J . Phys. Chem. 1990, 94, 194-199
194
During the deposition of AIN films utilizing pure N 2 plasma, the only expected source of hydrogen is residual water in the system. The absorption spectrum of an AIN film fabricated in a pure nitrogen plasma, Figure 4a, displays a strong AIN band and weak AI-N, and N H motions. This spectrum is of much poorer quality than the analogous spectrum obtained from an AIN film deposited in a hydrogen-nitrogen plasma. Visual inspection of the AIN absorption specimen prepared in pure N2 plasma revealed the presence of opalescence on the KBr disk, suggesting that the deposited material was quit rough. TEM and electron diffraction data indicate that ion-beam-fabricated AIN films are made up of crystallites ranging in size from 2 to 15 nm.3+4*8J3,20 We are now in the process of conducting morphological studies on our AIN films. Based on the above discussion, it is reasonable to assume that AIN tunneling barriers, fabricated under the conditions described in this work, are composed of a thin underlayer of alumina on which AIN is deposited. The electron tunneling process proceeds through both AIO, and the AI0,-AIN regions. The presence of hydrogen ions in the nitrogen plasma during the deposition of aluminum nitride clearly improves the quality of the tunneling barriers. It should also be pointed out that whereas the A1N junctions prepared in pure N, plasma required deposition of 1-2-nm (measured by the films-thickness monitor) thick insulating films in order to produce resistances of about 200 R, AIN diodes prepared in the hydrogen-enriched nitrogen plasma required barriers of only 0.4-nm apparent thickness to yield comparable resistances. It is not likely that tunnel barriers less than 1 nm thick will produce resistances of tens of ohms.2' It is likely that the H2-N2 beam reacts with the aluminum substrate during the early stages of the A1N deposition. The film-thickness monitor registers only the net amount of AIN deposited, while the amount of surface material formed due to beamsubstrate reaction is not measured. The measured thickness of A1N barriers is greater when pure N, plasma is employed because (1) the nitrogen beam reacts with
the AI substrate to a lesser extent than H2-N2 plasma and (2) more native oxide is formed in the absence of H2. We are presently evaluating the contribution of the plasma-substrate interaction to the AIN tunnel barriers.
Conclusion We have observed and identified for the first time surface species, other than AIN, in ion-beam-deposited aluminum nitride films. The structural analysis of AIN films based on tunneling data indicates the presence of AlN along with AI-H, AI-N,, H-AI-N2, and NH, surface species. Optical spectra of these AIN films corroborated most of the IETS results. IETS, however, proved to be a more sensitive surface-spectroscopic method than FT-IR techniques, yielding additional information about the composition of the AIN films. The possible existence of NH, surface species was suggested by others but has not been verified to date. These species were also linked with a possible mechanism for the ion-nitriding process. Our results provide a new insight into the structure of A1N films and are also relevant to the understanding of the mechanism of the ion-nitriding process. The AIN tunneling barrier prepared in a pure N2 plasma most probably consists of AIN aggregates scattered on an alumina layer that is formed due to the residual water in the deposition system. Thus, it is expected that electron tunneling occurs through both AIO, and AIN. The presence of hydrogen ions in the nitrogen plasma during the deposition of aluminum nitride yields smoother tunneling barriers with less oxygen. Morphological and reactivity studies of the ion-beam-fabricated AIN films are now in progress. Acknowledgment. We gratefully acknowledge the National Science Foundation and the Division of Chemistry for their support in the form of Grant CHE-8805612. We also thank Professor K. W. Hipps for many helpful discussions and valued assistance in acquiring the various reported spectra. Registry No. AI-N2, 24304-00-5; hydrogen, 1333-14-0; nitrogen, 7727-37-9.
Theoretical Study of the Vibrational Circular Dichroism of 1,&Dideuterioallene: Comparison of Methods A. Annamalai,t K. J. Jalkanen,f U. Narayanan,t M.-C. Tissot,+ T. A. Keiderling,*,t and P. J. Stephens*,* Department of Chemistry, University of Illinois at Chicago, Box 4348, Chicago, Illinois 60680. and Department of Chemistry, University of Southern California, Los Angeles, California 90089-0482 (Received: April 28, 1989)
Vibrational rotational strengths are calculated for allene-1,3-d2by using the fixed partial charge (FPC), localized molecular orbital (LMO), and atomic polar tensor (APT) models and the a priori theory of Stephens. The LMO model is implemented using semiempirical methods. The APT model and the a priori theory are implemented at the ab initio SCF level of approximation. Dipole strengths for allene-1,3-d2, -do, and -d4 are simultaneously calculated. Dipole strengths predicted a priori are in reasonably good agreement with experimental values; the LMO and FPC models give similar and very different results, respectively. Rotational strengths calculated from the FPC, LMO, and APT models overall bear little resemblance to those calculated from the a priori theory.
Introduction
Vibrational circular dichroism (VCD) has been measured for a wide variety of chiral molecules, and a number of structural applications have been reported.' Most of the latter have been based on empirical correlation of spectroscopic features among chemically similar molecules. A few have attempted to use one 'University of Illinois at Chicago. 'University of Southern California.
of the several theoretical formulations2of VCD to correlate spectra with structure. The latter approach requires a reliable theory, capable of practical implementation. In order to evaluate their reliability, the predictions of some of the proposed theories of VCD (1) Freedman, T. B.; Nafie, L. A. Top. Stereochem. 1987, 17, 113. Polavarapu, P. L. Vib. SpectraStruet. 1984,13, 103. Nafie, L. A. Ado. Infrared Raman Spectrosc. 1984, I I , 49. Keiderling, T. A. Appl. Spectrosc. Rev. 1981, 17, 189.
(2) Stephens, P. J.; Lowe, M. A. Annu. Rev. Phys. Chem. 1985, 36, 213.
0022-3654/90/2094-0194$02.5Q/O 0 1990 American Chemical Society
VCD of 1,3-Dideuterioallene have been compared to experimental VCD data. In a very few cases, several theories have been simultaneously compared to spectra for the same molecule. The most extensive comparisons have been made using the fixed partial charge3 (FPC) and localized molecular orbital4 (LMO) models (the latter implemented at the CNDO level of approximation and henceforth labeled LMO/C). In some cases, the FPC model has been successful in replicating portions of the VCD ~ p e c t r u m in ; ~ other cases6 it has not been so successful. The same is true for the LMO/C model. Where both approaches have been examined simultaneously, in some cases the FPC model is superior, in other cases vice Very recently, Stephens has introduced a rigorous a priori theory of VCD that allows direct computation of VCD spectra from molecular wave f u n c t i ~ n s . ~Specifically, ~~J~ computation is required of two sets of molecular tensors, P$ and Mkp, called the atomic polar and atomic axial tensors respectively. The atomic polar tensors, P$, are well-known'' and determine vibrational absorption intensities. The atomic axial tensors, M&, are new and determine the magnetic dipole transition moments additionally required for the calculation of rotational strengths and VCD intensities. Stephens' theory has been implemented at the ab initio, S C F level of apprroximation for a variety of molecules.'2-20 In studies of a number of small, chiral m o l e c ~ l e s , ' ~the J ~ gauge dependence and the basis set dependence of its predictions have been extensively studied. It has been shown that a gauge termed the Distributed Origin with origins a t nuclei gaugelo is superior to other obvious choices. Using this gauge, calculations of VCD spectra for trans-o~irane-2,3-d~,'~ propylene oxide,I6 trans- 1,2dicyanocyclopropane,I6 4-methyl-2-0xetanone,'~3-methyl-2-oxetanone,19and propylene sulfide,20using basis sets of medium size, have given good overall agreement with experimental spectra.
(3) Schellman, J. A. J . Chem. Phys. 1973, 58, 2882; Ibid. 1974, 60, 343. Deutsche, C. W.; Moscowitz, A. J . Chem. Phys. 1968,49, 3257; Ibid. 1970, 53, 2630. (4) Nafie, L. A.; Walnut, T. H. Chem. Phys. Lett. 1977,49,441. Walnut, T. H.; Nafie, L. A. J . Chem. Phys. 1977,67,1501. Nafie, L. A.; Polavarapu, P. J . Chem. Phys. 1981, 75, 2935. (5) Annamalai, A.; Keiderling, T. A,; Chickos, J. S. J . Am. Chem. SOC. 1984, 106, 6254, and references therein. (6) Lal, B. 8.; Diem, M.; Polavarapu, P. L.; Oboodi, M.; Freedman, T. B.; Nafie, L. A. J . Am. Chem. SOC.1982, 104, 3336. Freedman, T. B.; Diem, M.; Polavarapu, P. L.; Nafie, L. A. J . Am. Chem. SOC.1982, 104, 3343. (7) Annamalai, A.; Keiderling, T. A.; Chickos, J. S. J . Am. Chem. Soc. 1985, 107, 2285. (8) Narayanan, U.; Keiderling, T. A. J . Am. Chem. Soc. 1988,110,4139. (9) Stephens, P. J . J . Phys. Chem. 1985,89, 748. (IO) Stephens, P. J. J . Phys. Chem. 1987, 91, 1712. ( I I ) Person, W. B.; Newton, J. H. J . Chem. Phys. 1974,61, 1040. (12) Lowe, M. A.; Stephens, P. J.; Segal, G.A. Chem. Phys. Lett. 1986, 123,108. Lowe, M. A.; Segal, G . A.; Stephens, P. J. J. Am. Chem. Soc. 1986, 108, 248. (13) Amos, R. D.; Handy, N . C.; Jalkanen, K. J.; Stephens, P. J. Chem. Phys. Lett. 1987, 133, 21. (14) Jalkanen, K. J.; Stephens, P. J.; Amos, R. D.; Handy, N . C. Chem. Phys. Lett. 1987, 142, 153; J . Phys. Chem. 1988, 92, 1781. Amos, R. D.; Jalkanen. K. J.: Steohens. P. J. J . Phvs. Chem. 1988. 92. 5571. ( 1 5 ) Jalkanen, K: J.;Stephens, P. j.;Amos, R. D.;'Handy, N . C. J . Am. Chem. SOC.1988, 110, 2012. (16) Kawiecki, R. W.; Devlin, F.; Stephens, P. J.; Amos, R. D.; Handy, N . C. Chem. Phys. Lett. 1988, 145, 411. Kawiecki, R. W. Ph.D. Thesis, University of Southern California, 1988. (17) Stephens, P. J.; Jalkanen, K. J.; Kawiecki, R. W.; Amos, R. D.; Handy, N . C.; Lazzeretti, P.; Zanasi, R. Forty-Second Symposium on Molecular Spectroscopy; The Ohio State University: Columbus, 1987; paper WHIO. Jalkanen, K . J.; Kawiecki, R. W.; Stephens, P. J.; Amos, R. D., to be submitted. (18) Jalkanen, K. J.; Stephens, P. J.; Amos, R. D.; Handy, N . C. J . Am. Chem. Soc. 1987, 109, 7193. Jalkanen, K. J.; Stephens, P. J.; El-Azhary, A,; Keiderling, T. A., to be submitted. (19) Jalkanen, K. J.; Devlin, F.; Stephens, P. J.; Polonski, T.; Amos, R. D.: Handy, N . C. Forty-Third Symposium on Molecular Spectroscopy; The Ohio State University: Columbus, 1988; paper RH5. Jalkanen, K. J.; Devlin, F.; Polonski, T.; Stephens, P. J., to be submitted. (20) Dothe, H.; Lowe, M. A.; Alper, J. S. J . Phys. Chem. 1988,92,6246. Bursi, R.; Stephens, P. J . Forty-Third Symposium on Molecular Specrroscopy; The Ohio State University: Columbus, 1988; paper RH6. Bursi, R.; Devlin, F.;Forni, A.: Stephens, P. J., to be published.
The Journal of Physical Chemistry, Vol. 94, No. 2, 2990 195 It is of interest to compare the predictions of Stephens' theory with those of earlier, simpler theories which, while intrinsically less reliable, are calculationally more accessible. If, in some class of molecules or subset of normal modes, one of the simpler models could be shown to be qualitatively reliable, it would continue to have value. It should be emphasized that qualitative VCD predictions at the level of sign pattern alone can often discriminate between allowable conformations of a given molecule. At present, there are no rules by which one can choose the cases (if any) in which any of the simpler theories would be reliable. In this paper we compare the predictions of the FFC,LMO/C, and atomic polar tensor2' (APT) equations with those of the a priori theory for allene-2,3-dz. Allene, with its cumulative double bond structure, has long been studied by both vibrational and electronic spectroscopies in an effort to understand its bonding.22 Furthermore, when 1,3-disubstituted, the allene molecule becomes optically active and the electronic circular dichroism of this "intrinsically chiral chromophore" has been extensively studied. This work is being extended through studies of the VCD spectra of a variety of substituted a l l e n e ~ . In ~ ~the course of these studies a sample of allene-l,3-d2 was obtained from Prof. J. S. Chickos and its vibrational spectra were measured. The fundamental frequencies of this molecule provided additional data for further improvement of the force field of allene using both scaled quantum mechanical and empirical appro ache^.^^ At this time, the vibrational frequencies and normal coordinates of this and other isotopomers of allene can be accurately calculated. Given also its small size, allene-2,3-d2 is therefore ideally suitable for comparison of the predictions of alternative theories of VCD. Additionally, as in the case of trans-~yclobutane-l,2-d~,~,~ the symmetry of the molecule restricts the number of parameters needed in the FPC model, reducing its indeterminacy and allowing a more meaningful comparison with other theories. Unfortunately, experimental VCD data on allene-l,3-d2 could not be obtained due to insufficient optical resolution of the sample that was available to us. Attempts were made to detect its VCD with both dispersive' and FTIRZ5spectrometers. As a result, all VCD calculations are compared to the a priori results obtained with the largest basis sets used, under the assumption that these calculations provide a good approximation to the experimental VCD. This assumption is supported by previous studies on tr~ns-oxirane-2,3-d~,'~ propylene oxide,16 trans-1,2-dicyanocyclopropane,'* 4-methyl-2-oxetanone,I9 3-methyl-2-0xetanone,'~ and propylene sulfide.20 The prediction of vibrational rotational strengths requires the calculation of electrical and magnetic dipole transition moments. The electric dipole transition moments also determine the dipole strengths and absorption intensities. Despite the absence of VCD data for allene-1,3-d2 absorption intensities are available for allene-do and -dz6 and we have obtained approximate values for allene-2J-d2. In addition to the comparison of rotational strengths for allene-1,3-dzpredicted by the FPC, LMO/C, AFT, and a priori theories, we have therefore also compared the dipole strengths for allene-do, -d4, and -2,3-d2 predicted by these theories to each other and to the available experimental data. Methods FPC and L M O / C calculations of dipole and rotational strengths, D and R, were carried out as in earlier studies on c y ~ l o b u t a n e . ~All . ~ force field calculations were done with adaptations of the normal mode analysis packages of Schacht~chneider.~' Two geometries and force fields, described (21) Freedman, T. B.; Nafie, L. A. J . Chem. Phys. 1983, 78, 27. (22) Runge, W. In The Chemistry o f t h e Allenes; Landon, S . R., Ed.; Academic: London, 1982; Chapter 10. (23) Narayanan, U.; Keiderling, T. A,; Elsevier, C. J.; Vermecr, P.; Runge, W. J . Am. Chem. Soc. 1988, 110,4133. (24) Narayanan, U.; Annamalai, A.; Keiderling, T. A. Spectrochim. Acta 1988, 44A, 785. Hegelund, F.; Duncan, J. L.; McKean, D. C. J . Mol. Spectrosc. 1977, 65, 366, and references therein. (25) Malon, P.; Keiderling, T. A. Appl. Spectrosc. 1988, 42, 32. (26) Koga, Y . ;Kondo, S.;Nakanaga, T.; Saeki, S. J . Chem. Phys. 1979, 71, 2404.
196
The Journal of Physical C h e m i s t r y , Vol. 94, No. I , 1990
Annamalai et al.
TABLE I: Calculated Frequencies ( v ) , Dipole ( D ) Strengths, and Rotational ( R ) Strengths for 1,3-Dideuterioallene" a priori FPC APT TZ/2Pb 6-31G(ext)' 6-31G**b 6-31G(ext) (6-31G**) (arb) LMO/C v D R D R D R R D R D R D R sym and assignt 0.2 -3.3 0.1 -6.2 0.4 -8.7 -0.04 3.0 -38.1 0.8 -9.6 1.1 -19.1 306 I AC-Hsymstr 6.3 0.7 8.7 0.05 9.7 1.9 19.3 B C-H asym str 3053 0.2 3.3 0.3 5.0 38.6 1.4 226 I 1.3 0.4 1.1 2.2 0.6 2.2 0.5 5.1 17.7 4.4 7.2 1.8 7.4 B C-D asym str 2252 0.2 -0.5 0.2 -2.4 0.3 -2.4 2.1 -19.2 0.9 -7.8 -0.5 0.5 -7.9 A C-D sym str 1944 21.5 0.1 21.9 0.2 15.7 0.2 0.02 1.2 1.1 14.2 0.6 50.2 0.4 B C=C=C asym str 1335 0.0 1 . 1 0.0 1.7 0.0 0.3 0.3 -3.9 0.04 0.2 -1.2 0.2 -2.7 A CHD deform 0.1 -2.1 0.02 1262 0.4 -4.1 0.4 -5.3 17.3 10.3 2.5 4.0 0.6 5.1 B CHD deform 11.6 0.1 5.8 -0.1 1.4 -13.2 2.6 -9.1 9.7 0.4 0.7 -6.1 A C=C=C sym str 1052 0.3 867 1.7 -27.6 2.3 -33.1 0.6 -14.9 1.8 5.3 25.9 16.3 30.7 2.6 16.1 B CCH(D) deform 81.7 65.9 847 16.3 91.0 17.1 93.6 14.3 6.0 50.7 0.0 2.3 8.1 19.4 A allenic torsion + CCHD oop bend 0.8 -6.7 2.2 -8.3 9.5 838 1 . 1 -7.4 12.6 -0.2 20.8 -4.4 11.6 -20.1 A CCH(D) deform 758 24.6 -98.3 24.5 -96.7 25.0 -102.2 -104.2 23.8 -99.3 12.0 -38.4 27.7 -10.6 B CCHD oop bend 39.4 27.0 7.9 29.9 6.3 17.3 9.7 -1.2 A allenic torsion + CCHD oop bend 636 7.9 35.1 7.9 34.3 8.4 328 9.3 30.0 9.7 27.1 4.7 28.1 -8.3 2.2 5.9 35.2 -13.8 0.5 -1.0 BCCClinearbend 4.9 -27.9 8.4 2.3 -5.9 34.1 12.6 0.7 324 9.6 -29.6 10.0 -26.6 1.0 A CCC linear bend
'Units: frequencies are in cm-I, D in (esu.cm)*,and R in (esu.cm)*. All calculations were done using the experimental molecular geometry and the empirical force field of ref 24. FPC charge set I is from ab initio calculations using 6-31G** basis set and optimized geometry, +0.161el on C,, -0.381el on C,, and +0.151e( on H(D) atoms. FPC charge set 2 is arbitrary, +0.81el on C,, -0.51el on C,, and +0.05)el on H(D) atoms. bTZ/2P: [Ss4p] on C and [3s] on H (scale factor 1.25) of T. H. Dunnipg ( J . Chem. Phys. 1971, 55, 716), augmented by d(1.2.0.4) on C and p(1.5,O.S) on H. 6-31G(ext): 6-31G (Hehre, W. J.; Radom, L.; Schleyer, P. v. R.; Pople, J. A. A b Initio Molecular Orbital Theory; Wiley: New York, 1986) augmented by S(0.056), p(0.056), and d(0.8,0.266) on C and s(0.054) and p(0.75,0.25) on H. previously,24 were used. At the experimental geometry an empirical force field was obtained. At the 6-31G** optimized S C F geometry a scaled 6-31G** S C F force field was obtained. Both force fields were fit to experimental frequencies for the five iso-1,3-d2, and -d4. Rotational topomers: allene-do, -dl, -1,f-d2, strength calculations were carried out for S-allene-1,3-d2. In this paper, focus will be on results from the empirical force field, for the sake of brevity. All LMO/C calculations were carried out with the use of a program graciously supplied by Prof. P. L. Polavarapu of Vanderbilt University.28 For the FPC calculations, many sets of charge parameters were tried, but results from only two are presented here. The first set used Mulliken overlap populations, derived from a 6-31G** a b initio calculation, and the second used an empirical charge set chosen to improve the observed intensity patterns (vide infra). A priori calculations of dipole and rotational strengths were carried out as described p r e v i o ~ s l y . l ~Rotational -~~ strengths were calculated using the equation of Stephens and the distributed origin with origins at nuclei gauge.I0 The atomic polar and axial tensors, P;@ and M& were calculated at the S C F level of approximation using analytical derivative methods and the CADPAC program,29 as described earlier.I3 Three basis sets were used: the 6-31G** basis set of Pople and c o - w ~ r k e r and s ~ ~the larger 6-31G(ext) and TZ/2P basis sets of In calculations presented elsehere,'^,^' the 6-31G(ext) and TZ/2P basis sets have been shown to give very similar results for P:a and MkQtensors and to provide good approximations to Hartree-Fock limiting values. The smaller 6-3 IC** basis set gives results that are qualitatively similar while quantitatively less accurate. The atomic polar tensor (APT) equation for rotational strengths was first proposed by Freedman and Nafie2' as an approximation to the LMO equation. However, this equation was subsequently shown by Stephens'O to be an approximation to his a priori equation. In the distributed origin with origins at nuclei gauge, the equation of Stephens fo_r t_he rotati_on_alstrength is the sup of two terms, dubbed the " F M " and "P-L" terms.1° The "P-L" term contains only atomic polar tensors and is-inpependent of atomic axial tensors. The contribution of the "P-L" term to the rotational strength is identical in form with the APT equation. (27) Schachtschneider, J . H. Technical Report No. 231-64, 1964; Technical Report No. 57-65, 1964; Shell Development Co., CA. (28) Polavarapu, P. L. J . Chem. Phys. 1982, 77, 2273. (29) Amos, R. D. The Cambridge Analytic Derivatives Package, Version 3.0, Cambridge, 1986. (30) Hehre, W. J.; Radom, L.; Schleyer, P. v. R.; Pople, J . A. Ab Initio Molecular Orbital Theory; Wiley: New York, 1986. (31) Amos, R. D. Adc. Chem. Phys. 1987, 67. 99.
TABLE 11: Approximate Dipole Strengths for Vapor-Phase and Approximate Relative Dipole Strengths for Solid-Phase 1,J-Dideuterioallene" vapor phase solid phase Ub
D6
Ub
3046 2278 1951 I264
I .o
3025 226 1 1940 1250 848 759 638
;;:)
650
0.4 9.2 I .2 36.0d
Drd 0.2 0.9 9.2 3.0 19.0 21.4 7.5
'Area under an absorption band was estimated using the Digilab routines for the FTS-60 FTlR instrument. Impurity and combination bands were found to interfere with the C-H and C-D stretching bands. 'Frequencies are in cm-' and dipole strengths in (esu.cm)2. Dipole strength in (esuan)2calculated using D = 0.92 X 10-38s(c/v) du, c in M-I cm-I. CRelative dipole strengths were arbitrarily normalized so that the asymmetric C=C=C stretch has the same value in both data sets. dUnresolved in vapor phase. The predictions of the APT equation are therefore simply obtained from ihe_a priori calculations by neglecting the contributions of the "P-M" terms. Corresponding dipole strengths are identical with those calculated a priori. Results This project generated many D and R values for allene-1,3-d2 calculated with various theoretical approaches, geometries, and force fields. A subset of the results are given in Table I. Where possible, D values are compared to the experimental results given in Table 11. Available experimental allene-do and allene-d, intensitiesz6 are also compared to calculated D values in Table 111. The R values for allene-1,3-d2,in the absence of experimental VCD data, are compared to the most accurate a priori values (those obtained with the TZ/2P and 6-31G(ext) basis sets). With very few exceptions, where they were compared, the two force fields gave very similar D and R values. In the case of allene-f,3-d2 only for the two nearly degenerate A modes (v5 and v6)24 lying between 830 and 850 cm-' are the results sensitive to the choice of force field. Since these absorption bands overlap, and their VCD is unknown, throughout the following discussion we present only the results obtained using the empirically refined force field." A Priori Theory. As shown in Table I, dipole strengths for allene-f ,3-dz obtained with the three basis sets were comparable. The 6-3 lG(ext) and TZ/2P results are very similar. Experimental relative D values for the solid-state spectrum and estimated ab-
VCD of 1,3-Dideuterioallene
band/type dn
The Journal of Physical Chemistry, Vol. 94, No. 1, 1990 197
obsd freq
calcd freq
6-31G**
arb
LMO/C
6-31G**
TZ/2P
3085 3007 1957 1398 999 84 1 356 2330 2230 1921 1032 829 667 307
3092 3007 1974 1399 998 840 353 2305 2229 1909 1025 826 666 303
5.48 4.35 2.12 20.54 4.40 28.59 1.73 4.67 5.56 0.31 14.89 5.17 18.63 2.68
1.36 1.40 17.05 2.09 1 1.66 12.43 41.07 1.87 7.16 11.16 1.58 21.37 11.73 29.98
2.05 1.70 5 1.46 0.27 2.13 32.20 0.34 1.27 3.63 47.88 0.12 3.91 22.56 0.89
0.65 0.67 16.03 0.09 0.92 28.47 4.68 0.63 1.01 15.01 0.09 0.29 20.73 5.01
0.28 0.18 22.80 0.40 2.02 28.22 9.63 0.36 2.74 19.70 0.35 1.27 20.08 9.44
exptC 0.28 0.74 9.99 2.00 1.75 21.65 8.20 0.44 0.91 9.20 0.91 1.40 15.25 7.70
OUnits: frequency in cm-I, intensity in IO”’ (esu.cm)2. Experimental values derived from ref 26. Calculated intensities for A , symmetry modes at 3025, 1443, 1077 (2203, 1228, 868) cm‘l and the B, mode at 850 (601) cm-I for do (d4) have not been listed since they are identically zero. *Charge sets as in Table 1. cConverted from B values (km/mol) of ref 26 using D = (0.40 X 10-36)B/u. Values for E modes used (B/2) in place of B.
solute D values for some of the vapor-phase bands are given in Table 11. The differences in relative values between the two phases presumably arise primarily from crystal effects. The 6-31G(ext) and T Z / 2 P D values are in good agreement with the available experimental data. Overall, relative intensities are satisfactorily predicted. Absolute D values are reasonably close to experimental values, only rarely deviating by more than a factor of 2. The weak C-D stretching modes are predicted to be slightly stronger than the weak C-H stretching modes. Such a relative intensity pattern is consistent with the solid-state data but not with the gas-phase data. As observed, the asymmetric C=C=C stretch is predicted to be intense. The in-phase CHD scissor (1 335 cm-’) is calculated to be very weak, consistent with its having been observed only in the Raman spectrum. The 1262- and 1 0 5 2 - ~ m bands -~ are also calculated to be weak, but about equal in intensity and more intense than the 1335-cm-l band. Experimentally, both are observed; however, the 1262-cm-l band (primarily C=C-H deformation) is substantially more intense than the 1052-cm-’ band. The 847-cm-l and the 758-cm-l bands have the highest calculated intensity in this spectral region, which is consistent with our experimental solid-state data. The sum of the calculated D values for the bands at 867-636 cm-’ is in good agreement with both sets of experimental data. Calculated intensities for allene-doand -d4,together with the experimental intensities determined by Koga et aLZ6are given in Table 111. Experimental values for E modes were divided by 2 to give direct comparison with calculated values for single components. The agreement between 6-31G** and TZ/2P calculated D values is comparable to that found in allene-Z,3-d2. The TZ/2P calculated and experimental D values are also in comparable agreement to that found in allene-1,3-dz. With the TZ/2P basis set, the asymmetric C=C=C stretch is calculated to be about twice the intensity found experimentally for both isotopomers. The C-D stretches in allene-d4 also are calculated to be somewhat higher in intensity than found experimentally, while the C-H stretches in allene-do are calculated to be too small. D values for the mid-IR bands are within experimental error for both the do and d4 isotopomers. The overall pattern calculated thus reflects experiment well. R values for S-allene-I,3-d2 calculated with the 6-31G**, 631G(ext), and TZ/2P basis sets are also given in Table I. The results obtained using the 6-31G(ext) and T Z / 2 P basis sets are very similar, differing the most for the C-H and C-D stretching modes. The 6-31G** basis set gives results qualitatively identical with the larger basis sets, although quantitatively somewhat different. The R values of the lower frequency modes on average exhibit less basis set dependence than do the higher frequency modes. R values predicted by the APT equation have been obtained from the a priori calculations, using the 6-31G(ext) basis set, and
are also given in Table I. The R values given by the APT equation are overall significantly different from the a priori results, yielding as many sign disagreements as matches in the mid-IR and in addition having magnitudes severely at variance. The C-H, C-D, and asymmetric C = C = C stretch R values are in agreement with the a priori calculation in terms of sign but differ substantially in magnitude. In the case of the larger R values predicted by the a priori theory, in three cases (bands at 847, 758, and 636 cm-I) large R values of the same sign are also predicted by the APT equation while in four cases (bands at 1052, 867, 328, and 324 cm-’) the results are very different (in all cases differing in sign). FPC Model. FPC calculations for allene-1,3-d2 were carried out using several sets of charges. Even though allene’s small size and symmetry constrain the charges, a dimension of flexibility remains. The C-H bond dipoles and the charge on the central carbon atom can vary. We first chose to use charges based on Mulliken overlap population analysis; two sets were tried based on calculations using 4-31G and 6-31G** basis sets. These gave fairly similar results, but both led to anomalous relative absorption intensity distributions. In particular, the C=C=C asymmetric stretch was predicted to have a very small D value whereas experimentally it is one of the strong bands in the spectrum. Calculations with several other arbitrarily chosen charge distributions were then carried out to determine if changing the central carbon charge might correct this situation. Only by making the central carbon very positive with respect to the terminal ones could the asymmetric C==C==Cstretch D value be increased. However, even with a high effective charge separation in the C=C=C system, overall adequate dipole strengths were not obtained. In Table I are summarized the results for the 6-31G** derived charge set (C, = 0.16, C, = -0.38, and H = 0.15) and for an arbitrary charge set (C, = 0.8, C, = -0.5, and H = 0.05) which gives an improved D value for the asymmetric C=C=C stretch (but not for the lower energy modes). The asymmetric C=C=C stretch and the 1262-cm-’ band (primarily C=C-H deformation) appear to be coupled in that increasing the intensity of one by charge alteration decreases that of the other. The relative intensities for the other distinct spectral regions of the spectrum are only crudely represented by the FPC calculations. That is, the 636-cm-I band, 758-cm-I band, and the three bands around 850 cm-’ (taken together) are intense, the 1052- and 1335-cm-I bands are very weak, and the C-H and C-D stretches are moderate in intensity. The intensity pattern of the near-degenerate bands at 867, 847, and 838 cm-I and the intensities of the 328- and 324-cm-’ bands are highly sensitive to the charge set used and hence are virtually undetermined within the FPC model. As for allene-l,3-dz, the basic pattern of the allene-do and -d, intensities is only very crudely predicted by the FPC model (Table 111). Again the arbitrary charge set improves the representation
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The Journal of Physical Chemistry, Vol. 94, No. 1, 1990
of the D values for the higher energy modes (>lo00 cm-’) but not the lower energy ones. FPC R value calculations for allene-1,3-d2 gave a similar qualitative pattern with all the various charge sets that we have tried with the exception that using a negative charge on both the terminal C and H atoms gave some mid-IR sign changes. Results for the 6-31G** and arbitrary charge sets are given in Table I. Considering first the C-H and C-D stretching regions, VCD couplets are calculated for both pairs of modes. In all cases, the relative and absolute signs calculated were the same as given by the a priori theory. The magnitudes obtained are much larger than the a priori magnitudes especially using the 6-31G** charge set. The asymmetric C=C=C stretch is calculated to have very small positive VCD in agreement with the a priori result. Increase of its dipole strength by charge reallocation using the arbitrary set of charges decreases this value somewhat. The 1335-cm-’ in-phase C H D scissor mode (which is calculated to have a very small dipole strength and is observed only in the Raman spectrum) is predicted to have a negative rotational strength larger than that of the asymmetric C=C=C stretch; its sign is not in agreement with the a priori calculations. The R values of the out-of-phase CHD scissor at 1262 cm-I and the symmetric C=C=C stretch at 1052 cm-’ are predicted to be large and opposite in sign. These signs are opposite to the a priori predictions. In the 900-600-cm-’ region, intense VCD is predicted. These modes have strong contributions from the in-plane C C H bend, the out-of-plane CCHD deformations, and the allenic torsion. In both cases presented in Table I and with most other charge sets tried, the three overlapping bands centered at 850 cm-] are predicted to have large net positive VCD while the 758-cm-I band is strongly negative and the 636-cm-’ band is weaker but positive again. In these respects the FPC calculations are consistent with the a priori calculations. However, the FPC and a priori R values for the 867-cm-l band are opposite in sign and the FPC R values for the 847-cm-’ band are extremely sensitive to the charges used. Thus, in detail, the FPC and a priori predictions differ substantially. The FPC calculations predict oppositely signed R values for the C=C=C bending modes at 328 and 324 cm-I, as do the a priori calculations. However, the signs are very sensitive to the charges used and thus are indeterminate. LMO/C Model. The D values predicted by the LMO/C model (Tables I and 111) are closer to the a priori values, and to the experimental results, than in the case of the FPC model. In allene-l,3-d2 the overall pattern of intensities deviates significantly from the a priori calculations for the 838-, 328-, and 324-cm-I bands. In allene-do and -d4, similar differences are found in the 355- and 307-cm-I bands, respectively. R values for allene-1,3-d2 predicted by the LMO/C model (Table I), on the other hand, are much closer to the FPC results than to the a priori predictions. Only for the three lowest modes (636, 328, and 324 cm-l) are there differences in sign. As a result, in almost all cases where the a priori and FPC calculations predict the same sign, this sign is replicated by the LMO/C model; when the FPC prediction differs in sign, so does the LMO/C calculation.
Discussion Dipole strengths for allene-do, -d4, and -1 ,3-d2 predicted a priori using the TZ/2P and 6-31G(ext) basis sets are in good overall agreement with experiment. Deviations between theory and experiment are undoubtedly due to both theoretical and experimental errors and are typical in magnitude for S C F calculations using basis sets of comparable s i ~ e . ~ The ’ . ~ good ~ agreement provides strong support for the essential correctness of the assignment of the vibrational spectrum of allene and its isotopomers, of the force field, and of the normal coordinates derived thence.24 Dipole strengths predicted by the FPC model are in poor overall agreement with experiment and with the a priori results. In addition, they are sensitive to the choice of partial charges, and hence substantially uncertain. The FPC model approximates the (32) Yamaguchi, Y.; Frisch, M.; Gaw, J.; Shaefer, H . F.; Binkley, J. S . J . Chem. Phys. 1986, 84, 2262.
Annamalai et al. atomic polar tensor P& by a constant diagonal tensor:”
P& = qAsa+4
(1)
where qx is the partial charge of nucleus A. Our results show that for allene this approximation is extremely inaccurate for a wide range of choices of sets of partial charges. Dipole strengths predicted by the LMO/C model exhibit considerable similarity both to the a priori predictions and to the experimental data. Only in the case of the C=C=C bending mode are the results very different. Semiempirical calculations of vibrational absorption intensities have been widely reported. The accuracy of our results is typical. Rotational strengths predicted a priori using the distributed orign with origins-at nuclei gauge are the sum of two terms, the “P-L” and the ‘‘P~M“ terms.I0 The former involves only the atomic polar tensors; the latter also depends on the atomic_axial tensors. The APT equation is obtained by neglecting the “P-M“ terms.10 Our results for allene-l,3-d2 show that in this case_t_heAPT equation is overall a very poor approximation. The ‘‘PsL” terms are a dominant contributor to the rotational strengths in only three modes: @ose at 847, 758, and 636 cm-]. The signs of the “P-L” and “P-M“ terms are identical in 8 of the 15 modes. The equation for rotational strengths predicted by the FPC model can be obtained from the APT equation (in the distributed origin with origins at nuclei gauge) approximating the atomic polar tensors via eq 1.Io As discussed above, eq 1 is poorly satisfied, and the APT equation is a poor approximation. We therefore expect that the FPC model will yield inaccurate predictions of rotational strengths. Our results bear out this expectation. Rotational strengths predicted by the LMO/C model are very different overall from those predicted a priori and exhibit considerable similarity to the FPC results. The L M O model for rotational strengths rests on the assumptions that the electrons are localized and that their orbits are much smaller than the dimensions of the m ~ l e c u l e .These ~ assumptions are difficult to justify in the case of allene-f ,3-d2, and it does not seem surprising that the predictions of the LMO model are inaccurate. The LMO/C model is implemented at a very different level of approximation than that of the a priori calculations, of course. However, the much greater reliability of the dipole strengths than of the rotational strengths suggests that the inaccuracy of the latter arises principally from the fundamental approximations of the model and not simply from the level of accuracy of the calculations. For the specific case of allene-13-dl our calculations thus show that the predictions of the APT, FPC, and LMO/C models are in poor overall agreement with the predictions of the a priori theory. Even with respect to the signs of the rotational strengths, these models yield agreement over the entire spectrum insignificantly better than statistical with the a priori theory. If only signs are compared, one does find a constant pattern predicted by all calculations for the C-H and C-D stretching modes. The existence of oppositely signed couplets for these pairs of modes undoubtedly reflects the symmetry of the molecule and would be expected to be predicted by all theories. However, the fact that the absolute signs are invariant is more surprising, especially given the large variation in predicted absolute magnitudes and the fundamental deficiencies of the APT, FPC, and LMO/C models. At the present time, we have no detailed explanation of this result. Our calculations do not support the general use of the APT, FPC, and LMO/C models in predicting rotational strengths and VCD spectra. Of course, one could argue that allene-1,3-d2 is a pathological molecule and that calculations on other more normal molecules will lead to a different conclusion. However, calculations on NHDT,I4 NH2NHZ,l7NHF(OH),I7 HN=C=NH,I7 CH3CHDCD3,I7oxaziridine,17 trans-cyclopropane-l ,2-d2.17trans- 1,2dicyanocyclopropane,18trans-oxirane-2,3-d2,I5propylene oxide,16 and 4- and 3-methy1-2-0xetanones,~~ inter alia, comparing a priori theory and APT and FPC model predictions have also led to the conclusion that the APT and FPC models are overall very inaccurate. On this basis, we believe that (at least for those two models) the results for allene-f ,3-d2 are typical. It seems very likely that the same is true for the LMO model.
J . Phys. Chem. 1990, 94, 199-203 The primary purpose of our calculations of rotational strengths of allene-1,3-d2 was to illuminate the conditions under which the simple FPC, LMO/C, and APT models might yield predictions of usable accuracy. As discussed above, the results for this molecule do not support the general use of these models. Nevertheless, in some of the molecules studied using the FPC and LMO/C models some success has been achieved in replicating some regions of experimental VCD Much of that agreement has been found for higher energy, “characteristic” modes.5 At the level of sign pattern, considering only the C-H stretch and asymmetric C==C=C stretch modes, the same would be true of allene-l,3-d2. In a similar comparison of theoretical VCD calculationsI2it was found that FPC and a priori calculations of VCD for trans-cyclopropane-f ,2-d2had a consistent sign pattern for modes lying above 1000 cm-I. In some studies, the molecular
199
geometry and force field were not accurately known and the significance of the conclusions arrived at is unclear. However, in a few cases-such as, for example, the study of trans-cyclobutane-f ,2-d2-accurate geometries and force fields were availThe reasons for these specific successes in predicting VCD spectra from either FPC or LMO/C models remain unclear and deserve further study. Acknowledgment. This work was supported by grants to T.A.K. from the National Science Foundation (CHE 84-12087) and to P.J.S. from the National Science Foundation, National Institutes of Health, NATO, and the San Diego Supercomputer Center. We thank Professor James Chickos for the gift of a sample of allene- f ,3-d2. Registry No. Allene-I,3-d2,19487-21-9.
Infrared Matrix Isolation Investigation of the Molecular Complexes of CIF with Benzene and Its Derivatives Hebi Bai and Bruce S. Ault* Department of Chemistry, University of Cincinnati, Cincinnati, Ohio 45221 (Received: May 5, 1989)
The matrix isolation technique has been employed to investigate the complexes formed between C1F and benzene, along with a series of substituted benzenes. 1:l adducts were formed in each case, and characterized by the shift of the C1F stretching mode upon complexation. For example, for the CIF.C6H6complex this mode was observed at 710 cm-I, shifted from 770 cm-l for parent CIF. A number of perturbed vibrational modes of the base subunit were detected as well, and this indicated that the CIF subunit sits axially above the benzene ring, interacting with the a-electron density. For the complex of CIF with C6HSBr,two different 1:l complexes were tentatively identified, one in which the CIF is coordinated to the ring, and one in which the CIF is coordinated to the bromine. The magnitude of the shift of the CIF stretching mode varied with the substituent on the ring in a manner which agreed with the electronic character of the substituent.
Introduction Molecular interactions and the formation of molecular complexes or adducts have been of ongoing interest to chemists for many y e a r ~ . I - ~ These complexes are often described in the electron donor-acceptor framework developed by Mulliken and others. Electron donors may be either lone pair u-donors or 7-electron donors from localized or delocalized *-electron systems. Stable complexes of benzene and its derivatives have been known for a number of years,6-8 often with the heavy halogens I2 and Br,. Several of these complexes have been characterized in cryogenic matrices as well, where isolated 1:l complexes can be trapped and s t ~ d i e d . ” ~ Fredin and Nelander have suggested9J0 that the complexes of c1, and Br, with C6H6 are oblique, while the l2 complex is axial. Further, they suggest that IC1 forms two complexes with C6H6, one oblique with the c1 nearer the ring, and one axial with the I nearer the ring. However, a study by Brown and Person showed15that it is necessary to use very high dilutions to isolate monomeric C6H6,suggesting that the complexes observed by Fredin and Nelander might not be 1:l complexes. Chlorine monofluoride, CIF, is a more reactive interhalogen and has proven to be an excellent probe of Lewis acid-base interactions.’620 ClF serves as a Lewis acid as it accepts electron density into its u* antibonding orbital, lowering the CI-F force constant and stretching frequency. Consequently, the experimentally determined position of this stretching mode is a sensitive indicator of the strength of the molecular interaction. Andrews and co-workers21,22 have used H F extensively as a probe of hydrogen bonding to a wide variety of electron donors, including substituted benzenes; the Lewis acid complexes of CIF provide Author to whom correspondence should be addressed.
0022-3654/90/2094-0199$02.50/0
an excellent parallel to these hydrogen-bonded complexes. Additionally, theoretical calculations have been carried out by several g r o ~ p son ~ ~complexes ,~~ of CIF, including the complex of C1F with benzene. These calculations suggest a structure which is axial 6 symmetry of the benzene ring. and which preserves the c Consequently, a study was undertaken to isolate and characterize
(1) Jensen, W. B. The Lewis Acid-Base Concepts, an Oueruiew; WileyInterscience: New York, 1980. (2) Mulliken, R. S . J . Am. Chem. SOC.1950, 72, 600. (3) Collin, J.; DOr, L. J . Chem. Phys. 1955, 23, 397. (4) Ferguson, E. E. J . Chem. Phys. 1956, 25, 577. (5) Ferguson, E. E. Spectrochim. Acta 1957, 10, 123. (6) Ferguson, E. E. J . Chem. Phys. 1957, 26, 1357. (7) Hassel, 0.;Stromme, K. 0. Acta Chem. Scand. 1958, 12, 1146. (8) Hassel, 0.;Stromme, K. 0. Acta Chem. Scand. 1959, 13, 1781. (9) Fredin, L.; Nelander, B. Mol. Phys. 1974, 77, 885. (10) Fredin, L.; Nelander, B. J . Am. Chem. SOC.1974, 96, 1672. (11) Brown, K. G.; Person, W. B. J . Chem. Phys. 1977, 66, 8876. (12) Engdahl, A.; Nelander, B. J . Chem. Phys. 1982, 77, 1649. (13) Engdahl, A.; Nelander, B. J . Phys. Chem. 1982, 86, 670. (14) Engdahl, A,; Nelander, B. J . Chem. Phys. 1983, 78, 6563. ( 1 5 ) Brown, K. G.; Person, W. B. Spectrochim. Acta, Parf A 1978, 3 4 4 117. (16) (17) (18) (19) (20) (21) (22) (23) Pitman (24)
Machara, N. P.; Ault, B. S . Inorg. Chem. 1985, 24, 4251. Machara, N. P.; Ault, B. S . J . Phys. Chem. 1987, 91, 2046. Machara, N. P.; Auk, B. S . J . Phys. Chem. 1988, 92, 73. Machara, N. P.; Auk, B. S . J . Phys. Chem. 1988, 92, 2439. Ault, B. S. J . Phys. Chem. 1987, 91, 4723. Andrews, L. J . Mol. Struct. 1983, 100, 281. Andrews, L.; Johnson, G. L. J . Phys. Chem. 1982, 86, 3380. Molecular Interactions; Ratajczak, H., Orville-Thomas, W. J., Eds.; Press: London, 1981; Vol. 1. Lucchese, R. L.; Schaefer, H. F. J . Am. Chem. SOC.1975, 97,7205.
0 1990 American Chemical Society
