2.3 BOLS-NEP-LBA Notion
31
2.3.2 BOLS-NEP Notion for the Undercoordinated Atoms
2.3.2.1 BOLS: Undercoordination Induced Bond Contraction
According to the BOLS correlation premise [2, 12], bond order loss shortens and
strengthens bonds between undercoordinated atoms, as illustrated in Fig. 2.2b. Bond
contraction densifies the local bonding charge, binding energy, and atomic mass;
bond strength gain deepens the potential well and shifts the core levels accordingly.
The following formulates the BOLS notion [13],
⎧
⎪ ⎪ ⎨
⎪ ⎪ ⎩
C z = d z /d b = 2{1 + exp[(12 − z)/(8z)]}
−1
(bond length)
C
−m
z
= E z /E b
(bond energy)
C
−(m+λ)
z
=
E z /d
λ
z
/
E b /d
λ
b
(energy density)
z ib C
−m
z
= z E z /(z b E b )
( atomic cohesive energy)
(2.5)
The bond nature index m correlates the bond energy to its length of a specific
substance. λ = 1 defines a monoatomic chain and λ = 2 the monoatomic sheets or
single walled nanotube. λ = 3 is the general case of three-dimensional solid. The
C z is universal to match the CN-resolved atomic distance of carbon nanotubes, Au
nanoparticles, Au, Pt, Ir, Ti, Zr, and Zn atomic chains, as well as skins of Fe, Ni, Ru,
Re, W and diamond [12, 14].
The BOLS notion also defines the CN dependence of the reduced bond length
d z , bond energy E z , BE density E den , and atomic cohesive energy E coh at the undercoordinated atomic site in a dimensionless form. These key quantities determine the
behavior of a substance at these under-coordinated atomic sites, as they link the local
atomistic bonding identities to macroscopic properties, such as adhesion ability,
diffusivity, elasticity, reactivity, strength, wettability, and so on so forth [12].
2.3.2.2 NEP: Strong Localization
Conversely, the densely, locally entrapped bonding and core electrons in turn polarize
the nonbonding electrons of the undercoordinated rim atoms [15, 16]. The polarized
states (P) in turn screen and split the local potential that offsets the entrapped core
bands negatively. Negative CLS may not happen if the specific CL is too deep or the
extent of polarization is insufficiently high. Therefore, it is not surprising that some
materials show positive and some others show negative or mixed CLS [17].
However, the polarization is subject to the availability of nonbonding electrons
[12, 15]. The nonbonding electrons refer to those composed of dipoles induced by the
lone pairs of O, N, and F, the unpaired dangling bond of C and Si at defect edges, and
the otherwise conduction unpaired electrons of metals at undercoordinated atomic
sites. The polarization raises the nonbonding states in energy toward or cross over
the E F [15]. Such CN-resolved local bond strain, electron densification, entrapment,
polarization and its effect on potential screening and splitting may explain the “defect
31
2.3.2 BOLS-NEP Notion for the Undercoordinated Atoms
2.3.2.1 BOLS: Undercoordination Induced Bond Contraction
According to the BOLS correlation premise [2, 12], bond order loss shortens and
strengthens bonds between undercoordinated atoms, as illustrated in Fig. 2.2b. Bond
contraction densifies the local bonding charge, binding energy, and atomic mass;
bond strength gain deepens the potential well and shifts the core levels accordingly.
The following formulates the BOLS notion [13],
⎧
⎪ ⎪ ⎨
⎪ ⎪ ⎩
C z = d z /d b = 2{1 + exp[(12 − z)/(8z)]}
−1
(bond length)
C
−m
z
= E z /E b
(bond energy)
C
−(m+λ)
z
=
E z /d
λ
z
/
E b /d
λ
b
(energy density)
z ib C
−m
z
= z E z /(z b E b )
( atomic cohesive energy)
(2.5)
The bond nature index m correlates the bond energy to its length of a specific
substance. λ = 1 defines a monoatomic chain and λ = 2 the monoatomic sheets or
single walled nanotube. λ = 3 is the general case of three-dimensional solid. The
C z is universal to match the CN-resolved atomic distance of carbon nanotubes, Au
nanoparticles, Au, Pt, Ir, Ti, Zr, and Zn atomic chains, as well as skins of Fe, Ni, Ru,
Re, W and diamond [12, 14].
The BOLS notion also defines the CN dependence of the reduced bond length
d z , bond energy E z , BE density E den , and atomic cohesive energy E coh at the undercoordinated atomic site in a dimensionless form. These key quantities determine the
behavior of a substance at these under-coordinated atomic sites, as they link the local
atomistic bonding identities to macroscopic properties, such as adhesion ability,
diffusivity, elasticity, reactivity, strength, wettability, and so on so forth [12].
2.3.2.2 NEP: Strong Localization
Conversely, the densely, locally entrapped bonding and core electrons in turn polarize
the nonbonding electrons of the undercoordinated rim atoms [15, 16]. The polarized
states (P) in turn screen and split the local potential that offsets the entrapped core
bands negatively. Negative CLS may not happen if the specific CL is too deep or the
extent of polarization is insufficiently high. Therefore, it is not surprising that some
materials show positive and some others show negative or mixed CLS [17].
However, the polarization is subject to the availability of nonbonding electrons
[12, 15]. The nonbonding electrons refer to those composed of dipoles induced by the
lone pairs of O, N, and F, the unpaired dangling bond of C and Si at defect edges, and
the otherwise conduction unpaired electrons of metals at undercoordinated atomic
sites. The polarization raises the nonbonding states in energy toward or cross over
the E F [15]. Such CN-resolved local bond strain, electron densification, entrapment,
polarization and its effect on potential screening and splitting may explain the “defect