Abstract
Expressions for analytical molecular gradients of core-excited states have been derived and implemented for the hierarchy of algebraic diagrammatic construction (ADC) methods up to extended second-order within the core-valence separation (CVS) approximation. We illustrate the use of CVS-ADC gradients by determining relaxed core-excited state potential energy surfaces and optimized geometries for water, formic acid, and benzene. For water, our results show that in the dissociative lowest core-excited state, a linear configuration is preferred. For formic acid, we find that the O K-edge lowest core-excited state is non-planar, a fact that is not captured by the equivalent core approximation where the core-excited atom with its hole is replaced by the "Z + 1" neighboring atom in the periodic table. For benzene, the core-excited state gradients are presented along the Jahn-Teller distorted geometry of the 1s → π* excited state. Our development may pave a new path to studying the dynamics of molecules in their core-excited states.
Highlights
The concept of the potential energy surface (PES) represents a cornerstone in theoretical chemistry, constituting an effective way to visualize and understand the interplay between the electronic and nuclear degrees of freedom that, in turn, underlie the behavior and interactions between molecules
The second x-ray absorption spectroscopy (XAS) peak is assigned to a transition to the 2b2 molecular orbital (MO) and it corresponds to a bound core-excited state.[11,64]
Python module named adc_gradient is integrated with algebraic diagrammatic construction (ADC) connect[49] and is made available for download under GPLv3 license at https://gitlab.com/iubr/cvs-adc-grad. Sample illustrations of this development were provided for the lowest core-excited states of water, formic acid, and benzene, where we have determined optimized core-excited state geometries and relaxed potential energy surfaces
Summary
The concept of the potential energy surface (PES) represents a cornerstone in theoretical chemistry, constituting an effective way to visualize and understand the interplay between the electronic and nuclear degrees of freedom that, in turn, underlie the behavior and interactions between molecules. To reduce the size of the ADC matrix, one possibility is to pick up only the blocks relevant to the core-excitation process This is the idea behind the CVS approximation, which is based on the fact that the core and the valence orbitals are well separated spatially and energetically so that the core-excitation and valence-excitation spaces may be considered decoupled.[35,36]. Scitation.org/journal/jcp as well as core-excited state properties With this approximation, ADC has been successfully applied to describe the x-ray absorption spectroscopy (XAS) of molecules,[37–42] showing a high accuracy and precision at the CVS-ADC(2)-x level.[15,42] As they are of direct relevance in the present work, the explicit expressions for the CVS-ADC(2)-x matrix elements are provided in Appendix A
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