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The relative partial molar enthalpies and apparent molar volumes of aqueous solutions of L-alanylglycine and of DL-alanylglycine
M-1333 J. Chem.
Thermod.vnamics
1982,
14, 93-91
The relative partial molar enthalpies and apparent molar volumes of aqueous solutions C-alanylglycine and of DL-alanylglycine M. K. KUMARAN,
G. R. HEDWIG,
of
and I. D. WATSON
Departmentof Chemistry,Biochemistry,and Biophysics,Massey Liniversity, PalmerstonNorth, New Zealand (Received7 May 1981: in revi.yed,form20 Ju1.v1981) Enthalpies of dilution of aqueous solutions of the dipeptides L-aiany~y~ne and DLalanylglycine have been measured at 298.15 K and used to obtain the relative partial molar enthalpy I.., of water in the solutions. The partial molar vofumes of the dipeptides, obtained from density measurements at 298.15 K, are also reported. The results are compared with those for glycyl-L-alanine solutions.
1. Introduction The interaction of solvent water with a protein in aqueous solution plays an important role in determining the conformational stability of the macromolecule.“’ The difference in the interaction with water of non-polar and polar amino-acid side groups in the protein is considered to be a dominant factor in the solvent’s role in determining the conformation of the protein. (‘**) One approach towards a better understanding of side-chain hydration in proteins is to study an analogous effect in a series of model compounds. In previous studies of aqueous solutions of some amino acids and dipeptides,‘3q4’ we examined the effect of amino-acid substituent on solute-water interactions from a determination of the relative partial molar enthalpies and partial molar volumes of the solution components. The results suggested that for solutes with non-polar side groups, the interaction with water was dominated by the side group. As part of our continuing studies on peptide solutions, we report the enthalpy of dilution and density measurements at 298.15 K on aqueous solutions of L-alanylglycine and DLalanylglycine. From a comparison of these results with those determined earlier for glycyl-L-alanine, (4) the importance of methyl-group position in the solvation of the dipeptide can be assessed.
2. Experimental L-Alanylglycine and DL-alanylglycine, purchased from the Sigma Chemical Co., were both recrystallized from (water + ethanol) and dried under vacuum. Each ~~21-9614/82~01~3+05
~Ol.~/O
C 1982 Academic Press Inc. (London) Limited
94
M. K. KUMARAN.
G. R. HEDWIG,
AND 1. D. WATSON
dipeptide gave a single h.p.1.c. peak and a single t.1.c. spot. The optical purity of Lalanylglycine was checked using a Thorn Bendix Ltd. N.P.L. automatic polarimeter, model 143D. The estimated specific optical rotatory power of the substance is 0.00889 m2. kg- ‘. This is in good agreement with the value of 0.00884 m” kg ‘. reported by Erlanger and Brand.“’ Water for preparation of the solutions was deionized, glass-distilled, and, prior to use, freshly boiled to reduce the relative amounts of dissolved gases. The enthalpies of dilution were determined using a LKB 10700 flow microcalorimeter. Details of the apparatus and procedures used have been reported earlier.‘3.4’ Solution densities were determined by pyknometry as described previously. (4) Solutions were prepared by mass by weighing in a temperaturecontrolled room and correcting for the effect of air buoyancy. The resistance of the calibration heater was 49.760 Q. Electric currents between 1.3 and 3.2 mA were used to match the enthalpy changes due to dilution, The solutions were pumped at a constant rate of (3.992rt 0.005) mm3. s- ‘. The dilutions were done by pumping water at different rates between 3.808 mm3 .s-’ and 15.203 mm’.s-r. All these how rates were checked frequently.
3. Results The results of the enthalpy of dilution measurements are given in table 1. As detailed in a previous paper, t31 the molar enthalpy of dilution AHdig of solute is related to the relative enthalpies E and rf of the diluted and undiluted solutions, by the equation: AH,,, = (Lf-L’)jn,, where n2 is the amount TABLE
__II mi mol.kg-’
of substance of the solute. The quantity
L/n,, which is
1. Enthalpies of dilution of dipeptide solutions at 298.15 K; tni and tnf are the initial and final molalities ~ mr mol,kg-’
---&ii, J.mol-’
3 mol-kg-’
~..- mr mol.kg-’
a311 J.moI-’
Mi
i&i&p
4 mol.kg-’
~. mm J,mol-’
L-CH,CH(NH,)CONHCH,COOH 0.4715 0.4715 0.4715 0.6861 0.6861 0.6861
0.0975
0.5158 0.5158 0.5158 0.6504 0.6504 0.6504
0.2631 0.1765 0.1067 0.3318 0.2226
0.1614 0.2405 0.3513 0.2359 0.1428
-57.9 -46.1 -33.7 -46.8 -63.0 -78.7
0.7713 0.7713 0.7773 0.8689 0.8689 0.8689
0.3980 0.2673
-54.1 -75.5
0.1618
-91.7
0.9677 0.9677 0.9677
0.4446 0.2987 0.1807
-59.9 -80.6 -98.4
1.1105 1.1105 1.1105
0.4946 0.3320 0.2007 0.5665 0.3800 0.2296
-65.9 -88.6 - 108.4 -14.4 -98.9 -122.7
0.3542
-97.8 -76.3 -100.5 -126.1
DL-CH~CH~H~)CONHCH~COOH
0:1345
-37.8
-50.5 -65.4 -47.2 -62.8 -79.7
0.7742 0.7742 0.7742 0.9107 0.9107
1.0347
0.3957 0.2656 0.1606 0.4647 0.3117 0.5280
-55.9 -73.1 -91.7 -64.8 -86.7 -74.7
1.0347 1.1004 1.1004 1.1004
0.5615 0.3767 0.2278
ENTHALPIES
OF
DILUTION
AND
DENSITIES
OF
TRIPEPTIDE
95
SOLUTIONS
identical to the relative apparent molar enthalpy L, of the solute,@ can be expressed as a polynomial in molality m in the form t/n2 = A,m+A2m2+A3m3+.
. ..
(2)
where coefficients Aj are parameters. From equations (1) and (2) AHdil=
A,(m,-mi)+A,(mi-mz)+A3(m:-mm3)f.
“,
(31
the values of the coefficients Aj were obtained by fitting equation (3) to the quantities in table 1 using the procedures described earlier. (j’ The parameters so obtained are given in table 2 together with their estimated standard deviations. Also shown in the TABLE
Dipeptide
___--... Al J,kg.mol-’
L-Alanyiglycine DL-Alanyl~ycine
17+3 159+3
-.
2. Parameters _-. .- A,r - _J.kg’.mol-
of equation
(3)
_... .--- A.3 __ _ J,kg3.molV4
-1.152 -II+2
.-- 3 mol.kg-’ 0.47 to 1.11 0.52 to 1.10
table is the range of initial molality over which the dilutions agreement index R,‘4’ calculated from the equation :
R 0.014 0.020
were made, and an
where the superscripts Ohsand ca’c refer respectively to the experimental enthalpy of dilution and that calculated from equation (3). and U’i is the weighting factorC3.“’ for AH$‘;. The relative partial molar enthalpy L, of the solvent was calcuIated’3’ using the equation : L, = (L-n,L,)/n,
= -M,(A,m2+2,~1,m3$3A,m4f.~.),
(5)
where M, is the molar mass of the solvent. The values of L, are shown graphically in figure I. For the purposes of comparison, L, values for the aqueous solutions of glycylglycine, alanylalanine, and glycyl-L-alanine obtained earlierC4’ are also included. The apparent molar volumes V’ were calculated from the solution densities 11 using the standard expression : I;+ = (M2i’p)-(p-po)jmppo,
(6)
where M, is the molar mass of the solute, m is the molality of the solution and I+, is the density of water. The density p of the solutions, and the apparent molar volumes Vd,of each of the dipeptides are given in table 3. The apparent molar volume of both dipeptides appears to be linear in molality and. although there is no a priori reason why this should be so,@) we have obtained the value at infinite dilution (which is the partial molar volume Vi= of solute at infinite dilution) by means of a least-squares fit to the equation : Ii = V,’ +Sm. (7)
M. K. KUMARAN,
96
G. R. HEDWIG.
I
--c
AND 1. D. WATSON
E
I
0.4
0.8
I 1.6
1.2
m/(mol*kgm')
FTGURE 1. Relative partial molar enthalpies of water in aqueous solutions of some dipeptides at 298.15 K. A, glycylglycine; B, glycylalanine; C. L-alanylglycine; D, DL-alanylglycine; and E, alanylalanine.
TABLE 3. Densities p of peptide solutions and apparent molar volumes V, of the dipeptides at 298.15 K In
mol.kg-’
P
g.cin3
v,
cm3~mol-’
m
mol.kg-’
P
v,
g.cme3 cm3.mol-’
0.1447 0.4715
1.00429 95.5,+0.7 1.02003 95.3skO.2
0.6862
1.02970
95.5,f0.2
L-CH,CH(NH,)CONHCH,COOH 1.03363 95.7, +O.l 0.7773 0.8689 1.03762 95.7, +O.l 0.9677 1.04168 95.8,+0.1
0.2032
1.00718
95.4,*0.5
DL-CH3CH(NH2)C0NHCHl~00~ 0.6504 1.02800 95.7, + 0.2
0.3411
1.01380 95.5,+0.3
0.4272
1.01784
0.5431
1.02316 95.7,f.O.2
95.6,*0.2
0.6665 0.7742
0.9107
1.02871
95.7,f0.2
1.03335 95.9,+-0.1 1.03917 95.99&o.1
In
mol,kg-’
P
g,cm-’
b
crn’~mol-’
1.1105
1.04757 95.9,rtO.l
1.0347 1.1004
1.04434 96.0s + 0.1 1.04688 96.2,fO.l
ENTHALPIES
OF DILUTION
AND DENSITIES
OF TRIPE~IDE
SOLUTIONS
97
TABLE 4. Partial molar volumes at infinite dilution and values of S for aqueous dipeptides at 298.15 K .---
Dipeptide L-Alanyl~ycine DL-AIanyIgiycine Glycyl- L-alanine ’
V~/(cm3~mol-‘) .-~. 95.01+0.1 95.221-0.06 92.66kO.06
.--
S/(cm3.kg.mol- 2, .~~. ~0.X6&0.1 0.86-tO.07 1.63ri:O.OS
’ From reference 3.
Values of V;, S, and their uncertainties so obtained are given in table 4 together with values of the same functions for glycyl-L-alanine.‘4’ 4. Discussion Chiral effects are expected to be negligible in the interaction of solvent water with small peptides. (‘I Our L,‘s and 1/;“‘s for aqueous solutions of L and DL-alanylglycine are consistent with this view. The L, results shown in figure 1 indicate that the interaction with water of alanylglycine is intermediate between that for glycylglycine and alanylalanine. The negative values of L, and the trend with molality suggest that the alanyl portion of alanylglycine dominates the solute-water interaction. A similar effect is observed for solutions of glycy1alanine. 14) However, from the differences between the curves of L, against m and the Q*‘s for solutions of alanylglycine and glycylalanine, it is clear that a methyl group in close proximity to a AH, group results in a different interaction with water than when close to a CO; group. This can be interpreted in terms of the specific interaction of the functional groups with water. The electrostriction of water molecules under the influence of the electric field is much greater for -&H3 than for CO;.‘R’9’ Consequently, the shielding effect of an adjacent methyl group is more significant for -&H, than for the -CO; functional group.“’ The differences in 1; and the L, curves for alanyl~ycine and ~ycylalanine are consistent with this shielding effect. We are grateful to the New Zealand University Grants Committee for a grant to purchase the calorimeter. One of us (M.K.K.) gratefully acknowledges the award of a Research Fellowship by Massey University. REFERENCES 1. Franks, F.; Eagland, D. CRC Crir. Rev. Biochem. 1975, 3. 165. 2. Timasheff, S. N. Act. Chem. Res. 1970, 3. 62. 3 Humphrey. R. S.; Hedwig, G. R.; Malcolm. G. N.; Watson, I. D. J. Chem. Thermo+amic.s 1980. 12. 595. 4 Dyke, S. H.; Hedwig. G. R.; Watson, I. D. to be published. 5. Erianger, B. F.; Brand, E. J. Am. Chem. Sot. 1951, 73, 3508. 6. Franks. F.; Smith, H. T. Trans. Furu&zy Sot. 1%8,64, 2962. 7. Cohn, E. J.; Edsall, J. T. Proteins, Amino Acids and Peptides. Reinhold: New York. 1943, p. 194, 8. Shahidi. F.; Farrell, P. G. J. Chem. Sot. Faraday I 1978, 74. 858. 9. Zana, R. J. Phw Chem. 1977, 81, 1817.
Thermod.vnamics
1982,
14, 93-91
The relative partial molar enthalpies and apparent molar volumes of aqueous solutions C-alanylglycine and of DL-alanylglycine M. K. KUMARAN,
G. R. HEDWIG,
of
and I. D. WATSON
Departmentof Chemistry,Biochemistry,and Biophysics,Massey Liniversity, PalmerstonNorth, New Zealand (Received7 May 1981: in revi.yed,form20 Ju1.v1981) Enthalpies of dilution of aqueous solutions of the dipeptides L-aiany~y~ne and DLalanylglycine have been measured at 298.15 K and used to obtain the relative partial molar enthalpy I.., of water in the solutions. The partial molar vofumes of the dipeptides, obtained from density measurements at 298.15 K, are also reported. The results are compared with those for glycyl-L-alanine solutions.
1. Introduction The interaction of solvent water with a protein in aqueous solution plays an important role in determining the conformational stability of the macromolecule.“’ The difference in the interaction with water of non-polar and polar amino-acid side groups in the protein is considered to be a dominant factor in the solvent’s role in determining the conformation of the protein. (‘**) One approach towards a better understanding of side-chain hydration in proteins is to study an analogous effect in a series of model compounds. In previous studies of aqueous solutions of some amino acids and dipeptides,‘3q4’ we examined the effect of amino-acid substituent on solute-water interactions from a determination of the relative partial molar enthalpies and partial molar volumes of the solution components. The results suggested that for solutes with non-polar side groups, the interaction with water was dominated by the side group. As part of our continuing studies on peptide solutions, we report the enthalpy of dilution and density measurements at 298.15 K on aqueous solutions of L-alanylglycine and DLalanylglycine. From a comparison of these results with those determined earlier for glycyl-L-alanine, (4) the importance of methyl-group position in the solvation of the dipeptide can be assessed.
2. Experimental L-Alanylglycine and DL-alanylglycine, purchased from the Sigma Chemical Co., were both recrystallized from (water + ethanol) and dried under vacuum. Each ~~21-9614/82~01~3+05
~Ol.~/O
C 1982 Academic Press Inc. (London) Limited
94
M. K. KUMARAN.
G. R. HEDWIG,
AND 1. D. WATSON
dipeptide gave a single h.p.1.c. peak and a single t.1.c. spot. The optical purity of Lalanylglycine was checked using a Thorn Bendix Ltd. N.P.L. automatic polarimeter, model 143D. The estimated specific optical rotatory power of the substance is 0.00889 m2. kg- ‘. This is in good agreement with the value of 0.00884 m” kg ‘. reported by Erlanger and Brand.“’ Water for preparation of the solutions was deionized, glass-distilled, and, prior to use, freshly boiled to reduce the relative amounts of dissolved gases. The enthalpies of dilution were determined using a LKB 10700 flow microcalorimeter. Details of the apparatus and procedures used have been reported earlier.‘3.4’ Solution densities were determined by pyknometry as described previously. (4) Solutions were prepared by mass by weighing in a temperaturecontrolled room and correcting for the effect of air buoyancy. The resistance of the calibration heater was 49.760 Q. Electric currents between 1.3 and 3.2 mA were used to match the enthalpy changes due to dilution, The solutions were pumped at a constant rate of (3.992rt 0.005) mm3. s- ‘. The dilutions were done by pumping water at different rates between 3.808 mm3 .s-’ and 15.203 mm’.s-r. All these how rates were checked frequently.
3. Results The results of the enthalpy of dilution measurements are given in table 1. As detailed in a previous paper, t31 the molar enthalpy of dilution AHdig of solute is related to the relative enthalpies E and rf of the diluted and undiluted solutions, by the equation: AH,,, = (Lf-L’)jn,, where n2 is the amount TABLE
__II mi mol.kg-’
of substance of the solute. The quantity
L/n,, which is
1. Enthalpies of dilution of dipeptide solutions at 298.15 K; tni and tnf are the initial and final molalities ~ mr mol,kg-’
---&ii, J.mol-’
3 mol-kg-’
~..- mr mol.kg-’
a311 J.moI-’
Mi
i&i&p
4 mol.kg-’
~. mm J,mol-’
L-CH,CH(NH,)CONHCH,COOH 0.4715 0.4715 0.4715 0.6861 0.6861 0.6861
0.0975
0.5158 0.5158 0.5158 0.6504 0.6504 0.6504
0.2631 0.1765 0.1067 0.3318 0.2226
0.1614 0.2405 0.3513 0.2359 0.1428
-57.9 -46.1 -33.7 -46.8 -63.0 -78.7
0.7713 0.7713 0.7773 0.8689 0.8689 0.8689
0.3980 0.2673
-54.1 -75.5
0.1618
-91.7
0.9677 0.9677 0.9677
0.4446 0.2987 0.1807
-59.9 -80.6 -98.4
1.1105 1.1105 1.1105
0.4946 0.3320 0.2007 0.5665 0.3800 0.2296
-65.9 -88.6 - 108.4 -14.4 -98.9 -122.7
0.3542
-97.8 -76.3 -100.5 -126.1
DL-CH~CH~H~)CONHCH~COOH
0:1345
-37.8
-50.5 -65.4 -47.2 -62.8 -79.7
0.7742 0.7742 0.7742 0.9107 0.9107
1.0347
0.3957 0.2656 0.1606 0.4647 0.3117 0.5280
-55.9 -73.1 -91.7 -64.8 -86.7 -74.7
1.0347 1.1004 1.1004 1.1004
0.5615 0.3767 0.2278
ENTHALPIES
OF
DILUTION
AND
DENSITIES
OF
TRIPEPTIDE
95
SOLUTIONS
identical to the relative apparent molar enthalpy L, of the solute,@ can be expressed as a polynomial in molality m in the form t/n2 = A,m+A2m2+A3m3+.
. ..
(2)
where coefficients Aj are parameters. From equations (1) and (2) AHdil=
A,(m,-mi)+A,(mi-mz)+A3(m:-mm3)f.
“,
(31
the values of the coefficients Aj were obtained by fitting equation (3) to the quantities in table 1 using the procedures described earlier. (j’ The parameters so obtained are given in table 2 together with their estimated standard deviations. Also shown in the TABLE
Dipeptide
___--... Al J,kg.mol-’
L-Alanyiglycine DL-Alanyl~ycine
17+3 159+3
-.
2. Parameters _-. .- A,r - _J.kg’.mol-
of equation
(3)
_... .--- A.3 __ _ J,kg3.molV4
-1.152 -II+2
.-- 3 mol.kg-’ 0.47 to 1.11 0.52 to 1.10
table is the range of initial molality over which the dilutions agreement index R,‘4’ calculated from the equation :
R 0.014 0.020
were made, and an
where the superscripts Ohsand ca’c refer respectively to the experimental enthalpy of dilution and that calculated from equation (3). and U’i is the weighting factorC3.“’ for AH$‘;. The relative partial molar enthalpy L, of the solvent was calcuIated’3’ using the equation : L, = (L-n,L,)/n,
= -M,(A,m2+2,~1,m3$3A,m4f.~.),
(5)
where M, is the molar mass of the solvent. The values of L, are shown graphically in figure I. For the purposes of comparison, L, values for the aqueous solutions of glycylglycine, alanylalanine, and glycyl-L-alanine obtained earlierC4’ are also included. The apparent molar volumes V’ were calculated from the solution densities 11 using the standard expression : I;+ = (M2i’p)-(p-po)jmppo,
(6)
where M, is the molar mass of the solute, m is the molality of the solution and I+, is the density of water. The density p of the solutions, and the apparent molar volumes Vd,of each of the dipeptides are given in table 3. The apparent molar volume of both dipeptides appears to be linear in molality and. although there is no a priori reason why this should be so,@) we have obtained the value at infinite dilution (which is the partial molar volume Vi= of solute at infinite dilution) by means of a least-squares fit to the equation : Ii = V,’ +Sm. (7)
M. K. KUMARAN,
96
G. R. HEDWIG.
I
--c
AND 1. D. WATSON
E
I
0.4
0.8
I 1.6
1.2
m/(mol*kgm')
FTGURE 1. Relative partial molar enthalpies of water in aqueous solutions of some dipeptides at 298.15 K. A, glycylglycine; B, glycylalanine; C. L-alanylglycine; D, DL-alanylglycine; and E, alanylalanine.
TABLE 3. Densities p of peptide solutions and apparent molar volumes V, of the dipeptides at 298.15 K In
mol.kg-’
P
g.cin3
v,
cm3~mol-’
m
mol.kg-’
P
v,
g.cme3 cm3.mol-’
0.1447 0.4715
1.00429 95.5,+0.7 1.02003 95.3skO.2
0.6862
1.02970
95.5,f0.2
L-CH,CH(NH,)CONHCH,COOH 1.03363 95.7, +O.l 0.7773 0.8689 1.03762 95.7, +O.l 0.9677 1.04168 95.8,+0.1
0.2032
1.00718
95.4,*0.5
DL-CH3CH(NH2)C0NHCHl~00~ 0.6504 1.02800 95.7, + 0.2
0.3411
1.01380 95.5,+0.3
0.4272
1.01784
0.5431
1.02316 95.7,f.O.2
95.6,*0.2
0.6665 0.7742
0.9107
1.02871
95.7,f0.2
1.03335 95.9,+-0.1 1.03917 95.99&o.1
In
mol,kg-’
P
g,cm-’
b
crn’~mol-’
1.1105
1.04757 95.9,rtO.l
1.0347 1.1004
1.04434 96.0s + 0.1 1.04688 96.2,fO.l
ENTHALPIES
OF DILUTION
AND DENSITIES
OF TRIPE~IDE
SOLUTIONS
97
TABLE 4. Partial molar volumes at infinite dilution and values of S for aqueous dipeptides at 298.15 K .---
Dipeptide L-Alanyl~ycine DL-AIanyIgiycine Glycyl- L-alanine ’
V~/(cm3~mol-‘) .-~. 95.01+0.1 95.221-0.06 92.66kO.06
.--
S/(cm3.kg.mol- 2, .~~. ~0.X6&0.1 0.86-tO.07 1.63ri:O.OS
’ From reference 3.
Values of V;, S, and their uncertainties so obtained are given in table 4 together with values of the same functions for glycyl-L-alanine.‘4’ 4. Discussion Chiral effects are expected to be negligible in the interaction of solvent water with small peptides. (‘I Our L,‘s and 1/;“‘s for aqueous solutions of L and DL-alanylglycine are consistent with this view. The L, results shown in figure 1 indicate that the interaction with water of alanylglycine is intermediate between that for glycylglycine and alanylalanine. The negative values of L, and the trend with molality suggest that the alanyl portion of alanylglycine dominates the solute-water interaction. A similar effect is observed for solutions of glycy1alanine. 14) However, from the differences between the curves of L, against m and the Q*‘s for solutions of alanylglycine and glycylalanine, it is clear that a methyl group in close proximity to a AH, group results in a different interaction with water than when close to a CO; group. This can be interpreted in terms of the specific interaction of the functional groups with water. The electrostriction of water molecules under the influence of the electric field is much greater for -&H3 than for CO;.‘R’9’ Consequently, the shielding effect of an adjacent methyl group is more significant for -&H, than for the -CO; functional group.“’ The differences in 1; and the L, curves for alanyl~ycine and ~ycylalanine are consistent with this shielding effect. We are grateful to the New Zealand University Grants Committee for a grant to purchase the calorimeter. One of us (M.K.K.) gratefully acknowledges the award of a Research Fellowship by Massey University. REFERENCES 1. Franks, F.; Eagland, D. CRC Crir. Rev. Biochem. 1975, 3. 165. 2. Timasheff, S. N. Act. Chem. Res. 1970, 3. 62. 3 Humphrey. R. S.; Hedwig, G. R.; Malcolm. G. N.; Watson, I. D. J. Chem. Thermo+amic.s 1980. 12. 595. 4 Dyke, S. H.; Hedwig. G. R.; Watson, I. D. to be published. 5. Erianger, B. F.; Brand, E. J. Am. Chem. Sot. 1951, 73, 3508. 6. Franks. F.; Smith, H. T. Trans. Furu&zy Sot. 1%8,64, 2962. 7. Cohn, E. J.; Edsall, J. T. Proteins, Amino Acids and Peptides. Reinhold: New York. 1943, p. 194, 8. Shahidi. F.; Farrell, P. G. J. Chem. Sot. Faraday I 1978, 74. 858. 9. Zana, R. J. Phw Chem. 1977, 81, 1817.