Jeffrey A. Nichols

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.

Multiconfigurational electron propagator (MCEP) ionization potentials for general open shell systems

We have developed a multiconfigurational electron propagator (MCEP) technique for the theoretical determination of ionization potentials for general open shell and highly correlated atomic and molecular systems. In order to do this, we have used and extended the generalized spin‐symmetry adapted operators of Pickup and Mukhopadhyay. To properly account for correlation effects we have additionally included ionization and electron affinity operators analogous to the ‖Γ〉〈0‖ state transfer operators necessary in multiconfigurational linear response. MCEP ionization potentials and ionization process probabilities have been evaluated for both O2 and N2 and used to carry out detailed examination and interpretation of the respective PES and ESCA spectra. The MCEP results are extremely encouraging for both principal and shake‐up I.P.′s. For example, using 〈5s4p1d〉 contracted Gaussian basis sets the principal valence ionization potentials to bound ionic states are calculated within ±0.3 eV of experiment for both N2...

Theoretical study of C2 and C−2 : X 1Σ+g , a 3Πu , X 2Σ+g , and B 2Σ+u potentials

We employ multiconfigurational self‐consistent field and multiconfigurational electron propagator methods to characterize the X 2Σ+g and B 2Σ+u states of C−2 and the X 1Σ+g and a3Πu states of C2 over a wide range of bond lengths (1.0–1.9 A). We find a systematic difference of approximately 0.3 eV in the relative positioning of our anion‐ and neutral‐state potentials compared to the anion–neutral spacing in the best curves constructed from experimental data. Once this energy shift is taken into consideration, all four of our computed potential energy curves are in reasonably good agreement with experimental information. However, there remains a substantial difference in the relative positioning of our B 2Σ+u and a 3Πu curves, compared to the best available experimental data, at larger bond lengths. The relevance of this discrepancy and of our other data to the present state of experimental knowledge on C−2 /C2 is discussed.

COMPLETE BASIS SET LIMIT IONIZATION POTENTIALS OF O3 AND NO2 USING THE MULTICONFIGURATIONAL SPIN TENSOR ELECTRON PROPAGATOR METHOD (MCSTEP)

We have calculated low-lying principal vertical ionization potentials (IPs) of O3 and NO2 with the multiconfigurational spin tensor electron propagator method (MCSTEP) using several different basis sets. We obtain an estimate of complete basis set limit (CBS) MCSTEP IPs. This is the first time CBS estimates have been used with MCSTEP. We show that MCSTEP is accurate and reliable compared with experiment at the CBS limit for obtaining low-lying vertical IPs for open shell molecules such as NO2 and highly correlated molecules such as O3. Our results confirm previous assignments of photoelectron peaks based on calculations made using less accurate methods.

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.

The potential energy curves of the X 2Πg, a 4Πu, A 2Πu, b 4Σ−g, B 2Σ−g, 2Πu, and c 4Σ−u states of O+2 obtained using the multiconfigurational spin tensor electron propagator method

With electron propagator methods, electronic ionization and attachment energies are obtained directly. The multiconfigurational spin tensor electron propagator method (MCSTEP) is explicitly designed for systems with open shell and/or nondynamical correlation in the initial state. We apply MCSTEP to O2 at several internuclear separations and obtain and report the MCSTEP potential energy curves and the spectroscopic constants for the X 2Πg, a 4Πu, A 2Πu, b 4Σ−g, B 2Σ−g, 2Πu, and c 4Σ−u states of O+2.

The determination of electron affinities of the open shell systems C and CH2 using the multiconfigurational spin tensor electron propagator method

The multiconfigurational spin tensor electron propagator method (MCSTEP) is a Green’s function approach for accurately predicting and analyzing ionization potentials (IPs) and electron affinities (EAs). Unlike more traditional Green’s function approaches, MCSTEP is applicable to highly correlated and open shell systems as well as to closed shell systems with small correlation effects. We apply MCSTEP for the determination of EAs for C and CH2. This is the first time that MCSTEP has been used to determine the EAs for systems which have both open shell neutral and anionic ground states. Our best MCSTEP results for the EA of C and the adiabatic EA of CH2 are 1.2904 and 0.6356 eV, respectively, compared to 1.2607 and 0.6306 eV, respectively, obtained with large scale multireference configuration interaction (MRCI) using the same basis sets. Experimental values are 1.268 eV for C and 0.628±0.031 eV for CH2. We also show that accurate EAs for these systems can be obtained both with MRCI and especially with MCST...

Multiconfigurational spin tensor electron propagator vertical ionization potentials for O2: Comparison to some other forefront methods using the same basis sets and geometries

In a recent paper in The Journal of Chemical Physics, we showed the potential energy curves for several cation states of O2 obtained using the multiconfigurational spin tensor electron propagator method (MCSTEP) with a 〈5s4p3d〉 basis set. In this communication we present vertical ionization potential calculations to the same O2 states. However, for the results reported here, exactly the same basis sets and geometries are used that were used for two other forefront methods; the coupled‐cluster reference electron propagator theory (CC‐EPT) and the Fock space multireference coupled‐cluster method (FSMRCC). Hence, more direct comparisons and contrasts among these methods are now available.

Low‐lying ionization potentials of O3 and NO2 using the multiconfigurational spin tensor electron propagator method

The multiconfigurational spin tensor electron propagator method (MCSTEP) is a single particle Green’s function (or electron propagator) method for determining the low‐lying principal vertical ionization potentials (IPs) and electron affinities (EAs) of atoms and molecules. It was specifically designed to handle cases where the initial state has nondynamical correlation and/or is open shell. We have applied MCSTEP for the first time to triatomic molecules composed entirely of second row atoms. The two cases we present are O3 and NO2—for the former nondynamical correlation is present in the ground (initial) state and for the latter the ground (initial) state is open shell. MCSTEP results are accurate compared to experiment and other forefront theoretical techniques.