Influence of molecular geometry, type of exchange-correlation functional, and contraction scheme of basis set applied at the iron nuclei have been tested in the calculation of ^(57)Fe Mössbauer isomer shifts and quadrupole splittings for a wide range of ligand types, as well as oxidation and spin states, in inorganic and organometallic systems. It has been found that uncontraction of the s-part of Wachter's full-electron basis set at the iron nuclei does not appreciably improve the calculated isomer shifts. The observed correlations for all tested sets of geometries are close to each other and predominantly depend on the employed exchange-correlation functional with B3LYP functional being slightly better as compared to BPW91. Both hybrid (B3LYP) and pure (BPW91) exchange-correlation functionals are suitable for the calculation of isomer shifts in organometallic compounds. Surprisingly, it has been found that the hybrid B3LYP exchange-correlation functional completely fails in accurate prediction of quadrupole splittings in ferrocenes, while performance of the pure BPW91 functional for the same systems was excellent. This observation has been explained on the basis of relationship between the amount of Hartree-Fock exchange involved in the applied exchange-correlation functional and the calculated HOMO-LUMO energy gap in ferrocenes. On the basis of this explanation, use of only pure exchange-correlation functionals has been suggested for accurate prediction of Mössbauer spectra parameters in ferrocenes

Hadt, Ryan G.

Nemykin, Victor N.

Caltech Authors - Main

Supporting Information Figure 1. Correlation between experimental isomer 
shifts (δexp) and calculated  (B3LYP geometry test set) total electron density at 
the 57Fe nucleus (ρtotal) using: (A) B3LYP functional and Wf basis set; (B)
B3LYP functional and WfsU basis set; (C) BPW91 functional and Wf basis set; 
(D) BPW91 functional and WfsU basis set.
Nemykin & Hadt
-2 0 2
11610
11612
11614
11616
11618
ρ
t
o
t
a
l
δexp (mm/s)
EC: B3LYP
BS: Wf
A
-2 0 2
11566
11568
11570
11572
ρ
t
o
t
a
l
δexp (mm/s)
EC: B3LYP
BS: WfsU
B
-2 0 2
11614
11616
11618
11620
ρ
t
o
t
a
l
δexp (mm/s)
EC: BPW91
BS: Wf
C
-2 0 2
11572
11574
11576
11578
ρ
t
o
t
a
l
δexp (mm/s)
EC: BPW91
BS: WfsU
D
Supporting Information Figure 2. Correlation between experimental isomer 
shifts (δexp) and calculated  (BP86 geometry test set) total electron density at the 
57Fe nucleus (ρtotal) using: (A) B3LYP functional and Wf basis set; (B) B3LYP 
functional and WfsU basis set; (C) BPW91 functional and Wf basis set; (D)
BPW91 functional and WfsU basis set.
Nemykin & Hadt
-2 0 2
11610
11612
11614
11616
ρ
t
o
t
a
l
δexp (mm/s)
EC: B3LYP
BS: Wf
A
-2 0 2
11566
11568
11570
11572
ρ
t
o
t
a
l
δexp (mm/s)
EC: B3LYP
BS: WfsU
B
-2 0 2
11614
11616
11618
11620
ρ
t
o
t
a
l
δexp (mm/s)
EC: BPW91
BS: Wf
C
-2 0 2
11572
11574
11576
11578
ρ
t
o
t
a
l
δexp (mm/s)
EC: BPW91
BS: WfsU
D
-2 0 2
-2
0
2
δ
c
a
l
c
 
(
m
m
/
s
)
δexp (mm/s)
EC: B3LYP
BS: Wf
A
-2 0 2
-2
0
2
δ
c
a
l
c
 
(
m
m
/
s
)
δexp (mm/s)
EC: B3LYP
BS: WfsU
B
-2 0 2
-2
0
2
δ
c
a
l
c
 
(
m
m
/
s
)
δexp (mm/s)
EC: BPW91
BS: Wf
C
-2 0 2
-2
0
2
δ
c
a
l
c
 
(
m
m
/
s
)
δexp (mm/s)
EC: BPW91
BS: WfsU
D
Supporting Information Figure 3. Correlation between experimental (δexp) and 
calculated (δcalc) isomer shifts (B3LYP geometry test set) using: (A) B3LYP 
functional and Wf basis set; (B) B3LYP functional and WfsU basis set; (C)
BPW91 functional and Wf basis set; (D) BPW91 functional and WfsU basis set. Nemykin & Hadt
Supporting Information Figure 4. Correlation between experimental (δexp) and 
calculated (δcalc) isomer shifts (BP86 geometry test set) using: (A) B3LYP 
functional and Wf basis set; (B) B3LYP functional and WfsU basis set; (C)
BPW91 functional and Wf basis set; (D) BPW91 functional and WfsU basis set. Nemykin & Hadt
-1.0 -0.5 0.0 0.5 1.0 1.5
-1.0
-0.5
0.0
0.5
1.0
1.5
δ
c
a
l
c
 
(
m
m
/
s
)
δexp (mm/s)
EC: B3LYP
BS: Wf
A
-1.0 -0.5 0.0 0.5 1.0 1.5
-1.0
-0.5
0.0
0.5
1.0
1.5
δ
c
a
l
c
 
(
m
m
/
s
)
δexp (mm/s)
EC: B3LYP 
BS: WfsU
B
-1.0 -0.5 0.0 0.5 1.0 1.5
-1.0
-0.5
0.0
0.5
1.0
1.5
δ
c
a
l
c
 
(
m
m
/
s
)
δexp (mm/s)
EC: BPW91
BS: Wf
C
-1.0 -0.5 0.0 0.5 1.0 1.5
-1.0
-0.5
0.0
0.5
1.0
1.5
δ
c
a
l
c
 
(
m
m
/
s
)
δexp (mm/s)
EC: BPW91
BS: WfsU
D
Supporting Information Figure 5. Correlation between experimental (∆EQexp) 
and calculated (∆EQcalc) quadrupole splittings (B3LYP geometry test set) using: 
(A) B3LYP functional and Wf basis set; (B) B3LYP functional and WfsU basis 
set; (C) BPW91 functional and Wf basis set; (D) BPW91 functional and WfsU
basis set.
Nemykin & Hadt
-4 -2 0 2 4
-4
-2
0
2
4
∆
E
Q
c
a
l
c
 
(
m
m
/
s
)
∆EQexp (mm/s)
EC: B3LYP
BS: Wf
A
-4 -2 0 2 4
-4
-2
0
2
4
∆
E
Q
c
a
l
c
 
(
m
m
/
s
)
∆EQexp (mm/s)
EC: B3LYP
BS: WfsU
B
-4 -2 0 2 4
-4
-2
0
2
4
∆
E
Q
c
a
l
c
 
(
m
m
/
s
)
∆EQexp (mm/s)
EC: BPW91
BS: WfsU
C
-4 -2 0 2 4
-4
-2
0
2
4
∆
E
Q
c
a
l
c
 
(
m
m
/
s
)
∆EQexp (mm/s)
EC: BPW91
BS: WfsU
D
Supporting Information Figure 6. Correlation between experimental (∆EQexp) 
and calculated (∆EQcalc) quadrupole splittings (BP86 geometry test set) using: 
(A) B3LYP functional and Wf basis set; (B) B3LYP functional and WfsU basis 
set; (C) BPW91 functional and Wf basis set; (D) BPW91 functional and WfsU
basis set.
Nemykin & Hadt
-4 -2 0 2 4
-4
-2
0
2
4
∆
E
Q
c
a
l
c
 
(
m
m
/
s
)
∆EQexp (mm/s)
EC: B3LYP
BS: Wf
A
-4 -2 0 2 4
-4
-2
0
2
4
∆
E
Q
c
a
l
c
 
(
m
m
/
s
)
∆EQexp (mm/s)
EC: B3LYP 
BS: WfsU
B
-4 -2 0 2 4
-4
-2
0
2
4
∆
E
Q
c
a
l
c
 
(
m
m
/
s
)
∆EQexp (mm/s)
EC: BPW91
BS: Wf
C
-4 -2 0 2 4
-4
-2
0
2
4
∆
E
Q
c
a
l
c
 
(
m
m
/
s
)
∆EQexp (mm/s)
EC: BPW91
BS: WfsU
D
-4
-2
0
2
 
E
,
 
e
V
Fe dz2 
Fe dxy, dx2-y2
Fe dxz, dyz
π* Cp
Ferrocene
π Cp
Fe Fe
Supporting Information Figure 7. Bonding interactions between Cp- ligand
and FeII ion in ferrocene along with charge-transfer transitions.
Nemykin & Hadt
2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5
2
4
6
8
10
12
14
H
O
M
O
-
L
U
M
O
,
 
e
V
∆EQcalc 
FcCN
2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5
2
4
6
8
10
12
14
H
O
M
O
-
L
U
M
O
,
 
e
V
∆EQcalc 
FcCN3Vy
2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5
2
4
6
8
10
12
14
H
O
M
O
-
L
U
M
O
,
 
e
V
∆EQcalc
Fc, D5h
Supporting Information Figure 8. Correlation between calculated 
quadrupole splittings and HOMO-LUMO energy gap in ferrocene (Fc), 
cyanoferrocene (FcCN), and tricyanovinylferrocene (FcCN3Vy).
Nemykin & Hadt
-2 0 2 4
2
1
0
A
b
s
,
 
%
mm/s
Room-temperature Mössbauer spectrum of FcCN3Vy. Spectrum was recorded 
using NGRS-4 spectrometer in constant acceleration mode and referenced to 
sodium nitroprusside at room-temperature. The source was 57Co in a chromium 
matrix with initial activity of 50 mCi.
Nemykin & Hadt
Supporting Information Table 1. Comparison of correlation coefficients (r) and αrel for 
the test sets which utilize -0.18 mm/s and 0.00 mm/s (in parenthesis) values for isomer 
shift in Fe(CO)5 complex. 
 
  Method  
 BPW91/Wf BPW91/WfsU B3LYP/Wf B3LYP/WfsU 
X-ray geometry 
r 0.978(0.975) 0.977(0.974) 0.987(0.986) 0.985(0.983) 
αrel -0.337(-0.335) -0.357(-0.353) -0.304(-0.301) -0.320(-0.317) 
Β3LYP geometry 
r 0.965(0.961) 0.975(0.970) 0.969(0.967) 0.974(0.972) 
αrel -0.308(-0.305) -0.320(-0.317) -0.291(-0.288) -0.303(-0.300) 
ΒP86 geometry 
r 0.971(0.966) 0.971(0.966) 0.981(0.978) 0.980(0.978) 
αrel -0.313(-0.311) -0.331(-0.329) -0.294(-0.291) -0.308(-0.305) 
 
 
 


Influence of Hartree-Fock exchange on the calculated Mössbauer isomer shifts and quadrupole splittings in ferrocene derivatives using density functional theory

Influence of molecular geometry, type of exchange−correlation functional, and contraction scheme of basis set applied at the iron nuclei have been tested in the calculation of 57Fe Mössbauer isomer shifts and quadrupole splittings for a wide range of ligand types, as well as oxidation and spin states, in inorganic and organometallic systems. It has been found that uncontraction of the s-part of Wachter’s full-electron basis set at the iron nuclei does not appreciably improve the calculated isomer shifts. The observed correlations for all tested sets of geometries are close to each other and predominantly depend on the employed exchange−correlation functional with B3LYP functional being slightly better as compared to BPW91. Both hybrid (B3LYP) and pure (BPW91) exchange−correlation functionals are suitable for the calculation of isomer shifts in organometallic compounds. Surprisingly, it has been found that the hybrid B3LYP exchange−correlation functional completely fails in accurate prediction of quadrupole splittings in ferrocenes, while performance of the pure BPW91 functional for the same systems was excellent. This observation has been explained on the basis of relationship between the amount of Hartree−Fock exchange involved in the applied exchange−correlation functional and the calculated HOMO−LUMO energy gap in ferrocenes. On the basis of this explanation, use of only pure exchange−correlation functionals has been suggested for accurate prediction of Mössbauer spectra parameters in ferrocenes

Victor N. Nemykin

Ryan G. Hadt

CiteSeerX

Influence of Hartree−Fock Exchange on the Calculated Mo1ssbauer Isomer Shifts and Quadrupole Splittings in Ferrocene Derivatives Using Density Functional Theory

Supporting Information Figure 1. Correlation between experimental isomer 
shifts (δexp) and calculated  (B3LYP geometry test set) total electron density at 
the 57Fe nucleus (ρtotal) using: (A) B3LYP functional and Wf basis set; (B)
B3LYP functional and WfsU basis set; (C) BPW91 functional and Wf basis set; 
(D) BPW91 functional and WfsU basis set.
Nemykin & Hadt
-2 0 2
11610
11612
11614
11616
11618
ρ t
ot
al
δexp (mm/s)
EC: B3LYP
BS: Wf
A
-2 0 2
11566
11568
11570
11572
ρ t
ot
al
δexp (mm/s)
EC: B3LYP
BS: WfsU
B
-2 0 2
11614
11616
11618
11620
ρ t
ot
al
δexp (mm/s)
EC: BPW91
BS: Wf
C
-2 0 2
11572
11574
11576
11578
ρ t
ot
al
δexp (mm/s)
EC: BPW91
BS: WfsU
D
Supporting Information Figure 2. Correlation between experimental isomer 
shifts (δexp) and calculated  (BP86 geometry test set) total electron density at the 
57Fe nucleus (ρtotal) using: (A) B3LYP functional and Wf basis set; (B) B3LYP 
functional and WfsU basis set; (C) BPW91 functional and Wf basis set; (D)
BPW91 functional and WfsU basis set.
Nemykin & Hadt
-2 0 2
11610
11612
11614
11616
ρ t
ot
al
δexp (mm/s)
EC: B3LYP
BS: Wf
A
-2 0 2
11566
11568
11570
11572
ρ t
ot
al
δexp (mm/s)
EC: B3LYP
BS: WfsU
B
-2 0 2
11614
11616
11618
11620
ρ t
ot
al
δexp (mm/s)
EC: BPW91
BS: Wf
C
-2 0 2
11572
11574
11576
11578
ρ t
ot
al
δexp (mm/s)
EC: BPW91
BS: WfsU
D
-2 0 2
-2
0
2
δ c
al
c (
m
m
/s
)
δexp (mm/s)
EC: B3LYP
BS: Wf
A
-2 0 2
-2
0
2
δ c
al
c (
m
m
/s
)
δexp (mm/s)
EC: B3LYP
BS: WfsU
B
-2 0 2
-2
0
2
δ c
al
c (
m
m
/s
)
δexp (mm/s)
EC: BPW91
BS: Wf
C
-2 0 2
-2
0
2
δ c
al
c (
m
m
/s
)
δexp (mm/s)
EC: BPW91
BS: WfsU
D
Supporting Information Figure 3. Correlation between experimental (δexp) and 
calculated (δcalc) isomer shifts (B3LYP geometry test set) using: (A) B3LYP 
functional and Wf basis set; (B) B3LYP functional and WfsU basis set; (C)
BPW91 functional and Wf basis set; (D) BPW91 functional and WfsU basis set. Nemykin & Hadt
Supporting Information Figure 4. Correlation between experimental (δexp) and 
calculated (δcalc) isomer shifts (BP86 geometry test set) using: (A) B3LYP 
functional and Wf basis set; (B) B3LYP functional and WfsU basis set; (C)
BPW91 functional and Wf basis set; (D) BPW91 functional and WfsU basis set. Nemykin & Hadt
-1.0 -0.5 0.0 0.5 1.0 1.5
-1.0
-0.5
0.0
0.5
1.0
1.5
δ c
al
c (
m
m
/s
)
δexp (mm/s)
EC: B3LYP
BS: Wf
A
-1.0 -0.5 0.0 0.5 1.0 1.5
-1.0
-0.5
0.0
0.5
1.0
1.5
δ c
al
c (
m
m
/s
)
δexp (mm/s)
EC: B3LYP 
BS: WfsU
B
-1.0 -0.5 0.0 0.5 1.0 1.5
-1.0
-0.5
0.0
0.5
1.0
1.5
δ c
al
c (
m
m
/s
)
δexp (mm/s)
EC: BPW91
BS: Wf
C
-1.0 -0.5 0.0 0.5 1.0 1.5
-1.0
-0.5
0.0
0.5
1.0
1.5
δ c
al
c (
m
m
/s
)
δexp (mm/s)
EC: BPW91
BS: WfsU
D
Supporting Information Figure 5. Correlation between experimental (∆EQexp) 
and calculated (∆EQcalc) quadrupole splittings (B3LYP geometry test set) using: 
(A) B3LYP functional and Wf basis set; (B) B3LYP functional and WfsU basis 
set; (C) BPW91 functional and Wf basis set; (D) BPW91 functional and WfsU
basis set.
Nemykin & Hadt
-4 -2 0 2 4
-4
-2
0
2
4
∆E
Q
ca
lc
 (m
m
/s
)
∆EQexp (mm/s)
EC: B3LYP
BS: Wf
A
-4 -2 0 2 4
-4
-2
0
2
4
∆E
Q
ca
lc
 (m
m
/s
)
∆EQexp (mm/s)
EC: B3LYP
BS: WfsU
B
-4 -2 0 2 4
-4
-2
0
2
4
∆E
Q
ca
lc
 (m
m
/s
)
∆EQexp (mm/s)
EC: BPW91
BS: WfsU
C
-4 -2 0 2 4
-4
-2
0
2
4
∆E
Q
ca
lc
 (m
m
/s
)
∆EQexp (mm/s)
EC: BPW91
BS: WfsU
D
Supporting Information Figure 6. Correlation between experimental (∆EQexp) 
and calculated (∆EQcalc) quadrupole splittings (BP86 geometry test set) using: 
(A) B3LYP functional and Wf basis set; (B) B3LYP functional and WfsU basis 
set; (C) BPW91 functional and Wf basis set; (D) BPW91 functional and WfsU
basis set.
Nemykin & Hadt
-4 -2 0 2 4
-4
-2
0
2
4
∆
E
Q
ca
lc
 (m
m
/s
)
∆EQexp (mm/s)
EC: B3LYP
BS: Wf
A
-4 -2 0 2 4
-4
-2
0
2
4
∆E
Q
ca
lc
 (m
m
/s
)
∆EQexp (mm/s)
EC: B3LYP 
BS: WfsU
B
-4 -2 0 2 4
-4
-2
0
2
4
∆E
Q
ca
lc
 (m
m
/s
)
∆EQexp (mm/s)
EC: BPW91
BS: Wf
C
-4 -2 0 2 4
-4
-2
0
2
4
∆E
Q
ca
lc
 (m
m
/s
)
∆EQexp (mm/s)
EC: BPW91
BS: WfsU
D
-4
-2
0
2
 
E
, e
V
Fe dz2 
Fe dxy, dx2-y2
Fe dxz, dyz
π* Cp
Ferrocene
π Cp
Fe Fe
Supporting Information Figure 7. Bonding interactions between Cp- ligand
and FeII ion in ferrocene along with charge-transfer transitions.
Nemykin & Hadt
2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5
2
4
6
8
10
12
14
H
O
M
O
-L
U
M
O
, e
V
∆EQcalc 
FcCN
2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5
2
4
6
8
10
12
14
H
O
M
O
-L
U
M
O
, e
V
∆EQcalc 
FcCN3Vy
2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5
2
4
6
8
10
12
14
H
O
M
O
-L
U
M
O
, e
V
∆EQcalc
Fc, D5h
Supporting Information Figure 8. Correlation between calculated 
quadrupole splittings and HOMO-LUMO energy gap in ferrocene (Fc), 
cyanoferrocene (FcCN), and tricyanovinylferrocene (FcCN3Vy).
Nemykin & Hadt
-2 0 2 4
2
1
0
Ab
s,
 %
mm/s
Room-temperature Mössbauer spectrum of FcCN3Vy. Spectrum was recorded 
using NGRS-4 spectrometer in constant acceleration mode and referenced to 
sodium nitroprusside at room-temperature. The source was 57Co in a chromium 
matrix with initial activity of 50 mCi.
Nemykin & Hadt
Supporting Information Table 1. Comparison of correlation coefficients (r) and αrel for 
the test sets which utilize -0.18 mm/s and 0.00 mm/s (in parenthesis) values for isomer 
shift in Fe(CO)5 complex. 
 
  Method  
 BPW91/Wf BPW91/WfsU B3LYP/Wf B3LYP/WfsU 
X-ray geometry 
r 0.978(0.975) 0.977(0.974) 0.987(0.986) 0.985(0.983) 
αrel -0.337(-0.335) -0.357(-0.353) -0.304(-0.301) -0.320(-0.317) 
Β3LYP geometry 
r 0.965(0.961) 0.975(0.970) 0.969(0.967) 0.974(0.972) 
αrel -0.308(-0.305) -0.320(-0.317) -0.291(-0.288) -0.303(-0.300) 
ΒP86 geometry 
r 0.971(0.966) 0.971(0.966) 0.981(0.978) 0.980(0.978) 
αrel -0.313(-0.311) -0.331(-0.329) -0.294(-0.291) -0.308(-0.305) 
 
 
 


English

http://static.msi.umn.edu/rreports/2006/217.pdf

Influence of Hartree-Fock exchange on the calculated Mössbauer isomer shifts and quadrupole splittings in ferrocene derivatives using density functional theory

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