On the use of pseudostates to calculate molecular polarizabilities

Abstract

The polarizability of a molecule is an intrinsic property which is important for a large variety of problems. However, determining reliable values for these polarizabilities is not straightforward: for instance the standard sum over states formulation of the problem does not converge because of the need to include not only many excited states but also to allow for contributions from the continuum. Here a formulation of this technique is given which uses pseudostates to allow for physical and continuum states otherwise omitted from the expansion. The pseudostates are represented by even-tempered expansions of Gaussian-type orbitals at the molecular centre-of-mass. The method is tested for LiH, Li2, water and CO molecules. For LiH and CO, calculations for the polarizability of low-lying excited states are presented including that for the A 3Π state of CO, whose polarizability appears not to have been previously determined. It is suggested that the use of pseudostates provides a straightforward method of calculating static polarizabilities of molecules in both ground and excited electronic states. The extension of the method to the calculation of dynamic polarizabilities is discussed.

Low-energy electron scattering with the purine bases of DNA/RNA using the R-matrix method

“…The molecular R-matrix with pseudo-states (RMPS) method 48,49 has been demonstrated to systematically improve the polarization effects. 50,51 However, at present it is computationally too expensive to perform RMPS calculations for molecules of the size considered here. Indeed, the calculations presented in this work constitute the limit that could be achieved at this time.…”

Uncertainty estimates for theoretical atomic and molecular data

“…Studies [69,70] suggest that while the FD approach for transition dipoles shows improved convergence behavior compared to the EV approach, perhaps more so than for Spherically averaged polarizability of water in its equilibrium geometry computed using sum-over-states formula (1) [73]; the experimental value is corrected for vibrational effects [75].…”

R-matrix calculations of low-energy electron alkane collisions

“…The polarizabilities can be improved beyond those in the table by including more states in the target region, but the gains are small and the computational cost high. Even if all the states are included, this approach still leads to polarizabilities which converge to less than the true value (Jones and Tennyson 2010). The dependence of the polarizability on basis and model is slightly complicated as approximate wavefunctions are often more polarizable than their more exact counterparts.…”

“…The dependence of the polarizability on basis and model is slightly complicated as approximate wavefunctions are often more polarizable than their more exact counterparts. This means that the calculated polarizabilty may decrease as the calculation is improved (Jones and Tennyson 2010 2.2.2. Rydberg model.…”

“…For the smaller calculations the outer region is computationally straightforward. However when the number of target states involved becomes large, this is no longer so and to obtain a good polarizability, a large number of states are required in the sum over states expression (Jones and Tennyson 2010). For low energy, this is not an issue, as high-energy states can simply be dropped in the outer region calculation with no detriment to lower energy cross sections (Rabadán and Tennyson 1997).…”