–F) stretching modes, and all deformation modes, by 15–5 cm1 from their harmonic estimates. In consequence fundamental transitions of all but m6(B1) and m1(A1) modes are underestimated. This effect is most pronounced for ma(S–F) mode, where mean field (VSCF) anharmonic correction amounts to 12 cm1. Vibrations of SO2F2 are weakly anharmonic, with mean field effect having predominant influence on anharmonicity. Two-dimensional mapping of the diagonal (V(Qi)) and mode coupling (V(Qi,Qj)) potential [13] (Fig. 1),

124.6 136.5 294.2 83.4 1.9 2.1 7.0 0.0 0.159 1473.8 1222.9 543.9 536.5 306.4 301.8 291.4 240.4 131.9 125.0 135.0 289.3 84.1 2.1 2.4 7.3 0.0 0.157 ma(S@O) ms(S@O) ma(S–Cl) d(OSO) ms(S–Cl) qw(SO2) qr(SO2) qt(SO2) d(ClSCl) 23.3e

149.9 139.0 314.8 106.6 0.5 2.2 4.5 0.0 0.071 1492.2 1239.5 596.6 571.7 416.4 394.8 366.6 279.7 214.2

e

c

d

Refs. [6,36]. Ref. [8]. m – stretching, d – deformation, qr – rocking, qw – wagging, qt – twisting. cc-pVTZ basis on O, F, Cl, and Br atoms and cc-pV(T+d)Z basis on sulfur. RMSD in cm1.

20.8e 13.5e

b

13.5e

150.0 137.2 311.5 109.4 0.8 2.8 5.0 0.0 0.056 1502 1269 887.2 849.5 551.6 544.1 539.1 386.2 384 254.4 159.0 243.2 125.2 28.0 33.8 21.6 0.049 0.0 248.7 156.8 244.4 129.5 27.4 34.6 21.1 0.029 0.0 1527.0 1283.2 879.8 841.2 539.0 531.0 525.9 376.5 373.8

1551.9 1304.7 893.9 856.8 552.8 545.1 540.1 388.2 386.2

Int. m Int. m

a

Mode Exptl. cc-pV(T+d)Z cc-pVTZ

1463.7 1218.1 582.9 559.3 404.6 382.7 358.1 271.4 208.6 ma(S@O) ms(S@O) ma(S–F) ms(S–F) d(OSO) qr(SO2) qw(SO2) d(FSF) qt(SO2)

m

cc-pVTZ

Int.

m

Int.

1434 1205 586 577 408 388 362 282 218

Exptl. cc-pV(T+d)Z

d

SO2Cl2

c a d

SO2F2

8 N P > > jV ðnip Þj >N <

if

N P N > P > > jV ðnip ; njq Þj :

otherwise,

i ¼ j;

p¼1

p¼1 q¼1

1444.1 1201.8 531.1 525.1 298.0 292.0 281.1 232.4 129.1

Int. m m

cc-pVTZ

P ðQi ; Qj Þ ¼

b

Mode

c

SO2Br2

Int.

cc-pV(T+d)Zd

Modec

ma(S@O) ms(S@O) qw(SO2) d(OSO) qr(SO2) ms(S–Br) ma(S–Br) qt(SO2) d(BrSBr)

A.T. Kowal / Chemical Physics 324 (2006) 359–366 Table 2 Harmonic approximation wavenumbers (cm1) and infrared transition intensities (km/mol) of SO2X2 (X = F, Cl, Br) molecules, computed at MP2(FC)/cc-pVTZ and MP2(AE)/cc-pV(T+d)Z levels

362

where nip, njq are grid points and N is the number of grid points, shows that inter-mode coupling has substantial effect on anharmonicity only in case of ma(S@O), ms(S@O), ma(S–F), and ms(S–F) stretching modes (Table 3). The relative strength of the diagonal and mode coupling potential shows no dependence on the basis set used in the calculation (Fig. 2). Vibrational assignments and energy succession of m3, m7, m9 triad place m7qr(SO2) mode above m9qw(SO2) in both basis sets, in accord with the interpretation of high-resolution IR spectrum of SO2F2 [6]. The energy sequence of qt(SO2) and d(F–S–F) modes proposed recently [9] places d(F–S–F) mode at lower energy, based on the analysis of low temperature Ar matrix Raman spectrum of SO2F2 [36]. Reverted order of these modes follows from density functional computation [3], preliminary analysis of the infrared spectrum [6], as well as present work (Table 3), including harmonic approximation spectrum calculated on MP2/ccpV(T+d)Z level (Table 2). Raman intensity pattern of m4(A1) and m5(A2) modes calculated recently [8] also suggests that 384 cm1 band should be assigned to qt(SO2) transition whereas 386.2 cm1 band is likely to originate from d(F–S– F) mode. Nearly coincident positions and small anharmonic corrections of these two modes imply that the assignment of 769.1 cm1 band to 2m4 and 2m5 overtones is reasonable since the computed separation of these two overtones at CCVSCF level amounts to 0.5 cm1. On the other hand, the spacing of 1244.4 and1232.7 cm1 bands observed in the Raman spectrum of SO2F2 [36] makes their assignment to m2 + m5 and m2 + m4 combination modes [36] rather questionable, since these transitions are expected to nearly coincide. Anharmonic approximation of combination transitions in SBKJC(3df) basis suggests that these two bands can alternatively be assigned to m8 + m4(m5) and m2 + m4(m5) combination modes. Although Fermi resonance between m1(A1) fundamental at 1269 cm1 and m2 + m4(A1) combination at 1244.4 cm1 cannot be excluded, one would expect that such resonance will spread resonant states farther apart and decrease energy gap separating transitions assigned to m2 + m4 and m2 + m5 [36]. However, this is not the case, since 1244.4 and 1232.7 cm1 bands are spaced out by 11.7 cm1. The assignment of 1425.4 cm1 band observed in the Raman spectrum of sulfuryl fluoride [36] to m8 + m9(A1) combination transition is supported by CC-VSCF calculated wavenumber of this mode, 1402.5 cm1, even though its energy is slightly underestimated. CC-VSCF computation provides two other combination transitions, m8 + m7(A2) and m8 + m3(B2), close in energy to 1425.4 cm1 band, but their detection in the Raman spectrum is less likely because of much lower intensity [36]. Anharmonic spectrum of sulfuryl chloride computed by CC-VSCF method in SBKJC(3df) basis (Table 4) approximates wavenumbers of the observed fundamentals [8,9]

A.T. Kowal / Chemical Physics 324 (2006) 359–366

363

Table 3 Vibrational transitions (cm1) and infrared intensities of SO2F2 computed at MP2 level in 6-31G(df) and SBKJC(3df) basis sets Modea

6-31G(df)

1 2

3 4

5 6 7 8 9 RMSDe a b c d e

SBKJC(3df)

Harm

VSCF

PT2-VSCF

Int. (km/mol)

Harm

VSCF

PT2-VSCF

Int. (km/mol)

2599.8 1734.3 1539.8 1442.7 1299.9 1295.0 1288.0 1241.2 1234.2 920.9 867.1 748.0 734.1 539.8 532.4 521.8 374.0 367.0

2566.6 1712.7 1519.3 1423.7 1285.8 1275.7 1269.5 1227.0 1221.3 907.3 858.2 739.5 727.7 535.4 528.2 517.7 370.4 364.2

2555.3 1705.2 1516.7 1423.6 1280.1 1275.6 1269.5 1225.0 1219.3 905.4 854.5 738.5 727.4 534.9 528.2 517.6 369.8 364.0

0.36 0.35 246.1 0.01 157.1 0.24 0 0.03 0 231.5 118.6 0.02 0 34.0 37.5 26.9 0.1 0.0

2561.2 1698.2 1520.4 1420.5 1280.6 1268.8 1267.9 1233.4 1232.5 884.5 849.1 768.5 766.9 547.6 539.4 536.0 384.3 383.4

2536.9 1678.3 1503.6 1402.9 1271.0 1250.6 1250.3 1220.2 1220.2 872.1 841.2 760.6 759.4 543.6 535.5 532.2 380.8 380.2

2525.0 1669.8 1500.9 1402.5 1265.0 1250.2 1250.0 1218.0 1217.9 869.9 837.0 759.6 759.1 543.1 535.4 532.0 380.2 380.0

0.39 0.37 240.6 0 150.7 0.21 0.01 0.05 0 229.2 118.6 0.03 0 24.8 30.6 19.0 0.03 0.0

23.2

17.2

16.2

7.7

7.7

9.0

Exptl.b

Assignmentd

1502 1425.4c 1269 1244.4c 1244.4c 1232.7c 1232.7c 887.2 849.5 769.1c 769.1c 551.6 544.1 539.1 386.2 384

2m1 2m2 m6(B1)ma(S@O) m8 + m9 m1(A1)ms(S@O) m8 + m4 m8 + m5 m2 + m4 m2 + m5 m8(B2)ma(S–F) m2(A1)ms(S–F) 2m4 2m5 m3(A1)d(OSO) m7(B1)qr(SO2) m9(B2)qw(SO2) m4(A1)d(FSF) m5(A2)qt(SO2)

Fundamental transitions labeled in order of decreasing wavenumber. Ref. [6]. Ref. [36]. m – stretching, d – deformation, qr – rocking, qw – wagging, qt – twisting. In cm1, excluding overtone and combination transitions.

9

9

8

8

7

7

6

6

5

5

4

4

3

3

2

2

1

1 1

2

3

4

5

6

7

8

9

1

2

3

4

5

6

7

8

9

Fig. 1. Two-dimensional mapping of the diagonal (V(Qi)) and mode coupling (V(Qi,Qj)) potential of SO2F2 at MP2/SBKJC(3df) level. Modes are labeled in the order of decreasing wavenumber (first column of Table 3) and relative strength of the potential is coded in shades of gray (0 – white, 255 – black).

Fig. 2. Two-dimensional mapping of the diagonal (V(Qi)) and mode coupling (V(Qi,Qj)) potential of SO2F2 at MP2/6-31G(df) level. Modes are labeled in the order of decreasing wavenumber (first column of Table 3) and relative strength of the potential is coded in shades of gray (0 – white, 255 – black).

with RMSD of 6.5 cm1 while that obtained in 6-31G(d) basis shows larger deviation of 13.9 cm1. Harmonic approximation provides acceptable description of m(S–Cl) stretching and all deformation modes, while ma(S@O) and ms(S@O) modes are significantly overestimated. Anharmonic corrections calculated in the former basis set vary from 2–3 cm1 for deformation and m(S–Cl) stretching

modes to 15–20 cm1 in case of m(S@O) modes and are almost exclusively due to mean field (VSCF) effect. Mode coupling pattern of SO2Cl2 (Fig. 3) resembles that of sulfuryl fluoride (Fig. 1), except for much weaker strength of m1– m8 and m1–m2 coupling, leading to the conclusion that only m6, m1, m8, and m2 modes are weakly coupled to each other. Nonetheless, coupling between ms(S–Cl) and d(OSO),

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A.T. Kowal / Chemical Physics 324 (2006) 359–366

Table 4 Vibrational transitions (cm1) and infrared intensities of SO2Cl2 computed at MP2 level in 6-31G(df) and SBKJC(3df) basis sets Mode

6-31G(df)

1 2 3 4 5 6 7 8 9 RMSDb

SBKJC(3df)

Harm

VSCF

PT2-VSCF

Int. (km/mol)

Harm

VSCF

PT2-VSCF

Int. (km/mol)

2468.3 1143.5 1481.2 1234.2 612.8 571.7 417.3 393.4 366.6 264.0 209.2

2437.7 1138.1 1461.8 1221.0 607.7 569.4 413.3 389.8 363.4 263.7 207.8

2430.4 1135.4 1459.1 1216.1 607.0 568.9 413.0 389.5 363.3 263.4 207.8

0.5 0.1 168.0 148.5 342.7 130.4 0.1 0.3 11.0 0.0 0.01

2439.6 1138.9 1464.2 1219.8 594.0 569.4 419.1 397.3 365.1 279.2 217.8

2417.9 1131.6 1448.0 1211.3 589.5 566.2 415.8 394.2 363.1 277.9 216.1

2431.2 1130.3 1445.3 1206.2 588.9 565.6 415.5 393.9 363.0 277.7 216.1

0.4 0.1 140.5 129.6 288.4 98.0 0.4 2.1 3.5 0.0 0.12

22.0

15.0

13.9

12.8

7.3

6.5

Exptl.a

Assignmentc

1434 1205 586 577 408 388 362 282 218

2m1 2m2 m6(B1)ma(S@O) m1(A1)ms(S@O) m8(B2)ma(S–Cl) m2(A1)d(OSO) m3(A1)ms(S–Cl) m9(B2)qw(SO2) m7(B1)qr(SO2) m5(A2)qt(SO2) m4(A1)d(ClSCl)

Only overtone transitions with intensity exceeding 0.1 km/mol are listed. a Ref. [8]. b In cm1, excluding overtone transitions. c m – stretching, d – deformation, qr – rocking, qw – wagging, qt – twisting.

9 8 7 6 5 4 3 2 1 1

2

3

4

5

6

7

8

9

Fig. 3. Two-dimensional mapping of the diagonal (V(Qi)) and mode coupling (V(Qi,Qj)) potential of SO2Cl2 at MP2/SBKJC(3df) level. Modes are labeled in the order of decreasing wavenumber (first column of Table 3) and relative strength of the potential is coded in shades of gray (0 – white, 255 – black).

qw(SO2) modes is strong enough to rise the energy of d(OSO) deformation mode and lower that of qw(SO2) mode with respect to wavenumbers observed in the spectrum of SO2F2. As a result of this coupling, ms(S–Cl) and d(OSO) modes contribute evenly to transitions observed at 577 and 408 cm1 [9] whereas qw(SO2) mode enters into transitions at 586 and 388 cm1. Assignments of ma(S@O), ms(S@O), ma(S–Cl), and ms(S–Cl) stretching modes are unambiguous and their wavenumbers calculated by CCVSCF method in ECP/valence basis set are remarkably close to the experimental spectrum [8]. On the other hand, the assignment of SO2 rocking and wagging vibrations has been controversial. Energy sequence of q(SO2) deformation

modes analogous to that of SO2F2 (qr(SO2) 388 cm1 > qw(SO2) 362 cm1 > qt(SO2) 282 cm1) [8] has been revised recently upon reinvestigation of low-temperature infrared and Raman spectra in the range of m9, m7, m5 transitions [9] such that qw(SO2) mode is placed higher in energy than qr(SO2) one. The same ordering of these modes was obtained in anharmonic approximation in both basis sets (Table 4), whereas wavenumbers computed in ECP basis deviate from experiment by less than 6 cm1. Only 2m1(A1) and 2m2(A1) overtone transitions of sulfuryl chloride were found to have observable infrared intensity (Table 4) and their wavenumbers are very similar in both basis sets. There is no experimental evidence of SO2Br2 species thus far, and anharmonic spectra of sulfuryl bromide reported in Table 5 can be viewed as extension of data computed within SO2X2 series and an alternative to scaled quantum mechanical force field approach reported recently [9]. Vibrations of SO2Br2 are weakly anharmonic, with major part of the anharmonic correction coming from mean field effect and no significant influence of mode correlation, as evidenced by nearly coinciding VSCF and CC-VSCF wavenumbers. Inter-mode coupling potentials (Fig. 4) are significant for mode dyads comprising ms(S@O) mode paired with any of (SO2) deformation modes and ms(S–Br), ma(S–Br) mode pair. On one hand, the wavenumbers of qw(SO2) and d(OSO) modes of SO2Br2 computed by CC-VSCF are lower in energy than those of sulfuryl fluoride and have reversed order. On the other hand, a systematic decrease in the energy of ma(S@O), ms(S@O), qr(SO2), and qt(SO2) transitions can be noted on going along SO2F2, SO2Cl2, SO2Br2 series in both basis sets. Vibrational spectrum of sulfuryl bromide calculated from scaled quantum mechanics force field [9] is very close to the CCVSCF anharmonic approximation and spectral assignments resulting from either method are virtually identical. However, direct VSCF computation of the anharmonic

A.T. Kowal / Chemical Physics 324 (2006) 359–366

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Table 5 Vibrational transitions (cm1) and infrared intensities of SO2Br2 computed at MP2 level in 6-31G(df) and SBKJC(3df) basis sets Mode

6-31G(df)

1 2 3 4 5 6 7 8 9

Assignmenta

SBKJC(3df)

Harm

VSCF

PT2-VSCF

Int. (km/mol)

Harm

VSCF

PT2-VSCF

Int. (km/mol)

2440.2 1060.2 1464.4 1220.1 550.5 530.1 303.7 299.6 285.9 222.2 129.9

2410.3 1057.5 1445.1 1207.2 547.7 528.7 301.4 297.4 283.3 223.2 129.0

2408.6 1055.4 1442.5 1206.3 547.2 528.0 301.1 296.5 283.0 222.4 128.9

0.4 0.1 135.3 139.3 303.7 97.4 4.9 2.3 3.8 0.0 0.05

2404.9 1060.3 1445.4 1202.5 532.5 530.2 300.0 293.6 284.0 236.4 133.3

2384.1 1055.4 1429.4 1194.2 530.2 527.7 299.1 291.5 281.8 236.2 132.4

2381.6 1053.3 1426.7 1193.0 529.7 526.9 298.8 290.6 281.5 235.5 132.4

0.4 0.1 112.1 124.1 264.3 73.8 1.0 2.1 7.2 0.0 0.24

2m1 2m2 m6(B1)ma(S@O) m1(A1)ms(S@O) m8(B2)qw(SO2) m2(A1)d(OSO) m7(B1)qr(SO2) m3(A1)ms(S–Br) m9(B2)ma(S–Br) m5(A2)qt(SO2) m4(A1)d(BrSBr)

Only overtone transitions with intensity exceeding 0.1 km/mol are listed. a m – stretching, d – deformation, qr – rocking, qw – wagging, qt – twisting.

MP2/SBKJC(3df) level correctly describe experimental transitions of SO2F2 and SO2Cl2 with RMSD of 9.0 and 6.5 cm1, respectively. Accuracy of the predicted anharmonic spectrum of SO2Br2 is equivalent to that obtained by scaled quantum mechanical force field method [8]. Wavenumbers and intensities of overtone and combination transitions of sulfuryl halides were acquired without extra computational effort and are within 6–20 cm1 of their experimental counterparts in the case of SO2F2. Vibrations of SO2X2 species are weakly anharmonic with predominant contribution to the anharmonic correction coming from the mean field effect. Inter-mode coupling has pronounced effect on the wavenumbers of ma(S@O), ms(S@O) stretching modes of all sulfuryl halides and in particular d(OSO) and qw(SO2) modes of sulfuryl chloride.

9 8 7 6 5 4 3 2 1 1

2

3

4

5

6

7

8

9

Fig. 4. Two-dimensional mapping of the diagonal (V(Qi)) and mode coupling (V(Qi,Qj)) potential of SO2Br2 at MP2/SBKJC(3df) level. Modes are labeled in the order of decreasing wavenumber (first column of Table 3) and relative strength of the potential is coded in shades of gray (0 – white, 255 – black).

Acknowledgement A generous grant of the computer time from the Wrocław Center for Networking and Supercomputing (WCSS) is gratefully acknowledged. References

spectrum of SO2Br2 does not require any scaling procedure or calculation of the spectra of homologous species. 4. Conclusions Application of effective core potential–valence basis set SBKJC(3df) to the evaluation of equilibrium geometry and vibrational spectra of sulfuryl halides, SO2X2 (X = F,Cl,Br), on MP2 level of theory demonstrated that performance of ECP basis set is slightly inferior to that of all-electron basis of triple zeta quality. Direct VSCF calculation of the anharmonic spectra of SO2X2 halides in ECP basis provided first-principles based and computer efficient way of obtaining vibrational characteristics of these compounds. Vibrational spectra computed in anharmonic approximation by direct CC-VSCF method on

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