Y. A. Aoto, A. P. de Lima Batista, A. Köhn, A. G. S. de Oliveira-Filho,

Contributed by Theo Keane

When performing calculations of any kind, it is important to establish how accurate a method one intends to use is for a given application. Transition metals (TMs) are often problematic systems for computational chemists, because they exhibit “strong correlation”, i.e. either static or dynamic correlation is significant in systems that contain TMs (usually both). This paper adds to the existing literature of benchmark results for TM compounds by performing some rather high-level calculations on 60 diatomic TM compounds. I believe this is intended to improve upon the recent 3dMLBE20 set of Truhlar and co-workers,[1] which was criticised in a pair of papers published in early 2017.[2,3]

In this new benchmarking set, 43 molecules contain first row TMs, 7 contain Ru, Rh or Ag, and the remaining 10 contain Ir, Pt and Au. The multiplicities range from 1 to 7. For these molecules they have assembled experimental data, including bond length, harmonic vibrational frequency and bond dissociation energies. Single reference benchmark values were obtained via (RO/U)CCSD(T)/aug-cc-pwCVnZ-PP[4d, 5d metals]aug-cc-pwCVnZ[else], with n = T, Q, 5, and were extrapolated to the Complete-Basis-Set (CBS) limit. They also investigated the effect of core-valence correlation on the single-reference values. Furthermore, internally contracted Multi-Reference CCSD(T) (icMRCCSD(T)) calculations were performed in the aug-cc-pwCVTZ(-PP) basis, based on full-valence CASSCF reference wavefunctions to investigate the effect of static correlation – the full details of the chosen active spaces are provided in the SI (Table S6). Finally, relativistic effects were considered: scalar relativistic corrections were obtained by comparing frozen core CCSD(T)/aug-cc-pwCVTZ(-PP) calculations with and without the 2nd-order Douglas-Kroll-Hess (DKH2) Hamiltonian. For the 4d and 5d TM containing molecules, Spin-Orbit corrections were obtained from CASSCF calculations with full valence active spaces and the full, 2 electron Breit-Pauli operator. It is important to note that, with the exception of the SO correction, these corrections were not merely calculated for the equilibrium geometry, rather these were calculated at multiple points along the bond length. Overall, the authors have clearly spent a great deal of care ensuring that their ‘benchmark level’ calculations are truly deserving of the title.

An interesting thing to note is that multi-reference, spin-orbit and core-valence correlation corrections all appear to be very weak and sometimes do not improve the agreement with experiment (Table 3). CBS extrapolation is by far the major way to reduce error. This is very important to bear in mind when looking at previous benchmarking results. The authors also note that the usual ‘multireference’ diagnostics are practically useless: there is weak correlation between diagnostics and, more critically, there is very weak correlation between any of the diagnostics and the magnitude of any MR corrections. The M diagnostic[4] is the best performing one; however, it still fails for approximately 30% of cases and yields both false positives and false negatives. The authors also briefly investigate the effect of including 4f orbitals into the correlation treatment for Ir and Pt and find that this has a very weak effect on their results (SI, Table S5).

Finally, the authors use their new benchmark set to rank some functionals. Overall, at the DFT/aug-cc-pVQZ + DKH2 correction level, it appears that hybrid functionals performs on average the best for bond-dissociation energies and equilibrium distances, when compared to the fully corrected results (Table 7). On the other hand, pure functionals perform better for harmonic frequencies. In agreement with the conclusions of the original 3dMLBE20 paper, it is clear that many functionals beat plain CCSD(T)(FC)/aug-cc-pwCVTZ. This reinforces the critical need for CBS extrapolation when performing CC calculations.

(1) Xu, X.; Zhang, W.; Tang, M.; Truhlar, D. G. Do Practical Standard Coupled Cluster Calculations Agree Better than Kohn–Sham Calculations with Currently Available Functionals When Compared to the Best Available Experimental Data for Dissociation Energies of Bonds to 3 D Transition Metals? J. Chem. Theory Comput. 2015, 11 (5), 2036–2052 DOI: 10.1021/acs.jctc.5b00081.

(2) Cheng, L.; Gauss, J.; Ruscic, B.; Armentrout, P. B.; Stanton, J. F. Bond Dissociation Energies for Diatomic Molecules Containing 3d Transition Metals: Benchmark Scalar-Relativistic Coupled-Cluster Calculations for 20 Molecules. J. Chem. Theory Comput. 2017, 13 (3), 1044–1056 DOI: 10.1021/acs.jctc.6b00970.

(3) Fang, Z.; Vasiliu, M.; Peterson, K. A.; Dixon, D. A. Prediction of Bond Dissociation Energies/Heats of Formation for Diatomic Transition Metal Compounds: CCSD(T) Works. J. Chem. Theory Comput. 2017, 13 (3), 1057–1066 DOI: 10.1021/acs.jctc.6b00971.

(4) Tishchenko, O.; Zheng, J.; Truhlar, D. G. Multireference Model Chemistries for Thermochemical Kinetics. J. Chem. Theory Comput. 2008, 4 (8), 1208–1219 DOI: 10.1021/ct800077r.

*J. Chem. Theor. Comput.*, 2017Contributed by Theo Keane

Copyright 2017 American Chemical Society

When performing calculations of any kind, it is important to establish how accurate a method one intends to use is for a given application. Transition metals (TMs) are often problematic systems for computational chemists, because they exhibit “strong correlation”, i.e. either static or dynamic correlation is significant in systems that contain TMs (usually both). This paper adds to the existing literature of benchmark results for TM compounds by performing some rather high-level calculations on 60 diatomic TM compounds. I believe this is intended to improve upon the recent 3dMLBE20 set of Truhlar and co-workers,[1] which was criticised in a pair of papers published in early 2017.[2,3]

In this new benchmarking set, 43 molecules contain first row TMs, 7 contain Ru, Rh or Ag, and the remaining 10 contain Ir, Pt and Au. The multiplicities range from 1 to 7. For these molecules they have assembled experimental data, including bond length, harmonic vibrational frequency and bond dissociation energies. Single reference benchmark values were obtained via (RO/U)CCSD(T)/aug-cc-pwCVnZ-PP[4d, 5d metals]aug-cc-pwCVnZ[else], with n = T, Q, 5, and were extrapolated to the Complete-Basis-Set (CBS) limit. They also investigated the effect of core-valence correlation on the single-reference values. Furthermore, internally contracted Multi-Reference CCSD(T) (icMRCCSD(T)) calculations were performed in the aug-cc-pwCVTZ(-PP) basis, based on full-valence CASSCF reference wavefunctions to investigate the effect of static correlation – the full details of the chosen active spaces are provided in the SI (Table S6). Finally, relativistic effects were considered: scalar relativistic corrections were obtained by comparing frozen core CCSD(T)/aug-cc-pwCVTZ(-PP) calculations with and without the 2nd-order Douglas-Kroll-Hess (DKH2) Hamiltonian. For the 4d and 5d TM containing molecules, Spin-Orbit corrections were obtained from CASSCF calculations with full valence active spaces and the full, 2 electron Breit-Pauli operator. It is important to note that, with the exception of the SO correction, these corrections were not merely calculated for the equilibrium geometry, rather these were calculated at multiple points along the bond length. Overall, the authors have clearly spent a great deal of care ensuring that their ‘benchmark level’ calculations are truly deserving of the title.

An interesting thing to note is that multi-reference, spin-orbit and core-valence correlation corrections all appear to be very weak and sometimes do not improve the agreement with experiment (Table 3). CBS extrapolation is by far the major way to reduce error. This is very important to bear in mind when looking at previous benchmarking results. The authors also note that the usual ‘multireference’ diagnostics are practically useless: there is weak correlation between diagnostics and, more critically, there is very weak correlation between any of the diagnostics and the magnitude of any MR corrections. The M diagnostic[4] is the best performing one; however, it still fails for approximately 30% of cases and yields both false positives and false negatives. The authors also briefly investigate the effect of including 4f orbitals into the correlation treatment for Ir and Pt and find that this has a very weak effect on their results (SI, Table S5).

Finally, the authors use their new benchmark set to rank some functionals. Overall, at the DFT/aug-cc-pVQZ + DKH2 correction level, it appears that hybrid functionals performs on average the best for bond-dissociation energies and equilibrium distances, when compared to the fully corrected results (Table 7). On the other hand, pure functionals perform better for harmonic frequencies. In agreement with the conclusions of the original 3dMLBE20 paper, it is clear that many functionals beat plain CCSD(T)(FC)/aug-cc-pwCVTZ. This reinforces the critical need for CBS extrapolation when performing CC calculations.

(1) Xu, X.; Zhang, W.; Tang, M.; Truhlar, D. G. Do Practical Standard Coupled Cluster Calculations Agree Better than Kohn–Sham Calculations with Currently Available Functionals When Compared to the Best Available Experimental Data for Dissociation Energies of Bonds to 3 D Transition Metals? J. Chem. Theory Comput. 2015, 11 (5), 2036–2052 DOI: 10.1021/acs.jctc.5b00081.

(2) Cheng, L.; Gauss, J.; Ruscic, B.; Armentrout, P. B.; Stanton, J. F. Bond Dissociation Energies for Diatomic Molecules Containing 3d Transition Metals: Benchmark Scalar-Relativistic Coupled-Cluster Calculations for 20 Molecules. J. Chem. Theory Comput. 2017, 13 (3), 1044–1056 DOI: 10.1021/acs.jctc.6b00970.

(3) Fang, Z.; Vasiliu, M.; Peterson, K. A.; Dixon, D. A. Prediction of Bond Dissociation Energies/Heats of Formation for Diatomic Transition Metal Compounds: CCSD(T) Works. J. Chem. Theory Comput. 2017, 13 (3), 1057–1066 DOI: 10.1021/acs.jctc.6b00971.

(4) Tishchenko, O.; Zheng, J.; Truhlar, D. G. Multireference Model Chemistries for Thermochemical Kinetics. J. Chem. Theory Comput. 2008, 4 (8), 1208–1219 DOI: 10.1021/ct800077r.