The vibrations of borazine derivative—I the planar vibrations of borazine and N-trideuteroborazine

SpectrochimicaActa, 19(}7. Vol. 25A, pp. 2021 to 2028. PergamonPress Ltd. Printedin Northern Ireland

The vibrations oi borazine derivatives--I The planar vibrations of borazine and N-trideuteroborazine* E. SrLSER~_XX~ Molecular Spectroscopy Laboratory Buenos Aires University, Per~ 222 Buenos Aires, Argentina

(Received 7 November 1966) A b s ~ a c t - - T h e infra-red spectrum of HaBaNaH s has been measured with 0.5 c m -I resolution over the 4000-250 c m -I region, and with lower resolution to 10,000 c m -1. Complementing the data with the known R a m a n active frequencies and those of the HaBaNaD s infra-red spectrum, a normal co-ordinate treatment has been made. Using only one non-zero off-diagonal force constant (in s y m m e t r y c o - o r d i n a t e s ) , a better than 1 per cent agreement w i t h all the observed frequencies has been obtained, except for the N H bending mode, for which a 3 per cent discrepancy cannot be eliminated b y any reasonable value of the other interaction terms. The significance of the n e w force constants in terms of the electronic structure of borazol is discussed. ~NTRODUCTIOYW

I~ the course of a research programme on the physico-chemical properties of borazine and borazarene derivatives and on their possible use as neutron scintillators [1], we felt the necessity to have a reliable set of force constants for the basic molecules, in order to use them in the assignment work of the complicated derivatives. On the other hand, b orazine "is one of the most interesting of the boron hydrides" [2], and in spite it is known to be a planar molecule with Dan symmetry and lEoelectronic with benzene, the characters of the bonds and the charge distribution have recently been the subject of very contradictory reports [3, 4]. The knowledge of the force constants and the band intensities could be helpful for the elucidation of such problems. The only published force field calculation for borazine was made by CRAW~ORD and EDSAT,T, [2] and was based on their own infra-red and Raman spectra; they used a simple valence-force potential function which gave an unavoidable discrepancy of more than 10 per cent in one of the ring vibrations. PRICE et aZ. [5], u s i n g a b e t t e r prism spectrometer, r e - e x a m i n e d t h e i n f r a - r e d spectrum, made small corrections to the Crawford and Edsall fundamentals, and were able to measure and assign 34 overtones and combination bands. WATANABE * A preliminary report of this work was presented at the Ohio State University Symposium, June 1964. t Present address: Fisk University, Infrared Spectroscopy Institute, Nashville, Tennessee 37203, U.S.A. [1] G. V. V I D ~ A et al, Int. J. Appl. Radiation Isotopes 15, 611 (1964). ~2] B° L. CRAW'FORD,JR. and J. T. EDSALL, J. Chem. Phys. 7, 223 (1939). [3] D. W. DAWES, Trans. Faraday Soc. 56, 1713 (1960). [4] R. HOFFMAN, J. Ghem. Phys. 40, 2474 (1964). [51 W. C. PRICE, R. D. B. FRASER, T. S. ROBINSON and H. C. LONOUET-HIGGINS, Dittccta~on@ ~araday Soc. 131 (1950). 2021

2022

E. SrLB~.R~A~

et al. [6] used the Crawford and Edsall force constants in order to calculate t h e

distribution of potential energy among the internal co-ordinates for each normal mode of vibration of borazine and N-tricloroborazine. B u t the same authors [7] later obtained the spectrum of N-trideuteroborazine, which proved that the Crawford and Edsall assignments of the B H and N H bending vibrations, in plane as well as out of plane, had to be interchanged; moreover, a calculation of frequencies using Crawford and Edsall's force constants yields discrepancies of 13, 18 and 30 per cent, respectively, for the planar ring, B H bending and N D bending vibrations of the isotopic molecule. At that point it seemed worthwhile to us to re-examine the spectrum of borazine with a high resolution grating spectrometer, to explore the region behind 400 cm -1 (which was the limit in the previous works), to make approximate measurements of integrated intensities and to carry out a more general normal co-ordinate treatment, with the aim of having a better agreement between the observed and calculated frequencies. EXPERIMENTAL

Borazine is a very reactive substance. In order to be sure that the weaker bands of the spectrum did not belong to impurities or to products of polymerization, decomposition or chemical reactions with the stopcock grease, samples prepared b y three different ways were stored in the infra-red cell for about 20 days each, and the constancy of the spectrum verified during that period. The first two samples were prepared and purified b y G. J. Videla and M. A. Molinari (from the Argentine A.E.C.) starting from B-trichloroborazine (reduced with lithium borohydride and aluminium borohydride, respectively) and the third b y J. Lombardo (from Buenos Aires University) starting from diborane and ammonia. Due to the intensity ratio of 1 : 1400 between the strongest and weakest fundamental absorption bands, which increases to 1:10,000 if combination bands are taken into account, a wide range of pressures had to be used. A 10 cm gas cell with CsI windows was connected to a gas handling device which made possible to expand the sample b y a factor of approximately 2, and to re-evacuate the expander b y condensing its content in a cold finger at liquid nitrogen temperature. The pressure was in this w a y changed in 11 steps between 175 and 0.15 tort., and the sample completely recovered. The spectrum between 4000 and 400 cm -1 was run at each pressure with a Beckman I R 9 spectrophotometer at standard resolution (approx 1.5 cm-1), both in linear transmittance and absorbanees scales; at 175 tort the spectrum from the u.v. to 4000 em -1 was run with a Beckman DK2, and from 400 to 230 cm -1 with said I R 9 equipped with the CsI interchange. Figure 1 shows the spectrum between 4000 and 230 em -~ at the indicated pressures. Every band was then run again with higher resolution (0.3-0.5 cm -~) at the optimum pressure and the wavenumber of the absorption peaks were measured to ±0.25 cm -~. In addition to the maximum absorbance of all the bands, the approximate [6] H. WATANABE, ]~I. I~ARISADA, T. NAKAOAWA a n d M. KUBO, Spectrochim. Acta 16, 78 (1960). [7] H. WATA~ABE, T. TOWA~I, T. NAKAOAWAand M. KUBO, Spectrochim. Acta, 16, 1076 (1960).

The vibrations of borazine derivatives--I

2023

a p p a r e n t i n t e g r a t e d intensities o f t h e f u n d a m e n t a l s were d e t e r m i n e d f r o m the area u n d e r t h e c u r v e in t h e linear a b s o r b a n c e - l i n e a r w a v e n u m b e r spectra. I n order to eliminate t h e pressure, w h i c h was our less a c c u r a t e m e a s u r e m e n t , the relative ~0 0

~I

~!

:~~

i

~

i

i

Ir,

i ji

I: 0 4000

5600

3200

2800

2400

2000

4800 t600 t400 WAVENUMBER (cm- I )

4200

~000

800

600

400

200

Fig. 1. Infra-red spectrum of borazine. Approx spectral slit-width: 1.5 em-1. Pressure in ram of mercury: 4000-230 cm-1 curve = 175, A = 3, B = 3, C = 1, D = 6, E = 13. intensities o f pairs of b a n d s in the same s p e c t r u m were determined, a n d all the results were expressed as percentages of the i n t e n s i t y o f ~14. ASSIGNMENTS The a s s i g n m e n t s of the f u n d a m e n t a l b a n d s b y WATANABE et (~. [7] were a d o p t e d e x c e p t for small changes resulting f r o m our more a c c u r a t e m e a s u r e m e n t s a n d ext e n d e d range. T h e bigger shifts o c c u r r e d for: (1) their ~la a t 1605 cm -1, where we did n o t find a n y a b s o r p t i o n p e a k ; t h e r e are t w o n e i g h b o u r i n g b a n d s a t 1625.0 a n d 1587.5 cm -1, a n d we decided t o a d o p t t h e l a t t e r as ~la because it is the s t r o n g e r one, a n d since t h e first could easily be assigned to the s u m m a t i o n of t h e s t r o n g vls a n d ule f u n d a m e n t a l s ; (2) their 415 em -1 b a n d , assigned b y Crawford a n d Edsall t o t h e o u t - o f - p l a n e v i b r a t i o n vl0, w h i c h showed to be, w h e n t h e s p e c t r u m was e x t e n d e d b e y o n d 400 cm -1, t h e / ~ b r a n c h o f a b a n d whose Q b r a n c h is located a t 393.0 cm -1. Table 1 s u m m a r i z e s our m e a s u r e m e n t s of frequencies a n d intensities, as c o m p a r e d Table 1. Infra-red active fundamental frequencies of borazine P~ee Symm.

This work

v

Wavenumber

Peak int.

W'avenumber

E'

11 12 13 14 15 16 17

3490 2530 1605 1465 918 718 519

100 30 0.1 100 15 5 I

3483.0 2527.0 1587-5 1465.5 918.0 718-0 517.5

A2~

8 9 10

1088 649 415

1"5 2 3

1090.5 650.5 393"0

Peak int. 10 35 0.1 100 55 16 0-1 0-3 0"07 8

Integr. int. 10 50 0.05 100 15 9 0.02 0.04 0"002 10

2024

E. Table

2. Assignment

of the observed

Price

SILBERMAN and

binary

combination

bands

of borazine

This work Assignment and symmetry

v ( c m -1)

Int.

v(em-*)

Int.

-6880 6000

-1.0 0.3

10010 6825 6014

4965

0.3

4975

0.05

4850 4765 -4305 4274 4135 3985

0.3 0.2 -0-5 0.4 0"3 0.6

4859 4771 4430 4335 -4180 3997"0

0.03 0.02 0.08 0.07 -O'07 0.16

-0.5

3762.0 2933.5 2828.0~

8

2816.0/

0.002 0.4 0.03

--0.01 0"01 3 15 20(? 7 10 5 5 0"1 0"4 0"4 0.15 --

2807.0~ 2795.0] 2780.5] -2738'5 2668'0 2588-0 2519"0~ 2488"0) 2406"0~ 2398"0) 2222'5 2157"5~ 2143-5) 2001.5~ 1986.5)

0.01 0.16 2.7 0.04 sh 0.06sh 0.02 sh 0.02 -0"01 0.25 5"0 shon 2527 3"0 3"0 0"14 0"4 0"4 0.17 0.15

-1865

-0'2

1917.0 1862.0

0.09 0.24

1835

--

0.1 -----

1832"0~ 1818.0) 1740"0 1625'0 1579.5

0.13 0.12 0"05 0'06 0-05

1410 -1360

20 -1.0

-

-

2931 2830) 2810~ 2801J --2743 2734 2668 2592 2522 2493 2408~ 2400) 2197 2158 2144 2000 -

-

-

-

--

-

1310 --

0-2 --

1411-5 1400.0 1364.5

1313.0~ 1297.5)

10} 10 3

0.2 0-2

3483 X 3 = 10449 3483 × 2 = 6 9 6 6 3483+2535=6018 3483+2527=6010 3483+1587=5070 2535+2527=5062 2527 X 2 = 5 0 5 4 3483+ 1465=4948

(E') (E') (E')

(E') (E') (E') (E')

(E')

3483+ 1070=4553 3 4 8 3 + 9 1 8 = 4401

(As n) (E')

3483+ 3483+ 2535 + 3483 +

(E') (E') (E') (As H)

718=4201 5 1 8 = 4001 1465 = 4000 288 = 3778

1465 × 2 = 2 9 3 0

(E')

2527+288=2818

(As ~)

1465+1070=2535

(As")

1465+938=2403 1465+ 918=2383 1465+798=2263 1465+ 718=2183 1090+ 1070=2160 1090+ 938=2028 1 0 7 0 + 9 1 8 = 1988 1465+518=1983 1090+851~1941 1587+288=1875 1070+798=1868 918+938=1856 918 X 2 = 1 8 3 6 1465+288=1753 718+ 918=1636 798 × 2 = 1 5 9 6 1070+518=1589 718 × 2 = 1436 918+518=1436 1090+ 288=1378 851+518=1369 1070+288= 1358 938+ 393=1331 798+ 518=1316

(E')

(E') (Aa ~)

(E') (E')

(As") (As") (E') (A~~) (As H)

(E') (E') (E') (As H) (E') (E') (As ~) (E')~F

(E')) (E') (E') (E') (As ~) (A2 ~)

B r a c k e t s i n t h e first a n d t h i r d c o l u m n i n d i c a t e s t r o n g l y o v e r l a p p i n g b a n d s , sh = s h o u l d e r , F = possible Fermi resonance. F u n d a m e n t a l f r e q u e n c i e s (ore-l): A1 t = 851, 938, 2535, 3450; A 2" = u n k n o w n ; E ' = 518, 718, 918, 1465, 1587, 2527, 3483; Az n = 393, 650, 1090; E" = 288, 798, 1070. I n f r a - r e d a c t i v e b i n a r y c o m b i n a t i o n s : A 1" X E', A x" X A2", A 2' × E', E ' × E', E" × E", E" × E n. U n a s s i g n e d b a n d s m a y c o r r e s p o n d t o A 2' X E ' o r t e r n a r y c o m b i n a t i o n s . C a l c u l a t e d c o m b i n a t i o n s w h i c h i n c l u d e Ax t f u n d a m e n t a l s m a y look t o o low b e c a u s e t h a t f r e q u e n c i e s are o n l y k n o w n f r o m l i q u i d s t a t e m e a s u r e m e n t s .

The vibrations of borazino derivatives---I

2025

Table 2 (cont.) Price

This work Assignment

~(cm -1)

int.

~(cm -l)

--0.2 ----

1232.0~ 1212.0~ 1199.0[ 1186.0] 1066.0 1036.0

--

--

1002"0~

986 --

0"5 --0.1 -----

---

1175 ---

--

--

789 -----

and s y m m e t r y

int. sh sh 0.18 0.15 0.02 0.01

851-~ 718-~918-~798 + 7 9 8 -{-

0.16

989"5) 927-5 804"0~ 789-0) 674-5~ 669.0) 559.5~ 550-5J

518

0"2 7 0.17 0.32 0.02 0.025 0.08 0.07

7 1 8 -~6 5 0 -~1090 -5 1 8 -~393 ~1465 -288 1070 --

393 518 288 393 288

~ = = ~ ~

1244 1236 1206 1191 1086

(A**) (E')

× 2 288 288 288 288 288 798 × 2 518

~

1036

(E')

~ ~ ~ ~ ~ ~-~ ~ ~

1006 937 802 807 681 667 576 552

(A~ ~)

(As")

(E') (E')

(E') (E') ( A s n) (E') (As") (E') (A~ ~)

with Price's results, which were up to now the basis for all the discussions on the vibrations of borazine. Overtone and combination bands were assigned for borazine using our infra-red data and CRAWFORD and EDSAT,T,'S measurements of the R a m a n fundamentals (quoted in Table 4). All the active first overtones and combination bands which include the lowest vibrational excited state (288 cm-1), 23 in total, were found among the 56 measured bands, as shown in Table 2. NORMAL CO-ORDINATE AlVALYSIS The geometry and internal co-ordinates of a symmetrically substituted borazine molecule are shown in Fig. 2. The 4A1 ~- 3A 2' ~ 7E' normal vibrations constitute r, ii

% y2

73 ~

II 82

Fig. 2. I n t e r n a l co-ordinates of a symmetrically substituted borazine molecule,

the in-plane modes, of which A 1' and E ' are R a m a n active, only E' is infra-red active, and A S' is inactive in both spectra. The out-of-plane vibrations are of species 3A2" ~ 3E", the first being infra-red and the second R a m a n active.

2026

E. SILBERI~N

A normal co-ordinate treatment, applying WILSON'S FG matrix method [8], was carried out using a MERCURr--FERRANTI computer for the calculation of the {]-matrix elements, the eigenvalues and normalized eigenvectors of the secular equations, the derivatives of the frequencies with respect to the force constants, the potential energy distribution, and t o m a k e a final least squares refinement of the force constants. The following bond distances and angles were used: B - - N ---- 1.44 A, N---It = 1.02 A, all angles ---- 120 °. In addition to the infra-red frequencies measured in the present work, R a m a n data for liquid borazine and infra-red frequencies of gaseous N-trideuteroborazine, as reported b y C~AWFORD and EDSALL [2] and WATANABE I0o,

]

0

I

750

I

I

I

I

I

730 710 WAVENUMBER (¢rn"'1)

I 690

Fig. 3. High resolution run of the 718 em-1 borazine fundamental, showing the 50: 40: 9 : 1 abundance ratio of the four boron isotopio species.

et al. [7], respectively, were used for the adjustment of the force constants. The Jacobian of a first adjustment of a diagonal field based on Crawford and Edsall's force constants (taking in mind Watanabe's changes of assignments) showed t h a t : (1) the similarity of the G elements for the a and fl co-ordinates produces very resembling elements in the Jacobian matrix and prevents the separate adjustment of the corresponding force constants; we made them equal and the proposed value should be considered the average of the real ones; (2) the elimination of the discrepancies in the ring frequencies requires the introduction of the t~tj and ~ifl~ interactions; (3) it is unnecessary or meaningless to introduce the remaining interactions. B y making the latter equal to zero a refinement of the non-zero internal co-ordinateforce constants, except the BN stretchings and their interactions was possible; in fact, a lineal combination of F~ and the F~, t/s m a y be adjusted in the A', species and the values of other two combinations depend principally on ~la and h4 in the E' species, but these three equations are not enough to determine their individual values. Table 3 shows the set of force constants finally adopted and Table 4 the calculated frequencies and their percentual differences with the observed ones; the mean value of this difference amounts to 0.87 per cent. The discrepancy in the N H stretching A 1' frequency is actually much smaller than indicated because the measurement was [8] E. B. W~T.so~, J. C. DECIUSand P. C. CROSS,Molecular Vibrations. McGraw-Hill (1955).

The vibrations Table

3. F o r c e

constants

of borazine

2027

derivatives--I

for borazine

and

l~-trideuteroborazine

BH stretch NH stretch

Fa Fb F¢ + F~ °~ + F, °B + 2Ft "~ + F~~

BN stretch

F t -- ~¿.F~o~ .~- Ft o~) -- F t " ~ Ft~ F t -.t- ~(F~°N ~ Ft °B) -- Pc" -- F¢p

BH bend NH bend BNB bend NBN bend BNB-NBN interaction

Fr F0

3"428 m d y n / . ~ 6.765 m d y n ] . ~ 6.609 m d y n ] A 6.045 m d y n [ ~ 9.897 m d y n / A 0"778 m d y n . A 0"347 m d y n . A

F~} F~

0'957 m d y n .

Fa~ °

A

--0"05 mdyn..~

The notation corresponds to the potential function:

3

3

1

6

1

1

6

2F:~

1,3,5

2,4,6

3

3

3

A Q . At~+~ + 2Ft~ ~

A Q . AQ+s- ~- F~ ~

(A~)~ + FO ~

1

1

3

+

3

+ 1

1

(~,)2

1

3

+ 1

1

made in liquid phase and there is probably a significant gas-liquid shift, which amounts to 40 cm -1 in the corresponding frequency of B-trichloroborazine, as will be reported in the next paper of this series. Table 2 shows that the B H and N H stretching vibrations have anharmonicities of the order of 3 per cent; this number Table 4. Observed and calculated frequencies and percentage differences o f borazine and •-trideuteroborazine

(HBNH)a Symm. A 1'

~

E'

~obs (em -1 )

~calc

diff.

~obs

~ealc

diff.

(era -1 )

(~o)

(e m - I )

(e m - 1 )

(~oo)

3503 2530 944 843

(1.54) * 0-20 0"64 0-94

---

2576 2530 941 812

b

ring ring

3450 2535 938 851

~'H st BH st ring ring BH b l~H b ring

3483 2527 1588 1465 918 718 518

3504 2534 1594 1454 908 738 518

0"60 0"28 0.38 0.75 1-09 2"78 0"00

2607 2527 1589 1436 899 547 509

2583 2533 1575 1444 907 530 509

assign.

1

NH st

2 3

BH st

4 11 12 13 14 15 16 17

(HBND)s

---

--0"92 0"24 0.88 0.56 0-89 3-10 0"00

* See r e m a r k i n t h e S e c t i o n o n n o r m a l c o - o r d i n a t e a n a l y s i s .

gives an order of magnitude for the error with which such frequencies m a y be adjusted using a harmonic potential. REMARKS

AND

DISCUSSIONS

As compared with Price's spectrum, a significant difference derived from our measurements consists in the decrease, by a factor of 10, of the ratio of the intensities of the N H and BH stretching bands, a fact that agrees with a molecular orbital

2028

E. SILBERMA_~

calculation we made in order to elucidate the charge transfer in borazine [9]. The band shapes measured under the higher resolution will be discussed elsewhere, b u t an easily noticeable fact is that most of the fundamentals have half-widths of the order of 30 em -1 and hardly visible P Q R or isotopic structure; the 1XrI-I and B H bendings, instead, give rise to very sharp Q branches which, in the case of the 718 cm -1 band, makes it possible to resolve the complete B 1° isotopic structure. There are four isotopic species of borazine, depending on the number of B 1° atoms that the molecule contains; their relative abundance should be, on statistical reasons, approximately 50:40:9:1 for the species containing 0, 1, 2 or 3 B 1° atoms, respectively. Figure 2 is the high resolution run of the 718 cm -1 fundamental, showing how easily it could be used for the boron isotopic analysis of borazine. The most significant differences between Crawford and Edsall's and our force fields are the interchange of the N H and B H bending force constants and the introduction of interactions between the ring stretehings. The remarkable similarity between the borazine and benzene spectra and force fields (see page 228 of Ref. [2]) led us to investigate the possibility that the values of the ring interactions in borazine could follow one of the patterns that different authors [10-13] have proposed for the same interactions in benzene; all these patterns, based on considerations about how the vibrational deformation of the ring m a y affect the charge distribution of the highly mobile ~-electrons, have in common the ÷ -- + sequence of signs for the ortho, meta and para interactions, respectively. We have found that just this condition, applied to the three equations of Table 3, leads to very improbable values of the force constants and/or to imaginary values of some frequencies of the inactive A 2' species. To be sure, we tried modified U R E r BRADT.~Y force fields using all the above quoted patterns of interactions (p parameters) : all of them proved impossible to yield reasonable adjustments. We think that the main reason for this impossibility lies in the fact that, on stretching a B N bond, the B atom will give back to the N atom part of the electron density originally donated b y the latter in the equilibrium configura%ion. This effect would increase the electron density of the N side of the bond and decrease it on the other one, giving rise to two ortho interaction force-constants (Ft °~ and _Ft°B) of different sign. The meta interactions should be equal b y symmetry reasons, leadiug finally to five different stretch force-constants, which cannot be determined without some additional hypothesis, even if the inactive A2' vibrations would be known. This result should lead to extreme carefulness when using the possible consequences of the "isoelectronie" character of borazine and benzene. Acknowledgements

The author wishes to t h a n k his graduate students C. FAVELUKES and E. ttULER for writing the computer programmes used in the calculations. The spectrometer was purchased through a grant from the Ford Foundation. [9] [10] [11] [12] [13J

M. GLA~BIAOI, M. S. DE GIA~tBIAOIand E. S I T . ~ , R ~ ¢ Theoret. Chim. Acta 5, 435 (1966). S. C~FA-~O and B. CRAW~ORD,JR., Spectrochim. Aeta 16, 889 (1960). J. R. SOHERER and J. OV~REND, Spectroehim. Aeta 17, 719 (1961). J. R. SOHERER, J. Chem. Phys. 36, (1962). W. D. JO~rES, J. Meg. Spectry 10, 131 (1963).