J. Phys. Chem. 1902, 86, 4737-4745
--
4737
-
-
the Sl(?r,a*) So internal conversion is much slower than the Sl(a,?r*) (+AE)S2(n,7r*) T3(7r,7r*) Tl(n,7r*) intersystem crossing:2 aST= 1. In MMA and PMMA, where the energy of S2(n,7r*)is slightly higher than that of Sl(?r,?r*)and the photoreduction occurs, the nonradiative deactivation other than the intersystem crossing is observed. These results indicate that the nonradiative deactivation observed in MMA and PMMA is not the S1(?r,?r*) So internal conversion due to the proximity effect20of Sl(?r,?r*)and S2(n,?r*)but the deactivation to the ground state in the encounter state of photoreduction.
not measured. However, since the temperature dependence of DT in MMA is very similar to that in PMMA, the deactivation mechanism shown in Figure 6 is also applicable to the deactivation of acridine in MMA, even if the rate parameters for MMA are different from those for PMMA. The fact that aF = 5 X lo-, in MMA at 296 K is much less than @JF = 5 X in PMMA at 296 K indicates that the value of (k4 k," + k;) exp(-AE,/RT) for MMA is much larger than that for PMMA. If it is assumed that (k4 + k," + kns) exp(-AE,/RT) >> kf kd k1 + k 2 + k3 exp(-AE,/RT) in the range of 220-296 K, the fact that the value for changes from 0.62-0.70 a t 296 K to unity at about 220 K means that k 4 / ( k 4+ k," + knS) increases with decreasing temperature. This implies that the activation energy of the intersystem crossing through S2(n,?r*)differs from that of the reaction in S2(n,7r*): further thermal activation is necessary for the reaction in addition to the S1(?r,?r*) S2(n,a*)thermal activation. In benzene, where the energy of S2(n,7r*)is very close to that of Sl(a,?r*)and the photoreaction does not occur,
-
+
+ +
Acknowledgment. We thank Mr. F. Kadowaki for the measurement of aFin MMA and Miss C. Iwanaga for the purification of MMA. Financial support by the Ministry of Education, Science, and Culture is greatly acknowledged.
-
~
~~
~~~~
~
(20) Lim, E. C. "Excited States"; Lim, E. C.; Ed.; Academic Press: New York, 1977 Vol. 3, p 305.
Infrared and Raman Spectra and Normal Coordinate Analysis of Boranediamine D. C. Reuter;
L. R. Thorne,t and W. D. Gwinn
Depetiment of Chemlstty, Unlversny of Callfmk,M & y , Callfornle 94720 (Recelved: August 3, 1982)
Vibration transition frequencies obtained from moderate-resolution Fourier transform infrared (FT IR) spectra and low-resolution Raman spectra are reported for l1BH(NH2I2,1oBH(NH2)2, l1BH(ND&, and 1oBH(ND2)2. A force-constant refinement calculation using the observed frequencies allows the normal coordinates for the planar modes of boranediamine (BDA) to be determined in terms of 17 independent force constants. One of the two symmetry types of the out-of-plane normal coordinates is determined in terms of four independent force constants. The accuracy of the force field is tested by its ability to reproduce transition frequencies of 11BD(ND.J2and to reproduce observed centrifugal distortion constants of 11BH(NH2)2 and observed inertial defects of eight isotopically substituted species of boranediamine. The results are most consistent with a planar structure for the molecule. The B-N stretch force constant is found to be 6.0 mdyn/A and the N-H stretch force constant is 6.8 mdyn/8. These results are consistent with a partial double bond for B-N.
Introduction Boranediamine, BH(NH2)2,is the first of the unsubstituted aminoboranes to be isolated in its monomeric forma1 Because of its simplicity, this molecule is an ideal subject for the study of the physical characteristics of the B-N bond in boranamines. In these compounds there is a possibility for partial double-bond character in the B-N bond as a result of electron donation from the lone electron pairs of nitrogen to the vacant boron 2p, orbitals. In BH(NH2)2the amount of double-bond character plays a dominant role in determining the planarity of the molecule and the magnitude of the torsional barrier about the B-N bond. Recently, microwave spectra of eight isotopically substituted species of boranediamine (BDA) were studied.2 Results of this study showed that the rotational transitions of boranediamine do not exhibit the splitting pattern characteristic of molecules undergoing inversion or hindered internal rotation. Furthermore, the small negative *Address correspondence to this author at the following address: NRC/RRA Goddard Laboratory for Atmospheric Sciences, Code 911, NASA/Goddard Space Flight Center, Greenbelt, MD 20771. Present address: Sandia National Laboratories, Livermore, CA 94550.
values found for the inertial defect (Z,- Z, - Zb) indicate that there is a fairly deep minimum in the potential energy curve at the planar position. Finally, if the potential energy functions for either the torsional coordinates or the out-of-plane NH2 bend coordinates were very broad with a minimum at the planar position, effects of vibrational averaging would tend to cause the inertial defect to be large and negative. Therefore, the microwave results indicate that boranediamine is a relatively rigid, planar molecule. Normal coordinate analysis provides a means of verification of these conclusions. Specifically, the B-N force constant will reflect any multiple bonding. A significant double-bond character for the B-N bond is most consistent with a rigid planar molecule. In this study we report the vibrational spectrum of boranediamine as determined by the techniques of Fourier transform infrared (FT IR) spectroscopy and spontaneous Raman scattering spectroscopy. Data from a number of isotopically related species are used to determine an approximate harmonic force field for the molecule. The force constants so determined are extremely useful in developing (1) Briggs, T. S.;Gwinn, W. D.; Jolly, W. L.; Thorne, L. R. J. Am. Chem. SOC. 1978, 100, 7762. ( 2 ) Thome, L. R.; Gwinn, W. D. J. Am. Chem. SOC. 1982,104,3822.
0 1982 Amerlcan Chemical Society
4738
The Journal of Physical Chemistry, Vol. 86, No. 24, 1982
Reuter et al.
TABLE I : Rotational Constantsa for Some Isotopes of Boranediamine isotope
A , MHz
B , MHz
C, MHz
"BH(NH.L
52 383.141 53 154.364 40 069.299 40 991.392
9093.558 9092.563 7426.650 7425.909
1748.191 1711.605 6267.783 6289.4
loBH(NH;); "BH(ND,), 'OBH(ND,),
a qualitative description of the type of bonding in the molecule. The force field may be used to calculate centrifugal distortion constants and inertial defects for the various isotopic forms. These may be compared to the values determined from the microwave data, to provide a check on the consistency of the analysis. Experimental Section Boranediamine was synthesized by using an ammonolysis procedure developed by Briggs,' in which a stream of dry ammonia gas is passed over molten borane monoammoniate, BH3NH3 NH3 + BHsNH3 BH(NH2)2 + Hz (1) Following purification the product was transferred either to the infrared or Raman sample cells or to a sample container cooled to liquid-nitrogen temperature for storage for later use. Unfortunately, since this transferal required heating of the sample and because of the tendency of BDA to polymerize in liquid phase, some decomposition always occurred. Consequently BDA samples always contained detectable quantities of ammonia, one of the decomposition products. The deuterated species of BDA were synthesized by substituting ND, and BH3ND3for NH3 and BH3NH3in reaction 1. This synthesis also yielded BD(ND2I2as part of the product (the totally deuterated species comprised somewhat less then 10% of the product). The details of the synthesis of the various reactants and their precursors are given in ref 3. A Nicolet 7199 Fourier transform infrared spectrometer was used to obtain the infrared spectra in this study. A useful modification of this particular spectrometer is that all the optics are in a vacuum box which can be evacuated to approximately 0.01 torr. This removed most of the interference due to atmospheric C02 and H20. Two sample cells were used in the IR work. The first consisted of a 10-cm Pyrex tube with an inner diameter of 2 in. and cesium iodide windows. This cell was used in the 4oocT400-cm~'region. The second was a 10-cm Pyrex tube with an inner diameter of approximately 4 in. and polyethylene windows and was used for measurements in the 400-50-cm-' region. For the higher wavenumber region a beam splitter composed of Ge on a KBr substrate was used in conjunction with a TGS pyroelectric detector having a KBr window. In the low wavenumber region a 6.25-pm Mylar beam splitter was used with the same type of detector having a thin black polyethylene window. Spectra were recorded with resolutions ranging from 0.5 to 0.125 wavenumber and 200-500 scans were averaged. The sample pressure for the different spectra ranged from approximately 70 to 10 torr. For the gas-phase Raman scattering studies a Jobin Yvon Ramanor HG .25 Raman spectrometer was used. The laser excitation was provided by a Coherent Model CR-2 argon ion laser operated at either 4880 or 5145 A. The latter line was preferred since the slight increase in (3) Thorne, L. R. Ph.D. Thesis, University of California, Berkeley, CA, June 1979.
K
Pb
-0.939 I18
0.173 595 0.169 150 0.185345 0.181158
- 0.942I99
-0.931 431 - 0.934499
scattering intensity expected for the 4880-Aline was more than compensated by the greater power available in the 5145-A line. The sample cell was Pyrex with a square cross section with 1-in. sides and rectangular faces of approximately 2 X 1 in.2 The low scattering intensity of BDA required the use of a multipass mirror configuration. With careful alignment, it was usually possible to obtain 15-20 passes through the sample. Unfortunately, even with multiple passes of the excitation light the intensity of the scattered light was so low that only relatively low-resolution measurements could be made (M-cm-' resolution was about the best that could be obtained). Sample pressures were typically 300-200 torr. Because of the relatively high natural isotopic abundance of loB (loB:l1B 0.25), it was possible to measure some transitions due to 1oBH(NH2)2 and 'OBH(ND,), as well as the more abundant lrB species in both the Raman and infrared studies.
-
Anaylsis of Spectra In general, the rotational fine structure of the vibrational bands for an asymmetric top molecule is extremely complex, showing little regularity in pattern unless the molecule is close to one of the symmetric top limits. The rotational constants for the four isotopic species studied here have been determined from their microwave spectra2 and are given in Table I along with the value of K . Since K is close to -1, the infrared vibrational spectrum will retain some of the overall characteristics of the simpler spectrum of a prolate symmetric top ( K = -1). Because boranediamine has Czusymmetry, each of the infrared transition moments belongs to a different irreducible representation. The form of the rotational structure of a given infrared band will thus depend upon whether the transition dipole moment lies along the a, b, or c principal axis of the molecule. In other words, BDA is not expected to have hybrid fundamental transitions. With the resolution at which this study was carried out it was found that, in fact, the symmetric top model was sufficient for determining the band type and transition frequencies. In particular for P and R wings of A-type bands (B2in CZu),all the subbranches corresponding to a given value of J coalesce into a single spectral feature. The separation between "lines" of different J is between 2B and B C (-0.5 cm-'). Similarly the Q wings form an unresolved bunch near the band center. The type-B bands (A, in C2J were found to consist of a series of equidistant "lines" separated by about 2A (-3 cm-'). These are made up of unresolved Q wings of the subbands. The B-type bands are further characterized by an intensity minimum at the band center. Finally, the type-C bands (B, in Czu) are composed of unresolved Q-wing groups separated by about 2A (-3 cm-') and, since p (Ia/Ib)is relatively large (-0.2), there is a strong intensity maximum at the band center. The distinctive appearance of the various band types greatly aided the assignment of the infrared spectrum. The frequency of the sharp maximum absorbance for A- and C-type bands was taken as the transition frequency for these bands. The transition frequency of the B-type bands was estimated from the minimum in the
+
Analysis of Boranediamine
absorbance between the P and R branches. Band-center frequencies determined in this way are expected to be accurate to about 1 cm-' or better. The highest-resolution data were obtained from a spectrum averaged over 500 scans at 0.125-cm-l resolution and a cell pressure of -10 torr. This was not sufficient to resolve the bands into individual subbands. Attempts to use the maximum resolution available (0.062 cm-') were not successful, due to the fact that the longer times required to obtain a spectrum were so long that the BDA decomposed into, among other things, ammonia. This was probably due primarily to a reaction with residual water on the cesium iodide windows which was not removed even with long periods (>1week) of vacuum pumping. The Raman experiments were undertaken with the intent of measuring the infrared dipole forbidden A2 fundamentals. However, as might be expected, only the transitions corresponding to the totally symmetric A,-type modes were observed. Since the Raman selection rules only allow transitions between levels of the same rotational symmetry, and since AJ = 0 is allowed, a large number of Q wings coincide near the band origin, giving rise to a single relatively narrow spectral feature. The center of this feature was always within 2 cm-' of the measured positions of the infrared lines. A listing of the frequencies of the assigned lines is given in Table 11. The region from 1440 to 1350 cm-I contained at least four and perhaps five separate line centers. From the intensities of these lines, it was apparent that most of these transitions were due to 11BH(ND2)2and that the fundamental transition for this species, which is expected to fall in this region, is heavily perturbed. Therefore the B2 transition 1440.8 cm-' is assigned as 11BH(ND2)2 transition but is included with a low weight in the normal coordinate analysis to follow. Two other cases of strong perturbation were found in the normal species 11BH(NH)2.In both the infrared and Raman spectra the Al line at 1192 cm-l was followed by a line of slightly lower intensity at 1159 cm-'. Both of these lines could not be fundamentals since at most seven Al fundamentals will be observed in boranediamine; furthermore, the intensity ratio indicated that the weaker line was not due to a loB isotopic substitution. Similarly, the A, line observed in the Raman at 938.5 cm-l was paired with a slightly less intense line at 922.1 cm-l. These lines were very weak in the infrared spectrum but were the strongest lines found in the Raman spectrum. If it is assumed that the perturbation is relatively independent of rotational state (as for a Fermi-type resonance) and that the perturbing state would normally have a negligible transition moment, then it is possible to determine approximate unperturbed frequencies from a ratio of the integrated intensities of the lines and the orthonormality of the perturbed wave functions (see, for example, ref 4, pp 215-7). Evidence for the rotational independence of the perturbation comes from the infrared spectrum since the rotational structure of these lines is not different than for other Al-type lines. Furthermore, the Raman spectrum exhibits no appreciable broadening, which is also indicative of a rotationally independent term. Using the first assumption given above, one may write the perturbed vibrational wave functions +,, as a linear combination of two unperturbed basis set functions dl and 42.
(4) Hertzberg, G. 'Infrared and Raman Spectra";Van Nostrand: New York, 1945.
The Journal of Physical Chemistry, Vol. 86, No. 24, 1982 4739 TABLE 11: Observed Infrared and Raman Spectra dipole selection B B B B B B B A A A A A A
symmetry type-
wavenumbers, cm-l infrared
.
llBHf NH.',' L a a
2518.1 1191.7
Ra" 3551.2 3457.8 2516.4 1192.0 938.5 402.0
3555.7 3464.0 1605.3 1393.2 1351.4 832.6 914.3 586.0 422.0
C C C
'OBH(NH2), B B A A B A B B B B B B B A
2537.7 1212.3
a a
1612.0 1430.3 "BH(ND,), a 1515.6 l1BH(N D , ) , 2655 a
2503 1061.9 773.5
1080.4
2654.8 2548.9 2504.3 1263.8 1061.9 775.0 335.8
2658.0 2536.0 1492.8 1440.gb 1033.4 637.0 896.8 477.0 314.7
A A A A
A C C C
a These lines were observed in the infrared but were obThis line appears to be heavily scured by nearby bands. perturbed in the spectrum.
Now when the second assumption above is used, it is seen that the ratio of the integrated intensities of the two transitions will be proportional to the ratio of the squared expansion coefficients of the basis set which has a nonvanishing transition moment: (3) This ratio and the orthonormality condition define the transformation (7') which diagonalizes the Hamiltonian in the basis set: PH,T = H , = E, (4) 11/12
OC
al2/aZ2
where H p is the diagonal Hamiltonian in the J, representation. Now the diagonal elements of H p are given by the measured transition frequencies, E,, and thus the unperturbed energies may be found by using the transformation to obtain H,. Using this procedure, and the integrated Raman intensities (Illg2/11169 = 1.32;IgU/IB2 = 1.87), we found that the
4740
The Journal of Physical Chemistry, Vol. 86, No. 24, 1982
two perturbed lines at 1192 and 1159 cm-' corresponded to unperturbed levels at 1177.2 and 1172.4 cm-', with a perturbation term of 17.3 cm-', while the perturbed transitions at 938.5 and 922.1 cm-' corresponded to unperturbed levels at 932.8 and 927.8 cm-' with a perturbation term of 7.8 cm-'. In the Raman spectrum of "BH(ND,), it was found that only seven A,-type transitions were observed, thus lending credence to the assumption that all the intensity of both pairs of perturbed lines in 11BH(NH2),was due to the fundamental. Since in both cases the higher-frequency transition was found to be more intense, the higher-energy unperturbed levels must correspond to the fundamental. The unperturbed transition frequencies were included in the normal coordinate analysis with a somewhat reduced weight due to uncertainties in the measurement of the integrated intensities. It is interesting to note that there is an observed B1 transition at 586 cm-l whose second harmonic would be of the right symmetry and energy to perturb the A,-type mode at 1177 cm-l. Also, the normal coordinate analysis to follow predicts an A, level at 462 cm-', whose second harmonic is of A, symmetry and would be expected to be at about 920 cm-'. This is a possible candidate for the perturber of the A, level at 932 cm-'; however, as will be discussed below, the force field for the A, modes is somewhat uncertain. As a check on the assignments the Redlich-Teller product rule5 was calculated for each of the symmetry species for which transitions were observed. For the B,-type modes the expected value for this parameter is 0.5978 while the observed value is 0.5954. For the B,-type modes the calculated value is 0.2909 and the observed value is 0.30'79. The agreement for the B2 modes is not extremely good but is reasonable when perturbation of one of the B2transitions in l'BH(ND,), is considered. For A, modes the product rule could not be calculated for the observed transitions since one mode was not observed. However, the theoretical value for the product rule can be used to predict the unobserved transition frequency. The expected value is 0.2616 and thus the predicted value of the missing Al transition in "BH(NH), is 1658.5 cm-'. This value was used in the normal coordinate analysis, although with a weight corresponding to a 5% uncertainty.
Normal Coordinate Analysis The observed vibrational transitions of a molecule depend upon the geometry of the molecule, the masses of the atoms, and the force field in which the atoms move. Given the geometry (in this case from the analysis of the microwave data2),the object of a normal coordinate analysis is to deduce the best quadratic molecular force field. The internal coordinate system used to define the potential field is illustrated in Figure 1. In this figure r,, r,, r3, and r4 refer to N-H stretching motions, R1 and R, refer to B-N stretches, D refers to the B-H stretch, a, and a, refer to the H-N-H angle bends, 0 refers to the N-B-N angle bend, 4 refers to the in-plane wag of the bisector of N-B-N angle with respect to the B-H bond, and p1and 0,refer to the in-plane wag of the bisector of an H-N-H angle with respect to the B-N bond. The out-of-plane coordinates are defined as rl, T,, 6,, 6,, and y,where 6, and 6, are the changes in the angles between the perpendicular to the plane formed by the H-N-H groups and the B-N bonds, and y is the out-of-plane wag coordinate defined by the change in the angle between the perpendicular to the N-B-N plane and the B-H bond. r1 and r2 are tor(5) Redlich, 0. 2.Phys. Chem. Abt. B 1935,28, 371.
Reuter et al.
-( H
N
H
Y
* 61
H
Figure 1. Internal Coordinate system used to define the molecular potential; the symbol -t signifies motion out of the molecular plane.
sional coordinates of the NH2groups about the B-N bonds. Defined in this way there are no redundant internal coordinates. This coordinate system is identical in form with that used in a normal mode analysis of urea, OC(NHz),,6 a molecule which is expected, in some respects, to have a force field similar to that of boranediamine. For example, the N-H stretch and H-N-H bend force constants of boranediamine may be compared with the same force constants for urea in order that a qualitative idea may be gained as to the differences in types of bonding between the two molecules. For boranediamine with planar Czosymmetry there will be seven vibrations with A, symmetry, six with B, symmetry, three with B1 symmetry, and two with A,-type symmetry. The number of symmetry-allowed, independent force constants is 1 / 2 ~ s n s ( n s l ) , where n, is the number of modes of symmetry s. The maximum number of independent internal coordinate force constants will be 58. The normal coordinate analysis is carried out by using program NORCRD, which uses a method, described in ref 7, in which the potential is introduced in terms of internal coordinates and then transformed to mass-weighted Cartesian coordinates. Most of the program was written previous to this study and the details of its operation are explained in the Appendix. Basically, the program uses a nonlinear least-squares technique to refine estimated values for a harmonic force field such that the differences between observed and calculated vibrational transition frequencies is minimized in the least-squares sense. In the analysis to follow, the out-of-plane- and in-plane-type coordinates are treated separately since the transformation used to obtain the symmetry coordinates will never mix in-plane-type internal coordinates with out-of-plane-type coordinates. Thus, there are 49 independent in-plane force constants corresponding to the A, and B2symmetry types, and 9 independent out-of-plane force constants corresponding to the A2 and B1 symmetry types. For 11BH(NHJ2 only 15 modes were observed (6 A,, 6 B2, and 3 B,); for "BH(ND2), there were 16 modes observed (7 AI, 6 B,, and 3 B1with one of the B, modes being heavily perturbed). For the two ,OB isotopic species of the above two A, and two B, modes and one A, and one B2 mode, respectively, were observed. In no case were any A, modes observed. Thus, since only 37 modes were ob-
+
(6) Duncan, J. L. Spectrochim. Acta 1971, 27, 1197. (7) Gwinn, W. D.J. Chem. Phys. 1971, 55, 477.
Analysis of Boranediamine
The Journal of Physical Chemistty, Vol. 86, No. 24, 1982
TABLE IV
TABLE I11 Form of Force Field
Values of Force Constantsa force constant
In-Plane Vibrations
FI,
FlS F13-F15
61
62
Y
71
Fl, F14
71
k.20
71
F, 0
72
Symmetry Coordinates A1 SI = 2-l(rl + r, + r, + r,,) S, = 2-l(rl - r, + r3 - r,) S,= 2-l1,(R1 + R,) S, = D s, = 2-”2(a1 + C Y , ) s, = 2-’/2(p1- P , )
e
A2
B, S, = 2-l(r1 + r, - r3 - r 4 ) S9= 2-l(rl - r 2 - r3 + r 4 ) Slo= 2-’/’(R1 - R,) = 2-”2(a1 - a , )
s,, s1,= 2-1/2(P1+ 0,)
In-Plane Constants 6.8238 6.0050 3.4207 0.6411 0.8584 1.5015 1.3778 -0.0191 0.0106 -0.4571 0.0424 0.0859 0.3806 - 0.0880 0.8877 0.2030 0.0443
0.003 0.064 0.004 0.003 0,019 0.019 0.027 0.003 0.003 0.053 0.003 0.016 0.019 0.045 0.020 0.012 0.006
Out-of-Plane Constants 0.0098 0.3665 0.1749 - 0.0409
0.0004 0.001 0.0008 0.0001
Force Field in Terms of Symmetry Coordinates‘
B,
A1
6.8153 6.79410 5.5479 3.4207 0.6835 0.8584 1.3778 0.0443 0.0443 0.3806 -0.1245 0.2871
F1,l
F, ,
=6
Bl
F;:
served, not all 58 force constants are uniquely determinable. In fact, because of rules connecting the harmonic frequencies of the different isotopes, there are fewer than 37 independent pieces of information. For example, use of the product rule allows one of the B1 frequencies to be predicted from the other five and there are only five independent B, frequencies. Because of this, it is necessary to place some constraints on the form of the force field. For example, it was assumed that the N-H (N-D) and B-H stretches have interaction force constants among themselves but with no other coordinates. This is both a common and a reasonable assumption because of the large frequency separation of these modes from the other modes of the molecule. It was also assumed that terms ala2,and PlR2 and their symmetric equivasuch as a1R2, lents have zero force constants. In other words, the interaction force constant of the symmetric (NH,) bend with the symmetric B-N stretch was assumed to be equal to the interaction force constant of the asymmetric (NH,) bend with the asymmetric B-N stretch, etc. The results of the normal coordinate analysis are presented in Tables 111-V. Table 111 defines the form of the force field used, Table IV gives the force constants and their estimated errors from the least-squares calculation, and Table V gives the observed and calculated values for the transition frequencies. Because of the constraints placed upon the force field, the statistical errors in the force constants given in Table IV should probably be multiplied by at least a factor of 3. The experimental weight used in the analysis is taken as 1/ai2where at = ( 0 . 0 1 ~+~ ti2, ) ~ vi is the observed vibration transition fre-
uncertainty b
value
Out-of-Plane Vibrations
S,=
4741
;
F6.7
Fa,8 F. G : l O Fll.11
Fl*,lZ F,,,,, FlO.1, F10.1, F12,13
A, ’14,14
FlS,,,
6.8535 6.8323 6.4621 0.5987 0.8584 1.5015 0.3806 1.2554 0.1215
Bl 0.1749 0.0098
F16,16
F17.17
FIE,,, F16y18
0.1749 0.0098 0.3665 - 0.0578
a Angular coordinates are scaled by 1 A so that all force constants may be expressed in units of mdyn/A. Estimated uncertainty from least-squares fit. Obtained by transforming the force field given in the first half of this table; n o fit to symmetry coordinates was done.
‘
quency in cm-’, and ei is the experimental uncertainty. For transition frequencies taken from the infrared data ci is -0.3 cm-’ while for data taken from the Raman spectra ci is 1cm-’. The factor of 0 . 0 1 represents ~~ the unknown anharmonic contribution to the transition frequency and is a common assumption.8 Even with the constraints on the force field mentioned above it was found in the initial attempts at fitting, when the solution was far from a minimum, that the system of equations was extremely ill-conditioned. In order to determine which force constants were most significant in defining the force field, we added interaction force constants one at a time in various orders. In this manner it was found that the interaction force constant between the B-N stretches (Itl,R2) and the H-N-H bends (a1, a2)was
-
(8) Mills, I. M. In “Critical Evaluation of Chemical and Physical Structure Information”, Proceedings of a Conference at Dartmouth College, June 24-29, 1973; Lide, D.R.,Paul, M. A., Eds.; National Academy of Sciences: Washington, DC, 1974; pp 269-88.
Reuter et al.
The Journal of Physical Chemistry, Vol. 86, No. 24, 1982
4742
TABLE V : Observed and Calculated Transitions symselec- metrv tion type"
B B B B B B B A A A A A A
c C C
TABLE VI "BH( NH,), centrifugal distortion constants, MHz
wavenumbers, cm-' obsd
calcd
"BH(NH,), 3551.2 3558.3 3457.8 3463.7 2516.4 2525.5 1658.5' 1613.7 1177.2 1182.7 932.7 931.7 402.0 403.2 3555.7 3565.3 3464.0 3474.0 1605.3 1602.3 1393.2 1404.7 1351.4 1347.7 832.6 829.9 914.3 914.2 586.0 585.9 422.0 421.6 552.9 462.0
weight in fit 7.92 x 10-4 8.36 x 10-4 1.58 x 10-3 1.40 x 10-4 4.16 x 10-3 6 . 0 0 ~10-3 4.96 X 10.' 7.91 x 10-4 8.34 x 10-4 3.88 x 10-3 5.15 x 10-3 5.47 x 10-3 1.44X lo-' 1.19 x lo-* 2.91 X lo-' 5.61 X lo-' 0.00 0.00
Tam
Tbbbb T C V 71
TZC
obsd'
calcd
- 2.660 i. 0.251 -0.057 0.015 -0.029 f 0.011 -0.130 t 0.231 -0.041 t 0.035
- 2.444 - 0.047 - 0.020 0.144 - 0.002
*
amu
"BH(NH,), '"BH(NH,), "BH(ND,), loBH(ND,), "BHNDHND, "BHNDHND, "BD( ND,), 'aBD(ND,),
* obsda
*calcd
- 0.0013 - 0.0045 - 0.0308 -0.0310 - 0.0241 - 0.0203 - 0.0188 - 0.0204
0.0110 0.0090 -0.0070 - 0.0090 - 0.0068 0.0027 -0.0007 - 0.0019
a obsd calcd -0.0123 -0.0135 -0.0235 - 0.0220 - 0.0173 - 0.0230 - 0.0181 -0.0185
*
From ref 2. T1 = T'&p + T'bbcc + TfCcM; see ref 15. = (A'/S)T'bbcc t ( B ' / s ) T aacc + (C'/S)T aabb; See ref 15. Cis and trans refer to the positions of the amine hydrogens relative to the B-H bonded hydrogen. e Inertial defects. A = IC- I, - I b . a
B B A A
'"BH(NH,), 2537.7 2539.7 1212.3 1206.3 1612.0 1620.4 1430.3 1418.9
1.55 x 6.62 3.85 x 4.89 x
B A
l"BH(ND,), 1080.4 1082.9 1515.6 1518.6
6 . 6 2 ~10-3 3.85 x 10-3
"BH(ND,), 2654.8 2646.9 2548.9 2538.0 2504.3 2494.3 1263.8 1266.0 1061.9 1062.8 775.0 775.8 335.8 333.7 2658.0 2643.0 2536.0 2523.6 1492.8 1488.3 1440.8 1378.2 1033.4 1033.7 637.0 671.4 896.8 896.9 477.0 477.0 314.7 315.5 43 2.1 327.4
1.42 x 10-3 1.54 x 10-3 1.59 x 10-3 6 . 1 2 ~10-3 8.79 x 10-3 1.64 X lo-' 6.55 X lo-' 1.42 x 10-3 1.55 x 10-3 4.49 x 10-3 L O O X 10-4 9.36 x 10-3 2.41 X lo-' 1.24X lo-' 4.39 x lo-, 9.17 X 0.00 0.00
'lBD(ND,), 2528.8 2512.3 1880.8 1899.1 1038.0 1027.5 1480.6b 1468.2
0.0 0.0 0.0 0.0
B B B B B B B A
A A A A A C C
c
B B B A
7,
10-3 ~10-3 10-3 10-3
' Calculated from product rule; see text. This line is in a complex region of the spectrum and its assignment is somewhat uncertain; see text. small and made little difference in the variance no matter what other force constants were present (as long as the calculation was stable). Secondly, it was found that, while the interaction force constant (F14)between the B-N stretches (Rl, R,) and the N-B-N bend (0) was dependent on the form of the force field, the major effect of including it was to cause the diagonal B-N stretch force constant (F,) and the B-N stretch interaction force constant (Fl,,) to have unreasonable values. Those force constants which did explain a large amount of the variance, and which did not cause instabilities in other force constants, would stabilize at approximately the same value regardless of the form of the force field (again as long as the calculation was stable). Therefore, a cal-
culation was performed in which the force constant for the terms Rial and Rza2and the force constant for the term Rd were constrained to be zero, along with those force constants mentioned earlier. The force field from this calculation was then used as an initial estimate in a calculation where the force constant for the terms Rlal and Rza2 and the force constant for the term Rd were not constrained to be zero. The number of terms in the force field was then further reduced by eliminating those terms which were small (
