Self-terms of intermolecular force constants

Abstract

The self-terms of the intermolecular force constants are derived by employing the condition of translation invariance. The self-terms thus obtained ensure that the dynamical matrices of the crystal are always Hermitian. The role of the condition of rotation invariance is discussed. The expressions for the self-terms differ in part from those published by Dolling, Pawley & Powell [Proc. Roy. Soc. (1973). A333, 363-384]. The conditions under which the self-terms of these authors are identical with the present ones are discussed.

Coulombic nonbonded interatomic potential functions derived from crystal-lattice vibrational frequencies in hydrocarbons

“…On physical grounds, the dynamical matrix is required to be Hermitian. As noted by Scheringer (1974) and by actual calculations in this laboratory, Pawley's method does not strictly obey this constraint. Since the difference is small, the dynamical matrix is symmetrized by simply averaging the cross-diagonal terms.…”

Self terms in external-mode formalism

“…Generally speaking, these external forces on individual atoms by themselves do not vanish* and thus inclusion of the second term in (9) is obligatory. In writing his equation (14), Scheringer (1974) omitted the first-order derivative terms of the type ~0,~ (cf. Born & Huang, 1954, equations 23.22 and 23.23).…”

“…However, as pointed out above, these terms should have been retained in the external-mode approach. If one included the first-order-derivative terms and used the amended version of Scheringer's (1974) equation (19), one can at once retrieve the missing term, which has been derived by us using the higher-order terms in (4).…”

“…Venkataraman & Sahni (1970), whose notation we follow here, have discussed how, for this formulation, the force constants connecting different clusters, q~ x ¢ x' , can be related to the intvratomic force constants between atoms on the (~/') x' (Venkataraman & Sahni, 1970, two clusters ~0,~ k' equations II.A.58a-d may use the translational and rotational sum rules (Venkataraman & Sahni, 1970, equations II.A.16-19) to deduce their expressions. An alternative scheme for obtaining the self force constants was presented by Scheringer (1974 to zero for k 4= k'. However, one should not assume that by doing this we are implying that intracluster frequencies are zero; we are simply using an artifact to show that in discussing the external normal modes no internal distortions of the clusters are admitted.…”

“…The second term on the right side does not occur in Scheringer's (1974) expression (cf. his equation 13d), and to this extent his expression is incomplete.…”