Journal of Nuclear and Radiochemical Sciences,Vol. 3, No. 1, pp. 137–141, 2002

137

Theoretical Predictions of Properties and Chemical Behavior of Superheavy Elements
V. Pershina∗
Gesellschaft für Schwerionenforschung, D-64291 Darmstadt, Germany
Received: November 13, 2001; In Final Form: March 25, 2002
Fully relativistic electronic structure calculations have been performed for gas phase and aqueous phase compoundsof elements 104 through 108. Based on these calculations, volatility and complex formation, as well as trends inthese properties, have been predicted. The transactinide compounds were shown to exhibit properties very similar
to those of the lighter homologs in the respective chemical groups. Some deviations from the observed trends were
established.
1. Introduction
Fast progress in experimental investigations of chemical
properties of the heaviest elements gives further impact to theoretical studies. Most of them are aimed at prediction of chemical
behavior in sophisticated and expensive experiments with single
atoms.
Recently, elements 107 (Bh)1 and 108 (Hs)2 were chemically
identified using gas-phase chromatography techniques. They
were shown to form BhO3 Cl and HsO4 in analogy with lighter
elements in the chemical groups Re and Os, respectively. Besides, the behavior of Rf and Sg which had already been characterized chemically has meanwhile been further studied in moredetail. In some cases, deviations from trends in properties foundfor lighter homologs in the groups were observed or conflicting
results of experiments conducted at the same conditions werereported. Thus, for example, results of various experiments on
the extraction of Zr, Hf, and Rf from HF and HCl solutions3–6
disagreed concerning extraction sequences (see the review ofKratz5 ): Cation exchange separations (CIX) of Zr, Hf, and Rf
from HF solutions, have given the following trend in ascending
Kd values: Zr > Hf > Rf, while in the anion exchange (AIX) separations, Rf and Hf though behaving similar, were much less absorbed on the AIX than Zr.3 In contrast to results of Reference 3,
recent AIX separations4 of group 4 elements from aqueous HCl
solutions performed at the same conditions have shown an inversed sequence in rising Kd values: Rf > Zr > Hf. The TBP
extraction of group 4 elements from 8 M HCl, however, showed
the position of Rf in between those of Zr and Hf: Zr > Rf > Hf.6
Thus, extraction behavior of group 4 elements from HF and HClsolutions have not yet been established with a high certainty.
Another open question was the hydrolysis of Rf. In Reference 7, a conclusion about stronger hydrolysis of Rf in comparison with that of Zr has been drawn by studying sorption of group
4 elements and Th on cobalt ferrocyanite surfaces, while resultsof the AIX separations come to a different conclusion.8
Group 5 elements were also shown to exhibit an unexpected,
inversed, trend in the complex formation and extraction from
aqueous acidic HCl solutions Nb > Db > Ta.9
Solution chemistry on element 106 has shown first interesting
results: In experiments on the elution of group-6 elements from
cation exchange columns in 0.1 M HNO3 , Sg was not eluted
from the column in contrast to W.10 This non-tungsten-like behavior of Sg was tentatively attributed to its lower tendency tohydrolyze as compared to that of tungsten. All those open questions needed answers or theoretical interpretation.
In our previous research, numerous gas phase and aqueous
phase compounds were studied theoretically. Trends in various physico-chemical properties in the transition element groups
and along the last transition-element row have been defined, as
well as influence of relativistic effects of those properties has

been elucidated. The reviews of those works are given in References 11, 12. To assist new experimental efforts and to solve
the accumulated problems, our theoretical research has been extended to the consideration of the above mentioned processes
and compounds.
In the current publication, we overview results of the recent investigations of the electronic structure and properties ofgaseous species of Bh and Hs, as well as of hydrolysis and complex formation of Rf, Db, and Sg in aqueous acidic solutions
along with their homologs in chemical groups.
2. Method and Details of the Calculations
Calculations of the electronic structure of the above mentioned compounds were performed using the fully relativistic Density-Functional Theory (DFT) method with the General
Gradient Approximation (GGA) for the exchange-correlationenergy.13, 14 The method is a fully relativistic all-electron (orfrozen core, FC, if necessary) code with the spin-orbit coupling explicitly included. It uses four-component basis functions
which are transformed into molecular symmetry orbitals using
double point groups. Molecular integrals between these functions are calculated in a numerical, three-dimensional grid. The
most recent version of the method includes minimization of anerror in the total energy15 and the integration scheme of Boerrigter et al.,16 which altogether give much more accurate results
for total energies.
The Dirac Hamiltonian ishD = c α π + (β − 1)c2 +V ,(1)

where the potential is the sum of three parts
V = Vn +Vc +Vx ,(2)

with Vn the nuclear, Vc the Coulomb, and Vx is a functional
derivative of the exchange-correlation energy. The GGA of
Becke17 and Perdew18 is included perturbatively in order to consider non-local contributions. In the GGA calculations, the relativistic form of the exchange-correlation potential developed byEngel et al.19 was used.
The present calculations have been performed within the
FC approximation for the group 4, 5, and 6 aqueous phasecomplexes and for all-electrons for group 7 and 8 gas-phasecompounds. The number of integration points was 104 . The
Mulliken population analysis20 was applied for the electronic
density distribution. The results were then further used for somephysico-chemical models in order to link measured and calculated properties.
3. Results and their Discussion
3.1. Gas-phase Complexes
3.1.1. Group 7 Oxyhalides. Results of the RGGA DFT cal-∗E-mail: V.Pershina@gsi.de.

c 2002 The Japan Society of Nuclear and Radiochemical Sciences
Published on Web 6/30/2002

138 J.Nucl.Radiochem.Sci.,Vol. 3, No. 1, 2002

Pershina

TABLE 1: Effective charges (QM ), overlap populations (OP), ionization potentials (IP), dipole moments (µ), electric dipole polarizabilities (α), dissociation (atomization) energies (∆Hdiss ) for MO3 Cl,
where M = Tc, Re, and Bh.21

Property
TcO3 Cl
ReO3 Cl
BhO3 Cl
QM
1.28
1.21
1.13
OP
1.93
2.20
2.31
IP / eV
12.25
12.71
13.05
µ/D
0.93
1.29
1.95
α / 10−24 cm3
4.94
5.91
7.50
23.12
24.30a22.30∆Hdiss / eVaThermochemical ∆Hdiss calculated via a Born-Haber cycle is23.76 eV.
culations21 of the electronic structure of group 7 oxychlorides
MO3 Cl (M = Tc, Re, and Bh) are summarized in Table 1. Typically of the transition elements in groups 4–6, the electronic
structure of the Bh compound is very similar to those of Tc and
Re. The values of the effective charge (QM ) and overlap population (OP, which is a measure of covalence) show BhO3 Cl to be
the most covalent compound in the row. Dipole moments andelectric dipole polarizabilities of MO3 Cl increase in the groupfrom Tc to Bh.
To predict adsorption energy, ∆Hads , of BhO3 Cl on the quartz
surface of the gas chromatography column, needed for the gasphase chromatography experiments, the following model of physisorption was used. The quartz surface was supposed to becovered with adsorbed Cl. The molecule-surface interaction energy in this case was considered of consisting of three parts:
molecular dipole — effective charge on Cl, molecular polarizability — effective charge on Cl and molecular polarizability —polarizability of Cl, so thatε(molecule- surface Cl) = ε(µ, Qe) + ε(α, Qe) + ε(α, α)=−2µQe Q2 e2 α 3αα 1 2 .
−−x2
2x4
2 x6 1 + 1
hν1

(3)

hν2

Here, hν1 and hν2 denote approximately IP of the molecule andof ClQ− , with the latter being a function of Q (see Reference 21).
The only unknown value in eq 3 was that of x. It could be
deduced, e.g. for ReO3 Cl, by setting eq 3 equal to the experimentally measured ∆Hads = −61 kJ/mol for a typical value of
Q(Cl) = −0.4. This has given x = 3.38 Å. Taking this value asa benchmark and assuming that the molecule-surface distancewas directly related to the size of the interacting molecules,∆Hads = −48.2 kJ/mol for TcO3 Cl and ∆Hads = −77.6 kJ/mol
for BhO3 Cl were determined.21 The increasing adsorption enthalpies (due to increasing dipole moments) mean that volatilitychanges in the following order: TcO3 Cl > ReO3 Cl > BhO3 Cl.
The experimentally determined ∆Hads = −77.8 kJ/mol (Ref. 1)
agreed very well with these predictions.
3.1.2. Group 8 Tetroxides. In a similar way, volatility ofMO4 (M = Ru, Os, and Hs) was predicted in Reference 22. For
that purpose, the RGGA DFT fully relativistic calculations havebeen performed for those molecules. Results of the calculations
are summarized in Table 2. As in the case of group 7 oxychlorides, HsO4 was found to exhibit properties very similar to thoseof OsO4 , and it is the most covalent and stable compound in
the group, as the binding energies (∆Hdiss ) show. The QM andOP data are indicative of an increase in covalence from RuO4 to
HsO4 . Such an increase is typical of various other compoundsof the transactinides and is accounted for by strong relativistic
stabilization of the 7s and 7p1/2 valence orbitals. The calculated
IPs show very good agreement with the experiment for RuO4
and OsO4 (Table 2). The calculated polarizabilities show a “zigzag” behavior in the group, with the lowest value for OsO4 .
Predictions of adsorption enthalpies of MO4 (M = Ru, Os, andHs) were made in a similar manner as those for the group 7 oxychlorides. For that purpose, a molecule-slab interaction model

TABLE 2: Effective charges (QM ), overlap populations (OP), ionization potentials (IP), and dissociation energies (∆Hdiss ) for MO4 ,where M = Ru, Os, and Hs.22

Property
QM
OP
IP / eV (calc)
IP / eV (exp)a
α / 10−24 cm3∆Hdiss / eVaReference 23.

RuO4
1.45
1.92
12.25
12.19
6.48
27.48

OsO4
1.46
1.94
12.35
12.35
5.96
27.71

HsO4
1.39
2.17
12.28
6.26
28.44

was used where the interaction energy was integrated over thevolume of a solid. The molecule - quartz surface interaction energy was considered to be of a pure van der Waals type describedby the following expression22


3 ε−1
αmol


E(x) = −(4)16 ε + 21+ hν1mol x3hνslabwhere ε = 3.81 is the dielectric constant of quartz. The interaction distance x was defined for OsO4 in a similar way as it
was done for ReO3 Cl. Using experimental values of α andIP (Table 2) for OsO4 and setting eq 4 equal to −38 kJ/mol,x(OsO4 ) = 2.25 Å was deduced. Then, taking this distanceas a benchmark and assuming that the molecule-surface distance is directly related to the size of the adsorbed molecules,∆Hads = −40.4 kJ/mol for RuO4 and ∆Hads = −36.3 kJ/mol for
HsO4 were obtained.
Several other types of interaction of the molecules with thesurface, like interaction with adsorbed oxygen on the surface,were also considered. In summary, ∆Hads = −40.4 ± 1.5 kJ/moland −36.7 ± 1.5 kJ/mol, on the average, have been predicted
for RuO4 and HsO4 , respectively. Thus, HsO4 was expected
to be almost equally or slightly more volatile than OsO4 , withthe difference in the adsorption enthalpy being of the order ofthe experimental uncertainty. This conclusion would also be inagreement with the higher covalence of HsO4 as compared tothose of the lighter homologs.
3.2. Hydrolysis and Complex Formation of Group 4–6 Elements. In HF and HCl solutions, group 4–6 elements form
mostly anionic complexes in various degree of hydrolysis. Differences in hydrolysis of compounds of elements belonging to
the same chemical group are reflected by differences in theirKd (distribution coefficient) values, since more hydrolysed complexes are worse extracted than less hydrolysed ones. In thefollowing section, a model is described which defines stabilityof complexes being in equibrium with their hydrolysis products.
Using this model, trends in Kd were predicted for group 4, 5, and6 elements for ion exchange separations from aqueous acidic solutions.
3.2.1. The Model. Reactions of complex formation in equilibrium with hydrolysis are expressed in a general form by thefollowing equlibrium−−(xz−y−a)+xM(H2 O)z+w◦ + yOH + aL ⇔ Mx Ou (OH)y−2u (H2 O)w La+ (xw◦ + u − w)H2 O .

(5)

To calculate free energy of such a reaction in an efficient way,
the following procedure was proposed.24 The free energy of acompound was supposed to be decomposed into the following
parts25−∆G f (u, v, w)/2.3RT = ∑ ai + ∑ ai j − log(u!v! w! 2w )+ (2u + v + 1) log 55.5

(6)

and for a reaction
log K = −∆Gr /2.3RT ,(7)

Theoretical Predictions of Properties and Chemical Behavior
TABLE 3: Coulomb parts of the Gibbs free energies (EC ) and their
2−changes (∆EC ) for the reaction M(H2 O)4+
and M(H2 O)4+8 ⇔ MF6829⇔ MCl2−
6 , where M = Zr, Hf, and Rf.

Energy
/ eV
EC
EC
EC
∆E C
∆E C

Compound

Zr

Hf

Rf

M(H2 O)4+
8
MF2−
6
MCl2−
6
2−
M(H2 O)4+8 ⇔ MF6
4+
M(H2 O)8 ⇔ MCl2−
6−53.34−2.60−1.21−52.07−1.18−50.92

50.75
52.15

0.41
50.88
52.50

0.23
2.13
51.15
53.06

where ∆Gr is the difference in ∆G f between products and startersof the reaction. The first term on the right-hand side of eq 6,∑ ai , is the non-electrostatic contribution from all the constituent
atoms, ∑ ai = k OP. The next term, ∑ ai j , is a sum of each pairwise electrostatic (Coulomb) interaction:
E C = ∑ ai j = −B ∑ Qi Q j /di j

(8)

ij

where di j is the distance between moieties i and j; Qi and Q j
are their effective charges and B = 2.3RTe2 /ε is an independent
constant. The last two terms in eq 6 are statistical: one is a correction for indistinguishable configurations of the species, andthe other is a conversion to the molar scale of concentration for
the entropy.
It was further suggested24 to calculate ∑ ai j and ∑ ai foreach compound via the electronic density distribution data (theMulliken numbers) obtained as a result of the fully relativistic
DFT calculations of the electronic structure of the complexesof interest. The differences in those values for the left and theright parts of an equilibrium reaction plus the differences in theother terms of eq 6 define log K. For that purpose, calculationsof the electronic structure of numerous complexes of group 4–6
elements have been performed and free energies of the complex
formation or hydrolysis reactions were defined.24, 26–28 The results will be shown in the following subsections.
In all cases, the results have shown the hydrolysis/protonationor complex formation processes to be governed by changes inthe electrostatic interaction, ∆E C , so that prediction of an equilibrium can be made with sufficient accuracy just by calculating
electrostatic terms only. This electrostatic interaction should,
however, be defined using calculated relativistic electronic density distribution data and not formal charges. Thus, knowing
only ∆E C , log K could be defined for any reaction, as it is shownin the following sections for group 4, 5, and 6 complexes.
3.2.2. Complex Formation of Group 4 Elements in HF and
HCl Solutions. In mixed solutions at HF between 10−3 M and∼ 1, the complex formation
10−2 M and 0.1 M HNO3 , i.e. at pH =for group 4 elements can be described by the following equilibrium2−+
M(H2 O)4+(9)
8 + 6HL ⇔ ML6 + 8H2 O + 6H
where M = Zr, Hf, and Rf, and L = F or Cl. To predict log K ofreaction 9, the DFT calculations of the electronic structure were2−2−complexes,
performed for the M(H2 O)4+
8 , MF6 , and MCl629where M = Zr, Hf, and Rf. Geometry and bond lengths (Re )2−were selected on theof M(H2 O)4+8 (D2d -symmetry) and MF6
basis of analysis of the structural data for Zr and Hf and from
calculated Re for some simpler Rf gas-phase compounds.30
The calculated electronic structure data show that the Rf complexes are very similar to those of Zr and Hf: ∆E C for reaction 9(Table 3) indicate that Rf should form complexes in a similar
way as Zr and Hf, only at slightly higher HF concentrations. The
sequence in the complex formation was, therefore, predicted as
Zr > Hf > Rf, with the differences in the Kd values between thethree elements being very small.
The theoretically obtained sequence for Zr, Hf, and Rf proved
to be in agreement with the experimental sequence for descending Kd values in the sorption by CIX and for ascending Kd values for Zr and Hf in the sorption by AIX.3 The low sorption of

J.Nucl.Radiochem.Sci.,Vol. 3, No. 1, 2002

139

TABLE 4: Energies of EC and ∆EC for the hydrolysis reaction−
24
M(H2 O)5+6 ⇔ M(OH)6 , where M = Nb, Ta, Db, and Pa.

Energy Compound/ eV
EC
M(OH)−
6
M(H2 O)5+
6
∆E C

Nb

Ta

Db

Pa

−21.74−21.92−23.33−25.38−21.48−25.37−19.53−29.71

0.18

2.05

3.89

9.18

Rf at the AIX found in the experiments3 could be explained bya stronger competition of the counter ion NO−
3 for the bindingsites of the resin.
In HCl solutions, at the HCl concentrations above 6 M, complex formation should follow the same pattern as that for the HF
solutions (no hydrolysis takes place). Results of the theoreticaltreatment of equilibrium 9 with the formation of the chlorocomplexes are summarized in Table 3. The calculated ∆E C indicate
the same sequence in the complex formation, Zr > Hf > Rf, for
HCl solutions, as that for HF solutions.
3.2.3. Hydrolysis and Complex Formation of Group 5 Elements. As a cation, Nb is known to be stronger hydrolyzed as
Ta, though for the compounds of Nb and Ta the opposite trend
is observed.25 The hydrolysis reaction (also for Pa) proceeds
very fast with the formation of the utmost hydrolysis product
M(OH)−
6 :−+(M = Nb, Ta, and Pa). (10)
M(H2 O)5+6 ⇔ M(OH)6 + 6H

To study hydrolysis of Db in comparison with that of the lighter
homologs in the group, the free energy changes of reaction 10
were determined for Nb, Ta, Db, and Pa on the basis of the calculations of the electronic structure of the indicated complexes
using the DFT method.26 Geometry and bond lengths for the
Nb, Ta, and Pa complexes were taken from experimental values
on the basis of analysis of the numerous structural data. The
bond lengths for the Db complexes were estimated from the calculated ionic radii.31
The results of the calculations are shown in Table 4. One
5+can see that E C for M(OH)−
6 and M(H2 O)6 , where M = Nb, Ta,
and Db, are rather similar, while those of Pa are different: E C(absolute value) of Pa(OH)−
6 is lower than those of Nb, Ta, andDb, while E C of Pa(H2 O)5+
6 is much higher. Obviously, Pa holds
water molecules stronger than Nb, Ta, and Db. The differences,∆E C , also show strong resistance of Pa against hydrolysis, sothat the trend for hydrolysis of group 5 elements is:
Nb > Ta > Db  Pa .

(11)

Thus, in agreement with experiment25 Nb is confirmed to be
more hydrolyzed than Ta, and both of them to be much morehydrolysed than Pa. Db is less hydrolyzed than Nb and Ta, butmuch more than Pa.
The formation of fluoride, chloride, and bromide complexesof group 5 elements undergoes the following complexation reaction−(12)
M(OH)−
6 + nHL ⇔ MOn L6−n + 6H2 O
where L = F, Cl, and Br. As in the previous cases, calculations of
the electronic structures of all various complexes of the group 5
elements have been performed using the DFT method and ∆E C
were defined on their basis (Table 5).26, 27 The ∆E C data show
the following trend for formation of all the types of complexes:∆E C :Pa  Nb > Db > Ta .

(13)

Thus, the theoretically obtained data show that, for all the typesof complexes, those of Pa are formed in more dilute HCl solutions (starting with Pa(OH)2 Cl−
4 at 2–4 M), than those of Nb.
The complexes of Nb start to form next, while those of Ta areformed at the highest HCl molarities. Db was shown to form

140 J.Nucl.Radiochem.Sci.,Vol. 3, No. 1, 2002

Pershina−
TABLE 5: ∆EC (in eV) for reaction M(OH)−
6 ⇔M(OH)n Clm , where
M = Nb, Ta, Db, and Pa.26

Metal
Nb
Ta
Db
Pa

M(OH)2 Cl−
4
13.56
14.32
14.29
11.68

MOCl−
4
18.40
19.80
19.67
16.29

MCl−
6
19.57
20.78
20.46
17.67

Reaction−
TABLE 6: ∆EC (in eV) for reaction M(OH)−
6 ⇔ML6 , where M =Nb, Ta, Db, and Pa, and L = F, Cl, and Br.26, 27

Complex
NbL−
6
TaL−
6
DbL−
6
PaL−
6

F
12.20
12.69
12.38
12.19

Cl
19.57
20.78
20.46
17.67

Br
21.40
22.63
22.11
19.91

complexes between those of Nb and Ta. This theoretical conclusion (sequence 13) for Nb and Ta (sequence 12) is in agreementwith the electrodialysis experiments.32−
Comparison of the ∆E C values for M(OH)2 Cl−
4 , MOCl4 , and−MCl6 (Table 5) shows that in agreement with the experiment,
the M(OH)2 Cl−
4 species are formed at lower HCl concentration,
while MCl−atthe highest concentrations, so that with increas6
ing HCl concentration the complex formation changes in the order−−(14)
M(OH)2 Cl−
4 > MOCl4 > MCl6 .
The theoretical analysis26 of the extraction mechanism of Nb,
Ta, and Pa from aqueous HCl solution by anion exchange has
shown that the extraction sequence is determined by the complex formation and partition of complexes between organic andaqueous phases. Taking this into account, an extraction positionof Db from aqueous solutions above 4 M HCl was predicted as26
Pa  Nb ≥ Db > Ta .

TABLE 7: Coulomb parts of the free energy changes (∆EC ) for the28
step-wise protonation of MO2−
4 , where M = Mo, W, and Sg.

(15)

The theoretically predicted trend 15 was confirmed by the experiment on the extraction of Db and other group 5 homologs
from HCl solutions.9 Thus, trends in the complex formation andextraction known for Nb, Ta, and Pa turned out to be inversed ingoing to Db. This could not be predicted by any extrapolationof properties within the group, but came out as a result of considering real chemical equilibria and calculating relativisticallythe electronic structure of the complexes.
The calculations have also well reproduced the sequence inthe formation of ML−
6 (M = Nb, Ta, Db, and Pa; L = F, Cl, and−−Br) as a function of the ligand L, MF−
6  MCl6 > MBr6 , as thedata of Table 6 show.
3.2.4. Hydrolysis of Group 6 Elements. In HNO3 solutions,group 6 elements form oxocomplexes with a various degree ofhydrolysis. Mo is known to be more hydrolyzed than W.25 The
question about hydrolysis of Sg was open.
To study hydrolysis of group 6 elements, the following protonation equilibria (well-established for Mo33 ) have been considered28−
MO2−
4 ⇔ MO3 (OH) ⇔ MO2 (OH)2 (H2 O)2 ⇔6+
MO(OH)3 (H2 O)+2 ⇔ M(OH)4 (H2 O)2+2 ⇔ . . . ⇔ M(H2 O)6(16)
where M = Mo, W, and Sg. For that purpose, the electronic
structure calculations of all the molecular species indicated in
the equilibria 16 were performed28 using the DFT method. Geometry and bond lengths of the Mo and W complexes weretaken from experimental values by analyzing numerous structural data.34–36 The bond lengths for the Sg complexes were estimated on the basis of Re for some simpler Sg gas-phase compounds.37 The calculations were, as previously, restricted to thecalculations of the ionic (Coulomb) and covalent parts of themolecular-ligand interaction energy using Mulliken numbers.

+
−
MO2−
4 + H ⇔ MO3 (OH)−+
MO3 (OH) + H + 2H2 O⇔ MO2 (OH)2 (H2 O)2
MO2 (OH)2 (H2 O)2 + H+
⇔ MO(OH)3 (H2 O)+
2MO(OH)3 (H2 O)+2 + H+
⇔ M(OH)4 (H2 O)2+
2+
M(OH)4 (H2 O)2+
2 + 4H⇔ . . . M(H2 O)6+6

∆E C / eVMo
W
Sg−12.98 −13.13 −12.95−21.43−22.08−21.61

−5.84

−6.35

−6.65

−0.43

−0.76

−1.23

41.97

38.71

37.11

Results of the calculations of ∆E C for the step-wise protonation process 16 are given in Table 7. Comparing the ∆E C data ofTable 7 for negative complexes of Mo, W, and Sg one can see an
extremum on W for the first two protonation steps: the largest
negative values of ∆E C for W mean its strongest preference for
protonation, or the weakest preference for hydrolysis, which isin agreement with the experiments for Mo and W.25 Thus, forthe first two protonation steps involving the negative complexesof the elements, which are more covalent in comparison with
the neutral and positively charged ones, the trend is reversed:
W > Sg > Mo. For the further protonation processes with theformation of the positively charged complexes, ∆E C becomessmoothly more negative from Mo to W and to Sg, so that thetrend in the protonation is Sg > W > Mo.
Hydrolysis constants for Sg were then defined using the established relation between ∆E C and log K
Mo : log K1 /∆E1C = 3.7/12.98 = 0.29,
W : log K1 /∆E1C = 3.8/13.13 = 0.29,
Mo : [log K1 + log K2 ]/[∆E1C + ∆E2C ] = 7.50/34.01 = 0.22,
W : [log K1 + log K2 ]/[∆E1C + ∆E2C ] = 8.1/35.21 = 0.23 (17)(The log K values are from Reference 33). Thus, by using thefact that log K/∆E C = const (eqs 17) and knowing ∆E C for the
Sg reactions log K1 (Sg) = 3.73 and log K1 + log K2 (Sg) = 7.5
were defined. Other log K are given in Reference 28.
Thus, the calculated ∆E C s indicate that for the first two protonation steps involving more covalent compounds the increasing
trend from Mo to W is not continued with Sg: W > Sg > Mo. A
similar reversed trend was observed in group 5 for the formationof chloro-, bromo-, and fluoro-complexes: Nb > Db > Ta.9, 24
For the further protonation processes with the formation of thepositively charged complexes, ∆E C becomes smoothly morenegative from Mo to W, and to Sg, so that the trend in the protonation process is: Sg > W > Mo. These theoretically obtained
sequences are in agreement with the experimental data on hydrolysis of Mo and W25 and, recently, on Sg.10
4. Conclusions
The calculations of the electronic structures of various gasphase and aqueous-phase compounds of the transactinides andtheir homologs have shown that the former are full homologsof the lighter 4d and 5d elements and exhibit very similar properties. The predicted enthalpies of adsorption of BhO3 Cl andHsO4 indicate that trends in volatility known for the lighter compounds should be continued with the transactinides.
The study of the hydrolysis and complex formation both theoretically and experimentally has indicated that some trends
could be reversed in the groups, as it was in the case of thegroup 5 and 6 complex formation. A careful analysis of chemical equilibria and relativistic calculations proved, therefore, tobe indispensable in predictions of the outcome of liquid chromatography separation experiments.

Theoretical Predictions of Properties and Chemical Behavior
Acknowledgements. The calculations were performed on
the Linux station of the GSI, Darmstadt. The author thanks T.
Bastug for help in the calculations. The DFT program developed in the group of Prof. B. Fricke, University of Kassel, wasused for the calculations.
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