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P. Veerakumar et al.
the reaction, tunability of the catalyst, and the choice of solvent toward reactivity
and selectivity, etc. which play vital roles in catalysis [3]. The electronic structure
calculations by DFT are useful for characterizing the chemical and physical
properties of bare and functionalized materials [4, 5]. As such, many graphenebased nanomaterials and related catalysis have been explored and designed with
implementation of the classes.
Plane-wave density functional theory (DFT) is a powerful tool for gaining insight
into bulk and surface structures at accurate, atomic level. The delocalized nature of
the plane-wave basis set hinders the application of many powerful post-computation
analysis approaches, many of which rely on localized atom-centered basis sets [6].
Traditionally, this gap has been bridged via projection-based techniques from a
plane-wave to atom-centered basis. Many numerical methods have been developed
to solve plane-wave DFT. It has been popularly classified as three methods including
Gaussian basis set methods, linear-augmented-plane-wave (LAPW) methods, and
pseudopotential plane-wave (PSPW) methods. All three methods can be made very
accurate and have been capable of predicting structures, frequencies, and energetics
for a wide class of compounds [7]. However, the current consensus in the quantum
chemistry and condensed matter physics communities reflects that only the first two
of these three methods are straightforward to apply for first-row transition metals.
It would be beneficial for PSPW methods to work well for these systems, because
Gaussian basis set and LAPW methods lack certain capabilities. In particular, PSPW
methods can perform ab initio molecular dynamics extremely efficiently and treat
unit cells up to a few hundred atoms. Another advantage of PSPW methods is their
transferability from molecules to surfaces to solids. In contrast, Gaussian-based
methods have different basis set requirements for gas and solid phase applications,
complicating the transferability of these methods [8]. Plane-wave DFT calculations
were usually performed using commercially available programs such as VASP [9],
SIESTA [10], CASTEP [10], ABINIT [11], and Quantum ESPRESSO [12] program
packages.
Recently, the modern density functional theory is molecular orbital DFT (like
valence bond and molecular orbital theory) as a very efficient additional tool
in the arsenal of computational methods rather than a perfectly different theory,
which is used orthogonal to traditional approaches [13]. A wave function for a
single electron is called a molecular orbital (MO). The MO with spatial and spin
coordinates are called spin orbitals and are products of a spatial orbital and a spin
function. The lowest unoccupied molecular orbital (LUMO) in DFT has as much
meaning in describing electron addition as the highest occupied molecular orbital
(HOMO) in describing electron removal [14]. Molecular orbital DFT calculations
were performed using Gaussian [15], ADF [16], and TURBOMOLE [17] program
packages, to investigate important atomic and molecular properties as well as some
selected areas of application.
The DFT results over graphene-based catalysts have been widely used for
determining the rate-limiting step [18], active sites [19], adsorption and activation
mechanisms [20], activation energy [21], and catalytic pathways [22], which cover
almost all catalysis-related topics. Perhaps one of the most illustrious examples
P. Veerakumar et al.
the reaction, tunability of the catalyst, and the choice of solvent toward reactivity
and selectivity, etc. which play vital roles in catalysis [3]. The electronic structure
calculations by DFT are useful for characterizing the chemical and physical
properties of bare and functionalized materials [4, 5]. As such, many graphenebased nanomaterials and related catalysis have been explored and designed with
implementation of the classes.
Plane-wave density functional theory (DFT) is a powerful tool for gaining insight
into bulk and surface structures at accurate, atomic level. The delocalized nature of
the plane-wave basis set hinders the application of many powerful post-computation
analysis approaches, many of which rely on localized atom-centered basis sets [6].
Traditionally, this gap has been bridged via projection-based techniques from a
plane-wave to atom-centered basis. Many numerical methods have been developed
to solve plane-wave DFT. It has been popularly classified as three methods including
Gaussian basis set methods, linear-augmented-plane-wave (LAPW) methods, and
pseudopotential plane-wave (PSPW) methods. All three methods can be made very
accurate and have been capable of predicting structures, frequencies, and energetics
for a wide class of compounds [7]. However, the current consensus in the quantum
chemistry and condensed matter physics communities reflects that only the first two
of these three methods are straightforward to apply for first-row transition metals.
It would be beneficial for PSPW methods to work well for these systems, because
Gaussian basis set and LAPW methods lack certain capabilities. In particular, PSPW
methods can perform ab initio molecular dynamics extremely efficiently and treat
unit cells up to a few hundred atoms. Another advantage of PSPW methods is their
transferability from molecules to surfaces to solids. In contrast, Gaussian-based
methods have different basis set requirements for gas and solid phase applications,
complicating the transferability of these methods [8]. Plane-wave DFT calculations
were usually performed using commercially available programs such as VASP [9],
SIESTA [10], CASTEP [10], ABINIT [11], and Quantum ESPRESSO [12] program
packages.
Recently, the modern density functional theory is molecular orbital DFT (like
valence bond and molecular orbital theory) as a very efficient additional tool
in the arsenal of computational methods rather than a perfectly different theory,
which is used orthogonal to traditional approaches [13]. A wave function for a
single electron is called a molecular orbital (MO). The MO with spatial and spin
coordinates are called spin orbitals and are products of a spatial orbital and a spin
function. The lowest unoccupied molecular orbital (LUMO) in DFT has as much
meaning in describing electron addition as the highest occupied molecular orbital
(HOMO) in describing electron removal [14]. Molecular orbital DFT calculations
were performed using Gaussian [15], ADF [16], and TURBOMOLE [17] program
packages, to investigate important atomic and molecular properties as well as some
selected areas of application.
The DFT results over graphene-based catalysts have been widely used for
determining the rate-limiting step [18], active sites [19], adsorption and activation
mechanisms [20], activation energy [21], and catalytic pathways [22], which cover
almost all catalysis-related topics. Perhaps one of the most illustrious examples