SUPPLEMENTARY MATERIAL
COMPARATIVE ANALYSIS OF THE PERFORMANCE OF COMMONLY AVAILABLE
DENSITY FUNCTIONALS IN THE DETERMINATION OF GEOMETRICAL PARAMETERS FOR
COPPER COMPLEXES
Sérgio F. Sousa, Gaspar R. P. Pinto, António J. M. Ribeiro, João T. S. Coimbra, Pedro A. Fernandes, Maria João Ramos*
REQUIMTE, Departamento de Química e Bioquímica, Faculdade de Ciências, Universidade do Porto, Rua do Campo
Alegre, s/n, 4169-007, Porto, Portugal
Corresponding author
*E-mail: mjramos@fc.up.pt
With the supplementary material for this article, we provide complementary information and data
regarding the comparative analysis of the different combinations of functionals and basis sets in
geometry optimization, performed for the different Cambridge Structural Database (CSD) complexes.
The contents encompass the following: 1) complete list of the copper complexes extracted from the
CSD database; 2) MSE results for Cu-ligand bond-lengths considering the initial assessment; and 3)
MSE and MUE results for the extended analysis section involving the Cu-ligand bond-lengths and
ligand-Cu-ligand angles.
1
1) List and characteristics of the CSD complexes used in this study
Table S1. CSD complexes used in this study with information regarding: CSD identification code,
number of atoms, coordination number, coordination type (N-Nitrogen; O-Oxygen; S-Sulphur; Watwater), copper’s oxidation number, and reference. * Complexes used for the initial assessment.
†
Complexes used in the DFT-D3 evaluation.
CSD ID
No of atoms Coordination no Coordination type Cu oxidation no Reference
CENKUC
23
2
N-N
1
[1]
ETERIE
37
2
N-N
1
[2]
HEGQAM*
19
2
N-N
1
[3]
KOBVAZ*,†
29
2
S-S
1
[4]
MIZBAY*,†
13
2
N-N
1
[5]
RIXVEZ
51
2
N-N
1
[6]
SAWXAP
41
2
N-N
1
[7]
BIZSIN†
24
3
N-S-S
1
[8]
BOMCEL†
37
3
S-S-S
1
[9]
JUXWAA
48
3
N-N-Wat
1
[10]
KUKXET
43
3
N-N-N
1
[11]
LOYXIG
52
3
N-N-N
1
[12]
NANQAU
61
3
N-N-N
1
[13]
QORHAG
46
3
N-N-N
1
[14]
AVETOL
43
4
N-N-N-S
1
[15]
DIYKOL
51
4
N-N-S-S
1
[16]
FOTNOR*,†
41
4
N-N-S-S
1
[17]
GEVMEZ
33
4
N-N-N-N
1
[18]
GIGXOK01
45
4
N-N-N-N
1
[19]
IBISOC01
45
4
N-N-N-N
1
[20]
IYUXOP
73
4
S-S-S-S
1
[21]
LUSVUQ*,†
35
4
N-N-S-S
1
[22]
LUWBIO
51
4
N-N-N-N
1
[23]
2
RIQJUX
45
4
S-S-S-S
1
[24]
XUNSEE
45
4
N-N-N-N
2
[25]
CEFBEU02
49
4
N-N-N-N
2
[26]
CEWGER
17
4
S-S-S-S
2
[27]
CUOXNA10*,†
13
4
O-O-O-O
2
[28]
HAJJIM
47
4
N-N-N-N
2
[29]
HURTUJ
45
4
N-N-N-N
2
[30]
MIKLEY
47
4
N-N-O-O
2
[31]
PYRDCU01
43
4
N-N-N-N
2
[32]
REKROO*,†
44
4
N-N-S-S
2
[33]
SEVNUC
25
4
N-N-N-N
2
[34]
VAZBUT10
45
4
N-N-N-N
2
[35]
YUDCOP*
27
4
N-N-S-S
2
[36]
BAHTIN
50
5
N-N-N-N-N
2
[37]
FUZYIJ
46
5
N-N-N-N-N
2
[38]
INABEE
56
5
N-N-N-N-N
2
[39]
JEZLAB
45
5
N-N-N-N-N
2
[40]
PINBOD†
42
5
S-S-S-S-S
2
[41]
QAFCUW
48
5
N-S-S-S-S
2
[42]
ZURZOB*,†
39
5
N-N-N-N-N
2
[43]
BIPQUM
31
6
N-N-O-O-O-O
2
[44]
CIRRAW
43
6
O-O-S-S-S-S
2
[45]
COZVUI
49
6
O-O-S-S-S-S
2
[46]
DIBJAZ*,†
39
6
N-N-N-N-S-S
2
[47]
KIQNAZ
49
6
N-N-N-N-N-N
2
[48]
RELCUG01†
43
6
O-O-O-O-O-O
2
[49]
SUHCAZ
53
6
N-N-N-N-N-N
2
[50]
3
2) MSE results considering the initial assessment.
Table S2. Calculated Mean Signed Error (MSE) in the Cu-ligand bond-lengths (pm), regarding the
initial assessment.
Type
Functional
CEP-121G
LanL2DZ
SDD
6-31G(d)
6-31G(d,p)
6-31+G(d)
6-31+G(d,p)
average
GGA
BLYP
7.0
9.1
6.6
1.1
1.1
5.6
5.6
5.2
BP86
3.9
6.3
3.8
-1.6
-1.6
2.4
2.4
2.2
PBE
3.8
6.3
3.7
-1.8
-1.7
2.2
2.2
2.1
TPSS
3.5
6.0
3.3
-2.0
-1.9
1.7
1.7
1.8
VSXC
5.0
6.8
4.5
-0.3
-0.2
6.0
6.1
4.0
M06L
4.0
5.3
3.2
-1.2
-1.1
2.9
2.9
2.3
H-GGA
B3LYP
5.3
6.9
4.7
0.4
0.4
4.6
4.7
3.9
HM-GGA
M06
3.0
4.1
2.1
-1.7
-1.7
2.3
2.4
1.5
M06HF
8.5
8.9
7.9
3.6
3.7
7.9
7.9
6.9
TPSSh
3.2
5.4
2.9
-1.9
-1.9
1.6
1.6
1.6
B2PLYP
3.4
5.6
2.7
-1.3
-1.2
1.6
1.9
1.8
B2PLYPD
3.0
5.3
2.3
-1.7
-1.6
1.4
1.4
1.4
mPW2PLYP
3.4
5.4
2.6
-1.0
-1.0
2.0
2.1
1.9
mPW2PLYPD
3.2
4.8
2.2
-1.8
-1.0
1.6
1.7
1.5
CAM-B3LYP
3.3
4.6
2.5
-1.4
-1.3
2.4
2.5
1.8
LC-wPBE
1.3
3.4
1.1
-3.4
-3.4
0.0
0.0
-0.1
wB97XD
3.5
5.1
2.9
-1.2
-1.1
2.7
2.9
2.1
3.7
5.7
3.2
-1.3
-1.2
2.6
2.6
2.2
M-GGA
DH-GGA
LC-H-GGA
average
4
3) MSE and MUE results considering the extended analysis.
Table S3. Calculated Mean Signed Error (MSE) in the Cu-ligand bond-lengths (pm), regarding the
extended analysis.
Type
Functional
CEP-121G
LanL2DZ
LanL2DZB3LYP
SDD
6-31G(d)
6-31G(d,p)
TZV
TZVP
average
GGA
BLYP
6.7
8.4
7.8
6.2
1.2
1.2
7.5
7.8
5.8
M-GGA
M06L
3.2
4.1
3.8
2.5
-1.1
-1.1
3.7
4.1
2.4
H-GGA
B3LYP
5.1
6.4
5.8
4.4
0.7
0.6
5.8
6.1
4.4
HM-GGA
M06
2.5
3.2
2.8
1.6
-1.8
-1.7
2.5
3.3
1.6
DH-GGA
mPW2PLYP
2.9
4.5
3.9
2.1
-1.4
-1.3
3.7
3.6
2.3
LC-H-GGA
wB97XD
3.4
4.4
4.0
2.6
-1.2
-1.2
3.5
3.9
2.4
4.0
5.2
4.7
3.2
-0.6
-0.6
4.4
4.8
3.1
average
5
Table S4. Calculated Mean Unsigned Error (MUE) in the Cu-ligand bond-lengths (pm) by type of
coordination (to Oxygen, Nitrogen, or Sulphur), considering the extended analysis section.
Nitrogen
Type
Functional
CEP-121G
LanL2DZ
LanL2DZB3LYP
SDD
6-31G(d)
6-31G(d,p)
TZV
TZVP
average
GGA
BLYP
5.0
6.0
5.6
4.8
4.2
4.2
5.5
6.7
5.2
M-GGA
M06L
3.0
3.1
3.1
3.0
3.8
3.8
2.9
4.4
3.4
H-GGA
B3LYP
3.7
4.4
4.0
3.4
3.5
3.5
4.1
5.5
4.0
HM-GGA
M06
2.4
2.5
2.4
2.6
3.6
3.6
2.1
3.7
2.9
DH-GGA
mPW2PLYP
2.7
3.3
3.0
2.7
3.7
3.5
2.7
3.6
3.1
LC-H-GGA
wB97XD
2.6
3.1
2.8
2.3
3.4
3.4
2.5
3.7
3.0
3.2
3.7
3.5
3.1
3.7
3.7
3.3
4.6
3.6
average
Oxygen
Type
Functional
CEP-121G
LanL2DZ
LanL2DZB3LYP
SDD
6-31G(d)
6-31G(d,p)
TZV
TZVP
average
GGA
BLYP
8.2
8.2
7.5
11.2
5.6
5.5
7.1
7.6
7.6
M-GGA
M06L
4.2
1.7
4.2
1.7
1.7
1.7
5.2
4.1
3.0
H-GGA
B3LYP
4.3
3.2
3.0
3.3
3.0
3.0
3.3
7.6
3.8
HM-GGA
M06
2.2
2.5
3.8
2.2
2.0
2.5
3.3
3.6
2.8
DH-GGA
mPW2PLYP
2.4
4.7
2.3
6.6
6.6
2.3
2.4
2.5
3.7
LC-H-GGA
wB97XD
2.1
6.4
2.0
4.9
2.0
2.0
2.0
2.1
2.9
3.9
4.5
3.8
5.0
3.5
2.8
3.9
4.6
4.0
average
Sulphur
Type
Functional
CEP-121G
LanL2DZ
LanL2DZB3LYP
SDD
6-31G(d)
6-31G(d,p)
TZV
TZVP
average
GGA
BLYP
13
15
15
12
4.8
4.9
14
8.5
11
M-GGA
M06L
9.3
11
11
8.4
3.0
3.0
10
6.7
7.8
H-GGA
B3LYP
11
13
13
10
4.2
4.3
13
7.2
9.4
HM-GGA
M06
7.9
9.7
9.2
7.0
2.3
2.2
8.3
6.0
6.6
DH-GGA
mPW2PLYP
8.2
11
10
7.4
2.8
2.7
10
4.6
7.1
LC-H-GGA
wB97XD
8.8
11
10
8.1
2.7
2.6
9.7
5.5
7.4
9.6
12
11
8.9
3.3
3.3
11
6.4
8.2
average
6
Table S5. Calculated Mean Unsigned Error (MUE) in the Cu-ligand bond-lengths (pm) by copper’s
oxidation state, considering the extended analysis section.
Copper I
Type
Functional
CEP-121G
LanL2DZ
LanL2DZB3LYP
SDD
6-31G(d)
6-31G(d,p)
TZV
TZVP
average
GGA
BLYP
5.9
7.3
6.9
5.9
4.6
4.6
6.7
5.8
6.0
M-GGA
M06L
4.8
5.2
5.3
4.7
5.0
5.0
5.0
3.6
4.8
H-GGA
B3LYP
5.5
7.1
6.3
5.3
4.2
4.1
6.5
6.1
5.6
HM-GGA
M06
4.1
4.6
4.4
4.4
5.0
4.9
4.2
3.7
4.4
DH-GGA
mPW2PLYP
4.3
5.7
5.0
4.5
5.3
5.2
5.0
4.0
4.9
LC-H-GGA
wB97XD
4.6
5.7
5.0
4.1
4.5
4.5
4.9
4.4
4.7
4.9
5.9
5.5
4.8
4.8
4.7
5.4
4.6
5.1
average
Copper II
Type
Functional
CEP-121G
LanL2DZ
LanL2DZB3LYP
SDD
6-31G(d)
6-31G(d,p)
TZV
TZVP
average
GGA
BLYP
8.1
9.9
8.8
7.6
4.5
4.5
8.7
9.2
7.7
M-GGA
M06L
4.6
5.4
5.2
4.3
2.5
2.5
4.9
5.8
4.4
H-GGA
B3LYP
5.6
6.3
5.9
5.0
3.4
3.4
5.9
6.2
5.2
HM-GGA
M06
3.6
4.3
4.1
3.4
2.1
2.2
4.0
4.8
3.6
DH-GGA
mPW2PLYP
3.8
4.8
4.5
3.3
3.1
2.2
4.7
3.9
3.8
LC-H-GGA
wB97XD
4.0
4.9
4.8
3.7
2.2
2.3
4.0
4.1
3.8
5.0
5.9
5.6
4.6
3.0
2.8
5.4
5.7
4.7
average
7
Table S6. Calculated Mean Unsigned Error (MUE) in the ligand-Cu-ligand angles (º) by copper’s
oxidation state, considering the extended analysis section.
Copper I
Type
Functional
CEP-121G
LanL2DZ
LanL2DZB3LYP
SDD
6-31G(d)
6-31G(d,p)
TZV
TZVP
average
GGA
BLYP
4.3
4.4
4.3
4.3
4.9
4.9
4.5
3.6
4.4
M-GGA
M06L
3.6
3.9
3.9
3.8
4.7
4.6
3.8
3.9
4.0
H-GGA
B3LYP
4.2
4.4
4.1
4.3
4.9
4.8
4.6
3.8
4.4
HM-GGA
M06
3.7
3.8
3.8
3.7
4.5
4.5
4.0
3.8
4.0
DH-GGA
mPW2PLYP
4.6
4.6
4.0
4.6
5.8
6.0
4.6
4.2
4.8
LC-H-GGA
wB97XD
4.3
4.2
4.0
3.9
4.9
4.9
4.3
4.2
4.3
4.1
4.2
4.0
4.1
5.0
4.9
4.3
3.9
4.3
average
Copper II
Type
Functional
CEP-121G
LanL2DZ
LanL2DZB3LYP
SDD
6-31G(d)
6-31G(d,p)
TZV
TZVP
average
GGA
BLYP
1.5
1.8
1.6
1.5
2.0
2.0
1.7
2.1
1.8
M-GGA
M06L
1.2
1.4
1.4
1.3
1.7
1.7
1.4
1.7
1.5
H-GGA
B3LYP
1.4
1.5
1.5
1.4
1.7
1.7
1.6
1.7
1.6
HM-GGA
M06
1.4
1.4
1.4
1.4
1.4
1.4
1.3
1.4
1.4
DH-GGA
mPW2PLYP
1.3
1.6
1.9
1.3
4.0
3.2
2.1
1.9
2.2
LC-H-GGA
wB97XD
1.2
1.4
1.2
1.3
1.4
1.4
1.3
1.4
1.3
1.3
1.5
1.5
1.4
2.0
1.9
1.6
1.7
1.6
average
8
Table S7. Calculated Mean Unsigned Error (MUE) in the Cu-ligand bond-lengths (pm) by coordination
number (2, 3, 4, 5, and 6), considering the extended analysis section.
Coordination
Type
Functional
CEP-121G
LanL2DZ
LanL2DZB3LYP
SDD
6-31G(d)
6-31G(d,p)
TZV
TZVP
average
GGA
BLYP
2.2
3.9
3.5
1.8
4.6
4.5
3.3
3.4
3.4
M-GGA
M06L
2.3
2.6
2.4
2.2
5.0
4.9
1.9
2.0
2.9
H-GGA
B3LYP
2.0
3.9
3.4
1.6
4.0
4.0
3.3
3.7
3.2
HM-GGA
M06
2.1
1.9
1.9
2.6
5.2
5.1
1.5
1.7
2.8
DH-GGA
mPW2PLYP
1.6
3.7
3.1
1.7
4.7
4.6
2.6
2.6
3.1
LC-H-GGA
wB97XD
1.5
3.1
2.6
1.6
4.6
4.6
2.1
2.6
2.8
1.9
3.2
2.8
1.9
4.7
4.6
2.5
2.7
3.0
2
average
3
GGA
BLYP
5.7
7.6
6.8
5.5
3.8
3.7
6.4
6.9
5.8
M-GGA
M06L
4.5
5.3
5.2
4.1
4.6
4.6
5.0
4.4
4.7
H-GGA
B3LYP
5.4
7.7
6.6
5.0
3.2
3.2
6.6
6.9
5.6
HM-GGA
M06
3.9
4.9
4.5
3.9
4.5
4.4
4.3
4.4
4.3
DH-GGA
mPW2PLYP
4.6
6.8
5.8
4.4
4.7
4.6
5.2
5.3
5.2
LC-H-GGA
wB97XD
4.4
6.1
5.4
4.1
4.3
4.3
4.9
4.8
4.8
4.7
6.4
5.7
4.5
4.2
4.1
5.4
5.4
5.1
average
4
GGA
BLYP
7.1
8.5
8.2
7.0
3.9
3.9
7.9
7.0
6.7
M-GGA
M06L
5.1
5.7
5.8
5.0
3.6
3.6
5.4
4.3
4.8
H-GGA
B3LYP
5.8
6.9
6.4
5.6
3.5
3.5
6.4
5.8
5.5
HM-GGA
M06
4.1
4.7
4.5
4.0
3.5
3.4
4.1
3.6
4.0
DH-GGA
mPW2PLYP
4.7
5.4
5.0
4.7
3.6
3.6
4.6
3.6
4.4
LC-H-GGA
wB97XD
5.1
5.8
5.3
4.5
3.3
3.3
5.1
4.5
4.6
5.3
6.2
5.9
5.1
3.6
3.6
5.6
4.8
5.0
average
5
GGA
BLYP
8.2
9.4
9.2
8.0
4.4
4.9
8.9
8.2
7.7
M-GGA
M06L
4.5
5.0
5.0
4.3
3.6
3.6
4.8
4.6
4.4
H-GGA
B3LYP
5.9
6.7
6.5
5.6
3.8
4.1
6.4
6.2
5.6
HM-GGA
M06
4.0
4.2
4.0
3.7
3.1
3.2
3.5
3.7
3.7
DH-GGA
mPW2PLYP
4.0
4.8
4.6
3.6
2.8
2.6
4.5
3.8
3.8
LC-H-GGA
wB97XD
4.1
4.5
4.6
3.7
2.9
3.0
3.9
3.7
3.8
5.1
5.8
5.6
4.8
3.4
3.6
5.3
5.0
4.8
average
6
GGA
BLYP
9.8
11.9
9.4
8.9
6.5
6.5
9.9
12.0
9.4
M-GGA
M06L
5.0
5.7
5.5
4.8
2.1
2.1
5.4
8.1
4.9
H-GGA
B3LYP
6.4
6.2
5.8
5.4
4.2
4.2
6.3
7.5
5.7
HM-GGA
M06
3.8
4.8
4.5
3.9
1.6
1.8
5.2
8.2
4.2
DH-GGA
mPW2PLYP
3.6
4.8
4.6
2.9
4.7
2.3
6.5
5.0
4.3
LC-H-GGA
wB97XD
3.7
5.0
4.7
3.6
1.8
1.8
3.6
4.5
3.6
5.4
6.4
5.7
4.9
3.5
3.1
6.2
7.5
5.3
average
9
Table S8. Calculated Mean Unsigned Error (MUE) in the ligand-Cu-ligand angles (º) by coordination
number (2, 3, 4, 5, and 6), considering the extended analysis section.
Coordination
Type
Functional
CEP-121G
LanL2DZ
LanL2DZB3LYP
SDD
6-31G(d)
6-31G(d,p)
TZV
TZVP
average
GGA
BLYP
1.4
1.2
1.2
1.3
1.0
1.0
1.0
1.4
1.2
M-GGA
M06L
1.3
1.5
1.5
1.3
2.3
2.2
1.5
1.3
1.6
H-GGA
B3LYP
1.3
1.1
1.1
1.2
1.2
1.1
1.1
1.3
1.2
HM-GGA
M06
1.2
1.4
1.4
1.2
1.7
1.7
1.4
1.4
1.4
DH-GGA
mPW2PLYP
1.0
1.1
1.2
1.1
3.2
3.4
1.2
1.3
1.7
LC-H-GGA
wB97XD
1.2
1.1
1.1
1.2
1.9
1.9
1.3
1.3
1.4
1.2
1.2
1.3
1.2
1.9
1.9
1.2
1.3
1.4
2
average
3
GGA
BLYP
3.7
5.1
4.2
3.9
4.8
4.7
4.1
3.5
4.3
M-GGA
M06L
3.0
4.3
3.9
3.2
5.0
4.4
4.8
4.2
4.1
H-GGA
B3LYP
3.9
5.5
4.5
4.1
4.6
4.6
4.7
3.9
4.5
HM-GGA
M06
3.3
4.1
3.9
3.1
4.0
4.3
4.2
3.1
3.7
DH-GGA
mPW2PLYP
5.0
5.8
4.9
5.2
5.2
5.1
6.5
5.1
5.4
LC-H-GGA
wB97XD
5.0
5.5
5.1
4.0
4.4
4.4
5.0
4.4
4.7
4.0
5.0
4.4
3.9
4.7
4.6
4.9
4.0
4.4
average
4
GGA
BLYP
2.9
2.9
2.9
2.9
3.1
3.1
3.2
2.8
3.0
M-GGA
M06L
2.6
2.6
2.6
2.6
2.9
2.9
2.5
2.7
2.7
H-GGA
B3LYP
2.8
2.8
2.7
2.8
3.0
3.0
3.0
2.7
2.9
HM-GGA
M06
2.6
2.6
2.5
2.5
2.9
2.9
2.6
2.7
2.7
DH-GGA
mPW2PLYP
2.7
3.2
3.3
2.7
6.5
6.7
3.8
3.7
4.1
LC-H-GGA
wB97XD
2.6
2.6
2.6
2.6
3.1
3.1
2.8
2.9
2.8
2.7
2.8
2.8
2.7
3.6
3.6
3.0
2.9
3.0
average
5
GGA
BLYP
2.2
2.3
2.2
2.2
3.4
3.4
2.2
2.4
2.6
M-GGA
M06L
1.8
2.0
2.0
1.8
3.1
3.1
1.8
2.2
2.2
H-GGA
B3LYP
2.2
2.2
2.1
2.1
3.1
3.1
2.2
2.3
2.4
HM-GGA
M06
2.5
2.2
2.4
2.2
2.8
2.8
1.8
2.1
2.3
DH-GGA
mPW2PLYP
1.9
1.8
2.6
1.9
2.7
2.3
2.0
1.6
2.1
LC-H-GGA
wB97XD
1.9
2.1
1.7
1.9
2.5
2.5
1.9
1.9
2.0
2.1
2.1
2.2
2.0
2.9
2.9
2.0
2.1
2.3
average
6
GGA
BLYP
1.4
1.9
1.6
1.5
2.0
2.0
1.6
2.3
1.8
M-GGA
M06L
1.3
1.4
1.4
1.4
1.4
1.4
1.4
1.8
1.4
H-GGA
B3LYP
1.3
1.5
1.4
1.4
1.5
1.5
1.6
1.8
1.5
HM-GGA
M06
1.1
1.3
1.3
1.3
0.9
0.9
1.3
1.4
1.2
DH-GGA
mPW2PLYP
1.2
1.4
1.2
1.2
2.7
1.4
1.7
1.5
1.5
LC-H-GGA
wB97XD
1.1
1.3
1.3
1.3
1.1
1.1
1.2
1.3
1.2
1.2
1.5
1.3
1.3
1.6
1.4
1.5
1.7
1.4
average
10
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