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WIREs Comput Mol Sci
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The algebraic diagrammatic construction scheme for the polarization propagator for the calculation of excited states

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The algebraic diagrammatic construction (ADC) scheme for the polarization propagator provides a series of ab initio methods for the calculation of excited states based on perturbation theory. In recent years, the second‐order ADC(2) scheme has attracted attention in the computational chemistry community because of its reliable accuracy and reasonable computational effort in the calculation of predominantly singly excited states. Owing to their size‐consistency, ADC methods are suited for the investigation of large molecules. In addition, their Hermitian structure and the availability of the intermediate state representation (ISR) allow for straightforward computation of excited‐state properties. Recently, an efficient implementation of ADC(3) has been reported, and its high accuracy for typical valence excited states of organic chromophores has been demonstrated. In this review, the origin of ADC‐based excited‐state methods in propagator theory is described, and an intuitive route for the derivation of algebraic expressions via the ISR is outlined and comparison to other excited‐state methods is made. Existing computer codes and implemented ADC variants are reviewed, but most importantly the accuracy and limits of different ADC schemes are critically examined. WIREs Comput Mol Sci 2015, 5:82–95. doi: 10.1002/wcms.1206

This article is categorized under:

  • Structure and Mechanism > Molecular Structures
  • Electronic Structure Theory > Ab Initio Electronic Structure Methods
  • Theoretical and Physical Chemistry > Spectroscopy
Structures of the ADC matrix in the strict and extended second‐order schemes ADC(2)‐s and ADC(2)‐x, as well as the third‐order scheme ADC(3). The matrices of these schemes have the dimension of a CISD matrix, as they stay within the singles and doubles manifolds. For the individual blocks the level of perturbation theory is given (white: zeroth order; yellow: first order; orange: second order; red: third order).
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Effect of the core‐valence‐separation (CVS) approximation on structure and size of the ADC(2)‐x matrix. The restriction of one of the indexes of the occupied orbitals to correspond to a core orbital results in a significant reduction of the matrix dimension. The color of the blocks represents the order of perturbation theory (yellow: first order; orange: second order) and the shaded parts of the original ADC(2)‐x matrix (left) are set to zero in the CVS approximation.
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Effect of spin‐opposite scaling (SOS) on the size and structure of the ADC(2)‐x matrix. Neglect of the same‐spin (ss) component and scaling of the opposite‐spin (os) components leads to a reduction of the matrix dimension and the possibility to fit the semiempirical scaling factors (cos and cx) to known benchmark data. The color of the blocks represents the order of perturbation theory (yellow: first order; orange: second order). The shaded parts of the original ADC(2)‐x matrix (left) are neglected in the SOS approximation.
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