ISSN:0300-9238    

DOI:10.1039/F298783FX046

出版商:RSC    

年代:1987

数据来源: RSC

ISSN:0300-9238    

DOI:10.1039/F298783BX048

出版商:RSC    

年代:1987

数据来源: RSC

摘要:

ISSN 0300-9238 JCFTBS 83(12)21 83-2339 (1 987) JOURNAL OF THE CHEMICAL SOCIETY Faraday Transactions II Molecular and Chemical Physics CONTENTS 21 83 Dielectric Absorption of Various Symmetrically Substituted Compounds of the Type [CH3(CH2)J2X in a Polystyrene Matrix M. S. Ahmed and S. Walker 2 19 1 Photoredox and Electrochemical Reactions of Water-soluble Gold Por-phyrins T. Shimidzu, H. Segawa, T. Iyoda and K. Honda 2201 Absorption Spectra of Molecules adsorbed on Light-scattering Media. Part 2.- Interpretation of Diffuse Reflectance Data R. Gade, U. Kaden and D. Fassler 2211 An SCF-MS-Xa, Study of the Bonding and Nuclear Quadrupole Coupling in 1:l Complexes of Amines with Diatomic Halogens and Interhalogens G. Bowmaker and P. D. W. Boyd 2225 Large-amplitude Vibrations and Microwave Band Spectra.Part 1 .-Adamantan-1-01 G. Corbelli, A. Degli Esposti, L. Favero, D. G. Lister and R. Cervellati 2235 Large-amplitude Vibrations and Microwave Band Spectra. Part 2.-l-Adamant- amine G. Corbelli, A. Degli Esposti, L. Favero, D. G. Lister and R. Cervellati 2247 Are the Reactions Li + Na2 and Na+ K2 Direct or Indirect? A Dynamics Study of Semiempirical Valence-bond Potential-energy Surfaces V. M. F. Morais and A. J. C. Varandas 2261 Zero-field Pulsed Response and Dipolar Couplings in Systems of Spin I=1 Nuclei J. C. Pratt and A. Watton 2271 Ion Diffusion near Charged Surfaces. Exact Analytic Solutions D. Y. C. Chan 2287 An Ab Initio Molecular-orbital Study of the Structure and Spectroscopic Proper- ties of CH3A1H G.E. Quelch and I. H. Hillier 2295 Photophysical Properties of Ru-Cyano-poly( pyridine) Complexes. Acidity and Temperature Tuning of Luminescence Properties A. Juris, F. Barigelletti, V. Balzani, P. Belser and A. von Zelewsky 2307 A Chemical Interpretation of Vibrationally Induced Barriers to Hindered Internal Rotation T. A. Claxton and A. M. Graham 2319 Kinetic Study of the Reactions of Ground-state Silicon Atoms, Si(3 3c),with Buta-1,3-diene and But-2-yne S. C. Basu and D. Husain 2325 Measurement of Absolute Rate Data for the Reaction of Atomic Potassium, K(4*SIl2), with CF3C1, CF2C12, CFC13, CF3Rr and SF6 as a Function of Tem- perature by Time-resolved Atomic Resonance Absorption Spectroscopy at h = 4-404 nm [K(5 '8) K(4 2S1,2)].D. Husain and Y. H. Lee 2339 Corrigendum to Exchange Interaction in Linear Trimeric Copper( 11) Complexes with Ferromagnetic and Anti ferromagnetic Ground States S. Gehring, H. Astheimer and W. Haase

ISSN:0300-9238    

DOI:10.1039/F298783FP150

出版商:RSC    

年代:1987

数据来源: RSC

摘要:

J. Chem. SOC.,Faraday Trans. 2, 1987, 83(12), 2183-2189 Dielectric Absorption of Various Symmetrically Substituted Compounds of the Type [CH3(CH2)3]2Xin a Polystyrene Matrix Mohammed Saber Ahmed Department of Chemistry, Case Western Reserve University, Cleveland, Ohio 44106, U.S.A. Stanley Wa1ker* Department of Chemistry, Lakehead University, Thunder Bay, Ontario P7B 5E1, Canada Dielectric absorption studies have been made on symmetrically substituted compounds of the type [CH,(CH,),],X where X is: 0 NH, >S and \SnCl,/ / in a polystyrene matrix in the frequency range 10-155 Hz over a temperature range 80-25G K. A plot of loss factor vs. temperature at a fixed frequency reveals two absorption peaks for each compound. The enthalpy of activation for both the low- and high-temperature absorptions is reasonably indepen- dent of the variation of the type of polar group X.The enthalpy of activation for the low-temperature absorption seems to be characterized largely by segmental rotation about the C-C bonds, and the high-temperature absorp- tion may be attributed to molecular rotation. The movement of the polar group from the end to the centre of the hydrocarbon chain does not affect appreciably the enthalpy of activation of the molecular process. For the various polar groups, X, studied here, the nature and size of the polar group seem unimportant in determining the enthalpy of activation value for the intramolecular process. Dielectric absorption studies have been carried out by Dasgupta et al.' on n-heptane solutions of dialkyl ether and also on dialkyl sulphide at microwave frequencies, and the data were analysed into contributions from molecular and intramolecular relaxation times where the intramolecular motion involved rotational contributions about the C-0 and C-S bonds.Hasan and Klages' reported that the dielectric relaxation of several symmetrically substituted ethers was dominated by intramolecular rotation about the C-0 bond. From dielectric measurements on di-n-butyl ether in n-heptane solution, .~Johari et ~1 interpreted the intramolecular process as motion around the polar C-0 bond. Cr~ssley,~ from dielectric studies of several symmetrically substituted ketones in cyclohexane solutions, concluded that the dipole reorientation is dominated by intramolecular rotation, although when the size of the alkyl groups in the ketone is increased sufficiently, the contribution from the whole molecule rotation becomes more appreciable.The main objectives of the present investigation are: (1) to separate completely the molecular process from any intramolecular ones; (2) to determine the enthalpy of activation of the intramolecular process and see how it varies with the nature of X; and (3) to compare values with those from R(CH2),Y (Y=-CH,Br,' -NH2 and -COCH3),' where the enthalpy of activation for the intramolecular process was virtually constant for a fixed chain length and largely independent of the nature of the dipoles.6 2183 Dielectric Absorption in a Polystyrene Matrix '"I Fig.1. Dielectric loss, err, us. T(K) at 1.01 kHz for [CH3(CH2)3]2Xin a polystyrene matrix where X is: (4 \,co, (b) \/so, (4 \/soh (4 \/o, 0 \(e) '/9 (f) \ /SnCI,, (8) ,NH, (h) \/s. /' \H Experimental Dielectric measurements were made by the use of a General Radio 1616 precision (10-105) Hz capacitance bridge. The experimental techniques and the procedures for sample preparations have been described in detail in previous publications. 5*7-9 Special care was taken in preparing the polystyrene disc for the case of di-n-butyl phosphine oxide. Since it is air-sensitive, the disc preparation and the study with a parallel-plate capacitor cell were carried out in a nitrogen atmosphere. Results The treatment of experimental data, consideration of errors and the evaluation of Eyring parameters are given in our previous Plots of loss factor, E" vs.tem-perature at a fixed frequency are given in fig. 1 while the dielectric data are listed in tables 1-4. Some of the relaxation times have been obtained by extrapolation of an assumed linear Eyring plot. Eyring plots are given in fig. 2 and 3. Discussion From fig. 1 it is evident that the half-width (ATl,*)values for the variable temperature absorption at a fixed frequency of symmetrically substituted molecules having the general M. S. Ahmed and S. Walker Table 1. Relaxation times and Eyring activation parameters for the low-temperature absorption of [CH3(CH2)J2Xwhere X is in a polystyrene matrix relaxatior! time/s ~T range P AHEh ASE X /K range 100 K 150 K /kJ mol-' /.iK-' mK1 92- 100 0.22-0.28 3.2 x 2.5 x 10-7 16.9 -0.4 93- 112 0.21-0.30 4.4 x 10-~ 1.3x 10-~ 19.2 20 89- 107 0.23-0.26 1.8 x lop4 9.2 x lo-* 17.9 15 92- 108 0.26-0.29 3.4 x 10-~ 1.3 x 10-~ 18.6 17 93-113 0.18-0.29 4.0 x 3.8 x lo-* 22.1 51 86- 104 0.21 -0.26 7.0 x 1.3 x lo-' 20.4 47 90- 109 0.22-0.3 1 3.4 x 10-~ 1.5 x lo-' 18.2 13 95-117 0.21-0.33 3.5 x 10-~ 6.2 x lo-* 20.4 35 ~~ a Obtained by extrapolation of the Eyring plots.Obtained directly (uncertainty *5%). Obtained directly (uncertainty *20% ). Table 2. Methyl rotational barriers in (CH3)2Xmoleculesa calculated barrier experimental barrier X / kJ mol-' / kJ mol-' \O 12.5 11.3*0.2 / \S 7.5 8.9k0.1 / >co 5.4 4.2 f0.2 \NH 15.1 13.6*0.4 / Obtained by molecular orbital calculation and taken from ref.(11) and (12). Dielectric Absorption in a Polvstyrene Matrix Table 3. Relaxation times and Eyring activation parameters for the higher-temperature absorption of [CH3(CHJ3I2X where X is in a polystyrene matrix ~ relaxation time/s X T range /K P range 200 K 225 K" AHE /kJ mol -' ASE' /J K-' mol-' 0 '\H \/ 197-228 0.15-0.19 1.9 x lop3 5.6 x lo-' 50.6 64 2 10-240 0.12-0.16 8.6 x lo-' 3.2 x lo-' 47.6 36 202-207 0.09-0.10 3.9 x 10-~ 9.4 x 10-~(' 53.3 71 193-218 0.13-0.16 2.0 x 5.7 x lop6 51.6 87 197-228 0.11-0.17 1.9~ 5.6~lop5 51.1 66 21 2-245 0.12-0.14 2.5 x 8.3 x lo-' 49.0 56 187-212 0.12-0.15 3.3 x 1.2 x lo-' ' 47.9 48 191-212 0.11-0.13 4.8 x lo-' 2.0X lo-' 45.3 48 " Obtained directly (uncertainty *5'/0).Obtained directly (uncertainty i2Oo/0). Obtained by extrapolation of the Eyring plots. Table 4. Relaxation time and Eyring parameters for the higher-temperature absorption of l-amino-octane,6 nonan-2-one6 and 1-bromo-octane5 in a polystyrene matrix relaxation time/s T range P -AH," AS, absorbant /K range 200 K 225 K* /kJ mol-' /J K-' mol-' 1-amino-octane 196-223 0.20-0.25 1.9x 5.1 x " 50.5 63 2-nonanone 187-212 0.16-0.22 3.3 x lo-' 1.6x lop7 47.5 63 1-bromo-octane 205-249 0.14-0.19 5 x 3.3 x lop6 46.9 -1.2 Obtained directly (uncertainty *5O/b). Obtained directly (uncertainty *20%).' Obtained by extrapolation of the Eyring plots. M. S. Ahmed and S. Walker -0.3i ,Q D -0.9-h L v M -1.5-0 m -2.1 m -2.7 8.5 9.5 10.5 11.5 10'K/T Fig. 2. Eyring plot of log Tr us. 1/ T (K')for the low-temperature absorption of [CH3(CHJ3I2X in a polystyrene matrix where X is: formula [CH3(CH2)3]2X, where X is CO, SO, 0,SO,, HPO, NH, S and SnCl,, are very similar and lie in the range 45-55 K. The p values for the low-temperature absorptions of symmetrically substituted molecules are also very similar and lie in the range 0.18-0.33 between 80 and 120 K. Likewise, both the p and ATt,, values closely resemble those previously reported for the intramolecular process in the 1-bromoalkane work5 and in studies on 1 -aminoalkanes and the alkan-2-0nes.~ The low-temperature absorption in 1-bromoalkanes,' I-aminoalkanes and alkan-2- ones6 has been largely attributed to segmentalcrotation about the C-C bonds in the chain, involving the movement of the polar end groups (-CH,Br, -NH2 and -COCH3). Alkyl-group rotation alone cannot give rise to absorption of the magnitude observed5 nor to the variation in &Laxvalues in fig.1 for the low-temperature process as X is altered. The two feasible candidates for these segmental rotations are rotation about the C-C bond involving the movement of the polar group, X, and rotation about the bond from the carbon atom(s) to the X group. Table 2 shows that the rotational barriers about the C-0, C-S, C-CO and C-NH bonds differ from one another by a substantial margin.",'* Since the molecules listed in table 1 are almost the same size, if the intramolecular rotation had taken place solely about the carbon atom(s) adjacent to the X group, the enthalpies of activation would have been expected to differ from one another quite substantially.However, inspection of table 1 reveals that the enthalpy of activation and also the relaxation time values are very similar indeed. The similarities of the enthalpies of activation for the low-temperature absorption, despite the variation of the polar group, X, bear out that the intramolecular rotation detected has the characteristics of rotation about the C-C bonds with consequent movement of the polar group, X. No energy barriers for internal rotations in the [CH3(CH2)J2X type 4.0 4.4 4.8 5.2 lo3 K/ T Fig.3. Eyring plot of log TTus. 1/ T (K-') for the high-temperature absorption of [CH,(CH,),],X in a polystyrene matrix, where X is: 0 0,>NH; +, 'S;/ D, >SO; a, >co. of molecule appear to be available in the literature. The closest experimental studies seem to be those of Pethrick and coworkers. l3-I5 The Arrhenius activation energies obtained from these ultrasonic studies ranged from 9.8 to 14.9 kJ mol-' for the various methylpentane~'~ Earlier work had resulted in rotational isomeriz- and methylhe~anes.'~ ation activation energies which varied from 13.8 kJ mol-' for nonane to 19.3 kJ mol-' for tstradecane, l3 where the barrier increased with increasing chain length.A similar increment in AHEof 5 kJ mol-' was obtained by Huque and WalkerI6 from dielectric studies of C-C rotations from nonan-1-01 to tetradecan-1-01 at low concentrations in a polystyrene matrix. The AH, value for these long-chain polar compounds from dielectric data is at best a rough indicator of the magnitude of the barrier of the various types of C-C rotations which relax the dipole(s) at the end of the chain. The ultrasonic approach, however, yields more detailed information about the C-C rotational isomeric barriers in these long-chain compounds, including the energy differences between the stable rotational energy states. Thus, the ultrasonic approach can lead to the construction of a more precise model for intramolecular rotation.High-temperature Absorption The p values for the high-temperature absorption of symmetrically substituted com- pounds are relatively low and lie between ca. 0.10 and 0.20 at 190-250 K (table 3). Such low /3 values as 0.10 indicate a broad distribution of relaxation The mechanism of dielectric relaxation for the high-temperature process [CH3(CH2)3]2X would seem to be of a similar nature as in CH3(CH2),Y(where, for example, Y is -NH2, -CH,Br and -COCH3). Both the enthalpy of activation and relaxation time values are reason- able for a molecular relaxation process and compare favourably with the values for the molecular process in 1-amino-octane and nonan-2-one (table 4), which have AHE values M. S. Ahmed and S. Walker 2189 of 50.5 and 47.5 kJ mol-’ and T200K values of 1.9x and 5.3 X lop4s, respectively.6 Thus, for the [CH3(CHJ3I2X compounds we also consider the process to be a molecular one.However, both the corresponding AHE and T values for molecular relaxation exhibit no recognizable increasing sequence in terms of increasing size of the group X, although the variation in the size of X is relatively small compared with that of the molecule. In fact, the variation in AHEcould almost be accounted for by experimental error. However, the variation in T would seem significant and may possibly be accounted for by the different inclinations of the fixed dipole moment to the long axis of the molecule as X is varied. This is one of the factors identified by Davies” which influence the molecular relaxation time value.Conclusions The main conclusions to be drawn from the present investigation are the following. (1) The data presented in this work establish that the symmetrically substituted molecules of the type [CH3(CH2)3]2X in a polystyrene matrix exhibit two distinct absorption peaks (see fig. l), whereas previous investigators have been unable to separate the peaks. (2) The most likely interpretation of the low temperature absorption is that of intramolecular rotation. It appears that rotation about the C-C bonds dominates the corresponding Eyring enthalpy of activation values. (3) The variation of the dipole position from the end 10 the centre of the hydrocarbon chain at most has only a small effect on the intramolecular enthalpy of activation obtained.(4) For the polar groups studied in the [CH3(CHJ3I2X type of molecule, the nature and size of the polar group seem unimportant in influencing the AHE value of the intramolecular process. (5) The high-temperature absorption may be ascribed to molecular relaxation. We thank Mr B. K. Morgan for technical assistance and Mr M. A. Siddiqui for helping with computer analyses. S. W. expresses his gratitude to the National Research Council of Canada for continued financial support. References 1 S. Dasgupta, K. M. Abdul-El-Nour and C. P. Smyth, J. Chem. Phys., 1969, 50, 4810. 2 ‘4. Hasan and G. Klages, 2. Naturforsch., Teil A, 1978, 33, 687. 3 G. P. Johari, J. Crossley and C. P. Smyth, J.Am. Chem. Soc., 1969, 91, 1597. 4 J. Crossley, J. Chem. P/i,vs., 1972, 56, 2549. 5 M. S. Ahmed and S. Walker, J. Chem. Soc., Faraday Trans. 2, 1985, 81, 479. 6 M. S. Ahmed and S. Walker, to be published. 7 M. A. Desando, S. Walker and W. H. Baarschers, J. Chem. Phys., 1980, 73, 3460. 8 C. K. McClellan and S. Walker, Can. J. Chem., 1977, 55, 583. 9 M. Davies and J. Swain, Trans. Faraday Soc., 1971, 67, 1637. 10 S. P. Tay, S. Walker and E. Wyn-Jones, Adu. Mol. Relax. Processes, 1978, 13, 47. 11 M. H. Whan Gibo and S. Wolf, Can. J. Chem., 1977, 55, 2778. 12 S. Profeta Jr and N. L. Allinger, J. Am. Chem. Soc., 1985, 107, 1907. 13 M. A. Cochran, P. B. Jones, A. M. North and R. A. Pethrick, J. Chem. Soc., Faraday Trans. 2, 1972, 68, 1719. 14 A. M. Awwad, A. M. North and R. A. Pethrick, J. Chem. Soc., Faraday Trans. 2, 1982, 78, 1687. 15 4. M. Awwad, A. M. North and R. A. Pethrick, J. Chem. Soc., Faraday Trans. 2,1983, 79, 731. 16 Md. E. Huque and S. Walker, J. Chem. Soc., Faraday Trans. 2, 1936, 82, 511. 17 N. E. Hill, W. E. Vaughan, A. H. Price and M. Davies, Dielectric Properties and Molecular Behaviour (Van Nostrand, Reinhold, London, 1969). Paper 6/ 1452; Received 2 1si July, 1986

ISSN:0300-9238    

DOI:10.1039/F29878302183

出版商:RSC    

年代:1987

数据来源: RSC

摘要:

J. Chem. SOC.,Furuday Trans. 2, 1987, 83(12), 2191-2200 Photoredox and Electrochemical Reactions of Water-soluble Gold Porphyrins Takeo Shimidzu,* Hiroshi Segawa, Tomokazu Iyoda and Kenichi Honda Division of Molecular Engineering, Graduate School of Engineering, Kyoto University, Kyoto 606, Japan Photoredox and electrochemical reactions of water-soluble gold porphyrins (AuTMPyP, AuTPyP and AuTSPP) have been investigated in aqueous solution. AuTMPyP is the most durable photoredox catalyst for these porphyrins operating through the reductive electron transfer process. Photo- generated AuTMPyP (r-radical anion) is able to reduce water at pH<4, although it undergoes disproportionation to form a AuTMPyP(ph1orin). The AuTMPyP(ph1orin) is completely oxidized back to the parent AuTMPyP in the dark with the appropriate oxidant, but does not have sufficient potential for the reduction of water.The design of the photochemical energy conversion systems using a metalloporphyrin as a visible light sensitizer involves some fundamental knowledge of the photoelec- trochemistry of primary photochemical processes in natural photosynthesis.' Water is this planet's most abundant source of electrons, and its oxidation provides electrons for the reduction of organic compounds by photoreaction with metalloporphyrins. For the photoreduction of water, appreciable successes have been achieved using zinc por- phyrins.* For the photo-oxidation of water,3 however, some problems still remain: (a) conventional metalloporphyrins do not fulfil the thermodynamic requirements necessary for the photo-oxidation of water, and (b) the resulting oxidized species undergo undesired irreversible reactions.Approaches to solving the first problem include both attaching an electron-withdrawing group onto the ring structure and incorporating a central metal of high electronegativity. For instance a metalloporphyrin of high oxidizing power can be easily obtained by the incorporation of gold (electronegativity 2.54). As regards the second problem it is necessary to design a simple redox cycle without undesired reactions. In the preceding rep~rt,~ we suggested that AuTMPyP was suitable as a photo-sensitizer for the splitting of water in homogeneous aqueous solution because of its strong oxidizing power.Table 1 summarizes the absorption data and redox potentials of gold porphyrins. Overall, the redox potentials of the gold porphyrins were more positive than those5 of other metalloporphyrins. The reduction potentials in the excited state of these porphyrins [E(P*/P'-)I, which were obtained from the first reduction potential [E(P/P-)] and the triplet excitation energy, are also more positive!. For example, not only the ?r-radical cation but also the excited states of gold porphyrins satisfy the thermodynamic requirement for the oxidation of water. However, there are few studies on the photoredox reactions of water-soluble gold porphyrins. In this paper we present the photoredox reactions of these gold porphyrins (AuTMPyP, AuTPyP and AuTSPP) in detail.In particular, the photoreduction of AuTMPyP is examined to clarify the formation of AuTMPyP( phlorin) which involves the disproportionation of AuTMPyP (n-radical anion). The energetics for reduced products of AuTMPyP, with reference to the reduction of water, are also presented. 2191 2192 Photoredox and Electrochemical Reactions of Gold Porphyrins Table 1. Absorption data and redox potentials of the gold porphyrins reduction redox potentials in the ground state potential in the absorption excited triplet maxima oxidation reduction state porphyrin nm (log E) E(P+/P)/V E(P/P'-)V E(P-/P2-)/V Ared E(P*/P-)/V ref. AuTMPyP 406 (5.44) 1.70" -0.20 -0.50 0.30 1.57 4 481 (3.61) 523 (4.18) 558 (3.78) AuTPyP 405 (5.55) 1.70" -0.21 -this 482 (3*741b 2-30' -0.19 work 520 (4.29)' -0.75 0.56 AuTSPP 406 (5.57) 1.50" -0.36 1.64 4 483 (3.62) 1.7ou,c -0.28'522 (4.22) -0.76' 0.48' AuTPP 412 (5.52)d 2.02b 521 (4.30)d -0.38b -l.OOb 0.62h 1.38 4 Unless otherwise stated, all data are in aqueous solution.All redox potentials are with respect to NHE. " Peak potential is over the potential window of the adopted solvent. In dichloromethane. 'In N,N-dimethylformamide. In chloroform. Anode peak potential. Experimental Materials Chlorogold meso-tetrakis(4-N-methylpyridy1)porphinetetrachloride salt (AuTMPyP) and chlorogold meso-tetrakis(4-sulphopheny1)porphinetetrasodium salt (AuTSPP) were prepared according to the previously reported meth~d.~A new gold porphyrin, chlorogold rneso-tetrakis( 4-pyridy1)porphine (AuTPy P), was synthesized by refluxing metal-free meso-tetrakis(4-pyridy1)porphine(TPyP)' (400 mg) and KAuC1, (1.O g) in aqueous HCl (50 cm3; pH 1.8) for 15 h.Chlorogold tetraphenylporphine (AuTPP) was prepared by Rothemund's method.' Both AuTMPyP and AuTSPP are freely soluble in water, and AuTPyP is soluble in acidic solution, and their photoredox reactions in homogeneous aqueous solution were investigated. Colloidal Pt catalyst supported by polyvinyl alcohol (PVA) was prepared according to the literature.*' Other reagents were the best available grades and were used as received. Photochemical Measurements Steady-state photolysis studies were carried out using a 500 W Xe lamp (Ushio Electric; UXL-500-D) through a 420nm cut-off filter and a near-infrared cut-off filter (Toshiba, L-42and IR-25S,respectively; 420< h/nm <700 for the optical window).Photolysis solutions of porphyrins (5.0 x lop5mol dmp3 j in water, containing the appropriate amount of sacrificial electron donor or acceptor, were purged with argon before irradi- ation. A square quartz cell connecting a Pyrex tube (volume, 12cm3; optical path, 1cm) was used as a photolysis cell. U.v.-vis. absorption spectra were recorded with an SM-402 spectrophotometer (Union Giken). Near-infrared absorption spectra were recorded with a UV-365 spectrophotometer (Shimadzu). Quantum yields in the steady-state photoredox reactions were determined in the previously reported manner.2' The incident T. Shirnidzu, H.Segawa, T. Iyoda and K. Honda light intensity was 6.5 x mol s-I at 550* 3 nm according to Reinecke's salt chemical actinometry.8 Flash photolysis studies were made with PHOlAL RA412 and RA401 instruments (pulse duration 18 ps). Photolysis solutions were prepared as above. Luminescence spectra were recorded with an RF-503 fluorescence spectrophotometer (Shimadzu). Electrochemical Measurements An electrolysis solution was purged with nitrogen or argon. Cyclic voltammograms were recorded with an NPGS-301 potentiogalvanostat and an NFG-6 function generator (Nikko Keisoku). A three-electrode system was employed with a platinum working electrode, a platinum counter-electrode, and a saturated calomel electrode.The reduction potentials of the excited states of the porphyrins [E (P*/ P*-) = E (P/P'-) + Eoo]were obtained from the first reduction redox potential [E (P/ P-)]and the excitation energy (Eoo).Thin-layer electrolysis in a quartz cell (optical path length 1.0 mm) was performed using a platinum minigrid working electrode and a platinum wire counter-electrode. Rotating ring-disc electrode (RRDE) experiments were carried out with a DPGS-1 dual-potentiogalvanostat, an NFG-3 function generator, and an SC-5 motor speed controller (Nikko Keisoku) with a Pt(ring)-Pt( disc) electrode. Results and Discussion Reversibility of Photoredox Cycles of Gold Porphyrins An important factor in the design of efficient photocatalysts, is the durability of the photosensitizer during steady-state irradiation. With this in mind, the reversibility of photoredox cycles of gold porphyrins in aqueous solution containing sacrificial electron acceptors or donors was investigated.In the photocatalysis, two types of photoinduced electron-transfer process, namely, oxidative electron transfer (OET) and reductive elec- tron transfer (RET) were considered.' In the former, the excited state of the porphyrin is quenched by the electron acceptor and the quenching reaction leads to oxidation of the porphyrin. In the latter the excited state is quenched by the electron donor and the reaction leads to reduction of the porphyrin, as follows: D+xPorAP;r*x: t)+l-*Pori;---: D POT'+ Por* -Por OET RET where Por, D and A are the porphyrin, the electron donor and the electron acceptor, respectively.The photo-oxidized product of AuTMPyP (5.0 x lop5mol dmp3) with K2S208as the sacrificial oxidant, at pH 3.8 showed a strong absorption maximum at 650 nm without near-infrared absorption bands.4 The product was considered to be a 'dihydroxy por- phyrin' because of the similarity to the absorption spectra of corresponding zinc com- plexes.'' The photo-oxidized product was bleached upon further irradiation and could not be reduced back in the presence of an electron donor in the dark. As in the case of other metall~porphyrins,~ the formation of the dihydroxyporphyrin through the OET process completely obstructed the photoredox cycle. However, AuTMPyP (5.0 x mol dmp3) was photoreduced with various sacrificial electrons donors [e.g.ethyl-enediamine tetra-acetic acid (EDTA) and its metal complexes (Mg-EDTA, Ni-EDTA) and triethanolamine (TEA)]. In all cases the product was AuTMPyP(ph1orin) (A,,, = 475 and 770 nm) at pH <9 or AuTMPyP( r-radical anion) (A,,, =638,780sh and 935 nm) 2194 Photoredox and Electrochemical Reactions of Gold Porphyrins ~~ 400 500 600 700 800 A /nm Fig. 1. The absorption spectra of photoreduced AuTMPyP with EDTA from ref. (4). (-j AuTMPyP, (. --.) AuTMPyP(.rr-radical anion), (---) AuTMPyP(ph1orin). at pH 10 (fig. 1). The resulting absorption spectra of the reduced AuTMPyP were similar to those of the reduced ZnTPP." The AuTMPyP( v-radical anion) was completely oxidized back to the parent AuTMPyP with an appropriate oxidant such as 0, or K2S208 at pH > 9, whereas AuTMPyP(ph1orin) was oxidized back to the parent AuTMPyP with K2S208at pH 1-8.These reoxidation reactions after photoreduction proceed without bleaching of the porphyrins (QPB 3 x lop5at pH 8.4), and the restoration ratio of the porphyrins in the reoxidation reactions was not less than 0.98. Additionally, AuTMPyP(ph1orin) was oxidized back to parent AuTMPyP with FeC13 at pH 2. These results indicate that AuTMPyP is a relatively durable photocatalyst operating through the photo-induced RET process. Harriman et al. reported on photo-oxidation of aqueous ethanol with SnTMPyP through its reversible porphyrin-phlorin redox cycle, emphasis- ing advantages.12 The photo-oxidized product of AuTPyP (5.0 x mol dm-3) with K2S208at pH 3.8 showed an absorption maximum at 648 nm, which was similar to that of AuTMPyP, as shown in fig, 2.The photo-oxidized product was considered to be the undesired AuTPyP(dihydroxy porphyrin). In the photoreduction of AuTPyP with EDTA at pH 4.7, the products exhibited complicated absorption spectra (fig. 2), which indicated a mixture of AuTPyP( v-radical anion) (A,,, =650, 750 and 830 nm), AuTPyP(ph1orin) (A,,, =780 nmj, and AuTPyP(ch1orin) (A,,, = 610 nm). AuTPyP(ph1orin) and the AuT- PyP(v-radical anion) were oxidized back to the parent porphyrin in the dark with an appropriate oxidant such as K2S208,but AuTPyP(ch1orin) was not reoxidized. There- fore, re-oxidation of the mixture with K2S208at pH 4.7 yielded the AuTPyP(ch1orin).In the mild reoxidation of the mixture with 0, at pH 4.7, only the AuTPyP(nradica1 anion) was completely oxidized, to leave AuTPyP(ph1orin) and AuTPyP(ch1orin). This means that a durable redox cycle is not established with AuTPyP because of the irreversible formation of undesired products. In the case of AuTSPP, efficient photoredox reaction did not occur. Steady-state irradiation of AuTSPP (5.0x mol dm-3) in the presence of a sacrificial electron T. Shimidzu, H. Segawa, T. Iyoda and K. Honda 500 600 700 aoo A /nm Fig. 2. The absorption spectra of photoreaction products of AuTPyP. (-) AuTPyP, (. * * -. .) photo-oxidized products with K,S,08, (-* -* -), photoreduced products with EDTA, (..-. .-. . -) reoxidation of the photoreduced products with 02,chlorin and pholorin still remaining, (---) reoxidation of the photoreduced products with K2S208,chlorin still remaining. acceptor such as K2S208or [Co(NH,),Cl]CI, (2 x lo-, rnol dmP3) at various pH values resulted in no accumulation of photo-oxidized species of the porphyrin. Even after prolonged irradiation (e.g. several days), no oxidation of AuTSPP was observed other than slight bleaching. In the photoreduction of AuTSPP using TEA, triethylamine and L-ascorbic acid (0.025 mol dmP3) as the sacrificial electron donor, no photoreduced porphyrin was observed. Only a slight amount of AuTSPP(yh1orin) (A,,, =750 nm) was observed in photoreduction in the presence of EDTA (0.025 mol dmP3) for 3 h, and the quantum yield of the reaction was quite low.The low efficiency of the photoredox reactions of AuTSPP was attributed to the short lifetime of its excited state at room temperature. These results mean that AuTSPP is ineffective for photoredox catalysis. Consequently, the RET process of AuTMPyP is the most useful photoredox cycle of the gold porphyrins studied since it exhibits high efficiency and durability. In view of this the RET process of AuTMPyP was investigated in detail. Mechanism of AuTMPyP(ph1orin) Formation The clarification of the phlorin formation process is important for the control of the efficiency of these photoreactions. In this section, the mechanism of the phlorin forrna- tion is discussed.From the flash photolysis measurement of AuTMPyP (5.0 x loP5mol dm-3) with EDTA (1.0 x mol drnP3) at pH 4.8 (fig. 3), it was shown that the absorption at 643 nm assigned to photogenerated n-radical anion decayed according to second-order kinetics with a rate constant of 2.6 x lo5drn3 mol-' s-'. This second-order decay means that the AuTMPyP( n-radical anion) is converted to AuTMPyP(ph1orin) via bimolecular dispro- portionation. In fact, the absorbance at 770 nm assigned to AuTMPyP(phlorin) increased with the decay of absorbance at 643 nrn. The disproportionation of the AuTMPyP(m-radicai ailion) was also confirmed by the addition of HCI to the photogenerated m-radical anion solution.4 2196 Photoredox and Electrochemical Reactions of Gold Porphyrins1\-(a) -11;;-0.005 -0, I I I I I 0.015 1 -0.005 oi -I I I I I Fig. 3.Decay of AuTMPyP( .rr-radical anion) at A = 643 nm (a)and growth of AuTMPyP(ph1orin) at A = 770 nm (b) after photoreduction of AuTMPyP (5.0 x lo-’ mol dmP3)by flash photolysis at pH 4.8with EDTA (1.0 x mol dm-3). 50 40 3c 2c 1c C 01 2 3 4 5 r/min Fig. 4. Concentration-time courses of AuTMPyP (-a-),the .rr-radical anion (-A-)and the phlorin (4-)during photoreduction using MgEDTA at (a)pH 8.8 and (b) pH 5.2. Since the phlorin is a protonated species it is considered that phlorin formation should be dependent on the pH of the reaction solutions. Typical time courses in the photoreduction of AuTMPyP with MgEDTA at pH 8.8 and 5.2 is shown in fig.4.12 Photoreduced AuTMPyP products were quantitatively analysed by using ~523= 1.51 x lo4 2197T. Shimidzu, H. Segawa, T. Iyoda and K. Honda A/nm Fig. 5. The absorption spectral change due to disproportionation of the electrochemically gener- ated n--radical anion of AuTMPyP, which was proton-induced. (-) Spectrum of AuTMPyP( 7r-radical anion) solution at pH 10; (---) spectrum after the pH of the solution had been lowered to pH 3 with HCl. (a) AuTMPyP, (b)AuTMPyP( .rr-radical anion), (c) AuTMPyP(ph1orin). for AuTMPyP, €635 = 1.32 x lo4for its ar-radical anion, and E~~~ = 1.4x lo4for its phlorin. At pH 8.8, the ar-radical anion was formed in the first stage, followed by the phlorin. However, at pH 5.2, the r-radical anion was scarcely observed and the rate of phlorin formation was ca.ten times that at pH 8.8. Therefore, it is suggested that the disproportionation of the v-radical anion to the phlorin is accelerated by protons. In the thin layer electrolysis of an aqueous solution of AuTMPyP (3.3~ mol dm-3) containing Na2S04 (0.1 mol dm-3) at 0.26 V us. NHE, the electrochemi- cally reduced products were identified as AuTMPyP(ph1orin) at pH <9 and AuTMPyP( v-radical anion) at pH 10, which were similar to those from the photoreduc- tion. The resulting phlorin was a two-electron reduction product by coulometric titration. Since AuTMPyP was not electroreduced to the AuTMPyP( r-dianion) at -0.26 V us. NHE (see table 1, E(P'/P'-) = -0.50 V us.NHE), the AuTMPyP(ph1orin) was formed not through the n-dianion but through the disproportionation of the ar-radical anion in the bulk solution at pH <9. In addition, when the pH ( = 10) of the solution was lowered to pH3.0 with HC1, the v-radical anion was immediately converted into equimolar quantities of the phlorin and the parent porphyrin in the dark (fig. 5). Thus, the AuTMPyP( phlorin) formation uia disproportionation occurred in not only the photo- but also electro-chemical reduction. AuTMPyP( phlorin) formation in the dark electrolysis suggests that the disproportionation is the only reasonable process for phlorin formation and the sacrificial reagent in the photoreaction is not responsible for the conversion of the n-radical anion to the phlorin.Rotating ring-disc voltammograrns were obtained for solutions of AuTh.l?yP (1.O x 1 OP3 mol dm-3) containing Na,S04 (0.1 mol dm-3). At pH 10 the cathodic disc limiting current (I,) was observed in two steps corresponding to the first and the second reductions of AuTMPyP (fig. 6). If the reduction process involves no successive reactions in the bulk phase, the reduced products at the disc surface are reoxidized at the ring electrode with appropriate collection efficiency. In the first reduction region, an anodic ring current (IR)corresponding to reoxidation of the n-radical anion was observed at E,> -0.20 V us. NHE (ER= ring potential). In the second reduction region, however, 2198 Photoredox and Electrochemical Reactions of Gold Porphyrins us.NHE -0.6 -0.4 -0.2 0 0.2 disc E,/V us. NHE Fig. 6. Correlation of RRDE current-potential curves for reduction of AuTMPyP relating to ring potentials. ED, disc potential; I,, disc current, corresponding to the reduction of AuTMPyP; E,, ring potential; I,, ring current, corresponding to the reoxidation of reduced AuTMPyP. AuTMPyP (1.0~ mol dmP3) with Na,SO, (0.1 mol dmP3)was electrolysed at pH 10.5 using Pt(ring)-Pt(disc) electrodes. Redox potential was with respect to NHE. no ring current was observed. These phenomena were similarly observed when the disc rotating rate was varied in the range 200-4000 r.p.m. These observations indicated that the .rr-dianion of AuTMPyP was not stable and not converted into phlorin at pH 10.At lower pH (3-6), the collection efficiency (at E, <0.6 V us. NHE) of the AuTMPyP( T-radical anion) was smaller than that at pH 10 (85-90'/0). This indicates that the AuTMPyP(.rr-radical anion) is converted into the AuTMPyP(ph1orin) at a low pH. These observations suggest that the AuTMPyP( phlorin) is generated only via dispro-portionation of the .rr-radical anion. Reduction of Water by Photoreduced AuTMPyP Under potentiostatic electrolysis at -0.23 V vs. NHE, ca. 70% of AuTMPyP was reduced to phlorin for 200min, as confirmed by absorption spectroscopy. The cyclic voltam- mogram of the phlorin accumulating solution, showed a new anode peak at 0.66 V us. NHE (fig.7). This was assigned to the reoxidised phlorin. The potential difference between the AuTMPyP(ph1orin) and the AuTMPyP( .n-radical anion) [E(P/phlorin) -E(P/P-) =0.86 V] agreed with that of ZnTPP (0.85 V).13 The AuTMPyP( 7.r-radical anion) with E( P/P'-) = -0.20 V us.NHE had the potential ability to reduce water in a particular pH range. At pH(3.5, hydrogen was produced in the presence of AuTMPyP (3.0 x lo-" mol dmp3), colloidal Pt catalyst and EDTA 2.0 x lo-* mol dm-3), under visible-light irradiation (fig. 8). An analogous system using ZnTMPyP has also been reported.14 The threshold pH (3.5) of hydrogen production agrees with the relationship, E(P/P'-) == E(H'/H,) = (-0.059 x 3.5) V vs. NHE. Thus, the proton-reducing species in the hydrogen production was considered to be the AuTMPyP( .rr-radical anion) intercepted by the Pt catalyst, and not AuTMPyFiphiwriii).As mentioned above, the redox potential of AuTMPyP(ph1orin) is 0.66 V us. NHE, T. Shimidzu, H. Segawa, T. Iyoda and K. Honda 2199 I1 I I I -0.5 0.0 +0.5 +I .o E/V us. NKE Fig. 7. Cyclic voltammograms of AuTMPyP. (a) Normal cyclic voltammogram for 50 mV s-*; (b)Single-sweep voltammogram for 10 mV s-' after potentiostatic electrolysis at -0.23 V us. NHE. New anode peak for reoxidation of phlorin appeared at 0.66 V us. NHE. i 1.0 8-I 0 1 2 3 4 5 6 PH Fig. 8. The photoreduction of water through the RET process of AuTMPyP. AuTMPyP (3.0~ lop4mol dmP3), EDTA (2.0 x lop2mol dm-')), colloidal Pt catalyst supported by PVA, and buffer were contained in the photolysis solution. Generated hydrogen was anaiysed by gas chromato- graphy (5A molecular sieve column).which is insufficient to reduce water. In fact, the addition of colloidal Pt to the photogenerated AuTMPyP( phlorin) solution did not lead to the generation of hydrogen in the dark. Conclusion The RET process described for AuTMPyP provides a durable photocatalytic reaction. The visible light-induced electron-transfer process of AuTMPyP and its energetics are summarized in scheme 1. This RET process involves two pathways for the reduction of electron acceptors; one is via the .rr-radical anion and the other is via the phlorin. Since the former has higher reducing power [E(P/P'-) = -0.20V vs. NHE] than the later [E(P/phlorin) =0.66 V vs. NHE], the inhibition of the phlorin formation enables 2200 Photoredox and Electrochemical Reactions of Gold Porphyrins -0.20 v -0.50 V e e AuTMPyP e.rr-radical anion ss v-dianion \ -e -e disproportionation 2~-radicalanion + H+ phlorin +phlorin+ AuTMPyP 0.66 V Scheme 1.Reductive electron-transfer process of AuTMPyP in aqueous solution. Redox potentials were with respect to NHE. us to construct an efficient energy conversion system. Since phlorin formation involves the bimolecular process of disproportionation of the .n-radical anion, a separation of the .n-radical anion is expected to inhibit the phlorin formation reaction. However, the phlorin was stable in oxygen-free solution for several weeks and formed reversible so that it can be stored for conversion into photochemical energy on demand with only slight loss of energy.This work was partly supported by a Scientific Grant-in-Aid from the Ministry of Education of Japan. References 1 M. Gratzel, K. Kalyanasundaram and J. Kiwi, Struct. Bonding (Berlin), 1982, 49. 2 (a)K. Kalyanasundaram and M. Gratzel, Helv. Chim. Acta, 1979,62,1345; (b)A. Harriman, G. Porter and M. C. Richoux, J. Chem. SOC.,Faraday Trans. 2, 1981, 77, 833; A. Harriman and G. Porter, J. Chem. Soc., Faraday Trans. 2, 1979, 75, 1532; (c) T. Schimidzu, T. Iyoda, Y. Koide and N. Kanda, Nout;. J. Chim., 1983, 7, 21; T. Schimidzu, T. Iyoda and Y. Koide, J. Am. Chem. SOC., 1985, 107, 35. 3 P. A. Christensen, W. Erbs and A. Harriman, J. Chem. SOC., Faraduy Trans. 2, 1985, 81, 575.P. A. Christensen, A. Harriman, G. Porter and P. Neta, J. Chem. SOC.,Furuday Trans. 2, 1984, 80, 1451; A. Harriman, G. Porter and P. Walter, J. Chem. SOC.,Faraduy Trans. I, 1983, 79, 1335. 4 T. Shimidzu, T. Iyoda, H. Segawa and K. Honda, Now. J. Chim., 1986, 10, 213. 5 A. Harriman, M. C. Richoux and P. Neta, J. Phys. Chem., 1983, 87, 4957, K. Kalyanasundaram and M. Neumann-Spallart, J. Phys. Chem., 1982, 86, 5163. 6 A. D. Adler, F. R. Longo, J. D. Finarelli, J. Goldmacher, J. Assour and L. Korsakoff, J. Org. Chem., 1967, 32, 476. 7 P. Rothemund and A. R. Menotti, J. Am. Chem. SOC.,1948, 70, 1808. 8 E. E. Wegner and A. W. Adamson, J. Am. Chem. SOC.,1966,88, 394. 9 J. R. Darwent in Photogeneration @Hydrogen, ed. A. Harriman and M. A. West (Academic Press, London, 1982), p. 23; G. Porter, in Light, Chemical Change and Life, ed. J. D. Coyle, R. R. Hill and D. R. Roberts (Open University Press, London, 1982). 10 M. Richoux, P. Neta, P. A. Christensen and A. Harriman, J. Chem. SOC., Faraday Trans. 2, 1986,82,235. 11 R. H. Felton, Primary Redox Reactions of Metalloporphyrins vol. V, The Porphyrins (Academic Press, New York, 1978); J. G. Lanese and G. S. Wilson, J. Electrochem. SOC.,1972, 119, 1039. 12 J. Handman, A. Harriman and G. Porter, Nature (London), 1984, 307, 534. 13 J. G. Lanese and G. S. Wilson, J. Electrochem. SOC.,1972, 119, 1039. 14 A. Harriman and M. Richoux, J. Phorochem., 1981, 15, 335. Paper 6/2147; Received 4th November, 1986

ISSN:0300-9238    

DOI:10.1039/F29878302191

出版商:RSC    

年代:1987

数据来源: RSC

摘要:

J. Chern, SOC.,Faruduy Trans. 2, 1987, 83(12), 2201-2210 Absorption Spectra of Molecules Adsorbed on Light-scattering Media Part 2.-Interpretation of Diffuse Reflectance Data Reinhold Gade," Uwe Kaden and Dieter Fassler Sektion Chemie der Friedrich-Schiller- Universitat Jena, DDR-6900 Jena, German Democratic Republic A statistical model of a densely packed assembly of coated particles whose sizes are large compared with the wavelength of light is developed. Based on a description of the optical properties of the particle surface covered with an adsorbed overlayer, the suggested model relates the diffuse reflect- ance of the powdered sample to the optical constants of the substrate medium and the absorption cross-section of the adsorbate. The model has been tested by calculating the molar absorption coefficients of an adsorbed dye from diffuse reflectance data and, simultaneously, by using an immersion technique.Spectroscopic studies of molecules dissolved in optically homogeneous media have formed an important tool of physicochemical research and industrial control for many years. In contrast to the analysis of transmission spectra of solutions, the determination of absorption cross-sections of molecules adsorbed on light-scattering media such as powders, papers, suspensions or sintered materials is a complex problem which has not yet been satisfactorily solved. This difference is due to the fact that the optical observables for scattering materials depend on both the absorption behaviour of the adsorbate and the scattering properties of the particulate adsorbent. For a quantitative determination of the absorption spectrum of adsorbed molecules, therefore, two methods are possible: (1) exclusion of light scattering using a suitable experimental method or (2) explicit consideration of light scattering by modelling the propagation of light in the powdered material. An immersion technique involving the first method has been developed by Robin and Trueblood.' The method is based on minimizing light scattering by immersing the disperse adsorbent-adsorbate system in a solvent of similar refractive index.For a suitable solvent the difference between the refractive indices n, and n3 of solvent and adsorbent, respectively, must be close to zero in the spectral range considered.Then the transmittance of the immersed sample will be near unity. Perfecting this technique, Gunther and Fas~ler*>~were able to determine quantitively the molar absorption coefficients of photochrome organic compounds adsorbed on silica gel. Because of the lack of immersion liquids with sufficiently high refractive indices, however, only adsorbent materials with refractive indices n3< 1.7 can be studied in this way. In the present paper a method is proposed to evaluate absorption cross-sections of adsorbed molecules from diffuse reflectance spectra of powdered adsorbent-adsorbate systems for arbitrary values of n3. To this end, in a previous paper4 the averaged reflectances and transmittances of a particle surface covered with a submonomolecular overlayer have been calculated using a linear approximation of the Fresnel coefficients.The reflectances and the transmittances of the coated surface averaged over the direction of incidence are related to the absorption cross-section of the adsorbed molecules. Thus, taking into account the results obtained in this paper (referred to here as Part l), a 2201 Optical Properties of Adsorbed Molecules recently developed statistical model5 of the diffuse reflectance of powdered solids can be extended to the treatment of a densely packed assembly of coated particles with sizes large compared with the wavelength of light. Statistical Model for Particulate Adsorbent-Adsorbate Systems For a characterization of the absorption behaviour of molecules adsorbed on light- scattering materials it is necessary to relate the observable, i.e.the diffuse reflectance to the fundamental optical parameters of the disperse adsorbent-adsorbate such as the relative refractive index n = n,/n,, the absorption coefficient k of the adsorbent and the absorption cross-section caof the adsorbate.When this relation is being sought within the framework of statistical models of diffuse reflectance,6 disperse media are considered, consisting of rough-surfaced spherical particles, the mean diameter D of which should be large compared with the wavelength of light. Thus the scattering effect of a particle may be explained by means of reflections on the particle surface and the absorption of radiation inside the particle.In addition, the particle material is assumed to be isotropic and weakly absorbing. The reflectances of the surface are then only determined by the ratio of refractive indices of the particle and the ambient medium, respectively, and do not depend on the absorption index of the substrate medium, To derive a relationship between the diffuse reflectance and the optical parameters n, k and ag,the following step-by-step method is applied. Diffuse Reflectance, R,, related to the Characteristics of a Particle Layer The powdered sample studied here is usually assumed to be infinitely thick, so that its transmittance may be neglected. Regarding the radiant flux between a separated particle layer and the rest of the sample, we easily find co T~R,R,=R+T2R, C (RR,)"=R+p.n=O 1-RR, Eqn (1) can be solved to give R,={I+R'-T*-[(I+R~-T~)~-~R~]~/~}/~R(2) i.e.an expression for the diffuse reflectance R, of the non-transparent sample in terms of the reflectance R and the transmittance T of a single particle layer. Using the so-called Kubelka-Munk function F(R,) = (1-Rm)*/(2R,)eqn (2) also may be written as AF(R,) =-( T+ A/2) (31R where the absorptance A of the particle layer obeys the condition R + T+A = 1. Evaluation of the Characteristics of a Single Particle Layer An elementary layer which is usually imagined as a planar array of N spherical particles is homogeneously illuminated from the upper half space. Furthermore we suppose that the part q of the total radiant power P encountering the particle layer is transmitted throughout the voids between the powder particles without scattering or absorption.Hence, a radiant power P,=(l-q)P/N impinges on the surface of each particle. According to the picture of light scattering in a disperse medium the elementary layer is commonly irradiated with diffuse light. It is apparent that the fraction q then will be R. Gade, U. Kaden and D. Fassler negligibly small, i.e. qd"0. However, if the particle layer in a special case is perpendicularly illuminated the portion q will be given by the ratio of the geometrical cross-section of all voids to the total area of the layer. For a hexagonally densely packed array of spherical particles we thus have Because of the diffuse reflection on the surface and the multiple reflections in the interior of the particles, various fractions of Po are scattered backward, forward and to the side.The backward- and forward-travelling portions of Po immediately contribute to the reflectance and transmittance of the elementary layer. On the other hand, by impinging on the neighbouring particles in the layer the sideways-propagating light will again be scattered upwards, downwards and sidewards. The radiant powers Pkm' and Pkm' scattered by the mth particle towards the backward and forward directions, respectively, are thus related to the sideways-emitted powers by a set of balance equation^.^ Carrying out the summation over all particles of the layer then leads to5 lN R=-c Pa"' = ( -q)[Pe(Q/4+i)-k Tet (xkQ -k xR)l (5)P m=l A = 1 -R -T = (1 -q)(l -pe-T,t)(l+ Q) (7) where the quotient Q= (pe/2+~etxs)/(l-pe/2-Tetx$) (8) represents the ratio of the mean power emitted from the wall of adjacent particles toward the central one to Po.The total transmissivity t of a single powder particle gives that fraction of the radiant power entering the particle which returns from it after an infinite number of reflections and passages across the particle. Furthermore, the scattering factors xR, xT, xs and xk, x;, x&determine the probability that light which entered the particle and underwent multiple reflections emerges from it upwards, downwards and sidewards, respectively.The dashed quantities in each-case refer to fhe irradiation from the neighbouring particles. Finally, the quantities pe= R,,, and re= are the averaged external reflectances and transmittances of the coated particle surface. For light travelling from the optically dense medium to the interface the corresponding internal reflectance and transmittance are denoted by pi= and T,= F3zl,respectively. As was shown in Part 1," these averaged reflectances and transmittances of the covered particle surface depend not only on the refractive index n but also on the absorptance a of the adsorbed overlayer. According to the linear approximation method used here the abovementioned reflectances and transmittances can be written as Pe( n, a = R,3 ( n + aeP23 ( n ) (9) ~~(12,a)= 1-R,,(n)+ aeT2,(n) (10) pi(n, a>= R31(n)+aeh1(n) (11) Ti(n, a)= 1 -R,,(n)+ aeT21(n)= 7,/n2 (12) where R13 and R31 are the averaged external and internal reflectances, respectively, of the uncovered surface.' The coefficients of the absorptance a in eqn (9)-(12) also depend on the relative refractive index n and were evaluated in part 1." Optical Properties of Adsorbed Molecules Fig.1. Illustration of the beam as it is diffused by the rough surface of the powder particles. In modelling the scattering of light by a single powder particle the final problem is now to express the particle characteristics introduced above in terms of fundamental optical parameters of the powdered adsorbent-adsorbate. Determination of the Particle Characteristics from Optical Constants Assuming a diffuse illumination of the elementary layer from the upper half space the corresponding half of each particle is homogeneously irradiated with light of the radiant flux density I.=2P0/(rrD2).From any infinitesimal element of area df of the illuminated hemisphere the radiant power peIOdf is diffusely reflected, while the portion t,Iodf enters the particle. As illustrated in fig. 1, the radiance of the entering light is assumed to be that of a scattered wave, i.e. the superposition of unscattered beam and a diffuse radiation. The diffuse part of the entering light is apparently due to scattering by the rough surface and therefore vanishes in the limit as n + 1. The magnitude of this fraction is given by g,(n)=(n-l)/n =g,(n) (13) where gi( n) denotes the corresponding parameter for the emerging light.Because of the isotropic part of the radiance both the upper and the lower half of the internal boundary face will be illuminated by the elements of area of the upper hemisphere, as can be seen from fig. 1. Thus, after an infinite number of reflections and passages across the particle the following radiant powers are transferred to the upper (u) and lower (1) half of the boundary face:5 PoTeMpiM[2-piM(1 -ge)l P,u= P,, =___1+ge 4(1 -piM) where the former subscript in each case indicates the hemisphere from which the light returns. The evaluation of the mean transmittance of the spherical particle for a single pass yields’ M(~D)=2[1 -(k~+~>exp(-k~)]/(k~)’.(14) R. Gade, U. Kaden and D. Fassler To determine the scattering factors one must take into account that a fraction of light returning from any particle impinges on the wall of surrounding particles. Therefore, the radiant powers which are scattered from this particle upwards, downwards and sidewards, respectively, may be expressed by5 PR = d?lu(1 -ws)+ Puuwsl PT=Ti[Pu,(1-ws)+ PI1wsl (15) Ps= ~i[(Puu+P~1>(1-w,)+(p~u+p~~)wsl where nws=(n-l) ( n ln--n-1 9 represents the probability that upwards propagating light is scattered sideways and vice versa.5 The scattering factors, which are defined as follows: x, = pJ --.-PJ . J=R, S, TPR+ PT+ Ps POTet then become [2-( 1-ge)piMI[2-piM -2(1-piM)wsl XT = 4(1+gel (18) xR= 1-xS-XT.(19) As noted in the preceding section, the total transmissivity t is evidently defined by ( PR+ PT+ Ps)/( P0~,).t = Using eqn (15) then an explicit expression for t is obtained, viz: t = TjM/(l -pJ4) (20) The case when the powder particle is illuminated by the neighbouring particles in the layer is treated analogously. This gives xk = x; = ( 1 -x9/2. (22) By substituting expressions for the particle characteristics from eqn (17)-(22) into the formulae for R, T and A [eqn (5)-(7)] the Kubelka-Munk function F(R,) may be calculated from eqn (3) as a function of the fundamental optical parameters n, k and a. The resulting functional dependence of F(Rm)= da,n, w (23) on a and kD is illustrated in fig.2. For the absorptance, a, of the adsorbed monolayer the following expression was obtained in part 1,4 viz: a = [aa (24) where (T, is the absorption cross-section of the adsorbed molecules and 6 denotes their number per unit area. 2206 Optical Properties of Adsorbed Molecules 1.5 0.25 1 .o /h 8 0.30 v Q s:4 0.5 0.40 0.50 0 I .oo 0 0.05 0.1 a Fig. 2. Plots of the Kubelka-Munk function F( R,) vs. the absorptance a = of the overlayer for three different values of kD and n =1.464: (-) kD=0, (---) kD=0.05, (----) kD=O.l Calculation of Molar Absorption Coefficients of Adsorbed Molecules The statistical model of powdered adsorbent-adsorbate systems presented above enables us to evaluate absorption cross-sections a,( 2,) at discrete wavenumbers 2,(i = 1, .. . ,2) from diffuse reflectance data. For this purpose the diffuse reflectance spectra Rt (2) and R>(t)of both the corresponding particulate adsorbent-adsorbate system and the uncoated substrate powder are required. Before beginning this the experimental reflect- ance spectra must be transformed into thc I=( R,) representation. Then, using a numerical iteration procedure for a given set of experimental values F(RL,,);i = 1, . . . ,2 the attached quantities k,D are determined satisfying the condition -(PF(a =O, n, kD)I<A (25) where A is the chosen accuracy limit. Finally, by applying the same iteration method for each of the values F(R&) the corresponding absorptance is calculated,which obeys the relation \F(Rt,~)-(PF(an n,’k~D)[<A* (26) The required relative refractive index n can be taken from a handbook of physical chemistry, e.g.ref. (8), or must be measured with a refractometer. The absorption cross-sections a,(t,)are then calculated dividing the absorptance values a, by l.The number 6 of the adsorbed molecules per unit area, needed here, can be expressed by 5 = c’/fg, where fg (in cm2 g-’) is the specific geometric surface area of the powdered adsorbent and c’ (in mol g-’) denotes the specific concentration of the adsorbed dye. For spherical particles fg is given by 6f =-DPS where ps is the density of the substrate material. Based on a quantum-mechanical description of light absorption in molecular systems an expression for the absorption cross-section (T, was derived in Part 1 .4Since a, depends in the same manner on the transition moment as the molar absorption coefficient E, it R.Gade, U. Kaden and D. Fassler can only differ from E by a scaling factor. To determine this factor, an elementary layer is considered in the limit as n + 1. Because of the absence of light scattering in this case the particle layer here is assumed to be illuminated perpendicularly with parallel light. Then using the suggested statistical model the transmittance of a single elementary layer takes the form Tp(a,n = I, k~)= qp+ (1 -qp)(1 -a)2M(kD) (28) where the subscript p designates the perpendicular irradiation of the layer. As noted earlier the quantities a = and kD are commonly supposed to be small compared with unity.Expanding the expression on the right-hand side of eqn (28) in powers of a and kD and retaining up to first-order terms then gives TP((oa,n = 1, kD)= 1--rr [1-(1 -250,)( 1 -2kD/3)]. (29)2d3 On the other hand, by applying the immersion technique it is usually assumed that the optical density of the immersed sample can be represented as a sum of two terms, one of which is the contribution of the powdered substrate (S) and the other is that of the adsorbate (A). Since the substrate particles are usually small compared with the sample dimensions the adsorbate may be considered as homogeneously distributed with the concentration where NAis the number of adsorbed molecules being in the volume V of the layer.Therefore, the transmittance of a thin immersed particle layer of the thickness D can be expressed by T(D)= = exp(-sc~/~oge)[qp+ (1 -q,)~(k~)]. Expanding this expression in powers of the small quantities ECDand kD,and neglecting quadratic and higher-order terms, the following linear approximation of T(D) is obtained: T(D)= (1 -%.){ 1-5[1-(1 -5 kD)I}. Equating this expression to that from eqn (29) finally yields loge 1-2kD/3 log e E=Oa-= 0,-.2 1 -rrkD/(3d3) 2 The molar absorption coefficients E calculated from the absorption cross-sections O, of the adsorbed molecules by means of eqn (32)then apparently correspond to those which can be determined using the immersion technique. Comparison with Experimental Results and Discussion To test the method for evaluating molar absorption coefficients of adsorbed molecules, described above, the absorption spectrum of indigo adsorbed on silica gel has been determined both from diffuse reflectance data of the powdered material and the transmit- tance spectrum of the immersed sample.Silica gel (Merck, 60,70-230 mesh) has proved a suitable adsorbent because it obeys the conditions of the model with regard to particle size and isotropic refractive index. Moreover, by immersing the silica gel in an optimized mixture of toluene and cyclohexane with a refractive index of n = 1.464, samples of a Optical Properties of Adsorbed Molecules 0-51 U 0.5 1.0 1.5 2.0 2.5 c’/ lo-’ mol g-’ Fig.3. Plot of the F(R&) values of the coated silica gel versus the specific concentration of adsorbed indigo. The linear calibration curve has been determined employing a least-squares fitting procedure. high transparency may be obtained. In order to obtain reproducible results the silica gel was classified with sieves and the fraction of particles having diameters between 80 and 100 pm was used as adsorbent. On the other hand, choosing indigo as adsorbate a dye has been examined which is sufficiently stable in the adsorbed state and will not be desorbed when immersing the adsorbent particles in the toluene-cyclohexane mixture. In addition, no fluorescence emission of indigo adsorbed on silica gel could be detected, so that a corresponding deterioration of the diffuse reflectance spectra can be neglected.However, if the covered adsorbent exhibits a strong fluorescence a correction method’ must be employed to obtain true diffuse reflectance spectra of the powdered samples. Unfortunately, the solubility of indigo in the immersion liquid is poor and also the molar absorption coefficient of indigo in this solvent is not known. Therefore, the specific concentration, c’, of the adsorbed indigo has been determined taking into account the fact that the Kubelka-Munk function of the powdered adsorbent-adsorbate system depends linearly on the concentration c’.l0 For this purpose the indigo dye was dissolved in tetrachloromethane ( E,,, = 1660m2 mol-*)” and adsorbed on silica gel from this solution. From the carefully dried samples the diffuse reflectance spectra were measured with an M40 spectrophotometer (Carl Zeiss, Jena), and the F(R,) values at the wavenumber C = 15 870 cm-’ were plotted against the specific concentration c’, as shown in fig.3. To achieve samples of the high transparency needed for transmission studies, the adsorption was now carried out from a solution of indigo in the immersion liquid. By filling part of the resulting silica-gel-solvent slurry in cells with a 0.1 cm optical path length, ten samples were prepared as described in ref. (2). The number of powder particles per unit volume in the slurry may be characterized by the thickness deffof an equivalent compact layer of the adsorbent material in the cell used.For the ten samples considered the mean value of deffis given by deff= 0.0227 f0.0005 cm. The transmittance spectra of these immersed samples were then measured with the immersion liquid as reference. The average of these spectra is plotted in fig. 4 as a R. Gade, U. Kaden and D. Fassler T 22 20 18 16 14 v’/ lo3cm-’ Fig. 4. Averaged diffuse reflectance (-) and transmittance (---) spectra of the silica-gel-indigo samples (a) and the pure silica gel (b). dashed line. To eliminate the optical density of the adsorbent particles the transmittance of the immersed, uncoated silica gel has also been measured and is plotted us. v” in fig. 4. After the immersion liquid had been removed from the rest of the slurry and the powdered material dried, the diffuse reflectance spectra of both the silica-gel-indigo samples and the uncoloured silica gel were measured with MgO as reference.The corresponding absolute reflectance spectra averaged over a sequence of measurements are also plotted in fig. 4. Taking into account the reflectance value at t= 15 870 cm-’ the application of the above calibration method (see fig. 3) yields the following specific concentration of adsorbed indigo: c‘ = (1.67 f0.09) x lov7mol g-’. By studying the adsorption properties of a silica gel of the same kind de Mayo and coworkers have found a monolayer coverage c,,,, =4.95 x mol g-’ for pyrene.12 It is therefore apparent that the specific concentration c‘of the adsorbed indigo is consider- ably smaller than the monolayer coverage.From the transmission spectrum T(t)of the coated silica gel immersed in a toluene-cyclohexane mixture the molar absorption coefficients E(;) of the adsorbed indigo dye have been calculated according to the relationship where Ts(Y”) is the transmittance spectrum of the immersed pure silica gel and psis the density of the substrate medium. In addition, the absorption spectrum E( t)of indigo adsorbed on silica gel has been determined from the diffuse reflectance data of the powdered adsorbent-adsorbate system using the procedure described in the previous section. In fig. 5 the molar absorption coefficients E evaluated by both methods have been plotted versus the wavenumber G. Optical Properties of Adsorbed Molecules 22 20 18 16 14 ;/ lo3 cm-I Fig.5. Absorption spectra of indigo adsorbed on silica gel calculated from diffuse reflectance data (-1 and determined using the immersion technique (--.-). From fig. 5 it is evident that the absorption spectrum E( Y”) of the adsorbed indigo which is calculated from the R:( Zr) spectrum agrees sufficiently well with that determined by the immersion technique. In this way it has been shown that using the statistical model presented here molar absorption coefficients of adsorbed molecules can be determined from diffuse reflectance data of a disperse adsorbent-adsorbate system. References 1 M. Robin and K. N. Trueblood, f. Am. Chem. SOC., 1957 79, 5138. 2 D. Fassler and W. Gunther, Z. Chem., 1977, 17, 429.3 D. Fassler and W. Gunther, 2. Chem., 1978, 18, 69. 4 R. Gade, U. Kaden and D. Fassler, J. Chem. SOC., Faraday Trans. 2, 1984, 70, 1077. 5 R. Gade, f. Mod. Opt., in press. 6 H. G. Hecht, J. Res. Natl Bur. Stand. USA, Part A, 1976, 80, 567. 7 G. Duyckaerts, Spectrochim. Acta, 1955, 7, 25. 8 Handbook ofchemistry and Physics, ed. R. C. West and M. J. Astle (CRC Press, Cleveland, Ohio, 60th edn, 1980). 9 D. H. Alman, F. W. Billmeyer and D. G. Phillips, Proc. 18th session CIE, (London 1975) (Bureau Central de la CIE, Paris, 1976), pp. 237-244. 10 G. Kortiim, Re~exionsspektroskopie(Springer-Verlag, Heidelberg, 1969). 11 J. Griffith, Colour and Constirution of Organic Molecules (Academic Press, London, 1976). 12 R. K. Bauer, P. de Mayo, K. Okada, W. R. Ware and K. C. Wu, J. fhys. Chem., 1983, 87, 460. Paper 612367; Received 10th December, 1986

ISSN:0300-9238    

DOI:10.1039/F29878302201

出版商:RSC    

年代:1987

数据来源: RSC

摘要:

J. Chem. SOC.,Faraday Trans. 2, 1987, 83(12), 2211-2223 An SCF-MS-Xa Study of the Bonding and Nuclear Quadrupole Coupling in 1: 1 Complexes of Amines with Diatomic Halogens and Interhalogens Graham A. Bowmaker" and Peter D. W. Boyd Department of Chemistry, University of Auckland, Private Bag, Auckland, New Zealand SCF-MS-Xa calculations of the electronic structure of the 1: 1 complexes of pyridine with 12, IBr and ICl, and of the i : 1 trimethylamine-I, complex have been carried out to investigate the bonding and nuclear quadrupole coupling in these molecules. Good agreement (to within 10% in most cases) is obtained between the calculated and observed halogen nuclear quadrupole coupling constants for these molecules. The agreement in the case of the nitrogen quadrupole coupling parameters is not as good, but the calculations do support some of the previously reported conclusions concerning the changes in the nitrogen orbital populations which occur UPOF.complex formation. The results essentially support previous conclusions, based on Townes and Dailey analyses of the experimental quadrupole coupling data, concerning the extent of charge transfer and the distribution of the transferred charge in these molecules. They are, however, at variance with some of the results obtained from chemical shifts in the photoelectron spectra. The electric dipole moments of the molecules have also been calculated. These are ca. 30% higher than the highest reported experimental values, but show the expected trends from one compound to another.The chemical bonding in compounds known as charge-transfer or donor-acceptor complexes has been the subject of much experimental and theoretical study, the results of which are discussed in several books and reviews.'-' The properties of such complexes have often been discussed in terms of the charge-transfer theory developed by M~lliken.*,~ Complexes between molecules such as amines, which are capable of donating electrons from a lone-pair orbital, and the diatomic halogens, which are capable of accepting electrons into an antibonding orbital, are described as n-u complexes within Mulliken's clas~ification.~,~A number of X-ray crystal structure studies have shown that these molecules contain a linear N---X---Y arrangement of the nitrogen and halogen atoms, and that the nitrogen-halogen and halogen-halogen bond lengths are longer than the normal covalent bonds between the same A number of experimental studies (nuclear quadrupole resonance,16-20 MOs~bauer'~-~~ and photoelectron spectro~copy;~~ dipole and i.r.studies) have been carried out in order to try to measure the changes in electron distribution and the degree of charge transfer which takes place upon complex formation. The most detailed information of this type has been obtained from nuclear quadrupole coupling studies. Estimates of the degree of charge transfer (0.2-0.3 e) have been obtained from halogen nuclear quadrupole coupling constant^,'^"'3** and estimates of the changes in the nitrogen valence orbital populations have been obtained from 14N n.q.r.~tudies.'~**~ However, these conclusions are based on the Townes and Dailey method of analysis of the nuclear quadrupole coupling a method which relies on certain assumptions about the origins of the field gradients responsible for the quadrupole coupling, and about the types of orbital involved in the bonding. The validity of these assumptions can only properly be checked by 2211 SCF-MS-Xa Study of Nuclear Quadrupole Coupling calculations of the electronic structure and electric field gradients in the molecules concerned. We have previously shown that the SCF-MS-Xa molecular orbital method is capable of calculating nuclear quadrupole coupling constants of simple halogen-containing molecules with good acc~racy,~~-~' and that further insight into the electronic structure and the origins of the electric field gradients responsible for the coupling constants can be obtained from an analysis of the results of such calculations.We report here the application of this method to several amine-halogen complexes for which structural and nuclear quadrupole coupling data are available. Other workers have reported difficulties in obtaining good agreement between experimental and calculated 14N coupling constants for coordinated nitrogen donor molecules using the Xa method.38 However, good agreement has been obtained in the case of the free pyridine molecule.39 Thus the complexes pyridine-IX (X = I, C1, Br) would appear to be ideal subjects for a further investigation of the calculation of 14Nquadrupole coupling constants. We have also carried out calculations for the complex trimethylamine-I, because of its structural simplicity and high symmetry.No I4Ncoupling constant measurement has been reported for this molecule as yet. Electric dipole moment measurements played an important role in early studies aimed at determining the degree of charge transfer in the ground states of donor-acceptor complexes, and values for several amine-halogen complexes have been rep~rted.~~-,~ We have therefore calculated the electric dipole moments of the above molecules in order to test further the quality of the calculated wavefunctions. Method of Calculation All calculations were carried out using the SCF-MS-Xa program XASW.~',~~The atomic region a-values used were those of Sch~artz~~ for the free atoms, while the intersphere and outersphere values were taken as the average of the atomic values weighted by the valence electron number.The iterative SCF procedure was ended when the maximum relative change in potential was less than The parameters used in the calculations and the resulting virial ratios are given in table 1. The free-molecule molecular geometries for p~ridine'~ and trimeth~larnine~' were used in all calculations. The coordinate and atom-labelling systems used in the calculations are shown in fig. 1. The partial wave expansion was limited to 1= 4 for the outersphere, and to I = 1 for all atoms other than hydrogen.All of the calculations were carried out using atomic sphere radii determined by the Norman criterion (Norman reduction factor Rf= 0.88)y except in the case of the proton radii. It was found that charge-partitioning calculations for the calculation of molecular properties with these radii were not possible. This is due to the coarseness of the grid used for the expansion of the hydrogen radii during the charge-partitioning Accordingly, a slightly smaller value of 1.25 a.u. was chosen. Charges and electric field gradients were calculated using the method of Karplus and coworkers for the partitioning of inter- and outer-sphere ~harge.~',~' Electric field gradients, eq, in atomic units were converted into coupling constants, e2qQ, using the equation (e2qQ/h)/MHz =234.9(eq/a.u.)( eQ/ cm2).(1) The nuclear quadrupole moments used in the calculations are eQ/ cm2= -0.082 (wl); 0.29 (79Br);-0.69 (','I); 0.0205 ( *4N).47 Comparison of Calculated and Observed Nuclear Quadrupole Coupling Constants A comparison of the calculated and observed nuclear quadrupole coupling constants is given in table 2. For the iodine nuclei, the difference between the calculated and observed coupling constants is generally <10%. This agreement is comparable to that Table 1. Parameters used in the Xa calculations sphere radii (a.u.) molecule virial D-XY a ;nt R,hu, RH RC2 RC3 Rc4 RN Rx RY ratio " ~~~ ~ pyridine (py) 0.761 06 6.303 1.250 1.662 1.692 1.697 1.669 --1.994 90 PY'I2 0.741 65 10.799 1.250 1.66 1 1.692 1.697 1.650 3.029 3.298 1.999 64 py-IBr 0.742 61 10.421 1.250 1.661 1.692 1.697 1.647 2.988 2.959 1.999 48 py.IC1 0.745 32 10.178 1.250 1.661 1.692 1.697 1.649 2.980 2.699 1.999 35 Me,N 0.764 09 5.232 1.250 1.704 --1.645 --1.993 88 Me,N I2 0.741 69 8.397 1.250 1.702 --1.626 2.970 3.300 1.999 67 " aintis the intersphere value of a.R,,, is the outersphere radius. '. Virial ratio = -potential energy/kinetic energy. SCF-MS-Xa Study of Nuclear Quadrupole Coupling T (b) Fig. 1. Coordinate and atom-labelling systems used for (a) pyridine (x axis perpendicular to plane of ring) and (b) trimethylamine. obtained previously in a similar study of the diatomic halogen and interhalogen molecules XY,37and of the trihalide ions XY2.33In the case of the pyridine complexes the electric field gradient asymmetry parameter q at the halogen nuclei need not be exactly zero as it is in the free halogen molecules, since the axial symmetry of the halogen molecule is lost in the complex.Nevertheless, the calculated 7 values for the halogen nuclei are all very close to zero. This is in good agreement with experiment in the few cases where this quantity has been We note that there is a significant discrepancy between the 1271 coupling constants obtained for py*IC1 and py-IBr from Mossbauer spectros- copy21723compared with those obtained from the v(3++ 3/2) transition frequencies by nuclear quadrupole resonance spectroscopy. I6,l7 The Mossbauer values are ca.10% higher than the n.q.r. values. The reason for this is not clear at present. The experimental values given for these compounds in table 2 are derived from n.q.r. measurements. No experimental bromine quadrupole coupling data are available for pya IBr. The calculated chlorine coupling constant in py.IC1 is ca. 50% higher than the experimental value. Thus the best overall agreement between the Xa calculated and the experimental coupling constants is obtained for the iodine complexes py*12 and Me,N.I,. N coupling constants were calculated for the free amines pyridine and trimethyl- amine, as well for the halogen complexes, and the results are given in table 2. Reasonable Table 2. Bond lengths used in calculations, and comparison of calculated and experimental nuclear quadrupole coupling constants e2qQ/h, field gradient asymmetry parameters q,and molecular dipole moments ,u -_I___-bond length/pm (e2qQlh)lMHz rl p/ lo-" c m molecule ~-I___-D-XY NX XY ref.nucleus Xa exptl Xa exptl ref. Xa exptl ref. pyridine( py) ----5.39 -4.88" 0.396 0.405" 48 13.9 7.39 52 (-) 4.58 0.396 49 Q PY'I2 231h 283h 12 4.65 (-) 2.58 0.003 0.285 20 27.0 15-21 53 4 -2519 (--) 2680 0.007 0 18 (-) 2631 0.10 24 (-) 2600 -22 -1517 (-) 1439 0 -24 (-) 1300 -22 py.IBr 226 266 13 4.48 (-) 1.91 0.229 0.203 20 -2712 (-) 2971 0.008 C 16 421.5 -0 py.IC1 229 251 14 4.47 (-) 1.80 0.140 0.188 20 -2835 (-) 3095 0.007 C 16 17 -63.7 (-) 42.3 0 C 17 Me,N ----7.20 -5.47" 0 0" 50 (-) 5.19 0 51 Me3N-12 227 283 15 -4.56 -0 --25.7 21.7, 18.3 53, 55 -2313 (-) 2679 0 -16 (-) 2604d 0 -24 -1266 (-) 1261" 0 0.09 24 -~ " Gas-phase experimental values. Bond lengths for 4-methylpyridine-I,.'Assumed to be zero in calculating the experimental e2qQ/h. Experimental coupling constants for triethylamine. I,. SCF-MS-Xa Study of Nuclear Quadrupole Coupling Table 3. Gross atomic orbital populations for the nitrogen and halogen atoms molecule D-XY atom orbital PY py-IBr py.IC1 Me,N Me3N.12 N S 1.475 1.449 1.441 1.444 1 A46 1.448 P.; P, P: 1.372 1.099 1.442 1.429 1.093 1.263 1.436 1.095 1.243 1.438 1.096 1.260 1.080 1.080 1.561 1.100 1.100 1.324 X s 1.935 1.959 1.957 1.935 PI 1.993 1.992 1.993 1.965 P, P: 1.99 1 1.008 1.992 0.945 1.988 0.908 1.965 1.072 Y S 1.919 1.957 1.949 1.952 PY 1.991 2.004 2.010 1.984 P, PZ 1.998 1.323 1.998 1.424 2.001 1.447 1.984 1.384 agreement between the and calculated 14Ncoupling constants was obtained in the case of the free amines.However, agreement in the case of the pyridine-halogen complexes is much poorer. The reasons for this will be discussed below in the section on the analysis of the electric field gradients. Comparison of Calculated and Observed Electric Dipole Moments A comparison of the calculated and observed electric dipole moments of the molecules is given in table 2. The direction of the dipole moments is such that the positive end is at the left-hand end of the molecules as depicted in fig.1 in all cases except that of the free trimethylamine molecule, where the dipole lies in the reverse direction. It is probable that the signs of the calculated and experimental dipole moments are opposite in this case. The observed large increase in the magnitude of the dipole moment from the free molecule to the complex is well reproduced by the calculations. The main cause of this is the electronic charge transfer which takes place between the amine and the halogen molecule (see the discussion of the charge distributions below). The calculated increase in the dipole moments from the I2 to the IBr and IC1 complexes of pyridine is consistent with the greater degree of charge transfer which occurs along this series.However, no experimental values appear to have been reported for the latter two complexes. The observed direction of the dipole moments (with the negative end at the halogen atoms) supports the charge-transfer bonding theory. The calculated dipole moments for the complexes are, however, ca. 30% higher than the highest reported experimental values. This is the reverse of the situation found in a corresponding study of the free interhalogen molecules XY, where the calculated values were consistently smaller than the experi- mental values.37 Population Analysis The gross atomic orbital populations and atomic charges for the molecules (after charge partitioning) are given in tables 3 and 4. The populations of the halogen px and pv orbitals are all very close to 2, indicating that these orbitals are non-bonding.Thus the Xa calculations support the assumption which is often made in qualitative descriptions of the bonding in these compounds, namely that charge-transfer bonding involves the halogen (T orbitals only, and that there is no back-donation involving the out-of-plane G. A. Bowmaker and P. D. W. Boyd Table 4. Atomic charges molecule D-XY atom PY py-12 py-IBr py.IC1 Me,N Me3N.12 N -0.387 -0.233 -0.216 -0.236 -0.165 0.026 c2 0.091 0.109 0.118 0.119 0.1 18 0.098 c3 -0.079 -0.069 -0.055 -0.055 c4 0.032 0.005 0.023 0.023 H2 0.049 0.059 0.066 0.066 -0.032 -0.012 H3 0.083 0.075 0.078 0.078 -0.01 5 -0.007 H4 0.067 0.041 0.051 0.050 total D 0 0.161 0.272 0.253 0 0.242 X 0.07 1 0.111 0.154 0.064 Y -0.233 -0.384 -0.407 -0.305 total XY -0.162 -0.273 -0.253 -0.241 halogen T orbitals.The halogen s-orbital populations are significantly less than 2, indicating that there is a small degree of s-p mixing in the bonding orbitals. The extent of the halogen s-orbital involvement is similar to, but slightly less than that found in a similar study of the free halogen and interhalogen molecules.37 The populations of the centre halogen (X) pzorbitals are close to, but slightly ltss than those of the corresponding atom in the free halogen or interhalogen molecule^.^' The decrease in this population for the pyridine complexes is 0.08 (py.12), 0.06 (py-IBr), and 0.04 (py.IC1).In contrast, the populations of the terminal halogen (U) pz orbitals are considerably higher than those in the free molecules by 0.23 (py.Iz),0.25 (py-IBr), and 0.19 (py-IC1). This indicates that net charge transfer from the amine to the halogen molecule takes place upon complex formation and that all of the transferred charge resides on the terminal halogen atom. The centre iodine atom loses some electron density as a result of the formation of the charge-transfer bond with the amine nitrogen atom. These results are entirely in agreement with deductions made from an analysis of the halogen n.q.r. results for these and related complexes.16 The nitrogen orbital populations also undergo changes upon complex formation. The largest change in both the pyridine and trimethylamine complexes is a decrease in the population of the pz orbital.This is the result of transfer of electron density from the nitrogen ‘lone-pair’ orbital (which is an admixture of the nitrogen s and pz orbitals) to the halogen molecule. The other nitrogen p-orbital populations also change to varying degrees. In the case of the pyridine complexes, the main change is an increase in the out-of-plane px orbital population. As the halogen px populations are essentially unchanged from the value 2.0 found for the free halogen molecules, this increase cannot be due to ‘back-donation’ of welectron density from the halogen molecule. Rather, it is due to a redistribution of the .rr-electron density in the pyridine molecule upon complex formation.This is a consequence of the charge transfer from the nitrogen ‘lone-pair’ orbital, which reduces the electron density at the nitrogen atom. The nitrogen atom thus becomes more electrophilic, and attracts more electron density from the pyridine ring as a result. Apparently the more mobile r-electron density in the ring is affected in this way, since only the nitrogen out-of-plane p,-orbital population undergoes an increase; the population of the in-plane pv orbital (which is involved in the cr bonding in the ring) remains essentially unchanged upon complex formation. These results are in good agreement with deductions made from an analysis of the I4N n.q.r. results for these 2218 SCF-MS-Xa Study of Nuclear Quadrupole Coupling complexes.20 The Xa results indicate that a similar effect occurs in Me,N.12, as the nitrogen px-and p,-orbital populations show an increase upon complex formation.However, the total increase in these populations (0.04) is somewhat less than that for the corresponding pyridine complex (0.06), possibly reflecting the lower mobility of the D electrons in Me3N compared with the 7~ electrons in pyridine. Some of the above conclusions drawn from the orbital populations are reflected in the values of the atomic charges (table 4). In particular, a reduction of the negative charge on the nitrogen atom and an increase in the negative charge on the terminal halogen atom are consequences of the charge-transfer bond formation. An increase in the positive charge on the centre iodine atom is a consequence of the polarity of the N-I charge-transfer bond, as has been discussed previously.“ The total extent of charge transfer is indicated by the values of the total donor (D) and total halogen (XY) charges.The calculated values lie in the range 0.15-0.25, in good agreement with values deduced from hal~gen~~,*’>~~ n.q.r. results. In the case of py.IC1, for example, the calculated value of 0.25 can be compared with the experimental value of 0.26.17,20From the results in table 4 it can be deduced that the net change in the charge on the nitrogen atom in py.JC1 upon complex formation is +0.15. This is in excellent agreement with the value of +0.14 deduced from the 14Nn.q.r.data.20 This also agrees well with the value +0.1 estimated from the nitrogen 1s binding energy shift in this complex as measured by ESCA.25 There remains a discrepancy of ca. +0.1 between the increased positive charge on the nitrogen and the net negative charge gained by the ICl molecule. Analysis of the results in table 4 shows that this can be accounted for by an additional transfer of 0.1 e from the carbon atoms C2 and C3. Most of this arises from the inductive shift of the n-electron density in the pyridine ring to the nitrogen atom as discussed above. Although there is good agreement between the calculated change in the charge on the nitrogen atom in py.IC1 and that estimated from the nitrogen 1s binding energy shift measured by ESCA, the iodine 3d binding energy shift indicates a decreased positive charge on the iodine atom, in contradiction to the Xa and n.q.r.results.25 The reason for this discrepancy is not understood at present. Since the calculated changes in the nitrogen orbital populations agree qualitatively with those determined from the 14N quadrupole coupling parameters, it is of interest to make a quantitative comparison of the absolute populations determined by both methods. In the n.q.r. analysis” it was assumed that the nitrogen valence orbitals can be represented as three in-plane sp2hybrid orbitals and one out-of-plane p orbital. The populations of these orbitals are represented by a (out-of-plane p orbital), b (two sp2 hybrids involved in C-N bonding) and u (N-donor sp2hybrid orbital).As a result of the inductive effect discussed above, a and b depend on u according to the equations: a =a,+ B(2-a) (2) The nitrogen orbital populations can be expressed in terms of the above parameters as follows: n, = (cot’ e)u +(1 -Cot2e)b (4) n, = a n,. = b n,=(1-cot’8)a+(cot2 8)b (7) where 28 is the C-N-C angle. The values obtained for these populations for pyridine and py-IC1 from the nitrogen n.q.r. data are compared with the Xa values in table 5. Clearly the agreement between these values is not very good. There are several possible reasons for this. In view of the poor agreement between the observed and calculated G. A. Bowmaker and P. D. W. Boyd 2219 Table 5. Comparison between the Xa calculated N-orbital populations and those calculated from 14Nquadrupole coup- ling data molecule population Xa N n.q.r.a14 1.476 1.557 1.372 1.156 1.099 1.290 1.442 1.733 1.444 1.441 1.438 1.317 1.096 1.321 1.260 1.520 a Calculated from data in ref.(19) using eqn (2)-(7) and the parameters a, = 1.156, b, = 1.29, A = 0.446, B =0.087 and 219 = 117". 14N quadrupole coupling parameters, the most likely explanation is that the Xa popula-tions are incorrect. Table 5 shows that the main problem is the low value of n, obtained in the Xa calculations. Nevertheless, the main changes in the populations upon complex formation (the decrease in n, and n, as charge is transferred from the nitrogen donor orbital, and the resulting increase in n, arising from inductive transfer of n charge in the pyridine ring) are in the same direction for the two sets of numbers.These changes are somewhat smaller for the Xa calculated values, however, and the reason for this is not yet clear. Analysis of Electric Field Gradients An analysis of the various contributions to the field gradients at the halogen nuclei reveals that the total field gradient is very nearly equal to the sum of the one-centre valence-orbital field gradient integrals at that nucleus (see table 6). Thus the field gradient at these nuclei is due almost entirely to electron density in the valence orbitals centred on the nucleus concerned, as is assumed in the semiempirical Townes and Dailey method of analysis.32 Thus, to a good approximation, the origins of the field gradients at these nuclei can be discussed entirely in terms of the one-centre contributions, and these are given in table 7.Also included in table 7 are the average field gradients per electron, eq, (z = x, y, z), for the valence p orbitals p,, p),,p,. These are defined as eqi= yi/ni where V,, is the sum, over all occupied states, of the principal component, in the i direction, of the field gradient due to electron density in the valence piorbital in that state and ni is the gross population of the orbital pi (table 4). In a free atom the eqi values for the p,, p), and pz orbitals would be equal. The eqj values obtained for the halogen p orbitals show similar behaviour to that observed in studies of the diatomic halogen molecules XY and the trihalide ions XY2.33337 For example, the values for a particular nuclear species (e.g.1271) differ according to the chemical environment for that nucleus. We have previously shown that this is due to a dependence of the egj values on atomic charge in the case of the halogen orbital field gradients in diatomic halogen and interhalogen rn01ecules.~~ This dependence can be fitted to an equation of the form 2220 SCF-MS-XQ Study of Nuclear Quadrupole Coupling Table 6. Sum of one-centre valence field gradient integrals, yj,and the total field gradient moI ecul e atom j valence total PY’I2 N Y -0.4347 -0.4817 Y 0.9308 0.9661 .) -0.4961 -0.4845 IA X -7.719 -7.719 Y -7.825 -7.823 Z 15.545 15.542 1, X -4.675 -4.678 y -4.679 -4.682 Z 9.354 9.360 py.IC1 N X -0.4789 -0.5295 4’ 0.8942 0.9293 7 -0.41 53 -0.3997 I X -8.6850 -8.6842 Y -8.8083 -8.8050 Z 17.4934 17.4892c1 Y -1.6472 -1.6536 Y -1.6478 -1.6540 Z 3.2950 3.3077 pyridine N X 0.3803 0.3379 Y 0.7391 0.7808 7 -1.1194 -1.1187 pyridi n e( exp) ‘* N X -0.923 y -0.372 --1.296 Ref.(52). where n is the atomic charge. For F<< 1 this can be approximated as eq, = eq,( 1 + ns). (10) Thus plots of eq, us. n should be linear. In the previous study it was found that the most regular variation of this type is shown by the px and p,. orbitals, which are not involved in the bonding.” A plot of this kind for the iodine-p, and pb,orbitals in the diatomic halogen and interhalogen the trihalide ions,33 and the amine- halogen complexes studied in the present work is shown in fig.2. It is found that the data for the terminal iodine atoms follow a reasonably linear relationship, with s = 0.13 and eq, = -14.1 a.u. The value of P obtained is very close to the value of 0.12 originally estimated by Townes and Dailey from experimental data for the iodine atom,” and the value of eq, obtained is identical with the value for neutral atomic iodine (see footnote to table 7). The data for the central iodine atoms in the trihalide ions and the amine halogen complexes do not lie on the same line as that for the terminal iodine atoms, however. These data appear to lie on separate lines for the two different types of compound, These lines have similar E values to that for the terminal iodine atoms, but the eq, values (-14.7 a.u.for the trihalide ions, -15.2a.u. for the amine-halogen complexes) are significantly greater in magnitude than that for the terminal iodine atoms. This result suggests that a contraction of the central-atom px and p,, orbitals relative to those on the terminal aioms takes place. We have previously commented upon this effect in the case of the trihalide ions and have shown that it is capable of explaining the observation that the quadrupole coupling constant for the centre iodine atom in the Table 7. Valence p-orbital contributions to the field gradient, eq, and the field gradient per electron, eq; (a.u.) at the nitrogen and halogen atoms.________~-_____ -275 molecule D.XY py.IBr atom orbital N P\ 1.55 -2.26 1.91 -2.67 1.94 -2.70 1.92 -2.67 -1.49 -2.75 1.64 -2.99 P\ 1.43 -2.60 1.45 -2.65 1.47 -2.68 1.46 -2.67 1.49 -2.75 1.64 -2.99 2 P: -4.09 -2.84 -3.85 -3.05 -3.78 -3.04 -3.80 -3.02 -4.44 -2.84 -4.22 -3.18 X 15.20 -15.25 15.34 -15.41 15.36 -15.42 15.13 -15.40PY P\ 15.23 -15.30 15.39 -15.45 15.40 -15.50 15.13 -15.40 i’U P: -14.87 -14.75 -14.00 -14.81 -13.27 -14.62 16.00 -14.93 0 Y P\ 13.67 -13.73 10.76 -10.74 5.97 -5.94 13.11 -13.22 3 P\ 13.67 -13.68 10.76 -10.77 5.97 -5.97 13.11 -13.22 !? PZ -17.98 -13.59 -15.34 -10.77 -8.64 -5.97 -18.42 -13.31 ** -__.______~ _________ ____~ _______ ____ a Atomic values: eq,(I) = -14.1, eq,,(Rr) = -11.3, eq,(CI) = -5.7, eq,,(N) = -2.1 to -2.7 a.u.N N SCF-MS-Xa Study of Nuclear Quadrupole Coupling 15 t-erminaI iodineI atom 14 I I -0.2 0 0.2 0.4 atomic charge n Fig. 2. Dependence of the iodine pn orbital field gradient eqi (i = x, y) on atomic charge in some halogen and polyhalide compounds. tri-iodide ion is ca. 10% higher than that for atomic iodine, despite the fact that the electronic configurations are almost identical in these two cases.33 The reason for this effect is not yet known, but it appears to be even larger in the case of the centre iodine atom in the amine-halogen complexes. It appears that the main reason for the poor agreement between the calculated and observed I4N coupling constants in pyridine and its complexes is the failure of the Xa calculation to produce reasonable nitrogen p-orbital populations.Thus, despite the apparent good agreement between the calculated and observed e'qQ/h and 7 for pyridine (table 2), the relative magnitudes of the principal components of the field gradient tensor in the x and y directions are interchanged (table 6). The reason for this is that the relative magnitudes of the px and py orbital populations are incorrect (table 5). A previous minimum basis set ab initio SCF calculation also resulted in incorrect relative magnitudes for the x and y components of the nitrogen field gradient This situation was corrected in a later a6 initio calculation using a more extensive basis This appears to be a common problem associated with minimum basis set calculations on pyridine. It does not arise in the case of trimethylamine, where the px and py orbitals are equivalent by symmetry.In the case of the pyridine-halogen complexes, the Xa calculations result in pz orbital populations which are lower than those of the px orbital. This results in a change in the sign and direction of the principal component of the field gradient tensor at the nitrogen atom. The sign and direction of the principaI component of the nitrogen quadrupole coupling tensor have not been determined experimentally for these complexes, but it seems unlikely that such a change takes place. This point needs to be investigated further, but it appears that the Xa method is not well suited to calculating good absolute values of the nitrogen orbital populations and I4N quadrupole coupling parameters in pyridine complexes.References 1 G. Briegleb, Elektronen-Donator-Acceptor-Komplexe(Springer-Verlag, Berlin, 1961). 2 R. S. Mulliken and W. B. Person, Molecular Complexes, A Lecture and Reprint Volume (Wiley, New York, 1969). 3 J. Yarwood, Spectroscopy and Structure qf Molecular Complexes (Plenum Press, London, 1973). 4 S. P. McGlynn, Chem. Rev., 1958, 58, 1113. 5 J. N. Murrell, Q. Rev. Chem. Soc., 1961, 15, 191. 6 E. M. Kosower, Prog. Phys. Org. Chem., 1965, 3, 81. 7 R. Foster and C. A. Fyfe, Prog. Nucl. Magn. Reson. Specrrosc., 1969, 4, I. G. A. Bowmaker and P. D. W. Boyd 8 R. S. Mulliken, J.Am. Chem. Soc., 1952, 74, 811. 9 R. S. Mulliken, J. Chim. Phys., 1964, 61, 20. 10 0. Hassel and C. Rldmming, Q. Rev. Chem. Soc., 1962, 16, 1. 11 H. A. Bent, Chem. Rev., 1968, 68, 587. 12 0. Hassel, C. Romming and T. Tufte, Acta Chem. Scand., 1961, 15, 967. 13 T. Dahl, 0. Hassel and K. Sky, Acra Chem. Scand., 1969, 21, 592. 14 C. Romming, Acta Chem. Scand., 1972, 26, 1555. 15 K. 0. Stromme, Acra Chem. Scand., 1959, 13, 268 16 G. A. Bowmaker and S. Hacobian, Ausr. J. Chem., 1969, 22, 2047. 17 H. C. Fleming and M. W. Hanna, J. Am. Chem. Soc., 1971, 93, 5030. 18 R. Bruggemann, F. Reiter and J. Voitlander, 2.Narurjiorsch., Teil A, 1972, 27, 1525. 19 G. A. Bowmaker, .I. Chem. Soc., Faraday Trans. 2, 1976, 72, 1964. 20 G. V. Rubenacker and T. L.Brown, Inorg. Chem., 1980, 19, 398. 21 C. I. Wynter, J. Hill, W. Bledsloe, G. K. Shenoy and S. L. Ruby, J. Chem. Phys., 1969, 50, 3872. 22 S. Bukshpan, C. Goldstein, T. Sonnino, L. May and M. Pasternak, J. Chem. Phys., 1975, 62, 2606. 23 S. Bukshpan, M. Pasternak and T. Sonnino, J. Chem. Phys., 1975, 62, 2916 24 H. Sakai, Y. Maeda, S. Ichiba and H. Negita, J. Chem. Phys., 1980, 72, 6192. 25 A. Mostad, S. Svensson, R. Nilsson, E. Basilier, U. Gelius, C. Nordling and K. Siegbahn, Chem. Phys. Lett., 1973, 23, 157. 26 M. T. Rogers and W. K. Meyer, J. Phys. Chem., 1962, 66, 1397. 27 A. J. Hamilton and L. E. Sutton, J. Chem. Soc., Chem. Commun., 1968, 460; P. Boule, J. Am. Chem. Soc., 1968, 90, 517. 28 K. Toyoda and M. Imai, Bull. Chem. Soc. Jpn, 1975,48, 3393.30 J. Yarwood and W. B. Person, J. Am. Chem. Soc., 1968, 90, 594. 31 G. W. Brownson and J. Yarwood, J. Mol. Strucr., 1971, 10, 147. 32 E. A. C. Lucken, Nuclear Quadrupole Coupling Coupling Consranrs (Academic Press, London, 1969), chap. 7. 33 G. A. Bowmaker, P. D. W. Boyd and R. J. Sorrenson, J. Chem. Soc., Faraday Trans. 2, 1984,80, 1125. 34 G. A. Bowmaker, P. D. W. Boyd and R. J. Sorrenson, J. Chem. Soc., Faraday Trans. 2, 1985,81, 1023. 35 G. A. Bowmaker and P. D. W. Boyd, J. Mol. Srruct. Theochem., 1985, 122, 299. 36 G. A. Bowmaker, P. D. W. Boyd and R. J. Sorrenson, J. Chem. SOC.,Faraday Trans. 2, 1985,81, 1627. 37 G. A. Bowmaker and P. D. W. Boyd, J. Mol. Strucr. Theochem., 1987, 150, 327. 38 S. F. Sontum and D. A. Case, J.Phys. Chem., 1982, 86, 1596. 39 D. A. Case, M. Cook and M. Karplus, J. Chem. Phys., 1980, 73, 3294. 40 K. H. Johnson, Adv. Quantum Chem., 1973,7, 143; D. A. Case, Annu. Rev. Phys. Chem., 1982,33,151. 41 D. A. Case and M. Cook, Program XASW, personal communication. 42 K. Schwartz, Theor. Chim. Acta, 1974, 34, 225. 43 B. Beagley and A. R. Medwid, J. Mol. Strucr., 1977, 38, 229. 44 J. G. Norman Jr, Mol. Phys., 1976, 31, 1191. 45 D. A. Case and M. Karplus, Chem. Phys. Lett., 1976, 39, 33. 46 M. Co3k and M. Karplus, J. Chem. Phys., 1980, 72, 7. 47 C. M. Lederer and V. S. Shirley, Tables ofIsoropes (Wiley, New York, 7th edn, 1978), appendix 7; D. Sundholm, P. Pyykko, L. Laaksonen and A. J. Sadlej, Chem. Phys., 1986, 101, 219. 48 G. 0. Sldrensen, J. Mol. Spectrosc., 1967, 22, 325. 49 L. GuibC, Ann. Phyr., 1962, 7, 177. 50 M. T. Weiss and M. W. P. Strandberg, Phys. Rev., 1951, 83, 567. 51 C. T. O’Konski and J.T. Flautt, J. Chem. Phys., 1957, 27, 815. 52 G. 0. Sgrensen, L. Mahler and N. Rastrup-Andersen, J. Mol. Srmcr., 1974, 20, 119. 53 A. J. Hamilton and L. E. Sutton, J. Chem. Soc., Chem. Commun., 1968, 460. 54 D. R. Lide and D. E. Mann, J. Chem. Phys., 1958, 28, 572. 55 P. Boule, J. Am. Chem. SOC.,1968, 90, 517. 56 E. Kochanski, J. M. Lehn and B. Levy, Theor. Chim. Acra, 1971, 22, 111; 1979, 54, 93. 57 G. de Brouckkre and G. Berthier, Mol. Phys., 1982, 47, 209. Paper 71348; Received 23rd February, 1987

ISSN:0300-9238    

DOI:10.1039/F29878302211

出版商:RSC    

年代:1987

数据来源: RSC

摘要:

J. Chem. Soc., Faraday Trans. 2, 1987, 83( 12), 2225-2233 Large-amplitude Vibrations and Microwave Band Spectra Part 1 .-Adamantan-1-01 Giorgio Corbelli, Alessandra Degli Esposti, Laura Favero and David G. Lister* Istituto di Spettroscopia Molecolare del C. N. R., Via de' Castagnoli 1, 40126 Bologna, Italy Rinaldo Cervellati Dipartimento di Chimica 'G. Ciamician', Universita di Bologna, Via Selmi 2, 40126 Bologna, Italy and Istituto di Spettroscopia Molecolare del C.N. R., Via de' Castagnoli 1, 40126 Bologna, Italy The microwave spectra of adamantan-1-01 and [2Ht]adamantan-l-ol have been observed in the frequency range 8-40GHz at temperatures of 340- 350 K. The spectra consist of strong series of pa R-branch bands and in the case of adamantan-1-01 a weaker series of ,ubQ-branch bands.The separation of the pbQ-branch bands is almost twice that expected for a rigid rotor. An analysis using the internal axis method to treat the internal rotation of the hydroxy group and which assumes the molecule to be a symmetric rotor gives the approximate formula Y=(A-B+w)(~K+~) for the observed Q-branch bands. The parameter w arises from the internal rotation part of the Hamiltonian. The barrier to internal rotation in adamantan-1-01 is estimated to be V, = 4.9 (4) kJ mol-' [410 (30) cm-'I. The error in V, arises largely from the uncertainty in the moment of inertia of the hydroxy group about the internal rotation axis. Many heavier molecules under conditions of low resolution show microwave band spectra.' The main uses of these spectra have been in conformational analysis,* the study of intermolecular hydrogen-bonded cornplexe~'~~ and as the starting point for the analysis of high-resolution spectra.We have also found them useful in the identification of pyrolysis product^.^ In this and in the following paper6 we report studies of the band spectra of adamantan-1-01 (I, X = OH) and I-adamantamine (I, X = NH,) and show that they may be analysed to give information about the potential barriers hindering large- amplitude vibrations. In adamantan- 1-01 the large-amplitude vibration is the internal rotation of the hydroxy group, while in 1-adamantamine it is necessary to consider both the internal rotation and inversion of the amine group.X-Ray' and electron diffraction'^^ studies of adamantane (I, X = H) show the molecule to have a structure with almost equal carbon-carbon bond lengths and tetrahe- dral angles. Chadwick et a/."*" have studied the microwave spectra of some symmetric rotor 1-substituted adamantanes (X=F, C1, Br, I, CN) and conclude that, with the exception of the fluoride, the adamantane cage is distorted very little by substitution. Both adamantan-1-01 and 1 -adamantarnine are therefore expected to have almost undis- torted adamantane cage structures. Using the structures of the hydroxy group from methanol'' and the amine group from methylamine, 137'4 Ray's asymmetry parameter [K= (2B-A-C)/(A-C)] is found to be ca. -0.99 for both adamantan-1-01 and I-adamantamine.The moment of inertia? of the adamantyl group about its C3axis is ?For convenience and comparison with other work non-SI units have been used for moments of inertia, 1 x lo4mupm' corresponds to 1 a.m.u. A'. 2225 Large-amplitude Vibrations in Adamantan-1-01 X ca.300 x lo4mu pm2 while the moment of inertia of the hydroxy group about the internal rotation axis is 0.75 x lo4mu pm2 in methanol,I2 and that of the amine group is 3.33 x lo4mu pm’ in [2H2]methylamine.’4 The treatment of both the overall and internal rotation using the symmetric rotor approximation is therefore expected to be good for both adamantan-1-01 and 1-adamantamine. In the next section we summarize some of the internal axis method (IAM) treatment of internal rotation in a symmetric and discuss its application to molecules in which the internal rotor (OH, NH2) is very light compared to the rest of the molecule.Internal Rotation in Symmetric Rotors The potential energy hindering the internal rotation is expressed as v= VJ2(1-cos 34) (1) where 4 is the torsional angle of one group with respect to the other. Koehler and Dennison,” following Nielsen,” have shown that by a suitable choice of axis system the Hamiltonian for overall and internal rotation may be written as H = H,+Hi, (2) where H, is a symmetric-rotor rotational Hamiltonian and Hi, is an internal rotation Hamiltonian. For a prolate rotor El, gives energy levels EJK =BJ(J+l)+(A-B)K‘ (3) where the rotational constant B has been written as B as a reminder that for the molecules under consideration it is really the mean of the B and C rotational constants. The internal rotation Hamiltonian may be written in reduced form as Hi,=F[Pi+ V(1 -COS 34)] (4) where V= V3/2E The constant F is written in terms of the moment of inertia about the a inertial axis (Ia)and the moments of inertia of the internal rotor (I,) and the adamantyl cage (IA) about the internal rotation axis as G.Corbelli et al. 2227 and An important parameter in the treatment is 1,p =-. (7)Ia A consequence of writing the Hamiltonian in the form of eqn (2) is that the internal rotation wave functions of eqn (4)depend on the rotational quantum number K. They may be expanded in terms of the wavefunctions for free internal rotation [I/& exp (im+), rn =0,*I, *2,.. .I as In this basis the non-zero reduced matrix elements are Hi,(m,m)=(m-Kp)’+V (9) Hi,(m, m +3) = -V/2. (10) The Hamiltonian matrix factorizes into three blocks which may be labelled as T = 1,2, 3,18 corresponding to the sub-bases of the free internal rotor wavefunctions of eqn (8) 7‘1, m=3s (s=O,*l,f2 ,...) ~=2, m=3s-1 7=3, rn=3s-2. Fig. l(a) shows the behaviour of the three sub-levels W,, corresponding to the ground torsional state for F = 22.53 cm-’, V, =410 cm-’ and p =0.0025. These correspond to our final values for adamantan-1-01. It can be seen that for K =O the ~=2 and 3 levels are degenerate. For other values of K, the T = 1, +K and -K levels are degenerate, while the r =2, +K and T =3, -K levels are degenerate, as are the r =2, -K and T =3, +K levels.The curves corresponding to the three types of level oscillate with a period of CQ. 1200 in K, although of course only integral values of K are allowed. The long period in K has the important consequence that for the observed transitions which have K <40 the energy of the levels varies almost linearly with K. This is shown on an expanded scale in fig. l(b). A symmetry classification of the energy levels is useful in deriving the transition selection rules and nuclear spin statistical weights. Strictly, a high-order permutation inversion group’’ shou-ld be used, but for the present purposes the C, point group is and the levels have the following symmetry: TKO 1 2 3 1 A E2 El A 2 E2 El A E2 3 E, A E, El For a given T the symmetry of the levels varies cyclically with K in the order A, EZ,E,.This arises from the choice of p in eqn (7). The alternative choice of IA P=-1, Large-amplitude Vibrations in Adamantan-1-01 1 1 1 1 1 1 1 1 1 1 1 1 1 0 300 600 900 1200 K 15 10 s50'0iu Q -5 -1 0 -15 -20 Fig. 1. (a) Variation of the internal rotation energy levels with K for the ground torsional state for F = 22.53 cm-', V,= 410 cm-' and p = 0.0025. (b) The variation of the energy differences W,, -W,, with K for K =50. produces energy levels of a given T with the same symmetry, but these oscillate with a period of ca. 3 in K, leading to the same final result.The 215 (32 768) combinations of the nuclear spin wavefunctions of the protons of the adamantyl group form a reduced representation r = 10944A + 10 912E, + 10 912E2 (12) of the C, point group. The product of the internal rotation and nuclear spin wavefunc- tions must belong to the A irreducible representation.2032' The statistical weights for the internal rotation sub-levels are therefore A:E, :E,, 10944: 10 912: 10912, giving ratios of very nearly unity. This is not of great importance for adamantan-1-01, but has some consequence in 1-adamantamine, where it is necessary to consider also the pair of equivalent protons or deuterons of the amine group. The selection rules for the allowed transitions can be derived from the requirement that there is no change in the symmetry of the nuclear spin wavefunction. The allowed transitions are therefore: A * A, El * E, and E, * E2. For the R-branch transitions, AK =0 and there is no change in the internal rotation G.Corbelli et al. 2229 substate. From eqn (3) the frequencies are Y = 2B(J + 1) (13) where J is the rotational quantum number of the lower levels involved in the transitions. The allowed AK = +1 & Q-branch transitions are 7=2 + 3,l + 2 and 3 +-1. Approximate formulae for the Q-branch transitions may be derived in the following way. The curve representing the WK levels has a minimum at K = 0 and therefore for low values of K There is an approximate sum rule for the WK+: WK+ WK2+ WK = constant. (15) A discussion of this sum rule is given in the appendix of the following paper.6 Once eqn (14) is established, differentiation of eqn (15) with respect to K gives It is convenient to write Eqn (2), (3), (14), (16) and (17) give the following formulae for the AK = +I p,b Q-branch transitions: = (A-B+ w)(~K~23 + 1) (18) Y,~=(A-B-~/~W)(~K+I)- W-1/2~ (19) ~3~ = (A-B -1/2~)(2K+ 1)+ W+ 1/2~.(20) Experimental Adamantan-1-01 (99"/0 pure) supplied by EGA-Chemie was used without further purification. ['H,]adamantanol was prepared by dissolving adamantan- 1-01 in [2Hl]methanol (99.5 atom '/o 2H) supplied by EGA-Chemie and then removing the methanol under reduced pressure. A molar ratio of exchangeable '€3: 'H of 30: 1 was used. The relative intensities of the pa R-branch bands of adamantan-1-01 and ['H,]adamantan-1-01 indicated a deuteration of 80-90%.Adamantan-1-01 was found not to exchange with D20. Microwave spectra were observed at temperatures of 340-350 K using a computer-controlled Stark modulation spectrometer with a heatable Results Fig. 2 shows a recording of the R-band spectrum of adamantan-1-01. The members of the strong series of pa R-branch bands are labelled by their J quantum numbers. The measured band frequencies for adamantan-1 -01 and ['H,]adamantan-1-01 are given in table 1, together with the values of B derived by fitting the frequencies to eqn (13). In fig. 2 a second series of bands with a separation of ca. 2000 MHz is observed. Under conditions of higher resolution and lower Stark voltage these bands are found to consist of a strong absorption and a number of weaker lines (fig.3). The strongest feature can Large-amplitude Vibrations in Adamantan-1-01 14 15 18 i 27 29 31 33 35 37 GHz Fig. 2. The microwave spectrum of adamantan-1-01 between 27 and 38 GHz. Stark voltage = 800 V cm-'. The pa R-branch bands are labelled by their J quantum numbers and the pb Q-branch bands by their K quantum numbers. Table 1. Measured pa R-branch band frequencies and differences between observed and calculated frequencies (in MHz) for adamantan-1-01 and [*H,]adamantanol adamantan-1-01 ['H,]adamantan- 1-01 J ~~ obsd obsd -calcd obsd obsd -calcd ~ ~~~ ~ 3 9 395 2 9 197 2 4 11 743 2 11 496 2 5 14 090 0 13 793 0 6 16 439 1 16 092 0 7 18 785 -1 18 389 -2 8 21 138 3 20 687 -2 9 23 483 0 22 992 4 10 25 831 -0 25 286 -1 11 28 179 -0 27 584 -2 12 30 526 -2 29 889 4 13 32 876 0 32 180 -4 14 35 222 -2 34 483 1 15 37 573 0 36 781 -0 (Tn 1 2 B 1174.14 (2)' 1149.41 (5) Standard deviation of fit.'Standard error. G. Corbelli et al. 223 1 33750 33850 33950 M Hz Fig. 3. The K = 17 pb Q-branch band at a Stark voltage of 50 V cm-'. The measured band frequency is indicated by the arrow. Table 2. Measured pb Q-branch band frequencies and the separation between successive members (in MHz) for the T = 2 +3 series of adamantan-1-01 K obsd separation K obsd separation 4 8 458 1892 13 25 807 1989 5 10 350 14 27 796 2002 7 14 152 1915 15 29 798 2020 8 16 067 1924 16 31 818 2036 9 17 991 1935 17 33 854 2052 10 19 926 1947 18 35 906 2069 11 21 873 1960 19 37 975 2087 12 23 833 1974 20 40 062 be measured with an accuracy of *2 MHz.The separation between successive members decreases regularly on going to lower frequency, and 16 transitions between 8 and 40 GHz have been observed. The measured frequencies and the differences between successive members of the series are given in table 2. At the lowest frequencies, division of the band frequency by the band separation gives a number which is almost a half-integer. For the two lowest frequencies in table 2 these numbers are 4.47 and 5.47.This shows that the frequencies are approximately following eqn (18) and belong to the T = 2 +3 series. It also establishes the K quantum numbers. A graphical extrapolation of v/(2K+ 1) us. K to K =Ogives A -B+ w =935 MHz. A graphical extrapolation of Av vs. K to K =0 gives A-B+w=933 MHz. In order to extract information about the barrier height it is necessary to separate the coefficient of (2K + 1) into the components A -B and o.In the following paper we obtain IA=299.5 x lo4mu pm2 from I, for [2H2]1-admantamine. Assuming I, has Large-amplitude Vibrations in Adamantan-1-01 700 t 600 500 E--. a 400 3 00 350 4 00 4 50 V,/ cm-' Fig. 4. Variation of w [eqn (16)] with V, for I, = 0.70, 0.75, 0.80 ( x lo4mupm2).The horizontal line is the value of w deduced from the spectra. the same value as in methanol (I, = 0.75 x lo4mu pm2)12 gives A = 1683 MHz. Combining this with the experimental B from table 1 gives A -B = 508 MHz and for A -B + w = 934 MHz this gives w = 426 MHz. Fig. 4 shows the calculated variation of w for different barrier heights and I,, keeping IA fixed at 299.5 x lo4mu pm2. The values of I, chosen correspond to that of methanol and that of methanol k0.05x lo4mu pm'. The observed value of w gives barrier heights of 440, 410 and 390 cm-' for the three values of I,. Discussion In order to compare the value of V, obtained here with that of 376 cm-' in methanoli2 it is necessary to have some idea of its uncertainty.Fig. 4 shows this to arise primarily from the uncertainty in w and that in I,. The observed Q-branch band frequencies show considerably larger deviations from eqn (18) than the model frequencies calculated from the Hamiltonian of eqn (2). This may be attributed to contributions from higher- order rotation-internal rotation terms of the type discussed by Ki~~man.'~ Inspection of his expressions shows that for adamantan-1-01 these will add terms in K2, K3 etc. to the energy levels and therefore make some contribution to w.Since the band separations increase with K this implies these terms are making a positive contribution to w. The second source of error in the determination of w comes from the estimation of the rotational constant A.This was done using eqn (6) and transferring IA from [ 'H2] l-adamantamine and 1, from methanol. The uncertainty arises in the transferability of these quantities from one molecule to another. Chadwick et al.," after making the assumptions of a regular cage structure and rCH = 109 pm, found rcc to be 154.2 f0.2 pm for the three molecules for which they had data for more than one isotopic species. The value of rcc obtained from I, for ['H,]l-adamantamine with the same assumptions is 154.0 pm. The difference in rcc between l-adamantamine and adamantan-1-01 is there- fore unlikely to be more than 0.2 pm, and this translates into an uncertainty of 5 MHz on the rotational constant A. The error contributed to A by the uncertainty in I, is much less than this.The value of I, has a much larger effect on the calculated value G. Corbelli et al. 2233 of w since it enters into both F [eqn (5)] and p [eqn (7)]. For an OH bond length of 94.5 pm, as in methanol," the range of values of I, used to calculate the data for fig. 4 correspond to a change of 2-4" in the COH angle or 1-2" in the tilt of the CO bond with respect to the internal rotation axis. In phenol I, = 0.77 x lo4mu indicating that I, in adamantan-1-01 is very likely to lie within the range (0.7-0.8) x lo4mu pm'. It can. therefore be concluded that there is evidence for an increase of ca. 50 cm-' in the barrier to internal rotation in passing from methanol to adamantan-1-01. An interesting point about the spectrum of [*H,]adamantan-1-01 is our failure to observe Q-branch bands.The energy difference W [eqn (17)] is predicted to be ca. 15 GHz and so members of all three series, as well as some members of a AK = -1 series, should occur between 8 and 40GHz. The J dependence of the Q-branch transitions is sufficiently different for the two isotopic species to give recognizable bands for one but not the other. We would like to thank Dr Barry Landsberg, formerly of the University College of North Wales, Bangor, for suggesting that we study the microwave spectrum of adaman- tan-1-01 and for the gift of our original sample. We thank Mr L. Minghetti, Mr R. Pezzoli and Mr G. Tasini for the construction of the vacuum system and the fabrication of waveguide components used in this work.References 1 L. H. Scharpen and V. W. Laurie, Anal. Chem., 1972, 44,378R. 2 W. E. Steinmetz, J. Am. Chem. Soc., 1974, 96, 635. 3 C. C. Costain and G. P. Srivastava, J. Chem. Phys., 1961, 35, 1903. 4 E. M. Bellott and E. B. Wilson, Terrahedron, 1975, 31, 2898. 5 R. Cerveilati, G. Corbelli, A. Degli Esposti, D. G. Lister and P. Todesco, J. Chem. SOC.,Perkin Trans. 2, 1987, 585. 6 G. Corbelli, A. Degli Esposti, L. Favero, D. G. Lister and R. Cervellati, J. Chem. Soc., Faraday Trans. 2, 1987, 83, 2235. 7 W. Nowacki, Helv. Chim. Acta, 1945, 28, 1223. 8 W. Nowacki and K. Hedberg, J. Am. Chem. SOC., 1948, 70, 1497. 9 J. Hargittai and K. Hedberg, J. Chem. Soc., Chem. Commun., 1971, 1499. 10 D. Chadwick, A. C. Legon and D.J. Millen, J. Chem. Soc. A, 1968, 116. 11 D. Chadwick, A. C. Legon and D. J. Millen, J. Chem. Soc., Faraday Trans. 2, 1972, 68, 2064. 12 R. M. Lees and J. G. Baker, J. Chem. Phys., 1968,48, 5299. 13 D. Lide Jr, J. Chem. Phys., 1957, 27, 343. 14 K. Takagi and T. Kojima, J. Phy~.SOC.Jpn, 1971, 30, 1145. 15 J. S. Koehler and D. M. Dennison, Phys. Rev., 1940, 57, 1006. 16 C. H. Townes and A. L. Schawlow, Microwave Spectroscopy (McGraw-Hill, New York, 1955), chap. 12, p. 315. 17 H. H. Nielsen, Phys. Rev., 1932, 40, 445. 18 D. G. Burkhard and D. M. Dennison, Phys. Rev., 1951, 84, 408. 19 H. C. Longuet-Higgins, Mol. Phys., 1963, 6, 445. 20 C. C. Lin and J. D. Swalen, Rev. Mol. Phys., 1959, 31, 841. 21 J. E. Wollrab, Rorarional Spectra and Molecular Structure (Academic Press, New York, 1967), chap. 6, p. 153. 22 R. Cervellati, G. Corbelli, A. Dal Borgo, D. G. Lister and A. G. Giumanini, J. Mol. Struct., 1984, 117, 87. 23 B. Kirtman, J. Chem. Phys., 1962, 37, 2516. 24 T. Pedersen, N. W. Larsen and L. Nygaard, J. Mol. Struct., 1969, 4, 59. Paper 71439; Received 9th March, 1987

ISSN:0300-9238    

DOI:10.1039/F29878302225

出版商:RSC    

年代:1987

数据来源: RSC

摘要:

J. Chem. SOC.,Faraday Trans. 2, 1987, 83(12), 2235-2246 Large-amplitude Vibrations and Microwave Band Spectra Part 2.-1 -Adamantarnine Giorgio Corbelli, Alessandra Degli Esposti, Laura Favero and David G. Lister* Istituto di Spettroscopia Molecolare del C,N.R., Via de' Custugnoli 1, 40126 Bologna, Italy Rinaldo Cervellati Dipartimento di Chimica 'G. Ciamician', Universita di Bologna, Via Selmi 2, 40126 Bologna, Italy and Istituto di Spettroscopia Molecolare del C.N.R., Via dc' Castagnoli 1, 40126 Bologna, Italy The microwave spectra of 1-adamantamine, [*HI] 1-adamantamine and ['H2] 1-adamantarnine have been observed at room temperature in the frequency range 8-40GHz. The spectra consist of both F~ R-branch and F~ Q-branch bands. The paR-branch bands of the three isotopic species appear as doublets and this is attributed to the inversion of the amine group.A simple treatment of the internal rotation and inversion in which the molecule is regarded as a symmetric rotor shows that six series of AK = +l pc Q-branch bands should be associated with the ground vibrational state. The band frequencies are shown to follow approximately the formulae v = a(2K + 1) or v = a(2K+ l)+b where the constants a are the sum of the rotational constant A -B and contributions from the internal motions. The formulae are verified experi- mentally for ['H,]l-adarnantamine. The barrier to internal rotation in [2H,]1-adamantamine is determined to be V, = 9.0 (9) kJ mol-' [750 (70) cm-'1 and the inversion splitting to be A; = 1250 (30) MHz.In the preceding paper' it was shown that information about the barrier to internal rotation in adamantan-1-01 could be obtained from microwave band spectra. In this paper we show that similar information may be obtained for 1-adamantamine. In this molecule, as in meth~lamine,'-~ the internal rotation and inversion of the amine group are strongly coupled to each other and to the overall rotation. This can be seen from the projection diagrams of fig. 1. The molecule can pass from one conformation of minimum potential energy to another by an internal rotation of the amine group by f120". When the amine group inverts it is necessary that it is accompanied by an internal rotation of 160"in order to pass from one conformation of minimum potential energy to another.1-Adamantamine is very close to being a prolate symmetric rotor. Fig. 2 shows an energy-level correlation diagram for the ground vibrational state of a molecule of this type in which there is both inversion and internal rotation, the latter being hindered by a potential with threefold symmetry. In the limit of infinite potential barriers a given rotational energy leve! (J, K) is sixfold degenerate. For finite inversion but infinite internal rotation barriers the six levels split into two groups of three, which are labelled s (symmetric) and a (antisymmetric), depending on the symmetry of their wavefunctions with respect to the inversion coordinate. The separation of the two groups of levels is denoted by the inversion splitting A:.For finite internal rotation barriers each group of levels splits into three, and these are labelled by the index 7 [as in ref. (l)]. Finally, 2235 Large-amplitude Vibrations in 1 -Adamantarnine Fig. 1. Projection diagrams along the CN bond for 1-adamantamine showing [(a)and (b)]how the molecule passes from one conformation of minimum potential energy to another by internal rotation, but how an inversion of the amine group (c) must be accompanied by an internal rotation to achieve the same result (d). Fig. 2. Energy-level correlation diagram for the ground vibrational state of a symmetric rotor with inversion and internal rotation. (a>Infinite barriers: each J, K level is sixfold degenerate. (b)Finite inversion barrier: levels split into two groups of three.(c) Finite inversion and internal rotation barriers giving six levels. (d) Interaction between inversion and internal and overall rotation displaces levels relative to each other. the interaction of the two internal motions and their interaction with the overall rotation displaces the levels relative to each other. In 1-adamantamhe this interaction changes the order of the levels in both the s and a states. This discussion will be put in a more quantitative form in the next section, where expressions for the energy levels and transition frequencies will be given. The microwave spectra of some symmetric rotor 1 -adamantanes have been observed by Chadwick et al.637 They studied molecules with substituents X = F, C1, Br, I, CN and reached the conclusion that with the exception of the fluoride the adamantane cage is little distorted by substitution.The symmetric rotor spectra only give the moment of inertia perpendicular to the molecular symmetry axis. Chadwick et ai?’ used the moments of inertia of isotopically substituted molecules to derive the principal moment of inertia of the adamantyl group It was found that Icd showed little variation for the three molecules for which isotopic data (X = C1, Br, CN) was obtained. We are G. Corbelli et al. 2237 able to test their conclusion by deriving the moment of inertia of the adamantyl group about its symmetry axis from the A rotational constant of ['H,]l-adamantamine. Internal Rotation and Inversion in a Symmetric Rotor Itoh' and Kivelson and Lide3 have given theoretical treatments of the internal motions, their mutual interaction and their interaction with the overall rotation for methylamine.Many of their approximations and assumptions will be followed here. 1 -Adamantarnine will be treated as a symmetric rotor and it will be assumed that the s and a states have slightly different rotational constants. The energy levels are labelled EjKTs or EjKTa. Additional labels giving the internal rotation and inversion vibrational quantum numbers are dropped since only the ground vibrational state is being considered here. The energy levels are expressed as E~K~,= B,J(J+ 1) + (A,-13,)K + wKT-;AT( 1+ xK,) (1) where A and B are the rotational constants, WK,are the internal rotation energies' and the XK, are integrals which allow for the interaction of the internal motions and overall rotation.A term has been dropped from both eqn (1) and (2), representing the zero-point inversion energy. The integrals XKTare defined as3 where + is the internal rotation coordinate and the +KT are the internal rotation wave- functions.' The XKTare readily calculated once the internal rotation wavefunctions are expressed in terms of the free internal rotation wavef~nctions.~ In ref. (1) it was shown for adamantan- 1-01 that for relatively low values of K the W,, are almost linear functions of K. It was also shown that awKl -0 (4)aK and Eqn (4) is a consequence of WK having a minimum at K = 0, and eqn (5) follows from the approximate sum rule for the WKT.Fig.3 shows that the XK,are also nearly linear functions of K for relatively low values of K. XKlhas a maximum value at K=O and therefore 1 -0.aK Kivelson and Lide3 have shown that there is an approximate sum rule for the XKT 2238 Large-amplitude Vibrations in 1-Adaman tamine 0.02"03+7--L O-O't -0.031 Fig. 3. Variation of the integrals X,, with K for 1, =3.3 x lo4 mu pm2, F =5.12 cm-*, p =0.011 and V, =750 cm-' (values appropriate to [2H,]1-adamantamine). It is convenient to define and X =iAp(Xo,-X,,) (10) in order to be able to write simpler expressions for the energy levels given in eqn (1) and (2). Kivelson and Lide3 derived the sum rule for the X,, on the assumption that the internal rotation barriers were sufficiently high for the internal rotation wavefunctions to be regarded as simple harmonic oscillator wavefunctions localized in the regions of the potential minima.It has been shown that the WKT2" as Fourier series involving the angle Kp, where ' and the XK:78can be expressed I,,p =-. I, In Appendix 1 a demonstration of these sum rules for the W,, and XK, is given which also illustrates their approximate nature. The nuclear spin statistical weights and selection rules have been given for methyl- amir~e.~?~Those for 1-adamantamine may be derived in a similar way, making use of the results given for adamantan-1-01 in the preceding paper.' The energy levels may be classified using the irreducible representations of the C3point group to which a suffix s or a is added to denote the symmetry of the inversion part of the wavefunction.The nuclear spin statistical weights (gns)may be expressed as products of factors due to the internal rotation (gir)and inversion (gi)4 gns =$irgi -(12) In ref. (1) it was shown that the ratios gir(A):gir(E,):gir(E,)were very nearly unity. In deriving g,, it is therefore only necessary to consider the statistical weights of the amine group. Taking into account that protons follow Fermi-Dirac and deuterons Bose- Einstein statistics the ratios of the statistical weights for s to a levels is 1:3 for I-adamantamine and 2 : 1 for ['HJl-adamantamine. For ['H,]l-adamantamine, where there is no symmetry for the nuclear spin wavefunctions of the amine group, the ratio G.Corbeili et al. 2239 Table 1. a and b constants for the AK = + 1 pc Q-branch series a b T=2 t 3 S A,-tS+w-x a A, -B, + w + x T=1 -2 s A,-B2+1/2(-w+x) -W-X+1/2(w-x) a Aa-B,-1/2(w+x) -W+X+l/2(w+x) T=3 C 1 s A,-B,+ 1/2(-~+x) w+x+ 1/2(-w+x) a A, -B, -1/ 2(M? + x) w -x-1/2(W+X) of s to a levels is unity. The selection rules may be derived from the requirement that there is no change in the symmetry of the nuclear spin wavefunctions of either the adamantane or amine groups in an electric dipole transition. For the NH2 and ND2 species this gives s-s, a-a and A ++ A, El El, E2 ++ E2. Forthe NHD species, transitions between a and s levels are allowed, but as in adamantan- 1-01, the second requirement remains.Two series of paR-branch transitions with frequencies vs= 2B,(J + 1) (13) and va= 2Ba(J+ 1) (14) are expected. Using eqn ( 1) and (2) and the approximations of eqn (4), (5), (6)and (8) approximate formulae for the pcAK =+1 Q-branch transitions may be derived. For the NH2 and ND2 species the frequencies of the r = 2 +-3 transitions may be written as v = a(2K + 1) (15) and for the remaining transitions as v = a(2K + 1)+ b (16) where the constants a and b are given in table 1. Experimentai 1-Adamantamine (97% pure) supplied by Aldrich was used without further purification. The sample used to observe the spectrum of ['H,]l-adamantamine was prepared by dissolving 1-adamantamhe in the deuterated methanol recovered from the preparation of ['H],adamantan-l-ol' and removing the methanol under reduced pressure. The sample used to observe the spectrum of L2H2]1-adamantamine was prepared by twice dissolving 1-adamantamhe in deuterated methanol and removing the methanol under Large-amplitude Vibrations in 1-Adamantarnine reduced pressure.Spectra were observed at room temperature using a slow flow of sample through the cell. Results The pa R-branch bands of all three isotopic species appear as doublets. In the NH2 species the upper-frequency component is generally the stronger, in the ND2 species it is the lower-frequency component and in the NHD species both components are of equal intensity. This would suggest that the doubling is due to the inversion of the amine group and that the lower-frequency components belong to the s states and the upper-frequency components to the a states.Table 2 gives the measured band frequencies and the results of fitting them to eqn (13) and (14). Although all three isotopic species show pcQ-branch bands it has so far been possible to make a reasonably complete analysis for [2H,]1-adarnantamine. This is because the constants W and X of table 1 are <50 MHz, while A-B= 540 MHz for this isotopic species. For the-other two isotopic species these constants are comparable to if not larger than A -B. For K between 12 and 18 it has been possible to assign all six pcAK = +1 Q-branch bands for [2HH,]1-adamantamine. Fig.4 shows the K = 16 transition at ca. 18.1 GHz and it can be seen that the bands show approximately the 2 : 1 intensity ratios expected from the statistical weights. On the basis of the relative intensities and the constants given in table 1, the assignment of bands I, 111, IV and VI is straightforward. Bands I11 and IV are assigned to the T =2 +-3 transitions of the s and a states and bands I +-and VI to the T= 1 -2 and ~=3 1 transitions of the s state. Table 3 gives the measured band frequencies and the differences labelled I in this table are for fitting the band frequencies to eqn (15) or eqn (161, as appropriate. Two assignments are possible for bands I1 and V and the correct one depends on whether W is larger or smaller than X.Assignment of band I1 to the T = 1 +-2 transition of the a state gives W = 22 MHz and X = 7 MHz, while assignment of band I1 to the T= 3 +-1 transition of the a state gives W =. 7 MHz and X = 22 MHz. A choice between these two assignments was made using the separations between the T= 2 +3 bands and the property that the XKTmay be expressed as Fourier series (see Appendix 1). For this purpose the quantity p was estimated from the structure of the adamantane cageh37 and the structure of the amine group in meth~larnine.~” In this way X was found to be ca. 23 MHz, showing that the correct assignment of band I1 is to the T= 3 +1 transition of the a state, and that of band V is to the T = 1 +-2 transition of this state. Approximate values of the barrier height of V, (ca.760 cm-’) and for the inversion splittitting of A; (ca. 1200 MHz) were obtained from these values of W and X. These were used as the starting points for a series of fits to the observed band frequencies using eqn (1) and (2). In these fits the parameters Iu,F and p were kept fixed and the remaining parameters A, -B,, A,-B,, V, and A: were varied. I, was fixed at the value from CD3ND25and then F and p were obtained from the value of I, calculated from the a constants of table 4 and the B,constant from table 2. I, was changed by *lo% and the fits were repeated. The derived constants are given in table 5 and the differences between the observed and calculated frequencies for the first fit are given as I1 in table 3.Although the standard deviation for the fits is comparable to the estimated accuracy of frequency measurement (ca. 1-2 MHz), the T= 2 +3 and T=3 +-1 series of the a state show relatively large systematic deviations. Discussion Table 5 shows that, as in the case of adamantan-1-01,’ the height of the barrier to internal rotation is very sensitive to the value of I,. In both molecules the value of I,x has been Table 2. Measured pa R-branch band frequencies, differences between observed and calculated frequencies and B constants (in MHz) for 1-adamantarnine ~~ 1-adamantarnine [*HI]1-adamantarnine [2H,]1-adamantamine ____ ---~--__ S a S a S a ._____ ~_______ _--__~___I____ ____l__l____ J obsd obsd-calcd obsd obsd-calcd obsd obsd-cald obsd obsd-calcd obsd obsd-calcd obsd obsd-calcd ~ ~~ ~ ~~ 3 9 373 3 9 383 2 9 164 4 9 174 2 8 962 3 8 970 -1 4 11 450 0 11 462 -3 9 5 14060 3 14 074 -3 m\J 6 16398 -1 16 420 -3 16 029 -1 16 051 -0 15 680 1 15 704 5 %7 18 319 -1 18 347 3 17 922 3 17 943 1 5 8 21 088 3 21 110 -6 20 609 -1 20 637 -0 20 165 6 20 185 0 = 9 23425 -3 23 462 0 22 898 -2 22 932 2 22 394 -5 22 436 9 2 10 25771 0 25 803 -5 25 189 -1 25 222 --1 2 11 28111 -2 28 151 2 27 480 0 27 514 -2 12 30453 -3 30 502 2 29 774 4 29 807 -2 13 32801 2 32 849 2 32 060 0 32 102 --0 31 362 4 31 395 -3 14 35 137 -5 35 192 -1 34 343 -1 34 397 2 33 590 -8 33 641 0 15 37490 6 37 453 4 36 641 1 36 690 2 35 840 2 35 880 -4 16 38 927 -3 38 980 -1 38 078 0 38 125 -1 (7" 3 3 2 2 7 6-B 1 171.39 (5)h 1173.09(5) 1 144.99 (2) 1 146.51 (2) 1 119.94 (7) 1 121.37 (6) Standard deviation.Standard error in units of least-significant digit. N N ;f: Large-amplitude Vibrations in 1-Adamantarnine VI111 I 1I I I 18 060 18 100 18 150 18 200 M Hz Fig. 4. The K =16 transition of [2H,]1-adamantamine near 18.1 GHz. The assignments are (I) ~=1 1t 2s, (11) ~=3+--la, (111) 7=2+3s, (IV) ~=2+3a,(V) ~= -2a, (VI) ~=?+ls. transferred from the corresponding methyl compound and in estimating the uncertainty in the barrier height it has been assumed that in the 1-adamantanes I, may differ by up to *lo%. Takagi and Kojima' give barriers to internal rotation in CH,ND2 and CD3ND2of 679 and 672 cm-', respectively.Our result for ['H,]l-adamantarnine is somewhat higher than this. They also give inversion splittings of 2269 and 2218 MHz for CH3ND2 and CD3ND2,respectively, which are larger than the values found here. The low-resolution microwave spectra of adamantan-1-01 and 1-adamantamine indicate that the barriers to internal rotation are somewhat higher than in the corresponding methyl compounds. The smaller inversion splitting in ['H,] 1 -adamantamhe compared to ['H2]methylamine also indicates a higher inversion barrier. From the values of B,and A, -BSin tables 2 and 5 the smallest moment of inertia of ['H2]1-adamantamine is I, =302.8 x lo4mu pm2. Taking I, =3.3 x lo4mu pm' gives IA=299.5 x lo4mu pm2 for the moment of inertia of the adamantane cage about the .~~internal rotation axis.With the same assumptions as Chadwick et ~1 of a regular ~ cage and rCH =109 pm, the average carbon-carbon bond length is 154.0 (2) pm. The error in the bond length comes from an estimated error of 2 MHz in the value of the A rotational constant and the uncertainty of 10% in I,. The value of rCCfound here may be compared with those of 154.1 (11,154.2 (3) and 154.3 (1) pm found for 1-adamantanes with X =C1, Br, CN.7 For rCC =154.0 pm, the B values of all three isotopic species of 1-adamantamine give rCN=149 pm. This is ca. 2 pm larger than the value in methylamine (rCN=147.4 ~rn,~ rCN =147.1'). Similarly, with rcc =154.0 pm the B values of the OH and OD species of adamantan-1-01 give rCo =144 pm and this is ca.1-2 pm larger than the value found in methanol (rc0 =142.5 ~rn,~ =142.1 pm'*). Chadwick et al.' found, with the excep- rcc tion of the fluoride, CX bonds ca. 1 pm longer than those in the corresponding methyl compounds. D.G.L. thanks Prof. D. J. Millen and the Chemistry Department of University College London for their hospitality. Table 3. Measured AK = +1 pc Q-branch band frequencies (in MHz) for [*H2]1-adamantamine" r=3+-2 7E1-2 7-3-1 S a S a S a band: 111 IV I V VI II _____-obsd obsd -calcd obsd obsd -calcd obsd obsd -calcd obsd obsd -calcd obsd obsd -calcd obsd obsd -calcd K I I1 I 11 I I1 I I1 1 I1 I I1 7 8 237 1 1 8 241 0 -1 8 210 -0 -1 8 9 335 1 -0 9 340 0 -1 9 309 0 -0 9 366 0 1 9 10 432 -0 -1 10 407 -0 -1 10 464 -0 1 11 12 629 0 0 12 605 1 0 12 661 -0 1 12 13 727 0 -0 13 735 0 -2 23 702 -1 -1 13 746 -2 -1 13 760 1 1 13713 -1 3 13 14 825 0 -0 14 834 1 -2 14 801 -1 -1 14 847 1 2 14 858 -0 1 14812 0 4 14 15 923 0 -1 15 932 -0 -3 1.5 900 -0 -0 15 946 2 2 15 956 -0 1 1.5910 0 4 1.5 17 020 -1 -2 17 030 -1 -3 16 999 0 0 17 043 0 1 17 055 -0 1 17008 0 3 16 18 118 -1 -2 18 130 0 -2 18 097 0 -0 18 141 0 1 18 153 -0 1 18 107 1 4 17 19 218 1 -0 19 229 1 -2 19 196 0 0 19 239 -1 0 19 251 -0 1 19204 -0 3 18 20 316 1 -1 20 327 -0 -3 20 295 1 1 20 338 --0 1 20 349 -0 0 20302 -0 2 19 21 414 0 -1 21 425 -1 -4 21 393 0 -0 21 436 -0 1 21 449 1 2 20 22 512 0 -1 22 525 0 -3 22 492 0 0 22 535 0 2 22 547 0 1 21 23 609 -1 -2 23 624 0 -3 23 590 -0 0 23 633 -0 1 23 646 1 2 22 24 708 -0 -1 24 722 -0 -4 24 688 -1 -1 24 732 0 2 24 744 0 2 a The differences (I) are for fitting to eqn (15) or (16) and the differences (11) are for the fit to eqn (1) and (2) for I, = 3.3 x lo4mupm2, F = 5.12 cm-' and p =0.011.Large-amplitude Vibrations in 1 -Adamantarnine Table 4. a and b constants (in MHz) for the AK = +1 pc Q-branch bands of [-HJl-adamantamine a/MHz b/MHz cr/MHz" 7=2 -3 s 549.07 (l)b 0.7 a 549.38 (1) 0.6 r=l+-2 s 549.29 (2) -29.2 (6) 0.6 a 549.20 (5) 17.6 (1.7) 1.o r=3 + 1 s 549.22 (2) 29.0 (5) 0.5 a 549.06 (2) -12.8 (6) 0.6 " Standard deviation of fit. 'Standard error in units of least-significant digit. Table 5. Constants for the fits to eqn (1) and (2) for [2H2]1- adam an tamine I:/ 10' mu pm2 3.03 3.33 3.63 F"/cm-' 5.62 5.12 4.70 Pa 0.010 0.01 1 0.012 A,-B,/MHz 549.19 (1)' 549.19 (1) 549.19 (1) A, -Ba/MHz 549.25 (1) 549.25 (1) 549.25 (1) V,/crn-' 839 (11) 755 (12) 686 (12) AP/MHz 1286 (13) 1254 (15) 1228 (17) cr"/MHz 1.6 1.8 2.1 " Parameter fixed as described in the text.Standard error in units of least-significant digit. ' Standard deviation of fit. Appendix 1 The internal rotation energy levels may be expressed as Fourier series'-5 WK,=F(a,+a, cos yKT+a2cos2yK7+--.) where the angles yKTare defined as 27T YKI =-Kp3 27T YK*=-(l-KP)3 27T YK 3 = -3 ( 1+Kp and p is defined in eqn (11). Using the relation cos (a+p)=cos a cos p-sin (Y sin p the sum SWK = WK!+ WK2f WK3 G.Corbelli et al. 2245 Table Al. Coefficients for the expansion of W,, and X,, in Fourier series for values of p and V appropriate to (a)adamantan-1-01 and (b)[’HI]1-adamantamhe P: (a)0.0025 (b)0.01 1 V: 9.1 73.7 W nu X nu W nu X na 5.7 0 1.8 1 -1.3 -1 5.6 -1 -2.1 -4 2.5 -2 2.7 -3 -4.8 -9 -8.7 -5 1.7 -2 -5.5 -7 3.3 -6 -1.4 -7 7.7 -4 8.9 -9 8.4 -9 1.5 -5 <1 -8 5.1 -2 2.9 -6 ~ ~~ ~~~ The entries in the table are reported in the form 1.0x lo-”. may be expressed as Sw,=3Fao+F n=1,2 +sin (+)[sin TnKp (T)+sin (-?)]I.Since sin a = -sin (-a) the sin term in eqn (A7) is zero for all n. For n not a multiple of 3, the cos term is also zero. For n a multiple of 3, a, must be zero for SwK to be a constant.For high barriers the Fourier series eqn (Al) converges rapidly and a3is small compared to a,, a, and u2. In their work on methylamine, Takagi and Kojima’ used terms up to a2 in the expansion of the internal rotation energy levels. Tsuboi et ~1.~ have expressed the XK,in Fourier series of the form XK, = a, cos SK7+ a3cos3SK, + * * -(AS) where the angles SK, are defined as Making use of eqn (A5) the sum SXK =XK1+XK2+XK3 can be expressed in a form similar to eqn (A7). The sum rule for the X,, is then seen to require that a3,a,, . . . are zero. Takagi and Kojima’ used only the first term in eqn (AS) in their work on methylamine and this was also found to be satisfactory here. Two examples of the expression of the WK,and the XKras Fourier series and the validity of the sum rules are given in table A1 for values of p and the reduced barrier ( V = V3/2F)appropriate to (a) adamantan-1-01 and (b) [*H,]l-adamantamine.The Large-amplitude Vibrations in 1-Adamantarnine Fourier coefficients were found by least-squares fits to 25 values of WK or XK covering a cycle of WK and half a cycle in XK Table A1 also gives the maximum deviation of the sum SWK from the value of 3a, and also the maximum absolute values of the sum SxK. For the relatively high barrier case of ['HJ l-adamantamine the Fourier series are seen to converge rapidly and the sum rules are obeyed to a high level of accuracy. For the much lower barrier case of adamantan-1-01 it is necessary to include more terms in the Fourier series expansions and the sum rules are very approximate.References 1 G. Corbelli, A. Degli Esposti, L. Favero, D. G. Lister and R. Cervellati, J. Chem. Soc., Faraday Trans. 2, 1987, 83, 2225. 2 T. Itoh, J. Phys. SOC.Jpn, 1956, 11, 264. 3 D. Mivelson and D. R. Lide Jr, J. Chem. Phys., 1957, 27, 353. 4 D. R. Lide Jr, J. Chem. Phys., 1957, 27, 343. 5 K. Takagi and T. Kojima, J. Phys. SOC.Jpn, 1971, 30, 1145. 6 D. Chadwick, A. C. Legon and D. J. Millen, J. Chem. SOC. A, 1968, 1116. 7 D. Chadwick, A. C. Legon and D. J. Millen, J. Chem. Sue., Faraday Trans. 2, 1972, 68, 2064. 8 M. Tsuboi, A. Y. Hirakawa, T. Ino, T. Sasaki and K. Tanagaka, J. Chem. Phys., 1964, 41, 2721. 9 R. M. Lees and J. G. Baker, J. Chem. Phys., 1968, 48, 5299. 10 M. C. L. Gerry, R. M. Lees and G. Winnewisser, J. Mol. Spectrosc., 1976, 61, 231. Paper 7/440; Received 9th March, 1987

ISSN:0300-9238    

DOI:10.1039/F29878302235

出版商:RSC    

年代:1987

数据来源: RSC

摘要:

J. Chem. SOC.,Faraday Trans. 2, 1987, 83( 12), 2247-2260 Are the Reactions Li + Na, and Na + K, Direct or Indirect? A Dynamics Study of Semiempirical Valence-bond Potential-energy Surfaces Victor M. F. Morais? and Antonio J. C. Varandas* Departamento de Quimica, Universidade de Coimbra, 3049 Coimbra Codex, Portugal Quasiclassical trajectory calculations have been carried out for the Li + Na, (v=O,J=lO) + LiNa+Na and Na+K,(v=O,J=lO) + NaK+K reac-tions at collision energies of 3.5 and 2.3 kcalt mol-’, respectively, using realistic potentials based on an extended-LEPS method. Most dynamics features suggest that those reactions proceed at such energies via an indirect mechanism. However, the analysis of the product internal state vibrational distributions show, particularly in the case of Na+ K2,that it is not possible to assign a vibrational temperature to such distributions.The result from LIF experiments, which suggest a direct mechanism for Li + Na2 but are less conclusive for Na+ K2, are thus only partly corroborated by the present calculations. The exchange reaction of alkali-metal atoms with alkali-metal dimers, M’+ M2 -+ M’M + M, has been the subject of much study, both experimental and theoretical.’ Since alkali-metal atoms are highly polarizable, the van der Waals attractions are particularly important and should reflect into the dynamics. Measurements of cross-sections for the exoergic reactions M’= Na and K with M2= K2, Rb2 and Cs2 and for the marginally endoergic reactions M’ = Rb and Cs with M2 = K2 and Rbz, have shown a large reactive cro~s-section,~’~ur2 100 A’,§ which suggests that a major fraction of the collisions captured by the long-range attraction might lead to reaction.The systems M3= Na,, K3 and Cs3 have also been observed in molecular-beam studie~,~ and the e.s.r. spectra of Na35 and K36indicated that they are chemical species ’ rather than just van der Waals molecules. The lowest potential-energy surface is therefore expected to have a well at the valence region of the potential, which also reflects on the measured large cross- sections. More recently* internal-energy distributions of reaction products using laser- induced florescence (LIF) have been reported on the Li + Na2 and Na+ K2 exchange reactions.A non-statistical internal-state distribution of the MM’ products was observed for the former reaction, which led the authors to conclude that there was an incomplete randomization of energy, thus implying a direct reaction mechanism. With Na + K2, however, the vibrational distribution could be described by a temperature, a finding compatible with a long-lived complex at thermal energies.8 The alkali-metal trimers are amongst the simplest systems for which potential-energy surfaces have been studied by quantum-mechanical calculation^.^-' ’ Since the atoms have one valence electron in an s orbital, the semiempirical valence-bond approach known as the LEPS method is particularly appropriate for obtaining such surface in an analytic form. Earlier applications of the LEPS method have disregarded long-range forces by assuming Morse and anti-Morse functions to describe the potentials for the singlet and triplet states of the diatomic fragments, respectively.Although the surfaces ?Permanent address: Instituto de Cihcias Biomedicas Abel Salazar, Universidade do Porto, 4000 Porto, Portugal. $1 cal= 4.184 J. $Unless specified otherwise, atomic units are used throughout this work: bohr radius (au)= a.u. of length = 0.529 177 A = 0.052 9177 nm; hartree energy ( Eh)= a.u. of energy = 27.21 1 652 eV = 4.359 821 aJ. 2247 Trajectory Calculations of Li -k Na2 and Na + K2 thus obtained1*-l3 display a short-range minimum associated with chemically stable alkali-metal trimers, the most stable geometry of the homonuclear trimers was found to be linear and symmetric.This result is in poor agreement with that obtained from accurate ab initio CI electronic-structure calculations for Li39y10 and Na3,I1 which predict such structures to be Cz, 'obtuse' with an opening angle close to 70". Re~ently'~~''we suggested that the Coulomb and exchange integrals in the London equation should be calculated from reliable analytic potential-energy curves for the X 'X+ and a 3C+ states of the dimers. By further using an effective 3X+diatomic potential function with a single parameter, which has been introduced to mimic ionic contributions to the wavefunction and is determined from the condition that the potential should reproduce the experi- mentally known binding energy of Li3,I6 the most stable structure for the trimers has been found to have a geometry in close agreement with the best ab initio results.Quasiclassical trajectory calculations for the Li and Na systems have been previously carried out by Whitehead" using the Whitehead-Gri~e'~,'~ LEPS potentials for LiNa, and NaLi,. He concluded that these exchange reactions proceed via a long-lined complex; as the energy is increased the reaction dynamics become direct. Unfortunately, detailed product internal-state (rotational and vibrational) energy distributions have not been reported, and hence a comparison cannot be made with the more recent measure- ments of Breford et a1.8for the Li + Na, and Na+ K2 reactions. In this work we report a detailed study of the dynamics of these reactions and provide theoretical data for such a comparison using realistic potentials we have published elsewhere.l5 Potential-energy Surfaces for LiNa, and NaK, The potential-energy surfaces used for the calculations of the present work are of the extended-LEPS form described previou~ly;~~,~' the reader is referred to the original papers for details. Fig. 1 shows equipotential bond-stretching contour plots for the LiNa, and NaK, surfaces at the optimum interbond angles of LLiNaNa=46.9* and LNaKK = 49.9", respectively. Further bond-stretching contour plots of the LiNa, and NaK, potential-energy surfaces for which the interbond angles (LLiNaNa and LNaKK, respectively) have been varied at each point so as to give the lowest potential energy are presented in fig.2(a)-(c). The optimum angles obtained from this procedure are also shown as equiangle contours in plots (b) and (d) of this figure. We note that such plots, which aim to optimize the remaining hidden coordinate," are similar to those previously reported by Rynefors and Nordholm" for a model of the KNaCl system. Fig. 3 shows equipotential contour plots for the Li and Na atoms moving around the equilibrium homonuclear diatomics, Na, and K2, respectively, which lie along the x-axis and have their centre of mass fixed at the origin. Note that the most stable form of these trimers is found to be a symmetric bent structure with the light atom at the middle; the geometric properties of such structures have been given el~ewhere.'~"' We further observe that the surfaces are almost flat with a variation in the bending angle.As in previous calculations,12313 the asymptotic valleys show no barrier for reaction. Trajectory Calculations and Discussion Trajectories have been run using the quasiclassical method well documented in the literature.20'21 In choosing the step size for the trajectory numerical-integration procedure (based on a combination of a fourth-order Runge-Kutta and an eleventh-order Adams- Multon method,,') the requirement has been imposed that four or more figures were conserved both for the total energy and total angular momentum. Batches of 2500 trajectories each were run of both systems with the diatomic molecule initially set at the vibrational state u = 0 and rotational quantum number J = 10.These conditions 13 -00-14.55 11.50 13.05 10.00 11-55 C CI.-.5 8.50 lO.05 a: 7.00 8.55 5.50 7.05 I4.OO 5.55 I I I I 4.00 5.50 7.00 8.50 10.00 11.50 13.00 5.55 7-05 8.55 10.05 11.55 13.05 14.55 RLiNsi/aO RNaK/ '0 Fig. 1. Equipotential bond-stretching contour plots for the LiNaz (a)and NaK, (b)alkali-metal trimeric molecules. The interbond angles are fixed at the corresponding values for the equilibrium triatomic geometry. Contours are equally spaced by 0.04 and 0.03 eV, starting at A = -1.398 and -1.025 eV, respectively, for plots (a) and (b). h, h,wl 0 19.00 19.00 16.50 16.50 14 .OO 14.00 i?--.' 11.5C 11.502a: 9 .oc 6 .SO 4*QO Fig.2. Equipotential optimized bond-stretching contour plots for LiNa, (a)and NaK, (c). In these plots the interbond angles (LLiNaNa and LNaKK, respectively) are chosen to minimize the potential energy. The values of the optimum angles are shown as equiangle contours in plots (b)and (d).Contours in plots (a)and (c) are equally spaced by 0.04 and 0.03 eV, starting at A = -1.398 and -1.025 eV, respectively, for LiNaz and NaK,. Contours in plots (b) and (d)are equally spaced by 5", starting at A = 0". V. M. F. Morais and A. J. C. Varandas 225 1 ici Fig. 3. Equipotential contour plots for: (a)an Li atom moving around an equilibrium ground-state Na, molecule and (b)an Na atom moving around an equilibrium ground-state K2 molecule.In both plots the centre of mass of the diatomic species, which lies along the X axis, is kept fixed at the origin. Contours are equally spaced by 0.01 eV, starting at A = -1.328 and -0.94 eV, respectively, for plots (a)and (b). h -10.80 -9.00 -7-20 -5.40 -3.60 -1.80 0.00 1.80 3.60 5-40 7.20 9eOO 10.80 Xl% Fig. 3.-( continued) h,Nul w Trajectory Calculations of Li + Na, and Na + K2 1.0-h2 0.8-u a 2 v 0.6---3.- I iLDL Os4-Ic .-Y2 0.2-2 0.o i1.0 0.0 0.2 0.4 0.6 0.8 1.0 impact parameter (reduced) Fig. 4. Opacity function showing the dependence of the reaction probability P( b) on the relative impact parameter (b/b,,,) for the systems (a) Li + Na, (ZI = 0, J = 10) and (b) Na + K, ( ZI = 0, J = 10).The collision energies are 3.5 and 2.3 kcal mol-’, respectively. correspond approximately to those observed in supersonic molecular beams,” and have also been adopted in previous quasiclassical trajectory The values of the maximum impact parameters are 8 A(=15.1a0) and 9.8 A(=18.5a0), respectively, for Li + Na, and Na + K2. Calculations have been carried out for collision energies of 3.5 and 2.3 kcal mol-I, respectively, for the Li + Na, and Na+ K2systems, since these mimic those observed in the LIF measurements.’ The partitioning of the internal energy of the products into vibrational and rotational energy constituents has been accomplished by Mu~kermann’s~~procedure, using the spectroscopic data we gathered elsewhere.l4,I5 The boxing procedure used to assign the quantum numbers in the product diatomics has been the conventional histogramic method; for key references and a critical analysis of this method see, e.g. ref. (24) and (25). For Li + Na,, the calculated reaction cross-section at the present collision energy is ur= 68.44k 1.91 A*, in good agreement with the value obtained by interpolating White-head’s results” for the same collision energy (a‘=64 A2). For Na+ K,, we have obtained d= 134.57 f3.00 A’, which is ca. twice as large as the average cross-section (uLv= 65 A‘) reported in ref. 2 though being close to the capture cross-section reported in the same reference (acap140 A’) based on a simple van der Waals potential. This supports the= conclusion that the major fraction of collisions drawn into the small internuclear distance by the long-range van der Waals attraction undergo an exchange reaction.Fig. 4 shows the dependence of the reaction probability P(b) on impact parameter for Li + Na, and Na+ K, at these collision energies, Although the variation of reaction probability with impact parameter for Li+Na, seems to be nearly uniform, a slight tendency towards a bimodal distribution is also apparent (see later). For Na+K, the reaction probability increases from zero at the maximum impact parameter to a maximum value near the zero impact parameter. Given the similarity of the collision energies for both systems, the difference in the opacity functions may be attributed to the maximum (15,) orbital angular momentum, which is larger for Na + K2 (L, = 285 A for this system us.167 A for Li+ Na2),thus offsettingto a larger extent the attractive nature of the NaK, potential surface, itself containing a well less deep than that of LiNa?. Fig. 5 reports the differential cross-sections for the Li+ Na:, and Na+ K2 systems. The marked feature from both distributions is the nearly symmetrical shape around 0 = 90”with sharp forward and backward peaks. As noted by Whitehead,I3 this behaviour V. M. F. Morais and A. J. C. Varandas n 30 60 90 120 150 180 0 30 60 90 120 150 180 scattering angle/" Fig. 5. Centre-of-mass differential cross-sections for: (a) the product LiNa molecule from the reaction Li + Na, (u = 0, J = 10); (b) the product NaK molecule from the reaction Na+ K2 (u = 0, J = 10).0 = 0" corresponds to the initial atom direction. 1.o 0.8 .--2 0.6 1-1 D 0.4 a, .--Y d E 0.2 0.0 0.0 0.8 1.6 2.4 3.2 4.0 0.0 1.2 2.4 3.6 4.8 6.0 complex lifetime/ps Fig. 6. Histograms of the complex lifetimes for: (a> Li+ Na2 (v = 0, J = 10) and (b) Na+ K2 (u = 0, J = 10); see text for definition of complex lifetime. is to be expected at low collision energies in systems for which the maximum orbital angular momentum is much larger than the internal angular momentum (J = 10 A for both systems). The shape of the distribution in this osculating regime can be obtained from the ratio of the lifetime of the complex to its rotational period: where I is the moment of inertia of the complex and L its angular momentum.From this expression, Whitehead has estimated for Li+ Na2 a rotational period of ca. 1ps. We have performed a similar calculation, and obtained T = 1.98 ps and T = 5.36 ps, respectively, for Li +Na, and Na +K,. Such values may be compared with the complex averaged lifetimes of 0.82 ps, both for Li +Na, and Na+ K,, which are obtained from the analysis of the trajectories assuming that the complex lifetimes can be defined13 as the amount of time during which the atoms can be inscribed within a circle of diameter 6.5 A. The histogram representations of the complex lifetimes at the above collision energies are of the form displayed in fig.6, which shows the characteristic exponential Trajectory Calculations of Li + Na, and Na + K2 shape of a random lifetime distribution. Bond distance us. time plots showing typical indirect-type [(a)and (c)]and direct-type [(6) and (d)]reactive collisions are presented in fig. 7. The migratory trajectories which are observed can be attributed to the almost flat nature of the potential surface with variation in bending angle, as noted in the previous section. In an attempt to correlate the type of collision with impact parameter, we have made histogram representations of the reaction probability us.impact parameter, P(b), for trajectories lasting longer than 1 ps (taken as the indirect type or statistical) and for those which are shorter-lived than that length of time (the direct type).The results are shown in fig. 8. Indirect-type Li + Na, and Na+ K2trajectories arise preferentially from collisions with medium or large impact parameters. Thus, indirect-type trajectories seem to be mainly due to complexes which are trapped by the centrifugal barrier. Direct-type trajectories are therefore mainly due to collisions with small impact parameters. For Li + Na, the corresponding distribution shows a maximum at 6 = 0 and a relative peak at b/b,,, = 0.9; for Na+ K2 there is a single maximum at b/b,,, == 0.3. The product energy distributions obtained from the trajectory calculations for the Li + Na, and Na+ K2 systems are shown in fig. 9, and are compared with the results obtained from a statistical (shown by crosses).For completness, we summarize here the statistical formulae used. Thus, for a long-range type -C/R6 potential and large collisional angular momentum, the product energy distributions for a loose three- body complex are given by the form P(E:)= (EL/ B;)’/’( E’ -E:) E: < Bk (2a1 =(E’-E:) E:> B:, (26) for translation, and P( EL) = [ E’-Ef,-(2/5)BL]B:” EL d E’-Bk (34 = (3/5)(E’-Ek)5’3 EL> E‘-B; (3b) for both vibration and rotation. In eyn (2) and (3) B; is the maximum centrifugal barrier in the exit channel of the potential energy surface, which is given by B; = (p/~’)~’~(C6/CL)’/2E, (4) E and E: are the reactant and product translational energies, EL is the product vibrational or rotational energy, E’ is the total energy available to products, p and p’ are the reactant and product reduced masses, and C, and Ciare the leading van der Waals coefficients of the long-range entrance and exit channel potentials.Since accurate values of c6 and Ck are lacking in the literature, they have been approximated here by the sum of the van der Waals constants for the interactions involving the isolated atom and the terminal atoms of the partner diatomic, i.e. C6(A-BC)= C6(A-B)+ C6(A-C). Agreement with the statistical results is good for both the translational and rotational energies. However, it ranges from poor (in the case of Na+K,) to moderate (for Li+ Na,) in the case of the vibrational energy. The averaged values of these energy distributions are f (vib) :f(rot):f(trans) = 30 (32) :34 (52):36( 16) for Li + Na, =33 (27):27(55):40(15) for Na+K, where the values in parentheses represent those obtained from the LIF measurements, and the statistical results correspond to an equipartition of the total energy amongst the three energy modes.Again, our theoretical values for the product-averaged energy distributions seem to suggest an indirect-type mechanism proceeding mainly uia a long-lived complex which is non-rigid and non-linear. In fact, they generally corroborate the results reported previously by Whitehead for Li+Na,, despite the fact that the surfaces he used show significant differences from those used in the present study. V. M. F. Morais and A. J. C. Varandas h 'D v \iJ' Trajectory Calculations of Li + Na, and Na + K2 1 h, I:iI0.20.0 0.0 0.2 0.4 0.6 0.8 1.0 0.0 0.2 0.4 0.6 0.8 1.0 impact parameter (reduced) Fig.8. As fig. 4,but showing separately reacting trajectories which last shorter than 1 ps [(a)and (c)] and longer than 1ps [( b) and (d)]. Opacity functions (a) and (b)are for Li + Na,, while those labelled (c) and (d) are for Na+ KZ. Fig. 10 reports the vibrational-state distributions for NaLi formed in the reaction Li +Na, -+LiNa+ Na and for NaK formed in the reaction Na+ K2-+NaK+ K. Also shown for comparison are the experimental points of Breford et aL8 for Li + Na, and the Maxwell- Boltzmann vibrational distributions assuming a vibrational temperature of 300 K. [The vibrational energies employed in the calculation of the Maxwell- Boltzmann distributioo were obtained by solving the Schrodinger equation for the nuclear motion using the LiNa and NaK potential functions reported in ref.(151.1 The vibrational product distribution of LiNa extends up to u” =9, in good agreement with the experimentally observed value of z1= 7. For NaK the vibrational distribution extends as far out as v”= 14, whereas the maximum value of u’’observed in the LIF measurements was 2.”’ =4. Note the non-thermal nature of the vibrational distribution for NaK, which shows a plateau near v”= 2. Although the vibrational distribution from the present work shows no peak near o =2 for Li + Na,, it is nonetheless not unambiguous to assign a vibrational temperature to such a distribution.Finally, the discrepancies found between the quasiclassical trajectory calculations from the present work and the experimental resuits may justify a brief critical assessment of this approach. Since the quasiclassical trajectory method inherently misses quantum effects such as tunnelling, resonance and interference effects, one may question whether those discrepancies are genuine or a result of the quasiclassical approach. Obviously, a thorough answer to this question would require an accurate solution of the quantum- dynamical equations for the current alkali-metal atom-dimer reactions. However, this task is too formidable at present for all but a few simple systems and models. Among the real systems, the ground-state H+H2 exchange reaction is by far the most studied.V. M.F.Morais and A. J. C.Varandas :1.0 c.’ 7--0.6 t-71 1 i++bpl>*F* 0.ou 0.0~ 0.0 0.2 0.4 0.6 0.8 1.0 0:o 0.2 0.4 0.6 0.8 1.0 0.2 0.4 c fractional energy (T) fractional energy (R) fractional energy (V) Fig. 9. Translational (Tj, rotational (R) and vibrational (V) product energy distributions for: (a)-(c)Li + Na, (u = 0, J = 10) and (d)-(f) Na+ K2 (v =0, J = 10). Shown for comparison are the predictions of a statistical model. 0.8 0.6 0.4 0.2 10.c 0.01 3 579 vibrational quantum number Fig. 10. Vibrational product quantum-state distributions for the reactions (a)Li + Naz (u= 0, J = 10) and (b) Na+ K2 (u= 0, J = 10). Shown for comparison in the vibrational plots are the .~experimental LIF results (0) of Breford et ~1 Also shown in all plots are the Boltzmannian curves ( + ) assuming thermal equilibrium at T = 300 K.As previous studies of this H -tH2 reaction show [see, e.g., ref. (25) and references therein], the quasiclassical dynamics gives good overall agreement, in the sense of an average, with the quanta1 results, except near the reaction threshold. In addition, the greater masses of the colliding partners would lead us to anticipate that the quasiclassical method would be even more reliable for studying the alkali-metal atom-dimer reactions. Trajectory Calculations of Li i-Na, and Na + K2 However, it may be argued that the information from reaction dynamics on surfaces with barriers (such as H + H2) is hardly transferable to barrier-free surfaces and this prevents us from carrying this discussion further.In summary, from the theoretical side, the present discrepancies between trajectory calculations and experiments1 results are probably due to both inaccuracies in the dynamics approach and the potential-energy surfaces themselves. Conclusions We have shown that most features of the Li + Na, and Na+ K2 dynamics suggest an indirect reaction mechanics although some others are typical of a direct mechanism. Bearing in mind that these two mechanisms correspond to ideal extreme situations, it is no surprise that our calculations favour an indirect mechanism although they show a significant contribution from direct-type collisions. Since the experimental internal energy distribution measurements reported by Engelke et al.are non-specific with respect to the rotational-vibrational state of the reagent molecules, further trajectory calculations are needed to mimic their experimental conditions. In addition, it would be interesting to calculate by accurate ab initio methods the potential-energy surfaces of the hetero- nuclear alkali-metal trimers and use them for dynamics studies. Work along these lines is in preparation. This work was supported by the Instituto Nacional de Investigaqio Cientifica (INIC) Portugal. The allocation of computer time at the University of Oporto is also gratefully acknowledged. References 1 M. R.Levy, Prog. React. Kine?., 1972, 10, 86. 2 J. C. Whitehead and R. Grice, Faraday Discuss. Chem. SOC., 1973, 55, 324; 374. 3 D. J. Mascord, P. A. Gorry and R. Grice, Faraday Discuss. Chem. SOC., 1976, 62, 16. 4 D. M. Lindsay, D. R. Herschbach and L. A. Kwiram, Mol. Phys., 1976, 32, 1199. 5 G. A. Thompson and D. M. Lindsay, J. Chem. Phys., 1981, 74, 959. 6 P. J. Foster, R. E. Leckenby and E. J. Robbins, J. Phys. B,1968, 2, 478. 7 A. Herrmann, S. Leutwyler, E. Schumacher and L. Woste, Helv. Chim. Acra, 1978, 61, 453. 8 E. J. Breford, F. Engelke and G. Ennen, Chem. Phys. Lett., 1983, 100, 499. 9 W. H. Gerber and E. Schumacher, J. Chem. Phys., 1978, 69, 1962. 10 H-0. Beckmann, Chem. Phys. Left., 1982, 93, 240 and references therein. 11 R. L. Martin and E.R. Davidson, Mol. Phys., 1978, 35, 1713. 12 J. C. Whitehead and R. Grice, Mol. Phps., 1973, 26, 267. 13 J. C. Whitehead, Mol. Phys., 1975, 29, 177. 14 A. J. C. Varandas and V. M. F. Morais, Mol. Phys., 1982, 47, 1241. 15 A. J. C. Varandas, V. M. F. Morais and A. A. C. C. Pais, Mol. Phys., 1986, 58, 285. 16 C. H. Wu, J. Chem. fhys., 1976, 65, 3181. 17 J. C. Whitehead, Mol. Phys., 1976, 31, 549. 18 J. N. Murrell, S. Carter, S. Farantos, P. Huxley and A. J. C. Varandas, Molecular Porenrial Energy Functions, (Wiley, Chichester, 1984). 19 K. Rynefors and S. Nordholm, Chem. Phys., 1985, 95, 345. 20 M. Karplus, R. N. Porter and R. D. Sharma, J. Chem. Phys., 1965, 43, 3259. 21 J. T. Muckermann, Quantum Chemistry Program Exchange no. 229 (Indiana University, Bloomington, Indiana, 1973).22 M. P. Sinha, A. Schultz and R. N. Zare, J. C'hem. Phjvs., 1973, 58, 549. 23 J. T. Muckermann, J. Chem. Phys., 1971, 54, 1155. 24 J. Bowman and S. C. Leasure, J. Chem. Phyy., 1977, 66, 1756. 25 A. J. C. Varandas, Chem. Phys., 1982, 69, 295. 26 S. A. Safron, N. D. Weinstein, D. R. Herschbach and J. C. Tully, Chem. Phys. Left., 1972, 12, 564. 27 P. J. Dagdigian, H. W. Cruse, A. Shultz and R. N. Zare, J. Chem. Phys., 1974, 61, 4450. Paper 7/443; Received 10th March. 1987

ISSN:0300-9238    

DOI:10.1039/F29878302247

出版商:RSC    

年代:1987

数据来源: RSC