Pseudopotential-Based Correlation Consistent Composite Approach

Article pubs.acs.org/JPCA

Pseudopotential-Based Correlation Consistent Composite Approach (rp-ccCA) for First- and Second-Row Transition Metal Thermochemistry Sivabalan Manivasagam, Marie L. Laury, and Angela K. Wilson* Department of Chemistry and Center for Advanced Scientific Computing and Modeling, University of North Texas, Denton, Texas 76203-5017, United States S Supporting Information *

ABSTRACT: The relativistic-pseudopotential correlation consistent composite approach (rp-ccCA) was used to determine the enthalpy of formation (ΔHf) of 24 first row (3d) transition metal compounds. The rp-ccCA-derived ΔHf’s were compared to ΔHf’s previously obtained with an all-electron composite method for transition metals (ccCA-TM). For the 3d metal systems, rp-ccCA achieves transition metal accuracy, within 3 kcal/mol of reliable experimental data, overall. By utilizing pseudopotentials within the rp-ccCA methodology, we observed a significant computational time savings (53%) in comparison to the all-electron basis sets employed within ccCA-TM. With the proven reliability and accuracy of rp-ccCA, the methodology was employed to construct a calibration set of 210 second-row (4d) transition metal compounds and their ΔHf’s. The 4d calibration set is referred to as 4dHf-210. Within the 4dHf-210 set, there were 61 molecules with available experimental data. The average experimental uncertainty was 4.05 kcal/mol and the mean absolute deviation of rp-ccCA was 3.64 kcal/mol, excluding outliers (10 total). This study provides a large set of energetics that can be used to gauge existing and future computational methodologies and to aid experimentalists in reaction design.

■

and some transition metal compounds.14 Unfortunately, such calculations are often not computationally feasible for practical calculations of 4d transition metal (TM) systems, due to the high number of electrons associated with the metal centers and accompanying ligands.15 Density functional theory (DFT) provides a less computationally intensive means for determining thermodynamic data of second-row transition metals; however, functional choice can become challenging, as no single functional has been identified that works effectively for a range of metals, ligand type, and property, and the errors can become quite large for transition metal thermochemistry.16−20 Most functionals are not parametrized for transition metals due, in part, to the lack of large benchmark sets that include transition metal compounds.21−23 There have been a number of transition metal data sets that have helped in the analysis of density functional methods for properties including geometries, bond dissociation energies, ionization potentials, and enthalpies of formation. To highlight several examples, Furche and Perdew composed a set of 3d metal systems (M−X, X = M, H, O, N, F, CO) and examined reaction energies.24 For 3d, 4d, and 5d metals, test sets for equilibrium bond lengths have been generated by Bühl and co-

INTRODUCTION The second-row (4d) transition metals are of significant interest in the scientific community due to their range of oxidation and spin states, coordination sites, and ability to bond to various ligands, which makes them suitable candidates for catalyst design in areas including biomedicine and the petrochemical industry.1−5 Novel uses for 4d catalysts are continually developed, such as in organic synthesis with palladium-catalyzed alkyne reactions,6 water oxidation with ruthenium-based catalysts,7,8 and molybdenum biological catalysis.9 The application of newly developed 4d compounds relies largely on their thermodynamic properties; however, experimental data, such as enthalpies of formation (ΔHf’s) are scarce for 4d compounds, and often existing experimental data have large uncertainties (e.g., 20 kcal/mol for ZrI and 10 kcal/ mol for CdBr) due to factors including the reactivity of the 4d metals with oxygen, the formation of multiple oxides, and the incomplete combustion of 4d systems.10−13 Computational chemistry provides an alternative approach to experiment for determining thermodynamic data, where the theoretical results can supplement and help guide experimental work. Ab initio-based methods such as coupled cluster with singles, doubles, and perturbative triples [CCSD(T)] paired with a correlation consistent basis set of at least quadruple-ζ or quintuple-ζ quality have been shown to be useful in the determination of reliable thermochemical data for main group © 2015 American Chemical Society

Received: March 12, 2015 Revised: May 19, 2015 Published: May 22, 2015 6867

DOI: 10.1021/acs.jpca.5b02433 J. Phys. Chem. A 2015, 119, 6867−6874

Article

The Journal of Physical Chemistry A workers,25−27 as well as by Truhlar and co-workers for 3d transition metals.28,29 Riley and Merz examined functional performance for a set of 94 enthalpies of formation and 58 ionization potentials for first row transition metals.30 More recent sets in publication by Truhlar include 3d and 4d atoms and their ionization potentials and excitation energies and a set of 3d metal−ligand bond energies (3dMLBE70),17,31,32 which is a subset of our ccCA-TM/11 set (all of the enthalpies of formation with experimental uncertainties of 2.0 kcal/mol), and should be referred to using our notation, ccCA-TM/11-2, where the “2” represents energies with experimental uncertainties of 2.0 kcal/mol or less.66 Ab initio composite methods provide an alternative computational approach by combining lower level methods with large basis sets and high-level methods with small basis sets. The design of composite methods aims for the determination of accurate energetic properties with a reduced computational cost in comparison to a high level of theory with a large basis set (e.g., an all-electron CCSD(T)-DK calculation with an aug-ccpV5Z-DK basis set). Various composite methods have been developed, such as the popular Gaussian-n methods,33−37 Weizmann-n methods,38,39 HEAT methods,40−42 the Feller− Dixon−Peterson method,43−45 the multicoefficient correlation method (MCCM),46,47 and the correlation consistent composite approach (ccCA).14,48−55 Relativistic effective core potentials (ECP) provide a means to significantly reduce the cost for many-electron systems, while accounting for relativistic effects that are particularly important for heavy elements. ECPs are associated with a reduced computational cost because they decrease the number of electrons and basis functions in a calculation by replacing the core electrons and functions with an effective potential. A key component in the construction of an ECP is the core size. Small core pseudopotentials account for all core electrons except for the last noble-gas inner shell and valence electrons, whereas large core pseudopotentials account for all core electrons except the valence shell. Small core pseudopotentials are more accurate by allowing valence interactions with the outermost noble gas shell.56 Small core ECPs and their corresponding correlation consistent valence basis sets (ccpVnZ-PP) have been developed for the second-row transition metal elements (Y−Cd).57 These basis sets have provided opportunities for understanding thermochemistry for larger 4d systems that would be intractable with an all-electron set.58−62 When ECPs were examined for 3d and 4d metals, the energy separation between the core electrons included in the ECP and the valence electrons is greater for the 4d elements than for the 3d metals; therefore, the 3d core electrons have larger contributions to the overall energies than the 4d core electrons. Recently, the relativistic pseudopotential correlation consistent composite approach (rp-ccCA), combining the composite approach technique along with ECPs, was developed and the method has proven to be useful for 4d and lower pblock systems.63,64 In the initial rp-ccCA study, Laury and coworkers obtained accurate ΔHf’s (within 1.0 kcal/mol from reliable, well-established experiment for main group) for 25 4pcontaining molecules and observed a computational time savings of over 30% in comparison to all-electron composite methods.64 Laury and co-workers then applied rp-ccCA to a set of 30 4d transition metal compounds, achieving a mean absolute deviation (MAD) of 2.89 kcal/mol from experimental ΔHf’s. This initial 4p and 4d study demonstrated that rp-ccCA provides a significant computational savings through the use of

pseudopotentials for main group compounds and, overall, can achieve transition metal chemical accuracy (within 3 kcal/mol of reliable experiment) for 4d compounds. In this work, rp-ccCA was applied to a set of 24 3d (Cu and Zn) transition metal compounds (referred to as 3dHf-24) to compare accuracy and computational costs. Because rp-ccCA was developed for 4d systems, it was of interest to examine if the accuracy of the methodology was maintained for 3d molecules and to determine its time savings for transition metal species. rp-ccCA was then applied to a large molecule set of 210 4d transition metal compounds (referred to as 4dHf-210). The demonstrated performance of rp-ccCA for second-row transition metals supports the utilization of rp-ccCA for the determination of additional enthalpies of formation of secondrow transition metals. These newly determined enthalpies (ΔHf’s) are provided as a large 4d calibration set to aid in gauging current and future computational methodologies, such as density functionals, and to provide a better thermochemical understanding of second-row transition metals.

■

THEORETICAL METHODS The relativistic-pseudopotential correlation consistent composite approach (rp-ccCA) is one of the variants in the ccCA family developed by the Wilson group. The formulation for the rp-ccCA energy is E(ccCA) = Eref (CBS) + ΔEcc + ΔEcv + ΔESO + ΔEZPE (1)

where Eref(CBS) represents the MP2/aug-cc-pVnZ (n = D, T, Q) energies [aug-cc-pV(n+d)Z65 was used for second-row (chlorine) species] extrapolated to the complete basis set limit (CBS), ΔEcc represents the higher-order electron correlation calculated with CCSD(T), ΔEcv represents the core−valence electron correlation term, ΔESO represents the spin−orbit interaction term, and ΔEZPE represents the scaled zero-point energy term. A detailed explanation of the rp-ccCA methodology is given in the original rp-ccCA paper by Laury et al.64 As recommended in earlier rp-ccCA work, a spin-restricted Hartree−Fock (ROHF) reference was implemented.64,66 The MOLPRO67 software package was utilized for the rp-ccCA calculations. The rp-ccCA energy from eq 1 is utilized to determine the enthalpy of formation at 298 K via ° (298K) − HM ° (0K)] ΔHf°(M,298K) = ΔHf°(M,0K) + [HM −

∑

a(Ha°(298K) − Ha°(0K))

atoms

(2)

where the first term represents the molecular enthalpy of formation at 0 K, the second term is the scaled, computed thermal correction for the molecule, and the third term is the experimental thermal correction for the atoms. The molecular enthalpy of formation at 0 K is determined by ΔHf°(M,0K) =

∑

aΔHf°(a,0K)

atoms

− [ ∑ aEccCA (a) − EccCA (M) − EZPE(M)] atoms

(3)

The first term is the experimental atomic enthalpies of formation at 0 K and the second term is the computed dissociation energy of the molecule of interest. 6868


Article

The Journal of Physical Chemistry A Two molecule sets were composed for this study: 3dHf-24 and 4dHf-210. The 3dHf-24 set is composed of 24 copper and zinc-containing molecules from the ccCA-TM/11 set and the 4dHF-210 set is composed of 210 4d-containing molecules. The 4dHf-210 set of molecules ranges from diatomics to large organometallics and contains all 10 4d metals. The 4dHf-210 set is taken from the 3d set (ccCA-TM/11) that Jiang et al. compiled from experimental data for 3d compounds containing 2−20 atoms.66 Computationally derived enthalpies in 4dHf-210 that do not have experimental data to compare with were analyzed in comparison to their corresponding 3d transition metal compounds when possible. When available, enthalpies of formation for transition metal compounds were compared to experimental results from references including the NISTJANAF tables and the Yungman compendium.10,11,68

Table 1. Signed Deviations in kcal/mol of ROHF rp-ccCA and ccCA-TM Enthalpies of Formation (ΔHf) at 298.15 K As Compared with Experiment for the 3dHf-24 Set molecule Cu2 CuH CuO CuF CuF2 CuS CuCl CuGe CuSe CuBr (CuCl)3 (CuBr)3 Zn2 ZnH ZnCH3 Zn(CH3)2 ZnO ZnF2 ZnS ZnCl ZnCl2 ZnSe ZnBr ZnBr2

■

RESULTS AND DISCUSSION A. rp-ccCA and ccCA-TM 3d Transition Metal Set Comparison. To validate the reliability of rp-ccCA for first row (3d) transition metals, a comparison between rp-ccCA and ccCA-TM was carried out for a set of 24 copper- and zinccontaining compounds. Copper and zinc compounds from the ccCA-TM/11 benchmark set were chosen because all-electron and ECP correlation consistent basis sets are available for both metals.60,66 The enthalpies derived using ccCA-TM were obtained from a previous transition metal thermochemical study by Jiang and co-workers.66 The calculated ΔHf’s for the 3dHf-24 set can be found in Table 1. The rp-ccCA method yielded a mean absolute deviation (MAD) of 2.84 kcal/mol, whereas ccCA-TM resulted in an MAD of 2.10 kcal/mol from experimental ΔHf’s. As in the previous ccCA-TM study, CuOH, (ZnCl)2, and (ZnBr)2 were considered outliers and were not considered in the statistical analysis. Without these statistical outliers, the MADs for both rp-ccCA and ccCA-TM were within transition metal chemical accuracy (within 3 kcal/mol of experiment) and near the average experimental uncertainty (2.63 kcal/mol). The similarities often observed between copper and zinccontaining molecules may be partially attributed to both the copper and zinc atom having a fully filled 3d-shell. The rp-ccCA deviations are comparable between the two metal centers with MADs of 2.92 and 2.76 kcal/mol for copper and zinc, respectively. Though ccCA-TM slightly underestimated the copper ΔHf’s and overestimated the zinc ΔHf’s by the same magnitude, rp-ccCA only had a marginal underestimation for both metal centers. Examination of the statistical outliers did not yield a common solution to the deviations observed between theory and experiment. Both rp-ccCA and ccCA-TM underestimate the ΔHf of CuOH (−14.86 and −14.60 kcal/mol, respectively). The large D1 value (0.17) of ionic CuOH suggests the molecule may exhibit multireference character (multireference guideline diagnostic values: T1 > 0.05 and D1 > 0.15)69 and improved agreement with experiment may be obtained by using a multireference wave function-based method. Coupled cluster diagnostics for the dimeric and trimeric halides suggest that the single reference ccCA-TM and rp-ccCA methods likely are suitable for describing these systems. For (ZnCl)2, deviations of near equal magnitude are observed for rp-ccCA and ccCA-TM, suggesting experimental ΔHf’s, determined via extrapolation from zinc and copper monochloride values, may need to be revisited. In a previous ccCA-TM 3d study,66 large deviations were observed between experiment and ccCA-TM for TiCln

a e

ground state Σg+ 1

1

Σ 2 B1 1 Σ 2 Ag 2 B1 1 Σ 2 B1 2 B1 1 Σ 1 A1 1 A1 1 + Σg 2 Σ 2 A1 1 A1 1 Σ 1 Σg 1 Σ 2 Σ 1 Σg 1 Σ 2 Σ 1 Σg MSD MAD RMSD σ

rp-ccCA

ccCA-TM

2.7 −2.2 −1.0 1.0 1.8 −4.1 0.6 3.0 −3.8 2.8 4.6 7.3 −0.5 −0.5 −6.1 1.6 2.4 2.8 0.1 −5.2 −0.6 1.4 6.6 5.3 0.83 2.84 2.06 3.41

3.4 −2.3 −0.5 0.8 1.3 −4.5 0.0 2.1 −2.5 −0.7 4.8 5.2 −0.4 −0.3 −6.2 0.8 0.0 2.6 −0.9 −5.1 −1.0 0.5 3.5 −1.0 −0.02 2.10 1.85 2.80

Reference 11. bReference 72. cReference 68. Reference 74. fReference 10. gReference 75.

expt 115.3 ± 65.9 ± 73.2 ± 1.1 ± −66.0a 75.1 ± 21.8 ± 122.8 ± 70.3 ± 28.8 ± −61.8 ± −35.8 ± 60.7e 62.9 ± 45.5 ± 12.6 ± 55.2 ± −118.9 ± 62.9 ± 6.5 ± −63.5 ± 60.0 ± 24.3 ± −44.4a

1.3b 2.0a 10c 3.0d 5.0a 0.4c 4.2a 12a 6.0a 0.5c 2.1a 1.0a 4.0f 0.3f 1.0g 1.1a 0.5g 1.0a 0.4a 1.4g 7.0a

2.63

d

Reference 73.

systems. Recent re-examination of the experimental ΔHf’s for the titanium chlorides70 resulted in significantly better agreement with ccCA-TM. Zinc chlorides may also benefit from similar re-examination. The true anomalies are the bromide systems with more than one metal, (CuBr)3 and (ZnBr2)2. For these two molecules, the deviations of rp-ccCA and ccCA-TM were not in agreement [(CuBr)3 12.73 and 5.20 kcal/mol and (ZnBr2)2 15.23 and 12.3 kcal/mol, respectively]. The ground states and geometries obtained via both methods are in agreement, with the geometries only differing by a few hundredths of an ångstrom. If rp-ccCA calculations are run for the TM bromide systems where the DK basis sets are utilized for the bromine atoms in place of the ECP, the rp-ccCA deviations [(CuBr)3 7.31 kcal/mol and (ZnBr2)2 13.63 kcal/ mol] are in better agreement with ccCA-TM. As in the previous ccCA-TM study, (CuBr)3 was considered in the statistical analysis, whereas (ZnBr2)2 was not. It was determined when a single metal atom center system is studied, rp-ccCA in its native form is recommended. If there is more than one metal atom in the system of interest, ECPs should be used for the metal and DK basis sets for the substituents. Although there is a slight loss of accuracy for rp-ccCA for the copper and zinc compounds versus ccCA-TM, rp-ccCA still achieves transition metal chemical accuracy and describes the thermodynamics of the systems within the reported experimental uncertainties. Because rp-ccCA uses pseudopotentials, 6869


Article

The Journal of Physical Chemistry A

applied to 210 4d transition metal compounds (4dHf-210). The molecule set consists of a wide range of compounds, from dimers to carbonyl-containing compounds, with compounds of both single and multireference character included. Of the 210 compounds, 61 have experimentally determined ΔHf’s for comparison. The compounds are selected from the ccCA-TM/ 11 set, but with the replacement of the 3d metals with 4d metals, and optimization of the resulting structures. The complete 4dHf-210 set with ground states and rp-ccCA calculated ΔHf’s, as well as the 61 experimentally determined ΔHf’s, are included in the Supporting Information. The rp-ccCA results for the 4dHf-210 set are compiled in Table 3. The compounds with available experimental data included 31 halides, 15 chalcogenides, 3 oxohalides, 3 carbides, 3 dimers, 2 hydrides, 2 organometallics, and 2 carbonylcontaining compounds. The experimental data used for comparison with these compounds came primarily from the Yungman compendium of thermochemical substances, the Simões transition metal thermochemical reference compiled into the NIST database, and the JANAF tables by Chase and co-workers.10,11,68 The majority of the experimental works cited in these databases were published nearly half a century ago. These experimental values may benefit from an examination with newer experimental techniques, as evidenced by the observations for TiCln systems discussed in the previous section, which was improved by a re-evaluation of the enthalpy of sublimation utilized in the experimental evaluation.

there should be a significant computational cost reduction in comparison to ccCA-TM.64 A computational cost analysis was carried out between rp-ccCA and ccCA-TM, and rp-ccCA calculations were, on average, 53.4% faster than ccCA-TM (Table 2). The computational savings can be attributed to the Table 2. Percent Computational Time Savings of ROHF rpccCA Relative to ccCA-TM Calculations molecule

savings (%)

Cu2 CuH CuO CuF CuF2 CuS CuCl CuGe CuSe CuBr (CuCl)3 (CuBr)3

60.4 47.7 67.6 50.6 48.0 53.3 55.9 56.4 60.7 58.9 57.7 77.0

molecule

savings (%)

Zn2 ZnH ZnCH3 Zn(CH3)2 ZnO ZnF2 ZnS ZnCl ZnCl2 ZnSe ZnBr ZnBr2 average 53.42%

59.7 51.7 34.0 28.7 50.3 38.3 45.1 40.5 43.2 57.6 75.8 63.2

more efficient implicit electron treatment through the ECPs within the rp-ccCA methodology, in comparison to ccCA-TM’s explicit electron treatment. B. rp-ccCA 4d Transition Metal Set. Given the results from the copper and zinc molecule sets, rp-ccCA was then

Table 3. Signed Deviations from Experiment in kcal/mol for rp-ccCA Enthalpies of Formation (ΔHf) at 298.15 K for the 4dHf210 Molecule Set molecule YC2 YC4 YF YF2 YS YSe ZrO ZrO2 ZrS ZrCl ZrCl2 ZrCl3 ZrCl4 ZrBr ZrBr3 ZrBr4 NbO NbO2 NbF5 NbOCl3 NbCl4 MoO MoO2 MoO3 MoF MSD MAD a

deviation

expt

5.9 −2.8 −4.8 5.2 3.4 −7.5 1.3 6.2 7.7 −2.6 4.7 1.4 −0.3 5.5 8.4 3.7 3.5 4.3 1.1 −5.2 −2.1 −4.0 1.3 3.6 4.3

145.5 ± 4.0 192.0 ± 5.0a −22.6 ± 9.0a −152.1 ± 7.0a 39.6 ± 3.1a 53.1 ± 4.9a 22.1 ± 10.0a −70.0 ± 5.0a 70.8 ± 4.3a 67.6 ± 5.7b −34.9 ± 3.6b −124.7a −208.0 ± 0.6b 71.9 ± 0.5b −97.6a −166.0 ± 2.0b 47.8 ± 5.0a −50.1 ± 5.0a −416.6 ± 0.3a −180.0 ± 1.1a −132.1 ± 0.7a 95.5 ± 10.0a −3.2 ± 5.0a −86.7 ± 5.0c 67.6 ± 3.0a open shell 1.35 3.46 a

molecule

deviation

expt

MoF2 MoCl4 MoO2Cl2 MoBr4 Mo(CO)5 Mo(CO)6 RuO RhO Pd2 PdO PdCl2 Ag2 AgH AgO AgF AgCl AgBr Cd2 CdH Cd(CH3) Cd(CH3)2 CdF2 CdCl CdCl2 CdBr closed shell −0.95 3.92

−0.7 2.9 0.2 −7.8 −3.5 −9.5 0.2 2.2 −0.4 1.6 1.8 −2.8 −1.7 6.0 3.3 0.6 2.3 −5.1 −1.9 0.9 3.4 −6.4 4.4 5.6 0.7 overall 0.82 3.64

−38.9 ± 4.0a −82.3 ± 6.0b −150.7 ± 3.5a −40.9b −157.5 ± 5.0b −219.2 ± 1.1b 98.6a 98.0 ± 10.0a 162.6 ± 6.0a 92.6 ± 3.0d 30.7 ± 2.5a 97.29a 66.6 ± 3.0a 74.9 ± 4.3e 1.7a 22.1a 23.0 ± 2.1a 51.4b 62.3c 49.9 ± 4.0b 24.2a −94.4 ± 1.0a 6.55a −46.5 ± 1.1a 15.9a expt 4.05

Reference 11. bReference 10. cReference 68. dReference 76. eReference 77. 6870


Article


Figure 1. rp-ccCA computed enthalpies of formation versus experimental enthalpies of formation (where available) in kcal/mol for the 4dHf-210 set.

correlation between the deviation of rp-ccCA from experiment with metal type or bonding type was observed. When rp-ccCA deviations are observed with respect to metal center and similar ligands (e.g., silver metal center and halide ligands: AgF, AgCl, AgBr), rp-ccCA is observed to accurately and consistently determine enthalpies for compounds with similar bonding structure. Due to the high electronegativity of fluorine and the reactivity of metal oxides, the molecular ΔHf’s are often associated with larger experimental uncertainties. For examples, within the 4dHf-210 set, the average experimental uncertainties of the fluorine-containing molecules and the oxygen-containing molecules are 4.05 and 5.58 kcal/mol, respectively. A comparison between rp-ccCA MADs and average experimental uncertainties for subsets of the 4dHF210 set is reported in Figure 2. The MADs obtained via rpccCA are well within these experimental uncertainties (3.22 and 3.04 kcal/mol) and are near transition metal chemical accuracy. A similar accuracy level is observed for diatomic molecules, where the average experimental uncertainty is 5.24 kcal/mol and rp-ccCA yields an MAD of 3.23 kcal/mol. Outliers from the set are listed in Table 4, and are not restricted to a certain metal type (six different 4d metal centers are represented); therefore, the deviations are not systematically due to the method. If the multireference criteria of T1 > 0.05 and D1 > 0.15 based on 3d systems69 is considered for our 4d systems, diagnostics (T1 = 0.053, D1 = 0.156) for PdGe suggest that a multireference wave function treatment may be required and the deviation of the rp-ccCA value from the experimental value (−9.03 kcal/mol) is not unexpected. The multireference diagnostics of the remaining outliers indicate a single reference treatment should provide a reliable prediction. The oxides (PdO, RhO, RuO), in addition to PdGe, have salient multireference character based on the diagnostic values. These oxides provide an example of where the diagnostic values are not a guarantee of multireference behavior, because the single reference wave function based approach of rp-ccCA determines the ΔHf’s within or near transition metal chemical accuracy and/or experimental uncertainty. The palladium diatomic, PdGe, and oxides (PdO, RhO, and RuO) all exhibit multireference character based on diagnostics (Supporting

Overall, rp-ccCA achieved an MAD of 6.38 kcal/mol for the 61 compounds with available experimental ΔHf’s. The correlation between the rp-ccCA and experimental ΔHf’s is depicted in Figure 1. Of the 61 molecules with experimental data, 10 compounds in the set had significant rp-ccCA deviations (>10 kcal/mol) and can be considered statistical outliers in the 4dHf-210 set. The MAD of rp-ccCA for the remaining 51 compounds was 3.64 kcal/mol, in comparison to the average experimental uncertainty (where available) of 4.05 kcal/mol. The 10 statistical outliers are listed in Table 4 and the Table 4. T1 and D1 Diagnostics and rp-ccCA Signed Deviations for the Enthalpies of Formation (ΔHf) from Experiment in kcal/mol for the Statistical Outliers of the 4dHf-210 Molecule Set

a

molecule

T1

D1

rp-ccCA

YO YF3 ZrF3 ZrF4 ZrBr2 NbCl3 MoO2F2 RhCl2 RhCl3 PdBr2

0.035 0.016 0.021 0.019 0.021 0.022 0.028 0.037 0.024 0.029

0.059 0.035 0.047 0.052 0.054 0.056 0.091 0.109 0.093 0.127

−1.2 −272.8 −247.1 −380.4 −10.4 −67.0 −233.2 40.3 27.4 40.4

expt −11.6 ± −301.9 ± −264.0 ± −400.0 ± −42.0 ± −92.0a −268.0 ± 30.0 ± 16.0 ± 26.0 ±

2.6a 3.1a 4.0a 0.56a 10.00a 5.0a 3.0a 3.0a 3.0a

Reference 11.

experimental uncertainty for the set is 4.66 kcal/mol. Of the outliers, 7 of the molecules are similar to molecules that are well described by rp-ccCA. For example, because the ΔHf’s determined by rp-ccCA for YF and YF2 are within experimental uncertainties, rp-ccCA presumably should yield a similar accuracy level for YF3, yet YF3 is an outlier. Similar points could be made for the Nb, Mo, and Pd outliers. For these molecules, experimental values may need to be revisited. The overall accuracy of rp-ccCA was comparable for open-shell versus closed-shell systems (MADs of 3.46 and 3.92 kcal/mol, respectively), demonstrating that rp-ccCA is able to describe both open- and closed-shell systems similarly. No overall 6871


Article


Figure 2. Mean absolute deviations (MADs) of rp-ccCA in comparison to average experimental uncertainities in kcal/mol for subsets of the 4dHf210 set.

Information), but only PdGe (T1 = 0.053, D1 = 0.156) deviates significantly (9.03 kcal/mol) from experiment. With a new, larger set of molecules and the overall demonstrated utility of rp-ccCA to describe transition metal thermochemistry, rp-ccCA can be used to aid in examining prior experimental works. Table 5 lists eight sample compounds

(53.4%) was observed when pseudopotentials were utilized, in comparison to use of the all-electron basis sets in ccCA-TM. For transition metal systems, rp-ccCA has affirmed that the use of pseudopotentials in a composite approach leads to not only comparable accuracy but also a reduction in computational cost. A large set of 210 enthalpies of formation for 4d transition metal compounds was also generated to provide calibration data for the development of future computational methodologies and aid experimental work. Deviations of rp-ccCA for the 4dHf-210 set are within the 51 available experimental uncertainties, excluding outliers, (rp-ccCA MAD: 3.64 kcal/ mol, experimental uncertainty: 4.05 kcal/mol). A trend analysis between 3d and 4d metal compounds supports the reliability of the calculated enthalpies of formation. Overall, rp-ccCA is a useful methodology for the prediction of the enthalpy of formation for systems including main group and transition metals. For the 4d metal systems where experimental data is limited, the enthalpies of formation determined via rp-ccCA are recommended as a reference. The generation of the large 4d molecule set is a useful gauge for computational applications, such as the development of density functionals for transition metals, and as a complement to experiment, in areas such as catalyst design.

Table 5. Molecules with Multiple Reported Experimental Enthalpies of Formation (ΔHf) and rp-ccCA Values for ΔHf in kcal/mol molecule

expt 1

ZrCl ZrCl2 ZrCl4 ZrBr ZrBr4 MoBr4 PdO CdCH3

49.3h −43.4h −234.2 ± 0.3g 49.4a −181.8 ± 0.9f −67.7a 80.6c 34.4a

expt 2 67.6 ± −34.9 ± −208.0 ± 71.9 ± −166.0 ± −40.9b 92.6 ± 49.9d

5.7d 3.6d 0.6d 0.5b 2.0d 3.0e

diff between expt

rp-ccCA

18.3 8.5 26.2 22.5 15.8 26.8 12.0 15.5

64.98 −30.19 −208.39 77.40 −169.65 −48.66 91.03 50.76

a

Reference 11. bReference 68. cReference 78. dReference 10. Reference 76. fReference 79. gReference 71. hReference 80.

e

■

with multiple experimental values from the literature, which deviate significantly from one another. For these systems with conflicting experimental ΔHf’s, rp-ccCA can aid in the confirmation of experimental predictions. For example, experimental ΔHf’s predicted by Chase and Tsirel’nikov differ by 26.2 kcal/mol for ZrCl4, but rp-ccCA deviates from Chase’s result by only 0.39 kcal/mol.68,71

ASSOCIATED CONTENT

S Supporting Information *

Calculated ROHF-rp-ccCA enthalpies of formation at 298 K and molecular ground states for the 4dHf-210 set and experimental enthalpies of formation at 298 K, where available. The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jpca.5b02433.

■

■

CONCLUSIONS The relativistic-pseudopotential correlation consistent composite approach (rp-ccCA) was applied to 24 copper and zinc (3d) compounds (3dHf-24), as well as 210 4d transition metal compounds (4dHf-210), to obtain their enthalpies of formations. The rp-ccCA method achieves transition metal chemical accuracy (within 3 kcal/mol from experiment) for the 3d molecules and the rp-ccCA deviations from experimental enthalpies of formation are comparable to all-electron ccCATM. When applying rp-ccCA to a system with more than one metal center, ECPs are recommended for the metal and DK basis sets for the substituents. A significant average time savings

AUTHOR INFORMATION

Corresponding Author

*A. K. Wilson. Electronic mail: [email protected]. Notes

The authors declare no competing financial interest.

■

ACKNOWLEDGMENTS This material is based upon work supported by the National Science Foundation under Grant No. CHE-1362479 and CHE1213874. Computing resources were provided by the Academic Computing Services at the University of North Texas. S.M. thanks the Texas Academy of Math and Science for financial 6872


Article


(21) Swart, M. Accurate Spin-State Energies for Iron Complexes. J. Chem. Theory Comput. 2008, 4, 2057−2066. (22) Yang, K.; Peverati, R.; Truhlar, D. G.; Valero, R. Density Functional Study of Multiplicity-Changing Valence and Rydberg Excitations of P-Block Elements: Delta Self-Consistent Field, Collinear Spin-Flip Time-Dependent Density Functional Theory (DFT), and Conventional Time-Dependent DFT. J. Chem. Phys. 2011, 135, 044118. (23) Zein, S.; Poor Kalhor, M.; Chibotaru, L. F.; Chermette, H. Density Functional Estimations of Heisenberg Exchange Constants in Oligonuclear Magnetic Compounds: Assessment of Density Functional Theory versus Ab Initio. J. Chem. Phys. 2009, 131, 224316. (24) Furche, F.; Perdew, J. P. The Performance of Semilocal and Hybrid Density Functionals in 3d Transition-Metal Chemistry. J. Chem. Phys. 2006, 124, 044103. (25) Bühl, M.; Kabrede, H. Geometries of Transition-Metal Complexes from Density-Functional Theory. J. Chem. Theory Comput. 2006, 2, 1282−1290. (26) Waller, M. P.; Braun, H.; Hojdis, N.; Bühl, M. Geometries of Second-Row Transition-Metal Complexes from Density-Functional Theory. J. Chem. Theory Comput. 2007, 3, 2234−2242. (27) Waller, M. P.; Bühl, M. Vibrational Corrections to Geometries of Transition Metal Complexes from Density Functional Theory. J. Comput. Chem. 2007, 28, 1531−1537. (28) Schultz, N. E.; Zhao, Y.; Truhlar, D. G. Databases for Transition Element Bonding: Metal-Metal Bond Energies and Bond Lengths and Their Use to Test Hybrid, Hybrid Meta, and Meta Density Functionals and Generalized Gradient Approximations. J. Phys. Chem. A 2005, 109, 4388−4403. (29) Schultz, N. E.; Zhao, Y.; Truhlar, D. G. Density Functionals for Inorganometallic and Organometallic Chemistry. J. Phys. Chem. A 2005, 109, 11127−11143. (30) Riley, K. E.; Merz, K. M. Assessment of Density Functional Theory Methods for the Computation of Heats of Formation and Ionization Potentials of Systems Containing Third Row Transition Metals. J. Phys. Chem. A 2007, 111, 6044−6053. (31) Luo, S.; Averkiev, B.; Yang, K. R.; Xu, X.; Truhlar, D. G. Density Functional Theory of Open-Shell Systems. The 3d-Series TransitionMetal Atoms and Their Cations. J. Chem. Theory Comput. 2014, 10, 102−121. (32) Luo, S.; Truhlar, D. G. How Evenly Can Approximate Density Functionals Treat the Different Multiplicities and Ionization States of 4d Transition Metal Atoms? J. Chem. Theory Comput. 2012, 8, 4112− 4126. (33) Pople, J. A.; Head-Gordon, M.; Fox, D. J.; Raghavachari, K.; Curtiss, L. A. Gaussian-1 Theory: A General Procedure for Prediction of Molecular Energies. J. Chem. Phys. 1989, 90, 5622. (34) Curtiss, L. A.; Raghavachari, K.; Trucks, G. W.; Pople, J. A. Gaussian-2 Theory for Molecular Energies of First- and Second-Row Compounds. J. Chem. Phys. 1991, 94, 7221. (35) Curtiss, L. A.; Raghavachari, K.; Redfern, P. C.; Rassolov, V.; Pople, J. A. Gaussian-3 (G3) Theory for Molecules Containing First and Second-Row Atoms. J. Chem. Phys. 1998, 109, 7764. (36) Curtiss, L. A.; Redfern, P. C.; Raghavachari, K. Gaussian-4 Theory. J. Chem. Phys. 2007, 126, 084108. (37) Curtiss, L. A.; Redfern, P. C.; Raghavachari, K. G N Theory. Wiley Interdiscip. Rev. Comput. Mol. Sci. 2011, 1, 810−825. (38) Martin, J. M. L.; de Oliveira, G. Towards Standard Methods for Benchmark Quality Ab Initio thermochemistryW1 and W2 Theory. J. Chem. Phys. 1999, 111, 1843. (39) Boese, A. D.; Oren, M.; Atasoylu, O.; Martin, J. M. L.; Kallay, M.; Gauss, J. W3 Theory: Robust Computational Thermochemistry in the kJ/mol Accuracy Range. J. Chem. Phys. 2004, 120, 4129−4141. (40) Tajti, A.; Szalay, P. G.; Császár, A. G.; Kállay, M.; Gauss, J.; Valeev, E. F.; Flowers, B. A.; Vázquez, J.; Stanton, J. F. HEAT: High Accuracy Extrapolated Ab Initio Thermochemistry. J. Chem. Phys. 2004, 121, 11599−11613. (41) Bomble, Y. J.; Vázquez, J.; Kállay, M.; Michauk, C.; Szalay, P. G.; Császár, A. G.; Gauss, J.; Stanton, J. F. High-Accuracy Extrapolated Ab

support. Support from the United States Department of Energy for the Center for Advanced Scientific Computing and Modeling (CASCaM) is acknowledged.

■

REFERENCES

(1) Malcolmson, S. J.; Meek, S. J.; Sattely, E. S.; Schrock, R. R.; Hoveyda, A. H. Highly Efficient Molybdenum-Based Catalysts for Enantioselective Alkene Metathesis. Nature 2008, 456, 933−937. (2) Magano, J.; Dunetz, J. R. Large-Scale Applications of Transition Metal-Catalyzed Couplings for the Synthesis of Pharmaceuticals. Chem. Rev. 2011, 111, 2177−2250. (3) Martinez, R.; Simon, M.-O.; Chevalier, R.; Pautigny, C.; Genet, J.P.; Darses, S. C−C Bond Formation via C−H Bond Activation Using an in Situ-Generated Ruthenium Catalyst. J. Am. Chem. Soc. 2009, 131, 7887−7895. (4) Yamanoi, Y.; Nishihara, H. Direct and Selective Arylation of Tertiary Silanes with Rhodium Catalyst. J. Org. Chem. 2008, 73, 6671− 6678. (5) Stöcker, M. Gas Phase Catalysis by Zeolites. Microporous Mesoporous Mater. 2005, 82, 257−292. (6) Chinchilla, R.; Nájera, C. Chemicals from Alkynes with Palladium Catalysts. Chem. Rev. 2014, 114, 1783−1826. (7) Duan, L.; Bozoglian, F.; Mandal, S.; Stewart, B.; Privalov, T.; Llobet, A.; Sun, L. A Molecular Ruthenium Catalyst with WaterOxidation Activity Comparable to that of Photosystem II. Nat. Chem. 2012, 4, 418−423. (8) Karunadasa, H. I.; Chang, C. J.; Long, J. R. A Molecular Molybdenum-Oxo Catalyst for Generating Hydrogen from Water. Nature 2010, 464, 1329−1333. (9) Schwarz, G.; Mendel, R. R.; Ribbe, M. W. Molybdenum Cofactors, Enzymes and Pathways. Nature 2009, 460, 839−847. (10) Linstrom, P. J.; Mallard, W. G. NIST Chemistry WebBook, NIST Standard Reference Database Number 69; National Institute of Standards and Technology: Gaitherburg, MD, 2000. (11) Yungman, V.; Glushko, V. P.; Medvedev, V. A.; Gurvich, L. V. Thermal Constants of Substances; Wiley, Begell House: New York, 1999. (12) Deyonker, N. J.; Peterson, K. A.; Steyl, G.; Wilson, A. K.; Cundari, T. R. Quantitative Computational Thermochemistry of Transition Metal Species. J. Phys. Chem. A 2007, 111, 11269−11277. (13) Pedley, J. B.; Marshall, E. M. Thermochemical Data for Gaseous Monoxides. J. Phys. Chem. Ref. Data 1983, 12, 967. (14) DeYonker, N. J.; Cundari, T. R.; Wilson, A. K. The Correlation Consistent Composite Approach (ccCA): An Alternative to the Gaussian-N Methods. J. Chem. Phys. 2006, 124, 114104. (15) Weaver, M. N.; Yang, Y.; Merz, K. M. Assessment of the CCSD and CCSD(T) Coupled-Cluster Methods in Calculating Heats of Formation for Zn Complexes. J. Phys. Chem. A 2009, 113, 10081− 10088. (16) Cundari, T. R.; Arturo Ruiz Leza, H.; Grimes, T.; Steyl, G.; Waters, A.; Wilson, A. K. Calculation of the Enthalpies of Formation for Transition Metal Complexes. Chem. Phys. Lett. 2005, 401, 58−61. (17) Zhang, W.; Truhlar, D. G.; Tang, M. Tests of ExchangeCorrelation Functional Approximations Against Reliable Experimental Data for Average Bond Energies of 3d Transition Metal Compounds. J. Chem. Theory Comput. 2013, 9, 3965−3977. (18) Jiang, W. Y.; Laury, M. L.; Powell, M.; Wilson, A. K. Comparative Study of Single and Double Hybrid Density Functionals for the Prediction of 3d Transition Metal Thermochemistry. J. Chem. Theory Comput. 2012, 8, 4102−4111. (19) Laury, M. L.; Wilson, A. K. Performance of Density Functional Theory for Second Row (4 D) Transition Metal Thermochemistry. J. Chem. Theory Comput. 2013, 9, 3939−3946. (20) Tekarli, S. M.; Drummond, M. L.; Williams, T. G.; Cundari, T. R.; Wilson, A. K. Performance of Density Functional Theory for 3d Transition Metal-Containing Complexes: Utilization of the Correlation Consistent Basis Sets. J. Phys. Chem. A 2009, 113, 8607−8614. 6873


Article

The Journal of Physical Chemistry A Initio Thermochemistry. II. Minor Improvements to the Protocol and a Vital Simplification. J. Chem. Phys. 2006, 125, 64108. (42) Harding, M. E.; Vázquez, J.; Ruscic, B.; Wilson, A. K.; Gauss, J.; Stanton, J. F. High-Accuracy Extrapolated Ab Initio Thermochemistry. III. Additional Improvements and Overview. J. Chem. Phys. 2008, 128, 114111. (43) Feller, D.; Peterson, K. A.; Dixon, D. A. Further Benchmarks of a Composite, Convergent, Statistically Calibrated Coupled-ClusterBased Approach for Thermochemical and Spectroscopic Studies. Mol. Phys. 2012, 110, 2381−2399. (44) Feller, D.; Peterson, K. A.; Dixon, D. A. A Survey of Factors Contributing to Accurate Theoretical Predictions of Atomization Energies and Molecular Structures. J. Chem. Phys. 2008, 129, 204105. (45) Peterson, K. A.; Feller, D.; Dixon, D. A. Chemical Accuracy in Ab Initio Thermochemistry and Spectroscopy: Current Strategies and Future Challenges. Theor. Chem. Acc. 2012, 131, 1079. (46) Fast, P. L.; Corchado, J. C.; Sanchez, M. L.; Truhlar, D. G. Multi-Coefficient Correlation Method for Quantum Chemistry. J. Phys. Chem. A 1999, 103, 5129−5136. (47) Fast, P. L.; Truhlar, D. G. MC-QCISD: Multi-Coefficient Correlation Method Based on Quadratic Configuration Interaction with Single and Double Excitations. J. Phys. Chem. A 2000, 104, 6111− 6116. (48) DeYonker, N. J.; Mintz, B.; Cundari, T. R.; Wilson, A. K. Application of the Correlation Consistent Composite Approach (ccCA) to Third-Row (Ga-Kr) Molecules. J. Chem. Theory Comput. 2008, 4, 328−334. (49) DeYonker, N. J.; Wilson, B. R.; Pierpont, A. W.; Cundari, T. R.; Wilson, A. K. Towards the Intrinsic Error of the Correlation Consistent Composite Approach (ccCA). Mol. Phys. 2009, 107, 1107−1121. (50) DeYonker, N. J.; Grimes, T.; Yockel, S.; Dinescu, A.; Mintz, B.; Cundari, T. R.; Wilson, A. K. The Correlation-Consistent Composite Approach: Application to the G3/99 Test Set. J. Chem. Phys. 2006, 125, 104111. (51) Oyedepo, G. A.; Peterson, C.; Wilson, A. K. Accurate Predictions of the Energetics of Silicon Compounds Using the Multireference Correlation Consistent Composite Approach. J. Chem. Phys. 2011, 135, 094103. (52) Oyedepo, G. A.; Wilson, A. K. Multireference Correlation Consistent Composite Approach [MR-ccCA]: Toward Accurate Prediction of the Energetics of Excited and Transition State Chemistry. J. Phys. Chem. A 2010, 114, 8806−8816. (53) Riojas, A. G.; Wilson, A. K. Solv-ccCA: Implicit Solvation and the Correlation Consistent Composite Approach for the Determination of P K a. J. Chem. Theory Comput. 2014, 10, 1500−1510. (54) Mahler, A.; Wilson, A. K. Explicitly Correlated Methods within the ccCA Methodology. J. Chem. Theory Comput. 2013, 9, 1402−1407. (55) Das, S. R.; Williams, T. G.; Drummond, M. L.; Wilson, A. K. A QM/QM Multilayer Composite Methodology: The ONIOM Correlation Consistent Composite Approach (ONIOM-ccCA). J. Phys. Chem. A 2010, 114, 9394−9397. (56) Stoll, H. Large-Core vs. Small-Core Pseudopotentials: A Case Study for Au2. Chem. Phys. Lett. 2006, 429, 289−293. (57) Peterson, K. A.; Figgen, D.; Dolg, M.; Stoll, H. EnergyConsistent Relativistic Pseudopotentials and Correlation Consistent Basis Sets for the 4d Elements Y-Pd. J. Chem. Phys. 2007, 126, 124101. (58) Peterson, K. A.; Figgen, D.; Goll, E.; Stoll, H.; Dolg, M. Systematically Convergent Basis Sets with Relativistic Pseudopotentials. II. Small-Core Pseudopotentials and Correlation Consistent Basis Sets for the Post-D Group 16−18 Elements. J. Chem. Phys. 2003, 119, 11113. (59) Peterson, K. A. Systematically Convergent Basis Sets with Relativistic Pseudopotentials. I. Correlation Consistent Basis Sets for the Post-D Group 13−15 Elements. J. Chem. Phys. 2003, 119, 11099. (60) Peterson, K. A.; Puzzarini, C. Systematically Convergent Basis Sets for Transition Metals. II. Pseudopotential-Based Correlation Consistent Basis Sets for the Group 11 (Cu, Ag, Au) and 12 (Zn, Cd, Hg) Elements. Theor. Chem. Acc. 2005, 114, 283−296.

(61) Peterson, K. A.; Yousaf, K. E. Molecular Core-Valence Correlation Effects Involving the Post-D Elements Ga-Rn: Benchmarks and New Pseudopotential-Based Correlation Consistent Basis Sets. J. Chem. Phys. 2010, 133, 174116. (62) Peterson, K. A.; Shepler, B. C.; Figgen, D.; Stoll, H. On the Spectroscopic and Thermochemical Properties of ClO, BrO, IO, and Their Anions. J. Phys. Chem. A 2006, 110, 13877−13883. (63) Laury, M. L.; Wilson, A. K. Examining the Heavy P-Block with a Pseudopotential-Based Composite Method: Atomic and Molecular Applications of Rp-ccCA. J. Chem. Phys. 2012, 137, 214111. (64) Laury, M. L.; DeYonker, N. J.; Jiang, W.; Wilson, A. K. A Pseudopotential-Based Composite Method: The Relativistic Pseudopotential Correlation Consistent Composite Approach for Molecules Containing 4d Transition Metals (Y-Cd). J. Chem. Phys. 2011, 135, 214103. (65) Dunning, T. H.; Peterson, K. A.; Wilson, A. K. Gaussian Basis Sets for Use in Correlated Molecular Calculations. X. The Atoms Aluminum through Argon Revisited. J. Chem. Phys. 2001, 114, 9244. (66) Jiang, W.; DeYonker, N. J.; Determan, J. J.; Wilson, A. K. Toward Accurate Theoretical Thermochemistry of First Row Transition Metal Complexes. J. Phys. Chem. A 2012, 116, 870−885. (67) Werner, H. J.; Knowles, P. J.; Lindh, R.; Manby, F. R.; Schütz, M.; Al, E. MOLPRO, Version 2009.1, a Package of Ab Initio Programs, 2009. (68) Chase, J. M. W.; Davies, C. A.; Downey, J. J. R.; Frurip, D. J.; McDonald, R. A.; Syverund, A. N. NIST-JANAF Thermochemical Tables, 4th ed. J. Phys. Chem. Ref. Data 1998, 551. (69) Jiang, W.; DeYonker, N. J.; Wilson, A. K. Multireference Character for 3d Transition-Metal-Containing Molecules. J. Chem. Theory Comput. 2012, 8, 460−468. (70) Hildenbrand, D. L. Low-Lying Electronic States and Revised Thermochemistry of TiCl, TiCl2, and TiCl3. J. Phys. Chem. A 2009, 113, 1472−1474. (71) Efimov, M. E.; Prokopenko, I. V.; Medvedev, V. A.; Tsirel’nikov, V. I. Enthalpy of Zirconium Tetrachloride Formation. Zh. Fiz. Khim. 1986, 60, 2364−2365. (72) Gingerich, K. A. Experimental and Predicted Stability of Diatomic Metals and Metallic Clusters. Faraday Symp. Chem. Soc. 1980, 14, 109. (73) Ehlert, T. C.; Wang, J. S. Thermochemistry of the Copper Fluorides. J. Phys. Chem. 1977, 81, 2069−2073. (74) Gutsev, G. L.; Bauschlicher, C. W. Chemical Bonding, Electron Affinity, and Ionization Energies of the Homonuclear 3d Metal Dimers. J. Phys. Chem. A 2003, 107, 4755−4767. (75) Von Szentpály, L. Atom-Based Thermochemistry: Predictions of the Sublimation Enthalpies of Group 12 Chalcogenides and the Formation Enthalpies of Their Polonides. J. Phys. Chem. A 2008, 112, 12695−12701. (76) Norman, J. H.; Staley, H. G.; Bell, W. E. Mass Spectrometric Study of Gaseous Oxides of Rhodium and Palladium. J. Phys. Chem. 1964, 68, 662−663. (77) Smoes, S.; Mandy, F.; Auwera-Mahieu, A.; Vander Drowart, J. Determination by the Mass Spectrometric Knudsen Cell Method of the Dissociation Energies of the Group IB Chalcogenides. Bull. Soc. Chim. Belg. 1972, 81, 45−56. (78) Norman, J. H.; Staley, H. G.; Bell, W. E. Mass Spectrometric Knudsen Cell Measurements of the Vapor Pressure of Palladium and the Partial Pressure of Palladium Oxide. J. Phys. Chem. 1965, 69, 1373−1376. (79) Tsirel’nikov, V. I. Thermodynamic Functions of Lower Zirconium Halides in Gaseous State. Zh. Fiz. Khim. 1974, 48, 2135. (80) Farber, M.; Fisch, M. A.; Grenier, G.; Ko, H. C.; Harris, S. P. Investigation of the Thermodynamic Properties of Rocket Combustion Products; Defense Technical Information Center: Ft. Belvoir, VA, 1967.

6874


Pseudopotential-Based Correlation Consistent Composite Approach

Recommend Documents