W. E. Wentworth, G. W. Drake, Walter Hirsch, and Edward Chen University of Houston
Houston, Texas
I
I
Molecular Charge Transfer Complexes A group experiment in physical chemistry
In the usual physical chemistry course for undergraduates, the student is introduced to the various concepts used t o explain intermolecular interaction such as dipole-dipole, dipole-induced dipole, London dispersion forces, and finally hydrogen bonding, which possibly may or may not include the previously mentioned forces to some degree. However, in the past decade or so, extensive work has been carried out on another very significant interaction, namely, charge transfer forces, which should be ranked equally with the other intermolecular forces. As u-ill become obvious from the later discussion, the name charge transfer forces is representative of the theory explaining the origin of the interaction which was given by A'lulliken (1). There is a voluminous amount of literature on the subject which includes several excellent reviews (2-5). The reader should consult these works for a more thorough treatment of the theoretical aspects of the subject and for a better feeling for the broad applications to various types of molecular complexes than will be presented in this paper. A book has also been published on the subject which reviews the material up to 1961 (6). By and large, experimental results agree remarkably well with the theory, but, as in any other area of science, studies are still incomplete. In view of the extensive amount of work done on this subject and the apparent wide application to various nlolecular interactions, it seems only logical that this topic be included within the discussion of molecular interactions as presented to the undergraduate student. I n recent years the texts available for physical chemistry have included a more quantitative discussion of the principles of quantum mechanics and their application to chemistry. With this background, the theory of charge transfer complexes can be covered quite readily within certain limitations. For example, Moore's textbook (7) is used for the physical chemistry course a t this university; chapters 12 and 13 contain the wave mechanical theory and give examples to the application of the variational method. As a matter of fact, the charge transfer theory presents a good, yet simple example of the variational method and the results can be readily correlated with experiment. It is for this reason that a physical chemistry experiment on charge transfer complex formation can he carried out on a group basis. The purpose of this paper is to describe such an experiment which has been carried out for the past two years a t this university. I n a paper by Leisten (S), a group experiment was described where the rate constants of the second order
hydrolysis of esters by aqueous alkali were correlated with Hammett sigma-rho values. A different ester was assigned to each student and the correlation of the results of the group was made at the end of the semester. The same type group experiment was carried out in our experiment with charge transfer complexes. As we will see later, the frequency of the charge transfer band and the standard free energy change for the complex are related to the electron affinity of the acceptor molecule (acid in the Lewis acid-base concept) and the ionization potential of the electron donor molecule. If the electron acceptor molecule remains the same in a series of molecular complexes, then a correlation exists between the above mentioned parameters of the complex and the ionization potential of the varying electron donor molecules. In this case, each student or pair of students is assigned a different electron donor molecule and a common electron acceptor. The results of all of the students in the group are reproduced and distributed when the series of experiments are completed, and each of the students carries out the correlation with ionization potential. Obviously, the student gets the benefit of the results of the other students without extra work on his part. I n general, there is considerable added interest in this type of experiment when the student sees his own data, along with the othera, correlated with theory. Of course, the student also obtains the valuable experience of obtaining equilibrium data, use of the spectrophotometer, and observation of the effect which a solvent can have upon the spectra. In our experiment tetracyanoethylene was used as the common electron acceptor and various methylbenzenes as electron donors. These were selected for their stability and availability. However, it certainly is not necessary t o restrict the selection to these compounds. Upon consulting the literature, one will find a wide choice of complexes that could be used in the experiment. Theory
The actual quantum mechanical theory of charge transfer was first developed by Mulliken some 10 years ago ( 1 ) . Prior to this time there were several suggestions that the force of attraction may arise from this type of phenomenon, but the actual quantitative presentation was given by R'lulliken. Much of the following discussion arises from this reference. Mulliken used perturbation theory to derive the desired ground state and excited state energies. An Volume 41, Number 7. July 1964
/ 373
alternative procedure using the variational method was given by McGlynn (5). The latter derivation is basically followed in this paper since only the variational method is covered in the undergraduate lecture. In order to obtain more details of the theory, the reader is referred hack to these original references. The type of molecular complexes which may he included in this theory might consist of inorganic or organic molecules or ions. I n general, they consist of an electron acceptor (acid in the Lewis acid-base theory), which will he represented by A, and an electron donor (Lewis base), which will he represented by B. The reaction which is of concern is the formation of a somewhat weak intermolecular complex AB. In this discussion, only a single 1:l complex will be considered, although in general it may be necessary to include higher order complexes consisting of more than one electron donor or acceptor. It is assumed that both A and B are in totally symmetric singlet electronic ground states; i.e., all valence electrons are paired. In the molecular complex AB there will he a certain force of attraction between the two molecules as a result of the now classical dipole and polarization forces. Let us designate the wave function for this resonance structure as the no-bond wave function. According to the theory of charge transfer complexes, the resulting wave function of the ground state of the molecule consists of not only this contribution of the no-bond wave function, hut also an ionic contribution arising from the transfer of an electron from the electron donor molecule to the electron acceptor molecule. The wave function for the ground state of the complex AR can then he approximated by:
Then upon substituting equations (2) and (4) into (3)
Using the following nomenclature H , = f *(A,B)H+(A,B)d, = E,
- B+)H+(A- - B i ) d r - B+)dr
Hz, = f + ( A -
Hal
=
=
Et
f +(A,B)H+(A-
equation (5) becomes E N = alRo
+ 2abH0, + beE,
(6)
According to the variation method we wish to minimize the energy of the ground state with respect to the parameters a and b in equations (4) and (6) which can he combined as follows:
Taking the partial derivative of equation (7) with 1.espect to the parameters a and b and setting equal to zero to find the minimum energy
+
E ~ ( 2 a 2bS) = 2aE0
+
E ~ ( 2 b 2aS) = 2bE1
+ 2bHm + 2aH0,
(8)
I n order for these two simultaneous equations which are linear with respect to a and b to have a solution, other than the trivial one in which a = b = 0, the determinant must be zero (10).
where a and b are constants which govern the relative contributions of $(A,B) and +(AB f ) to +N. $(A.B) is essentially a no-bond wave function since there is no covalent bond formed between A and B as the result of paired electrons. $(A- - B+) is the dative wave function arising from the transfer of an electron from B t o A and the formation of a weak covalent bond between the odd electrons on A- and B+. In all three wave functions $(A,B), $(A- - B+) in equation (2), it would he necessary to include contributions from polarization of the moleoules to he completely accurate. Furthermore, the wave function +(A+ - B-) has been neglected since it is assumed that one of the molecules has a much greater electron accepting power relative to the other molecule. The energy of the ground state would then he given (7, 9)
Expanding the determinant
where H is the exact Hamiltonian operator including nuclei and electrons in both molecules of the complex. If $N, $(A,B) and + ( A - B+) are all normalized then one equation relating a and b is
There also exists an excited state whose energy should be approximately El, the energy of the dative resonance form. Let us represent the wave funetaion for this excited state by
-
One may assume in complexes of this nature that the wave function $(A,B) is the major contribution to the ground state wave function qN; i.e., b
