The Fe(III)-cyanide chemical bond in the hexacyanoferrate (III) anion : a theoretical study of linkage isomerism and of spin-state isomers

              
Rev. Acad. Canar. Cienc., XIII (Núms. 1-2-3), 105-113 (2001) (publicado en Julio de 2002)
The Fe(III)-cyanide chemical bond in the hexacyanoferrate (111) anion.
A theoretical study of linkage isomerism and of spin-state isomers
Pedro Gil(, Eduardo Medina de la Rosa·, Pedro Martín-Zarza and Pablo A.
Lorenzo-Luis
Departamento de Química Inorgánica, Facultad de Farmacia, Universidad de La
Laguna, Tenerife, Canary Islands, Spain
Abstract
The aim of this work is to study the Fem-cN- bond in [Fem(CN)6]3- because Fe111 that
is a hard cation prefers the carbon atom which is a soft atom in the CN- anion. The
electronic structures and molecular properties of CN- free ligand, the [Fem(CN)6]3-
anionic complex together with its linkage isomer [Fe111(NC)6]3- and spin-state isomers
(low spin LS and high spin HS) for the linkage isomers, using the density functional
theory (DFT) are studied. Equilibrium geometries, vibrational frequencies and
electronic spectra are calculated and compared with the experimental data.
Keywords: Computational chemistry, coordination chemistry, hexacyanoferrate(III)
Introduction
The cyanide ligand act as a strong nucleophile, occupies a high position in the
spectrochemical series, gives rise to a large nephelauxetic effect, produces a large trans
effect and is probably the most stable carbanion (1,2). A review devoted to the
chemistry oftransition metal cyanide compounds has been published (3).
The CN- ligand presents a variety of binding modes in different complexes ( 4). Thus,
in the KJ[Fem(CN)6] (5), [Cu11(dien)h[Fem(CN)6h·6Hiü (6) compounds, the Fe111-CN­bond
is forrned through the carbon atom. This same behaviour is presented by the
isomorphous complexes of general formula K3[M(CN)6] (7), M = Mnm and Co111• On
the other hand, in Prussian blue Fe4m[Fe11(CN)6]-xH20 (8) both Fe11-C and Fem-N bonds
exist in the crystal structure.
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The first issue unresolved in the literature consulted is to explain why the hard cation
Fem prefers the carbon atom which is a soft atom in the CN- ligand, in addition to
which, this ligand is a soft base (9).
In order to answer this question it is necessary to know first the electronic structure and
molecular properties of the CN- free ligand. Therefore, the aim of this work is to study
the electronic structure and molecular properties of the CN- free ligand, the
[Fem(CN)6] 3- anionic complex together with its linkage isomer [Fem(NC)6) 3- and spin­state
isomers (low-spin LS and high-spin HS) for the linkage isomers, using the density
functional theory (DFT). The impressive success of the DFT in modeling the molecular
and electronic structures oftransition metal complexes has been shown (10).
Experimental Procedure
K3[Fem(CN)6] was commercially available (Merck) and used without further
purification. The IR transmission spectrum was recorded with a Bruker ITS 55 using
KBr as support, in the 4000-400 cm-1 spectral range. The electronic spectrum in
aqueous solution (10-5 M in K3[Fem(CN)6]) was performed on a Shimadzu UV-2101 PC
spectrophotometer in the 600-190 nm spectral range.
Theoretical Calculations
The energy according to DFT includes the nuclear, core and Coulomb terms as the
Hartree-Fock energy, yet replaces the Hartree-Fock exchange energy by an exchange
functional, Ex(P), and adds a correlation functional, Ec(P).
EDFT = E"uclear + Ecore + ECoulom + Ex(P) + Ec(P)
Both of the latter are functions of the electron density, P (11-14). DFT treats the
electronic energy as a function of the electron density of ali electrons simultaneously
and thus includes electron correlation effects. DFT comprises severa! types of
functionals. In this paper, we use the Becke-Perdew (11-14) (pBP86/DN .. ) functional in
which the non-local corrections are introduced perturbatively with full polarization basis
set.
Total energy and equilibrium geometries were calculated. Normal mode analysis was
performed to obtain vibrational frequencies. The frequencies calculated were not scaled.
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The electroruc spectrurn was also calculated using DFT (pBP86/DN ). Calculations
were made with the Spartan Pro program (15). This program predicts vibrational
frequencies and allows animated visualization of normal mode vibrations. Calculations
were run in direct mode on a Pentiurn II PC.
(!)
(II)
RESULTS AND DISCUSSION
In Table 1 are given the structural data of equilibriurn geometries as well as the er
ofCN-, [Fe111(CN)6]3- and [Fe111(NC)6]3- species theoretically calculated.
Table 1. Structural pararneter of the equilibriwn geometries for CN- (!), [Fe111(CN)6]3- (LS and
HS) (11) and [Fe111(NC)6] 3- (III) (in Á and deg.)
Species C-N Fe-C Fe-N < Fe-C-N Area Vol. Enegie
(CPK) A2 (CPK) Á3 (KcaVmol)
1.190 -58287 .1323
LS 1.18 1.96 - 1.97 179.9 209.93 -1142858.599 228.86
HS 1.182 2.23 179.8- 179.9 227.56 -1142799.594 253.46
LS 1.180 1.950- 1.960 180.0 219.32 -1142786.987 247.62
(III)
HS 1.184 2.136 179.9- 180.0 230.71 -1142772.900 264.42
*Surface area and volwne of space-filling model CPK (Corey-Pauling-Koltwn) calculated by
DFT; LS and HS = low and high spin, respectively.
In Table 2 are found the experimental structural data. A good concordance is ob
between the experimental structural parameters and those calculated by DFT for
[Fem(CN)6]3- and [Fem(NC)6]3- low spin anions.
It is observed in Table 1, that while the C - N bond distances and Fe - C - N bond
theoretically calculated, not change practically in LS and HS anions, the Fe - C and Fe - 1'
distances are function ofthe spin states, being largest in HS anions.
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Table 2. Experimental structural parameters for CN- (I), [Fe111(CN)6]3- (II) species (in A and deg).
For comparative proposes Na2[Fe(CN)s(N0)]·2H20 (III) and fe4(fe(CN)6h"xH20 (IV) are
included
Species C-N Fe-C Fe-N < Fe-C-N Reference
(I) 1.15 (17)
(II) 1.13(2) 1.93(1)-1.97(2) 176(2)-179(2) (5)
1.12(2) - 1.18(2) 1.93(2) - 1.99(2) 172(2) - 179(1) (6)
(III) 1.14(2) - 1.19(2) 1.90(2) - 1.93(2) 177(1) - 179(1) (18)
(IV) 1.12 - 1.15(2) 1.906 - 1.945(2)* 2.012 - 2.039(9) (8)
*in this case Fe11
This fact is due to the occupation of eg orbitals in the HS complexes; as consequence
the CPK volumes ofthe anions are larger than the LS corresponding anions (Table 1).
The linkage isomerization energy for [Fem(CN)6]3- (LS)~ [Fem(NC)6]3- (LS) transition
is 71.612 Kcal/mol. On the other hand, the energy for [Fem(CN)6]3- (LS)~
[Fem(CN)6]3- (HS) spin-state isomers transition is 59.005 Kcal/mol. Both the linkage
isomerization energy and later the transition energy indicate that the more stable species
at room temperature is [Fem(CN)6]3- (LS), as observed experimentally. The difference
in energy between LS and HS for [Fe111(CN)6)3- is: -2~o + 2P, where ~o is 35,000 cm-1
(100.1 Kcal/mol) (16) and Pis the electron-pairing energy. From the above equation, P
= 70.59 Kcal/mol is obtained. As ~o > P it is more favorable for electrons to pair in the
t2g level and therefore a low spin complex is obtained. The value obtained for P is 83%
ofthe value of P for Fem free (85.42 Kcal/moÍ) (9). For the transition [Fem(NC)6]3- (LS)
~ [Fem(NC)6]3- (HS), the energy is 14.087 Kcal/mol. Also in this case the more stable
species is [Fem(NC)6]3- (LS).
The Mulliken atomic charges calculated from the Mulliken population analysis are
given in Table 3.
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Table 3. Mulliken atomic charges for CN-, [Fe(CN)6]3- and [Fe(NC)6]3- anions
CN- [Fe(CN)6]3- [Fe(NC)6]3-
LS HS LS HS
e -O.S32 Fe -0.474 0.2S3 0.032 0.49S
N -0.468 Cl -0.048 -0.180 -0.409 -0.3S9
C2 -0.046 -0.181 -0.366 -0.3SS
C3 -0.048 -0.181 -0.362 -0.3SS
C4 -0.046 -0.181 -0.366 -0.3SS
es -0.048 -0.181 -0.362 -0.3SS
C6 -0.047 -0.180 -0.410 -0.3S6
NI -0.389 -0.361 -0.131 -0.222
N2 -0.3S8 -0.362 -0.123 -0.227
N3 -0.374 -0.362 -0.124 -0.227
N4 -0.389 -0.362 -0.123 -0.227
NS -0.3S8 -0.362 -0.124 -0.227
N6 -0.374 -0.362 -0.131 -0.228
Total -1.000 -3 .000 -3.000 -3.000 -3.000
LS and HS = low and high spin
lt is interesting to observe that in the CN" free anion, the carbon atom presents one
negative charge larger than the nitrogen atorn, this latter atom being more
electronegative than the carbon atom. This explains why the Fe(III) hard ion prefers
links to, in the case of CN-, the more "hard" atom of C. The values are in good
agreement with the those in reference (3) although our calculations show a higher
negative charge over the carbon atom. The HOMO of the CN- anion a1so in our
calculations is slightly antibonding and principally localised over the carbon atom.
However, in the [Fem(CN)6]3- (LS and HS) the charge of the nitrogen atom is more
negative than the carbon atom. Therefore, the Fe-C bond favours the back-bonding and
the Fe-C bond distance is shorter than the Fe-N bond distance (Table 2).
For [Fem(CN)6]3- or [Fem(NC)6]3- (both with LS and C2v symmetry) and
[Fe111(CN)6]3- or [Fem(NC)6]3- (both with HS and C4v symmetry), there are 33 normal
modes of vibration. The calculated vibrational frequencies and the standard
thermodynamic quantities of these species are given in Table 4. lt is observed that a
good agreement exists between the calculated and the experimental frequencies.
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Table 4. Main vibrational frequencies (cm-1) calculated by DFT for [Fe(CN)6]3- (I), [Fe(NC)6]3- (TI). For comparative purpose are included the
experimental vibrational frequencies (cm-1) of [Fe(CN)s(N0)]2- (III). CN- (IV) free ligand is also include. Standard thermodynamic quantities at 298.15
K and 1.00 atm.
. D.H (Kcal/mol) D.S (cal/mol K)
Species Symmetry Frequencies Symmetry Frequencies Energ. D.H1raslati D.Hrotatio D.Hvibral D.Straslational D.Srotational D.Svibrationa
(Calcd.) (Exper.) (Ref.) (Kcal/mol)
(I) LS B 1 425 (Fe-C stretch) 416 (Fe-C stretch) (6) 30.552 0.889 0.889 35.126 41.957 29.914 27.502
B2 589 (Fe-C==N bend) 583 (Fe-C=N bend)
Bl 2044-2127 (C==N stretch) 2094 - 2126 (C==N stretch)
2076- 2026 (C==N stretch)**
HS 2428 (C==N stretch) 27.626 0.889 0.889 37.865 41.957 29.096 81.556
,~_.
o
(TI) LS Bl 440 (Fe-N stretch) 28.539 0.889 0.889 33.709 41.957 29.686 31.998
B2 519 (Fe-N=C bend)
Al 2069(N==C stretch)
HS 2276 (N==C stretch) 27.488 0.889 0.889 37-363 41.957 28.712 67.177
(III) 420--450 (Fe-C stretch) (18)
470-515 (Fe-C==N bend)
2140--2182 (C==N stretch)
(IV) 2047 (C==N stretch) 2080 (C==N stretch) (19) 2.927 0.889 0.592 2.927 35.703 11.374 lx!0-3
*zero-point vibrational energy; **this work
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The simulation of the UV-visible spectra of the [Fem(CN)6]3- (HS and LS) and
[Fem(NC)6]3- (HS and LS) species has been performed using DFT. The most interesting
feature emerges from the HOMO-LUMO transition (Tables 5 and 6), because according
to our calculations, it demands an energy for [Fe111(CN)6]3- LS of 3.8441 eV, which
corresponds to a wavelength of 323 mn. close to the band experimentally observed at
320 nm (5,15) 2T2(t5) ~ 2A2(t4e) in the electronic spectrum and which accounts
moreover, for the yellow colour of this compound. lt is one band identified as Fem
crystal-field transition.
Table 5. Energies corresponding to HOMO-LUMO molecular orbitals
Species HOMO (eV) LUMO(eV) Transition (e V)
[Fe(CN)6]3- LS 4.6683 8.5124 3.8441 (323 nm)
[Fe(CN)6]3- HS 5.0646 9.5431 4.4785 (277 nm)
[Fe(NC)6]3- LS 4.3232 7.0139 2.6907 (461 nm)
[Fe(NC)6]3- HS 4.2098 9.7009 5.4911 (225 nm)
*Ls and HS = low and high spin
Table 6. Electronic spectrum of [Fe(CN)6]3- LS
Type MO > MO ~E (e V) A.(nm) Exp. (nm)
a > a 54 > 55 (*) 4.03 308 302.5
a > a 53 > 55 4.04 307
a > a 52 > 55 4.15 298 290
a > a 51 > 55 5.04 245 250
p > p 53 > 55 3.95 314 302.5
p > p 52 > 55 3.99 311
p > p 51 > 54 1.62 765
HOMO > LUMO 3.84 323 320.5
(Spartan)
7t(CN) > 7t(CN-) • 192
*the number shows the order MO energies as they are output calculations. We have not
considered symmetry argument like do the Spartan program
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Continued Table 6 Electronic spectrum of [Fe(CN)6]3-LS
Type MO>MO ~E (eV) A.(nm) Exp. (mn)
7t(CN") > HOMO 4.14 300
(Spartan)
7t(CN") > HOMO (av) 34,35,36 > 54 (av) 2.93 423 418.5
charge transfer
a> p (spin forbidden) 53 > 55 4.56 271 260.5
a> p (spin forbidden) 52 > 55 4.69 264
The experimental spectrum is shown in Fig. 1. A good concordance is observed
between the experimental spectrum and that theoretically calculated.
0,3 - ----------------- ------------- -- ---- -,
A
0,2
0,1
O!---~~~~~~~~~~~~~__::::::::;:====:::::===:::::;::::;
150 250 360 450 550
nm
Figure l. Experimental electronic spectrum ofK3[Fe(CN)6] in water
From Table 5 it is observed that the HS species absorb in ultraviolet in the electronic
spectra. These species may therefore be expected to be pale colour or colourless.
The[Fe111(NC)6]3- (LS) anion should present a more intense yellow colour than
Fe111(CN)6]3- (LS).
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