228
M. J. Toda et al.
ligation. However, more noticeable changes are apparent when substituents of the
conjugated ring are changed [16].
6 Importance of Electronically Excited States: Relevance of
DFT and TD-DFT in Electronic Structure Calculations
The ground- and excited-state properties of cobalamins can be represented well by
using DFT and TD-DFT methods, respectively. Although wave function-based methods are more accurate, they are simply far too expensive to apply to systems as large
as cobalamins. Alternatively, DFT is a method not based on the wave function but
is based on inhomogeneous electron gas, typically referred to as electron density.
DFT efficiently scales with system size and is applicable to large systems. TDDFT can be viewed as an extension of DFT but is used to study properties related to
time-dependent potentials. Analogous to the Hohenberg–Kohn theorem in DFT is the
Runge–Gross theorem in TD-DFT [74]. In TD-DFT, the many-body time-dependent
Schrodinger equation is replaced with a set of time-dependent single-particle equations [10]. TD-DFT has become a widely used tool to study the electronically excited
states of complex systems, including cobalamins. Vertical excitation energies and
transition dipole moments at a particular geometry can be calculated using TD-DFT.
Excitation energies tend to agree with experiment within 0.3 eV, but typically calculated excitation energies require a shift to the red to yield much better agreement
with experiment [65]. With that being said, the proper description of electronically
excited states within the TD-DFT framework is dependent on functional choice. A
common practice is to rely on benchmark studies to determine the most appropriate functional to use for a particular system. There have been several studies that
sought to determine the proper functionals to use for both ground- and excited-state
properties of cobalamins, and these will be discussed in detail in Sects. 7 and 8.
7 Co–C Bond Strength: Key to Theoretical Benchmarks
There are several challenges to overcome when studying cobalamins computationally, including the system size and the presence of a transition metal. The former
can be resolved by using a truncated cofactor in simulations (Fig. 1). This typically
involves replacing all side chains with hydrogens, replacing the lower axial DBI base
with a much simpler imidazole (Im) ligand, while maintaining the structural integrity
of the upper axial ligand. These truncated models have less than 70 atoms and provide
a good agreement with relevant known structural details from high-quality crystal
structures. Due to system size, DFT has become the method of choice for studying cobalamins. The ground-state prediction by DFT of various cobalamins is well
understood. This is exemplified by the results of a theoretical investigation of the
M. J. Toda et al.
ligation. However, more noticeable changes are apparent when substituents of the
conjugated ring are changed [16].
6 Importance of Electronically Excited States: Relevance of
DFT and TD-DFT in Electronic Structure Calculations
The ground- and excited-state properties of cobalamins can be represented well by
using DFT and TD-DFT methods, respectively. Although wave function-based methods are more accurate, they are simply far too expensive to apply to systems as large
as cobalamins. Alternatively, DFT is a method not based on the wave function but
is based on inhomogeneous electron gas, typically referred to as electron density.
DFT efficiently scales with system size and is applicable to large systems. TDDFT can be viewed as an extension of DFT but is used to study properties related to
time-dependent potentials. Analogous to the Hohenberg–Kohn theorem in DFT is the
Runge–Gross theorem in TD-DFT [74]. In TD-DFT, the many-body time-dependent
Schrodinger equation is replaced with a set of time-dependent single-particle equations [10]. TD-DFT has become a widely used tool to study the electronically excited
states of complex systems, including cobalamins. Vertical excitation energies and
transition dipole moments at a particular geometry can be calculated using TD-DFT.
Excitation energies tend to agree with experiment within 0.3 eV, but typically calculated excitation energies require a shift to the red to yield much better agreement
with experiment [65]. With that being said, the proper description of electronically
excited states within the TD-DFT framework is dependent on functional choice. A
common practice is to rely on benchmark studies to determine the most appropriate functional to use for a particular system. There have been several studies that
sought to determine the proper functionals to use for both ground- and excited-state
properties of cobalamins, and these will be discussed in detail in Sects. 7 and 8.
7 Co–C Bond Strength: Key to Theoretical Benchmarks
There are several challenges to overcome when studying cobalamins computationally, including the system size and the presence of a transition metal. The former
can be resolved by using a truncated cofactor in simulations (Fig. 1). This typically
involves replacing all side chains with hydrogens, replacing the lower axial DBI base
with a much simpler imidazole (Im) ligand, while maintaining the structural integrity
of the upper axial ligand. These truncated models have less than 70 atoms and provide
a good agreement with relevant known structural details from high-quality crystal
structures. Due to system size, DFT has become the method of choice for studying cobalamins. The ground-state prediction by DFT of various cobalamins is well
understood. This is exemplified by the results of a theoretical investigation of the