The fourth-order algebraic diagrammatic construction scheme for the polarization propagator

Abstract

Until today, perturbation-theoretical consistent algebraic diagrammatic construction (ADC) schemes for the polarization propagator had been derived and implemented up to third order. They have turned out to be versatile and reliable {\em ab initio} single-reference methods for the quantum chemical investigation of electronic transitions as well as excited-state properties. Here we present, for the first time, the derivation of consistent fourth-order ADC(4) schemes exploiting novel techniques of automated equation and code generation. The accuracies of the resulting ADC(4) excitation energies have been benchmarked against recent high-level, near exact reference data. The mean absolute error of both schemes turns out to be smaller than 0.1 eV. These developments open also new avenues towards highly accurate ADC methods for electron-detached and attached states.

Classification of doubly excited molecular electronic states

“…For example, the CC3 (ref. 18) and ADC(4) methods 19 are considered appropriate, whereas even ADC(3) 20 can be problematic. 19,21 Moreover, in a multireference framework, 22 one can produce accurate descriptions of doubly excited states.…”

“…18) and ADC(4) methods 19 are considered appropriate, whereas even ADC(3) 20 can be problematic. 19,21 Moreover, in a multireference framework, 22 one can produce accurate descriptions of doubly excited states. However, these methods are accompanied by the ever-present problems of choosing an appropriate active space and related parameters.…”

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

“…For the improvement of the accuracy of ADC schemes, the natural way to proceed is to increase their perturbation theoretical order. This has recently been realized by the EE-ADC(4) scheme and will also be extended to IP- and EA-ADC. These methods will serve as important benchmarks for lower-order ADC methods and less accurate quantum chemical electronic structure methods in general.…”

“…In other words, ADC schemes can be derived via the ISR, for which no corresponding propagator is known, for example, spin-flip EE-ADC methods . Also, the ISR formalism allows for automated equation generation, that is, for the derivation of higher-order ADC schemes like ADC(4), which otherwise would require prohibitive human effort. It has to be noted that all quantitites accessible via the ISR formalism may also be derived by means of the effective Liouvillian (EL) formalism, and this approach has been followed in a number of recent ADC developments. − …”

“…Previous error analyses, taking also doubly excited states and also larger organic molecules into account, showed a slightly better performance of EE-ADC(3) compared to EE-ADC(2), as it would be expected considering the associated formal computational effort of N 5 and N 6 arithmetic operations, respectively, with N denoting the number of basis functions used for the representation of the electronic system under consideration. A substantial step forward in accuracy of excitation energies is made at the fourth-order level of EE-ADC(4) with a mean absolute error of only 0.09 eV, however, at the cost of considerably increased memory requirements and arithmetic scaling (cf. Table ).…”