Gas-phase models for the evolved planetary nebulae NGC 6781, M4-9 and NGC 7293

We have studied the chemistry of the molecular gas in evolved planetary nebulae. Three pseudo-time-dependent gas-phase models have been constructed for dense (10(4)-10(5) cm(-3)) and cool (T similar to 15 K) clumpy envelopes of the evolved nebulae NGC 6781, M4-9 and NGC 7293. The three nebulae are modelled as carbon-rich stars evolved from the asymptotic giant branch to the late planetary nebula phase. The clumpy neutral envelopes are subjected to ultraviolet radiation from the central star and X-rays that enhance the rate of ionization in the clumps. With the ionization rate enhanced by four orders of magnitude over that of the ISM, we find that resultant abundances of the species HCN, HNC, HC3N and SiC2 are in good agreement with observations, while those of CN, HCO+, CS and SiO are in rough agreement. The results indicate that molecular species such as CH, CH2, CH2+, HCl, OH and H2O are anticipated to be highly abundant in these objects.