Longitudinal polarizability

Figure 1 Evolution as a function of the number of unit cells (N) of the longitudinal polarizability per unit cell, AoIl(N) = l(N) - 0[l(N-1) for prototypes of saturated (polyethylene) and unsaturated (polyacetylene) polymers.

The main quantity providing the dynamic longitudinal polarizability of closed-shell infinite periodic systems is the polarization propagator which at the RPA level takes the form [23-25] ... 

Table I Longitudinal polarizability per unit cell as a function of the number of H, units cells, N in comparison with the polymeric value.

Figure 3 Frequency-dispersion curves of the longitudinal polarizability per unit cell of infinite periodic chains of hydrogen molecules according to the method used (RPA (bottom) and UCHF (top)). AH the values are in a.u.. The position of the first excitation energies which corresponds to the poles is indicated by vertical bars.

The computed 6-31G values for the longitudinal polarizability and longitudinal hyperpolarizability per unit cell are given in Table 7. It can be observed that the longitudinal polarizability and longitudinal hyperpolarizability increase with the chain length. However, the rate of variation of these magnitudes decreases with N, in such a way that ay/N... 

TABLE 7. Static longitudinal polarizabilities oil (in a.u.) and longitudinal hyperpolarizabilities yl (in 104 a.u.) per unit for linear C2nH2 +2 polyenes"... 

Further work on long polyenes, including vibrational distortion, frequency dispersion effects and electron correlation, would be important for evaluating more accurate asymptotic longitudinal polarizabilities and hyperpolarizabilities. 

The Htickel method predicts that in the case of a long polyene chain the longitudinal polarizability of n electrons varies as the cube of the molecular length, while the o polarizability should increase only linearly 18>. Refined molecular orbital calculations (taking into account bond alternation etc.) do not exhibit this abnormal asymptotic behaviour. 

Mosley et al. have applied different density functional methods for a molecular hydrogen chain.134 The results obtained with the aid of Romberg s extrapolation procedure135 overestimate the static longitudinal polarizability as compared to the CHF results. 

X and Y represent halogens) with m = 2 for H—X the expressions of Brown and Denbigh are numerically almost the same. Longitudinal polarizabilities, however, sometimes increase as r decreases Le Ffevre (1958) therefore advanced (31)... 

The static dipole polarizabilities of alkali dimers have been calculated as a function of the internuclear distance and of the vibrational index for both their electronic ground state and lowest triplet state. The method is based on /-dependent pseudopotentials for atomic core representation, Gaussian basis sets, effective core potentials to account for core polarization, the evaluation of molecular orbitals by the restricted HF method, and then a full valence Cl treatment. For all alkali pairs, the parallel and perpendicular components of the ground state a at equilibrium distance Rg scale as the cube of Re, which can be related to a simple electrostatic model of an ellipsoidal charge distribution. So, for the ground state, the longitudinal polarizability exhibits a maximum at a distance corresponding to 1.3-1.5 times the equilibrium distance. 

B. Kirtman and M. Hasan, Chem. Phys. Lett., 57, 123 (1989). Ab Initio Longitudinal Polarizabilities and Hypeipolarizabilities for Polydiacetylene and Polybutatriene Oligomers. For the long-chain semiempirical calculations, see B. Kirtman, Int.. Quantum Chem., to be published. Finite Chain Approximation for Linear and Non-Linear Polarizabilities of Polydiacetylene and Polybutatriene. 

---