New-Generation Electron Propagators for Molecules, Ions, and Clusters

Abstract

New ab initio electron propagator self-energies (one-particle Green’s function methods) for calculating electron binding energies and Dyson orbitals have been derived from an intermediately normalized, Hermitized superoperator metric. No adjustable or empirical parameters are tolerated in the derivation of the new self-energies or their reference Hartree-Fock orbital bases. The cubically scaling diagonal second order method (D2) has been demonstrated to systematically underestimate (overestimate) ionization energies (electron affinities). To ameliorate this deficiency, same-spin correlation is neglected in the opposite-spin second order method (os-D2) that significantly improves accuracy and efficiency. Renormalizations of the ring and ladder terms in the diagonal 2ph-TDA self-energy lead to the diagonal ring (DR) and diagonal ladder (DL) methodologies that have achieved improved efficiency and accuracy. Modification of the Outer Valence Green’s Function (OVGF) method because of the new choice of intermediately normalized, Hermitized superoperator metric leads to the derivation of the approximately renormalized linear third order (L3+). Simplification of the L3+ method leads to the approximately renormalized quasiparticle third order (Q3+) and the approximately renormalized partial third order method (P3+). When the approximate estimation of post-third-order terms is replaced by the explicit evaluation of all contributions from the expansion of inverted matrices, the resulting explicitly renormalized variants of L3+, Q3+, and P3+ are obtained, referred to as RL3, RQ3, and RP3, respectively. Restoration of off-diagonal matric elements leads to the NRL3, NRQ3 and NRP3 self-energies. In addition, non-Dyson (nD) versions of D2, os-D2, OVGF, L3+ and RL3 self-energies are obtained by deactivating energy dependence in 2ph denominators for electron detachment energies calculations and in 2hp denominators for electron attachment energies calculations. This deactivation is achieved by setting the E = εp in the Σpq(E) self-energy terms with these denominators. The non-Dyson version has improved efficiency in electron detachment energies calculations as the arithmetic bottlenecks are no longer iterative. This advantage does not necessarily occur for electron attachment energies calculations. Performance of the new methods has been evaluated using extensive experimental and computational benchmark databases for vertical ionization energies (VIEs), vertical electron affinities (VEAs), and vertical electron detachment energies (VEDEs) of anions. For VIEs and VEDEs, the best compromises of accuracy and cost, expressed in terms of mean absolute errors (MAEs) in eV, and arithmetic efficiency, expressed in terms of powers of occupied (O) and virtual (V) orbital dimensions in bottleneck operations, are os-nD-D2, Q3+, nD-L3+, and nD-RL3 diagonal self-energies. The corresponding MAEs and arithmetic scaling factors respectively are: (~0.18, OV2), (~0.15, O2V3), (~0.08, OV4), and ~0.07, OV4). NRL3 is the best non-diagonal method with an MAE of ~0.06 eV and a non-iterative O2V4 scaling. For VEAs, the best compromises of accuracy and cost are D2, nD-L3+, and nD-RL3 diagonal self-energies. Their corresponding MAEs and arithmetic scaling factors respectively are: (~0.18, OV2), (~0.08, OV4), and (~0.07, OV4). NRL3 is the best non-diagonal method with an MAE of ~0.06. Tests on open-shell atoms, molecules, and ions show similar trends except that MAEs generally increase by ~0.05 eV due to spin contamination. For molecules with nuclei of the fourth or higher periods, RL3 and nD-RL3 are the best methods with MAEs of ~0.14 eV. For core 1s ionizations, the Brueckner doubles with triple field operators (BD-T1) method exhibits the highest accuracy with a MAE of ~0.39 eV. It shows excellent agreement with experimental data and minimal systematic bias. Composite schemes that incorporate the new methods for estimating basis-set effects have enabled highly accurate calculations of VIEs and VEDEs for organic photovoltaic molecules, which are important for optimizing solar energy devices, achieving MAEs that approach chemical accuracy (average errors of 0.04 eV). The new methods and their composite schemes also produce excellent predictions and clear interpretations based on Dyson orbitals for the photoelectron spectra of DNA nucleotide anions and green fluorescent protein (GFP) chromophore anions. Because the new methods developed in this dissertation require no adjustable or empirical parameters and the accuracy of several of them approaches chemical accuracy, they are reliable for predictions on novel molecules, ions, and clusters. Therefore, the existence, stability and VEDEs of OnH2n+1– and NH4-(H20)n double Rydberg anions have been predicted. These clusters are predicted to have well separated VEDEs and experimentally accessible total energies and therefore are expected to appear in mass-selected, anion photoelectron spectra that typically detect low-lying isomers.