Ionization energies below 20 eV of 10 molecules calculated with electron propagator techniques employing Hartree-Fock orbitals and multiconfigurational self-consistent field orbitals are compared. Diagonal and nondiagonal self-energy approximations are used in the perturbative formalism. Three diagonal methods based on second-and third-order self-energy terms, all known as the outer valence Green's function, are discussed. A procedure for selecting the most reliable of these three versions for a given calculation is tested. Results with a polarized, triple < basis produce root mean square errors with respect to experiment of approximately 0.3 eV. Use of the selection procedure has a slight influence on the quality of the results. A related, nondiagonal method, known as ADC(3), performs infinite-order summations on several types of self-energy contributions, is complete through third-order, and produces similar accuracy. These results are compared to ionization energies calculated with the multiconfigurational spin-tensor electron propagator method. Complete active space wave functions or close approximations constitute the reference states. Simple field operators and transfer operators pertaining to the active space define the operator manifold. With the same basis sets, these methods produce ionization energies with accuracy that is comparable to that of the perturbative techniques.
The trust-region self-consistent field (TRSCF) method is presented for optimizing the total energy E(SCF) of Hartree-Fock theory and Kohn-Sham density-functional theory. In the TRSCF method, both the Fock/Kohn-Sham matrix diagonalization step to obtain a new density matrix and the step to determine the optimal density matrix in the subspace of the density matrices of the preceding diagonalization steps have been improved. The improvements follow from the recognition that local models to E(SCF) may be introduced by carrying out a Taylor expansion of the energy about the current density matrix. At the point of expansion, the local models have the same gradient as E(SCF) but only an approximate Hessian. The local models are therefore valid only in a restricted region-the trust region-and steps can only be taken with confidence within this region. By restricting the steps of the TRSCF model to be inside the trust region, a monotonic and significant reduction of the total energy is ensured in each iteration of the TRSCF method. Examples are given where the TRSCF method converges monotonically and smoothly, but where the standard DIIS method diverges.
We propose and develop the multiconfigurational spin-tensor electron propagator (MCSTEP) technique for the theoretical determination of vertical ionization potentials (IPs) and electron affinities (EAs) for general open-shell and highly correlated atoms and molecules. We obtain these equations from a Green’s function or electron propagator approach where we properly couple electron removal and addition tensor operators to a multiconfigurational tensor state. To account for important shake-up effects and to achieve a ‘‘balance’’ in initial and final state correlation corrections, we include in MCSTEP ionization and electron affinity operators analogous to the ‖c〉〈0‖ state transfer operators necessary in multiconfigurational linear response. In repartitioned MCSTEP (RMCSTEP) we augment the MCSTEP operator manifold with operators of the form a+iajak by first employing partitioning theory to estimate their contributions and then repartitioning only the important operators into the primary space. In this way, important shake-up processes to diffuse orbitals are accurately and reliably handled with RMCSTEP at the same level of approximation, i.e., as part of the primary space operator manifold . Initial application of these methods is extremely encouraging for both principal and shake-up IPs. Using a 〈5s5pld〉 contracted Gaussian valence basis set augmented with two diffuse s, two diffuse p, and two diffuse d functions, the RMCSTEP ionization potentials to the low-lying (<∼24 eV) 2S and 2P bound ionic states (including diffuse states) for Be are calculated within ±0.07 eV of experiment. The IP to the lowest 2D state is calculated 0.14 eV from experiment.
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