ABSTRACT
Density functional theory (DFT) calculations were used to optimize the
geometry of cyclopentadienyl thallium (Cp-Tl). DFT calculations were
also used to calculate the Van der Waals structures and interaction
energies of cyclopentadienyl thallium benzene (Cp-Tl-C5H5),
cyclopentadienyl thallium acetylene (Cp-Tl-C2H2),
and cyclopentadienyl ethylene (Cp-Tl-C2H4)
complexes. All calculations were done using the following combination
of non-local exchange and correlation functionals: B3LYP, BPW91, MPW1PW91.
The optimized geometry of Cp-Tl was compared to the experimental microwave
structure of Cp-Tl. The calculated Cp-Tl structure shows that modified
Perdew-Wang exchange and correlation functionals, MPW1PW91, gives better
values of the thallium-carbon bonding distance. Both Cp-Tl
thallium-carbon(Cp) and thallium-Cp(centroid) bond lengths are 0.066
A longer than the experimental value. The results obtained using
Becke's exchange functional seemed to give longer thallium-carbon bonding
distance even if a larger basis set was used. Becke's exchange functionals
over estimates the thallium-carbon(Cp) bond length by as much as 0.165
A using the smaller basis set. The relativistic effect
due to thallium was considered in the calculation to obtain more accurate
Cp-Tl thallium-carbon bond length. The Cp-Tl bond length using
ADF with ZORA relativistic potentials calculations gives good results.
The Van der Waals structure of Cp-Tl-C5H5,
Cp-Tl-C2H2, and Cp-Tl-C2H4
were calculated using MPW1PW91/cc-vPTZ/SDD and PW91/ADF/ZORA level
of calculations. Microwave study to confirm the existence of the above
weakly bound complexes are planned in the near future.
INTRODUCTION
Cyclopentadienyl
thallium complex (Cp-Tl) is an example of a 'half-sandwich' complex that
is stable at room temperature. The open coordination geometry of
the heavy metal makes this complex a challenging and ideal molecular
system for studying the effect of metal-ligand weak bonding interactions
using density funtional theory (DFT) and microwave spectroscopy.
As the metal become 'heavier', the DFT calculations of metal-ligand bond
lengths maybe less accurate because the relativistic effect and spin orbit
become increasingly important factors in the calculation. It has
been reported that the heavier elements in third row transition metal often
shows the metal-atom bond length to be about 0.1 A longer than the experimental
value (1). Therefore, in order to obtain more accurate Cp-Tl
structure and energy, the relativistic effective potential must be considered
in DFT calculations. The DFT method has been successfully used to
calculate the structures, reaction dynamics, bonding energy, vibration
frequencies, and Van der Waals interaction energies of many first and second
rows transition metal complexes (2,3). However, there are small numbers
of experimental and theoretical studies on a third row transition metal
complexes, especially of weakly bound complexes. Hopefully, the continuous
development of better exchange-correlation functionals, relativistic effective
potentials, and larger basis sets for the third row transition metals
make it possible to carry out accurate DFT calculations on heavy
organomettallic complexes.
The gas phase structure
and Van der Waals interactions between Cp-Tl and common organic ligands
are not well understood. Up to date, there are no theoretical and experimental
studies available for these weakly bound complex systems.
Because the Van der Waals interactions are weak bonding interactions,
these Cp-Tl-ligand complexes may have interesting physical and chemical
properties. For instance, it is known that many weakly bound complexes
exhibit large amplitude internal motion and vibrational predissociation
which are not commonly found in a stable metal-ligand complex (4).
The interesting question, which is central to our understanding of chemical
reation, is how does Cp-Tl influence the eletronic structures,
geometry,and energy of a ligand. Our recent experimental and DFT
studies of rhenium complexes, (C2H2)(CH3)ReO2,
demonstrated that the third row transition metals can have significant
effect on the electronic structure, bond length, and bond angles of ligand.
In the case of rhenium, the rhenium metal forces partial sp2
hybrid on acetylene electronic structure (19). To help us gain insight
into the thallium-ligand interactions, we are using the DFT to study
the geometry of the cyclopentadienyl thallium (Cp-Tl) and to calculate
the structure and binding energies of the following proposed systems:
cyclopentadienyl thallium benzene (Cp-Tl-C5H5),
cyclopentadienyl thallium acetylene (Cp-Tl-C2H2),
and cyclopentadienyl ethylene (Cp-Tl-C2H4)
complexes. The existence of these weakly bound complexes will be
verified using the microwave spectroscopy. The result of DFT calculation
on Cp-Tl will be compared to the experimentally determined gas phase structure
of Cp-Tl which has been obtained earlier in our laboratory using Fourier
transformed microwave spectroscopy (5).
Cp-Tl Cp-Tl-Acetylene
STRUCTURAL BACKGROUND
Cyclopentadienyl thallium (Cp-Tl)
structure has been measured here in our laboratory using a Fourier transformed
microwave spectrometer (5). Deuterated samples of CpTl were
prepared to obtain spectra for deuterium-substituted isotopomers. Analysis
of the spectra allowed the determination of the following structural parameters:
the bond lengths between Tl-C(Cp) = 2.413(3) A, C-C =1.421(10) A,
C-H =1.082(9) A, and the angle C-H = 0.9(2) degree. There are no
theoretical and experimental studies available for these weakly bound complex
systems. The Van der Waals structures between Cp-Tl and C2H2,
C2H4, and C5H5
will be determined from various computational methods: Gaussian 98 DFT
and ADF ((Amsterdam density functional) calculations. The results
form gaussian 98 DFT will be compared with ADF. All results
will be compared to the experimentally determined Cp-Tl structure.
RELEVANT PRINCIPLES
The relativistic effect
and spin orbit interaction due to thallium must be considered in the calculations
if one to obtain the more accurate predictions of structures and energies
of these complexes. The heavier elements in third row transition
metal often shows the metal-atom bond length to be about 0.1 A longer than
the experimental value (1). The shape consistent relativistic
effective potential (REPs) for thallium was obtained from Christiansen
and Wildman (18). The REPs potential has been shown to work very
well in the simple system such as Tl-H. The REPs potential will be used
with Gaussian 98 DFT calculations. The ZORA relativistic potentials
will be considered in the ADF calculations.
COMPUTATIONAL AND EXPERIMENTAL METHODS
All density functional
calculations were performed on TINTIN IBM computer cluster using the GAUSSIAN
98 program at the University of Arizona CGF (computing graphic facilities)
(6). The Molekel visualization solftware was used to aid in visualize
the electrostatic potential surfaces and molecular orbitals of Cp-Tl and
Cp-Tl-ligand complexes. All computations were done on the hartree
computer located in CGF. The Cp-Tl structure was first optimized
using different exchange correlation funcionals, effective core potentials,
and basis sets to calibrate the Cp-Tl system. The following non-local
Becke's three-parameter and modified Perdew Wang's exchange functionals,
and Lee, Yang, Parr, Perdew, and Wang's correlation functionals were used:
B3LYP, BPW91, B3PW91, MPW1PW91 (7,8,9,10). Many different basis sets
were chosen for carbon and hydrogen atoms including are Pople's 6-311G,
and the 6-311G with diffusion polarization functions p, d, and f
(11 ), Dunning's correlation consistent triple zeta basis set cc-pVTZ
(12 ), and Aldrich basis sets SVP(13),TZV(14). There are two basis
sets availble in Gaussian 98 for thallium metal which are the Los
Almos double zeta basis set, LANL2DZ, and Stuttgart/Dresden SDD basis set
(15,16).
The effective core potentials
(ECP) for thallium used in calculation were of SDD and LANL2DZ types and
are available in Gaussian 98. The shape consistent relativistic effective
potential (REPs) for thallium was obtained from Christiansen and Wildman
(18). For computational compatibility on Gaussian 98, the spin-orbit was
deleted and assumed to be very small. The REPs replaces 68 thallium
electrons leaving 5d, 6s, and 6p electrons in the valence subshells.
The thallium basis set was adjusted to make the thallium basis
set equivalent to the carbon basis set by free up the outer components
of thallium s, p, and d obitals. The calculation involving thallium relativistic
effect was done at MPW1PW91/cc-pVTZ/REPs level. The calculated Cp-Tl structure
and bond lengths were compared to the gas phase Cp-Tl experimental values.
It turned out that the calculation at MPW1PW91/cc-pVTZ/SDD level provided
the best calibration for the system using standard Gaussian98 basis sets
and ECP. DFT calculations of the proposed weakly bound
structures cyclopentadienyl thallium benzene (Cp-Tl-C5H5),
cyclopentadienyl thallium acetylene (Cp-Tl-C2H2),
and cyclopentadienyl ethylene (Cp-Tl-C2H4)
complexes were done using MPW1PW91/cc-pVTZ/SDD level of calculation as
well as MPW1PW91/cc-pVTZ/REPs. The frequency analysis was performed
for all the complexes to verify that there are no negative frequencies
and that indeed the structures were at the minimum of potential energy
surface. Basis set superposition error (BSSE) was not calculated.
The structure of Cp-Tl is
also optimized using Amsterdam density functional calculations (ADF). The
advantage of the ADF calculations is that we can include the relativistic
potential of each atom in the calculations. The DFT methods used
in ADF calculations will be BLYP and PW91. B3LYP and B3PW91 methods.
Becke's three parameters are not available in ADF. The same basis
sets used in Gaussian 98 DFT calculations will be used in ADF.
The calculation of bond
interaction energies can be estimated substracting the total energies
of the optimized products and reactants, similar to the determination
of enthalpy of reactions. Such calculation should give good estimates of
weak bonding energies without any knowlege of dissociation bond energies.
MX(n) + X ----> MX(n+1) 1)
dE = E(product) - E(reactants)
2)
Experimental verification of the weakly bound complexes will be performed
using a Flygare-Balle-type pulsed beam Fourier transformed microwave spectrometer
(18). The structure of Cp-Tl was determined in our lab using this same
instrument. The Van der Waals complexes can be formed by racting
Cp-Tl with ligands under the appropriate experimental condition.
A high density of complexes can form by adjusting the temperature, gas
pressure, and pulsed rate......
STRUCTURAL ANALYSIS
DFT calculations using
Gaussian 98 over estimates the thallium-carbon bonding distance by
as much as 0.165 A using the smaller basis set. This best calculated
value without the relativistic potential is about 0.066 A longer than the
experimental value. The calculation using REPs gives the thallium-carbon
bond length equal to...... The ADF calculations....
ELECTRONIC POTENTIAL
Figure3:Electrostatic potential energy surface Cp-Tl-NH3
Figure4:Electrostatic
potential energy surface Cp-Tl
COMPUTATIONAL RESULTS AND DISCUSSION
The optimized structure of
Cp-Tl was compared to the experimental gas phase Cp-Tl structure (Table
I). The thallium- carbon bond length using Beck's non-local exchange
functionals gave longer Cp-Tl bond length comparing to the modified
Perdew Wang exchange functionals. However, both method did not produce
the Cp-Tl bond lengths that agree will with the experimental value.
The best DFT method of calculation without relativistic effective potential
turned out to be MPW1PW91/cc-pVTZ/SDD
and
the calculated the Cp-Tl thallium-carbon bond length to be 2.755
A. Figure 1: Optimized
structure cyclopentadienyl thallium. This best calculated value
is about 0.34 A longer than the experimental value. Although
MPW1PW91/cc-pVTZ/SDD
method
didnot produce very accurate thallium-carbon bond length value, it
was used to optimize the geometry of the Cp-Tl-Acetylene complex to see
if the method can converge. The calculation of CP-Tl-C2H2
did converge. The optimized Cp-Tl-C2H2
is shown in Figure 2: Optimized
structure cyclopentadienyl thallium acetylene. The thallium-carbon(Cp)
is increased to 2.764 A with the acetylene present. The thallium-carbon(C2H2)
is 4.642 A, about 40% longer than the thallium-carbon(Cp). The small
increase in thallium-carbon(Cp) bond length implies that there are weak
interactions between thallium and acetylene pi orbitals. The
acetylene appeared to be very weakly bound to thallium. The binding
energy is estimated using equation1 and 2 to be about...........
Figure 3 shows G98 optimized
Van der Waal structure of cyclopentadienyl thallium benzene.
The optimazation of Cp-Tl
using ADF with Zora relativistic gives improved results. Both MPW1PW91
and B3PW91 with Tl5d double zeta basis set gives the Tl-Cp(centroid) bond
length = 2.430 A, which is only 0.017 A longer than the experimental value.
ADF/Zora
optimized structure of cyclopentadienyl thallium
ADF/Zora
optimized structure of cyclopentadienyl thallium benzene
Table I. Gaussian 98 DFT Calculation of Tl-C(Cp) and Tl-Cp(centroid)
bond lengths for Cp-Tl
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Relativistic potential (REPs) |
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Notation: Method/ C, H basis set/ Tl basis set and core potential
Table II. ADF Calculations of Tl-C(Cp) and Tl-Cp(centroid)
bond lengths for Cp-Tl
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Tl.4f |
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| Experimental value |
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Table III. Gaussian 98 DFT MPW1PW91/cc-pVTZ/SDD:
Optimized Van der Waals geometry of Cp-Tl-ligand complexes
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Table IV ADF MPW1PW91 optimized Van der Waals geometry
of Cp-Tl-ligand complexes
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Table V Optimized Van der Waal geometry using MP2 methods
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CONCLUSIONS
It is clear that the Becke's
exchange function over estimated the Cp-Tl bond lengths as much as 6% larger
than the experimental value. These results supported the arguement by Zhang
et al. and Wesoloski et al that the Becke's exchange functional can not
accurately evaluate the weak bonding interaction because of its erroneous
asymptotic behavior at low density (19,20). The results from MPW1PW91
did better job of calculation. The Cp-Tl bond lengths using MPW1PW91 without
the relativistic potential is off by about 0.066 A. This is
a good value since many Gaussian 98 DFT calculations of heavy metal complexes
without relativistic potential often over estimated the bond length by
about 0.1 A. The REPs relativistic potential, however,
did not work well with these systems.
The ADF calculation using
Zora relativistic gave the Tl-Cp(centroid) bond length closest to the experimental
value.
NEXT STEP
The next important
step is to verify the existence of these weakly bound complex structures
experimentally. The structural investigation of these complexes using
a microwave spectroscopy should give new insights and spectroscopic informations
about the physical properties and dynamics of internal rotations associated
with these systems. The study should give us some new insight about
the chemical reactivity of Cp-Tl.
ACKNOWLEDGEMENTS
Dr. Stephen G. Kukolich for his guidance
Dr. Michael Barfield for his help with Gausssian technicalities
Dr. Phil Christiansian for his help with REPs relativistic effective potential
Dr. Dennis Lichtenberger for introducing various computational methods
Dr. Matt Lynn for his help with ADF
TA: Mauricio Cafiero for his help with Gaussian technicalities
Chakree Tanjaroon
Email: ctanjaro@u.arizona.edu