Coupled-Cluster in Real Space. 2. CC2 Excited States Using Multiresolution Analysis

Abstract

We report a first quantized approach to calculate approximate coupled-cluster singles and doubles CC2 excitation energies in real space. The cluster functions are directly represented on an adaptive grid using multiresolution analysis. Virtual orbitals are neither calculated nor needed in this approach. The nuclear and electronic cusps are taken into account explicitly regularizing the corresponding equations exactly. First calculations on small molecules are in excellent agreement with the best available LCAO results.

Electron collisions with BeH2 below 20 eV

“…In the equilibrium ground state configuration the 1σ g 1σ u and 2σ g orbitals are doubly occupied. In the present calculations we have used a bond length of 1.332Å(2.513 a 0 ) obtained from calculations with the coupled-cluster approximation (CC2) method using the aug-cc-pVTZ basis set [17] (Calculations using these two geometries yielded practically identical cross sections, but the CAS-CI energies are slightly lower for the latter). In addition, as is standard in quantum chemistry calculations, we have used the Abelian D 2h point group (rather than the D ∞h ).…”

“…The orbitals were generated with MOLPRO [29]. For comparison, the coupled-cluster approximation (CC2) using multiresolution analysis (MRA) [17] and equation of motion -coupled clusters singles and doubles (EOM-CCSD/cc-pVTZ) calculations [20] of excited states were used.…”

“…Experimentally determined geometry and vibrational frequencies of the ground state were published only a few years ago [14]. A few publications are available concerning its potential energy surface, investigated using high-order ab initio methods, as well as its excited states and thermodynamic properties [15][16][17][18]. There are two publications concerning cross sections of BeH 2 , one presenting electron impact ionization cross sections [19], the other covering lower energy scattering [20].…”

“…Ground state energy in Hartree and vertical excitation energies in eV for first 21 excited states of BeH2 using the SA-CASSCF approach and the (aug)-cc-pVDZ basis sets. Earlier theoretical data is also listed: (a) EOM-CCSD[20], (b) CC2-MRA[17] and (c) CAS-CI[20].…”

Reducing qubit requirements while maintaining numerical precision for the Variational Quantum Eigensolver: A Basis-Set-Free Approach

“…Initial treatment of correlated methods beyond density functional theory aimed at representing multi-electron wavefunctions directly, resulting in basis-set-free and virtual-orbitalfree approaches. [23][24][25][26] Recently, an approach to directly determine MRA-represented pair natural orbitals (MRA-PNOs) on the level of Møller-Plesset perturbation theory of second order (MP2) was demonstrated. This approach allows to grow near-optimal system-adapted PNOs from scratch without the use of a global basis set.…”