Theoretical study of the atomization energy and geometry of sulfur dioxide and sulfur monoxide

Theoretical study of the atomization energy and geometry of sulfur dioxide and sulfur monoxide

Journal of Molecular Structure (Theochem) 467 (1999) 187–193 Theoretical study of the atomization energy and geometry of sulfur dioxide and sulfur mo...

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Journal of Molecular Structure (Theochem) 467 (1999) 187–193

Theoretical study of the atomization energy and geometry of sulfur dioxide and sulfur monoxide Branko S. Jursic Department of Chemistry, University of New Orleans, New Orleans, LA 70148, USA Received 24 August 1998; accepted 8 September 1998

Abstract Computational studies with complete basis set, hybrid, gradient-corrected, and local spin density approximation density functional methods were performed on sulfur dioxide and sulfur oxide with target to compute their structure, bond dissociation energies, vibrational spectra, and atomization energies. The obtained results are compared with the experimental results. It was demonstrated that the complete basis set ab initio method and the hybrid DFT method were accurate for computing bond dissociation energies. The total atomization energy is better described using the gradient-corrected density functional method. It was demonstrated that sulfur dioxide is a very difficult computational system that requires a larger basis set and a high order electronic interaction for its proper description. q 1999 Elsevier Science B.V. All rights reserved. Keywords: Atomization energy; Sulfur dioxide; Sulfur monoxide

1. Introduction There is no question that sulfur dioxide and sulfur oxides are very important species in view of atmospheric pollution. There are at least two ways in which sulfur dioxide influences the environment; through the formation of a strong H2SO3 mineral acid with its reaction with moisture in the air, and by incorporating sulfur dioxide in photosynthesis instead of carbon dioxide. This molecule has been the subject of numerous spectroscopic studies [1–3]. Its vibrational spectrum at high excitation is considered to be a classic example of the normal mode limit behavior. On the other hand, sulfur oxide (SO) has a very intriguing chemistry. The major source of sulfur monoxide in planetary and terrestrial atmospheres is through the photodissociation of SO2 1 hn , giving SO 1 O, at 194 nm [4]. Although sulfur dioxide and sulfur oxide are relatively small chemical systems, one can expect that the

chemical and physical properties of such small chemical systems should be well described by computational methods. That is true when the couple cluster ab initio computational method with the spdfg basis set quality is used. This theory well describes most, but not all, of the sulfur dioxide properties [5,6]. Geometric parameters for the structures are not in good agreement with the experimental values. In the paper of application of Gaussian-1 (G1) model to second-row molecules [7], it was pointed out that in the computation of the total atomization energy (TAE) of sulfur dioxide, the G1 exhibits an unusually high error (7.4 kcal/mol). Recently, this problem was addressed again through the basis set convergence study on the sulfur dioxide atomization energy [8]. Some of the DFT computational studies [9,10] on this problem were performed recently, as well as complete basis set ab initio [11] computational studies. Here, we would like to present a systematic study of the sulfur dioxide atomization energy, as well

0166-1280/99/$ - see front matter q 1999 Elsevier Science B.V. All rights reserved. PII: S0166-128 0(98)00484-9

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Table 1 Structural parameters for SO2 and SO computed with ab initio and density functional theory methods

Theory

˚ r1/A

a1/8

˚ r2/A

HF/6-31G(d’) MP2/6-31G(d’) B3LYP/6-31G(d) BLYP/6-31G(d) SVWN/6-31G(d) B3LYP/6-311G(2d) BLYP/6-311G(2d) SVWN/6-311G(2d) B3LYP/6-311G(3df) BLYP/6-311G(3df) SVWN/6-311G(3df) B3LYP/6-31111G(3df) BLYP/6-31111G(3df) SVWN/6-31111G(3df) Experimental

1.411 1.471 1.464 1.490 1.467 1.445 1.436 1.471 1.436 1.460 1.438 1.461 1.447 1.438 1.432

118.8 119.9 119.1 119.1 119.3 119.2 119.4 119.0 119.3 119.0 119.3 119.1 119.4 119.5 119.5

1.464 1.521 1.518 1.545 1.517 1.499 1.525 1.498 1.488 1.513 1.487 1.488 1.513 1.488 1.481

as the relative stability of singlet and triplet sulfur oxide by using both CBSQ and three of the most common density functional theory methods.

2. Computational methods All computational studies are performed with the Gaussian 94 [12] computational package with ab initio methods as implemented in the computational package. The complete basis set (CBS) method was developed by Petersson and coworkers [13–16]. The family name reflects the fundamental observation underlying these methods that the largest error in the ab initio calculations results from basis set truncation. The energy of the chemical system is computed from a series of calculations. The initial calculation starts with geometry optimization and frequency calculation at HF/6-31G(d’) theory level (see Ref. [17] and references therein). The geometry is further optimized at MP2/6-31G(d’) [18–20] theory level with single point energy calculation at QCISD(T)/6311G(d’) [21]; MP4(SDQ)/CBSB4 [22]; and MP2/ CBSB3. The model also has empirical corrections

for spin contamination and a size-consistent, highorder correction. An explanation for basis set abbreviation can be found elsewhere [23]. All energies are computed on fully optimized structures of anions, cations, and neutral molecules. Throughout the text, if the theory level is not specified then the discussed energies are obtained through CBSQ (0 K) computational studies. We believe that these are currently the most accurate energies obtained by computational studies. Density functionals used in this study are as they are incorporated in the Gaussian 94 computational package [12]. There are three commonly used density functional theory methods: hybrid B3LYP, gradientcorrected BLYP, and local spend density approximation SVWN were used in combination with the 6-31G(d,p), 6-311G(2d,2p), and 6-311G(3df,3pd) basis sets. The Gaussian B3LYP implementation is a slight version of Becke’s three-parameters hybrid functional [24]. The Gaussian Becke’s threeparameter functional has the following form: (1 2 a0) × Ex(LSDA) 1 a0 × Ex(HF) 1 ax × Delta 2 Ex(B88) 1 ac × Ec(LYP) 1 (1 2 ac) × Ec(VWN), where the energy terms are the Slater exchange, the Hartree–Fock exchange, Beckes 1988 exchange functional correction [25], the gradient-corrected correlation functional of Lee et al. [26], and the local correlation functional of Vosko et al., [27] respectively. The values of the coefficients determined by Becke are as follows: a0 ˆ 0.20, ax ˆ 0.72, and ac ˆ 0.81. Gradient-corrected BLYP is a combination of Becke’s 1988 exchange functional [25] and Lee et al. [26] correlation functional. The local spin density approximation (LSDA or SVWN) is a combination of Slater’s exchange functional [28–30] and exchange functional provided by Vosko et al. [27]. The 631G(d), 6-311G(2d), 6-311G(3df), and 631111G(3df) basis sets were used for density functional theory study. For their explanation see Ref. [23].

3. Results and discussion It was noted that there are certain discrepancies between the G1 computed sulfur dioxide atomization energies, but we should also note that there is a discrepancy between the computed geometry and the

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Table 2 Total energies (a.u.) for singlet sulfur dioxide (EI), triplet sulfur oxide (EII), triplet sulfur atom (EIII) and triplet oxygen atom (EIV) computed with complete basis set ab initio and various density functional theory methods Theory level

EI

EII

EIII

EIV

CBSQ (0 K) CBSQ B3LYP/6-31G(d) B3LYP/6-31G(d)(0 K) B3LYP/6-311G(2d) B3LYP/6-311G(2d)(0 K) B3LYP/6-311G(3df) B3LYP/6-311G(3df)(0 K) B3LYP/6-31111G(3df) B3LYP/6-31111G(3df)(0 K) BLYP/6-31G(d) BLYP/6-31G(d)(0 K) BLYP/6-311G(2d) BLYP/6-311G(2d)(0 K) BLYP/6-311(3df) BLYP/6-311G(3df)(0 K) BLYP/6-31111G(3df) BLYP/6-31111G(3df)(0 K) SVWN/6-31G(d) SVWN/6-31G(d)(0 K) SVWN/6-311G(2d) SVWN/6-311G(2d)(0 K) SVWN/6-311G(3df) SVWN/6-311(3df)(0 K) SVWN/6-31111G(3df) SVWN/6-31111G(3df)(0 K)

2 548.035079 2 548.031092 2 548.587480 2 548.580682 2 548.685803 2 548.678915 2 548.710075 2 548.703017 2 548.715962 2 548.708945 2 548.573567 2 548.567313 2 548.674217 2 548.667862 2 548.696535 2 548.690001 2 548.703505 2 548.697016 2 546.813813 2 546.807133 2 546.918015 2 546.911234 2 546.941686 2 546.934746 2 546.947110 2 546.940223

2 472.841843 2 472.838522 2 473.352481 2 473.349930 2 473.411051 2 473.408483 2 473.422622 2 473.419987 2 473.426985 2 473.424349 2 473.337110 2 473.334752 2 473.398659 2 473.396287 2 473.409462 2 473.407019 2 473.414348 2 473.411907 2 471.919696 2 471.917155 2 471.982756 2 471.980193 2 471.994237 2 471.991608 2 471.957574 2 471.954950

2 397.656892 2 397.654532 2 398.104993 2 398.10493 2 398.132265 2 398.132265 2 398.133505 2 398.133505 2 398.134498 2 398.134498 2 398.087011 2 398.087011 2 398.117100 2 398.117100 2 398.118311 2 398.118311 2 398.119129 2 398.119129 2 397.017672 2 397.017672 2 397.047577 2 397.047577 2 397.050559 2 397.050559 2 397.051716 2 397.051716

2 74.987061 2 74.984700 2 75.060623 2 75.060623 2 75.085571 2 75.085571 2 75.086464 2 75.086464 2 75.090915 2 75.090915 2 75.046962 2 75.046962 2 75.073567 2 75.073567 2 75.074454 2 75.074454 2 75.080286 2 75.080286 2 74.643341 2 74.643341 2 74.669060 2 74.669060 2 74.669824 2 74.669824 2 74.674557 2 74.674557

experimentally determined geometry. It actually does not come as a surprise that MP2, as well as the lower level of ab initio methods with a modest basis set, cannot properly describe geometries of molecules such as sulfur dioxide and sulfur oxide. The reason for this is these molucules are small and polar, and for their property description, the computational method with a high level of electron correlation is required. Some of the density functional theory methods [31– 34] are becoming the method of choice for generating the geometries of such demanding chemical systems [35–46]. The best experimental estimation of sulfur dioxide ˚ for the S–O bond distance (r1) and 109.58 is 1.432 A for the O–S–O bond angle (a1) [47–49], and for sulfur oxide the S–O bond is estimated to be ˚ (r2). The computed sulfur dioxide structure 1.481 A with various basis sets are presented in Table 1. As expected, the computed geometries of these two

compounds with small basis sets, such as 6-31G(d) are far from the experimental values. The HF/631G(d) computed bond distances are too short, and the MP2/6-31G(d) bond distances are too long. The B3LYP with 6-31G(d) generate better structures for both sulfur dioxide and sulfur oxide, although with such a small basis set, the computed geometries are still quite far from the experimental geometries. With larger basis sets, all three density functional theory methods produce satisfactory SO2 and SO geometries. The best geometries are obtained with the B3LYP/6311G(3df) theory model (Table 1). Let us now compute the total atomization energies for sulfur dioxide and sulfur oxide [50,51]. Total energies for sulfur dioxide, sulfur oxide, sulfur, and oxygen atoms computed with various theory levels are presented in Table 2. In some of our previous studies, we have demonstrated that complete basis set ab initio methods can produce accurate bond

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Table 3 Computed total atomization energies (kcal/mol) for SO2 (TAE(SO2)) and the SO (TAE(SO)) and their difference (kcal/mol) from experimental values (DTAE(SO2) and DTAE(SO)). BDE(SO2) ˆ the S–O bond dissociation energy in the SO2; DBDE(SO2) ˆ difference between experimental (123.60 kcal/mol) and computed S–O bond dissociation energy in the SO2; AE(SO) ˆ the S–O bond dissociation energy (atomization energy) for the SO; DAE(SO) ˆ difference between experimental (125.67 kcal/mol) and computed atomization energy for SO; TAE(SO2) ˆ total atomization energy for SO2; DTAE(SO2) ˆ difference between experimental (259.30 kcal/mol) and computed total atomization energy for SO2 Theory level

BDE(SO2)

DBDE(SO2)

AE(SO)

D AE(SO)

TAE(SO2)

DTAE(SO2)

CBSQ (0 K) CBSQ B3LYP/6-31G(d) B3LYP/6-31G(d)(0 K) B3LYP/6-311G(2d) B3LYP/6-311G(2d)(0 K) B3LYP/6-311G(3df) B3LYP/6-311G(3df)(0 K) B3LYP/6-31111G(3df) B3LYP/6-31111G(3df)(0 K) BLYP/6-31G(d) BLYP/6-31G(d)(0 K) BLYP/6-311G(2d) BLYP/6-311G(2d)(0 K) BLYP/6-311(3df) BLYP/6-311G(3df)(0 K) BLYP/6-31111G(3df) BLYP/6-31111G(3df)(0 K) SVWN/6-31G(d) SVWN/6-31G(d)(0 K) SVWN/6-311G(2d) SVWN/6-311G(2d)(0 K) SVWN/6-311G(3df) SVWN/6-311(3df)(0 K) SVWN/6-31111G(3df) SVWN/6-31111G(3df)(0 K) CCSD(T)/AVTZ CCSD(T)/AV5Z CCSD(T)/AV5Z 1 2d1f Experimental

129.37 130.44 109.42 106.76 118.71 116.00 126.12 123.35 124.28 121.53 118.91 116.46 126.75 124.25 133.42 130.85 131.07 128.52 157.36 154.76 167.04 164.39 174.21 171.50 197.65 194.97

2 5.77 2 6.84 14.18 16.84 4.89 7.60 2 2.52 0.25 2 0.68 2.07 4.69 7.14 2 3.15 2 0.65 2 9.82 2 7.25 2 7.47 2 4.93 2 33.76 2 31.16 2 43.44 2 40.79 2 50.61 2 47.90 2 74.05 2 71.37

124.18 125.05 117.26 115.70 121.24 119.63 127.16 125.51 126.49 124.83 127.47 125.99 130.51 129.03 135.98 134.44 134.87 133.34 162.32 160.73 166.99 165.38 171.84 170.19 145.14 143.49 117.26 124.38 124.81 125.67

1.49 0.62 8.41 9.97 4.43 6.04 2 1.49 0.16 2 0.82 0.84 2 1.80 2 0.32 2 4.84 2 3.36 2 10.31 2 8.77 2 9.20 2 7.67 2 36.65 2 35.06 2 41.32 2 39.71 2 46.17 2 44.52 2 19.47 2 17.82 8.41 1.29 0.86 0.0

253.55 255.49 226.68 222.45 239.95 235.63 253.29 248.86 250.77 246.37 246.38 242.45 257.26 253.28 269.40 265.30 265.94 261.87 319.69 315.49 334.03 329.77 346.05 341.70 342.79 338.47 236.67 255.72 257.14 259.30

5.75 3.81 32.62 36.85 19.35 23.67 6.01 10.44 8.53 12.93 12.92 16.85 2.04 6.02 2 10.10 2 6.00 2 6.64 2 2.57 2 60.39 2 56.19 2 74.73 2 70.47 2 86.75 2 82.40 2 83.49 2 79.17 22.63 3.58 2.16 0.0

123.60

0.0

dissociation energies for relatively small chemical systems [52–54]. This is also true for hybrid B3LYP with an adequate basis set, as well as for some molecular systems for gradient-corrected BLYP [55–60]. Therefore, one can expect that the experimental S–O bond dissociation energies for both sulfur dioxide and sulfur oxide should be reproduced well with these computational methods. The S– O bond dissociation energy (D0) in sulfur dioxide is estimated experimentally to be 123.60 kcal/mol or 5.359 eV [50,51]. To our surprise, the CBSQ (0 K) computed bond dissociation energy is 6.84 kcal/mol higher than the experimental value (Table 3). Usually

this method generates energies that are 1–2 kcal/mol away from the experimental values [61–65]. There is a widespread belief that the density functional theory methods display low basis set sensitivities, and that relatively good computational results can be obtained with a modest size basis set such as 6-31G(d). In the case of the S–O bond dissociation energy for sulfur dioxide, it is obvious that this is not true. The B3LYP/ 6-31G(d) computed bond dissociation energy is 16.84 kcal/mol lower than the experimental value (Table 3). By increasing the size of the basis set to 6-311G(2d) the B3LYP computes an S–O bond dissociation energy that is 7.6 kcal/mol lower than the

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Table 4 Density functional theory computed harmonic frequencies (v , cm 21) with 6-311G(3df) basis set

v1 v2 v3 SOD a

cc-pVTZ a

VQZ a

AVQZ 1 1 a

B3LYP

BLYP

SVWN

Exp.

513.47 1148.6 1353.8 56.0

520.0 1161.7 1369.4 20.8

519.5 1166.1 1376.2 10.1

521.8 1185.7 1390.5 26.5

489.2 1092.1 1286.6 204

502.6 1167.1 1276.7 125.5

522.2 1167.9 1381.8 0.0

Computed with CCSD(T) ab initio method with these two basis sets; SOD ˆ sum of the frequency deviation from the experimental values.

experimental value. After adding the f functional to the basis set, the computed and experimental values actually become almost identical, only exhibiting a difference of 0.25 kcal/mol. Adding the diffusion functional to the basis set does not produce a better agreement with the experimental data. On the contrary, it generates a larger computational error (Table 3). The gradient-corrected BLYP actually produced a better S–O bond dissociation energy for sulfur dioxide with the 6-311G(2d) basis set than with the 6-311G(3df) basis set. The computed error is 0.65 kcal/mol (Table 3). On the other hand, regardless of the basis set size, the S–O bond dissociation energy for sulfur dioxide computed with local spin density approximation (LSDA or SVWN as used in Gaussian) substantially underestimates the bond dissociation energy. The bond dissociation energy for sulfur oxide is also the atomization energy. Here we have a much better agreement between the CBSQ computed value and the experimental value (Table 3). The computational error is only 0.62 kcal/mol, a difference that would be expected for such an accurate computational method as CBSQ. Again, the best agreement with the computed and experimental bond dissociation energy was obtained with the B3LYP/6-311G(3df) theory model. The computed error is only 0.16 kcal/mol, a much better agreement than that which was obtained with the complete basis set ab initio method (Table 3). The other DFT methods behave in the same manner as in the case of the sulfur dioxide bond dissociation energy. Now we will examine the total atomization energy for sulfur dioxide. As it was mentioned before, the total atomization energy computed with the G1 ab initio method is 7.4 kcal/mol lower than the experimental value. Here, again, we have demonstrated the superiority of the complete basis set ab initio method

for computing thermodynamics of chemical systems, with regard to Gaussian computational approaches. The atomization energy is underestimated by only 3.81 kcal/mol (Table 2). To our surprise, B3LYP/6311G(3df), which computes the most accurate S–O bond dissociation energies for sulfur dioxide and sulfur oxide, underestimates the total atomic energy for sulfur dioxide even more than the G1. The computed error is 10.44 kcal/mol (Table 3). The best agreement was obtained with the gradientcorrected BLYP density functional methods. The computational error varies with the size of the basis set from 2.04 kcal/mol to 10.10 kcal/mol (Table 3). When these results are compared with CCSD(T) ab initio studies [8], by using relatively large basis sets (for basis set explanation, see Refs. [8,66–70]), the quality of the computed bond dissociation, as well the atomization energies, are comparable with those computed with hybrid and gradient-corrected density functional theory methods (Table 3). On many previous occasions, we have demonstrated that hybrid B3LYP, and in some cases BLYP gradient-corrected DFT methods with appropriate basis sets, can very accurately compute vibrational spectra for small chemical systems [71–74]. The frequencies for sulfur dioxide are determined experimentally [1–3] as 522.2; 1167.9, and 1381.8 cm 21 (Table 4). Unscaled density functional generated vibrations are compared with both experimental and some CCSD(T) obtained frequencies. Again, we have demonstrated that the hybrid DFT methods compute relatively good vibrational spectra for chemical systems. The sum of the deviation from the experimental values is 26.5 cm 21, which is comparable with the spectra computed with CCSD(T)/VQZ. Surprisingly, not as good an agreement was obtained with the gradient-corrected BLYP density functional theory method.

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4. Conclusion The S–O bond dissociation energies and atomization energies for sulfur dioxide and sulfur oxide have been studied with the complete basis set ab initio method, hybrid gradient-corrected, and local spin density approximation density functional methods. In addition, the CCSD(T) ab initio method was used, and a vibration spectra of sulfur dioxide was computed. It was clearly demonstrated that for such a unique molecular system, such as sulfur dioxide, a relatively larger basis set is necessary. The addition of the f polarization functional seems to be crucial for the correct evaluation of the atomization energy. The best agreement between computed and experimental S–O bond dissociation energies for sulfur dioxide and sulfur oxide were obtained with the hybrid B3LYP/ 6-311G(3df) theory model, while the best SO2 atomization energy was obtained with BLYP gradientcorrected density functional theory method. The CBSQ ab initio method is more accurate than the G1 ab initio method. The frequencies, as well as geometries, of these two molecules are best described with the hybrid DFT method. The DFT methods outperform many ab initio methods and will produce energies as accurate as CBSQ or CCSD(T) ab initio methods with large basis sets. In summary, it can be said that computing the atomization energy of sulfur dioxide is proven to be as demanding computationally as it is with ab initio methods. In general, it can be concluded that hybrid and gradient-corrected DFT methods should well describe these two chemical systems, and the information obtained from this calculation should be reliable. References [1] W.J. Lafferty, A.S. Pine, J.M. Flaud, C. Camy-Peyret, J. Mol. Struct. 157 (1993) 499. [2] F.J. Lovas, J. Phys. Chem. Ref. Data 14 (1985) 395. [3] R.D. Shelton, A.H. Nielsen, W.H. Fletcher, J. Chem. Phys. 21 (1953) 2178. [4] T. Klaus, S.P. Belov, A.H. Saleck, E. Herbst, J. Mol. Spectrosc. 168 (1994) 235. [5] Y. Pak, R.C. Woods, J. Chem. Phys. 104 (1996) 5547. [6] K. Raghavachari, G.W. Trucks, J.A. Pople, M. Head-Gordon, Chem. Phys. Lett. 157 (1983) 479. [7] L.A. Curtiss, C. Jones, G.W. Trucks, K. Raghavachari, J.A. Pople, J. Chem. Phys. 93 (1993) 2537.

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