R . D.Singh and D. R. F e r r o
970
ployed in this work was purchased with the aid of National Science Foundation Grant No. GP-18397. References a n d Notes (1) J. R. Wasson, G . M. Woitermann, and H. J. Stoklosa, Top. Current Chem., 35, 65 (1973). (2) J. R. Wasson, lnorg. Chem., 10, 1531 (1971) (3) B. J . McCormick, J. L. Featherstone, H. J. Stoklosa and J. R . Wasson, lnorg. Chem., 12, 692 (1973). (4) N. D. Yordanovand D. Shopov, Chem. Phys. Lett., 16,60 (1972). (5) R. K. Cowsik and R . Srinivasan, Chem. Phys. Lett., 16, 183 (1972). (6) R. G. Caveli, E. D. Day, W. Byers, and P. M . Watkins, Inorg. Chem., 11, '1591 (1972). (7) J R. Wasson, Chem.-Anal., 56, 36 (1967). ( 8 ) 6. M . Woltermann and J. R. Wasson, J. Phys. Chem., 77, 945 (1973). ( 9 ) B. J. McCormick, Can. J . Chem., 47, 4283 (1969). (10) 6 .Durgaprasad, D. N. Sathyanarayana, and C. C. Patel, Can. J. Chem., 47, 631 (1969); K. A. Jensen, B. M . Dahl, P. H. Nielsen, and G. Borch, .Acta Chem. Scand., 25, 2029 (1971): 26, 2241 (1972). (11) H. J. Stoklosa. H. L . Huffman, and J. R . Wasson, J. Inorg. NucI. Chem., 35,2584 (1973) (12) A. D. Toy, S . H. H. Chaston, J. R . Pilbrow, and T. D. Smith, lnorg. Chem., 10, 2219 jl97'1). (13) P. W. Atkins and M . C. R. Symons, "The Structure of Inorganic Radicals," Arnericc-inElsevier, New York, N. Y., 1967, pp 20-22, (14) P. E. Rakita, S . J. Kopperl, and J. P. Fackler, Jr., J. lnorg. Nucl. Chem., 30, 2139 (1968). (15) P.. Muller, V V ti. Rao, and E. Diemann, Chem. Ber., 104, 461 ( 1 97.1 ) , (16) C. J. Bailhausen and H. B. Gray, Inorg. Chem., 1, 111 (1962); J, Selbin, Chem. Rev., 65, 153 (1965); Coord. Chem. Rev.. 1, 293 ( 1966). ( 1 7) M. Shiro and U. Fernando, Chem. Commun., 63 (1971).
(18) A. L. Companion and M . A. Komarynsky, J. Chem Educ.. 41, 257 (1964). (19) J . R. Wasson and H. J. Stoklosa, J. Chem. Educ., SO, 185 (1973). (20) H. J. Stoklosa and J. R . Wasson, J. lnorg. Nucl. Chem., 36, 227 (1974); D. K. Johnson, H. J. Stokiosa, J. R. Wasson. and H. E. Montgomery, /bid., in press. (21) E. R . Price and J. R . Wasson, unpublished results. (22) C. K. J$rgensen, Struct. Bonding (Berlin), 1, 3 (1966); €3. N. Figgis, "Introduction to Ligand Fieids," Interscience, New York, N. Y., 1966, pp242-245. (23) M . V. Valek, W. A. Yeranos, G. Basu, P. K. Hon, and R . L. Belford, J. Mol. Spectrosc., 37, 228 (1971). (24) H. A. Kuska and P.-H. Yang, "Bonding Studies of Bis(tetramethy1urea)dichlorooxovanadium(lV)," submitted for publication; Abstracts of the 5th Central Regional Meeting of the American Chemical Society, Cleveland, Ohio, May 13-15, 1973. (25) R . A. D. Wentworth and T. S. Piper, J. Chem. Phys., 41, 3884 (1964). (26) D. E. C. Corbridge, Top. Phosphorus Chem., 3, 57 (1966) (27) R. Hoffmann, J. Chem. Phys., 39, 1397 (1963). (28) R . S. Mulliken, J. Chem. Phys., 23, 1833, 1841 (1955). (29) R. T. Sanderson, "Inorganic Chemistry," Reinhold, New York, N. Y., 1967; H. J . Stoklosa, J. Chem. Educ., 50, 290 (1973). (30) H. Basch, A. Viste, and H. B. Gray, J. Chem. Phys., 44, 10 (1966). (31) J. H. Schachtschneider, R . Prins, and P. Ros, lnorg. Chim. Acta, 1, 462 (1967). (32) C. J. Ballhausen and H. B. Gray, "Moiecuiar Orbital Theory," W. A. Benjamin, New York, N. Y . , 1964, p 122. (33) M. Wolfsberg and L. Hemiholz, J. Chem. Phys.. 20,837 (1952) (34) W. A. Yeranos. J. Chem. Phys., 44, 2207 (19661. (35) M . Zerner and M. Gouterman, lnorg. Chem., 5, 1699 (1966); Theor. Chim. Acta, 4, 44 (1966), (36) E. Clementi and D. L. Raimondi, J. Chem. Phys., 38, 2686 (1963) (37) F. N. Tebbe and E. L. Muetterties, lnorg. Chem., 9, 629 (1970) (38) J. J. Kaufman, lnt. J. Quantum Chem., 15, 485 (1967). (39) C. P Keijzers, H. J. M. de Vries, and A . van der Avoid, Inorg. Chem., 11, 1338 (1972). (40) C. Furlani, P. Porta, A. Sgamellotti, and A. A. G . Tomiinson, Chem. Commun., 1046 (1969).
C N D 0 / 2 Study of NH-0.O Hydrogen Bonds in Ions, Zwitterions, and Neutral Molecules R . D. Singh and D. R. Ferro* lstitufo di Chimica d e l e Macromoiecoie del CNR, 20133 Milano, Italy (Received November 30, 1973) Publication costs assisted by the lstituto di Chimica delle Macromolecole
CND0/2 calcuhtioiis have been carried out 011 a number of hydrogen bonded systems, including ammonia, ammonium, imidazole, and glycine as proton donors and formic acid, formate ion, and glycine as acceptors. The interaction energy a t intermolecular separations larger than the equilibrium distance has ~ each H bond. been interpreted as the sum of the electrostatic energy and an attractive potential U H for A moderate dependence of UHBon the nonlinearity of the H bond is observed, while in the case of two H bonds or of a bifurcated H bond, the additivity of U H B is found to hold with good approximation. The magnitude of UHBgreatly increases when varying the donor and/or the acceptor from neutral molecule to zwitterion and to ion.
Introduction Considerable attention has been given to the study of hydrogen bonds of N-H.n.0 type, which play an important pole in stabilizing the secondary and tertiary struttures of polypeptides. In a recent paper McGuire, et al.,l have pointed out the importance of a suitable empirical hydrogen bond potential function for the study of the conformations of macromolecules. They have derived hydroThe Journai of Physical Chemistry, Vol 78, No. 10, 1974
gen bond potentials in a variety of relevant systems by calculating the interaction energy between simple molecules using CND0/2 and empirical methods. Such functions may be useful in the empirical expression of the conformational energy Of a macromolecule. Thus One can write total conformational energy2 as Econf
=
ZUtms
ZUnb -!-
ZUHB
-k
Eel
(1)
C,MQ0/2 Study of N H - ~ OHydrogen Bonds
91
where the four components on the right-hand side represent the torsional, nonbonded, hydrogen bond and the electrostatic energies, respectively.3 However, the energetics of the hydrogen bonds formed between a proton donor and a proton acceptor, of which either or both bear an electric charge, is little known and only few theoretical papers have dealt with it.4 The main reason for this lack of interest is that the ionic groups of molecules of b i o ~ o g ~ csignificance a~ in water are normally ~ d v a t e dand their interaction is therefore screened by the e other hand, the protein structures deterX-ray diffraction show examples of ionic bonds, while at times H bonds and electrostatic interactiom appear to stabilize the substrate-enzyme or haptenantibody compIexes.5--7 Amino acids and oligopeptides are found as ions and zwitterions in the solid state and as such me linked by strong hydrogen bonds; similar H bonds may, th~!refore,be formed also between the ioniza?A?groups of ~ n a . ~ r o ~ o ~ ewhen c u ~ efavorable s conditions are met. From their nmr and esr studies of angiotensin 11, Weinkam and JorgensenR have concluded that in this octapeptide and its several analogs the C terminus tripeptide hispro-phe, exists in EL cyclic structure stabilized by an iondipole interactiton between the COO- group and the histidine ring. In an attempt to study the conformation of angiotensin XI and to confirm the findings of these authors by conformatioxlal energy calculations, we were faced with the problem of using an appropriate empirical hydrogenbond pot,ential function for the COO- .H-N type of interaction. Due to the lack of the experimental information on such interncti.ona, we had to resort to independent quantum nieckanaical calculations in order to gain insight about the hgidrlqen bond potential function to be used in our empirical expression of the conformational energy. We ha.ve, therefore, undertaken a systematic study of hydrogen bonds of the type N-H...O in small systems r:onsi,sting of ions, ~ w ~ t t e r i o n sand , neutral molecules, using Pop1.e and 8egal's9 CND0/2 method. In all these systems, ammonia, aanmonium, imidazole, and both the canonical and (;he zwitterion forms of glycine have been taken as proton donors; formic acid, format,e ion, and both t h e forms of glycine as acceptors. The present &udy is, therefore, aimed at seeing whether in the c o n f o r ~ ~ ~ calcidations ~ . o ~ a ~ on systems in which charged groups foran I.$ bonds (a) one can apply the computational scheme of eq I, i.e., describe the hydrogen 'Imnding, also in such cases, by a simple function to be added to the e ~ e ~ ~ ~ o and s t ~nonbonded tic energies; and if n ~ , t . i ~tJHB ~ i sare the same as for a normal hy-
-.
Since the most ihportant quantities responsible for the intermolecular interaction are the charge distribution and tbus the electrostatic energy, we have used the complete neglect of differential overlap (CNDO/2) method which yields a reasonable charge distribution. This method has been applied to such calculations1 and its details referred to elsewhere.9 In the study of intermolecurogcn bonds, it is generally observed that upon the optimikation wi.th respect to internal coordinates CNDO/2 predicts too short -IIdistances and overestimates the tlianerization energies. However, when the two monomers iiire held rigid and calculations are done a t experimental
-
hydrogen bond length, a fairly reasonable value is obtained for the energy of formation of hydrogen bond. Since CND0/2 underestimates the repulsive interactions, it follows that this method can provide satisfactory information only in the attraction region of the potential energy, and some other method is required to determine the depth of the minimum and the shape of the potential in the repulsion region. The information obtained by these two methods, in the two regions, when compounded together with proper weight to reproduce some experimental quantities, could lead to the complete ~ y d r o g e n , b o ~pod tential. Due to the lack of experimental knowledge of hydrogen bonds in our systems, we, a t present, have restricleel our studies in the attraction region; even in this region, however, it remains to be seen if the quantitative validity of the derived potential is based on experimental facts. We have used the CNDO/2 method to calculate the intermolecular interaction in several systems formin, one or more hydrogen bonds of the N-H type, 8,s a function of O--.H distance (EoH),limiting the analysis of O W results t,o the range of RoH above its a p p r o x ~ ~ i aequiiibri~e urn value of 1.75 A. The interaction energy E(&) between the two molecules, defined as the difference bel tween the energy of the dimer and the sum of the energies of the two isolated components, has been calculated by n g of holding rigid the two molecules arid ~ r a n ~ ~ a t ione them along a straight line (shown by the a r ~ o win the figures). A modification was made to Sepal's original programlo which enabled us to use the final ~noleculmorbitals of one calculation as the initial guess for the fdowing one; this led to a significant reduction of the computer time required for calculating the curve5 E ( R o H ) . The interaction energy calculated using ab initio MO methods in hydrogen bonded systems when split into electrostatic, exchange, charge transfer, polarization, and dispersion i.nteraction components appears to provide a physically meaningful interpretation.lI A similar but more simplistic decomposition of the total interaction energy is impl.icd in the empirical calculations. Thus irr the case of two interacting rigid molecules eq 1. I-momes
-
and we analyze the CNDO/2 results t o see whether the behavior of E supports such an ernpirikall expression of the interaction energy. The first term of Eiilteri s the painvise sum of the nonbonded interactions (extended over all the atom pairs except the O s S e H ones . involved in hydrogen bonding), each represented by a repulslve part and the attractive dispersion energy. At the intermolecular distances we are dealing with, the repulsive contribution to the nonbonded term is negligible; whereas CNDO/2, which is an approximate SCF rraelhocl: neglects the dispersion energy. We may, therefore, conclude th.at .ZU,3bis not included in E. The second term XUETB arises from each intermolecular hydrogen bond, and each UHB is a function of only the distances between the atoms directly involved in the hydrogen bonding (H, 8:and perhaps C and N as well). 'Thus in order for eq 2 l,o be of general application it xnust be possible to express the difference between the total interaction and hhe clectrcistatic energy by a simple sum of berms
E -- E,,
=
ZUHH
(3
independently of (a) the relative orientation of the molecules, (b) the number of hydrogen bonds formed, and (c) The Journal of Physical Chemistry, VO/. 78, No. IO, 7974
R . 0. Singh and D. R. Ferro
972
TABLE I:5 Internal Coordinates of the Isolated Monomers Glycineb Zwitterion
-
1.46 1.45 1.30
1.46 1.47 1.27
c '-0
1.30
CU-H N-R 0-H
1.00
1.36 1.09 1.00 1.00
C"-c '==O C*-C'-O N-C"-C' C
1.09
119.5 119.5 109.5 109 . 5
ImidazoleC
Canonical form
C"-C' C"-N c '=O
123.0 116.0 109.5 109.5
CrC2 Cz-N3
Neutrak
1.36 1.36 1.31 1.32 1.39
" 3 4 4
CrNj Ns-Ci
C i-CrN3 CrNrC4 N3-cc-N~ CrNsCi Nj-Ci-CZ
Formic acid
107.0
110.0 109.0
C-N
c=o c-0 0-H
0-c=o
1.08 1.24
Ion
1.09 1.25
1.31 1.00
124.3
H-C=O H-C-0
117.85 117.85
C-0-H
107.8
124.0 118.0 118.0
108.0
106.0
All the bond lengths are in angstrom units and angles in degrees. All H atoms are tetrahedrally attached to C" and N, with one N H bond lying in the NCaC'O plane. Each hydrogen is placed in the ring plane a t 1.00 .i on the bisector of the corresponding ring angle.
131(2i0
in small systems, but it would have been a few times bigger in the case of larger systems as glycine-glycine (see Results and Figure 8). (b) We calculate the electrostatic energy in the usual monopole approximation
q L and q r being the fractional charges on the atoms i and j , respectively, calculated by CNDO/2 population analysis, and rlj being their separation. On the contrary, McGuire, et al., calculate the charge distribution by
Figure 1. C N D 0 / 2 and C N D O / 2 (ON) (in parentheses) net charges on the atoms for the above conformations of the molecules participating in the intermolecular interaction. The values given should be divided by 1000 to obtain electronic charge
units.
the substituents attached to the atoms forming the hydrogen bond. Therefore E - E,, was plotted as a function of RotI for different configurations of the dimers, and eq 3 was fitted by the least-squares method. First UHBwas expressed as a function of ROHonly, i.e., the effect of nonlinearity of the hydrogen bond was neglected. However, it was found that the fitting is significantly improved by introducing a direction-dependent term to account for the nonlinearity of N-H...O bond. The final form for UHB selected for the attraction range of the &H distance is
UHB= -ARoH-"[I - a sin' (NH...O)] (4) Our approach to the study of the nature of the hydrogen bond is very similar to that of McGuire, et d.,l but we deviate from them in the following three points. (a) As discussed above, to derive the hydrogen bond potential we do not substract the nonbonded term from the total interaction energy. The error due to this term, not accounted for by CNDO/2, is of the order of 0.5 kcal/mol The Journal of Physical Chemistry, Vo/. 78, No. 10. 1974
means of a population analysis based on overlap normalization.12 Although the overlap normalized (ON) charges may represent a better approximation to the true electron distribution, they are not consistent with the CNDO scheme, and a fictitious dielectric constant equal to 2 had to be added to obtain the convergence of Eel to E at large distances. The dipole moment calculated by CND0/2 is in agreement with the experimental value when the atomic dipoles, arising mainly from the lone pairs, are added to the dipole calculated from the net charges. We agree then that these charges must be altered to reproduce the total dipole moment by means of a point charge distribution only; but they are consistent with the CNDO energy and must be used as such to interpret E in terms of Eel and other contributions. (c) Finally, unlike McGuire, et al., we have not tried to determine the repulsive part of U,,. For each curve also the nonbonded interactions were calculated and only the points corresponding to negative values of ZUnb were included in the fitting of E - E,,. This procedure avoided errors due to omission of the repulsive interactions, but in the case of distorted hydrogen bonds it restricted the range of fitting above R O H = 2 A. In most cases, however, it is found that inclusion of points corresponding to even smaller value of E O M , and thus, to a (small) positive value of ZU,,, does not significantly affect the fitting. Definition of the Dimers. The monomers of the hydrogen bonded dimers treated in the present paper are illustrated in Figure 1, where the fractional CNDQ/2 and ON charges (in parentheses) are given for each atom. The molecular internal coordinates used in our calculations are reported in Table 1. The values for the two forms of glycine are those reported by Oegerle and Sabin,13 except for the CCO angle of the carboxylate group, which here corre-
CMD&)/2 Study of NHv-sC Hydrogen Bonds
973
p Figure 2. Conformations of linear, distorted, bifurcated, mono-, and multihydrogeri bonded dimers of ammonia and formate ions. T h e arrows indicate the directions of translation of one molecule with respect to the other and the dotted lines are used to repre-
sent hydrogen bonds.
Figure 4. Dimers of glycine. The upper part shows the dimer zwitterionic glycine...glycine (B), and the lower part glycine ...g lycine (D). The dotted lines represent the hydrogen bonds and the arrows indicate the directions of translation of one molecule with respect to the other.
2, which i s restricted to the system A, i . e , ammoniumformate, shows all the relative orientations of the interacting molecules. The corresponding arrangements for systems B, C, and D can be obtained from Figure 2 by removing one of the free protons (the one lying above the plane of the figure in the cases a through e) from ammonium and/or by adding one proton to the free oxygen. Only the dimers a, d, and e have been considered for the combinations C and D. In all the cases the heavy atoms are coplanar; the configuration of case d is similar to the bifurcated H bond formed in the crystal of a-glycine by the COO- groups of two parallel molecules; e is derived from d by removing one acceptor molecule. Dimers of glycine were then studied, as this is the simplest example of a zwitterion. The structures considered are shown in Figures 3 and 4. Except in case a of Figure 3, where the two molecules were set on the same plane to form a linear H bond, a preliminary scan was performed to find favorable orientations of the dimers by empirical energy calculation. In the case of two zwitterions three energy minima were found; the two most stable, c and d, showing a center and an axis of symmetry, respectively, are compact structures in which van der Waals contacts are important and they gave rise to practical difficulties in translating the molecules; therefore the curve E .- E,, was not calculated for them. The constraint of exact linearity was applied to obtain the dimer of case €3, and two almost linear and equivalent hydrogen bonds were obtained in case D. We examined the linear hydrogen bonds formed by imidazole with the formate ion and the glycine zwitterion. The first system is shown in Figure 5a; in the latter case the formate ion is replaced by the glycine molecule oriented as the mirror image of the donor of Figure 3a. Finally, for a comparison with the hydrogen-bonded dimers also a few pairs of molecules not linked by H bonds were studied; those discussed in the next section are presented in Figure 5 b, 5g, and 5h.
...
fbJ
(CI
ldJ
Figure 3. Zwitterionic dimers of glycine The inter- and intramolecular hydrogen bonds are shown by dotted lines The directions of translation in cases a and b are indicated by the arrows sponds to m lower value of the CNDO/2 energy of the isolated molecule. In a first set of calculations ammonium and ammonia as proton donors were allowed to form the hydrogen bonds with formate ion and formic acid in all the four possible combinations taking two a t a time: A (ammonium. .formate), B (ammonium ...formic acid), C (ammonia.s.farmate), and D (ammonia ...formic acid). Figure
-
The Journalof Physical Chemistry, Vol. 78, No. 10, 1974
R . 0 . Singh and D. R. Ferro
974 80 I I I
I
I I
I I I
I I
Q
fa i
tb)
d
Figure 5. Hydrogen bonded (a) and nonhydrogen bonded (b) dimers of imidazole and formate ion. g and h represent two differently oriented nonhydrogen bonded dimers of ammonia and formate ion. Arrows indicate the directions of translation of one molecule with respect lo the other.
Results and Discussion Illustrative examples of the interaction energy E, calculated by using the CNDOIB method, the electrostatic energy calculated from the CND0/2 charges, and the difference E - E,, are shown in Figures 6-8. The order of magnitude of E differs considerably in the three systems. In each case, for values of Ron greater than 6 A, Eel converges to E within an uncertainty of the order of the computational errors (0.05 kcal/mol). In the case of the glycine dimer shown in Figure 8, subtraction of the nonbonded energy contribution from E - E,, leads to a physically inconsistent result, since a positive value of the order of 2 kcal/mol i s predicted for the hydrogen bond potential a t the O...H distance of ca. 2.5 A. These facts quantitatively support our interpretation of the CNDOIB interaction energy in terms of the electrostatic and the hydrogen bond components only. The values of E and E - Eel calculated at some ROH distances, together with the corresponding fitted values ZlY,,, are listed in Tables 11-IV. The coefficients A and CY were determined by the least-squares fitting for several integral values of n in the expression ( 5 ) of UHB; all the structures of Tables 11-IV, except the dimers c and d of the glycine zwitterion, were included. In all the cases the best fit corresponded either to n = 5 or 6, except for imidazole...formats where it was 4; therefore the A's and the CY'Sfor the values 5 and 6 of n are reported in Table V, where we give also the root-mean-square deviation corresponding to the best potential UH, = -ARoH-n. In the following paragraphs we will examine the difference E E,, as a function of R O H separately for the types of systems described in the previous section. Ammonium (or Ammonia). ..Formate (or Formic The Journal of Physical Chemistry, Vol. 78, No. 10, 1974
Figure 6. ROH dependence of
the CND0/2 interaction energy E, the intermolecular electrostatic energy E,,, and their difference E - E,, in case b of the ammonium.. .formate dimer,
,)rC
______----------
.;:
/' / ' I
dependence of CNDO/2 interaction energy E, intermolecular electrostatic energy Eel, ana their difference € €,I in the case of imidazole.. .formate dimer. Figure 7. ROH
Acid). The collection of dimers shown in Figure 2 constitutes a variety of situations sufficient to investigate the ROHdependence of E - E,, and its additivity in multihydrogen bonded systems. A cumulative inspection of Fig-
CNDQ/2 Study of l\lH.-.O Hydrogen Bonds
75
TABLE 11: Interaction Energies for Hydrogen Bonded Dimers at Various ROBDistances RqH, Configuration
A
E, kcal/mol
-
E
Eel, kcal/mol
E, ZUHB
kcal/mol
-25.17 -18.04 -11.30 -7.32 -2.96 -0.17 -19.99 -11.96 -5.22 -0.38 -13.23 -8.93 -5.53 -0.34 -17.40 -11.68 -8.08 -1.73 -8.70 -5.84
-9.55 -7.88 -5.80 -4.25 -2.34 -0.62 -7.49 -5.82 -3.29 -0.98 -6.90 -5.25 -3.67 -0.83 -8.41 -6.94 -5.58 -2.47 -4.00 -3.24 -2.56 -1.07 -2.97 -2.23 -0.92
E
&I,
kcal/mol
".__.I-
a
1.75 1.85
'0
2.00 2.15 2.50 4.00 2.02 2 . '17 2 " 51
C
4.01 2.15 2.30 2.50 4 00 I
d
2.06) 2.15 2.30
3.00 e
2.00
2 :I5 I
2.30
3.00 f
2.55
2.135 3.30
- 119.38 - 111.20 - 101.10 -93.25 -80.80 -57.00 - 132.60 -121.70 - 103.58 -69.35 - 119.36 - 110.01 - 100.20 -65.98 -209.28 - 194.91 - 183.06 -147.88 - 107.09 -99.32 -92.97 -74.63 - 112.70 - 1.00.33 -69.19
NH4'. . .HCQO-22.99 -17.95 -12.12 -8.11
-3.32 -0.48 -16.76
--11.81 -4.78 -0.47 -12.97 -8.91 -5.32 -0.44 -18.58 -13.79 -9.96 -2.75 -9.85 -7.05 -4,94 - 1. .17 -4.92 -2.66 -1.19
-4.04
-0.86 -6.81 -3.51 -1.48
NU,. .HCOO-7 75 -6 25 -4 33 -3 on
XUHH
.l_ll
-8.36 -6.33 -4.29 -3.00
-1 37 -0 19 -5 2 3 -3 81 -1 73
-1.40 -0.13 -6.38 -4.43
-0 23
-0.23
- 5 33 -3 84 -2 44 -0 29 -6 60 -5 23 -3 98 -i 31 - 3 05 -2 35 -1 72 -0 47 -1 60 -1 00 -0 49
-5.00
-2.18
-3.65 -2.49 -0.25 -5,.24
-3.93 -3.30 -0.88
-2.62 -1.97
-1.51 -0.44 --.2 . 16
-1,28 -0.64
TABLE 111: Interaction Energies for Hydrogen Bonded Dimers at Various ROEDistances RON,
E,
Configuration
A
kcal/mol
a
1.75 1.85
-23.73 -20.38 -16.36 -13.39 -9.20 -3.95 -32.80 -27.63 -23.49 -13.59 -16.85 -14.21 -12.11 -7.01
E
- Eel,
kcal/mol
. .HCOOH -11.82 -9.35 -6.43 -4.40 -1.94 -0.39 -10.44 -7.59 -5.36 -0.81 -4.94 -3.54 -2.46 -0.51 Imidazole. . 'Formate -11.23 -9.07 -6.47 -5.15 -2.27 -0.24
ZUHB
E,
E - Eel,
kcal/mol
kcal/mol
NHd'.
2.00 2.15
2.50 d
4.00 2.00
2.15 2.30 e
a
3.00 2 00 a:. 151 2 30 3 001
1.75 1 858 2.00
2.10 2.50 4.00
__
I_
___l_____l
-18.57 -15.94 -12.72 -11.05 -7.03 -3.15
ures 9-12 gives an idea of the relative strengths of various t,ypes of hydrogen bonds. First of all one observes that the lowest curve in all the fi6wres always corresponds to the linear hydrogen bond (a), while the curves of cases b through e, all representing variously distorted H bonds, lie close to it. This fact suggesls that, besides being a function of R O H , U H , must possess a moderate dependence on the nonlinearity of atoms PJ, H, and (9. Secondly the three E - E,, curves of cases e (one H bond), b (two equivalent H bonds), and c (two H bonds Raving the donated proton in common) fall fairly close to each other when normalized to one hydrogen bond. An
-12.01 -9.09 -6.16 -4.30 -2.01 -0.19 -10.22 -7.30 -5.34 -1.49 -5.11 -3.65 -2.67 -0.75
-3.65 -3.14 -2.32 -1.61 -0.65 -0.09 -2.86 -2.35 -1.73 -0.44 -1.41 -1.17 -0.87 -0.22
-11.07 -8.87 -6.49 -5.34 -2.65 -0.08
-4.07 -3.74 -3.31 -2.96 -2.32 --1.03
NH,. . .HCQOM -3.09 -2.65 -1.91 -1.27 -0' 43 -0.03 -2.36 -1.89 -1.31 -0.19 -1.14 -0.92 -0.65 -0.09 Imidazole. . . fGly -6.25 -5.06 -3.49 -2.38 -0.93 -0.11
ZUHB
-3.29 -2.49 -1.68 -1.17 -0.55 -0.05 -.2.38
-1.74 -1.31 -0.38 -1.19 -0.87 -0.65 -0.10 -6 44 -4.88 -3.30 ~
-2.30
-1.08 -0.10
even stronger indication of the additivity of E - E,, stems from the comparison of curves d and e (Figures 11-13); the interaction of the proton with two acceptor molecules (bifurcated H bond) yields a value of E - Eel per II bond almost equal to that with one acceptor in the same condition. A note of caution should however be added while making a quantitative comparison of the interaction energies; since we are studying the effect of hydrogen bonding when acceptor and donor approach each other, the isolated acceptor in case d is defined as the complex of the two formate (or formic acid) molecules a t the 0-0 separation of 3.2 A, and E,, is therefore computed using the charge distribution of this complex. In systems A and B, because The Journal of Physical Chemistry, Vol. 78, No. 70,1974
R . D.Singh and D.R, Ferro
976
TABLE IV: Interaction Energies for Hydrogen Bonded Dimers a t Various ROHDistances
-23.97 -20.81 -16.91 -14.01 -9.78 -4.01 -29.64 -18.44 -13.18 -8.09 -42.75 -43.54
1.75 1.85 2.00 2.15 2.50 4.00 2.80 2.49 2.99 3.98
a
b
e
d
-Gly + . . . -G]y -e -9.88 -7.74 -5.17 -3.40 -1.29 -0.13 -7.77 -2.15 -0.65 -0.16 -10.38 -9.47
-10.44 -7.48 -4.68 -3.04 -1.23 -0.07 -7.75 -2.16 -0.76 -0.15 -6.59 -7.16
1.85 1.96 2.50 4.00
-7.37 -6.00 -4 42 -1.97 -0.19
1.87 2.02 2.17 2.63 4.10
-6.97 -5.04 -3.74 -1.24 -0.17
2.10
-Gly+, . .Gly -5.03 -3.97 -2.74 -0.98 -0.11 G l y . . .Gly -5.49
I
-3.80
-2.10 -0.60
+Q.01
-5.11 -3.82 -2.71 -1.13 -0.11 -5.73 -3.61 -2.35 -0.74 -0.05
....... €fib
....... E - E i E ,
R,,
(A)
Figure 8. Variation of different types of intermolecular energies with ROH in the case of the glycine...glycine dimer. E n b is the empirical nonbonded interaction term; of particular interest is the fact that E Eel Enb is largely positive at ROH N 2.50
-
A.
-a
_-.-_ _ bc
-
......
........ f
R0"h
-
Figure 10. A plot of f €,I vs. Row for various conformations. of the a m m o n i a . - - f o r m a t e dimer. Curves b and c are normalized to one H bond.
--a
b
-- c
______ e
........ f
3 ROB t i )
2
4
-
Figure 9. A plot ot E €,I vs. ROH for various conformations of the ammonium...formate dimer. Curves a, b, c, e, and f refer lo the corresponding situations of Figure 2. For comparison the curves b and c: have been normalized the one H bond by dividE,, by 2, ing E
-
The Journalof Physical Chemistry, Vol. 78, No. 10, 1974
of the mutual polarization of the two anions, Eel so computed differs significantly (almost by 4 kcal/mol at R O H 2 A in A) from the value relative to the charge distribution of the isolated formate ion. There is then a lack of additivity of the total interaction energy arising from E,] rather than from UHB;in fact it does not occur with systems C and D where the acceptor is a neutral molecule. The configuration of dimer f is obtained from b by rotating th.e donor by 90" about the C-N axis, so that for any given C-N separation the distances ROH only differ in the two structures. Upon rotation it is observed that E increases much more than &,; the result is a large positive change of E - Eel ( e . g . , 11 and 3.5 kcal/mol, respectively, in A and B for ROHin b equal to 2 A), which then is due only to the breaking of two hydrogen bonds partially balanced by the formation of four long and more distorted ones. This result shows that with good approximation, also in the case of charged molecules, E - E,, does not
CND0/2 Study of Mh.&.OHydrogen Bonds
3
2
R,,
4
til
Figure 11. A plot of normalized E - E,, vs. ROH for the various conformations of ammonium...formic acid dimer. Curves a, d , and e refer to the corresponding dimer conformations.
RbH(H1
Figure 13. Comparison between the normalized E - E,) curves of cases d and e for the systems ammonium...formate ( A ) and ammonia...formate ( B ) .
-
Figure 12. A plot of normalized E E,) YS. ROH for the various conformations of the ammonia-.-formlc acid dimer. Curves a, d, and e refer to tne corresponding dimer conformations.
arise from the polarization induced by ions or dipoles independently of the positions of the hydrogens, but it is essentialiy a function of the coordinates of the atoms forming the H bonds. If this statement were exact then E,, should equal E when two polar molecules interact without hydrogen bonding, whereas a certain polarization effect is to be expected. An estimate of the amount of E - E,, not arising from hydrogen bonding can then be obtained by comparing the curves relative to configurations g and h (Figure 5) of HCO2 - ...NH3 with those of the hydrogen bonded dimers; in particular, cases b, c, and h differ from each other only by a rotation through N. The comparison (Figure 14) is very rough, since E - E,, is plotted as a function of the dislance RCN,taken rather arbitrarily as a measure of the intermolecular separation. It shows any way that in nonbonded systems, at intermolecular distances Corresponding to normal hydrogen bonds, the correction to E,, due to the charge redistribution is only a
Figure 14. A plot of E - Eel vs. RCN for the nonhydrogen bonded dimers g (- -) and h ( - . .) of ammonia..*formate, compared with the curves of the hydrogen bonded cases b (--) and c ( - - -).
-
-
small fraction of the hydrogen bond energy. The calculation also offers an estimate of a typical error committed in the empirical calculations of the conformational energy The Journal of Physical Chemistry. Vol 78, No. IO, 1874
R. D. Singh and D. R . Ferro
978
TABLE V: Best Fit Coefficients A .
and n of the Potential Function UHB
CY.
n = 5 Donor
Acceptor
NH.z NH, NH, NH, -Gly + GlY GlY Imidazole Imidazole
WCOO HCOO HCOOH WCOOH -Gly -Gly ~i GlY HCOO -Gly
+
'I
+
~
+
A, kcal/mol
:\K
383 137 197 54 163
a
U
0.53 0.61 0.27 0.46 0.65
1.01 0.48 0.30 0.11 0.24
111 63
194 106
n = 6
__
.-
A, kcal/mol .&e
m
U
uoa
723 256 366
0.36 0.41
0.92 0.55 0.44
100
0.31 0.48
1.36 0.71 0.47 0.22 0.57
300 213 122 356
0.10
0.21 0.36 0.14
0.10
0.20
0.78 0.29
195
Root-mean-square deviation for a = 0.The values reported correspond to the best n, which varies from 5 to 7 .
0.16
0.23 0.16
>' Represents -OQC-CH?-NHs
-.
0
-2
-Y E . -.
-1,
m
Y
.x
'ii w
-6
w
-8
Figure 15. A plot of the charge QT transferred (per H bond) from donor to acceptor, for cases d (--) and e ( - - -) of the
-10
four combinations ammonium. sformate ( A ) , ammonia...formate (B), ammonium.-.formic acid, (C) and ammonia. .formic acid (D)
-
where the charge distribution is kept constant while varying the molecular conformation. The features of the results discussed above are common to the four systems considered. However, the magnitude of E - E,, a t a given RoEI greatly increases in going from the dipole...dipole to the ion-.dipole and to the ion ..ion type of interaction. This fact i s quantitatively expressed by the best fit coefficients A of {Jtfk3, reported in Table V. The improvement of the two-parameter fitting (1 e , accounting for the angular dependence) over the one, can be immediately visualized by comparing the root-mean-square deviations D O in the iast column of this table, with the lowest value of o. In genera!, the error i s almost halved when the nonlinearity of the hydrogen bond is accounted for in the present way. The residual error may be partially due to the analytical form selected for CrHL1,but is mainly contributed by the different situations which we try to fit with the same potential. Although the discrepancies do not show a regular trend, cases b seem the most deviating ones. While we do not attempt to interpret the potential UHB quantitatively in terms of the charge transfer and the polarization components, the results indicate that both must be important For example, one observes rather a good correlation between the magnitude of the coefficients A of the four types of hydrogen bonds and the total charge QT transferred from the proton acceptor to the donor. Figure
.
The Journal O f Physical Chemistry, Vol. 78, No. IO, 1974
R,, t i )
normalized E - €,I vs. RON for the glycine dimers. Curves A(a), A ( b ) , C , and 0 refer to the corresponding situations in Figures 3 and 4,
Figure 16. A plot of
15 shows also that the transferred charge in the bifurcated case approaches the corresponding value in the equally distorted single hydrogen bonds but the differences are larger than those between their energies. We finally observed a moderate dependence of QT on the distortion of the H bonds. On the other hand, the charge transfer and the hydrogen bond energy are greatly enhanced when the donor and/or the acceptor is an ion. A comparison of cases B and C shows that this effect grows with the polarizability of the molecule interacting with the ion. Glycine Dimers. The three combinations A, B, and D of the two forms of glycine (Figures 3 and 4) differ from the ones described previously for the replacement of the ion with the zwitterion. The effect is that the differences between the strengths of the hydrogen bonds in the three cases are reduced, probably because the polarization caused by the binding ion is partially balanced by the opposite ion on the other side of the molecules. The E - E,, curves for these systems are reported is Figure 16. The two forms a and b of the zwitterion dimer show again that there is a significant effect of distortion on the hydrogen bond energy and on the total charge transferred. The latter can be seen in the upper part of Figure 17, whereas the
CNC)0/2 Study of N H - 0 - O Hydrogen Bonds
2
5
.
97
8
6
-057
R,, t i )
I
I
L
5
R"*(i)
Figure 17. Charge redistribution due to hydrogen bonding in the dimers of zwitterionic glycine. Dashed lines refer to one linear H bond (case a ) , while solid lines refer to two distorted H bonds (b). Upper half shows the variation of QT vs. ROH. Lower half
shows the behavior of the fractional CND0/2 charges on hydrogen bonded hydrogens and oxygens. In the case of two hydrogen bonds the variation of the charges on the two bonded hydrogens is exactly the same, whereas on the two oxygens is different because one of them (01) is intramolecularly bonded, VVorth noting is the susceptibility of these charges even at large intermolecular distances, in contrast to QT and E - E,, which approach zero at Row 'v 3 A. lower part of this figure shows the behavior of the net charges on the atoms directly involved in the hydrogen blonding. An important feature of these curves that deserves a special mention is the nature of QT and the net charges a t large distances. It can be noticed that while QT drops to zero at Row 3.5 A, the net charges remain experiencing the influence of the interacting molecule up to much larger distances. The charge redistribution due to the H-bond formation qualitatively agrees with the one normally found by other MO calculations,ll namely, an increase of the electron density on the electronegative atom carrying the proton and also on the electronegative atom forming the bond, and a decrease on the hydrogen tind on the atom (C here) bonded to the electronegative atom. However, the variation of the individual charges does not appear to be correlated with the H-bond potential. A redistribution 6f the charges in the dimer upon the €orormation of the hydrogen bond and a good correlation of the variation of Qrr with that of hydrogen bond energy supports the fact that the hydrogen bonding is a collective interaction. The three E - E,, curves A, B, and D referring to the linear H bonds are much closer to each other than those in, ion...ion and related systems. Thus, while the coefficient A is not very different in gly.-.gly and ammonia . ..formic acid as one should expect, in t,he case of the zwitterionic dimer it is less than a half the value of MCQO- .NH4+ Yet the differences in the hydrogen 3:2:1) to conbond strengths are large enough (A:B:D vince one not to use the same M-bond potential function for neutral and charged groups. Concerning the large dis-
-
I
3
-
Figure 18. A plot of E - Eel vs. RNO for the hydrogen bonded dimers imidazole...formate (--) and imidazole..ozwtttertonic glycine (---.-.), and for the nonhydrogen bonded imidazole-..formate dimer agreement between E - Eel and ZU,, for the two cases c and d of the zwitterionic dimer, we notice that both structures present several very distorted H bonds; the error may arise from having overestimated the distortion parameter a. Imidazole as a Proton Donor. Since the aromatic ring of imidazole is more polarizable than ammonia one could expect stronger hydrogen bonds when the former acts as the proton donor. Such appears to be the case when imidazole forms a linear hydrogen bond with the formate ion (Figure 5a); the coefficient A is 40% larger than that in ammonia-e-formate and a similar behavior is offered by Qr. When the imidazole molecule is rotated until the nonprotonated N is colinear with the C=O bond (Figure 5b), E - E,, becomes small compared with its value in the hydrogen bonded configuration at the same RON distance. Again the polarization effect is small unless the O and H atoms come close, and so the increase o f R when imidazole replaces ammonia is mainly due to the strengthening of the H bond. Contrary to this, such an increase is not observed when imidazole replaces a glycine molecule bonded to the zwitterion of glycine. Table V shows that the coefficient A of imidazole ...*g ly- is even slightly smaller than that of giy...rgly . Caiculations on some more systems are, therefore, needed to analyze the importance of the substituents.
Conclusions The results of the present CNDO/2 calculations support the empirical representation of the interaction energy between the hydrogen bonded molecules as the sum of the intermolecular electrostatic energy and one potential tiHR (function of ROH and N...O) for each hydrogen bond being formed; to these terms the dispersion energy, not accounted for by CNDO, should be added. Of particular interest is the result that the additivity of UHKholds also in the case of bifurcated hydrogen bonds. The Journal of Physical Chemistry, Vol. 78, No. 10, 1974
980
J . B.
The attractive coefficients A determined by us show that the parameters of the hydrogen bond potential functions to be used in the empirical energy calculations vary greatly according to whether neutral molecules, zwitterions; or ions participate in the hydrogen. bonding. Further work is needed to test the applicability of UHBand to extend it to shorter distances; for this purpose lattice energy calculations of 'crystals of the above molecules may be useful.
Acknowledgment. One of us (R. D. S.) wishes to express his thanks to the National Research Council of Italy for having assisted him financially throughout the course of this investigation. References and Notes (1) R . F. McGuire, F. A. Momany, and H . A. Scheraga, J. Phys. Chem., 76, 375 (1972)
Nagy, 0 . B. Nagy, and A . Bruyiants
(2) H. A. Scheraga, Advan. Phys. Org. Chenr.. (3) In this work we are not concerned with ?he torsional energies. It suffices to say that usually they are represented by a cosine function of the dihedral angle, such that when added to nonbonded and electrostatic contributions reproduce the experimental barriers to rotation in small model systems. (4) (a) P. A. Kollman and L. C:Allen, J. Amer. Chem. Soc., 92, 6101 (1970); (b) P. J . Hay, W. J. Hunt, and W. J. Goddard, ibid., 94, 8301 (1972) ( 5 ) R . E. Dickerson and I. Geis, "The Structure and Action of Proteins." Harper and Row, New York, N. Y . , 1969, pp 73,83, and 93. (6) M . Yudkin and R . Offord, "A Guidebook to Biochemistry," University Press, Cambridge, 1971, pp 24 and 46-49. (7) A. S. V . Burgen, 0. Jardetzsky, J. C. Metcalfe, and N. W. WadeJardetzsky, Proc. Nat. Acad. Sci. U. s., 58, 447 (1967). (8) R . J . Weinkam and E. C. Jorgensen, J. Amer. Chem. SOC., 93, 7033 (1971);ibid., 93,7038 (1CiTlI. (9) J. A. Pople and G. A. Segal, J. Cfiem. Phys., 44, 5289 (1966). (10) G. A. Segai, Quan?um Chemica! Exchange Program. No, 91, QCPE, Indiana University. (11) P. A . Kollman and L. C. Allen. Chem. Rev., 72, 283 (1972). (12) J . F. Yan. F. A. Momany, R. Hoffmann, and H. A. Scheraga, J. Phys. Chem., 74, 420 (1970). (13) W. R . Oegerle and J . R. Sabin, J. Mol. Slrucr., 15, 131 (1973)
r Complexes in Organic Chemistry. XI.' Effect of Acceptors on the
harge-Transfer Complexes Formed by Cyclic Anhydrides agy,2 6.B. Nagy," and A. Bruylants iaborafoire de Chimie Generale et Organique. Universite Catholique d e Louvain. lnstitut Lavoisier, Place L. Pasteur. B-1348 louvain-la-Neuve, Belgium (Received July 27. 1973: Revised Manuscript Received January 74. 1974)
r-T and ri-r type charge-transfer complexes with fixed donor moiety and variable acceptor moiety were examined. The thermodynamic and spectroscopic properties of these complexes were analyzed as a function of the properties of the acceptors. Several new electron affinity values for the acceptors were determined and their magnitude was interpreted in the light of the molecular electronic structure.
In a previous paper3 we examined the variation of the properties of charge-transfer complexes (CT complexes) formed by tetrachlorophthalic anhydride (TCPA) with aromatic T donors when the latter were changed. In the present paper we wish to report a similar study on the n-a and r--s type CT complexes of several cyclic anhydrides (Table I). The main purpose i s to examine the behavior of various CT complexes when their acceptor moiety is varied. Although the different presently known acceptors were already compared and their acceptor strength carefully a n a l y ~ e d only , ~ a few studies were devoted to closely related acceptors. The homologous series of polynitrobenzenes4-6-8 and of substituted p-benzoquinones4 7-9 were studied in detail. The importance of this type of study should be emphasized since it permits one to establish how the properties of the acceptor molecule may influence those of the whole CT complex. According to the theoiy o f weak complexes a direct relationship exists between the CT band position ymax and the electron affinity of the acceptor, EA4
The Journal of Physical Chemistry, Vol. 78, No. 10, 1974
C1 and Cz are constants characteristic mainly of the donor moiety. Since the last term on the right-hand side of eq 1 turns out to be negligible, one should obtain a straight line with unit slope when plotting hvcr against E A both expressed in eV units. This prediction has already been verified experimentally by BriegleblO and by Foster8 who used either the actual electron affinity values or the half-wave reduction potentials, E I : ~ ,which are closely related to themlo
E,
= -E,,>
4- 1.41
(2)
The intercept of eq 1is given approximately by
c, = I ,
4- E , --
w,,
(3)
where I , is the ionization energy of the donor; Ec represents the Coulomb interaction energy of the two oppositely charged ions resulting from the complete transfer of one electron from the donor to the acceptor; Wo represents the interaction energy between the donor and the acceptor due to other factors than charge-transfer. Since in practice 1 I D + &I >> 1 Wol, eq 3 reduces to
c, =: I" IEc (41 It is noteworthy that only very few E l values are known at present and their reliability is often questionable.10
