Knowledge Bank

Generalization of previous $ideas1$ gives a simple quantum-mechanical theory of molecular complexes. Let A be an electron acceptor (Lewis acid) and B a base (electron donor). Typically, A may be a neutral molecule or a positive atom-ion, B a neutral molecule or negative atom-ion. For example A may be $I2$ or $Ag+$; B may be benzene or $I-$. Most often, A and B have even-electron diamagnetic structures. Then A and B, and therefore the complex A-B in its ground state, have totally symmetrical singlet $(1A1)$ wave functions. These can be $written2$ as \begin{equation}\psi_{N} = a\psi_{0} + b\psi_{1} +\ldots\end{equation} Here $\psi 0$ is usually a no-bond function $\psi (A,B)$, and $\psi 1$ a dative function $\psi (A--B+)$ with covalent bond between $A-$ and $B+$ (weak in loose complexes, strong in molecules such as $R3N\ast BX3$. Complementary to $\psi$ of Eq. (1), the complex (in addition to states with A or B alone excited) has a characteristic excited electronic state $\psi E=a\prime \psi 1-b\prime \psi 0+\dots$ An intense absorption band $\psi N-\psi E$ is predicted, even for a loose complex. Essentially, this probably often accounts for the colors observed when molecular complexes are formed. These N---E spectra may be called (in general, intermolecular) charge-transfer spectra. They constitute a generalization of the familiar intense interatomic charge-transfer (N---V) spectra of molecules. The N---E oscillator strength, f, is easily computed. For the $Bz\cdot I$ complex (Bz = benzene), assuming the $I2$ axis to lie parallel to the Bz plane with its center on the z-axis (Bz symmetry axis), $f=(4.704\times 10-7)\gamma \mu EN\mathrm{<mrow\; data-mjx-texclass="ORD">2</mrow>}(\gamma incm-1,\mu ENinDebyeunits),with\mu EN=a\prime be(zBz-zI2)+(aa\prime -bb\prime )eS(zBz-z\to ),$ where S is an overlap integral of estimated value 0.1. Hildebrand and Benesi's strong $\lambda 3000$ transition may be identified as N---E of $Bz\backslash cdotI2$. Using Flarbrother's dielectric constant measurements on $I2$ in Bz solution, 0.7D is then obtained for the permanent dipole moment of $Bz\backslash cdotI2$. This yields 0.17 for b in Eq. (1) $(b2=0.028)$. From b and $S,a,a\prime$, and $b\prime$, and then estimating $zBz-ZI2$ as $3.4\backslash AA,\mu EN$ and f can be computed. The computed and observed $b2$-values are 0.19 and 0.30 respectively, a satisfactory agreement. The theory outlined appears capable of explaining the structure and spectra of Ar-Hl complexes in general (Ar = aromatic hydrocarbon, Hl = halogen molecule) and of numerous other types of complexes. The ``charge-transfer'' forces corresponding to resonance of $\psi 1$ with $\psi 0$ in Eq. (1) to some extent resemble London's dispersion forces. However, they should have strong orientational properties, of possible importance in determining how molecules pack in crystals or liquids. This is because resonance requires that $\psi 1$ and $\psi 0$ have the same group-theoretical symmetry. Thus in $Ag+Bz,\psi 1(Ag-Bz+)$ violates this requirement if the silver atom is either on the benzene sixfold axis or in the ring plane.$\mathrm{<mrow\; data-mjx-texclass="ORD">1</mrow>}$ An intermediate location is thus indicated. This prediction is supported by experimental evidence. In $Bz\cdot I2$, similar symmetry considerations point to the model assumed above.