1. Coordination Chemistry - 1
Prepared By
Dr. Krishnaswamy. G
Faculty
DOS & R in Organic Chemistry
Tumkur University
Tumakuru
2. Molecular Compounds (or) Addition compounds
Complex salts
Double salts
Combination of simple molecular inorganic salts in the stoichiometric
proportions produce molecular compounds or addition compounds.
Depending upon the behavior molecular compounds can be
classified into two groups
A double salt is simple aggregates of
two inorganic salt and splits into the
constituents ions in solution and
individual identities are retained.
Examples:
Potash Alum: K2SO4.Al2(SO4)3.24H2O
Mohr’s salt: (NH4)2SO4.FeSO4.6H2O
Complex salts
Double salts
A complex salt is simple aggregates of
two inorganic salt and splits into the
new complex ion in solution and
individual identities are lost.
Examples:
Potassium ferrocyanide:
4KCN.Fe(CN)2 or K4[Fe(CN)6]
Potassium ferricyanide:
3KCN.Fe(CN)2 or K3[Fe(CN)6]
3. Potash Alum represented by K2SO4.Al2(SO4)3.24H2O is an example of double salt
and prepared by crystallization of solution containing equimolar K2SO4 and
Al2(SO4)3.
K2SO4(aq) + Al2(SO4)3(aq) → K2SO4. Al2(SO4)3.24H2O(s)
K2SO4. Al2(SO4)3.24H2O(s) → 2K+(aq) + 2Al3+ (aq) + 4SO4
2-(aq)
and it ionizes in solution as follows
Potassium ferrocyanide represented by 4KCN.Fe(CN)2 or K4[Fe(CN)6] is an
example of complex salt and prepared by the action of KCN on FeSO4.
example of complex salt and prepared by the action of KCN on FeSO4.
2KCN + FeSO4 → K2SO4 + Fe(CN)2
4KCN + Fe(CN)2 → K4 [Fe(CN)6]
and it ionizes in solution as follows
K4 [Fe(CN)6] → 4K+ + [Fe(CN)6]4-
4K+ + 6CN- + Fe2+
Complex ion
4. A complex ion is an ion in which a metal cation is attached to ligands by
coordinate bonds.
Coordination chemistry is the branch of inorganic chemistry which
concerns the study of coordination compounds.
In the structural formula of a coordination compound, the central metal cation or
atom and the ligands attached to it are written in a square bracket [ ] called a
coordination sphere.
coordination sphere.
The cation or anion outside the coordination sphere is called the ionization
sphere or counter ion.
The atom in a ligand that is directly attached to the metal cation or atom is called
donor atom and the number of donor atoms attached to metal cation or
atom is called the coordination number.
5. C+ / A- [Mn+/ M (L)x]
Coordination sphere
Coordination number
Metal Cation
Metal atom
Ionization sphere
Ligands
Metal atom
Ionization sphere
The ligands remaining within the coordination sphere ligate the metal center to
determine the stereochemistry of the complex.
The ligands are the Lewis bases, the metal centres are the Lewis
acids and the complexes are the Lewis acid-base adduct.
6. Ligands
classification
Organic and inorganic nature of ligands
Organic ligands example oxalate, ethylenediamine;
Inorganic ligands example H2O, NH3, halides
Hard-Soft character of ligand
Hard ligands example H2O, NH3, OH-, F-
Soft ligands example CO, CN-, C2H4
Charge bearing properties of ligands
Cationic – NO+
Anionic – Halides, OH-
Neutral- H O, NH
classification
Neutral- H2O, NH3
Mode of binding of ligands to metal
Pi- acid ligands – CO, CN- (σ – donor & π - acceptor)
Pi-donor ligands - OH-, F- (σ – donor & π - donor)
Sigma donor ligands - H2O, NH3 (σ – donor )
Number of donor sites (Denticity) of the ligand
Monodentate ligands
Polydentate ligands
7. Number of donor sites (Denticity) of the ligand
Monodentate Didentate
Latin word meaning tooth
A ligand which shares
electron pair of single
donor atom with metal
atom or ion.
A ligand which have two
donor atom which attach
to metal atom or ion.
Polydentate
(Chelating)
A ligand which have more
than two donor atom
which attach to metal
atom or ion.
atom or ion.
Bridging
Eg: 4, 4’-bipyridine
Chelating
Symmetrical
(AA)
Eg: Oxalato
Unsymmetrical
(AB)
Eg: Glycinato
atom or ion.
8. Polydentate ligands depending on the number of binding sites, the ligands
are tridentate, tetradentate, pentadentate, hexadentate etc.
9. Ambidentate ligands are monodentate ligands which have two or more
different donor atoms can coordinate to a metal cation through either of
the two different atoms.
Example: -NO2
- , -SCN-, -S2O3
2-
Nitrogen atom Oxygen atom
Nitrogen atom
coordinated to
metal
Oxygen atom
coordinated to
metal
Macrocyclic ligands are special class of chelating ligands which contain
large size rings with several donor atoms can coordinate to a metal cation.
Example: Chlorophyll, Hemoglobin and Vit B12
10. Homoleptic complex in which a metal is bound to only one type of
donor atoms.
Example: [Co(NH3)6]3+
Heteroleptic complex in which a metal is bound to more than one type
of donor atoms.
Example: [Co(NH3)4 Cl2]+
Example: [Co(NH3)4 Cl2]+
11. IUPAC Nomenclature of Coordination compounds
1) If coordination compound is ionic, the
cation is named first followed by anion.
2) In naming complex ion [M(L)x]n±
3) First name the ligand in alphabetical order.
(i) If Anionic ligands are present name end
with “–O” by replacing the last letter “–e”.
-ide → -ido
-ite → -ito
-ate → -ato
(ii) If neutral ligands are present common
name are preferred.
H O → Aqua
(ii) If the complex is anionic, then the metal
name ends with suffix “-ate” or replace –
ium, -en, -ese.
Cobalt → Cobaltate
Titanium → Titanate
Tungsten → Tungstate
Manganese → Manganate
Iron → Ferrate
7) Oxidation state of the metal is written in
Roman numeral in the parenthesis ().
8) Prefix “µ” is used if bridging ligands are
present.
H2O → Aqua
NH3 → Ammine
4) Greek prefixes di-, tri-, tetra-, penta- and
so forth are used to designate number of
each type of ligand.
5) If the name of the ligand itself contain a
Greek prefix, then prefixes bis-, tris-,
tetrakis- are used.
6) After naming the ligand, write the name of
the metal
(i) If the complex is cationic or neutral, the
usual name of the metal is used.
present.
9) Geometrical isomers are named by using
prefixes cis- & trans- (or) fac- & mer-.
10) Optical isomers are designated by d (or) l.
11) Number of water molecule are designated
in the last.
H2O → monohydrate
½ H2O → sesquihydrate
14. Structure and Isomerism in Coordination compounds
Coordination number and geometry of the complexes are related to one
another.
For example, complexes with coordination number 4 are either have
tetrahedral or square planar geometry.
The coordination number and geometry of the complexes depends upon the
following factors:
1. The size of metal atom or ion.
2. Size of the ligands and the steric interaction between the ligands.
3. Electronic interaction and the number of d-electrons in metal
atom or ion.
4. Whether the ligands form pi- bonds with metal ion or atom.
In general, the metal atoms or ions of larger size favour the formation of
complexes of higher coordination number because steric repulsion
decreases with increase in size of central metal ion.
15. In general, the coordination number of metals in complexes are found to be
2 to 9, out of which coordination number 2, 4 and 6 are most common.
Coordination number – 2:
A few number of complexes are known.
They are limited to the d10 species i.e. Cu+, Ag+, Au+ and Hg2+ ions.
These complexes have linear geometry.
Some examples are
Some examples are
[H3N-Cu-NH3]+, [Cl-Cu-Cl]-, [H3N-Ag-NH3]+, [NC-Hg-CN]
These complexes are typically unstable react with additional ligands to
form complexes of higher coordination number.
[Cu(CN)2]-
+ 2CN-
[Cu(CN)4]3-
[Ag(NH3)2]+
+ 2NH3 [Ag(NH3)4]+
16. Coordination number – 3:
Rare number of complexes are known.
These complexes have trigonal planar and trigonal pyramidal geometry.
Some examples are
K[Cu(CN)2], HgI3
- and pyramidal SnCl3
-.
C
N
Cu
Sn
Cl Cl
-
C
Cu
C
N
N
Cu Cu
Many compounds appear to be three coordinate as judged from
stoichiometry are found to have higher coordination number.
Eg: CsCuCl3 (Infinite single chain, -Cl-CuCl2-Cl- with C.N = 4)
KCuCl3 (Infinite double chain, -Cl4-(Cu2Cl2)-Cl4- with C.N = 6)
Cl
Cl
Cl
17. Coordination number – 4:
Second most important coordination number in coordination chemistry.
These complexes have tetrahedral and square planar geometry.
Tetrahedral complexes are favored by larger ligands like Cl-, Br- & I- and
small metal ion or atoms with
(i) d0 and d10 configuration
(ii) dn configuration where square planar or octahedral is not
favored such as Fe2+ (d6), Co2+ (d7), Ni2+ (d8), Cu2+ (d9) ions
which for tetrahedral complexes with Cl-, Br- ions.
Square planar complexes are less favored sterically than tetrahedral
complexes.
Square planar complexes are thus formed by only a few metal ions. The
best known are the d8 species such as Ni2+.
18. Ni
Cl
2-
Ni
NC CN
2-
Prerequisite for stability of these square planar complexes is the presence
of non bulky strong field π - acceptor ligand such as CN-.
The metal ions belonging to 4d- and 5d- transition elements such as Rh+,
Pd2+, Pt2+ & Au3+ form invariably square planar complexes
regardless of the π – donor or π – acceptor character of the ligands.
Ni
Cl
Cl
Cl
Ni
NC CN
Pd
Cl
Cl
Cl
Cl
2-
Pt
Cl
Cl
Cl
Cl
2-
Tetrahedral Square planar
Square planar
19. Coordination number – 5:
The complexes of CN – 5 are less common than that of CN – 4 & 6.
These complexes have Square pyramidal or trigonal bipyramidal geometry.
These two geometries can be interconverted by small change in bond
angles because these two geometries differ little in energy from one
another.
[CdCl5]3-
[Co(C6H7NO)5]2+
[Ni(CN)5]3-
[Sb(C6H5)5
,
Trigonal
bipyramidal Intermediate geometries
Square
pyramidal
[Ni(CN)5]3- ion exist as both square pyramidal and trigonal bipyramidal in
the same crystal.
Ni
NC
NC
CN
CN
3-
Ni
NC
CN
CN
CN
3-
Trigonal
bipyramidal
Square
pyramidal
CN
CN
20. Coordination number – 6:
This is the most common and enormously important coordination number
for transition metal complexes.
The possible geometries corresponding to CN – 6 may be hexagonal
planar, trigonal prismatic, octahedral or tetragonally distorted octahedron.
In a regular octahedral complex all the M-L bond distances are equal and
the complexes have plane as well as centre of symmetry i.e. regular
octahedral complexes are symmetric and have Oh symmetry.
octahedral complexes are symmetric and have Oh symmetry.
L
M
L
L
L
L
L
[Co(NH3)6]3+
[Cr(H2O)6]3+
[Co(H2O)6]3+
[Fe(CN)6]4-
[Ni(NH3)6]2+
21. There are some complexes of CN – 6 which have all the six ligands same
but undergo some sort of distortion due to the electronic effect. This type of
distortion is Jahn-Teller effect.
L L
L
L L
L
L L
L
Tetragonal elongation
L
M
L
L
L
M
L
L
Tetragonal compression
Trigonal prismatic
L
M
L
L
22. Coordination number – 7:
This coordination number is not common. Few 3d and some 4d & 5d
complexes are known. Because of larger metal ion size it can accommodate
more than six ligands.
The possible geometries corresponding to CN – 7 are pentagonal
bipyramidal, a capped octahedron and a capped trigonal prism.
Examples are
[Os(CN) ]3- [ZrF ]3- [NbF ]2-
[Os(CN)7]3- [ZrF7]3- [NbF7]2-
pentagonal bipyramidal capped octahedron capped trigonal prism
23. Coordination number – 8:
This coordination number is also not common. Only few complexes are
known.
The possible geometries corresponding to CN – 8 are distorted cubic
structures i.e. square antiprismatic and trigonal dodecahedral.
Examples [Mo(CN)8]4-
Square antiprismatic trigonal dodecahedral
24. Coordination number – 9:
This coordination number requires larger transition metals and f-block
elements.
The possible geometry corresponding to CN – 9 is tricapped triogonal
prismatic.
Examples includes [Sc(H2O)9]3+, [La(H2O)9]3+ as well as [TcH9]2- and [ReH9]2-
25. Isomerism in Coordination compounds
The compounds having same chemical composition but different properties
due to the structural difference are called isomers and the phenamenon of
existence of isomers is called isomerism. (isos means same; meros means
parts).
Isomerism in Coordination compounds
Structure / Constitutional
isomerism
Spin isomerism Stereoisomerism Conformational
or polytopal
isomerism
Ionization Hydrate Linkage Coordination Ligand Polymerization
Low Spin High Spin Geometrical Optical
26. Structural isomerism arises due to different bonding between metal and ligands.
Ionization isomerism: There is exchange of ligands b/w coordination and
ionization sphere and give different ions when dissolved in water.
[Co(NH3)5Br]SO4 [Co(NH3)5 (SO4)]Br
Hydrate isomerism: There is exchange of water molecule b/w coordination and
ionization sphere.
[Cr(H2O)6]Cl3 [Cr(H2O)5Cl]Cl2. H2O
Linkage isomerism: When ambidentate ligands can coordinate to a metal
through either of the two different donor atoms.
[Co(NH3)5(SCN)]Cl2 [Co(NH3)5(NCS)]Cl2
[Co(NH3)5(SCN)]Cl2 [Co(NH3)5(NCS)]Cl2
Coordination isomerism: Observed in the coordination compounds having both
cationic and anionic complex ions and there may be exchange of ligands.
[Co(NH3)6][Cr(CN)6)] [Cr(NH3)6][Co(CN)6)]
Ligand isomerism: If a ligand itself exists in two or more isomeric form, then the
complex containing such ligands also exists in isomeric forms.
[Co(pn)2Cl2]+
pn- propylenediamine [Co(tn)2Cl2] +
tn- trimethylenediamine
Polymerization isomerism: It occurs between compounds having the same
empirical formula but different molecular weight.
[Pt(NH3)2]Cl2 ; [Pt(NH3)4Cl4] ; [Pt(NH3)3Cl]2 [PtCl4]
27. The isomers in which the same type and number of ligands are coordinated to the
metal atom or cation but with different spatial arrangements are called
stereoisomers.
Stereoisomers is classified into two types
(1) Geometrical isomerism
(2) Optical isomerism
Geometrical isomers are the one in which relative position of the ligands
round the metal ion is different.
round the metal ion is different.
Geometrical isomers exist only in pairs, one isomer with two ligands
adjacent to each other (cis) and in the other two ligands are opposite to each
other (trans).
Geometrical isomerism is most common in complexes having coordination
number of 4 and 6.
The complexes having coordination numbers 2 and 3 do not exhibit
geometrical isomerism.
28. Geometrical isomerism in complexes having coordination number - 4
ML4
Square planar
[MA4]n±, [MA3B]n±, [M(AA)2]n±,
[M(AA)AB]n± and [M(AA)A ]n±
Do not exhibit geometrical isomerism
Tetrahedral
[MA4]n± (or) [MABCD]n±
[M(AA)AB]n± and [M(AA)A2]n±
Do not exhibit geometrical isomerism
whether all ligands are same or
different because all the ligands in this
geometry are at adjacent positions
relative to each other.
Above types square planar complexes
do not exhibit geometrical isomerism
because all the possible spatial
arrangement of the ligands in this
geometry are same.
M
A
A
A A
n±
M
A A
A A
n±
29. [MA2B2]n±
type complexes
M
A B
A B
n±
M
A B
B A
n±
Cis Trans
Examples of this type of complexes are [Pt(NH3)2 Cl2], [Pt(py)2 Cl2] etc
Pt
H3N Cl
H3N Cl
Pt
H3N Cl
Cl NH3
Cis Trans
Geometrical isomers possible is 2
30. [MA2BC]n±
type complexes
Examples of this type of complexes are [Pt(Py)2(NH3)Cl]+, [Pt(NH3)2PyCl]+
etc
M
A B
A C
n±
M
A B
C A
n±
Trans
Cis
etc
Pt
Py NH3
Py Cl
Pt
Py NH3
Cl Py
Cis Trans
+ +
Geometrical isomers possible is 2
31. [MABCD]n±
type complexes
M
A B
D C
n±
M
A C
B D
n±
A D
n±
Cis Cis
Cis
Trans Trans
M
A D
C B
Trans
This type of complexes exists in three isomeric forms. The three isomers
are obtained by fixing one ligand at corner and then placing the other
three ligands one by one trans to the fixed ligand.
32. Examples of this type of complexes are [Pt(Py)(NH3)ClBr],
[Pt(NH3)(C2H4)ClBr] etc
Pt
H3N Py
Br Cl
Pt
H3N Cl
Br Py
Pt
H3N Py
Cl Br
Geometrical isomers possible is 3
33. M
A A
B B
n±
Cis
[M(AB)2]n± type complexes exists in two isomeric forms
AB is unsymmetrical ligand in which A and B are two different donor
atoms.
B B
M
A B
B A
n±
Trans
35. [M2A2B4]n± Bridged binuclear square planar complex
M
A
B
n±
Cis
M
B A
B B
A
n±
B B
This type complex
exists in three
isomeric forms (Cis,
Trans
M
B
M
B A
M
A
A
n±
M
B B
B B
Unsymmetric
isomeric forms (Cis,
trans and
unsymmetric).
36. Example of this type of complex is [Pt2(PEt3)2 Cl4]
Pt
Et3P
Cl
Cis
Pt
Cl PEt3
Cl Cl
Et3P Cl Cl
Trans
Pt
Cl
Pt
Cl PEt3
Pt
Et3P
Et3P
Pt
Cl Cl
Cl Cl
Unsymmetric
37. Square planar complexes with symmetric ligands carrying one or
more substituents can form geometrical isomers.
Example of complex with one substituent [Pt(pn)2]2+
pn = propylenediamine
Pt
H2
N
Cis
H2
N
H3C
CH3
2+
N
H2
Trans
N
H2
H3C
CH3
H H
Pt
H2
N
N
H2
H2
N
N
H2
H3C
H
H CH3
2+
38. Example of complex with two substituent [Pt(bn)2]2+
bn = butylenediamine
Pt
H2
N
N
H2
Cis
H2
N
N
H2
H3C
CH3
H H
2+
H3C CH3
H H
Trans
Pt
H2
N
N
H2
H2
N
N
H2
H3C
H
H CH3
2+
H3C H
H CH3
39. Geometrical isomerism in complexes having coordination number - 6
ML6
L L
L
1
2
5
Octahedral complex if the two ligands
occupy either of the positions
(1,2), (1,3), (1,4), (1,5)
(2,3), (3,4), (4,5), (5,2)
(6,2), (6,3), (6,4), (6,5)
it is cis isomer
L
M
L
L
3
4
6
it is cis isomer
Octahedral complex if the two ligands
occupy either of the positions
(1,6), (2,4), (3,5)
it is trans isomer
42. [MA4BC]n±
type complexes A
M
A
C
B
A
A
n±
A
M
A
A
A
B
C
n±
Cis Trans
Examples of this type
of complexes are
H3N
Co
H3N
OH2
Cl
NH3
NH3
2+
H3N
Co
H3N
NH3
NH3
Cl
OH2
2+
Cis Trans
of complexes are
[Co(NH3)4 Cl(H2O)]2+,
[Co(NH3)4 (Py)Cl]2+
etc.
The complex of this
type exist in two
isomeric forms.
43. [MA3B3]n±
type complexes A
M
A
B
B
A
B
n±
A
M
A
B
A
B
B
n±
facial meridional
Examples of this type
of complexes are
H3N
Co
H3N
Cl
Cl
NH3
Cl
H3N
Co
H3N
Cl
NH3
Cl
Cl
fac mer
of complexes are
[Co(NH3)3 Cl3],
[Cr(NH3)3 Cl3]
etc.
The complex of this
type exist in two
isomeric forms.
44. Facial isomer (1,2,3-isomer) three identical donor atoms lie on the
corner of a triangular face and all three bond angles (B-M-B) are 90o .
Meridional isomer (1,2,4-isomer) three identical donor atoms lie on
the corner of a plane bisecting the complex and two bond angles (B-M-
B) are 90o and one (B-M-B) is 180o.
A
n±
B
n±
4
Facial and Meridional isomers
A
M
A
B
B
B
A
M
A
B
A
B
facial meridional
1
2
3
1
2
45. [M(AB)3]n±
type complexes
AB-Unsymmetrical ligand
Examples of this type
of complexes are
[Co(gly)3],
[Cr(gly)3]
facial meridional
B
M
A
B
A
B
A
n±
A
M
A
B
A
B
B
n±
[Cr(gly)3]
etc.
The complex of this
type exist in two
isomeric forms.
fac mer
O
Co
N
O
N
O
N
N
Co
N
O
N
O
O
gly
gly
gly
gly
gly
gly
H2C
H2N
CO
O
gly =
46. [MA2B2C2]n±
type complexes
Examples of this
type of complexes
are
[Pt(NH ) (Py) Cl ]2+
H 3 N
P t
H 3 N
C l
P y
P y
C l
H 3 N
P t
C l
C l
N H 3
P y
P y
C is tra n s
2 + 2 +
H 3 N C l
P y
2 +
P y C l
N H 3
2 +
[Pt(NH3)2(Py)2Cl2]2+
etc.
The complex of this
type exist in five
isomeric forms.
H 3 N
P t
C l
P y
P y
P t
C l
N H 3
H 3 N
P t
H 3 N
P y
P y
C l
C l
2 +
47. [MABCDEF]n± type complexes
There is only one coordination compound of this type and it can exist in fifteen
(15) possible isomeric forms.
[Pt(NH3)(Py)(NO2)(Cl )(Br)(I)]
Py
H3N
Pt
O2N
Br
Cl
I
48. [M(AA)2B2]n±
type complexes
Examples of this
type of complexes
Cis Trans
A
M
A
B
B
A
A
n±
A
M
A
A
A
B
B
n±
type of complexes
are
[Co(en)2Cl2]+
[Co(en)2 (NO2)2]+
[Rh(C2O4)2Cl2]3-
etc.
The complex of this
type exist in two
isomeric forms.
Cis Trans
N
Co
N
Cl
Cl
N
N
+
N
Co
N
N
N
Cl
Cl
+
en
en
en en
52. O
C o
N
Py
N H 3
O
N
+
gly
gly
O
C o
N
N H 3
Py
O
N
+
gly
gly
N N H 3
O
+
gly
O N H 3
N
+
gly
[M(AB)2CD]n±
type complexes
Examples of this
O
C o
N
O
N
N H 3
Py
+
gly gly
N
C o
Py
O
gly
O
C o
N
N
O
N H 3
Py
+
gly gly
O
C o
Py
3
N
gly
Examples of this
type of complex is
[Co(gly)2(NH3)(Py)]+
The complex of this
type exist in six
isomeric forms.
53. To distinguish cis- and trans- isomers
Dipole moment
measurement
Infrared
spectroscopy
Chemical
method
Trans isomers has
Zero dipole
Trans isomers are
IR inactive
Grinberg’s
method
Zero dipole
moment
Cis isomers has
some value of
dipole moment
IR inactive
Cis isomers are
IR active
method
Trans isomers
form non chelated
complex
Cis isomers form
chelated complex
55. Optical isomerism in complexes having coordination number - 4
ML4
Square planar
[MA4]n±, [MA3B]n±, [M(AA)2]n±,
[M(AA)AB]n± and [M(AA)A ]n±
Do not exhibit optical isomerism.
Tetrahedral
[MA4]n±
[M(AA)AB]n± and [M(AA)A2]n±
Do not exhibit optical isomerism.
Square planar complexes do not exhibit
optical isomerism because all the four
ligands and metal ion are in the same
plane and hence posses plane of
symmetry.
56. [MABCD]n± type of tetrahedral complex exhibits optical isomerism.
For example, [As(CH3)(C2H5)(S)(C6H5COO)]2+ exists as optical isomers
S S
2+ 2+
As
H3C
C2H5
OOCC6H5
As
CH3
C2H5
C6H5COO
57. Some complexes of Pd (II) and Pt (II) square planar complexes are optically
active.
58. Optical isomerism in complexes having coordination number - 6
ML6
Octahedral complex
[MA6]n± and [MA5B]n±
A
M
A
A
A
A
A
n±
[MA6]n± and [MA5B]n±
Above types of octahedral
complexes do not exhibit optical
isomerism because of presence of
plane of symmetry.
A
M
A
A
A
B
A
n±