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Predicting the properties of the 113-120 transactinide elements

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Abstract

The information indices, recently introduced for the description of the electronic structure of atoms, are used as a more convenient basis than atomic number (or period number) for correlations with the properties of the chemical elements within the main groups of the periodic table. When the derived equations are extrapolated, the expected values for a number of properties or characteristics of the 113 to 120 transactinide elements are obtained: entropies in the gas and solid state, heats of melting and sublimation, melting and boiling points, first and second ionization potentials, atomic volumes, densities, covalent radii, and orbital exponents. Some corrections to the predictions were made by proceeding from the similarity in the trend of the expected values for elements 113 to 120 and the known data on elements 81 to 88. Some properties of elements 85 to 88, missing from the literature, were also calculated.
J,
Phys.
Chem.
1981,
85,
1177-1186 1177
Predicting the Properties
of
the
11
3-120
Transactinide Elements
Danall Bonchev” and Verglnla Kamenska
Department
of
Physical Chemistty, The Higher School
of
Chemical Technology, 8010 Burgas, Bulgaria (Received: May 9, 1980;
In
Final Form: November
11,
1980)
The information indices, recently introduced for the description of the electronic structure of atoms, are used
as a more convenient basis than atomic number (or period number) for correlations with the properties of the
chemical elements within the main groups of the periodic table. When the derived equations are extrapolated,
the expected values for a number of properties
or
characteristics of the 113-120 transactinide elements are
obtained: entropies in the gas and solid state, heats of melting and sublimation, melting and boiling points,
first and second ionization potentials, atomic volumes, densities, covalent radii, and orbital exponents. Some
corrections to the predictions were made by proceeding from the similarity in the trend of the expected values
for elements 113-120 and the known data on elements 81-88. Some properties of elements 85-88, missing from
the literature, were also calculated.
Introduction
During the last
35
years the periodic table of chemical
elements was considerably extended when the
15
trans-
uranium elements up to element 106 were ~ynthesized.l-~
The prediction of islands
of
nuclear ~tability~-~ around
elements 114 and 164 has prompted greatly the efforts to
synthesize new superheavy elements as well as to search
for some of them in nature.*-1° Relativistic Hartree-
Fock-Slater
(or
Dirac-Slater) cal~ulations~~-’~ have been
carried out for chemical elements up to 172 providing
estimates of their most stable electron configurations. The
prospect of further evolution of the periodic table has been
a
subject of considerable interest.l4-lg All this has en-
couraged attempts to predict the physical and chemical
properties of superheavy elements by extrapolating the
properties of the known elements in Mendeleev’s style,
as
well as by using various approximate
method^.^*^^
(1)
G.
T.
Seaborg, “Man-Made Transuranium Elements”, Prentice-
Hall, Englewood Cliffs, NJ
1964.
(2)
G.
T.
Seaborg,
Ann.
Res.
NucE.
Sci.,
18, 53 (1968).
(3) I.
Zwara, Y.
T.
Chuburkov, R. Tsaletka,
T.
S.
Tsarova, M. R.
Shelevsky, and B.
V.
Shilov,
Sou.
J.
At. Energy,
21,709 (1966);
Radiok-
himiya,
9, 231 (1967);
Sou.
Radiochem.,
9,
226 (1967).
(4)
G.
N. Flerov and
I.
Zvara, Preprint
OIYAI, D7-6013,
Dubna,
1971.
(5)
W.
Myers and W. Swiatecki, Report
UCRL-11980,
1965.
(6)
S.
G.
Nilsson,
S.
G.
Thompson, and C.
F.
Tsang,
Phys.
Lett.
B,
28,
458 (1969);
C.
F.
Tsang and
S.
G. Nielson,
Nucl.
Phys.
A140,289 (1970).
(7)
J.
Grumann,
U.
Mosel, B. Finkand, and W. Greiner,
2.
Phys.,
228,
371 (1969).
(8)
G.
T.
Seaborg, Robert A. Welch Foundation Conference, The
Transuranium Elements, Houson, TX, Nov
1969.
(9)
G. N. Flerov and
V.
P.
Perelygin,
At. Energiya,
26, 520 (1969).
(10)
G.
Herrmann,
Nature (London),
280, 543 (1979).
(11)
J.
Waber, D. I. Cromer, and D. Libermann,
J.
Chem.
Phys.,
51,
(12)
E!.
Fricke, W. Greiner, and
J.
Waber,
Theor.
Chim. Acta
(Berl.),
(13)
R.
Fricke and
J.
Waber,
J.
Chem.
Phys.,
66,
3246 (1972).
(14)
B.
B. Cunningham,
Ann.
Reu.
NucE.
Sci.,
14, 323 (1964).
(15)
G.
T.
Seaborg,
J.
Chem.
Educ.,
46, 626 (1969).
(16)
N.
N. Semenov, Ed.,
“100
Let Periodicheskogo zakona khimi-
(17)
R.
Fricke and
J.
T.
Waber,
Actinides
Rev.,
1,433 (1971).
(18)
IC.
Keller, “The Chemistry of the Transuranium Elements”,
(19)
B.
M. Kedrov and D. N. Trifonov,
“0
Sovremennikh Problemakh
(20)
A.
V.
Grosse,
J.
Znorg.
Nucl.
Chem.,
27, 509 (1965).
664 (1969).
21, 235 (1971).
cheskikh elementov”, Nauka, Moscow,
1969.
Chemie Gmbh,
1971.
Periodicheskoi sistemi”, Atomisdat, Moscow,
1974.
A question may arise whether the method
of
predicting
the properties of superheavy elements by continuation of
the trends
in
chemical groups
has
not lost its meaning since
relativistic quantum mechanical calculations allow us, in
principle, to do this in a more rigorous way. Only a few
quantities, however, like ionization potentials, atomic
and
ionic radii, etc., can be directly calculated. Even in these
cases theoretical calculations do not seem to be entirely
satisfactory. As shown by Keller et al.23 a systematic
correction, determined from experiment, improves the
theoretical values of the ionization potential. The quantum
mechanical calculations of atomic and ionic radii
for
most
of the 7p elements, as pointed out by Fricke et al.,12J3J7
are inaccurate since it
is
not possible to define the atomic
radius as the radius of the principal maximum of the
outermost electron shells.
“If
one continues, however, the
trends in the behavior of metallic or ionic radii, as it done
by Grosse,20 Keller et al.,23 and Cunningham,21 one gets
results which will be quite accurate” (ref 17). In light of
these comments, attempts to improve the extrapolation
technique for predicting the properties of the superheavy
elements seem justified.
Recently, we have applied the information theory26” to
the characterization of the electronic structure of atoms.wB
In general, the proposed concept of atomic information
indices is
a
suitable mathematic model which is likely to
be homomorphic to the periodic table. The information
approach was used in the analysis of the quantitative as-
pects of periodicity, by deriving information equations for
(21)
B. B. Cunningham, ref
140
in ref
1.
(22)
B.
B.
Cunningham, Robert
A.
Welch Foundation Conference.
The Transuranium Elements, Houston, TX, Nov
1969.
(23)
0.
L. Keller, Jr.,
J.
L.
Burnett,
T.
A.
Carlson, and C.
W.
Nestor,
Jr.,
J.
Phys.
Chem.,
74, 1127 (1970).
(24)
0.
L.
Keller, Jr., C. W. Nestor, Jr.,
T.
A.
Carlson, and
B.
Fricke,
J.
Phys.
Chem.,
77, 1806 (1973).
(25)
0.
L.
Keller, Jr., C. W. Nestor, Jr., and B. Fricke,
J.
Phys. Chem.,
78,
1945 (1974).
(26)
C. E. Shannon and W. Weaver, “Mathematical Theory of
Communication”, University of Illinois, Urbana,
1949.
(27)
L. Brillouin, “Science and Information Theory”, Academic Press,
New York,
1956.
(28)
(a)
D.
Bonchev,
V.
Kamenska, and
D.
Kamenski,
Monatsch
Chem.,
108, 487 (1976);
(b)
D.
Dimov and D. Bonchev,
Math.
Chem.
(MATCH),
2, 111 (1976);
(c) D. Bonchev,
V.
Kamenska, and C. Tash-
kova,
ibid.,
2, 117 (1976).
(29)
(a)
D.
Bonchev and
V.
Kamenska,
Monatsch
Chem.,
109, 551
(1978);
(b)
Croat.
Chim.
Acta,
51,19 (1978);
(c)
Monatsch
Chem.,
110,
607 (1979);
(d)
Math.
Chem.
(MATCH),
7, 113 (1979).
0022-3654/81/2085-1177$01.25/0
0
1981
American Chemical Society
1178
groups and periods in the periodic table, as well as re-
vealing correlations between information indices and
properties of chemical elements. By reflecting adequately
on the details of the electronic structure of atoms, the
information indices seem to be much more promising than
the atomic number (which equals only the total number
of electrons) in the search for structure-property correla-
tion~.~~~
In the present paper we shall use the atomic information
indices for predicting various properties of elements
113-120 which belong to the main groups 111-VI11 of pe-
riod VII, and main groups I and
I1
of period VIII. The
correlations between the properties and information ind-
ices, which have been derived for each of these groups, are
extrapolated to the superheavy elements of interest.
The properties of element 116 have not, up
to
now, been
a subject of a detailed study. Some of the examined
properties of the other seven elements (boiling and melting
points, ionization potentials, density, etc.) have already
been treated by Grosse20
(z
=
118), Cunningham2I
(z
=
117-120), and Keller et al.
(z
=
113, 114,23
11526),
making
use mainly of correlations (within a chemical group) with
the row number or atomic number. These works are ex-
cellent examples of predictions on the basis of extrapola-
tion of known properties of lower homologues in the per-
iodic table. Still, a reexamination of the predicted prop-
erties of these elements might be of interest since atomic
information indices are supposed to be a more appropriate
basis for correlations and extrapolations. In addition to
the expected more reliable “vertical” correlations, such a
systematic study of the superheavy elements of the eight
main groups of the periodic table makes it possible to use
a “horizontal” correlation by comparing the trend in the
period formed with that of the preceding period. It is
hoped, in compliance with Mendeleev’s ideas, that in such
a way the predictive power of the periodic table could be
used more effectively.
Met
hod
An atom having
z
electrons will be considered. If certain
criterion are used, the set of electrons can be partitioned
into
k
subsets, having
zl,
z2,
...,
zk
electrons, respectively.
A
finite-probability scheme for the set can be constructed
so
that it specifies a definite probability
p1
=
zi/z
for a
randomly chosen electron to be in the ith subset:
cardinality
probability
[
pl,
pZ,
p3,
.
.
.,
Pk
subset
we can define the average
entropy for the probability distribution of electrons over
subsets in bits per electron as
The
Journal
of
Physical Chemistry,
Vol.
85,
No.
9,
1987
1
1,
2,
3,
...,
k
zl,
z2,
z3,
.
.
.,
zk
Using the Shannon
Bonchev
and
Kamenska
not a measure of entropy since it does not express the
average uncertainty per structure having
z
elements of a
given ensemble of all possible structures having the same
number of elements.
I
is rather the information content
of the structure under consideration in relation
to
a system
of transformations leaving the strucqure invariant. In this
paper we shall term the quantities
I
and
I
as information
indices. More details concerning the terminology can be
found in ref 31.
Various information indices can be introduced for the
atoms of chemical elements depending on the criterion
used for grouping electrons into different subsets. Within
the one-electron approximation the different atomic
quantum numbers and some of their combinations can be
taken as criteria. It is possible in principle to define an
atomic information index in such a way that the valence
electrons are given a larger weight than the innermost
electrons. Such an index might be of interest in chemistry
since the outermost electrons are those which determine
the chemical properties of the atoms. The different
weights of the valence and inner electrons can, however,
be introduced only empirically. Therefore, it seems logical
to
develop
first
the information approach
to
the description
of the atomic electron shells without any additional as-
sumptions. The essential role of the valence electrons
could be more effectively taken into account in a future
development of the approach.
Related to the above, atomic information indices were
defined in our preceding
publication^^^^^^
by taking each
electron with an equal weight. The following electron
subsets in the atom were used:
(1)
electron shells,
(2)
subshells, (3) atomic orbitals,
(4)
spin orbitals,
(5)
(nlj)
subshells, as well as groups of electrons having the same
quantum number, (6) angular momentum
(I),
(7)
magnetic
(m),
(8)
magnetic spin
(mJ,
(9) inner
(j),
and
(10)
total
magnetic
(mj).
In this paper we use the first tyo criteria
only, i.e., the mean information indices
I,,
and
I,l
are used
in parallel with the total information indices
I,,
and
InL.
These indices are readily calculated from the known
electron configurations of the chemical elements.
As
for
the superheavy elements of interest, their electronic
structure is
also
regarded as well established on the basis
of quantum mechanical
calculation^.^^-^^
Thus, the 7p
subshell should become populated in elements 113-118 by
1-6 electrons, respectively, while the valence electronic
configuration of elements 119 and 120 is expected to be
8s1
and
8s2,
respectively.
The procedure developed for the prediction of the
properties of elements 113-120 includes deduction by
comparison of equations correlating a certain property
of
the elements of the corresponding main group in the pe-
riodic table with one of their four information indices
I,,,
Inl,
I,,,
and
fn1
(denoted in what follows by
11,
12,
13,
and
Z4,
respectively), as well as with their atomic number
z.
The latter was considered not only for the purpose
of
comparing results with those obtained by means of the
information indices, but the information indices are ex-
pected to be, in general, more reliable for structure-
property correlations than the atomic number. The limited
variety of such indices used in the present paper (only two
out of
10
indices specified above) in some cases may,
however, result in a worse correlation as compared with
the atomic number and, hence, in a less precise prediction
of
the properties of the superheavy elements.
Each of the above five correlations was obtained by
least-squares fitting to eight different versions of trial
equations. The latter are expected
to
be mainly different
The total entropy of the probability distribution of
electrons in the atom can also be specified by using an
equation derived16 from
(1):
k
i=
1
I
=
21
=
z
log,
2
-
czi
log,
zi
(2)
There is no general agreement in the literature about
how to name the quantities defined by eq
1
and
2.
Some
authors prefer
to
call them the mean and total information
content of the system under consideration, respectively.
For instance, according to Mowshovit~~~ the quantity
f
is
~~ ~~~~~
(30)
A.
Mowshovitz,
Bull.
Math.
Biophys.,
30,
225
(1979).
(31)
D.
Bonchev,
Math.
Chem.
(MATCH),
7,65
(1979).
Properties
of
Elements
113-120
power
or
exponential type of functions (eq
5-8),
due to the
logarithmic dependence between the atomic information
indices and the number of electrons in the atom and its
electron subsets:
y=A+Bx (3)
(4)
y
=
AxB
(5)
(6)
y
=
10BXA (7)
(8)
y
=
A
+
Bx
+
Cx2
y
=
AxB
+
C
y
=
10BXA
+
C
The Journal
of
Physical Chemistry,
Vol.
85,
No.
9, 198
1
1
179
X
y=m
x
-
X1
y=-
A
+
Bx
+
y1
(9)
Using a computer program we have selected out of the
40
equations the best correlation for a given property the
one which displays the lowest mean relative error.
The predictions of the properties of elements
113-120,
made on the basis of the best-group correlation, if neces-
sary
can be corrected in the second stage of
our
procedure.
The similarity in the trend at the end of periods
VI
and
VII, and the beginning of periods
VI1
and VIII, is regarded
here as another criterion for the reliability of the predic-
tions. This assumption originates from Mendeleev’s ideas
for the properties
of
a certain element being an arithmetic
mean of the properties of its neighbors both in the vertical
(group) and horizontal (row) directions. An additional
justification of this assumption is the similarity in the trend
of the properties of elements along the eight main groups.
With few exceptions, which will be discussed in the next
section, the properties examined have the same (increasing
or
decreasing) trend along each of the main groups exam-
ined in the periodic table.
Results
and
Discussion
After selecting the properties to be dealt with, we have
proceeded from the available experimental
or
theoretical
data taking into account that some of the properties of the
superheavy elements of interest have already been satis-
factorily predicted by other a~thors.’l-~~flJ~P* This holds
in particular for the chemical properties like oxidation
states,32 ionic and metallic radii, etc.
Though failing
so
far, there is still some hope of finding
in nature small amounts of some superheavy elements
that
are within the predicted regions of nuclear stability. Re-
lated to this, some macroscopic properties, already treated
or not by other authors, were
also
taken
into
consideration.
Thus, the following properties of chemical elements were
studied: entropy in the gas and solid heats of
melting33-36 and ~ublimation,~~ melting and boiling
point^,^^^^^
first and second ionization
potential^,^^
atomic
(X-ray) densities,34 Pauling’s covalent
and orbital
exponent^.^^^^'
The best-group correlations found for each of the
12
properties under study are given in Table I. Every entry
contains the type of equation (eq
3-10
are marked
as
1-8,
(32) R.
S.
Drago,
J.
Phys.
Chem.,
62,
353 (1958).
(33)
B.
P.
Nikolskii, Ed., “Khimicheskie Dannie”, Vol. 1, Ghoskhim-
(34)
G.
V. Samsonova, Ed., “Svoistva Elementov”, Vol.
1,
Metalurgiya,
(35)
A.
S.
Shchukarev, “Neorganicheskaya Khimia”, Vol.
1,
Visshaya
(36)
E.
Clementi and D.
L.
Raimondi,
J.
Chem.
Phys.,
38,2686 (1963).
(37)
E.
Clementi,
D.
L.
Raimondi, and
W.
P.
Reinhardt,
J.
Chem.
isdat, Moscow, 1963.
Moskow, 1976.
Shkola, Moscow, 1970.
Phys.,
47,
1300 (1967).
.U
=b
“I‘
i
0
u
a6
,
015
115
111
105
225
50
75
8,
4
;5
INFORMATION INDEX
1,
bilo
ATOMIC
NUMBER
Flgure
1.
The
covalent radlus
of
elements
of
group
VI1
vs. (a) atomic
number and (b) information index
1,.
respectively), then the variable used (the type of infor-
mation index
Il
to
14,
or
the atomic number
z),
followed
by the mean relative error in percent. Coefficients
A,
B,
and
C
from eq
3-10
are presented in the next three lines.
Four different symbols a,
b,
c, and d may also appear there
as superscripts to
I
or
z.
The first three refer to cases
where the number of data used in the correlation is not
the maximum one;
c
indicates cases where no data are
available for the heaviest known element in the group;
a
and
b
refer to cases
(27
and
8
in number, respectively),
where the first,
or
first and second elements, respectively,
in the group is excluded from the correlation. The latter
was made in order to improve the correlations since the
first and second elements in the group often behave dif-
ferently from the other elements. Thus, a certain property
could have a minimum
or
maximum in the second
or
third
element of the group, the elements after the extremum
being of importance only for the extrapolation of the
function to higher
z.
15
other cases are denoted by the
superscript d. They refer to cases in which the function
changes its slope from negative to positive,
or
vice versa,
for the element which is forelast in the group. It is hard
to judge in such cases if this change will continue in the
next superheavy element
or,
contrary
to
it, if the extremum
is a starting point for a zig-zag like trend for the curve.
All
these cases are discussed later in detail.
Seven places in Table
I
are empty. In five cases (groups
VI1 and VIII) this is due to lack of data for some of the
properties. The heats of melting and the elements from
group IV do not display a common regularity because of
the different crystal modifications of these elements. The
boiling points of elements from group V are of type d,
described above, which makes their prediction unreliable.
Analysis of Table
I
reveals that the correlations with the
information indices substantially prevail on those made
with the atomic number of chemical elements
(66
against
23
cases). The decrease
in
the mean relative error achieved
when replacing the correlations with the atomic number
by those with the information indices is in some cases very
impressive:
Sosofid
(group IV),
0.9%
instead of
6.5%;
Rkov
(group
VII),
0.14%
instead of
3.2%;
VA
(group
I),
2.4%
instead of
10.6%;
AHM
(group VIII),
3.7%
instead of
17.970,
etc. Still greater prevalence of the information
indices was found in a preceding study
(36
against
1
cases)
where polynomial-type functions were solely examined in
the correlations.29d The atomic number proved to be of
greater importance only for the density and entropy in the
gas phase
(5
out of
8
group correlations). One could,
however, expect the systematic examination of the other
eight information indices, mentioned in the previous sec-
tion, to demonstrate also in the remaining cases the ad-
vantage of the information indices for group correlations
in the periodic table. Being detailed and flexible charac-
teristics of the electronic structure of atoms, the infor-
mation indices are capable of describing more adequately
1180
The
Journal
of
Physical
Chemistry,
Vol.
85,
No.
9,
1981
I
116
6.
5.
Bonchev and Kamenska
T
"
116'
i42i
w
41
/I/
IV
v
MAIN
VI
GROUPS
VI1 Vlll
I II
Figure
2.
Entropy in the
gas
state of elements 81-88 (experimental)
and 113-120 (predicted). The dashed line shows the correction for
element 114 according to the horizontal correlation (the similarity in
the trends of the two neighboring periods).
chart
I
group
IV
So,
cal
deg-'
(eatom)-'
Si
5:';;
A,
=
-0.02
40:24
A2
=
+0.14
Ge
A3=
+1.65
Sn
Pb
41.89
than the atomic number
or
row number the structure-
dependent properties of the chemical elements.
As
an
illustration we show the change in the trend of the covalent
radius of the elements from group VI1 from irregular, when
expressed vs. atomic number, to a linear one for the in-
formation index
7,
(Figure la,b).
It
should be taken into account that, in several cases,
Table
I
does not present the best correlations defined on
the basis of the lowest mean relative error. Using the
horizontal correlation aa a second criterion we gave pref-
erence to cases where the correlation with an information
index had a larger mean relative error than that for the
corresponding correlations with atomic number
(pR,
group
The opposite correction was made in two other cases
(rmv,
group I,
E,
=
3.30
>
cI
=
1.24;
12,
group VII,
E~
=
3.47
>
=
2.45).
The accuracy attained in the correlation, presented in
Table
I,
is as follows: in 30 cases the mean relative error
is less than 1%, in 50 cases it is within the 1-5% range,
and only in 9 cases it is larger than 5%. The large mean
relative error in the later cases is a result of the irregular
trend of some properties. Some
of
them will be discussed
later.
In Table
I1
we present the values for 13 macroscopic
properties
or
atomic characteristics of elements 113-120,
as predicted according to our extrapolation scheme. The
corresponding values of the same properties, which were
found in the literature as calculated by other authors, are
given for the sake of comparison in Table
111.
Entropy in the Gas State.
A
fairly good coincidence in
the entropy trend is manifested in Figure
2
for the two last
periods in the periodic system of chemical elements. The
only exception is element 114 for which the extrapolated
value of 44.8-45.0 cal deg-' (g-atom)-' seems
too
high. The
analysis made for the entropies of the elements of group
IV reveals the reason for the unsatisfactory prediction for
element 114. The change in entropy on going from
Si
to
Ge and from Ge to Sn is very small (Chart
I),
while on
going from Sn to Pb it is (in cal deg-' (g-atom)-l) consid-
erable
(A,
>>
A2 AJ.
The mathematical functions used
in the correlation provide for a further fast increase of
So,
V,
EI
=
10.11
>
eZ
=
7.23;
{,
POUP
VI,
€1
=
1.28
>
E,
=
0.94).
27
I
119
Ill
N
V
VI
VI1
Vlll
I
II
MAIN
GROUPS
Flgure
3.
Entropy in a solid state of elements 81-88 (experimental)
and 113-120 (predicted):
(0)
values predicted by Keller et al.23,25
No
data for groups
VI1
and
VIJI.
Dl
.
111
IV
v
v1
VI1 Vlll
I
II
MAIN
GROUPS
Figure
4.
Heats of melting
of
elements 81-88 (experimental) and
113-120 (predicted). The points 113' and 116' are predicted by using
the correlations for groups
111
and
VI,
respectlvely (Illustrated in the
upper
part
of
the
figure). Points 113 and 116 are obtained by assuming
AH,(period
VII-VI)
=
AHM (period
VI-V).
No
data for group
VII.
(A4
=
SO114
-
Sopb
>>
A,).
If we assume, however, that the
increase in entropy is approximately the same for a pair
of neighboring periods
(Al
=
A2,
A,
=
A4)
a value of 41.89
+
1.65
=
43.52 cal deg-l (g-atom)-l is obtained for element
114. The same value can be determined directly from
Figure 2 by assuming a parallel trend of the two curves
also
in the region of element 114 (the dashed line in Figure
2).
Thus, the horizontal correlation between the elements
of periods
VI
and VI1
also
manifests good predicting power.
The lack of
experimental data for groups
VI1
and VI11 makes it dif-
ficult
to
compare fully the last two periods. Nevertheless,
the curves have similar trends with the exception of group
IV where both predicted values, ours and that of Keller23
(18.6-19.0 and
20
cal deg-l (g-atom)-', respectively) are
overestimates. The horizontal correlation results
in
a lower
value for the entropy of element 114 within the range
17.4-17.5 cal deg-' (g-atom)-'. On the other hand, the
entropy of elements 113 and 115 is nearly the same in our
calculations and those by Kelle$3B
(z
=
113: 17.1 and 17.0
cal deg-' (g-atom)-l, respectively;
z
=
115: 15.4-15.5 and
Entropy
in
the Solid State
(Figure 3).
Properties
of
Elements
1
13-
120
The Journal
of
Physical Chemistry,
Vol.
85,
No.
9, 1981
1181
II
I
44
I
0
R
0
im
h
W
c1
8
?
M
Y
3
i!
Y
I
P
R*
a
%
E?
4
M
M
B
k
1182
The
Journal
of
Physical Chemistry,
Vol.
85,
No.
9,
1981
Bonchev and Kamenska
60
j5,:
-
-
1
2
I
-
40
30
4
z
lI.
0
I-
4
m
-I
3
vl
20-
g
10-
TABLE
11:
Predicted Properties
of
Elements 113-120 and 84-88 According
to
the Equations
of
Table
Ibic
81
$;\
- -
113
115
',
"
\\
\
,:,)a
\;\
\\
'?
\'
0
'\;a
03
86
111
IV
V
VI
VI1
Vlll
I
II
pry-
ertiesa 113 114 115 116 117
118
119 120
So,, 44.5-44.6 43.4-43.5b 45.7-45.9 46.1-46.3 45.7-45.9 43.3-43.5 44.6-44.8 43.3-43.5
8'
solid
17.1-1 7.2 18.6-1 9.0 15.4-1 5.5 16.8-1 7.2 24.9-26.6 18.5-19.5
AH, 1.26' 1.41-1.43 1.82' 0.80-0.86 0.48-0.49 1.92-2.05
AHs 32.2-32.7 17.2-17.7 58.1-58.9 28.5-28.6 5.14-5.26 15.1-15.8 39.2-42.8
TM 724-730 265-340 340-358 637-780 765-769 250-260 295-297 900-1020
TB 1370-1420 1640-1760 1035-1135' 825-860 252-266 928-942 1770-1890
I1
5.92-6.08 7.8-8.0' 6.6-7.2 7.60-8.00 8.43-8.71 9.30-9.66 3.69-3.80 5.33-5.55
12
18.4-19.4 16.4' 21.3' 18.3-19.2 18.5-19.9 19.2-19.8 20.3-21.4 9.28-9.52
VA
17.9-18.6 20.6-20.8 22.4-25.2 29.4-30.8 44.4-44.5b 55.5-61.1 92.5-96.9 44.3-46.1
P
14.5-17.1 13.4-14.0 12.5-13.0b 11.0-11.4 7.1-7.3 4.9-5.1 3.7-4.0 5.2
R,,, 1.72-1.80 1.71-1.77 1.56-1.68 1.62-1.66 1.56-1.57 2.63-2.81 2.06-2.10
5
2.15-2.21 2.15-2.19 2.32-2.36b 2.48-2.54 2.69-2.75 2.88-2.94 1.18-1.22 1.35-1.39
VA~
=
23.9-25.0;
VA'~
=
33.9-34.5;
VA&
=
45.4-49.8;
,A''=
78.3-82.1;
,A"=
40.3-41.9;p8'= 6.2-6.5;~'~
=
4.4-4.5;
pa'
=
2.8-3.0;~"
=
4.4;
Rc0v85
=
1.43;
Rc0,''
=
2.58; RCov8'
=
2.05;
5''
=
1.13-1.17;
ts8
=
1.23-1.27
a
Same dimensions as in Table
I.
Values found by horizontal correlation in Figure 2-13.
'
Values found by the condi-
tion
XvII
-
XvI
-
XvI
-
XV
or similar considerations.
TABLE
111:
and Fricke et
al.12*1347
Some Properties
of
Transactinide Elements
113-1
20, as Predicted by Grosse,Zo Cunningham,21 Keller et al.,23325
propertiesa, 113*3 11423 115" 116 117'l
118"
llgzl
1202'
so
solid
17 20 16
34 10 34 5.6
7
00
340 -700 620-820 258 273-303 950
*Hs
TM
I,
7.4 8.5 5.2 9.3 9.8 3.4-3.8 5.4
I
112
7.5 8.5 5.9 6.8 8.2 9.0 4.1 5.3
12
16.8 18.1 16 15 23 10
VA
18
21 45 50 80-90 45
P
16 14 13.5" 12.9'' 5.7
3
7
€2
CO"
1.7
1.8
2.3 2.6' 2.0'
TB 1400 420 -1400 880 263 900 1970
P
l2
14.7 15.1 14.7 13.6 4.6 7.2
2.212
Rat13 1.13
1.21
1.77 1.51 1.38 1.31 2.55 2.16
a
Same dimensions
as
in Table
I.
The references cited in the columns should be taken into account only when there
is
no citation in the rows.
'
Atomic radius.
16 cal deg-l (g-atom)-l, respectively.
Heats
of
Melting
(Figure 4). The coincidence between
the two periods is not very good. The heats of melting of
elements 118,119, and 120 are nearly the same as those
of the corresponding elements 86,
87,
and 88 of the pre-
ceding period. On the other hand, the situation denoted
in Table I by superscript d occurs in groups I11 and
VI.
It is illustrated in Figure 4 above points 113 and 84. The
correlations given in Table I provide the values of 0.73-0.87
and 4.8-6.6 kcal (g-atom)-l
for
elements 113 and 116, re-
spectively (denoted as 113' and 116' in Figure
4).
Alter-
natively, we can suppose, however, that the extrema in the
curves
of
groups I11 and
VI
are the initial points of an
increasing,
or
decreasing, branch
of
these curves, respec-
tively. Assuming the same change
on
going from period
VI to VI1 as on going from period
V
to VI we obtain for
elements 113 and 116 that the heats of melting are 1.26
and 1.82 kcal (g-atom)-l, respectively. The choice between
the two estimates for elements 113 and 116 needs addi-
tional argumentation. For this reason we present in Figure
4 both estimates
for
each element although chemical in-
tuition may point to the values calculated in analogy with
the preceding periods.
Heats
of
Sublimation
(Figure
5).
Similar to heats
of
melting, the heats
of
sublimation
of
elements 118-120 are
very much the same as those of elements 86-88.
A
very
good coincidence was found between
our
result and that
of
GrosseZ0 for element 118
(5.2
and 5.6 kcal (gatom)-',
respectively).
One should not expect the curve for elements 113-116
to
be parallel with that for elements 81-84 since the heats
of
sublimation in group V tend to increase with atomic
(38)
K.
S.
Pitzer,
J.
Chem.
Phys.,
63,
1032
(1975).
Properties of Elements
1
13-120
The
Journal
of
Physical
Chemistry,
Vol.
85,
No.
9, 1981
1183
l14w5
-..__>
:le
200
.
111
IV V
VI
VI1
Vlll
I
I1
MAIN
GROUPS
Figure
6.
Melting points
of
elements
81-88
(experimental) and
113-120
(predicted):
(0)
values predicted in ref
20
(z
=
1
la),
ref
21
(z
=
117, 119, 120),
and ref
23
(z
=
113, 114).
Two predictions are
made for elements
114
and
116
following the two possible extrapo-
lations of the melting points of the elements of groups IV arid VI shown
in the upper part of the figure. Points
114'
and
116'
are obtained by
the corresponding equations in Table
I
while points
1
14
and
116
are
obtained
by
the conditions: ATdperiod VII-VI)
>
ATdperiod VI-V),
and A T,(period VII-VI)
=
A
T,(period VI-V), respectively.
Chart
I1
group
IV
mp,
K
group
VI
mp,
K
Si
Ge
Sn
Pb
114
i!!:
AI
=
578
A%=
605
505
A3=95
6oo
A4
?
S
Se
Te
Po
116
392
AI=%
490
A2=
233
723
A3=
196
527
A4
?
Since this element is believed to have a closed p1/22 shell
it is expected to be a gas or a very volatile liquid.
A
sim-
ilarity in the properties
of
elements
113
and
115
is also
expected due to their similar electronic structure
(z
=
113,
plI2l;
z
=
115,
p3l2l).
Hence, one could conclude that the
heats of sublimation of elements
114
and
115
predicted
by Keller23v25 seem consistent with the real electronic
structure of these elements.
Melting Points
(Figure
6).
Again, the values obtained
for elements
118-120
are close to those of elements
86-88.
A good coincidence is manifested with the values predicted
by Keller et al.23 for elements
113
and
114,
by Cunning-
hamz1 for elements
117,119,
and
120
(here we have taken
the mean value of
720
K from the range of
350-550
"C
reported21 for element
117),
by Grosse20 for element
118.
By considering the horizontal correlation, one can see
from Figure
6
that the trend of melting points on going
from elements
81
through
85
cannot be reproduced for
elements
113
to
117.
This is due
to
two different reasons.
Primarily, the trend in melting points with increasing
atomic number is not the same for all groups. Thus, it
increases for groups
I11
and
VII,
whereas it decreases for
the heavy elements of group
V.
As
a result, points
113
and
117
lie above the curve of period
VI,
while the point
115
lies below. Another complication occurs in groups
IV
and
VI:
the trend in melting points changes in the last known
element of each of these groups (this is illustrated by the
corresponding curves above elements
114
and
116
in Figure
6)
(Chart
11).
The correlations reported in Table
I
yield, with a mean
relative error of
10-12%,
the melting points of elements
114
and
116
(points
114'
and
116'
in Figure
6)
in the range
265-340
and
637-780
K, respectively.
If
one assumes,
however, that the extrema, appearing in period
V
both in
(39)
0.
L.
Keller in "Predictions in the Study of Periodicity",
B.
M.
Kedrov and
D.
N.
Trifonov,
Ed.,
Academy of Sciences, USSR, Institute
of Science and Technology,
Moscow,
1976,
pp
202-203
(in Russian).
9'"l
600.
0
200
Ill
IV
v
VI
VI1
Vlll
I
I1
MAIN
GROUPS
Figure
7.
Boiling points of elements
81-88
(experimental) and
113-120
(predlcted).
(0)
values predicted in ref
20
(z
=
1
la),
ref
21
(z
=
117, 119, 120),
and ref
23
(z
=
113, 114).
The trend in groups
V, VI, and
I
is shown in the upper part of the figure.
No
estimate for
element
115
is given. Points
115', 118',
and
119'
are obtained by
the
correspondlng equations in Table I, point
116
Is
obtained by assumlng
AT,(period VII-VI)
C
AT,(period VI-V), while for point
119
the
condition
A
T,(period VU-VI)
=
A T,(period VI-V)
is
used.
groups
IV
and
VI,
were the initial points for a new branch
of a parabolic type of curve, the opposite predictions can
be made. Assuming also that the change from periods
VI
to
VI1
is the same
as
that for periods
V
to
VI,
one obtains
for element
116 T,,,
=
330
K, while for element
114 TM
=
695
K.
It
seems reasonable, however,
to
take a higher value
for element
114
since
A3
<<
A2,
assuming
A4
>
A3.
For
this
reason we propose the second possible value for the melting
point of element
114
to be regarded as being within the
range
695-800
K. Evidently, one should go beyond the
criteria used in this paper to make a choice between the
two alternatives for elements
114
and
116.
The Lindeman
formula used by Keller et for element
114,
can be
regarded
as
such an additional criterion. Since the melting
point obtained on this basis
(340
K) coincides with our
value obtained from the equations in Table
I
we present
these values for elements
114
and
116
in Table
11.
Boiling Points
(Figure
7).
The tendency in elements
118-120
to have their heats of melting and sublimation,
as
well
as
their melting points near
to
the respective values
of elements
86-88
seems
to
hold
also
for the boiling points.
On the other hand, the curves of periods
VI
and
VI1
(groups
I11
to
VIII)
intersect due to the tendency of the
boiling points to diminish with atomic number along
groups
I11
and
IV,
and to rise along groups
VI1
and
VIII.
As
can be seen from Figure
7
our predictions practically
coincide with those of Keller et
al.23
for element
113,
and
Cunningham21 for elements
117
and
119.
The boiling and
melting points of element
118
found in our study
(-14
f
7
and
-18
f
5
OC) agree quite well with those previously
calculated by GroeseZ0
(TB
=
-10
"C
and
TM
=
-15
"C).
The boiling point of element
114 (420
K) reported in ref
23,
however, seems more reliable than ours, due to rela-
tivistic effects.
In
groups
V, VI,
and
I
there is once again
the situation where the trend in the group alters for the
last known element (superscript d in Table
I)
(Chart
111).
The change in boiliig point around the minimum of group
I is very small. This makes the estimate based on the
respective correlation of Table
I
(TB
=
928-942
K) close
to the second estimate denoted in Figure
7
as point
119
(TB
=
957
K) in the increasing part of the curve for group
I
on going from period
VI
to
VIII.
The estimates for elements
115
and
116
are not
straightforward. The correlation given in Table
I
yields
for element
116
the value of
1430-1520
K. This seems
1184
chart
I11
The
Journal
of
Physical
Chemistry,
Vol.
85,
No.
9,
7981
group
V
bP,
K
group
VI
Bonchev and Kamenska
N
P
As
Sb
Bi
A,
=
470.7
A3
=
1013
885
A2
=
337
i:::
A,=-68
0
S
Se
Te
Po
11
5
?
116
II
IV
v
VI
VI1
VI11
I
I1
Figure
8.
First ionization potentials
of
elements
81-88
(experimental)
and
113-120
(predicted):
(0,X)
values obtained
in
ref
21, 23, 25
and
in
ref
12,
respectively. The
two
possible extrapolations
for
group
IV
are
given
in
the upper part
of
the figure.
Point
114'
is
obtained
by
the
corresponding equations
of
Table
I
while point
114
is obtained
by
assumlng Al,(perlod
VII-VI)
C
Al,(perlod
V-IV).
unrealistic especially when compared with the boiling
points of
Po
and Te
(1235
and
1285
K,
respectively). On
the other hand, analysis of the boiling points in group VI
indicates a characteristic behavior: the change is larger
on going from one period to another of the same size
(A,
=
628",
A1V-v
=
355O)
than on going from a smaller to a
larger period
(AIII-Iv
=
212O,
AV-VI
=
50a),
both effects
decreasing with the atomic number. Then, if this trend
still holds for period VII, one should expect
AVI-VII
to be
within the
100-200°
range. This leads to
TB
=
1035-1135
K
for element
116.
The prognosis
for
element
115
was
quite uncertain since no clear regularity was found for the
boiling points of group
V.
Ionization Potentials.
The trend for the first ionization
potentials of element
113-120
was found to parallel that
of elements
81-88
(Figure
8).
Two expected values can
be given for element
114
due to the change in the behavior
of group IV in Pb (see below). The correlation presented
in Table
I
yields a value for element
114
that is lower than
that of Pb by
0.1-0.2
eV. Treating the minimum point
for
Sn
as
the onset of an ascending part of the curve, however,
we predict a value higher than that for Pb
(Il
=
7.8-8.0
eV, point
114,
connected with a dashed line in Figure
8).
Although the horizontal correlation shown in Figure
8
looks
very attractive, the agreement with the data predicted by
other authors (Table 111) is not quite satisfactory. Our
results are close to those of Cunningham2' for elements
119
and
120,
Fricke, Greiner, and Waber12
for
elements
117,
118,119,
and
120,
and Grosse20 for element
118.
The point
114
in Figure
8
also approaches the value predicted in both
ref
23
and
12.
The largest disagreement occurs for element
113
(Chart IV).
Analysis of the data for group I11 reveals a tendency for
Il
to decrease when no new type of electron subshell ap-
pears in the next period
(All
>
0
on going from period I1
to 111, and from IV to
V)
and to increase in the opposite
case
(AI,
<
0
on going from period I11 to IV (d subshell),
and from V
to
VI
(f
subshell)). Then, it is logical to expect
that a small decrease will occur again in element
113
as
compared with
T1.
The quantum mechanical calcula-
tions,12J4 however, provided the value
of
7.4-7.5
eV which
MAIN
GROUPS
Li
Na
K
Rb
cs
Fr
1615
1151
1032
119
?
Chart
IV
group group
I11 IP. eV IV IP. eV
113
?
114
?
22t
115
,
0
111
IV
v
VI
VI1 Vlll
I
II
MAIN
GROUPS
Flgure
9.
Second ionization potentials of elements
81-88
(experl-
mental) and
113-120
(predicted):
(0)
values obtained
in
ref
23,
25,
and
21
for
elements
113, 114; 115;
and
117-120,
respectively. The
points denoted as
114'
to
120'
are obtained
by
the corresponding
equations
in
Table
I
while
points
114
and
115
are obtained
by
assuming
AJ,(period
VII-VI)
i=
Al,(perlod
V-IV).
is much larger than that of Tl(6.1 eV). This increase in
the first ionization potential of element
113
is due to the
strong spin-orbit coupling occurring in the superheavy
elements. Such new physical effects appearing at higher
atomic numbers obviously reduce the predictive power of
the periodic table related to some properties of the su-
perheavy elements such
as
ionization potentials and atomic
radii. Still, periodicity could be of use for the improvement
of such quantum mechanical calculations by a systematic
empirical correction within a chemical group
or
period
as
demonstrated by Keller et al.23y26 and Fricke et a1.,12 re-
spectively.
The prediction of the second ionization potentials is not
straightforward. In six out of eight cases two prognoses
can be made, due to the minimum that appears in the
penultimate known element in main groups 11, IV-VIII.
We present in Figure
9
the values obtained by extrapo-
lating the corresponding equations from Table
I.
All
these
values are lower than the values of their lower homologues
in the groups.
Our
prognoses for elements
117-119
seem
more plausible than those of Cunningham21 and are close
to them for element
120.
Due to the spin-orbit coupling
between
7p1p
and
7p3,2
levels,12J7 however,
our
estimates
for elements
114
and
115
seem underestimated and will
be changed below.
Properties of Elements 113-120
2.9
The
Journal
of
Physical
Chemlstty,
Vol.
85,
No.
9, 1981
1185
.
x
0
U
Ill
IN
V
VI
VI1
Vlll
I
II
MAIN
GROUPS
ai
,
Flgure
10.
Atomic volumes of elements 49-56, 81-83 (experimental),
84-88 (dashed line), and 113-120 (expected):
(0)
values predicted
in ref 23 for
z
=
113, 114, ref 20 for
z
=
118, and ref 21 for
L
=
117,
119, and 120.
An alternative prognosis could be made in dealing with
the minimum in the second ionization potential of group
11, IV-VI11 as an initial point of the group correlation
curve. An analysis similar to that presented above for
Il
for the elements of group IV, and specifically the condition
A12(YII-VI)
=
AIz(V-IV), could result in another series
of
I2
values for elements
114-118
and
120.
The uncertainty
in such a prediction is, however, too high. Moreover, in
view of the quantum mechanical calculations12 revealing
a tendency
for
the first ionization potentials to increase
for 7p1/2 and to decrease for
7p3j2
levels, the values thus
predicted for elements
116-118
would be strongly over-
estimated. For this reason we present in Figure
9
two more
plausible predictions of this kind made for element
114
(I2
16.4
eV), which is close to the estimate of Keller et
al.23
(1,
=
16.8
eV), and element
115
(I2
=
21.3
eV). The
prediction made by Keller et
aLZ5
for the second ionization
potential of element
115
is, however, closer to our initial
estimate
(18.1
vs.
18.4
eV). Elements
49-56
have
been taken here as analogues
of
the transactinide elements
113-120
since data on the next homologues within the eight
main groups have been found in the literature only for
elements
81-83.
The coincidence in the trends
of
the two
periods
is
satisfactory. The results obtained are very much
the same as those
of
Keller et al.23 for elements
113
and
114,
and CunninghamZ1 for element
120,
and are somewhat
higher than those reported by CunninghamZ1 (elements
17
and
119)
and Grosse20 (element
118).
Using the similarity
in the trends of the neighboring periods we have corrected
the value
VA1l7
=
53-54
cm3 (g-atom)-l, obtained by the
best group correlation,
to
VA
=
44-45
cm3 (g-atom)-' which
also coincides with the Cunningham value.21 We also
present in Figure
10
and Table I1 the atomic volumes of
elements
84-88
calculated by us according to the corre-
sponding equations of Table
I.
Our value of
47.6
f
2.2
cm3
(g-atom-l for emanation (element
86)
is close to the es-
timate presented by Grosse20
(42.3
cmm3 (g-atom)-l).
Densities
(Figure
11).
A
horizontal correlation is shown
with the data available for four elements of the preceding
period
(81-84)
and the elements
49-56.
On this basis, the
expected value of
pl15
=
9.5-11.7
g
~m-~, obtained by group
correlation (Table I), is corrected
to
a higher one
(12.5-13.0
g ~m-~). Accord with the results of other authors17,20~21~23
using the continuation
of
trends of the known elements
(see Tables I1 and 111) is good for elements
113, 114, 115,
118,
and
119.
For elements
116
and
120
our values are
lower by
1.7
and
1.8
g ~m-~, respectively.
A
systematic
deviation from the results of Fricke et al.13 was, however,
Atomic Volumes
(Figure
10).
21
I
\5
5/
Ill
IV
v
VI
VI1 Vlll
7
II
M4lN
GROUPS
Figure
11.
Densitles of elements 113-120 and
85-88
obtained In this
work, as well as those obtained by Fricke et
(z
=
113, 114), ref 16
(z
=
115, 116), Grosse'O
(z
=
118), and
Cunningham"
(z
=
119, 120):
(0)
comparison with the experimental
densities
of
elements 81-84 and 49-56.
(X);
Keller
et
''1
1!3
,lL
T
MAIN
GROUPS
Flgure
12.
Pauling's covalent radii for elements 49-56 and 81-84
(experimental): elements
85,
87,
88
(X
and the dashed line) and
113-120 (expected):
(0)
covalent radii reped by Fricke and Waber"
(z
=
114, 119, and 120), Cunningham'
(z
=
117), and Grosse20
(z
=
118).
found within the range of
1-2
g ~m-~. The densities of
elements
85-88,
calculated by extrapolations of the cor-
responding equations of Table
I,
are also presented in
Figure
11
and Table
11.
Again,
our
estimate for emanation
(element
86)
and that of Grosse,20 taken at
0
K, are rela-
tively close
(4.45
f
0.05
and
5.25
g ~m-~, respectively).
Pauling's Coualent Radii
(Figure
12).
The extrapolated
values
for
elements
113-120
are compared with those of
elements
49-56
and
81-84.
The radii of elements
85,87,
and
88,
calculated in this work, are also shown in Figure
12
and Table
11.
(The van der Waals' radii of group VI11
elements are not presented there.) Our results coincide
very well with those of Keller et
al.=
for element
114,
and
those
of
Fricke et al." for elements
119
and
120.
In the
light of the recent quantum mechanical calc~lations~~J~J~
showing
that
the relativistic effeds increase the contraction
1186
The
Journal
of Physical Chemisfry,
Vol.
85,
No.
9, 1981
Bonchev and Kamenska
in the correlations with these indices than in the correla-
tions with atomic numbers.
On the other hand, the great flexibility to reflect the
atomic electronic structure that is the principal advantage
of information approach may
or
may not be entirely re-
alized in a certain correlation depending on the type of the
mathematical function used. Taking into account the fact
that the functions used in the present paper cannot always
express in the best way the trend of a certain property in
a group of elements, we have completed our procedure by
examining also the trend within the periods (vertical and
horizontal correlations, respectively). We suppose that the
combined use of the atomic information indices for cor-
relations within groups and periods is
the
most promising
way
for the prediction of properties of the superheavy
elements by means of extrapolations. Naturally, making
use of a greater variety of indices and functions for the
correlations, some of the expected values, reported in this
paper, could be further improved. An additional refine-
ment of the extrapolation procedure may come from
modification of the atomic information indices
so
as
to
take
into account the major role of the outermost electrons in
the chemistry and including them with larger weights in
the information functions.
The reliability of the extrapolation methods will, how-
ever, in some cases be insufficient. Two reasons should
be taken into account. Primarily, the trend of a certain
property can drastically change in the last
known
element
of the group in the periodic table
(14
our of
96
cases ex-
amined above).
Tko
opposite extrapolations result in these
cases and additional criteria (some rules
or
approximate
formulas) are needed to choose between them. What
prediction could, however, be done if such a drastic change
did occur in the superheavy element of a chemical group?
The method of extrapolations based on the periodicity of
the chemical elements is in principle incapable of pre-
dicting neither the appearance of new effects nor their
magnitude. As shown by quantum mechanical calcula-
tions, such important effects are the strong spin-orbit
coupling in the superheavy elements and the large rela-
tivistic contraction of their orbitals with a low angular
momentum. They cause a considerable change in the
ionization potentials and a decrease in the size
of
atoms
which cannot be obtained by extrapolations. Still, the
periodicity could be of use in the prediction of such atomic
properties, providing empirical corrections
to
the calculated
magnitudes as shown in the most convincing way in the
studies of Keller et al.,a* Fricke et
al.,"
and other authors.
One can conclude that, although limited
to
some extent,
the periodicity of the chemical elements has not lost its
importance for the prediction of the properties of super-
heavy elements up to
z
=
120.
Acknowledgment.
It is a pleasure
to
express our thanks
to Dr.
I.
Zvara (Dubna), Dr. G. Nikolov (Sofia), and Pro-
fessor
0.
Kastano Gonzales (Sofia)
for
their comments
which substantially improved the presentation of this
manuscript.
Flgure
13.
Orbital exponents by Clementi et a1.38,37 for elements
81-86, as
well
as the expected values for elements 87, 88, and
113-120.
A
correction
is
made for element 115 on the basis
of
the
similarity in the
two
curves
(E
=
2.32-2.36).
of
the outermost shells, some of our estimates, particularly
those for elements
113
and
114
(7p1/,
subshell), seem,
however, overestimated.
Orbital Exponents
(Figure
13).
As
an addition to the
various properties
of
transactinide elements
113-120
we
have also extrapolated the orbital exponents of the atomic
wave functions used by Clementi et a1.36137 for elements
1-86.
The horizontal correlation presented in Figure
13
shows that the values expected for elements
113-118
manifest in general the same trend as the exponents of
elements
81-86.
The only exception is element
115
where
the correlation within group
V
leads to a higher value
(tl16
=
2.44-2.64).
Making use of the similarity in trends of the
two curves, we have corrected the value expected for ele-
ment
115
to
2.32-2.36.
Predictions for elements
87
and
88
are also presented in Figure
13
(la,
=
1.13-1.17,
tsa
=
1.23-1.27).
Concluding
Remarks
The great capability of the periodic table to predict
properties
of
chemical elements is known since the time
of Mendeleev. Numerous correlations have been obtained
in which a certain property of the chemical elements in
a group
or
period is expressed as a function of the atomic
number or the period number. The latter two numbers,
however, are equal to the total number of electrons in the
atom, and the number of electron shells, respectively.
Thus, extrapolations made for the properties of the su-
perheavy elements are not based on a
detailed
description
of the electronic structure of atoms. The information
indices proposed recently for the description of atoms seem
to provide a better basis for the prediction of structure-
dependent properties of chemical elements since they re-
flect the electronic structure of atoms in details. Hence,
it is logical to expect that more precise extrapolations can
be made within the group of the periodic table making use
of atomic information indices. These expectations are
additionally supported by the greater precision reached
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