Heats of Formation for

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Prediction of Bond Dissociation Energies/Heats of Formation for Diatomic Transition Metal Compounds: CCSD(T) Works Zongtang Fang,† Monica Vasiliu,† Kirk A. Peterson,*,‡ and David A. Dixon*,† †

Department of Chemistry, The University of Alabama, Shelby Hall, Tuscaloosa, Alabama 35487-0336, United States Department of Chemistry, Washington State University, Pullman Washington 99164-4630 United States

‡

S Supporting Information *

ABSTRACT: It was recently reported (J. Chem. Theory Comput. 2015, 11, 2036−2052) that the coupled cluster singles and doubles with perturbative triples method, CCSD(T), should not be used as a benchmark tool for the prediction of dissociation energies (heats of formation) for the first row transition metal diatomics based on a comparison with the experimental thermodynamic values for a set of 20 diatomics. In the present work the bond dissociation energies as well as the heats of formation for those diatomics have been calculated by the Feller−Peterson−Dixon approach at the CCSD(T)/ complete basis set (CBS) level of theory including scalar relativistic corrections and correlation of the outer shell of core electrons in addition to the valence electrons. Revised experimental values for the hydrides are presented that are based on new heterolytic R−H bond dissociation energies, which are needed for analysis of the mass spectrometry experiments. The agreement between the calculated bond dissociation energies and the revised experimental values of the hydrides is good. Good agreement of the calculated bond dissociation energies/heats of formation is also found for most of the chlorides, oxides, and sulfides given the experimental error bars from experiment and those of the transition metal atoms in the gas phase. Thus, reliable results can be achieved by the CCSD(T) method at the CBS limit. The use of PW91 orbitals for the CCSD(T) calculations improves the predictions for some compounds with large T1 diagnostics at the HF-CCSD(T) level. The optimized bond distances and calculated vibrational frequencies for the diatomics also agree well with the available experimental values.

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INTRODUCTION

range of functionals that can be used for such thermodynamic predictions. Recently, Truhlar and co-workers22 suggested, on the basis of a comparison with a database of thermodynamic values (their 3dMLBE20) mostly developed by Wilson and co-workers,17 that CCSD(T) does not handle the prediction of the bond dissociation energies (heats of formation) for first row transition metal diatomics any better than does density functional theory (DFT) with many functionals and suggest that CCSD(T)-based methods should not be used as a benchmark electronic structure approach for such systems. Their results are in contrast to those from our groups23−31 as well as that of Wilson,15−19 which show for sets of polyatomic transition metal compounds that DFT methods do not perform as well as CCSD(T)-based approaches for a range of thermodynamic properties. In addition, we have recently demonstrated that using DFT-based orbitals for the CCSD(T) calculations or Brueckner orbitals32−38 in BCCD(T) calculations can significantly improve the predicted heats of formation of chromium oxides and UCl6.39 As part of our efforts to provide approaches for the reliable prediction of thermodynamic properties, we have evaluated the heats of formation/bond dissociation energies (BDEs) for the diatomics reported by Truhlar and co-workers22 using the FPD

There is substantial interest in having a capability to predict reliable thermodynamic properties, especially for compounds containing transition metals, by using electronic structure methods. For such compounds, it is difficult to make measurements on small gas phase species so there are a smaller number of reliable values available to serve as benchmarks for computational electronic structure approaches as compared to those for main group or organic compounds.1−3 Such thermodynamic values are of practical importance as many catalysts contain transition metals and reliable thermodynamic quantities can play an important role in catalyst design. We have developed a composite approach, the Feller− Peterson−Dixon approach,4−8 for the prediction of thermodynamic quantities for all atoms in the Periodic Table. At its core for most molecules is coupled cluster theory with single and double excitations and a perturbative triples correction (CCSD(T))9−12 extrapolated to the complete basis set (CBS) limit using the correlation-consistent basis sets13 for the valence electrons followed by additional corrections for core−valence interactions, relativistic effects, and of course the zero-point energy. There are a number of other similar approaches including a range of correlation consistent composite approach (ccCA) methods for transition metals,14−19 and Gaussian-X for transition metals.20,21 Of course, there are also density functional theory methods with a wide © 2017 American Chemical Society

Received: September 30, 2016 Published: January 12, 2017 1057

DOI: 10.1021/acs.jctc.6b00971 J. Chem. Theory Comput. 2017, 13, 1057−1066

Article

Journal of Chemical Theory and Computation Table 1. CCSD(T) (HF Orbitals) Optimized Bond Distances in Å and Frequencies in cm−1 for Diatomic MXa

a

molecule

Re(5)

Re(CBS)

Re(expt)

ωe(5)

ωe(CBS)

ωexe(5)

ωexe(CBS)

TiCl VH VO VCl CrH CrO CrCl MnS MnCl FeH FeCl CoH CoCl NiCl CuH CuCl ZnH ZnO ZnS ZnCl

2.2661 1.6850 1.5851 2.2292 1.6304 1.6127 2.1704 2.0654 2.2368 1.5479 2.1761 1.5049 2.0752 2.0542 1.4593 2.0506 1.5897 1.7000 2.0445 2.1293

2.2642 1.6840 1.5839 2.2273 1.6293 1.6116 2.1688 2.0633 2.2355 1.5478 2.1751 1.5049 2.0749 2.0539 1.4593 2.0498 1.5899 1.6989 2.0427 2.1274

2.26462345(15)67 1.7367 1.589365 2.214566 1.6554111(57)65 1.61564 2.193952(2)63 2.0763 2.243 calc22 1.6367 2.179b,22 1.5367 [1.5424]65 2.087b,22 2.073b,22 1.4626364 2.05118364 1.594964 1.867 2.167 2.167

404.8 1656.4 1030.9 410.2 1753.0 931.8 434.7 491.8 385.9 1868.0 408.2 1895.4 417.6 421.4 1946.4 417.4 1613.6 745.2 462.3 393.3

404.2 1657.1 1033.6 410.6 1755.1 930.4 435.9 490.8 386.6 1858.8 409.4 1893.2 417.6 423.0 1944.6 418.5 1611.4 747.1 464.3 395.3

1.1 12.2 4.2 1.3 27.1 8.3 1.4 1.8 1.4 26.1 1.6 33.0 1.7 1.7 38.1 1.6 51.0 5.6 2.0 1.6

0.7 5.3 4.2 1.1 27.8 7.7 1.5 1.2 1.4 22.3 1.7 32.0 1.6 1.9 38.2 1.6 49.7 5.6 2.0 1.5

ωe(expt)

ωexe(expt)

404.3370 1011.364 417.466 1656.05115(54)65 898.464 396.662172

4.8664 1.0,71 3.566 30.4965 6.7564

[382.4]64 (409.9)64

(2.2)64

1941.2664 415.2964 1607.664

37.5164 1.5864 55.1464

390.564

1.564

b

(5) = aug-cc-pwCV5Z-DK. Calculated at the DFT M06 level.

guesses of the bond distances are obtained from the “experimental” values used by Truhlar and co-workers.22 As discussed below, not all of these experimental values have experimental sources. The heats of formation for the diatomic molecules are predicted at the Feller−Peterson−Dixon (FPD) level.4−8 Either the CCSD(T) energies with n = T, Q, and 5 are extrapolated to the complete basis set (CBS) limit using a mixed Gaussian/exponential (eq 1)51

approach. Although Truhlar and co-workers quote BDEs, we note that in a number of cases, BDEs were not directly available from experiment but are actually derived from heats of formation. We come to two conclusions. (1) The FPD method based on using CCSD(T) works for most of the compounds to within experimental error when the uncertainties in the experimental heats of formation of the metal atoms, which are required for our predicted heats of formation or for the experimental BDEs, are included. In cases where the direct experimental measurement is a bond dissociation energy, notably for the hydrides, we also obtain good agreement with corrected experimental values. Thus, CCSD(T) is an appropriate benchmark tool for transition metal compounds. (2) There are issues with the experimental data, especially for the hydrides, and the computational values are more reliable than the current uncorrected experimental values used in 3dMLBE20. Thus, one must take care in benchmarking computational methods against experimental data that are inaccurate. At the same time as our work was being competed, we were made aware of a similar study by Cheng et al. using a similar approach,40 also with a reassessment of the experimental data for VH and CrH used in 3dMLBE20.

E(n) = ECBS + A exp[− (n − 1)] + B exp[− (n − 1)2 ] (1)

or the energies with n = Q and 5 are extrapolated to the CBS limit with eq 2.52 E(n) = ECBS + B /(n + 1/2)4

(2)

The total atomization energy (TAE = D0) is obtained using eq 3. D0 = ΔE(CBS) + ΔE(SO) + ΔE(ZPE)

(3)

The contribution ΔE(CBS) accounts for the electron correlation of both valence and outer-core electrons as well as scalar relativistic effects. The anharmonic-corrected zeropoint energy is calculated as 1/2ωe − 1/4ωexe, where ωe and ωexe values are obtained from the fitted CCSD(T)-DK/aug-ccpwCV5Z-DK potential energy functions. The spin orbit corrections, ΔE(SO), for the ground state atoms were taken from experiment53−55 and the ΔE(SO) for molecules were from Truhlar and co-workers.22 Rather than focusing on De, we focus on the actual experimental value, which is either a D00 or a heat of formation. The heats of formation at 0 K are derived from their TAE and the experimental heats of formation of the atoms.56 The thermal corrections at 298 K are obtained using the normal statistical mechanical expressions.57 The heats of formation at 298 K are calculated using the equation by Curtiss et al.58 The calculated heats of formation at 298 K and the experimental enthalpies of the atoms at 298 K are used to derive the BDE corrections from 0 to 298 K (Supporting Information).

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COMPUTATIONAL METHODS The equilibrium bond distances are obtained via a seven-point polynomial fit,41 where the single point energies for the fit are calculated at the CCSD(T) level using the second-order Douglas−Kroll−Hess Hamiltonian42−44 and the aug-ccpwCVnZ-DK (n = T, Q, 5) basis sets.45−48 Both the valence and outer-core electrons (1s for O and F, 2s2p for Cl, and 3s3p for the metals) are correlated in the CCSD(T) calculations. The electronic structures of the open-shell species were calculated with the R/UCCSD(T) approach where a restricted open shell Hartree−Fock (ROHF) calculation was initially performed and the spin constraint was then relaxed in the coupled cluster calculation.49,50 The R/UCCSD(T) method is equivalent to the ROHF-based implementation in other codes and has been shown to provide reliable results. The initial 1058

DOI: 10.1021/acs.jctc.6b00971 J. Chem. Theory Comput. 2017, 13, 1057−1066

Article

Journal of Chemical Theory and Computation Table 2. Components for Bond Dissociation Energies for Diatomic MX in kcal/mola HFb

HFb

MX

ΔECBS(T,Q,5)

ΔECBS(Q,5)

ΔEZPE

ΔESO22

TiCl VH VO VCl CrH CrO CrCl MnS MnCl FeH FeCl CoH CoCl NiCl CuH CuCl ZnH ZnO ZnS ZnCl

97.99 57.11 152.20 99.33 50.87 106.60 88.47 67.18 82.32 44.54 82.35 52.50 80.81 90.01 64.47 88.00 21.54 35.60 33.72 50.54

98.20 57.19 152.45 99.53 50.89 106.76 88.94 67.45 82.49 44.68 82.53 52.66 81.12 90.32 64.49 88.18 21.56 35.75 33.95 50.72

−0.58 −2.37 −1.47 −0.59 −2.49 −1.32 −0.62 −0.70 −0.55 −2.64 −0.58 −2.68 −0.60 −0.60 −2.75 −0.60 −2.27 −1.06 −0.66 −0.56

−0.90 −0.40 −1.10 −1.30 0.00 0.20 −0.80 −0.60 −0.80 −0.10 −0.90 −0.20 −1.00 −2.10 0.00 −0.80 0.00 −0.20 −0.60 −0.80

PW91b

D00CBS(T,Q,5)

D00CBS(Q,5)

96.51 54.34 149.63 97.43 48.38 105.47 87.37 65.88 80.97 41.79 80.87 49.63 79.21 87.31 61.72 86.60 19.26 34.34 32.47 49.18

96.72 54.42 149.88 97.64 48.40 105.63 87.52 66.15 81.14 41.94 81.05 49.78 79.52 87.62 61.74 86.77 19.29 34.50 32.70 49.36

D00CBS(T,Q,5) 97.05 55.00 152.39 98.11 50.38 107.27 90.07 66.77 81.17 42.08 81.10 50.79 80.80 89.17 62.20 86.99 19.57 34.71 32.30 49.37

[63.31]i [88.05]i [35.22]i [32.64]i

expt D00CBS(Q,5)

97.26 55.08 152.64 98.32 50.41 107.43 90.23 67.04 81.35 42.22 81.29 50.94 81.11 89.48 62.45 87.42 19.33 34.80 32.55 49.29

[63.56]i [88.46]i [34.87]i [33.15]i

D00 95.7 ± 2.5,88 100.1 ± 290 50.1 ± 4.4,82,c 53.7 ± 1.5d 149.5 ± 2,92 147.864 101.9 ± 291 46.1 ± 3.3,82,c 49.1 ± 1.5e 101.1 ± 7,94 110 ± 2,93 109.8 ± 2.695,c 89.6 ± 1.687 69.7 ± 3,86,c 80.2 ± 1.687 37.0 ± 3.1,83,c 42.2 ± 1.5f 77.9 ± 1.687 47.8 ± 3.1,84,c 51.9 ± 1.5,g 49.3 ± 1.5h 79.9 ± 1.687 89.2 ± 1.687 60.3 ± 4.8,84 60.785 89.6 ± 1.8,89 87.2 ± 0.356 19.5 ± 0.586,j 37.1 ± 1.097 48.4 ± 3.086,j 53.5 ± 1.086,j

a ΔECBS(T,Q,5) = electronic energy from eq 1. ΔECBS(Q,5) = electronic energy from eq 2. ΔESO = spin orbit correction from ref 22. ΔEZPE from CBS extrapolation. D00 = bond dissociation energy at 0 K. bHF = HF orbitals. PW91 = PW91 orbitals. See text. cRe-evaluated experimental numbers. See text. dFrom reaction with (CH3)2NH. See Table 3. eFrom reaction with (CH3)3N. See Table 3. fFrom reaction with c-C3H6. See Table 3. gFrom reaction with iso-C4H10. See Table 3. hFrom reaction with c-C3H6. See Table 3. iBCCD(T) values in brackets []. jFrom heat of formation at 298 K corrected to 0K and includes error in the heat of formation of that atoms.

The CCSD(T)-DK calculations were carried out with MOLPRO 2012.1.59,60 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 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.

Analysis of IR transitions in VCl gives an experimental value that is 0.015 Å shorter than our value.66 For VH, the experimental bond distance is taken from the poster compilation of Bolydrev and Simons67 (see also Jensen et al.68) and our optimized value is >0.05 Å shorter, showing the estimated value is too long. For MnS, our value is within 0.005 Å of the value from the poster compilation of Bolydrev and Simons.67 For FeH, our value is almost 0.08 Å shorter than the poster compilation of Bolydrev and Simons.67 For CoH, our calculated value is 0.025 Å shorter than the value given by Bolydrev and Simons67 and 0.037 Å shorter than the value given by Huber and Herzberg.64 For MnCl, no experimental value has been reported and our CCSD(T)/CBS value is similar to the previously reported calculated value22 at the M06 density functional theory level. For FeCl, we are consistent with the previously reported calculated value.69 For CoCl and NiCl, only calculated values are available.22 For ZnO, ZnS and ZnCl, the only available “experimental” values are from the poster of Bolydrev and Simons67 and are only given to one decimal place in Å. Our value for ZnO is 0.1 Å shorter, that for ZnS, 0.056 Å shorter, and that for ZnCl, 0.03 Å longer than the Bolydrev and Simons values. Frequencies. The calculated harmonic frequencies ωe at the CCSD(T)-DK/aug-cc-pwCV5Z-DK level show differing amounts of agreement with experiment. For TiCl,70,71 VCl,66 MnCl,64 FeCl,64 CuH,64 CuCl,64 ZnH,64 and ZnCl,64 the harmonic values are within 10 cm−1 of experiment and the anharmonic ωexe terms are within a few cm−1 of experiment. The calculated value of ωe for VO is within 20 cm−1 of experiment,64 for CrO it is within 34 cm−1 of experiment,64 and that for CrCl is within 38 cm−1 of experiment.72 There is a significant difference between the CCSD(T)-DK/aug-cc-

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RESULTS AND DISCUSSION Geometries. The optimized geometries are shown in Table 1. The calculated bond distances and frequencies were extrapolated to the CBS level by extrapolating the individual energies from the seven-point fits at the Q5 level. For TiCl, VCl, and CrCl, Kardahakis and Mavrides provide a good overview of experimental and computational values of these chlorides.61 We first describe the agreement of our calculated values with the more reliable experimental values. For TiCl, the experimental value is from submillimeter-wave spectroscopy62 and our aug-cc-pwCV5Z-DK result differs by