THERMODYNAMIC PROPERTIES OF IODINE PENTAFLUORIDE 871
Potential Constants and Thermodynamic Properties of Iodine Pentafluoride
By G. NAGARAJAN
Department of Physics, Annamali University, Annamalainagar, South India (Z. Naturforschg. 17 a, 871—874 [1962] ; eingegangen am 10. November 1961)
An orthonormalized set of symmetry coordinates satisfying the transformation properties has been constructed for the iodine pentafluoride molecule having the tetragonal pyramidal structure
with the symmetry point group Cjv . Utilising these symmetry coordinates and a potential function consisting of the ordinary valence force terms and central force terms, the elements of potential and kinetic energy matrices have been obtained. From the observed RAMAN and infrared funda- mental frequencies the potential constants and thermodynamics properties such as heat content, free energy, entropy and heat capacity have been calculated for a rigid rotator, harmonic oscillator approximation.
BRAUNE and PINNOW 1 obtained electron diffrac- potential constants on the basis of WILSON'S group tion patterns of Iodine pentafluoride from which theoretical method7 and the calculation of thermo- they concluded that its structure was probably a tri- dynamic properties such as heat content, free energy, gonal bipyramid with the point group D-3h . This entropy and heat capacity for the ideal gaseous state conclusion has been questioned on the basis of more at one atmospheric pressure for different tempera- recent electron diffraction experiments by BOGERS, tures using a rigid rotator and harmonic oscillator WAHRHAFTIG and SCHOMAKER 2. The RAMAN and in- approximation. frared absorption spectral studies were carried out 3 by LORD and his coworkers proposing the C4V 1. Symmetry and Selection Rules model for IF5. This model has four fluorine atoms On the basis of the tetragonal pyramidal struc- in a square, with the iodine atom and the fifth ture, the Iodine pentafluoride molecule is character- fluorine atom on the four fold axis normal to the ised by three symmetry axes (X, Y, Z) of which square and perfectly agrees with the structure pre- the Z axis is perpendicular to the plane of the dicted by GUTOWSKY and HOFFMAN 4. Further, the tetragon and passing through the iodine and the C4V model is in accord with expected bond hybridi- fluorine atoms, two vertical planes of symmetry zation of d2p3 orbitals. Moreover, PAULING 3 has (2 av) each containing the iodine atom and three pointed out that in atoms with an unshared pair of fluorine atoms and two diagonal planes of symmetry electrons, the unshared pair tends to "occupy" one (2 0(j) each containing one atom of iodine and one of the corners of the coordination polyhedron as though to replace the shared pair of the bond, and that for a central atom with five bonds and one un- shared pair, the five bonds should be directed to- ward the five corners of a square i. e. the structure should be C4V. Recently, BAUER 6 also by the elec- tron diffraction study has confirmed the Cjv model for Iodine pentafluoride molecule.
The assignment of the vibrational frequencies given by LORD and his coworkers 3 has been taken in the present investigation for the evaluation of
1 BRAUNE and PINNOW, Z. phys. Chem. B 35, 239 [1937]. 5 L. PAULING, The Nature of Chemical Bond, Cornal Univer- 2 ROGERS, WAHRHAFTIG and SHOMAKER, Abstracts, Atlantic city sity Press, Ithaca, New York 1940, p. 110. meeting, American Chemical Society, April 1947. 6 S. H. BAUER, J. Phys. Chem. 56, 343 [1952]. 3 R. C. LORD, M. A. LYNCH JR., W. C. SCHCMB and E. J. SLO- 7 E. B. WILSON JR., J. Chem. Phys. 7, 1047 [1939] ; 9, 76 WINSKI, J. Amer. Chem. Soc. 72, 522 [1950], [1941]. 4 H. S. GUTOWSKY and C. J. HOFFMAN, J. Chem. Phys. 19, 1259 [1951]. 872 G. NAGARAJAN atom of fluorine (Fig. 1). ordinary valence or central force type potential func- From the characters and other relevant features tions. In order to describe the Iodine pentafluoride of the point group C4V for this molecule it is seen molecule more realistically and at the same time that the expected modes of vibration are nine of keep within the number of independent force con- which three come under A, species and active both stants, potential functions are made up of terms in RAMAN and infrared absorption spectra, two come representing possible important interactions taken under BJ species and active in BAMAN but inactive from the general potential function. It is not found in infrared, one comes under B2 species and active possible to describe the Iodine pentafluoride mole- in RAMAN but inactive in the infrared and three cule by such a potential function. Direct interactions come under E species and active both in RAMAN and of the central force type between the terminal atoms infrared absorption spectra. are then investigated. It is found that a potential function consisting of the ordinary valence terms 2. Symmetry Coordinates and two additional terms representing central force type interactions between the nonbonded fluorine Thirteen internal coordinates are taken to de- atoms best describes the Iodine pentafluoride mole- scribe the twelve vibrational degrees of freedom cule. Such a potential function has been taken here and they are the changes in the interbond distances for the evaluation of valence as well as nonbonded AD, Ad,, Ad,, Ad3 and _lo?4 and the changes in force constants. the interbond angles AS,, A&2 . AS3 , AS4 , A R, = AD, #2= (Ad, + Ad2 + Ad3 + Ad4)/2, gon, fq representing the force between the nonbond- R3 = (A&, + A&2 + A63 + A&4- A®, - A$2 ed fluorine atoms in the tetragonal plane, fq' re- presenting the force between nonbonded fluorine -A^-A&JIV8, atom of the tetragonal plane and fluorine atom of R0 = (A&, + A&2 + ASs + AQ4 + A4>, + A&2 the symmetry axis and several stretching-stretching, + A Ro = (A&,- A(P2 + A , For the B2 type vibration, F12 = 2(fDd + A 0B'0f'q), R1= (AS,-AS2 + AS3-ASi)/2. F,3 = V2D DUE - foe) ~V2 A'QC'Q F'Q, 2 2 For the E type vibrations, F22 = fd + 2 fdd + fdd+(A0 + B0) fq + Bo f'q , F23 = d (fde + fd0 — 2 fdO ~ fde~~ i fd 3. Potential Energy For the B , type vibrations, Fn = fd-2 fdd + f'dd + (A0 - Bo) 2Jq + Bo2 /;, It has been a matter of general experience that F\2 = d (fdo ~ 2fd0 + fd0) + Bq CO fq, fluorine-bearing molecules cannot be described by F22 = d2 (/ 0— 2 f00 + f For the B2 type vibration, AQ= (D-d cos &) fq'; 2 2 F\I = d {f Q — 2 fe@ + /©©) + CQ fq; Co = G? (sin 0) fq; For the E type vibrations, B'0= (d-D cos 0) fq'; 0 Fu =fd-idd + (Al + Bpfq + B'0f,q, and C' = D d (sin Q) fq'. The potential function adopted here is very simi- Fit = d(f d the case of COF2 molecule. 2 F22 = d (f 0 — J®®) + C0- /9 , F23 = C?2 (/ — f00), 4. Kinetic Energy ^33 = d2{fe — fee) + Co fa; 5 where The G matrix elements are as follows: For the type vibrations, fy = Mi' ^0 = 50 = (/(l — cos ©)fq; Gn = iUF + /*I» G12 = 2 Hi cos 0, G1S = V2 ¡uT {sin 0 sin 0 - 2 (1 - cos 0) cos 0}/ (J sin 0), £22 = /¿F + /-¿i (1 + 2 cos 0 + cos 2 0), £23 = -pI {2 1/2 sin 0(1 - cos 0) (1 + 2 cos 0 + cos 2 0) -sin 0(1-cos 0) (1 + 2 cos 0 + cos2 $+4 cos 0) }/(2 c/ sin 0 sin 0), £33 = ^1 {sin2 0(1-cos 0)2 (5 + 8cos 0 + 2 cos 0 + cos2 0) + 4 sin2 ^(l-cos 0)2(1 + 2 cos 0 +cos2 0) -4 sin 0 sin 0(1-cos 0) (1- cos 0) (1 + 2 cos 0 + cos2 0 + 4 cos 0) }/(2 d2 sin2 0sin2 0) + {sin2 0 sin2 0+2 sin2 0(1 + 2 cos 0 - 2 cos2 0) - 4 sin 0 sin 0 cos 0 (1 - cos 0) + sin2 0(1+2 cos 0 + cos 2 0 -4cos2 0) }/(2 d2 sin2 0 sin2 0); For the type vibrations, Gli=pF + pi(l -2 cos 0 + cos2 0), G12= -^(1 - COS 0) (1 -2 cos 0 +cos 2 0)/((f sin 0), C22 = /^F/C?2 + M F (1 ~ 2 cos 0 + cos 2 0) / ( For the B2 type vibration, Gn = 2 (1 — cos 2 0)/ (d2 sin2 0); For the E type vibrations, G11 = ^F + /ii(l-cos2 0), G12= -jui(l-cos 0) (1 — cos 2 0) / ( G13= — /¿j(1 — cos 0) (1 — cos 2 0) / (e? sin 0), G22 = juF/d2 +11 F (1 - cos 2 0) / (if2 sin2 0) + ^ (1 - cos 0)2 (1 - cos 2 0) / (d2 sin2 0), G23 = //Fcos 0(1 -COS 0)/(G?2 sin 0 sin 0) + /¿i(l -cos 0) (1 -cos2 0) (1 -cos 0) /(d2 sin 0 sin 0), G33 = 2 /¿F/CT2 + 2 /¿I (1 — cos 0)2 (1 — cos 2 0) / (d2 sin2 0) where G\j = G-}{, d is the distance between iodine and fluorine atoms, is the reciprocal mass of fluorine atom and jui is the reciprocal mass of iodine atom. The secular equations for the various irreducible representations can now be constructed by applying the usual principles 7. 5. Results 275 cm"1 (Bx), 572 cm"1 (B2), 645 cm"1 (E), 375 cm"1 (E) and 192 cm"1 (E). The molecular The fundamental frequencies given by LORD and parameters given by LORD and his coworkers 3 are his associates3 for IF5 occur at 710cm-1 (Ax), as follows: 1 1 1 693cm" (Aj), 317cm- (Aj), 605 cm" (Bx), 0 = 86° 12', 0=105° and F> = d=1.75A. It is not possible to evaluate all of the force con- 8 R. J. LOVELL, C. V. STEPHENSON and E. A. JONES, J. Chem. Phys. 22, 1953 [1954]. stants and hence most of the interaction constants 874 THERMODYNAMIC PROPERTIES OF IODINE PENTAFLUORIDE 874 have been neglected. The obtained valence force The repulsion constant fq in the tetrahedron of IF5 and nonbonded force constants are given in Table 1. is not much deviated from the value of the constant fq in the pentagonal plane of IF7. Similarly the repulsion The repulsion constants and the distances of the constant fq is also similar to that of the value of the two fluorine atoms are given in Table 2. When the constant fq in IF7. obtained force constants were introduced in the equations it was found that the calculated frequen- cies were in good agreement with those of the ob- 6. Thermodynamic Properties served values. The force constants of IF7 are also given in Table 1 for comparison. The heat content, free energy, entropy and heat capacity were calculated for 15 temperatures from Iodine Iodine 100° to 1300 °K using the fundamental frequencies Constant pentafluoride heptafluoride * given by LORD and his associates 3. A rigid rotator, harmonic oscillator model was assumed and the ID 3.696 3.490 fd 3.324 3.003 values were calculated for the ideal gaseous state U 0.449 0.501 at one atmospheric pressure. Nuclear spins and iso- 0.282 0.322 fq topic mixing were neglected. Using the molecular 0.403 0.252 fe 0.251 0.213 parameters given above the moments of inertia for fOD 0.226 IF5 are as follows: fdd 0.652 0.582 fdd 0.154 Ixx ^ Izz = 182.2727 AWU A2 fd 0.139 fee 0.159 0.082 (302.7785 xl0~40 gem2) and f Table 1. Force constants in 105 dynes per cm of IF5 and IF7 . The symmetry number used for this calculation is 4. The values for the thermodynamic properties of IF5 Repulsion constant are given in Table 3. Molecule Distance in A in 105 dynes per cm. IFs 2.392 0.449 ~(Fo-E°0) 2.777 0.282 T{° K) (.H0-E°0)/T S° c; IF7 2.145 0.501 T 2.581 0.322 100 9.05 40.41 49.46 11.83 200 12.27 47.64 59.91 18.91 Table 2. The repulsion constant and the distance of the two 273.16 14.58 51.81 66.40 22.70 fluorine atoms. 298.16 15.30 53.11 68.42 23.70 300 15.36 53.22 68.58 23.77 It is seen from the Table 1 that the I-F stretching 400 17.84 57.99 75.83 26.56 force constant f in the tetrahedron is less than that of 500 19.77 62.20 81.97 28.19 d 600 21.26 65.91 87.16 29.18 the axial I-F stretching constant in iodine penta- 700 22.43 69.27 91.70 29.82 fluoride. Similarly the I-F stretching constant in the 800 23.36 72.27 95.63 30.25 girdle is less than that of the axial I-F stretching con- 900 24.16 75.11 99.27 30.56 stant in the case of IF7. The axial I-F stretching con- 1000 24.81 77.66 102.47 30.79 stant in IF5 is slightly greater than that of the axial 1100 25.37 80.13 105.51 30.96 I-F stretching constant in IF7 and the I-F stretching 1200 25.84 82.36 108.20 31.09 1300 26.25 110.74 31.19 constant in the tetrahedron of IF5 is also slightly 84.49 greater than that of the I-F stretching constant in the Table 3. Heat content, free energy, entropy and heat capacity girdle of IF7 . of Iodine pentafluoride for the ideal gaseous state at one The fluorine-iodine-fluorine bending constant f& in atmospheric pressure. T is the temperature in degrees Kelvin, the tetrahedron is slightly greater than that of the -1 -1 the other quantities are in cal deg mole and E0° is the fluorine (tetrahedron) - iodine - fluorine (axial) bending energy of one mole of perfect gas at absolute zero temperature. constant in IF5 . The stretching-stretching interaction constant fdd in the tetrahedron of IF5 is similar to that of the stretching- The author expresses his heartful thanks to Dr. K. stretching interaction constant fdd in the girdle of IF7 . VENKATESWARLU for his encouragement during the pro- The bending-bending interaction constants fee and gress of this work and to the University Grants com- of IF5 are greater than that of the values of the mission, Government of India for the award of a Post- respective constants in IF7 . Graduate Research Scholarship.