Joseph T. Golab

Comparison of perturbative and multiconfigurational electron propagator methods

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 Greens 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 ζ 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 multiconfigurational spin‐tensor electron propagator method for determining vertical principal and shake‐up ionization potentials for open shell and highly correlated atoms and molecules

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, ...

Proper characterization of MC SCF stationary points

Abstract We discuss several characteristics that an MC SCF stationary point should fulfill in order to be a proper representation of the exact N th state in energy of a certain symmetry. We derive an MC SCF iterative scheme that invokes some of these characteristics directly as conditions on the iterative algorithm. Numerical examples demonstrate that convergence is obtained rapidly and reliably to a stationary point with this algorithm. Numerical examples also demonstrate one main point of this paper, i.e. the importance of carefully examining the characteristics of an MC SCF stationary point before assigning it to be an approximate representation of a state. Several different stationary points have been determined for BeO that satisfy some or all of the conditions for being an approximate representation of the same state and it is often not at all clear which stationary point should be chosen as a representative of the desired state. This difficulty may be present in all current and previous MC SCF calculations.

Photoionization cross sections involving an explicitly correlated initial state: Combination of multiconfigurational linear response and the stieltjes—tchebycheff moment theory

Abstract We have performed outer valence photoionization cross section calculations for N 2 and O 2 . To do this we have combined several linear response techniques, in particular time-dependent Hartree—Fock (TDHF), multiconfigurational time-dependent Hartree—Fock (MC TDHF), and a modification of MC TDHF (MMC TDHF) with Stieltjes—Tchebycheff moment theory (STMT). To our knowledge, these MC TDHF and MMC TDHF calculations are the first which combine explicitly correlated Green function approaches with STMT. Since, in addition, these calculations are fully coupled, we expect the MC TDHF and in particular the MMC TDHF—STMT results to be highly reliable. For both N 2 and O 2 our MC TDHF—STMT and MMC TDHF—STMT results are in overall agreement with previous static exchange STMT results; however, there are a few significant differences and differences in detail in the partial and total photoionization cross sections. In particular, for example, for N 2 we note that the MMC TDHF—STMT does not give a “hump” resonance in the cross section for the (1π u −1 )A 2 Π u ionic state. In O 2 we note that the (3σ g −1 ) cross section obtained using MMC TDHF—STMT is substantially lower than the static exchange results.

Multiple stationary point representations in MC SCF calculations

Abstract By using a complete second-order Newton-Raphson multiconfigurational self-consistent field (MC SCF) procedure combined with the Fletcher restricted step constraint algorithm and a modification of the surface walking procedure of Simons et al., an MC SCF energy hypersurface at fixed geometry has been examined in considerably more detail than had been done previously. By calculational example, it is shown that there may exist several MC SCF stationary points which fulfill all four structural criteria we require of a state for being a “good” representation of an exact state. The problem with the existence of several stationary point solutions may be reduced if care is taken in the selection of the MC SCF configuration space. Calculational examples also demonstrate that near-lying stationary points exist which fulfill some, but not all, of these four structural criteria. Hence, stationary points should be obtained with a global MC SCF method which automatically eliminates convergence to as many as possible of these unwanted stationary points. Upon convergence, structural criteria which are not automatically fulfilled should be examined in detail.

Implementation of the direct SCF and RPA methods on loosely coupled networks of workstations

The use of a cluster of workstations as an alternative supercomputer resource is demonstrated using the ab initio direct SCF and RPA code DISCO. DISCO was implemented using several different mechanisms to achieve the requisite parallelization. The various parallel software mechanisms are characterized based upon several different criteria, including portability, ease of use, and relative efficiency. The application of direct SCF and RPA techniques to study the static polarizability of paranitroaniline is described.

The ionization potentials of NH2: The multiconfigurational spin‐tensor electron propagator method (MCSTEP) applied to a polyatomic open‐shell radical

The multiconfigurational spin‐tensor electron propagator method (MCSTEP) gives accurate ionization potentials (IPs) and electron affinities (EAs) for both closed‐shell and open‐shell molecules, including for highly correlated systems. Both principal and lower‐lying shakeup IPs can be accurately obtained and straightforwardly characterized using MCSTEP. To further test this new technique, we have applied the MCSTEP approach to the open‐shell, polyatomic radical NH2. We report and characterize vertical IPs 0–20 eV, including several ionizations that have not, as yet, been observed experimentally. IPs to both singlet and triplet states of NH+2 are accurately calculated using the same MCSCF reference state. We predict the presence of previously undetected, observable vertical PES IPs to states of 3A2, 1A1, and 1A2 symmetries at 16.86, 18.00, and 18.26 eV, respectively. Also, we calculate adiabatic IPs by a modified application of the procedure. By examining the two lowest adiabatic IPs with both MCSTEP and Δm...

The ionization potentials of F2: A comparison of multiconfigurational electron propagator (MCEP) with other large scale methods using the same basis set

The multiconfigurational electron propagator technique (MCEP) gives reliable vertical ionization potentials (I.P.s) and electron affinities (E.A.s) for atoms and molecules, including open‐shell and highly correlated systems. Shake‐up and inner‐valence I.P.s can be accurately obtained and characterized. In contrast, perturbative‐type Green’s function (PTGF) approaches are useful for closed‐shell systems with relatively little correlation. Perturbative‐type Green’s functions cannot consistently reliably predict shake‐up and inner‐valence I.P.s. We have applied the MCEP method to F2 at 2.68 a.u. using 〈4s3p1d〉 and 〈5s4p2d〉 basis sets. In F2, the complete active space of all valence orbitals is small. Hence, reliable MCEP results should be obtained for all valence ionization processes. In addition, comparison calculations are given using other large scale techniques, i.e., ΔSCF, ΔMCSCF, PTGF, and Δ multireference CI using the same basis sets. The photoelectron spectrum of F2 below 30 eV is not well characteri...

Multiconfigurational spin tensor electron propagator electron affinities for F, BO, CN, OH, and NH2

We applied the multiconfigurational spin tensor electron propagator method (MCSTEP) to the systems F, OH, NH2, BO, and CN for the determination of vertical and adiabatic electron affinities (EAs). These are the first MCSTEP EA calculations for systems that are not pseudo two‐electron systems and the first time MCSTEP is used for EAs of molecules. Using standard Dunning core‐valence basis sets supplemented with diffuse functions and with relatively small complete active spaces, MCSTEP results are in very good to excellent agreement with experiment. Comparisons with EAs determined by other methods using exactly the same basis sets show that MCSTEP is generally more consistent and reliable.

Ionization potentials of CH2: A comparison of the multiconfigurational spin tensor electron propagator method with benchmark full configuration interaction and large scale multireference configuration interaction calculations

Using the same basis sets and geometries as were previously used in ‘‘benchmark’’ full configuration interaction (FCI) calculations we compare the multiconfigurational spin tensor electron propagator method (MCSTEP) with FCI for the vertical ionization potentials (IPs) in CH2 below 19.0 eV. Our results show that MCSTEP using a full valence complete active space MCSCF initial state accurately obtains the lowest several principal vertical ionization potentials. We also determine vertical and adiabatic IPs in CH2 with MCSTEP using larger bases and compare to accurate large scale multireference singles and doubles CI with quadruple excitations estimated via a Davidson correction.