Ramaswamy, K.

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Indian J. PkyB. 49,1-6 (19'76)Unique force field for boron trihalidesK. Ramaswamy and L. J ayaramanDepartment of Physics, Anmmalai University, Anmmalainagar, Tamil Nadu 608101,(Received 24 June 1974, revised 5 September 1974)An attempt has been made to fix the unique Ibrce field for the de­generate species of boron trihalidos through parametric representa­tion method using isotopic frequencies and observed Coriolis coupling constants. The parameter <j> was found to bo 26°16', 14^ " and 9" for BFg, BCI3 and BBrg respectively. Other molecular constants like mean amplitudes of vibration, Coriolis coupbng constants and rota­tional distortion constants wore also calculated.1 . IntroductionEvaluation of potential enei’gy matrix (F) making use of a set of observed vibra­tional frequencies alone has posed a problem since for N  values of A (— there exist N(N-\-1)/2 solutions for force constants. To isolate the true F matrix, the different kinematic methods (Herranz & Castano 1966, Torkington 1949, Strey 1967, Billes 1966) have been proposed. For the unique determination of the force field additional data like the Coriolis coupling constants (Duncan & Mills 1964a), moan amplitude of vibration (Morino et al 1960), rotational distor­tion constants (Duncan & Mills 1964b) and infrared band intensities (Levin 1970) are generally used. The use of isotopic data in conjunction with Green’s function (DeWamos et al 1964a, 1964b, 1966, Ramaswamy & Rangarajan 1971, Rama- swamy & Shanmugam 1972) and or the parametric methods (Jordanov & Nikolova 1972a, 1972b, 1972c, Ananthakrishnan & Aruldhas 1972) have also been widely used.In the present paper BY3 (Y =  F, Cl, Br) planar type molecules (D^ point group) have been taken for a general study of these methods with a view to fix the unique force field. Force constants for the (1x1) species A^ and Ag can be determined directly from the observed frequencies by a first degree secular equation. The parametric representation of Jordanov Si Nikolova (1972a, 1972b, 1972c) and Ananthakrishnan & Aruldhas (1972) were used to get unambiguous force constants for the degenerate species e. Other molecular parameter’s like mean vibrational amplitude, Coriolis coupling constants and rotational distortion constants were also calculated for these boron trilrolides. The vibrational frequencies, bond lengths and Coriolis coupling constants used in the presentK. Ramaswamy and L. JayaramanoaloulationB are summarized in table 1 along with the referonoes from which they are taken.Table 1. Vibrational frequencies (om"^), bond lengths (A) and Coriolis coupling constants for some XYg planar type moleculesCoriolisMolecule Vo Vg Bond length couplingA constant886 1481.9 485.461.2115 -0 .8 1 ± 0 .0 2 < '888 1428.8 483.74 -0 .8 0 9 “471 993.7 2431.73iiBCla 471 964.2 243282.6 856 1651.87282.5 819 165» Ladd et al (1963); Duncan (1964);  ^ Qinn ct al (1970).2 . T h EOBETIOAL CONSXBEBATIONSFor an N  dimensional problem, jV(Y-—1)/2 free parameters are neces»sary to achieve a unique solution for 0. T]\o c]?,oice of the parameter differs in various methods. The F  and G matrices are goAT^ erned by the relation ,andF ^  L-^AL \G ^ L  L( 1 )(2)A matrix — VT'  ^ was constructed using F, the eigen Abactor matrix and T, the eigen value matrix of 6-. This matrix is related to the true L  matrix by tho relationL — ^0^7 (3)wJt,ere A is an orthogonal matrix. For N  ^ 2 ,  we need a single parameter and hence tli,e matrix A is given bycos 0 “Hiii0sin0COS0(4 )JordanoA'' & Nikolova (1972a, 1972b, 1972c) fixed the A  matrix by using the iso­topic frequencies as additional parameter. They expressed the force constant matrices F  and F^ of two isotopic species by the relationsUnique force field for boron trihalides F =  Lo-^AAAL^~^and=  4 - 1* A*A*A*L„-^*.Tho Born-Oppenheimer approximation {F = F*) yields A* =  A {Ln-^*)AAA{Lf'^Lo*)A*.... (5 ) . . .  (6)... (7)Th(’ asterisk stands for the isotopic molociilo. Assuming A “ A*, A* was calculated for various values of ^ ranging from 0 to 180 .^ A graph was drawn between <f> and the calculated isotopic frequencies. The intersection of the frequency curves ^vith the experimental values plotted as straight lines parallel to the abscissa were taken as the true value of ^ to represent the A matrix. Force constants were calculated for the boron trihalides from relation (5) and the results arc given in tables 2 and 3.Table 2. Symmetrized force constants (mdyn/A) of BF3 calculated by differentmethods.Method Parameter<!>F a?Jordanov & Nikolova 27°16' 8.8459* 6.9240 0.5032 -0.5300Using :-0.81:i:0.02 25° 15' 8.8459 6.5439 0.5194 -0.3938: -0.809 25nS' 8.8459 6.5548 0.6190 -0.3970Most probable value 26°16' 8.8459 6.7642 0.5129 -0.4717Ginn et al (1970) — — 6.683±0.05 0.609b±0.002 -O .377drO.O2• This number of significant figures is retained to aoeuro internal consistency in cal­culations.Table 3. Valence force constants (mdynik) of BFg, BCI3 and BBPg.ValenceforceconstantsBF3 BCI3 BBrsPresentworkDeWames et al (I960)PresentworkDeWames et al (1966)PresentworkDeWames et al (1966)fa 7.4580* 7.1478 3.7612 3.7881 3.1291 3.0669faa 0.6939 0.8378 0.4096 0.4192 0.2683 0.3445fda 0.1572 0.1064 0.0661 0.0677 0.0749 0.0614raa -0 .3 1 4 4 -0 .2 1 2 8 -0 .1 3 0 3 -0 .1 3 6 4 -0 .1 4 9 7 -0 .1 2 2 7f a a -0 .1 7 0 8 -0 .1 7 6 8 -0 .0 7 6 6 -0 .0761 -0 .0 6 6 6 -0 .0 6 7 9f a 0.3416 0.3617 0.1612 0.1623 0.1333 0.1368^ As undsr table 2,Witii a proper A matrix, tho relations governing (f> and  ^ values arc tan (f) — (*^ 33 ^44)!*^ u  ^44) I*— Clil)4 K. Ramaswamy and L. Jayaramanandtan (p =('^ 33- ^ 44)^^34lb[^34’^ (*^33 9^3)(*^ 44~“ 3^8)1^(*^ 44 ^^33)(8)(9)witli J ~ L^  ^  ^ where C is the matrix (Meal & Polo 1956) which depends031 the mass and geometry of the moleculcj. For planar type molecules, the eJemonts of tho C matrix areC33 =  3/2/«^ : ^  (3/2/ta;H-/ty); /ix.These valm^s are essentially the same as the one reported by liristianson & Cyvin (1963). Using the observed f  value of Duncan (1964) and Ginn el al (1970) the solution of <p was fixed from relation (8). The force constant matrix F  was cal- eulated from relation (5) and the results are given in table 2.The mean vibrational amplitudes, Coriolis coupling constants and rotational distortion constants werci calculated from the well kxiown relations of Cyvin (1959), Meal & Polo (1956) and Kivolson & Wilson (1952, 1953) and the results are given in table 4,Table 4. Mean amplitudes of vibration (A), Coriolis coupling constants and rotational distortion constants (cm~ )^ of BF3, BCI3 and BBrg.MolociulfiMeanamplitudes of vibrationCoriolis coupling constants Botational distortion constants X 10-'  ^(cm-^)o*A'-r(A) D j D k D jkBP, 0.0430* 0.789 -0 .7 8 9 2.8515 1.9972 -4 .8 5 0 0(0.0431)» (-0.809)fr (4 x l0 -'')‘* (2 x 10- ’^ )'^BCl, 0.060 0.881 -0 .8 8 1 0.2991 0.2192 -0 .4 9 0 0(0.060) ( -0 .8 7 4 ) ‘>BBr, 0.0515 0.940 -0 .9 4 0 0.0419 0.0298 -0 .0 6 7 7(0.0518)« (-0 .903 )c« Cyvm (1969o);  ^ Ginn et al (1970); c Kriatianaen & Cyvin (1963);  ^ Ginn et al (1908).* As under table 2.3. DiscussionLadd et al (1963) in their attempt to fix unique force constants for the E  species have drawn a graph between F33 and a function of y?, incorporating theUnique force field for boron trihalides 5force oonataiits of “ 5 7 ,  and and chose P,, corresponding to a minimumvalue. The remaining force omisfcants and wero calculated from the force constant ellipses drawn between ^^ 34 and F^  ^ and F^ .^ Lindeman & Wilson (1956) fixed the force constants of BF^ by transferring the potential constants from other related molecules to the one in question. DeWames et al (1964a, 1964b, 1966) used the isotopic frequencies as the additional parameter and there­by fixed tho force field through Green’s function analysis. Duncan (1964) and McKean (1966) fixed the force field of BF^ by drawing a graph between F^  ^ and 7^ 33, i 4^4 and C44 and chose the correct set corresponding to the inteo-section of the calculated £ curve with the observed values. Ananthala‘isji.nan k  Anildlxas (1972) fixed the force constants for BF^ in the parametric representation using the observed f  value.Fig. 1. Plot of frequency va* of BFg versus the angle 0 for tho degenerate species of tho isotopic pair °^BFa and ^^ BFg.Plot of frequency v^ * of BFg versus the angle tp for the degenerate species of the isotopic pair “^BFa and “ BFg.In calculating the force constants of BF^ by Jordanov & Nikolova’s (1972c) method, using relation (7) A* and honoe v* was calculated. Graphs were drawn between and v,* and and shown in figure 1 , Jt is seen from the gra i^h that6 K. Ramaswamy and L* Jayaramanthere are two .-golutionsi for <f> correBpotiding to the intoriaection of the calculated and obfiijrvod iRotopic frcqucnoieR. The mean values are 27°15' and 170°. Using these twa) values for 0, A matrix was constnicted and force constants were calculated from relation (5). Tt was found that the B-F  band force constant calculated using 0 — 170° leads to abnormal values for BF  stretching force constant.Duncan (1904) computed as — 0.81:£0.02 by comparing the calculated band contour with, tlu  ^ observed one. Using this ?44 tl\e* parametfjr 0 was calculat(id from relation (8) and it w as found to be 25°15'. Subsequently Ginn et al (1970) reported a value of —0.809 for ?44 from the \\ band analysis. The value of 0 obtained for — —0.809 was 25°18'. A mean value of 0 — 26°10' whioli, will reproduce both the isotopic frequencies and the Coriolis coupling constants was chosen to represent the correct parameter 0 for BF. .^ With this value of 0 — 2G°K)', the F matrix elements (F.^  ^— 0.7642 mdyn/A; F»  ^— —0.4717 mdyn/A; F^  ^— 0.5125 mdyn/A) obtained arc in good agi'eemont with the values {F^ .^  — 0.08 mdyn/A; .F,,^  ^  —0.37 mdyn/A: F^^ — 0.509 mdjux/A) reported by Ginn ft al (1970).The moan amplitudt^ of vibration (0.0430 A) calculated for the B-F  bond at 0 26“10' is in agreement with the value. (0.043 A) rey)ortcd by Cyvin (1969c).The Coriolis coupling constant .789) is in agreement with the value(—0.809) observed by Ginn ft al (1970). TJu' rotational distortion constants (Ihc -  1.9972x10^'^ cm“ ;^ 7ijK - —4.85x10"" cm~ )^ are in good agreement Avith the values (Djc — 2x10 "’ em~ ;^ Dju — — 5xl0~’ cm~ )^ reported by Ginn ct al (1908).Utiing relation (7), A* and hence v* way calculated for BCI3. Since tlioro IB no change in the bending frequency due to isotopic substitution the graph was drawn between 0 and alone and is shown in figure 2. It is seen from tlui figure that there are two solutions for (j> corresponding to the observed value of the isotopic frequency. The two solutions ai'e 14° and 170°30\ The value of (j> =  14° has boon taken as th.o true solution for this molecule. As seen from table 3 the valence force constants calculated for <j> =  14° are in good agreement with the reported work of DeWames et al (1966). The bonded mean amplitude vibration (0.050 A) ejaculated for BCI3 compares well with the value (0.050 A) n^ported by Oyvin (1969c) and the electron diffr action value of (0.045^0.003 A) Hedberg (1966). The Coriolis coupling (jonstant calculated for the degenerate species E —0.881) is in good agreoirKuit with th,e value (^ 44— —0.874)given by Kristiansen & Cyvin (1963).Unique force field for boron trihalides 73. of (Voqijoncy M3’ of BHi’y versus tho angle (fi lor tho dogonorate spccios of theI’y aiulPor BBrgA* and hence v* was calculated from relation (7). A graph was drawn between (f> and vg* and it is shown in figure 3. I t was found that the isotopic frequencies wore reproduced at 0 =  9° and 175°. Tho value of 0 =  9° represents the true state of affair for this molecule and the I’orce constants were calculated at 0 =  9° from relation (5) and tho results are given in table 3. As seen from table 3 tho valence force constants are in general agreement with the work of DeWames et al (1966). The calculated moan amxditudo of vibration (0.0515 A) and the Coriolis coupling constant (^ 44 =  —0.940) are in agreement with the values (0.0518 A) and (^ 44 =  —0.903) reported by Cyvin (1969c) and Kristiansen & Oyvin (1963), respectively.K .  E a m a s w a m y  a n d  L .  J a y a r a m a nAOENOWIjEDGMBITTOne of th,e authors (L.J.) is thankful to the Council of Scientific and Indus­trial Besearch, Government of India, New Delhi for the award of a Junior Research Fellowship.BErEHENOESAnanthaki'ishiian T. R. & Aruldhas 0 . 1972 J. Mol. ISirml. 13, 163.BilloB F. 1900 Acta, Ohim. Acad. Set. Hung. 47, 53.Cyvin S. J. 1969 S'pectrochim Acta 15, 828.Oyvin S. J. 1969 Kgi. Norsko Viclenskab, SolBkabs Skrifier No. 1.DeWamoH R. E., Base G. D., Lynds L. & Wolforam T. 1964a J. Chem. Fhys. 40, 3611. HoWamcH R. E. & Wolfram T. 1964b J. Chem. Phys. 40 853.DoWamos H. E., BaBs, C. P ., Lyiids L, & Wolfram T. 1960 Bull. Chem, Boc. Japan  39, 201. Duncan J. L. & Mills I. M. 1964a Spectrochim Acta. 20, 1089.Duncan J. L. & Mills 1. M, 1964b Spectrochim Acta. 20, 523.Duncan J. L. 1964 J. Mol. Spectrosc. 13, 338.Ginn S. G. W., Brown 0. W., Konnoy J. K, & John Ovorond 1968 J. Mol. Spectrosc. 28, 509. Ginn S. G. W., Dorothy Johanson & John Overend 1970 J. Mol, Spectrosc. 36, 448.Hodbr3i*g K. 1966 Trans. A jh. Crystallogr. Assoc. 2, 79.Horranz J. & Castano F. 1966 Spectrochim Acta. 22, 1966.Jordanov B. & Nikolova B. 1972a J. Mol. Struct. 13, 21.Jordanov B. & Nikolova B. 1972b J. Mol. Struct. 15, 7.Jordanov B. & Nikolova B. 1972c J. Mol. Struct. 15, 19.Kivolson D. & Wilnon Jr. E. B. 1952 J. Chem. Phys. 20, 1575.Kivelson D. & Wilson Jr. E. B, 1953 J. Chem. Phys, 21, 1229.Kristiansen L. & Cyvin S. J. 1963 J. Mol. Spectrosc. 11, 185.Ladd J. A., Orville-Thomas W. J. & Cox Bortmin C. 1963 Spectrochim Acta. 19, 1911. *Levin I. W. 1970 J. Chem. Phys. 52, 2783.Lindeman Louis F. & Kent Wilson M. 1956 J. Chem. Phys. 24, 242.McKean D. C. I960 Spectrochim Acta. 22, 269.Meal J. H. & Polo S. R. 1956 ,7. Chem, Phys, 24, 1119.Morino Y., Nakamura Y. & Takao Ijima 1960 J. Chem, Phys. 32, 043.Ramaswomy K. & Rangarajan S. 1971 Spectroscopic Molecular 20, 1.Ramaswamy K. & Shanmugam G. 1972 Acta Phys. Folonica. 42A, 635.Stroy G. 1967 J . Mol. Spectrosc. 24, 87.Torkington P. 1949 J. Chem. Phys. 17, 1026.

Unique Force Field for Boron Trihalides

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Unique Force Field for Boron Trihalides

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