We propose an iterative method for computing vibrational spectra that significantly reduces the memory cost of calculations. It uses a direct product primitive basis, but does not require storing vectors with as many components as there are product basis functions. Wavefunctions are represented in a basis each of whose functions is a sum of products (SOP) and the factorizable structure of the Hamiltonian is exploited. If the factors of the SOP basis functions are properly chosen, wavefunctions are linear combinations of a small number of SOP basis functions. The SOP basis functions are generated using a shifted block power method. The factors are refined with a rank reduction algorithm to cap the number of terms in a SOP basis function. The ideas are tested on a 20-D model Hamiltonian and a realistic CH 3 CN (12 dimensional) potential. For the 20-D problem, to use a standard direct product iterative approach one would need to store vectors with about 10 20 components and would hence require about 8 × 10 11 GB. With the approach of this paper only 1 GB of memory is necessary. Results for CH 3 CN agree well with those of a previous calculation on the same potential.

Abstract. The definition of instantaneous eigenstate populations for a dynamical non-self-adjoint system is not obvious. The naïve direct extension of the definition used for the self-adjoint case leads to inconsistencies; the resulting artifacts can induce a false inversion of population or a false adiabaticity. We show that the inconsistency can be avoided by introducing geometric phases in another possible definition of populations. An example is given which demonstrates both the anomalous effects and their removal by our approach.

We present calculations for the action of laser pulses on vibrational transfer within the H + 2 and Na 2 molecules in the presence of dissipation due to photodissociation of the molecule. The laser fields perform closed loops surrounding exceptional points in the laser parameter plane of intensity and wavelength. In principle the process should produce controlled vibrational transfers due to an adiabatic flip of the dressed eigenstates. We directly solve the Schrödinger equation with the complete time-dependent field instead of using the adiabatic Floquet formalism which initially suggested the design of the laser pulses. Results given by wavepacket propagations disagree with predictions obtained using the adiabatic hypothesis. Thus we show that there are large non-adiabatic exchanges and that the dissipative character of the dynamics renders the adiabatic flip very difficult to obtain. Using much longer durations than expected from previous studies, the adiabatic flip is only obtained for the Na 2 molecule and with strong dissociation.