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Spin-Orbit Effect on the Molecular Properties of TeX (X=F, Cl, Br, and I; n=1, 2, and 4): A Density Functional Theory and Ab Initio Study Jiwon Moon, and Joonghan Kim J. Phys. Chem. A, Just Accepted Manuscript • DOI: 10.1021/acs.jpca.6b06176 • Publication Date (Web): 07 Sep 2016 Downloaded from http://pubs.acs.org on September 9, 2016

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The Journal of Physical Chemistry

Spin-Orbit Effect on the Molecular Properties of TeXn (X=F, Cl, Br, and I; n=1, 2, and 4): A Density Functional Theory and Ab Initio Study Jiwon Moon and Joonghan Kim* Department of Chemistry, The Catholic University of Korea, Bucheon 14662, Republic of Korea

*Email: [email protected] Tel: +82-2-2164-4338 Fax: +82-2-2164-4764

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ABSTRACT Density functional theory (DFT) and ab initio calculations, including spin-orbit coupling (SOC), were performed to investigate the spin-orbit (SO) effect on the molecular properties of Tellurium halides, TeXn (X=F, Cl, Br, and I; n=1, 2, and 4). SOC elongates the Te−X bond and slightly reduces the vibrational frequencies. Consideration of SOC leads to better agreement with experimental values. The Møller-Plesset second-order perturbation theory (MP2) seriously underestimates the Te−X bond lengths. In contrast, B3LYP significantly overestimates them. SO-PBE0 and multireference configuration interactions with the Davidson correction (MRCI+Q), which include SOC via a state-interaction approach, give the Te−I bond length of TeI2 that matches experimental value. On the basis of the calculated thermochemical energy and optimized molecular structure, TeI4 is unlikely to be stable. The use of PBE0 including SOC is strongly recommended for predicting the molecular properties of Te-containing compounds.


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INTRODUCTION The chemical reactivity of a molecule is closely related to its molecular structure. Therefore, determination of the molecular structure is a prerequisite for understanding the chemical reactivity. A powerful method for obtaining molecular structures is gas-phase electron diffraction (GED). GED provides detailed information about the molecular structure in the gasphase; thus, GED results can serve as a standard for determination of the reliability of quantum chemical methods. Recently, Shlykov et al. determined the molecular structures of TeBr2, TeI2, TeF4, and TeCl4 using the GED technique.1-2 They also performed quantum chemical calculations using the Møller-Plesset second-order perturbation theory (MP2) to support their GED experiments. They concluded that the GED results were well reproduced by MP2 with a triple-ζ level basis set. For this reason, the same level of theory was applied to chalcogen tetrahalides (MX4; M= S, Se, and Te, X= F, Cl, Br, and I) to elucidate their molecular structures.3 Although numerous quantum chemical studies of tellurium halides, TeXn (X=F, Cl, Br, and I; n=1, 2, and 4) have been performed, these studies have only considered the scalar relativistic effect.1-4 However, since Te is a 5p-block element, its spin-orbit coupling (SOC) is considerable. For example, SOC increases the bond length in I2 by ~0.015 Å.5 Therefore, SOC should be considered when comparing the calculated results with those of GED experiments. In this respect, a systematic study that considers the SO effect on molecular properties is still lacking. In the present work, density functional theory (DFT) and high-level ab initio calculations that included SOC were performed to investigate molecular properties, such as molecular structures, vibrational frequencies, and thermochemical values of TeXn (X=F, Cl, Br, and I; n=1,



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2, and 4). Consideration of SOC is crucial to obtain highly accurate geometrical parameters that are very close to the experimental values determined by GED.1-2 This work will provide a guide to inform the selection of appropriate theoretical methods to support GED experiments.

COMPUTATIONAL DETAILS Geometry optimizations and subsequent harmonic vibrational frequency calculations were performed using the DFT6-7 method. We used PBE08-9 as the exchange-correlation functional because PBE0 has shown good performance for the molecular properties of mercury halides (HgXn, X=F, Cl, Br, and I; n=1, 2, and 4), which are similar to tellurium halides.10 In addition, PBE0 gave comparable results with those of CCSD(T) in the recent theoretical investigation of PtCN and PdCN.11 We also used B3LYP12-13 to compare the results with those of PBE0. The relativistic effective core potentials (RECPs) were used to treat the scalar relativistic effect for Te14, Br14, and I15 atoms. These RECPs have 28, 10, and 28 electrons as a core size for Te, Br, and I atoms, respectively, viz. small-core RECPs. Quadruple-ζ level basis sets were used for the valence electrons of Te, Br, and I; dhf-QZVPP was used for Te and I.16 The absence of dhfQZVPP for Br meant that cc-pVQZ-PP14 was instead used. The def2-QZVPP all-electron basis sets were used for F and Cl.17 A two-component spin-orbit DFT (SODFT)18 method was used to examine the SO effect on the molecular properties of TeXn (X=F, Cl, Br, and I; n=1, 2, and 4). SODFT calculations used the SO potentials of dhf-QZVPP for Te and I, and the cc-pVQZ-PP for Br. In SODFT calculations, [2p1d] functions were augmented to the valence basis sets of Te and I.16 For SODFT calculations of Br, we used the uncontracted cc-pVQZ-PP basis sets rather than the contracted equivalent. This was because the contracted basis set with SO potential cannot


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reasonably describe the SO effect.10 All DFT and SODFT calculations were performed using the NWChem6.1.1 program.19 We also performed ab initio calculations to check the validity of the DFT calculations. We used the MP220 and coupled cluster singles and doubles with perturbative triples (CCSD(T))21 methods. In all ab initio calculations, only the scalar relativistic effect was considered. The 4s and 4p electrons of Te and I, the 3s and 3p electrons of Br, the 1s, 2s, and 2p electrons of Cl, and the 1s electrons of F, were not correlated in the MP2 and CCSD(T) calculations. All MP2 and CCSD(T) calculations were performed using the Gaussian09 program.22 In addition, the anharmonic effect of the vibrational frequency and empirical dispersion23 (Grimme’s D3 with Becke and Johnson damping) were considered using the Gaussian09 program.22 To examine the validity of treating the SO effect by SODFT, we also performed ab initio calculations that included SOC for TeI2 only. We used the complete active space self-consistent field (CASSCF)24 method for generating the reference wave function. The active orbitals contained three p orbitals of each Te and I atoms, CAS(14,9) and are shown in Figure S1 in the Supporting Information. The two states-averaged CASSCF wave function for the 1A1 state was used for subsequent multireference configuration interaction (MRCI) with the Davidson correction (+Q).25-27 The molecular structure of the ground state (1A1 state) of TeI2 was optimized at the MRCI+Q level. In the MRCI+Q calculations, the same number of electrons as in the CCSD(T) calculations were correlated. We used the state-interaction approach to consider SOC. In the SOC calculations, total twelve states (two 1A1, 1B1, two 1B2, 1A2, 3A1, two 3B1, 3B2, and two 3A2 states) of MRCI+Q calculations were used as the spin-free states. In all multireference ab initio calculations, we used dhf-QZVPP RECP, as in the DFT and CCSD(T)



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calculations. A previous theoretical study of PtCN has shown that the dhf-QZVPP RECP describes SOC well.11 The grid points (0.001 Å and 0.1 °) of the potential energy surface (PES) including SOC were used to optimize the molecular structure of TeI2. All multireference ab initio calculations were performed using the molpro2012 program.28

RESULTS AND DISCUSSION 1. TeX (X=F, Cl, Br, and I) The molecular structures of TeXn (X=F, Cl, Br, and I; n=1, 2, and 4) are shown in Figure 1. The optimized bond length and the calculated vibrational frequency of TeX (X=F, Cl, Br, and I) are summarized in Table 1. As shown in Table 1, both PBE0 and CCSD(T) give almost identical results for the Te−X (X=F, Cl, Br, and I) bond length. In contrast, B3LYP significantly overestimates the Te−X bond length, compared with the bond length calculated by CCSD(T). The Te−F bond length that was optimized by MP2 is almost identical to that obtained using CCSD(T). However, MP2 underestimates the Te−X (X=Cl, Br, and I) bond length compared with CCSD(T), and the magnitude of underestimation gradually increases on changing from F to I. The SO effect, which can be seen from the difference between results of DFT and SODFT calculations, slightly increases the Te−X (X=F, Cl, Br, and I) bond length. In the PBE0 calculations, consideration of SOC results in Te−X bond lengths that are close to the experimental values.29-30 For example, the bond length (1.906 Å) of TeF as optimized by SOPBE0 is almost identical to the experimental value (1.907 Å, see Table 1).30 Therefore, PBE0 and SO-PBE0 show good performance for calculating the Te−X bond length. Since B3LYP has 6 ACS Paragon Plus Environment

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already been shown to overestimate the Te−X bond length, consideration of SOC results in values that are further from the experimental values.29-30 As can be seen from Table 1, B3LYP underestimates and PBE0 overestimates the vibrational frequency of TeX, compared with the experimental values.30-31 It is worth noting that the vibrational frequencies of TeX calculated by PBE0 are very close to those of CCSD(T). Since bond lengths are increased by SOC, it follows that the vibrational frequency is also reduced by SOC. As expected, all vibrational frequencies of TeX calculated using SODFT were found to have reduced. As shown in Table 1, PBE0 calculations that include the SO effect on the vibrational frequency of TeF and TeCl are in close agreement with the experimental values (The SO effect on the vibrational frequency of TeBr and TeI is negligible).30-31 However, these calculated values still show some deviation from the experimental values. To examine the source of the discrepancy, we performed vibrational frequency calculations of TeF and TeCl that included the anharmonic effect; the results are shown in Table 1. The anharmonic effect reduces the vibrational frequency of TeF and TeCl by 6 and 3 cm-1, respectively. The anharmonic effect of TeF is thus not negligible. When the reduction in vibrational frequency from SOC (6 cm-1) is added to the anharmonic effect-corrected value (628 cm-1), the vibrational frequency of TeF is 622 cm-1 (= 628 – 6), which is closer to the experimental value of 616.3 cm-1. The same situation is observed for the vibrational frequency of TeCl. Therefore, both SOC and anharmonic effects should be considered to obtain very accurate vibrational frequencies.

2. TeX2 (X=F, Cl, Br, and I)



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The molecular structure of TeX2 (X=F, Cl, Br, and I) has a bent structure (C2v) shown in Figure 1. The optimized geometrical parameters and the calculated vibrational frequencies for these species are summarized in Table 2. As can be seen from Table 2, the same variations between the theoretical methods are seen in the molecular structures of TeX2 as for TeX; the Te−X bond lengths of TeX2 calculated by PBE0 are very close to those of CCSD(T), but are significantly overestimated by B3LYP. On changing from F to I, the magnitude of underestimation of Te−X bond lengths in TeX2 by MP2 also increases. All methods give similar results for the bond angles of TeX2. The previous study of TeX2 concluded that MP2 with a triple-ζ basis set showed close reproduction of the experimental results measured by GED.1 To clarify this issue, we also performed MP2 calculations with triple-ζ level basis sets (Te and I: dhf-TZVPP, Br: cc-pVTZPP, Cl and F: def2-TZVPP) and the calculated results are summarized in Table 2. As shown in Table 2, MP2 calculations with triple-ζ basis sets overestimate the Te−X bond lengths, compared with MP2 calculations with quadruple-ζ basis sets. The dependence on whether a triple-ζ or quadruple-ζ basis set is used increases on changing from F to I. It is worth noting that the results of MP2 calculations with triple-ζ basis sets closely match those of CCSD(T) with quadruple-ζ basis sets (see Table 2). If the level of the basis set is the same, MP2 calculations significantly underestimate the Te−X bond lengths, compared with those using CCSD(T). In the MP2 calculations, the basis set dependence is considerable, thus, using triple-ζ basis sets results in overestimation of the Te−X bond lengths. Therefore, error cancellation occurs in MP2 calculations using triple-ζ basis sets. In summary, MP2 is not an appropriate method for calculating the molecular properties of TeX2, especially the Te−X bond lengths. In addition, the triple-ζ basis set is not sufficiently large to describe the Te−X bond lengths accurately. 8 ACS Paragon Plus Environment

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As can be seen in Table 2, the SO effect lengthens the Te−X bonds, as in the case of TeX. Contrary to TeX, the magnitude of lengthening by SOC increases on changing from F to I. The amount by which bonds are elongated by SO-B3LYP is slightly larger than for SO-PBE0. The elongation of SO-PBE0-optimized Te−X (X= Cl, Br, and I) bond lengths by SOC provides results that are in excellent agreement with the experimental values observed by GED.1 Therefore, SO-PBE0 is an appropriate method to support GED experiments. In the SO-B3LYP calculations, the deviation from experimental values increases, as in the case of TeX. B3LYP is thus not recommended to support GED experiments. In a previous study of TeX2, it was mentioned that CCSD(T) slightly overestimates the Te−X bond lengths.1 This overestimation is ascribed to the use of triple-ζ basis sets. As can be seen from Table 2, CCSD(T) gave almost identical results to PBE0. If SOC is considered in CCSD(T) calculations, the results obtained will be quite close to the experimental values, as in the case of SO-PBE0. This result also indicates that quadruple-ζ basis sets are necessary to obtain reasonable molecular structures of TeXn. To validate the ability of two-component SODFT to describe SOC, MRCI+Q including SOC via a state-interaction approach was used to calculate the molecular structure of TeI2. First, the molecular structure of TeI2 was optimized using MRCI+Q/dhf-QZVPP, which gave r(Te−I) = 2.682 Å and ∠I−Te−I = 101.0 °. These values are very close to those given by PBE0 and CCSD(T); PBE0, CCSD(T), and MRCI+Q all give an almost identical molecular structure for TeI2. With the addition of SOC to MRCI+Q calculations, the optimized molecular structure of TeI2 is r(Te−I) = 2.691 Å and ∠I−Te−I = 100.8 °. These values show that the elongation of the Te−I bond length, arising from the addition of SOC to the MRCI+Q-SO calculations, is exactly same as that of SO-PBE0. Therefore, both SO-PBE0 and MRCI+Q-SO give identical Te−I bond 9 ACS Paragon Plus Environment


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lengths for TeI2. Both two-component DFT and state-interaction approaches consistently describe SOC. The electronic configuration of the reference wave function in the MRCI+Q calculations of the 1A1 state (ground state) of TeI2 occupies all active orbitals except the a1(3) and b2(3) orbitals (see Figure S1 in the Supporting Information). These two orbitals of Te−I bond have anti-bonding character because of the nodal plane between Te and I, as is clearly seen in Figure S1. The electronic configurations of triplet excited states should occupy the a1(3) and b2(3) orbitals, σ*(Te−I) orbitals. The SO coupled ground state resulted from mixing the first 1A1 state (97.20 %) with the first 3B1 (0.34 %), the second 3B1 (0.59 %), the first 3B2 (0.87 %), the first 3A2 (0.18 %), and the second 3A2 (0.82 %). All mixed triplet states have anti-bonding character in the Te−I bond because they occupy the a1(3) and b2(3) orbitals. These results explain the elongation of the Te−I bond of TeI2 after consideration of SOC in MRCI+Q-SO calculations. It is noteworthy to mention that even very small amounts of mixing contribute to the elongation of Te−I bonds. Table 2 show that MP2 overestimates the vibrational frequencies of TeX2, while B3LYP underestimates these frequencies, compared with those calculated by CCSD(T). The vibrational frequencies of TeX2 calculated by PBE0 are quite close to those of CCSD(T). Therefore, we conclude that PBE0 is a reliable and efficient method for calculating the vibrational frequencies of TeX2. Consideration of SOC gives slightly reduced vibrational frequencies; thus, the vibrational frequencies of TeCl2 calculated by SO-PBE0 approach the experimental values. As in the case of TeX2, inclusion of the anharmonic effect for TeCl2 also leads to slightly reduced vibrational frequencies. Vibrational frequencies of TeCl2 that were corrected for SOC and anharmonic effects, in an additive manner, (389−3=386 and 129−3=126 cm-1) were much closer to experimental values (377 and 125 cm-1).32 10 ACS Paragon Plus Environment

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3. TeX4 (X=F, Cl, Br, and I) The molecular structure of TeX4 (X=F, Cl, Br, and I) is known to adopt a see-saw structure (C2v) shown in Figure 1, and the optimized geometrical parameters of TeX4 are summarized in Table 3. B3LYP again overestimated the Te−X bond length, as in the case of TeX2. Furthermore, B3LYP assigns the lowest energy molecular structure of TeI4 as the Td structure, which, is different to the outputs of all other methods. Therefore, B3LYP is an inappropriate method to describe TeX4 molecules. MP2 also underestimates the Te−X bond lengths (except for TeF4) compared with those of the CCSD(T) method. We also performed MP2 calculations with triple-ζ basis sets to compare the results with previous theoretical results.2-3 As shown in Table 3, the same situation occurs as seen in TeX2; the basis set dependence is significant in TeX4 and a triple-ζ basis set is not sufficiently large. Therefore, MP2 is also an inappropriate method to describe TeX4 accurately. PBE0 gives reasonable results for TeF4 and TeCl4, as compared with those of CCSD(T). However, in TeBr4 and TeI4, the geometrical parameters of PBE0 slightly deviated from those of CCSD(T). Especially, the PBE0-calculated ∠Iax−Te−Iax bond angle (167.6 °) significantly differs from that (174.3 °) of CCSD(T). In contrast, as mentioned in the previous section, the geometrical parameters of TeI and TeI2 calculated by PBE0 are very close to those of CCSD(T). This discrepancy in TeI4 originates from dispersion interactions. To check this issue, PBE0 calculations including empirical dispersion interactions (hereafter, PBE0-D3BJ) were performed, and the calculated results are listed in Table 3. As shown in Table 3, inclusion of dispersion interactions makes the results match those of CCSD(T) more closely. Therefore, dispersion interactions are crucial for TeI4 systems. As mentioned above, B3LYP predicts the minimum energy structure of TeI4 to be a Td structure (see Table 3). This discrepancy may arise 11 ACS Paragon Plus Environment


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from the deficiency in B3LYP’s ability to describe the dispersion interactions. Further investigation on this issue is underway in our group. The difference between PBE0-D3BJ and CCSD(T) in the calculated ∠Iax−Te−Iax bond angle is still large, and improvement of the empirical dispersion is therefore still needed in DFT calculations. As shown in Tables 3 and 4, the geometrical parameters (r(Te−Ieq) and ∠Ieq−Te−Ieq) of TeI4, calculated by MP2 and CCSD(T), are almost identical to those for TeI2. These results indicate that TeI4 exists as TeI2 and 2I units; with a dispersion interaction causing attachment of two I atoms to TeI2, rather than a chemical bond. In contrast, the geometrical parameters (r(Te−Xeq) and ∠Xeq−Te−Xeq) of TeX4 (X=F, Cl, and Br) differ from those of TeX2. As can be seen in Table 3, the SO effect on the molecular structures of TeF4 and TeCl4 is negligible. These results can be ascribed to the large electronegativity of F and Cl, such that Te in Te(IV)X4 (X=F and Cl) behaves like Te4+; it is readily expected that its SOC is very weak. However, in TeX4 (X=Br and I), the low electronegativity of these halides means that the SO effect is observed in the molecular structures. As previously mentioned, the molecular structure of TeI4 can be considered to have two I atoms, which are attached to TeI2 by dispersion interactions, lying in axial positions, while I lies at the equatorial position. Therefore, I atoms located at the axial position display relatively large SOC, which leads to a large SO effect being evident in the geometrical parameters, including the axial positions of I. The calculated vibrational frequencies of TeX4 are listed in Table S1 in the Supporting Information. Since the trend among the theoretical methods is the same, similar reasoning to that discussed for TeX4 can be applied. In TeBr4 and TeI4, the vibrational frequencies calculated by MP2 are very close to those of CCSD(T). These results are in contrast to those for TeX2 and TeX. PBE0 is deficient in its description of dispersion interactions, so that in TeBr4 and TeI4 where 12 ACS Paragon Plus Environment

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dispersion interactions are not negligible, the vibrational frequencies of PBE0 do not closely match those of CCSD(T). As shown in Table S1 in the Supporting Information, the SO effect on the vibrational frequencies of TeX4 is not large.

4. Thermochemistry of TeXn (X=F, Cl, Br, and I; n=1, 2, and 4) Various thermochemical energies of TeXn (X=F, Cl, Br, and I; n=1, 2, and 4) have been calculated and the obtained results are summarized in Table 4. As can be seen from Table 4, B3LYP and PBE0 reasonably describe the thermochemical energies, compared to the results of CCSD(T) calculations. The thermochemical energies calculated by PBE0 are in excellent agreement with those of CCSD(T); all energies calculated by PBE0 and CCSD(T) differ by less than 3 kcal/mol, except for two values: the dissociation energy of TeCl, and the atomization energy of TeCl4. MP2 overestimates the thermochemical energies compared with CCSD(T) values; all values calculated by MP2 are larger than those of CCSD(T). In particular, the values for TeX4 → TeX2 + X2 (X=F, Cl, Br, and I), and the atomization energy of TeX4 (X=F, Cl, Br, and I), are considerably overestimated. Therefore, one should exercise caution when using MP2 calculations to examine thermochemical energies. We find that PBE0 and B3LYP are superior to MP2 in calculations of thermochemical energies. As can be seen in Table 4 from the difference between B3LYP and SO-B3LYP (31.8 kcal/mol), there is a considerable SO effect on the atomization energy of TeI4 (TeI4 → Te + 4I). However, the magnitude of this difference is questionable because both B3LYP and SO-B3LYP predict that TeI4 possesses the Td structure, in contrast with all other methods. In five types of thermochemical energy calculations, PBE0 and SO-PBE0 show that the SO effect shows 13 ACS Paragon Plus Environment


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consistently on changing from F to I. It is of note that the difference of the SO effect among halogen atoms is not large; the thermochemical energies of TeIn only slightly differ from those of TeXn (X=F, Cl, and Br). Generally, the SO effect on thermochemical energies (1) and (2) is larger than on other thermochemical energies (see Table 4). As shown in Table 4, the value of the atomization energy of TeX4 → TeX2 + X2 (X=F, Cl, Br, and I) gradually decreases on changing from F to I. In particular, the energies of TeI4 → TeI2 + I2 (CCSD(T): 6.2, PBE0: 6.9, and B3LYP: 5.4 kcal/mol) are small in comparison with those of other TeX4 (X=F, Cl, and Br). This suggests that TeI4 is unstable, and therefore decomposes at high temperatures, becoming undetectable. Indeed, TeI4 has never been observed in hightemperature GED experiments, except for in TeBr4 GED experiments, where it cannot be analyzed due to its presence in very small amounts.1 This result is consistent with the experimental observations.1

CONCLUSIONS Systematic quantum chemical calculations that included SOC were performed to calculate the molecular properties of TeXn (X=F, Cl, Br, and I; n=1, 2, and 4). PBE0 describes the molecular structure of TeXn (n=1 and 2) well; the geometrical parameters of TeXn (n=1 and 2) calculated by PBE0 are quite close to those of CCSD(T) and MRCI+Q. However, in TeX4 (X=Br and I), the geometrical parameters optimized by PBE0 differ slightly from those optimized by CCSD(T). B3LYP significantly overestimates the bond length of TeXn (X=F, Cl, Br, and I; n=1, 2, and 4). The dependence upon valence basis sets is significant in the MP2 calculations. MP2 calculations significantly underestimate the bond length of TeXn (X=F, Cl, Br, and I; n=1, 2, and 4). The 14 ACS Paragon Plus Environment

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previously reported good performance of MP2 calculations with triple-ζ basis sets was found to arise from error cancellation. SOC increases the bond lengths, and reduces the vibrational frequencies of TeXn. The calculated results that include SOC are quite close to the experimental values observed by GED. Therefore, SOC plays a crucial role in predicting the molecular structure of Te containing compounds. SO-PBE0 and MRCI+Q-SO give identical bond lengths of TeI2. In order to obtain accurate vibrational frequencies, both SO and anharmonic effects should be considered. B3LYP and PBE0 are superior to MP2 for thermochemical energy calculations. The thermochemical energies calculated by PBE0 match those of CCSD(T) particularly closely. For these reason, we recommend PBE0 including SOC for predicting the molecular properties of Te containing compounds. On the basis of the calculated thermochemical energy and optimized molecular structure, TeI4 is unlikely to be stable. This result is consistent with recent experimental observations. We hope that this work will aid the analysis of future GED experimental data.

ASSOCIATED CONTENTS Supporting Information The active orbitals of CAS(14,9) for TeI2 are shown in Figure S1. The calculated vibrational frequencies of TeX4 (X=F, Cl, Br, and I) are summarized in Table S1. This material is available free of charge via the internet at http://pubs.acs.org.

AUTHOR INFORMATION



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Corresponding Author *E-mail: [email protected] (J. K.)

ACKNOWLEDGMENTS This research was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Science, ICT & Future Planning (NRF2014R1A1A1007188). This work was also supported by the National Institute of Supercomputing and Network/Korea Institute of Science and Technology Information with supercomputing resources including technical support (KSC-2016-C1-0002).


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REFERENCES (1) Shlykov, S. A.; Oberhammer, H.; Titov, A. V.; Giricheva, N. I.; Girichev, G. V., A Combined Gas‐Phase Electron Diffraction/Mass Spectrometric Study of the Sublimation Processes of TeBr4 and TeI4: The Molecular Structure of Tellurium Dibromide and Tellurium Diiodide. Eur. J. Inorg. Chem. 2008, 2008, 5220-5227. (2) Shlykov, S. A.; Giricheva, N. I.; Titov, A. V.; Szwak, M.; Lentz, D.; Girichev, G. V., The Structures of Tellurium (iv) Halides in the Gas Phase and as Solvated Molecules. Dalton Trans. 2010, 39, 3245-3255. (3) Oberhammer, H.; Shlykov, S. A., Gas Phase Structures of Chalcogen Tetrahalides MX4 with M= S, Se, Te and X= F, Cl, Br, I. Dalton Trans. 2010, 39, 2838-2841. (4) Christe, K. O.; Zhang, X.; Sheehy, J. A.; Bau, R., Crystal Structure of ClF4+ SbF6-, Normal Coordinate Analyses of ClF4+, BrF4+, IF4+, SF4, SeF4, and TeF4, and Simple Method for Calculating the Effects of Fluorine Bridging on the Structure and Vibrational Spectra of Ions in a Strongly Interacting Ionic Solid. J. Am. Chem. Soc. 2001, 123, 6338-6348. (5) Lee, H. S.; Cho, W. K.; Choi, Y. J.; Lee, Y. S., Spin–Orbit Effects for the Diatomic Molecules Containing Halogen Elements Studied with Relativistic Effective Core Potentials: HX, X2 (X= Cl, Br and I) and IZ (Z= F, Cl and Br) Molecules. Chem. Phys. 2005, 311, 121-127. (6) Hohenberg, P.; Kohn, W., Inhomogeneous Electron Gas. Phys. Rev. B 1964, 136, 864-871. (7) Kohn, W.; Sham, L. J., Self-Consistent Equations Including Exchange and Correlation Effects. Phys. Rev. A 1965, 140, 1133-1138. (8) Adamo, C.; Cossi, M.; Barone, V., An Accurate Density Functional Method for the Study of Magnetic Properties: The PBE0 Model. J. Mol. Struct. THEOCHEM 1999, 493, 145-157. (9) Ernzerhof, M.; Scuseria, G. E., Assessment of the Perdew–Burke–Ernzerhof Exchange Correlation Functional. J. Chem. Phys. 1999, 110, 5029-5036. (10) Kim, J.; Ihee, H.; Lee, Y. S., Spin-Orbit Density Functional and Ab Initio Study of HgXn (X= F, Cl, Br, and I; n= 1, 2, and 4). J. Chem. Phys. 2010, 133, 144309. (11) Moon, J.; Kim, T. K.; Kim, J., Ground and Low-Lying Excited States of PtCN and PdCN: Theoretical Investigation Including Spin–Orbit Coupling. Theor. Chem. Acc. 2016, 135, 127. (12) Becke, A. D., Density-Funtional Thermochemistry .3. The Role of Exact Exchange. J. Chem. Phys. 1993, 98, 5648-5652. (13) Lee, C.; Yang, W.; Parr, R. G., Development of the Colle-Salvetti Correlation-Energy Formula into a Functional of the Electron Density. Phys. Rev. B 1988, 37, 785-789. (14) Peterson, K. A.; Figgen, D.; Goll, E.; Stoll, H.; Dolg, M., Systematically Convergent Basis Sets with Relativistic Pseudopotentials. II. Small-Core Pseudopotentials and Correlation Consistent Basis Sets for the Post-d Group 16–18 Elements. J. Chem. Phys. 2003, 119, 1111311123. (15) Peterson, K. A.; Shepler, B. C.; Figgen, D.; Stoll, H., On the Spectroscopic and Thermochemical Properties of ClO, BrO, IO, and their Anions. J. Phys. Chem. A 2006, 110, 13877-13883. (16) Weigend, F.; Baldes, A., Segmented Contracted Basis Sets for One-and Two-Component Dirac–Fock Effective Core Potentials. J. Chem. Phys. 2010, 133, 174102. (17) Weigend, F.; Ahlrichs, R., Balanced Basis sets of Split Valence, Triple Zeta Valence and Quadruple Zeta Valence Quality for H to Rn: Design and Assessment of Accuracy. Phys. Chem. Chem. Phys. 2005, 7, 3297-3305.



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(18) Nichols, P.; Govind, N.; Bylaska, E. J.; De Jong, W. A., Gaussian Basis Set and Planewave Relativistic Spin−Orbit Methods in NWChem. J. Chem. Theory Comput. 2009, 5, 491-499. (19) Valiev, M.; Bylaska, E. J.; Govind, N.; Kowalski, K.; Straatsma, T. P.; Van Dam, H. J.; Wang, D.; Nieplocha, J.; Apra, E.; Windus, T. L., NWChem: A Comprehensive and Scalable Open-Source Solution for Large Scale Molecular Simulations. Comput. Phys. Commun. 2010, 181, 1477-1489. (20) Frisch, M. J.; Head-Gordon, M.; Pople, J. A., Semi-Direct Algorithms for the MP2 Energy and Gradient. Chem. Phys. Lett. 1990, 166, 281-289. (21) Raghavachari, K.; Trucks, G. W.; Pople, J. A.; Head-Gordon, M., A Fifth-Order Perturbation Comparison of Electron Correlation Theories. Chem. Phys. Lett. 1989, 157, 479483. (22) Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Scuseria, G. E.; Robb, M. A.; Cheeseman, J. R.; Scalmani, G.; Barone, V.; Mennucci, B.; Petersson, G. A.; et al. Gaussian 09, revision D.01; Gaussian, Inc.: Wallingford, CT, 2009. (23) Grimme, S.; Ehrlich, S.; Goerigk, L., Effect of the Damping Function in Dispersion Corrected Density Functional Theory. J. Comput. Chem. 2011, 32, 1456-1465. (24) Roos, B. O., Advances in Chemical Physics; Ab Initio Methods in Quantum Chemistry Ⅱ. John Wiley and Sons: Chichester, England, 1987. (25) Langhoff, S. R.; Davidson, E. R., Configuration Interaction Calculations on the Nitrogen Molecule. Int. J. Quantum Chem. 1974, 8, 61-72. (26) Knowles, P. J.; Werner, H. J., An Efficient Method for the Evaluation of Coupling Coefficients in Configuration Interaction Calculations Chem. Phys. Lett. 1988, 145, 514-522. (27) Werner, H. J.; Knowles, P. J., An Efficient Internally Contracted MulticonfigurationReference Configuration Interaction Method. J. Chem. Phys. 1988, 89, 5803-5814. (28) Werner, H.-J.; Knowles, P. J.; Knizia, G.; Manby, F. R.; Schütz, M.; Celani, P.; Korona, T.; Lindh, R.; Mitrushenkov, A.; Rauhut, G.; et al. MOLPRO, version 2012.1, a package of ab initio programs, 2012. http://www.molpro.net. (accessed June 18, 2014) (29) Ziebarth, K.; Setzer, K.; Fink, E., High-Resolution Study of the X22Π1/2→ X12Π3/2 FineStructure Transitions of 130TeF and 130Te35Cl. J. Mol. Spectrosc. 1995, 173, 488-498. (30) Uibel, C., Hochauflösende Fourier-Transform-Emissionsspektroskopie: Elektronenübergänge Der Zweiatomigen Radikale As2, Sb2 und TeF. in thesis 1999. (31) Hubert, K.; Herzberg, G., Molecular Spectra and Molecular Structure, vol. IV. Van Nostrand Reinhold: 1979. (32) Beattie, I.; Perry, R., Gas-Phase Raman Spectra and Resonance Fluorescence Spectra of Some Halides of Germanium, Tin, Lead, and Tellurium. J. Chem. Soc. A 1970, 2429-2432.


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Tables Table 1. Optimized molecular structures (in Å) and calculated vibrational frequencies (in cm-1) of TeX (X=F, Cl, Br, and I). B3LYP

SO-B3LYP

PBE0

SO-PBE0

MP2

CCSD(T)

Exp.

1.906 630

1.900 637

1.901 634

1.90675b 616.3b

2.315 393

2.298 404

2.315 391

2.31684(5)c 386d

2.460 276

2.434 286

2.455 275

267.4d

2.678 2.685 2.643 2.647 r(Te− −I) 210 224 [223]a 224 211 [211]a Σ a: the anharmonic effect is included in values in the square brackets.

2.618 232

2.647 222

217.3d

TeF r(Te− −F) Σ

1.920 612 [611]a

1.926 606

1.902 636 [628]a

r(Te− −Cl) Σ

2.338 377 [375]a

2.346 372

2.309 396 [393]a

TeCl

TeBr r(Te− −Br) Σ

2.487 262 [261]a

2.494 263

2.455 277 [275]a TeI

b: reference 30 c: r0 value, reference 29 d:

reference

19

ACS Paragon Plus Environment

31


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Table 2. Optimized molecular structures (bond length in Å and bond angle in °) and calculated vibrational frequencies (in cm-1) of TeX2 (X=F, Cl, Br, and I). B3LYP

SO-B3LYP

PBE0

SO-PBE0 TeF2 (C2V) 1.891 94.2 660 209 634 TeCl2 (C2V) 2.323 99.2 389 129 365 TeBr2 (C2V)

r(Te− −F) ∠F− −Te− −F A1 (symm.) A1 (bending) B2 (asymm.)

1.904 94.9 633 [632]a 205 [203]a 618 [614]a

1.909 94.6 626 200 611

1.887 94.5 658 [656]a 213 [210]a 642 [638]a

r(Te− −Cl) ∠Cl− −Te− −Cl A1 (symm.) A1 (bending) B2 (asymm.)

2.348 99.9 370 [371]a 125 [123]a 357 [354]a

2.355 99.9 368 122 353

2.318 99.2 392 [389]a 131 [128]a 378 [372]a

r(Te− −Br)

2.508

2.516

2.474

∠Br− −Te− −Br A1 (symm.) A1 (bending) B2 (asymm.)

101.3 251 [251]a 81 [80]a 247 [245]a

101.5 239 78 235

100.5 267 [266]a 85 [83]a 263 [261]a

r(Te− −I)

2.720

2.732

2.681

2.690

∠I− −Te− −I A1 (symm.) A1 (bending)

102.9 195 [195]a 61 [60]a

103.3 200 59

101.9 209 [209]a 64 [62]a

102.3 203 61

2.480 100.6 261 82 261 TeI2 (C2V)

MP2

CCSD(T)

1.883 (1.888)b 94.4 (94.8) b 661 (659)b 215 (214)b 644 (643)b

1.882 94.0 662 217 646

2.303 (2.311)b 98.1 (98.5)b 404 (400)b 133 (133)b 389 (386)b 2.447 (2.463)b 98.8 (99.2)b 279 (274)b 86 (86)b 275 (270)b 2.649 (2.670)b 99.7 (100.3)b 220 (213)b 64 (63)b

20


Exp.

2.318 98.3 392 130 378

2.331(3)c, 2.323(4)d 97.2(6)e 377f 125f

2.468

2.480(5)c, 2.472(6)d

99.1 268 84 265

99.0(6)e

2.679

2.693(3)c, 2.686(10)d

100.3 209 62

103.1(22)e

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B2 (asymm.)


196 [195]a

202

210 [209]a

204

221 (214)b

a: the anharmonic effect is included in values in the square brackets. b: Te: dhf-TZVPP and X (X=F, Cl, Br, and I):def2-TZVPP c: r0 in reference 1 d: re in reference 1 e: reference 1 f: reference 31

21


212


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Table 3. Optimized molecular structures (C2v, bond length in Å and bond angle in °) of TeX4 (X=F, Cl, Br, and I). B3LYP

SO-B3LYP

PBE0

SO-PBE0

MP2

CCSD(T)

Exp.

1.842 1.909 101.0 84.5 162.5

1.835 (1.839)a 1.904 (1.907)a 99.7 (99.8)a 84.9 (84.9)a 164.0 (164.3)a

1.833 1.899 100.6 84.4 162.4

1.846(4)b 1.899(4)b 99.5(3)b 84.9(7)b 164.3(12)b

2.290 2.424 101.1 88.4 174.9

2.289(3)b 2.428(4)b 102.5(7)b 88.9(6)b 176.7(10)b

TeF4 r(Te− −Feq) r(Te− −Fax) ∠Feq−Te− −Feq ∠Feq−Te− −Fax ∠Fax−Te− −Fax

1.857 1.927 100.4 85.0 164.2

1.857 1.928 100.4 85.0 164.2

1.842 1.909 100.9 84.5 162.6 TeCl4

r(Te− −Cleq) r(Te− −Clax) ∠Cleq−Te− −Cleq −Clax ∠Cleq−Te− −Clax ∠Clax−Te−

2.326 2.469 100.5 90.3 179.0

2.327 2.470 100.5 90.3 179.1

2.296 2.433 101.1 89.1 177.3

r(Te− −Breq) r(Te− −Brax) ∠Breq−Te− −Breq ∠Breq−Te− −Brax −Brax ∠Brax−Te−

2.502 2.661 100.5 92.9 171.0

2.506 2.664 100.5 92.9 171.0

2.464 2.619 101.2 90.9 177.1

2.296 2.434 101.1 89.1 177.3

2.276 (2.284)a 2.414 (2.422)a 100.1 (100.2)a 88.7 (89.0)a 175.9 (176.9)a

2.465 2.621 101.2 90.9 177.1

2.429 (2.445)a 2.583 (2.601)a 100.0 (100.0)a 89.9 (90.3)a 179.7 (179.2)a

2.699 2.888 101.7 93.5 169.1

2.647 (2.667)a 2.837 (2.864)a 99.8 (100.0)a 92.0 (92.9)a 173.9 (171.1)a

TeBr4 2.449 2.601 101.1 89.7 179.0

TeI4 2.847 2.845 2.693 r(Te− −Ieq) 2.847 2.845 2.878 r(Te− −Iax) 109.5 109.4 101.4 ∠Ieq−Te− −Ieq 109.5 109.5 93.9 ∠Ieq−Te− −Iax 109.5 109.4 167.6 ∠Iax−Te− −Iax a: Te: dhf-TZVPP and X (X=F, Cl, Br, and I):def2-TZVPP b: reference 2


2.679 2.869 101.1 91.8 174.3

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Table 4. Thermochemical energies (in kcal/mol) of TeXn (X=F, Cl, Br, and I and n=1,2, and 4). B3LYP (1) TeF → Te+F (2) TeF2 → TeF+F (3) TeF2 → Te+F2 (4) TeF4 → TeF2+F2 (5) TeF4 → Te+4F (1) TeCl→ Te+Cl (2) TeCl2 → TeCl+Cl (3) TeCl2 → Te+Cl2 (4) TeCl4 → TeCl2+Cl2 (5) TeCl4 → Te+4Cl (1) TeBr → Te+Br (2) TeBr2 → TeBr+Br (3) TeBr2 → Te+Br2 (4) TeBr4 → TeBr2+Br (5) TeBr4 → Te+4Br (1) TeI → Te+I (2) TeI2 → TeI+I (3) TeI2 → Te+I2 (4) TeI4 → TeI2+I2 (5) TeI4 → Te+4I

83.8 89.7 138.2 141.7 350.5 62.7 61.4 69.3 36.7 215.6

SO-B3LYP 83.3 85.0 133.0 139.6 343.1 62.0 57.0 64.1 35.0 208.7

55.5 52.6 59.8 21.7 178.3

54.7 47.6 54.3 20.7 170.9

49.0 43.6 49.2 5.4 141.5

42.1 31.6 43.3 5.5 109.7

PBE0 TeFn 81.4 88.8 136.9 145.4 349.0 TeCln 64.9 65.0 70.9 41.0 229.9 TeBrn 57.7 56.2 62.2 25.9 191.5 TeIn 51.4 47.5 51.9 6.9 152.8

SO-PBE0

MP2

CCSD(T)

85.9 85.1 137.6 143.3 347.7

83.8 97.0 142.1 154.0 373.5

80.8 90.7 136.4 145.7 352.3

69.2 61.4 71.6 39.3 228.9

62.6 68.6 73.0 45.6 235.0

61.8 64.4 70.2 39.9 222.1

62.1 51.9 62.6 25.0 190.4

56.4 61.5 64.9 32.3 203.2

55.7 57.0 61.7 25.5 189.2

55.6 42.0 52.0 7.0 150.1

50.6 54.1 55.1 14.8 169.2

49.2 48.4 51.3 6.2 150.1



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Figure 1. Molecular structures of TeXn (X=F, Cl, Br, and I; n=1,2, and 4).


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