J. Phys. Chem. B 2008, 112, 15867–15874
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High Pressure Raman Spectroscopic Study of Deuterated γ-Glycine Ajay K. Mishra, Chitra Murli,* and Surinder M. Sharma High Pressure Physics DiVision, Bhabha Atomic Research Centre, Mumbai 400 085, India ReceiVed: July 19, 2008; ReVised Manuscript ReceiVed: October 10, 2008
Raman spectroscopic investigations of deuterated γ-glycine, carried out up to 21 GPa, indicate emergence of a new phase, which is similar to the δ-phase, reported to be formed from the undeuterated γ-glycine at 3 GPa and the transformation to this phase is complete by 6 GPa. Observed pressure -induced variations in CD2 and N-D stretching modes indicate significant changes in the hydrogen-bonding interactions. Around ∼15 GPa, splitting of CD2 and C-C stretching modes and discontinuous changes in the slope of CO2 and N-D stretching modes indicate another structural rearrangement across this pressure. The Raman spectra of retrieved phase at ambient conditions suggest that it may be a layered structure similar to the ζ-phase reported to be formed on decompression of the nondeuterated δ-glycine. Introduction Pressure-induced changes in the hydrogen-bonding interactions in diverse compounds such as ice, mineral dihydroxides, e.g. M(OH)2 (M ) Mg, Ni, Ca, Co, etc.), proteins, amino acids, and many organic as well as inorganic compounds have been reported in the literature. The high pressure behavior of the materials with hydrogen bonds depends on the nature and the number of hydrogen bonds present in a material. In the case of M(OH)2 mineral dihydroxides, which have been investigated with the anticipation that the hydrogen bonds would strengthen under pressure, these compounds are found to show pressureinduced disorder in the hydrogen sublattice at higher pressures.1 In the case of ice, which have several polymorphs, hydrogenbonding interactions change significantly across different phases. At very high pressures ∼60 GPa, symmetrization of hydrogen bonds have been claimed.2 Study of hydrogen bonds in various materials, in particular, biologically significant compounds is important as their contribution to the overall intermolecular interactions is quite significant. In the case of amino acids, which are characterized by more than one hydrogen bond, the compressibility of hydrogen bonds were found to have diverse character.3 The polymorphs of glycine, the simplest amino acid display structural phase transitions to structures with altogether new kind of hydrogen-bonded networks.4-12 Though neutron diffraction studies would be ideal to study hydrogen-bonding interactions, a first hand knowledge of changes in these interactions can be provided by spectroscopic studies. Deuteration of the hydrogen-bonded materials also make it much more suitable for studying hydrogen-bonding interactions as the vibrational modes related to hydrogen-bonding interactions are well resolved and can be studied in more detail. Investigation of spectral changes on deuteration is also found to have relevance in the context of understanding sensory perceptions. In fact there have been efforts to correlate the olfactory discrimination of normal and deuterated glycine by fish with their different vibrational properties.13,14 Standard conventions of spectral changes associated with hydrogen bonds is that when an X-H----O (X ) O, N, C, etc.) hydrogen bond is formed, X-H covalent bond elongates and * To whom correspondence should be addressed. E-mail: chitrakmg@ yahoo.com.
consequently X-H stretching frequency red shifts.15 Using the natural bond orbital analysis, Weinhold et al.16 have shown that the charge transfer from lone pair of an electron donor is directed to the σ* antibonding orbital of the proton donor, X-H bond. The increase of electron density in the σ* antibonding orbital weakens the X-H bond which leads to elongation and reduction in the X-H stretching frequency (red shift). Red shift has been commonly associated with the increase in the hydrogen bond strength. However there are many recent investigations which report blue shifting of X-H stretching mode when hydrogen bonds are formed.17-21 The red shifting of X-H stretching mode is attributed to the conventional H-bonding and the blue shifting of the same has been attributed to improper H-bonding. There have been theoretical calculations as well as vibrational studies of many hydrogen-bonded complexes that have been aimed at understanding of the nature of different kinds of hydrogen-bonding formations.22 Hobza et al. have proposed that blue-shifting hydrogen bonding can be explained by charge transfer from proton acceptor to remote atoms in X instead of the σ* antibonding orbitals of the X-H bond, which is followed by structural reorganization of proton donor framework resulting in the contraction of C-H bond.23 Another theory by Scheiner et al.21 has proposed that improper and proper hydrogen bond leads to similar change in the remote parts of the hydrogen bond donor. The difference between proper (red-shifting) and improper (blue-shifting) hydrogen bonding have been explained in terms of the more dominant interaction energy involved in the process.22 For red-shifting hydrogen bond complexes, the ratio of the induction and dispersion energy is larger than one and the opposite is true for improper hydrogen bond complexes.22 In the blue-shifting complexes, dispersion interaction helps to contract the X-H bond and therefore causes the blue shift.22 In the case of investigations of hydrogen-bonding interactions under pressure, there are various situations, such as red shifting, blue shifting, negligible change, and so forth, under pressure.24,25 As the increase in the density of sample under pressure can cause blue shifting, it is rather nontrivial to discriminate the contribution of hydrogen bonds to the blue shifting of the vibrational modes. In the light of above discussions, it is of importance to look in to changes in the X-H stretching modes
10.1021/jp806381e CCC: $40.75 2008 American Chemical Society Published on Web 11/17/2008
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Figure 1. Raman spectra of deuterated γ-glycine at few representative pressures during compression in the spectral region (a) 100-250; (b) 250-850; (c) 800-1300 cm-1.
(X ) C, N, O, etc.) of various compounds under pressure in the context of hydrogen-bonding interactions as it would help to resolve the issues related to spectroscopic manifestations of hydrogen-bonding interactions under pressure. High pressure investigations of various amino acids have been carried out rather extensively in the recent years.4-12,26-37 However, so far only one high pressure neutron diffraction study of deuterated amino acid L-serine has been reported in the literature.30 The results obtained when studying pressure-induced phase transitions in deuterated samples30 were similar to those reported previously for the nondeuterated samples37,38 although not identical with them. In the case of undeuterated L-serine, while Moggach et al. reports single crystal to single crystal phase
transition from L-serine-I to an orthorhombic high-pressure phase, L-serine-II, in the pressure range 4.8 -5.4 GPa, Boldyreva et al. has reported two phase transitions into this compound at 5.3 and 7.8 GPa. In comparison to these studies, in the case of deuterated L-serine the occurrence of the new high pressure phases are identical to the undeuterated one with transition pressures nearly same, which are 4.6-5.2 GPa and 7.3-8.1 GPa.30 High pressure X-ray diffraction and Raman studies on γ-glycine, report a phase transition to a new phase δ at 3 GPa.11,8,10 It may be noted here that two high pressure groups have carried out structural investigations of the undeuterated γ-glycine using X-ray diffraction. An irreversible phase transi-
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Figure 2. Raman spectra of deuterated γ-glycine at few representative pressures during compression in the spectral region 1400-2400 cm-1; dashed arrows indicate emergence of new blue-shifted modes; ! and * indicate unidentified peaks.
Figure 3. Raman spectra of deuterated γ-glycine at few representative pressures during decompression in the spectral region 100-1300 cm-1.
tion in the γ-glycine was first reported by Boldyreva’s group and this phase is termed as δ phase and its crystal structure was reported to be Pn,10 which on release of pressure at 0.6 GPa transforms to another new phase ζ and both the new phases were reported to have a layered structure. Another group from Edinburgh has termed the new high pressure phase observed at 3 GPa as ε phase. X-ray diffraction studies of Edinburgh’s group report that in the high pressure phase, there is a likelihood of C-H---O hydrogen bonds getting strengthened at the cost of the N-H---O bonds.11,10 Though Raman studies on undeuterated glycine report breaking of the weakest N-H---O hydrogen bond across the transition, the nature of pressure-induced changes in the other hydrogen-bonding interactions have not been reported. It would therefore be of interest to investigate deuterated γ-glycine under
pressure using Raman spectroscopy to look for changes in the high pressure behavior, if there is any, compared to the normal undeuterated γ-glycine and utilize the distinct spectroscopic signatures to understand pressure-induced changes in the hydrogen-bonding interactions in more detail. As no high pressure studies are available for deuterated γ-glycine and also high pressure data for undeuterated γ-glycine are available only up to 8 GPa, we have carried out high pressure Raman spectroscopic investigations of fully deuterated γ-glycine at higher pressures up to 21 GPa. These studies on fully deuterated γ-glycine, in which both N-H and CH2 stretching modes are replaced by well resolved N-D and CD2 stretching modes would be useful to understand pressure-induced changes in the N-D---O as well as C-D---O hydrogen-bonding interactions.
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Figure 4. Raman spectra of deuterated γ-glycine at few representative pressures during decompression in the spectral region 1400-2400 cm-1.
Structural Details. In the structure of γ-glycine, glycine molecules are linked by two hydrogen bonds N-D1---O1 and N-D2---O2 to form helices around the crystallographic 32 screw axes.10 A third lateral hydrogen bond N-D3---O1 connects the helices thus forming a three-dimensional network. The structural refinement of the neutron diffraction data collected on polycrystalline samples of commercially available (fully deuterated) d5-glycine from Aldrich Chemical Co., Inc. at Dhruva reactor (situated at our center) could be fitted to fully deuterated γ-phase.39 The refined structural parameters of γ-glycine are a ) 7.0280(4) Å, c ) 5.4814(5) Å, and V) 234.478(1) Å3 at ambient conditions and are in good agreement with the earlier reported values.40 Hydrogen bond parameters obtained for deuterated γ-glycine are D1---O1 ) 1.774 Å, D2---O2 ) 1.787 Å, and D3---O1 ) 1.914 Å, while the corresponding values reported for the undeuterated γ-glycine are 1.763, 1.828, 1.960 Å respectively.40 Two of the hydrogen bond parameters, D2--O2 and D3---O1, are not found to obey the Ubbelohde effect.41 Experimental Details Powder crystalline samples of deuterated γ-glycine were loaded into hole of diameter 140 µm drilled in a stainless steel gasket indented to a thickness of 70 µm in a Mao-Bell type of diamond anvil cell. Raman spectra were recorded using our indigenously developed micro Raman system around HR 460 spectrograph, a super notch filter, and a liquid nitrogen-cooled Spectrum One CCD detector. Laser line (532 nm) of diodepumped solid-state laser was used as excitation wavelength. Neon lines were used for the calibration of Raman as well as ruby spectra which were recorded for pressure measurement in a diamond anvil cell. The assignments of various Raman modes recorded under ambient conditions have been carried out by comparing the Raman spectrum reported for normal undeuterated glycine.42 For the assignment of some of the modes we have also used the high pressure behavior of Raman modes of the undeuterated γ-glycine.10 Results and Discussion High pressure Raman spectra of deuterated γ-glycine in the spectral regions 100-250, 250-850, 850-1300, and 1400-2500
cm-1 are shown in Figures 1a-c and Figure 2, respectively. Figure 3 and Figure 4 show the Raman spectra on release of pressure from 21 GPa. Variation of Raman shifts with pressure in the spectral regions (100-850 cm-1), (850-1300 cm-1) and (1400-1700 cm-1) are shown in Figures 5a-c, respectively. Pressure-induced changes in the frequency of the N-D and C-D stretching modes are shown in Figures 6 and 7, respectively. Comparison of the Raman spectra at ambient, high pressure, and retrieved (released from 20 GPa) phase are shown in Figure 8. As seen from Figure 1 and Figure 2, the observed variations in several Raman modes suggest that this compound has undergone significant structural changes across 3 GPa. The intensity of the COO rocking mode (∼475 cm-1) reduces drastically prior to the transition and across the transition a new mode appears adjacent to it. ND3 torsional mode appears as a weak broadband around 350 cm-1. This mode is found to split at higher pressures. However, as this mode is very weak, individual peaks could not be fitted and hence is fitted as a single peak. As shown in Figure 5a, this mode is found to show stiffening with a small slope change across 3.8 GPa and remains nearly constant up to 11.6 GPa beyond which again shows stiffening. The high pressure behavior of this mode is found to be somewhat similar to that of N-D stretching band (I) (2098 cm-1) associated with strongest intralayer hydrogen bond (discussed in the subsequent section). Above the transition pressure, COO wagging mode (∼521 cm-1) is replaced by a new blue-shifted mode adjacent to it while ND3 rocking mode (812 cm-1) is replaced by a red-shifted one. C-C stretching (∼870 cm-1), CD2 wag (∼971 cm-1), CD2 rock (∼728 cm cm-1), CD2 torsional (∼961 cm-1), and CD2 bending modes (∼1078 cm-1) show stiffening, C-N stretch (∼1026 cm-1) shows softening, and the mode at 950 cm-1, which may be assigned to one of the ND3 rocking modes, starts picking up intensity across the transition pressure. The spectral changes due to the phase transition that started at 3 GPa are found to be complete by 6 GPa and the new phase is found to be stable up to 10 GPa with no further discontinuous changes. The Raman spectra of the new phase are similar to the Raman spectra of the δ phase reported for undeuterated glycine.10 Structural
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Figure 5. Variation of Raman mode frequencies with pressure (a) 100-850 cm-1; (b) 850-1300 cm-1; (c) 1400-1600 cm-1; closed symbols denote data on compression; open symbols denote data on decompression.
changes above 10 GPa are discussed separately. The high pressure behaviours of N-D and CD2 stretching modes would be discussed in detail in the subsequent sections. N-D Stretching Modes. As shown in Figure 2, broadband observed around 2100 cm-1 corresponds to the N-D stretching band (I) which is associated with the shortest hydrogen bond N-D1---O1. The band observed at 2300 cm-1 corresponds to the N-D stretching band (III) which represents the longest hydrogen bond N-D3---O1. The N-D stretching band (II) that appears around 2250 cm-1 may correspond to the medium strength hydrogen bond N-D2---O2. All the N-D bands were found to occur at frequencies that are lower by a factor of ∼1.3 to those of the undeuterated γ-glycine. From the observation of N-D stretching band (I) as presented in Figure 6, due to large error bars it is difficult to discern a
clear trend up to ∼3 GPa. However, one can see that there are no drastic changes in this mode across the transition pressure. It displays very small variation in the pressure range 3-10 GPa. This is consistent with the earlier reports on undeuterated glycine and implies that the strongest hydrogen bond is relatively less compressible.11,8,10,7 On further increase of pressure our data is suggestive of a slope change across 10 GPa with stiffening as well as broadening. The broadening of this N-D stretching mode (I) in particular may be due to disorder in the hydrogen sublattice associated with it.1 As high pressure experiments have been carried out under nonhydrostatic conditions (no pressure transmitting medium was used to ensure that there is no degradation of the sample), it is not possible to conclude with certainty whether the disorder is intrinsic in nature. In addition, it is of interest to note that the relative intensity of the N-D
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Figure 6. Variation of N-D stretching modes with pressure. Closed symbols denote data on compression; open symbols denote data on decompression. For compression data solid lines are drawn as an aid to eye; full width half-maxima of the modes are given as error bars.
Figure 7. Variation of C-D stretching modes with pressure. closed symbols denote data on compression; open symbols denote data on decompression. For compression data solid lines are drawn as an aid to eye and the dotted lines are for decompression; full width halfmaxima of the modes are given as error bars.
stretching band (I) increases at higher pressures. Though in the case of infrared absorption the increase in the intensity is attributed to strengthening of hydrogen bonds, for Raman intensity such a correlation is not straightforward. However, it would be of interest to do neutron diffraction studies to find out whether this suggestive stiffening of N-D band (I) at pressures above 10 GPa is just due to increase in density or it is an indication of strengthening of improper hydrogen bonds. N-D stretching band (II) shows a small discontinuous change across 3 GPa and remains nearly constant up to 10 GPa. Above
Mishra et al. this pressure it is not possible to follow this mode as it is merged in the background of C-D bands. The N-D stretching band (III) softens up to a pressure of 3 GPa. As shown in Figure 6, above this pressure it shows discontinuous stiffening to a frequency higher by nearly 80 cm-1, which is lower than the value of ∼100 cm-1, which is reported for undeuterated glycine.10 It is also interesting to note that the full width half-maximum as well as relative intensity show a decreasing trend at higher pressures above 10 GPa, which may be a consequence of breaking of this hydrogen bond as reported for normal undeuterated γ-glycine during the transition from γ to δ phase.11,10,8,7 CD2 Stretching Modes. As shown in Figure 2, in deuterated γ-glycine, there are three intense peaks appearing in the region 2100-2300 cm-1. Modes appearing at 2178 cm-1 and 2258 cm-1 are assigned as symmetric and asymmetric CD2 stretching modes respectively. Compared to the undeuterated glycine, symmetric and asymmetric CD2 stretch bands appear at a value decreased by a factor 1.36 and 1.32, respectively. In addition there are weak shoulder peaks adjacent to these two modes which may be due to Davydov splitting as suggested for deuterated alanine.43 The mode appearing at 2129 cm-1 may be due to Fermi resonance as reported for C-deuterated glycine.44 As shown in Figure 7, CD2 stretching modes show a small stiffening with a dν/dP, 2.27 cm-1/GPa for symmetric stretch and 3.12 cm-1/GPa for asymmetric stretch up to a pressure of 2 GPa. As seen in Figure 2, new blue-shifted CD2 stretching modes start developing at the cost of old ones at 3 GPa and these changes are complete at 6 GPa. Appearances of new modes suggest a phase transition to a new phase. In the new phase, in the pressure range up to 10 GPa, the CD2 stretch modes are found to stiffen at a higher rate with dν/dP, 3.75 cm-1/GPa for symmetric stretch and 4.6 cm-1/GPa for asymmetric stretch. It is also noted that dν/dP for CO2 symmetric stretch mode (1407 cm-1), before the transition is 5.19 cm-1 and after the transition is 3.12 cm-1/GPa. The mode at 2129 cm-1 reduces in intensity and becomes unobservable at pressures above 11 GPa. As displayed in Figures 2 and 7, at the transition pressure, CD2 stretching modes show a blue shift of nearly 32 cm-1 and CO2 symmetric stretching mode (1407 cm-1) show a red shift of ∼17 cm-1. C-N stretching mode also shows softening across the transition. It may be noted that in the case of improper hydrogen bonds, electron density is transferred to the remote part of the donor and thereby it is expected that there is elongation of the bonds associated with it which results in the red shift of its frequency.19,20,45 In the case of deuterated γ-glycine under pressure, we observe blue shifting of CD2 stretching mode accompanied by the red shift of not only the CO stretch but also the C-N stretch modes. Hence it is of interest to verify whether the blue shifting of CD2 stretching modes do imply formation of improper C-D---O hydrogen bonds. It may be noted that across the transition, a large reorganization of atomic positions is also expected. Moreover blue shifting of the vibrational modes can also arise due to increase in the density under pressure. As we have mentioned in the introduction it is difficult to establish whether the observed blue shifting is due to hydrogen-bonding interactions without detailed structural analysis. It may be noted that X-ray diffraction studies of normal undeuterated glycine do indicate the possibility of strengthening of C-H---O hydrogen bonds in the high pressure ε phase (same as δ phase reported by Boldyreva’s group).11 However, neutron diffraction studies which can provide reliable hydrogen bond
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Figure 8. Comparison of Raman spectra of the initial phase, completely released, and the high pressure phase at 6 GPa.
distances are required for understanding the observed changes in the CD2 stretching modes in terms of hydrogen-bonding interactions. Pressures above 10 GPa. The rate of stiffening of many of the modes is found to increase above 10 GPa. We also observe significant broadening of both N-D and CD2 stretching modes above this pressure. At pressure ∼ 15 GPa, as shown in Figures 1 and 2, C-C stretch (870 cm-1) as well as CD2 asymmetric stretch (2258 cm-1) show splitting. Above this pressure N-D stretching band (III) is no more discernible. Though the splitting of CD2 stretching modes are generally seen in the deuterated compounds, which are attributed to Davydov correlation splitting, other spectral changes such as splitting of C-C stretching modes, discontinuous changes in the slope of CD2, CO2, N-D stretching modes, and so forth, suggest that there could be a phase transition around this pressure. It would be of interest to investigate whether the simultaneous splitting of C-C and CD2 stretching modes correspond to any new hydrogen bond formation at higher pressures. Structural investigation would be useful to resolve this issue. Structural Changes on Release of Pressure. On release of pressure, the splitting of the CD2 asymmetric stretching band is found to persist until 3 GPa. The band corresponding to 2129
cm -1, which had disappeared after 10 GPa during compression, reappears on release at 15 GPa. It is of interest to note that the blue-shifted C-D bands observed in the new phase do not red shift accordingly on release of pressure. There is a remnant blue shift of CD2 stretching mode on release. The shoulder peaks of the CD2 bands are also not well resolved on release. In the case of ND stretching band (I) there is a remnant red shift on release. It is also found that the frequency of ND (III) is found to be lower than the new high pressure δ phase but higher than (blueshifted) the initial phase. On release around 0.9 GPa, there are a number of spectral features such as splitting, a small slope change, and so forth, which indicate a structural rearrangement though not as drastic as the phase transition observed while compressing to 3 GPa.10 The spectral features of the released phase suggests that this phase may be similar to the ζ phase as well as the other layered polymorphs of undeuterated glycine, such as R, β, and so on, and not the initial γ phase which is characterized by helical network of hydrogen bonds. As shown in Figure 8, the retrieved phase is found to have a remnant disorder which is indicated by increase in the width of some of the observed Raman modes. To summarize, deuterated γ-glycine undergoes a structural phase transition to new crystalline phase at ∼3 GPa which is
15874 J. Phys. Chem. B, Vol. 112, No. 49, 2008 similar to δ phase observed earlier in the undeuterated γ-glycine. The high pressure δ phase is found to be stable up to 10 GPa. Beyond 10 GPa, the observed spectral features indicate onset of disorder. Around ∼15 GPa, splitting of CD2 stretch modes and other spectral changes indicate structural rearrangement in particular in the C-D sublattice. On release of pressure, this splitting persists until 3 GPa. The Raman spectra of the retrieved phase are similar to the ζ phase of undeuterated glycine and other layered polymorphs of glycine. The natures of pressureinduced structural transitions in γ-glycine do not seem to be altered much by deuteration. High pressure structural investigations of this compound using neutron diffraction study which can provide hydrogen bond parameters would be helpful to understand the spectroscopic implications of hydrogen-bonding interactions under pressure. Acknowledgment. Authors would like to thank Himanshu Poswal for his useful suggestions. References and Notes (1) Murli, C.; Sharma, S. M.; Kulshreshtha, S. K.; Sikka, S. K. Physica B 2001, 307, 111. (2) Aoki, K.; Yamawaki, H.; Sakashita, M.; Fujihisa, H. Phys. ReV. B: Condens. Matter. 1996, 54 (22), 15673. (3) Boldyreva, E. V. Acta Cryst. A. 2008, 64, 218–231. (4) Murli, C.; Sharma, S. M.; Karmakar, S.; Sikka, S. K. Physica B 2003, 339, 23. (5) Boldyreva, E. V.; Ahsbahs, H.; Weber, H. P. Z. Kristallogr. 2003, 218, 23. (6) Boldyreva, E. Cryst. Eng. 2004, 6, 235–254. (7) Boldyreva, E.; Ivashevskaya, S.; Sowa, H.; Ahsbahs, H.; Weber, H. P. Dokl. Phys. Chem. 2004, 396, 358–361. (8) Boldyreva, E. V.; Ivashevskaya, S. N.; Sowa, H.; Ahsbahs, H.; Weber, H. P. Z. Kristallogr. 2005, 220, 50. (9) Goryainov, S. V.; Kolesnik, E. N.; Boldyreva, E. V. Physica B 2005, 357, 340. (10) Goryainov, S. V.; Kolesnik, E. N.; Boldyreva, E. V. Chem. Phys. Lett. 2005, 419, 49. (11) Dawson, A.; Allan, D. R.; Belmonte, S. A.; Clark, S. J.; David, W. I. F.; McGregor, P. A.; Parson, S.; Pulham, C. R.; Sawyer, L. Cryst. Growth Des. 2005, No. 4, 1415. (12) Bordallo, H. N.; Boldyreva, E. V.; Buchsteiner, A.; Koza, M. M.; Landsgesell, S. J. Phys. Chem. B 2008, 112 (29), 8748–8759. (13) Hara, J. Experientia 1977, 33, 618–619. (14) Turin, L. Chem. Sens. 1996, 21, 773. (15) Krishnan, R. S.; Krishnan, K. Proc. Indiana Acad. Sci. 1964, 60A, 11. (16) Weinhold, F. A. J. Mol. Struct. 1997, 398, 181. (17) Chang, H. C.; Jiang, J. C.; Lai, W. W.; Lin, J. S.; Chen, G. C.; Tsai, W. C.; Lin, S. H. J. Phys. Chem. B 2005, 109, 23103. (18) Su, C. C.; Chang, H. C.; Jiang, J. C.; Wei, P. Y.; Lu, L. C.; Lin, S. H. J. Chem. Phys. 2003, 119 (20), 10753–10758.
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