Algebraic Diagrammatic Construction Schemes Employing the Intermediate State Formalism: Theory, Capabilities, and Interpretation

Abstract

Algebraic diagrammatic construction (ADC) schemes represent a family of ab initio methods for the calculation of excited electronic states and electron-detached and -attached states. All ADC methods have been demonstrated to possess great potential for molecular applications, e.g., for the calculation of absorption or photoelectron spectra or electron attachment processes. ADC originates from Green’s function or propagator theory; however, most recent ADC developments heavily rely on the intermediate state representation or effective Liouvillian formalisms, which comprise new ADC methods and computational schemes for high-order properties. The different approaches for the calculation of excitation energies, ionization potentials, and electron affinities are intimately related, and they provide a coherent description of these quantities at equivalent levels of theory and with comparable errors. Most quantum chemical program packages contain ADC methods; however, the most complete ADC suite of methods can be found in the recent release of Q-Chem.

responsefun: Fun with Response Functions in the Algebraic Diagrammatic Construction Framework

“…Since the ADC scheme for the polarization propagator and its ISR have already been explained in detail in numerous other places, the basic concepts are only briefly outlined in the following. − The ADC equations are formulated in the basis of the so-called intermediate states {Ψ̃ J }, which are obtained by first applying physical excitation operators to the correlated ground-state wave function and then successively orthonormalizing the resulting correlated excited states with respect to the ground state and each other in a Gram–Schmidt-like procedure. The matrix representation of the Hamiltonian shifted by the ground-state energy in the IS basis is given by matrix M with elements M I J = ⟨ Ψ̃ I | Ĥ − E 0 | Ψ̃ J ⟩ where the indices I and J label physical excitations, i.e., singly, doubly, etc.…”

On the performance of second-order approximate coupled-cluster singles and doubles methods for non-valence anions

“…The computational cost of CC2 scales as N 5 and the memory requirements can be reduced from N 4 to N 3 by applying the resolution-of-the-identity (RI) approximation or Cholesky decomposition to the electron-repulsion integrals. 44–46 As a consequence, CC2 and the closely related algebraic diagrammatic construction through second order (ADC(2)) 47,48 are well established as excited-state methods for molecules beyond the application range of EOM-CCSD.…”

Particle-Breaking Unrestricted Hartree–Fock Theory for Open Molecular Systems

“…We include noninteracting orbitals of zero energy in the orbital space to generate a linear combination of determinants containing both even and odd numbers of electrons. These noninteracting orbitals (hereafter referred to as bath orbitals) have been used for the computation of ionization potentials and electron-attached states in coupled cluster theory, − the algebraic diagrammatic construction scheme, − and time-dependent density functional theory . Furthermore, bath orbitals have recently been employed to obtain a spin-adapted coupled cluster model .…”