The influence of relativistic effects on electronic energy levels in metal tetraiodides MI4 (M = Ti, Zr, Hf, Th)

Article abstract of DOI:10.1016/j.poly.2015.03.014

The influences of scalar relativistic effects and spin orbit coupling on electronic energy levels in TiI₄, ZrI₄, HfI₄ and ThI₄ have been explored by density functional theory. Calculated ionization energies are

Full text of DOI:10.1016/j.poly.2015.03.014

Polyhedron 93 (2015) 1–7
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Polyhedron
journal homepage: www.elsevier.com/locate/poly
The influence of relativistic effects on electronic energy levels in metal
tetraiodides MI4 (M = Ti, Zr, Hf, Th) q
⇑
Jennifer C. Green , Russell G. Egdell
Department of Chemistry, University of Oxford, Inorganic Chemistry Laboratory, South Parks Road, Oxford OX1 3QR, UK
a r t i c l e i n f o
a b s t r a c t
Article history:
The influences of scalar relativistic effects and spin orbit coupling on electronic energy levels in TiI4, ZrI4,
HfI4 and ThI4 have been explored by density functional theory. Calculated ionization energies are com-
pared with previously published He(I) and He(II) photoelectron spectra of TiI4, ZrI4 and HfI4 and with
new experimental data for ThI4.
Received 12 January 2015
Accepted 19 March 2015
Available online 27 March 2015
Ó 2015 Elsevier Ltd. All rights reserved.
Keywords:
Photoelectron spectroscopy
Relativistic effects
Group 4 iodides
Spin-orbit coupling
Density Functional Theory
1. Introduction
molecules [9–11] and solids [8]. However it is important to bench-
mark the approaches now being used against experimental data for
There is a growing realization that relativistic effects have a
strong influence on the energetics, bonding and functional proper-
ties of compounds of the heavy elements [1,2]. For example it has
recently been shown that the unusual quasi-linear stereochemistry
found in HgO arises from relativistic stabilization of the valence 6s
orbitals of Hg along with indirect destabilization of the Hg 5d
levels [3]. The consequent small separation between the 5d and
6s orbitals then allows oxygen mediated mixing between them
in the D4h coordination environment: shallow core d level mixing
with O 2p levels is much less pronounced in ZnO and CdO where
the d levels are deeper in energy and these oxides have respec-
tively regular tetrahedral and octahedral coordination around the
metal [4]. Elsewhere Pykko and coworkers have explored the
energetics of the lead acid battery using first principles calculations
of thermodynamic parameters and conclude that the battery volt-
age of around 2 V would be very much lower in the absence of rela-
tivistic stabilization of the 6s levels of Pb [5]. More recently
relativistic stabilization of Pb 6s orbitals has been shown to be very
important in determining the optical properties of lead-based per-
ovskite iodides now exciting great interest as absorber materials in
a new generation of solar cells [6–8].
simple molecular systems. Here we explore the influence of scalar
relativistic effects and spin–orbit coupling on the molecular elec-
tronic energy levels in the simple tetraiodides TiI4, ZrI4, HfI4 and
ThI4. The calculated molecular ionization energies are compared
with previously published photoelectron spectra of the three tran-
sition metal halides [12]. The paper also presents experimental
He(I) and He(II) photoelectron spectra of ThI4. The dominant scalar
effect transpires to be stabilization of the molecular a1 level in HfI4
and ThI4, paralleling stabilization of the atomic 6s and 7s orbitals in
Hf and Th respectively. Spin–orbit coupling in these molecules
involves a complex interplay between spin–orbit coupling based
on iodine with an increasingly important contribution from the
metal atom as one progresses through the series from TiI4 to ThI4.
2. Experimental
ThI4 was prepared by direct combination of the elements. A
weighed lump of the metal (ca. 2 g) was placed in a quartz tube
(ꢀ1.5 cm OD) and a constriction was worked into the upper end
of the tube. The tube was dried under dynamic vacuum and a stoi-
chiometric quantity of iodine was then sublimed from another ves-
sel onto the cooled (liquid N2) metal. The tube was then sealed at
the constriction. Reaction was initiated by radio-frequency
induced heating and was sustained until the thorium had com-
pletely reacted with the iodine. Analysis: % I calc. 68.6, found 68.3.
PE spectra were measured on a Perkin-Elmer PS 16/18 spec-
trometer, modified for He(II) measurements by the inclusion of a
Developments in computational techniques have allowed rela-
tivistic calculations to be performed on increasingly more complex
q
We dedicate this paper to Professor Mike Mingos, an esteemed colleague and
friend.
⇑
Corresponding author. Tel.: +44 01865 272600.
E-mail address: jennifer.green@chem.ox.ac.uk (J.C. Green).
http://dx.doi.org/10.1016/j.poly.2015.03.014
0277-5387/Ó 2015 Elsevier Ltd. All rights reserved.

2
J.C. Green, R.G. Egdell / Polyhedron 93 (2015) 1–7
Table 3
Table 1
Kohn–Sham orbital energies (eV) and Mulliken populations for MI4.
Calculated and experimental interatomic distances (Å) for MI4.
1t1
3t2
1e
2t2
2a1
M
Method
Ti
Zr
Hf
Th
TiI4
ZrI4
HfI4
ThI4
Energy
%I 5p
%Ti 3d
%Ti 4s
%Ti 4p
ꢁ6.79
ꢁ7.63
84
9
ꢁ7.84
75
25
ꢁ8.21
71
19
ꢁ9.01
M–I
Exp
NR
ZORA
SO
ZORA/SO
2.546 [21]
2.58
2.57
2.57
4.19
2.660 [21]
2.73
2.71
2.71
4.43
2.662 [21]
2.72
2.69
2.69
4.39
2.91 [22]
3
2.95
2.95
4.82
100
81
15
6
6
I–I
Energy
%I 5p
%Zr 4d
%Zr 5s
%Zr 5p
ꢁ6.97
ꢁ7.61
89
4
ꢁ7.92
74
27
ꢁ8.34
73
21
ꢁ8.93
100
80
Table 2
15
Kohn–Sham orbital energies (eV) for MI4 without and with the inclusion of scalar
relativistic effects.
8
1
Energy
%I 5p
%Hf 5d
%Hf 6s
%Hf 6p
ꢁ6.95
ꢁ7.65
88
5
ꢁ7.92
75
24
ꢁ8.34
74
19
ꢁ9.41
100
73
MI4
TiI4
NR
ZrI4
NR
Hf I4
NR
ThI4
NR
ZORA
ZORA
ZORA
ZORA
22
7
3
1t1
3t2
1e
2t2
2a1
ꢁ6.88 ꢁ6.79
ꢁ7.73 ꢁ7.63
ꢁ7.94 ꢁ7.84
ꢁ8.28 ꢁ8.21
ꢁ7.03
ꢁ7.67
ꢁ7.89
ꢁ8.38
ꢁ8.81
ꢁ6.97
ꢁ7.61
ꢁ7.92
ꢁ8.34
ꢁ8.93
ꢁ7.05
ꢁ7.69
ꢁ8.03
ꢁ8.41
ꢁ8.89
ꢁ6.95
ꢁ7.65
ꢁ7.92
ꢁ8.34
ꢁ9.41
ꢁ7.29
ꢁ7.23
ꢁ7.67
ꢁ7.96
ꢁ8.00
ꢁ7.14
ꢁ7.28
ꢁ7.69
ꢁ8.06
ꢁ8.57
Energy
%I 5p
%Th 5f
%Th 6d
%Th 7s
%Th 7p
ꢁ7.14
92
7
ꢁ7.28
ꢁ7.69
ꢁ8.06
73
2
ꢁ8.57
76
3
94
80
ꢁ9.01
ꢁ9.01
20
20
17
4
hollow cathode discharge lamp and high current power supply
(Helectros Developments). The discharge lamp heats the sample,
which was contained in a quartz tube. An adequate vapour pres-
sure for measurement of spectra was obtained with a sample tem-
perature of 500 °C.
5. Electronic structure
With neglect of spin–orbit coupling, the 32 valence electrons of
the Group 4 tetrahalides occupy orbitals with the general ordering
Samples were introduced into the spectrometer under an argon
filled dry bag. Spectra were calibrated using He(I
a), He(Ib) and
He(II ) excited signals of admixed inert gases and N2. Band areas
a
1t1 > 3t2 > 2e > 2t2 > 2a1 > 1t2 > 1a1
were corrected to allow for variation in analyzer transmission
function with electron kinetic energy.
The 1a1 and 1t2 orbitals are predominantly I 5s in character and
are not considered in the subsequent discussion as they are not
observed in the experimental spectra.
The effect of inclusion of scalar relativistic effects (ZORA) is
shown in Table 2.
3. Computational methods
Density functional calculations were carried out using the
Amsterdam Density Functional program suite, ADF 2012.01
[13,14]. TZP basis sets were used with triple-n accuracy sets of
Slater-type orbitals [15,16], with polarization functions added to
all atoms. Relativistic corrections were made using the ZORA
(zero-order relativistic approximation) formalism, and the spin–
orbit formalism. The BP functional was employed [17–20]. The core
electrons were frozen up to 2p for Ti, 3d for Zr and 4p for Hf and I
and 4f for Th. The geometries of MI4 (M = Ti, Zr, Hf, Th) were opti-
mized with a Td symmetry constraint. Frequency calculations con-
firmed energy minima. The effect of freezing the core orbitals was
tested with single point all electron spin–orbit calculations. Only
small differences in orbital energies were found (see ESI).
Vertical ionisation energies were calculated by direct unrestricted
calculations on the molecular ions in their ground and appropriate
excited states, and subtraction of the energy of the neutral mole-
cule. Cartesian coordinates for the optimized structures are given
in the electronic Supplementary information.
The most striking effect on the orbital energies is the stabiliza-
tion of the 2a1 level for HfI4 and ThI4 on inclusion of the scalar cor-
rections. Kohn–Sham orbital energies, calculated with scalar
relativistic corrections but without spin–orbit coupling, and their
compositions are given in Table 3 and plotted in Fig. 1a.
In all cases the orbital ordering is the same. The spread of ener-
gies is strongly influenced by through space interactions between
the I 5p orbitals and is therefore a function of the I–I distance.
Thus the 1t1 orbital involves out of phase through space antibond-
ing interactions which become less important as the I–I separation
increases. It follows that TiI4 has the highest energy 1t1 orbital.
Conversely, the 2a1 orbital involves in-phase through space inter-
actions and this orbital is at lower energy in TiI4 than in ZrI4 and
ThI4. However the 2a1 orbital is much more stable in HfI4 than in
ZrI4, even though the bond lengths are almost identical in the
two compounds. The increased stability of the 2a1 orbital of HfI4
mirrors stabilisation of the 6s orbital in Hf as compared to Zr and
is influenced by two effects. Hf occurs in the periodic table after
the filling of the 4f shell. The 4f orbitals have no radial nodes and
are unable to shield the highly penetrating 6s orbitals from the
increase in nuclear charge across the lanthanide series. At the same
time the 6s orbital in atomic Hf is strongly stabilised by scalar rela-
tivistic effects, which become increasingly important with increas-
ing atomic number. Thus the valence s ionisation energies in Ti, Zr
and Hf are respectively 6.828 eV, 6.634 eV and 6.825 eV. The 2a1
bonding orbitals have a contribution from their respective metal
ns orbitals (Table 3) and thus the increase from ZrI4 to HfI4 mirrors
the increase in the atomic ionisation energy.
4. Results and discussion
Density functional calculations were carried out for the four MI4
molecules (M = Ti, Zr, Hf, Th) at three different levels. The first
neglected relativistic effects (NR), the second included scalar rela-
tivistic effects (ZORA) and the third included the effect of spin orbit
coupling (SO). The geometries of the four MI4 molecules were opti-
mized at these three levels. The resulting tetrahedral geometries
are given in Table 1. Inclusion of relativistic effects reduce the cal-
culated M–I bond length, the effect increasing down the group.
Addition of spin–orbit coupling makes little difference to the
geometry.
The energies of the orbitals tend to rise for all of the orbitals in
ThI4, apart from the 1t1 orbital, which is the most stable of the
Group IV set. The stability maybe in part a consequence of the

J.C. Green, R.G. Egdell / Polyhedron 93 (2015) 1–7
3
Fig. 1. (a) Kohn–Sham orbital energies (ZORA) for MI4 (b) Kohn–Sham orbital energies with spin–orbit corrections (SO) for MI4 (c) calculated IE (ZORA) for MI4 (d) calculated
IE including SO coupling (SO) for MI4. (Colour online.)
greater I–I distance but, whereas the 1t1 combination has no sym-
metry match among the valence orbitals of the d-block metals, Th
is able to form a bonding combination with its 5f orbitals, and the
calculations suggest a small (7%) contribution to the MO in this
case (Table 3).
Table 3 reveals a high degree of I 5p character to all orbitals
consistent with the bond polarity. The 2a1 orbital in ThI4 has a rela-
tivistic stabilisation (0.57 eV) even bigger than that in HfI4
(0.52 eV). The influence of relativistic effects on the energy of the
7s orbital in Th may be discerned by comparing the atomic ion-
isation energies of Ce (5.539 eV) and Th (6.307 eV). There is an
increase of 0.768 eV despite an increase in the principal quantum
number from 6 to 7.
Representative iso-surfaces for the orbitals of HfI4 are shown in
Fig. 2.
In principle there is no
but iso-surfaces show that the 3t2 orbital is principally
ter and non-bonding, and 2t2 principally and bonding. The 3t2
orbitals show a small amount of mixing with the metal (n ꢁ 1)d
and np orbitals but the principal bonding interaction is enshrined
r
p
separability for tetrahedral molecules
in charac-
p
r
r
in the 2t2 orbital between I 5p and metal (n ꢁ 1)d orbitals, the
metal np orbitals have a very minor role. The 2e orbital gives
p
bonding exclusively with the metal (n ꢁ 1)d orbitals.
It is now well established that for early actinides the shallow
core 6p shell can also be involved in metal–ligand bonding
[23,24]. Its energy and radial distribution are favorable for mixing

4
J.C. Green, R.G. Egdell / Polyhedron 93 (2015) 1–7
Fig. 2. Isosurfaces for the top occupied Kohn–Sham orbitals of HfI4 observed along a C2 axis. (Colour online.)
Table 4
Table 6
Descent of symmetry from Td to Tꢂ .
Calculated splittings of the orbital energy levels (eV) and in parenthesis shifts in the
mean of SO split energy levels (eV) on inclusion of spin–orbit coupling for MI4.
d
Tdꢂ
Td
M
1t1
3t2
1e
2t2
2a1
A1
E
T1
T2
E0 (E1/2
U0 (U3/2
U0 + E0 (U3/2 + E1/2
U0 + E00 (U3/2 + E5/2
)
)
Ti
0.41 (ꢁ0.07)
0.41 (ꢁ0.05)
0.43 (ꢁ0.04)
0.42 (ꢁ0.09)
0.20 (ꢁ0.1)
0.12 (ꢁ0.09)
0.25 (ꢁ0.09)
0.05 (ꢁ0.07)
0 (ꢁ0.08)
0 (ꢁ0.03)
0 (ꢁ0.02)
0 (0.03)
ꢁ0.04 (0.19)
0.11 (0.19)
0.11 (0.16)
0.31 (0.13)
0 (0.05)
0 (0.06)
0 (0.03)
0 (0.09)
Zr
Hf
Th
)
)
ꢁmeans less stable, + means more stable.
Table 5
Energies (eV) of the spin–orbitals of MI4.
Table 7
M
5U0
3E0
4U0
3E00
3U0
2E00
2U0
2E0
Calculated ionization energies (eV) for MI4 molecules.
Ti
ꢁ6.61
ꢁ6.78
ꢁ6.77
ꢁ6.91
ꢁ7.02
ꢁ7.19
ꢁ7.20
ꢁ7.33
ꢁ7.46
ꢁ7.48
ꢁ7.48
ꢁ7.19
ꢁ7.66
ꢁ7.6
ꢁ7.76
ꢁ7.89
ꢁ7.90
ꢁ7.72
ꢁ8.37
ꢁ8.57
ꢁ8.57
ꢁ8.40
ꢁ8.41
ꢁ8.46
ꢁ8.46
ꢁ8.09
ꢁ9.06
ꢁ8.99
ꢁ9.45
ꢁ8.66
M
1t1
3t2
1e
2 t2
2a1
Zr
Hf
Th
ꢁ7.73
ꢁ7.26
Ti ZORA
Ti SO
8.98
8.86 U0
9.84 E0
9.84
9.71 U0
9.90 E00
10.06
10.03 U0
10.46
10.68 E00
10.71 U0
11.25
11.38 E0
Zr ZORA
Zr SO
9.04
9.69
10.03
10.49
11.05
8.91 U0
9.34 E0
9.61 U0
9.72 E00
10.05 U0
10.66 U0
10.77 E00
11.19 E0
with the valence orbitals of smaller ligands. In the case of our
calculations on ThI4 the 6p orbitals were included in the basis set
but gave no contribution to the t2 set of orbitals, which instead
mixed to some extent with the 7p orbitals. Presumably the greater
bond length and the diffuse nature of the I 5p orbitals results in
poor overlap with the pseudo core orbitals of the Th 6p set. The
behavior found here for ThI4 contrasts with that found for both
HfCl4 [25] and OsO4 [26,27]. where mixing with shallow core 5p
levels gives measurable spin orbit splitting in the outer occupied
t2 level.
Hf ZORA
Hf SO
9.04
8.9 U0
9.35 E0
9.74
9.62 U0
9.86 E00
10.00
10.06 U0
10.50
10.65 U0
10.79 E00
11.55
11.66 E0
Th ZORA
Th SO
9.14
8.94 U0
9.37 E0
9.25
9.21 U0
9.27 E00
9.68
9.76 U0
10.11
10.18 U0
10.49 E00
10.6
10.75 E0
many years ago [28]. In the absence of interaction between the I 5p
orbitals and orbitals of the central atom (as is the case for the tran-
sition metal iodides) and further ignoring the need for normaliza-
tion due to I–I overlap, the 1t1 level should be split by ꢁ3fI6p/4,
where fI6p is the spin–orbit coupling constant for I 5p orbitals.
This value is basically half that found for a free iodine atom and
predicts the U0 ionic state to lie at lower energy than the E0 state.
This simple expression is potentially modified in the case of Th
as the t1 orbitals are no longer exclusively I 5p based, but the Th
5f orbital spin–orbit splitting and the contribution to the 1t1 orbital
6. Spin–orbit energy levels
The effects of spin–orbit coupling on metal tetrahalides has
been considered previously [12,24,28,29]. Inclusion of the spin
orbit effects splits the 2T levels as shown in the descent of symme-
try table (Table 4).
Before looking at the calculation results it is useful to summar-
ize the conclusions from a phenomenological approach developed

J.C. Green, R.G. Egdell / Polyhedron 93 (2015) 1–7
5
are too small to have a noticeable effect. The value of fI6p for an I
atom is 0.628 eV [30] giving an estimate of 0.47 eV for the 5U0–
3E0 separation.
The splitting of the t2 orbitals is considerably more complex as
the magnitude and sign of the splitting are a function of the degree
of rp mixing and also the contribution from metal d and p orbitals
may well be significant. However for a pure I 6p system with no
I-metal overlap and neglecting the normalization constant arising
from I–I overlap, a pure t2(
p
) set would be split by ꢁ3fI6p/4 and
a t2( ) set would have a zero splitting. Mixing between the two
r
can however lead to a full restoration of the atomic spin orbit split-
ting found in a free I atom (i.e. ꢁ3fI6p/2) in the uppermost t2 level
where
r and p contributions are out-of-phase and a splitting of
half this magnitude with the opposite phase (i.e. +3fI6p/4) in the
lower in-phase t2 combination, where the U0 ionic state is now at
higher energy than the E00 state. This situation pertains when the
wavefunctions for the two t2 combinations can be written as:
qffiffi
3t2 ¼ 23t2ð
qffiffi
qffiffi
p
p
Þ ꢁ 1t2ð
r
Þ
Þ
3
qffiffi
2t2 ¼ 13t2ð
Þ þ 2t2ð
r
3
The results for the orbital energies with spin–orbit coupling
(SO) included are given in Table 5. The energy levels are plotted
in Fig. 1b. Table 6 gives the calculated splittings of the various
levels and the degree to which the energy mean of the split SO
levels shifts from the ZORA value.
Due to I 5p dominance of orbital composition the I 6p orbitals
are expected to dominate the SO splitting. The 1t1 splitting is con-
sistent down the group with 5U0 < 2E0 and the energy trend of the
spin–orbit components reflects that of the parent orbital. The mag-
nitude of the splitting is 0.41–0.43 eV which compares favorably
with the 0.47 eV estimated above. The 1e and 2a1 levels are unsplit
and relatively unshifted.
Fig. 3. He I (hm = 21.2 eV) and He II (hm = 40.8 eV) photoelectron spectra of ThI4.
Table 8
With the 3t2 and 2t2 levels, possible interaction between the
p
) is U0 < E00 and for
Experimental vertical ionization energies (eV) for MI4 molecules and suggested
assignments.
sets should be considered. If splitting for 3t2(
2t2(r
) E00 < U0, interaction between E00 levels will reduce the SO
Ti
Zr
Hf
Th
splitting of both sets, leading to low values calculated for t2 split-
tings. There is evidence for this in that the means for the spin–orbit
components of these two sets show greater shifts than the other
means and move apart. The significantly larger splitting of the
2t2 orbital for ThI4 is attributed to the admixture of the Th 6d orbi-
tals, the spin–orbit coupling constant for Th 6d being sufficiently
large for only a 20% contribution to be effective. The spin–orbit
coupling constant for Pa4+ has been measured as 0.23 eV [31],
and has been calculated as 0.38 eV [32], that for Th4+ will be less
as the nuclear charge is less.
a
9.22(sh),
9.32
5U0
9.49(sh),
9.61
5U0
9.48(sh),
9.57
5U0
a
9.47(sh), 9.67
5U0
b
c
9.77
10.03
10.05
b
10.02
3E0
3E0
3E0
4U0
10.32
4U0
10.45
3E00
10.33, 10.51
4U0
10.51
3E00
10.37, 10.56
4U0
10.67
3E00
10.26
3E00 + 3E0
10.62, 10.82
3U0
c
10.68
3U0
10.77, 10.96
3U0
10.82, 10.95
3U0
10.97, 11.19
2U0
d
e
11.19
11.35, 11.49
11.45, 11.56
d
e
11.49
2E00
2U0
2U0
2E00
7. Ionization energy calculations
11.34
2U0
11.92
2E0
11.68
2E00
12.00
2E0
11.68
2E00
12.47
2E0
IE calculations were performed both with and without spin–or-
bit coupling (ZORA and SO). The calculated ionization energies are
given in Table 7 and plotted in Fig. 1(c) and (d).
11.76
2E0
From inspection of Fig. 1 it is evident that the trends in calcu-
lated IE are the inverse of the trends in orbital energies and hence
they have the same underlying causes.
Table 9
8. Assignment of photoelectron spectra
Relative band intensities in the He I and He II spectra of MI4.
TiI4
ZrI4
HfI4
He I
ThI4
Photoelectron spectra of the transition metal tetraiodides MI4
(M = Ti, Zr, Hf) have been reported previously [12]. That of ThI4
has not been published previously, although experimental data
for the other thorium tetrahalides is available [24,29]. The He I
and He II spectra of TiI4 are shown in Fig. 3. A listing of identifiable
vertical ionization energies for all four iodides is given in Table 8
together with possible band assignments.
He I
He II
He I
He II
He II
HeI
He II
a
b
c
d
e
2.0 (2)
1.1 (1)
5.2 (5)
3.4 (3)
0.9 (1)
2.0
1.3
9.2
5.8
1.7
2.0 (2)
1.0 (1)
4.6 (5)
2.8 (3)
1.1 (1)
2.0
1.0
17.1
12.8
2.7
2.0 (2)
1.0 (1)
5.1 (5)
3.7 (3)
0.8 (1)
2.0
1.1
9.1
6.3
1.6
2.0 (2)
4.4(4)
4.2(4)
0.8 (1)
0.9 (1)
2.0
4.5
6.4
1.8
0.8

6
J.C. Green, R.G. Egdell / Polyhedron 93 (2015) 1–7
Fig. 4. Comparison of experimental (a) and calculated (b) vertical ionization energies (eV) of MI4 M = Ti, Zr, Hf and Th. (Colour Online.)
The eight spin orbits, which ionize in the energy region below
calculations reproduce well the trends observed in the spectra. In
particular the predicted groupings of the bands in the calculations
concur with the intensity observations, notably the 2:1:5:3:1 pat-
tern observed for the d-block elements as opposed to the 2:4:4:1:1
pattern for ThI4 (Table 9). In addition the observed increases in
relative intensity of bands in the He II spectra are in the calcula-
tions associated with spin–orbitals derived from orbitals with the
highest d content, 1e and 2t2. The trends down the group of the
bands 5U0, 3E0 and 2E0 which may be identified without ambiguity
are very well reproduced by the calculations.
13 eV, should give rise to eight primary ionization processes.
However in some of the spectra more than eight features are
identifiable. This is a consequence of Jahn–Teller (J–T) splitting of
2
the U0 states in the molecular ion. We may anticipate that such
J–T splitting is greater for states involving a hole with bonding
character than for non-bonding ones such as 2T1 states.
Changes in relative intensity of bands with photon energy can
identify the states arising from ionization of electrons from orbitals
with metal d character as these tend to increase in relative inten-
sity in the He II spectra. The dominance of I character in the orbi-
tals leads to band intensities in the He I spectra reflecting the
degeneracies of the contributing states. Both these criteria are used
to assist band assignment. Band intensities are given in Table 9.
The number of states that must be assigned to each region is
given in parentheses in Table 9. We may also conclude that regions
c and d arise from orbitals with metal d character.
10. Concluding remarks
The excellent agreement between the observed pattern of
experimental ionization energies for the metal tetraiodides shown
in Fig. 4 and those calculated by density functional theory methods
after inclusion of both scalar relativistic effects and spin–orbit cou-
pling give one considerable confidence in the ability of current
computational techniques to explore and understand the com-
plexities of electronic structure in complex heavy atom systems.
Publication of experimental photoelectron spectra of ThI4 com-
pletes the experimental data set of photoelectron spectra for the
thorium tetrahalides.
Assignment of the 5U0 and 2E0 states as to the lowest and high-
est IE bands respectively is unambiguous, as is the 3E0 state to the
second band b for M = Ti, Zr and Hf. For ThI4, the assumption of a
SO splitting similar to its congeners places the 3E0 states within
the band at 10.22 eV.
The He I/He II intensity variations suggest that the 2E00, 3U0 and
4U0 states contribute to the higher IE bands in regions d and c,
though for the d block elements the lower IE region of band c
shows a smaller intensity increase with photon energy. The inten-
sity considerations together with the calculations suggest the
assignments given in Table 8.
Molecular photoelectron spectroscopy should continue to pro-
vide an important technique for benchmarking electronic structure
calculations as is the case for solid state materials.
Acknowledgements
We thank the SRC for the purchase of a spectrometer and the
Salter’s Company for a scholarship (R.G.E.). We also gratefully
acknowledge the contribution of Tony Orchard to the inception
of this work.
9. Comparison of experimental and calculated ionization
energies
The experimental and calculated ionization energies are shown
in Fig. 4. Where splitting of a 2U0 state is observed the mean is plot-
ted in Fig. 4. Overall the calculated IE are too low when compared
with experiment [33]. Such underestimates are common when
Appendix A. Supplementary data
using density functional techniques and the
crepancy normally increasing with increasing IE. In general the
D
SCF method, the dis-
Supplementary data associated with this article can be found, in
the online version, at http://dx.doi.org/10.1016/j.poly.2015.03.014.

J.C. Green, R.G. Egdell / Polyhedron 93 (2015) 1–7
7
[15] J.C. Slater, Theory of Molecules and Solids. Vol. 4: The self-Consistent Field for
Molecules and Solids, Mc-Graw-Hill, New York, 1974.
References
[16] J.S. Slater, The Calculation of Molecular Orbitals, Wiley, New york, 1979.
[17] A.D. Becke, Phys. Rev. A 38 (1988) 2398.
[18] J.P. Perdew, Phys. Rev. B 33 (1986) 8822.
[1] P. Pyykko, Ann. Rev. Phys. Chem. 63 (2012) 45.
[2] M. Barysz, Y. Ishikawa (Eds.), Relativistic Methods for Chemists, Springer,
Dordrecht, 2010.
[3] P.A. Glans, T. Learmonth, K.E. Smith, J. Guo, A. Walsh, G.W. Watson, F. Terzi,
R.G. Egdell, Phys. Rev. B 71 (2005) 235109.
[4] P.A. Glans, T. Learmonth, C. McGuinness, K.E. Smith, J.H. Guo, A. Walsh, G.W.
Watson, R.G. Egdell, Chem. Phys. Lett. 399 (2004) 98.
[5] R. Ahuja, A. Blomqvist, P. Larsson, P. Pyykko, P. Zaleski-Ejgierd, Phys. Rev. Lett.
106 (2011) 018301.
[6] X. Zhu, H.B. Su, R.A. Marcus, M.E. Michel-Beyerle, J. Phys. Chem. Lett. 5 (2014)
3061.
[7] E. Menendez-Proupin, P. Palacios, P. Wahnon, J.C. Conesa, Phys. Rev. B 90
(2014) 045207.
[8] F. Brivio, K.T. Butler, A. Walsh, M. van Schilfgaarde, Phys. Rev. B 89 (2014)
155204.
[9] N. Kaltsoyannis, B.E. Bursten, J. Organomet. Chem. 528 (1997) 19.
[10] L. Andrews, X. Wang, Y. Gong, G.P. Kushto, B. Vlaisavljevich, L. Gagliardi, J.
Phys. Chem. A 118 (2014) 5289.
[11] S.G. Minasian, J.M. Keith, E.R. Batista, K.S. Boland, D.L. Clark, S.A. Kozimor, R.L.
Martin, D.K. Shuh, T. Tyliszczak, Chem. Sci. 5 (2014) 351.
[12] R.G. Egdell, A.F.J. Orchard, Chem. Soc. Farad. II 73 (1977) 485.
[13] SCM, 2002.2 ed., Theoretical Chemistry, Vrije Universiteit: Amsterdam, 2002.
[14] G. te Velde, E.J. Baerends, J. Comp. Phys. 99 (1992) 84.
[19] J.P. Perdew, Phys. Rev. B 34 (1986) 7046.
[20] S.H. Vosko, L. Wilk, M. Nusair, Can. J. Phys. 58 (1980) 1200.
[21] G.V. Girichev, E.Z. Zasorin, N.I. Giricheva, K.C. Krasnov, V.Zh. Spiridovnov,
Strukt. Khim. 18 (1977) 42.
[22] R.J.M. Konings, D.L. Hildebrand, J. Alloys Comp. 271 (1998) 583.
[23] R.G. Denning, J.C. Green, T.E. Hutchings, C. Dallera, A. Tagliaferri, K. Giarda, N.B.
Brookes, L. Braicovich, J. Chem. Phys. 117 (2002) 8008.
[24] J.M. Dyke, N.K. Fayad, A. Morris, I.R. Trickle, J. Chem. Phys. 72 (1980) 3822.
[25] N. Kaltsoyannis, Chem. Phys. Lett. 274 (1997) 405.
[26] B.E. Bursten, J.C. Green, N. Kaltsoyannis, Inorg. Chem. 33 (1994) 2315.
[27] P. Pyykkö, J. Li, T. Bastug, B. Fricke, D. Kolb, Inorg. Chem. 32 (1993) 1525.
[28] J.C. Green, M.L.H. Green, P.J. Joachim, A.F. Orchard, D.W. Turner, Philos. Trans.
R. Soc. A 268 (1970) 111.
[29] L.J. Beeching, J.M. Dyke, A. Morris, J.S. Ogden, J. Chem. Phys. 114 (2001) 9832.
[30] M. Montalati, A. Credi, L. Prodi, T. Gandolfi, Handbook of Photochemistry,
Taylor and Francis, CRC Press, 2006.
[31] N. Edelstein, W.K. Kot, J.C. Krupa, J. Chem. Phys. 96 (1992) 1.
[32] L. Seijo, Z. Barandiaran, B. Ordejon, Mol. Phys. 101 (2003) 73.
[33] J.C. Green, P. Decleva, Coord. Chem. Rev. 249 (2005) 209.