Non-adiabatic and time-resolved photoelectron spectroscopy for molecular systems

We quantify the non-adiabatic contributions to the vibronic sidebands of equilibrium and explicitly time-resolved non-equilibrium photoelectron spectra for a vibronic model system of Trans-Polyacetylene. Using exact diagonalization, we directly evaluate the sum-over-states expressions for the linear-response photocurrent. We show that spurious peaks appear in the Born-Oppenheimer approximation for the vibronic spectral function, which are not present in the exact spectral function of the system. The effect can be traced back to the factorized nature of the Born-Oppenheimer initial and final photoemission states and also persists when either only initial, or final states are replaced by correlated vibronic states. Only when correlated initial and final vibronic states are taken into account, the spurious spectral weights of the Born-Oppenheimer approximation are suppressed. In the non-equilibrium case, we illustrate for an initial Franck-Condon excitation and an explicit pump-pulse excitation how the vibronic wavepacket motion of the system can be traced in the time-resolved photoelectron spectra as function of the pump-probe delay

Origin and Implication of Ellipticity in High-order Harmonic Generation from Aligned Molecules

We address theoretically and numerically the possibility of observing ellipticity in high-order harmonic generation (HHG) from aligned molecules driven by linearly polarized fields—a subject of controversy in the recent literature with significant implications. To that end we develop a numerical method for solution of the electronic dynamics and extend a recently developed theory of HHG from aligned molecules. Our numerical results are in good agreement with recent experimental data. The theory explains analytically several observations of polarization experiments. We note the conditions under which ellipticity can be observed and the information content of elliptically polarized harmonics regarding the molecular system

The Exchange Energy of a Uniform Electron Gas Experiencing a New, Flexible Range Separation

The exchange energy of a uniform electron gas which experiences a two-parameter separation of the Coulomb interaction is derived as a local functional of the electron density. The two parameter range separator allows separate control of where and how rapidly the Coulomb interaction is switched off. The usefulness of the functional is briefly assessed by combination with a recently published pair of exchange and correlation functionals. The self-interaction error of noble-gas dimer cation dissociation is found to be reduced while thermochemistry is relatively unperturbed. These results suggest that changes in attenuator shape can improve range-separated functionals

Scaled Opposite Spin Second Order Moller-Plesset Correlation Energy: An Economical Electronic Structure Method

A simplified approach to treating the electron correlation energy is suggested in which only the alpha-beta component of the second order Moller-Plesset energy is evaluated, and then scaled by an empirical factor which is suggested to be 1.3. This scaled opposite spin second order energy (SOS-MP@) yields results for relative energies and derivative properties that are statistically improved over the conventional MP2 method. Furthermore, the SOS-MP2 energy can be evaluated without the 5th order computational steps associated with MP2 theory, even without exploiting any spatial locality. A 4th order algorithm is given for evaluating the opposite spin MP2 energy using auxiliary basis expansions, and a Laplace aproach, and timing comparisons are given

Assessment of tuning methods for enfacing approximate energy linearity in range-separated hybrid functionals

A range of tuning methods, for enforcing approximate energy linearity through a system-by-system optimization of a range-separated hybrid functional, are assessed. For a series of atoms, the accuracy of the frontier orbital energies, ionization potentials, electron affinities, and orbital energy gaps is quantified, and particular attention is paid to the extent to which approximate energy linearity is actually achieved. The tuning methods can yield significantly improved orbital energies and orbital energy gaps, compared to those from conventional functionals. For systems with integer M electrons, optimal results are obtained using a tuning norm based on the highest occupied orbital energy of the M and M + 1 electron systems, with deviations of just 0.1–0.2 eV in these quantities, compared to exact values. However, detailed examination for the carbon atom illustrates a subtle cancellation between errors arising from nonlinearity and errors in the computed ionization potentials and electron affinities used in the tuning