Comparison of explicitly correlated local coupled-cluster methods with various choices of virtual orbitals

Abstract

Explicitly correlated local coupled-cluster (LCCSD-F12) methods with pair natural orbitals (PNOs), orbital specific virtual orbitals (OSVs), and projected atomic orbitals (PAOs) are compared. In all cases pair-specific virtual subspaces (domains) are used, and the convergence of the correlation energy as a function of the domain sizes is studied. Furthermore, the performance of the methods for reaction energies of 52 reactions involving 58 small and medium sized molecules is investigated. It is demonstrated that for all choices of virtual orbitals much smaller domains are needed in the explicitly correlated methods than without the explicitly correlated terms, since the latter correct a large part of the domain error, as found previously. For PNO-LCCSD-F12 with VTZ-F12 basis sets on the average only 20 PNOs per pair are needed to obtain reaction energies with a root mean square deviation of less than 1 kJ mol(-1) from complete basis set estimates. With OSVs or PAOs at least 4 times larger domains are needed for the same accuracy. A new hybrid method that combines the advantages of the OSV and PNO methods is proposed and tested. While in the current work the different local methods are only simulated using a conventional CCSD program, the implications for low-order scaling local implementations of the various methods are discussed.

Perspective: Explicitly correlated electronic structure theory for complex systems

“…Krause and Werner proposed a scheme to combine the advantages of OSV and PNO. 143 Independently, Hättig, Tew, and co-workers developed a hybrid OSV-PNO scheme for F12 using auxiliary PNOs (X-PNOs) and reported PNO-CC-F12 implementations. 144,145 The recent development of the domain-based local PNO MP2-F12 (DLPNO-MP2-F12) for the O(N) scaling exhibits subquadratic scaling for quasi one-dimensional n-alkanes.…”

“…The steep scalings needed to generate PNOs can be avoided using local variants that employ intermediates with PAO domains or the orbital-specific virtuals (OSVs) 142 often generated from extended PAO domains to attain asymptotic linear scalings. 135,143,144 Among the choices of virtual orbitals, PNOs provide the most compact representation of domains with high accuracy. Krause and Werner proposed a scheme to combine the advantages of OSV and PNO.…”

Experimental and Theoretical Determination of Dissociation Energies of Dispersion-Dominated Aromatic Molecular Complexes

“…Also various explicitly-correlated variants of (PNO-based) local correlation methods have been implemented. 101,[104][105][106][107][108] In view of the progress made in recent years, one is tempted to conclude that basically from today on, explicitlycorrelated -that is, near complete-basis-set limit -CCSD(T) calculations can be performed with computational effort (computation time and other computer resources) that scales linearly with the size of the molecular system. This would render more approximate and much less accurate approaches redundant, except perhaps for optimizing the required equilibrium structures as long as analytical nuclear gradients have not yet been implemented for the (explicitly-correlated) PNO-based LCC methods.…”

The orbital-specific virtual local triples correction: OSV-L(T)

“…37. Hybrid PAO/OSV/PNO schemes, which exploit and combine the advantages of the different schemes and avoid the O(N 4 ) scaling of the OSV and PNO generation, have also been proposed 37 and are currently being efficiently implemented. 40 Similar methods are also being developed by other groups.…”

“…Obvious examples are the Cholesky [10][11][12][13][14] and singular value decompositions, 15 and density fitting. [16][17][18][19][20][21][22] Also schemes defining new occupied and virtual orbital sets, such as the projected atomic orbital (PAO) based local correlation, [23][24][25][26][27] the pair natural orbital (PNO), [28][29][30][31][32][33][34][35][36][37] and the orbital specific virtual (OSV) 38,39 methods can be interpreted as tensor factorizations. All these methods substitute the delocalized occupied Hartree-Fock orbitals by (still mutually orthogonal) localized molecular orbitals (LMOs), obtained by a unitary transformation of the former.…”