Studies in theoretical chemistry.

Abstract

REFINED ANTISYMMETRIC MOLECULAR ORBITAL CALCULATIONS OF THE ENERGY LEVELS OF BENZENE AND HEXAMETHYLBENZENE The calculation of the energy levels of benzene using the method of Parr, Craig and Ross (1950) was repeated at a higher degree of refinement; the method was also extended to hexamethylbenzene. The extra detail comprises the inclusion of terms involving (i) the exchange interaction between pi-electrons and core, (ii) the contribution of the hydrogen atoms to the core potential, (iii) the carbon—hydrogen or carbon-methyl ionic terms. A description is therefore given of the antisymmetric molecular orbital method as applied to benzene (including configuration interaction), together with the additional refinements made in our calculations. An attempt is then made to interpret the results obtained in the light of (i) experimental data, (ii) previous theoretical work, notably the calculation of Parr, Craig and Ross (1950).

THE NON-EMPIRICAL CALCULATION OF THE SINGLET-TRIPLET SEPARATION FOR THE XI AND ZETA COPPER BONDS IN BINUCLEAR COPPER ACETATE X-ray studies of crystalline copper acetate (Niekerk and Shoening, 1953) have shown it to be binuclear, the copper atoms being bridged by four acetate groups which act as bidentate chelates. There is no direct bond of any strength between the two coppers in this picture. To help explain certain-anomalous properties (such as the diamagnetic susceptibility and its variation with temperature) of copper acetate, Figgis and Martin (1950) postulated a delta-bond between the copper atoms. This implies that a "localised" triplet state is present, with energy low enough to be significantly populated thermally at modest temperatures less than the decomposition temperature of the complex. On ligand field theory, such a bond should have been between either 3dz2 or 3dxy orbitals, the latter being the more likely because, although the overlap of orbitals is very much less, the bond energy is also less by about 12000 cm^-I. The excitation energy from the singlet state to the triplet (denoted as -J) is only 300 cm^-I. However, the system affords excellent opportunity for the testing out of d--orbital bonding theory, as this is a case where an isolated d-orbital bond occurs, and first order interaction of other bonding systems is not present.

THEORY OF THE METHODS OF CALCULATION OF MOLECULAR POLARISABILITY Quantum-mechanical calculations have been carried out on atomic and simple molecular systems by many workers, notable among whom are Buckingham (1937), Kirkwwod (1932) and Hellmann (1983). The methods which have so far been successful are either of the perturbation or variation type. In fact, the reduction of the methods to a few equations, in which atomic or molecular orbitals may be substituted, is discussed here. The method thus obtained (Rahman, 1953) is presently restricted to systems of well-known wave-function (owing to the sensitivity of polarisability to charge distribution) if accurate results are required. Even when the wave-functions of the ground and all the excited states are known, there is certainly a contribution (Guy and Tillieu, I953) due to transitions to continuous levels. This means that some kind of approximate calculation needs to be employed, preferably only using groundstate wave-functions. It turns out that a reasonably easy formula can be deduced, but it is only good, in general, for systems with a symmetry property such that the matrix elements of their wave-functions with respect to the applied field vanish. It is also found (Guy and Harrand, 1952) that polarisabilities obtained in this way are not strictly additive, the criterion of additivity being that the "bond” polarisabilities. considered can be represented accurately by localised wave-functions. When the method is applied to conjugated systems, apparently (Coulson and Davies, 1952) a fairly accurate result can be obtained if an accurate delocalised wave-function for the whole system is known. The latest calculations (Weislinger, I958) which utilise the formulas of Barriol and Regnier (1953) indicate that the direct theoretical approach, even when applied with precision, does not give as good an answer at this stage in the theory as one which utilises some empirical constants. The inclusion of any empirical parameters alters the character of his calculations to such an extent as to dominate completely the final result, or, on the contrary, (Buckingham, 1937, and references) to increase the accuracy by such a small amount as to be superfluous. This is mainly because the result depends, as far asparameters go, very directly upon the initial wave-functions used. Now, Slater orbitals, with only one parameter, usually have to be used for a manageable calculation to result, and these just depend upon the atomic screening parameter. The importance of this factor is seen by the calculations of Rahman (1958), who evaluated the polarisability of the hydrogen molecule, using a very precise wave-function. This gave a result probably accurate to +/-3%. Valence-bond wave-functions, using Slater atomic orbitals (Bell and Long, 1950), give a value of +/-25% for the hydrogen molecule, and, unfortunately, only types of wave-functions of equal simplicity can normally be used in the more complex systems which it is desired to investigate. However, the formulae given here may be used for a consideration of simple and symmetrical systems; for larger systems it appears impossible to perform anything but comparative calculations at the present state of the theory.