Chapter 2
Computational Methods in Rh-Catalyzed
C–H Functionalization
Cheng-Xing Cui, Song Liu, Chun-Xiang Li, Ruopeng Bai, and Yu Lan
2.1 DFT Method
The theoretical treatment of a polyatomic molecular involves the ab initio method,
the semiempirical method, the density-functional theory (DFT) method, and the
molecular-mechanics method. An ab initio method [1–4] calculates the electronic
wavefunction of a molecule by using the correct Hamiltonian [5] to solve the
Schrödinger equation. However, a semiempirical molecular quantum mechanical
method [6, 7] uses a simpler Hamiltonian than the correct molecular Hamiltonian.
In the semiempirical method, experimental data or results from ab initio calculations
were adopted to adjust the values of parameters. A DFT method [8, 9] calculates
the molecular electron probability density ρ rather than molecular wavefunction
and then calculates the molecular electronic energy from ρ. A molecular mechanics
method [10] views the polyatomic molecule as a collection of atoms, which are held
together by bonds. The molecular mechanics method obtains the molecular energy
without wavefunction but in terms of force constants for bond bending, stretching,
torsion, and other parameters. Consequently, the molecular mechanics method is not
a quantum mechanical method.
The solution of Schrödinger equation with ab initio method needs to deal with
3n variables for an n-electron system. Meanwhile, only three variables should be
considered for the electron probability density ρ in the DFT method. As a result,
for the computational studies of Rh-catalyzed C–H bond activation, DFT method
was always the first choice, which could give an adequate compromise between
computational consumption and accuracy.
There is no unified standard for the classification of density functionals in the physical chemistry field. As shown in Fig. 2.1, J. P. Perdew proposed using the “Jacob’s
ladder” to classify the level of functionals [11]. The ground in “Jacob’s ladder” is HF
theory, which is an imprecise method including neither exchange energy nor correlation energy. The first rung in “Jacob’s ladder” is the functional based on L(S)DA,
the variable in this kind of functional is the local spin density. The second rung in
© The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2021
Y. Lan et al., Computational Advances of Rh-Catalyzed C–H Functionalization,
SpringerBriefs in Molecular Science,
https://doi.org/10.1007/978-981-16-0432-4_2
19
Computational Methods in Rh-Catalyzed
C–H Functionalization
Cheng-Xing Cui, Song Liu, Chun-Xiang Li, Ruopeng Bai, and Yu Lan
2.1 DFT Method
The theoretical treatment of a polyatomic molecular involves the ab initio method,
the semiempirical method, the density-functional theory (DFT) method, and the
molecular-mechanics method. An ab initio method [1–4] calculates the electronic
wavefunction of a molecule by using the correct Hamiltonian [5] to solve the
Schrödinger equation. However, a semiempirical molecular quantum mechanical
method [6, 7] uses a simpler Hamiltonian than the correct molecular Hamiltonian.
In the semiempirical method, experimental data or results from ab initio calculations
were adopted to adjust the values of parameters. A DFT method [8, 9] calculates
the molecular electron probability density ρ rather than molecular wavefunction
and then calculates the molecular electronic energy from ρ. A molecular mechanics
method [10] views the polyatomic molecule as a collection of atoms, which are held
together by bonds. The molecular mechanics method obtains the molecular energy
without wavefunction but in terms of force constants for bond bending, stretching,
torsion, and other parameters. Consequently, the molecular mechanics method is not
a quantum mechanical method.
The solution of Schrödinger equation with ab initio method needs to deal with
3n variables for an n-electron system. Meanwhile, only three variables should be
considered for the electron probability density ρ in the DFT method. As a result,
for the computational studies of Rh-catalyzed C–H bond activation, DFT method
was always the first choice, which could give an adequate compromise between
computational consumption and accuracy.
There is no unified standard for the classification of density functionals in the physical chemistry field. As shown in Fig. 2.1, J. P. Perdew proposed using the “Jacob’s
ladder” to classify the level of functionals [11]. The ground in “Jacob’s ladder” is HF
theory, which is an imprecise method including neither exchange energy nor correlation energy. The first rung in “Jacob’s ladder” is the functional based on L(S)DA,
the variable in this kind of functional is the local spin density. The second rung in
© The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2021
Y. Lan et al., Computational Advances of Rh-Catalyzed C–H Functionalization,
SpringerBriefs in Molecular Science,
https://doi.org/10.1007/978-981-16-0432-4_2
19