A
Combined
DFT
and
Restricted
Open-Shell
Configuration Interaction Method Including SpinOrbit Coupling: Application to Transition Metal LEdge X-Ray Absorption Spectroscopy
Michael Roemelt,1 Dimitrios Maganas,1 Serena DeBeer
1,2
and Frank
Neese 1a
1
Max-Planck Institute for Chemical Energy Conversion, Stiftstrasse 34-36, D-45470 Mülheim
an der Ruhr, Germany
2
a
Department of Chemistry and Chemical Biology, Cornell University, Ithaca, NY 14853, USA
Author
to
whom
frank.neese@cec.mpg.de
correspondence
should
be
addressed:
Electronic
mail
I.
Matrix elements of the BO Hamiltonian
S’ = S
See Roemelt, M; Neese, F “Excited State of large open-shell molecules: An efficient,
general and spin-adapted approach based on a restricted open-shell ground state wavefuntion”
(in preparation)
S’ = S -1
i
t 
u 
Hˆ BO  j    A12  S    ij FtuI   tu FijO 
 SOMO

I
I
   ij  Ftu   tw | uw     tu  Fij   iw | jw  

 wwtu

 SOMO

SOMO




  ij | tu    it | ju    ij tu  Tw | Tw  
 

T

 wt 

 A22  S    wu

SOMO
SOMO



 
 1   tu    ij | tu    ij  FtuO    tv | uv     tw | uw   

v u
wt

 



SOMO SOMO

  

  wv | wv  

 ij tu  

wt v u



SOMO
SOMO


 A1  S   A2  S   2  tu  1 it | ju    tu   iv | jv    tu   iw | jw  
v u
wt



t  
i
 SOMO



b  
BO
ˆ
H u
  A1  S   A3  S   iu | tb   A2  S   A4  S      it | ub   1   tu  iu | tb  
 wwtu



i
t 
b 
Hˆ BO  j   A1  S   A5  S    ij FbtI   it | jb 
SOMO
 


 A1  S   A6  S    ij  FbtO    tu | ub     ij | tb  
u

 

 SOMO

 A2  S   A6  S      ij FbtI    ij | tb  
 wt

SOMO
 SOMO 

O


2
F

2
tw
|
wb



 tv | vb 



ij
ij
bt

vw


 wt
 A2  S   A7  S   
SOMO SOMO
SOMO

 ij    tu | ub    2  ij | tb 



u
w t
wt
w u


 ta   Hˆ BO  ub    A32  S    tu FabI   ab FtuO   tu | ab 
SOMO




2 A3  S  A4  S  1   tu  ta | ub     tu  wa | wb  
wt


SOMO
 SOMO 
 O

O

F

wa
|
wb


F

wt
|
wu





 wT | wT 
 ab  tu
   tu  ab

T


 wwtu 


SOMO
SOMO


 
2
I
 A4  S   1   tu   ab Ftu   tu | ab    ab   wt | wu    ab   vt | vu   
wt
v u

 

SOMO
SOMO
SOMO


    ab  wv | wv     ta | ub    tu | ab 

wt
 wt v u



t 
a 
b 
Hˆ BO  j   A3  S   A5  S    ab FjtO   jt | ab 
SOMO


 A3  S   A6  S    ab FjtI    ab  ut | uj    jt | ab  
u


SOMO


 A4  S   A5  S      ab FjtO  2  ta | jb    jt | ab  
 wt

SOMO


 A4  S   A6  S      ab FjtI   jt | ab 
 wt

 ia   Hˆ BO  bj    A52  S    ij FabI   ab FijI   ij | ab 
 SOMO

2 A5  S   A6  S      ab  it | jt    ij  at | bt 
 t

SOMO


A62  S     2 ij FabC  2 ab FijC  2  ij | ab 
 t

SOMO SOMO


2 A6  S   A7  S      2 ab  it | jt   2 ij  ua | ub 
 t u t

 SOMO SOMO 2 ij FabO  2 ab FijI  4 ij  ta | tb   4 ab  it | jt  

  



t
w  t  4 ij ab  tw | tw   2  ij | ab 





A72  S    SOMO SOMO SOMO

SOMO SOMO SOMO

4 ij ab  tw | tw      4 ij ab  tT | tT  
w 
 

t
u t
t
w t
T


u t
where the spin coupling coefficients An  S   are given by
A1  S    A3  S   
2S   1
2S   2
1
2S   2 2S   1
A2  S     A4  S   
A5  S   
A6  S    
A7  S   
2S   1
2S   3
 S   1
2
 S 2
1
S   1 2S   3 2S   2 2
2
1
S   1 2S   3 2 2S   2 2S   1
S’ = S + 1
ia   Hˆ BO bj     ij FabO   ab FijI   ij | ab 
II.
Parameterized diagonal elements of the DFT/ROCIS matrix
The parameterized diagonal elements of the CI matrix in the DFT/ROCIS method in the
basis of CSF’s with S   S are given by:
O KS
C KS
 ti Hˆ DFT / ROCIS  it  Ftt    Fii    c1  ii | tt   c2  it | it  
SOMOs

T
 Hˆ
a
t
DFT / ROCIS

a
t
O  KS 
aa
F
C  KS 
tt
F
1


cHF  tT | tT    iT | iT  
2


 c1  tt | aa   c2  ta | ta 
C KS
C KS
 ia Hˆ DFT / ROCIS  ia  Faa    Fii    c1  ii | aa   2c2  ia | ia 
O KS
O KS
C KS
O KS
 taiw Hˆ DFT / ROCIS  atwi  Faa    Ftt    Fii    Fww   c1  ii | ww   c1  tt | aa 
c1  ii | tt   c1  ww | tt   c1  ii | aa   c1  ww | aa 
1


cHF  tT | tT    iT | iT  
2


T
2
4
C KS
C KS
 Faa    Fii    c1  tt | tt   c1  ii | aa   2c2  it | it   c2  ta | ta 
3
3
SOMOs
1
2

   c2  tT | tT   cHF  iT | iT  
3
3

T
(1.1)
c2  it | it   c2  wa | wa  
 tait Hˆ DFT / ROCIS  tiat
SOMOs

Off-diagonal matrix elements of two “trip-doublet“ basis functions  tiat
and  uiau , that
share the same internal and external labels i and a but have different active labels t and u, are
treated as diagonal elements with respect to the parameterization.
1
1
1
1
2
 tait Hˆ DFT / ROCIS  uiau  FaaC  KS   FiiC  KS   c2  it | it   c2  iu | iu   c2  tu | tu 
3
3
3
3
3
1
1
1
 c1  ii | aa   c2  ta | ta   c2  ua | ua 
3
3
3
Likewise, the parameterized diagonal elements of CSF’s with S   S  1 read to:
 ia   Hˆ DFT / ROCIS  ia    FaaO KS   FiiC  KS   c1  ii | aa  
SOMOs

T
1
cHF  iT | iT 
2
Eventually, the parameterized diagonal elements with S   S 1 are given by:
 ti    Hˆ DFT / ROCIS  ti   
 FttO KS   FiiC  KS   c1  ii | tt 



 A12  S    SOMOs
1


  cHF  tT | tT    iT | iT  
2


 T

 FttO KS   FiiC  KS   c1  ii | tt   c1  tw | tw   c2  it | it   c2  iw | iw  
SOMOs




1
   SOMOs 

 wt   c2  tT | tT   cHF  tT | tT   cHF  tT | tT  

 A22  S   
2

 T 

 SOMOs SOMOs



c2  vw | vw 

 

v t
wt
2 A1  S   A2  S  
t 
a 
a 
 c  iw | iw 
wt
2
SOMOs
 O KS

a 
O KS
Hˆ DFT / ROCIS  t    A32  S    Faa    Ftt    c1  tt | aa    cHF TT | aa  
T


O
KS
O
KS





F

 Ftt
 c2  tw | tw   c1  tt | aa 
 SOMOs  aa

SOMOs

  
 wt c2  ta | ta   c2  wa | wa    c2  wT | wT  
2
 A4  S   

T

 SOMOs SOMOs



w c2  vw | vw
 

v t
2 A3  S   A4  S  
i 
SOMOs
SOMOs
 c  wa | wa 
wt
2
SOMO
 O KS

a 
O KS
Hˆ DFT / ROCIS  i    A52  S    Faa    Fii    c1  ii | aa    cHF Ta | Ta  
T



2 FaaC  KS   2 FiiC  KS   2c1  ii | aa  
SOMOs




   SOMOs
 t   2c2  tT | tT 
2

 A6  S   
 T

 SOMOs SOMOs

2

c2  tu | tu 

 

t
u




 F C  KS   F C  KS   c  ii | aa   c  ta | ta   c  wa | wa  
ii
1
2
2
 SOMOs SOMOs  aa



2
 A7  S      2 c2  iw | iw   c2  it | it   2c2  tw | tw 

 t wt  SOMOs


  c2  wT | wT   c2  tT | tT   1 cHF  iT | iT   

 T 
2
 
2 A5  S   A6  S  
SOMOs
 c   it | it    ta | ta 
2
t
2 A6  S   A7  S  
SOMOs SOMOs
  c  iw | iw   it | it    wa | wa   ta | ta 
t
wt
(1.2)
2
With the spin coupling coefficients
A1  S    A3  S   
2S   1
2S   2
1
2S   2 2S   1
A2  S     A4  S   
A5  S   
A6  S    
A7  S   
III.
An  S  
2S   1
2S   3
 S   1
2
 S 2
1
S   1 2S   3 2S   2 2
2
1
S   1 2S   3 2 2S   2 2S   1
Experimental Details of Ti Data Collection
[Cp2TiCl2] and [CpTiCl3] (99+%) were purchased from Strem Chemicals and were used
without further purification. Samples were finely ground and spread across double-adhesive
conductive carbon tape, which was attached to a copper paddle. Ti L-edge data were
measured at Stanford Synchrotron Radiation Lightsource using the 31-pole wiggler beam line
10-1. A spherical grating monochromator was used for energy selection. The data were
measured at room temperature as total electron yield spectra utilizing a Galileo 4716
channeltron electron multiplier as a detector. Three to four scans were measured in order to
check reproducibility; the presented data represent a single scan. TiO2 was used as a
calibration reference with the maximum of the L3 edge assigned to 458.2 eV and the highest
energy L2 feature set to 465.8 eV. In all cases, a linear background was fit to the pre-edge
region and was subtracted from the entire spectrum. Normalization was accomplished by
fitting a straight line to the post-edge region and normalizing the edge jump to 1.0. Due to the
presence of a significant oxygen background, at ~520 eV, there is a significant error in the
absolute normalizations.
IV.
Reduced matrix elements of the SOC operator
C01 0 zˆ m 0 
SOMO

m
zTT
T
1
0
0 zˆ 
m
C
  z mju
u
j
m
C01 0 zˆ m  bu  zub
C01 0 zˆ m  bu
0
vj
2 m
z jb
6
C01 0 zˆ m  bu

uj
C01  ti zˆ m  uj   ij tu
SOMO

m
zTT
  tu z mji   ij ztum
T
1
0
C
 zˆ 
t
i
m
b
u
0
C01  ti zˆ m  bj 
1
 ij ztbm
2
C01  ti zˆ m  bu
  ij tu zvbm
vj
C01  ti zˆ m  bu

uj
1
2
 ij ztbm 
 ij tu zubm
6
6
C01  ta zˆ m  bu   tu ab
SOMO

m
m
zTT
  tu zab
 zutm
T
C01  ta zˆ m  bj
1

 ab z mjt
2
C01  ta zˆ m  bu
  ab tv z mju
vj
C01  ta zˆ m  bu

uj
2
1
 ab z mju 
 ab z mjt
6
6
SOMO
1
m
C01  ia zˆ m  bj   ij ab  zTT
2
T
C01  ia zˆ m  bu
0
vj
C01  ia zˆ m  bu

uj
2
 ij zabm   ab z mji 

12
C01  taiw zˆ m  bu
  ij tu vw ab
vj
SOMO

m
zTT
T
   z
m
ij vw ab tu
m
 ij tu ab zvw
m
 ij tu vw zab
 tu vw ab z mji
C01 taiw zˆ m bu

uj
2
m
 ij ab wu ztum   ij ab tu zuw


6
4
 SOMO m

C01  tait zˆ m  bu
  ij tu ab   zTT
 zutm 
uj
6
 T

SOMO
2
m
  ij ab  zTT
6
TT
4
m
  ij tu zab
6
4
  ab tu z mji
6
b 
C1 0 zˆ m  j   z mjb
C1  ti zˆ m  bj     ij ztbm
C1  ta zˆ m  bj     ab z mjt
C1  ti zˆ m  bj     ij ztbm
C1  ia zˆ m  bj   
1
 ij zabm   ab z mji 

2
C1  taiw zˆ m  bj     ij ab ztwm
C1  tait zˆ m  bj   
2
1
1
 ij ab zttm 
 ij ab zabm 
 ab z mji
6
6
6
1
0
C

t 
i
t 
SOMO


m
ˆz m  uj     A12  S    ij tu  zTT
  tu z mji   ij ztum 
T


SOMO
 SOMO 
m
m
m
m 





tu
ij tu  zTT  2 ij tu zww   tu z ji   ij ztu  


T


 A22  S    wwtu


m
 1   tu   ij ztu

C01  i 
b 
zˆ m  u   0
C01  i 
b 
zˆ m  j     A1  S   A5  S    A1  S   A6  S    ij ztbm 
t 
 SOMO 
  A2  S   A6  S    2 A2  S   A7  S     ij  ztbm 
 wt

SOMO

m
m 
C01  ta   zˆ m  ub    A32  S    tu ab  zTT
  ab zutm   tu zab

TT


SOMO
SOMO


m
m 
 tu ab  zTT
  tu ab 2 zutm   ab zutm   tu zab





TT

 A32  S    wwtu 


m
 1   tu   ab zut

C01  t 
a 
b 
zˆ m  j     A3  S   A5  S    A3  S   A6  S     ab z mjt
  A4  S   A6  S    2 A4  S   A7  S     ab
SOMO

wt
z mjt
SOMO

m
m 
C01  ia   zˆ m  bj    A52  S    ab ij  zTT
  ab z mji   ij zab

T


SOMO SOMO



m
 A62  S    ij ab    2 zTT
 4 zttm 
t
 T


 SOMO SOMO 

 SOMO m
m 
m
m 
A72  S       ij ab   2 zTT
 4 zttm  4 zww
  2 ab z ji  2 ji zab 
 T

 t wt 

u 
C1 0 zˆ m  j    A1  S   z mju
m
C1 0 zˆ m  bu    A3  S   zub
C1 0 zˆ m  uj     A5  S   z mjb
SOMO


m
C1  ti zˆ m  uj     A1  S    ij tu  zTT
  tu z mji   A2  S    ij z mju
T


C1  ti zˆ m  ub    0
b 
C1  ti zˆ m  j   A6  S    ij ztbm
C1  ta zˆ m  uj     0
 SOMO

b 
m
C1  ta zˆ m  u   A3  S    tu zab
 A3  S      ab tu zvvm   ab zutm 
 v u

C1  ta zˆ m  bj     A6  S    ab z mjt
C1  ia zˆ m  uj    
A1  S  
C1  ia zˆ m  bu    
C1  ia zˆ m  bj   
 ij Cm zaum
2
A3  S  
2
A5  S  
2
 ab zuim

z   ab z mji 
m
ij ab
m
C1  itwa zˆ m  uj     A2  S    ij tu zaw
C1  itwa zˆ m  ub     A4  S    ab uw ztim
m
C1  itwa zˆ m  bj    A7  S    ij tu zaw
C1  tait zˆ m  uj    
b 
C1  tait zˆ m  u  
C1  tait zˆ m  bj   




A1  S  
6
A3  S  
6
 ij zaum 
 ab z 
2 A2  S  
6
2 A4  S  
6
2 A5  S    2 A6  S  
2 A7  S  
6
1   tu   ij zaum
1   tu   ab zuim
 ab z mji
 ij zabm
6
2 A7  S    2 A6  S   SOMO
A5  S  

6
 ab z mji 
A5  S  
 2 
ij
u
z mji
u
6
A6  S   SOMO
6
ab
6
m
ab uu
z
 ij zabm
where
2S
C01 
S  S  1
2 2S  1
2S  3
C1 
C1  2
1 x
y
z pq  iz pq


2
z pq1  
z pq1 
1 x
y
z pq  iz pq


2
z
z 0pq  z pq
and
A1  S    A3  S   
2S   1
2S   2
1
2S   2 2S   1
A2  S     A4  S   
A5  S   
A6  S    
A7  S   
2S   1
2S   3
 S   1
2
 S 2
1
S   1 2S   3 2S   2 2
2
1
S   1 2S   3 2 2S   2 2S   1
Matrix elements between wavefunctions  SM
and  SJ M  are evaluated as follows:
I
1,0,1
 1 S
m
ˆ tot  S M       E  S      1m C C  S
 SM
H
I
J
IJ SS MM
I
 I J 
  zˆ  

M
m
M
 
m


where the summation of  and  is over all ROCIS basis functions.
V.
Coordinates of [CuCl4] in D2d and D4h symmetry
D2d
Cu
Cl
Cl
Cl
Cl
-0.000031 -0.000016 -0.000234
2.146470 -0.000040
0.870967
-2.146442
0.000048
0.870932
-0.000043
2.146466 -0.870845
0.000046 -2.146458 -0.870819
D4h
Cu
Cl
Cl
Cl
Cl
0.000008
2.336259
-2.336248
-0.000007
-0.000012
0.000011
-0.000012
-0.000017
2.336263
-2.336245
0.000000
0.000000
0.000000
0.000000
0.000000
VI.
DFT/ROCIS spectra of D2d – [CuCl4]2- using ZORA
Figure S1. DFT/ROCIS spectra of [CuCl4]2- in D2d symmetry using no relativistic correction
(top), ZORA (middle) and ZORA including picture change effects (bottom).
VII.
Scalar Relativistic effect on L-edge of [FeCl4]2-
Figure S2. DFT/ROCIS spectra of [FeCl4]2- using no relativistic correction (black), ZORA
(red) and the DKH2 approximation (blue).
VIII.
Basis set dependence on SOC splitting
Figure S3. ROCIS spectrum of [CuCl4]2- in D2d symmetry using the def2-TZVP (black),
QZVP (red) and CP(PPP) basis set (blue).
IX.
Effect of density on the L-edge of [Cp2TiCl2]
.
Figure S4. DFT/ROCIS spectrum of [Cp2TiCl2] using the ground (red) and excited state
(black) density for the evaluation of SOMF integrals. Both curves virtually overlay each
other.
X.
Charges of effective core potentials and point charges for non-heme iron
complexes
Large supercells that contain a few thousand atoms were extracted from the crystal strctures
of the non-heme iron complexes.1-3 The supercells were divided into three parts. The first part
is the region that is treated by quantum chemical methods (QR) comprising the non-heme iron
complex. The second part is the sphere of counterions, called boundary region, (BR) that are
approximated by effective core potentials according to Fuentealbe and co-workers.4 The third
part comprises a large number of point charges (PC) that mimicks the effect of the remaining
part of the supercell. Three distribution of charges were applied to the effective core
potentials, each obeying a set of boundary conditions. Two common boundary conditions of
all three models are that the total charge of the supercell has to be close to zero (~10 -12-10-14
charge units) and that the charge of a given ion has to be as close as possible to its charge as
defined in the sense of the electrostatic potential model introduced by Breneman and Wiberg.5
Model A has been chosen with regard to these conditions. For model B the charge of the QR
plus the charge of the BR also has to equal zero. Model C is equivalent to model B but also
applies the conductor-like screening model with an infinite dielectric.6
Model A:
Atom
Fe
Cl
N
Na
K
Co
[FeCl4]20.836
-0.709
1.000
-
[FeCl6]42.042
-0.804
1.050
1.052
-
[FeCl6]31.610
-0.778
0.386
0.689
[Fe(tacn)2]2+
0.424
-0.982
0.220
-
[Fe(tacn)2]3+
0.588
-0.984
0.486
-
[FeCl4]2-0.707
0.615
-
[FeCl6]40.500
0.500
-
[FeCl6]30.064
0.116
[Fe(tacn)2]2+
-0.500
-
[Fe(tacn)2]3+
-0.5
-
[FeCl4]20.837
-0.696
0.983
-
[FeCl6]42.043
-0.802
1.050
1.054
-
[FeCl6]31.609
-0.780
0.410
0.685
[Fe(tacn)2]2+
0.426
-1.001
0.223
-
[Fe(tacn)2]3+
0.584
-0.979
0.496
-
Model B:
BR
Atom
Fe
Cl
N
Na
K
Co
PC
Atom
Fe
Cl
N
Na
K
Co
XI.
Fitting of DFT/ROCIS parameters
18 mononuclear complexes were chosen for this study featuring a variety of metal centers in
different coordination environments, oxidation- and spin states. The data set consist of the
iron complexes [Fe(III)Cl6]3- (1) and Fe(II)(tacn)2 (2), the Titanium complexes Ti(IV)Cp2Cl2 (3)
and Ti(IV)CpCl3 (4) and the Vanadium complexes K2[V(V)O(O2)2C5H4NCOO)] (5),
V(V)O2(R,R’L1)] , R=Me, R’=Ph (6), R=H, R’=Me (7), R=H, R’=Ph (8), R=H, R’=4-O2NPh
(9), V(IV)O(HRL2), R=H (10)7, Me (11), Et (12), Cl (13), V(IV)O(acac)2 (14), V(IV)O(acac)2Py
(15) V(IV)O(salen) (16) , V(IV)O(TPP) (17) and V(III)(acac)3 (18). In the foregoing list the
following abbreviations were used for the ligands: L1 = oxyoxime,8 L2 = salicylaldoxime,8
acac = acetylacetonato, salen = N, N’-bis(salecylidene)ethylendiamine and TPP = 5,10,15,20Tetraphenyl-21H,23H-porphine. Complexes 1-5, 14, 17-18 were purchased or synthesized
according to common published procedures. Complexes 1-4 are discussed in this work, while
further details will be given in an upcoming manuscript for complexes 5-18. V L-edge data
for complexes 6-13, 15-16 have been reported previously8 and kindly offered from professor
Nigel Young in a personal communication. The BP86/def2-TZVP(-f) optimized structures of
the above complexes are presented in Figure S5.
Figure S5. The BP86/def2-TZVP(-f) optimized structures of the eighteen model complexes
used for the parameterization procedure.
Description of the parameterization procedure
In the course of the parameterization procedure a constrained multigaussian least square fitting
on the experimental spectrum employing the Lavenberg-Marquardt algorithm was performed
over the calculated transition energies (calculated spectra). The chosen gaussians have the
general form:
f  x   Amp 
1
2  FWHM
2
e

 x Centroid 2
2 FWHM
Where Amp is the amplitude, FWHM is the full width at half maximum and Centroid is the
position of the defined Gaussian. Tight convergence criteria are used for the relative error in
the approximate solution (xtol=10-8) as well as for the desired sum of squares (ftol=10-8). The
The quality of the fit is measured with the aid of the following parameters: First,
SSerr   
 y
gridpoints
2
exp
i
 yimodel  

2
i
where SSerr , is the regression sum of the squares which is the sum of the squares of the
deviations of the predicted values yimodel from the experimental values yiexp . Second,
SStot 
 y
gridpoints
model
i
 y  

2
i
where SStot is the total sum of the squares of the deviation of the predicted values yimodel from
the average experimental value yimodel and eventually
R2  1 
SSerr
SStot
where R2 is usually referred to as the coefficient of determination. It provides a measure for
the goodness of fit and takes values between 0 and 1. In this work R2 is used as a normalized
version of SSerr and is used as an indicator of the quality of the fitting throughout the
parametrization procedure.
Fitting protocol
The parametrization was performed in three steps. At first, a one-digit fitting was performed
in which c1, c2 and c3 parameters were varied in the range between 0.0-1.0 taking steps of 0.1
intervals. This step was followed by a second-digit fitting procedure in a more spotted region
of c parameters. For all these calculations the def2-SVP basis set was used. A final refinement
of the optimized parameters was performed with the larger def2-TZVP(-f ) basis set (2000
calculations/functional). The calculated spectra were generated with the orca_mapspec utility
by applying a constant line shape gaussian broadening of 0.2 eV. All calculated spectra have
been energy shifted in order to match the maximum experimental and calculated L3 intensity.
(V(B3LYP)= 10.9 eV, V(BHLYP)= -4.8 eV, Fe(B3LYP)= 13.9 eV, Fe(BHLYP)= -3.9 eV, Ti(B3LYP)= 11.8
eV, Ti(BHLYP)= -2.8 eV). We should note that slightly different shifts are reported in the main
text for iron and titanium in which the shifts refer to a linear correlation between
experimentally observed and calculated transition energies. Such corresponding shifts for
vanadium will be reported elsewhere.
1.00
1.00
0.98$
0.98$
0.98
0.98
0.98
0.98
0.97$
B3LYP$
0.96
0.96
0.97
0.97
0.97
0.97
BHLYP$
0.97$
0.97$
0.96$
0.96$
0.95
0.95 0.95
0.95$0.95
0.94 0.94
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0.90
0.90
0.90
0.88
0.88
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0.93$
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0.87$
0.86
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33
44
55
66
77
88
99
18 Average
1010 11 11 12 12 13 13 14 14 15 15 16 16 17 17 18 Average
Figure S6. Best-fit values between experimental and calculated spectra expressed in terms of
R2 for the data set. Blue and green columns visualize the individual contributions for B3LYP
and BHLYP functionals, respectively along the data set, whereas red and purple columns
represent the corresponding average contributions.
XII.
Comparison to RAS-PT2 results
In a recent publication, Odelius and co-workers calculated the Ni L-edge of [Ni(H2O)6]2+ as
well as the Fe L-edge of [Fe(tren(py)3)]2+ and its high spin analogue [Fe(tren(6-methyl-py)3]2+
with the RAS-PT2 methodology.9 In order to compare the performance of the RAS-PT2
method with DFT/ROCIS for the calculation of transition metal L-edges, analogous
calculations were conducted with DFT/ROCIS. Prior to the L-edge calculations, geometry
optimizations were carried out utilizing the BP86 functionalref together with the def2-TZVP(f) basis set.ref During the optimizations molecular charges were absorbed by the conductor-
like screening model (COSMO).ref Transition energies and moments were calculated
according to the computational setup introduced in section IIIB of the main manuscript. All
DFT/ROCIS spectra are shifted by +17 eV (Ni) or 16.2 eV (Fe).
Figure S7 presents a comparison of the experimental Ni L-edge of [Ni(H2O)6]2+ (top panel)
with the calculated Ni L-edges as obtained from RAS-PT29 (middle panel) and DFT/ROCIS
(bottom panel) calculations. Experimentally, the L3 edge exhibits a sharp main feature at
853.4 eV and a small satellite at higher energies (~855.5 eV). On the other hand, the L2 edge
consists of two almost equally intense features at about 870.2 eV and 871.5 eV. The RASPT2 spectrum reproduces the relative energy and intensity of all spectral features with high
accuracy. The DFT/ROCIS spectrum does not reach such a high degree of accuracy for the Ni
L-edge. In the L3 edge, the small satellite feature is predicted much too close to the main
feature and the calculated L2 edge has only a single band.
Figure S7. Comparison of the Ni L-edge of [Ni(H2O)6]2+ (top panel) with the calculated Ni
L-edges as obtained from RAS-PT29 (middle panel) and DFT/ROCIS (bottom panel)
calculations.
The octahedral [Fe(tren(py)3)]2+ complex has a 1A1g ground state while the corresponding
methylated analogue [Fe(tren(6-methyl-py)3]2+ features a 5T2g ground state. As expected, the
change of the spin state strongly influences the Fe L-edge of the complex. In Figure S8 the
experimental Fe L-edges of [Fe(tren(py)3)]2+ and [Fe(tren(6-methyl-py)3]2+ (top panel) are
compared to the calculated Fe L-edges as obtained from RAS-PT2 (middle panel) and
DFT/ROCIS (bottom panel). In the experimental spectrum the L3 edge of [Fe(tren(py))3]2+
consists of an intense main band at 709.4 eV and two small satellite features that appear as
shoulders at the low energy side of the main band around 711.4 eV and 713.2 eV. The shape
of the L2 edge is similar to the shape of the L3 edge with the exception that the two shoulders
have merged to a single feature. Upon introduction of methyl groups to the pyridine ligands
and the concomitant change of the spin state of the Fe center, the Fe L-edge moves about 2 eV
to higher energies. Furthermore, the two edges become broader, resulting in lower maximal
intensities. At the lower energy side of the L3 edge, a shoulder appears around 706.0 eV.
RAS-PT2 correctly predicts the shift in energy as well as the intensity loss in the L2 edge. In
particular, the L2 edge is reproduced quite accurately. However, in contrast to the findings
made for [Ni(H2O)6)]2+, the RAS-PT2 spectra of [Fe(tren(py)3)]2+ and [Fe(tren(6-methylpy)3)]2+ considerably deviate from the corresponding experimental spectra. For example, the
loss in intensity in the L3 edge with the change of the spin state is not reproduced.
Furthermore, the RAS-PT2 spectra of both species exhibit intense features at the low energy
side of the main L3 band that are not experimentally observed. The DFT/ROCIS calculations
on the other hand do not only correctly reproduce the shift in energy and intensity but also
produce realistic spectral shapes for both Fe-complexes.
In summary, we have found that while the RAS-PT2 calculations for [Ni(H2O)6]2+ are of
higher accuracy than the corresponding DFT/ROCIS calculations, DFT/ROCIS yields better
results for the two octahedral Fe complexes. Hence, on the basis of the obtained results none
of the two approaches can be classified as the more (or less) reliable. In our opinion, both
methods have their strengths and weaknesses arising from their different construction
schemes. Most probable, the relative performance of the two methods will be case sensitive
for future applications.
Figure S8. Comparison of the Fe L-edge of [Fe(tren(py)3)]2+ and [Fe(tren(6-methyl-py)3]2+
(top panel) with the calculated Fe L-edges as obtained from RAS-PT29 (middle panel) and
DFT/ROCIS (bottom panel) calculations.
XIII.
1.
2.
3.
4.
5.
6.
7.
References
J. K. Beattie and C. J. Moore, Inorg. Chem. 21 (4), 1292-1295 (1982).
J. C. A. Boeyens, A. Forbes, R. D. Hancock and K. Wieghardt, Inorg. Chem. 24 (19),
2926-2931 (1985).
J. W. Lauher and J. A. Ibers, Inorg. Chem. 14 (2), 348-352 (1975).
P. Fuentealba, H. Stoll, L. Szentpaly, P. Schwerdtfeger and H. Preuss, J. Phys. B 16,
L323 (1983).
C. M. Breneman and K. B. Wiberg, J. Comput. Chem. 11 (3), 361-373 (1990).
A. Klamt and G. Schüürmann, Journal of the Chemical Society-Perkin Transactions 2
(5), 799-805 (1993).
For complex 10 no reliable data were availiable (see ref 7). Hence for the calibration
procedure experimental data were taken from the isostructural complex 11.
8.
9.
D. Collison, C. D. Garner, J. Grigg, C. M. McGrath, J. F. W. Mosselmans, E. Pidcock,
M. D. Roper, J. M. W. Seddon, E. Sinn and P. A. Tasker, J. Chem. Soc., Dalton Trans.
(13), 2199-2204 (1998).
I. Josefsson, K. Kunnus, S. Schreck, A. Föhlisch, F. M. F. de Groot, P. Wernet and M.
Odelius, The Journal of Physical Chemistry Letters 3 (23), 3565-3570 (2012).