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- Abstract
- 1. Introduction
- 2. Computational Methodology
- 3. Results and Discussion
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Mol Phys. Author manuscript; available in PMC 2010 June 15.

Published in final edited form as:

Mol Phys. 2009 January 1; 107(8-12): 1251–1259.

doi: 10.1080/00268970902953596PMCID: PMC2885807

NIHMSID: NIHMS177666

Department of Chemistry, Quantum Theory Project, 2328 New Physics Building, University of Florida, Gainesville, FL 32611-8435, 352-392-6973

Kenneth M. Merz, Jr.: ude.lfu.ptq@zrem

See other articles in PMC that cite the published article.

Heats of formation for nine complexes of the form CuX_{n} (X = Cu, H, O, OH, S, F, F_{2}, Cl, Cl_{2}) were calculated using the CCSD and CCSD(T) coupled cluster methods with the 6-31G** and TZVP basis sets as well as the LANL2DZ basis set/pseudopotential on Cu with both the 6-31G** and TZVP basis sets applied to the nonmetal atoms. These values were compared with literature heat of formation values. A second order Douglas-Kroll-Hess relativistic correction was applied at the CCSD/TZVP and CCSD(T)/TZVP levels of theory. Overall, the CCSD(T)/TZVP level of theory with the relativistic correction was most suited for the heat of formation calculations possessing low absolute average error and RMSD and the ability to analyze each copper complex, except for the problematic case of copper(II) fluoride. Finally, experimental geometric parameters were compared with the calculated structures in such cases where these data were available. None of the investigated levels of theory predicted bond lengths consistently better than other methods, and it was determined that the most accurate bond length does not necessarily result in the most accurate calculated heat of formation value for a given complex.

Copper is an extremely relevant transition metal and is contained in a wide range of chemical systems, including biological molecules such as proteins, catalysts, reagents for enantioselective synthesis and building blocks for molecular magnets.^{1}^{-}^{6} With its rich chemistry, copper containing systems have been the subject of much study both experimentally and theoretically.

Copper systems have been the subject of a wide range of theoretical treatments over the last two decades. Ahlrichs in 1990 studied small CuX systems and their dimers using coupled pair functional calculations, including first order relativistic effects.^{7} Other CuX systems, including tellurides, have been probed using pseudopotentials and MP2 calculations and such calculations were found to predict spectroscopic parameters that compared favorably with experiment.^{8} Terreux and coworkers probed the interactions of Cu^{2+} with glucosamine and *N*-acetylglucosamine using density functional methods and were able to successfully analyze the energetics of the various complex conformers.^{9} Further density functional calculations investigated the structure of copper clusters, structural and spectroscopic relationships in blue copper proteins and complexes of copper with dinitrogen.^{10}^{-}^{12} DFT methods have additionally been applied in the mechanistic study of Cu-involving reactions, including alkene insertion into Cu—B bonds and cuprate conjugate addition.^{13}^{,}^{14} Cascella and coworkers applied hybrid TDDFT-Molecular Dynamics simulations to study the optical spectra of the Cu^{2+}—azurin complex and found these methods appropriate for the faithful reproduction of experimental data.^{15} High level CCSD(T) calculations have been used to investigate the reactivity of copper atoms with CS_{2}.^{16} CCSD(T) calculations including relativistic effects have further been implemented in the study of metal fluorides, including CuF.^{17}

Numerous high-quality heat of formation studies on small organic molecules are present in the literature. Of particular interest to us are methodologies incorporating coupled-cluster methods. In 2001, Dixon and coworkers showed that Δ*H _{f}* values for NH

Several groups have undertaken the task of performing high quality calculations on transition metal containing systems. Balabanov and Peterson describe accurate basis sets (extracted towards the CBS limit) for transition metals Sc through Zn.^{22}^{,}^{23} Further work by Peterson and coworkers describes the application of the correlation consistent Composite Approach to the thermochemistry of transition metal systems.^{24} Finally, Lu and coworkers have recently published high level calculations on transition metal-ammonia complexes at the CCSD(T) level extrapolated to the CBS limit in order to accurately predict ionization potentials.^{25} While it may not be practical to apply the highly accurate CCSD(T)-CBS extrapolated model to larger transition metal containing systems, we desired to probe the efficacy of CCSD and CCSD(T) calculations with smaller basis sets in predicting the heats of formation of such systems, since to our knowledge this has not been examined closely.

Recently, we have conducted density functional studies incorporating twelve popular DFT methods on a series of 94 transition metal complexes using the 6-31G** and triple-ζ quality TZVP basis sets as well as the pseudopotential based LANL2DZ.^{26}^{,}^{27} We have also conducted studies on a series of nine ZnX_{n} complexes using the coupled cluster methods CCSD and CCSD(T) with the 6-31G** and TZVP basis sets alone and in combination with LANL2DZ.^{28} Herein we extend our coupled cluster treatment to include a series of nine CuX_{n} complexes and report calculated Δ*H _{f}* values. We additionally compare the copper-nonmetal bond lengths with literature geometries where available.

Table 1 contains a summary of the best density functional and basis set combination for each of the nine CuX_{n} complexes where in each case “best” is taken as the density functional/basis set pairing producing the heat of formation closest to the experimental value. As was observed with Zn complexes, there is no universal best density functional for use in the prediction of heats of formation for CuX_{n} systems, with the mostly widely applicable combination being BB1K/6-31G** for five of the nine systems considered. While it is simple for small systems to choose a best functional from the list or even test several, it is desirable to have a computational methodology that is effective for a larger range of compounds. This is especially important when considering the study of larger, more substituted systems. We hypothesized that utilizing more computationally elaborate coupled-cluster methods will provide a more broad approach to the calculation of these values in Cu complexes and test this on the nine selected CuX_{n} complexes.

All calculations were carried out on a SUN cluster featuring dual 2.5GHz Opteron nodes using the Gaussian 03^{31} suite of programs. All geometry optimizations incorporated standard gradient methods. For all single point calculations, the SCF=TIGHT keyword was used. Additionally, the SCF=XQC keyword was applied in all instances, as SCF convergence was often problematic, especially for higher energy multiplets and this is a standard procedure for attempting to correct such difficulties. CCSD and CCSD(T) calculations were run as implemented in Gaussian 03.^{32}^{-}^{37} Where applicable, calculations were done at the UCCSD at UCCSD(T) levels. All other calculations are closed shell. Frequency calculations were conducted on all geometries (at the minimum energy multiplicity) to insure all calculated lowest energy structures resided at local minima on the potential energy surface. The results of the frequency analysis, once deemed acceptable minima, were used in the heat of formation calculation. The 6-31G** and triple-ζ quality TZVP basis sets were used as implemented in Gaussian 03.^{38}^{-}^{40} LACVP** calculations were run using the GEN keyword for the basis set. In these calculations, the LANL2DZ basis/pseudopotential was used for copper and the 6-31G** basis set for the nonmetal atoms. A second set of calculations was run which applied the TZVP basis set to the nonmetals while retaining LANL2DZ on the copper atom.

For all CuX_{n} species considered, it was initially desired to optimize the 1, 3, 5 and 7 multiplicities for even electron species and the 2, 4, 6 and 8 multiplicities for odd electron species as done in our previous DFT work.^{26} This worked well for most CCSD calculations, although high energy multiplicities were sometimes difficult to converge. CCSD(T) calculations failed for a large number of high energy multiplicities especially in the larger systems, although the CCSD ground state could always be converged for smaller complexes using CCSD(T) calculations.

Heats of formation (Δ*H _{f}*) for all complexes were computed using the method outlined in the Gaussian white paper on Thermochemistry in the Gaussian 03 online manual.

$$\begin{array}{c}\Delta {H}_{f}\phantom{\rule{0.1em}{0ex}}(\text{M},298\text{K})=\Delta {H}_{f}\phantom{\rule{0.1em}{0ex}}(\text{M},0\text{K})+(({H}_{M}\phantom{\rule{0.1em}{0ex}}(298\text{K})-{H}_{M}\phantom{\rule{0.1em}{0ex}}(0\text{K}))\hfill \\ \phantom{\rule{6.5em}{0ex}}-\sum \text{x}({H}_{x}(298\text{K})-{H}_{x}(0\text{K}))\hfill \end{array}$$

(1)

$$\begin{array}{c}\Delta {H}_{f}\phantom{\rule{0.1em}{0ex}}(298\text{K})=627.5095({E}_{\text{CORR}})+80.64-627.5095({E}_{\text{Cu}})+\hfill \\ \phantom{\rule{5em}{0ex}}(\Delta {H}_{f}\phantom{\rule{0.1em}{0ex}}(\text{atom},298\text{K})-627.5095({E}_{\text{atom}})\hfill \end{array}$$

(2)

Equation 2 is in terms of the output provided by Gaussian, for convenience, where *E*_{CORR} is the sum of electronic and thermal enthalpies provided in output of the frequency calculation (which includes thermal and ZPE corrections to the energy). *E*_{Cu} and *E*_{atom} are the energies of the copper and nonmetal atoms at a given level of theory. The constant 80.64 (kcal/mol) in Equation 2 is the Δ*H _{f}* (Cu, 298K) taken from the NIST chemistry WebBook

$$\sqrt{\frac{1}{n}\sum _{i}^{n}{({x}_{i}-\overline{x})}^{2}}$$

(3)

The results of calculations using the CCSD and CCSD(T) coupled-cluster methods with the 6-31G** and LACVP** basis sets are summarized in table 2 and figure 1. CCSD(T) calculations failed for ^{2}CuF_{2} using both basis sets, but were successfully completed for all remaining entries. Generally, the CCSD(T) level was an improvement over CCSD level calculations. Excluding ^{1}CuF_{2} values, as these were not obtainable at the CCSD(T) level, the average unsigned error at CCSD(T)/6-31G** was a 3.4 kcal/mol improvement over CCSD/6-31G**, although the RMSD was actually slightly larger at the CCSD(T) level, by 1.3 kcal/mol. The same trend was observed using the LACVP** basis set, with CCSD(T) improving the average unsigned error by 1.3 kcal/mol, with a 0.5 kcal/mol higher RMSD value. For this set of calculated Δ*H _{f}* values, the CCSD(T)/6-31G** level of theory provides the best results in five of the eight studied CuX

The failure in predicting the heat of formation for ^{2}CuF_{2} at the CCSD(T)/6-31G** theory level is due to lack of convergence in the SCF on submitting the frequency job. Efforts to alleviate this problem included taking the initial guess from the checkpoint file, enforcing maximal symmetry and the removal of all symmetry constraints, to no avail. For the methods where ^{2}CuF_{2} could be evaluated, the results were not very good. The errors associated with these values approached 20 kcal/mol. Methods excluding CCSD(T)/6-31G** were also very poor at evaluating the heat of formation in ^{2}CuS, with very large errors. Conversely, the error in ^{2}CuS with CCSD(T)/6-31G** was very low at 2.2 kcal/mol. In the table 2 data set, nearly all calculated Δ*H _{f}* values are overestimates when compared to the literature values, with two exceptions.

Results of CCSD and CCSD(T) calculations with the TZVP and LANL2DZ basis sets are presented in table 3 and figure 2. All calculated values are overestimations of the literature heats of formation in this data set, with no exceptions as were observed in the 6-31G** and LACVP** data. Of the four methodologies, the CCSD(T)/TZVP level provides the best predictions of the Δ*H _{f}* values with an average unsigned error of 14.1 kcal/mol and an RMSD value of 4.8. The CCSD(T)/TZVP results are systematic improvements over their CCSD counterparts. CCSD(T)/LANL2DZ-TZVP results showed a similar improvement over their CCSD/LANL2DZ-TZVP counterparts, with average unsigned errors of 17.6 and 19.1 kcal/mol respectively. These average errors were larger than those observed using only the TZVP basis set. For each of the nine CuX

CCSD and CCSD(T) calculated vs. experimental Δ*H*_{f} values with the TZVP and LANL2DZ-TZVP basis sets.

Overall, for the eight methodologies employed, the best Δ*H _{f}* values are calculated with the CCSD(T) coupled-cluster method and the 6-31G** and TZVP basis sets. A comparison of these two levels of theory is shown in figure 3. CCSD(T)/6-31G** Δ

We decided to further our investigation by applying a Douglas-Kroll-Hess 2^{nd} order relativistic correction (DKH) to calculations at the CCSD/TZVP and CCSD(T)/TZVP levels of theory as implemented in Gaussian 03.^{44}^{-}^{48} This correction was applied during the course of both the geometry optimizations and frequency analyses and these results are summarized in tables 4 and and5.5. At the CCSD/TZVP theory level, the average unsigned error drops by 2.7 kcal/mol with the addition of this correction, with eight of the nine calculated values improving over the uncorrected values. The lone entry that does not improve is ^{2}CuS, whose predicted Δ*H _{f}* value worsens by 0.6 kcal/mol. It should be pointed out that the experimental error bar in

CCSD/TZVP Δ*H*_{f} values with and without 2^{nd} order DKH relativistic correction CuX_{n} complexes.

CCSD(T)/TZVP Δ*H*_{f} values with and without 2^{nd} order DKH relativistic correction CuX_{n} complexes.

Inclusion of the DKH relativistic correction at CCSD(T)/TZVP provides a slightly better improvement in the calculated Δ*H _{f}* values over their CCSD counterparts.

Calculated bond lengths are compared to available experimental values in Table 6. The CCSD/LACVP** level of theory most closely predicts the metal-nonmetal distance in ^{2}CuO, ^{1}CuF and ^{2}CuF_{2}. The CCSD(T)/TZVP theory level is best at predicting this distance in ^{1}Cu_{2} and ^{2}CuCl_{2}. The remaining closest values are scattered amongst the remaining levels of theory. It is worth pointing out that while CCSD/LACVP** may be suitable for predicting bond lengths closer to the experimental, the resulting heat of formation values in these instances were poor in comparison with some of the other methods that did not reproduce the bond length as well. In ^{2}CuS, while there is no experimental distance to compare with, it can be pointed out that the CCSD and CCSD(T) distances with the 6-31G** basis set are lower than the other six entries that are grouped more closely together.

Comparison of calculated and experimental^{29} bond lengths. All values are in Ångstroms. Closest calculated values are in **bold** font.

For ^{2}CuF_{2} and ^{2}CuCl_{2} the experimental bond angles are 180 degrees and this was observed in most instances. The notable exceptions are in ^{2}CuF_{2} at the CCSD/6-31G** and CCSD(T)/6-31G** levels of theory. Here, the linear geometry was predicted to be a transition state and the optimized ground state structure possessed a F-Cu-F angle of approximately 172 degrees, a deviation of eight degrees from the experimental value. This geometric discrepancy surely contributed to the poorly predicted heats of formation for this complex. The Cu-O-H angel in ^{1}CuOH is 110.2 degrees. The calculated bond angles at CCSD/TZVP, CCSD(T)/LACVP** and CCSD(T)/LANL2DZ-TZVP were with 0.2 degrees of the experimental, and all other theory levels agreed within 2.4 degrees. There seems to be no trend relating accuracy in the geometry prediction with the determination of accurate Δ*H _{f}* values.

Heats of formation were calculated for nine CuX_{n} complexes using the CCSD and CCSD(T) coupled cluster methods in conjunction with the 6-31G**, LACVP**, TZVP and LANL2DZ-TZVP basis sets. The best correlation with experimental values were obtained with the CCSD(T)/6-31G** and CCSD(T)/TZVP levels of theory. Applying a second order Douglas-Kroll-Hess relativistic correction at the CCSD(T)/TZVP level of theory resulted in reduction of the absolute average error and RMSD, while a slightly lesser overall improvement was achieved applying the same correction at the CCSD/TZVP level. Clearly for determining Δ*H _{f}* values in these copper complexes the CCSD(T)/TZVP level of theory including a second order DKH relativistic correction is most appropriate when considering standard coupled cluster calculations in conjunction with reasonable basis sets. The fact that the best results were obtained at the CCSD(T)/TZVP level of theory with a relativistic correction for these copper systems is not a trivial observation. Previous DFT studies show that increasing the basis set does not always produce better results, nor does raising the quality of the applied density functional method.

The most accurate prediction of metal-nonmetal bond distances was scattered across the levels of theory investigated. There was also observed to be no correlation between accurate bond length prediction and the determination of an accurate Δ*H _{f}* value. Multiplicities in these CuX

We thank the NIH (GM066859 and GM44974) for supporting this research. MNW wishes to thank the NIH for support in the form of an NRSA postdoctoral fellowship (F32GM079968).

**Supporting Information Available:** Spreadsheets detailing all heat of formation calculations at all investigated levels of theory.

1. Klinman JP. Chem Rev. 1996;96:2541. [PubMed]

2. Solomon EI, Szilagyi RK, DeBeer George S, Basumallick L. Chem Rev. 2004;104:419. [PubMed]

3. Jorgensen KA, Poulsen TB. Chem Rev. 2008;108:2903. [PubMed]

4. Stanley LM, Sibi MP. Chem Rev. 2008;108:2887. [PubMed]

5. Rorabacher DB. Chem Rev. 2004;104:651. [PubMed]

6. Ruiz E, de Graaf C, Alemany P, Alvarez S. J Phys Chem A. 2002;106:4938.

7. Kolmel C, Ahlrichs R. J Phys Chem. 1990;94:5536.

8. Mahe L, Boughdiri SF, Barthelat JC. J Phys Chem A. 1997;101:4224.

9. Terreaux R, Domard M, Viton C, Domard A. Biomacromolecules. 2006;7:31. [PubMed]

10. Balbuena PB, Derosa PA, Seminario JM. J Phys Chem B. 1999;103:2830.

11. Pierloot K, De Kerpel JOA, Ryde U, Olsson MHN, Roos BO. J Am Chem Soc. 1998;120:13156.

12. Elustondo F, Mascetti J, Papai I. J Phys Chem A. 2000;104:3572.

13. Dang L, Zhao H, Lin Z, Marder TB. Organometallics. 2007;26:2824. 4.

14. Yamanaka M, Nakamura E. Organometallics. 2001;20:5675.

15. Cascella M, Cuendet MA, Tavernelli I, Rothlisberger U. J Phys Chem B. 2007;111:10248. [PubMed]

16. Dobrogorskaya Y, Mascetti J, Papai I, Nemukhin A, Hannachi Y. J Phys Chem A. 2003;107:2711.

17. Illias M, Furdik P, Urban M. J Phys Chem A. 1998;102:5263.

18. Dixon DA, Feller D, Peterson KA. J Chem Phys. 2001;115:2576.

19. Feller D, Dixon DA. J Chem Phys. 2001;115:3484.

20. Feller D, Dixon DA, Francisco JS. J Phys Chem A. 2003;107:1604.

21. Pollack L, Windus TL, de Jong WA, Dixon DA. J Phys Chem A. 2005;109:6934. [PubMed]

22. Balabanov NB, Peterson KA. J Chem Phys. 2005;123:064107. [PubMed]

23. Balabenov NB, Peterson KA. J Chem Phys. 2006;125:074110. [PubMed]

24. DeYonker NJ, Peterson KA, Steyl G, Wilson AK, Cundari TR. J Phys Chem A. 2007;111:11269. [PubMed]

25. Li S, Peterson KA, Dixon DA. J Chem Phys. 2008;128:154301. [PubMed]

26. Riley KE, Merz KM. J Phys Chem A. 2007;111:6044. [PubMed]

27. Yang Y, Weaver MN, Merz KM. Assessment of the 6-31+G**/LANL2DZ Basis Set Coupled with Density Functional Theory Methods: Prediction of Heats of Formation and Ionization Potentials for Third Row Transition Metal Complexes. J Phys Chem A. 2008 Submitted for publication. [PMC free article] [PubMed]

28. Weaver MN, Yang Y, Merz KM. Assessment of the CCSD and CCSD(T) Coupled-Cluster Methods in Calculating Heats of Formation for Zn Complexes. J Phys Chem A. 2008 Submitted for publication. [PMC free article] [PubMed]

29. Yungman VS, editor. Thermal Constants of Substances. Vol. 4 Wiley; New York: 1999.

30. Bredow T, Geudtner G, Jug K. J Comput Chem. 2001;22:861.

31. Frisch MJ, Trucks GW, Schlegel HB, Scuseria GE, Robb MA, Cheeseman JR, Montgomery JA, Jr, Vreven T, Kudin KN, Burant JC, Millam JM, Iyengar SS, Tomasi J, Barone V, Mennucci B, Cossi M, Scalmani G, Rega N, Petersson GA, Nakatsuji H, Hada M, Ehara M, Toyota K, Fukuda R, Hasegawa J, Ishida M, Nakajima T, Honda Y, Kitao O, Nakai H, Klene M, Li X, Knox JE, Hratchian HP, Cross JB, Bakken V, Adamo C, Jaramillo J, Gomperts R, Stratmann RE, Yazyev O, Austin AJ, Cammi R, Pomelli C, Ochterski JW, Ayala PY, Morokuma K, Voth GA, Salvador P, Dannenberg JJ, Zakrzewski VG, Dapprich S, Daniels AD, Strain MC, Farkas O, Malick DK, Rabuck AD, Raghavachari K, Foresman JB, Ortiz JV, Cui Q, Baboul AG, Clifford S, Cioslowski J, Stefanov BB, Liu G, Liashenko A, Piskorz P, Komaromi I, Martin RL, Fox DJ, Keith T, Al-Laham MA, Peng CY, Nanayakkara A, Challacombe M, Gill PMW, Johnson B, Chen W, Wong MW, Gonzalez C, Pople JA. Gaussian 03 Revision D.01. Gaussian, Inc.; Wallingford CT: 2004.

32. Cizek J. Adv Chem Phys. 1969;14:35.

33. Purvis GD, Bartlett RJ. J Chem Phys. 1982;76:1910.

34. Scuseria GE, Janssen CL, Schaefer HF., III J Chem Phys. 1988;89:7382.

35. Scuseria GE, Schaefer HF., III J Chem Phys. 1989;90:3700.

36. Pople JA, Head-Gordon M, Raghavachari K. J Chem Phys. 1987;87:5968.

37. Bartlett RJ. J Phys Chem. 1989;93:1697.

38. For references describing the standard abbreviations and basic ab initio methods see the following: **(a) **Hehre WJ, Radom L, Schleyer PvR, Pople JA. Ab Initio Molecular Orbital Theory. Wiley-Interscience; New York: 1986. ** b. **Clark TA. A Handbook of Computational Chemistry. Wiley-Interscience; New York: 1985.

39. Rassolov VA, Pople JA, Ratner MA, Windus TL. J Chem Phys. 1998;109:1223.

40. Schafer A, Huber C, Ahlrichs R. J Chem Phys. 1994;100:5829.

41. The Gaussian white paper dealing with thermochemistry is available on the web at the following URL: http://www.gaussian.com/g_whitepap/thermo.htm.

42. The NIST chemistry WebBook is accessible at the following URL: http://webbook.nist.gov/chemistry/.

43. Langhoff SR, Bauschlicher CW., Jr Chem Phys Lett. 1986;124:241.

44. Douglas M, Kroll NM. Ann Phys. 1974;82:89.

45. Hess BA. Phys Rev A. 1985;32:756. [PubMed]

46. Hess BA. Phys Rev A. 1986;33:3742. [PubMed]

47. Jansen G, Hess BA. Phys Rev A. 1989;39:6016. [PubMed]

48. deJong WA, Harrison RJ, Dixon DA. J Chem Phys. 2001;114:48.

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