Page 1

Superheavy Elements

A Prediction of Their Chemical and Physical Properties

Burkhard Fricke

Gesamthochschule Kassel, D-3500 Kassel, Heinrich-Plett-Str. 40, Germany and

Gesellschaft für Schwerionenforschung, D-6100 Darmstadt, Postfach 541, Germany

Table of Contents

I. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .90

11. Predictions of Nuclear Stability .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .92

111. Basis für the Predictions of Chemical and Physical Properties

1. The Electronic Structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

a) Continuation of the Periodic Table

b) Ab-initio Atomic Calculations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

2. Trends of the Chemical and Physical Properties . . . . . . . . . . . . . . . . . . . . . . . . . ..

a) Trends Emerging from the Calculations

b) Empirical and Semi-empirical Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

97

97

97

98

102

102

107

IV. Discussion of the Elements

1. The 6d transition Elements Z = 104 to 112 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ..

2. The 7p and 8s Elements Z = 113 to 120 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ..

3. The 5g and 6/ Elements Z = 121 to 154 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ..

4. The Elements Z = 155 to 172 and Z = 184. .. .. . .. . . . . . .. . . . .. . . . . . . . . . . . .

111

111

118

127

130

V. Critical Analysis of the Predictions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .137

VI. Application of the Chemical Predictions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ..139

VII. References..............................................................142

89

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J. Introduction

Very recently Oganesian, Flerou and coworkers (1) in Dubna announced the

discovery of element 106. Although they observed less than 100 fission tracks of

the decaying nuclei of this element, formed after the heavy-ion bombardment of

Crionson Pb, they were able to measure a half-life of about 20 msec for one isotope

and 7 msec for another. At about the same time Ghiorso and coworkers (2) in Ber-

keley found a new alpha activity for which they established the genetic link

with the previously identified daughter and grand-daughter nuclides

aa

o:

263106 ~

259104

----+

3 sec

255102

----+

3 min

0.9 sec

This evidence indicates that a new element has been added to the periodic

table, thus presenting a new challenge to scientists.

Until 1940 the heaviest known element was uranium with the atomic number

92, and at that time (about 1944) the actinide concept of Seaborg (3) was just a

hypothesis. It is thus apparent that great progress has been made since then.

Fourteen new elements have been added to the periodic system and much chem-

ical and physical information has been gathered concerning this region of ele-

ments. Hence we can expect that element 106 is probably not the last element

but only a step toward an even longer periodic table. The approach used in the

experiments up to now to produce even heavier transuranium elements has been

to proceed element by element into the region of atomic numbers just beyond the

heaviest known by bombarding high-Z atoms with small-Z atoms. There have

been very difficult and laborious attempts to proceed even further (4, 5). The

upper limit of this method is determined by experimental feasibility; it cannot

now be predicted with certainty but will be about element 108 or 109. The other

way to proceed is to bombard two very heavy elements with each other, thus

producing superheavy elements directly. This method will probably overlap

with the first method at its lower end.

This second method, which must be the result of bombardments with relatively

high Z heavy ions, is still in preparation at several places in the world, i. e. Dubna

in the USSR, Berkeley in the USA, Orsay in France, and Darmstadt in Germany.

If this method is successful, it should lead to the nearly simultaneous discovery

of a number of new elements.

There is general agreement that theoretical predictions of nuclear stability,

which we discuss briefly in the next paragraph, define a range of superheavy

elements with sufficiently long half-lives to allow their study, provided they can

be synthesized. What cannot be predicted is whether there exist nuclear reactions

for such synthesis in detectable amounts on earth.

The known elements heavier than uranium are usually called by the very

unspecific name of transuranium elements. In the upper range this term is ex-

90

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Superheavy Elements

pected to overlap with the equally ill-defined expression superheavy elements.

To clarify the situation from a nuclear physics point of view, one may define

the end of the transuranium elements and the beginning of the superheavy ele-

ments as the element where the nuclear stability of the longest-lived isotope in-

creases again with increasing Z. The observed strong decrease of the half-Jives of

the transuranium elements known up to now can be seen in Fig. 1. The question

is where and if this trend to even smaller half-lives is likely to end.

From a chemical point of view the elements, including the unknown super-

heavy elements, are well defined by their location in the periodic table. The ele-

ments up to 103 are the actinides or the 51 transition elements. Chemical reviews

of these are given by Seaborg (6, 7), Cunningham (8), Asprey and Pennemann (9),

and Keller (10). The 6d transition series starts with element 104. Of course, the

first chemical question to be answered is whether this simple series concept of the

periodic table still holds for the superheavy elements. A very comprehensive review

of elements 101 to 105, discussing the nuclear stability and chemical behavior of

the predicted elemcnts, was given by Seaborg (5) in 1968. Several other articles

dealing mainly with the chemical behavior of superheavy elements, the search for

superheavy elements in nature, and the electronic structure of these elements

have since been published. The references are given in the discussion below.

In this summary of the very quickly developing field of the superheavy ele-

ments, the main emphasis lies on the prediction of their chemical properties. Apart

from the general interest of the question, this knowledge is expected to be very

important because chemical separation will be one of the methods used to detect

superheavy elements.

91

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11. Predictions of Nuclear Stability

Like the well-known effect of the elosed shells in the atomie eleetron eloud at

Z ==2, 10, 18,36,54,86, whieh is the physieal basis for the strueture of the periodie

table, the effeet of elosed nueleon shells together with a large separation to the next

unoccupied shell also makes for considerable nuclear stability. The nucleus

consists of two kinds of particles, protons and neutrons, so that we have two

series of so-ealled magie numbers. These are for protons 2, 8, 20, 28, 50, 82, and

for neutrons 2, 8, 20, 28, 50, 82, and 126. Nuelei where both protons and neutrons

are magie, (160, 40Ca or 208Pb, for example) are called double-magie nuclei and

are partieularly stable. As we go to even heavier nuclei, the effect whieh most

heavily influenees stability to ex-decay or fission (the most important decay modes)

is the inereasingly large repulsion of the nueleonie eharges against the attraetive

nuelear forces, which severely shortens the half-lives of the nuclei (11), as can be

seen from Fig. 1. This suggests the question: Is the stabilizing effect of the next

1021

1018

_

lI)

o

Z

o

U

tg 109

1015

1012

W 106

u,

:::J

J

103

u..

--'

<{

:r:

10-3

10-6

10-9

1 0 - 1 2 ~ " " " " " - " " ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' - - & o . . . I - . L - J . - ~ . . . . . \ - o I - - I - . . I . . . . J . . : . . I

Fig. 1. The longest-lived isotopes of transuranium elements as a function of Z for spontaneous

fission and a decay (11)

92

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Superheavy Elements

double-magie configuration large enough to counteract this repulsion and to

lengthen the half-lives yet again?

Because it was assumed that the next protonic magie number was 126 (by

analogy with the neutrons), early studies of possible superheavyelements did not

receive much attention (12-15), since the predicted region was too far away to

be reached with the nuclear reactions available at that time. Moreover, the ex-

istence of such nuclei in nature was not then considered possible. The situation

changed in 1966 when Meldner and Röper (16, 17) predicted that the next proton

shell closure would occur at atomic number 114, and when Myers and Swiatecki

(18) estimated that the stability fission of a superheavy nucleus with elosed

proton and neutron shells might be comparable to or even higher than that of

many heavy nuclei.

These results stimulated extensive theoretieal studies on the nuclear properties

of superheavy elements (19). The calculations published so far have been based

on a variety of approaches. Most ealeulations were performed by using a phenom-

enologieal deseription within the deformed shell model (20-23). In this model

the nucleons are considered to move in an average potential and the shape of the

potential and other parameters are chosen by fitting single-partiele levels in well-

investigated spherical or deformed nuclei. Regardless of the approach followed,

the authors agree in predicting a double-magie nueleus298114, although several

other magie proton and neutron numbers near these values have been diseussed.

There are also several self-consistent calculations (17, 24-27) but suitable

parameters have to be used, beeause the nueleon-nueleon force is not known from

general considerations. Most authors also accept the magie numbers Z === 114 and

N === 184.

In addition to the proton magie number 114, a seeond superheavy magic proton

number was investigated at Z === 164 (23, 28). Although the realization of such a

nueleus seems to be far from any praetieal possibility at the moment, one should

bear this region in mind because many most interesting questions could be an-

swered if it were possible to produce these elements. One way to actually proeeed

o

28 50 82126184196318

NEUTRONS

Fig. 2. Schematic drawing of the stability of the nuclei as a function of the number of protons

and neutrons. The expected islands of stability can be seen near Z = 114 and Z = 164 (29)

93

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B. Frieke

into this region is the observation of the X-rays from the quasi-moleeular systems

whieh are transiently formed during heavy ion eollission (109).

These predietions are depieted very schernatically in Fig. 2 in an allegorieal

fashion (29). The long peninsula eorresponds to the region of known nuelei. The

grid lines represent the magie numbers of protons (Z) and neutrons (N). The third

dimension represents the stability. The magie numbers are shown as ridges and

the double-magie nuelei, like 208Pb, are represented as mountains. The two regions

near Z ==114 and Z ==164 show up in Fig. 2 as "islands of stability" within the

large "sea of instability".

The detailed ealeulations quoted above predict potential barriers against

fission, i. e. the total energy of the nucleus is caleulated as a funetion of the

deformation, beeause a deformation parameter describes at the one extreme the

spherieal nucleus and at the other the two separated nuclei after fission. All of

these ealeulations indieate a maximum (or two) at a small deformation, whereas

we get a dip of a few MeV at zero deformation and a trough of a few hundred MeV

for very large deformations. The result of such a ealeulation is shown in Fig. 3

o[

298114

>

Q)

- 2100

1

T 8 MeV

~

>-

~

0::

l.LJ

Zw

-2200

-J

<t

i=

z

l.LJ

~0a..

-- 2300

ENERGY RELEASE ~

310 MeV

o

-2400

.....1

DEFORMATION -------

Fig. 3. Total energy as a funetion of the deformation of the expeeted double-magie nueleus

298114. The small minimum at the deformation zero is expeeted to be the reason for the very

long lifetime of this nucleus (32)

for the expected double-magie nucleus298114. This small minimum at zero de-

formation plays an important role ; it keeps the nucleus in spherical shape and

prevents rapid deeay in the fission path. Spontaneous fission ean oeeur only by the

extremely slow proeess of tunneling through the several MeV high barrier.

94

Page 7

108

126

Superheavy Elements

Thus, the height and width of this barrier playamost important role in the

predietion of the half-lives against fission (31). For the double-magie nueleus298114

a height of between 9 and 14 MeV is predieted, depending on the method used.

This yields spontaneous fission half-lives of between 107and 1015years.

These first results were very promising and stimulated a very extensive but

up to now unsueeessful seareh for superheavy elements in nature. A most corn-

prehensive review of this subjeet was given by G. Herrmann (32). But, besides

spontaneous fission, a nueleus ean deeay by other deeay modes like o: deeay,

ß deeay, or eleetron eapture. The most eomprehensive study of half-lives in the

first superheavy island was performed by Fiset and Nix (33). Figure 4 is taken

from their work.

126

120

114

NI

ffi

CD

108

~:J

Z

Zoi-

o

0:::

0..

120

114

172

178

184

190172178184

NEUTRONNUMBER .t:!.

190

Fig. 4. Summary of predictions of the half-lives of the nuclei at the :first island of stability.

(a) spontaneous-:fission half-Iives, (b) cc-decay half-lives, (c) electron-capture and ß-decay

half-lives, and (d) total half-lives. The nurnbers give the exponent of 10 of the half-lives in

years (33)

The results show that, as one moves away from the double elosed-shell nueleus

298114, the ealeulated spontaneous fission half-lives in Fig. 4a deerease from 1015

y for nuclei on the inner contour to 10-5y (about 5 min) for nuclei on the outer

contour. With respect to spontaneous fission, the island of superheavy nuclei is

a mountain ridge running north and south, with the descent being most gentle in

the northwest direction. The calculated «-decay half-lives in Fig. 4b, however,

95

Page 8

B. Fricke

decrease, rather smoothly with increasing proton number from 105y for nuclei

along the bottom contour to 10-15y (about 30 nsec) for nuclei along the top

contour. The discontinuities arise from shell effects. The ß-stability valley crosses

the island from the southwest to the northeast direction.

The calculated ß-decay and electron-capture half-lives in Fig. 4c decrease

from 1 y for nuclei along the inner contour to 10-7y (about 3 sec) for nuclei at

the outer contour. The total half-lives in Fig. 4d are obtained by taking into ac-

count all three decay modes. The longest total half-life of 109years is found for the

nucleus294110. A three-dimensional plot of these results (35) is given in Fig, 5,

where the island character of this region of relative stability is beautifully demon-

strated.

Fig. 5. Same as Fig. 4 d in a three-dimensional plot (35)

In considering such results (34), one should be aware of the great uncertainties

associated with the extrapolation of nuclear properties into the unknown region.

The calculations are associated with large errors. The total uncertainty for all

three decay modes discussed here is as large as 1010for the half-lives.

The half-lives for the second island of stability are even smaller. In the most

optimistic estimates, they are not more than a few hours, and the uncertainty

of 1010brings them down into the region of nsec. The second assumption of course,

which has still to be proved, is that these nuclei can in fact be produced.

In conclusion, one may say that there is general agreement that theoretical

predictions of nuclear stability define a range of superheavy elements in the vicin-

ity of element 114with sufficiently long half-lives to allow their study, provided

they can be synthesized.

96

Page 9

111. Basis for the Predictions of Chemical and Physical Properties

1. The Electronic Structure

When M endeleev constructed his periodic system in 1869 he had actually found the

most general and overall systematics known in science. He developed this table

from his comparison of the chemieal and physical properties of the elements,

without knowing the underlying reason for it. Since the early stages of quantum

mechanics in the 1920's, it has become clear that the similarity of the properties

of the elements depends strongly on the outer electronic structure. The filled-shell

concept is in accord with the periodicity of the chemical properties that formed

the basis for the concept of the periodic table.

Thus it is obvious that the first step toward predicting chemical and physical

properties is to predict the electronic structure of the superheavy elements. An

excellent review article on this subject will be published by}. B. Mann (35) in

the near future.

a) Continuation of the PeriodicTable. As early as 1926M adelung (36) found the

empirical rules for the electron-shell filling of the ground-state configurations of

the neutral atoms. His rules are simple:

1. electron shells fill in order of increasing value of the quantum number sum

(n+l), where nis the principalquantumnumber and lthe orbitalquantum number;

2. for fixed (n+l), shells fill in order of increasing n.

In Fig. 6 we show one of the many published schemes based on these rules,

which demonstrates the filling of the electrons. This systematics provides an

almost correct explanation of all known neutral atomic configurations in the

known region of elements. This simple law was therefore used by Gol'danskii (37)

and by Seaborg (5) to predict the electron structure of the superheavy elements.

Seaborg designated the 32 elements of the Sg and 61 shells as the "superactinide

series" and placed them as elements 122 to 153 by analogy with the actinide series

1

3

15

25

2

4

5

13 3p 18

4p 36

49 5p

81 6p 86

112 113 7p

2p 10

11

19 45

37 55 38

55 65

87 75 88

119 85 120

35

12

20

21 3d 30

39 4d 48

71 5d 80

31

54

56

157 "f 70

89 5f 102 103 6d

6 f

-----

118

(n+l)

1

2

3

4

5

6

7

8

f121

~

597d8P 1681 169 95 170 I

---~-

9

-----------------~

Fig. 6. The filling of the electron shells according to the simple rule of Madelung (36)

97

Page 10

B. Fricke

90 to 103 following actinium. Since there were already in the known region of

elements a few deviations from M adeiung's simple rules, especially in the lanth-

anides and actinides, Chaikkorskii (38) and later Taube (39) tried to predict these

anticipated deviations. In Table 1 we show the predictions of Gol'danskii, Seaborg,

Table 1. Predictions of the ground-state configurations of Gol'danskii (37), Chaikkorskii (38),

Taube (39) and Seaborg (5) for elements 121 to 127 and 159 to 168, using the principle of the

extrapolation within the periodic table. The main quantum numbers (5g, 61, 7d, 85) are not

shown. This table is taken from Mann (35)

Element

Taube (39)

Gol'danskii (37)

Seaborg (57)

Chaikkorskii (38)

121

d52

g52

d52

d52

122

123

Id52

g252

g252

d252

gjd52

g352

g352d352

124

125

g2/d52

g452

g452

12d252

g3 jd52

g552

g552

g2 j2 d52

126

g41d52

g652

- g652

g3 12d52

127

159

g5 jd52

g752

g752

g5 d2s2

d752

d752

d752

160

161

d852

d852

d951

d952

d952

dl O51

162

163-168

dl O52

dl O52

dl O52

S52spn (n = 1 - 6) for all columns

Chaikkorskii and Taube for elements 121 to 127 and 159 to 168. Apart from small

discrepancies in these somewhat uncertain regions, there was general agreement

that the unfinished 8th row of the periodic table would be finished by the 6d

elements ending at element 112 and the 7p elements at 118. From a conservative

point of view, every extrapolation into the region starting with element 121 is

expected to be very speculative. Nevertheless, the reliability of the location of the

elements in the periodic table seems to be relatively unambiguous.

b) Ab-initio Atomic Calculations. The prediction ofthe electronicconfigurations

of the superheavy elements became much more reliable when ab-initio atomic

calculations became available and accurate enough to be used in the field of

the superheavy elements.

In the following paragraph we give a very brief description of the principles

used in the calculations. For the details, especially the exact formulas used, we

refer to the literature. All the calculations that are useful in this connection are

based on the calculation of the total energy ET of the electronic system, given by

the expression

98

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Superheavy Elements

where 1jJ is the total wave function and H the Hamiltonian of the system. The

physical solution is found when ET is at the total minimum after the variation of

1jJ.

Depending on the ansatz for the total wave functions 1jJ and the Hamiltonian

H of the system, this minimalization of the total energy leads to a set of different,

usually coupled differential equations. The solution oi these equations gives the

total wave function and hence the total energy. These methods, usually called

Hartree and Hartree-Fock methods, are described in detail in various texts and

papers (40). For those planning to do suchcalculations, R.D. Hartree's "Calculation

of Atomic Structure" (41), and "Atornic Structure Calculations" (42) by F. Herr-

mann and S. Skillman are recommended. A review article by J. P. Grant (43)

gives an excellent description of relativistic methods. A good summary is also

given by]. B. Mann (35).

Let us discuss very briefly the various methods that have been used. The first

group of calculations is done by using the non-relativistic Hamiltonian (ignoring

spin-orbit interaction)

Here the first term with v the Nabla operator is the kinetic energy, the second

is the potential energy due to the nuclear charge, and the last term is the total

electrostatic interaction energy over all pairs of electrons.

Hartree's method (H) considers the total wave function to be a product of

one-electron wave functions 1p === II f[Ji; this leads, after the variation of the total

i

energy, to a set of second-order homogeneous differential equations that have

to be solved for the radial wave functions of the electrons of each shell. The last

term due to the interaction of the electrons is given by the potential generated

by all the other electrons. In this respect the set of the differential equations is,

of course, already coupled. This was the basic method used by Larson et al. (44)

for the first atomic claculations in the region of superheavy elements Z === 122 to

127.

Hartree-Fock method (HF). Here the total wave function is assumed to be an

antisymmetric sum of Hartree functions and can be represented by a Slater

determinant

1p === (N 1)- t If[J1(1) f[Jl(2) •.••• f[JN(N) r

which automatically obeys the Pauli principle.

The effect of the determinantal wave function is to greatly complicate the

resulting differential equations by adding exchange potential terms, giving rise to

an inhomogeneous equation, for which the correct solutions becomes much more

difficult and time-consuming. For the exact equations, see for example]. B. Mann

(35). A program using this method was developed by C. Froese-Fischer (45).

Hartree-Fock-Slater method (HFS). In this method the inhomogeneous parts

of the equations used in the Hartree-Fock method are approximated by a local

99

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B. Fricke

potential, as proposed in 1951 by Slater (46). This approximation yields much

simpler homogeneous differential equations in which the potential terms are

identical for every orbital of the atom, which makes the actual computation

less time-consuming by a factor of about 5 to 10, although the results are nearly

as good as with the Hartree-Fock method,

For heavy elements, all of the above non-relativistic methods become in-

creasingly in error with increasing nuclear charge. Dirac (47) developed a relativist-

ic Hamiltonian that is exact for a one-electron atom. It includes relativistic mass-

velocity effects, an effect named after Darwin, and the very important interaction

that arises between the magnetic moments of spin and orbital motion of the elec-

tron (called spin-orbit interaction). A completely correct form of the relativistic

Hamiltonian for a many-electron atom has not yet been found. However, excellent

results can be obtained by simply adding an electrostatic interaction potential of

the form used in the non-relativistic method, This relativistic Hamiltonian has

the form

(i c rx(k) . \l (k) - ß(k) c2-

~

H = ~~ )

+~

.'. ,

r»

r»

~

k k<j

where o:and ßare 4 x4 matrices and \l is the Nabla operator. Using the variation-

al method in the same manner as before and taking a Slater determinant as the

wave function, one obtains two sets of first-order inhomogeneous differential

equations to be solved for all electrons of the atom. This most complicated ver-

sion of atomic calculations is called the relativistic Hartree-Fockmethod or Dirac-

Fock method (DF) (48). Various papers calculating the ground-state configurations

of superheavy atoms by this method have been published since 1969 (49-51). A

complete discussion is given by J. B. Mann (35).

These very complicated inhomogeneous coupled differential equations can

again be simplified by using Slater's approximation. This method is therefore called

the relativisticHartree-Fock-SlaterorDirac-Fock-Slater (DFS) (52-53) calculations,

and they have also been done by several authors for the superheavy elements

(54-56).

The results for the ground-state configurations of all superheavy elements up

to 172 and for element 184 are given in Table 2 (35,50,56-60). In only very few

cases are the results different for the two best methods, DF and DFS, but the

differences are so small that no final decision can be made.

The first difference that becomes obvious in comparison to the empirical

continuation of the electron filling discussed above (29, 37-39) occurs at elements

110 and 111. The calculated ground-state is s2d8and s2d9, respectively, which is

not at all common in the homologs of the two elements.

Also, beginning with element 121, every element has a different ground-state

configuration than that predicted by simple extrapolations. The main reason for

this behavior is that, unexpectedly, an 8p electron state becomes occupied at

element 121, and at least one of these electrons remains bound through all the

following elements. In the 160 region the difference between the simple predictions

and the results of the calculations is already so large that the position of the

elements in the periodic table is changed drastically. (For an overview and com-

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Page 13

Table 2. Atomic ground-state configurations for the neutral elements 103 to 172 and 184 according to Mann (35) and Pricke and Waber (85,60), using

self-consistent Dirac-Fock calculations

Element

Rn core + 5/14+

Element

Z = 120 core +

Element

Z = 120 core +

+ 8pr/2 +

Element

Z = 120 core +

+ 8pr/2 5g1S6/14+

103

7527p

7526d2

7526d3

7526d4

7526d5

121

8p

139

5g136/27d2

5g146/37d1

5g156/27d2

5g166/27d2

5g176/27d2

5g1S6/17d3

5g1S6/37d2

6/47d2

6/57d2

6/67d2

6/67d3

6/67d4

6/S7d3

6/97d3

6/117d2

6/127d2

6/137d5

6/147d2

157

7d3

104

122

8p 7d

140

158

7d4

7d4951

7d5951

7d6951

7ds

105

123

8p 7d 6/

8p 6/3

141

159

106

124

142160

107

125

8p 6/35g

8p 7d 6/25g2

8p2 6/25g3

8p 26/25g4

8p2 6/25g5

8p2 6/25g6

8p2 6/25g7

8p2 6/25gS

8p2 6/35gS

8p2 6/45gS

143

161

108

7526d6

7526d7

7526dS

7526d9

7526d1O

7526d107p

7526d107p2

7526d107p3

7526d107p4

7526d107p5

7526d107p6

7526d107p6 85

7526d107p6 852

126

144

162

109

127145

163

7d9

7d1O

7d10951

7d10952

7d109529pi/2

7d109529pr/2

7d109529pr/2 8 P ~ / 2

7d109529pr/2 8 P ~ / 2

7d109529pr/2 8pg/2

7d109529pr/2 8pi/2

Z = 172 core +

6g57/48d3

110

128

~ 4 6

164

111

129

147

165

112

130

148

166

113

131

149

167

114

132

150

168

115

133

151

169

116

134

152

170

Cf)

117

135

8p2 6/45g9

8p2 6/45g1O

8p2 6/37d 5g11

8p2 6/37d 5g12

153

171

~"0

CD

~P"

CD

~

<

~

118

136

154

172

137

155

119

120

138

156

184

~

CDS

CD

.....,.

0

.....,.

~c-t-

r.Jl

Page 14

B. Fricke

parison, see the periodic table in Fig. 21, incorporating the results of the prediction

of the elements up to 172 taken from Fricke et al. (56)). This disagreement with

the results expected from a simple continuation of the periodic table is of course,

a result of the interpretation of the periodic system in terms of chemical behavior,

but the primary reason is the surprising order of filling of the outer electron shells

in this region.

If we try to proceed to even heavier elements, the calculations come to a halt

at Z = 174 because at this element the ls level reaches the negative continuum of

the electrons at a binding energy of 2mec2 ==1 MeV and the calculation breaks

down. To proceed further, Fricke (61) introdueed a phenomenologieal description

of the quantum-eleetrodynamical effects into the SCF caleulations (60), which

shifts the binding energies of the inner electrons back to lower values. Using this

method, he was then able to study the electron configurations of the elements

beyond Z == 174.

2. Trends of the Chemieal and Physical Properties

The detailed and sophistieated caleulations of the electronic-ground states of the

atoms are very worthwhile as an important, though only the first step toward

predieting the ehemical and physical properties of superheavy elements, beeause

chemistry consists not only of the properties of the atoms but also of the molecules

and their behavior. Ab-initio ealeulations of molecules were introduced for small

moleeules and small Z, and the state of the art is still far away from the point

that allows actual calculations of the chemieal properties of superheavy molecules.

A first step in this direction has been taken by Averill et al, (62), who ealeulated

the wave function of (110)F 6 using a muffin-tin method.

a) Trends Emerging from the Calculations. Althoughwe are not able to ealeulate

the properties of superheavy moleeulesat the present time, the atomic calculations

give us more than just the electronie structure of the neutral elements.

One has to bear in mind that two elements from the same ehemieal group,

which often have the same outer eleetronie strueture will be chemically and physi-

eally slightly different. This can be to some extent explained as the effeet of their

somewhat different sizes, changed ionization potential, and the different energies

and radial distributions of the wave functions between analogous shells. These

quantities are also determined directly by the atomic calculations. The size of the

atom or ion correlates strongly with the principal maximum of the outermost

electronicshell, as found by Slater (63),thus giving a first estimate of this important

magnitude. Sometimes the expectation value of <r> of the outermost shell is

used as the radius, but the agreement with experiment is not so good.

There is eonsiderable agreement that the ionization potentials have to be

ealculated in the adiabatie approximation, in which it is assumed that during the

removal of an electron sufficient time elapses for the other electrons to rearrange

themselves, so that the ionization potentialis given by thedifference in total energy

of the two calculations with m and m-l electrons. The other method, taking the

calculated energy eigenvalues (64), can only be used as an approximation to this

physical quantity.

102

Page 15

Superheavy Elements

In the first part of the periodic table it is relatively easy to make the connection

between these quantities and a chemical interpretation because of the few shells

involved and their large separation. Moreover, the influence of the inner electron

shells is rather small so that the outer electron configurations are very similar in

the same chemical group at different periods. When we proceed to higher elements

at the end of the periodic table, the number of shells increases, the binding energy

of the last electrons decreases, and there is competition between shells; hence the

influence of the inner electrons becomes more significant. This rather complex

behavior is further complicated by the fact that relativistic effects now begin

to be important and the coupling between the angular momenta of the elec-

trons changes from LS to intermediate or j-j coupling. All these effects and their

relative influences are taken into account in the ab-initio calculations. Of course,

to prove their reliability in the superheavy region of elcmcnts, they have to

reproduce the complex structure and its relationship to chemical behavior in the

known part of the periodic table, which in all cases is done for example for the

groundstate configurations of the atoms. The main change due to relativistic effects

is the splitting of all shells with l i=0 into two subshells with j ===l+1/2 and

j ==l -1/2. This means that, for example the pstate splits into the Pl/2 subshell

DIRAC- SLATER- EIGENVALUES

VALENCE ELECTRONS FORsp'p CONFIG.

0------------_

164

o

25 5075 100125150

PROTON OR ATOMIC NUMBER

-10

;: -20

<l>

>-

C)

n::

~

-30

w

-40

-50

SiGe

Sn

Pb

8 d ~

0

2

Fig. 7. Comparison of the eigenvalues of the ns, npl/2 and np3/2 electrons in the group-IVA

elements using DFS calculations. This figure illustrates the very strong dependence of the spin-

orbit splitting between the two p states as a function of the atomic number. For element 164,

the 9s and 8d 3/2 levels are also drawn (85)

103