# Predicting the properties of the 113 to 120 transactinide elements

**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.

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**ABSTRACT:**This chapter reviews possible experimental aspects of relativistic effects in heavier Main Group elements and their compounds. Attention is focused on the sixth, seventh and eighth Period elements, for which the relativistic contribution to their physical and chemical properties is significant. Superheavy elements through Z = 120 are also discussed. This review may increase interest of theoreticians in chemistry-oriented problems that require use of relativistic methods of quantum chemistry. KeywordsRelativistic effects-Sixth-seventh and eight periodic elements-Superheavy elements04/2010: pages 63-97; - [Show abstract] [Hide abstract]

**ABSTRACT:**A nonorbital representation of the many-electron atomic systems is proposed. It is obtained by considering a certain equivalence class of mappings ƒ: ϵ → Π from the set ϵ of N electrons into the set Π of Z protons. Total binding energy of the systems (Z = 3,4,…, 18; Z − N = k = 0, 1,…, 8) arranged according to the Periodic Table criterion, turns out to be the linear function of ZIr, where Ir is an information functional related to our representation.International Journal of Quantum Chemistry 10/2004; 25(5):755 - 766. · 1.17 Impact Factor - SourceAvailable from: Peter Daniel Grünwald[Show abstract] [Hide abstract]

**ABSTRACT:**We compare the elementary theories of Shannon information and Kolmogorov complexity, the extent to which they have a common purpose, and where they are fundamentally different. We discuss and relate the basic notions of both theories: Shannon entropy versus Kolmogorov complexity, the relation of both to universal coding, Shannon mutual information versus Kolmogorov (`algorithmic') mutual information, probabilistic sufficient statistic versus algorithmic sufficient statistic (related to lossy compression in the Shannon theory versus meaningful information in the Kolmogorov theory), and rate distortion theory versus Kolmogorov's structure function. Part of the material has appeared in print before, scattered through various publications, but this is the first comprehensive systematic comparison. The last mentioned relations are new.CoRR. 01/2004; cs.IT/0410002.

Page 1

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~-~

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~~-’~

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^.^*^^

around

have been

(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,

(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,

664 (1969).

1965.

(12) E ! . Fricke, W. Greiner, and J. Waber, Theor. Chim. Acta (Berl.),

21, 235 (1971).

(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-

cheskikh elementov”, Nauka, Moscow, 1969.

(17) R. Fricke and J. T. Waber, Actinides Rev., 1,433 (1971).

(18) IC. Keller, “The Chemistry of the Transuranium Elements”,

Chemie Gmbh, 1971.

(19) B. M. Kedrov and D. N. Trifonov, “0 Sovremennikh Problemakh

Periodicheskoi sistemi”, Atomisdat, Moscow, 1974.

(20) A. V. Grosse, J. Znorg. Nucl. Chem., 27, 509 (1965).

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

Page 2

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-

t i o n ~ . ~ ~ ~

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:

probability [

Using the Shannon

cardinality

p l , pZ,

p3, . . ., Pk

we can define the average

subset

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

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,

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

(9) inner (j),

and (10) total

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).

Page 3

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 + B x

y = A + Bx + Cx2

(3)

(4)

(5)

(6)

(7)

(8)

y = AxB

y = AxB + C

y = 10BXA

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*

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 i n t o consideration.

Thus, the following properties of chemical elements were

studied: entropy in the gas and solid

melting33-36 and ~ublimation,~~

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,

This holds

heats of

melting and boiling

(32) R. S. Drago, J. Phys. Chem., 62, 353 (1958).

(33) B. P. Nikolskii, Ed., “Khimicheskie Dannie”, Vol. 1, Ghoskhim-

isdat, Moscow, 1963.

(34) G. V. Samsonova, Ed., “Svoistva Elementov”, Vol. 1, Metalurgiya,

Moskow, 1976.

(35) A. S . Shchukarev, “Neorganicheskaya Khimia”, Vol. 1, Visshaya

Shkola, Moscow, 1970.

(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.

Phys., 47, 1300 (1967).

. U

=b

“I‘ i

0 u

a6

,

015

115

111

105 2 2 5

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. A l l

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

Page 4

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)-'

5:';;

40:24

A 2 = +0.14

A 3 = +1.65

41.89

Si

Ge

Sn

Pb

A , = -0.02

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

V, EI = 10.11 > eZ = 7.23; {, POUP VI, €1 = 1.28 > E, = 0.94).

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,

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.

D l

.

111

IV

v

v1 VI1 Vlll

I

II

M A I N

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).

(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.

Entropy in the Solid State (Figure 3).

No data for group VII.

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

Page 5

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

B

k

M

Page 6

1182

The Journal of Physical Chemistry, Vol. 85, No. 9, 1981

Bonchev and Kamenska

60

j5,:

- - 1

2

I - 40

30

4

z

l I .

0

I-

4

g 1 0 -

m

3

vl

-I

2 0 -

TABLE 11: Predicted Properties of Elements 113-120 and 84-88 According to the Equations of Table Ibic

p r y -

ertiesa 113 114 115

So,, 44.5-44.6 43.4-43.5b 45.7-45.9

8 ' solid

17.1-1 7.2 18.6-1 9.0 15.4-1 5.5

AH, 1.26' 1.41-1.43

AHs 32.2-32.7 17.2-17.7 58.1-58.9

TM 724-730 265-340 340-358

TB 1370-1420 1640-1760

I 1

5.92-6.08 7.8-8.0' 6.6-7.2

1 2

18.4-19.4 16.4' 21.3'

VA

17.9-18.6 20.6-20.8 22.4-25.2

P

14.5-17.1 13.4-14.0 12.5-13.0b

R,,, 1.72-1.80 1.71-1.77 1.56-1.68

5

2.15-2.21 2.15-2.19 2.32-2.36b

V A ~

= 23.9-25.0; VA'~ = 33.9-34.5; VA& = 45.4-49.8; ,A''=

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.

81 $;\

\ ; \

\ \

'? \'

- - 113 115 ', "

\ \

\

, : , ) a

0

'\;a

03

111

86

IV

V

VI

VI1

Vlll

I

II

116 117

118

119 120

46.1-46.3

16.8-1 7.2

1.82'

28.5-28.6

637-780

1035-1135'

7.60-8.00

18.3-19.2

29.4-30.8

11.0-11.4

1.62-1.66

2.48-2.54

45.7-45.9 43.3-43.5 44.6-44.8

24.9-26.6

0.48-0.49

15.1-15.8

295-297

928-942

3.69-3.80

20.3-21.4

92.5-96.9

3.7-4.0

2.63-2.81

1.18-1.22

43.3-43.5

18.5-19.5

1.92-2.05

39.2-42.8

900-1020

1770-1890

5.33-5.55

9.28-9.52

44.3-46.1

5.2

2.06-2.10

1.35-1.39

= 4.4-4.5;

0.80-0.86

5.14-5.26

250-260

252-266

9.30-9.66

19.2-19.8

55.5-61.1

4.9-5.1

765-769

825-860

8.43-8.71

18.5-19.9

44.4-44.5b

7.1-7.3

1.56-1.57

2.69-2.75 2.88-2.94

40.3-41.9;p8'= 6.2-6.5;~'~ 78.3-82.1; ,A"=

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

propertiesa, 113*3

so solid

17

34

7 00

TM

TB 1400

Some Properties of Transactinide Elements 113-1 20, as Predicted by Grosse,Zo Cunningham,21 Keller et al.,23325

11423

20

10

340

420

115"

16

34

-700

-1400

116 117'l

118"

llgzl 1202'

5.6

258

263

620-820

880

273-303

900

950

1970

*Hs

I ,

I 112

1 2

VA

P

P l2

7.4

7.5

8.5

8.5

16.8

21

14

15.1

5.2

5.9

18.1

9.3

8.2

16

45

9.8

9.0

15

50

5.7

3.4-3.8

4.1

23

80-90

3

4.6

5.4

5.3

10

45

7

7.2

6.8

18

16

14.7

13.5"

14.7

12.9''

13.6

€2 CO"

1.7 1.8 2.3

2.212

1.31

2.6' 2.0'

Rat13 1.13

1.21

1.77 1.51 1.38 2.55 2.16

a Same dimensions as in Table I.

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

The references cited in the columns should be taken into account only when there is

(38) K. S . Pitzer, J. Chem. Phys., 63, 1032 (1975).

Page 7

Properties of Elements 1 13-120

The Journal of Physical Chemistry, Vol. 85, No. 9, 1981 1183

l 1 4 w 5

-..__> :le

200

.

1 1 1

IV V

VI

VI1 Vlll

I

I1

M A I N GROUPS

Figure 6.

113-120 (predicted): (0)

(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 1 1 4 ' and 1 1 6 ' 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.

Melting points of elements 81-88 (experimental) and

values predicted in ref 20 (z = 1 l a ) , ref 2 1

Chart I1

group IV

Si

Ge

Sn

Pb

114

mp, K

group VI

S

Se

Te

Po

116

mp, K

i ! ! :

505 A 3 = 9 5

6oo A4

?

A I = 578

A % = 605

392 A I = %

490 A 2 = 233

723 A 3 = 196

527

A 4

?

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

I 1

M A I N GROUPS

Figure 7.

113-120 (predlcted). (0)

(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 1 1 5 ' , 1 1 8 ' , and 119' are obtained by the

correspondlng equations in Table I, point 116 I s 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

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 T M = -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

Boiling points of elements 81-88 (experimental) and

values predicted in ref 20 (z = 1 l a ) , ref 2 1

for element 114, can be

Page 8

1184

chart I11

The Journal of Physical Chemistry, Vol. 85, No. 9, 7981

group V

N

P

As

Sb

Bi

11 5

bP, K

group VI

0

S

Se

Te

Po

116

Bonchev and Kamenska

A , = 470.7

A 3 = 1013

A,=-68

885 A 2 = 337

i : : :

?

II

IV

v

VI

VI1

VI11

I

I 1

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

119

1615

1151

1032

?

Chart IV

group

I11

group

IV IP. eV IP. eV

113

22t

?

114

?

115 ,

0

111

IV

v

MAIN GROUPS

V I

VI1 Vlll

I

II

Flgure 9. Second ionization potentials o f 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. A l l 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.

Page 9

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

a i

,

Flgure 10. Atomic volumes of elements 49-56, 81-83 (experimental),

84-88 (dashed line), and 113-120 (expected): (0)

in ref 23 for z = 113, 114, ref 20 for z = 118, and ref 21 for L = 117,

119, and 120.

values predicted

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).

Atomic Volumes (Figure 10).

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 - ~ ,

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,

obtained by group

2 1

I

Ill

\ 5

5/

7

IV

v

VI

VI1 Vlll

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)

densities of elements 81-84 and 49-56.

comparison with the experimental

(X); Keller et

''1

1!3

, l L

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 r e p e d 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 - ~ .

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 - ~ ,

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

The densities of

respectively).

Page 10

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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- Available from Danail Bonchev · Jun 10, 2014
- Available from Danail Bonchev · Jun 10, 2014