Supporting Information for
The Reliability of DFT Methods to Predict Electronic
Structures and Minimum Energy Crossing Point for
[FeIVO](OH)2 Models: A Comparison Study with
MCQDPT Method
Kun Liu,*,a Yuxue Li,b Jialing Su,a Bin Wang*a
a
Tianjin Key Laboratory of Structure and Performance for Functional Molecules; Key Laboratory of
Inorganic-Organic Hybrid Functional Material Chemistry, Ministry of Education; College of Chemistry,
Tianjin Normal University, 393 Bin Shui West Road, Tianjin 300387, P. R. China
b
State Key Laboratory of Organometallic Chemistry, Shanghai Institute of Organic Chemistry, Chinese
Academy of Sciences, 345 Ling Ling Road, Shanghai 200032, China
* To whom correspondence should be addressed.
E-mail: bnulk2010@gmail.com; wangbin1980@gmail.com
Table of Contents
Section S1. Selecting active space.
Section S2. A simple prove: The gradients of two states are proportional at MECP.
Section S3. Wavefunctions information of MCQDPT(10e,13o) and CASSCF(10e,16o) calculation for
various states of [FeIVO](OH)2.
Section S4. Locating the MECPs.
Section S5. Optimized internal coordinates at MCQDPT(10e,13o)/ TZVP level. (the MECPs are located
at CASSCF(10e,16o)/TZVP level)
Section S1, Selecting active space
For CASSCF calculation, we tried several kinds of active spaces before we determined the final
choice of the 10 electron distributed in 16 orbitals. The active orbitals consist of iron 3dz2, 3dxz, 3dyz,
3dxy, 3dx2-y2, 4dz2, 4dxz, 4dyz, 4dxy, 4dx2-y2, and oxygen 2pz, 2px, 2py, 3pz, 3px, 3py. The eight diffused-like
orbitals (five iron 4d orbitals and three oxygen 3p orbitals) were in the active space to account the
double shell effect (the radial correlation in the outer shell). These orbitals are shown in Figure S1.
Considering the calculation cost, the (10e/13o) space was employed for MCQDPT calculations without
7π, 8π, and 4σ in Figure S1.
Figure S1. The schematic orbitals in CASSCF(10e/16o)/MCQDPT(10e/13o) active space for
[FeIVO](OH)2.[a]
[a] The graph is drawn using MacMolPlt 7.4.4.[1]
[1] Bode, B.M.; Gordon, M.S. J. Mol. Graphics Mod. 1998, 16, 133-138
The active spaces were chosen based on a series of calculations as shown in Table S1, Table S2,
Figure S2 and Figure S3. Taking the geometries of various electron configurations optimized at
MCQDPT(10e,13o)/TZVP levels, the single point calculations were performed using various active
spaces. The results of comparison were listed in Table S1 and Figure S2. With the increase of active
space, the relative energies of those configurations become gradually close to each other. The
differences between the results of CASSCF(10e,16o)/TZVP and MCQDPT(10e,13e)/TZVP are very
small except the two highest electron configurations, 5A2 and 7A2.
Using CASSCF(10e,16o)/TZVP and MCQDPT(10e,13e)/TZVP, the geometries of various electron
configurations were optimized with C2v symmetry and the results were shown in Table S2 and Figure
S3. As expected, the equilibrium geometries of 5A2 and 7A2 were obviously different, but excellent
agreement was obtained for other electron configurations.
We guess (perhaps wrongly, but reasonably) single-reference correlated treatments out of the question
for high-energy excited states of this Fe-O unit. In order to ensure the reliability of the results, the two
highest energy states are not used as references in this study. In spite of MCQDPT(10e,16o)/TZVP is
expected to provide a better result, the calculation is too expensive. In this paper, we select the
MCQDPT(10e,13e)/TZVP results as a reference. Unfortunately, multi-reference perturbation theory
lacks analytic gradients in GAMESS program. For the calculations about the minimum energy crossing
point (MECP), the CASSCF(10e,16o)/TZVP results were chosen as a reference.
Table S1. Relative energies (in kcal/mol) of various electron configurations of [FeIVO](OH)2, optimized
with MCQDPT(10e,13o)/TZVP using various active spaces a b.
State
Energy
5A
1
5A
2
5B
1
5B
2
3A
1
3A
2
3B
1
3B
2
7A
1
7A
2
7B
1
7B
2
CAS(10e,11o)
0.0
50.8
-1.7
-6.6
- c.
34.7
27.8
24.9
29.3
44.8
1.7
-1.7
CAS(10e,13o)
0.0
45.9
2.1
-3.6
- c.
32.4
20.2
17.1
34.6
34.1
6.5
2.9
CAS(10e,16o)
0.0
40.5
5.5
-0.7
- c.
27.8
24.6
21.7
37.3
30.7
9.3
5.2
MCQDPT
(10e,11o)
0.0
44.3
8.4
1.3
34.6
30.4
28.1
23.7
41.8
50.1
14.1
9.9
MCQDPT
(10e,13o)
0.0
50.3
5.6
-1.2
36.2
31.6
28.0
24.0
38.8
41.0
11.0
6.7
[a] These orbitals are shown in Figure S1. [b] Stable spin states are shown in bold. [c] This run found 0
CI eigenvectors with S= 1.00.
Figure S2. Mean deviation of calculated energy gaps with CASSCF/MCQDPT methods using various
active spaces
Table S2. Geometric parameters and relative energies of various electron configurations of
[FeIVO](OH)2, optimized at MCQDPT(10e,13o)/tzvp and CASSCF(10e,16o) /tzvp level respectively a
State
Energy
R1
5
A1
1.65
5
A2
1.95
5
5
3
1.81
1.77
1.78
B1
B2
A1
b
3
3
3
7
7
7
7
1.72
1.66
1.63
1.83
2.80
1.88
1.87
A2
B1
B2
A1
A2
B1
B2
(Fe1-O2)
(1.66)
(6.86)
(1.83)
(1.79)
(- )
(1.76)
(1.66)
(1.64)
(1.85)
(2.98)
(1.90)
(1.89)
R2
1.79
1.79
1.81
1.81
1.79
1.78
1.78
1.77
1.81
1.83
1.81
1.81
b
(Fe1-O3)
(1.79)
(1.82)
(1.81)
(1.81)
(- )
(1.79)
(1.78)
(1.77)
(1.81)
(1.83)
(1.81)
(1.80)
A1
110.7
98.7
120.2
120.2
105.4
108.1
109.0
112.7
119.6
95.1
118.9
116.3
b
(O4-Fe1-O2)
(110.3)
(90.7)
(120.0)
(119.8)
(- )
(106.3)
(108.7)
(112.0)
(119.7)
(94.3)
(118.8)
(116.3)
A2
133.1
137.4
134.2
133.5
133.7
134.6
135.8
135.3
133.9
144.6
134.0
138.8
(H6-O4-Fe1)
(132.9)
(146.8)
(134.2)
(134.1)
(-b)
(134.7)
(135.4)
(135.3)
(133.7)
(143.6)
(134.0)
(139.0)
Relative
energy
0.0
50.3
5.6
-1.2
36.2
31.6
28.0
24.0
38.8
41.0
11.0
6.7
(27.5)
(24.5)
(21.6)
(37.2)
(30.6)
(9.2)
(5.2)
(0.0)
(49.7)
(5.4)
(-0.8)
b
(- )
[a] The CASSCF(10e,16o) /tzvp values were listed in parentheses. Bond lengths in Å, angles in degree
and relative energies in kcal/mol. [b] This run found 0 CI eigenvectors with S= 1.00.
Figure S3. Mean deviation of calculated geometric parameters between MCQDPT(10e,13o)/tzvp and
CASSCF(10e,16o) /tzvp
Section S2, A simple prove: The gradients of two state are proportional at MECP.
According to Morokuma's work (N. Koga, K. Morokuma, Chem. Phys. Lett. 1985, 119, 371.), the
method is based on the minimization of the Lagrangian function L( R )  E1 ( R)  [ E1 ( R)  E2 ( R)] ,
where R is nuclear coordinates, E1(R) and E2(R) are the energies of the state 1 and state 2 considered as
functions of R, and λ is Lagrange multiplier.
From the stationary condition (R* , λ* ) of the Lagrangian,
*
E2 ( R* )
L( R* * ) E1 ( R* )
* E1 ( R )



[

]
R*
R*
R*
R*
and therefore the following relationship exists,
0  g1 ( R* )   *[ g1 ( R* )  g 2 ( R* )]
where g1 and g2 are vectors of first derivatives of E1 and E2 with respect to the coordinates R at the
stationary point.
Then,
g1 ( R* )  kg 2 ( R* ) k 
g1 ( R* )
g 2 ( R* )
k   * / (1   * ) (There is a clerical error here in the original literature.)
Section S3, Wavefunctions information of MCQDPT(10e,13o) and CASSCF(10e,16o)
calculation for various states of [FeIVO](OH)2
Table S3. The natural occupation number of MCQDPT(10e,13o) calculation for various states of
[FeIVO](OH)2.[a]
State[b]
3
A1
3
A2
3
B1
3
B2
5
A1
5
A2
5
B1
5
B2
7
A1
7
A2
7
B1
7
B2
1σ
1π
2π
1δ
2δ
3π
4π
2σ
3σ
5π
6π
3δ
4δ
1.826
1.839
1.868
1.862
1.767
1.601
1.967
1.963
1.000
1.989
1.971
1.971
1.957
1.986
1.669
1.949
1.928
1.998
1.355
1.958
1.971
1.000
1.000
1.971
1.959
1.582
1.939
1.715
1.934
1.022
1.970
1.431
1.973
1.000
1.974
0.999
0.996
0.998
0.998
0.999
0.997
0.995
0.998
0.998
0.998
0.996
0.998
0.998
0.996
0.995
1.960
1.947
0.996
0.995
0.999
0.999
0.998
1.986
0.999
0.999
1.018
1.935
0.333
1.023
1.050
1.977
0.639
1.018
1.005
0.996
0.992
1.005
1.026
0.452
1.039
0.301
1.046
0.975
1.007
0.563
1.004
0.997
1.004
0.993
0.176
0.168
0.136
0.147
0.230
0.400
1.007
1.011
0.992
0.999
1.004
1.004
0.005
0.005
0.005
0.006
0.006
0.004
0.023
0.022
0.009
0.011
0.023
0.023
0.015
0.021
0.008
0.018
0.020
0.015
0.008
0.022
0.024
0.005
0.008
0.024
0.016
0.008
0.016
0.008
0.018
0.005
0.021
0.008
0.022
0.004
0.022
0.008
0.004
0.004
0.005
0.005
0.004
0.004
0.002
0.002
0.002
0.004
0.002
0.002
0.007
0.007
0.022
0.022
0.004
0.006
0.003
0.004
0.002
0.014
0.003
0.003
[a] The orbitals of active space were shown in Figure S1.
[b] See Figure 1 in paper for correspondence states.
8
Table S4. The information on the multiconfigurational wavefunctions from the CASSCF(10e,16o)
calculation[a]
State[b]
A1[c]
3
3
A2
3
B1
3
B2
5
A1
5
A2
5
B1
Orbital order
ALPHA
BETA
COEFFICIENT
-
1111110000000000
1110111000000000
1111000000000000
1110001000000000
0.7366939
-0.3039125
1111110000000000
1111000000000000
0.7890278
1111110000000000
1111000000000000
0.8041888
1111111000000000
1110000000000000
0.8637268
1111111000000000
1110000000000000
0.8129670
1111111000000000
1111111000000000
1101111100000000
1111111000000000
1101111100000000
1110000000000000
1100000100000000
1100000100000000
1110000000000000
1100000100000000
0.6669632
-0.4672299
-0.3490798
0.7363462
-0.3436192
1100000000000000
0.9272120
1100000000000000
0.9675294
1100000000000000
0.9400121
1100000000000000
0.9332141
1π-3π-1σ-2π-1δ-2δ-4π-2σ
3σ-5π-6π-3δ-4δ-7π-8π-4σ
2δ-2π-1σ-1π-4π-1δ-3π-2σ
3σ-5π-6π-3δ-4δ-7π-8π-4σ
2δ-1π-1σ-2π-3π-1δ-4π-2σ
3σ-5π-6π-3δ-4δ-7π-8π-4σ
2π-1π-1σ-3π-4π-1δ-2δ-2σ
3σ-5π-6π-3δ-4δ-7π-8π-4σ
1π-3π-1σ-2π-2δ-1δ-4π-2σ
3σ-5π-6π-3δ-4δ-7π-8π-4σ
2π-1σ-1π-4π-2σ-1δ-2δ-3π
3σ-5π-6π-3δ-4δ-7π-8π-4σ
1σ-1π-2π-3π-2σ-1δ-2δ-4π
3σ-5π-6π-3δ-4δ-7π-8π-4σ
2π-1π-3π-4π-1σ-1δ-2δ-2σ
7
A1
1111111100000000
3σ-5π-6π-3δ-4δ-7π-8π-4σ
2δ-1σ-2π-1π-4π-1δ-3π-2σ
7
A2
1111111100000000
3σ-5π-6π-3δ-4δ-7π-8π-4σ
2π-1σ-2σ-4π-1δ-3π-2δ-1π
7
B1
1111111100000000
3σ-5π-6π-3δ-4δ-7π-8π-4σ
1σ-1π-2σ-3π-1δ-4π-2δ-2π
7
B2
1111111100000000
3σ-5π-6π-3δ-4δ-7π-8π-4σ
[a] The orbitals of active space were shown in Figure S1.
[b] See Figure 1 in paper for correspondence states.
[c] This run found 0 CI eigenvectors with S=1.00.
5
B2
9
Section S5, Locating the MECP
The MECPs of 5A1/5B2 and 3B2/5B2 were located at the M06/TZVP level using the NewtonLagrange method. The geometry, energies and energy gradients of the two MECPs were listed in Table
S4. Using the same method, the MECPs have been located by a variety of DFT functionls.
Table S4. Energies (in hartree) and Energy Gradients (g, in hartree/bohr) of the Minimum Energy
Crossing Point (MECP) of the 5A1/5B2 and 3B2/5B2 at M06/TZVP level
MECP(5A1/5B2)
MECP(3B2/5B2)
E(5A1) = -1490.5026868 a.u.
E(3B2) = -1490.4847519 a.u.
E(5B2) = -1490.5026864 a.u.
E(5B2) = -1490.4847518 a.u.
Geometric parameters
g (5A1)
g (5B2)
g(5A1)/g(5B2)
B1 (O2-Fe1)
-0.03783
0.02436
-1.55
0.00450
0.10038
0.045
B2 (O3-Fe1)
-0.00472
0.00304
-1.55
0.00145
0.03230
0.045
B3 (H5-O3)
0.00120
-0.00078
-1.54
-0.00007
-0.00170
0.041
A1 (O3-Fe1-O2)
-0.03371
0.02170
-1.55
0.00195
0.04372
0.045
A2 (H5-O3-Fe1)
0.00518
-0.00333
-1.56
-0.00026
-0.00599
0.043
D1 (O4-Fe1-O2-O3)
0.0
0.0
-
0
0
-
D2 (O5-O3-Fe1-O2)
0.0
0.0
-
0
0
-
-λ/(1-λ)
-1.55
g (3B2)
g (5B2)
g(3B2)/g(5B2)
0.045
10
Section 6, Optimized internal coordinates at MCQDPT(10e,13o)/ TZVP level (the
MECP are located at CASSCF(10e,16o)/TZVP level)
3
3
A1
A2
Fe
Fe
O 1 1.77553
O 1 1.72058
O 1 1.78826 2 105.398
O 1 1.78463 2 108.130
O 1 1.78826 2 105.398 3 180.0000
O 1 1.78463 2 108.130 3 180.0000
H 3 0.93563 1 133.706 2 0.0000
H 3 0.93537 1 134.618 2 0.0000
H 4 0.93563 1 133.706 2 0.0000
H 4 0.93537 1 134.618 2 0.0000
3
3
B1
B2
Fe
Fe
O 1 1.65802
O 1 1.62984
O 1 1.77668 2 108.992
O 1 1.77309 2 112.667
O 1 1.77668 2 108.992 3 180.0000
O 1 1.77309 2 112.667 3 180.0000
H 3 0.93553 1 135.841 2 0.0000
H 3 0.93549 1 135.308 2 0.0000
H 4 0.93553 1 135.841 2 0.0000
H 4 0.93549 1 135.308 2 0.0000
5
5
A1
Fe
O 1
A2
Fe
1.65023
O 1
1.95197
O 1 1.79018 2 110.657
O 1 1.79488 2 98.654
O 1 1.79018 2 110.657 3 180.0000
O 1 1.79488 2 98.654 3 180.0000
H 3 0.93608 1 133.104 2 0.0000
H 3 0.93485 1 137.410 2 0.0000
H 4 0.93608 1 133.104 2 0.0000
H 4 0.93485 1 137.410 2 0.0000
5
5
B1
Fe
O 1
B2
Fe
1.80862
O 1
1.76692
O 1 1.81022 2 120.204
O 1 1.80805 2 120.209
O 1 1.81022 2 120.204 3 180.0000
O 1 1.80805 2 120.209 3 180.0000
H 3 0.93601 1 134.200 2 0.0000
H 3 0.93604 1 133.454 2 0.0000
H 4 0.93601 1 134.200 2 0.0000
H 4 0.93604 1 133.454 2 0.0000
11
7
7
A1
Fe
O 1
A2
Fe
1.83404
O 1
2.79563
O 1 1.80645 2 119.569
O 1 1.83143 2 95.085
O 1 1.80645 2 119.569 3 180.0000
O 1 1.83143 2 95.085 3 180.0000
H 3 0.93597 1 133.876 2 0.0000
H 3 0.93277 1 144.582 2 0.0000
H 4 0.93597 1 133.876 2 0.0000
H 4 0.93277 1 144.582 2 0.0000
7
7
B1
B2
Fe
Fe
O 1 1.88480
O 1
O 1 1.80912 2 118.890
O 1 1.80515 2 116.297
O 1 1.80912 2 118.890 3 180.0000
O 1 1.80515 2 116.297 3 180.0000
H 3 0.93604 1 133.960 2 0.0000
H 3 0.93506 1 138.833 2 0.0000
H 4 0.93604 1 133.960 2 0.0000
H 4 0.93506 1 138.833 2 0.0000
MECP (5A1/5B2)
MECP (3B2/5B2)
Fe
Fe
O 1 1.7137454
O 1 1.5681918
O 1 1.8019117 2 114.8155090
O 1 1.7564021 2 109.8146962
O 1 1.8019117 2 114.8155090 3 180.0000
O 1 1.7564021 2 109.8146962 3 180.0000
H 3 0.9358952 1 134.1600714 2 0.0000
H 3 0.9355199 1 135.2184089 2 0.0000
H 4 0.9358952 1 134.1600714 2 0.0000
H 4 0.9355199 1 135.2184089 2 0.0000
1.87263
12