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Far-infrared spectra of imidazole monocrystals
Vohimr HO. number 3
H.R. ZELSMAXN ’ _P. EWZFFON ’ md Y. MARECWAL ’ Drboraroke de R&onance ~~f~gn&&e. D&arremenr de RedrercJxeFondamenru!e. Cent-e d %rudesn’ickire~ de Grenoble-85X. F38ojl Grenoble Cede-q Fr~re Keceised 17 Ma)’ 19S4; in final form 6 JuIy I984
The spectm of imidatok monocrysralshxing their c nis (the averagedirection of H-lmndst in the obsmarion plane have ken recorded in rhsnnge 50-500 cm-’ _ 7&e tt*o prtramrrcrsstied are umpsr;irure and pokr&.ation. From the xo-iation of pobriwtion. tie are able to gjw 3 clear rtssi_gnmenr of all vibr~~%o~,arid particularly of those stiIl lxking in the iitrrxure. The chsngcs of tie spectra with temperature cm be inrerpreted, in s f=sr z+pprati5oon, by assuming rhar alf modes are mod&ted by a vibntion lihich has _Ifrequency f&ins betueen 30 md 60 cm-’ _
1- Introduction In tbe far-IR r&on_ H-bonds X-H.--Y arc ar rhe origin of bands corresponding. in a first appro_Gmation. to the relative vibrations of the two molecuks X-H and Y. These vibrations bag been shorn to influenc2 srrongfy the pS ribrations fl---G] and ro be at the or@ of their rhermsl sensitivities. They may even be thoughr to influence srrongly mosf of the proprties of H-bonds_ which hss importanr biofogical consequences_ esspctc.ialIuy wr‘rlr regard ro r.he sensitivity of biological reactions to tempirarure variations- As 3 consequence, a precise knowlrdse of these far-IR vibrarions of H-bonds appears to be of a crucial importance_ Despite this gear interest, the number of reported studies concerning these vibrations is quite small ~5--8] _ This is certain& due to zhe diffkulry encountered in Utis region of obtaining good qua&y spectra. With the recent developrncnt of Fourier rransform techniques. howeb*r. the qua&y of FIR spectra has been si_gn.ificant& improved and may ncnv be compared with that usual& attained in r.he classical 1R region f8] _ 1n this letter, we present the first psrz of our FIR *_ ---
mid-IR region [9]_ In ties2 c~ssals, the five-membered rings of irnidazole molecules are linked rogerher by Hbonds and form infmire chains whose average orienrations coincide witirh the c axis_ Consequently. FIR bands wiJl be mostly due EOthe relative M7radons ofmofec&s eked by H-bonds and _partIy ro rhe r&&e sibrations of chains, The two physic4 parameters which we have varied in these studies are temperature and polarization_ This iarser parameter is mosr useful for obraining a clear rtuigunenr of the VtioW Ities. Ihe fiirsz (remp+raZure) will provr3 essential for Obtaining information concerning the mi?chaniis of H-bonds and panicuEarly the anharmonicities of rZie various v&radons due fo H-bon&_
2. Experimental
conditkms
Imidazole was of -com~erciC' purity grade from Fluka. After crystallkzrion in water, the producz was sublimed ar 5O”C_ A saturated solution of imidazofe in a nzkture of benzene @O%~and acetone &!EZ) was *ha.. ,-.L*----1 -
\r~lumr 110, number 3
CHEMCAL
78 September
PHYSICS LElTERS
setwtion. The thickness of the sample was then reduced to some 200 &ml. The s~tttple was mounted on an Air Liquide CRCS I‘Q ustat which was itttroduwd into a Polytec interferometer. The length swept by the moving mirror corresponded to an effective resolution of better than 2 Cl11-' . The specrr.tl elements were calculated for every 0.5 c‘nt- I. Tltcse wuditious were ueczssary to septrate ttc.trly coinciding b.mds and to approach their real httcktpcs. as some of t'ttt‘scb,mds become rather 113rrow at tetnpmmtri’s below 70 Ii.
3. Results sud discussiott The spectra obktitted with such tnottoc~st~ls having thci,r c ascs in the pl,~~~ of obsen~tiun .we displayed in tip. 1 (Eflc) srd tis. 2 (Elc) Gx viu-ious tetup=xwtres. 1‘Lwc .I& of irrtidtzolz it: the .twr+e direction of Mbottds (1 O] _Tfw ordin&e &WI in these tigttres is
coordinate calculations [I 1- I3f which we clearly find at 77 aud BS cm-l _A cotnplete assignment of all the vibrations is given itt table I_ The band at 154 cm-1 deserves some special comments. because it is strong and saturates (-4(w) Z 2) at some polarizaGon angles_However. we can show that it has two distinct components (fis. 3). one of which has a polarization perpendicular to c sud the other at *XI0 from c in the pkme of obsarrstion. This is corroborated by recent results of inelastic neutron-s~tte~tt~ experiments [ 131. With the help of norm&coordinate calculations. we 1113~ 3ssuxn~ that OII~ of the components is Au. because such a polarization is expected at 133 [ 121 or 110 cm-l [ 111. We assign the other cwntponettt to the batId quoted as ‘hot observed” [ 1 1.121 which has B, symmetry. Witlt these assigntnents. we see all tlte frequencies that are predicted from the symmetry elements of the unit cell of imidttzole. The seaxtd pxzttnetet which WC hsve vxied is temperature. Frottt a rapid .tnslysis of the c_trkttions of the spectra with T, we obtain two kinds of information.
.-\t low tztnpetxtures. the specrr~ shown in tip. I dud 2 zshihit sharp fexures that are dose to the resotution limit <~,fthe aptwratus. They enable us to acwunt for all S A,, Gbtxtiotts thst should be observed. especially the two still-lxking frequencies sppexing in normal-
The ftrst has tn do with the band at 214 cm-1 (at 6 K} which is polarized thong c_ Frotn the t-aristions of its width (fig. I). which increases mu& more rapidly km the widths of the other bands. we infer that it is a corn-hination band. The candidates for such a combinlttion are the bands at 155 cd (A,, or B,) and a band at 160 cm-l which appears in the Ratnan spectrum of itnidazole. This latter hmd will be either _L. z in which
IMIDRZCLE
293 K ------:Ei t 5,‘sK
_...a._._
Fig. 1. Speztrd 2S6
oi
1984
intid.tzole monocrystals at wious temperatures. The polarization direction is Fade1
to c.
Volume I IO, number 3
CHEWCAL
28 Scprember
PHYSICS LETI-ERS
1984
it.25
fMIDi=iZOLE - ~_IE
._._.___ 293 _---_ 298
K K
. . . , 50.0
106
15%
2m
258
333
FREQUENCY ~cm-11
due 10 ~harmoiticirics
no chzz+
fin ‘the harmonic approximation occws With temp+rzturzj_ _Acompfere ana?ysk
of rhe r-ariarions of these bands wixh tempeprature is complicated by the strong overlapping oi all bznxls and requires some further consider&on_ WC mzy neverthe-
70
a) Direction
gc 1)
of the E vector.
d)Frequency quotedasnot
b, Frequency not yet zzxiged. obsemd in refs. [i1,12].
cl !&e text_
z37
2.258
28 September 1984
CHEMICAL PHYSICS LEVITITERS
~~o’ofurne 110, number 3
F
T=6K
Po?arrzation ----__
I 11B”
90” ____. . .._
8.888~~~
*.
50.00
“. 100.0
‘.
‘.
158.8
.
.
*
‘.
200.0
.
a.
FREQUENCY Fig.
less obtain some information
3. The
‘.
250.0
.
70”
*.
(cm-11
band at 154 CZR-~as a function of the polarization angle at 10 K.
from the shifts of the
maxima of these bands when the temperature is varied. These are easily measurable quantities which we may attribute in a first approsimation, to the shifts ofthe
centres of gravity of the same bands. We show some of
these quantities in fig. 4. The remarkable feature shown in fig. 4 is that all vibrations exhibit the same behaviour whatever their frequencies at 6 K. More precisely, all
t-
.900 -
0.000
s
300.0
180.0
200.0
308.0 T
(Kelvin)
Fig. 4. Relative variations of the maxima of various bands i with temperature.
Volume 110, number 3
these vibrations show no shifts at low temperatures and a linear variation with temperature at temperatures higher than 100 K. When extrapolating this linear variation towards low temperature, we intersect the value 1 at temperatures Tf5 which falI between 40 and 80 K for all vibrations i (fig. 4)_ This enables us to eliminate a one-dimensional anharmonicity (such as encountered in Morse or double-well potentials) as being at the origin of the shifts of all these maxima with temperature. For such potentials, we expect T& to increase with Ihe value ojTzo of the frequency of the ith vibration at low temperatures_ In the case of a Morse-type potential, for instance, whose levels are of the form
E; =(n+;)ai2ifI
-(n+~)~,f,
(2
where ?ii is the anharmonicity parameter, the centre of gravity 0’. of all tz -+ II + 1 transitions will be such that
W’l-
2S,(Z, - I)
-=1-
1 - 26,
+=o
28 September 1984
CHEhiICAL PHYSICS LE-ITERS
+ $(d212j/dQ’)((Q
- (Q),)‘>,
c.+ = wkzo + (tfl;lfS2)(Z - 1) d”%/dQ’.
= 1 - exp[-fin&l
- ai)/k_T] ,
(4)
so that we find
kT; =;fiQ,(l
- i$)
This equation clearly sho\?rs that kT& is nearly equal to the observed frequency wzTzo at 0 K. which does not fit with the results shown in fig. 4. We may consequently suspect anharmonic CGUphgS to be at the origin of the observed shifts with temperature_ The simplest way to introduce these anharmonic couplings is to assume that the potential r’j for the ith mode sj is that Gf an harmonic oscillator having a frequency SLi which is modulated by some vibration Q which is the same for all modes i: Vi = ;MsLi” (Q)q; .
This gives, within the adiabatic appro.ximation (the frequency of the Q mode is assumed to be less than those of all other modes i):
(61
(a
in eq. (4) with 6 is we deduce
kT’o =ii!Ll.
(Z’)-’
(7)
where ( >T means the thermal average for the Q variable. As shown by neutron-diffraction experiments [I 5j _ the variation of (Q>* between 77 and 300 K is less than 0.01 A. This suggests that the term 521(
H.R. ZELSMAXN ’ _P. EWZFFON ’ md Y. MARECWAL ’ Drboraroke de R&onance ~~f~gn&&e. D&arremenr de RedrercJxeFondamenru!e. Cent-e d %rudesn’ickire~ de Grenoble-85X. F38ojl Grenoble Cede-q Fr~re Keceised 17 Ma)’ 19S4; in final form 6 JuIy I984
The spectm of imidatok monocrysralshxing their c nis (the averagedirection of H-lmndst in the obsmarion plane have ken recorded in rhsnnge 50-500 cm-’ _ 7&e tt*o prtramrrcrsstied are umpsr;irure and pokr&.ation. From the xo-iation of pobriwtion. tie are able to gjw 3 clear rtssi_gnmenr of all vibr~~%o~,arid particularly of those stiIl lxking in the iitrrxure. The chsngcs of tie spectra with temperature cm be inrerpreted, in s f=sr z+pprati5oon, by assuming rhar alf modes are mod&ted by a vibntion lihich has _Ifrequency f&ins betueen 30 md 60 cm-’ _
1- Introduction In tbe far-IR r&on_ H-bonds X-H.--Y arc ar rhe origin of bands corresponding. in a first appro_Gmation. to the relative vibrations of the two molecuks X-H and Y. These vibrations bag been shorn to influenc2 srrongfy the pS ribrations fl---G] and ro be at the or@ of their rhermsl sensitivities. They may even be thoughr to influence srrongly mosf of the proprties of H-bonds_ which hss importanr biofogical consequences_ esspctc.ialIuy wr‘rlr regard ro r.he sensitivity of biological reactions to tempirarure variations- As 3 consequence, a precise knowlrdse of these far-IR vibrarions of H-bonds appears to be of a crucial importance_ Despite this gear interest, the number of reported studies concerning these vibrations is quite small ~5--8] _ This is certain& due to zhe diffkulry encountered in Utis region of obtaining good qua&y spectra. With the recent developrncnt of Fourier rransform techniques. howeb*r. the qua&y of FIR spectra has been si_gn.ificant& improved and may ncnv be compared with that usual& attained in r.he classical 1R region f8] _ 1n this letter, we present the first psrz of our FIR *_ ---
mid-IR region [9]_ In ties2 c~ssals, the five-membered rings of irnidazole molecules are linked rogerher by Hbonds and form infmire chains whose average orienrations coincide witirh the c axis_ Consequently. FIR bands wiJl be mostly due EOthe relative M7radons ofmofec&s eked by H-bonds and _partIy ro rhe r&&e sibrations of chains, The two physic4 parameters which we have varied in these studies are temperature and polarization_ This iarser parameter is mosr useful for obraining a clear rtuigunenr of the VtioW Ities. Ihe fiirsz (remp+raZure) will provr3 essential for Obtaining information concerning the mi?chaniis of H-bonds and panicuEarly the anharmonicities of rZie various v&radons due fo H-bon&_
2. Experimental
conditkms
Imidazole was of -com~erciC' purity grade from Fluka. After crystallkzrion in water, the producz was sublimed ar 5O”C_ A saturated solution of imidazofe in a nzkture of benzene @O%~and acetone &!EZ) was *ha.. ,-.L*----1 -
\r~lumr 110, number 3
CHEMCAL
78 September
PHYSICS LElTERS
setwtion. The thickness of the sample was then reduced to some 200 &ml. The s~tttple was mounted on an Air Liquide CRCS I‘Q ustat which was itttroduwd into a Polytec interferometer. The length swept by the moving mirror corresponded to an effective resolution of better than 2 Cl11-' . The specrr.tl elements were calculated for every 0.5 c‘nt- I. Tltcse wuditious were ueczssary to septrate ttc.trly coinciding b.mds and to approach their real httcktpcs. as some of t'ttt‘scb,mds become rather 113rrow at tetnpmmtri’s below 70 Ii.
3. Results sud discussiott The spectra obktitted with such tnottoc~st~ls having thci,r c ascs in the pl,~~~ of obsen~tiun .we displayed in tip. 1 (Eflc) srd tis. 2 (Elc) Gx viu-ious tetup=xwtres. 1‘Lwc .I& of irrtidtzolz it: the .twr+e direction of Mbottds (1 O] _Tfw ordin&e &WI in these tigttres is
coordinate calculations [I 1- I3f which we clearly find at 77 aud BS cm-l _A cotnplete assignment of all the vibrations is given itt table I_ The band at 154 cm-1 deserves some special comments. because it is strong and saturates (-4(w) Z 2) at some polarizaGon angles_However. we can show that it has two distinct components (fis. 3). one of which has a polarization perpendicular to c sud the other at *XI0 from c in the pkme of obsarrstion. This is corroborated by recent results of inelastic neutron-s~tte~tt~ experiments [ 131. With the help of norm&coordinate calculations. we 1113~ 3ssuxn~ that OII~ of the components is Au. because such a polarization is expected at 133 [ 121 or 110 cm-l [ 111. We assign the other cwntponettt to the batId quoted as ‘hot observed” [ 1 1.121 which has B, symmetry. Witlt these assigntnents. we see all tlte frequencies that are predicted from the symmetry elements of the unit cell of imidttzole. The seaxtd pxzttnetet which WC hsve vxied is temperature. Frottt a rapid .tnslysis of the c_trkttions of the spectra with T, we obtain two kinds of information.
.-\t low tztnpetxtures. the specrr~ shown in tip. I dud 2 zshihit sharp fexures that are dose to the resotution limit <~,fthe aptwratus. They enable us to acwunt for all S A,, Gbtxtiotts thst should be observed. especially the two still-lxking frequencies sppexing in normal-
The ftrst has tn do with the band at 214 cm-1 (at 6 K} which is polarized thong c_ Frotn the t-aristions of its width (fig. I). which increases mu& more rapidly km the widths of the other bands. we infer that it is a corn-hination band. The candidates for such a combinlttion are the bands at 155 cd (A,, or B,) and a band at 160 cm-l which appears in the Ratnan spectrum of itnidazole. This latter hmd will be either _L. z in which
IMIDRZCLE
293 K ------:Ei t 5,‘sK
_...a._._
Fig. 1. Speztrd 2S6
oi
1984
intid.tzole monocrystals at wious temperatures. The polarization direction is Fade1
to c.
Volume I IO, number 3
CHEWCAL
28 Scprember
PHYSICS LETI-ERS
1984
it.25
fMIDi=iZOLE - ~_IE
._._.___ 293 _---_ 298
K K
. . . , 50.0
106
15%
2m
258
333
FREQUENCY ~cm-11
due 10 ~harmoiticirics
no chzz+
fin ‘the harmonic approximation occws With temp+rzturzj_ _Acompfere ana?ysk
of rhe r-ariarions of these bands wixh tempeprature is complicated by the strong overlapping oi all bznxls and requires some further consider&on_ WC mzy neverthe-
70
a) Direction
gc 1)
of the E vector.
d)Frequency quotedasnot
b, Frequency not yet zzxiged. obsemd in refs. [i1,12].
cl !&e text_
z37
2.258
28 September 1984
CHEMICAL PHYSICS LEVITITERS
~~o’ofurne 110, number 3
F
T=6K
Po?arrzation ----__
I 11B”
90” ____. . .._
8.888~~~
*.
50.00
“. 100.0
‘.
‘.
158.8
.
.
*
‘.
200.0
.
a.
FREQUENCY Fig.
less obtain some information
3. The
‘.
250.0
.
70”
*.
(cm-11
band at 154 CZR-~as a function of the polarization angle at 10 K.
from the shifts of the
maxima of these bands when the temperature is varied. These are easily measurable quantities which we may attribute in a first approsimation, to the shifts ofthe
centres of gravity of the same bands. We show some of
these quantities in fig. 4. The remarkable feature shown in fig. 4 is that all vibrations exhibit the same behaviour whatever their frequencies at 6 K. More precisely, all
t-
.900 -
0.000
s
300.0
180.0
200.0
308.0 T
(Kelvin)
Fig. 4. Relative variations of the maxima of various bands i with temperature.
Volume 110, number 3
these vibrations show no shifts at low temperatures and a linear variation with temperature at temperatures higher than 100 K. When extrapolating this linear variation towards low temperature, we intersect the value 1 at temperatures Tf5 which falI between 40 and 80 K for all vibrations i (fig. 4)_ This enables us to eliminate a one-dimensional anharmonicity (such as encountered in Morse or double-well potentials) as being at the origin of the shifts of all these maxima with temperature. For such potentials, we expect T& to increase with Ihe value ojTzo of the frequency of the ith vibration at low temperatures_ In the case of a Morse-type potential, for instance, whose levels are of the form
E; =(n+;)ai2ifI
-(n+~)~,f,
(2
where ?ii is the anharmonicity parameter, the centre of gravity 0’. of all tz -+ II + 1 transitions will be such that
W’l-
2S,(Z, - I)
-=1-
1 - 26,
+=o
28 September 1984
CHEhiICAL PHYSICS LE-ITERS
+ $(d212j/dQ’)((Q
- (Q),)‘>,
c.+ = wkzo + (tfl;lfS2)(Z - 1) d”%/dQ’.
= 1 - exp[-fin&l
- ai)/k_T] ,
(4)
so that we find
kT; =;fiQ,(l
- i$)
This equation clearly sho\?rs that kT& is nearly equal to the observed frequency wzTzo at 0 K. which does not fit with the results shown in fig. 4. We may consequently suspect anharmonic CGUphgS to be at the origin of the observed shifts with temperature_ The simplest way to introduce these anharmonic couplings is to assume that the potential r’j for the ith mode sj is that Gf an harmonic oscillator having a frequency SLi which is modulated by some vibration Q which is the same for all modes i: Vi = ;MsLi” (Q)q; .
This gives, within the adiabatic appro.ximation (the frequency of the Q mode is assumed to be less than those of all other modes i):
(61
(a
in eq. (4) with 6 is we deduce
kT’o =ii!Ll.
(Z’)-’
(7)
where ( >T means the thermal average for the Q variable. As shown by neutron-diffraction experiments [I 5j _ the variation of (Q>* between 77 and 300 K is less than 0.01 A. This suggests that the term 521(
T) in eq. (7) is hard& temperaturede~ndent. The orher term in CfQ - (Q$&may be estimated with the assumption that Q is governed, in a first approximation. by an harmonic potential of frequency 12 and mass Al’ (introducing eventual anharmonic one-dimensional terms in Q would make a vary slightly with T). With this assumption we fmd
where Z(a) is the s3me as Zj(stj, equal to zero. From this equation
+ O(ls,)‘l,
+ _._,
j
(9)
wl~icl~ shows that T,$ is the same for all modes i and that fis2 consequently fails between 30 and 60 cm-l (fig_ 4). This mode Q does not appear in the FIR spectrum_ It may be the totally symmetric (A-) vibration that corresponds to a translation parallel Fo c,[ 11. lz] and which has strong components in the v,(X--H...s) and
loc&zed
vibrations
of a single H-bond_
References [ 11 S. Bnros and D. Had& in: The hydrogen-bond:
Recent progress in theory and experiments. eds. P_ Schuster, G. Zundel and C. Smdorfy (North-l%oilrind, Amsterdam. 1976) ch. 12.
[2]
S. Bntos, J. Lmmnbe and A. Novak, in: Molecular inter-
actions, eds. H. Ratajczak and WJ. Oniile-Thomas C\\Xey, h’ew York, 1980) ch. 9 and referentxs therein. f3] G-L_ Hofacker. Y. Mz&chzl and MA_ Ratner, in: The hydrosen-bond: Recent progress in theory and esperiments, eds. P. Schuster, G. Zundel and C. Sandorfy (North-Holland, Amsterdam, 1976) ch. 6 and references therein.
239
Volume 110, member 3
CHEMICAL PHYSICS LErl-ERS
[4] Y. Md%al, in: Molecular interactions, eds. l-l. Ratajcwk and W.J. Orville-Thomas (Wiley, New York, 1980) ch. 8 and reference3 therein. [S] K.D, Wller and WC. Rothschild, Far-infrared spectrascopy (W%ey,New York, 1971) ch. 6. [6] S.G.W. Ghm and f.L. Wood, 3. Chem. Phys. 46 (1967) 2735. f7] C. pwehard and A. Novak, J. Chem. Phys. 48 (1968) 3079. ($1 f. Bandekar. L. Gcnzel, F. Kremer and L. Santa, Spectrochim. Acta 39A (1983) 357. [9] P. Excoffon and Y. Mar&al. Chem. Phys. 52 (1980) 237, 245: J. Chim. Phys. 78 (1981) 353.
28 September 1984
[lo] S. XlartinezCarrera, Acts Cryst. 20 (1966) 783. [ 1 l] R. Majoube and G. Vergoten, J. Chem. Phys. 76 (1982) 2838. [ 121 L. Colombo, P. Bleckmann. B. Schmder. R. Schneiderand Th. Plesser, J. Chcm. Phys. 61(1974) 3270. [13] ~V.~n~~,Z.K~~.129(1969)211. [14] KR. Link. H. Grimm. B. Domer, H. Z~~~n, H. Stiller and P. Bleckmann, 3. Phys. Chem. Sol., submitted for publicMoon. [IS] B.M. Craven. RX. McMulland. J.D. Bell and H.C. Frwman, Acta Cryst. B33 (1977) 2585.