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IL'III’IIHWdefiIIIIIIfiIIIIIIIIII IIII‘IIILI lflllllllllglflllLllllllllllllllflfllfll LIBRARY Michigan State University This is to certify that the thesis entitled VIBRATIONAL SPECTRA OF POLYCRYSTALLINE ETHANES presented by Mas soud Hassanpour has been accepted towards fulfillment of the requirements for Ph.D. Chemistry degree in gay/kg mite; Major professor Date September 7, 1979 0-7 639 OVERDUE FINES: 25¢ per day per item RETURNING LIBRARY MATERIALS: Place in book return to remove charge from circulation records VIBRATIONAL SPECTRA OF POLYCRYSTALLINE ETHANES By Massoud Hassanpour A DISSERTATION Submitted to Michigan State University in partial fulfillment of the requirements for the degree of DOCTOR OF PHILOSOPHY Department of Chemistry 1979 ABSTRACT VIBRATIONAL SPECTRA OF POLYCRYSTALLINE ETHANES By Massoud Hassanpour The Raman spectra of polycrystalline C2H6 and CZD6 in the solid (II) phase are presented and shown to be con- sistent with the recent crystal structure reported by Van Nes and Vos. The spectra strongly support Ci as the site sym- metry, which has been under question in the literature. The mid-infrared and/or Raman spectra of the neat, partially-deuterated ethanes: C2H5D, 1,1-C2HuD2, CH3CD3 and C2HD5, and of dilute mixed crystals of the partially- deuterated ethanes in one another have been obtained to learn more about the intermolecular force field of ethane and those of molecular crystals in general. The retention of the symmetry of the parent (C2H6) crystal as an "effective" symmetry in the partially-deu- terated crystals was concluded from the data obtained. Various sets of atom-atom interaction potentials were used to calculate the lattice frequencies of the C2H6 crystal with the aid of recent single crystal x-ray data. Massoud Hassanpour The "best" interaction potential was used to calculate the lattice frequencies of the partially-deuterated ethanes, assuming that the crystal structure and symmetry are un- changed by deuteration. From a comparison of the observed and calculated frequencies, it was determined that the lattice modes of the partially-deuterated crystals are amalgamated and can be described in the virtual crystal limit. Consistent with the virtual crystal theory, mutual exclusion was retained for the lattice modes of these dis- ordered solids, illustrating the "effective" Ci site sym- metry. Translational lattice frequencies of the partially- deuterated ethanes were also calculated using the potential which best predicted those of the C2H6 and C2D6 crystals. In the dilute-mixed crystal spectra, the guest modes often exhibit multiplet structure arising from different relative orientations of the neighboring molecules. The number of energetically-inequivalent orientations is diagnostic of the "effective" site symmetry of the host lattice (i424; symmetry in the spectroscopic rather than the mathematical sense), which was found to be Ci for each of the partially-deuterated ethanes. The magnitudes of the site (gas-to-crystal) shift, site-splitting and orienta- tional effect show no significant isotope effect, but they are sensitive to vibrational type. This indicates that the intermolecular force constants remain unchanged in going from the 02H6 to the C2D6 crystal. Due to the "effective " Ci site symmetry, the internal Massoud Hassanpour modes of CH3CD3 can be treated in the pure crystal exciton formalism and are quite similar to the internal mode spectra of C2H6 and C2D6. However, the internal modes of CZHSD’ l,l-C2H4D2 and C2HDS must be treated as mixed- crystal‘modes. To the heroic and toiling masses of Iran 11 ACKNOWLEDGMENTS I wish to thank Dr. George E. Leroi for his interest, advice and encouragement throughout the entire doctoral program. Advice from Dr. D. D. Ward regarding the interpretation of the crystallographic data and generation of the orienta- tion matrix is gratefully acknowledged, as are many helpful discussions with Dr. R. G. Whitfield. I am also thankful to the members of the Molecular Spectroscopy Group for their friendship and cooperation. Special thanks to Dr. Steve Gregory for his help regarding the use of Normal Coordinate Analysis program. Thanks are also extended to the faculty and staff of the Department of Chemistry for making my stay here a very pleasant and memorable experience. Financial support from MSU and NSF is gratefully acknowledged. iii Chapter TABLE OF CONTENTS LIST OF TABLES. . . . . . . . . LIST OF FIGURES . . . . . . . . . . . . . CHAPTER I. A. Introduction B. Background Information on Ethane In Condensed Phase . . . CHAPTER II. THEORETICAL TREATMENT OF CRYSTAL VIBRATIONS . . . . . . . . . . . A. The Vibrations and Selection Rules in Molecular Crystals B. The Crystal Structure of Ethane. . . . . . . . . . . C. Theoretical Approach to the CHAPTER III. CHAPTER IV. I A. Calculation of Molecular Crystal Vibrations. . . . 1. Calculation of Crystal- Vibrational Frequencies 2. Vibrational Exciton Tech- nique . . . . . . Site-Group Splitting. . The Orientational Effect. EXPERIMENTAL. nstrumentation . . . . . . . . . . RAMAN PHONON MODES IN CRYSTALLINE D6 AND PARTIALLY DEUTERATED ETHANES. . . . . . . . . . . Phonons in Disordered Crystals. iv Page vii xi 10 l8 l8 25 3A 36 Al A3 A6 A6 Chapter CHAPTER V. CHAPTER VI. CHAPTER VII. Page B. The Potential Function of Ethane. . . . . . . . . . . . . . . 50 C. The Librations of the Ethanes . . . 59 D. Raman Phonon Modes in the Meta- stable Solid Phase of Ethanes . . . '7A E. Conclusions . . . . . . . . . . . . 78 THE ORIENTATIONAL EFFECT, A MEANS FOR PROBING THE SITE SYMMETRY OF THE PARTIALLY-DEUTERATED CRYSTAL- LINE ETHANES. . . . . . . . . . . . . .. 79 A. Theory. . . . . . . . . . . . . . . 79 B. Experimental. . . . . . . . . . . . 81 C. Site Shifts . . . . . . . . . . . . 97 D Conclusions . . . . . . . . . . . . 100 THE RAMAN SPECTRA or NEAT CRYSTALLINE c H C2D AND SOEID THEIR MUTUAL S LUTIONS IN THE INTERNAL REGION . . . . . . . . 102 THE INTERNAL MODES OF THE PARTIALLY—DEUTERATED ETHANES. . . . . 11“ A. Introduction. . . . . ._. . . . . . 11“ B. The Internal Modes of CH3CD3. . . . llS Neat Solid (II) CH3CD3. . . . 132 Mixed Crystals. . . . . . . . . . . 136 C. The Internal Modes of CZHSD’ l’l-CZHL‘D2 and C2HD5. . . . o o o . 136 CszD . . . . . . . . . . . . . . . 138 1,1-02HuD2. . . . . . . . . . . . . 162 ' CZHDS . . . . . . . o . . . . . o . 163 D. Conclusion. . . . . . . . . . . . . 166 Chapter Page CHAPTER VIII. DISCUSSION AND SUGGESTIONS FOR FUTURE WORK. . . . . . . . . . . 167 REFERENCES. . . . . . . . . . . . . . . . . . . . . 169 vi Table LIST OF TABLES Page Lattice Parameters and Orientation Matrix for the Ethane Crystal . . . . . 13 Structural Parameters for free Ethane Molecule and Molecule in Crystal . . . . . . . . . . . . . . . . lS Correlation Table for INTERNAL Modes of Solid Ethane . . . . . . . . . 16 Table 3. Continued. Correlation Table for EXTERNAL Modes of Solid Ethane. . . . . . . . . . . . . . 17 Number of Energetically—Inequivalent Orientations for C2H6 Isotopes in Sites of C1 and cl. . . . .'. . . . . . 39 Nonbonded Potential Parameters, 6 + B (-Cr) + where ViJ = -Ar exp -1 QiQJr o o o o o o o o o o o o o o o o 52 The Observed and Calculated Lattice Frequencies (cm-1) of Solid (II) Ethane . . . . . . . . . . . 5A The Observed and Calculated Lattice Frequencies (cm-l) of Solid (II) C2D6 . . . . . . . . . . . . 56 vii Table 10 ll l2 13 1A 15 Calculated Translational Fre— quencies (cm-l) of Ethanes From Potential Set VIII. The Observed and Calculated Librational Frequencies (cm‘l) of Ethanes. . . . . . . . The Crystal Normal Coordinates of the Librations of the Ethanes. Perturbation Strengths of the Ethane Librations . . . . The Librational Lattice Fre- quencies (cm-1) of Ethanes in the Metastable Phase. . Observed 02HD5 Fundamentals in the Infrared Spectrum of a 3% C2HD5/C2H5D Mixed Crystal . . . . . Observed Infrared Funda- mental Frequencies (cm-l) of C2HSD Diluted in CH3CD3 and CZHDS . . . . . . . . . . . . . Observed l,l-C2HuD2 Funda- mentals in the Infrared Spectra of 15% l,l-C2HuD2/CH30D3 and H% 1,1-CZHuD2/02HD5 Mixed Crystals. viii Page 58 63 65 7O 77 9O 91 92 Table Page 16 Orientational "Splitting", 60E, of Partially Deuterated Ethane Guests in Dilute-Mixed Crystals. . . . . . . . . . . . . . . . 96 17 Gas-to-Mixed Crystal Shifts of the Ethanes. . . . . . . . . . . . . 99 18 Observed Raman Fundamental Frequencies (cm'l) of Pure Polycrystalline (Solid II) Ethane and its Dilute Solid Solution in C2H6. . . . . . . . . . . . 10A 19 Observed Raman Fundamental Frequencies (cm-l) of Pure Crystalline Ethane-d6 (Solid II) and its Dilute Solid Solu- tion in C2H6. . . . . . . . . . . . . . 105 20 Internal Fundamental Frequencies (cm'l) of CH3CD3. . . . . . . . . . . . 119 21 Observed Frequencies of CH3CD3 Fundamentals in Dilute Mixed Crystals of CH3CD3/C2H6 . . . . . . . . 121 22 Observed Frequencies (cm-l) of CH3CD3 Fundamentals in 2% CH3CD3/C2H5D . . . . . . . . . . . . 122 ix Table Page 23 Site Splitting for Degenerate Modes of CH3CD3 in Dilute Mixed Crystals. . . . . . . . . . . . . 137 2“ Internal Fundamental Fre— quencies (cm-1) of Solid (II) C2H5D. . . . . . . . . . . . . . . 139 25 Observed Fundamental Fre- quencies of Solid (II) 1,1-02HuD2. . . . . . . . . . . . . . . 1A1 26 Internal Fundamental Fre- quencies (cm-l) of Solid (II) C2HD 142 5. . . . . . . . . . . LIST OF FIGURES Figure Page 1 Packing of the Monoclinic Phase of C2H6 (From Reference 27) . . . . . . 13 2 Schematic ExCiton structure of Raman-active bands in crystalline ethane. . . . . . . . . . . 33 3 The Orientation of C2H5D in C2H6' . . . . . . . . . . . . . . . . . 37 A The Raman Lattice region of C2H6, CH3CD3 and CZD6. The peaks marked with an asterisk are laser fluorescence lines. . . . . . 6O 5 The Raman lattice region of Solid (II) c2H5D, 1,1-CZHuDé and 02HD5. The peaks marked with an asterisk are laser fluores- cence lines . . . . . . . . . . . . . . 61 6 The calculated librational fre- quencies versus the number of deuterium atoms . . . . . . . . . . . . 67 7 The observed librational fre- quencies versus the number of xi Figure 10 ll 12 deuterium atoms The Raman lattice modes of crystalline C2H6 and deuterated species. Relative intensities within each species are denoted by the vertical lines. Shoulders in the experimental spectra are indicated by dotted lines The Raman lattice region of CH3CD3 and C2HDS in metastable phase. The peaks marked with an asterisk are laser fluores- cence lines The Raman lattice region of C2H6 and C2D6 in the presence of both stable and metastable phases. The peak marked with an asterisk is a laser fluores- cence line. Part of the infrared spectrum of 3% C2HD5/02H5D; v1, v5, v7 (a"), V8 (a"), v10 (a' and a") and v11 (a") of C2HD5' . . . Part of the infrared spectrum of 3% C2HD5/C2H5D; v3, v6, V8 (a') xii Page 68 73 75 76 82 Figure 13 14 lSPa l6 17 Page v9 (a' and a"), v11 (a') and v12 (a') bands of C2HD5 . . . . . . . . 83 Part of the infrared spectrum Of 3% C2H5D/CH3CD3; V3: v7 (a'), ”8 (a'), v9 (a', a"), v11 (a") and v12 (a') bands of CZHSD . . .'. . . . . . . . . . . . . . 84 Part of the infrared spectrum v9 (a' and a"), v11 (a') and v12 (a') bands of C2H5D . . . . . . . . 85 Part of the infrared spectrum of 1.5% 1,1-02HuD2/CH3CD3; v3, v6, ”8 (a'), v9 (a' and a"), and v12 (a') of 1,1- C2HL‘D2. o o o o o o o o o o o o o o o o 86 Part of the infrared spectrum of 1.5% 1,1-C2HuD2/CH3CD3; v2, v5 and oil (a' and a") bands of 1,1-C2HuD2 . . . . . . . . . . 87 Part of the infrared spectrum Of 14% 1,1'C2HuD2/C2HD5; V2, V5, v7 (a' and a") and ”8 (a") bands of 1,1-C2HuD2. The peak marked with an asterisk is due to the V5 band of the host . . . . . . . . . . 88 xiii Figure 18 19 20 21 22 Part of the infrared spectrum of 4% 1,1-02HuD2/C2HD5; v3, V6, v9 (a' and a") and v12 (a' and a") bands of 1,1-02HuD. Part of the Raman spectrum of solid (II) ethane. The peak marked with an asterisk is attributed to v3 of C-13 substituted ethane molecules. Part of the Raman spectrum of solid (II) C2H6 (v1 and v10). The peak marked with an asterisk is attributed to v1 of C-13 substituted ethane molecules. The Raman spectrum of solid (II) C2D6. The peak marked with an asterisk is attributed to C-l3 substituted ethane-d6 molecules The Raman spectrum of solid (II) ethane-d6 in a A% solu- tion of C2D6 in C2H6. xiv Page 89 106 107 108 109 Figure 2A 25 26 27 Part of the IR spectrum of solid (II) CH3CD3; v2, v6, v9, v11 and v12. The peaks marked with an asterisk are attributed to 0-13 substituted molecules of CH3CD3 and that marked with the double asterisk is attributed to v9 (a") of l’l‘C2HuD2 -Part of the IR spectrum of solid (II) CH3CD3; v1, v5, v7, v8, v10 and 2V11 (2v6). The peaks marked with an asterisk are attributed to 0-13 substituted molecules of CH3CD3. . The v3, v12, v11 and v6 regions of the Raman spectrum of solid (II) CH3CD3. The peak marked with an asterisk is attributed to 0-13 substituted molecules of CH3CD3 Raman scattering from internal modes of solid (II) CH3CD3; v2, V8 and v5. The peak marked with an asterisk is attributed to C-l3 substituted molecules. XV Page 123 12“ 125 126 Figure 28 29 30 Page Raman scattering from internal modes of solid (II) CH3CD3; v1, v7 and v10. The peak marked with an asterisk is attributed to C-13 substituted molecules of CH3CD3 and that marked with the double aster- isk is assigned to an overtone of V6 and v11 in Fermi resonance with v10. . . . . . . . . . . . . . . . 127 Part of IR spectrum of 3% CH3CD3/02H6; v2, v3, v5, V6’ ”9’ V10, V11 and v12 of CH3CD3. The peak marked with an asterisk is attributed to C—13 substituted molecules of CH3CD3 and that marked with the double asterisk is attributed to v9 (a") of l’l'CzHuD2' . . . . . . . 128 Part of the Raman spectrum of at CH3CD3/C2H6 v2, v3, “6’ v10, v11 and v12 of CH3CD3. The peak marked with an asterisk is attributed to the overtone combination of V6 and v11 in Fermi resonance with v10. . . . . . . . 129 xvi Figure 31 32 33 3A 35 36 37 Page Part of the IR spectrum of 2.5% CH3CD3/C2H5D; v3, v5, v6, v9, v10, v11 and v12 of CH3CD3. The peak marked with an asterisk is attributed to C-13 substituted molecules and those with the double asterisk are attributed to v9 (a") of 1,1-02HuD2. . . . . . . .‘ 130 Part of the Raman spectrum of 2% CHBCD3/CZHD5; v2, v3, v10 and v12 of CH3CD3 . . . . . . . . . 131 Part of the IR spectrum of solid (II) C2H5D; v1 (a'), vs (a'), v7 (a") and v10 (a") . . . . . 143 Part of the IR spectrum of solid (II) C2H5D3 v7 (a'), ”8 (a") and v11 (a'). . . . . . . . . .I. . . . . . 1““ Part of the IR spectrum of solid (II) CZHSD; v2 (a'), v8 (a'), v11 (a") and v12 (a') . . . . . . 1A5 Part of the IR spectrum of solid (II) C2H5D; v9 (a') and v9 (a") . . . . . . . . . . . . . .' 1A6 Raman scattering from internal modes of solid (II) C2H5D; v6, v9 (a') and v12 . . . . . . . . . . . . 1A7 xvii Figure 38 39 A0 41 A2 “3 AM Page Internal modes of part of the Raman spectrum of solid (II) C2H5D; v3 and v7 (a'). The peaks marked with an asterisk are attributed to 0-13 substi— tuted molecules.[See also the text] . . 1A8 Part of the Raman spectrum of solid (II) C2H5D; v1, v5, v7 (a") and v10 (a"). . . . . . . . . . 1A9 Internal modes of solid (II) 1,1-C2H4D2. v1, v5, v7, v10 and ”8' . . . . . . . . . . . . 150 Internal modes of solid (II) 1,1-C2HuD2; v2, v3, V6’ v9, v12 and v11 (a"). . . . . . . . . . 151 Internal modes of solid (II) 1,1-C2HuD2; v9, and v3. The peak marked with an asterisk is attributed to C-l3 substi- tuted molecules . . . . . . . . . . . . 152 Internal modes of solid (II) 1,1-C2HuD2; v2, v6, V8 and v12 . . . . . . . . . . . . . . . . . . 153 'Internal modes of solid (II) 1,1-C2HuD2; v1, v5, v7 and v10. . . . . 15A xviii Figure 45 A6 A7 A8 A9 50 Internal modes of C2HD5; v v9 (a") and v 12 33 Internal modes of C2HD5; v6, V8 (a"), v11 (a') and vii (a"). Internal modes of C2HDS; Internal modes of C2HD5; v1 and v5. with an asterisk is attributed to C-13 substituted molecules of CZHD 50 The peak marked Internal modes of C2HD5; " v1, v7, and v10 (a ). Internal modes of C 2 5’ V6 (a'), v8, v9 and v11. The peak marked with an asterisk is attributed to C-l3 substituted molecules of CZHD 50 xix Page 155 156 157 158 159 160 CHAPTER I A. Introduction It has been known for several decades that vibrational spectra of molecules in the solid state provide valuable information concerning crystal structure, rotational and vibrational motions of the molecules in the unit cell and the nature of the intermolecular forces responsible for them.]'-3 The first and the most significant papers on the sub- Ject published by Halford (19A6),u Hornig (19A8)5 and by Winston and Halford (19A9,l951)6’7 enhanced tremendously the amount of experimental and theoretical work in this area. The introduction of lasers as Raman sources and the consequent availability of commercial Raman spectrometers, as well as the availability of sophisticated far—infrared instruments, have undoubtedly also played a significant role in the development of the field. Much of the initial work was devoted toward a qualitative understanding of the vibrational spectra. The first model quantitative inter- pretation was reported in 1962 when Dows attempted to calculate the vibrational spectrum of the ethylene crystal.8 The early work in vibrational spectroscopy 9 of molecular crystals has been reviewed by Dows 10 (lattice modes). The more 11 (internal modes) and Schnepp recent work in this area has been discussed by Baily, Pawley12 and by Schnepp and Jacobi.13 Many researchers have focused their studies on molecular crystals of simple aliphatic hydrocarbons, such 15-17 and ethane,18 and on the 19 as acetylene,lu ethylene simple aromatic hydrocarbons, such as benzene and naph- thalene,2O in order to develop a more quantitative under- standing of the intermolecular forces of the solids. These simple hydrocarbons are particularly attractive for study because they usually crystallize with two or four molecules per unit cell, and only three types of atom- atom interactions need be considered. This greatly sim- plifies the model calculations which are done to obtain a better understanding of the vibrational spectrum of a molecular crystal. B. Background Information on Ethane in Condensed Phase Although the IR and Raman spectra of ethane and of various deuterated ethanes in the gas and liquid phase have been studied by many workers,21 little and incomplete work has been done on the solid phases. The first work on the ordered crystalline (solid II) 1 ethane was a report on the IR spectrum in the 600-3000 cm- region by Avery and Ellis (19A2).22 [See Chapter II for the description of the solid phases of ethane.] Schwartz, 33 a1. (1971)23 have studied the far-infrared spectra of crystalline C2H6 and 02D6 at various tempera- tures between 25°K and 90°K. Each compound showed two absorption bands, which the isotopic frequency shifts revealed to be translational lattice modes. Leroi (1970)2A studied the torsional fundamental near 300 cm'1 in ordered solid (II) 02H6, CH3CD3 and C2D6. Preliminary Raman spectra of neat C2H6’ CH3CD3 and C2D6 in the crystalline phase were obtained by Leroi and Getty (1970)25 in this laboratory. The observed spectra revealed that the (hex- agonal) crystal structure proposed by Mark and Pohland (1925)26 on the basis of an x-ray powder pattern was in— correct, since it predicts neither site nor correlation field splitting correctly. By working through the pos- sible site and factor groups which give predictions in accord with the observations, Leroi and Getty suggested a Ci site with C2h factor group symmetry and two molecules per unit cell for crystalline ethane. Later Eggers and TeJada (1975)18 published the IR spectra of ordered solid (II) C2H6, 02D6 and their mutual solid solutions in the region of the internal fundamentals. From their studies, Eggers and TeJada tentatively proposed a slightly distorted hexagonal structure with two molecules in the unit cell, but they rejected Ci as the site symmetry. However, it was our belief from the beginning of this research that the most probable site symmetry would be Ci’ Just as for 02H2, 02Hu,benzene, naphthalene and several other hydro- carbons, all non-polar compounds. The observed Raman and infrared spectra of crystalline C2H6 and C2D6 were completely consistent with inversion site symmetry. It was not until recently (and well after the work des- cribed in this thesis was initiated) that Van Nes and Vos (1978)27 reported the single crystal x-ray analysis of two modifications of solid ethane - the plastic and the anisotropic phases - which confirmed our prediction of C1 as the site symmetry for anisotropic (ordered) crystalline ethane. In a very recent report on Raman and Infrared spectra of stable (ordered) crystal and a newly- found metastable solid phase of C2H6 and C2D6, Eggers and Wisnosky (1979)28 came to the conclusion that the site symmetry for the stable phase of crystalline ethane is indeed 01' Their work also includes a theoretical cal- culation of the fundamental frequencies of C2H6 and CZD6’ as well as a calculation of the relative intensity of the external modes of crystalline C2H6' The present study of the vibrational spectra of 02H6, 02D6 and partially deuterated ethane crystals: d1, 1,1-d2,'1,1,1-d3, and d5 has been conducted to learn more about the intermolecular force field of ethane, and of simple molecular crystals in general. We also wished to determine whether the symmetry of the parent (C2H6) crystal is retained as an "effective" symmetry in the partially deuterated crystals. This provides some under- standing of the effects of perturbations arising from dis- order in these crystals (vide infra) on the intermolecular force fields. The retention of effective symmetry enables interpretation of the spectrum of the partially deuterated ethanes on the basis of pure crystal theories. Because of the relationship between neat crystals and isotopically mixed crystals, useful information about neat crystal) intermolecular interactions can be obtained by studying the mixed crystals. This method has been shown to be very informative in the case of deuterated benzene,29’3O and similar work on the deuterated ethylenes in this 1aboratory17 has been of immense diagnostic help in the study of that system. CHAPTER II THEORETICAL TREATMENT OF CRYSTAL VIBRATIONS A. The Vibrations and Selection Rules in Molecular Crystals A distinguishing characteristic of molecular crystals is that in such crystals the molecules preserve their individuality in the first approximation. This is because the interaction forces between molecules, i;g;, inter- molecular forces, are much weaker than the forces acting between the atoms of a single molecule - the intramolecular forces. Therefore, all possible atomic vibrations in molecular crystals can be classified into two groups: I. INTERNAL VIBRATIONS, which are essentially those of the free molecule (i;g;, stretching and bending, etc. of chemical bonds in the molecule) subject to solid state interactions. II. EXTERNAL or LATTICE VIBRATIONS, which arise from (approximately) rigid body motion of molecular groups as a whole. The external modes are entirely solid state vibrations, and are characterized by their low frequency '1). (usually less than 200 cm Lattice modes can be further divided into two types: (a) TRANSLATIONAL modes which arise from changes in position of the center of gravity of the molecules and (b) ROTATIONAL or LIBRATIONAL modes which involve hindered or quasi-rotation of the molecular groups about their centers of gravity. Lattice modes are important in connection with crystal structure and make a large contribution to the specific heat of solids. Their energies vary considerably (in the 0-200 cm"1 range) and depend strongly on the molecular masses and moments of inertia, as well as on the nature of the bonding between the molecules. They are a property (mainly) characteristic of the solid state, and are not seen in the gas phase, although they are sometimes observed in liquids, indicating a quasi-crystalline struc- ture in those cases. Their width, frequency and intensity are temperature- and pressure-dependent. The coupling of internal and external vibrations, normally ignored in the analysis of the vibrational spectra of crystals, could become important as the internal and external modes approach one another in energy. From the theory of crystal dynamics, the selection rules for a molecular vibration to be observed via infrared or Raman spectroscopy require that X = 0, where X is the wave vector of a vibrational excitation travelling through the crystal with wave-like character. This arises because the interaction of a vibrational excitation with a photon must satisfy conservation of linear momentum. Therefore, the value of the wave vector of the vibrational excitation must be of the same order as that of the probing radia- tion.* In order that K 5 O, the vibrations of (transla- tionally) equivalent atoms in different unit cells of a molecular crystal must be identically in phase. Accordingly, the optically-active vibrations of the bulk crystal are the vibrations of a unit cell carried through the crystal, in the same phase, by the operation of translation. Con- sequently, a consideration of the normal modes of vibra- tion of the unit cell suffices to enumerate the genuine modes of the crystal as a whole. The implication of the above discussion is that the number of optically-observ- able fundamental vibrational degrees of freedom in a molecular crystal which contains in the unit cell m mole- cules, each having N atoms, is simply 3 mN. Three of 5 Consider, for example, the possible excitation of a given optical mode by infrared absorption, assuming this process to be allowed by symmetry. Of course, conservation of energy then requires that the photon frequency and the vibrational frequency be the same. But also, momentum must be conserved in the process. A quantized lattice vibration (phonon) acts for most practical purposes as if it possessed a momentum MK, where K is in the range of the first Brillouin Zone (-n/2a :,K g w/2a). It is thus required that MQ = MK, where Q is the wave vector (= 2n/A) of the observed photon. Since the wavelength of infrared light is large compared to the lattice constagt (a), is very small (103 cm-1 as compard to K = cm“ l).Q Optical transitions will then occur essentially at K = O. The same applies to Raman scattering processes. In this case, when a phonon is created by the inelastic scattering of a photon whose change in frequency causes its wave vector to change from Q to Q', it is required that HQ - MQ' = MK. Since Q and Q' are both small, clearly their vector difference is also small. these degrees of freedom are associated with the acoustic modes, whose frequencies are zero at K = O; the remaining 3 mN-3 modes are optical modes. (The acoustic modes cor- respond to the pure translation of the entire lattice in space). Of 3mN-3 optical modes 3(m-l) are translational vibrations, 3m belong to librational modes and the remain- ing (3N-6)m are accounted for by internal modes, assuming a non—linear molecule. .Therefore, if no degeneracies are present, the internal region would consist of 3N-6 vibra- tions each showing m components, usually referred to as the Davydov or factor group components. Degenerate modes of the free molecule can also be split because of the lower local symmetry in the crystal, which may no longer be consistent with the degeneracy. This latter splitting, usually called static field or site splitting, thus in- creases the number of components for degenerate vibrations to a maximum of 2m. The vibrational excitations of a molecular crystal may be classified as either phonons or excitons. Phonons, which are quantized lattice vibrations, are delocalized excitations in the crystal. The internal vibrations, which are localized, are usually classified as excitons. Since the phonons are delocalized, they are quite dependent on K whereas the localized excitons are only slightly de- pendent on §.l' The number and activity of the vibrational modes of 10 a molecular crystal are usually derived from a symmetry consideration of the crystal. Several types of symmetry groups need be considered, including the space group, the unit cell or factor group, and the site-group sym- metries of the lattice. The space group entirely des- cribes the symmetry relations among the molecules in the lattice, including the translational symmetry. The space group symmetry minus the translational symmetry is the unit-cell symmetry, which describes the symmetry relations of the molecules in the unit cell. The site group des- cribes the symmetry of the static field in which the molecules in the crystal interact. A correlation3l'33 of the free molecule symmetry with the site and unit cell symmetries provides information concerning the activity and number of Davydov and site group splitting components of the molecular crystal modes. B. The Crystal Structure of Ethane In the literature, contradictory information is avail- able regarding the symmetry of solid ethane. Wyckoff (1966)3u reports a hexagonal structure (P63/m 2/m 2/c, Z = 2) at 88 K. This structure was found from optical studies (Wahl (191A);35 Mark and Pohland (l925)26) of a solid sample of ethane Just below the melting point, combined with the structural information obtained by 11 Mark and Pohland (1925) from Debye-Scherrer diagrams taken with Zn, Cu and Cr radiation. According to Mark and Poh- land, the powder 1ines correspond quite well to a hexagonal unit cell. No definite conclusion was made concerning the space group(P63/m 2/m2/c was mentioned as one of the possibilities). However, this structure is inconsistent with the infrared and Raman spectra, as previously mentioned. According to an optical and dilatometric study by Eggers (1975),36 ethane shows the following transforma- tions: liquid——->isotropic solid——>anisotropic solid 90.2710.02K 89.82i0.02K A pressure-temperature phase diagram reported at the same time by Straty and Tsumura (1976)37 confirms the existence of the isotropic phase Just below the melting point. Proton magnetic resonance measurements by Givens and McCormick (1977)38 have given temperatures of 90.37 and 89.72 (0.05) K for the above transitions and very narrow lines for the isotropic solid. From his study, Eggers suggests that the isotropic solid is a plastic crystalline form, and that the symmetry of the anisotropic solid is lower than hexagonal. On the basis of IR spectra of the latter phase of 02D6, TeJada and Eggers (1975)l8 tenta- tively proposed a slightly distorted hexagonal structure with two molecules in the unit cell related by either a 12 glide plane or a screw axis. A very recent x-ray analysis of single crystals of ethane by Van Nes and Vos27 (1978) revealed that the (plastic) modification of crystalline C2H6 solid (1) at 90°K is cubic. In the cubic phase, which has symmetry Im3m, and two molecules in the unit cell, strong orienta- tional disorder is present. The anisotropic phase of ethane, solid (II), was determined to be monoclinic with space group P21/n and two molecules per unit cell. The two molecules in the cell lie at the inversion centers (0,0,0) and (8,8,8) and have a staggered conformation. Recently Wisnosky and Eggersza’39 reported a new phase for solid ethane. This new phase has been found to be metastable with a crystal structure different from the other solid phases of ethane. The pure metastable phase may be obtained at an optimum deposition temperature of A7°K, but when heated will rapidly and irreversibly trans- form to the stable phase, solid (II), at about 70°K. Sample deposition at temperatures above 60°K results in the formation of the stable phase. The metastable solid was sometimes formed during the course of this work. However, the current investigation is concerned with the vibra- tional spectra of the stable phase only. The crystal structure of ethane in the stable mono- clinic phase (solid II) is shown in Figure 1. Table 1 lists the lattice parameters and the orientational matrix 13 A01; ‘5 “‘33 "a. '3‘? -t’ Fig.9. ‘ Figure 1. Packing of the monoclinic phase of c Reference 27). 2 96(from a b Table l. Lattice parameters and orientation matrix for the ethane crystal. a = n.226 A b = 5.623 A c = 5.8A5 A = 90.0° s = 90.u1° y = 90.0° X y _ Z a .263A .A996 .8252 b -.6859 -.50A6 .52AA c .678A -.70A1 .2098 aFrom Reference 27. bSee text. 1A for an ethane molecule centered at the origin and initially oriented with C-C bond along the x-axis and two trans hydrogens in the xy plane. The unit cell lengths a, b and 0 correspond with Figure l; a,E3and Y are the angles between b and c, c and a, and between a and b, respec- tively. (Note that the unit cell is essentially ortho- rhombic.) The orientation matrix arises from rotations about the x, y and z axes by angles of -73.A1, -A2.72, and ~69-0 degrees respectively. The bond lengths, bond angles, and the changes caused by deuteration of the free molecule, and of the molecule in the crystal, are given in Table 2. H(l), H(2) and H(3) denote the hydrogens belonging to the same carbon atom in the molecule. The 6's are the changes in bond lengths and angles caused by deuteration. The correlation table for solid (II) ethane is given in Table 3. Six doublets (A-modes) and six quartets (E-modes), three of each Raman-active and three of each IR-active, are predicted for the internal modes. Six Raman—active librations and three IR-active translations are expected in the lattice region (after subtraction of the three acoustical modes). The vibrational spectra of C2H6 and 02D6 have been found to be consistent with the crystal structure recently determined by x-ray analysis and the above prediction, except that only two of the three predicted infrared-active translations have been observed,23 and that in a few cases fewer components are resolved for the internal modes. 15 Table 2. Structural parameters for Free Ethane Molecule and Molecule in Crystal. a Gas Crystal r (C=C) 1.5335 A 1.532 A r (C-H) 1.0955 A 1.096 A < (H(l)-C-H(2)) 107.76° 107.1° < (H(l)-C-H(3)) . 107.76° 111.A° < (H(2)-C-H(3)) 107.76° 108.3° < C-C-H(l) 111.10° 109.5° < C-C-H(2) 111.10° 111.8° < C~C-H(3) 111.10° 108.8° 6r (CH—CD) .0019 A 6<(HCC-DCC) -.010° 6r (cc—1300) .0001A A r (CC) -5 x 10"5 A for each successive deuterium substitution. 8‘Gas phase values and 6's from Reference A0. bFrom Reference 27. $333930." 33:33 89935 new :28: manage“ E was m .m G . w . h M- 3: G /—.-< Q\=Hfl \u k 3 m. = 3.u<"°°““‘°‘ TOW) E" / 33“ IR (2 .. acoustics) ~R and IR indicate Raman and infrared activity, respectively. 18 C. Theoretical Approach to the Calculation of Molecular Crystal Vibrations In the following discussion, two theoretical descrip- tions of the vibrations in molecular crystals are reviewed. The first, which is a semiclassical treatment and follows closely the work of Taddei gt_al,ul was used to calculate the external frequencies of ethanes in solid phase II. “2 The second, called the vibration exciton technique and ”3 assists in the discussion of developed by Davydov, experimental data for both pure and mixed crystals of the partially-deuterated ethanes. 1. Calculation of Crystal-Vibrational Frequencies In the conventional theory of lattice dynamics developed by Born and Huanguu the potential energy function of a molecular crystal is divided into two parts: U = vo + Ve , (1) where Vo represents the intramolecular part, £;2L, the internal energy of all molecules in the crystal, and Ve is the intermolecular potential energy and is the collection of all terms which refer to more than one molecule. For a piece of crystal large enough to fulfill the cyclic boundary conditions, the infinitesimal linear l9 displacements of the atoms are described in terms of the normal coordinates of the molecule and the external dis- placement coordinates. The external displacement co- ordinates are the Eckart-mass-weighted translational and torsional coordinates. As usual in the vibrational problem, the potential energy is expanded in a Taylor series about the equilibrium configuration in terms of the internal and external co- ordinates, 3N-6 l 2 2 2 U‘ 2“? <3V|aQ )Q E-au n 0 aun o aun BM 2 + g; 2; (3 ve/aQaulaQva)oQauzstm3 , (2) where u, v label the molecule in the unit cell, a, B the unit cell and 2, m, n the external and internal co- ordinates. The first (3N-6) coordinates are the internal coordinates for a non-linear molecule, and the last six coordinates are the external coordinates. The force field of the free molecule may be assumed for V0 if the equilibrium configuration of the molecule is not deformed severely in the crystal. However, V0 in principle should be the intramolecular potential rela- tive to the molecule in the site, and uncoupled to the other molecules in the lattice. It should also be noted 20 that the second derivative of V0 is taken with respect to the internal normal modes only. The form of V8 will be specified later. The second derivative of the intermolecular potential energy is ex- pressed with respect to both the internal coordinates and the external coordinates. The first derivatives of V0 and Ve have been assumed to be zero.“5 These terms may be excluded only when the interaction terms between the intra- molecular and intermolecular potentials are actually negligible and if Ve has a minimum for the observed crystal structure. The neglect of the third and higher derivatives of the potentials obviously confines such a treatment to the harmonic approximation. The problem may now be simplified by expressing equation (2) in terms of the symmetry coordinates va (g) which belong to the irreducible representation of the transla- tional group. These symmetry coordinates are given as follows: va (x) = L'l/2 E Qva exp (2nig°£8) , (3) where L is the number of unit cells in the crystal, £8 is a position vector connecting the 8th cell with an ar- bitrary reference cell which will be labeled 1, and § is the wave vector. The potential energy in terms of these symmetry 21 coordinates becomes, * Vm it E [EMQM (MQHME) + 5 12m Fu2(§)%£(}§)va(g)l u - ( ) where, F:?(é) = g (32Ve/8Qlu23QBum)o exp(-2n1x-g8) . . (5) The frequencies of the crystal normal modes v(g) can be calculated by solving the secular equation: |F:§(g) - [x<§) - A235 = o (6) uvalm where A(§) = uw2v2(§) and A2 = HnZvE. The via are the frequencies of the free molecule. The form of the intermolecular potential energy, Ve, must be specified in order to evaluate FX?(§). When only pairwise interactions are considered, V=§ZZVBV ufivwhena=8. (7) e a ’ a8 uv u th Here V3: is the pairwise interaction between the p molecule 22 th th in the a molecule in the 8th unit cell. unit cell and the v Therefore, in terms of Equation (7), um g _ , 2 Bu Fu£(§) 2 exp( 2ni§ £B)(a Vlu/anulaQva) o 871 if u=v 2 8T + 6 Z Z (a Vlu/anuzanum)0 if u=T (8) The molecule-molecule interactions are usually expressed as a sum of atom-atom interactions, _ l BvJ BvJ v - z 2: 2 v (r ) , (9) e Z’GB uv iJ aui aui where i labels the atoms belonging to molecule an, and J the atoms belonging to molecule 8v. The interatomic ij aui' of the atom—atom potentials, the second derivatives in distance between atoms 1 and J is given by r In terms Equation (8) are given by: 23 32V?“ 2 32V11 ari ear-11 Br Br 3V Br Br Br Br J , 1,1 + 11 i , 11 1 , 11 , aQva 3rJ ariJ anul 3ri BQva arJ BvJ where for simplicity, VBvJ and raui aui have been replaced u1,u6 have by ViJ and r13, respectively. Taddei, gt El- pointed out that traditionally the second term in the above equation has been ignored. They have calculated the lattice frequencies of benzene with and without this term. The inclusion of this "first derivative" term caused a 2% to 15% reduction in the calculated lattice frequencies, showing that the effect of this term is not negligible. Kobayashil47 also points out that his calculation indicates that the effect of inclusion of the linear terms on the normal fre- quencies of polyethylene crystals is non-negligible for the librational lattice modes (it lowers the frequencies by as much as 20 cm'l), while its effect is not drastic for the translational lattice modes or for the correlation splitting of the internal modes. Agreement between the observed and calculated frequencies of the lattice modes is improved significantly by inclusion of the linear terms. Therefore, this term was included in the calculation of lattice 24 frequencies of the solid ethanes. The solutions of the above secular equation [Equation (6)] will give the frequencies of the crystal normal modes over the entire Brillouin zone. However, § selection rules make it possible to observe only the optically-active vibrations, that is vibrations with 5 = 0, via infrared absorption and Raman scattering. It should be noted that § arises from the translational symmetry of the crystal; therefore if the translational symmetry is destroyed it may no longer be a "good" quantum number. As noted earlier, the intermolecular potential is usually specified as the sum of molecule-molecule pair- wise interactions which are expressed as a sum of atom-atom interactions. The atom-atom interaction potential for hydrocarbons is often expressed as a Buckingham potential (exp-6): ViJ = B exp(-CriJ) - Ari? , (ll) and sometimes includes Coulombic interactions (exp-6-l): -6 -l ViJ = B exp(-Crij) - AriJ + QiQJriJ (l2) 25 where r13 is the nonbonded interatomic distance, i;g;, the interatomic distance between atom i of molecule a and atom J of a molecule other than a in the crystal. A, B and C are adjustable parameters which are obtained by refinement to non-spectroscopic crystal properties such as heats of sublimation and crystal lattice energies. The parameters Q1 and QJ are point charges on atoms 1 and 3, respectively. . The actual calculations of the crystal frequencies of the ethanes were made using program TBON, a computer pro- gram written by Taddei and Bonadeo. 2. Vibrational Exciton Technique Over the past 30 years two complementary theoretical approaches have been taken to solve the problem of Frenkel excitons.“8 The first, the Halford-Hornig approach, is almost purely group theoretical in nature. The second ap- proach, called the Davydov theory,“3 is a technique for obtaining general crystal energy levels. The following discussion is a review of the modified form of Davydov's theory given by Bernstein gt_al.19 to be used in the qualitative discussion of static and dynamic effects in molecular crystals, iagaa the Splitting and shifts of modes in the solid state in comparison to those of the free molecule (see also Reference “9, Chapter 6). 26 The above-mentioned technique first quantizes the local, molecular modes (tight—binding formalismso), and then forms delocalized wave functions for the whole crystal. In the limit of the tight-binding (Frenkel) approximation, the zeroth-order crystal states, representing localized vibra- tional excitation f on a particular molecule at a given site nq in the crystal, is given by: f f O , (13) wnq 3 ¢nq n&;ntqt ¢ntqt where n labels the unit cell, q labels the site in the unit cell, f refers to the fth excited state of the molecule, and ¢nq is a crystal site function. It is assumed that the various f states do not mix and that the localized excita— tion functions are orthogonal, i.e., f f' (wnqlwntqt> = Gnn'éqq'aff' . (1“) Then, from these functions one can generate the one-site exciton functions (excitons in which any amount of excita- tion is on a single molecule) in the Bloch representation, N X exp(i :R )w n=l § nq f _ -1/2 f wq - L nq , (15) 27 where N is the total number of molecules in the crystal denotes the position of the center of a molecule th and an located at the qth site in the n unit cell with respect to a common origin. (16) with En being the vector from an arbitrary crystal origin th to the origin of the n unit cell and gnq a vector from the origin of the unit cell to the molecule in the qth site in the same unit cell. It is convenient to divide the Hamiltonian, H, into a one-site Hamiltonian H° and an intersite interaction Hamil- tonian H'; H = H° + H' , _ (17) where G _ o = o H n21 qgl an (18) and H' = (19) H, nqfig'q' nq’n'q' 28 The Hfiq n'q' terms represent the pairwise interactions of 3 the molecules in the crystal. The eigenfunctions of H° are Just the crystal site nq functions ¢nq introduced in Eq. (13). H° is (considered nq to be) the Hamiltonian of the free molecule whose nuclear framework has been distorted to match that of the molecule in the crystal. Using the one-site exciton functions of Eq. (13) as zero-order functions, the first-order Hamil- tonian matrix element for the excited states of crystalline ethane, corresponding to the fth excited state of the mole- cule, are: Lf ( ) - )3] ex [(1K)( )]< f lHl f > (20) qql 5 ‘ n'=l p m Enq’fintqt wnq wntqt ° Separating the H-independent terms from the H-dependent terms, f _ f r f qu,(§) _ (a +D )5qq, + qu.(§) , (21) where f _ r f e - = <¢nq|ngl¢nq (22) is the g-independent free-molecule excitation energy, and 29 Df = = 2 <¢ nq nq nq#n'q' f o f o is the H—independent contribution to the environmental shift. The H-dependent term consists of both a diagonal part, f _ f f qu(§) - ngh' exp[1§(finq-fin.q.)J . (2“) which represents the interactions of the translationally- equivalent molecules, and off-diagonal parts, f — qul(£) - nfi' expEiE(finq-fingq.)] f , f , <2u) representing the interactions of the translationally in- equivalent molecules in the crystal. 30 Band Energies - The crystal excitation energy, for a particular value of K, now can be found by solving a o x a determinant of H. For the ethane crystal where a = 2, the crystal energies would be:u9 12%;)1 = sf + Df + %{qu(§) + L§.q.(g)3 z %{[qu(§)-qu,(g)12 + AEqu.(§)12}1/2 , (25) where Ef(0)+ and Ef(o)' are the energies of the two Davydov components for the internal vibration f, separated by f f 2 f 2 1/2 {Equ(§) - qu.(g>1 + utqu.fiuomlcm5mm mo opsuospum :ouaoxm oapwsonom .m madman WW W : K t A8 332.0 till: llllll 30 flIIMflII IIIIIIIIII IIIIIIIIIIIIIIIIIII: IIIII I It... s 3 h ouulx .o coo: .6339 18351.81. 0 A GO 3 .0359 $33.: 0 3o” .128. 23.5 ‘ 3.5 30 3“ to the shift. Therefore, the static and dynamic effects can be separated experimentally by observing the spectra of isotopic dilute mixed crystals, where it is E’+ A, not 'E + A + Lf(o), that determines the position of the guest energy levels in the ideal case. Site-Group Splitting - Another type of splitting which is observed in the spectra of molecular crystals like CZHS is site-group, or static-field splitting. This is caused by the destruction of molecular degeneracies when the gas phase molecular symmetry is lowered in the crystal. Bern- stein gt al.19’29 have suggested that the site-group splitting be defined phenomenologically as the splitting obtained for the guest in an ideal-mixed crystal, where there exist no resonance interactions between the molecules in the crystal. The ideal-mixed crystal is defined as one in which: (a) The guest is infinitely dilute, (b) Guest and host differ only by isotopic substitution, (c) Guest and host have the same symmetry and dimension, (d) Quasi-resonance interactions between guest and host (Q in Figure 2) are negligible, and (e) The effect of isotopic substitution on A can be neglected. 35 In the ideal mixed crystal, therefore, the site-group splitting of a degenerate gas-phase band will be quanti- tatively identical to the difference in the A terms of the originally degenerate components. Symbolically this can be written as (Ax’Ay) where x and y designate the degenerate components (see Figure 2b). In the neat crystal there are additional resonance contributions to the splitting of free-molecule degenerate states; i;g;, once degeneracy has been removed by static- field interactions, the degenerate levels may be further coupled by the dynamic (fi-dependent) interactions or by quasi-resonance interactions in the mixed crystal. The essence of the above statement is that whenever both site group and factor group splitting are expected together, the total effect cannot be treated as a simple superposition of the two independent effects. A separation of the two effects would be Justified as a first approximation only if: (a) The site-group interaction is at least an order of magnitude larger than the resonance interaction; and (b) the site-group components are of different symmetry; or (c) the resonance interactions are much larger than the site-group splitting. 36 Except for the first two cases, the so-called site-group splitting in a neat crystal will contain contributions not only from the phenomenological site-group splitting in the ideal mixed crystal, but also from resonance interactions. The Orientational Effect - The effect of the crystal site on degenerate molecular states was considered in the last section. However, another site effect, referred to as Orientational "splitting" may be observed for non- degenerate modes in the spectra of dilute mixed crystals of partially deuterated ethanes in comparison to mixed 02H6/C2D6 crystals. This arises because the guest molecules can have different specific orientations with respect to the environmental field of the host; i;g;, the guest mole- cule can orient itself in more than one way in this field, and the differently oriented vibrational transitions may have different "static" energies which appear as a "splitt- ing" in the experimental spectrum. This is illustrated in Figure 3 for a dilute mixed crystal of CZH D in 02H6 5 (or CZHD5 in CZD6)' However, of the six distinct transla- tionally-inequivalent orientations, 3(a) and 3(b) are energetically equivalent on the Ci site of the host as are 3(c) and 3(d), and 3(e) and 3(f). This is easily understood by examining the nearest neighbor interactions. The orientational splitting therefore depends upon the site symmetry of the host. If the CszD (or C2HD5) guest Figure 3 _ The orientations of C2H5D in C2H6 . 38 molecule resides on a C1 site (which in a rigorous mathe- matical sense would apply, for example, to dilute mixed crystals of the dl-isotope in the dS-isotope), obviously the six orientations 3(a) - 3(f) would be energetically- inequivalent and a sextet is expected for the non-degenerate guest modes. Thus the number of components observed in the spectrum for a given vibration is an indication of the "ef- fective" site symmetry.. The orientational effect has been observed for a number of isotopically-substituted molecules, including the par- tially deuterated ethylenes in our laboratory17 and the partially deuterated benzenes by Bernstein.29 Bernstein mentions in his report that the orientational "splitting" observed in mixed crystals occurs also in a neat crystal, but usually serves to broaden the exciton structure. A group theoretical method described by KopelmanSl may be used to determine the number of translationally- inequivalent orientations and the number of energetically- inequivalent orientations which exist for a given isotope. The number of energetically-inequivalent orientations which exist for the different partially-deuterated ethanes in a C1 or C1 site are tabulated in Table h. As was pointed out earlier, the site splitting and orientational effect are similar and both are static effects. Therefore, the orientational "splitting" is also equivalent to the difference between A's in the dilute-mixed 39 Table H. Number of Energetically-Inequivalent Orientations for C2H6 Isotopes in Sites of C1 and C l. Substituted Molecular No. of Orientations Compound Symmetry In Site of C1 Cl Ethane-dl and-d5 CS 3 5 Ethane-1,2-d2 and l,l,2,2 du Cé 3 6 02h 1 3 Ethane l,l--d2 and l,l,l,2-du Cs 3 6 Ethane l,l,l-d3 C3v l 2 Ethane 1,1,2-d3 CS 3 6 C 6 l2 U0 isotopic crystals. It should be noted that partial deuteration of ethane destroys not only the D3d symmetry of the free C2H6 molecule, but also results in the destruction of the translational as well as the C1 site symmetry of the crystal lattice, because in the partially-deuterated ethanes the molecules assume translationally-distinct orientations in the crystal. However, the disordered crystals may show an "effective" Ci site. This can be understood if one ignores the substituents on the C-C frame, and notes that the same crystal structure as the parent 02H6 is retained assuming negligible changes in the lattice parameters upon deuteration. One goal of this research was to ascertain whether the effective site sym- metry in the partially-deuterated ethane crystals was C1 or 01‘ CHAPTER III EXPERIMENTAL Research grade ethane (C2H6) was obtained from MG Scientific Gases and had a stated minimum purity of 99.99%. The -d1, -l,l-d2, -l,l,l-d3, -d5 and “d6 isotopic species of ethane were obtained from Merck, Sharp and Dohme of Canada; their minimum isotopic purities were stated to be 96.3u atom zD, 98 atom Z D, 98 atom ZD, 99 atom %D and 99 atom ZD, respectively. All samples were used without further purification. The mass spectrum of each compound was obtained using electron bombardment beam energies of 15 eV, 20 eV and 70 eV, but no additional information on impurities could be determined. The gas phase samples were sprayed onto the cold cell substrate for both Raman and infrared experiments. The vapor-deposition technique was used because it is more convenient and controllable than growing polycrystalline samples from a drop of liquid (a technique sometimes em- ployed in such studies), in that it allows samples of dif- ferent thickness to be studied in the infrared and samples of good scattering quality to be obtained for Raman in- vestigation. Both the back pressure and flow rate of the “l H2 sample were found to be important and critical in obtain- ing deposits of high scattering quality for Raman investi- gation. When the samples were deposited and a needle valve was used to control the flow in such a way that more sample was deposited on one side of the cold substrate, the sample looked snowy and very good scattering was obtained from that side. To get such a deposit, one starts to open the needle valve slowly until the beginning of the (white) condensate on the substrate is observed. Then the flow of the sample should be increased and controlled to maintain more deposition on one side. If the flow is slower than it should be, then a uniform deposit is obtained which has poorer scattering quality. The Raman samples were deposited at low temperature (~20°K) and then annealed at approxi- mately 70°K for 15-30 minutes prior to recooling for spectroscopic observation. Annealing was important to be sure that the sample was in the stable ordered solid phase of ethane, the phase we were interested in studying. Annealing above 75°K (the melting points of the ethanes52 are W9O°K) produced solid samples with many cracks and of poor scattering quality. The infrared samples were deposited at about 70°K and maintained at that tempera- ture for 5-10 minutes for annealing, and then slowly cooled for spectroscopic observation. The dilute'mixtures were made by mixing predetermined amounts of gas phase samples of the guest and host. A “3 high vacuum line with calibrated volumes was used, and the pressure of the gases was measured with a mercury manometer. The amount of the mixture made was such that it would yield a back pressure similar to that of the pure samples. Instrumentation An Air Products model CS-202 or CSA-202 Displex cryo- genic helium refrigerator system was used for cooling the samples. Typical temperatures were between l6-23°K when the spectra were recorded, as measured by a gold (0.07% iron) gs. chromel thermocouple imbedded in the cold sub- strate. The higher temperature limit usually applied for the Raman experiments. The higher temperature is believed to be caused by the size of the Raman cell and the fact that the cell and shroud were not nickel plated. The temperature of the samples was controlled with either a cryodial model ML lhOO automatic temperature regulator or an Air Products temperature controller with calibrated platinum resistor for temperature sensing. For IR experiments, CsI was used for the outer windows and the cold substrate. Quartz was used for the outer windows and copper for the substrate in the Raman work. Thin sheets of indium were placed between any two parts of the cryostats required to be in good thermal contact. an The Raman cell which was used has been described pre- viously by Elliott and Leroi.15 It is a closed cell which enabled evacuation independent to that of the shroud. The vacuum in the sample cell was about 2 x 10-5 torr be- fore the cell was cooled and the sample deposited. The following spectrometers were employed: A Perkin-Elmer Model 225 IR grating spectrometer (“000- 200 cm'l), with resolution better than 1 cm"1 above 500 cm-1 and between 1-2 cm'1 below 500 cm'l. should be accurate to 11 cm'l. Reported frequencies A Raman spectrometer comprised of a Jarrell-Ash model 25-100 double Czerny-Turner monochromator coupled with a thermoelectrically-cooled RCA 031034 Photomultiplier tube and a spectra physics Model 16h Ar+ ion laser as the ex- citation source. Both the 51MB 3 and h880 A lines of the Ar+ ion laser were used as exciting lines for all Raman experiments in order to distinguish laser-fluorescence lines. In some cases the lattice spectra were also observed with the “765 A line of the argon-ion laser as the exciting line in order to positively eliminate interference from laser-fluorescence lines. The resolution in the Raman 1 spectra was 1 cm' or better for the fundamentals and lattice modes. Most of the reported infrared and Raman frequencies 1 are believed to have an accuracy of :1 cm' , especially 145 for those of sharp and strong bands; for poorly resolved bands this accuracy is $2 cm'l. However, for very broad bands in both the infrared and Raman the accuracy may fall to :3 to 15 cm'l, as well as for overtones and combination bands. CHAPTER IV RAMAN PHONON MODES IN CRYSTALLINE C2H6, C2D6 AND PARTIALLY DEUTERATED ETHANES A. Phonons in Disordered Crystals It was pointed out in Chapter II that isotopic substi- tuion in molecular ethane causes the molecular point group symmetry, D3d’ of the parent (02H6) molecule to be lost with the formation of lower molecular symmetries. There- fore, isotopically substituted molecular ethanes, CZHSD’ CH3CD3, 02HD5 . . ., 222. can assume several different relative orientations upon solidification, and crystals of these molecules are translationally disordered. This might be a disaster in the interpretation of the experi- mental results, because the mutual exclusion of the lattice phonon modes is expected to be destroyed in the absence of Ci site symmetry, and the "M-selection rule" may no longer be applicable due to lack of translational symmetry. Recently there has been much interest in the study of phonons and excitons of heavily doped mixed crystals. More studies, however, have been centered on excitons rather than phonons. ”6 A7 Phonons of simple disordered systems of heavily doped isotopic mixed crystals like: benzene-h6:benzene-d6;53 naphthalene-hm:naphthalene-dlo;5)4 durene-hlu:durene-dlu 55 have attracted investigators the most. Their studies of the mixed crystals have provided information regarding the nature of phonon bands, the validity of the separation between librational and translational motions, line broaden- ing, band mixing, and localization vs. delocalization in the mixed crystals. It has been observed that the phonon states of isotopic-mixed crystals are in the amalgamation limit;53’56 that is, the same number of phonon bands are observed for mixed crystals as in the pure crystal, while the corresponding phonon bands shift almost linearly as a function of the concentration, between the positions of the two pure constituents. It appears as though the two substances are completely amalgamated to yield another new crystal with perfect periodicity. The mixed crystal can then be regarded as a virtually perfect crystal. Hong and Kopelman53 have shown, in their coherent potential approximation for interacting bands in the weak perturbation limit (virtual crystal limit57’58), that the phonon energies of the mixed isotopic crystals can be ex- pressed as follows: w = wA/(l-CBAf) , (3o) A8 where “A is the frequency of the pure host and C is the B mole fraction concentration of the guest. The parameter Af is called the perturbation strength of the band and is defined as (ni-ng)/n£, where f designates the degree of R T freedom (i.e., Rx: Ry’ z, x’ Ty, T2) and n is the mass (for translations) or moment of inertia (for librations). f If A is very small, Equation (30) can be rewritten as l w = wAu + 5 CBAf) , , (31) which predicts a linear dependence of the frequencies on the guest concentration. The weak perturbation assumption holds perfectly in substitutionally disordered systems, where the intermolecular force constants of the mixed crystals are the same as those of the pure crystal. It follows that, in substitutionally disordered systems: (a) The §-selection rule is still valid; (b) all the phonons are delocalized; and (c) the normal coordinates described in the mass- or moment-of-inertia-weighted coordinate system remain unchanged in going from the pure host crystal to the pure guest crystal. It can be concluded, then, that the spectroscopic activity of the lattice modes should remain unchanged. Thus, mutual exclusion would be retained if the pure crystal has 49 a centrosymmetric site symmetry. No significant changes in the phonon band widths are predicted in the virtual crystal limit. However, the relative intensity of the phonon modes may be altered relative to the pure crystal if Af is different for different degrees of freedom. Hong and Kopelman53 have indicated in their theoretical develop- ment that within the virtual crystal limit, the total intensity of the Raman spectra of the mixed crystal is f is usually equal to that of the pure crystal, but since A different for each rotation, this would lead to mixing of intensities among different Raman bands. However, the infrared spectrum of mixed crystals should have the same intensity pattern as that of the pure crystal because Af is always equal for all the translations. Whitfieldl6 has demonstrated that the neat, partially deuterated ethylene solids can be considered as isotopic- mixed crystals. Certainly this is true for partially- deuterated ethanes too, where the nearest neighbor atoms are either hydrogens cn° deuteriums as in a mixture of CZD6:C2H6‘ Thus the intermolecular interactions are quite similar to those in a mixture of C2H6 and C2D6. The fact that the phonon energies of isotopic mixed crystals are mass-dependent leads to the conclusion that an analogy can be drawn between the percent deuteration of a partially deuterated ethane and the concentration of the guest in a C2D6‘C2H6 mixed crystal. For example, solid CH3CD3 50 is in many respects analogous to a mixed crystal con- taining equimolar C2H6 and C2D6. Since in the virtual crystal limit the force constants and "effective" symmetry, i;gL, the spectroscopically ob- served symmetry, of the crystal remain unchanged, the phonon frequencies of the partially deuterated crystals in this limit can be calculated assuming they are pure crystals. Therefore, the semi-classical method of calculating the phonon frequencies (TBON) discussed in Chapter II should still apply. The crystal symmetry and potential function remain the same for each ethane unit; only the masses of the molecules are different. B. The Potential Function of Ethane During the last decade there has been a great deal of interest in the normal vibrations of molecular crystals.149 The intermolecular forces in crystals are of particular im- portance because of their close relation to the physical properties of solids. In most cases, as was mentioned in Section C-1 of Chapter II, it is assumed that the intermolecular potential can be approximated as the sum of pairwise interactions between non-bonded atoms, each being expressed by an empirical or semi-empirical function.59'6l This type of intermolecular force field has been used extensively in previous normal coordinate treatments of various molecular 51 crystals such as crystalline benzene,ul’62 901Y- ethylene, Several atom-atom potentials have been proposed re- cently, and their derivations have been extensively dis- cussed, especially by Kitaigorodskiisg and Williams.60’6l’65’66 In particular, Williams has collected a large number of ex- perimental data for entire classes of molecules and has obtained several potential functions by simultaneous fitting of crystal structures, heatscfi‘sublimation, and elastic constants. Several such potential functions have been used in the calculation of the lattice frequencies of ethane in order to determine which potential best fits the observed lattice frequencies. Table 5 lists the parameters of the potentials tested. The calculations were based on the use of a fore- shortened bond length of C-H equal to 1.026 A (reduced from the gas phase value by 0.07 A). This was required for a consistent application of Williams' potentials, because in deriving the parameters from crystal data, Williams had to shift the location of the repulsion-attrac- tion center by 0.07 A toward the C atom along the C-H bond.67 The choice of 6 A for truncation of the inter- action radius was made because it is sufficient to ensure the convergence of the calculated frequencies to a constant value.68 The unit cell dimensions from the x-ray work by Van Nes and Vos27 were used without any refinement for .A_O_3N=o=oo_o 2.2382393.Amd B o c3 82. 98 o .35 a; .3 c on.” ocean 3m .5 m... 8 o 3.” «mom «.3 o so.» 83 mm. o 8.." 808 com _> z. c on; «.83 n.8, o moo.» «.83 of... o as.» :32. Son > 3 o BA...” 933 3.3 a mom.» 935 on. o :3 Home ~83. >. E o E.» 32 to. .. o B. a com..— com o and o 5% so . _= 5 o 3..» owns «.3 o 8.” coo: on. c on.” 236 mom . __ 5 o 2..» 33 an o B..." 9.8. 5 o 8..” one? com _ 5.0 o m < .06 o m < 5.0 o A m < .3... :5... =.....o . o....o .8 P.105 + touzxom + :3: II. __> 22.3 .2808an .2223. 0023.82 l m 035. i 53 minimum crystal energy.72 Potential functions I, II and III were obtained by Williams61 from a least-squares fit of observed and cal- culated crystal data of aliphatic hydrocarbons only. Po- tential IX was obtained by a least-squares fit of observed and calculated crystal data for aromatic hydrocarbons,60 while potentials VI, VII and VIII were obtained by least squares refinement between the observed and calculated crystal structures of both saturated and aromatic hydro- carbons.61’69 Potential functions IV and V have been ob- tained by Taddei,§£_al,ul by a least-squares refinement of potential functions VI and IX to obtain the best agree- ment between the calculated and observed lattice frequen- cies of benzene, whereas potential X recently obtained by Williams66 from 18 saturated and aromatic hydrocarbon crystal structures, includes an optimum net point charge of .159 E'on the hydrogen and carbon atoms. Each interaction potential was used to calculate the lattice frequencies of ethane and the results compared to the observed values. The results are tabulated in Table 6 which includes also the standard deviations. The best agreements with the observed librational frequencies are obtained with potential functions I, II and VI. The agree- ment for translations is best with potentials V and VIII; however, the low frequency librational modes calculated with these potentials fit more poorly the experimental 5H Aoado Iqu 9 >vuww u may .popmm msmswmlcwoslpoono .mm monopommm 809mb .moUoE HMCOHumHmCMQp can HMCOfiumanHH npon Eonm soapsnfihpcoo o>w£ heap mocum .Uowcmnommpcfi on canoe mmmnem .m\aim:\m m:.:H mm.~m mm.a m:.mm mfl.m Ho.OH Am.m mm.HH mo.m Ho.m omen «.mHH mma HOH m.emH OHH HOH m.moa HHH OHH m.soa naoa sea moa mm 20H mm m.zw mm :.mm mm am 9mm mm mm as pm me m.mm as us m.mu m.me mCOfipmHmcwnB m.mmH m.mAH mmfl m.HsH Had m.mmH m.o=H m.ssa flea OMH m.HmH m.:mH mma m.mHH .mma mud mHH mmfl 02H m.HmH sud omH mm.mHH ana m.moH med mHH m.moa mHH NNH mHH m.OHH Ada m.mHH omH mm mHH OOH mm mm m.moa moa mm «OH mm mm m.=s mm m.om m5 ms mm mm mm m.mm mm m.mm m.o~ mm us me m.Hs m.=m m.ms as AA x on S: H; g > E HHH E H . moo macapmpnaq pom Hmfipcmuom .mcmnpm AHHV oHHom mo AHIEoV mmaocosuomm oofippmq oopMHSono new oo>pmmno one .m manna 55 values compared to the predictions of potentials I, II and VI. As a result, the overall agreement for both trans- lational and librational frequencies is best with potential functions I, II and VI, as is clear from the calculated root- mean-square error shown in Table 6. Although potential I fits the observed lattice frequencies of C2H6 better than II, and II is slightly better than VI, it was found that the reverse is true for C2D6 and the partially— deuterated species. The best potentials for CZH6 were used to calculate the lattice frequencies of CZD6' The calculated and observed frequencies of C2D6 are listed in Table 7. Comparison of the standard deviation for the observed and calculated librational and translational frequencies of C2D6 indicates that potential II is pre- ferred to I and VI with the agreement being poorest for potential I. Therefore it was concluded that potential II is superior among the potentials tested, and that po- tentials VI and I are the next best potentials for the crystalline ethanes. It may be noted that recently Eggers and Wisnosky have been involved in similar calculations for crystalline ethane.28 They employed‘a different program and their con- clusions differ from those drawn above. Prior to the calculation of the normal mode frequencies they performed an energy minimization calculation for the crystal struc- ture, which leads to a structure slightly different from 56 Table 7. The Observed and Calculated Lattice Frequencies (cm'l) of Solid (II) 0206. Observed -Librations I II VI VIII 57 57.5 61 59 5“ 81 68 69 67 62 8A.5 83.0 85.5 8A 77 98.5 85.0 ' 92 91.5 83 -_-- 96 101 100 91 103 99.5 109 109 98.5 Translations -_-- 69.0 70 69.0 63 76.5a 85.5 8u.5 8H. 77.5 91.5a 98.0 100.5 100.5 92 rms 9.02 7.99 8.38 . 10.71 aFrom Reference 23. 57 the experimental one. They have tested only three poten- tial functions (here numbered VI and VIII, and one of ).68 They seleCted the Williams' Coulombic potentials Coulombic potential as the best intermolecular interaction function for ethane, based on the fairly good agreement with the translational lattice modes and the slightly better fit to the splitting observed for the internal modes. It is unlikely that this is the best choice. From Table 6 it may be noted that the Coulombic potential gave poor agreement, on the average, with the observed librations and translations. It is not safe to choose the best potential on the basis of only three models. In contrast, a broad range of potential functions were used in the calculations reported here, and the transferability of potential II, which was obtained by a least-squares refinement to the crystal data of aliphatic hydrocarbons, in calculating the lattice frequencies of the (aliphatic hydrocarbon) ethane crystal is not suprising. The claim that potential II is the best one, and the rejection of the Coulombic one in the calculation of the lattice fre- quencies of ethane is supported by a statement by Wil— liams65 that "the Coulombic contribution to the lattice energies of aliphatic hydrocarbons (n—pentane, n-hexane, n-octane) is less than 1%, while it reaches a value of 29% of the total lattice energy of benzene. As a final point, it should be mentioned that potential 58 II is not necessarily the best overall potential function for crystalline ethane; an examination of how well the various potentials predict the internal mode frequencies is required for a better Judgment. Only two of the three expected infrared-active transla- tions of C2H6 and C2D6 have been observed.23 The energies of these phonons are 83 cm"1 and 101 cm"1 for ethane-h6 and 76.5 and 91.5 cm‘1 for ethane-d6. The third optically active translational mode has been calculated to be at lower frequency (see Tables 6 and 7). Potential VIII also provided the best agreement for the translational frequencies of C2D6 (Table 7). Therefore the translational frequencies for all isotopic Species of ethane were calculated using potential VIII; they are tabulated in Table 8. It is to be noted that potential VIII predicts the exact value of Table 8. Calculated Translational Frequencies (cm-1) of Ethanes From Potential Set VIII. 06s.a Calc. Obs.a Calc. -- 70 68.5 67.5 66.5 65.5 6u.5 --- 63 83 85 84 82.5 81.0 80.0 79.0 76.5 77.5 101 101 99.5 98.0 96.5 95.0 94.0 91.5 92 aFrom Reference 23. 59 the highest translational frequency of both C2H6 and C2D6’ while the second highest calculated translational frequency for C2H6 and C2D6 is higher by 2 and l om“1 than the ob- served ones, respectively. This is certainly expected to be true for isotopic species of ethane as well. C. The Librations of the Ethanes The Raman spectra in the lattice region of the stable phase Of ethane-d0, ethane-d6 and several partially deu- terated species are shown in Figures A and 5. Six bands for C2H6, and at least five bands for C2H5D, CHDZCHB, CH30D3, CZHD5 and 02D6 were observed, with a second-highest frequency band of 02H5D, CHD20H3 and CZHDS appearing as shoulders. A comparison of the observed and calculated (from potentials II and VI) librational frequencies of ethane-d0, ~d1, -l,l-d2 and d5 was used to estimate the "missing" band for CH3CD3 and C2D6- The situation is complicated because the librational modes which lie second and third-highest in ethane-dO "cross" positions with increasing deuteration, according to the eigenvector distri- bution (see Table 10). For CH3CD3 these two modes are predicted at 110.5 cm‘1 and 105 em'l by potential II, and their eigenvectors are mixed. However, if the difference between the calculated and observed frequencies of these two vibrations from 02H6, CZHSD’ 1,1-C2HuD2 and C2HD5 6O * c:2 H6 * * CH3 CD3 * c2 ”6 *. * 140 100 AD. (cm'1) 50 l_ l . l 1 I l 1 1 1 1 Figure 4 _The Roman lattice region of C2H6 , CH3CD3 and C2 Db“ The peaks marked with an asterisk are laser- fluorescence lines. 61 szufl) * at e * czuns 130 I 90 A17 (cmd) 50 L 1 1 L l 1 L 1 l Figures ._. The Raman lattice region of solid (ll) C2HSD, 1,] -C2H4D2 and C2HDS; the peaks marked with an asterisk are laser fluorescence lines. 62 are interpolated to CH3CD3 then both can be expected to lie near 108 cm'l. A band is indeed observed in CH3CD3 at 108.5 cm"1 (see Table 9), which is relatively stronger in comparison to the other librational intensities than one might expect from the other isotopic ethanes. Perhaps it encompasses both of the bands expected in this range. In C2D6 the two vibrations retain the distinctive normal mode distribution found for C2H6, the expected correlation being (in cm‘l), 120 (do): 92 (d6) and 117 (do): 101 (06). Extrapolation of the frequencies observed for the other ethanes suggests that the former would lie in the 97-100 cm'1 range and the latter would fall between 98 and 101 cm‘l. Again a single band is observed for C2D6 in this region, at 98.5 cm-l, which may belong to both librational modes. The frequencies of the lattice modes of the partially- deuterated ethanes were calculated using interaction po- tential II. It was assumed that deuteration causes only a change in the mass of the molecule and that the symmetry of the lattice remains unchanged. The slight changes in bond lengths and bond angles upon deuteration were also neglected, since these should have only a minor effect on the calculated frequencies. The calculated and observed librational frequencies are given in Table 9. The agree- ment between the calculated and observed values is as good as that for ethane-dO and ethane-d6. .HH pom Hmapaopoa co comma mGOHumHaonom 63 moa m.moa m.mHH sea Hma m.mHH ANH m.oNH mma m.mmH flea m.HmH Hoa eoa m.moa m.oHH m.mHH mad NNH mHH m.HmH oma m.mm m.moa mm mm m.ooa mod oaa NHH m.=HH mHH mHH AHA m.mm m.:w m.hm pm m.mm mm m.mm mm m.mm mm NOH NOH me an H» m.mm mm mm m.es mm om mm mm m.mm Hm hm mm m.mm mm m.:© H5 m.>m m.:~ m.Hw m.m> >5 .Hno .noo .Hoo .noo. .H60 .660 .Hoo .noo .H60 .660 .Hoo .moo bomo mommo moommo Noemmoua.a ommmo ammo «.mocmnpm mo AHIEoV moHocoaooam Hmaoapmanaq oopwaaoamo can oo>nomno 039 .m manna 6A The crystal normal coordinates obtained from TBON for the librations of the crystalline ethanes are given in Table 10. The eigenvectors provide a direct measure of the degree of mixing of molecular rotations or of trans- lations in each normal mode. It is to be noted that mixing of the translational and rotational degrees of freedom was strictly forbidden, since the frequencies were calculated assuming centrosymmetric site symmetry for each ethane crystal. The eigenvectors listed in Table 10 show that in most cases it is impossible to think of a crystal normal mode as being a pure rotation around a given principal molecular axis. In fact, it is seen from Table 10 that some modes are mixed by more than 20%, and even up to 50% (the highest and the lowest frequency modes). However, the relative contribution of each rotation to each normal coordinate remains essentially unchanged in going from C2H6 to C2D6, except for the eigenvectors for the second- and third-highest frequencies of 02H6, which "mix" and "cross" at C2HuD2 and C2H3D3. The calculated and observed librational frequencies are plotted against the number of deuterium atoms per molecule in Figures 6 and 7, respectively. A virtually linear dependence between the frequencies and number of deuteriums are predicted for the four lowest frequency vibra- tions in Figure 6. (Note that the fifth lowest frequency of ethane d3-d6 corresponds to the fourth lowest frequency 65 Table 10. The Crystal Normal Coordinates of the Librations of the Ethanes. Crystal Vcalc. (cm'l)a Rx R? R2 C2H6 78.5 .63 -.03 .77 83 .ll -.11 -.99 102 .11 .99 .05 119 .2H -.97 .03 131.5 .96 .2h .10 lul. .77 -.ll . .63 CZHSD 70.5 .66 -.03 -.75 80 .12 -.01 -.99 98.5 -.11 -.99 -.06 110.5 .39 -.92 .05 122 .91 .39 .11 133 -.7u .12 -.66 0211402 71 .69 -.02 -.72 77.5 .13 -.01 -.99 95.5 -.11 -.99 -.08 110 .61 _ -.79 .09 115.5 .78 .62 .10 127 .72 -.13 .69 C2H3D3 68 .71 -.02 -.70 75 -.1’4 .01 .99 92.5 -.11 -.99 -.09 105 .81 -.57 .12 110.5 -.57 -.82 -.07 121 .70 -.IU .70 66 Table 10. Continued. Crystal Vcalc. (cm-l)a. Rx y z C2H2Du 65 -.73 .01 .69 73 .15 .01 .99 90 -.ll .99 .10 100.5 -.90 .A2 .1“ 107 -.Al .91 .05 116.5 .68 .15 .72 02HD5 63 -.7A .01 .67 71 -.16 .01 .99 87.5 -.11 .99 .11 96.0 -.93 .32 .16 10A -.32 .95 .Oh 112.5 .66 .15 .73 C2D6 61 -.75 .Ol .66 69 .17 .Ol .98 85.5 -.11 .99 .11 92 -.95 .27 .17 101 -.26 .96 .0A 109 .65 .16 .7” aCalculations based on potential set II. 67 Amen") 150 - 100 - sob ‘ Figure 6.-‘l’he calculated librational frequencies versus the number of deuterium atoms. 68 150 - " loo " 50 " "' 1 l l l I I l Figure 7 -The observed librational frequencies versus the number of deuterium atoms. 69 of ethane dO-dzJ This is expected also on the basis of the low perturbation strengths calculated from moment-of- R R inertia data (A y a A Z = -.uu), and Equation (31). There- fore, the frequency dependence on the percentage deutera- tion should be described by Equation (31) for these bands. Non-linear behavior is predicted for the two highest fre- quency bands of ethane-dO and their counterparts in the deuterated species, suggesting that Equation (30) should describe the curves for these bands. f, of the calculated fre- The perturbation strengths, A quencies are given in Table 11 along with the experimentally observed values of Ar, and those calculated for pure rota- tions about the principal axes from the moments-of—inertia of C2H6 and CZD6' The Af's of the calculated frequencies were determined by calculating the perturbation strength for each point with Equation (30), and then finding the average Af for the band. (The averages, in fact, were very close to those calculated for the CH3CD3 bands.) The experimental perturbation strengths were found by determining the slopes of the lines shown in Figure 7 and using Equation (31) to determine Ar. If one wishes to draw a line straight through the points of the two highest frequency bands, it is necessary to increase the uncertainty of the peaks at 113.5 cm'1 for CH3CD3 and 98.5 cm".1 for 1, respectively, even though the 1. C2D6 to 12.5 and :2 cm- experimental uncertainty is closer to :1 cm- 70 Table 11. Perturbation Strengths of the Ethane Librations. Rx R R A = -.99 A Y = —.uu A z = -.uu Libration (C2H6) cm'l Afiexp)a Alcalc)b 77 -.A1 -,55 98.5 -.3u -.us 102 ' -.36 -.02 117 -.36 -.A0 120 -.N8 -1.02 131.5 -.63 -,57 —— aFrom Figure 7. bFrom Figure 6. 71 The values of the experimentally-determined perturba- tion strengths are consistent with those expected for rota- tional motions (A = -0.2), given in Table 11. granslation' The greater experimental uncertainty of the measured value of the second-highest frequency band may account for the somewhat larger discrepancy. As also is indicated by the normal coordinate calculation, the Af's for the four lowest frequency (C2H6) librations are primarily motions about the y and z principal rotational axes of the molecule. However, it will be noticed from Table 10 that the lowest and highest frequency bands are in fact strong mixtures of rotations about the x- and z-axes. This mixing accounts for the strong intensity of these bands relative to expec- tations based on the oriented gas model71 for librations primarily around the C-C axis. The fact that only five or six Raman-active phonons are observed for the partially deuterated ethanes, and their energies vary smoothly with the degree of deuterium substitution, indicates that the librational motions of the ethane crystals are amalgamated. Furthermore, the applicability of Equation (31) to five of the modes, and of Equation (30) to the sixth, shows that solid ethane can be treated in the virtual crystal limit. This conclusion is supported by the close agreement between the experi- mental perturbation strengths and those calculated on the basis of the virtual crystal approximation. The virtual 72 crystal limit implies that the partially-deuterated mole- cules form substitutionally disordered crystals. Moreover, this implies that the effective lattice symmetry of the partially-deuterated ethane crystals is the same as that of the C2H6 and CéD6 lattice, and that the intermolecular force constants remain unchanged. The relative intensities of the Raman lattice modes of crystalline ethane and deuterated species are shown in Figure 8. No significant changes in the relative intensi- ties of the librations are observed for the partially- deuterated ethanes, although this is permitted by the R Rz R virtual crystal theory, since for ethane A x f A y = A The apparent higher intensity of the highest frequency mode in CH3CD3, CZHD5 and C2D6 is believed to be due to some contribution from an "unobserved" component (the second highest frequency band) in the above crystals. At the same time, Figure 8 nicely shows the smooth decrease of librational band energies with the degree of deuterium substitution, as is expected. It is also interesting to note that the lowest and the highest energy librational bands, which according to the normal coordinate calculation both have contribution from rotation about x and z principal axes, move faster to lower frequency than other modes in the deuterated species. 73 1L ,1] rue...- Lil PIC..- .. h— — A17 (cm"1 ) 120 100 so 60 l l l l l Figure 8 -The Raman lattice modes of crystalline (Isz and deuterated species. Relative intensities within each species are denoted by the verti- cal lines. Shoulders in the experimental Spectra are indicated by dotted lines. 7A D. Raman Phonon Modes in the Metastable Solid Phase of Ethanes In the course of this research we were notified by 70 of a newly-found phase for ethane, called the Eggers metastablephase, indicating its behavior. A complete description of this phase and the conditions under which it is obtained in pure form are given elsewhere.39 After learning of the existence of such a phase we noticed that some of our earlier spectra belonged to either the pure metastable phase or to a mixture of both crystalline phases. The spectra of the metastable phase show many regions of marked difference from those of the stable phase (II), especially in the lattice region, where the location, relative intensities and the number of phonon bands are different. This fortunate difference in the Raman lattice region then permitted us to check for purity of the ordered stable phase (II), which was the primary subject of the present investigation. Because our main interest was the study of the ordered stable phase (II) of the ethanes, here we only show, in Figures 9 and 10, examples of the Raman lattice region of the pure metastable phase of CH3CD3 and CZHDS’ and of a mixture of metastable and stable phases of C2H6 and C2D6. The spectra were taken at 23°K for C2H6, CH3CD3 and C2HD5, and at 30°K for C2D6; the annealing temperature was 38°K for C2H5 and about 50°K for the other 75 89 98 CH3CD3 "4.5 120 no 100 90 so I l l l l Ail'(cm‘1) Figure 9_The Raman lattice region of CH3CD3 and C2H05 in metastable phase. The peaks marked with an asterisk are laser-fluorescence lines. 76 98.5 106.5 135 » 77 13L5 120 140 120 100 80 104.5 91 83} lOO 110 90 70 5° 1 1 1 1 1 1 Afilcm“) h- Figure IO_The Raman lattice region of (2sz and C206 in the Presence of both stable and metastable Phases. The peak marked with an asterisk is a laser— -fluorescence line. 77 three crystals. The metastable phase, as exemplified in Figure 9, shows three bands in the Raman lattice region, two bands of essentially equal intensity separated by about 8 cm'1 and a less intense peak at higher frequency. It was noted, from the comparison of the stable and metastable phase spectra, that the two intense peaks in the meta- stable phase have similar components in the stable phase, 1, and that the but of weak intensity, separated by 3-A cm- third band corresponds to the highest-frequency band in the lattice region of the stable phase. Therefore, the presence of the metastable phase can be distinguished by the two intense peaks described above. Table 12 below lists the librational frequency modes of 02H6, C2D6, CH3CD3 and C2HDS in the metastable solid phase. 1) Table 12. The Librational Lattice Frequencies (cm- of Ethanes in the Metastable Phase. C2H6 CH3CD3 C2HD5 C2D6 98.5 89 83 83 106.5 98 91.5 , 91 135 ll”.5 108 109.5 78 E. Conclusions The following conclusions have been drawn in this chapter: (a) The interaction potential II, which has been obtained by a least-squares refinement to the crystal data of aliphatic hydrocarbons, is the best overall po- tential function for ethane. This also confirms the transferability of such an interaction potential to other aliphatic hydrocarbons. (b) The librations of the ethanes are amalgamated and can be described in the virtual crystal limit. This implies that: (l) The effective lattice symmetry of the par- tially-deuterated ethane crystals is the same as the lattice symmetry of the C2H6 and 02D6 crystals; there- fore H is still a "good quantum number" and the ef- fective site symmetry is 01' (2) The intermolecular force constants and the lattice normal coordinates remain unchanged in going from the C2H6 to the C2D6 crystal. (3) The bands observed in the Raman phonon region are the librations - no interference from the transla- tions was observed, consistent with a C site. i (c) The observed Af's predict a mixing of the rotations about the principal axes, as does the frequency calculation. CHAPTER V THE ORIENTATIONAL EFFECT, A MEANS FOR PROBING THE SITE SYMMETRY OF THE PARTIALLY-DEUTERATED CRYSTALLINE ETHANES A. Theory In the previous chapter it was shown that mutual ex- clusion for the lattice vibrations of the partially-deuter- ated ethanes is retained, and it was concluded that the lattice vibrations of these crystals experience an "ef- fective" Ci site symmetry. In this context "effective" means that the electronic distribution of the neighbors, but not their isotopic composition, governs the inter- molecular interactions. Thus it can be said that the molecules cannot distinguish between hydrogens and deuteriums on the neighboring molecules. A knowledge of the "effective" site symmetry is neces- sary for the interpretation of the spectra of the internal modes of the neat partially-deuterated ethanes because the orientational effect may complicate these modes, and the number of energetically inequivalent orientations depends on the site symmetry. However, the orientational effect may also be used to probe the "effective" site symmetry 79 80 of the partially-deuterated crystals. The discussion in Chapter II showed that the number of orientational components observed for the guest modes of a dilute isotopic mixed crystal is governed by the site symmetry of the host as well as the guest point-group sym- metry. A group theoretical procedure as described by 51 can be used to determine the number of orienta- Kopelman tional components expected for the partially-deuterated ethanes in sites of Cl’ C1 or any other symmetry. Our approach in Chapter II, however, was of a more straight- forward and physical nature. The results for the number of energetically inequivalent orientational components determined for a Cl or Ci site were listed in Table A. All of the partially-deuterated ethanes can be used as probes of the site symmetries of the other partially deuterated ethanes. CH3CD3 shows no orientational "splitting" in a site of C symmetry, because of its higher i point-group symmetry, viz. C3v' However, it is seen from Table A that three components for each (nondegenerate) mode of C2H5D, 1,1-C2HHD2 and 02HD5 as guest molecules diluted in C2H6, C2D6 or any deuterated species of ethane are expected if the effective site symmetry is C while six components 13 should be observed in sites without any symmetry (Cl)' 81 B. Experimental The orientational effect was studied on transitions of C2H5D’ 1,1-C2HuD2 and C2HD5 (see Figures 11-18). Tables 13-15 list the observed guest frequencies of the following dilute-mixed crystals of the partially-deuterated ethanes: Experiment Number Guest/host 1 . W2HD5/C 5D 2 C2 HSD/CHBCD3 1,1-C2HuD2/CH3CD3 3 C2 HSD/C2HD5 1,1-C2HuD2/C2HD5 Experiments 1, 2 and 3 were utilized to probe the effective site symmetry of ethane-d1, -d3 and -d5, respectively. At the same time, experiments 2 and 3 provided information about the effect of the host and guest molecules on the magnitude of the orientational "splitting", SOE’ of certain vibrational modes. There are some general observations to be made about the data obtained. First, in no case were more than the three components expected on the basis of Ci site sym— metry observed for the guest fundamental bands. However, only in a few cases were three bands resolved. Second, in most cases, doublets were observed, often with an .mommo so Aesv Ha; one Ass pee .sv ea; .Aeev we .Aesv so .mo .H mommmoxmommo am so assesses ooasaasa one do than .HH enemas ? to; a3 a} .5. \\ . _ _ _ _ _ _ _ _ _ comp mom p thN Bow mg“ was m3" mmpu mom N can“ 83 .mommo mo momma A.mv mH> can A.mv HH> Ass one .mvm> .A.wv w> .m9 .m> mammmo\mammo mm mo Sappooam oopmamcfi one mo whom .NH opswfim «— a . a r), _ . . . _ . . . _ _ ooh moo o8 moo ooo. o5. moo. o8. on: on: .ommmo co noose .6 NH; eds es Ha» .Aes ..sv m5 .A.sv we .A.sv so .mo mmoommo\ ommmo am so asbestos ooashasa one do ease .mH enemas 8A _ . _ _ _ _ _ . nus o2. m6 moo ooo 2: a: on“. mon— 85 .Qmmmo MO mUCQD Apmv NH? Ucm A.MV HH? «Azm USN —NV 0? .Aemv m> .mp mmnmm0\ammmo am no Sappoodm bonehead on» no need .aa opswfim .. .. .. = a .s a... so a; e on . _ _ . . . _ 2.: me. was mg .563 mm: at? 08' an: 86 .mozmmo1ana mo A.mv mH> can .Aem can .mv m9 A.sv we .ee .me ”moommo\moemmona.fl em.a do Espresso ooasaoea one do some .mH enemas \\ o‘- em- a. e e. ., mom can can 9!. mam mg 05.. mac— hF— mu: 2140 2085 1380 1360 1305 1285 Figure 16. Part of the infrared spectrum of 1.5% l’l’coHuDg/ CH3CD3; 02, V5 and V11 (a' and a") bands of 88 ' 2975 2950 2130 2115 1460 1450 1335 1305 l l l | I I l I V8 3’ *- VS a v7 Figure 17. Part of the infrared spectrum of A% 1,1-C2Hu02/ C2HD5; v2, v5, 07 (a' and a") and V8 (a") bands of 1,1-C2HuD2. The peak marked with an asterisk is due to the v5 band of the host. .moqrmoua.a so noose Aes poo .ev mH> one Aes one .sv m5 1: .@> .n: mmmzm0\mD::m01H.H &: mo Enhpomam UmmeMCH ecu no when .mH mpsmflm _ _ _ _ _ _ hum mam was mvh mam 0mm Chow mmo— no: mu: 90 Table 13. Observed C2HD5 Fundamentals in the Infrared Spectrum of a 3% C2HD5/C2H5D Mixed Crystal. Assign- Wavenumber Assign- Wavenumber menta (cm‘l) ment (cm’l) 01 a' 2150.5 (ms) v10 a' 2255 (w) 21A9.3 (m,shld) ' 03 a' 862.8 (vw) a" 2225.2 (s) 2222.6 (s) 05 a' 2121.5 (w) 2219.8 (5) V6 a' 1067 (ms) 1063.7 (5) V11 a' 1057.9 (w) v7 a" 2208.8 (m) a" 1291.0 (w) 2207.0 (m, Shld) 1287.8 (w) v8 a' 1127.3 (mw) v12 a' 1005.8 (w) a" 1297.6 (s) 1003.8 (mw) 09 a' 598.0 (ms,sh) 600.2 (8, sh) a" 631.9 (3, sh) 633.6 (ms, sh) 8The a' and a" assignments in this and the following tables are from the gas phase assignment. 91 Table 1A. Observed Infrared Fundamental Frequencies (cm-l) of C2H5D Diluted in CH3CD3 and C2HD5° Assignment 2% C2H5D in CH3CD3 3% C2H5D in C2HD5 V3 a' 977.2 (m) 977.5 (W) vs a' 1379.8 (ms) 07 a' 2172.5 (m,sh1d) 2169.5 (8) a" 2968 (vs) V8 a' 1303 (ms) 1301 (w,shld) a" 1A61.5 (s). 1A58.0 (8) v9 a' 717.2 (s) 717.1 (s) 71A.0 (s) 71A.2 (s) a" 805.2 (s) 805.5 (ms) 802.A (s) 802.1 (ms) V11 a' <1AA7.2 (ms) 1AA1.9 (ms, shld) 1AAO.5 (s) a" 1292.2 (s, shld) 1291.0 (8) v12 a' 1119.5 (ms) 1119.8 (mw) 111A.7 (ms) 1111.6 (w) 92 Table 15. Observed 1,1-02111402 Fundamentals in the Infrared Spectra ofl.5% 1,1-02HMD2/CH3CD3 and A% 1,1- CthDg/CQHD5 Mixed Crystals. 0’ - ”I - 1.5m 1,1 C2HAD2/CH CD3 At 1,1 CZHADg/C2HD5 - 3 ASSIgnment Wavenumber (Gm-l) Wavenumber (cm‘l) 02 a' 1379-9 (m) 137A.8 (s) 137A.A (w) 1367.2 (w) 1370.0 (mw) 03 a' 9A6.0 (W) 953.1 (W) 9A3.2 (mw) V5 8' 2128.5 (8) 2125.5 (ms) 2120.0 (8) 2120.A (S) 2113.0 (ms, shld) 2117.0 (ms) V6 a' 1118.5 (m) 1119.2 (mw) 1118.2 (m) 111A.5 (m) 07 a' 2968.2 (vs) a" 296A.8 (vs) V8 a' 1A82.0 (vw) 1A82.5 (vw) 1479- (w) 1A79.8 (mw) V8 a" 1A63.2 (ms) 1A57.0 (m) 1A55.6 (m) 93 Table 15. Continued. 1.5% 1,1-C2HuD2/CH3CD3 A7 1,1-C2HuD2/C2HD5 Assignment Wavenumber (cm-1) Wavenumber (cm-l) v9 a' 737.A (ms) 737.7 (mS) 735.3 (s) 735.5 (s) a" 688.6 (m) 686. (s) 685.8 (s) 68A.5 (ms) 683.2 (ms) 011 a' 1300.2 (mw) 1297. (mw) 1296. (mw) a" 1293.0 (S) 1293. (s) 012 a' 1077. (m) 1078.6 (m) 107A.5 (mw) a" 1109.5 (m) 1107.7 (mw) 9A intensity ratio of 2:1, and in some cases singlets were recorded. In the latter case the bands were usually weak (compare, for example, the 03 hand of the three species in dilute mixed crystals) and that is possibly one reason why they do not show "splitting”. In cases where doublets or (stronger) singlets were observed it can be assumed that the orientational "splitting" is too small to allow the components to be observed, or that the resolution is hampered by the sample quality. In any event, the orienta- tional components were resolved in many cases, and hence the determination of the site symmetries of the partially- deuterated ethanes by way of the orientational effect should be applicable. The observed orientational "splittings" varied from unresolved to 8.5 cm-l. It is to be noted that it is impossible for all bands in all dilute mixed crystals to compare isotOpic guest or host effects on the magnitude of the orientational "splitting". Problems arise when guest bands are obscured by host bands (especially in the wavenumber ranges 1300- l and 2800-3000 cm-l) or the guest bands are dif- lAOO cm- ficult to assign due to the presence of extraneous im- purities (other than the guest molecules) and/or the pres- ence of host overtones and combination bands. The frequency region lower than approximately 1200 cm-1 was considered best to most definitively observe the guest modes of the dilute mixed crystals (09 for example). 95 The presence of doublets and triplets in dilute-mixed crystal spectra clearly indicate an "effective" centro- symmetric site symmetry. Table 16 lists the magnitude of the orientational "splitting", 50E, for vibrational modes of ethane-d1, 1,1-d2 and -d5 in dilute-mixed crystals. The 09 (a') and 09 (a") fundamentals are the only modes which were observed in all dilute-mixed crystals. They show doublets in all cases, with an intensity ratio often close to 2:1. The intensity difference between the two components is possibly due to the third, unresolved or- ientational component. It can be seen that the effect of host or guest isotopic Substitution on the orientational "splitting" is negligible; however, the orientational ef- fect is different for different vibrational modes. The following bands have shown a different number of orientational components in different hosts: 33 (121‘025A221 - exhibits two components in the C2HD5 host, at 9A3.2 cm'1 and 9A6 cm-l, but shows only one com- ponent, at 9A3.l cm“1 in the CH3CD3 host. The absence of the higher frequency component in CH3CD3 is believed to be due to its weakness and the poorer sample quality. 36 (1,1-C2H422) - shows three components in the C2HD5 host, at 1119.2 cm‘l, 1118.2 em'1 and 111A.5 cm‘l, but shows only one component, at 1118.5 cm-l, in the CH3CD3 host. Undoubtedly the two unobserved lower frequency bands are hidden by the 96 band of the CH3CD3 host. 96 Table 16. Orientational "splitting", 60E, of Partially Deuterated Ethane Guests in Dilute-Mixed Crystals.a 05/01 01/03 Dl/DS 1,1-02/03 1,1-02/05 v1 1 2 --- —-- --- -—- v2 --- --- --- 7.6 5.5, A.A. 03 0 O 0 O 2.8 v5 0 --—. —-- 8.5, 7.0 5.1, 3.A 06 3.3 --- 0 0 3.7,11.0 v7 a' -—- 3.0 --- --- O a" 1.8 --- O --- 0 08 a' O 2.0 --- 3 0 2 7 a" 0 --- 3.5 --- 6 2, l A 09 a' 2.2 3.2 2.9 2.1 2.2 a" 1 7 2 8 3.A 2 1 2 6, 2 6 v10 a' O --- -—- --- --- a" 2.6, 2.8 —-— --- -—- ——- 011 a' o --- 5.3, 1.A 3.2, 1.0 --- a" 3.2 1.2 --- 0.7 --- 912 a' 1.2 --- 5.1, 3.1 0 A.l a" --- ---' --- --- 1.8 aZeros in the Table indicate unresolved bands; no entry (-) means that the guest band could not be observed in the dilute-mixed crystal. 97 39 (1’1'023A221.' shows three components in the C2HD5 host, at 688.6 cm'l, 685.8 cm"1 and 683.2 cm-l, but shows only two components, at 686.6 cm'1 and 68A.5 cm-1 in the CH3CD3 host. Probably the better sample quality in the former case enables three components to be observed. 112 (111‘C25A221 — shows two components in the C2HD5 host, at 1078.6 cm-1 and 107A.5 cm'l, but shows only one component, at 1077.5 cm?1 in the CH3CD3 host. This dis- crepancy is also possibly due to the poorer sample quality in the latter case, where a very weak but indistinct band is seen around 1073 cm.1 in the CH3CD host. 3 XZ—LLL13925A221 — shows three components in the C2HD5 l and 1370 cm'l, but shows 1 host, at 1379.9 om‘l, 137A.A cm- only two components, at 137A.8 cm- and 1367.2 cm"1 in the CH3CD3 host. Obviously the high frequency band is hidden by V2 of the CH CD host. 3 3 C, Site Shifts The experimental site shifts A can be determined from Of particular the tables of data as Egas - Emixed crystal' interest are whether or not such shifts are present, what trends in the shifts can be determined as a function of vibrational state, and what the host or guest isotope effects are on these shifts. However, it must be noted that the contribution of various symmetry coordinates (that is the atomic motions) to any particular fundamental 98 vibration will change upon deuteration. Thus a strict com- parison between different molecules may not be possible. These changes, however, are expected to have a more pro— nounced effect on the band width of the vibrations, which arise from dynamic interaction between the molecules, and less effect on the static interactions; that is, the orientational "splittings" and the A's - the gas to crystal field shifts - should be less dependent on the poten- tial energy distribution. The inaccuracy of the gas phase data (see Chapter VII) gives rise to uncertainties in the site shift measurements in several cases. Therefore, only those vibrations for which it is believed these complications are minimized will be discussed in Table 17. The values tabulated for the site shifts are the mean A's measured from Raman and infrared experiments and/or in different hosts. A comparison of the host effect on the site shifts is not possible because not all experiments were done in the same host. Therefore, the above data give only a rough idea of the size of the site shifts for 01, 02, 03, V8 and 09 for the different isotopes of ethane. Generally the differences in the A's for a given vibrational mode between infrared and Raman spectra among different hosts varied between O-3.0 cm'l. Small site shifts for the v3 C-C stretching and 09 bending modes, which appear relatively constant for all isotopes, indicate small interaction with the surrounding field. 99 Table 17. Gas-to-Mixed Crystal Shifts of the Ethanes. d 01 1,1-d2 d3 d d6 "1 A CH(CD) str. 19.0 --- ---- ---- 13.1 1A.5 \) A 2 CH3(CD3) def. 11.0 -_- 1A.A 12.8 ---- 7.5 \) A 3 0-0 str. —0.1 0.5 0.9 2.0 3.2 0.7 09(a') A Bend. 1.u 2.u -0.1 v9(a") 0.6 0.7 0.2 A Bend 1.2 A.l -1.8 V8(a') A CH3(CD3) def —-- 5.9 -—-- 5.7 u.u 11.0 \) (at!) A CH3(CD3) def. 5.5 11.A ---- 11.A 100 In contrast, for the 01 CH(CD) stretching, and the 02 and V8 CH3(CD3) deformation modes, larger site shifts (m15,5 cm'l, mll.0 cm"1 and m6.0-11.0 cm-l, respectively) are observed which are not nearly as constant with isotopic substitution. The greater site shifts for the latter vibrations imply a greater interaction with the static field. It is seen from the given A values that the site shifts for vibrations involving deuterium motion rather than hydrogen motion tend to be smaller (compare for instance the A's of 01, 02 and 09). Generally a large site shift is expected to be observed for any given vibration which is perturbed by Fermi resonance interaction with a nearby band. Although all the available data have not been inter- preted in detail, it is possible to conclude from the above discussion that there is no significant isotope effect on the A term for the ground vibrational states of ethanes. D. Conclusions The following conclusions can be drawn from the obser- vations of the guest modes of the dilute-mixed crystals of the partially-deuterated ethanes in each other. The "effective" site symmetry of the partially- deuterated ethane crystals is C Therefore the ethane 1' molecules cannot distinguish between hydrogens and CHAPTER VI THE RAMAN SPECTRA OF NEAT CRYSTALLINE 02H6 C2D6 AND THEIR MUTUAL SOLID SOLUTIONS IN THE INTERNAL REGION The Raman and infrared spectra of solid (II) ethane and C2D6 are consistent with the recent crystal structure reported by Van Nes and Vos.27 Observation of a maximum of four components for the 09 (en) vibrational mode in the ir spectrum (already reported by Eggers and TeJadalB) indicates the existence of at least two molecules per unit cell. The site symmetry of C1 for crystalline ethane is strongly supported, since the mutual exclusion rule holds in the ir and Raman spectrum. If the correlation diagram (Table 3), for C2H6 of molecular symmetry D3d on a C1 site with C2h factor group symmetry is considered, one can see that all the degenerate modes can be split at the site into two components as a result of reduction in symmetry of the molecule from D3d to the C1 site symmetry. Furthermore, any of the funda- mentals can be split by factor group coupling into two components, one with symmetry "a" and the other of sym- metry "b". Consequently one would expect to observe a 102 103 maximum of four resolved components for degenerate modes and two resolved components for non-degenerate modes in both the infrared and the Raman spectra of solid (II) ethane. The observed Raman fundamental vibrational frequencies of C2H6, C2D6 and their dilute mutual solid solutions are listed in Tables 18 and 19. The observed spectra are shown in Figures 19-23. For two of the three nondegenerate g-modes two components are indeed observed for both C2H6 and C2D6, while for the third non-degenerate mode only a singlet has been resolved, with an apparent shoulder for the C2H6 crystal. Also, three components have been re- solved for two of the degenerate g-modes in both compounds, while the third eg vibrational mode appeared as a doublet. In the following we consider these vibrational modes and their components in more detail. ll—Lglgl - This fundamental is observed as a single intense peak in the Raman spectra of both C2H6 and C2D6. However, a second component of moderate intensity is seen as a shoulder for C2H6 which could not be resolved. This, if not the second component of 01, might be assigned to an overtone of V8 in Fermi resonance with 01. Two mod- erately intense peaks in the Raman spectra of C2D6’ at 2121 and 21Al.6 cm-l , are tentatively assigned to the overtones of 06 and 08. Single peaks on the low frequency side of the 01 au vibration of both compounds, at 2861.6 cm.1 (C2H6) 10A Table 18. Observed Raman Fundamental Frequencies (cm-l) of Pure Polycrystalline (solid II) Ethane and its Dilute Solid Solution in C2H6.a Assignment Gas Phaseb Pure Crystalline 5% C2H6/C2D6 01 8.1g 2899 287A (VS) 2880.0 ' 2873.u (m, shld) v a 1AOO 1A00.A (m) 2 1g ' 137A.8 (w) 1389 c V3 31g 993 978.“ (W) 992.0 (5, sh) 995.1 (8, sh) 99A.O V10 8g 2955 2959.5 (s) 2958.“ 295A.5 (s) 2955 c 011 eg 1u60 1A33.0 (w) 1AA5.3 (ms) 1AA8.9 (w) 1A60.8 (s) lA56.0 V12 eg 1190 1190.2 (w) 1191.8 (w) 1191.0 1198.3 (vw) 1197.1 Key to Table: av = very, s = strong, m = moderate, w = weak, sh = sharp shld = shoulder. bGas phase values are from Reference 21(d) and 21(m). CThese frequencies are attributed to C-l3 substituted molecules. 105 Table 19. Observed Raman Fundamental Frequencies (cm‘l) of Pure Crystalline Ethane-d (solid II) and its Dilute Solid Solution in C2H6° Assignment Gas Phasea Pure Crystalline 9% C2D6/C2H6 C D 2 6 2083 2067.2 (vs) 2068.5 1 3lg 2061.u (vw)C v2 alg v3 als 1155 843 2225 10M1 970 1145 1152 823. 836. 8&8 2210 2215 2217 1091 1051. 1057. 963. 966. .25 (m) .35 (w) 7 (we 05 (s) .25 (S) .9 (VS) .2 (vs) .3 (shld, ms) .MO (m) 60 (m) 15 (m) 65 (w) 35 (m) 11U7.5 8h2.25 2212.95 2215.75 10U8.3 96H.2 aGas phase values from Ref. 21(g). bFrom Reference 21(n). CThese frequencies are attributed to C-13 substituted mole- cules. 106 meanpm omusufipmnsm mane co m .mmazooaoe > 6» ompsnappum ma xmfipmumm am no“: powaE xmma one .mcmnpm AHHV UHHom mo sapwoodm cmemm on» mo whom .mH opswam \NI msm GOO— ?i a. m_£ nous asap 22am: 0v?— Ay3=s nKQp 107 V1 (‘12) 930(el) 2965 2865 l 1 . Figure 20. Part of the Raman spectrum of solid (II) C2H5 (v1 and v10). The peak marked with an asterisk is attributed to v1 of C-13 substi— tuted ethane molecules. .moasomaoe mclmcmnuo cops» umnzm malo op oopsnfipppm ma xmfipoumm cm and: woxame xmmd one . Qmo AHHV UHHOm mo Esmpooom cmsmm one .Hm mpswfim 108 |\\ \\ q A ~ ova _ § q q q . LR _ 1 fix . m3 mne— moop on: on: coca n3“ 8.9a. mama a ing? . Auov N... A2; a. 30V...— 15 .3 Auov 2.. Ans "a .mmmo ca memo mo soapsaom a: m CH molmcwzpm AHHV UHHom mo Esauomdm :mEmm one .mm ohswfim xx xx xx xx 109 . mo xx _ . xx 001 _ u xx _ 4 xx . q m8 o 96 o3 o— coo. 3: mm: 89.. £2 32. m3“ E... 1...: A55. 3.. 110 ‘3 “EH ”2 (‘19) 1200 1185 985 ' 1 n u 1 L If ”1(319) V (0 ) 9 2985 2950 2885 2875 1465 1450 l I 11 l I 4/ l I If If Figure 23. Part of the Raman spectrum of solid (11) ethane in a 5% solution of C2H6 in C2D5; v V10, V11 and V12 Of 02H6. V 1’ V2: Q: 111 and 2061.“ cm'1 (C2D6), are assigned to v1 of the cor- responding molecule containing one C-13 atom. Their low intensity, 2.5% and 3% of the parent (C2H6 and C2D6’ respectively) peak, is in good agreement with this assign- ment. 32_(a1g) - This fundamental, a CH3 deformation mode, appears with two components in both the C2H6 and C2D6 Raman spectra, one weak component and the other moderately intense. In the spectra of isotopically dilute solutions, the two components are replaced by a singlet in the region between the original pair of peaks, indicating the factor group origin of the components. The splitting of the com- ponents in C2H6 (25.6 cm—l) is much larger than for C2D6 (6.1 cm-l)- 33—Lélgl — An intense doublet is observed for v3, the C—C stretch, mode, in both cases, with no such splitting found in the mixed crystal. These observations are con- sistent with predictions from the correlations previously given. The l3C-120 stretch is seen at 978.“ (C2H6) and 823.7 (C2D6) cm-1 as a single satellite of v3 which ex— hibits correlation field splitting only. This feature may be considered to be the v3 stretch mode for a matrix- isolated species. These isotopic peaks have m2.2% of the intensity of the corresponding parent peak, are consistent with double the natural aboundance of 13C (1.1%) and lie, 112 as expected, on the low frequency side of the factor group components of the host. XlO—LEgl - v10, a CH(CD) stretch mode, is an eg mode. Now, an eg mode may exhibit both site and factor group splitting. However, C2H6 shows only two of the four ex- pected components for v10, while in 02D6, three components are observed (two strong peaks and one of moderate intensity). The le-spectra of isotopically dilute solutions of C2H6 in C2D6 and vice-versa, however, consist of two components of equal intensity at nearly the same frequency as the strong bands observed for the pure solids. These observa- tions validate the site and factor group predictions postu- lated on the basis of the crystal structure, and exemplify the utility of mixed crystal spectra. Because the crystal structures of the pure host and guest are identical, the site symmetry is unchanged and thus the site splittings are unaffected. 0n the other hand,the neighboring molecules that interact with the guest species are now no longer identical oscillators, thus causing the resonance inter— actions which give rise to the correlation field splitting, to vanish. g mode. This fundamental was observed with three components 211_(§g) — v11, a CH3(CD3) stretch mode is also an e for both C2H6 and C2D6, although the pattern of intensities for the three peaks reveals obvious differences in the two 113 cases. For C2D6, the three components are all of com- parable intensity, with the central peak slightly more intense. For C2H6, the three components consist of two more intense peaks and a weak one in between. However, in the spectra of the dilute solid solutions only a single peak, broader than in the pure spectra, could be resolved, thus providing no further information. 312—iggl - The v12 band, the Raman-active bending mode, consists of three components in the spectrum of C2H6, but only two components were observed for C2D6, with the intensities markedly different in the two cases. For C2H6, the three components consist of two moderately intense neighboring peaks and a weak component on the high fre- quency side. The corresponding C2D6 feature appears as a weak peak and a moderately strong higher frequency peak. However, in the spectra of the isotopic dilute solutions, this fundamental appears as a doublet for C2H6 and a singlet for C2D6 guests. The bands are somewhat broader than in the pure crystals, and thus one can be certain that the extra components observed for the pure solids are due to factor group splitting. CHAPTER VII THE INTERNAL MODES OF THE PARTIALLY-DEUTERATED ETHANES A. Introduction It has been shown in Chapters IV and V that the crystals of the partially-deuterated ethanes have an "effective" Ci site symmetry. This leads to the existence of only one energetically distinguishable orientation of the molecules in the CH3CD3 crystals, and three energetically inequivalent orientations in the C2H5D, 1,1-C2HuD2 and C2HD5 crystals (see Table A). This chapter is therefore divided into three sections. Section B concerns the assignments of the internal modes of CH3CD3 in neat crystals and in dilute solid solutions in C2H6 and C2H5D hosts; Section C deals with the observed fundamental vibrations of C2H5D, 1,1- C2HuD2 and C2HD5 neat crystals. A comment on the assign- ments of the observed frequencies is in order. The free molecules of the partially-deuterated ethanes are of lower symmetry than the D3d symmetry of ethane. Therefore, fundamentals, overtones and combinations which were in- active for the 02H6 and C2D6 crystals may now become active. Fermi resonance may also become more prevalent in the 11” 115 crystals of the partially-deuterated ethanes due to the lower symmetry of the molecules. Moreover, the neat samples contained some impurities, and natural abundance C-13 im- purity was present in all the samples. Thus the spectra of the neat partially-deuterated samples exhibit many bands and assignment of these is at best tenuous. (A calculation of C-13 harmonic shifts from the free molecule C-l2 fre- quencies of the partially-deuterated ethanes, using standard normal coordinate analysis, has been under way, but was not finished at the time when this thesis was completed.) The assignments given in this chapter are based on gas phase frequencies, relative intensities and observed dilute- mixed crystal frequencies. Also, mutual exclusion was not observed, so a comparison of infrared and Raman data aided in the assignments. Only bands assigned as fundamentals are presented in the wavenumber tables in this chapter, together with their relative intensities. B. The Internal Modes of CH3QQ3 The CH3CD3 molecule is of interest among other isotopic species of ethane, in that substantial symmetry remains and thus it shows no orientational effect in dilute- mixed isotopic crystals. The absence of the orientational effect in the internal mode spectrum of CH3CD3 might lead to an analogy between the internal modes of CH3CD3, C2H6 116 and C2D6. However, it must be noted that CH3CD3 is still disordered because of the existence of the translationally inequivalent orientations. Therefore the usefulness of the g = 0 selection rule may be questionable. Unfortunately there have been only a few studies of the internal modes of disordered molecular crystals.73"76 Most of these have dealt with isotopic mixed crystals whose 56 and the goal has modes are in the separate band limit, been to identify the nature of the splitting in the pure crystal spectrum. Little effort has been concentrated on 56 the internal modes in the amalgamation limit. However, studies of the phonons of the isotopic mixed molecular crystals have revealed the usefulness of § in the amalga- mation limit (see Chapter IV). The most important parameter which determines to which type a given mixed crystal belongs is the ratio of the difference A of the energies of the host and guest to the width T of the energy band. When this ratio is large, the energy band is split into a number of bands which correspond approximately to the guest and host, and each band gives rise to its own absorption peak(s). This is the case in the separate band limit or persistence type.56 The amalga- mation limit, on the other hand, is achieved when this ratio is small; i;g;, when the energy difference between the host and guest vibration is less than the bandwidth of the pure-crystal mode. A crystal containing molecules 117 in energetically-inequivalent orientations can be considered a mixture of different "pure crystals", each containing molecules in a simple orientation. The orientational "splitting" then corresponds (approximately) to the guest- host difference, A. Formally one can say that the energy difference between the orientational components of CH3CD3 is zero. That is, for each vibration all orientations have only one energy, and thus the energy difference is zero. Zero is certainly less than the bandwidth of the vibra- tion, and thus the internal vibrations of these crystals are in the amalgamation limit. Excitons are more localized than phonons, and thus the phonons of a crystal probe the periodicity of the lat- tice over a larger range than do the vibrational excitons. If H is a "good quantum number" for the phonons of a dis- ordered solid in the amalgamation limit, it is likely to be a "good quantum number" for the vibrational excitons of the disordered (CH CD3) solid in this limit as well. If g 3 selection rules still apply to this disordered solid, then the bands should show the same number of Davydov components as do the corresponding bands of ethane and ethane-d6. In other words, one would expect to observe a doublet for the non-degenerate modes and a maximum of a quartet for the degenerate modes in the infrared and Raman spectra of solid (II) CH3CD3. A breakdown of g selection rules would most likely lead to broad, structureless bands. 118 The observed fundamental vibrational frequencies of solid CH3CD3 are listed in Table 20. Tables 21 and 22 include the observed frequencies of CH3CD3 fundamentals in dilute mixed crystals of C2H6 and C2H5D. The mixed, crystal spectra will aid both in the assignment of CH3CD3 fundamental bands and in finding the origin of the neat CH3CD3 band splittings. In the neat crystal, singlets were observed for all non-degenerate modes (except for the Raman spectrum of v3) and doublets were observed for the degen- erate modes in both spectra (except for the IR spectrum Of v If it is true that the CH3CD3 crystal still 12)' possesses a spectroscopically "effective" Ci site sym- metry, like C2H6 and C2D6, then the "a" mode doublets, etc. would arise from Davydov interactions and they should dis- appear in the dilute-mixed crystals. C-l3 isotope shifts were observed for three of the twelve fundamentals of CH3CD3. It is to be noted that for this molecule two different C-13 species exist, each with 1.1% natural abundance. The Raman and IR spectra of the fundamental modes of neat crystalline CH3CD3, and of its dilute solid solutions in C2H6 and C2H5D hosts, are shown in Figures 2H-32. Table 20. Internal Fundamental Frequencies (cm-l) of CH 119 CD 3 3° Neat-Crystal Mode Description IR Raman 01 (a1) CH str. 2881.3 (vs) 2878.1 (vs) 2876.0 (w)C 287u.8