J . Phys. Chem. 1990, 94, 6603-6607
and/or r’(Re2)+r(Re2), and such assignments are reasonable for the weak transient absorptions in the visible region. A clear distinction between the two types of excited states only arises when we consider o-u* transitions. The v u * transition of the 3(0-u*) excited state is spin forbidden and therefore cannot give rise to an intense transient absorption band. On the other ’ hand, the ’(n+u*)-type states have the ( u ) ~ ( u * )configuration; thus there should be a spin-allowed u+u* transition for these excited states. Note that this type of excited state retains a metal-metal bond order of I/,, which means that it will be bound regardless of ligand constraints. The energy and intensity of the excited-state PU* transition can be predicted by comparison with isoelectronic ground-state molecules that have been reduced by ’ While one electron, yielding the same ( u ) ~ ( u * )configuration. one-electron reduction of Re2(CO)loand its phosphine derivatives has been accomplished by low-temperature radiolysis and the products have been characterized by ESR methods,22no reports of the optical absorption spectra have appeared. However, the d7-d7compounds of the type Rh2(1,3-diisocyanopropane),(L):+, where L is a neutral or anionic axial ligand, have ground-state absorption spectra that are very similar to those of the d7-d7 M 2 ( C 0 ) 1 0compounds.23 Spectral data are available for the one-electron reduced dinuclear Rh compounds.24 These (U)~(U*), radicals show a very intense PU* transition at 450-500 nm that is red-shifted, as might be expected, from those of their present d7-d7 dimers. We would expect 3(~--w*) excited states to show intense u+u* transitions at similar wavelengths. Since the observed transient spectrum actually shows only very weak absorptions to the red of the ground state ‘ ( v u * ) transition (Figure (22) Symons, M. C. R.; Wyatt, J.; Peake, B. M.; Simpson, J.; Robinson, B. H. J . Chem. Soc., Dalton Trans. 1982, 2037. (23) Miskowski, V. M.; Smith, T. P.; Loehr, T. M.; Gray, H . B. J. Am. Chem. SOC.1985, 107, 7925. (24) (a) Miskowski, V. M.; Sigal, 1. S.; Mann, K. R.; Gray, H. B.; Milder, S. J.; Hammond, G . S.; Ryason, P. R. J . Am. Chem. SOC.1979, 101, 4383. (b) Milder, S. J.; Goldbeck, R. A.; Kliger, D. S.; Gray, H. B. J . Am. Chem. Soc. 1980, 102,6761. (c) Boyd, D. C.; Matsch, P. A.; Mixa, M . M.; Mann, K. R. Inorg. Chem. 1986, / 2 5 , 3331.
6603
S), we conclude that the transient excited state must be the 3 ( ~ + u * ) state.
Energy ofthe )(u+u*) State. It is the 3 ( ~ u *state ) of d7-d7 metal dimers that correlates electronically to the 17-electron radical fragments that result from metal-metal bond homolysis.17 Consequently, it is the population of this triplet state that gives rise to much of the photochemistry observed for this class of metal dimers. Unfortunately, the associated singlet-triplet absorption band appears to be very weak and has never been observed in the absorption spectrum of the decacarbonyls (Mn2(CO)loor Re2(CO),,) nor is it present in the absorption or excitation spectrum of the title compound. However, the low-temperature emission (A, = 700 nm) does provide a lower limit for the energy of the relaxed )(u+u*) state of this compound from the wavelength, -600 nm, at which the emission becomes vanishingly weak. This lower limit agrees fairly well with those derived from semiempirical calc~lations.l~~ The only other experimental bound on the energy of 3(u+u*) comes from the work of Poe and coworkers, who reported that the emissive triplet state of biacetyl (relaxed energy 19 700 cm-’ (508 nm)) was quenched by Mn2(CO),, and Re2(C0)8(P(C6H5)3)2,yielding the normal photoproducts of metal-metal dissociation. This gives an approximate ) for these comupper bound for the energy of the 3 ( ~ u *state pounds at -510 nm, which is similar to the value we estimated for Re2(CO),( dmpm),. Acknowledgment. We would like to thank Dr. G. G. Christoph for helpful discussions. D.R.T. acknowledges the National Science Foundation for support of this research. Some of the research described in this paper was carried out by the Jet Propulsion Laboratory, California Institute of Technology, under a contract with the National Aeronautics and Space Administration. Supplementary Material Available: Full crystallographic details for Rez(Me2PCH2PMe2)2(CO)6 (5 pages); observed and (1 2 calculated structure factors for Re2(Me2PCH2PMe2)2(CO)6 pages). Ordering information is given on any current masthead page.
Raman Matrix Isolation Spectroscopy of Hydrogen. 4. Rotational and Vibrational Spectra of Monomeric Species and Aggregation Processes in Solid Nitrogen M. E. Alikhani and J. P. Perchard* Laboratoire de Spectrochimie MolZculaire (AssociP au CNRS, UA SOS), UniversitZ Pierre et Marie Curie, 4 Place Jussieu, 75252 Paris Cedex 05, France (Received: November 20, 1989; In Final Form: March 5, 1990)
The rotational and vibrational Raman spectra of H2, D2,and HD trapped in solid nitrogen have been recorded at 9 K. After D2)lines. The corresponding deposition, monomeric species are identified by either one Q(0) (HD) or two Q(J), J = 0 and 1, (H2, So(J) rotational transitions display a doublet pattern with a splitting ranging from 22 to 26 cm-I. After annealing at about 25 K, totally different spectra are observed. In the Q(J)region the new features behave as those obtained in the same conditions in rare gas matrices while the S o ( J ) transitions are identified as single but broad lines with frequencies close to that of the free molecules and line widths strongly decreasing upon increase in temperature. These results suggest that hydrogen, because of its mobility and its low solubility in N2, migrates in annealing conditions and forms microcrystals with spectral properties comparable to those observed for the crystalline phase.
Introduction
As a first step in matrix studies devoted to the reactivity of dihydrogen with respect to small molecules (N2,CO, C2H2)in the presence of metal atoms, we have examined in detail the Raman spectra of H2, HD, and D2 trapped in inert matrices. In three previous papers (refs I , 2, and 3, referred to as I, 11, and (1) Alikhani, M. E.; Silvi, E.; Perchard, J . P.; Chandrasekharan, V. J . Chem. Phys. 1989, 90, 5221.
0022-3654190f 2094-6603$02.50/0
111) we have examined the spectral responses of monomeric and polymeric dihydrogen species embedded in solid rare gases. The purpose of this paper is to extend the spectral analysis to the case of N z matrices, with two main goals: on the one hand to get the (2) Alikhani, M. E.; Manceron, L.; Perchard, J . P. J. Chem. Phys. 1990, 92, 22. ( 3 ) Alikhani, M. E.; Manceron, L.; Perchard, J. P. Chem. Phys. 1990,140, 51.
0 1990 American Chemical Society
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Thp ,Journal of Physical Chemistry, Vol. 94, No. 17, 1990
true spectra of the monomers, which, as seen below, was not the case in the previous work^;^.^ on the other hand to examine in detail the aggregation process occurring on sample annealing, which was shown in 11 and I l l to lead to phase separation for Ar and Kr matrices, respectively. In the previous studies on the trapping of hydrogen in solid nitrogen4ss the rotational as well as the vibrational Raman bands of hydrogen had been characterized by complicated patterns. In ref 4 the S o ( J ) lines ( J = 0, 1) are split into quadruplets with irregular spacings; the existence of multiplets instead of single sharp rotational lines, as observed in the case of rare gas matrices, was considered by the authors as a proof of hindered rotation of H, in solid nitrogen. In ref 5 each rotational transition was identified as a triplet, the components of which display strongly temperature-dependent relative intensities. Such a complex pattern was interpreted in terms of site effect and rotational hindering. As for the Q branch, it was seen to exhibit a triplet and a quadruplet pattern in refs 4 and 5, respectively, whose origin is matter of controversy: aggregation in ref 4, vibration-translation coupling of monomeric species in ref 5. The observations made in our first experiments on the H 2 / N 2system appeared quite different from those previously reported and prompted us to reexamine carefully the Raman spectra of the three isotopic species. It will be seen that the comparison of the spectra of H2 and D2 with those of HD, which was not studied in the previous works, is of great help in ascertaining some of the assignments. Experimental Section The spectrometer, cryogenic apparatus, and experimental techniques have been described in detail in I. Nitrogen matrices of H,, HD. and D2 were prepared by deposition of premixed gases a t a rate of 50 pmol h-l for 15-20 h onto a Be-Cu alloy sample holder maintained at I O K. Raman spectra were recorded with a Coderg P H O spectrometer equipped with a Spectra Physics Model 164 argon ion laser delivering 800-900 mW power at 488 nm and a photon counting system (PAR 11 IO). The cryostat was an Air Products Model CS-202 closed-cycle helium refrigerator. A dielectric filter transmitting about 30% of the light power was employed to prevent unwanted plasma emission lines from appearing in the spectra. Raman line positions were accurately measured by superimposing one Ne emission line on the spectrum during the running scan. The frequency accuracy is 0.3 cm-I for the narrow Q lines and 1 cm-' for the weaker and broader rotationai and rovibrational lines. But the splitting between the components of the multiplets are measured with a better accuracy: 0.7 and 0.5 cm-! for the Q I ( J ) and S o ( J ) lines, respectively. Spectral slit widths, of the order of 1-2 cm-I for rotational lines, were decreased to 0.8 cm-' for the narrower Qi(J) lines. As discussed in I, the trapping efficiency of hydrogen with respect to that of nitrogen was checked by comparing the intensity of the Q branch of N, with respect to that of H2 in a binary matrix for :: given H 2 / N 2 molar ratio measured in the gas phase prior to deposition. From the knowledge of the cross section of H, and N, it nas concluded that the H2/N2 molar ratio in the solid matrix is half as much as that of the gaseous mixture. That is to say that, for our experimental setup, the relative trapping efficiency of hydrogen versus nitrogen gas is about 50%. Only the corrected values will be given in what follows. Results I . Spectra Recorded before Annealing. ( a ) Q Branches. Spectra recorded just after deposition at 10 K (Figure 1) are characterized by two lines for H 2 and D, and one line for HD, with frequencies reported in Table I. For H, the splitting is 7.0 f 0.2 cm-', the intensity of the low-frequency component at 41 38.5 cm-' being in most experiments about 2.5 times stronger than that of the high-frequency one (4145.5 cm-I). For D, the splitting is 2.8 f 0.2 cm-I, the low-frequency line being about 2.5 times (4) Prochaska. F. T.; Andrews. L. J . Chem. Phys. 1977, 67, 1140. (5) Bier. K. D.;Jcdl, H. J.; Daiifer, H. Can. J . Phys. 1988, 66. 708. (ti! Stoicheff. B. P. Can.J . Phys. 1957. 31. 730.
Alikhani and Perchard
hi__ . -L 330
370
600
--
-~ 4150
580
'nr*
Figure 1 . Typical rotational and vibrational Raman spectra of the three isotopic species of dihydrogen trapped in solid nitrogen. These spectra were recorded a t 10 K just after deposition a t IO K, with spectral slit widths of 2 cm-I for the S,(J) and 0.7-0.8 cm-' for the QI(J) lines. Dotted line: For comparison, S o ( J )lines of H2dissolved in liquid N2 at 75 K.
TABLE 1: Rotational and Vibrational Frequencies of H2, HD, and D2 (Natural o/p Abundances) Trapped in Nitrogen at 9 K before (M) and after (P)Annealing at 27 K assignH10 H D' D,O mentb
354.0
Qi(0) Qi(l)
586.5 4145.5 (4161.2) 41 53.5 4138.5 (4155.2) 4146.5
261. I
178.8
3617.7 (3632.1) 3621.9
2980.7 (2993.6) 2987. I 2977.9 (2991.5) 2985.0
I n parentheses are gas-phase values taken from lit (ref ti). mer: P. aggregate.
P M P M P M P
* M. mono-
weaker in intensity than the high-frequency one. These features are assigned to isolated hydrogen molecules. H2 and D2 monomers are expected to produce two Q ( J ) transitions, J = 0 and 1, but H D only one Q(0) transition. The difference, of course, arises from the symmetry forbidden o p nuclear spin conversion for H, and D,, which precludes the J = 0 state to be the only level populated at 9 K . The Qi(I)/Ql(0) intensity ratio is not very different from the room temperature value expected in absence of spin conversion (3.0 for H,, 0.5 for D,). However, in some experiments, these ratios were found to be much smaller, suggesting partial spin conversion, probably due to the presence of 0, impurity traces in the matrix sample. These intensity considerations, and also the spacing between the two lines close to the corresponding gas-phase value, are very strong arguments for the proposed assignment. These conclusions differ from those reported by the previous authors who have observed more intricate spectra. On the one hand Prochaska and Andrews4 assigned only one line at 4141 cm-I to the H, monomer without further comments; on the other hand Bier et aL5 observed a quartet in the Q ( J ) region of H 2 that they assigned to the H 2 monomer. The two low-frequency lines at 4139-4147 cm-l were assigned to the QI( 1 ) and Ql(0) transitions, respectively, in relatively good agreement with our own values; the two other features at about 41 53.5-41 59.5 cm-' were assigned to vibration-translation coupled transitions. In our experiments none of these two high-frequency features was observed after deposition; however, as discussed below, matrix annealing leads to the appearance of one new line at about 4153.5 cm-' assignable to polymers (see below). ( b )S,(J) Lines. Figure 1 compares the pure rotational spectra of HZ, HD, and D, recorded at I O K after deposition; the corresponding frequencies are included in Table I. All the observed transitions are reproducibly split into doublets framing the gas-
-
Raman Matrix Isolation Spectra of Hydrogen
~
The Journal of Physical Chemistry, Vol. 94, No. 17, 1990 6605
~
4150
4140
cm-1
Figure 2. Effect of the annealing temperature on the Q branch of H2 in solid N 2 ( H 2 / N 2 = 2/100). Spectra recorded at IO K: (a) after deposition, no annealing; (b) after 5 min annealing to 24 K; (c) after 15 min annealing to 26 K; (d) after 15 min annealing to 28 K.
phase S o ( J ) lines; the splitting between the components varies between 22 and 27 cm-', the larger values being observed for the So(0) transitions (26.5, 23.7, and 27.0 for H2, HD, and D2, respectively). The So( 1 ) doublet has been observed only for H2, with a splitting of 22.0 cm-l. In all cases the low-frequency component is the stronger and the narrower. These observations differ from those described in ref 4 and 5 , in which extra features were reported at intermediate frequencies between the two components of the doublet. It will be seen below that one of these features appeared in our spectra, but after annealing only. 2. Spectra Recorded after Annealing. ( a ) Q Branches. Raising the temperature from 10 to 25-27 K leads to irreversible spectral changes together with weakening of the Raman signals due to loss of dihydrogen from the matrix. The new spectra are characterized by the appearance of one (HD) or two (H2, D2) lines, hereafter referred to as P, blue-shifted with respect to those observed before annealing (Figures 2 and 3 and Table I). The main properties of these new features are as follows: (i) their intensity increases at the expense of that of the monomeric lines upon successive annealings at increasing temperatures; (ii) their widths are remarkably narrow, less than 0.5 cm-'; (iii) their position is not only dependent on the recording temperature (shift of 0.30, 0.20, 0.15 cm-' K-l for H2, HD, D,, respectively), but also on the annealing temperature; (iv) for H2 the frequencies and relative intensities of the two components are dependent on the ortho/para concentration ratio. Observation (i) is clearly demonstrated in the spectra of a H2/N2 sample recorded at IO K after successive annealings between 24 and 28 K (Figure 2). Comparison of the spectra obtained before and after annealing shows that the Q( 1) monomeric line at 41 38.5 cm-', prominent after deposition, strongly decreases in intensity upon annealing at 24 K; at the same time one strong band at 4144.4 cm-' and a weaker feature at 4152.3 cm-' have appeared, the first one overlapping the weak Q(0) line of parahydrogen monomer. Increase of the annealing temperature leads to progressive disappearance of Q( 1) and to weak but significant blue shifts of the polymeric lines. The frequencies reported in Table I are those measured after annealing at 27 K. The frequency blue shifts of the P lines on increasing the annealing temperature could be tied to the partial desorption process of hydrogen evidenced by the decrease of the Raman signals. Indeed in the desorption process the matrix sticking to the sample holder gets spoiled, leading to a lowering of the thermal exchanges and to an uncontrolled temperature increase of the sample. Since the band frequencies are noticeably temperature dependent, a temperature increase of a few kelvins would be enough to account
+
+
lM dka 2990
2980
cm-l
Figure 3. Vibrational Raman spectra of D2 trapped in solid N2, recorded at IO K: (a) D 2 / N 2 = 2/100, after deposition; (b) same sample as a, after annealing to 27 K; (c) D 2 / H 2 / N 2 = 1/3/100, after annealing to 26 K. A
+
2988 2985 cm-'
Figure 4. Comparison between experimental (a) and calculated (b), spectra of H 2 (left) and D2 (right) trapped in solid N1 Spectra recorded at IO K after annealing at 27 K. Left: lower traces, H 2 / N 2 = 2/100, o/p = 1.5; upper traces, H 2 / 0 2 / N 2 = 2/0.2/100, o/p = 0.25. Right: lower traces, D2/N2 = 2/100, o/p = 3; upper traces, D 2 / H 2 / N 2 = I,/ 3/100, o/p = 3. The synthetic spectra are calculated for a hexameric close packing aggregate, using gaussian band profiles for each component with fwhm = 0.8 cm-I. For H 2 u0 = 4146.0, up = 4152.5 cm-I; for Dz u0 = 2987.2, up = 2985.0 cm-l; in both casesf,, = -150 andf,,, = -30 dyn cm-I.
for the blue shift. Observation (iv) is displayed in Figure 4 which compares the spectra of H 2 polymers for two values of the ortho/para molar ratio, as measured from the intensity ratio of the Q( 1) and Q(0) lines of monomeric H2 recorded after deposition. On the lower trace, which corresponds to an ortho/para ratio of 2.4, the two bands are measured at 4146.5 and 4153.5 cm-' with an intensity ratio of the order of 4.2. For the upper trace the ortho/para ratio is 0.9 and the polymeric lines are measured at 4146.4 and 4151.3 cm-l, the intensity ratio between these two bands being close to 1.O. Thus these bands have to be associated with ortho and para molecules embedded in some kind of (H2)" aggregate but are not simply assignable respectively to each kind
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Alikhani and Perchard
The Journal of Physical Chemistry, Vol. 94, No. 17, 1990 H2
- Q(1) significantly greater than in the gas phase (7.0 against
Np
C
JL
Figure 5. Effect of the recording temperature on the So(J)lines of H2 trapped in solid N,: (a) after deposition, no annealing; recording temperature T, = IO K; (b) after annealing to 27 K; T, = 10 K; (c) same as b, T, = 25 K .
of molecules. A more striking example is encountered in the D,/N2 spectra (Figure 3), where the intensity ratio of the highfrequency/low-frequency components is 2.5 for the Q(O)/Q( 1) monomeric doublet and 0.43 for the 2987.1 /2985.0 cm-' polymeric one. These differences suggest that vibrational coupling takes place between molecules within the aggregate, as will be discussed in the next section. ( b ) So(J) Lines. As the vibrational spectra, the rotational spectra experience irreversible transformations upon annealing. The most significant results for H, are displayed in Figure 5; for each S o ( J ) transition the doublet observed before annealing is replaced by one line whose frequency is very close to that measured in the gas phase (ugas - v N 2less than 0.4 cm-I). The profiles of these new features are strongly temperature dependent, the line widths decreasing reversibly from 7 cm-I at 9 K to about 2 cm-' at 27 K. These lines were observed after deposition by Bier et aL5 who mentioned a comparable temperature dependence for the band profiles. 3. Q ( J ) Branches of Isotopic Mixtures. Double doping experiments involving two isotopic species of hydrogen were performed to demonstrate vibrational decoupling effects. The main differences with respect to the Q(J) spectra of polymers obtained in binary matrices are reported below. ( a ) H D Q Branch. Two experiments were carried out, in which H D was diluted with either H 2 or D,, at H 2 / H D and D 2 / H D molar ratios of 2.1 and 2.7, respectively. In both cases the H D polymeric band observed after annealing clearly displays a blue shift of the order of 2 cm-' with respect to its position in binary H D / N 2 matrices. This band is narrow, with observed fwhm of 1.0 cm-' for a spectral slit width of 0.7 cm-I. ( b ) D2 Q Branch. The vibrational spectrum of polymeric D2 diluted with H2 or H D is characterized by frequency blue shifts and by intensity inversion of the two bands with respect to those observed in binary D 2 / N 2matrices. Figure 3 shows the spectral evolution from a binary D,/N, = 2/100 to a H 2 / D 2 / N 2= I / 3/ 100 ternary mixture. Upon isotopic dilution both components experiment a 1 .O f 0.1 cm-I blue shift and recover the relative intensity measured for the monomeric Q(O)/Q( 1) lines. These spectral changes agree with those previously reported in I1 and 111 for rare gas matrices and, consequently, will have to be interpreted according to the same model of vibrational coupling within large aggregates.
5.93 cm-' for H2, 2.8 against 2.10 cm-' for D2) and with an intensity ratio IQcl,/lao close to the one expected in absence of ortho para conversion. Their positions suggest two comments. On the one hand the gas/matrix frequency shift is smaller than in rare gas matrices, an expected result if one remembers that the main contribution to the vibrational shift arises from the dispersion term of the matrix-hydrogen pair potential. This dispersion term, characterized by the C, coefficient of the Lennard-Jones potential, increases in the order N,/Ar/Kr/Xe in the ratio 1 / 1.2/ 1.8/2.2,' as the vibrational shifts ( 1 / 1.2/ 1.8/2.4 according to I). On the other hand the increase of the AQ splitting with respect to the gas-phase value may arise from two different causes: either (i) an increase in the vibration-rotation coupling constant a, or (ii) a rotational dependence of the vibrational perturbation. In the first case, if one considers that the AQ splitting is close to 2a, the increase of cy from the gas to the matrix is of the order of 17% for H2 and 27% for D,. Such large changes, tied to differential matrix effect on the internuclear distance in the L' = 0 and u = 1 vibrational states, should involve much larger vibrational perturbations than experimentally observed. As a consequence the second hypothesis seems to be more realistic. While the assignments in the Q(J) regions are straightforward, those in the rotational region are rendered difficult by the presence of a doublet for each transition with the following properties: The low-frequency component is stronger and narrower than the high-frequency one. But the relative intensities vary according to the transition considered and to the isotopic species. The splitting is roughly isotopically independent and decreases from So(0) to So(l). The mean frequency shift s o ( 0 ) = So(0)gas - s,(o), where So(0)is the mean frequency of the two components, is positive for H, and D, (+3.6 and +1.6 cm-', respectively) but negative for H D (-1.5 cm-I). For H,, A S 0 ( J ) varies from +3.6 cm-' for J = 0 to -2.2 cm-' for J = I . The splitting of the So(0) rotational transition has previously been observed for solid H, and D2 at 2 K by Welsh and coworkersE who observed in both cases a triplet pattern at 351.84-353.85-355.83 (parahydrogen) and 176.8-1 79.4-182.0 cm-' (orthodeuterium). These observations were accounted for by Van Kranendonk9 in term of M-degeneracy lifting of the J = 2 rotational level due to the anisotropic (quadrupolar) interaction between nearest neighbors. The larger splitting for D2 than for H2 (2.6 against 2.0 cm-I) was explained by a smaller intermolecular distance in solid D,. In the same way we suggest that the anisotropic N,-H2 interaction potential is at the origin of the splitting in solid nitrogen, with the following remarks: (i) According to Van Kranendonk et al.,9 since the crystal structure of a N, is fcc, the Raman lines have twofold instead of threefold split.ting expected in case of hcp structure. (ii) The value of the quadrupole moment of N, (2.3 times greater in absolute value than that of H,) is at the origin of the larger splitting. (iii) Matrix distortion around the H, molecule (contraction of the N, molecules around the substitutional site and symmetry loss) could also increase the anisotropic potential and contribute to enlarge the splitting. (iv) The rotational Raman lines of H 2 dissolved in liquid nitrogen in the temperature range 70-80 K undergot0 a huge broadening (Figure 1) which is, in our opinion, another manifestation, in a disordered medium, of the electrostatic contribution to the intermolecular potential. (v) For H, trapped in solid O,,which is another quadrupolar matrix, there also exists a splitting of the So(0) transition;" the
-
~~~~
Discussion 1. Monomers. Owing to their simplicity, the Q ( J ) branches recorded after deposition characterize exclusively monomeric species, They display one Q(0) line for H D and two Q(J), J = 0 and I , narrow lines for H 2 and DZ.with the splitting AQ = Q(0)
~~
~~
~
(7) Hirschfelder, J. 0.; Curtis, C. F.; Byrd, R. B. Molecufar Theory o j Gases and Liquids, Wiley: New York, 1964. (8) Bhatnagar, S. S.; Allin, E. J.; Welsh, H. L. Can. J . Phys. 1962, 40, 9. (9) Van Kranendonk, J.; Karl, G. Reo. Mod. Phys. 1968, 40, 531. (IO) Marsault, J . P. Unpublished results. ( I 1 ) Alikhani. M . E.; Perchard, J. P. To be published.
Raman Matrix Isolation Spectra of Hydrogen splitting is of the order of 7 f 2 cm-I, roughly in the ratio of the quadrupole moments (-5.1 for N2 against -1.3 for 02,in C m2). (vi) In the case of HD, the negative value of AS(0) is expected on the basis of the rotation-translation coupling already observed in rare gas matrices.' Aggregates. The vibrational spectra observed after annealing behave like those obtained in the same experimental conditions in rare gas matrices and, consequently, will be analyzed within the model of coupled oscillators described in 11. The analysis is based on three typical properties to be accounted for by the calculations: (i) the existence of one polymeric line for H D and of two lines for H2 and D,; (ii) the blue shift of the frequency upon isotopic dilution, for H2 and D,, and relative intensity decrease of the low-frequency component; (iii) for H2, a decrease of the splitting betwen the two components when the ortho/para molar ratio decreases. A hexameric aggregate in a close-packing arrangement, which corresponds to the upper limit for tractable calculations, was chosen since it was shown in ref 2 to give the best fit to the observed spectra. The molecules are identified with spheres whose centers are set at the apexes of an octahedron (Ohsymmetry). Four force constants have then to be introduced: two diagonal ones, Fo and Fp,respectively associated to ortho and para molecules, and two off-diagonal,S,, andf,,, between nearest neighbors and next nearest neighbors, respectively. These off-diagonal constants were shown in ref12 to arise from the H2-H2 dispersion potential and, as a consequence, are negative with a Rd dependence, where R is the intermolecular distance. Then, since the distances between n n n and nn molecules are in the ratio 2Il2, it follows that f,, = Sf,,,. Calculations have been performed according to the usual G F method. For H 2 and D2 12 ortho/para mixed species were considered, with relative abundance calculated by assuming that the ortho/para molar ratio has the value deduced from the intensity ratio of the monomer Q(J)lines. The line intensities are calculated by neglecting the polarizability anisotropy, which is well justified owing to the low value of the depolarization ratio of the Q branches of H 2 and D, in the gas phase.I3 Accordingly the relative intensity I,,,. of the mth mode of one hexamer p is given by the following relationship
The Journal of Physical Chemistry, Vol. 94, No. 17, 1990 6607 molecules of this hexamer. The spectrum was synthesized by adding the 12 spectra, assuming a Gaussian profile for each component. This model accounts for all the spectral properties of the aggregates. On the one hand vibrational decoupling upon isotopic dilution gives rise to a shift toward high frequency with respect to the position of the P signals of undiluted species, with, in the case of D, (Figure 4),intensity inversion of the two components. As discussed in I1 and 111, this last effect arises from the strong coupling between the vibrations of the orthodeuterium and paradeuterium molecules in (Dz)" aggregates, which tends to increase the intensity of the low-frequency symmetrical modes (the totally in phase mode being located at the lowest frequency because of the negative values of the interaction force constants). In the case of H, the ortho/para vibrational mixing is not so strong because of the larger difference between orthohydrogen and parahydrogen frequencies; the coupling experimentally evidenced by changes in frequencies and relative intensities of the two P components according to the ortho/para ratio can also be well accounted for with the help of interaction force constantsf,, and f,,, of the same order of magnitude as those used for H D and D2. Conclusions
where (an/&)is the isotropic polarizability tensor derivative with respect to the stretching coordinate r, Q,. the normal coordinate associated to the mode m,and N,, the relative abundance of the hexameric species p, the summation being extended over the six
With respect to the results obtained in rare gas matrices, there is one important difference in the Raman spectral response of dihydrogen embedded in solid N2 at 10 K: the behavior of the rotational lines of monomeric species which appear as doublets with splitting not significantly different for H2 and D,. We suggest that this property, also observed in other molecular matrices, arises from the M degeneracy lifting of the rotational levels due to the quadrupolar contribution to the interaction potential. The observations relating to the aggregation processes, on the contrary, are remarkably close to those made in solid rare gases and suggest the formation of microcrystals for annealing temperatures of the order of 25 K. Spectral simulation with a hexameric model does not correspond to a mean aggregation number of six but only to the upper limit for exact calculations. We rather think that these microcrystals involve a much larger number of molecules, as suggested by the spectral changes in the rotational region where the monomeric &(J) doublets are replaced by single more or less broad lines with frequencies close to that measured in solid dihydrogen, which are themselves close to that of the free molecule. In these conditions one may consider that these lines arise from molecules embedded in large clusters and are no longer sensitive to the electric field arising from the quadrupolar N, molecules. Complementary IR studies on the vibrational spectra of hydrogen in solid nitrogen are planned in this laboratory in the near future. In spite of the foreseeable broadness of the absorption bands, significant changes are expected from monomers to polymers.
(12) Van Kranendonk, J. Physica 1959.25, 1080; Can. J . Phys. 1960.38, 240. ( 1 3) Holzer, W.; Le Duff, Y.; Altmann, K . J . Chem. Phys. 1973,58,642.
Acknowledgment. We gratefully acknowledge Dr. L. Manceron for his help in setting up the experimental device. We also thank Dr. J. P. Marsault for giving us results prior to publication.
