Bond Dissociation Energies for Diatomic Molecules Containing 3d

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Bond dissociation energies for diatomic molecules containing 3d transition metals: Benchmark scalarrelativistic coupled-cluster calculations for twenty molecules Lan Cheng, Jürgen Gauss, Branko Ruscic, Peter B. Armentrout, and John F. Stanton J. Chem. Theory Comput., Just Accepted Manuscript • DOI: 10.1021/acs.jctc.6b00970 • Publication Date (Web): 12 Jan 2017 Downloaded from http://pubs.acs.org on January 17, 2017

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Journal of Chemical Theory and Computation

Bond dissociation energies for diatomic molecules containing 3d transition metals: Benchmark scalar-relativistic coupled-cluster calculations for twenty molecules

Lan Cheng,1, 2, a) Jürgen Gauss,3, b) Branko Ruscic,4, 5, c) Peter B. Armentrout,6, d) and John F. Stanton1, e)

1)

Institute for Theoretical Chemistry, Department of Chemistry,

The University of Texas at Austin, Austin, Texas 78712, USA

2)

Department of Chemistry, The Johns Hopkins University, Baltimore,

Maryland 21218, USA

3)

Institut f¨ ur Physikalische Chemie, Universit¨ at Mainz, D-55099 Mainz,

Germany

4)

Chemical Sciences and Engineering Division, Argonne National Laboratory,

Argonne, Illinois 60439, USA

5)

Computation Institute, The University of Chicago, Chicago, Illinois, 60637,

USA

6)

Department of Chemistry, University of Utah, 315 S. 1400 E. Room 2020,

Salt Lake City, Utah, 84112, USA ACS Paragon 1 Plus Environment


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Benchmark scalar-relativistic coupled-cluster calculations for dissociation energies of the twenty diatomic molecules containing 3d transition metals in the 3dMLBE20 database (Xu et al., J. Chem. Theory Comput. 2015, 11, 2036) ) are reported. Electron correlation and basis set effects are systematically studied. The agreement between theory and experiment is in general satisfactory. For a subset of sixteen molecules, the standard deviation between computational and experimental values is 9 kJ/mol with the maximum deviation being 15 kJ/mol. The discrepancies between theory and experiment remain substantial (more than 20 kJ/mol) for VH, CrH, CoH, and FeH. In order to explore the source of the latter discrepancies, the analysis used to determine the experimental dissociation energies for VH and CrH is revisited. It is shown that, if improved values are used for the heterolytic C-H dissociation energies of di- and tri-methyl amine involved in the experimental determination, the experimental values for the dissociation energies of VH and CrH are increased by 18 kJ/mol, such that D0 (VH) = 223 ± 7 kJ/mol and D0 (CrH) = 204 ± 7 kJ/mol (or De (VH) = 233 ± 7 kJ/mol and De (CrH) = 214 ± 7 kJ/mol). The new experimental values agree quite well with the calculated values, showing the consistency of the computation and the measured reaction thresholds.

a)

Electronic mail: [email protected]

b)


c)


d) e)



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I.

INTRODUCTION

Thermochemical quantities such as bond dissociation and atomization energies, and enthalpies of formation are of fundamental interest in chemistry.1–7 With the rapid growth of computing power and developments of quantum-chemical methods and algorithms, computational thermochemistry has become a useful alternative/complement to experimental determinations. Theoretical model chemistries with systematic treatment of electron correlation and basis set effects have been shown to provide accurate results.8–20 For example, when electron correlation effects are taken into account using coupled-cluster methods21 with inclusion of up to quadruple excitations, subchemical accuracy (sub-kJ/mol) can be achieved for bond energies of molecules containing first-row elements, provided that basis set effects are accurately treated via extrapolation schemes and other important corrections are included, such as scalar-relativistic, spin-orbit, anharmonic zero-point vibrational, and diagonal Born-Oppenheimer corrections.16,17 On the other hand, although coupled-cluster methods have been often used for thermochemistry of transition-metal containing systems,22–25 the accuracy of the CC methods for these systems has been criticized.26 The treatment of the often pronounced electron correlation in transition-metal compounds is challenging. In particular, it is often difficult to tell whether a multireference treatment is necessary to obtain accurate results for a 3d metal containing system. For example, a number of diagnostics have been employed to assess the multireference character of the metal-containing molecules and no simple criteria proposed so far turn out to be sufficient.27 Therefore, benchmark coupled-cluster calculations on transition-metal compounds at levels beyond the common CCSD(T) approach28 with detailed basis set treatments are valuable. By examining the contributions from higher exACS Paragon 3 Plus Environment


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citations (those beyond CCSD(T)), useful information can be obtained on the convergence of the coupled-cluster series for these molecules. In the present paper, we report systematic scalar-relativistic coupled-cluster calculations on the bond dissociation energies for the diatomic transition metal containing molecules in the 3dMLBE20 database recently set up by Truhlar and coworkers.26 It is convenient to compare the equilibrium (i.e. bottom-of-the-well) dissociation energies computed in the present work with the corresponding “experimental values” for De compiled for the 3dMLBE20 set in Ref. 26 by subtracting the computed thermal corrections and zero-point-energies from measured dissociation energies at 298 K. In our calculations, the scalar-relativistic effects have been treated using spin-free exact two-component theory,29,30 and the HEAT protocol17 is employed for the treatment of electron correlation and basis set effects. Namely, allelectron CCSD(T) results obtained using systematic correlation-consistent basis sets have been extrapolated to estimate the basis set limit values, which are then augmented with contributions from higher excitations (full triples and quadruples) obtained using smaller basis sets within the frozen-core approximation. When comparing the present computational results with experimental values, it is found that, for a subset of sixteen molecules in the 3dMLBE20 database, the computational results compare favorably with the experimental ones. For the remaining four molecules, VH, CrH, FeH, and CoH, the discrepancies between theory and experiment are considerably larger. This has motivated us to reinvestigate the experimental values, and here we present such a reanalysis for VH and CrH, which were studied using the same basic experimental approach.31,33 The experimental studies for these hydrides first measured the energy threshold for the hydrogen abstraction reactions between the atomic metal cations and mono-, di-, and tri-methyl amines. Then the experimental values for the bond dissociation energies of ACS Paragon 4 Plus Environment

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the metal hydrides were derived using measured reaction thresholds together with heterolytic C-H bond dissociation energies of the mono-, di-, and tri-methyl amines as well as the ionization energies of the metals and the electron affinity of hydrogen, all of which were taken as the standard values in the literature at that time. It is found that the “standard values” for the heterolytic C-H bond dissociation energies at the time the experiments were carried out deviate from the more accurate values in Active Thermochemical Tables (ATcT)32 by roughly 17 kJ/mol, a finding that tends to ameliorate the (apparent) large errors in the present calculations for these molecules. Using the reaction thresholds measured and the latest available ATcT values for the C-H dissociation energies, which are also supported by high-level quantum-chemical calculations, the correspondingly updated experimental values for bond dissociation energies of VH and CrH agree quite well with the current computations. This finding verifies the reliability of both the computational results presented here and the experimental measurements reported in Ref. 33.

The paper is organized as follows. Computational details are given in Section II. In Section III, the convergence of the computational results with respect to electron correlation and basis set effects is analyzed. The issues surrounding the multireference character of these molecules are also discussed. The computational results are compared with the experimental data as well as previous coupled-cluster results in Section IV. The updated determination for the experimental values of bond dissociations energies for VH and CrH is reported in Section V. A preliminary revisitation for the experimental values of FeH and CoH is also presented in Section VI. Finally the conclusion and outlook are given in Section VII. ACS Paragon 5 Plus Environment


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II.

COMPUTATIONAL DETAILS

Scalar-relativistic coupled-cluster calculations have been carried out to analyze electron correlation and basis set effects. Throughout our calculations, the spin-free exact twocomponent theory in its one-electron variant (SFX2C-1e)29,30,35 has been used for an accurate and efficient treatment of scalar-relativistic effects. Systematic correlation-consistent basis sets with scalar-relativistic contraction coefficients36 including aug-cc-pwCVXZ-DK (augcc-pCVXZ-DK for O, S, and Cl), aug-cc-pVXZ-DK, and cc-pVXZ-DK sets with X=T, Q, 5,37–40 have been employed in CCSD(T)28,41 calculations to assess the treatment of the basis set effects. The valence and core-valence correlation basis sets will be abbreviated as aVXZ and aCVXZ in the following. Basis-set extrapolation techniques42,43 have been used to estimate the Hartree-Fock self-consistent-field (HF-SCF) energies and CCSD(T) correlation energies in the basis set limit. We note that the contraction coefficients of these basis sets have been obtained for the second-order Douglas-Kroll-Hess (DKH2)36,44 method. Since 3d transition metals are not too heavy, the contraction coefficients of DKH2 and SFX2C-1e do not differ very much. Therefore, the error introduced by using the DKH2 contraction in SFX2C-1e calculations is negligible for valence properties such as bond dissociation energies. We have verified this by comparing results obtained here with those from calculations with uncontracted basis sets. We mention that scalar-relativistic effects make siginificiant contributions to the bond dissociation energies of the molecules studied here. The scalar-relativistic corrections have been calculated as the difference between SFX2C-1e and non-relativistic all-electron CCSD(T) results using aCVTZ and aCVQZ basis sets and are summarized in Table I. The largest scalar-relativistic contribution occurs for NiCl and amounts to -35.1 kJ/mol. These results ACS Paragon 6 Plus Environment

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are consistent with those in Ref.26 , with the deviation originating from the difference in the basis sets used: in Ref.26 , aug-cc-pwCVTZ basis sets and aug-cc-pVTZ basis sets were used for metals and light elements, respectively. The basis set dependence of scalar-relativistic corrections seems insignificant, as aCVTZ and aCVQZ results differ by at most 0.4 kJ/mol. However, since SFX2C-1e CC calculations are as efficient as the non-relativistic ones, in the present study we used the SFX2C-1e approach throughout. High-level correlation contributions, i.e., electron correlation contributions beyond CCSD(T), have been obtained via additivity schemes. The full triples contributions have been obtained as the difference between extrapolated CCSDT45 and CCSD(T) values using cc-pVTZ and cc-pVQZ basis sets within the frozen-core approximation. Corrections due to quadruple excitations have been calculated as the difference between CCSDTQ46 and CCSDT results using cc-pVDZ basis sets within the frozen-core approximation. All the CC calculations have been performed using the CFOUR program package47–49 except the CCSDTQ calculations, which have been carried out using MRCC.50,51 In order to compare our calculations with those of Xu et al.,26 the computational results described above have been obtained with the same geometries as reported in Ref.26 . In addition, we have computed the geometries at CCSD(T) level with a variety of correlationconsistent basis sets. The corresponding corrections to the energy (the difference between the CCSD(T)/aug-cc-pwCVQZ energy calculated using CCSD(T)/aug-cc-pwCVQZ geometry and that obtained using the geometry compiled in Ref. 26) are reported as ∆geo . As will be shown, they are significant for FeH and ZnO, modest for VH and ZnS, and negligible for the remaining 16 molecules. Although we have directly obtained the CCSD(T) electron correlation contributions from all-electron aug-cc-pwCVXZ calculations and the corresponding basis-set extrapolation proACS Paragon 7 Plus Environment


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cedure, we divide the electron correlation contributions into valence and core-valence correlating contributions to facilitate a comparison with previous results. For this purpose, frozen-core CCSD(T) calculations using aug-cc-pVXZ basis sets have been carried out and the results are used in the basis set extrapolation to obtain the valence correlation contributions in the basis set limit. The extent to which the valence and core-valence correlating contributions are additive (as is tacitly assumed in most studies) is also discussed by comparing core-valence correlating contributions obtained as the difference between all-electron and frozen-core results using various options of basis sets.

Spin-orbit corrections have been taken from Ref. 26 and added on top of the scalarrelativistic coupled-cluster results. Both spin-orbit corrections and ∆geo are included when we compare the computational results with experiment.

Further, to analyze the discrepancies between the computation and available experimental results for VH and CrH,31 we have performed calculations of the heterolytic C-H bond dissociation energies in mono-, di- and tri-methyl amines, as these data have been used in the derivation of experimental values for the bond dissociation energies of VH and CrH. The calculations of the bond dissociation energy for methyl amine have employed the HEAT345Q protocol18 for the calculations of the heat of formation for the corresponding compounds. Calculations with an approximate version of HEAT (mHEAT)52 are also carried out for methyl amine and compared with the HEAT results as well as the results in Active Thermochemical Tables (ATcT) database.32 This mHEAT method is then used for the calculations for heterolytic C-H bond dissociation energies in di-methyl amine and tri-methyl amine. ACS Paragon 8 Plus Environment

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III.

COMPUTATIONAL RESULTS AND DISCUSSIONS

In this section we systematically analyze various contributions to the equilibrium bond dissociation energies for the twenty diatomic molecules containing 3d transition-metal elements in the 3dMLBE20 database, including electron correlation contributions, basis set effects, and the effect of geometries, to critically assess the reliability of the computational results. Aspects regarding the multireference character of these molecules are discussed as well.

A.

Electron correlation contributions and the convergence of the

coupled-cluster series

As expected, electron correlation plays a central role in the calculation of equilibrium dissociation energies De for the diatomic molecules studied here. As is shown in Table II, the HF-SCF results for De are often qualitatively wrong; for CrO, FeH, CoH, ZnO, and ZnS, HF-SCF calculations predict the molecules to be unstable. While CCSD calculations are capable of recovering the bulk of electron correlation contributions, the inclusion of perturbative triples corrections is essential for numerical accuracy. For example, the perturbative triples correction in CCSD(T) nears 80 kJ/mol for the bond energies of both VO and CrO. In contrast, the high-level correlation (hlc) contributions, including the full triples corrections as well as the corrections due to quadruple excitations, are significantly smaller: they are typically of the order of a few to several kJ/mol. Further, for about half of the molecules studied here, the full triples correction and the quadruples correction tend to cancel, a behavior also characteristically found in studies of first-row compounds. For example, in VO, they amount to -5.6 and 4.7 kJ/mol, respectively, therefore ACS Paragon 9 Plus Environment


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amounting to only -0.9 kJ/mol in total. The largest hlc contribution occurs in the case of CoH, where the full triples contribution and the quadruple contribution have the same sign and take the values of 2.1 and 5.4 kJ/mol, respectively, yielding a total value of 7.5 kJ/mol. Interestingly, there appears to be no correlation between the magnitude of the perturbative triples corrections and that of the high-level correlation contributions. CrO has the largest perturbative triples contribution of 79.6 kJ/mol, but the corresponding high-level correlation correction amounts to only 1.2 kJ/mol. In the case of CoH with the largest highlevel correlation correction of 7.5 kJ/mol, the corresponding perturbative triples correction takes a moderate value of 27.5 kJ/mol. The steady decrease of the magnitude of CCSD, triples, and quadruples contributions clearly shows a rapid convergence of the coupled-cluster series in the present calculations. The CCSD contributions are typically 5-10 times greater than the triples contributions, which are in turn 3-20 times larger than the corresponding quadruples corrections. Therefore, the remaining electron correlation corrections due to even higher excitations (the difference between CCSDTQ and full configuration interaction) will further decrease and thus can be neglected in the present study. The rapid convergence of the CC series is also a clear indication that these molecules are “single-reference” systems. This aspect will be addressed in more detail below.

B.

Basis set effects

As has been observed in many calculations of thermochemical properties in the literature, basis set effects on the electron correlation contributions to the dissociation energies are pronounced. As shown in Tables III and IV, although calculations using augmented triplezeta basis sets (aVTZ) can provide HF-SCF contributions that compare reasonably well ACS Paragon10 Plus Environment

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with those extrapolated to the basis set limit, the same is definitely not true for the CCSD contributions. For example, aVTZ results and those extrapolated to the basis set limit often differ by more than 10 kJ/mol (as much as 20 kJ/mol for NiCl). Therefore, it is necessary to accurately account for basis set effects on the correlation contributions to obtain qualitatively correct results that allow for objective analysis of the merits of the methods employed.

While basis set effects for the triples contributions are less significant than those for the singles and doubles, the basis set error for the perturbative triples corrections obtained from aVTZ calculations can still amount to around 4 kJ/mol, e.g., in the case of CoCl as shown in Table IV. The basis set effects for the full triples corrections, demonstrated in Table VI, behave similarly to those of the perturbative triples contributions, although the magnitude of the effect is smaller. Therefore, it is necessary to perform a basis set extrapolation for both the perturbative and full triples corrections to obtain accurate results, similar to what is done in high-accuracy thermochemistry protocols. Due to the high computational cost of the CCSDT calculations, the practically feasible option adopted here for accounting for the full triples correction is to perform an extrapolation using cc-pVTZ and cc-pVQZ results, as suggested by the HEAT protocol.17

In contrast, basis set effects for quadruples corrections shown in Table VI are much less significant than those for the CCSD and triples contributions. The difference between the quadruples corrections calculated using cc-pVTZ and cc-pVDZ basis sets are in most cases less than 0.5 kJ/mol, with the largest difference being 1.7 kJ/mol in the case of CrO. Therefore, an estimation of quadruples corrections using cc-pVDZ basis sets appears to be adequate and can be recommended as a cost-effective option. This is also in line with previous findings based on calculations of molecules containing first-row elements.53 ACS Paragon11 Plus Environment


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C.

Core-valence correlation effects

The core-valence correlation contribution at the CCSD(T) level is formally defined as the difference between all-electron and frozen-core CCSD(T) results; both in the complete basis set limit. We thus use the difference between the all-electron CCSD(T)/aug-cc-pwCV∞Z result and the frozen-core CCSD(T)/aug-cc-pV∞Z result as ∆CV , which are summarized in the last column of Table VII and also shown in Table I. The core-valence correlation contributions to the bond energies span a range of a few tenths to more than 20 kJ/mol. For eight of the twenty molecules studied here, the core-valence correlation contributions are greater than 10 kJ/mol, with the largest value of 22.5 kJ/mol for the VO molecule. The inclusion of core-valence correlation contributions clearly improves the agreement between computed and experimental values, as illustrated in Figure 1. An efficient but approximate scheme for obtaining core-valence correlation contributions is to take the difference between all-electron and frozen-core results computed using a given basis set or a more approximate extrapolation scheme. In Table VI we present results obtaining using aCVXZ (X=T, Q, 5) basis sets and the extrapolation scheme using tripleand quadruple-zeta basis sets (“aCV∞Z(3,4)”) or quadruple- and quintuple-zeta basis sets (“aCV∞Z(4,5)”). It is shown that basis set effects on core-valence correlation contributions are also significant. It is necessary to go beyond triple-zeta basis sets to obtain reasonably accurate descriptions. The “aCV∞Z(3,4)” scheme shows errors less than 4 kJ/mol for all the molecules studied here, and might be a cost-effective option. We emphasize that the valence and core-valence correlation contributions are not strictly additive in practice, since the frozen-core results estimated in the basis set limit using aug-cc-pwCVXZ and aug-cc-pVXZ basis sets are different. In another word, the coupling ACS Paragon12 Plus Environment

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between valence correlation and the core-correlating basis functions is not negligible.19 This is represented as the difference between the last two columns in Table VII. As we can see, the largest discrepancy can amount to 3 kJ/mol in the case of VO. Therefore, for the present benchmark calculations, we do not assume that the valence and core-valence correlation contributions are additive. Instead, we make sure that the sum of valence and core-valence correlation contributions corresponds to the all-electron CCSD(T)/aug-cc-pwCV∞Z results.

D.

Corrections due to geometrical effects

The bond lengths of the molecules have been calculated at SFX2C-1e/CCSD(T) level with a variety of basis sets, and the results are summarized in Table VIII. While diffuse functions do not have significant effects on the calculated bond distances, the core-valence correlation contribution amounts to 0.02-0.04 ˚ A for six of the molecules studied here and thus has to be taken into account for accurate calculations. The agreement between the SFX2C-1e/CCSD(T)/aug-cc-pwCVQZ geometries and the geometries compiled in Ref. 26 varies in this test set. For twelve molecules in this test set, the differences between the two bond lengths are less than 0.02 ˚ A. However, the largest discrepancy appears for ZnO and is about 0.10 ˚ A. As the correction to the Zn-O bond length due to high-level correlation effects (estimated as the difference between CCSDTQ and CCSD(T) results) is only around 0.005 ˚ A, it appears that the SFX2C-1e/CCSD(T)/aug-cc-pwCVQZ value for the bond length is more reliable. The corresponding corrections to the dissociation energies (∆geo ) are computed as the difference between the SFX2C-1e/CCSD(T)/aCVQZ results calculated with CCSD(T)/aCVQZ geometries and those with the geometries given in Ref. 26. As is listed in Table II and VIII, the corrections due to the geometries are small for most of the molecules presented here. ACS Paragon13 Plus Environment


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However, the correction for the ZnO molecule amounts to 10.3 kJ/mol. The inclusion of this correction is critical for achieving good agreement between the computed and experimental values for the dissociation energy of ZnO. The corresponding corrections for FeH and ZnS amount to 3.8 and 2.0 kJ/mol, respectively, and are also not negligible.

E.

A remark on “multireference character” A number of diagnostics54–58 have been proposed in the literature to assess the multiref-

erence character of molecules. On the other hand, it has been shown in an extensive and thorough study27 that it is difficult to use a simple criterion for systems containing 3d transition metals. In this subsection we refrain from using simple criteria, and directly base our analysis of this issue on the information of the coupled-cluster wave functions. The information about the singles and doubles amplitudes in the CCSD wave functions is summarized in Table IX. max{|t1 |} and max{|t2 |} are the largest absolute values for singles and doubles amplitudes. The values of

P

t22,αβαβ are used to compare the contributions of

doubly excited determinants to CCSD wavefunctions, and the values of

P

t21,αα represent

the total contribution of single excitations in CCSD wavefunctions. Among the molecules presented here, ZnO is the only one that has a t2 amplitude larger than 0.1. In other words, one doubly excited determinant is substantially more important than other excited determinants in the CCSD wave function of ZnO, but is still much less important than the reference determinant. Therefore, ZnO might be termed as having a slight biradical character. This is consistent with the reasonably good performance of CCSD(T) for this molecule as well as the non-negligible contribution from quadruple excitations to the dissociation energy (5.2 kJ/mol). Meanwhile, large t1 amplitudes are ubiquitous in these transition-metal compounds; 12 ACS Paragon14 Plus Environment

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of them have t1 amplitudes greater than 0.1 and a t1 amplitude of 0.40 is found in CrH. However, as single excitations take care of orbital-relaxation effects, large singles amplitudes do not necessarily imply a multireference character. To understand this further, Brueckner CCD (BCCD)59,60 calculations have been carried out. It is shown in Table VIII that the BCCD results are of similar quality to CCSD, and the reference determinants composed of Brueckner orbitals have similar t2 amplitudes to the CCSD calculation. This indicates that the large singles amplitudes in CCSD result from significant orbital-relaxation effects, whereas the wave function is dominated by a single determinant if one uses Brueckner orbitals to construct the reference determinant. This is consistent with the rapid convergence of the coupled-cluster series as well as the good performance of CCSD(T); the contributions diminish rapidly when one goes to higher excitations.

IV.

COMPARISON WITH THE EXPERIMENTAL RESULTS AS WELL

AS PREVIOUS COUPLED-CLUSTER CALCULATIONS

As is illustrated in Figure 1, for the subset of 16 molecules with four hydrides VH, CrH, FeH, and CoH excluded, the frozen-core CCSD(T)/aug-cc-pV∞Z results compare reasonably well with the experimental values. Further inclusion of core-valence correlation effects as well as high-level correlation effects (those beyond CCSD(T)) systematically improves the agreement between computed and experimental values. The root mean square deviation between the best computed results and the experimental values is below 8 kJ/mol, while the largest absolute deviation is 15.0 kJ/mol. This agreement is reasonable. If one assumes that both the experimental and computed results have uncertainties of roughly 8 kJ/mol, the experimental and computed results overlap for all these sixteen molecules. However, for VH, CrH, FeH, and CoH, the best computed values are higher than the ACS Paragon15 Plus Environment


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experimental values by more than 20 kJ/mol (Table I). The maximum absolute deviation (41.4 kJ/mol) occurs in the case of CoH. Further, the agreement between computed and experimental results for these four molecules becomes worse when more rigorous treatments are adopted, as can be seen from Tables II and X. For this reason, the statistical analysis including all twenty molecules (Table X) does not show systematic improvements when the theoretical treatment gets more complete. It should be noted that the high-level correlation contributions amount to 0.8, 3.6, 1.7, and 7.5 kJ/mol for VH, CrH, FeH, and CoH, respectively. Therefore, it is unlikely that the remaining correlation contributions are as large as 20 kJ/mol. In the next section, we present a revisitation of the experimental values for VH and CrH, as a first step towards understanding the remaining discrepancies. We note that our CCSD(T)/aVTZ results are similar to those reported by Truhlar and coworkers,26 indicating that the SFX2C-1e scheme provides a treatment of scalar-relativistic effects of similar quality to the DKH2 method adopted there. The major difference between the present results and those reported by Truhlar and coworkers thus originates from the basis set effects beyond triple-zeta basis sets. Our calculations at the CCSD(T)/awCV∞Z level compare favorably with recent results of Fang et al.61 It should also be mentioned that our results for the FeH molecule agree well with those of DeYonker and Allen,62 and our results of CuH and VO are consistent with those of Bross et al.63

V.

REVISITATION OF THE EXPERIMENTAL VALUES FOR THE BOND

DISSOCIATION ENERGIES OF VH AND CRH

The experimental measurement of the bond dissociation energies for VH and CrH by Armentrout and coworkers31 utilizes the hydrogen abstraction reactions of (mono-, di-, and ACS Paragon16 Plus Environment

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tri-) methyl amines M+ + Cn H2n+3 N → MH + Cn H2n+2 N+ , M = Cr, V and n = 1, 2, 3.

(1)

The threshold energies Ethr measured for the reactions involving di- and tri-methyl amines were combined with the corresponding heterolytic C-H bond dissociation energies in Cn H2n+3 N, the ionization energies of the metal atoms, as well as the electron affinity of the hydrogen atom to determine the dissociation energies of the metal hydrides D0 (M-H) = −Ethr − IE(M) − EA(H) + D(Cn H2n+2 N+ -H− ).

(2)

While the ionization energies of Cr and V as well as the electron affinity for the hydrogen atom have been accurately known for many years, the accurate determination of bond dissociation energies, or of thermochemical parameters in general, for organic molecules has been a challenging task. A recent landmark in this field is the development of the Active Thermochemical Tables (ATcT) approach,32 which is based on a thermochemical network linking the species included in the network. By requiring self consistency within the thermochemical network, the errors for the heats of formation for the compounds included in the network are greatly reduced. The derivation of the dissociation energies of VH and CrH reported in Ref. 33 in 1996 took the values of 9.34 eV, 8.81 eV, and 8.51 eV for the heterolytic C-H dissociation energies of (mono-, di-, and tri-) methyl amines, respectively,64 which deviate substantially from the most current ATcT results that are based on a slightly expanded ver. 1.112d of the ATcT Thermochemical Network (TN)65,66 (9.471 ± 0.007 eV at 0 K, 9.520 eV at 298 K; 9.002 ± 0.010 eV at 0K, 9.053 eV at 298 K; 8.685 ± 0.011 eV at 0 K, 8.745 eV at 298 K). As the C-H bond dissociation energies for di- and tri-methyl amines in ATcT are greater than the previously adopted values by 0.192 eV (18.5 kJ/mol) and 0.175 eV (16.9 kJ/mol), the bond dissociation energies in VH and CrH were both underestimated ACS Paragon17 Plus Environment


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by 17.7 kJ/mol in the previous derivation of experimental values. Thus, combining the threshold measurements of Ref. 33 with the updated ATcT thermochemistry for the di- and tri-methyl amine shifts the 0 K bond dissociation energies D0 to 223.2 ± 6.7 kJ/mol for VH and 203.9 ± 6.7 kJ/mol for CrH. The corresponding “experimental” De values in Table II are then 232.8 kJ/mol and 213.5 kJ/mol for VH and CrH, respectively. The differences between computed and experimental values are consequently reduced to 9.4 kJ/mol for VH and 4.3 kJ/mol for CrH, and thus are in line with those for the other molecules in the 3dMLBE20 database. When the revised experimental values of VH and CrH are used in the statistical analysis, the standard deviation for the subset of 18 molecules in the 3dMLBE20 database (with CoH and FeH excluded) amounts to 8.5 kJ/mol and is consistent with that for the subset of 16 molecules with VH, CrH , CoH, and FeH excluded (8.8 kJ/mol). The ATcT values for the C-H bond dissociation energies of interest are supported by high-level ab initio calculations for the heats of formation of Cn H2n+3 N, Cn H2n+2 N+ (n=1, 2, 3), and H− . First we carried out calculations using the HEAT345-Q protocol for the smallest variants (CH3 NH2 and CH2 NH+ 2 ) and compared the results with those available in ATcT. As is shown in Table XI, the heat of formation obtained from HEAT calculations agree very well with and those in ATcT, with a deviation of -0.6 kJ/mol and 0.7 kJ/mol for CH4 N+ and CH5 N, respectively. This is consistent with the performance of the HEAT protocols demonstrated in many applications.67,68 The C-H bond dissociation energy derived using these computed heats of formation is 912.4 kJ/mol, in very good agreement with the ATcT value of 913.8 kJ/mol. Then we performed more approximate calculations using an approximate version of HEAT (mHEAT)52 for these molecules. As can be seen in Table XI, the more approximate mHEAT model provides a value of 914.4 kJ/mol for the CH dissociation energy, which is 2.0 kJ/mol larger than the HEAT value and 0.6 kJ/mol ACS Paragon18 Plus Environment

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greater than the ATcT value. Therefore, the approximate version of HEAT, which is feasible for calculations of the larger methyl amines, may not reach subchemical accuracy for the thermochemical parameters of interest, but is clearly sufficient for the present purpose, which is concerned with discrepancies on the order of 20 kJ/mol. The mHEAT model was then used to calculate thermochemistry for the di- and tri-methyl amines and the results are summarized in Table XII. The calculated C-H bond dissociation energies for di- and trimethyl amines (8.995 eV and 8.679 eV) agree well with those values in ATcT (9.002 ± 0.010 eV and 8.685 ± 0.011 eV), verifying the high accuracy of the ATcT values and supporting the rederivation of the experimental values for the dissociation energies of VH and CrH.

VI.

PRELIMINARY ANALYSIS FOR FEH AND COH

For FeH and CoH, the bond dissociation energies were measured by Armentrout and coworkers, again by utilizing hydrogen abstraction reactions but now from alkanes or acetaldehyde: M+ + RH → MH + R+

(3)

for M = Co, RH = ethane, propane, iso-butane, and cyclo-propane and M = Fe, RH = acetaldehyde, cyclopentane, n-butane, propane, and cyclopropane.

Thresholds measured

for these reactions were again combined with the heterolytic R-H bond dissociation energies, IE(M), and EA(H) to yield the metal hydride bond energies: D0 (M-H) = −Ethr − IE(M) − EA(H) + D(R+ -H− ).

(4)

Here updated ATcT values are available for the heterolytic bond energies at 298 K for ethane, propane (at the 2 position), cyclopropane, and acetaldehyde. These values (1132.1 ± 0.3, 1055.9 ± 0.3, 1184.8 ± 4.0, and 970.2 ± 0.6 kJ/mol at 298.15 K, all from the same ACS Paragon19 Plus Environment


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ver. 1.122d of the ATcT TN65,66 ) again differ in some cases from those available in the literature at the time of the guided ion beam studies (1132 ± 6, 1049 ± 2, 1161 ± 3, and 964 ± 2 kJ/mol). Thus, although the value for ethane is essentially unchanged, those for the other three molecules are lower by 7, 24, and 6 kJ/mol, respectively. These studies also utilized n-butane, isobutane, and cyclopentane, molecules for which no update of the thermochemical data is available. In the case of CoH, hydride abstraction reactions with ethane, propane, isobutane, and cyclopropane were studied. Using updated ATcT thermochemistry and correcting for thermal effects as suggested in Ref. 33, the D0 (Co-H) values obtained are 1.89 ± 0.06 eV from ethane, 1.86 ± 0.10 eV from propane, and 2.11 ± 0.11 eV from cyclopropane. Using extant thermochemistry, the value obtained from isobutane in Ref. 33 was 2.05 ± 0.20 eV. Given the changes found in the updated thermochemical data for propane and acetaldehyde, it seems plausible that the latter value could increase by about 6 kJ/mol, making it very similar to the value obtained from the updated cyclopropane data. The average of all values is 1.99 ± 0.14 eV (192 ± 13 kJ/mol), which is 12 kJ/mol higher than the value from Ref. 33, but still 29 kJ/mol below the value calculated here. Experimentally, the thresholds for these reactions could be shifted upward by competition with other reactions, an effect that was not explicitly included in these studies. Such competition means that the higher values for the CoH bond energies are probably the best experimental values. In this case, the updated cyclopropane result, which is consistent with an empirically adjusted isobutane result, suggests that D0 (CoH) = 204 ± 13 kJ/mol. When adjusted to De of 215 ± 13 kJ/mol, it now lies a substantial 17 kJ/mol below the theoretical value of 232 kJ/mol. In the case of FeH, the hydride donors utilized were acetaldehyde, cyclopentane, n-butane, propane, and cyclopropane, for which updated thermochemical data is not available for the ACS Paragon20 Plus Environment

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heterolytic bond energies of cyclopentane and n-butane. Using updated ATcT thermochemistry for the other three molecules leads to D0 (FeH) values of 1.65 ± 0.07, 1.50 ± 0.06, and 1.73 ± 0.07 eV for acetaldehyde, propane, and cyclopropane. The cyclopentane and n-butane reactions yield values of 1.34 ± 0.09 and 1.44 ± 0.08 eV, which are plausibly increased by 6 kJ/mol (0.06 eV) to account for anticipated updates in thermochemistry. The average of all five values is 1.56 ± 0.13 eV (150 ± 13 kJ/mol) or De (FeH) = 160 ± 13 kJ/mol, compared to the theoretical value of 192 kJ/mol. Accounting for competition, the values derived from the acetaldehyde and cyclopropane experiments provide a plausible experimental value of 1.69 ± 0.07 eV (163 ± 7 kJ/mol), or De = 173 ± 7 kJ/mol, again 19 kJ/mol below theory. To provide an independent assessment of such manipulations, we reexamine the CuH system as well, which was done in parallel with CoH for all four alkanes. Here the average of all four 0 K bond energies using updated ATcT thermochemistry is 2.61 ± 0.19 eV (252 ± 18 kJ/mol), identical to the 251 ± 6 kJ/mol value reported in Ref. 33. If only the cyclopropane result (which again provides the highest BDE measured) is utilized, D0 (CuH) = 2.87 ± 0.07 eV (277 ± 7 kJ/mol). Converting to De , these two values are 268 and 293 kJ/mol, compared to the theoretical value of 272 kJ/mol. Clearly in this case, the average experimental value provides the best agreement, and the plausible bond energy of 293 kJ/mol is 21 kJ/mol above theory. Although the use of the maximum experimental values for both CoH and FeH is somewhat speculative, these values are plausibly the most correct values obtained from these experiments. On the other hand, the case of CuH shows that such an interpretation may not be correct. Nevertheless, using these speculative values, the remaining discrepancy between theory and experiment for CoH and FeH of 19 kJ/mol is just outside of the experimental unACS Paragon21 Plus Environment


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certainty of about 10 kJ/mol, but comparable to the combined experimental and theoretical uncertainties. Overall, these comparisons suggest that further experimental explorations of these systems to confirm or deny the accuracy of the present calculations would be useful.

VII.

SUMMARY AND OUTLOOK

Systematic relativistic coupled-cluster calculations on diatomic molecules containing 3d transition metals in the 3dMLBE20 set are reported. It is shown that all the molecules in this database lack “multireference character” and coupled-cluster results are reliable provided that scalar-relativistic and basis set effects are adequately taken into account. The agreement between computational and experimental results are fair for a subset of sixteen molecules in the database (excluding VH, CrH, CoH, and FeH), with a standard deviation of 9 kJ/mol and a maximum deviation of 15 kJ/mol. For the remaining four molecules (VH, CrH, CoH, and FeH), the discrepancies between theory and experiment remain substantial. As a step towards understanding the remaining discrepancies, a reinvestigation of the experimental values for VH and CrH has been undertaken. By correcting values for the heterolytic C-H dissociation energies of mono-, di-, and tri-methyl amines, which serve as intermediate quantities in the derivation of experimental values for the dissociation energies of VH and CrH, the experimental values for the bond dissociation energies of VH and CrH are increased by 18 kJ/mol and the new values of equilibrium dissociation energies (233 kJ/mol for VH and 214 kJ/mol for CrH) agree well with computation (242 kJ/mol for VH and 218 kJ/mol for CrH). A preliminary revisitation for the experimental values of FeH and CoH is also presented, and it would seem worthwhile to revisit the experimental measurements of CoH and FeH, in order to elucidate the remaining discrepancies between theory and experiment. The coupledACS Paragon22 Plus Environment

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cluster results presented here can also serve as benchmarks for validating and testing density functionals for calculations of compounds containing 3d transition metals.

ACKNOWLEDGMENTS

This work has been supported by National Science Foundation under Grant No. CHE1361031 (L. C. and J. F. S.) , the Deutsche Forschungsgemeinschaft (DFG Grant GA 370/6-1 and 6-2) (J. G.), the U.S. Department of Energy, Office of Science, Office of Basic Energy Sciences, Division of Chemical Sciences, Geosciences and Biosciences under Contract DEAC02-06CH11357 (B. R.), and National Science Foundation under Grant No. CHE-1359769 (P. B. A.). L. C. is grateful to Kirk Peterson (Washington State University) and David Dixon (University of Alabama) for sharing their CCSD(T)/awCV∞Z results prior to publication.

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TABLE I. Bond dissociation energies De (in kJ/mol) obtained from all-electron CCSD(T) calculations. Scalar relativistic corrections (∆Rel ) are given as the difference between SFX2C-1e and non-relativistic results. aCVTZ

aCVQZ

Ref. 26

Nonrel SFX2C-1e

∆Rel

Nonrel SFX2C-1e

∆Rel

∆Rel

TiCl

401.6

394.9

-6.7

413.6

406.7

-6.8

-6.3

VH

240.9

233.1

-7.9

247.0

238.9

-8.1

-7.9

VO

621.0

617.9

-3.1

635.6

632.3

-3.3

-3.3

VCl

409.3

400.5

-8.8

421.7

412.7

-9.0

-8.8

CrH

204.8

211.1

6.3

207.3

213.4

6.1

6.3

CrO

416.9

433.1

16.1

425.5

441.4

16.0

15.9

CrCl

354.9

359.4

4.5

364.2

368.5

4.3

-7.5

MnS

267.6

260.3

-7.3

283.9

276.2

-7.6

-7.1

MnCl 337.9

331.0

-6.9

349.1

342.1

-7.0

-6.7

FeH

184.9

171.4

-13.5

194.1

180.3

-13.8

-13.4

FeCl

338.3

329.2

-9.1

350.0

340.7

-9.3

-9.2

CoH

227.3

208.3

-19.1

237.4

218.1

-19.3

-18.8

CoCl 343.4

315.4

-28.0

360.8

332.4

-28.4

-28.0

NiCl

390.8

355.5

-35.4

403.4

371.5

-35.4

-35.1

CuH

257.6

268.4

10.8

260.5

271.4

10.8

10.9

CuCl 355.6

355.1

-0.5

365.7

364.9

-0.7

-0.4

ZnH

93.9

88.3

-5.7

96.5

90.9

-5.7

-5.9

ZnO

139.0

127.8

-11.1

147.3

136.1

-11.2

-11.3

ZnS

130.9

121.9

-9.0

143.3

134.1

-9.1

-8.8

ZnCl

209.0

196.9

-12.1

219.5

207.2

-12.3

-12.1



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 49 50 51 52 53 54 55 56 57 58 59 60

Page 30 of 41

TABLE II. Contributions to the equilibrium bond dissociation energies De (in kJ/mol). VXZ and aVXZ represent cc-pVXZ and aug-cc-pVXZ basis sets, respectively. HF-SCF

CCSD

∆(T)

∆T

∆Q

∆CV

aV∞Z(3,4,5) aV∞Z(4,5) aV∞Z(4,5) V∞Z(3,4) VDZ see text

∆SO Ref.26

∆geo see text

De Cal.

Exp.

Cal.-Exp.

TiCl

342.6

55.6

12.0

1.7

1.4

4.5

-3.8

0.0

414.1

421.7(8.4)

-7.7

VH

177.0

51.6

0.4

0.9

-0.1

13.0

-1.7

1.1

242.2

215.1(6.7)

27.2

VO

156.4

385.6

76.9

-5.6

4.7

22.5

-4.6

0.0

636.0

631.8(8.4)

4.2

VCl

350.3

49.7

9.6

-1.0

0.4

10.8

-5.4

0.1

414.6

426.3(8.4)

-11.8

CrH

105.2

107.9

3.7

3.7

-0.1

-2.9

0.0

0.4

217.8

195.8(6.7)

22.0

CrO

-56.7

427.7

79.6

-2.0

3.2

-3.4

0.8

0.1

449.4

438.1(5.0)

11.3

CrCl

274.8

93.7

11.6

2.2

0.7

-7.4

-3.3

0.4

372.6

377.0(6.7)

-4.4

MnS

48.4

194.9

32.8

1.3

0.8

11.4

-2.5

0.0

287.2

295.0(8.4)

-7.8

MnCl

320.2

21.3

6.4

-0.9

0.4

1.0

-3.3

0.0

345.1

337.6(6.7)

7.5

FeH

-80.6

232.1

21.4

0.5

1.2

14.0

-0.4

3.8

191.9

154.4(3.3)

37.6

FeCl

313.2

25.8

6.9

-2.9

0.5

3.5

-3.8

0.0

343.4

328.4(6.7)

15.0

CoH

-57.9

238.5

27.5

2.1

5.4

16.5

-0.8

0.5

231.8

190.4(5.0)

41.4

CoCl

75.4

223.0

31.4

1.0

4.8

17.2

-4.2

0.1

348.6

336.8(6.7)

11.8

NiCl

103.1

234.7

33.1

-1.8

2.1

15.4

-8.8

0.3

378.0

368.2(4.2)

9.8

CuH

141.0

120.2

10.1

0.0

0.4

0.6

0.0

0.0

272.4

261.9(5.9)

10.5

CuCl

262.8

97.2

12.3

-0.5

0.7

0.0

-3.3

0.0

369.1

366.9(1.7)

2.2

ZnH

71.0

24.2

-3.2

1.2

0.0

1.0

0.0

0.0

94.2

90.4(2.1)

3.8

ZnO

-166.9

263.9

44.5

-0.6

5.2

0.3

-0.8

10.3

155.7

158.6(3.8)

-2.8

ZnS

-5.6

122.2

25.5

-1.3

2.2

-0.5

-2.5

2.0

141.9

143.5(4.2)

-1.6

ZnCl

193.6

16.6

4.3

0.0

0.6

-0.2

-3.3

0.6

212.3

223.8(4.2)

-11.6


Page 31 of 41

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 49 50 51 52 53 54 55 56 57 58 59 60


TABLE III. HF-SCF contributions to De (in kJ/mol) computed with correlation-consistent basis sets of various sizes as well as the corresponding extrapolated values. Molecule cc-pVTZ cc-pVQZ cc-pV5Z cc-pV∞Z (3,4,5) aug-cc-pVTZ aug-cc-pVQZ aug-cc-pV5Z aug-cc-pV∞Z (3,4,5) TiCl

341.2

341.7

342.2

342.5

341.9

341.9

342.3

342.6

VH

176.2

176.8

176.9

176.9

176.7

176.9

177.0

177.0

VO

154.1

155.6

156.0

156.1

155.3

156.0

156.3

156.4

VCl

348.1

349.3

349.9

350.2

349.4

349.6

350.0

350.3

CrH

103.5

104.7

105.0

105.0

104.2

104.9

105.1

105.2

CrO

-61.9

-57.9

-57.2

-57.1

-57.7

-57.2

-56.9

-56.7

CrCl

270.6

273.4

274.3

274.6

273.0

273.9

274.5

274.8

MnS

43.2

46.4

47.5

48.0

46.0

47.0

47.9

48.4

MnCl

316.8

319.1

319.7

320.0

319.4

319.6

320.0

320.2

FeH

-82.1

-80.9

-80.5

-80.4

-80.9

-80.7

-80.6

-80.6

FeCl

309.6

312.2

313.0

313.3

312.1

312.5

313.0

313.2

CoH

-59.8

-58.5

-58.2

-58.1

-58.3

-57.9

-57.9

-57.9

CoCl

70.8

73.5

74.6

75.1

73.8

74.5

75.0

75.4

NiCl

97.8

100.9

102.2

102.8

101.4

102.2

102.8

103.1

CuH

139.1

140.0

140.5

140.6

140.4

140.8

140.9

141.0

CuCl

258.4

260.6

261.7

262.3

261.1

261.7

262.4

262.8

ZnH

70.0

70.6

70.7

70.7

70.4

70.8

70.9

71.0

ZnO

-179.9

-171.3

-168.0

-166.3

-166.8

-166.8

-166.9

-166.9

ZnS

-12.3

-8.4

-6.8

-6.1

-8.2

-7.0

-6.1

-5.6

ZnCl

188.9

191.8

192.8

193.2

191.9

192.6

193.3

193.6



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 49 50 51 52 53 54 55 56 57 58 59 60

Page 32 of 41

TABLE IV. The CCSD contributions to De (in kJ/mol) computed with correlation-consistent basis sets of various sizes as well as the corresponding extrapolated values. Molecule cc-pVTZ cc-pVQZ cc-pV5Z cc-pV∞Z (4,5) aug-cc-pVTZ aug-cc-pVQZ aug-cc-pV5Z aug-cc-pV∞Z (4,5) TiCl

36.7

47.4

51.7

56.3

41.2

50.0

52.7

55.6

VH

45.8

49.4

50.5

51.8

48.0

50.2

50.9

51.6

VO

366.2

376.0

380.8

385.8

369.8

378.9

382.2

385.6

VCl

29.5

40.9

45.6

50.5

35.6

44.1

46.9

49.7

CrH

104.1

106.2

107.1

108.0

106.0

107.0

107.5

107.9

CrO

410.6

418.3

423.0

428.0

414.9

422.0

424.8

427.7

CrCl

75.5

85.4

89.7

94.3

81.3

88.8

91.2

93.7

MnS

169.0

183.0

189.2

195.7

176.1

187.5

191.1

194.9

MnCl

2.4

12.9

17.2

21.6

7.4

16.1

18.7

21.3

FeH

223.4

228.1

230.1

232.2

226.0

229.6

230.8

232.1

FeCl

6.4

16.9

21.2

25.8

11.4

20.4

23.1

25.8

CoH

226.5

233.5

236.3

239.3

230.3

235.4

236.9

238.5

CoCl

195.0

210.1

216.8

223.9

202.8

215.0

218.9

223.0

NiCl

205.9

221.7

228.5

235.6

214.2

226.8

230.6

234.7

CuH

122.0

121.4

120.9

120.3

119.1

120.1

120.2

120.2

CuCl

83.6

90.4

93.5

96.8

83.5

91.6

94.3

97.2

ZnH

23.5

24.3

24.3

24.3

22.2

23.9

24.1

24.2

ZnO

250.5

256.9

260.0

263.2

253.9

260.1

262.0

263.9

ZnS

104.0

113.6

117.2

121.0

106.2

115.6

118.8

122.2

ZnCl

0.0

8.8

12.2

15.9

2.1

10.7

13.6

16.6


Page 33 of 41

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 49 50 51 52 53 54 55 56 57 58 59 60


TABLE V. The perturbative triples corrections to De (in kJ/mol) computed with correlationconsistent basis sets of various sizes as well as the corresponding extrapolated values. Molecule cc-pVTZ cc-pVQZ cc-pV5Z cc-pV∞Z (4,5) aug-cc-pVTZ aug-cc-pVQZ aug-cc-pV5Z aug-cc-pV∞Z (4,5) TiCl

9.9

10.9

11.5

12.1

10.8

11.3

11.7

12.0

VH

0.4

0.4

0.4

0.4

0.4

-0.4

0.4

0.4

VO

76.4

78.2

78.9

79.7

76.5

78.3

77.6

76.9

VCl

7.4

8.5

9.0

9.6

8.4

8.9

9.2

9.6

CrH

3.4

3.5

3.6

3.7

3.7

3.7

3.7

3.7

CrO

75.5

77.6

78.6

79.6

75.6

77.8

78.7

79.6

CrCl

9.2

10.4

10.9

11.5

10.4

10.9

11.2

11.6

MnS

28.5

30.6

31.6

32.7

29.8

31.3

32.0

32.8

MnCl

4.6

5.4

5.7

6.2

5.2

5.7

6.0

6.4

FeH

15.6

19.0

20.3

21.6

17.6

19.8

20.6

21.4

FeCl

5.3

6.0

6.3

6.7

5.7

6.3

6.6

6.9

CoH

23.3

25.8

26.7

27.7

25.3

26.7

27.1

27.5

CoCl

24.6

28.3

29.8

31.4

27.4

29.6

30.5

31.4

NiCl

25.8

29.8

31.4

33.1

29.1

31.2

32.1

33.1

CuH

10.5

10.6

10.4

10.3

9.8

9.9

10.0

10.1

CuCl

10.7

11.8

12.0

12.2

10.6

11.2

11.7

12.3

ZnH

-1.5

-2.2

-2.8

-3.4

-2.7

-3.0

-3.1

-3.2

ZnO

40.6

42.6

43.4

44.3

41.9

43.3

43.9

44.5

ZnS

22.7

24.3

24.7

25.0

23.4

24.3

24.9

25.5

ZnCl

3.6

4.1

4.0

3.9

3.4

3.6

4.0

4.3



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 49 50 51 52 53 54 55 56 57 58 59 60

Page 34 of 41

TABLE VI. Full triples and quadruples corrections to De (kJ/mol). ∆T

∆Q

Molecule cc-pVDZ cc-pVTZ cc-pVQZ cc-pV∞Z (3,4)

a

cc-pVDZ cc-pVTZ

TiCl

3.4

2.2

1.9

1.7

1.4

/

VH

0.4

0.6

0.8

0.9

-0.1

-0.1

VO

-1.3

-4.1

-5.0

-5.6

4.7

5.2

VCl

-0.3

-0.9

-1.0

-1.0

0.4

/

CrH

0.8

3.8

3.7

3.7

-0.1

0.4

CrO

3.9

0.1

-1.1

-2.0

3.2

4.9

CrCl

2.7

2.6

2.3

2.2

0.7

/

MnS

3.5

2.0

1.6

1.3

0.8

/

MnCl

-0.3

-0.8

-0.8

-0.9

0.4

/

FeH

8.4

3.3

1.7

0.5

1.2

1.0

FeCl

0.1

-3.0

-2.9

-2.9

0.5

/

CoH

9.0

4.8

3.2

2.1

5.4

5.8

CoCl

9.1

4.3

2.4

1.0

4.8

/

NiCl

4.0

0.4

-0.9

-1.8

2.1

/

CuH

0.9

0.3

0.1

0.0

0.4

0.4

CuCl

0.9

0.0

-0.3

-0.5

0.7

/

ZnH

0.7

0.8

1.0

1.2

0.0

-0.1

ZnO

2.9

0.5

-0.2

-0.6

5.2

/

ZnS

0.9

-0.7

-1.1

-1.3

2.2

/

ZnCl

0.5

0.0

0.0

0.0

0.6

/

a

Due to limited resources, CCSDTQ/cc-pVTZ Calculations have only been

carried out for hydrides as well as VO and CrO.


Page 35 of 41

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 49 50 51 52 53 54 55 56 57 58 59 60


TABLE VII. Core-correlation contributions to De (kJ/mol). “ACXZ” represents the difference between all-electron (ae) CCSD(T)/aug-cc-pwCVXZ and frozen-core (fc) CCSD(T)/aug-cc-pwCVXZ results. The last column of the table gives the difference between ae-CCSD(T)/aug-cc-pwCV∞Z and fc-CCSD(T)/aug-cc-pV∞Z results. Molecule ACTZ ACQZ AC5Z AC∞Z(3,4) AC∞Z(4,5) AC∞Z(4,5)-A∞Z(4,5) TiCl

0.0

2.8

3.6

4.9

4.5

4.5

VH

7.6

11.1

12.1

13.8

13.2

13.0

VO

12.8

17.6

18.5

21.1

19.5

22.5

VCl

5.8

9.2

9.9

11.6

10.6

10.8

CrH

-2.5

-2.3

-2.8

-2.1

-3.3

-2.9

CrO

-1.4

-2.3

-3.4

-2.9

-4.5

-3.4

CrCl

-5.7

-5.8

-6.9

-5.8

-8.0

-7.4

MnS

5.7

8.6

9.6

10.6

10.6

11.4

MnCl

-1.7

0.2

0.6

1.5

1.1

1.0

FeH

6.1

10.6

11.9

13.8

13.3

14.0

FeCl

-0.9

1.3

2.3

2.9

3.3

3.5

CoH

8.8

12.8

14.3

15.8

15.9

16.5

CoCl

7.4

11.2

13.9

13.9

16.7

17.2

NiCl

7.2

10.6

12.8

13.0

15.1

15.4

CuH

-0.7

0.7

0.6

1.8

0.5

0.6

CuCl

-1.4

-0.4

-0.1

0.4

0.1

0.0

ZnH

-1.4

-0.6

0.2

0.0

1.0

1.0

ZnO

-1.3

-0.4

-0.1

0.2

0.2

0.3

ZnS

-0.5

0.4

0.5

1.0

0.5

-0.5

ZnCl

-1.2

-0.3

-0.2

0.4

0.0

-0.2



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 49 50 51 52 53 54 55 56 57 58 59 60

Page 36 of 41

TABLE VIII. Equilibrium bond lengths Re (in ˚ A) computed at the SFX2C-1e-CCSD(T) level with a variety of correlation-consistent basis sets. Molecule cc-pVTZ cc-pVQZ aug-cc-pVTZ aug-cc-pVQZ aug-cc-pwCVTZ aug-cc-pwCVQZ Ref.26 TiCl

2.306

2.306

2.313

2.309

2.273

2.266

2.265

VH

1.710

1.708

1.713

1.709

1.688

1.682

1.730

VO

1.596

1.595

1.600

1.597

1.590

1.586

1.589

VCl

2.256

2.255

2.259

2.257

2.235

2.229

2.215

CrH

1.650

1.649

1.653

1.651

1.631

1.628

1.656

CrO

1.620

1.620

1.625

1.622

1.618

1.613

1.621

CrCl

2.200

2.198

2.201

2.198

2.174

2.169

2.194

MnS

2.096

2.089

2.096

2.089

2.075

2.067

2.070

MnCl

2.253

2.251

2.256

2.252

2.243

2.236

2.243

FeH

1.556

1.558

1.559

1.559

1.548

1.547

1.630

FeCl

2.193

2.189

2.194

2.189

2.183

2.176

2.179

CoH

1.502

1.504

1.507

1.507

1.504

1.502

1.530

CoCl

2.087

2.083

2.087

2.081

2.080

2.075

2.087

NiCl

2.068

2.062

2.066

2.059

2.061

2.053

2.073

CuH

1.452

1.455

1.459

1.458

1.460

1.455

1.463

CuCl

2.060

2.056

2.062

2.054

2.058

2.051

2.050

ZnH

1.580

1.583

1.589

1.587

1.591

1.587

1.590

ZnO

1.698

1.699

1.707

1.702

1.706

1.700

1.800

ZnS

2.057

2.051

2.059

2.050

2.055

2.048

2.100

ZnCl

2.134

2.137

2.140

2.133

2.138

2.131

2.100


Page 37 of 41

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 49 50 51 52 53 54 55 56 57 58 59 60


TABLE IX. The electronic energies (Hartree) as well as information about the singles and doubles amplitudes obtained from CCSD and Brueckner CCD (BCCD) calculations using aug-cc-pCVTZ basis sets. max{|t1 |} and max{|t1 |} are the largest absolute values for singles and doubles amplitudes. The values of

P

t21,αα (

P

t22,αβαβ ) represent the norm of singly (doubly) excited determinants

of the given spin combination to the total wavefunctions. CCSD P

BCCD

t21,αα max{|t2 |}

Molecule

energy

max{|t1 |}

TiCl

-1314.8951

0.12

0.25

0.02

VH

-949.3741

0.21

0.43

VO

-1024.0732

0.11

VCl

-1410.3538

CrH

P

t22,αβαβ

P

t22,αβαβ

energy

max{|t2 |}

0.36

-1314.8940

0.02

0.36

0.03

0.28

-949.3726

0.03

0.27

0.31

0.04

0.36

-1024.0662

0.03

0.35

0.19

0.36

0.02

0.36

-1410.3523

0.02

0.35

-1050.9467

0.40

0.71

0.03

0.28

-1050.9457

0.03

0.26

CrO

-1125.5850

0.22

0.38

0.05

0.37

-1125.5798

0.05

0.35

CrCl

-1511.9206

0.47

0.78

0.02

0.36

-1511.9194

0.02

0.35

MnS

-1557.2943

0.23

0.30

0.05

0.40

-1557.2900

0.04

0.39

MnCl

-1619.6873

0.04

0.09

0.02

0.34

-1619.6863

0.02

0.34

FeH

-1272.7503

0.36

0.60

0.02

0.34

-1272.7515

0.03

0.31

FeCl

-1733.7353

0.05

0.12

0.02

0.36

-1733.7337

0.02

0.35

CoH

-1393.3763

0.16

0.31

0.03

0.32

-1393.3732

0.02

0.31

CoCl

-1854.3355

0.22

0.34

0.02

0.39

-1854.3272

0.02

0.38

NiCl

-1981.6562

0.13

0.24

0.02

0.38

-1981.6518

0.02

0.38

CuH

-1654.9146

0.08

0.15

0.02

0.31

-1654.9101

0.02

0.30

CuCl

-2115.8665

0.08

0.14

0.02

0.38

-2115.8622

0.02

0.37

ZnH

-1796.0028

0.08

0.14

0.03

0.29

-1796.0005

0.03

0.29

ZnO

-1870.5845

0.06

0.14

0.15

0.42

-1870.5783

0.14

0.40

ZnS

-2194.5690

0.06

0.11

0.10

0.41

-2194.5659

0.10

0.41

ZnCl

-2256.9607

0.06

0.10

0.02

0.36

-2256.9584

0.02

0.36



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 49 50 51 52 53 54 55 56 57 58 59 60

Page 38 of 41

TABLE X. Deviation of computed De (in kJ/mol) from experimental values. Spin-orbit contributions (∆SO ) and geometrical corrections (∆geo ) have been included. The high-level correlation contributions ∆hlc is the sum of ∆(T) and ∆Q given in Table I. Molecule

fc-CCSD(T)

+∆CV +∆hlc

Molecule

aug-cc-pVTZ aug-cc-pVQZ aug-cc-pV5Z aug-cc-pV∞Z

TiCl

-31.7

-22.3

-18.8

-15.3

-10.8

-7.7

VH

9.4

11.1

12.7

13.4

26.4

27.2

VO

-34.7

-23.2

-20.3

-17.4

5.0

4.2

VCl

-38.2

-29.0

-25.5

-22.0

-11.2 -11.8

CrH

18.5

20.3

20.9

21.4

18.5

22.0

CrO

-4.3

5.4

9.4

13.5

10.1

11.3

CrCl

-15.2

-6.3

-3.0

0.1

-7.2

-4.4

MnS

-45.6

-31.7

-26.4

-21.4

-9.9

-7.8

MnCl

-9.0

0.5

3.7

6.9

8.0

7.5

FeH

11.7

17.8

19.8

21.8

35.9

36.8

FeCl

-3.0

7.0

10.4

13.8

17.3

15.0

CoH

6.5

13.4

15.4

17.4

33.9

41.4

CoCl

-36.9

-21.8

-16.5

-11.1

6.1

11.8

NiCl

-31.9

-16.4

-11.1

-5.8

9.5

9.8

CuH

7.5

9.0

9.3

9.5

10.1

10.5

CuCl

-15.1

-5.7

-1.8

2.0

2.0

2.2

ZnH

-0.4

1.3

1.5

1.6

2.6

3.8

ZnO

-20.1

-12.6

-10.2

-7.6

-7.3

-2.8

ZnS

-22.6

-11.1

-6.4

-1.9

-2.5

-1.6

ZnCl

-29.2

-19.6

-15.7

-12.0

-12.2 -11.6

Maximum deviation

-45.6

-31.7

-26.4

-22.0

35.9

41.4

Mean deviation

-14.2

-5.7

-2.6

0.3

6.2

7.7

Mean unsigned deviation

16.4

12.6

11.8

11.2

12.3

12.5

Standard deviation

19.3

16.1

15.0

14.1

14.6

15.0

Maximum deviation (16)a

-45.6

-31.7

-26.4

-22.0

17.3

15.0

Mean deviation (16)a

-20.6

-11.0

-7.6

-4.2

0.6

1.7

Mean unsigned deviation (16)a

17.6

11.9

10.5

9.4

8.2

7.7

Standard deviation (16)a

19.0

14.3

13.0

12.0

9.4

8.8

a The

results obtained with VH, CrH, FeH, and CoH excluded from the analysis.


Page 39 of 41

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 49 50 51 52 53 54 55 56 57 58 59 60


TABLE XI. Heats of formation (at 0 K, in kJ/mol) for CH4 N+ , H− , and CH5 N, as well as the bond dissociation energies (BDEs) derived from them. CH4 N+ ATcT

H−

CH5 N

BDE

BDE (eV)

763.5 ± 0.7 143.3 ± 0.0 -7.0 ± 0.3 913.8 ± 0.7 9.471 ± 0.007

HEAT345-Q

762.9

143.3

-6.3

912.4

9.457

mHEAT(CV34)

762.3

143.3

-8.8

914.4

9.477



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 49 50 51 52 53 54 55 56 57 58 59 60

TABLE XII. Heats of formation (at 0 K, in kJ/mol) computed using the mHEAT model, as well as the bond dissociation energies (BDEs) derived from them. Cn H2n+2 N+ H− Cn H2n+3 N BDE BDE (eV) ATcT (eV) n=1

762.3

143.3

-8.8

914.4

9.477

9.471 ± 0.007

n=2

727.2

143.3

2.6

867.9

8.995

9.002 ± 0.010

n=3

693.9

143.3

-0.2

837.4

8.679

8.685 ± 0.011


Page 40 of 41

Page 41 of 41


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 49 50 51 52 53 54 55 56 57 58 59 60 ACS Paragon Plus Environment

Bond Dissociation Energies for Diatomic Molecules Containing 3d

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