Spectrophotometric determination of the formation constants of some transition metal cations with a new synthetic Schiff base in dichloromethane and chloroform using rank annihilation factor analysis

Article abstract of DOI:10.1016/j.molstruc.2010.10.025

The complex formation between a new synthesized Schiff base and the cations Ni²⁺, Co²⁺, Cu²⁺, Zn²⁺ in dichloromethane (DCM) and chloroform solutions was investigated spectrophotometrically using rank annihilation factor analysis (RAFA). The results of mole ratio plots and continuous variation data show the stoichiometry of complexation were found to be 1:1, and 2:1 metal ion to ligand. The stoichiometry was obtained as 1:1 metal ion to ligand ratio for Co²⁺, Ni²⁺ and Zn²⁺ in chloroform and 2:1 for Cu²⁺. In DCM the stoichiometry was obtained as 1:1 for Co²⁺ and 2:1 for Ni²⁺ and Zn²⁺ and a consecutive 2:1 metal ion to ligand ratio was obtained for Cu²⁺. Formation constants of these complexes were estimated by application of RAFA on spectrophotometric data. In this process the contribution of ligand was removed from the absorbance data matrix when the complex stability constant acts as an optimizing object and simply combined with the pure spectrum of the ligand, the rank of the original data matrix can be reduced by one by annihilating the information of the ligand from the original data matrix.

Full text of DOI:10.1016/j.molstruc.2010.10.025

Journal of Molecular Structure 985 (2011) 86–90
Contents lists available at ScienceDirect
Journal of Molecular Structure
journal homepage: www.elsevier.com/locate/molstruc
Spectrophotometric determination of the formation constants of some
transition metal cations with a new synthetic Schiff base in dichloromethane
and chloroform using rank annihilation factor analysis
a
a
a
Abbas Afkhami a, , Tayyebeh Madrakian , Hassan Keypour , Saeid Soltanbeygi ,
⇑
Farzad Khajavi a, Majid Rezaeivala b
a Faculty of Chemistry, Bu-Ali Sina University, Hamedan 65174, Iran
b Department of Chemical Engineering, Hamedan University of Technology, Hamedan 65155, Iran
a r t i c l e i n f o
a b s t r a c t
The complex formation between a new synthesized Schiff base and the cations Ni2+, Co2+, Cu2+, Zn2+ in
dichloromethane (DCM) and chloroform solutions was investigated spectrophotometrically using rank
annihilation factor analysis (RAFA). The results of mole ratio plots and continuous variation data show
the stoichiometry of complexation were found to be 1:1, and 2:1 metal ion to ligand. The stoichiometry
was obtained as 1:1 metal ion to ligand ratio for Co2+, Ni2+ and Zn2+ in chloroform and 2:1 for Cu2+. In
DCM the stoichiometry was obtained as 1:1 for Co2+ and 2:1 for Ni2+ and Zn2+ and a consecutive 2:1 metal
ion to ligand ratio was obtained for Cu2+. Formation constants of these complexes were estimated by
application of RAFA on spectrophotometric data. In this process the contribution of ligand was removed
from the absorbance data matrix when the complex stability constant acts as an optimizing object and
simply combined with the pure spectrum of the ligand, the rank of the original data matrix can be
reduced by one by annihilating the information of the ligand from the original data matrix.
Ó 2010 Elsevier B.V. All rights reserved.
Article history:
Received 18 August 2010
Received in revised form 12 October 2010
Accepted 13 October 2010
Available online 20 October 2010
Keywords:
Schiff base
RAFA
Formation constant
Spectrophotometry
1. Introduction
spectra of different chemical species involved in the equilibria
is an important problem, because it makes the determination of
Schiff base metal complexes have been widely studied because
they have industrial, antifungal, antibacterial, anticancer and her-
bicidal applications [1]. Chelating ligands containing N, S and O do-
nor atoms show broad biological activity and are of special interest
because of the variety of ways in which they are bonded to metal
ions [2]. It is known that the existence of metal ions bonded to bio-
logically active compounds may enhance their activities [3,4].
Stability constants can be key parameters for the investigation
of equilibria in solution. They are very important in many fields
such as industrial chemistry [5], environmental studies [6],
medicinal [7] and analytical chemistry [8]. Therefore complexa-
tion reactions of metal ions with different ligands have been
widely studied [9–11]. Several methods such as potentiometric
titration [12], conductometry [13], and spectrophotometry [14],
have been reported for the determination of stability constants.
Among the methods used for the determination of stability con-
stants, spectrophotometric methods have the advantage of sensi-
tivity and are suitable for determination of stability constants in
solution under different experimental conditions. Overlapping of
stability constants by classical methods difficult or even impossi-
ble, and can cause great uncertainties in the obtained results. This
problem can be easily overcome using chemometric methods
[15,16], where one can analyze whole spectra, thereby utilizing
all spectral information.
Rank annihilation factor analysis (RAFA) was originally devel-
oped by Ho et al. as an iterative procedure [17]. It was modified
by Lorber to yield a direct solution of a standard eigen-value
problem [18] and can be employed to quantitatively analyze gray
systems with an unknown background. RAFA has been used in dif-
ferent fields including the spectrophotometric study of chemical
kinetics [19,20], spectrophotometric determination of acid dissoci-
ation constants and the formation constants of metal–ligand com-
plexation [21–25]. In the present work we used RAFA for the
determination of the stability constants of some transition metal
ions with a recently synthesized Schiff base in different solvents.
2. Theory
The basis of the application of RAFA in the determination of the
formation constants for 1:1 and 2:1 (metal to ligand) complexes
was described in our previous works [24,25].
⇑
Corresponding author. Tel./fax: +98 811 8272404.
E-mail address: afkhami@basu.ac.ir (A. Afkhami).
0022-2860/$ - see front matter Ó 2010 Elsevier B.V. All rights reserved.
doi:10.1016/j.molstruc.2010.10.025

A. Afkhami et al. / Journal of Molecular Structure 985 (2011) 86–90
87
For a consecutive 2:1 metal to ligand complexation reaction, the
equations are as follows
cells and the measurements were performed at 25 0.1 °C. All
experiments were performed with analytical reagent grade
chemicals. The Schiff base was synthesized in the laboratory.
DCM, chloroform, diethyl ether, sodium sulfate, 3,5-di-tert-
butylsalycilaldehyde, silica gel, chloride and nitrate salts of
Ni2+, Cu2+, Co2+ and Zn2+ were purchased from Merck (Darms-
tadt, Germany) and N,N0-bis(3-aminopropyl)piperazine was sup-
plied from Sigma–Aldrich Chemical Companies and used
without further purification. All solutions were prepared freshly
prior to the measurements. All calculations were performed in
MATLAB 6.5 (Math Works, Cochituate Place, MA) and Microsoft
Excel 2003.
M þ L ! ML
ML þ M ! M2L
½MLꢀ
ð1Þ
ð2Þ
Kf1
¼
ð3Þ
ð4Þ
½Mꢀ½Lꢀ
½M2Lꢀ
Kf2
¼
½MLꢀ½Mꢀ
CL ¼ ½Lꢀ þ ½MLꢀ þ ½M2Lꢀ
ð5Þ
ð6Þ
3.2. General procedure for synthesis of Schiff base N,N0-bis
(2-((3-propylimino)methyl)-4,6-di-tert-butylphenol)piperazine (PTBP)
CM ¼ ½Mꢀ þ ½MLꢀ þ 2½M2Lꢀ
where [L], [M], [ML] and [M2L] are the equilibrium concentrations
of ligand, metal ion and the complexes, respectively. Kf1 and Kf 2
are the stepwise stability constants of the complexes, CL is the total
concentration of ligand, which remains constant, and CM is the total
concentration of metal ion, which is varied when employing the
molar ratio method.
3,5-Di-tert-butylsalicylaldehyde (1 mmol, 0.234 g), N,N0-bis
(3-aminopropyl)piperazine (0.5 mmol, 0.1 g) and silica gel (0.5 g)
were mixed together in a tube and irradiated in a microwave oven.
The progress of the reaction was monitored by gas chromatogra-
phy upon completion of the reaction, the crude product was re-
crystallized from ethanol and then dried over sodium sulfate. The
solvent was evaporated and the product was washed with diethyl
ether and dried. The product was identified by melting point, mass
spectrum, elemental analysis, and IR and 1H and 13C NMR spectra.
Anal. Calc. for C40H64N4O2ꢂ0.5H2O (MW: 632.5): C, 74.27; H, 10.77;
N, 8.66. Found: C, 74.18; H, 11.10; N, 8.50%. Yield: 0.28 g (90%).
By combination of Eqs. (3)–(6) as a function of the free ligand
concentration [L] yields
3
2
K2f1 ꢁ 4Kf1Kf2½Lꢀ þ ðK2 CM ꢁ K2 CL ꢁ 4Kf1Kf2ðCM ꢁ 2CLÞÞ½Lꢀ
f1
f1
2
ꢁ ðKf1CM þ Kf1Kf2ðCM ꢁ 2CLÞ þ 1Þ½Lꢀ þ CL
¼ 0
ð7Þ
m.p. (124.0–126.0) °C. IR (Nujol, cm-1): 1631 [
t(C@N)], 1162(s)
[t
(CAO)]. MS (EI): m/z = 632 [M]+. 1H NMR (90 MHz, CDCl3, ppm)
If the values of CM, CL and Kf 1 and Kf2 are known, it is possible to
obtain the free ligand concentration [L] from the roots of the asso-
ciated polynomial.
dH: 1.33 (s, 18H, H-3), 1.47 (s, 18H,7-H), 1.90 (b m, 4H,13-H),
2.51 (b m, 12H, 14-H and 15-H), 3.64 (t(3J = 8.0 Hz), 4H, 12-H),
7.10–7.39 (m, 4H, 1-H and 5-H), 8.37 (b s, 2H, AC@N), 13.89(s,
2H, AOH). 13C NMR (400 MHz, CDCl3, ppm) dC: 28.1 (t, C-13),
29.4(q, C-3), 31.5(q, C-7), 34.1(s, C-4), 35.0(s, C-8), 53.3(t, C-15),
56.1(t, C-14), 57.6(t, C-12), 117.8 (s, C-10), 125.7, 126.8 (d, C-1,
C-5), 136.7, 139.9 (s, C-2, C-6), 158.2 (s, C-9) (aromatic ring),
166.0(d, C-11, AC@N) [28]. Scheme 1 shows the structure of the
synthesized Schiff base.
A two-way data matrix can be formed by measuring absorbance
under different wavelengths at a series of metal to ligand molar ra-
tios with constant analytical concentrations of the ligand. By
removing the contribution of one component from the original
absorption data matrix using RAFA, the rank of the residual matrix
decreases by one. By substitution of different values of Kf1 and Kf2
in Eq. (7) for a given amount of CM and CL, different vectors of li-
gand concentration will be obtained. The molar absorptivity of
the ligand can be obtained from the spectrum of the pure ligand.
Therefore the absorption spectra for the ligand at different
metal–ligand molar ratios are obtained by multiplying the concen-
tration profile of the ligand by its molar absorptivity. RAFA uses the
iterative procedure to find the best Kf so that by removing the
ligand spectra from the original absorption data matrix, the rank
of the residual matrix reduces by one.
3.3. Experiment procedure
Stock solutions of PTBP and metal ion salts were prepared in
DCM and chloroform. The analytical ligand concentration was kept
constant and different concentrations of metal ions were added to
the PTBP solution. Then after 30 min the spectrum of the solution
was obtained between 270 and 500 nm in 1 nm intervals. The
molar ratio data was used to determine the stoichiometry of the
metal–ligand complexes and the RAFA program was used to calcu-
late the complex formation constant. All specific details are given
in the next section.
Based on principal component analysis (PCA), the RSD (Relative
Standard Deviation) method is widely used to determine the num-
ber of principal components [26,27]. The RSD is a measure of the
lack of fit of a principal component model to a data set. The RSD
is defined as:
P
ꢀ
ꢁ
1=2
c
gi
nðic¼nꢁþ11Þ
RSDðnÞ ¼
ð8Þ
where gi is the eigenvalue, n is the number of considered principal
components and c is the number of samples. The RSD was used as a
formula to obtain the optimum stability constant.
3. Experimental
3.1. Apparatus and materials
Absorption spectra were obtained with a Perkin–Elmer Lamb-
da 45 UV–VIS spectrophotometer using 1 cm path length glass
Scheme 1. The structure of the synthesized Schiff base.

88
A. Afkhami et al. / Journal of Molecular Structure 985 (2011) 86–90
4. Results and discussion
0.05
0.04
0.03
4.1. Simulation for a 2:1 metal to ligand consecutive complexation
reaction
Fig. 1 shows the simulated absorbance spectra of a 2:1 metal–
ligand consecutive complex system at a fixed concentration of li-
gand (8.0 ꢃ 10ꢁ5 mol Lꢁ1) and various concentrations of metal
ion with molar ratios of 0–2.0 with a certain stability constant
(log Kf1 = 5.20 and log Kf2 = 5.60). Concentration profiles of the li-
gand and complexes (ML and M2L) were obtained through the
appropriate equations. The pure spectra of the ligand and com-
plexes were simulated by Gaussian function with the characteris-
tics of: kmax(L) = 450 nm, kmax(ML) = 500 nm and kmax(M2L) = 520,
spectral band width of 20 nm for ligand, 22 nm for ML complex
and 25 nm for M2L complex, and maximum molar absorptivity of
2500 L molꢁ1 cmꢁ1 for ligand, 2200 L molꢁ1 cmꢁ1 for ML complex
and 2000 for M2L complex. The simulated absorbance matrix was
constructed by multiplying the concentration profiles matrix into
the pure spectra matrix. Then the noise equal to 0.001 absorbance
unit was added to the data matrix. PCA results show that there are
three principal components in the absorbance data matrix. The
synthetic data matrix was processed by the RAFA method and
the relationship between the RSD of the residual matrix and the
stability constants (Kf1 and Kf2) is shown in Fig. 2.
RSD
0.02
0.01
0
log Kf2
log Kf1
Fig. 2. The relationship between RSD and stability constants, Kf1 and Kf2 for a
consecutive 2:1 metal–ligand complex formation system, obtained log (Kf1) = 5.20
and log (Kf2) = 5.60.
1
0.8
Cu
0.6
Ni
4.2. Real data
0.4
Zn
Co
The electronic absorption spectra of PTBP ligand between the
0.2
0
L
cations of the first transition series (i.e. Co2+, Ni2+, Cu2+ and Zn2+
)
in CHCl3 solution are shown in Fig. 3. The PTBP ligand has an absor-
bance band with a kmax at 329 nm, while each of cations does not
show any absorption band in the investigated region. With the
addition of M2+ ion to PTBP ligand solution, strong shift (50–55
nm) toward higher wavelengths in comparison to free PTBP ligand
were observed where neither cation nor PTBP ligand have any
absorption in this region. This is a clear indication for the formation
of complexes. The absorption bands for Co2+, Ni2+ and Zn2+, mix-
tures appeared at 379, 387 and 383 nm, respectively, whereas
the absorbance at 329 nm (due to PTBP ligand) decreased (Fig. 4).
The stiochiometry of complex was examined in CHCl3 solution
by the continuous variations method and found a maximum at
XPTBP value of 0.33 and 0.5 that emphasis on formation of a 2:1
Cu2+ – PTBP complex and 1:1 for Co2+, Ni2+ and Zn2+ ions in this
solvent.
300 320 340 360 380 400 420 440 460 480 500
Wavelength, nm
Fig. 3. Visible spectra of PTBP and its complexes with Co2+, Ni2+, Cu2+and Zn2+ in
CHCl3 solution.
0.8
2
0.7
0.6
14
0.5
0.4
0.3
0.2
0.1
0
The PCA results show that the ratio of two consecutive eigen-
values is large at the second eigenvalue, so there are two principle
components (absorptive species) in the absorbance data matrix for
all complexes in CHCl3. One of the species is the ligand and the
2
1
0.25
0.20
0.15
0.10
0.05
0.00
300.0
350.0
400.0
450.0
500.0
Wavelength, nm
Fig. 4. Experimental absorption spectra for Ni2+ (1); PTBP (2) and complex with
PTBP in chloroform with different concentrations of metal in the range of 0.0–2.0 M
ratio of metal to ligand.
other is the complex. Therefore even for M2L complexes, the exis-
tence of two species (L and M2L) was observed and the ML species
was not detected. The value of the stability constant for each com-
plex was optimized by applying RAFA on the data matrix shown in
Fig. 4.
350
400
450
500
550
600
650
Wavelength, nm
Fig. 1. Simulated absorbance spectra of a consecutive 2:1 metal–ligand complex
formation system at a fixed concentration of ligand and various concentrations of
metal ions. log Kf1 = 5.20, log Kf2 = 5.60, kmaxðLÞ ¼ 450 nm , kmaxðMLÞ ¼ 500 nm and
kmaxðM2LÞ ¼ 520.
Complexes in DCM showed a 1:1 metal to ligand stoichiometry
for the Co2+ and a 2:1 metal to ligand stoichiometry for the Ni2+

A. Afkhami et al. / Journal of Molecular Structure 985 (2011) 86–90
89
and Zn2+. The wavelength of maximum absorbance for the ligand
in DCM was observed at 329 nm. The wavelengths of maximum
absorbance for complexes were observed at 379 nm, 384 nm and
382 nm for Co2+, Ni2+ and Zn2+ respectively. But, Cu2+ formed two
complexes ML and M2L in DCM solution which their wavelengths
of maximum absorbance were 396 nm and 362 nm respectively.
PCA results show that there are two principal components for
Co2+, Ni2+ and Zn2+ complexes in DCM (Schiff base and the com-
plex) and there are three principal components for Cu2+ complexes
in DCM. (Schiff base, ML, and M2L complexes). The plots of singular
values versus number of components for the metal complexes in
DCM are shown in Fig. 5. As seen in Fig. 5 there are three principal
components for Cu2+ complex in DCM and there are two principal
components for Co2+, Ni2+ and Zn2+ complexes in DCM.
Table 1
Formation constants estimated for Schiff base complexes with metal ions in two
solvents.
Cation
Solvent
CHCl3 (D = 4.81a, DN = 4.0b)
DCM (D = 9.08a, DN = 1.6b)
Metal/ligand
log Kf
Metal/ligand
log Kf
Co2+
Ni2+
Cu2+
1:1
1:1
2:1
5.00 0.02
5.60 0.03
6.00 0.01
1:1
2:1
1:1
2:1
2:1
6.30 0.02
8.08 0.02
5.47 0.02
4.83 0.02
7.58 0.03
Zn2+
1:1
5.65 0.02
a
D: dielectric constant (25 °C).
DN: Gutmann donor number.
b
(a)
30
(a)
8.00
25
20
15
10
5
L
M2L
ML
4.00
0.00
0
0
2
4
6
8
10
12
14
0
0.5
1
1.5
2
2.5
Number of components
Cm/CL
60
50
40
30
20
10
0
40000
30000
20000
10000
0
(b)
(c)
(b)
M2L
L
ML
0
2
4
6
8
10
12
14
16
Number of components
271
321
371
421
471
Wavelength (nm)
30
25
20
15
10
5
Fig. 6. Concentration profiles (a) and spectral profiles (b) of the components of Cu2+
complex with PTBP in DCM.
RAFA was applied on the data matrices and stability constants
of the complexes were obtained in minimum RSD Table 1 shows
the stability constants for Co2+, Ni2+, Cu2+ and Zn2+ complexes with
PTBP in chloroform and DCM solutions.
Cu2+ forms a 2:1 metal to ligand complex in DCM and also the
intermediate complex (ML) was seen in the absorbance data
matrix. After applying RAFA on the data matrix and obtaining the
stability constants (Kf1 and Kf2), concentration profiles of the com-
ponents (L, ML, M2L) were obtained using the appropriate equa-
tions (Eqs. (3)–(6)), then by projection of absorbance data matrix
on the concentration profiles, the spectral profiles were obtained
using:
0
0
2
4
6
8
10
12
14
16
Number of components
30
(d)
25
20
15
10
5
S ¼ CþD
ð9Þ
where C+ is the pseudo-inverse of the concentration matrix, D is the
absorbance data matrix and S is the spectrum matrix. Fig. 6 shows
the concentration and spectral profiles of the formed components of
Cu2+ complex with PTBP in DCM.
From Table 1, it is obvious that the stability of the complexes in
general was higher in DCM. It is well known that the Gutmann do-
nor number and dielectric constant of solvents [29] is an important
measure in complexation reactions. It should be noted that DCM,
0
0
2
4
6
8
10
12
14
16
Singular value
Fig. 5. The plots of singular values versus number of components for complexes of:
(a) Co2+, (b) Cu2+, (c) Ni2+ and (d) Zn2+ with PTBP in DCM.

90
A. Afkhami et al. / Journal of Molecular Structure 985 (2011) 86–90
and CHCl3 possess similar dipole moments (i.e. DCM: 1.55, CHCl3;
1.01), but have quite different donor numbers. It is obvious that the
stability of complex increases significantly by decreasing the donor
number of the solvents. Therefore, as expected, the type of solvent
can have a great effect on stoichiometry and stability constant of
the complex.
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5. Conclusions
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absorption spectra and concentration profiles of species in several
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Acknowledgments
The authors acknowledge the Bu-Ali Sina University Research
Council and Center of Excellence in Development of Chemical
Methods (CEDCM) for providing support to this work.
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