Assessment of Perturbative Explicitly Correlated Methods for Prototypes of Multiconfiguration Electronic Structure

Abstract

The performance of the [2]S and [2]R12 universal perturbative corrections that account for one-and manybody basis set errors of single-and multiconfiguration electronic structure methods is assessed. A new formulation of the [2]R12 methods is used in which only strongly occupied orbitals are correlated, making the approach more amenable for larger computations. Three model problems are considered using the aug-ccpVXZ (X = D,T,Q) basis sets: the electron affinity of fluorine atom, a conformational analysis of two Si2H4structures, and a description of the potential energy surfaces of the X 1Σg+, a 3Πu, b 3Σg-, and A1Πu states of C2. In general, the [2]R12 and [2]S corrections enhance energy convergence for conventional multireference configuration interaction (MRCI) and multireference perturbation theory (MRMP2) calculations compared to their complete basis set limits. For the electron affinity of the F atom, [2]R12 electron affinities are within 0.001 eV of the experimental value. The [2]R12 conformer relative energy error for Si2H4 is less than 0.1 kcal/mol compared to the complete basis set limit. The C2 potential energy surfaces show nonparallelity errors that are within 0.7 kcal/mol compared to the complete basis set limit. The perturbative nature of the [2]R12 and [2]S methods facilitates the development of a straightforward textbased data exchange standard that connects an electronic structure code that can produce a two-particle density matrix with a code that computes the corrections. This data exchange standard was used to implement the interface between the GAMESS MRCI and MRMP2 codes and the MPQC methods is used in which only strongly occupied orbitals are correlated, making the approach more amenable for larger computations. Three model problems are considered using the aug-cc-pVXZ (X = D,T,Q) basis sets: the electron affinity of fluorine atom, a conformational analysis of two Si 2 H 4 structures, and a description of the potential energy surfaces of the X 1 Σ g + , a 3 Π u , b 3 Σ g -, and A 1 Π u states of C 2 . In general, the [2] R12 and [2] S corrections enhance energy convergence for conventional multireference configuration interaction (MRCI) and multireference perturbation theory (MRMP2) calculations compared to their complete basis set limits. For the electron affinity of the F atom, [2] R12 electron affinities are within 0.001 eV of the experimental value. The [2] R12 conformer relative energy error for Si 2 H 4 is less than 0.1 kcal/mol compared to the complete basis set limit. The C 2 potential energy surfaces show nonparallelity errors that are within 0.7 kcal/mol compared to the complete basis set limit. The perturbative nature of the [2] R12 and [2] S methods facilitates the development of a straightforward text-based data exchange standard that connects an electronic structure code that can produce a two-particle density matrix with a code that computes the corrections. This data exchange standard was used to implement the interface between the GAMESS MRCI and MRMP2 codes and t...

Semi-stochastic full configuration interaction quantum Monte Carlo: Developments and application

“…From these 2-RDM estimates, [2] R12 corrections were calculated via the MPQC code 45 . The binding in Be 2 is primarily due to dispersion interactions, and requires very high angular momentum atomic orbitals for an accurate description.…”

Assessment of multireference approaches to explicitly correlated full configuration interaction quantum Monte Carlo

“…The spin-free [2] R12 approach developed by Valeev and co-workers can be employed a posteriori to reduce the basis set incompleteness error of an arbitrary multi-reference calculation 55,56,64 . The [2] R12 correction to the energy is evaluated in an internally contracted, second-order perturbative fashion via the Hylleraas functional.…”

“…In our work, the 2-body RDMs are sampled with the FCIQMC method along with the correlation energy using the stand-alone code NECI 68 . Whilst we have also implemented our own program for the [2] R12 corrections 59 , in this work we use the interface to the [2] R12 implementation within MPQC 69,70 , reading in the sampled density matrices and orbital information using an interface developed by Roskop et al 64 .…”

C n ( n =2−4): current status

“…Since then, C 2 has been the subject of extensive ab initio MRCI [30][31][32][63][64][65][66][67][68][69][70][71], full CI [72,73], quantum Monte Carlo [74] and explicitly correlated MR [75] calculations aiming at obtaining accurate analytic representations of the various PECs (and their avoided crossings [30][31][32]), electronic excitation energies, dissociation energies and expectroscopic parameters. Note that these latter approaches frequently rely on extrapolations to the one-and/or N -electron basis sets, core and core-valence correlation contributions, and also relativistic corrections.…”

“…Note that these latter approaches frequently rely on extrapolations to the one-and/or N -electron basis sets, core and core-valence correlation contributions, and also relativistic corrections. As argued several times [72][73][74][75], the presence of various low-lying excited electronic states and its unusual bonding behaviour makes C 2 a notoriously challenging benchmark test for quantum chemical methods. Recently, with the aid of high-level MR calculations and state-of-the-art experimental techniques, Krechkivska et al reported the existence of novel 4 3 Π g -a 3 Π u [69] and 3 3 Π g -a 3 Π u [71] systems (referred to as Krechkivska-Schmidt bands) and provided an accurate value for the carbon dimer ionization energy [70].…”