A Density-Based Basis-Set Correction for Wave Function Theory

Abstract

We report a universal density-based basis-set incompleteness correction that can be applied to any wave function method. e present correction, which appropriately vanishes in the complete basis set (CBS) limit, relies on short-range correlation density functionals (with multideterminant reference) from range-separated density-functional theory (RS-DFT) to estimate the basis-set incompleteness error. Contrary to conventional RS-DFT schemes which require an ad hoc range-separation parameter µ, the key ingredient here is a range-separation function µ(r) that automatically adapts to the spatial non-homogeneity of the basis-set incompleteness error.As illustrative examples, we show how this density-based correction allows us to obtain CCSD(T) atomization and correlation energies near the CBS limit for the G2 set of molecules with compact Gaussian basis sets.Contemporary quantum chemistry has developed in two directions -wave function theory (WFT) 1 and density-functional theory (DFT). 2 Although both spring from the same Schrödinger equation, each of these philosophies has its own pros and cons.WFT is a ractive as it exists a well-de ned path for systematic improvement as well as powerful tools, such as perturbation theory, to guide the development of new WFT ansätze. e coupled cluster (CC) family of methods is a typical example of the WFT philosophy and is well regarded as the gold standard of quantum chemistry for weakly correlated systems. By increasing the excitation degree of the CC expansion, one can systematically converge, for a given basis set, to the exact, full con guration interaction (FCI) limit, although the computational cost associated with such improvement is usually high. One of the most fundamental drawbacks of conventional WFT methods is the slow convergence of energies and properties with respect to the size of the one-electron basis set. is undesirable feature was put into light by Kutzelnigg more than thirty years ago. 3 To palliate this, following Hylleraas' footsteps, 4 Kutzelnigg proposed to introduce explicitly the interelectronic distance r 12 = |r 1 − r 2 | to properly describe the electronic wave function around the coalescence of two electrons. 3,5,6 e resulting F12 methods yield a prominent improvement of the energy convergence, and achieve chemical accuracy for small organic molecules with relatively small Gaussian basis sets. [7][8][9][10][11][12] For example, at the CCSD(T) level, one can obtain quintuple-ζ quality correlation energies with a triple-ζ basis, 13 although computational overheads are introduced by the large auxiliary basis used to resolve three-and four-electron integrals. 14 To reduce further the computational cost and/or ease the transferability of the F12 correction, approximated and/or universal schemes have recently emerged. [15][16][17][18][19][20] Present-day DFT calculations are almost exclusively done within the so-called Kohn-Sham (KS) formalism, which corresponds to an exact dressed one-electron theory. 21 e a ractiveness of DFT originates from its very favor...

Plane wave basis set correction methods for RPA correlation energies

“…In practice, one would have to perform additional convergence tests for each value of µ or resort to more elaborate schemes. 41 For the sake of simplicity, we omit these convergence tests throughout and use the large cutoffs E χ max = 2/3 E max for all values of µ, compare Table I. Fig.…”

Density-Based Basis-Set Incompleteness Correction for GW Methods

“…where s(r) = ∇n(r)/n(r) 4/3 is the reduced density gradient and the correlation energy per particleε srPBE c,md n, s, µ interpolates between the usual PBE correlation energy per particle 95 at µ = 0 and the exact large-µ behavior 92,96,97 using the on-top pair density of the Coulombic uniform electron gas (see Ref. 57). Note that the information on the local basis-set incompleteness error is provided to these RS-DFT functionals through the range-separation function µ B (r).…”

Chemically Accurate Excitation Energies With Small Basis Sets

“…In other words, the correction vanishes in the CBS limit, hence guaranteeing an unaltered limit. 20 Note that in Eqs. (1a) and (1b) we have assumed that the same density functionalĒ B can be used for correcting all excited-state energies, which seems a reasonable approximation since the electron-electron cusp e ects are largely universal.…”

“…19 and further developed in Ref. 20, we have shown that one can e ciently approxi-mateĒ B [n] by short-range correlation functionals with multideterminantal (ECMD) reference borrowed from RS-DFT. 46 e ECMD functional,Ē sr c,md [n, µ], is a function of the rangeseparation parameter µ and admits, for any n, the following two limits…”

“…11,12 Instead of F12 methods, here we propose to follow a different route and investigate the performance of the recently proposed density-based basis set incompleteness correction. 19 Contrary to our recent study on atomization and correlation energies, 20 the present contribution focuses on vertical and adiabatic excitation energies in molecular systems which is a much tougher test for the reasons mentioned above. is density-based correction relies on short-range correlation density functionals (with multideterminant reference) from a) Corresponding author: emmanuel.giner@lct.jussieu.fr b) Corresponding author: loos@irsamc.ups-tlse.fr range-separated density-functional theory [21][22][23][24][25][26][27][28][29][30][31][32][33][34][35][36] (RS-DFT) to capture the missing part of the short-range correlation e ects, a consequence of the incompleteness of the one-electron basis set.…”