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Force constants, coriolis coupling constants and mean amplitudes of vibration of GaF63− and FeF63−
421 Journal of iviolecrdar Structwe, 15 (1973) 42 1424 0 Elsevier Scientific Publishing Company, Amsterdam
- Printed in The Netherlands
FORCE CONSTANTS, CORIOLIS COUPLING CONSTANTS AMPLITUDES OF VIBRATION OF GaF, 3- AND FeF, 3B. B. SRIVASTAVA, Department A.
AND
MEAN
A. K. DUBLISH
of Physics, Meerut
Unioersity,
Meerut
(India)
N. PANDEY
Department
of Physics,
Meerut CoNege, Meerut (India)
(First received 8 May 1972; in final form 9 October 1972)
ABSTRACT
The force constants, Coriolis coupling constants and mean amplitudes of vibration at 0, 298.16 and 500 K for GaFe3 - and FeFb3- have been reported for the first time employing recent vibrational data. The results are discussed in the light of available information.
INTRODUCTION
So far only a few spectroscopic studies have been made for the complex fluorides of the type A,MF, in which the metal atom M is in octahedral, or approximately octahedral, coordination. Recently Weighardt and Siebert’ reported the fundamental vibrational frequencies with their assignments, on the basis of octahedral symmetry for hexafluoroanions, of gallium and iron. The anions belonging to 0, point group give rise to six fundamental vibrational frequencies. The fundamental frequencies vr(ar,J, vz(eg) and vs(fi,) are Raman are infrared active while the vg($&) is forbidden in active and v3(fiu) and v&J both. Since the vibrational frequencies of these systems are now available, it was thought worthwhile to compute the molecular parameters like force constants, Coriolis coupling constants and mean amplitudes of vibration which have not yet been reported. ‘The results will be helpful in the interpretation of the rotationvibration spectra oi‘ the present species. Wilson’s GI; matrix method2 was employed to evaluate the force constants using general quadratic potential function. The constants, in turn, were used to calculate the Coriolis coupling constants c3 and & forf,, xfi, by Cyvin’s method3. The mean amplitudes of vibration were calculated for bonded as well as for non-bonded atom pairs at 0,298.16 and 500 IS. The 2 x 2 determinant of species f,, consisting of three unknowns were solved by Peacock and Miiller’s procedure4.
422 TABLE
I
VIBRATIONAL CONSTANTS
Symbol
(in cm-‘),
WAVENUMBERS OF GaFs3-
GaFG’-
AND
FeFG3-
FORCE
(in mdyn/A)
CONSTANTS
GQPF
GaFs3-
FeF,
3-
“1
525
511
fr
1.863
I.731
1'2
358
368
Lr
0.275
0.235
1’3
455
v‘s 1’5
385 266 188.1
447 268 252 178.2
f,, J&-&n f,f,... &-&, f,.-f&p
0.121 0.172 0.34, 0.072 0.073
0.255 0.09 0.20 0.011 0.01,
v6
AND
CORIOLIS
COUPLING
FeFs3-.
Ea. g-s
GaFe’-
FeF6’-
0.353
0.405
0.147
0.095
The fundamental frequencies employed in the present computation are listed in Table 1.
RESULTS AND
DISCUSSION
The results of the force constant computations and Coriolis coupling constants are presented in Table 1. The valence force constants used here are:f,, the bond stretching constant for the metal-halide bond;f,,, the constant for the interaction between a bond being stretched and an adjacent bond;&, the constant for interaction between a bond being stretched and a bond opposite to it; f,,, the interaction constant between an angle and one of the bond forming its side; f,,,., the interaction constant between an angle and a bond in its plane but not forming one of its sides; f,, the bending force constant; f,, the interaction constant between an angle and an adjacent angle in the same plane; f,,, the interaction constant between an angle and an angle when one bond is common to both bending pairs and others are opposite; fadl,,, the interaction constant between an angIe and an angle in the adjacent plane butwith no bond in common, andy,..,, the interaction constant between an angle and an angle when bending angles are opposite to each other. c3 and c4 are Coriolis constants forf,, xfr,, typeFrom Table 1 it can be observed that all the force constants except &of GaFe3- are greater than those of FeFG3- wh.ich shows that the interaction between opposite bonds is larger in transition metal fluoroanions compared to that in the non-transition metal fluoroanions. The ratio of the interaction constants& for the fluoride anions considered in the third oxidation state is 1-l corn-pared to 2.9 in the case of the hexafluoroanions5 in the fourth oxidation state. From comparison of the stretching force constants in the transition metal hexafluoroanions belonging to first transition series, MnF6’- (2.97 mdyn/A), FeFs3-
423 (1.73, mdyn/A) and NiF, 2- ( 3. 18, mdyn/A), it is found that there is no regular variation with increase in the number of d electrons, therefore it is inferred that the fluoride anions of the metal in the fourth oxidation state are more stable than those in the third oxidation state. The mean amplitudes of vibration for bonded as well as for non-bonded atom pairs at 0, 298.16 and 500 Kare summarized in Table 2. It can be seen from TABLE 2 VIBRATIONAL
MEAN
AMPLITUDES
Distance
F
Fe_ _ F
OF
Temperature (K)
M-F F__.
(in A)
0 298.16 500 0 298.16 500 0 298.16 500
(linear) (non-linear)
GaFs3-
AND
FeFe3-
Mean amplitudes GaF63-
FeFs3-
0.05 11 0.0583 0.0693 0.0666 0.0778 0.0935 0.0737 0.0954 0.1176
0.0525 0.0598 0.07 11 0.066 1 0.0768 0.0921 0.0779 0.1046 0.1300
this table that the mean amplitudes of vibration for bonded and non-bonded atom pairs are in the order M-F -c F - - - F (linear) -C F - - - F (non-linear). The mean amplitude values, corresponding to bonded atom pairs increase with decrease in atomic weight of the central atom as well as with the decrease in the number of d electrons while the respective force constants show the opposite trend. It will be interesting to compare the mean amplitude values in the isoelectronic series GaFe3-, GeFe2-, As F,-, and SeF, . The values are listed in Table 3. TABLE
3
COMPARISON
OF
MEAN
AMPLITUDES
OF
VIBRATION
(itI
A)
FOR
MF6”-
AT
Fhoroanions
M-F
Distance F.. . F (linear)
F---F (non-linear)
GaF,“GeFe2AsFsSeFs FeFs 3RuFs OsFs MnFe2NiFs2-
0.0583 0.0478 0.0428 0.0399 0.0598 0.0405 0.0385 0.0485 0.0466
0.0778 0.0643 0.0570 0.0533 0.0768 0.0551 0.0527 0.0639 0.0623
0.0954 0.0889 0.0812 0.0717 0.1046 0.0939 0.0907 0.0989 0.0964
ROOM
TEMPERATURE
The mean amplitude values of other systems are taken from the literature6. It is observed from this table that the mean amplitude corresponding to respective atom pairs are in decreasing order as one proceeds from low to high atomic weights. It is also noticeable that the values decrease with the decrease of charge on the fluoroanions. From this variation it is inferred that as one moves from a more ionic bond to a covalent bond the mean amplitude values decrease. In other words, the mean amplitudes are smaller for stronger bonds. Such an observation has also been reported in literature for other chloro, bromo and iodo species. Comparison of vibrational amplitude values from Table 3 for FeFS3-, RuF6 and OsF,, where the central atoms belong to the samecolumn of the periodic table, shows that the value decreases from Fe to OS. The mean amplitude values show no regular variation for the series MnF62-, FeFc3and NiF,‘where the central atoms belong to the same row of the periodic table as is also evident from the discussion of the force constants. The mean amplitudes increase with rise in temperature as is expected.
ACKNOWLEDGEMENTS
The authors wish to thank Prof. Dr. A. Miiller, University of Dortmund, Germany for constant encouragement and Prof. S. J. Cyvin for helpful comments. They also thank Prof. Dr. S. P. Khare for providing the necessary facilities in the department of Physics, Meerut University, Meerut.
REFERENCES 1 K. WEIGHARDT AND H. SIEBERT, J. Mol. Strttcture, 7 (1971) 305. 2 E. B. WI~N JR., D. C. DECIUSAND P. C. CROSS,Molecular Vibratiotzs, McGraw-Hill, New York, 1955. 3 S. J. CYVIN, Molecular Vibrations and Mean Square Amplitudes, Elsevier, Amsterdam, 1968. 4 C. J. PEACOCKAND A. MOLLER, J. Mol. Spectrosc., 26 (1968) 454. 5 V.K. GUPTA,RAMBABU,A.N.PANDEYANDZ.H.ZAIDI, IndianJ.PureAppLPhys., inpress. 6 B. P. SINGH, A. N. PANDEY AND H. S. SINGH, Indian J. Pure Appt. Phys., 8 (1970) 193.
- Printed in The Netherlands
FORCE CONSTANTS, CORIOLIS COUPLING CONSTANTS AMPLITUDES OF VIBRATION OF GaF, 3- AND FeF, 3B. B. SRIVASTAVA, Department A.
AND
MEAN
A. K. DUBLISH
of Physics, Meerut
Unioersity,
Meerut
(India)
N. PANDEY
Department
of Physics,
Meerut CoNege, Meerut (India)
(First received 8 May 1972; in final form 9 October 1972)
ABSTRACT
The force constants, Coriolis coupling constants and mean amplitudes of vibration at 0, 298.16 and 500 K for GaFe3 - and FeFb3- have been reported for the first time employing recent vibrational data. The results are discussed in the light of available information.
INTRODUCTION
So far only a few spectroscopic studies have been made for the complex fluorides of the type A,MF, in which the metal atom M is in octahedral, or approximately octahedral, coordination. Recently Weighardt and Siebert’ reported the fundamental vibrational frequencies with their assignments, on the basis of octahedral symmetry for hexafluoroanions, of gallium and iron. The anions belonging to 0, point group give rise to six fundamental vibrational frequencies. The fundamental frequencies vr(ar,J, vz(eg) and vs(fi,) are Raman are infrared active while the vg($&) is forbidden in active and v3(fiu) and v&J both. Since the vibrational frequencies of these systems are now available, it was thought worthwhile to compute the molecular parameters like force constants, Coriolis coupling constants and mean amplitudes of vibration which have not yet been reported. ‘The results will be helpful in the interpretation of the rotationvibration spectra oi‘ the present species. Wilson’s GI; matrix method2 was employed to evaluate the force constants using general quadratic potential function. The constants, in turn, were used to calculate the Coriolis coupling constants c3 and & forf,, xfi, by Cyvin’s method3. The mean amplitudes of vibration were calculated for bonded as well as for non-bonded atom pairs at 0,298.16 and 500 IS. The 2 x 2 determinant of species f,, consisting of three unknowns were solved by Peacock and Miiller’s procedure4.
422 TABLE
I
VIBRATIONAL CONSTANTS
Symbol
(in cm-‘),
WAVENUMBERS OF GaFs3-
GaFG’-
AND
FeFG3-
FORCE
(in mdyn/A)
CONSTANTS
GQPF
GaFs3-
FeF,
3-
“1
525
511
fr
1.863
I.731
1'2
358
368
Lr
0.275
0.235
1’3
455
v‘s 1’5
385 266 188.1
447 268 252 178.2
f,, J&-&n f,f,... &-&, f,.-f&p
0.121 0.172 0.34, 0.072 0.073
0.255 0.09 0.20 0.011 0.01,
v6
AND
CORIOLIS
COUPLING
FeFs3-.
Ea. g-s
GaFe’-
FeF6’-
0.353
0.405
0.147
0.095
The fundamental frequencies employed in the present computation are listed in Table 1.
RESULTS AND
DISCUSSION
The results of the force constant computations and Coriolis coupling constants are presented in Table 1. The valence force constants used here are:f,, the bond stretching constant for the metal-halide bond;f,,, the constant for the interaction between a bond being stretched and an adjacent bond;&, the constant for interaction between a bond being stretched and a bond opposite to it; f,,, the interaction constant between an angle and one of the bond forming its side; f,,,., the interaction constant between an angle and a bond in its plane but not forming one of its sides; f,, the bending force constant; f,, the interaction constant between an angle and an adjacent angle in the same plane; f,,, the interaction constant between an angle and an angle when one bond is common to both bending pairs and others are opposite; fadl,,, the interaction constant between an angIe and an angle in the adjacent plane butwith no bond in common, andy,..,, the interaction constant between an angle and an angle when bending angles are opposite to each other. c3 and c4 are Coriolis constants forf,, xfr,, typeFrom Table 1 it can be observed that all the force constants except &of GaFe3- are greater than those of FeFG3- wh.ich shows that the interaction between opposite bonds is larger in transition metal fluoroanions compared to that in the non-transition metal fluoroanions. The ratio of the interaction constants& for the fluoride anions considered in the third oxidation state is 1-l corn-pared to 2.9 in the case of the hexafluoroanions5 in the fourth oxidation state. From comparison of the stretching force constants in the transition metal hexafluoroanions belonging to first transition series, MnF6’- (2.97 mdyn/A), FeFs3-
423 (1.73, mdyn/A) and NiF, 2- ( 3. 18, mdyn/A), it is found that there is no regular variation with increase in the number of d electrons, therefore it is inferred that the fluoride anions of the metal in the fourth oxidation state are more stable than those in the third oxidation state. The mean amplitudes of vibration for bonded as well as for non-bonded atom pairs at 0, 298.16 and 500 Kare summarized in Table 2. It can be seen from TABLE 2 VIBRATIONAL
MEAN
AMPLITUDES
Distance
F
Fe_ _ F
OF
Temperature (K)
M-F F__.
(in A)
0 298.16 500 0 298.16 500 0 298.16 500
(linear) (non-linear)
GaFs3-
AND
FeFe3-
Mean amplitudes GaF63-
FeFs3-
0.05 11 0.0583 0.0693 0.0666 0.0778 0.0935 0.0737 0.0954 0.1176
0.0525 0.0598 0.07 11 0.066 1 0.0768 0.0921 0.0779 0.1046 0.1300
this table that the mean amplitudes of vibration for bonded and non-bonded atom pairs are in the order M-F -c F - - - F (linear) -C F - - - F (non-linear). The mean amplitude values, corresponding to bonded atom pairs increase with decrease in atomic weight of the central atom as well as with the decrease in the number of d electrons while the respective force constants show the opposite trend. It will be interesting to compare the mean amplitude values in the isoelectronic series GaFe3-, GeFe2-, As F,-, and SeF, . The values are listed in Table 3. TABLE
3
COMPARISON
OF
MEAN
AMPLITUDES
OF
VIBRATION
(itI
A)
FOR
MF6”-
AT
Fhoroanions
M-F
Distance F.. . F (linear)
F---F (non-linear)
GaF,“GeFe2AsFsSeFs FeFs 3RuFs OsFs MnFe2NiFs2-
0.0583 0.0478 0.0428 0.0399 0.0598 0.0405 0.0385 0.0485 0.0466
0.0778 0.0643 0.0570 0.0533 0.0768 0.0551 0.0527 0.0639 0.0623
0.0954 0.0889 0.0812 0.0717 0.1046 0.0939 0.0907 0.0989 0.0964
ROOM
TEMPERATURE
The mean amplitude values of other systems are taken from the literature6. It is observed from this table that the mean amplitude corresponding to respective atom pairs are in decreasing order as one proceeds from low to high atomic weights. It is also noticeable that the values decrease with the decrease of charge on the fluoroanions. From this variation it is inferred that as one moves from a more ionic bond to a covalent bond the mean amplitude values decrease. In other words, the mean amplitudes are smaller for stronger bonds. Such an observation has also been reported in literature for other chloro, bromo and iodo species. Comparison of vibrational amplitude values from Table 3 for FeFS3-, RuF6 and OsF,, where the central atoms belong to the samecolumn of the periodic table, shows that the value decreases from Fe to OS. The mean amplitude values show no regular variation for the series MnF62-, FeFc3and NiF,‘where the central atoms belong to the same row of the periodic table as is also evident from the discussion of the force constants. The mean amplitudes increase with rise in temperature as is expected.
ACKNOWLEDGEMENTS
The authors wish to thank Prof. Dr. A. Miiller, University of Dortmund, Germany for constant encouragement and Prof. S. J. Cyvin for helpful comments. They also thank Prof. Dr. S. P. Khare for providing the necessary facilities in the department of Physics, Meerut University, Meerut.
REFERENCES 1 K. WEIGHARDT AND H. SIEBERT, J. Mol. Strttcture, 7 (1971) 305. 2 E. B. WI~N JR., D. C. DECIUSAND P. C. CROSS,Molecular Vibratiotzs, McGraw-Hill, New York, 1955. 3 S. J. CYVIN, Molecular Vibrations and Mean Square Amplitudes, Elsevier, Amsterdam, 1968. 4 C. J. PEACOCKAND A. MOLLER, J. Mol. Spectrosc., 26 (1968) 454. 5 V.K. GUPTA,RAMBABU,A.N.PANDEYANDZ.H.ZAIDI, IndianJ.PureAppLPhys., inpress. 6 B. P. SINGH, A. N. PANDEY AND H. S. SINGH, Indian J. Pure Appt. Phys., 8 (1970) 193.