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Compensation effect in the thermodynamics of conformational equilibria
Specfrochimica
Acta, Vol.
46A. No. 7, pp. 1037-1043, 1990
05~39/90 s3.00+ o.LNl @ 1990 Pergamon Press plc
Printed in Great Britain
Compensation
effect in the thermodynamics
of conformational
equilibria
A. I. FISHMAN* and A. A. STOLOV Kazan State University, Lenin Street 18, Kazan 42OW8, U.S.S.R.
A. B. REMIZOV Kazan Chemistry Technology Institute, Karl Marx Street 68, Kaxan 420015, U.S.S.R. (Receiued
1 June 1989; in final form 23 October 1989; accepted 26 October 1989)
Abstract-The solvent dependence of thermodynamic parameters of conformational equilibria in trans-1,2dichlorocyclohexane and rraans-1,2-bromochlorocyclohexane was-investigated by infrared absorption spectra. The results obtained show the existence of a compensation effect in the thermodynamics of conformational equilibria: the enthalpy (AH,) and entropy (AS,) differences change in the same direction when going from one solvent to another. A semi-quantitative estimation of the effect is given on the basis of the equations of statistical thermodynamics. It is shown that the temperature dependence of the A& value must be taken into account when determining the enthalpy difference of the conformers. This yields the equality of the true and observed AH, values.
INTRODUCTION
and temperature dependence of the parameters of conformational equilibria are nowadays the subject of intense studies [l, 21. In many studies devoted to this problem, the solvent dependences of the values AH, or AG,, (enthalpy and free enthalpy differences of the conformers) are analysed. However, there is little data concerning the entropy difference of the conformers, AS,,, and its variation with a solvent. The latter fact is probably due to experimental difficulties in determining the AS,, values. The lack of experimental data seems to be responsible for the following assumptions having different forms: (1) AS, = 0 or AS, = R In y, where y is the statistical weight ratio of the conformers [3]; (2) A&# 0, but is independent of solvent [l, 41; (3) AS,#O, but is independent of temperature [l]. It is perfectly clear that, in the common case, the entropy difference of the conformers depends on the solvent and temperature. Therefore, it becomes important to find out if those dependences are sufficient or not, i.e. to evaluate the experimental errors appearing due to the usage of assumptions (l)-(3). To answer this question, it is necessary to determine AS,, values for several model compounds under different experimental conditions. In this paper, the values AH,,, AGo, AS,, and also AH’ and AS’ are obtained for two di-substituted halocyclohexanes in polar and non-polar solvents. The modification of the i.r. spectroscopic method proposed earlier [5], was used. On the basis of the data obtained, an attempt is made to answer the above questions. THE SOLVENT
MATERIALS
Trans-l,2-dichlorocyclohexane(I)andtrans-l,2-bromochlorocyc1ohexane(II)wereused as models. In the liquid and solution these compounds exist in the form of a mixture of diaxial (A) and diequatorial (B) conformations [6,7]. The molecule I is one of the basics in analysing the general principles of conformational analysis: thermodynamic parameters of conformational equilibria in I dissolved in different liquids have been determined previously by different methods [ 11. The conformational equilibria in II have not been studied quantitatively. * Author to whom correspondence
should be addressed. 1037
A. I. FISHMAN et al.
1038
Non-polar propane (E = 1.61 [S]) and polar CFzClz (E = 2.5 when T= 220 K and E = 3.5 when T= 120 K) were used as the solvents. Since the dipole moments for A and B conformers are sufficiently different (3.13 and 0.37 D for the B and A form of I, respectively [l]), then, according to Ref. [l], the essential solvent dependence of all thermodynamic parameters may be expected. EXPERIMENTAL
The i.r. spectra were obtained with a UR-20 spectrometer and processed by a computer. The integral intensities of the absorption bands 498 (A) and 514 cm-’ (B) of I; 484 (A) and 505 cm-’ (B) of II [6,7] were studied. Concentrations of I and II were less than 10-3mol I-‘. The temperature range was 85-225 K. For temperatures c 145 K, the “freezing” state of the conformational equilibria occured [5]. The values of AH, were determined by the slope of the dependence of ln(l,/Z,) upon l/T (for the temperature range T > 145 K). The changes of the integral absorption coefficients aA and ua with temperature were taken into account [5,9]. Free enthalpy differences (AC,,), activation enthalpy (AH’), entropy (AS’) and the ratio aA : aB were determined by investigating the kinetics of conformational transitions. The experimental techniques used for studying the kinetics have been described in detail previously [5, lo]. The results obtained are listed in Table 1.
RESULTS AND DISCUSSION
The solvent dependence
of the ratio aA : aB
It can be seen from Table 1 that the ratio of integral absorption coefficients for the bands belonging to different conformers changes when going from propane to CF2Clz. This fact does not seem to be surprising, since the sufficient solvent dependence of i.r. band intensities is well known [ll]. Nevertheless, the assumption of independency of aA : aB on the media is frequently used [l, 4, 12, 131. In our case, the systematic errors which would appear, if we assume that aA.* aB is constant, are rather small: 70 cal mol-’ for AGo and 0.4cal mol-’ K-’ for A&. However, in the common case they are unpredictable. It should be noted that, according to our normal coordinate analysis of I and II, the bands 498 (I, A), 484 cm-’ (II, A) and 514 (I, B), 505 cm-’ (II, B) correspond to the vibrations having practically the same form. This closeness of the vibrational forms seems to be responsible for the closeness of the values of aA : aB for I and II and for their similar dependence on a solvent. The observed and true AH0 values
According to Ref. [l], when analysing the experimental AH, values it is necessary to take into account the dependence of AH, upon temperature. If AH, is a function of T, Table 1. Thermodynamic and spectroscopic characteristics of the conformers of I and II in propane and CFzClz Compound
Compound Parameter aala, AH& (kcal mol-‘) AS& (cal mol-’ K-‘) AGO(B- A)* (cal mol-‘) AHo(B - A)? (cal mol-‘) AS,(B - A) (cal mol-’ K-‘)
Propane 1.9kO.l 13.5 20.7 15+5 330 + 20 485 + 20 0.95 + 0.15
CF, Cl, 2.4kO.2 13.6+0.5 18+5 110+50 0+40 - 0.65 + 0.35
Propane 2.OkO.l 12.4kO.6 9+4 620 f 30 650 f 30 0.20+0.35
CF; Cl2 2.65 +0.3 320 f 70 90+70 - 1.4OkO.85
* The values AGo correspond to T= 167 K. t The values AH, within the limits of the experimental errors were found to be independent of T. They correspond to the average temperature for the interval 225-145 K.
Thermodynamics of conformational equilibria
1039
then the observed values (AHEb”.) differ from the true ones (AHAm’). ABRAHAM and BRET~NYDERobtained the following expression [ 11:
AH;“.=AHg”‘-T and proposed to use a reaction field model for calculating the term T(dAHhNeldT). The values T(dAH$“VdT) are sufficient when a polar solvent, or a solvent with large de/dT is used. For example, we have obtained for the solution of I in CF2Clz : T(dAHAmeldT) = 460 cal mol- ’ (T= 167 K). All the parameters used were taken from Ref. [ 11. However, when derivating (l), ABRAHAM and BRET~NYDERassumed the entropy difference of the conformers to be independent of temperature. Taking into account this dependence, instead of (1) we have a strict expression:
(2) When AH,, is measured under constant pressure (a widely used situation), the latter expression may be simplified. From the well known thermodynamic equation (for example Ref. [14]):
(s),=
T(z)P
(34
AHgbS.= AHF.
(3b)
one obtains:
It should be noted that the latter expression is derived from the fundamental thermodynamic laws, and hence it is strict. Thus, the experimental value of AH,, is equal to the true one and calculation of the term T(dAH,ldT) is not necessary. Therefore, some results obtained by ABRAHAMand BRET~NYDER[l] are to be corrected. It should be also noted, that, according to Eqn (3a), from the fact AH,=f(T) it follows that AS, also depends on temperature, and vice versa, if AH, is a constant, then AS, is a constant too. Unfortunately, nowadays it is difficult to find out if AH, is a function of T or not, because the accuracy of i.r. or NMR methods seems not to be sufficient. Compensation effect The values AH,, and AS,, (see Table 1) decrease when going from the solution in propane to that in CF2C12. Therefore, AC, decreases due to the enthalpy term, and at the same time it increases due to the contribution of TAS,. The similar results obtained in thermodynamics of non-specific [15] and specific [16] solvation are known as a compensation effect [17]: varying the solvent, one changes the AH, and AS,, values; the dependence of AS,, upon AH, is close to linear with a positive leading coefficient (AASJAAH,). In our case these coefficients are 3.3 x 10e3 K-’ for I and 2.8 x 10e3 K-’ for II (see Table 1). For the first time, the existence of the compensation effect in conformational equilibria was noted [18,19]. Below we shall try to substantiate the effect on the basis of a simple model. Let us consider the dependence of enthalpy upon a coordinate of internal rotation, q, for a molecule having two conformations A and B (Fig. l-continuous line, corresponding to the first solvent). For the molecules in the A form, torsional vibrations take place near qL, and the full energy of such vibrations is: E_
M2 I K4(qx4
2
4L12 ’
\u
1040
A. I. FISHMAN et al. A
K
I
I
\ \ \
H
I/
\\
’\
L
I
’
/
5H~
/’
\ L
Fig. 1. The dependence
of the enthalpy
upon a coordinate
of the internal
rotation
for a
molecule
in two solvents (continuous and dashed lines).
where M is the momentum moment, I,, is the reduced inertia moment and KA is the force constant. The statistical integral for the torsional vibrations can be written in the form: m exp( - EJRT)dM dq.
z=c II-m
(5)
Here, c is a constant taking into account the dimension of the integral. Combining the expressions (4) and (5) and integrating gives: z = ~xcRT(Z,A/KA)“‘.
(6)
Furthermore, we shall consider only torsional terms and their contribution to the value AS,. Here we assume that the structure of the surroundings of a solute is practically independent on its conformation, and hence the integrals over intermolecular degrees of freedom are equal for different conformers. The entropy of the A form can be calculated from the integral z [20]: SA= R{1n[2JccRT(~,,/KA)“*] + l}. The expression for the entropy difference, one obtains:
(7)
of the B form is similar. Thus, for the entropy
AS,=S,-&=iRln
(8)
All the characteristics of the curve H(q) are changed when we take the second solvent (Fig. l-dashed line). Since the structure of stable conformations weakly depends on a solvent, the changes in coordinates qL and qN, corresponding to energy minima, are neglected. For the change of the enthalpy difference with a solvent, one obtains: AAH,, = AH;, - AH, = AH, - AH,,
(9)
and for the change of AS,: AAS,,=AS&-A&=iRln
(10)
Thermodynamics
of conformational
1041
equilibria
where Ka, KL, AH; and A$, are the force constants, enthalpy and entropy differences of the conformers in the second solvent. Let us draw the relationship between AAH,, and AAS-,. Supposing L to be the beginning of a coordinate system, one obtains, for a segment of the curve KLM, an approximate expression: Hz-
Ar-f”B [l - cos(n * q)],
(11)
where AH& is the activation enthalpy and n characterizes curve H(q). From (11) it follows:
K*2?
a number of minima on the
A%B
aq2 s=o=2n2.
(12)
Obtaining similar expressions for Ki, KB and Kb and substituting them into Eqn (lo), one obtains: AH& + AH, AH:,+
AH,
(13)
*
It should be noted that the latter expression is obtained for the case of such internal rotation, when only one coordinate q varies. However, in the common case, several internal coordinates may be responsible for a conformational transition. For example, the inversion of a six-membered ring is accompanied with the rotation around all the six C-C bonds. If m coordinates are responsible for the internal rotation process, the statistical integral will have a form of a multiplication of the terms written in Eqn (6) and the entropy, a sum of the terms written in Eqn (7). Hence, taking into account Eqn (9), one obtains: AAS,,=;
AH:B
R In 3.
BA
AH,a+
AH,+
AAH,,
AH:, + AHA
’
(14)
Since for a great number of systems AAH,= AHA-AH~G AH’, expression (14) can be expanded in power series. Taking into account only the first two terms of the expansion, one obtains:
From (15) it is seen that the value, AA&,, strongly depends on AAH, and weakly on AH,. The tangent of the slope of the dependence AAS,=f(AAH,) is proportional to the number of coordinates responsible for the internal rotation and to the reciprocal value of the activation enthalpy: AA& R m -AAH,,-% AH+’
W-9
Thus, for the inversion of a six-membered ring, AH’= 10 kcal mol-‘, m = 10 and AASJAAH,, = 10e3 K-l. So, the order of the magnitude of the experimental value agrees with the estimated one. We see that the contribution of the entropy term TAA&, to AAG,, may be essential: when AA&lAAH,,= 10m3K-’ and T= 300 K, it compensates 30% of the AAH,, contribution. At the same time it should be noted that our consideration of the compensation effect in the thermodynamics of conformational equilibria takes into account only the contribution of torsional vibrations to AS,, values, and therefore it is not complete. Furthermore,
1042
A. I. FISHMANet al.
-1
-2 A/i,, (kcal
Fig.2.The dependence
0
mol-‘1
of AS, upon AH, for o-iodophenol in 12 solvents. values are taken from Ref. [21].
All AH, and AS,
the symmetry of the surroundings of the solute may be dependent on its conformation, and this fact may alter also the AS,, value. Thus, the estimations obtained may only reveal the general tendency of the behaviour of the thermodynamic parameters when the solvent is varied: (1) When AH,, is independent of a solvent, the changes in the entropy difference are, as a rule, small. (2) When AH,, changes sufficiently, AS,,, as a rule, changes also, the tangent of the dependence AH,, =f(A&) being positive. (3) The magnitude of AA& could be estimated with the help of expression (16).
Other literature data
There are several works in the literature in which the effect of the solvent upon the enthalpy and entropy differences of the conformers is investigated. Thus BAKER and SHULGIN [21]have studied the conformational equilibria in 12 solutions of o-iodophenol. When determining A&,, the authors of Ref. [21] used a doubtful assumption (aA = aB in all the solvents) and hence the obtained AS0 values are systematically shifted from the true ones, the results obtained are in good agreement with the described tendency (Fig. 2). For o-iodophenol, the value AA&/AAH,, was found to be equal to 1.3 x 10m3K-l.
1
1
I
1
2 A Ho tkcat mot-’ 1
Fig. 3. The dependence
of AS, upon AH,, for different compounds
studied in Refs [22, 23)
Thermodynamics
of conformational
equilibria
1043
The solvent dependence of conformational equilibria in 1,3,2-dioxophosphorinanes (equilibrium chair * chair) and in 2-substituted-5,6-benz-1,3-ditiepines (chair & boat) was investigated in Refs [22,23] by NMR spectroscopy. Figure 3 shows the diagram produced using the data obtained in those studies. One can observe the compensation dependence, the values AAS,lAAH, being within the limits (0.9-1.5) x 10m3K-l, which are in good agreement with our estimations. Acknowledgemenu-The authors are grateful to E. N. KLIMOVIT~KY and M. B. TIMIRBAEVfor synthesizing and purifying the samples and to M. D. BORISOVERand 0. E. KISELEVfor a fruitful discussion.
REFERENCES [l) R. J. Abraham and E. Bretsnyder, in Inrernnl Rotation in Molecules (edited by W. J. Orville-Thomas) (1974). [2] V. V. Samoshin and N. S. Zefirov, Zh. Vses. Khim. Obshch. 29, 521 (1984). [3] G. A. Beresneva, L. V. Khristenko, 0. D. Ulyanova and Yu. A. Pentin, Zh. Phys. Khim. 60, 1045 (1986). [4] A. F. Vasiljev, Zh. Prikf. Spectrosk. 6, 485 (1967). [5] A. I. Fishman, A. A. Stolov and A. B. Remizov, Spectrochim. Actu 41A, 505 (1985). [6] A. B. Remizov and L. M. Sverdlov, Zh. Prikl. Spectrosk. 9, 113 (1968). [7] P. Klaboe, Actu Chem. &and. 25, 695 (1971). [8] Ya. Yu. Akhadov, Dielektricheskie Svoistva Chistikh Zhidkostei, (Dielectric Properties of Pure Liquids). Izdarelsrvo Standartov, Moscow (1972). [9] A. I. Fishman, A. B. Remizov and A. A. Stolov, Dokl. Akad. Nauk SSSR 260, 683 (1981). [lo] A. I. Fishman, A. B. Remizov and A. A. Stolov, Zh. Prikl. Spectrosk. 40, 604 (1984). [ll] A. J. Barnes and W. J. Orville-Thomas (Editor), Vibrational Spectroscopy. Modern Trends. Elsevier, Amsterdam (1977). [12] 0. Exner, Z. Fried1 and P. Fiedler, Coil. Czech. Chem. Cornmun. 48, 3086 (1983). [13] Z. Friedl, P. Fiedler, J. Biros, V. Uchitilova, I. Tvaroska, S. Bohm and 0. Exner, CON. Czech. Chem. Commun. 49,205O (1984). [14] P. W. Atkins, Physical Chemistry. Oxford University Press, Oxford (1978). [15] B. N. Sotomonov, V. V. Gorbatchuk and A. I. Konovalov, Zh. Obshch. Khim. 52, 2688 (1982). [16] G. C. Pimentel and A. L. McClellan, The Hydrogen Bond. Freeman, San Francisco (1960). [17] S. G. Entelis and R. P. Tiger, Kinetika Reaktsii v Zhidkoi Faze (Reaction Kinetics in the Liquid Phase).
Khimiya, Moscow (1973). [18] A. I. Fishman, A. A. Stolov, A. B. Remizov and I. S. Pominov, Zh. Prikl. Spectrosk. 44, 330 (1986). [19] A. B. Remizov, A. A. Stolov and A. I. Fishman, Zh. Phys. Khim. 61, 2909 (1987). [20] I. N. Godnev, Vichisleniye Termodinamicheskikh Funktsii po Molecularnim Dannim, (Calculation of Thermodynamic Functions by Molecular Data). GITTL, Moscow (1956). [21] A. W. Baker and A. T. Shulgin, Spectrochim. Acta 22, 95 (1966). [22] V. V. KIotchkov, A. V. Aganov, Yu. Yu. Samitov and B. A. Arbuzov, Izv Akad. Nauk SSSR, Ser. Khim. 316 (1985). [23] V. V. KIotchkov, Sh. K. Latipov, L. K. Yuldasheva, A. V. Aganov, A. V. Ilyasov and B. A. Arbuzov, 1.7~. Akad. Nauk SSSR, Ser. Khim. 545 (1987).
Acta, Vol.
46A. No. 7, pp. 1037-1043, 1990
05~39/90 s3.00+ o.LNl @ 1990 Pergamon Press plc
Printed in Great Britain
Compensation
effect in the thermodynamics
of conformational
equilibria
A. I. FISHMAN* and A. A. STOLOV Kazan State University, Lenin Street 18, Kazan 42OW8, U.S.S.R.
A. B. REMIZOV Kazan Chemistry Technology Institute, Karl Marx Street 68, Kaxan 420015, U.S.S.R. (Receiued
1 June 1989; in final form 23 October 1989; accepted 26 October 1989)
Abstract-The solvent dependence of thermodynamic parameters of conformational equilibria in trans-1,2dichlorocyclohexane and rraans-1,2-bromochlorocyclohexane was-investigated by infrared absorption spectra. The results obtained show the existence of a compensation effect in the thermodynamics of conformational equilibria: the enthalpy (AH,) and entropy (AS,) differences change in the same direction when going from one solvent to another. A semi-quantitative estimation of the effect is given on the basis of the equations of statistical thermodynamics. It is shown that the temperature dependence of the A& value must be taken into account when determining the enthalpy difference of the conformers. This yields the equality of the true and observed AH, values.
INTRODUCTION
and temperature dependence of the parameters of conformational equilibria are nowadays the subject of intense studies [l, 21. In many studies devoted to this problem, the solvent dependences of the values AH, or AG,, (enthalpy and free enthalpy differences of the conformers) are analysed. However, there is little data concerning the entropy difference of the conformers, AS,,, and its variation with a solvent. The latter fact is probably due to experimental difficulties in determining the AS,, values. The lack of experimental data seems to be responsible for the following assumptions having different forms: (1) AS, = 0 or AS, = R In y, where y is the statistical weight ratio of the conformers [3]; (2) A&# 0, but is independent of solvent [l, 41; (3) AS,#O, but is independent of temperature [l]. It is perfectly clear that, in the common case, the entropy difference of the conformers depends on the solvent and temperature. Therefore, it becomes important to find out if those dependences are sufficient or not, i.e. to evaluate the experimental errors appearing due to the usage of assumptions (l)-(3). To answer this question, it is necessary to determine AS,, values for several model compounds under different experimental conditions. In this paper, the values AH,,, AGo, AS,, and also AH’ and AS’ are obtained for two di-substituted halocyclohexanes in polar and non-polar solvents. The modification of the i.r. spectroscopic method proposed earlier [5], was used. On the basis of the data obtained, an attempt is made to answer the above questions. THE SOLVENT
MATERIALS
Trans-l,2-dichlorocyclohexane(I)andtrans-l,2-bromochlorocyc1ohexane(II)wereused as models. In the liquid and solution these compounds exist in the form of a mixture of diaxial (A) and diequatorial (B) conformations [6,7]. The molecule I is one of the basics in analysing the general principles of conformational analysis: thermodynamic parameters of conformational equilibria in I dissolved in different liquids have been determined previously by different methods [ 11. The conformational equilibria in II have not been studied quantitatively. * Author to whom correspondence
should be addressed. 1037
A. I. FISHMAN et al.
1038
Non-polar propane (E = 1.61 [S]) and polar CFzClz (E = 2.5 when T= 220 K and E = 3.5 when T= 120 K) were used as the solvents. Since the dipole moments for A and B conformers are sufficiently different (3.13 and 0.37 D for the B and A form of I, respectively [l]), then, according to Ref. [l], the essential solvent dependence of all thermodynamic parameters may be expected. EXPERIMENTAL
The i.r. spectra were obtained with a UR-20 spectrometer and processed by a computer. The integral intensities of the absorption bands 498 (A) and 514 cm-’ (B) of I; 484 (A) and 505 cm-’ (B) of II [6,7] were studied. Concentrations of I and II were less than 10-3mol I-‘. The temperature range was 85-225 K. For temperatures c 145 K, the “freezing” state of the conformational equilibria occured [5]. The values of AH, were determined by the slope of the dependence of ln(l,/Z,) upon l/T (for the temperature range T > 145 K). The changes of the integral absorption coefficients aA and ua with temperature were taken into account [5,9]. Free enthalpy differences (AC,,), activation enthalpy (AH’), entropy (AS’) and the ratio aA : aB were determined by investigating the kinetics of conformational transitions. The experimental techniques used for studying the kinetics have been described in detail previously [5, lo]. The results obtained are listed in Table 1.
RESULTS AND DISCUSSION
The solvent dependence
of the ratio aA : aB
It can be seen from Table 1 that the ratio of integral absorption coefficients for the bands belonging to different conformers changes when going from propane to CF2Clz. This fact does not seem to be surprising, since the sufficient solvent dependence of i.r. band intensities is well known [ll]. Nevertheless, the assumption of independency of aA : aB on the media is frequently used [l, 4, 12, 131. In our case, the systematic errors which would appear, if we assume that aA.* aB is constant, are rather small: 70 cal mol-’ for AGo and 0.4cal mol-’ K-’ for A&. However, in the common case they are unpredictable. It should be noted that, according to our normal coordinate analysis of I and II, the bands 498 (I, A), 484 cm-’ (II, A) and 514 (I, B), 505 cm-’ (II, B) correspond to the vibrations having practically the same form. This closeness of the vibrational forms seems to be responsible for the closeness of the values of aA : aB for I and II and for their similar dependence on a solvent. The observed and true AH0 values
According to Ref. [l], when analysing the experimental AH, values it is necessary to take into account the dependence of AH, upon temperature. If AH, is a function of T, Table 1. Thermodynamic and spectroscopic characteristics of the conformers of I and II in propane and CFzClz Compound
Compound Parameter aala, AH& (kcal mol-‘) AS& (cal mol-’ K-‘) AGO(B- A)* (cal mol-‘) AHo(B - A)? (cal mol-‘) AS,(B - A) (cal mol-’ K-‘)
Propane 1.9kO.l 13.5 20.7 15+5 330 + 20 485 + 20 0.95 + 0.15
CF, Cl, 2.4kO.2 13.6+0.5 18+5 110+50 0+40 - 0.65 + 0.35
Propane 2.OkO.l 12.4kO.6 9+4 620 f 30 650 f 30 0.20+0.35
CF; Cl2 2.65 +0.3 320 f 70 90+70 - 1.4OkO.85
* The values AGo correspond to T= 167 K. t The values AH, within the limits of the experimental errors were found to be independent of T. They correspond to the average temperature for the interval 225-145 K.
Thermodynamics of conformational equilibria
1039
then the observed values (AHEb”.) differ from the true ones (AHAm’). ABRAHAM and BRET~NYDERobtained the following expression [ 11:
AH;“.=AHg”‘-T and proposed to use a reaction field model for calculating the term T(dAHhNeldT). The values T(dAH$“VdT) are sufficient when a polar solvent, or a solvent with large de/dT is used. For example, we have obtained for the solution of I in CF2Clz : T(dAHAmeldT) = 460 cal mol- ’ (T= 167 K). All the parameters used were taken from Ref. [ 11. However, when derivating (l), ABRAHAM and BRET~NYDERassumed the entropy difference of the conformers to be independent of temperature. Taking into account this dependence, instead of (1) we have a strict expression:
(2) When AH,, is measured under constant pressure (a widely used situation), the latter expression may be simplified. From the well known thermodynamic equation (for example Ref. [14]):
(s),=
T(z)P
(34
AHgbS.= AHF.
(3b)
one obtains:
It should be noted that the latter expression is derived from the fundamental thermodynamic laws, and hence it is strict. Thus, the experimental value of AH,, is equal to the true one and calculation of the term T(dAH,ldT) is not necessary. Therefore, some results obtained by ABRAHAMand BRET~NYDER[l] are to be corrected. It should be also noted, that, according to Eqn (3a), from the fact AH,=f(T) it follows that AS, also depends on temperature, and vice versa, if AH, is a constant, then AS, is a constant too. Unfortunately, nowadays it is difficult to find out if AH, is a function of T or not, because the accuracy of i.r. or NMR methods seems not to be sufficient. Compensation effect The values AH,, and AS,, (see Table 1) decrease when going from the solution in propane to that in CF2C12. Therefore, AC, decreases due to the enthalpy term, and at the same time it increases due to the contribution of TAS,. The similar results obtained in thermodynamics of non-specific [15] and specific [16] solvation are known as a compensation effect [17]: varying the solvent, one changes the AH, and AS,, values; the dependence of AS,, upon AH, is close to linear with a positive leading coefficient (AASJAAH,). In our case these coefficients are 3.3 x 10e3 K-’ for I and 2.8 x 10e3 K-’ for II (see Table 1). For the first time, the existence of the compensation effect in conformational equilibria was noted [18,19]. Below we shall try to substantiate the effect on the basis of a simple model. Let us consider the dependence of enthalpy upon a coordinate of internal rotation, q, for a molecule having two conformations A and B (Fig. l-continuous line, corresponding to the first solvent). For the molecules in the A form, torsional vibrations take place near qL, and the full energy of such vibrations is: E_
M2 I K4(qx4
2
4L12 ’
\u
1040
A. I. FISHMAN et al. A
K
I
I
\ \ \
H
I/
\\
’\
L
I
’
/
5H~
/’
\ L
Fig. 1. The dependence
of the enthalpy
upon a coordinate
of the internal
rotation
for a
molecule
in two solvents (continuous and dashed lines).
where M is the momentum moment, I,, is the reduced inertia moment and KA is the force constant. The statistical integral for the torsional vibrations can be written in the form: m exp( - EJRT)dM dq.
z=c II-m
(5)
Here, c is a constant taking into account the dimension of the integral. Combining the expressions (4) and (5) and integrating gives: z = ~xcRT(Z,A/KA)“‘.
(6)
Furthermore, we shall consider only torsional terms and their contribution to the value AS,. Here we assume that the structure of the surroundings of a solute is practically independent on its conformation, and hence the integrals over intermolecular degrees of freedom are equal for different conformers. The entropy of the A form can be calculated from the integral z [20]: SA= R{1n[2JccRT(~,,/KA)“*] + l}. The expression for the entropy difference, one obtains:
(7)
of the B form is similar. Thus, for the entropy
AS,=S,-&=iRln
(8)
All the characteristics of the curve H(q) are changed when we take the second solvent (Fig. l-dashed line). Since the structure of stable conformations weakly depends on a solvent, the changes in coordinates qL and qN, corresponding to energy minima, are neglected. For the change of the enthalpy difference with a solvent, one obtains: AAH,, = AH;, - AH, = AH, - AH,,
(9)
and for the change of AS,: AAS,,=AS&-A&=iRln
(10)
Thermodynamics
of conformational
1041
equilibria
where Ka, KL, AH; and A$, are the force constants, enthalpy and entropy differences of the conformers in the second solvent. Let us draw the relationship between AAH,, and AAS-,. Supposing L to be the beginning of a coordinate system, one obtains, for a segment of the curve KLM, an approximate expression: Hz-
Ar-f”B [l - cos(n * q)],
(11)
where AH& is the activation enthalpy and n characterizes curve H(q). From (11) it follows:
K*2?
a number of minima on the
A%B
aq2 s=o=2n2.
(12)
Obtaining similar expressions for Ki, KB and Kb and substituting them into Eqn (lo), one obtains: AH& + AH, AH:,+
AH,
(13)
*
It should be noted that the latter expression is obtained for the case of such internal rotation, when only one coordinate q varies. However, in the common case, several internal coordinates may be responsible for a conformational transition. For example, the inversion of a six-membered ring is accompanied with the rotation around all the six C-C bonds. If m coordinates are responsible for the internal rotation process, the statistical integral will have a form of a multiplication of the terms written in Eqn (6) and the entropy, a sum of the terms written in Eqn (7). Hence, taking into account Eqn (9), one obtains: AAS,,=;
AH:B
R In 3.
BA
AH,a+
AH,+
AAH,,
AH:, + AHA
’
(14)
Since for a great number of systems AAH,= AHA-AH~G AH’, expression (14) can be expanded in power series. Taking into account only the first two terms of the expansion, one obtains:
From (15) it is seen that the value, AA&,, strongly depends on AAH, and weakly on AH,. The tangent of the slope of the dependence AAS,=f(AAH,) is proportional to the number of coordinates responsible for the internal rotation and to the reciprocal value of the activation enthalpy: AA& R m -AAH,,-% AH+’
W-9
Thus, for the inversion of a six-membered ring, AH’= 10 kcal mol-‘, m = 10 and AASJAAH,, = 10e3 K-l. So, the order of the magnitude of the experimental value agrees with the estimated one. We see that the contribution of the entropy term TAA&, to AAG,, may be essential: when AA&lAAH,,= 10m3K-’ and T= 300 K, it compensates 30% of the AAH,, contribution. At the same time it should be noted that our consideration of the compensation effect in the thermodynamics of conformational equilibria takes into account only the contribution of torsional vibrations to AS,, values, and therefore it is not complete. Furthermore,
1042
A. I. FISHMANet al.
-1
-2 A/i,, (kcal
Fig.2.The dependence
0
mol-‘1
of AS, upon AH, for o-iodophenol in 12 solvents. values are taken from Ref. [21].
All AH, and AS,
the symmetry of the surroundings of the solute may be dependent on its conformation, and this fact may alter also the AS,, value. Thus, the estimations obtained may only reveal the general tendency of the behaviour of the thermodynamic parameters when the solvent is varied: (1) When AH,, is independent of a solvent, the changes in the entropy difference are, as a rule, small. (2) When AH,, changes sufficiently, AS,,, as a rule, changes also, the tangent of the dependence AH,, =f(A&) being positive. (3) The magnitude of AA& could be estimated with the help of expression (16).
Other literature data
There are several works in the literature in which the effect of the solvent upon the enthalpy and entropy differences of the conformers is investigated. Thus BAKER and SHULGIN [21]have studied the conformational equilibria in 12 solutions of o-iodophenol. When determining A&,, the authors of Ref. [21] used a doubtful assumption (aA = aB in all the solvents) and hence the obtained AS0 values are systematically shifted from the true ones, the results obtained are in good agreement with the described tendency (Fig. 2). For o-iodophenol, the value AA&/AAH,, was found to be equal to 1.3 x 10m3K-l.
1
1
I
1
2 A Ho tkcat mot-’ 1
Fig. 3. The dependence
of AS, upon AH,, for different compounds
studied in Refs [22, 23)
Thermodynamics
of conformational
equilibria
1043
The solvent dependence of conformational equilibria in 1,3,2-dioxophosphorinanes (equilibrium chair * chair) and in 2-substituted-5,6-benz-1,3-ditiepines (chair & boat) was investigated in Refs [22,23] by NMR spectroscopy. Figure 3 shows the diagram produced using the data obtained in those studies. One can observe the compensation dependence, the values AAS,lAAH, being within the limits (0.9-1.5) x 10m3K-l, which are in good agreement with our estimations. Acknowledgemenu-The authors are grateful to E. N. KLIMOVIT~KY and M. B. TIMIRBAEVfor synthesizing and purifying the samples and to M. D. BORISOVERand 0. E. KISELEVfor a fruitful discussion.
REFERENCES [l) R. J. Abraham and E. Bretsnyder, in Inrernnl Rotation in Molecules (edited by W. J. Orville-Thomas) (1974). [2] V. V. Samoshin and N. S. Zefirov, Zh. Vses. Khim. Obshch. 29, 521 (1984). [3] G. A. Beresneva, L. V. Khristenko, 0. D. Ulyanova and Yu. A. Pentin, Zh. Phys. Khim. 60, 1045 (1986). [4] A. F. Vasiljev, Zh. Prikf. Spectrosk. 6, 485 (1967). [5] A. I. Fishman, A. A. Stolov and A. B. Remizov, Spectrochim. Actu 41A, 505 (1985). [6] A. B. Remizov and L. M. Sverdlov, Zh. Prikl. Spectrosk. 9, 113 (1968). [7] P. Klaboe, Actu Chem. &and. 25, 695 (1971). [8] Ya. Yu. Akhadov, Dielektricheskie Svoistva Chistikh Zhidkostei, (Dielectric Properties of Pure Liquids). Izdarelsrvo Standartov, Moscow (1972). [9] A. I. Fishman, A. B. Remizov and A. A. Stolov, Dokl. Akad. Nauk SSSR 260, 683 (1981). [lo] A. I. Fishman, A. B. Remizov and A. A. Stolov, Zh. Prikl. Spectrosk. 40, 604 (1984). [ll] A. J. Barnes and W. J. Orville-Thomas (Editor), Vibrational Spectroscopy. Modern Trends. Elsevier, Amsterdam (1977). [12] 0. Exner, Z. Fried1 and P. Fiedler, Coil. Czech. Chem. Cornmun. 48, 3086 (1983). [13] Z. Friedl, P. Fiedler, J. Biros, V. Uchitilova, I. Tvaroska, S. Bohm and 0. Exner, CON. Czech. Chem. Commun. 49,205O (1984). [14] P. W. Atkins, Physical Chemistry. Oxford University Press, Oxford (1978). [15] B. N. Sotomonov, V. V. Gorbatchuk and A. I. Konovalov, Zh. Obshch. Khim. 52, 2688 (1982). [16] G. C. Pimentel and A. L. McClellan, The Hydrogen Bond. Freeman, San Francisco (1960). [17] S. G. Entelis and R. P. Tiger, Kinetika Reaktsii v Zhidkoi Faze (Reaction Kinetics in the Liquid Phase).
Khimiya, Moscow (1973). [18] A. I. Fishman, A. A. Stolov, A. B. Remizov and I. S. Pominov, Zh. Prikl. Spectrosk. 44, 330 (1986). [19] A. B. Remizov, A. A. Stolov and A. I. Fishman, Zh. Phys. Khim. 61, 2909 (1987). [20] I. N. Godnev, Vichisleniye Termodinamicheskikh Funktsii po Molecularnim Dannim, (Calculation of Thermodynamic Functions by Molecular Data). GITTL, Moscow (1956). [21] A. W. Baker and A. T. Shulgin, Spectrochim. Acta 22, 95 (1966). [22] V. V. KIotchkov, A. V. Aganov, Yu. Yu. Samitov and B. A. Arbuzov, Izv Akad. Nauk SSSR, Ser. Khim. 316 (1985). [23] V. V. KIotchkov, Sh. K. Latipov, L. K. Yuldasheva, A. V. Aganov, A. V. Ilyasov and B. A. Arbuzov, 1.7~. Akad. Nauk SSSR, Ser. Khim. 545 (1987).