On the basis of the most recently reported spectroscopic data on vibrational modes in TeCl4 and structural parameters of TeCl4, an estimation of its main force constants complemented with the calculation of mean amplitudes of vibration in a wide temperature range have been performed. Also thermodynamic functions for the ideal gaseous state of the molecule calculated, using the statistical mechanics approach.Facultad de Ciencias ExactasCentro de Química Inorgánic

Barán, Enrique José

Zeitschrift für Naturforschung A

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Vibrational Properties of Tellurium Tetrachloride
Enrique J. Baran
Centro de Química Inorgánica (CEQUINOR/CONICET. UNLP). Facultad de Ciencias Exactas. 
Universidad Nacional de La Plata. C. Correo 962. 1900-La Plata. Argentina
Reprint requests to Prof. E.J. B.; Fax: (054) 0221 4259485; E-mail: baran@quimica.unlp.edu.ar
Z. Naturforsch. 60a, 408-410 (2005); received March 2. 2005
On the basis of the most recently reported spectroscopic data on vibrational modes in TeCfi and 
structural parameters of TcCIq. an estimation of its main force constants complemented with the 
calculation of mean amplitudes of vibration in a wide temperature range have been performed. Also 
thermodynamic functions for the ideal gaseous state of the molecule calculated, using the statistical 
mechanics approach.
Key words: TeCQ: Force Constants; Mean Amplitudes of Vibration; Thermodynamic Functions.
The gas phase infrared and Raman spectra as well 
as the corresponding spectra in Ar and N2 matrixes of 
TeClq have been reported more than thirty years ago by 
Beattie et al. [1]. However, the vibrational description 
remained incomplete since only seven of the nine fun­
damental vibrations can be found in these studies. The 
vibrational assigmnent of this molecule was only com­
pleted recently, performing a new measurement of the 
gas phase IR spectrum, complemented by an ab initio 
molecular orbital calculation at the MP2 level [2],
Using the spectroscopic and structural data reported 
in this study, we have now performed the calculation 
of the most important vibrational properties and ideal 
gas phase thermodynamic functions of this molecule.
The molecular geometry of TeClq is consistent with 
VSEPR theory [3], It can formally be derived from 
the sp3d hybridization of the central atom, with the 
lone pair occupying one of the equatorial positions 
of the trigonal pyramidal arrangement. The computed 
geometrical parameters are the following: Te-Cleq = 
2.13 A; Te-Clax = 2.441 A; Cleq-Te-Cleq = 100.2° and 
Clax-Te-Clax = 176.6° [2], The large space require­
ment of the electronic lone pair is shown by the Cleq- 
Te-Cleq angle less than 120° and by the tilt of the axial 
chlorines towards the equatorial ones, as well as by the 
longer axial bonds. Notwithstanding, and as discussed 
below, an alternative approach, based on a well-known 
empirical semi-ionic model, may be more adequate for 
a better description of the Te-Cl bonds.
In order to attain a wider insight into the bond char­
acteristics we have made an approximate calculation of 
the principal force constants, using the valence force 
field proposed by Siebert for Y2XZ2 molecules of C2v 
symmetry [4], but neglecting coupling effects between 
species of the same symmetry. The results are shown 
in Table 1. In this table, f refers to Te-Cl bonds, f to 
bond/bond interactions. fa to Cleq-Te-Cleq and fp to 
Clax-Te-Clax angles.
As it can be seen from the data presented in Table 1. 
the Te-Cl equatorial bonds are appreciable stronger 
than the axial ones, in agreement with the estimated 
greater length of these last bonds. The value estimated 
for the Te-Cleq bond compares reasonably well with 
that calculated for the Te-Cl bonds in the pyramidal 
TcCF cation(2.27 mdyn/A) [5],
Using these calculated force constants for the two 
types of Te-Cl bonds it is possible to make a rough es­
timate of their bond orders, using the empirical method 
of Siebert [5,6], This calculation shows that the equa­
torial bonds present a bond order of about of 1.2, 
whereas the axial bonds are weaker with a bond or­
der of only 0.8, pointing also to substantial differences 
in the bond strength and characteristics of both bond 
types.
These results are in agreement with the semi-ionic 
three center-four electron (3c-4e) bond model [3,7,8], 
In the frame of this model, the equatorial Cl atoms are 
bound by regularly localized two center-two electron 
(2c-2e) bonds via sp2 hybridized orbitals on the cen­
tral atom, with the lone pair on the remaining lobe of 
this hybrid orbital. Then, the axial F atoms must be 
in 3c-4e bonds, using the remaining p orbital of tel­
lurium, and generating more ionic and weaker bonds 
[9.10],
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E. J. Baran • Vibrational Properties of TeC14 409
Table 1. Approximate force constants (in mdyn/A) for TeCL.
/(Te-Cleq) /(Te-Clax) /'(Te-Cleq) /'(Te-Clax) fa .fß
2.39 1.48 0.30 0.0 0.20 0.04
Table 2.
TeCl4.
Calculated mean .amplitudes of vibration (in A) for
T(K) "Te-Cl(eq) "Te-Cl(ax) "Cl...Cl(eq:) HCl...Cl(ax) HCl(eq)...Cl(ax)
0 0.0400 0.0448 0.066 0.057 0.079
100 0.0401 0.0454 0.071 0.058 0.089
200 0.0427 0.0502 0.086 0.065 0.111
298.16 0.0470 0.0567 0.101 0.074 0.132
300 0.0471 0.0568 0.101 0.074 0.132
400 0.0519 0.0636 0.115 0.083 0.151
500 0.0566 0.0699 0.128 0.092 0.168
600 0.0612 0.0759 0.140 0.100 0.183
700 0.0656 0.0816 0.150 0.107 0.198
800 0.0697 0.0869 0.161 0.114 0.211
900 0.0737 0.0919 0.170 0.121 0.224
1000 0.0774 0.0967 0.179 0.127 0.236
Table 3. Statistical thermodynamic functions (in cal/deg mol) 
ofTeCl4.
T(K) CP
100 16.86 11.81 56.83 68.65
200 22.07 15.86 66.38 84.24
298.16 23.90 18.25 73.20 91.45
300 23.92 18.29 73.31 91.60
400 24.70 19.81 78.79 98.60
500 25.09 20.83 83.33 104.16
600 25.31 21.56 87.20 108.76
700 25.45 22.11 90.56 112.67
800 25.54 22.53 93.54 116.08
900 25.60 22.87 96.22 119.09
1000 25.64 23.14 98.64 121.79
1100 25.68 23.37 100.86 124.23
1200 25.70 23.57 102.90 126.47
1300 25.72 23.73 104.79 128.53
1400 25.74 23.87 106.56 130.43
1500 25.75 24.00 108.21 132.21
For a wider characterization of the tellurium­
chlorine bonds, we have also calculated the mean am­
plitudes of the vibrations of TcCT 4. These calculations 
were performed with the method of characteristic vi­
brations of Muller et al. [11] (cf. also [12,13]). The 
obtained results, in the temperature range between 0 
and 1000 K, are shown in Table 2.
The results of these calculations are in excellent 
agreement with the calculated force constants and with 
the discussed bond characteristics, as the equatorial 
bonds present lower mean amplitude values than the 
axial ones, in the full temperature range. On the other 
hand, and in agreement with the coimnented simi­
lar value of the force constants, the Te-Cl bond in 
the Ted;, cation presents an identical mean ampli­
tude value (0.047 Á at 298 K) [12] as for the Te-Cleq 
bonds.
A comparison with the octahedral TcCL,1 2 3 anion, 
also containing Te(IV), is interesting too. The force 
constant of 1.20 mdyn/Á calculated for the Te-Cl 
bonds in this case [14] immediately shows weaker 
bonds than in Ted 4. Consequently, the mean ampli­
tudes of vibration of TcCT r,2 are also relatively higher 
(0.0484 Á at 0 K and 0.0649 A at 298 K [14]) than 
those of both types of Te-Cl bonds in TcCT 4.
[1] I.R. Beattie, O. Bizri, H. E. Blayden, S.B. Brum- 
bach, A. Bukovszky, T. R. Gilson, R. Moss, and B. A. 
Phillips, J. Chem. Soc. 1974, 1747.
[2] A. Kovacs and R. J. M. Konings. J. Mol. Struct. 
410/411,407(1997).
[3] J. E. Huheey. E.A. Keiter, and R. L. Keiter, Inorganic
Finally, we have calculated the thermodynamic 
functions in a wide temperature range, for the ideal 
gaseous state (unit fugacity) using the rigid rotator, har­
monic oscillator approximation [15,16], The moments 
of inertia were calculated with the MOLDRAW pro­
gram [17], The symmetry number is 2.
The results, specific heat (Cp). reduced enthalpy 
[(H° —Ho°)/T], reduced free enthalpy [(G° — Ho°)T] 
and entropy (S'0), in the temperature range between 
100 and 1200 K, are presented in Table 3.
To conclude, these calculations provide a wider in­
sight into the vibrational properties of TcCT 4. an in­
teresting representative of the rather uncoimnon XY 4- 
type molecules, containing a central heavy metal atom, 
and possessing C2,, symmetry.
Acknowledgements
Tins work was supported by the Universidad Na­
cional de La Plata (Project 11/X339) and the “Consejo 
Nacional de Investigaciones Científicas y Técnicas de 
la República Argentina”. The author is a member of 
the Research Career of this organism.
Chemistry. Principles of Structure and Reactivity, 4th 
Ed., Harper-Collins, New York 1993.
[4] H. Siebert, Z. Anorg. Allg. Chem. 275, 210 (1954).
[5] H. Siebert, Anwendungen der Schwingungsspektro­
skopie in der Anorganischen Chemie, Springer, Berlin 
1966.
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410 E. J. Baran • Vibrational Properties of TeCLj
[6] A. Fadini and F. M. Schnepel. Schwingunsspektro- 
skopie. Methoden. Anwendungen. Thieme. Stuttgart 
1985.
[7] G. C. Pimentel. J. Chem. Phys. 10. 446 (1951).
[8] R.E. Rundle. J. Am. Chem. Soc. 85. 112 (1963).
[9] O. J. Curnow. J. Chem. Educ. 75. 910 (1998).
[10] E. J. Baran. Z. Naturforsch. 56a. 333 (2001).
[11] A. Müller. C. J. Peacock. H. Schulze, and U. Heidborn. 
J. Mol. Struct. 3.252 (1969).
[12] A. Müller. E. J. Baran, and K. H. Schmidt. Characteris­
tic Mean Amplitudes of Vibration; in: Molecular Struc­
tures and Vibrations (Ed. S. J. Cyvin). Elsevier. Ams­
terdam 1972.
[13] E. J. Baran. An. Asoc. Quim. Argent. 61. 141 (1973).
[14] M.N. Avasti and M. L. Mehta. Z. Naturforsch. 25a. 
566 (1970).
[15] K. S. Pitzer. Quantum Chemistry. Prentice Hall. New 
Jersey 1953.
[16] G. Allen and H. O. Pritchard. Statistical Mechanics and 
Spectroscopy. Butterworths. London 1974.
[17] P. Ugliengo. D. Viterbo, and G. Chiari. Z. Kristallogr. 
207. 9 (1993).
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Vibrational properties of tellurium tetrachloride

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Vibrational properties of tellurium tetrachloride

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