Computational Methods in Organometallic Catalysis. Yu Lan
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In DFT, electron density functional is used instead of wavefunction, which provides a better accuracy than HF method. In Kohn–Sham DFT framework, the most difficult multielectron interaction is simplified to a problem of the motion of electrons in an effective potential field without interaction, which includes the influence of external potential field and Coulomb interaction between electrons, such as exchange–correlation interaction. Therefore, DFT method provides an excellent computational efficiency.
In computational organometallic chemistry, the two results we are most concerned about are the activation energy for one pathway and the difference of activation energy between two pathways, which represent the reaction rate and selectivity, respectively. The precision orders required by those two results are 1 and 0.1 kcal/mol, respectively. Although the accuracy of DFT method seems to be insufficient to meet the requirements, the error cancelation makes the accuracy sufficient for the DFT calculations of reaction rate and selectivity.
2.5.2 How to Choose a Density Functional
Strictly, this paragraph may be the least serious part in this book, because the selection of a functional in computational organometallic chemistry has many other reasons, even might be that I like this functional. If there must be a way, the selection of density functional can be based on the targeted benchmark results because of the lack of clear physical meaning leading to the inestimable error. However, there are often insufficient data for that in a specific organometallic system. Therefore, it is rather hard to choose a density functional for computational organometallic chemistry.
Until now, B3LYP functional has always been the preferred functional for theoretical study of reaction mechanism, although it has been proposed for more than 20 years. There are hundreds of density functionals, many of which would perform better than B3LYP in their own field of expertise. However, very few of them have more comprehensive performance than B3LYP, which leads to popularity of that functional. There are two main weaknesses in B3LYP: (i) disregard of dispersion interaction and (ii) the bad performance on charge transfer and Rydberg excitations. The first problem can be completely modified by DFT‐D3 correction without additional computing time. The second one can be solved by the variant CAM‐B3LYP functional. These amendments continue to extend the service life of B3LYP functional.
From a large number of calculation results, M06‐2X, which is a Minnesota series functional proposed by Truhlar in 2007, proved to be one of the best alternative functionals of B3LYP. In this functional, dispersion effect is introduced in its fitting parameters, which reveals good weak interactions. The 54% HF exchange component leads to a better performance on the calculation of charge transfer and Rydberg excitation. The shortcoming is that Minnesota series functionals require much higher accuracy of DFT integration grid than B3LYP. It could be solved by improvement of that; however, it will obviously be more time consuming. Moreover, M06‐2X functional is parameterized for the main group elements; therefore, it is unsuited for the calculation of transition metal involved system. As an alternative, M06‐L functional can be used in this case. It is noteworthy that MN15, also proposed by Truhlar in 2016, achieves a good balance between main group and transition metal elements in computational study.
The ωB97XD functional is another alternative of B3LYP, which is proposed by Head‐Gordon group in 2008 [94, 95]. This functional included empirical dispersion at DFT‐D2 level, which gives a good accuracy of weak interaction. Moreover, the introduction of long‐range correction into ωB97XD gives a good result in the calculation of charge transfer and Rydberg excitation. The time consumed for ωB97XD is also significantly higher than that of B3LYP.
Based on the author's experience, it is better to use hybrid‐GGA or hybrid‐meta‐GGA functionals involving dispersion correction on the geometry and thermodynamics calculation of organometallic system.
2.5.3 How to Choose a Basis Set
Generally, the time taken for DFT calculations is mostly used in the calculation of double‐election integral, which is positively correlated with N4, in which N is the total Gaussian‐type functions for a specific molecule. Therefore, the calculation of time taken for a specific molecule is dependent on the selectivity of basis set for all atoms in this molecule. In fact, the selection of the basis set is also arbitrary, which even could be based on experience and preferences. Fortunately, the accuracy of most DFT methods is not too dependent on the size of selected basis set, while most of large enough basis sets can yield a same result in DFT calculations. Additionally, when the number of base functions for using a basis set is the same, the time spent can be saved by using a basis set with less Gaussian‐type function under the same precision. Therefore, segmented contraction basis sets, such as Pople's basis sets and def2 series of basis sets, are better choice in DFT calculations.
For DFT calculations, regular polarization functions (d,p) are necessary, which can improve the accuracy to a great extent. However, the larger angular momentum functions are unnecessary. A triple‐zeta basis set is usually slightly better than a double‐zeta one. As an example, the basis set of 6‐311G(d,p) for DFT calculations is better than that of 6‐31G(d,p); however, the basis set of 6‐311(3df,2pd) has not shown improvement over that of 6‐311G(d,p). Following this idea, 6‐31G(d) is the smallest acceptable basis set in modern computational organometallic chemistry. The basis set of 6‐311G(d,p) is a better choice for both accuracy and efficiency. When def2 series of basis set is used, def2‐SVP is acceptable, while def2‐TZVP is a better one. In an anionic molecule, defuse function is necessary; therefore, 6‐31+G(d) is the acceptable basis set, while 6‐311++G(d,p) would provide a good accuracy.
For the DFT calculation onto transition metals, employing a pseudo potential basis set is strongly recommended for the consideration of both accuracy and efficiency. In this area, LANL2DZ is the smallest basis set for transition metals, which provides only acceptable accuracy for some geometry optimization. The larger ones, such as LANL2TZ, LANL08, LANL08(d), and LANL08(f), are recommended for 4–6th periodic elements involving transition metals.
Notably, because the accuracy is not obviously dependent on the basis set in geometry optimizations and harmonic vibrational frequency calculations, while the time consumption is large, a smaller basis set usually can be chosen, such as 6‐31G(d), 6‐31+G(d), def2‐SVP, or LANL2DZ. By contrast, larger basis sets are often more suitable in the single‐point calculations with high accuracy, such as 6‐311G(d,p), 6‐311+G(d,p), def2‐TZVP, LANL08 series. Additionally, for some highly parameterized functionals, a basis set consistent with that used in parameterizations is recommended in both geometry optimization and single‐point energy calculation. As an example, a basis set of 6‐311+G(d,p) is recommended for the DFT calculation with M06‐2X functional by that reason.
2.6 Revealing a Mechanism for An Organometallic Reaction by Theoretical Calculations
It has been more than 20 years since the computational tool became a powerful and popular way to reveal the mechanism for organic and organometallic reactions, which starts with the development of density functionals that gave excellent geometries and reasonable energetics for organic and organometallic compounds. Generally, the approach to the exploration of reaction mechanism and catalytic cycle involves the use of calculations to test hypotheses.
Collaboration with experimental chemists is helpful for the theoretical study of reaction mechanism. The proposed reaction mechanism can be assumed based on the known reaction conditions, phenomena obtained from experiments, and previous experience. Several possible mechanisms can be presumed, but each of them should be reasonable and not contradictory to the present experimental observations. In computational organometallic chemistry, the proposed reaction mechanism needs to involve all stationary points on the whole reaction