Ab initio Study of Exchange Coupling for the Consistent Understanding
of the Magnetic Ordering at Room-Temperature in V[TCNE]x
Bogdan Frecusa,b Corneliu I. Oprea,b Petre Panait,b Marilena Ferbinteanu,c Fanica Cimpoesu,d* and
Mihai A. Gîrţub*
5
a
Department of Theoretical Chemistry, Royal Institute of Technology, Stockholm, S-106 91, Sweden.
Department of Physics, Ovidius University of Constanţa, Constanţa 900527, Romania; E-mail: mihai.girtu@univ-ovidius.ro, Phone: +40721703344
c
Department of Inorganic Chemistry, University of Bucharest, Bucharest, 020462, Romania
d
Department of Theoretical Chemistry, Institute of Physical Chemistry, Bucharest 060021, Romania, E-mail:cfanica@yahoo.com
b
10
Contents
15

Table SM1: Results of BS-DFT band calculations

Table SM2: Results of BS-DFT calculations on dinuclears

Table SM3: Results of CASSCF calculations on dinuclears

Table SM4: Results of CASSCF calculations on symmetric
40
trinuclears

35
Table SM5: Results of CASSCF calculations on asymmetric
Table SM2. Total energy, expectation value of the square of the spin,
and the exchange coupling parameters determined by means of
unrestricted BS-DFT/B3LYP/6-31G* calculations on
{(HCN)5VII[TCNE]}+ molecular models for different spin projections Sz =
2 (HS) vs. Sz = 1 (BS), and various selections of fragments with respect
of the defined (a), (b) and (c) species. The estimation of coupling
parameter is done comparatively by Eq. (9) (penultimate column) and Eq.
(10) (last column).
Sz
<S2>
1
2
2.802
6.035
-1857.90779
-1857.89975
V-[TCNE](b)
Table SM6: Results of MRPT2 calculations on symmetric
1
2
2.800
6.035
-1857.91465
-1857.90654
V-[TCNE](c)
1
2
2.802
6.035
-1857.90359
-1857.89543
trinuclears
20

Table SM7: Results of MRPT2 calculations on asymmetric
trinuclears
25
J12,H-d (K)
J12,I-d (K)
-784.4
-845.8
-791.5
-853.5
-796.5
-859.0
V-[TCNE](a)
trinuclears

Ecalc(a.u.)
Table SM1. Total energy, expectation value of the square of the spin,
and the V-TCNE exchange coupling parameter J12 determined by means
of unrestricted BS-DFT band calculations, with the 6-31G* basis set, of
the ideal V[TCNE]2 lattice for different spin multiplicities, based on Eq.
(4).
E (a.u.)
<S2>
45
-1839.05728811
8.7583
LS (BS)
-1839.09822458
1.7259
HS
-1832.537282
8.7562
LS (BS)
-1832.594380
1.1551
ELS (a.u.)
EHS (a.u.)
J12 (K)
V-TCNE(a)
-1852.03229
-1852.03050
-141.3
V-TCNE(b)
-1852.03850
-1852.03639
-166.6
V-TCNE(c)
-1852.03382
-1852.03195
-147.6
J12, I-PBC (K)
DFT/U-BLYP/6-31G*
HS
Table SM3. The energies of the low-spin and high-spin states and the
exchange coupling parameters determined by means of Eq. (13) based on
CASSCF(6,7) calculations for the {(HCN)5VII[TCNE]}+ dinuclears cut
from the unit lattice along each of the three christallographic directions.
-718.2
DFT/U-SVWN/6-31G*
-1001.7
30
1
15
5
Table SM4. The energies of the symmetrical [TCNE]-V-[TCNE]
trinuclears, with respect to the low-spin state for the four possible spin
eigenstates and various geometry sequences, computed using the
CASSCF(9,9) method and fitted using the relations in Table 5 with
parameters given in Table 4.
State
Ecalc(K)
Ecalc(a.u.)
20
Efit(K)
S
S13
1/2
3/2
3/2
5/2
1
1
0
1
2
Au
4
Au
4
Ag
6
Au
-2204.27917
0.0
-2204.27782
427.1
-2204.27679
751.4
-2204.27539
1194.9
TCNE(b)-V-TCNE(b)
1/2
3/2
3/2
5/2
1
1
0
1
2
-2204.28559
0.0
-2204.28400
501.8
-2204.28277
891.7
-2204.28111
1416.7
TCNE(c)-V-TCNE(c)
1/2
3/2
3/2
5/2
1
1
0
1
2
Table SM6. The energies of the symmetrical [TCNE]-V-[TCNE]
trinuclears, with respect to the low-spin state for the four possible spin
eigenstates and various geometry sequences, computed using the MRPT2
method and fitted using the relations in Table 5 with parameters given in
Table 4.
State
10
Au
Au
4
Ag
6
Au
4
Au
Au
4
Ag
6
Au
-2204.27170
-2204.27029
-2204.26922
-2204.26775
4
0.0
441.9
751.4
1178.4
1/2
3/2
3/2
5/2
1
1
0
1
2
Au
-2208.21704
0.0
4
Au
-2208.21383
1012.7
4
Ag
-2208.21148
1754.6
6
Au
-2208.20839
2730.8
[TCNE](b)-V-[TCNE](b)
0.0
1013.9
1754.6
2703.8
0.0
498.7
891.7
1329.9
1/2
3/2
3/2
5/2
1
1
0
1
2
0.0
1131.9
1938.6
3018.4
0.0
482.6
784.4
1286.9
1/2
3/2
3/2
5/2
1
1
0
1
2
[TCNE](a)-V-[TCNE](a)
0.0
445.3
784.4
1248.9
Table SM5: The energies of the asymmetric [TCNE]-V-[TCNE]
trinuclears, with respect to the low-spin state for the four possible spin
eigenstates and various geometry sequences, computed using the
CASSCF(9,9) method and fitted using Eq. (15) with parameters given in
Table 4.
S
Ecalc(a.u.)
Efit(K)
S13
TCNE(a)-V-TCNE(a)
Ecalc(a.u.)
Ecalc(K)
S
Ecalc(K)
25
-2204.28648
0.0
-2204.28523
396.5
-2204.28425
704.4
-2204.28292
1123.7
TCNE(a)-V-TCNE(c)
0.0
464.5
702.8
1254.2
1/2
3/2
3/2
5/2
-2204.25822
0.0
-2204.25658
519.0
-2204.25557
839.1
-2204.25395
1350.6
TCNE(b)-V-TCNE(c)
0.0
460.4
839.3
1232.6
1/2
3/2
3/2
5/2
-2204.26206
-2204.26056
-2204.25944
-2204.25799
0.0
490.3
827.5
1308.4
0.0
472.1
827.6
1283.9
-2208.27391
-2208.27052
-2208.26757
-2208.26372
0.0
1070.7
2003.4
3220.3
0.0
1177.2
2003.4
3139.3
Ecalc(a.u.)
Ecalc(K)
Efit(K)
[TCNE](a)-V-[TCNE](b)
TCNE(a)-V-TCNE(b)
1/2
3/2
3/2
5/2
Au
Au
4
Ag
6
Au
4
-2208.22561
0.0
-2208.22228
1049.5
-2208.21947
1938.6
-2208.21562
3154.1
[TCNE](c)-V-[TCNE](c)
Table SM7: The energies of the asymmetric [TCNE]-V-[TCNE]
trinuclears, with respect to the low-spin state for the four possible spin
eigenstates and various geometry sequences, computed using the MRPT2
method and fitted using Eq. (15) with parameters given in Table 4.
S
Efit(K)
Au
Au
4
Ag
6
Au
4
2
1/2
3/2
3/2
5/2
-2208.28058
0.0
-2208.27734
1024.6
-2208.27499
1765.0
-2208.27170
2803.7
[TCNE](a)-V-[TCNE](c)
0.0
1064.5
1764.5
2861.1
1/2
3/2
3/2
5/2
-2208.27370
0.0
-2208.27061
977.0
-2208.26824
1724.6
-2208.26421
2997.9
[TCNE](b)-V-[TCNE](c)
0.0
1077.8
1721.7
2921.5
1/2
3/2
3/2
5/2
-2208.22020
-2208.21670
-2208.21397
-2208.21084
0.0
1153.5
1967.7
3078.8
0.0
1105.7
1967.8
2956.7