Beyond the electric-dipole approximation: A formulation and implementation of molecular response theory for the description of absorption of electromagnetic field radiation

Abstract

Beyond the electric-dipole approximation: A formulation and implementation of molecular response theory for the description of absorption of electromagnetic field radiation, 2015, Journal of Chemical Physics, (142) We present a formulation of molecular response theory for the description of a quantum mechanical molecular system in the presence of a weak, monochromatic, linearly polarized electromagnetic field without introducing truncated multipolar expansions. The presentation focuses on a description of linear absorption by adopting the energy-loss approach in combination with the complex polarization propagator formulation of response theory. Going beyond the electric-dipole approximation is essential whenever studying electric-dipole-forbidden transitions, and in general, non-dipolar effects become increasingly important when addressing spectroscopies involving higher-energy photons. These two aspects are examined by our study of the near K-edge X-ray absorption fine structure of the alkaline earth metals (Mg, Ca, Sr, Ba, and Ra) as well as the trans-polyenes. In following the series of alkaline earth metals, the sizes of non-dipolar effects are probed with respect to increasing photon energies and a detailed assessment of results is made in terms of studying the pertinent transition electron densities and in particular their spatial extension in comparison with the photon wavelength. Along the series of trans-polyenes, the sizes of non-dipolar effects are probed for X-ray spectroscopies on organic molecules with respect to the spatial extension of the chromophore. C 2015 AIP Publishing LLC.[http://dx

Applications to metal K pre-edges of transition metal dimers illustrate the approximate origin independence for the intensities in the length representation

“…The problems associated with origin dependence can be overcome by switching from the length to the velocity representation or even more elegantly to the exact expression as presented by List et al [23]. The List et al [23] approach also avoids the unphysical total negative intensities observed in [27] in the velocity representation and in the length representation in this work irrespectively of the choice of basis set.…”

“…The List et al [23] approach also avoids the unphysical total negative intensities observed in [27] in the velocity representation and in the length representation in this work irrespectively of the choice of basis set.…”

“…[23] However, this requires the calculation of new types of integrals that are not readily available in most codes. An isotropic tensor averaging, known from the terms in the multipole expansion, is not known for the exponential form of the wave vector.…”

X-ray spectroscopies through damped linear response theory

“…In Ref. [190] it was demonstrated that the contraction is almost inversely proportional to Z, while the transition energy goes as Z 2 -as expected for hydrogenic systems. This gives a kr depending close to linearly with Z.…”

“…The origin-dependent inclusion of higher-order terms in the perturbative field has been developed by Bernadotte et al, 189 and expanded by List et al 190 It has been demonstrated that an origin-independent inclusion of higher-order contributions can be achieved if all contributions to the same order in the wave vector is included consistently. Higher-order terms can break symmetry rules in the dipole approximations, yielding, e.g., 1s → nd transitions.…”