Static polarizability and second hyperpolarizability of closed- and open-shell pi-conjugated polymers

The static longitudinal linear polarizability (alpha) and second order hyperpolarizability (gamma) for neutral and charged, closed- and open-shell trans-polyacetylene (PA) chains C(2n)H(2n+2), C(2n-1)H(2n+1), C(2n-1)H(2n+1) (+), C(2n)H(2n+2) (+), and C(2n)H(2n+2) (2+) are systematically investigated and compared. The polarizabilities are calculated within the Pariser-Parr-Pople model, and the electron correlation effect is included through density matrix renormalization group. It turns out that for both alpha, and gamma, two neutral PA chains C(2n)H(2n+2) and C(2n-1)H(2n+1) give similar values, while both singly charged and doubly charged systems present significantly larger magnitude of alpha and gamma values than the two neutral chains. The two singly charged PA chains C(2n-1)H(2n+1) (+) and C(2n)H(2n+2) (+) give more apparent nonlinear optical responses than doubly charged case C(2n)H(2n+2) (2+) and both present negative second order hyperpolarizabilities for short to medium sized oligomers. The sign inversion of gamma values in singly charged PA molecules is anticipated to take place at the much longer length than ever observed due to the significant effects of electron correlation and geometry.