2891
STRUCTURE OF bV&Hi3-3,6-DIMETHYL-2,5-PIPERAZINEDIONE
The Crystal and Molecular Structure of trans-3,6-Dimethyl-2,5-piperazinedione
by Ettore Benedetti, Paolo Corradini, and Carlo Pedone Polymer Research Institute of the Polytechnic Institute of Brooklyn, Brooklyn, N e w York 1 1 ~ 0 1 (Received January 22, 1969)
The crystal structure of trans-3,6-dimethyld,5-piperazinedione (meso cyclic dimer of alanylalanine) has been determined. The unit cell is monoclinic with a = 6.349, b = 6.214, c = 9.040 li; b = 95.8'. The space group is PZ1/n with two molecules per unit cell. The structurehas been solved by the application of close-packing criteria and has been refined to an R value of 5.6%, for 521 nonzero independent reflections (Cu KO radiation). The piperazinedione ring is found to be essentially planar. A comparison of our results with the data for bond distances and bond angles of the cyclic dimer of glycine and with the suggestedvalue for the cis-peptideunit is made. The crystal structure is held together by formation of hydrogen-bonded layers of molecules approximately in the (101) plane.
Introduction
Structure Determination
The study of trans-3,6-dimethyl-2,5-piperazinedione (~-alanyl-~-alanyl-2,5-diketopiperazine, LD-DKP) is part of a program of research on the crystal structure of small molecules of biological interest containing amide groups now being carried out in our laboratory. The only X-ray structure established to date of a diketopiperazine is that of the unsubstituted 2,5-piperazinedione' and many researchers have felt the need of additional results concerning related molecules in particular2 and the conformation of a cis-peptide unit in generaL3
The molecules are expected to form hydrogen bonds in the crystal. Two of the simplest ways of possible association of the molecules to form hydrogen bonds are schematically shown in Figure 1 and correspond, respectively, t o the formation of a hydrogen-bonded chain (a) or to the formation of a hydrogen-bonded layer of molecules (b). Both models are consistent
Experimental Section Crystals suitable for the X-ray analysis were obtained by slow evaporation of an aqueous solution. On the basis of Weissenberg photographs taken with Cu Ka: radiation, the crystals were found to belong to the monoclinic system. The extinctions of h01 with h 2 = 2n 1and OkO = 2n 1 indicated the space group as P21/n. A crystal of approximately spherical shape was centered on a Picker automatic diffractometer equipped with a PDP-8 digital computer. The setting angles of 12 reflections were used in a least-squares program for the determination of the lattice constantse (Table I). The experimental density (Dexptl= 1.33 g/cm3 by flotation method) agrees with the X-ray density (Dx-R= 1.33 g/cma) on the basis of two molecules per unit cell. This result requires that the center of symmetry of the molecule must be retained in the structure as a crystallographic element of symmetry. For the structure determination the intensities of 529 nonzero independent reflections were collected using Ni-filtered Cu K a radiation in the range of 28 0-130', using the 8-28 scan mode and a range of 1.5". Two stationary crystal-stationary counter background counts of 10 sec were taken a t each end of each scan.
+
+
+
Table I : Unit Cell Dimensions trans-3,6-Dimethyl-2,5-piperazinedione:CBHloNzOz Mol w t = 142.16 F(000) = 152 Monoclinic, space group P21/n, 2 = 2 a = 6.349 & 0 . 0 0 5 4 b = 6.214 rtr 0.005A c = 9,040 5 0.006A p = 95"60' =I=10' Dx-R = 1.33 g/cm3 Dexptl= 1 . 3 3 g/cma
with the retention of the symmetry center of the molecule in the crystal. The presence of rows of molecules has been found in the crystal structure of the unstbstituted diketopiperazine' (repeat distance = 6.11 A). I n our case, the molecules must have their symmetry centers in O,O,O and '/2,l/2, '/z. Moreover, the orientation of the plane of the ring must be such as to justify the intcnsity of a few extremely strong reflections, such as the :101,202,202. (1) R. Degeilh and R. E. Marsh, Acta Cryst., 12, 1007 (1959). (2) D. W.Urry, Ann. Rev. Phys. Chem., 19,477 (1968). (3) G.N.Ramachandran and C. N. Venkatachalam, Biopolymers, 6 , 1255 (1968). (4) W.R. Busing and H. A. Levy, Acta Cryst., 22,457 (1967).
Volume 78,Number 0 September 1960
E. BENEDETTI, P. CORRADINI, AND C. PEDONE
2892 Table I1 : F, us. Fc ( x 10)
H
K L
0
0
2 217
0
0
5
-1
r
0 0
4 156 -157 6 33 29
-I
0
4
8
-1
3 3 3 3 3 3 3 3 3
R 9 8 7
F ,
F,
H K L F,
227
-1
-
f'
24 24 0 I O 112 1 1 4 1 10 3 3 28 I 9 76 75 I tl 6 9 70 I 7 21 23 1 6 3 4 - 30 I 5' 169 -170 1 4 53 51
0
I
3
2
2 2 2 2
I20 7b 2 78 3 96 93 4 153 -t44
2
I?
0 II
t 0
c
f!
0
r, c C. C
I 125
(!
2
0
2
5 6 7
0
2
8
2
Y
c it
C'
C 0 0
0 0 0 0
c 11
G
0
c rt G 0 0 C
0 L:
c (.
c.
r
C 1
1
I -I -1 -1
-1 -1 -1 I I 1
I
I 1
I I I 1 1
I
I I
la - 2 1
-
-1 -1 -1 -1 -1
-I -I -I 1 1 1
I I
4
3
3 3 3 3 3 3 3 3 3
6
5 4 3 2
1 0
I 2 3 4
-
-
1
26 29 39 - 4 3 47 - 4 9 61 65 3 4 1 4 E 3 5 22 26 3 4 15 15 3 3 I 7 2 -163 3 2 145 1 4 2 3 I 34 34 4 0 1 2 1 116 4 1 27 - 3 0 4 z 58 bo 4 3 126 119 4 4 11 12 4 5 15 21 4 b 25 25 4 7. 1 0 9 - 1 0 6 4 8 12 I3 5 5 52 52 5 4 12 11 5 3 TI 70 5 2 91 91 5 1 75 74 6 L1 90 91 6 1 66 66 6 2 R - 7 6 1 @ 3 102 6 0 hC 68 6 I 29 25 5 5 s3 55 5 4 66 -6b9 43 5 3 49 5 2 77 77 '5 1 1 3 9 142 5 I? 3 1 3U
1
2
1 1
2
a 20
2 2 2 2 2
7 72 6 8 5 115 4 134 3 176 2 38 I 18 0 99 1 ic6 2 24 3 176 4 113
-
2 10 3 9
3 3
-
8 1
2
--
-I -1
2 2
--
-1
5
0
123 89 4b 2a ?
-I -1
4 4 4
-1
4
1
-A
2
-I
2 2
-I -1 -I -I -I -1 -1
1 1
1
0
-1 -I
-2
41
41
35
I I
0 O
2
S
I
1 I
-1 -2
4
I I
I I I 1
-1
21
1
1 1 1 1 0
-1
49
I I I
lb3
52 12 41
1 1 I
1
- 1I 17
17 12
1
-I
I 1 I I
-2
72
6 7
'd 9 9
0 U
0
0
2 2 2
2
2 2
L 2 -2 -2 -2 -2 -2 -? -2 -2 -/
-2
-1
-toe
2 2
21 -174
2 2.
-
-11c
13
II
-
-
L
z Z
1 I 1 1 1
I 1 1
I I 1 1 2 2
2 2 2 2 2 2 2 2 2
2 2 2
2 2 2
3
3 1 3 9 -140
2 78 84 I 84 79 0 1 2 4 -121 I 114 - 1 1 1 2 5 IC 3 90 - 86 4 38 38 5 85 - 0 7 6 84 E4
r
8
9
E 1
3
3
z
3
L
3
-7
-2
3 3
-2 -7
3 3
5 4 2
I 0 I
- 2,
3
2 3 4 5
-2 -2 -2
3
6
3 3
8
-2 -2
3
9
4
8 7
-2 -2
-2 -2 -2 -2 -2
90
2
30
2 2 2 2
4 4 4 4
4 4 4 4
2 2 2
2 -? -2 -2 -2 -3 -3 -1 3 3
7
6 5 4
3 2
1 0 1 2
4 4 4 4 4
3 4 5
4
6
4 4
R
7
30 24 6
-
-
21 21
2 27
30
9 6 63 64 57 61 2') 32 10 6 23 22 4R 53 85 82 195 - 1 9 6 12 - 74 43 39 123 - I 2 5 1 2 5 124 6 0 - 63 19 22 41-40 5 b 32 36 61 - 56 3/ 34 135 -139 0 I 43 43 81 -63
-
-
-
5s
-
57
53 - 5 7 20 I6 31 35 93 93 7a 79 130 1 2 9 2 3 13
16 - 1 9 22 19
-
5 5
5 5 5 5 5 5 5
5
3
5 5 5 5 5 4
3
4
4
4
3
4 4 4 4 4 4 4 4 4
3
--
l
>,
46 - 45, 43 - 4 3
2
3 d .J
,4 -3
-3 -3 -1
-3
-3 -3 - 3 -3 -3
4 4
77 43
19
40
t
7 - 1
0
65 - 7 3 31 2Y
1 2
3 4 .3 2 1
0 1 2 7 6 5 4 3
2
I 0
1 2 3 4
5 6
45 48 32 35 2 8 -30 so 54 26 30 34 39 5 0 - 5 4 59 - b 2 33 - 3 3 19 -144 48 46 20 22 65 64
7
-18
6
19 2U 62
20 32 63 42 42 17 I7 11 82 - 8 5 16 7 9h 95
-
-
-
-
-3
-3
1 5 I 4
1 3
3
3 3 3 3 3
-
-
-3 -3
-3
-
4 7 19 - 1 6 4 8 3 5 3 6 3 9 14 - 1 1 3 8 24-76 -3 7 29 - 3 3 -3 3 6 27 24 -3 3 5 21 12 -3 3 4 191 193 -'3 3 3 58 - 54 -3 3 2 53-54 -3 3 1 5 9 '5 3 0 6 4 - 6 1 'I 3 I 19 22 3 3 2 51 52 .% 3 3 7 0 71 '3 3 4 41 41 5 3 5 46 47 > 3 6 70 71 5 3 7 35' 35 A 3 8 17-14 3 L 8 27 25 3 2 7 17 15 3 2 6 I7 15 3 2 5 91 94 ,j 2 4 62 63 3 2 3 89 90 3 .2 2 38 33 3 2 1 182 -185 3 2 0 Rb 85 -5 2 1 4 8 - 4 4 -3 2 2 105 - 1 0 3 -3 2 3 33 34 -3 7. 4 2 4 20 -3 2 5 154 158 -3 2 6 119 121 -3 2 1 I 2 6 123 - 3 2 8 8 3 -3 2 9 41-45 -3 1 IO 50 51 -7 1 9 41 42 -3 I 8 23 19 -9 1 7 117 12'4 - 3 1 6 96 95
29 46
75
L 2 77
These considerations, together with the application of close-packing criteria, enabled us to conclude that we must deal with hydrogen-bonded layers of molecules, in the plane (101). Further considerations of some intense high angle reflections, such as the 0 0 10, 3 0 11, 7 0 10 led us to a set of coordinates leading to a disagreement factor ( R = 21 1P.l - 1F.l 1/21F01) of 0.38. The structure was then refined by standard procedures.6 Two cycles of isotropic full-matrix least squares brought the R factor to a value of 0.15 which, upon introduction of anisotropic thermal parameters, dropped to 0.09. A The Journal of Physical Chemistry
44
4 49 3 !i
E-
F, H K L F , F, H K L F , F , H K L F -,
HKLF,
-
L 2
65
40 0
- 35 - 67
-
6
2
39
4
4 40 -3A 3 164 170 I 85 78 0 190 195 1 5Y 60 2 65 80 3 148 -148 4 224 22h 5 40 35 6 73 7b 7 113 1 1 5 8 l2M 129 9 16 I6 IC 13 I 3 10 5 1 51 9 r I R l Z R 7 72 72 6 89 89 5 95 95 4 39 - 36
3 3 3
42
4%
1 1
2 2 3
2
a
1 7 1 6 1 5
2
31 -1;:
1
2
41 89
47
0 6 1 2 0 8 36 1 9 1 0
2 2 2 7
2 L 2 2
::1
0
2
-2
22 23 9 5tJ 58 E IOU 98 7 23 22 6 I l 9 5 38 30 4 1q5 - 1 8 8 3 Z h 2 259 2 32 31 I 35 37 0 169 183 3 R8-85 4 10-13 5 8b 81 6 1 1 1 -107 7 10 I1 0 19 20 9 23 22 10 4 1 40 9 74 70 7 139 5 3 2 - 3 2 3 149 -140 I 223 228 3 178 - 1 7 5 5 1 0 7 109 7 26 24 9 103 1 0 2
: 4:
2
I6
6 117 115 7 51 54 r) 36 35 9 2 3
0 0 10 0 8 0 6
2
7 -119 -128 I75 34 -103
F,
HKLF,,
-i -2 -2 -2 -2 -2 -2 -2
18 - 7 2
5 183 -tan
2 10 1 10
-1 -1 -1
2 I7 i 2t 23 0 19 14 1 1 0 - 5 3
2 2 2 2 2
2 121 3 94 4 47 a 32 7 4 6 IO 5 12 4 164 3 7
4
1
-I
1
-1
I 1
-1 -1
5 5 5 4 4 4
-1
1
z
5
4 4 4 4 4
1
-I
-
4
1
5
34 29 36 - 3 3 12 10 35 - 3 7 13 15 34 32 34-28 12 20 142 - 1 3 1 253-245 13 4 49 52 116 1 1 7 51-53 56 55 72-69 15-14 0 0 8 - 4 67-668 14-10 35-34
20 - 1 7 65 - 6 1 81 83 31 27 I - 6
1 1 1 1
Fc
6 152 -154
--
30 45
- 76 68
1 1
lot -iio
1 0 112 -112 1 1 107 -104 1 2 5 3 1 3 241 - 2 5 9
-4 -4
80 43 29
-4
1 1
4 5
7 4
J
l
6
?
3 3 1 J 3 1 3
1 7 2 3 1 0 2 9 1 9 11 0 '9 3H 0 7 0 0 0 5 41 0 3 44 0 1215 0 I 2?0 n 3 13n 0 5 42 0 7 61 0 9 I3 0 8 2fl 0 6 51 0 4 99 o 2 117 0 0 184 0 2 0 4 64 0 6 I1 0 8 24
3 -I -3
-3 -3
-1 -4 -4
-4 -4
4 4 I+
4
4
4
1
4
1 1
4
4
1 1
4
I
4
4 4 4 -4 -4 -4
-4 -4
1 1
I 1 1 1 1
2 104 3 29 4
5
1
7
-4
1
8 9
-h
-4 -4
-4 -L
4
4 4 4
2 2
2 2 2 2
-
28 7 37 bO - 4 5 43 22? -237 -131 31 - 6 5
-
-
- 25
-
54
99
-123
--
-187
-
9
8 7
19 51 E
2
2
7
4
2
2
-5
4 4 4 4
3 7 5 3 3 6 8 -
4
3
>
3
4
3 3
3 2
3
1
30
3
0
30
-4 3 -4 3 -4 3
1
-
44 24 12-
6
-5
5 7
54 62 19 - 2 2
-6 -6
0 0 :I
4 b
40 7 6 - 4 E32
2
29 28 q - 5 32 29 29-20
0
I 2
3 4
5 6 4 3 2
I 0 1 2 3 4
5 6 7
-5
3 3 3
6
-5 -5
-5
3 3
-'i
j
-'I
9
3
5 2
3 3
h
3
5 5 2 L I
3 3 2 L 2
I'
8
-5
-5 -5
14
-5 -1,
-'J
2
2 2 2 2 2 2 2 2 7 2 2 1 1
5
0
7
-
29
8 -
-
31 8 47 1017 b2 24
-
17 47 25 2 34
9
58 21
- I2
16 17
-
16
32 34 7 2 56 - 54 25 24 112 l o b 6 1
4 3 2 1c3 1 b 0 37 I 38 2 24 1 23 4 45 14 6 23 5 30 4 29 3 41 2 9 1 27
0 48 I I30 2 91 3 105 4 54 5 74 6 22 7 56 n 46
----
40 26
22 I 15 22 31 25 J6
0
23 49 I29
-
8
53-
7
4b 7 16
94
111 52 73 24 58
43 53 47 I 18 13 17 16 58
-5
20
5 5 5
I 1 1 1
6
5
1
3
- 33 94 - 94 ,185
%
5 5
1 1
5
1
5
5
I 4 5
I3
2 2 - 18 10h 20 - 16 I
6 7 '
T i
0' r 0 5
I I
3 2 1 0
1219-
6 0 6 -6 -6
-6 -6
-6 -fi
-6
-6 -6
-b -f -6
t h
t h h
54 3 45
30
4
h
I
I1
1
4 31
-$
22
6
9~
3
-s
6 h
49 9
- 13
3
0 0 0 2 0 4 I s
h 6
- 76 1 a2 - 85 26 - 26
.25 2 13 1 57 0 7 4 I 125 122 2 47 45
-5
6
73 3
15 48
0
s a
PO
23
-5
-5
5
3a ?3
I 6 I 5 I 4 1 3
34
2 3 1A6
34 34 3 3 7 7 - 75 63 59 15 9 21 21
4 3
->
82
-
7
7
0 0
-4
-5 -5
-
-5
3 2 I
-4 -4 4 4 4 4 4 4 4 9 5 5 5 5 -5 -5 -5 -5
-5
9 5 LE 14 3 23 17 4 104 1 0 5 5 55 52 6 49 51
1
2
o
21
4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4
-4
90
2 2
0
8
4
109 55 57 73
-
-5 -5
4
- 6 1 55 19-15 5 3 9 - 3Y 13 16 -,
HI 21
P7
- 3R
-4
10
-.
98
40 40
0 3 I 45 - 4 7 1 156 -159 3 4 a
-4
61
6 92 5 112 4 52 3 57 2 74
3 3
4 5 6 7
6 5
-4
48 5 R
20 10
3 3
3 4 4 4
- 14
1
2
-4 -4
104 26
2 2
4 4 4
4 4 4
IO
-
-4
2 2
- 20
-
6
-4
1-
-
.-4
I
9 7
27 65 17 -28 8 2 1 I 15 15 6 20 19 5 33 31 4 50 50 3 14 9 2 7 5 - 76 I 82 81 O 53 50 1 46-46
I I
-4 -4 -4
-4
b
-
-
~
-6 -6
3
1
E
3 3 3 3
0 I
12 49 38 81 76 62 16 41
-6 6
3 3 4 4 4 4
0
4
7 I -7 -I -I -I -7 -i
2 2 2 2 2
-h -6
-6
2 3 4 5 3 2 I 0
2
I
I
2 1 I
0
: I
38
75 75
- 57
16 44
- 41
I C -
l
I
8
44
26 5 21
46
25 6
- 35 - 24 I2 - 1 1
2 0
-
3n 24
4 3
l
28 6 27 47 28
- I1
9 -
3
1
o
46
1 I 0 I
I I I I
7 7 7 7 -7
n
I I 32-20
30-24 31 30 5 - 3 82 81 I I 31 31 I 2 46 4H t l 3 9 4 I 4 64 63 I 5 10 - I 1 1 6 14 9 I 7 27 - 27 2 6 15 10 z 5 38 38 2 4 35 35 2 3 21 18 2 2 43 44 2 1 59 59 2 0 25 2~. 2 2 1 31 30 2 2 5 0 - 4 8 2 3 Ih 13 2 4 @ - U 3 3 l k - 1 6 1 3 2 I I
1 1
h h -6 -6
-
-
7 29 45 13 7 19
1*740
4
I 28 42
IO I 20
232
i
9
19
difference Fourier synthesis, at this point, disclosed the positions of only two of the five hydrogen atoms; that is, only the hydrogen atoms bonded to the ac carbon and to the nitrogen atom gave clear and well-resolved (5) The atomic scattering factors used for all the atomic species were taken from Hanson, et al. [H. P. Hanson, F. Herman, J. D. Lea, and S. Skillman, Acta Cryst., 17, 1040 (1964)l. The Busing-Levy leastsquares and function-error programs were used (Oak Ridge National Laboratory Reports 59-4-37,59-12-13,1959). A unitary weight was assigned t o each reflection with the exception of those reflections indicated by an asterisk in Table I1 to which zero weight was assigned during the calculation because extinction seemed to be important.
2893
STRUCTURE OF h'""'~S-3,6-DIMETHYL-2,5-PIPERAZINEDIONE
peaks in the difference synthesis. The positional parameters of the hydrogen atoms of the methyl group were calculated on the assumption of stereochemically staggered C H bonds, and their lengths were assumed to be 1.08 A. A final cycle of anisotropic full-matrix leastsquares refinement with fixed parameters for the hydrogen atoms yielded an R factor of 5.6%. I n Table 11:a list of the observed and the calculated structure factors is reported.
Discussion of the Structure I n Table 111are reported the final atomic parameters together with their standard deviations computed by inversion of the least-squares variance-covariance matrices. I n Table IV a list of bond lengths and bond angles is tabulated. -~
Table IV : Molecular Dimensions
A. Bond lengths (e.s.d. X 10-3) C'-0 C'-c"
1.240 1.470 1.509 1.462 1.325 1.03" 0.94"
Figure 1. Simplest ways of association for diketopiperazines: (a) formation of hydrogen-bonded rows of molecules; (b) formation of hydrogen-bonded layers of molecules.
ca-cB
Table I11 : Final Atomic Parameters
0-C'-N C'-N-C" N-Ca-CB N-C"-C' 0-Cf-C" C'-Ca-CB N-C'-C" C'-N-" c*-N-H~ N-C"-Hca C'-Ca-Hc~ C'-C"-Hca
Ce-N C'-N Ca-Hca N-HN
(3) (5) (51 (4) (4)
B. Bond angles: deg A. Final positional parameters (e.s.d. X 10-4)b Atom'
C' Ca CB
2.
e.8.d.
Y
e.8.d.
2
e.8.d.
0.0442 0.1146 0.3263 0.0790 0.1377 0.241 0.061 0.387 0.429 0,315
4 4 5 3 3
-0.1654 0.2073 0.2647 -0.3122 0.0252 0.054 0.340 0.137 0.297 0.388
5 4 5 3 3
-0,1045 -0.0059 0.0760 -0,1917 -0.1054 -0.170 -0.066 0.135 0.003 0.146
3 3 3 2 2
122.9 127.9 110.1 112.8 117.8 109.7 119.2 121 111 110 107 106
" The e.s.d. of this bond length is 0.04. a The mean e.s.d. for the angles involving heavy atoms is 0.5"; for thoseinvolving hydrogen atoms it is 3".
B. Anisotropic thermal parameters (e.s.d. X lo-*)* T = exp[ - (Puh2
C' e.s.d. C" e.s.d. C' e.s.d. 0 e.s.d. N e.s.d.
+ Pzzk' + Pad2 4-2P12hk + 2 h h l + 2Rzskl)l
811
PPZ
888
166 8 157 7 220 10 340 8 183 7
153 9 119 9 350 14 166 7 163 9
61 3 74 3 136 5 115 3 73 3
PIP
16 8
- 11 7 -112 9 -9 6 20 6
-
Pia
8%
39 4 52 4 52 6 111
3 5 -14 5
4
73 3
-762
-59 4 -14
a A fixed isotropic thermal factor ( B =; 3.5) was assigned to the hydrogen atoms. e.8.d. = estimated standard deviation.
A molecular model of trans-3,6-dimethyl-2,Bpi-perazinedione is shown in Figure 2. The piperazinedione ring is planar. The mean square plane6 of the molecule, centered at (O,O,O) with all eight heavy atoms weighted equally, is defined by the equation 4.28062
- 2.1704~+ 5.22402 = 0
All the atoms are almost exactly coplanar, their deviation from the mean-square plane being: C', +0.002 A; C", $0.010 A; N, -0.010 A: 0,+0.007 A. It may be of interest to compare the internal coordinates of the molecule as obtained in this study with I
.
(6) V. Sohomaker, J. Waser, R. E. Marsh, and B. G. Bergman, Acta Cryat., 12, 600 (1959).
volume 78, Number 9 September 1969
2894
E. BENEDETTI, P.CORRADINI, AND C. PEDONE
P
Figure 2, Molecular model of trans-3,6-dimethyl-2,5-piperaninedionewith bond distances and angles calculated from the final set of parameters.
Table V : Internal Coordinates of 2,5-Diketopiperazines Marsho
C'-c"
C'-N-C" C'-N-"
1.499 1.239 1.325 1 449 0,86 122.6' 118.9' 118.5' 126.0' 123'
c~-N-H~
111O
C'-0 C'-N Ca-N N-HN N-C'-0 C"-C'-N
ca-c'-o
I
Ramaohandranb
This investigation
1.53 1.24 1.32 1.47 1.0 123' 118' 119" 126' 121O 113'
1 470 (5) 1.240(3) 1.325(4) 1.462 (4) 0.94(4) 122.9' 119.2' 117,8' 127.9' 121' 111' I
Figure 3. A packing drawing of the molecules of trans-3,6-dimethyl-2,B-piperazinedioneviewed along the (100)projection.
nor unexpected since the deformation of one bond angle a t a methylene carbon atom is easier than that at a methine carbon atom.8 Accordingly, since the sum of the angles in a planar hexagonal ring must be (2 X 360"), the angles a t C' and N are slightly larger (Table VI. The mode of packing of the molecules requires only a few additions to what has been mentioned above. In Figure 3 a view of the crystal structure along t h e 3 Table VI : Hydrogen Bond Parameters 1.96 zk 0,04A 2.88 f 0.01A 165 f 1.5' 128.8 It 0.5' 10 =t1.5' 103.2f 0.5' 145.7 f 0.5' 150 i 1.5'
' The "limits of error" in bond distances and bond angles involving the heavy atoms are, respectively, 0.007 A and 0.3". Errors were not quoted.
'
those obtained by Marsh' for the unsubstituted 2,5-piperazinedione and with the values of the recommended standard cis-peptide unit, calculated by Ramachandran8 using potential energy functions which take into account also the possible variation of bond angles and the internal rotation angles' around the peptide bond. If one uses fixed bond lengths and bond angles for the diketopiperazine ring, according to the Ramachandran values, the angle in the ring at Ca would be 117". I n the unsubstituted 2,5-piperazinedione this angle is found to be 115.1' and the bond angle strain resulting from the deviation of the angle from the tetrahedral value is distributed over the other angles in the ring. For the disubstituted molecule the same angle at C" is found to be even lower (112.8') and closer to the tetrahedral value. Once again, this is neither surprising The Journal of Physical Chmistrzl
Table VII: The RootMean-Square Component of Thermal Displacement along the Three Principal Axes of the Ellipsoid (in A)
C' C"
CB 0 N
Axis 1
Axis 2
Axis 3
0.144 0.143 0.184 0.133 0.122
0.175 0.152 0.204 0,213 0.174
0.202 0,206 0.318 0.295 0.232
(7) J. T. Edsall, P. J. Flory, J. C. Kendrew, A. M. Liquori, G. NBmethy, and G. N. Ramachandran, Biopolymers, 4, 121 (1966); J . Mol.
Bwl., 15,399 (1966); J . Bwl. Chem.,241,1004 (1966). (8) P. Corradini, P. Ganis, C. Pedone, A. Sirigu, and P. A. Temusai, J . Polym. Sci., Part C, 16,2877 (1967).
ACTIVITY COEFFICIENTB FOR Two TERNARY SYBTEMS
2895
axis is reported together with the shortest interatomic distances. The nonbonded interactions of the methyl groups with the surrounding atoms indeed govern the packing of the layers of hydrown-bonded md~cules. The bond distances and bond lengths involving hydrogen bonds are reported in Table VI; finally, in Table VI1 are listed the root mean square components of the
thermal displacement along the three principal axes of the ellipsoid (1, 2, 3).
Acknowledgment, We wish to thank Professor M, Goodman for useful discussions. We also gratefully acknowledge the support of research grants from the National Science Foundation (GB 7558) and the National Instit,utes of Health (GM 08974).
Activity Coefficients for Two Ternary Systems:
Water-Urea-Tetramethylammonium Bromide and Water-Urea-Tetrabutylammonium Bromide at 25” ’ by Wen-Yang Wen and Chun-meei L. Chen Department of Chemistry, Clark University, Worcester, Massachusetts
01610
(Receiued January 29,1969)
Isopiestic vapor pressure measurements have been made for two ternary systems, HzO-urea-MerNBr and H20-urea-BucNBr at 25”. A method similar to that employed by Bower and Robinson was used for evaluating the activity coefficients of urea and salts. In the concentration range studied, it was found that each solute component is “salted in” by the other as shown by the considerable lowering of the activity coefficients in the presence of the other solute. The “salting-in” effect was found to increase greatly with the cationic size of the tetraalkylsmmoniumsalt. The lowering of the activity coefficients of urea and BudNBr found in this study may be due either to the water-structure breaking effect of urea or to the formation of some complex-like aggregates between urea and the tetraalkylammoniumsalt in aqueous solutions. The free energies of transfer of tetraalkylammonium bromides from water to urea solutions have been calculated. The results indicate that the transfer can proceed spontaneously from water to urea solution.
Introduction Thermodynamic properties of ternary systems in which water is one of the components are now under active investigation in various laboratories. The isopiestic vapor pressure method has been used to study many aqueous ternary systems containing two electrolytes,2 an electrolyte and a nonelectrolyte,8-6 and two nonelectrolyte^.^^^ In this paper we are reporting the results of our isopiestic vapor pressure measurements on two ternary systems, water-urea-tetramethylammonium bromide and water-urea-tetrabutylammonium bromide at 25”. This study was stimulated by the discovery in our laboratory that various crystalline complexes of urea and symmetrical tetraalkylammonium halides can be prepared from aqueous solutions a t room t e m p e r a t ~ r e . ~ Saito, Lee, and Weng also found that the solubility of urea in water increases with the addition of a tetraalkylammonium salt until the formation of a crystalline complex takes place. These observations suggest a
possible “salting-in” effect of these salts toward urea. It is, therefore, of great interest to study the salt-urea interaction in water by measuring the activity coefficients.
Theory The theoretical aspect of determination of activity coefficients for the ternary system containing one elec(1) Abstracted in part from the Ph.D. thesis of Chun-meei L. Chen submitted to Clark University in 1968. (2) See, e.g., H. S. Harned and R. A. Robinson, “Multicomponent Electrolyte Solutions,” Pergamon Press, London, 1968. (3) F.J. Kelly, R. A. Robinson, and R. H. Stokes, J . Phys. Chem., 65, 1958 (1961). (4) R. A. Robinson and R. H. Stokes, ibid., 66, 506 (1962). (5) V. E. Bower and R. A. Robinson, ibid., 67, 1524 (1963). (6) V. E.Bower and R. A. Robinson, ibid., 67, 1540 (1963); J . Res. Nut. Bur. Std., A69, 131 (1965). (7) R. A. Robinson and R. H. Stokes, J . Phys. Chem., 65, 1964 (1961). (8) H. D. Ellerton and P. J. Dunlop, ibid., 70, 1831 (1966). (9) S. Saito, M.Lee, and W. Y . Wen, J. Amer. Chem. Soc., 88, 6107 (1966). Volume 73, Number 9 September 1969
