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The SciTech, Journal of Science & Technology
Vol-1, Issue-1, p-40-50, 2012.
Article information:
Article Received: 16 March 2012 Article Accepted: 18 March 2012
Article Online: 16 April 2012
Journal homepage: www.thescitechpub.com
Article No: STJST201211002
DOI:…………………………..
Research Article
RELATIONSHIP BETWEEN ATOMIC ORBITAL EXPONENT AND ATOMIC HARDNESS
N. Islam
Department of Basic Science & Humanities/ Chemistry,
Techno Global- Balurghat, Balurghat-733103,
India.
Email: [email protected]
Fax: +91-3522271101
Abstract:
Considering hardness of atom as the attraction of a nucleus upon the valence shell electron, in this paper a
simple approach for the calculation of the global hardness of atoms in terms of their orbital exponents is presented.
The basic tenet of the present method is to use our newly computed atomic orbital exponent values to compute the
global hardness of the atoms. The express periodicity of periods and groups of periodic table exhibited by the
computed atomic hardness, correlation with some other existing hardness data, correlation of the some of the most
important physico-chemical properties of atoms etc speak volume of the efficacy of the present method in
computing atomic global hardness.
Keywords: effective nuclear charge, effective principal quantum number orbital exponents, global hardness,
periodicity.
η Ghosh Islam(ev)
H
Li
B
N
F
Na
Al
P
Cl
K
Sc
V
Mn
Co
Cu
Ga
As
Br
Rb
Y
Nb
Tc
Rh
Ag
In
Sb
I
Cs
La
Pr
Pm
Eu
Tb
Ho
Tm
Lu
Ta
Re
Ir
Au
Tl
Bi
At
Fr
Ac
Pa
Np
Am
Bk
Es
Md
Lr
Orbital exponent
ξ
Global hardness
Graphical abstract:
Atoms
©The SciTech Publishers, 2012. All Right Reserved
40
The SciTech, Journal of Science & Technology
Vol-1, Issue-1, p.40-50, 2012.
N. Islam
Relationship between atomic orbital exponent & hardness..
Introduction:
For the rationalization and prediction of various chemo-physical phenomena scientists are engaged in
introducing new concepts. The law of nature is simple but subtle and that one of the main goals of the natural
sciences is the formulation of simple models in concepts in terms of which the observed phenomenon can be
classified, understood and finally described. The chemical hardness is one of the fundamental chemical properties of
atoms and molecule relating to the intrinsic resistance toward the chemical reactivity of molecules, atoms and ions
by holding the electron cloud tightly to the species [1,2].The concept of hardness was basically introduced to justify
the acid base chemical interactions known as hard-soft acid base theory[2]. Chemical hardness fundamentally
signifies the resistance towards the deformation or polarization of the electron cloud of the atoms, ions or molecules
under small perturbation of charge cloud [1-12].
For a system of N electrons with ground state energy E [N,v] using the essence of the density functional theory
(DFT)[3,13], Parr et al [14] showed that(1)
µ=–χ = [∂E(ρ)/∂N]v
where µ is the chemical potential, E(ρ) is the energy, N is the number of electrons and v is the external potential.
The curvature of E vs. N curve, i.e. [∂2E(ρ)/∂N2] is identified as the hardness of the system[4]
2η = [∂2E(ρ)/∂N2]
(2)
It is now established that the rigorous evaluation of hardness η in terms of the Eq. (3) is difficult [6-12, 15, 16].
However, Parr and Pearson [4] invoking the calculus of finite difference approximation suggested an approximate
and operational formula of hardness as under:
(3)
η=½(I-A)
where I is the ionization potential and A is the electron affinity of atoms, ions or molecules
By invoking the Hartree-Fock SCF theory and Koopmans’ theorem, Pearson [17] connected the hardness concept
and the Hartree Fock SCF theory as under
η = - [εHOMO - εLUMO] / 2
(4)
where the orbital energy of the Highest Occupied Molecular Orbital (HOMO), εHOMO = –I and the orbital energy of
the Lowest Unoccupied Molecular Orbital (LUMO), εLUMO = –A
The effective nuclear charge:
The effective nuclear charge (Zeff.) is the net positive charge experienced by an electron in a multi
electronic atom[18]. The effective nuclear charge is somewhat lower than the actual nuclear charge (Z) and it is a
parameter which characterizes any atom or ion.
Thus, Zeff = Z – point charge at the nucleus representing the average electron repulsion.
Or simply,
Zeff = (Z-S)
(5)
where the screening constant or shielding constant, S, accounts for the average inner electronic repulsion on the
outer electron of interest.
©The SciTech Publishers, 2012. All Right Reserved
41
The SciTech, Journal of Science & Technology
Vol-1, Issue-1, p.40-50, 2012.
N. Islam
Relationship between atomic orbital exponent & hardness..
The effective nuclear charge, Zeff and the effective principle quantum number, n* are the two very important
conceptual
ptual terms. Both factors are opposing in nature. The effective nucleus
nucleus- electron attraction is proportional to
the effective nuclear charge and inversely proportional to the effective principal quantum number. The effective
nuclear charge increases gradually
lly while we are going across a period where the effective quantum number remains
constant. Thus, along a period, the effective attraction depends mainly on the effective nuclear charge as other factor
(n*) remains constant. But in the next period, they bo
both
th jump in number. The second factor, the effective principal
quantum number is the dominating factor while we are going across a group. Thus the consideration of only
effective nuclear charge to explain the periodicity of periods and groups is erroneous.
The ratio of the effective nuclear charge and the effective principle quantum numbers i.e., Zeff : n* is known as the
orbital exponent- physically represents the effective attraction power of the nucleus upon the electron. Thus the
“effective nucleus –electron”
lectron” attraction can be well documented by the orbital exponent.
Thus, the orbital exponent, ξ is defined as
asξ = Zeff/n*
(6)
In this work, we have proposed a simple formula of computing hardness of atoms based on the orbital exponent of
the atoms.
Radial dependent electrostatic formula of computing hardness of atoms:
Pearson [19] pointed out that a simple formula of computing hardness of atoms could be derived from
simple electrostatic considerations using atomic size. Dutta and Hati [20] have used the formula derived by Pearson
to calculate the hardness of a series of atoms. We [6] derived the electrostati
electrostatic formula for computing the hardness of
atoms asη ∝ e2/2r
where e is the electronic charge in esu and r is the ab
absolute
solute or most probable radius of atom in cm.
(7)
In atomic unit, this equation becomes
η ∝1/2r
(8)
In a recent
nt work, working on the electrostatic definition of the hardness and relying the classic Bohr model of
hydrogenic atom, [21] we have explored a new route for calculating the global hardness of atoms using
spectroscopy.
The suggested spectroscopic atomic ha
hardness model is
η= e2/{(2e2/ hc )+ (4π2Zeff 2 e4m/h2 n*2)}]
(9)
where h is the Planck constant, c is the velocity of light, m is the mass of electron.
Method of computation:
Computation of atomic orbital exponents:
Recently considering the pairing energy for p and d orbitals, Reed[15] modified Slater’s[18] grouping of
orbital and proposed two set of rules for the computation of the screening co
constants.
©The SciTech Publishers, 2012. All Right Reserved
42
The SciTech, Journal of Science & Technology
Vol-1, Issue-1, p.40-50, 2012.
N. Islam
Relationship between atomic orbital exponent & hardness..
Now goaded by the periodic law and following Reed, we[22-24] have evaluated the effective nuclear charge and the
orbital exponents for the atoms of the118 elements of the periodic Table with some modifications as under:
We have considered Reed’s suggestions for the evaluation of screening constants of the s, p and d block elements
and extended Reed’s rule for the evaluation of screening constants of f block elements. When electron entire in the
5f, 6p and higher we have used the contribution of 4f as 1. In the same shell f electrons shield each other by a factor
0.3228.
It is significant to mention here that in order to evaluate the orbital exponent, we have used the Eq.(4) and
the value of n* proposed by Slater 16 for n=1 to n=6 and for n=7, we have used the value of n*= 4.3 proposed by
Ghosh and Biswas[25].
Now, the hardness refers to the resistance of the electron cloud of the atomic and molecular systems under
small perturbation of electrical field. It is now well established that the hardness originate from the electron
attracting power of the screened nuclear charge of the atom [6-12].
The attraction of a nucleus upon the valence shell electron is directly proportional to the effective nuclear charge
(Zeff) and inversely proportional to its radius. Now, as the absolute radius or most probable radius is directly
proportional to the effective principal quantum number (n*)[26], we can safely and reasonably conclude that the
attraction of a nucleus upon the valence shell electron is inversely proportional to the n*.
i.e., η ∝ Zeff and η ∝1/ n*
At this point, to propose an algorithm to correlate the hardness, the effective nuclear charge and the effective
principal quantum number, we may simply consider the expression as
η ∝ Zeff /n*
(10)
or, η ∝ ξ
(11)
or, η = K (Zeff/n*) = K ξ
(12)
However, an equation can also be suggested for computing the hardness of the atoms based upon the conjoint action
of the two parameters– the effective nuclear charge (Zeff) and the effective principal quantum number as follows–
η = a (Zeff) + b (1/ n*) + c
(13)
where K is the correlation constant. It is constant throughout a period of the periodic table.
Now as the aim of the paper is to establish a simple relation between two parameters– the global hardness and the
orbital exponent of the atoms, we have relied upon the simple expression, the Eq.(12).
At this point it is necessary to discuss here some analogous formulae for the computation of atomic
hardness.
Following the Slater’s definition[18] that the maximum of the radial density function of the orbital of the
valence shell might be considered as a measure of the theoretical atomic radius and using the radial part of the
Slater’s one-electron function (STO’s) we [26] derived the formula for calculation of theoretical radii (r) is derived
as
r = n*/ξ
(14)
where n* is the effective principal quantum number and n is the orbital exponent.
©The SciTech Publishers, 2012. All Right Reserved
43
The SciTech, Journal of Science & Technology
N. Islam
Vol-1, Issue-1, p.40-50, 2012.
Relationship between atomic orbital exponent & hardness..
If we put the value of r (Eq 14) in to the electrostatic definition of hardness (Eq.10) the formula for hardness looks
like
η ∝ξ /2n*
(15)
Putting ξ = Zeff/n* in the above equation, we get
η ∝ Zeff/n*2
(16)
Based on the commonality in the basic philosophy of the origin and the operational significance of the
electronegativity and the hardness, in a recent work [27], we have also proposed a new scale of computing global
hardness of atoms asη = a ( Zeff /r ) + b
(17)
The global hardness data of the 103 elements of the periodic table is computed using the suggested algorithm,
Eq.(12) and the computed orbital exponent data of the corresponding atoms.
In order to evaluate K parameters for each period separately we have just divided the global hardness data of Ghosh
and Islam [6] with our computed orbital exponent data of the all the elements present in that period.
Result and Discussion:
The computed orbital exponents of atoms of 118 elements of the periodic table are presented in Table-1.
Table- 1: Computed orbital exponent of atoms of 118 elements of the periodic table
Atom
ξ
Atom
ξ
Atom
ξ
Atom
ξ
Atom
ξ
H
1.00000
Mn
0.92241
Tb
2.16171
Ac
0.71398
Uut
3.10888
He
1.67720
Fe
0.94557
Dy
2.32295
Th
0.73391
Uuq
3.26637
Li
0.66340
Co
0.96873
Ho
2.48419
Pa
1.02895
Uup
3.42386
Be
1.00200
Ni
0.99189
Er
2.64543
U
1.18644
Uuh
3.58135
B
1.34060
Cu
1.01505
Tm
2.80667
Np
1.34393
Uus
3.73884
C
1.67920
Zn
1.03822
Yb
2.96790
Pu
1.63898
Uuo
3.89633
N
2.01780
Ga
1.22124
Lu
2.98831
Am
1.79647
O
2.35640
Ge
1.40427
Hf
3.00871
Cm
1.95395
1.97388
F
2.69500
As
1.58730
Ta
3.02912
Bk
Ne
3.03360
Se
1.77032
W
3.04952
Cf
2.26893
Na
0.76907
Br
1.95335
Re
3.06993
Es
2.42642
Mg
0.99480
Kr
2.13638
Os
3.09033
Fm
2.58391
Al
1.22053
Rb
0.57680
Ir
3.11074
Md
2.74140
Si
1.44627
Sr
0.74610
Pt
3.13114
No
2.89888
P
1.67200
Y
0.75178
Au
3.15155
Lr
2.91881
S
1.89773
Zr
0.78895
Hg
3.17195
Rf
2.93874
Cl
2.12347
Nb
0.81038
Tl
0.92557
Db
2.95867
Ar
2.34920
Mo
0.83180
Pb
1.08681
Sg
2.97860
K
0.62357
Tc
0.85323
Bi
1.24805
Bh
2.99853
Ca
0.80659
Ru
0.87465
Po
1.40929
Hs
3.01847
Sc
0.82976
Rh
0.89608
At
1.56945
Mt
3.03840
Ti
0.85292
Pd
0.91750
Rn
1.73176
Uun
3.05833
V
0.87608
Ag
0.93892
Fr
0.53656
Uuu
3.07826
Cr
0.89924
Cd
0.96035
Ra
0.69405
Uub
3.09819
©The SciTech Publishers, 2012. All Right Reserved
44
The SciTech, Journal of Science & Technology
N. Islam
Vol-1, Issue-1, p.40-50, 2012.
Relationship between atomic orbital exponent & hardness..
Now, in order to justify the proposed algorithm, the Eq.(12), we have just plotted the computed orbital
exponents and the Ghosh and Islam’s global hardness data[6] of atoms in Figure-1
η Ghosh Islam(ev)
Orbital exponent
Global hardness
ξ
H B F Al Cl Sc Mn Cu As Rb Nb Rh In I La Pm Tb Tm Ta Ir Tl At Ac Np Bk Md
Atoms
Figure-1: Comparative study of the computed orbital exponents and the Ghosh and Islam’s global hardness data of atoms
A look at the Figure 1 revels that the nature of variation of the two periodic parameters are the same.
Hence, the assumption that “the two fundamental atomic periodic parameters– the atomic hardness and the atomic
orbital exponent are directly proportional to each other” is justified.
The global hardness data for 118 elements of the periodic table, evaluated through the Eq.(12) along with
the Ghosh and Islam’s hardness data[6] are presented in Table 2.
©The SciTech Publishers, 2012. All Right Reserved
45
The SciTech, Journal of Science & Technology
N. Islam
Vol-1, Issue-1, p.40-50, 2012.
Relationship between atomic orbital exponent & hardness..
Table-2: Computed hardness in eV of atoms of 118 elements of the periodic table as a function of their atomic number
Atom
Hardness in
eV
η Ghosh
Islam(ev)
Atom
Hardness in
eV
η Ghosh
Islam(ev)
Atom
Hardness in
eV
η Ghosh
Islam(ev)
H
6.954876
6.429954
Nb
2.787379
2.825974
Tl
1.469533
1.704349
He
11.66472
12.54491
Mo
2.861073
2.92213
Pb
1.725531
1.941353
Li
2.278412
2.374587
Tc
2.934766
3.018371
Bi
1.98153
2.178492
Be
3.441315
3.496763
Ru
3.00846
3.114598
Po
2.237528
2.415812
B
4.604219
4.619009
Rh
3.082154
3.210756
At
2.491825
2.652778
C
5.767122
5.740979
Pd
3.155848
3.306947
Rn
2.749524
2.889955
N
6.930026
6.862467
Ag
3.229542
3.403195
Fr
1.004025
0.988253
O
8.092929
7.985436
Cd
3.303235
3.499376
Ra
1.298722
1.28195
F
9.255833
9.106475
In
3.885562
3.916369
Ac
1.336016
1.349725
Ne
10.41874
10.23034
Sn
4.467889
4.333233
Th
1.37331
1.417526
Na
2.224257
2.444141
Sb
5.050216
4.750079
Pa
1.92541
1.936857
Mg
2.877112
3.014651
Te
5.632543
5.166979
U
2.220108
2.230558
Al
3.529967
3.584907
I
6.21487
5.583887
Np
2.514805
2.52412
Si
4.182821
4.155131
Xe
6.797197
6.000897
Pu
3.066905
3.043613
P
4.835676
4.725804
Cs
0.872178
0.682915
Am
3.361602
3.416868
S
5.488531
5.295979
Ba
1.075102
0.920095
Cm
3.6563
3.404984
Cl
6.141386
5.866186
La
1.160573
1.157089
Bk
3.693594
3.92442
Ar
6.794241
6.436619
Ce
1.640173
1.394276
Cf
4.245694
4.218081
K
2.13075
2.327318
Pr
1.896172
1.631473
Es
4.540391
4.511593
Ca
2.756159
2.758724
Nd
2.15217
1.868439
Fm
4.835089
4.805093
Sc
2.835305
2.858192
Pm
2.408168
2.105658
Md
5.129786
5.098982
Ti
2.914451
2.95783
Sm
2.664166
2.342665
No
5.424483
5.392605
V
2.993597
3.057341
Eu
2.920165
2.579815
Lr
5.461777
5.460699
5.499071
Cr
3.072743
3.156725
Gd
3.175785
2.817026
Rf
Mn
3.151889
3.256383
Tb
3.432161
3.054037
Db
5.536365
Fe
3.231034
3.355931
Dy
3.68816
3.291169
Sg
5.573659
Co
3.31018
3.455609
Ho
3.944158
3.528297
Bh
5.610954
Ni
3.389326
3.555013
Er
4.200156
3.765525
Hs
5.648248
Cu
3.468472
3.654418
Tm
4.456154
4.002555
Mt
5.685542
5.722836
Zn
3.547618
3.75416
Yb
4.712153
4.239478
Uun
Ga
4.173027
4.18552
Lu
4.744549
4.476583
Uuu
5.76013
Ge
4.798436
4.616627
Hf
4.776946
4.706522
Uub
5.797424
As
5.423845
5.066215
Ta
4.809343
4.950847
Uut
5.817442
Se
6.049255
5.479496
W
4.84174
5.187931
Uuq
6.112139
Br
6.674664
5.9111
Re
4.874136
5.425608
Uup
6.406836
Kr
7.300073
6.341847
Os
4.906533
5.661914
Uuh
6.701533
Rb
1.983971
2.120458
Ir
4.93893
5.900043
Uus
6.996231
Sr
2.566298
2.53737
Pt
4.971326
6.136715
Uuo
7.290928
Y
2.585817
2.633547
Au
5.003723
6.37413
Zr
2.713685
2.729753
Hg
5.03612
6.610266
The K values for each period are given in Table-3.
©The SciTech Publishers, 2012. All Right Reserved
46
The SciTech, Journal of Science & Technology
N. Islam
Vol-1, Issue-1, p.40-50, 2012.
Relationship between atomic orbital exponent & hardness..
Table 3. Computed Kn parameters for each period along with effective principal quantum numbers.
Period
Effective principal quantum number(n*)
Kn values
1
2
3
3.7
4
4.2
4.3
0.2305
0.06213
0.05579
0.065
0.071
0.0305
0.0205
st
1
2nd
3rd
4th
5th
6th
7th
To explore whether the evaluated data exhibit periodicity, we have plotted the computed global hardness as a
function of atomic number in Figure 2.
14
12 He
Ne
10
Hardness in eV
F
O
8
Kr
H
N
Ar
Cl
C
6
Al
Be
Sn
Ga
In
Na
K
Cl
Sc
Zn
Cu
Ni
Co
Fe
Mn
VCr
Ti
Sc
Ca
Al
Mg
Li
Sb
Ge
Si
4
Te
As
P
B
I
Se
S
Uuo
Uus
Uuh
Uup
Uuq
Uut
Uub
Uuu
Uun
Mt
Hs
Bh
fSg
LR
rDb
No
Md
Fm
Es
Cf
Xe
Br
Cd
Ag
Pd
Rh
Ru
Tc
Mo
Nb
Zr
Y
Sr
Rb
2
tHg
OsIrPAu
Re
HTa
fW
Lu
Yb
Tm
Er
Ho
Dy
Bk
Cm
Tb
Am
Gd
Pu
Eu
Rn
Sm
Np
At
Pm
Po
U
Nd
Bi
Pa
Pr
Pb
Ce
Tl
Th
Ac
Ra
La
Ba
Fr
Cs
t
Uu
t
Uu
s
b
M
d
D
M
p
Bk
N
At
Ac
Ir
Tl
Ta
Tb
Tm
I
La
Pm
In
Rh
b
Nb
R
u
As
n
C
M
F
B
H
0
Atoms
Figure 2: Plot of computed global hardness of atoms as a function of their atomic numbers.
The strength of any model is its ability to explain experimental observations. But the atomic hardness is neither
experimentally observable quantity nor it can be evaluated quantum mechanically [6-12,27]. We, therefore, in
absence of any such benchmark for absolute hardness data, rely upon our experience of hardness behavior goaded
by periodic law, and the comparative study of our newly computed hardness data with some other available sets of
hardness data as a validity test. To examine the nature of variation of such different sets of hardness data vis-à-vis
the result of present effort, we have plotted the two sets of data in Figure 3.
©The SciTech Publishers, 2012. All Right Reserved
47
The SciTech, Journal of Science & Technology
N. Islam
Vol-1, Issue-1, p.40-50, 2012.
Relationship between atomic orbital exponent & hardness..
14
η cal(eV)
η Ghosh Islam(ev)
12
Hardness in eV
10
8
6
4
2
M
t
U
ut
U
us
D
b
M
d
Bk
N
p
A
t
Ac
Ir
Tl
Ta
Tm
Tb
Pm
I
La
In
R
h
N
b
As
R
b
C
u
Sc
M
n
A
l
C
l
F
B
H
0
Atoms
Figure 3: Comparative study of the computed hardness data vis-à-vis the hardness data computed by Ghosh and Islam.
We have presented the result of DFT calculation of Sen and Vinayagam [16] and the corresponding data of present
calculation and Ghosh and Islam[6] in Table 4. For a better visualization of the comparative study, we have plotted
the above three sets of hardness data in Figure 4.
Table-4: Comparative study of the hardness of the present calculation vis-à-vis the DFT calculation of Sen and Vinayagam and Ghosh Islam
Atom
η calculated(eV)
η
DFT(eV)
η Ghosh
Islam(ev)
Li
2.278411609
2.33
2.374586656
B
4.604218576
4.07
4.619008972
C
5.767122059
5
5.740978922
N
6.930025542
5.91
6.862466529
O
8.092929026
6.8
7.985435701
F
9.255832509
7.66
9.106475372
Na
2.224256852
2.23
2.44414136
Al
3.529966578
2.69
3.584907074
Si
4.182821442
3.33
4.1551309
P
4.835676305
3.91
4.725803974
S
5.488531168
4.45
5.295979241
Cl
6.141386031
4.98
5.866186484
©The SciTech Publishers, 2012. All Right Reserved
48
The SciTech, Journal of Science & Technology
N. Islam
Vol-1, Issue-1, p.40-51, 2012.
Relationship between atomic orbital exponent & hardness..
10
η calculated(eV)
η DFT(eV)
η Ghosh Islam(ev)
9
8
7
Hardness
6
5
4
3
2
1
0
Li
B
C
N
O
F
Na
Al
Si
P
S
Cl
Atoms
Figure 4: Comparative study of the computed hardness data vis-à-vis the hardness data computed by Ghosh and Islam and Sen and Vinayagam
From Figures 2 and 3 and Table 2 it is evident that computed hardness values of the atoms of 118 elements exhibit
perfect periodicity of periods and groups. Each period begins with the hardness of a representative element and ends
with a noble gas atom. The hardness of the inert gas atoms occur at the top of the curve.
It is evident from Table 4 and Figure 4 that the trend of variation of the hardness data of the twelve elements is
similar to the results of Sen and Vinayagam [16] and Ghosh and Islam [6]. It is further observed that the result of
present calculation is free from the anomalous pattern of variation of the hardness values of these elements evident
in the various finite difference approximation calculations[19,28].
It transpires from a comparative study of the numerical values of the hardness data in Table 4 that the results of
present work have close agreement with the results of Sen and Vinayagam[16] . From Figure 5 it is more transparent
that at least for 12 cases, results of the present semi empirical calculation have close agreement with a sophisticated
DFT calculation[16].
It is the rule of nature that high hardness means less deformability under small perturbation. It is also well known
that the lanthanide elements are soft and easily deformable. It is well known fact [19] that size of atoms of f-block
elements undergoes a steady but slow contraction and the effect is well reproduced in the radii of such elements. It is
distinct from Table 2 and Figure 2 that the magnitude of hardness of all the lanthanide elements is small. It is
distinct from Table 2 and Figure 2 that the global hardness values of the inert gas elements are highest in each
period.
The global hardness of Cs is significantly small compared to those of other elements. The strong chemical reactivity
of the element Cs is well documented.
The chemical inertness of Hg and its state of aggregation is attributed to its small size and least deformability under
small perturbation. Table 2 and Figure 2 reveal that the hardness value of Hg atom is quite high placing it in the
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The SciTech, Journal of Science & Technology
Vol-1, Issue-1, p.40-51, 2012.
N. Islam
Relationship between atomic orbital exponent & hardness..
group of inert gas elements. Thus, the present work can well correlate the significant and characteristic properties of
elements in terms of its computed global hardness values.
Conclusion:
Relying upon the general relationship between global hardness of atoms and the electrostatic force of
attraction of the screened nucleus upon the valence shell electron, we have suggested an orbital exponent dependent
ansatz of computing the global hardness of atoms and have evaluated the global hardness of the atoms of 118
elements of the periodic table. The express periodic behavior and correlation of the most important physicochemical
properties of elements suggest that the present semi empirical approach is a meaningful venture of evaluating global
hardness of atoms.
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