Ab Initio Calculation of Total X-ray Scattering from Molecules

Abstract

We present a method to calculate total x-ray scattering cross sections directly from ab-initio electronic wavefunctions in atoms and molecules. The approach can be used in conjunction with multiconfigurational wavefunctions and exploits analytical integrals of Gaussian-type functions over the scattering operator, which leads to accurate and efficient calculations. The results are validated by comparison to experimental results and previous theory for the molecules H 2 and CO 2. Importantly, we find that the inelastic component of the total scattering varies strongly with molecular geometry. The method is appropriate for use in conjunction with quantum molecular dynamics simulations for the analysis of new ultrafast x-ray scattering experiments, and to interpret accurate gasphase scattering experiments.

Simulation of ultrafast excited-state dynamics and elastic x-ray scattering by quantum wavepacket dynamics

“…This has recently been confirmed by comparison to ab initio-derived scattering signals, and the largest deviations were seen for very small molecules, such as H 2 . 22 This is because the electron density of these systems is dominated by valence electrons, for which the IAM fails. On the other hand, for larger molecules, the IAM performs significantly better.…”

“…18 They found moderate discrepancies from the widely adapted independent atom model (IAM) utilizing the Debye scattering equation, but only for wide angle X-ray scattering (WAXS). Theoretical frameworks for the simulation of TR X-ray scattering of molecules 19,20 are under continuous development; most recent contributions were achieved by Kirrander et al [21][22][23] Their ab initio method is based on the evaluation of matrix elements of the scattering operator, utilizing high-level multiconfigurational electronic wave functions and nuclear wavepackets (WPs) obtained from quantum dynamics (QD) simulations. Their approach did not only yield high-accuracy results, but also accessed the inelastic and coherent mixed components 20,[24][25][26] of the scattering signal, in addition to elastic X-ray scattering.…”

On the use of the Obara–Saika recurrence relations for the calculation of structure factors in quantum crystallography

“…Over the years several research groups have faced this problem, from the initial efforts by McWeeny (1953), Chandler & Spackman (1978) and Barua & Weyrich (1986), to the more recent work of the Kirrander group in the context of the ab initio X-ray diffraction (AIXRD) method (Northey et al, 2014;Moreno Carrascosa et al, 2019;Northey & Kirrander, 2019). However, so far in this context the most efficient technique remains the one proposed by Jayatilaka (1994), who extended the McMurchie-Davidson (MD) recurrence relations used in quantum chemistry to evaluate molecular integrals (McMurchie & Davidson, 1978).…”

Theory of ultrafast x-ray scattering by molecules in the gas phase

“…The elastic and the inelastic signals are usually integrated on the detector and the inelastic contribution cannot generally be assumed to be constant. 28,29 The reorganization of the electron density due to bonding or electronic excitation is furthermore not accounted for in the framework of the IAM. 30,31 A particularly dramatic failure of the assumption that the time-dependent scattering signal is elastic was demonstrated in a seminal paper by Dixit, Vendrell, and Santra, who showed that the scattering signal of an electronic wave packet deviates substantially from the Fourier transform of the time-dependent electron density.…”