Supporting materials
SI Theoretical Backgrounds
SI.1 Breaking of orbital and spin symmetries
In the supporting material a brief explanation of our generalized molecular orbital (GMO)
approach to unstable molecule is presented in comparison with the valence-bond (VB) approach
since the mathematical formulation is completely neglected in the text. The closed-shell molecular
orbital (MO) picture often breaks down in the case of unstable molecules with diradical character,
indicating the existence of more stable broken-symmetry (BS) solutions.
Therefore we first
construct BS Hartree-Fock (HF), BS Kohn-Sham density functional theory (DFT) and their hybrid
solutions such as UB3LYP for diradical and polyradical species.
In order to obtain the localized
MO (LMO) picture used in Fig. 2 (see text), the first-order density matrix ( 1(r1,r2 )) of these BS
solutions is diagonalized as [91]
1(r1,r2 )    i†i ds   nii†i ,
i

i
(S1)
where  i denotes the BS MO i, and  i and n i mean, respectively, the natural molecular orbitals
(NMO) and the occupation number. The BS MOs are expressed with the bonding and antibonding


NMOs pair as
 i  cos i + sin  i*


(S2a)
 i–  cos i  sin  i*


(S2b)
where  denotes the orbital mixing parameter.
Since  i and  i* are symmetry-adapted and
usually belong to different spatial symmetries, BS MOs are often spatially symmetry-broken.
The orbital overlap Ti between BS MOs under the NMO approximation is defined as


(S3)
Ti = i+ i–  cos2 .
Then Ti becomes 1.0 in the case of the closed-shell case;  i+   i–   i , whereas Ti is 0.0 for the
complete mixing case (= /4). In order to express the decrease of chemical bonding via orbital
 the effective bond order b is defined by
symmetry breaking,

n i  n *i 1 cos2   1 cos2 
bi 

(S4a)
2
2
 cos2  Ti,

where n i and n *i denote the occupation numbers of the bonding and antibonding NMOs,
respectively. The effective bond order (b) is nothing but the orbital overlap between BS MOs under

the generalized MO approximation. The localized MO (LMO) are defined as the completely spin


polarized BS MOs as
i+    4 

(S4b)
1
i  i*  LMOa

2
(S5a)
1
i–    4 
1
 i   i*   LMOb,

2
(S5b)
where LMOa and LMOb are more or less localized on the sites a and b of molecular systems,

respectively. The LMOs are utilized for derivation of localized MO pictures of unstable molecules
as illustrated in Fig. 2 in the text.
However, it is noteworthy that LMOs are quite different from the
atomic orbitals (AO) in the simple valence-bond (VB) theory since LMO are orthogonal and still
molecular orbitals in nature.
Then the expression of LMOs with AO-like orbitals in Fig. 2 is
symbolic and qualitative for lucid understanding of diradicals and polydiradical species. We can
depict their exact shapes with the computer graphics as shown in this series of papers.
The delocalized MO picture via NMO can be transformed into LMO picture. To this end, the
BS MOs in eq. S2 are re-expressed with LMOs as follows


 i  cos LMOa + sin  LMOb
(S6a)
 i–  cos LMOb + sin  LMOa ,
(S6b)
where the mixing parameter  is given by    4 .
Then the BS MO configuration can be
expanded with using LMOs as
BSI   i i


 cos LMOa +sin  LMOb  cos LMOb +sin  LMOa








1
 2 cos2SD  2TD  sin2ZWa  ZWb ,
2
(S7a)
(S7b)
where the pure singlet (SD) and triplet (TD) diradical wavefunctions are given by


(S8a)


(S8b)
SD 
1
LMOa LMOb  LMOb LMOa
2
TD 
1
 LMOa  LMOb   LMOb  LMOa .
2
On the other hand, zwitterionic (ZW) configurations are resulted from the charge transfer from
LMOa to LMOb (vice versa) as follows:
ZWa  LMOa LMOa , ZWb  LMOb LMOb .
(S9)
The low-spin (LS) BSI MO configuration involves the pure triplet DR (TD) component, showing the

spin-symmetry breaking property. This in turn indicates that BS solution more or less
overestimates the diradical character, suggesting the necessity of careful examination of diradical
mechanism concluded with the BS calculations in general.
Similarly, the low-spin (LS) BSII MO
configuration is expressed by
BSII   i– i
(S10)
1
2
cos2



2

sin2




.
 ZWa ZWb 

SD
TD
2
The LS BSII MO solution also involves the pure triplet component. Thus both orbital and spin


2
symmetry breakings are inevitable for diradical species in the case of the single-determinant
(reference) BS solution on the basis of the independent particle model.
However, both orbital and
spin symmetries are conserved in finite systems, leading to the recovery of them.
SI.2 Recovery of symmetry breaking
The BSI and BSII solutions are degenerate in energy.
Then the quantum-mechanical
resonance of them is feasible as follows:
RBS(+) 


RBS(–) 



1
BSI  BSII 
2
(S11a)
1
 2 cos2SD  sin2ZWa  ZWb ,
2
(S11b)
1
BSI  BSII 
2
(S12a)
 TD.
(S12b)
Thus the in- and out-of-phase resonating BS (RBS) solutions are nothing but the pure singlet and
triplet states wave functions, respectively.
The chemical bonding between a and b sites is
expressed with the mixing of the SD and ZW configurations under the LMO approximation. The
valence-bond (VB)-type configuration interaction (CI) explanation of electronic structures becomes
feasible under the LMO approximation. For example, the effective bond order becomes zero for
the pure SD state, but it increases with the increase of mixing with the ZW configuration until the
ZW/SD ratio becomes 1.0, namely closed-shell limit: it is noteworthy that BS solutions in eqs. (S7b)
and (S10) involve the ZW configuration partly in the VB CI scheme.
In order to obtain the effective bond order for the RBS(+) solution, it is transformed into the
symmetry-adapted NMO expression as
1 cos2   1 cos2  ,
2(1 T )
1
RBS(+) 
i
2
*
i
i
(S13)
*
i
i
where the first and second terms denote the ground and doubly excited configurations, respectively,

in the MO-CI and 2x2 CASSCF approaches. The effective bond order (B) for RBS( ) is given by
n i RBS ()  n *i RBS ()
B
2
1 T   1 T 
21 T 
2




2
i
i
2
i

(S14a)

2Ti
1 Ti2
(S14b)
2bi
 bi .
1 bi2
(S14c)
The effective bond order (B) after elimination of triplet contamination part is larger than that (b) of

the BS solution itself. The diradical character (y) is defined by the weight of the doubly excited
configuration under the NMO approximation as
3
1 T 

2
y  2W D
i
1 Ti
2
 1
2Ti
1 Ti2
(S15a)
 1 B.


(S15b)
Thus the diradical character y is directly related to the decrease of the effective bond order B. The
chemical indices, b, B, and y, are mutually related in the GMO approach.
B and y values are also
obtained by using the MO-CI and CASSCF methods.
The simple pairing relation in eqs S2 and S6 is lost beyond BS approximation. Information
entropy is introduced as an alternative to the effective bond orders as
Ii  ni ln ni .
(S15c)
Then the information entropy for closed-shell pair is given by




Ic  2ln 2.
(S15d)
The normalized information entropy is defined as
2ln 2  ni ln ni
(S15e)
I˜i 
.
2ln 2
The I˜i values is zero for closed-shell orbital with ni  2 , whereas it becomes 1.0 for the singly
occupied orbital with n 1. The I˜i value is also a measure of decrease of the bonding property
i
and it is applicable even for RBS and MR wave functions where the pairing property of the
occupation numbers ni  n*i  2 is lost. These chemical indices for transition-metal complexes


in biology have been presented in this series of papers.
 structure of compound I
SI. 3 Electronic
Compound I (CpdI) is consisted of the Fe(IV)=O core and ligand radical (·L) parts. Here,
CpdI is regarded as the three-center system (O-Fe-L) for simple explanation. Three -orbitals with
the A1, S and A2 symmetries are available in the x-z plane as illustrated in Fig. S1, and the A1 and S
orbitals are doubly occupied under the closed-shell approximation. The S and A2 orbitals are
HOMO and LUMO, respectively. Similarly three -orbitals with the A1, S and A2 symmetries are
also formed in the y-z plane and the A2 orbital becomes the singly occupied MO (SOMO). This A2
orbital is mainly consisted of the dyz orbital of iron (Fe) ion, and therefore it is regarded as a
localized MO; LMO(Fe).
CpdI is formally regarded as a doublet species with the restricted open-shell MO
configuration;  (S)LMO (Fe) (S) .
However, the energy gap between the S (HOMO) and A2
(LUMO) orbital is small in the case of CpdI, leading to the HOMO-LUMO mixing under the BS
approximation


 cosS  sin A2 .
(S16)
Then the localized natural molecular orbitals (LMO) are defined by

  (   4) 
1
S  A2  LMO (O),
2
(S17a)
4

 – (   4) 
1
S  A2  LMO (L).
2
(S17b)
These LMO are mainly localized on the oxygen (O) and ligand (L) parts, respectively.

The
electronic structure of the -electron system in the x-y plane is more or less spin-polarized like
1,3-diradical species. The electronic structure of CpdI is regarded as an exchange coupled state
between diradical and doublet radicals.
Having obtained the MOs, we now consider the electronic structures of eight configurations in
Fig. 1. The three localized MO (LMO) are used to define the LMO configurations in Fig. 1 (see
text) as follows:
(4 1)  LMO (O)LMO (Fe)LMO (L),
(S18a)
( 1)  LMO (O)LMO (Fe)LMO (L),
(S18b)
( 1)  LMO (O)LMO (Fe)LMO (L),
(S18c)
( 1)  LMO (O)LMO (Fe)LMO (L).
(S18d)
2
2




2
These configurations correspond to the LMO descriptions of the active radical states depicted in
On the other hand, the charge transfer from LMO(O) to LMO(L) (vice versa) provides the
Fig.2.
doublet zwitterionic (ZW) configuration:
(2 1)  LMO (L)LMO (Fe)LMO (L),
( 1)  LMO (O)LMO (Fe)LMO (O). 


(S19a)

2
(S19b)
The four doublet configurations (21, 21', 21'', and 21''') are used to describe the diradicaloid state in
the x-z -electron system with extra one spin in eq. 4 (see text)
 RBSCI  C1 ( 2 1) C 2 ( 2 1) C 3( 2 1) C 4 ( 2 1),
(S20)
where Ci means the CI coefficient in the resonating BS (RBS) configuration interaction (CI). The

RBS CI description is also possible for transition structures and intermediates of hydroxylation
reactions as discussed in the text.
The key points of the RBS CI is that increase of the weight of the
ZW configuration with CI gives rise to the increase of the effective bond order of local singlet
diradical bond as shown in eqs. S13-S15.
This means that rebound step becomes stereoselective
because of decrease of diradical character (y) (see text).
As an extension of configuration
correlation diagrams at the BS level, RBS CI provides potential curves and states correlation
diagrams for hydroxylation reactions, which are under progress in our group.
SI. 4 Spin polarization of the d-p bond of Fe(IV)=O
The d-p bond of Fe(IV)=O core embedded in the strong ligand field is usually strong,
exhibiting no biradical character as illustrated in Fig. S2. However, the energy gap between the
bonding () aand antibonding (*) orbitals often becomes small in the case of weak ligand field,
giving rise to the HOMO-LUMO mixing. This entails the BS MOs as shown in Fig. S2.


   cos ( )  sin  ( * ),
(S21a)
 *  sin  ( )  cos ( * ).
(S21b)
5
The oxygen radical character is not negligible in this situation. The up-spin  (HOMO) orbital is
more or less localized on the iron site because of the exchange stabilization (see below).
On the
other hand, the up-spin * (LUMO) orbital (  * ) is more or less localized on the oxygen site and
acts as an electron acceptor as shown in Fig. 5 (see text).
The spin polarization is enhanced if the iron site becomes high-spin (HS) because of the

stabilization of the Coulombic exchange interaction. The closed-shell ()2 pair is triplet-unstable at
the HS state, providing the triplet (*)2 configuration. Then the sextet and quartet configurations
in Fig. 1 are contributable to the hydroxylation as



( 6 1)   LMO (O) LMO (Fe) LMO (L) ( ) ( * ),
(S22a)
( 4 1)   LMO (O) LMO (Fe) LMO (L) ( ) ( * ) ,
(S22b)
( 4 1)   LMO (O) LMO (Fe) LMO (L) ( ) ( * ) ,
(S22c)
( 4 1)   LMO (O) LMO (Fe) LMO (L) ( ) ( * ) .
(S22d)
Since these HS configurations have the reactive *-LUMO, the hydrogen abstraction reaction is
expected as illustrated in Fig. 6 (see text).

The LMO descriptions of orbital reorganization
processes along the radical reaction pathways as illustrated in Fig. 2.
The key conclusion
elucidated with this analysis is that the spin exchange coupling modes in the configurations
determine local singlet (SD) and triplet (TD) diradical mechanisms for rebound process in
hydroxylation reactions with CpdI as summarized in Table 1. This is the reason why the spin
exchange coupling modes in metalloenzymes have been investigated thoroughly in this series of
papers. The local SD and TD mechanisms for CpdI are regarded as an extention of previous SD
and TD mechanisms on the basis of the isolobal analogy among O, O2 and Fe(IV)=O (see text).
SI. 5 Pair and spin correlation functions
The spin densities appear under the BS approximation even in the low-spin (LS) singlet-type
BS configuration, though they should disappear in the exact singlet state. So, there is a basic
question what is spin density in the LS BS solution; only spin contamination errors?
Important
roles of spin densities emerge via the analysis of pair and spin correlation functions derived from
second-order density matrices of the BS solutions as shown in previous papers [92,93]. The on-site
pair function (P2) for electrons with different spins is given by
P2 (r1 ,r1;r1 ,r1 )  P1 (r1 ,r1 ) 2 Q(r1 ,r1 ) 2  2,
(S23)
where P1 (r1 ,r1 ) 2 and Q1 (r1 ,r1 ) 2 denotes, respectively, the density and spin density. This means
that the magnitude of spin density is parallel to the size of Coulombic hole for electrons with


different spins, namely electron correlations. Then the unpaired electron density U responsible for

deviation from the single determinant [94] is expressed by the sqaure of spin density under the BS
6
approximation as
U (r1 )  Q(r1 ,r1 ) 2  Q(r1 ) 2 .
(S24)
The magnitude of spin densities reported in various recent BS calculations can be understood from

the view point of nondynamical correlations between electrons with different spins [23-27].
Next, how about the sign of spin densities is a basic problem under the BS approximation.
In
order to elucidate this problem, the spin correlation function is introduced since it can be observed in
the case of infinite systems with neutron diffraction technique [23-27].
In fact, the spin correlation
function K 2 (r1 ,r2 ) is approximately given by
K 2 (r1 ,r2 ) 

 s(1) s(2)P (r ,r ;r ,r )ds
2
1
2
1
(S25a)
2
 Q(r1 )Q(r2 ).

where P2 denotes the second-order density matrix.
(S25b)
This means that the spin correlation is
singlet-type if the sign of spin density product is negative; () or (). Thus the sign of spin

density is closely related to the spin correlation function. Although the spin densities arising from
the first-order density P1 (r1 ,r2 ) disappears at the pure singlet state, the unpaired electron density


(U) and spin correlation function (K2) still exist as important indices of spin and electron correlations
even in the resonating BS (RBS) and symmetry-adapted MR wave functions such as CASSCF and

CASDFT. Therefore sign and magnitude of spin densities in several tables in this article should be
understood from the above theoretical view points in eqs. S23, S24, and S25. The pair and spin
correlation functions can be used to elucidate the nature of chemical bonds in the case of RBS and
MR approaches as alternative indices for spin density at the BS level of theory.
The above theoretical formulations in turn mean that discrimination between local singlet (SD)
and triplet (TD) diradical mechanisms in Table 1 works well even at RBS and MR levels of theory,
though the spin correlation function (K2) should be used as an alternative to spin density. More
detailed derivations of eqs (S23-S25) are given in the refs [92-94].
It is noteworthy that recent
many BS calculations of metalloenzymes are understood and analyzed from these theoretical
viewpoints as described in the text.
The present local SD and TD mechanisms are also applicable
for binuclear transition metal oxides with antiferromagnetic and ferromagnetic exchange couplings
as shown elsewhere [95]. Therefore it is concluded that magnetic coupling modes in several
transition-metal oxides cores in metalloenzymes determine local exchange coupling modes for
rebound diradical pairs, which are directly responsible for radical reaction pathways of oxygenations.
Thus magnetism and chemical bond is a basic and fundamental notion even in the theory of chemical
reaction mechanisms as shown in this series of papers.
SII.
Supporting Figures
Figures S1-S6 are given here as the supporting materials for MO-theoretical illumination of
local SD and TD mechanisms of hydroxylation with CpdI.
7
Figure S1.
Isoelectronic analogy among O, O2, Fe(IV)=O, Cu(III)=O and Au(III)=O.
Figure S2. Orbital interaction schemes of substrates with the compound I (CpdI) along the
diradical-type reaction pathway for 2[3(↑Fe(IV)=O↓) 2(•L↑)] (21’’)(see text).
Figure S3. Orbital interaction schemes of substrates with the compound I (CpdI) along the
diradical-type reaction pathway for 4[3(↓Fe(IV)=O↑) 3(↑*↑) 2(•L↑)] (41’) (see text).
Figure S4. Orbital interaction schemes of substrates with the compound I (CpdI) along the
diradical-type reaction pathway for 4[3(↓Fe(IV)=O↑) 3(↑*↑) 2(•L↑)] (41’’) (see text).
Figure S5. Orbital interaction schemes of substrates with the compound I (CpdI) along the
diradical-type reaction pathway for 4[3(↓Fe(IV)=O↑) 3(↑*↑) 2(•L↑)] (41’’’) (see text).
Figure S6. Molecular structures of substrates for hydroxylations.
SIII.
Supporting Tables
Tables S1-S5 are given here as the supporting materials.
Table S1
Opimized geometrical parameters and activation barriers for campjor (III)
Computational results for camphor by the B3LYP method are taken from
several groups.
Table S2
The optimized geometrical parameters and x-values for the transition
structures (4TS1 and 2TS1’ ) of IV-XII by UB3LYP. The geometrical
parameters are taken from refs [36-50].
Table S3
The spin density population on key groups of CpdI at the transition
structures (4TS1 and 2TS1 ) of I, II, III and IV-XII by UB3LYP.
Table S4
The spin density population on key groups of CpdI at the transition
structures (4TS1 ) of I, II, III and IV-XII by UB3LYP.
Table S5
The spin density population on key groups of CpdI at the transition
structures ( 2TS1’ ) of II and IV-XII by UB3LYP.
8
Fig. S1
K. Yamaguchi et al.
9
Fig. S2
K. Yamaguchi et al.
10
Fig. S3
K. Yamaguchi et al.
11
Fig. S4
K. Yamaguchi et al.
12
Fig. S5
K. Yamaguchi et al.
13
Fig. S6
K. Yamaguchi et al.
14
Table S1 Optimized geometrical parameters and x-values for transition structures of hydroxylation of
camphor with CpdI by hybrid DFT (HDFT) calculations
No.
III (a)
R1
R2
Rt
q
x (%)
DE‡(DFT)
Ref.
1.173
1.365
2.538
–
53.8
18.0
[53]
TS1 (SD)
1.124
1.424
2.548
–
55.9
20.2
TS1 (TD)
1.154
1.408
2.562
166.9
55.0
20.6
TS1 (SD)
1.158
1.390
2.548
166.4
54.6
19.5
TS1 (TD)
1.188
1.369
2.557
167.8
53.5
21.6
TS1 (SD)
1.195
1.359
2.554
167.6
53.2
20.8
TS1 (TD)
1.181
1.362
2.543
171.6
53.6
19.5
TS1 (SD)
1.152
1.371
2.523
170.6
54.3
19.5
TS1 (TD)
1.157
1.389
2.546
169.8
54.6
17.96
TS1 (SD)
1.129
1.404
2.533
170.4
55.4
18.39
TS1 (TD)
1.20
1.38
2.58
–
53.5
20.6
Spin State
4
TS1 (TD)
2
III (b)
4
2
III (c)
4
2
III (d)
4
2
III (e)
4
2
III (f)
4
15
[41]
[41]
[41]
[50]
[54]
Table S2
Optimized geometrical parameters, x-values, bond dissociation energies and activation barriers for hydroxylation with CpdI obtained by HD
No.
Substrates
Spin State
R1
R2
Rt

x (%)
E(BDE)
E‡(DFT)
IV
ethane
HS(TD)
1.136
1.427
2.563
170.2
55.7
107.51
21.32
LS(SD)
1.215
1.327
2.542
174.0
52.2
HS(TD)
1.123
1.427
2.550
166.3
56.0
LS(SD)
1.198
1.321
2.519
168.2
52.4
HS(TD)
1.141
1.427
2.568
170.2
55.6
LS(SD)
1.220
1.327
2.547
173.6
52.1
HS(TD)
1.257
1.337
2.594
170.6
51.5
LS(SD)
1.318
1.244
2.562
171.3
48.6
HS(TD)
1.126
1.426
2.552
171.8
55.9
LS(SD)
1.215
1.300
2.515
172.3
51.7
HS(TD)
1.203
1.449
2.652
169.8
54.6
LS(SD)
1.426
1.209
2.635
172.6
45.9
HS(TD)
1.259
1.310
2.569
170.7
51.0
LS(SD)
1.377
1.222
2.599
172.3
47.0
HS(TD)
1.252
1.404
2.656
172.8
52.9
LS(SD)
1.227
1.402
2.629
172.2
53.3
HS(TD)
1.240
1.324
2.564
163.5
51.6
LS(SD)
1.289
1.269
2.558
166.6
49.6
V
VI
VII
VIII
i-propane
n-propane
propene
methylphenyl-
20.23
103.39
19.05
17.68
107.98
21.47
20.36
91.48
14.68
15.15
103.66
18.28
cyclopropane
IX
isopropylphenyl-
17.31
95.92
16.03
cyclopropane
X
XI
XII
dimethylaniline
toluene
phenylethane
16
15.05
95.72
7.66
6.65
94.45
14.81
14.78
91.30
14.57
14.21
Table S3
Spin density populations for 4TS1, 2TS1 and 2TS1’’ of I, II and III.
No.
Type
Fe
O
Por
SR
H
Alk
I (2TS1)
SD
1.01
0.42
-0.58
-0.48
-0.08
0.70
III (2TS1)
SD
1.00
0.45
-0.48
-0.51
-0.04
0.58
II (2TS1)
SD
0.97
0.52
-0.33
-0.72
-0.07
0.63
II (2TS1’’)
TD
-1.00
0.37
0.34
0.74
-0.07
0.61
III (2TS1a)
SD
1.038
0.504
-0.827
-0.210
-0.057
0.560
III (2TS1b)
SD
1.157
0.546
-0.892
-0.257
-0.072
0.500
III (2TS1c)
SD
0.963
0.502
-0.437
-0.518
-0.047
0.522
III ( TS1a)
TD
0.887
0.594
0.761
0.191
-0.060
0.647
III (4TS1b)
TD
0.947
0.612
0.717
0.211
-0.066
0.553
III (4TS1c)
TD
1.269
0.681
0.123
0.397
-0.035
0.576
4
17
Table S4
Spin Density Populations for HS (4TS ) state of I-XII
No.
Type
Fe
O
Por
SR
H
Alk
Q a)
Ib)
TD
0.89
0.52
0.46
0.48
-0.06
0.72
0.35
II b)
TD
1.35
0.61
0.07
0.38
-0.06
0.72
0.27
III c)
TD
1.34
0.60
0.08
0.39
-0.03
0.62
0.35
IV c)
TD
1.35
0.61
0.07
0.38
-0.04
0.63
0.35
V c)
TD
1.40
0.64
0.05
0.36
-0.02
0.58
0.35
VI c)
TD
1.35
0.60
0.06
0.38
-0.04
0.64
0.35
VII c)
TD
1.28
0.69
0.14
0.40
-0.03
0.53
0.29
VIII c)
TD
1.38
0.63
0.05
0.36
-0.03
0.61
0.35
IX c)
TD
1.39
0.68
0.05
0.36
-0.01
0.52
0.36
X c)
TD
1.50
0.65
-0.05
0.25
0.00
0.66
0.49
XI c)
TD
1.32
0.66
0.11
0.38
-0.03
0.55
0.31
XII c)
TD
1.35
0.66
0.12
0.38
-0.02
0.52
0.31
a)Q: charge transfer from substrates
b) Ref. [61]
c) Refs [36-50].
18
Table S5
Spin density populations for 2TS1’ of IV-XII
No.
Type
Fe
O
Por
SR
H
Alk
Q a)
IIb)
SD
1.93
-0.20
-0.18
-0.09
0.05
-0.51
0.28
IVc)
SD
1.86
-0.07
-0.19
-0.09
0.03
-0.54
0.37
Vc)
SD
1.87
-0.05
-0.22
-0.17
0.02
-0.45
0.34
VIc)
SD
1.85
-0.07
-0.19
-0.08
0.03
-0.54
0.37
VIIc)
SD
1.82
0.12
-0.31
-0.24
0.01
-0.40
0.30
VIIIc)
SD
1.82
-0.03
-0.22
-0.12
0.02
-0.47
0.36
IXc)
SD
1.83
0.11
-0.29
-0.28
0.00
-0.37
0.34
Xc)
SD
1.71
0.21
-0.23
-0.15
-0.01
-0.52
0.47
XIc)
SD
1.81
0.11
-0.30
-0.22
0.01
-0.41
0.31
XIIc)
SD
1.83
0.16
-0.32
-0.29
0.00
-0.39
0.31
a) Q: charge transfer from substrates
b) Ref. [61]
c) Refs [36-50].
19