Femtosecond x-ray absorption spectroscopy of pyrazine at the nitrogen K-edge: on the validity of the Lorentzian limit

Abstract

We calculate the femtosecond X-ray absorption spectrum of pyrazine at the nitrogen K-edge including the wavepacket dynamics in both the valence and core-excited state manifolds. We do not invoke the widely used short-time (or Lorentzian) approximation which neglects the nuclear dynamics after the X-ray probe excitation. Instead, we calculate the X-ray-induced polarization in the time-domain where the optical pump as well as X-ray probe pulses are explicitly described. While the non-adiabatic population transfer following the optical excitation is well reproduced in the Lorentzian limit the transient X-ray absorption spectra obtained under this approximation lack some vibronic features, even when considering the short core-hole lifetime of nitrogen. We further demonstrate the effect of an increasingly longer pulse on the observed photo-triggered wavepacket dynamics which are blurred to the point that the X-ray probe response becomes effectively time-independent.

Nonlinear Molecular Electronic Spectroscopy via MCTDH Quantum Dynamics: From Exact to Approximate Expressions

“…TA is not the only type of spectroscopic method that can be simulated with the current protocol. Extension of the technique in the X-ray regime is straightforward − and will facilitate simulations of transient near-edge X-ray absorption fine structure (NEXAFS) spectra. The overlap term appearing in eqs and can be seen as the matrix element of the simplest operator (i.e., the identity operator).…”

Time-Dependent Resonant Inelastic X-ray Scattering of Pyrazine at the Nitrogen K-Edge: A Quantum Dynamics Approach

“…The full Hamiltonian H employed in the nuclear quantum dynamics simulations consists of a molecular Hamiltonian H mol supplemented by the interaction with an external electromagnetic field H int acting as a time-dependent perturbation boldH ( t ) = H normalm normalo normall + H int ( t ) Following the semi-classical ansatz of ref , the coupling to the external field is assumed to be accurately captured by the dipole approximation H int false( α β false) ( Q , t ) = prefix− μ α β · scriptE ( t ) where scriptE is the electric field of the photon beam and μ αβ is the transition dipole moment between the electronic states |α⟩ and |β⟩, and where the Condon approximation and a single polarization direction are assumed. Within the rotating wave approximation, the electric field is represented by scriptE ( t ) = scriptA ( t ) · e − i ω 0 ( t − t 0 ) with the temporal envelope function scriptA of the laser pulse centered at t 0 and with carrier frequency ω 0 .…”

“…As in ref , we decouple the valence and core-excited states, , yielding the following matrix representation of the molecular Hamiltonian H normalm normalo normall = ( lefttrue boldH normalv 0 0 boldH normalc ) where H v and H c are sub-Hamiltonians acting on the manifolds of the valence and core-excited electronic states, respectively. In both subspaces, a vibronic coupling model up to second order ,, is employed, leading to coupled potential energy surfaces (PESs) in a diabatic representation. , In this framework, each submatrix in eq is expressed as H x = H false( 0 false) + W x , boldx ∈ { v , c } where the zeroth-order Hamiltonian is constituted by the ground-state Hamiltonian in the harmonic approximation H false( 0 false) = prefix∑ i ω normali 2 ( − ∂ 2 ∂ Q i 2 + Q i 2 ) bold1 with ω i representing the frequency of mode Q i .…”

“…As in ref ( 78 ), we decouple the valence and core-excited states, 79 , 80 yielding the following matrix representation of the molecular Hamiltonian where H v and H c are sub-Hamiltonians acting on the manifolds of the valence and core-excited electronic states, respectively. In both subspaces, a vibronic coupling model up to second order 47 , 48 , 81 is employed, leading to coupled potential energy surfaces (PESs) in a diabatic representation.…”

Time-Resolved X-ray Absorption Spectroscopy: An MCTDH Quantum Dynamics Protocol

“…The short-time approximation (STA) invoked in ref ( 34 ) computes static absorption signals on top of a WP dynamics in the valence manifold, thereby completely neglecting the WP evolution projected by the probe pulse in the manifold of higher-lying states. Its validity for X-ray probe pulses has been studied by Freibert et al 35 who compared LVC/STA results with the highest LVC/WPO approach. They report that STA accurately reproduces the positions of the transient signals and their broadening, but as expected it lacks a fine vibronic structure, which becomes more visible the longer the lifetime of the core-excited states.…”