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Charge transfer properties of the hydrogen bond
431 Journal of Molecular Structure, 17 (1973) 43 I-433 @ Elsevier Scientific Publishing Company, Amsterdam - Printed in The Netherlands
CHARGE
TRANSFER
PROPERTIES
OF THE HYDROGEN
BOND
PART 4. ON THE CND0/2 MOLECULAR ORBITAL CALCULATIONS AND THE PROBLEM OF THE RELATION BETWEEN THE ENERGY AND THE AMOUNT dF CHARGE TRANSFERRED WITHIN HYDROGEN BONDED SYSTEMS
HENRYK RATAJCZAK Institure
of
Chemistry,
University
of
WroctOw, Wroctaw, III. Joliot-Curie I4 (Poland)
(Received 2 February 1973)
Recently attention has been paid to the charge transfer theorylm6 of the hydrogen bond but so far agreement has not been reached on the importance of this mechanism for understanding the properties7 and structure’ of hydrogen bonded systems. Even Kollman and Allen’, on the basis of a general discussion of the theory of the hydrogen bond have come to the conclusion that the hydrogen bond should not be examined by a charge transfer model, since “a more fundamental reason against the charge-transfer model to understand hydrogen bonding is that as the hydrogen bond gets stronger, the amount of charge transferred does not increase”. However this statement is in disagreement with the empirical relation found recently by Ratajczak and Orville-Thomas’ between the energy and the enhancement of the dipole moment of hydrogen bonded systems which is similar to the correlation found for iodine-amine charge transfer complexesg. The purpose of the present note it; to give some additional support in favour of the charge transfer theory of the hydrogen bond. This will be given by showing that the relation1 previously found between the energy and the amount of charge transfer is also satisfied by the data obtained from molecular orbital calculations carried out for hydrogen bonded systems recently1 O. The data are listed in Table 1 and presented in Fig. 1 as a relation between the energy of complex formation and the amount of charge transfer [Aq(e,]*. Theoretical justification for this correlation was obtained by Ratajczak and Orville-Thomas’ by usjng an extension of Mulliken’s charge transfer theory,
432 TABLE
I
CALCULATED CNDO
No.
1 2 3 4 5 6 7 8 9
ENERGIES
CHARGE
TRANSFER
FOR SOME HYDROGEN
BONDED
Proton
Proton
accepror Y
donor
H*CO
HNH, HNH+ HNHz H-OH H-OH HF HOW HF HF
3.6 4.5 5.8 7.2 8.7 9.4 II.2 13.2 15.4
0.032 0.039 0.036 0.041 0.059 0.061 0.064
0.13 0.14 0.18 0.20 0.19 0.20 0.24 0.25 0.25
IZF
19.4
0.093
0.30
20.0 59.7 72.2 102.1
0.097 0.289 0.365 0.350
0.31 0.54 0.60 0.59
Hz0 H3N HlCU I-I,0 HF H3N HzCO Hz0
IO 11 12 13 14
AND
SYSTEMS
USING
THE
METHOD=
%N Hz0 HOF-
w-x
HF HOI& + HOH HF
0.017 0.019
-
4.4 5.0 6.8
32.0 35.0 40-60
a Taken from ref. 10.
Fig. i. The relation between the energy of formation and the amount of chargetransferred in the hydrogen bonded complexes described in Table I. I, calcufated values of LLE, II, experimental values of An.
433 for weak electron donor-acceptor complexes, which leads to the relation
where AH is the energy of formation of the complex, /3e1 = (Ye is the nonbond and Yy, the dative bond wave function), pl is the dipole moment of the dative structure, AZ;cr is the contribution to the observed enhancement of the dipole_ moment of the hydrogen bond complex due to the presence of charge transfer in the ground state and We contains the classical eIectrostatic energy terms as well as the closed shell repulsion term. , From Fig. l,T the values of /3,,r and W,, can be estimated which are - 3.4 eV and 7 kcal/moI respectively. These values are much larger than those obtained from the empirical correlation between the energy and the enhancement of dipole moment of hydrogen bonded systems’, which are /3er = - 1.5 eV and We = (O-6-2) kcaI/mol. One of the reasons for the observed disagreement as far as the values of PO1 and W, are concerned might be due to the fact that the calculated energy and charge distribution are over-estimated in comparison to those determined experimentahy”. It is interesting to note that the discrepancy between the calculated and experimental values of energy increases as the hydrogen bond becomes stronger (see Table 1 and Fig. 1). However the most important aspect of this note was to show that the behaviour of the hydrogen bond is quite similar to the charge transfer interactions as far as the relation between the energy and the amount of charge transfer is concernedgS ‘I.
1 H. RATAJCZAKAND W. J. ORVILLE-THOMAS,J. Chew. Phys., 58 (1973) 971, Part 3 of this series. 2 S. BRATO& in P. 0. L~WDIN (editor), Adounces in Q~untunr Cizemistry, Vol. III, Academic Press, New York, 1967, p. 209. 3 H. B. FRIEDRICH AND W. B. PERSON, J. Chem. Phys., 44 (1966) 2161. 4 R. S. MULLXKEN AND W. B. PERSON, Molecular Complexes, Wiley-Interscience, New York, 1969. 5 H. RATAJCZAK, J. Phys. Chem., 76 (1972) 3000. 6 H. RATAJCZAK, J. Phys. Chem., 76 (1972) 3991. 7 P. A. KOLLMAN AND L. C. ALLEN, Chem. Rev., 72 (1972) 283. 8 P. A. KOLLMAN, J. Amer. Chem. Sot., 94 (1972) 1837. 9 H. RATAJCZAK AND W. J. ORVILLE-THOMAS,J. Mol. Structure, I4 (1972) 149. 10 P. SCHUSTER,Theor. Chirn. Acta, 19 (1970) 212. 11 K. MAZUR AND H. RATAJCZAK, to be published.
CHARGE
TRANSFER
PROPERTIES
OF THE HYDROGEN
BOND
PART 4. ON THE CND0/2 MOLECULAR ORBITAL CALCULATIONS AND THE PROBLEM OF THE RELATION BETWEEN THE ENERGY AND THE AMOUNT dF CHARGE TRANSFERRED WITHIN HYDROGEN BONDED SYSTEMS
HENRYK RATAJCZAK Institure
of
Chemistry,
University
of
WroctOw, Wroctaw, III. Joliot-Curie I4 (Poland)
(Received 2 February 1973)
Recently attention has been paid to the charge transfer theorylm6 of the hydrogen bond but so far agreement has not been reached on the importance of this mechanism for understanding the properties7 and structure’ of hydrogen bonded systems. Even Kollman and Allen’, on the basis of a general discussion of the theory of the hydrogen bond have come to the conclusion that the hydrogen bond should not be examined by a charge transfer model, since “a more fundamental reason against the charge-transfer model to understand hydrogen bonding is that as the hydrogen bond gets stronger, the amount of charge transferred does not increase”. However this statement is in disagreement with the empirical relation found recently by Ratajczak and Orville-Thomas’ between the energy and the enhancement of the dipole moment of hydrogen bonded systems which is similar to the correlation found for iodine-amine charge transfer complexesg. The purpose of the present note it; to give some additional support in favour of the charge transfer theory of the hydrogen bond. This will be given by showing that the relation1 previously found between the energy and the amount of charge transfer is also satisfied by the data obtained from molecular orbital calculations carried out for hydrogen bonded systems recently1 O. The data are listed in Table 1 and presented in Fig. 1 as a relation between the energy of complex formation and the amount of charge transfer [Aq(e,]*. Theoretical justification for this correlation was obtained by Ratajczak and Orville-Thomas’ by usjng an extension of Mulliken’s charge transfer theory,
432 TABLE
I
CALCULATED CNDO
No.
1 2 3 4 5 6 7 8 9
ENERGIES
CHARGE
TRANSFER
FOR SOME HYDROGEN
BONDED
Proton
Proton
accepror Y
donor
H*CO
HNH, HNH+ HNHz H-OH H-OH HF HOW HF HF
3.6 4.5 5.8 7.2 8.7 9.4 II.2 13.2 15.4
0.032 0.039 0.036 0.041 0.059 0.061 0.064
0.13 0.14 0.18 0.20 0.19 0.20 0.24 0.25 0.25
IZF
19.4
0.093
0.30
20.0 59.7 72.2 102.1
0.097 0.289 0.365 0.350
0.31 0.54 0.60 0.59
Hz0 H3N HlCU I-I,0 HF H3N HzCO Hz0
IO 11 12 13 14
AND
SYSTEMS
USING
THE
METHOD=
%N Hz0 HOF-
w-x
HF HOI& + HOH HF
0.017 0.019
-
4.4 5.0 6.8
32.0 35.0 40-60
a Taken from ref. 10.
Fig. i. The relation between the energy of formation and the amount of chargetransferred in the hydrogen bonded complexes described in Table I. I, calcufated values of LLE, II, experimental values of An.
433 for weak electron donor-acceptor complexes, which leads to the relation
where AH is the energy of formation of the complex, /3e1 = (Ye is the nonbond and Yy, the dative bond wave function), pl is the dipole moment of the dative structure, AZ;cr is the contribution to the observed enhancement of the dipole_ moment of the hydrogen bond complex due to the presence of charge transfer in the ground state and We contains the classical eIectrostatic energy terms as well as the closed shell repulsion term. , From Fig. l,T the values of /3,,r and W,, can be estimated which are - 3.4 eV and 7 kcal/moI respectively. These values are much larger than those obtained from the empirical correlation between the energy and the enhancement of dipole moment of hydrogen bonded systems’, which are /3er = - 1.5 eV and We = (O-6-2) kcaI/mol. One of the reasons for the observed disagreement as far as the values of PO1 and W, are concerned might be due to the fact that the calculated energy and charge distribution are over-estimated in comparison to those determined experimentahy”. It is interesting to note that the discrepancy between the calculated and experimental values of energy increases as the hydrogen bond becomes stronger (see Table 1 and Fig. 1). However the most important aspect of this note was to show that the behaviour of the hydrogen bond is quite similar to the charge transfer interactions as far as the relation between the energy and the amount of charge transfer is concernedgS ‘I.
1 H. RATAJCZAKAND W. J. ORVILLE-THOMAS,J. Chew. Phys., 58 (1973) 971, Part 3 of this series. 2 S. BRATO& in P. 0. L~WDIN (editor), Adounces in Q~untunr Cizemistry, Vol. III, Academic Press, New York, 1967, p. 209. 3 H. B. FRIEDRICH AND W. B. PERSON, J. Chem. Phys., 44 (1966) 2161. 4 R. S. MULLXKEN AND W. B. PERSON, Molecular Complexes, Wiley-Interscience, New York, 1969. 5 H. RATAJCZAK, J. Phys. Chem., 76 (1972) 3000. 6 H. RATAJCZAK, J. Phys. Chem., 76 (1972) 3991. 7 P. A. KOLLMAN AND L. C. ALLEN, Chem. Rev., 72 (1972) 283. 8 P. A. KOLLMAN, J. Amer. Chem. Sot., 94 (1972) 1837. 9 H. RATAJCZAK AND W. J. ORVILLE-THOMAS,J. Mol. Structure, I4 (1972) 149. 10 P. SCHUSTER,Theor. Chirn. Acta, 19 (1970) 212. 11 K. MAZUR AND H. RATAJCZAK, to be published.