Partial molar volumes-insights into molecular structure

LIQUIDS ELS EVI E R

Journal of Molecular Liquids 81 (1999) 37-45

Partial m o l a r volumes-Insights into molecular structure W.Zielenkiewicza, J.Poznafiskia, b a)Institute of Physical Chemistry, Polish Academy of Sciences, 01-224 Warsaw, Kasprzaka 44/52, Poland b)Institute of Biochemistry and Biophysics, Polish Academy of Sciences, 02-106 Warsaw, Pawifiskiego 5a, Poland SUMMARY The applications of a new model describing the solute - solvent interactions of organic hydrophobic compounds to the calculation of experimental volumetric data are discussed. The proposed model is based on the interpretation of volumetric properties of aqueous solutions: partial molar volume V~, molecular volume V2~ and volume of solvation shell Vl,solv. Calculations were made on reported V2° data for amides, N-alkyl amides and N,Ndialkylamides. The structural parameters of the compounds were obtained by use of the molecular mechanics methods, INSIGHT (Biosym, San Diego, USA) or SYBYL (Tripos Ass. St. Louis, USA), whereas for calculations of the molecular surface areas and molecular volumes the algorithm GEPOL version 12.1 was applied. It was demonstrated, that the ratio of V~ - V2 to the Vl,solv , defined as a relative density of solvation shell, co, is a convenient parameter when used to compare solutes with different structure and polarity. It was also shown that the patterns characterizing the dependence ofcx on the structure and polarity of the compounds are the same although the derived results depend on the applied method of calculation of structural parameters of a solute and "a priori" assumed dimension of solvation shell. © 1999 Elsevier Science B.V.All rights reserved. 1. INTRODUCTION The determination of volumetric properties is of great importance in the characterization of aqueous solutions. It is well known [1] that when a small non polar organic molecule is transferred from a non polar solvent to water, a large reduction in its partial molar volume is observed. This volume change is considered to be a manifestation of the hydrophobic effect, which is treated as one of the most important forces governing the structure and interaction of all biological molecules [ 1-4]. So far there is no consensus on the physical background of this effect [5-8]. Exist a great number of precise V~° data for aqueous solutions of organic hydrophobic compounds [9-12], e.g. alkanes, amines, amides. Many of these compounds are treated as model compounds for proteins and nucleic acids. The determination of partial molar volumes Acknowledgement:We gratefullyacknowledgethe financial supportfrom KBN (grant No 3T09A05611).

0167-7322/99/$ - see front matter © 1999 Elsevier Science B.V. All rights reserved. PII S0167-7322(99) 00030-6

38 of the solutions of proteins, nucleic acids and nucleic acid bases solutions were also subject several investigations [ 13-16]. Much effort has been also made to obtaining from V~° data information about solutesolvent interactions. To elucidate local changes of solvent structure caused by neutral or charged solute molecules, the simple additivity scheme [9], based on the examination of the contribution of the functional groups of the compounds is used. The notion of packing density [17-19] of a solute in solution, defined as the ratio of van der Waals volume V w to the partial molar volume V2° of solute species, is applied for comparing solutes with different structures and volumes. Terasawa et al [20] proposed a convenient linear dependence of V~° on V w for calculating the empirical constants characterizing several classes of organic compounds [2025], e.g. homologous strain-chain series of hydrocarbons, alcohols and porphyrine derivatives. A new model of solute solvent interactions, based on volumetric properties of the solution, was described in our previous paper [26]. According to this model each solute molecule has its own solvation shell of well defined volume. The solution is infinitely diluted so that solute-solute interactions can be theoretically neglected. It was demonstrated that parameter c~, defined as the relative density of soivation shell which characterizes the organization of the structure of water around the solute molecule, is a property convenient to use in comparing solutes with different structure and polarity. It was stated, that the values of c~ depend strongly on the number of CH 2 groups in a given series of compounds as well as on the number of polar groups. A linear dependence between the value cc and of the polarity P, defined as a ratio of molecular surface of the polar groups and atoms exposed to the solvent to the total molecular surface, has been found [26-27]. The ct value is always negative thereby indicating an average water density in the hydration shell to be lower than for pure water. That observation has led to the "iceberg" structure proposed originally by Franks and Ewans [28]. A conclusion about the dependence of the c~ value on the structural properties was formulated on the base of the calculations in which the geometrical parameters of each molecule were determined by the method of molecular mechanics according to the INSIGHT program (Biosym Technologies, San Diego, USA). The molecular accessible surface areas and molecular volumes were calculated by use of the algorithm GEPOL Version 12.1 [29]. In this work the results of cc and a = f(P) determinations, based on the evaluation of structural parameters of compounds was studied by two methods of molecular mechanics. Calculations were made taking into consideration various atomic radii as well as various dimensions of solvation shells. We attempted to verify, how the choice of the calculation method may affect the derived c~ value and it's mathematical formula as a function of polarity, ~=

f(P).

The calculations presented therein were made for amides, N-alkylated amides and N,Ndialkylamides. 2. M E T H O D S Assuming that d~.~ represents mean water density in the solvation shell, the relative density of hydration shell cc is given by the following expression [26]:

39

a .

d, ,on - d0 . . .

do

V ~ - V,°

V,.~

(1)

where do is the pure solvent density, Vu is the molecular volume, V~ is the partial molar volume and Vl,solv is the volume of the hydration shell. Calculations were based on reported V2° data [30]. The values of V:u and Vl,solv were evaluated on the base of determined structural parameters. The atomic coordinates of the molecules studied were obtained by INSIGHT of Biosym or SYBYL of Tfipos packages. In SYBYL calculations tripos forcefield [31] with Pullman atomic charges [32] was used, in INSIGHT cvff forcefield [33], respectively. Various types of optimization of the structure were assumed. In order to mimic water screening in the absence of explicit water molecules in both methods electrostatic interactions were scaled by setting a distance dependent dielectric constant to a value 1/4r. All alkyl groups were analyzed in extended conformation and sp2 hybridization of nitrogen. N-alkylated amides were assumed to be in trans configuration of HN, C=O. The influence of the used structural constraints on the cc=f(P) relation were additionally tested for the following conformational changes: 1) cis-trans isomerization of the amide bond in N-methylamides; 2) rotamer equilibrium undergoing in alkyl groups; 3) semiempirical calculation of the nitrogen sp2 to sp 3 hybridization change (performed by MOPAC 6.0 in PM3 parameterization). Molecular volumes V2u and volumes of solvation shells Vl,solv as well as molecular surface areas SM and their atomic partitions S A were estimated semiempirically using the GEPOL package 12.1 elaborated by Silla et al [29]. The water radius was set to 1.4A. The volume of the first solvation shell Vl,solv was assumed to be equal to the volume determined by rolling a sphere of water molecule diameter over the solute surface. Most of the calculations were done assuming nv-1 solvation shell. To visualize how varying the number of solvation shells affects the value o f ~ , the results are also presented for nv=l.5, 2. Similarly various combinations of forcefield geometry and radii optimization in a solvent accessibility semiempirical estimation were assumed. The calculations were made applying: la/ Insight with cvff forcefield and radii belonging to cvff" forcefield [0.95A(H), 1.5A,(I-I), 1.4A(N),I.4A(O)]; lb/Insight with cvff" forcefield and radii belonging to Tripos forcefieid [1.08A(H), 1.52A(C), 1.45A(N), 1.36A,(O)]; 2a/ Tripos forcefield and radii corresponding to Insight cvff; 2b/Tripos forcefield and radii belonging to Tfipos forcefield.

3. RESULTS AND DISCUSSION In Table 1 are listed the values of partial molar volumes V2°; index i, denoting the applied A A A calculation method (la, lb, 2a, 2b); the calculated values of Vzu , Vl,solv, So,S•,S,(N),S

M

,P

and cz for the compounds studied. Inspection of the results demonstrated, that the value of ct is always negative and depends strongly on the number of substituted CH 2 groups as well as on the place of their substitution on the skeleton. Generally it can be concluded that the c~ value is decreasing when the hydrophobicity of the solute increases. The cc value depends linearly on the polarity of the compounds (Table 2) according to the relation: cz = % + 13pP

(2)

40 Table 1. Partial Molar Volumes, Polarities and Relative Densities o f Solvation Shells. Volume [cm3-mol4l Surfacelk21

Compound N,N-Dimethylformamide N,N-Dimethylformamide N,N-Dimethylformamide N,N-Dimethylformamide N,N-Diethylfonnamide N,N-Diethylformamide N,N-Diethylformamide N,N-Diethylformamide N,N-Dimethylacetamide N,N-Dimethylacetamide N,N-Dimethylacetamide N,N-Dimethylacetamide N,N-Diethylacetamide N,N-Diethylacetamide N,N-Diethylacetamide "N,N-Diethylacetamide N,N-Dipropylacetamide N,N-Dipropylacetamide N,N-Dipropylacetamide N,N-Dipropylacetamide N,N-Dimethylpropanamide N,N-Dimethylpropanamide N,N-Dimethylpropanamide N,N-Dimethylpmpanamide N,N-Diethylpropanamide N,N-Diethylpropanamide N,N-Diethylpropanamide N,N-Diethylpropanamide N-Methylformamide NoMethylformamide NoMethylformamide N-Methyiformamide N-Ethylformamide N-Ethylformamide N-Ethylformamide N-Ethyiformamide N-Propylformamide N-Propylformamide N-Propylformamide N-Propylformamide N-Methylacetamide N-Methylacetamide N-Methylacetamide N-Methylacetamide N-Ethylacetamide N-Ethylacetamide N-Ethylacetamide N-Ethylacetamide N-Propylacetamide

I la lb 2a 2b la lb 2a 2b la lb 2a 2b la lb 2a 2b la lb 2a 2b la lb 2a 2b la lb 2a 2b la lb 2a 2b la lb 2a 2b la lb 2a 2b la lb 2a 2b la lb 2a 2b la

So 74.5 74.5 74.5 74.5 107.2 107,2 107,2 107,2 90.5 90.5 90.5 90.5 121.7 121.7 121.7 121.7 154.2 154.2 154.2 154.2 105.4 105.4 105.4 105.4 137.7 137.7 137.7 137.7 56.8 56.8 56.8 56.8 74.0 74.0 74.0 74.0 87.9 87.9 87.9 87.9 74.0 74.0 74.0 74.0 90.7 90.7 90.7 90.7 105.1

35.6 39.5 35.4 39.1 52.7 59.3 52.5 59.0 43.9 48.8 43.3 48.4 61.4 68.9 60.9 68.2 77.1 87.6 77.1 87.2 52.1 58.7 51.7 58.4 69.8 78.8 69.2 78.2 26.9 29.8 26.8 29.9 35.0 39.3 34.8 39.3 42.8 48.7 42.8 48.7 35.2 39.3 35.1 39.0 43.0 48.4 42.8 48.2 50.9

380.7 396.6 378.8 395.4 463.7 483.0 456.8 478.6 420.3 438.4 419.4 436.0 492.7 521.3 490.5 516.7 598.6 627.6 589.1 615.9 463.9 488.9 462,0 486.0 540.7 568,0 539.3 562.5 337.8 348.7 336.9 351.6 389.8 403.7 390.3 402.3 439.1 454.9 439.4 454.2 386.0 401.1 380.9 399.7 438.0 458.1 433.7 454.9 485.9

14.8 13.4 14.7 13.2 14.2 12.9 13.5 12.1 14.1 12.4 13.7 12.0 13.2 11.7 12.6 10.9 13.2 11.6 12.4 10.8 13.1 12.1 13.1 I 1.5 12.5 11.3 12.0 10.3 15.9 14.3 16.0 14.6 16.0 14.3 16.0 14.6 15.9 14.4 16.0 14.5 14.2 12.9 14.1 12.5 14.4 12.8 14.0 12.4 14.3

SM 3.7 3.6 3.6 3.7 2.1 2.2 2.0 2.0 3.9 3.8 3.7 3.7 2.1 2.3 2.0 2.1 2.3 2.1 2.0 2.1 3.5 3.6 3.6 3,6 1,8 2.0 1.8 2.0 6.6 5.8 6.5 5.7 5.4 5.0 5.6 5.2 5.4 5.1 5.6 5.2 5.8 5.4 5.9 5.6 5.2 5.0 5.5 5.0 5.3

0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 5.0 6.7 5.2 6.8 4.5 6.0 4.6 6.0 4.6 6.0 4.6 6.0 4.7 6.2 4.8 6.4 4.3 5.5 4.4 5.7 4.3

80.0 84.0 80.0 85.5 103.0 108.9 103.2 106.9 94.9 100.8 93.1 98.7 ll4.1 121.3 113.7 119.8 141.3 148.8 139.4 147.3 104.9 109.4 104.6 llO.5 129.1 133.6 125.0 130.8 67.8 71.3 67.6 71.2 78.9 82.7 82.7 84.7 97.2 98.2 97.1 98.2 79.7 84.1 80.1 86.0 96.8 99.9 96.0 99.3 108.9

tx 0.23 0.20 0.23 0.20 0.16 0.14 0.15 0.13 0.19 0.16 0.19 0.16 0.13 O.ll 0.13 O.11 O.ll 0.09 0.10 0.09 0.16 0.14 0.16 0.14 O.11 0.10 O.ll 0.09 0.40 0.38 0.41 0.38 0.33 0.31 0.32 0.30 0.27 0.26 0.27 0.26 0.31 0.29 0.31 0.29 0.25 0.23 0.25 0.23 0.22

-0.102 -0.088 4). 103 -0.090 -0.117 -0.099 -0.120 -0.101 -0.111 -0.095 -0.113 -0.097 -0.122 -0.101 -0.124 -0.103 -0.129 -0.106 -0.131 -0.109 -O.115 -0.095 -0.116 -0.097 -0.126 -0.104 -0.127 -0.106 -0.088 -0.077 -0.089 -0.077 -0.100 -0.086 -0.100 -0.086 -0.103 -0.086 -0.103 -0.086 -0.101 -0.087 -0.102 -0.088 -0.109 -0.092 -0.1lO -0.094 -0.112

41 Table 1. cont. Partial Molar Volumes, Polarities and Relative Densities o f Solvation Shells. Volume [cm3.mol"11 Compound I V~ 2 VM Vl,solv SO SN SH(N) SM

SuffacelAal

N-Propylacctamide N-Propylacctamid¢ N-Propylacctamide N-Methylpropanamide N-Methyipropanamide N-Methylpmpanamide N-Methylpropanamide N-Ethyipropanamide N-Ethylpropanamide N-Ethylpropanamide N-Ethylpropanamide N-Propylpropanamide N-Propyipropanamide N-Propylpropanamide N-Propylpropanamide • Formamide Formamide Formamid¢ Formamide Acetamide Acetamide Acetamide Acetamide Propanamide Propanamide Propanamide Propanamide Butanamide Butanamide Butanamide Butanamide Hexanamide Hexanamide Hexanamide Hexanamide

lb 2a 2b la lb 2a 21) la lb 2a 2b la lb 2a 2b la lb 2a 2b la ib 2a 2b la lb 2a 2b la lb 2a 2b la lb 2a 2b

105.1 105.1 105.I 89.8 89.8 89.8 89.8 105.4 105.4 105A 105.4 121.5 121.5 121.5 121.5 38.5 38.5 38.5 38.5 55.8 55.8 55.8 55.8 71.5 71.5 71.5 71.5 87.1 87.1 87.1 87.1 119.2 119.2 119.2 119.2

58.3 50.9 57.8 43.3 48.9 43.0 48.7 51.5 58.5 50.9 58.2 59.2 68.0 58.9 67.5 18.8 20.4 18.8 20.5 26.4 29.5 26.6 29.4 34.9 39.4 34.9 39.1 42.8 48.7 43.0 48.8 58.7 67.7 58.8 67.8

507.5 484.0 504.4 433.7 455.9 426.7 449.9 482.8 510.9 476.0 503.3 536.3 563.6 528.0 554.7 274.7 286.4 276.4 289.3 326.9 341.8 326.4 343.4 376.5 394.2 374.2 395.5 427.8 447.1 427.0 447.1 526.3 552.1 527.7 552.7

12.8 14.0 12.4 13.9 12.3 13.7 12.2 13.7 12.1 13.6 12.2 13.8 12.1 13.6 12.1 15.2 13.8 15.9 14.3 14.9 13.2 15.2 13.6 14.6 12.9 14.8 13.2 14.5 12.9 14.9 13.3 14.5 12.6 14.9 13.2

4.8 5.5 5.0 6.1 5.4 5.5 5.1 4.9 4.6 5.1 4.6 4.9 4.6 5.0 4.6 10.0 9.4 10.2 9.1 9.6 9.1 9.6 8.8 9.5 9.1 9.1 8.4 9.4 9.1 9.1 8.3 9.5 9.0 9.1 8.3

5.4 4.4 5.7 4.6 5.9 4.4 5.8 4.1 5.0 4.0 5.0 4.1 5.0 4.0 5.0 9.9 13.6 10.4 14.2 9.5 13.0 10.1 13.4 9.4 12.1 9.5 13.0 9.5 12.8 9.6 13.0 9.4 12.2 9.6 13.0

111.9 110.3 113.0 95.2 98.7 93.4 98.2 106.1 109.9 110.0 111.8 122.1 123.5 124.1 124.8 50.8 53.0 52.7 54.7 64.5 69.5 65.9 70.1 79.6 81.4 79.1 81.7 93.1 95.9 93.6 95.8 122.0 122.0 121.7 123.2

P

ct

0.21 -0.092 0.22 -0.112 0.20 -0.094 0.26 -0.107 0.24 -0.090 0.25 -0.110 0.24 -0.091 0.21 -0.112 0.20 -0.092 0.21 -0.114 0.19 -0.094 0.19 -0.116 0.18 -0.095 0.18 -0.119 0.17 -0.097 0.69 -0.072 0.69 -0.063 0.69 -0.071 0.69 -0.062 0.53 -0.090 0.51 -0.077 0.53 -0.090 0.51 -0.077 0.42 -0.097 0.42 -0.082 0.42 -0.098 0.42 -0.082 0.36 -0.104 0.36 -0.086 0.36 -0.103 0.36 -0.086 0.27 -0.115 0.28 -0.093 0.28 -0.114 0.28 -0.093

Derived values o f ~ and 13p are listed in Table 2. It appears, that in spite o f a scatter resulting from the applied calculation methods, the linear dependence o f the function ct--f(P) is always the same. For the series o f amides and N-alkyl amides, in spite o f different parameterization o f function ct--ffP), presented graphically on Figure 1, the derived values o f cto are close (Table 2), whereas the oto value obtained for N,N-alkylamines differs significantly from the others. W e analyzed the influence o f the applied method o f calculation on the obtained results o f volumetric parameters o f molecule, V ~ and Vl,solv , and likewise on the value oftx. Examining the data in Table 1 indicates that the structural parameters values calculated by cvff

42

-0.07

AN,N-dialkylamides

S

~

-0.08 -0.09 -0.10 -0.11

-0.12 0

0.1

0.2

0.3

0.4

0.5

0.6

P

Figure 1. Dependencies ¢t=f(P) for amides, N-alkylamides and N,N-dialkylamides/2b forcefield/

Table 2. The cto and I~n values for various atomic radii. i

nv

la lb 2a 2b 2b 2b

1 1 1 1 1.5 2

la lb 2a 2b 2b 2b

! 1 1 1 1.5 2

la lb 2a 2b 2b* 2b 2b

1 1 1 1 1 1.5 2

2b*

1

ao

I~p

Amides 4). 14 Ix'-0.002 0.099:L-0.008 -0.112i-0.001 0.070:£-0.003 -0.141:[-0.002 0.100i-0.005 -0.113i-9.001 0.073:£-0.003 -0.058i-0.001 0.044+0.002 -0.035i-0.001 0.028:t-0.002 N-alkyled amides -0.138x'-0.001 0.122i-0.008 -0.1 lOx'-0.001 0.081 x'-0.007 -0.14 hk-0.002 0.126:t0.009 -0.113i-0.002 0.094:£-0.009 -0.058!-0.006 0.058i-0.007 -0.035i-0.001 0.038i-0.002 N,N-dialkyled amides -0.150:£-0.001 0.207x'-0.013 -0.1192-0.001 0.155x'-0.011 -0.152i-0.001 0.214:£-0.012 -0.122:£-0.002 0.164x'-0.018 -0.115i-0.002 0.120:t-0.018 -0.064:£-0.001 0.074:t-0.005 -0.038:L-0.001 0.074:k0.005 All compounds (final correlation) -0.117i-0.002 (O) 0.144i-0.022 (N) 0.113:L-0.026

R2 0.991 0.995 0.993 0.994 0.994 0.994 0.974 0.941 0.968 0.944 0.944 0.944 0.981 0.974 0.968 0.954 0.900 0.954 0.945 0.970

43

forcefield do not differ from those obtained using the Tripos forcefield (Table 1, the values of parameters located in rows denoted by indexes la, 2a and lb, 2b). As a consequence, parameters % and I~p are also identical (Table 2). Whereas, the assumed radii values affect significantly the calculated results of structural parameters (Table 1, the values of the parameters located in rows denoted by indexes la, 2a and lb, 2b) and also the values of a o and 13p (Table 2). This conclusion is confirmed by calculations performed by assuming varying number of solvation shells nv=l, 1.5,2 (Table 2). Increase of V l,soiv results in decrease of the a value. Assuming, that a o depends on density, difference between solvation shell of completely non polar molecule and pure solvent, we conclude that its value should be the identical for different series of compounds. Looking for the reason for observed divergence of results we performed the calculations of structural parameters for the series of N,N-dialkyl amides assuming hybridization sp 3 instead of formerly used hybridization sp2. Derived results of calculations indicate (Table 2, index 2b*) the improvement of a o conformity for all series of compounds considered. It therefore seems that the a parameter is responding to the changes in the molecule structure. Additional semiempirical calculation performed for formamide and N-methyl-formamide proved the existence only one minimum corresponding to the nitrogen sp2 hybridization whereas in the case of N,N-dimethylformamide there are two minima corresponding to sp2 and sp3 hybridization respectively. So far only the dependencies between a and polarity of the molecule were analyzed. Now let us consider the more complex dependence of a on the molecule polar atom accessibility: N, O, H(N). Thus the equation (1) may be written as (3): = ~0 4- ~NXN + ~ o X o 4-- ~H(N)XH(N)

(3)

This equation, although formally correct, was impossible to resolve because of the strong exceeding 90°,6, correlation of the atomic partitions of nitrogen (X N ) and polar hydrogen XH0q). Decreasing the number of parameters only to: 13NXN and 13oXO we obtained following values of the parameters ao= -0.117 -- 0.002, 13N=0.144 _+0.022, 130--0.113 ± 0.026 (Table 2). The derived dependence describes the data of the partial molar volumes of the studied compounds with a very good accuracy. In addition, when defined in such a way data were used according to the simple additivity scheme to the calculation of partial molar volumes, we obtained the increment values of V~ related with the substitution of CH 2 on i'4= and C- atoms of the molecule skeleton, corresponding to 17.01 _+ 0.36 cm3.mo1-1 and 15.83 ± 0.19 cm3.mol "1, respectively. These results are in a good agreement with the data obtained by applying directly the additivity scheme to the calculation of the increment V2° values for CH 2 substitutions on N or C atoms: VCH2 (N- substituted) 17.41 ± 0.23 cm3.mo1-1 whereas VCHz (C-substituted) was found to be: - 15.93 ± 0.12 cm3.mo1-1 . The influence of the possible conformational changes on a = f(P) has been also verified. In the case of N-methylamides, where two forms of N-C(O) bond are possible, used method for all compounds, apart N-methylformamide, shows the dominant role of t r a n s isomers (Fig2).

44

CL • o.N--..,.°. -0.07

-0.08

-0.09

-0.10 0.2

0.3

0.4

0.5

0.6

P

Figure 2. The ot = f(P) relations for different conformational states of amides./2b forcefield/

Table 3 The a n and P values for different conformational states Compound Isomer Side chain rotamer N-Methylformamide t N-Methylformamide c N-Methylacetamide t N-Methylacetamide c N-Methylpropanamide t g+ N-Methylpropanamide t t N-Methylpropanamide c g+ N-Methylpropanamide c t Propanamide g+ Propanamide t Butanamide g+gButanamide g+g+ Butanamide g+t Butanamide tg+ Butanamide tt Formainide Acetamide

P

~t

0.375 0.384 0.286 0.306 0.236 0.235 0.266 0.251 0.422 0.416 0.358 0.360 0.364 0.353 0.357 0.690 0.510

-0.077 -0.078 -0.088 -0.089 -0.092 -0.091 -0.094 -0.094 -0.082 -0.082 -0.087 -0.087 -0.086 -0.087 -0.086 -0.062 -0.077

Conformer population 0.80 0.20 0.98 0.02 0.55 0.44 0.00 0.01 0.54 0.46 0.14 0.3 l 0.24 0. l 1 0.20

The obtained results are generally agree with molecular mechanics calculation of conforrnational energy, showing that cis isomers are destabilized by N-methyl C-alkyl steric interaction (Table 3). In contrast conformational changes o f the aliphatic side chains do not significantly change either ct or P values. Thus it appears, that the presented new model is not only providing new information about solute-solvent interactions but also broadens the range o f possible applications o f the methods presently used for interpretation of partial molar volume data.

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