Use of Improved Orbitals for CCSD(T) Calculations for Predicting

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Use of Improved Orbitals for CCSD(T) Calculations for Predicting Heats of Formation of Group IV and Group VI Metal Oxide Monomers and Dimers and UCl

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Zongtang Fang, Zachary Lee, Kirk A. Peterson, and David A Dixon J. Chem. Theory Comput., Just Accepted Manuscript • DOI: 10.1021/acs.jctc.6b00327 • Publication Date (Web): 11 Jul 2016 Downloaded from http://pubs.acs.org on July 19, 2016

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Journal of Chemical Theory and Computation

Use of Improved Orbitals for CCSD(T) Calculations for Predicting Heats of Formation of Group IV and Group VI Metal Oxide Monomers and Dimers and UCl6 Zongtang Fang,a Zachary Lee, a Kirk A. Peterson,b and David A. Dixon,a,* a

Department of Chemistry, The University of Alabama, Shelby Hall, Tuscaloosa, Alabama

35487-0336, USA b

Department of Chemistry, Washington State University, Pullman WA 99164-4630 USA

Abstract The prediction of the heats of formation of group IV and group VI metal oxide monomers and dimers with the coupled cluster CCSD(T) method has been improved by using Kohn-Sham density functional theory (DFT) and Brueckner orbitals for the initial wave function. The valence and core-valence contributions to the total atomization energies (TAE) for the CrO3 monomer and dimer are predicted to be significantly larger than when using the Hartree-Fock (HF) orbitals. The predicted heat of formation of CrO3 with CCSD(T)/PW91 is consistent with previous calculations including high order corrections beyond CCSD(T) and agrees well with the experiment. The improved heats of formation with the DFT and Brueckner orbitals are due to these orbitals being closer to the actual orbitals. Pure DFT functionals perform slightly better than the hybrid B3LYP functional due to the presence of exact exchange in the hybrid functional. Comparable heats of formation for TiO2 and the second and the third row group 4 and group 6 metal oxides are predicted well using either the DFT PW91 orbitals, Brueckner orbitals, or HF orbitals. The normalized clustering energies for the dimers are consistent with our previous work except for a larger value predicted for Cr2O6. The prediction of the reaction energy for UF6 +

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3Cl2 → UCl6 + 3F2 was significantly improved with the use of DFT or Brueckner orbitals as compared to HF orbitals.


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Introduction Transition metal containing compounds are important in catalysis as these d-block elements exhibit unique chemical properties such as low ionization energies coupled with a rich variety of oxidation states. We are especially interested in transition metal oxides (TMOs) which show Lewis acid-base and redox chemistry. 1,2 TMOs are widely employed in the energy areas of solar energy conversion, fuel cells, and biomass conversion as well as for environmental remediation. 3, 4, 5 TMO nanoclusters have lower band gaps and higher surface areas as compared to the bulk, making them more reactive. 6,7,8,9

Thermochemical data of these nanoclusters is

important for understanding catalytic reaction mechanisms. The heats of formation of transition metal species are difficult to predict using electronic structure methods. Currently, the composite Feller-Peterson-Dixon (FPD) method, 10, 11, 12, 13, 14, the correlation consistent composite approach (ccCA) 15 , 16 , 17 and the G4 method 18 usually provide heats of formation with error bars of ± 3 kcal/mol as compared to experiment, so called ‘transition metal chemical accuracy’. The FPD method uses at least single reference CCSD(T) 19,

20, 21, 22

theory at the complete basis set (CBS) limit with a series of additional

additive corrections to achieve the desired accuracy. The ccCA method extrapolates secondorder Møller–Plesset perturbation theory23 to obtain an estimate of the CBS limit in conjunction with a small basis set CCSD(T) or multireference calculation depending on the flavor of the ccCA approach used. G4 uses fourth-order Møller–Plesset perturbation theory to estimate the CCSD(T)/CBS limit.

Use of the explicitly correlated CCSD(T)-F12 methodology 24 , 25 can

provide accelerated convergence to the CBS limit. 26,27,28,29,30,31 Higher order corrections beyond CCSD(T) are not always needed to obtain chemical accuracy for transition metal compounds. However, for first row transition metal species, for 3 ACS Paragon Plus Environment


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example CrO3, there can be substantial multi-reference character (as indicated by high values of the T1 diagnostic 32) and higher order calculations beyond CCSD(T) are required to get accurate heats of formation for such molecules. 33 , 34 , 35 , 36 CrO3 is estimated to have a 4.5 kcal/mol correction to the atomization energy due to inclusion of the full T (-2.6 kcal/mol) and full Q (7.1 kcal/mol) corrections to CCSD(T).33,34 This yields a calculated value of ΔHf(298K) = -67.6 kcal/mol. This value is in agreement with the JANAF value 37 of 70 ± 10 kcal/mol considering the large experimental error bars, but not in as good agreement with the other reported value of 77.3 ± 1 kcal/mol.38 The JANAF value is based on assessing a number of different experimental values which range from -59 to -76 kcal/mol, whereas the latter value is based on one set of experimental measurements. 39 In this case, we feel that the computational value with the higher order correlation corrections represents the best available value. Higher order correlation calculations beyond CCSD(T) are computationally expensive and are not possible for larger molecules (CCSDT scales approximately as iterative N8 and CCSDTQ as N10 for N basis functions). This study demonstrates an improvement in the FPD approach for the prediction of accurate heats of formation for the TMO’s that require higher order correlation corrections. The goal is to avoid these high order corrections and/or expensive multi-reference calculations. Following the FPD approach used in our previous work, 40 the total atomization energy (TAE) is obtained using equation (1) TAE = ∆E (CBS) + ∆E (CV) + ∆E (SR) + ∆E (PP, Corr) + ∆E (SO) + ∆E (ZPE)

(1)

where the components are the frozen-core valence (we simply call valence in the following part) correlation energy, core-valence correction, scalar relativistic correction, pseudopotential correction, spin orbital correction, and zero point energy correction, respectively. 4 ACS Paragon Plus Environment

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For our first approach, we propose using the Kohn-Sham orbitals obtained by density functional theory (DFT) instead of the canonical Hartree-Fock (HF) orbitals for the valence and core-valence contributions to the TAE calculated at the CCSD(T) level. The second approach we propose is to use Brueckner orbitals 41,42,43,44,45,46,47 in the coupled cluster calculations. Brueckner doubles with perturbative triples [BCCD(T)] calculations eliminate the singles amplitudes in the CCSD wavefunction via appropriate orbital rotations. Friesner and coworkers36 showed a lower total energy for CrO3 with BCCD(T) than calculated with CCSD(T) starting from the HF orbitals. We have previously found that the use of DFT PW91 48,49 or Brueckner orbitals as the starting point for the coupled cluster calculations performs better than the use of HF orbitals for the prediction of the potential energy surfaces for the reactions of H2O with actinide oxides. 50 In this work, CCSD(T) calculations with the orbitals taken from selected DFT functionals and BCCD(T) calculations are carried out for some TMO clusters, the monomers and dimers of the Group 6 MO3 and Group 4 MO2 TMOs, and UCl6. The Group 4 oxides are in the +4 oxidation state and are closed shell. They nominally have no 3d orbital occupancy and any 3d occupancy comes from ligand back-bonding. The Group 6 compounds are in the +6 oxidation state and also should have no 3d occupancy except from back-bonding. UCl6 provides a good test for another type of metal, one containing f orbitals in the valence space. The U is in the +6 oxidation state so there should formally be no 5f or 6d occupancy except for backbonding. Computational Methods The geometries of the transition metal oxides are taken from our previous work.40 The selected DFT functionals used to generate the improved orbitals include the hybrid B3LYP 51,52 and M06, 53 the pure BP86, 54,55 PW91,48,49 and PBE, 56 and the local SVWN5.57,58 To perform the CCSD(T) calculation with the DFT orbitals, a standard DFT calculation is done and the 5 ACS Paragon Plus Environment


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resulting orbitals are processed through a single HF iteration with the resulting orbitals being used for the subsequent correlation step. Thus, both the core orbitals and the valence orbitals are from DFT. To unambiguously compare the effect of using the DFT orbitals vs. the HF orbitals in the valence CCSD(T) calculations, the frozen-core (valence correlation) calculations with the valence basis sets are performed with only the valence orbitals from DFT and the core orbitals from the HF (so that in all cases the frozen-core orbitals are identical). Those calculations are done as follows: (1) An initial Hartree-Fock (HF) calculation is done and the orbitals are saved. (2) A DFT calculation with the chosen functional is carried out and the Kohn-Sham orbitals are saved. (3) The two sets of orbitals are merged with the core (non-correlated) orbitals taken from the HF calculation and the remaining orbitals to be correlated are taken from the DFT calculation but are not re-optimized. This set of orbitals is then orthonormalized. (4) A single HF iteration is then carried out to provide a consistent set of orbital eigenvalues for the correlation calculation. For each DFT functional, the total CCSD(T) electronic energies are calculated at the CBS limit, which are obtained by extrapolation using a mixed Gaussian/exponential formula 59 from the energies calculated with aug-cc-pVXZ (-PP for the metals ) (X = D, T, Q) basis sets.40,60,61, 62 The basis set is labeled as aX. Core-valence (CV) correlation corrections are also calculated at the CCSD(T) level with the aug-cc-pwCVXZ (X = D, T, Q) basis sets for O and the corresponding aug-cc-pwCVXZ-PP basis set for the metals, and the corrections are extrapolated to the CBS limit using the same formula. These basis sets are denoted as awX. The total contribution including valence and core-valence energies to the TAE corresponds to the CCSD(T)/CBS energy extrapolated from the energies with the awX basis sets with both valence and outer-core electrons correlated. The results with various DFT functionals are denoted as


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CCSD(T)/DFT (DFT is the tested functional), in contrast to CCSD(T)/HF energies for which the HF orbitals are used. For the frozen-core electron correlation calculation with the valence basis set or the corevalence calculation with the core-valence basis set, a standard BCCD(T) calculation is done starting from the HF orbitals. In order to obtain the core-valence correlation correction, the corevalence calculation with the core-valence basis set is first carried out. The resulting Brueckner orbitals are saved and processed through a single HF iteration (purely for technical reasons internal to Molpro). The frozen-core calculation is then done with the core taken from the frozen Brueckner orbitals from the core-valence calculation. This ensures that a consistent set of outercore orbitals are used in both steps. It should be noted that in the Molpro implementation, the non-correlated orbitals are unmodified in the BCCD iterations. All of the calculations are done for the TiO2 and CrO3 monomers and dimers. On the basis of the performance of the selected DFT functionals, we choose the PW91 functional for benchmarks of the heats of formation of ZrO2, HfO2, MoO3 and WO3 monomers and dimers. BCCD(T) calculations are also performed for the second and the third row oxides.

The

pseudopotential corrections (ΔEPP,Corr) for Ti, Zr, Cr and Mo oxides in this work are derived from the calculations with both valence and core-valence electrons correlated using the HF orbitals. The scalar relativistic (SR) corrections, the zero point energy (ZPE) corrections, and the spin orbital (SO) corrections were taken from previous work.40 The TAE at 0 K is calculated as the energy difference between the ground states of the atoms and that of the cluster. We calculated CCSD(T) energies for the ground state atoms with the various DFT orbitals. It should be noted that the use of non-HF orbitals generally required the Fock operator to be block diagonalized before the perturbative triples contribution was 7 ACS Paragon Plus Environment


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calculated (which is done automatically in Molpro). With the correlation of both valence and core-valence electrons, CCSD(T)/DFT at the CBS limit predicts slightly more negative total electronic energies than does CCSD(T)/HF for O, Ti, and Cr. Various functionals give close total energies for Ti and Cr with differences up to 0.03 kcal/mol. The total energies between CCSD(T)/DFT and CCSD(T)/HF can differ by up to 0.18 kcal/mol for Ti and Cr. This difference for O is much less and is not important. CCSD(T)/PW91 at the same level gives ~ 0.8 and 0.7 kcal/mol more negative total energies than does CCSD(T)/HF for Zr and Mo. The total electronic energies for Hf and W predicted by CCSD(T)/PW91 are ~ 0.9 kcal/mol less negative than CCSD(T)/HF. In this work, for the TAE calculations at the CCSD(T)/DFT level, the energies of the ground states of the atoms and the molecules are chosen from the same functional. We use CCSD(T)/HF energies for the ground states of the atoms at the BCCD(T) level as we do not have a convenient open-shell Brueckner orbital code. The heats of formation at 0K are derived from its TAE and the experimental heats of formation of the atoms. The heats of formation at 298K are calculated using the equation by Curtiss et. al. 63 The normalized clustering energy (NCE), ΔEnorm, n, is defined as ΔEnorm, n = {n E(MOm) – E[(MOm)n]} / n

(1)

The NCE is the average binding energy of the monomers in a cluster. This follows from our previous work.40 The CCSD(T) and BCCD(T) calculations were carried out with MOLPRO 2012.1. 64, 65 The calculations were performed on the local Xeon and Opteron based Penguin Computing clusters, the Xeon based Dell Linux cluster at the University of Alabama, the Opeteron and Xeon based Dense Memory Cluster (DMC) and Itanium 2 based SGI Altix systems at the Alabama


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Supercomputer Center, and the Atipa 1440 Intel Xeon-Phi Node FDR-Infiniband Linux cluster at the Molecular Science Computing Facility at Pacific Northwest National Laboratory. Results and Discussion Valence contributions using DFT starting orbitals or Brueckner orbitals (both with a HF core) with the valence basis set are shown in Table 1. They are compared to the valence contributions at the CCSD(T)/HF level. The contributions of valence electronic energies for the group 4 and 6 TMO monomers and dimers with the use of selected DFT orbitals and Brueckner orbitals are shown in Table 2. For the ZrO2, HfO2, MO3, and WO3 monomers and dimers, we chose the PW91 functional for the CCSD(T) calculations. The TAE and the heats of formation for all the studied oxides based on the improved wave functions are shown in Table 3. The normalized clustering energies for the dimers are summarized in Table 4. The average bond dissociation energies are shown in Table 5. The contributions with different basis sets and the raw electronic energies with different staring orbitals are given in the Supporting Information (SI) together with more results from the BCCD(T) calculations. Sample inputs for CrO3 calculations with the CCSD(T)/PW91 and BCCD(T) methods are also shown in the SI. We discuss the UCl6 results separately below. Valence and Core-Valence Contributions with Various DFT Orbitals In general in the FPD approach,10,11,12,13 the valence and valence + core electrons CCSD(T) calculations are done separately, with the CBS extrapolation done with the former and a more modest basis set used for the latter to reduce the total computational cost. As the valence + core correlations are also extrapolated to the CBS limit in this work, the valence contributions with valence basis sets (aX) are less accurate than the valence CBS limits obtained with the awX basis sets. We first compare the valence correlation energy between DFT and HF orbitals with the non-correlated electrons 9 ACS Paragon Plus Environment


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described by the HF orbitals. We then examine the core-valence corrections using the DFT orbitals for the core and valence electrons. Table 1 shows the valence contributions to the TAE using DFT starting orbitals or Brueckner orbitals, which are compared to those using HF orbitals. The use of different functionals does not strongly impact the valence-only results for the CrO3 and TiO2 monomers and dimers. For the CrO3 monomer, the use of DFT orbitals gives valence contributions that are 2.5 to 3 kcal/mol larger than the use of HF orbitals. For the TiO2 monomer, using DFT orbitals increases the valence contributions by up to 0.5 kcal/mol in comparison with the use of HF orbitals. The valence contributions predicted by the Brueckner orbitals are ~ 2 kcal/mol larger for the CrO3 monomer and ~ 1 kcal/mol smaller for the TiO2 monomer than that by the HF orbitals. Similar results are predicted for the CrO3 and TiO2 dimers and the differences are generally twice that of the monomers. For the second and third row TMOs, the valence contributions predicted by the CCSD(T)/PW91 method are up to 0.5 kcal/mol larger for the monomers and 1.5 kcal/mol larger for the dimers than the CCSD(T)/HF results. Similar to the TiO2 monomer and dimer, the use of Brueckner orbitals slightly decreases the valence contributions by up to 0.7 kcal/mol for the second and the third row TMOs. Thus, the increase of the valence contributions using the DFT orbitals for the first row TMOs, especially the CrO3 monomer and dimer, is more significant than that for the second the third row TMOs. The valence components using DFT orbitals with a DFT core are shown in Supporting Information. In general, using DFT orbitals with a DFT core gives larger contributions for the valence correlation than with a HF core. They differ by up to 2 kcal/mol for the monomers and 4 kcal/mol for the dimers, which are larger than the differences between the CCSD(T)/DFT with a HF core and the CCSD(T)/HF results for most clusters. 10 ACS Paragon Plus Environment

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Table 2 shows ∆ECVV, which is the CBS value of the electronic energy contribution to the TAE with all of the core and valence electrons correlated, as well as the energy of the valence electrons with the awX basis sets ∆EVal'; the difference ∆ECV = (∆ECVV - ∆EVal') is also reported. We use ∆ECVV for the final calculation of the TAE and heats of formation. For the CrO3 monomer at the CCSD(T) level, the use of Kohn-Sham orbitals from DFT for all electrons increases the TAE by 4 to 5 kcal/mol in comparison to the use of HF orbitals for the valence-only electronic contribution. The use of different functionals does not strongly impact the valenceonly results. The core-valence contribution is generally on the order of 1.5 kcal/mol larger than the HF core-valence correction so the TAE is ~ 5 to 6 kcal/mol larger using the DFT orbitals than with the HF orbitals. The B3LYP orbitals give a comparable CV correction as the HF CV value. The CV correction predicted by the SVWN5 orbitals is 3.5 kcal/mol larger than that by HF orbitals. The use of generalized gradient approximation (GGA) DFT orbitals yields a slightly larger ∆ECVV than the use of orbitals from the hybrid B3LYP and M06 functionals. These latter two functionals contain some component of HF exchange. The use of the local SVWN5 orbitals gives the largest valence and core-valence electronic contribution. The use of the awX basis sets gives a valence contribution that is only 0.1 kcal/mol larger with the HF orbitals but is ~0.6 kcal/mol larger with the DFT orbitals. Thus the additive approximation used in the FPD approach could have errors on the order of 0.5 kcal/mol when using DFT orbitals due to a larger basis set effect on the valence electrons when using DFT orbitals. The results suggest that one should use the same set of orbitals for the valence and core-valence corrections as shown in the Supporting Information. Similar results are predicted for the CrO3 dimer. Both the valence electronic contribution and the core-valence corrections to the TAE are increased using the DFT orbitals as the starting 11 ACS Paragon Plus Environment


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orbitals. The differences between CCSD(T)/DFT and CCSD(T)/HF for Cr2O6 are generally twice that of the CrO3 differences with respect to various contributions shown in Table 2. For the TiO2 monomer, the use of the CCSD(T)/DFT method does not have as large an impact on the TAE. This is consistent with its smaller T1 diagnostic compared to CrO3 (0.035 vs. 0.044). The valence contributions and the CV corrections with the use of DFT orbitals are comparable to those with the use of HF orbitals for most DFT functionals. CCSD(T)/DFT gives ~ 1 kcal/mol larger valence electronic contributions. The use of orbitals from B3LYP decreases the CV correction by 1 kcal/mol. An increase of 0.5 kcal/mol is predicted by CCSD(T)/SVWN5. The ∆ECVV contributions with the use of DFT orbitals are slightly larger than the use of HF orbitals and they differ by up to 1 kcal/mol, significantly smaller than for CrO3. The use of DFT orbitals from the three different pure GGA functionals gives nearly identical ∆ECVV predictions. The valence contributions are not as basis set dependent on whether the CV or valence-only basis set is used for TiO2 with differences of only 0.2 kcal/mol. The performance of different DFT orbitals for Ti2O4 is consistent with that for TiO2 with slightly larger differences for various components. As a further test of the concept that improved orbitals yield improved TAEs and hence ΔHf’s, the coupled cluster calculations were also carried out using Brueckner orbitals for the CrO3 and TiO2 monomers and dimers (Table 2). For CrO3, the valence electronic contribution with the use of Brueckner orbitals is 2 kcal/mol larger than with use of HF orbitals, ~ 2 kcal/mol less than using the DFT orbitals. The CV correction predicted by the BCCD(T) method is 2.7 kcal/mol larger than from CCSD(T)/HF. The ∆ECVV with the use of Brueckner orbitals is thus 4.6 kcal/mol larger than using HF orbitals. The ∆ECVV obtained from BCCD(T) is comparable to the


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use of hybrid DFT functionals such as B3LYP and M06 and is 1 kcal/mol less than the use of pure DFT functionnals. Similar trends are predicted with the BCCD(T) method for Cr2O6. For the TiO2 monomer and dimer, the coupled cluster calculations using Brueckner orbitals give a lower valence electron contribution to the TAE and a larger core-valence contribution so that the value of ∆ECVV at the BCCD(T) level is only slightly smaller than that using the HF orbitals. Consistent with the CrO3 monomer and dimer, the ∆ECVV prediction with use of Brueckner orbitals is smaller than the result from the use of DFT orbitals. For the second and third row transition metal oxides, the valence and core-valence contributions to the TAE calculated with the use of PW91 or Brueckner orbitals are also shown in Table 2. CCSD(T)/PW91 increases the valence contributions and decreases the core-valence contributions compared to the use of HF orbitals for most clusters except for the WO3 monomer and dimer. Use of either the PW91, Brueckner, or HF orbitals does not significantly change the TAEs for WO3 and W2O6. The use of both PW91 and Brueckner orbitals gives results that are slightly smaller for ∆ECVV for the ZrO2 monomer and dimer. For the other oxides, CCSD(T)/PW91 gives slightly larger ∆ECVV components and BCCD(T) gives slightly smaller ∆ECVV components as compared to CCSD(T)/HF predictions. They differ by up to 1 kcal/mol for the monomers and 3 kcal/mol for the dimers. In summary, as shown for the CrO3 monomer and dimer, both the valence electronic contribution and the CV correction using HF orbitals underestimate the TAE as compared to the use of DFT orbitals. The hybrid functionals do not perform as well as the pure functionals, presumably because of the presence of some fraction of exact exchange with the hybrid functionals. The ∆ECVV’s with the use of Brueckner orbitals are also larger than the use of HF



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orbitals. For the other TMO monomers and dimers, DFT or Brueckner orbitals generally predict comparable TAE’s compared to the use of HF orbitals. The improvement in the TAE’s with CCSD(T)/DFT or BCCD(T) is important for the CrO3 monomer and dimer and not for the TiO2 monomer and dimer. Our previous studies7,9 suggest that there is some multi-reference character for the Cr metal oxides and possibly for the Ti metal oxides. The T1 diagnostics32 for CrO3 and TiO2 monomers and dimers calculated at the CCSD(T)/aWT level with the use of different starting orbitals are shown in the Supporting Information. The T1 diagnostics for the CrO3 monomer and dimer are larger than for the TiO2 monomer and dimer with the use of HF orbitals, perhaps indicating that there is more multireference character of Cr than Ti. The use of various DFT orbitals decreases the T1 diagnostic of the TMOs dramatically from ~ 0.045 and ~ 0.034 to ~ 0.015 for M = Cr and M = Ti respectively. These results demonstrate that the HF starting orbitals are a poor approximation to the actual orbitals and the use of the DFT orbitals is a marked improvement. Heats of Formation The heats of formation based on the core-valence and valence contributions to the TAE calculated with CCSD(T)/PW91 and BCCD(T) methods are shown in Table 3. The other components including the scalar relativistic (SR) corrections, the zero point energy (ZPE) corrections, and the spin orbit (SO) corrections are taken from our previous work40 and the pseudopotential corrections are shown in the Supporting Information. It should be noted that the heats of formation predicted by CCSD(T)/HF (Table 3) are slightly different from our previous study,40 where the core electrons were not correlated to calculate the pseudopotential corrections and the CV corrections were calculated at the triple zeta level to get the TAE. The differences among the CCSD(T)/PW91, BCCD(T) and the CCSD(T)/HF methods are consistent with the


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∆ECVV differences. CCSD(T)/PW91 gives slightly more exothermic heats of formation than the BCCD(T) method for the studied oxides. The predicted heat of formation of CrO3 with CCSD(T)/PW91 at 298 K, 67.7 ± 1.1 kcal/mol (error just from the atomic heats of formation) agrees well with the previous work with high order correlation corrections,33,34,35 including the best results of -67.6 kcal/mol.35 The heat of formation of CrO3 calculated by BCCD(T) differs by 1.2 kcal/mol for the CCSD(T)/PW91 value and is also in excellent agreement with the prior work. We note that the experimental results for CrO3 are not really reliable so we focus on the capture of the higher order corrections by using the BCCD or DFT orbitals. The heat of formation of Cr2O6 using the DFT PW91 orbitals and Brueckner orbitals are ~ 14 kcal/mol more negative than the value obtained by using HF orbitals. For the heats of formation of TiO2 and Ti2O4, the differences between CCSD(T)/PW91 and BCCD(T) are less than 1 kcal/mol for the monomer and 3 kcal/mol for the dimer. The heats of formation are slightly more exothermic with CCSD(T)/PW91 and slightly less exothermic with BCCD(T) when compared to CCSD(T)/HF for TiO2. Our derived experimental value for the experimental heat of formation for TiO2 is based on prior experimental work 66 and the CODATA value 67 for ΔHf(Ti(g)). The CCSD(T)/PW91 value is within 1 kcal/mol of this experimental value and within 1 kcal/mol of the experimental heat of formation of the dimer of TiO2 obtained from the experimental dimerization energy of TiO2.

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The experimental

dimerization energy of TiO2 to form Ti2O4 is -119 ± 10 kcal/mol at about 2260 K in excellent agreement with our calculated 298 K values of -120.8, -120.0, and -120.4 kcal/mol at the CCSD(T)/PW91, BCCD(T), and CCSD(T)/HF levels respectively.



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Consistent with the ∆ECVV difference discussed above, the heats of formation for the other TMOs are slightly more exothermic using the PW91 orbitals and less exothermic using Brueckner orbitals in comparison to CCSD(T)/HF. The difference is usually less than 0.5 kcal/mol for the BCCD(T) method and up to 3 kcal/mol for the CCSD(T)/PW91 method. All of the calculated heats of formation for ZrO2 are in agreement with experiment, considering the large error bars. For MoO3, all of the values are in agreement with experiment given the ± 5 kcal/mol error bars and we note that all of the results are less negative than the experimental value. The dimerization of MoO3 to form Mo2O6 has been measured at 1600 K to be −110.2 ± 8 kcal/mol 69 and -112 kcal/mol 70 at 1800 K. Both values are in excellent agreement with our calculated values of -112.6, -112.5, and -112.0 kcal/mol at 298 K at the CCSD(T)/PW91, BCCD(T), and CCSD(T)/HF levels respectively. We calculated the experimental value for ΔHf(Mo2O6) from the experimental heat of formation of MoO3 and the experimental dimerization energy. The apparent larger discrepancy with experiment and theory for Mo2O6 is an issue with the heat of formation of MoO3. We thus recommend that the heat of formation of MoO3 be re-measured. In contrast to MoO3, the calculated heats of formation for WO3 are more negative than the experimental value by about -10 kcal/mol. Again, we recommend that the experimental heat of formation of WO3 be re-measured. Given the error in the experimental heat of formation of the monomer, the calculated heats of formation for W2O6 are actually in just as good agreement with experiment as the monomer. We note that the dimerization energy of WO3 to form W2O6 has been measured70 to be -127 kcal/mol at 1800 K in excellent agreement with our calculated values at 298 K of -127.2, -127.3, and -126.7 kcal/mol at the CCSD(T)/PW91, BCCD(T), and CCSD(T)/HF levels respectively.


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Normalized Clustering Energies Table 4 presents the normalized clustering energies for the studied dimers with CCSD(T)/PW91 and BCCD(T) methods. For Ti2O4 and Cr2O6, the valence and core-valence contributions with various DFT functionals are shown in Supporting Information. For Ti2O4, CCSD(T)/DFT generally gives up to 0.3 kcal/mol larger contributions than CCSD(T)/HF, and BCCD(T) gives slightly smaller contributions than CCSD(T)/DFT. For Cr2O6, the results from the use of DFT orbitals and HF orbitals differ by up to 1 kcal/mol. The pure functionals perform slightly better than the hybrid functionals. The contribution with the use of Brueckner orbitals is slightly larger than that with the use of pure DFT functionals. The energies differ by only 0.1 kcal/mol. We chose the CCSD(T)/PW91 results (Table 4) for the following discussion due to the small errors among the results obtained from selected DFT orbitals. The sum of valence and core-valence contributions to the NCEs with the CCSD(T)/PW91 and BCCD(T) methods are nearly identical. The contributions of pseudopotential corrections with the correlation of both valence and core-valence electrons for both Ti2O4 and Cr2O4 are ~ 1.0 and ~ 0.5 kcal/mol less than previous work40 respectively, where the correction was derived from the energies with the valence electrons correlated only. The pseudopotential corrections for Zr2O4 and Mo2O6 are also ~ 0.5 kcal/mol less than our previous study. We use the other contributions such as scalar relativistic corrections as well as zero-point-energies from the previous study. Compared to the CCSD(T)/HF method,40 slightly larger NCEs are predicted. The difference is in the order of 1 kcal/mol for Cr2O6 and 0.3 kcal/mol for the other oxides. Again, our predictions in terms of NCEs are consistent with available experiments for Ti2O4, MO2O6 and W2O6. UCl6 The UCl6 molecule represents another test case for our proposed approach. Due to issues with calculating the energies of actinide atoms, for example U, we use isodesmic-type reaction 17 ACS Paragon Plus Environment


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approaches to calculate the heat of formation of the actinide complex. A good test case is the heat of formation of UCl6 as its experimental value is well-established. In addition, it is in the +6 oxidation state with 5f and 6d orbitals in the valence space. We can use the following reaction to determine the heat of formation of UCl6 from the accurately known heats of formation of UF6 71 UF6 + 3Cl2 → UCl6 + 3F2

(2)

The experimental value for this reaction is 278.0 ± 1.7 kcal/mol at 298 K. The various components to calculate the reaction energy are given in Table 5. The CCSD(T) values using HF orbitals are clearly not in agreement for this reaction, being too large by nearly 8 kcal/mol. Similar poor results were found using reactions (3) and (4). UF6 + 6HCl → UCl6 + 6HF

(3)

UF6 + ThCl4 + Cl2 → UCl6 + ThF4 + F2

(4)

We note that there are no issues in the calculation of the heats of formation of ThCl4 and ThF4 using the FPD approach. 72,73 We used both the BCCD(T) and CCSD(T)/B3LYP approaches as described above and found excellent agreement with experiment, within 1 kcal/mol in both cases. The T1 diagnostic for UF6 is 0.032 with the HF starting orbitals and the largest T1 amplitudes correspond to F 2p → U 5f (0.08 for each F atom). The corresponding T1 diagnostic for UCl6 is 0.038 with the HF starting orbitals and the largest T1 amplitudes are from Cl 3p → U 5f (0.11 for each Cl atom). Thus there is more backbonding into the U from the Cl ligands than from the F ligands. Average Bond Dissociation Energies The average bond dissociation energies predicted by the CCSD(T)/PW91 and BCCD(T) methods are shown in Table 6. We assume that the average M=O (metal oxygen double) bond energies in the monomer are identical with that in the dimer. The details of the derivation of the metal oxygen bond energies can be found in our previous study.40 18 ACS Paragon Plus Environment

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As the average bond dissociation energies are derived from the TAE, the difference between two methods is consistent with the TAE difference shown above. Again, CCSD(T)/PW91 gives slightly stronger bond energies than BCCD(T) in most cases. The order of group IVB and VIB meal oxygen bond energies are consistent with our previous work. The calculated M=O bond energies with CCSD(T)/PW91 for M = Ti and M = Cr are 0.5 and 2.0 kcal/mol stronger than that predicted by CCSD(T)/HF. This difference for the other TMOs is small. Conclusions The heats of formation of the group IV and group VI metal oxide monomers and dimers as well as for UCl6 have been predicted with the coupled cluster method using both DFT and Brueckner orbitals as the input orbitals. Significantly more negative heats of formation, -6 and 14 kcal/mol, are predicted for the CrO3 monomer and dimer, respectively, with the use of DFT or Brueckner orbitals when compared with the use of HF orbitals. The improved values due to using the DFT or Brueckner orbitals include contributions at both the valence and core-valence levels. The predicted heat of formation of CrO3 at the CCSD(T)/PW91 or BCCSD(T) levels is consistent with previous calculations with higher order electron correlation corrections included.33,34,35 Thus all of the available computational results suggest that the heat of formation of CrO3(g) needs to be re-measured to at least reduce the error bars and to confirm the computational results. We note that the corrections obtained using the DFT or Brueckner orbitals for CrO3 and Cr2O6 are far larger than the value of ± 3 kcal/mol defined as chemical accuracy for heats of formation of transition metal compounds given in the Introduction. The heat of formation of UCl6 from reactions (2) – (4) is also significantly improved by using DFT or Brueckner orbitals. The improved prediction of the heats of formation is predominately attributed to the use of more accurate orbitals, DFT or Brueckner, in the coupled cluster 19 ACS Paragon Plus Environment


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calculations, resulting in smaller values (decreasing from ~ 0.045 to ~ 0.015 in the case of DFT orbitals) of the T1 amplitudes that might otherwise be attributed to multireference character. For CrO3/Cr2O6 and UCl6, there are significant interactions of the ligand orbitals with the empty d(Cr) or f(U) orbitals which could lead to increased multireference character. The results suggest that the use of DFT or Brueckner orbitals generates better orbitals for the correlation calculations than do the HF orbitals. Thus we recommend for cases where there is potential for multireference character, that one use either DFT or Brueckner orbitals in addition to the HF orbitals to determine if the TAE is significantly changed. The heats of formation of the other transition metal oxides including the TiO2 monomer and dimer and the second and third row group IV and group VI metal oxides are not as strongly dependent on the starting set of orbitals as are CrO3, Cr2O6, and UCl6. For these other oxides, the heats of formation are predicted to be slightly more exothermic by CCSD(T)/DFT and slightly less exothermic by BCCD(T) as compared to CCSD(T)/HF. The heats of formation with use of different starting orbitals generally differ by up to 1 kcal/mol for the monomers and 3 kcal/mol for the dimers. Among the selected DFT functionals, the pure functionals such as PW91 perform better than the hybrid functional due to the presence of exact exchange from Hartree-Fock in the hybrid functionals. The results for the heats of formation show that there is little difference between the use of DFT or BCCD orbitals and the HF orbitals when there are no higher level correlations that are important. This is likely due to more ionic-like behavior and less backbonding of the ligands to the metal so that the HF orbitals provide a good initial description of the bonding. The consistency of the calculated results also points to the fact that most of the experimental data for the heats of formation of the monomers have issues. We note that the experimental dimerization energies are in excellent agreement with the calculated values 20 ACS Paragon Plus Environment

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showing that issues with many of the heats of formation of the larger clusters are due to errors in the monomers. The normalized clustering energies for the dimers with the use of improved wave functions are generally consistent with the use of HF theory except for Cr2O6, where slightly a more than 1 kcal/mol larger NCE is predicted in this study. The average bond dissociation energies predicted by the use of PW91 orbitals or Brueckner for M = Cr are generally stronger than the use of HF orbitals. For the other TMOs, there no significant change with the use of different starting orbitals for coupled cluster calculations. We thus recommend that one should examine the T1 diagnostic and any large T1 amplitudes in the CCSD calculation. For molecules that may have multi-reference character as evidenced by these checks or by chemical insight even though they are closed shell, we then recommend performing BCCD(T) or CCSD(T)/DFT calculations to look for improvements in the total energies leading to improved atomization energies when extrapolated to the CBS limit. We further note that one should be consistent when performing such calculations in terms of the valence and core-valence corrections and not to mix orbital sets for these different levels. Acknowledgments This work was supported by the Chemical Sciences, Geosciences and Biosciences Division, Office of Basic Energy Sciences, U.S. Department of Energy (DOE) under grant no. DE-FG02-03ER15481 (Catalysis Center Program). KAP gratefully acknowledges the support of the U.S. Department of Energy Office of Science, Office of Basic Energy Sciences, Heavy Element Chemistry Program through Grant No. DE-FG02-12ER16329. DAD also thanks the Robert Ramsay Chair Fund of The University of Alabama for support. Part of this work was performed on the computers in the Molecular Sciences Computing Facility at the W. R. Wiley Environmental Molecular Sciences Laboratory, a national scientific user facility sponsored by 21 ACS Paragon Plus Environment


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DOE’s Office of Biological and Environmental Research and located at Pacific Northwest National Laboratory, operated for the DOE by Battelle. Supporting Information. Valence and core-valence electronic contributions using DFT orbitals or Brueckner orbitals with different basis sets. Various components to the TAE. T1 diagnostics at the CCSD(T)/aWT level with correlation of core-valence electrons. CCSD(T) electronic energies using DFT orbitals for the atoms and oxides for different starting orbitals and basis sets. This material is available free of charge via the internet at http://pubs.acs.org.


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(61) Peterson, K.A.; Figgen, D.; Dolg, M.; Stoll, H. Energy-Consistent Relativistic Pseudopotentials and Correlation Consistent Basis Sets for the 4d Elements Y-Pd. J. Chem. Phys. 2007, 126, 124101-1 - 124101-12. (62) Figgen, D.; Peterson, K.A.; Dolg, M.; Stoll, H. Energy-Consistent Pseudopotentials and Correlation Consistent Basis Sets for the 5d Elements Hf – Pt. J. Chem. Phys. 2009, 130, 164108-1 - 164108-12. (63) Curtiss, L. A.; Raghavachari, K.; Redfern, P. C.; Pople, J. A. Assessment of Gaussian-2 and Density Functional Theories for the Computation of Enthalpies of Formation. J. Chem. Phys. 1997, 106, 1063-1079. (64) Knowles, P. J.; Manby, F. R.; Schütz, M.; Celani, P.; Knizia, G.; Korona, T.; Lindh, R.; Mitrushenkov, A.; Rauhut, G.; Adler, T. B.; Amos, R. D.; Bernhardsson, A.; Berning, A.; Cooper, D. L.; Deegan, M. J. O.; Dobbyn, A. J.; Eckert, F.; Goll, E.; Hampel, C.; Hesselmann, A.; Hetzer, G.; Hrenar, T.; Jansen, G.; Köppl, C.; Liu, Y.; Lloyd, A. W.; Mata, R. A.; May, A. J.; McNicholas, S. J.; Meyer, W.; Mura, M. E.; Nicklass, A.; Palmieri, P.; Pflüger, K.; Pitzer, R.; Reiher, M.; Shiozaki, T.; Stoll, H.; Stone, A. J.; Tarroni, R.; Thorsteinsson, T.; Wang, M.; Wolf, A. MOLPRO, version 2010.1, a package of ab initio programs. See http://www.molpro.net. (65) Werner H.-J.; Knowles, P. J.; Knizia, G.; Manby, F. R.; Schütz, M. Molpro: A General‐ Purpose Quantum Chemistry Program Package. WIREs Comput. Mol. Sci. 2012, 2, 242-253. (66) Balducci, G.; Gigli, G.; Guido, M. Mass Spectrometric Study of the Thermochemistry of Gaseous EuTiO3 and TiO2. J. Chem. Phys. 1985, 83, 1909-1912. (67) Cox, J. D.; Wagman, D. D.; Medvedev, V. A. CODATA Key Values for Thermodynamics; Hemisphere Publishing Corp.: New York, 1989.


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(68) Balducci, G.; Gigli, G.; Guido, M. Identification and Stability Determinations for the Gaseous Titanium Oxide Molecules Ti2O3 and Ti2O4. J. Chem. Phys. 1985, 83, 1913-1916. (69) Burns, R. P.; DeMaria, G.; Drowart, J.; Grimley, R. T. Mass Spectrometric Investigation of the Sublimation of Molybdenum Dioxide. J. Chem. Phys. 1960, 32, 1363-1366. (70) Norman, J. H.; Staley H. G. Thermodynamics of the Dimerization and Trimerization of Gaseous Tungsten Trioxide and Molybdenum Trioxide. J. Chem. Phys. 1965, 43, 3804-3806 (71) Guillaumont, R.; Fanghånel, T.; Neck, V.; Fuger, J.; Palmer, D. A.; Grenthe, I.; Rand, M. H. Chemical Thermodynamics 5: Update on the Chemical Thermodynamics of Uranium, Neptunium, Plutonium, Americium and Technetium, Elsevier, Amsterdam, 2003. (72) K. S. Thanthiriwatte, M. Vasiliu, S. R. Battey, Q. Lu, K. A. Peterson, L. Andrews, and D. A. Dixon, Gas Phase Properties of MX2 and MX4 (X=F, Cl) for M = Group 4, Group 14, Ce, and Th, J. Phys. Chem. A, 2015, 119, 5790-5803. (73) Peterson, K.A. Correlation Consistent Basis Sets for Actinides. I. The Th and U Atoms. J. Chem. Phys. 2015, 142, 074105-1 - 074105-14.



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Table 1. Valence Contributions (∆EVal) to the TAE using DFT Starting Orbitals with a HF core or Brueckner Orbitals for Group IV and Group VI Monomers and Dimers.a Molecule CrO3 Cr2O6 TiO2 Ti2O4 ZrO2 HfO2 MoO3 WO3 Zr2O4 Hf2O4 Mo2O6 W2O6 a

HF 341.47 776.46 299.44 721.23 330.92 329.87 417.38 475.74 790.30 809.63 946.81 1080.32

B3LYP 344.40 781.95 299.66 722.41

BP86 344.18 783.50 299.82 722.94

PW91 344.23 783.51 299.90 723.07 331.28 329.97 417.70 475.75 791.64 810.31 948.32 1081.15

PBE 344.13 783.32 299.81 722.90

M06 343.94 782.93 299.89 722.88

SVWN5 344.31 783.68 299.71 722.70

BCCD(T) 343.29 782.14 298.27 719.21 330.29 329.35 417.08 475.25 789.41 808.90 946.76 1079.93

CBS value for the valence electron contribution extrapolated from the CCSD(T)/aX energies.


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Table 2. Valence and Core-Valence Contributions to the TAE using DFT Starting Orbitals or Brueckner Orbitals for CrO3 and TiO2 Monomers and Dimers.a Molecule

CrO3

Cr2O6

TiO2

Ti2O4

ZrO2

HfO2 MoO3

Start Ψ HF B3LYP BP86 PW91 PBE M06 SVWN5 BCCD(T) HF B3LYP BP86 PW91 PBE M06 SVWN5 BCCD(T) HF B3LYP BP86 PW91 PBE M06 SVWN5 BCCD(T) HF B3LYP BP86 PW91 PBE M06 SVWN5 BCCD(T) HF PW91 BCCD(T) HF PW91 BCCD(T) HF

∆EVal' 341.58 346.31 346.26 346.39 346.28 345.38 345.53 343.75 776.69 787.45 787.25 787.39 787.24 785.41 785.31 782.71 299.61 300.76 300.76 300.78 300.73 300.26 300.10 298.44 721.40 723.92 723.67 723.74 723.65 722.62 721.61 719.37 330.84 333.55 330.22 329.97 331.51 329.45 417.50

∆ECVVc 343.46 348.12 349.54 349.57 349.49 348.70 350.01 348.33 783.28 794.40 797.54 797.44 797.36 795.58 798.38 795.12 304.57 304.76 305.36 305.44 305.37 305.18 305.53 304.31 733.22 733.92 735.30 735.40 735.28 734.73 735.61 732.42 336.70 335.62 335.97 333.80 334.36 333.18 416.88 33

∆ECV = ∆ECVV - ∆EVal' 1.88 1.81 3.28 3.18 3.21 3.32 4.48 4.58 6.59 6.95 10.28 10.06 10.12 10.17 13.07 12.41 4.96 4.00 4.61 4.65 4.64 4.91 5.43 5.87 11.82 10.00 11.63 11.66 11.63 12.12 14.00 13.05 5.86 2.07 5.75 3.83 2.85 3.72 -0.62

ACS Paragon Plus Environment


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WO3

Zr2O4

Hf2O4

Mo2O6

W2O6

PW91 BCCD(T) HF PW91 BCCD(T) HF PW91 BCCD(T) HF PW91 BCCD(T) HF PW91 BCCD(T) HF PW91 BCCD(T)

419.23 417.19 476.11 477.30 475.62 789.98 796.39 789.09 809.67 813.81 808.94 946.92 950.76 946.87 1081.00 1083.95 1080.60

417.19 416.84 474.52 475.67 474.09 803.13 801.54 802.04 819.15 820.73 818.27 948.07 949.20 948.58 1077.89 1080.80 1077.65

-2.04 -0.36 -1.59 -1.62 -1.53 13.15 5.15 12.96 9.48 6.91 9.33 1.15 -1.57 1.72 -3.10 -3.16 -2.95

a

CBS value for the valence electron contribution extrapolated from the CCSD(T)/awX energies. The HF calculations use an HF core for the valence-only correlation calculations. The DFT calculations use a DFT core for the valence only calculations. b CBS value extrapolated from the CCSD(T)/ awX energies with the metal 3s23p6 and oxygen 1s2 electrons correlated. This is the value used for the TAE and heats of formation calculations.


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Table 3 Total Atomization Energies and Heats of Formation for the Ground State Metal Oxide Monomers and Dimers.

Molecule

∆ECVV a

CCSD(T)/PW91 ΣD0,0Kb ΔHf,0Kc ΔHf,298Kd

∆ECVV a

BCCD(T) ΣD0,0Kb ΔHf,0Kc

ΔHf,298Kd

CCSD(T)/HF ΔHf,298Ke

Expt f

TiO2

305.44

300.27

-69.9

-70.5

304.31

299.14

-68.8

-69.4

-69.6

331.21

-67.8

-68.4

-69.2

-73.0 ± 3 -71.4 ± 3 g,h -68.4 ± 11

ZrO2

335.62

330.86

-67.4

-68.1

335.97

HfO2

334.36

318.32

-52.7

-53.4

333.18

317.14

-51.5

-52.2

-52.9

CrO3

349.57

338.23

-66.8

-67.7

348.34

337.00

-65.6

-66.5

-61.6

-78.0

-78.9

416.83

411.65

-77.6

-78.6

-78.6

-70.0 ± 10 -77.3 ± 1i -82.8 ± 5

MoO3

417.19

412.00

WO3 Ti2O4

475.67

459.60

-79.6

-80.7

474.09

458.02

-78.0

-79.1

-79.5

-70.0 ± 7

735.40

720.71

-260.0

-261.8

732.43

717.73

-257.0

-258.8

-259.6

-262.2 ± 11 j

Zr2O4

801.54

789.13

-262.0

-264.2

802.04

789.63

-262.7

-264.7

-265.8

Hf2O4 Cr2O6

820.73

785.88

-254.6

-256.5

818.27

783.42

-252.1

-254.0

-254.9

797.44

771.52

-228.6

-231.0

795.12

769.20

-226.3

-228.7

-216.9

Mo2O6

949.20

936.20

-268.1

-270.4

948.58

935.59

-267.5

-269.7

-269.2

-280.8 ± 13 k

W2O6

1080.80 1046.41

-286.3

-288.6

1077.65

1043.26

-283.2

-285.5

-285.7

-278.2 ± 10

a

Valence and core-valence contributions (∆ECVV) taken from CCSD(T)/PW91 and BCCD(T) respectively.

b

ΣD0, 0K = ΔECVV+ ΔEZPE + ΔESR+ ΔESO +ΔEPP,corr. The last four contributions were taken from our previous work.40

c

ΔHf, 0K [(MOm)n] = n ΔHf, 0K (M) + m*n ΔHf, 0K (O) − ΣD0, 0K [(MOm)n]. See Ref. 40 for the detail.

d

ΔHf,298K [(MOm)n] = ΔHf,0K [(MOm)n] + ΔH0K→298K [(MOm)n] − n ΔH0K→298K (M) − n*m ΔH0K→298K (O). See Ref. 40 for the detail. 35 ACS Paragon Plus Environment


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48

e

See Ref. 40 for additional details. ECVV taken from CCSD(T)/HF at the CBS level.

f

All experimental values from Ref. 37 unless noted.

g

Ref. 66.

h

Obtained using the CODATA heats of formation for Ti. The heat of formation for Ti is given in ref. 67 at 298.15 K. The heat of

formation of Ti at 0 K is obtained from this value with the correction from 0 to 298 K given in the JANAF table, ref. 37. i

Ref. 38 based on data from Ref. 39.

j

Using the heat of formation of -71.4 ± 3 kcal/mol for TiO2 and the dimerization energy from Ref. 68

k

The experimental value for ΔHf(Mo2O6) is from the experimental heat of formation of MoO3 and the experimental dimerization

energy from Ref. 69 corrected to 298 K.


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Table 4. Normalized Clustering Energies at 0 K (∆E0K) for the Ground State Dimers Calculated at the CCSD(T)/PW91 and BCCD(T) Levels. Molecule

ΔEZPEa

Ti2O4 Zr2O4 Hf2O4 Cr2O6 Mo2O6 W2O6

-1.08 -0.92 -0.94 -1.05 -0.85 -0.68

ΔESRb -0.33 -0.12 -0.11 -0.43 -0.16 -0.15

ΔEPP,Corrc -0.77 -0.41 -0.34 -0.14 -0.30 -0.29

CCSD(T)/PW91 ∆ECVV d ∆E0K e 62.26 60.1 65.15 63.7 76.00 74.6 49.15 47.5 57.41 56.1 64.72 63.6

BCCD(T) ∆ECVV ∆E0K e 61.90 59.7 65.05 63.6 75.96 74.6 49.22 47.6 57.45 56.1 64.74 63.6

CCSD(T)/HF Expt ∆E0Kf 59.9 59.4 ± 5g 63.4 74.4 46.6 55.8 57.5 ± 4h 63.3 69.4 ± 9i

a

BP86/aD.

b

CISD/aT level.

c

Pseudopotential corrections. They are derived from the calculations with both valence and core-valence electrons correlated. See

Ref. 40 for details. d

e

Valence and core-valence contributions (∆ECVV) taken from CCSD(T)/PW91 results. ΣD0, 0K = ΔECVV+ ΔEZPE + ΔESR +ΔEPP,corr. The last three components were taken from our previous work, Ref. 40.

f

∆ECVV taken from CCSD(T)/HF at the CBS level.

g

Ref. 68.

h

Ref. 69.

i

Ref. 37. 37 ACS Paragon Plus Environment


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Table 5 Composite results for the reaction enthalpy of UF6 + 3Cl2 → UCl6 + 3F2 in kcal/mol.

Method

a

CCSD(T)/HF BCCD(T)/HF CCSD(T)/B3LYP

FC-VQZ

FC-CBS

ΔCV U 5s5p5d

286.35 280.56 279.44

286.77 280.84 279.91

+1.76 +0.05 +0.47

ΔCV Cl 2s2p/F 1s

ΔSO

ΔQED

ΔZPE

ΔHr(298)

-0.55 -0.55 -0.55

-1.54 -1.54 -1.54

0.36 0.36 0.36

-0.22 -0.22 -0.22

285.93 278.29 277.78

a

These results use the Douglas-Kroll-Hess 3rd-order (DKH3) Hamilitonian throughout with cc-pVnZ-DK3/cc-pwCVnZ-DK3 basis sets on U and aug-cc-pVnZ-DK/aug-cc-pwCVnZ-DK sets on all other atoms. Details of the SO and QED calculations, as well as the CBS extrapolation method, can be found in Ref. 73. The CV effect for the Cl and F core orbitals, as well as the frequencies needed for the ZPE correction, were obtained using pseudopotential-based cc-pVnZ-PP basis sets on U.73


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Table 6. Average Bond Dissociation Energies in kcal/mol from the Total Atomization Energies of the Monomers and Dimers Calculated at the CCSD(T)/PW91, BCCD(T), and CCSD(T)/HF Levels. Method CCSD(T)/PW91

BCCD(T)

CCSD(T)/HF

Bond M=O

M = Ti

M = Zr

M = Hf

M = Cr

M = Mo

M=W

150.1

165.4

159.2

112.7

137.3

153.2

M−O

105.1

114.6

116.9

80.1

96.7

108.4

M=O

149.6

165.6

158.6

112.3

137.2

152.7

M−O

104.6

114.6

116.6

80.0

96.7

108.1

149.7

166.0

158.9

110.7

137.2

152.8

104.8

114.7

116.6

78.6

96.5

108.1

M=O M−O



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For Table of Contents Use Only Use of Improved Orbitals for CCSD(T) Calculations for Predicting Heats of Formation Zongtang Fang, Zachary Lee, Kirk A. Peterson, and David A. Dixon

TOC Graphic

∆Hr(298)

+ 3Cl2

+ 3F2 UCl6

UF6

CCSD(T)/HF BCCD(T)/HF CCSD(T)/B3LYP Experiment

∆Hr = 285.9 kcal/mol ∆Hr = 278.3 ∆Hr = 277.8 ∆Hr = 278.0 ± 1.7


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Use of Improved Orbitals for CCSD(T) Calculations for Predicting

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