Analysis of the errors in explicitly correlated electronic structure theory

The explicitly correlated approach is one of the most important breakthroughs in ab initio electronic structure theory, providing arguably the most compact, accurate, and efficient ansatz for describing the correlated motion of electrons. Since Hylleraas first used an explicitly correlated wave function for the He atom in 1929, numerous attempts have been made to tackle the significant challenges involved in constructing practical explicitly correlated methods that are applicable to larger systems. These include identifying suitable mathematical forms of a correlated wave function and an efficient evaluation of many-electron integrals. R12 theory, which employs the resolution of the identity approximation, emerged in 1985, followed by the introduction of novel correlation factors and wave function ansätze, leading to the establishment of F12 theory in the 2000s. Rapid progress in recent years has significantly extended the application range of explicitly correlated theory, offering the potential of an accurate wave-function treatment of complex systems such as photosystems and semiconductors. This perspective surveys explicitly correlated electronic structure theory, with an emphasis on recent stochastic and deterministic approaches that hold significant promise for applications to large and complex systems including solids. Published by AIP Publishing. [http://dx

Section: Introductionmentioning

confidence: 99%

Perspective: Explicitly correlated electronic structure theory for complex systems

Grüneis

Hirata

Ohnishi

et al. 2017

“…All the F12 integrals are evaluated using density fitting, 27,28 and approximating the Slater-type geminal function to a weighted 24 linear combination of six Gaussian-type geminal functions. 29 The CABS is constructed from the union of OBS and auxiliary basis sets by projecting out the OBS components. 19,30 For the B intermediate, we have used the so-called approximation C, 31 whose working equations can be found, for instance, in Ref.…”

mentioning

confidence: 99%

Communication: Second-order multireference perturbation theory with explicit correlation: CASPT2-F12

Shiozaki

Werner

2010

120

“…However, their computation has been thoroughly studied in the literature. 14,15,35,41,42,44,45,56,[65][66][67][68][69][70][71][72][73][74] Similarly, the nuclear attraction integrals can be easily obtained by taking the large-exponent limit of a s-type shell-pair.…”

Section: Three-and Four-electron Operatorsmentioning

confidence: 99%

Three- and four-electron integrals involving Gaussian geminals: Fundamental integrals, upper bounds, and recurrence relations

Barca

Loos

2017

We report the three main ingredients to calculate three-and four-electron integrals over Gaussian basis functions involving Gaussian geminal operators: fundamental integrals, upper bounds, and recurrence relations. In particular, we consider the three-and four-electron integrals that may arise in explicitly-correlated F12 methods. A straightforward method to obtain the fundamental integrals is given. We derive vertical, transfer and horizontal recurrence relations to build up angular momentum over the centers. Strong, simple and scaling-consistent upper bounds are also reported. This latest ingredient allows to compute only the O N 2 significant three-and four-electron integrals, avoiding the computation of the very large number of negligible integrals.