Multiconfigurational Spin Tensor Electron Propagator Research Articles

The complex-scaled multiconfigurational spin-tensor electron propagator method for low-lying shape resonances in Be−, Mg− and Ca−

We further apply the complex scaled multiconfigurational spin-tensor electron propagator method (CMCSTEP) for the theoretical determination of resonance parameters with electron-atom systems including open-shell and highly correlated (non-dynamical correlation) atoms and molecules. The multiconfigurational spin-tensor electron propagator method (MCSTEP) developed and implemented by Yeager and his coworkers for real space gives very accurate and reliable ionization potentials and electron affinities. CMCSTEP uses a complex scaled multiconfigurational self-consistent field (CMCSCF) state as an initial state along with a dilated Hamiltonian where all of the electronic coordinates are scaled by a complex factor. CMCSTEP is designed for determining resonances. We apply CMCSTEP to get the lowest 2P (Be−, Mg−) and 2D (Mg−, Ca−) shape resonances using several different basis sets each with several complete active spaces. Many of these basis sets we employ have been used by others with different methods. Hence, we can directly compare results with different methods but using the same basis sets.

Electron-atom scattering resonances: Complex-scaled multiconfigurational spin-tensor electron propagator method forB−shaperesonances

We develop the complex-scaled multiconfigurational spin-tensor electron propagator (CMCSTEP) technique for the theoretical determination of resonance parameters with electron-atom--molecule systems including open-shell and highly correlated (nondynamical correlation) atoms and molecules. The multiconfigurational spin-tensor electron propagator method developed and implemented by Yeager and his coworkers in real space gives very accurate and reliable ionization potentials and electron affinities. The CMCSTEP method uses a complex-scaled multiconfigurational self-consistent field state as an initial state along with a dilated Hamiltonian where all of the electronic coordinates are scaled by a complex factor. We apply the CMCSTEP and the related ${\text{M}}_{1}$ methods to get the ${\text{B}}^{\ensuremath{-}}$ shape resonance parameters using $14s11p$ and $14s11p5d$ basis sets with $1s2s2p3s$, $1s2s2p3s3p$, $1s2s2p3d$, $2s2p3s3p$, $2s2p3d$, and $2s2p3s3p3d$ complete active spaces. The CMCSTEP and ${\text{M}}_{1}$ resonance positions and widths are obtained for the $1{s}^{2}2{s}^{2}2{p}^{2}{\phantom{\rule{0.16em}{0ex}}}^{1}D$, $1{s}^{2}2s2{p}^{3}{\phantom{\rule{0.16em}{0ex}}}^{3}D$, and $1s2{s}^{2}2{p}^{3}{\phantom{\rule{0.16em}{0ex}}}^{3}D$, ${}^{3}S$, and ${}^{3}P$ shape resonances.

Electron-atom resonances: The complex-scaled multiconfigurational spin-tensor electron propagator method for the2PBe−shape resonance problem

We propose and develop the complex-scaled multiconfigurational spin-tensor electron propagator (CMCSTEP) technique for theoretical determination of resonance parameters with electron-atom and electron-molecule systems including open-shell and highly correlated atoms and molecules. The multiconfigurational spin-tensor electron propagator (MCSTEP) method developed and implemented by Yeager and co-workers in real space gives very accurate and reliable ionization potentials and attachment energies. The CMCSTEP method uses a complex-scaled multiconfigurational self-consistent field (CMCSCF) state as an initial state along with a dilated Hamiltonian where all of the electronic coordinates are scaled by a complex factor. The CMCSCF was developed and applied successfully to resonance problems earlier. We apply the CMCSTEP method to get ${}^{2}P\phantom{\rule{0.16em}{0ex}}{\text{Be}}^{\ensuremath{-}}$ shape resonance parameters using $14s11p5d,\phantom{\rule{0.16em}{0ex}}14s14p2d$, and $14s14p5d$ basis sets with a $2s2p3d$ complete active space. The obtained values of the resonance parameters are compared to previous results. Here CMCSTEP has been developed and used for a resonance problem. It appears to be among the most accurate and reliable techniques. Vertical ionization potentials and attachment energies in real space are typically within $\ifmmode\pm\else\textpm\fi{}0.2\phantom{\rule{0.28em}{0ex}}\text{eV}$ or better of excellent experimental results and full configuration-interaction calculations with a good basis set. We expect the same sort of agreement in complex space.

Obtaining positions and widths of scattering resonances from a complex multiconfigurational self‐consistent field state using the M1 method

AbstractWe present a complex multiconfigurational self‐consistent field (CMCSCF)‐based approach to investigate electron‐atom scattering resonances. It is made possible by the use of second quantization algebra adapted for biorthogonal spin orbitals, which has been applied to develop a quadratically convergent CMCSCF method. To control the convergence to the correct CMCSCF stationary point, a modified step‐length control algorithm is introduced. Convergence to a tolerance of 1.0 × 10−10 a.u. for the energy gradient is found to be typically within 10 iterations or less. A method involving the first block of the M matrix defined in the multiconfigurational spin tensor electron propagator method (MCSTEP) based on the CMCSCF reference state has been implemented to investigate 2P Be− shape resonances. The position and width of these resonances have been calculated for different complete active space choices. The wide distribution of the position and width of the resonance reported in the literature is explained by the existence of two distinct resonances which are close in energy. © 2009 Wiley Periodicals, Inc. Int J Quantum Chem, 2010

Equivalent orbitals for multiconfigurational spin‐tensor electron propagator method (MCSTEP): The vertical ionization potentials of B, NO, CF, and OF

AbstractThe multiconfigurational spin tensor electron propagator method (MCSTEP) was developed as an implementation of electron propagator/single particle Green's function methods for ionization potentials (IPs) and electron affinities (EAs). MCSTEP was specifically designed for open shell and highly correlated (nondynamically correlated) initial states. For computational efficiency the initial state used in MCSTEP is typically a small complete active space (CAS) multiconfigurational self‐consistent field (MCSCF) state. If in a molecule there are some degenerate orbitals which are not fully or half occupied, usual MCSCF calculations will make these orbitals inequivalent, i.e., the occupied ones will be different from the nonoccupied ones, so that the degeneracy is broken. In this article, we use a state averaged MCSCF method to get equivalent orbitals for the initial state and import the integrals into the subsequent MCSTEP calculations. This gives, in general, more reliable MCSTEP vertical IPs. © 2008 Wiley Periodicals, Inc., 2008

Approximate MCSCF optimization for multiconfigurational spin-tensor electron propagator method (MCSTEP): The vertical ionization potentials of CO, HCN, HNC, H2CO, and O3

The multiconfigurational spin tensor electron propagator method (MCSTEP) was developed as an implementation of electron propagator/single particle Green's function methods. MCSTEP was specifically designed for open shell and highly correlated (nondynamically correlated) initial states. The initial state used in MCSTEP is typically a small complete active space (CAS) with multiconfigurational self-consistent field (MCSCF) state. In some cases, because of our use of a small CAS in MCSTEP, the Lagrangian eigenvalues of the MCSCF reference state are in an undesired order (u). The desired order (d) can usually be obtained by excluding one or more orbital rotations in MCSCF optimization between the doubly occupied and partially occupied orbitals. We systematically examine several cases where the undesired order occurs for the low-lying vertical MCSTEP ionization potentials (IPs) of the molecules CO, HCN, HNC, H2CO, and O3 with our recently established CAS choices for MCSCF/MCSTEP. By excluding one or more orbital rotations between the partially and doubly occupied orbitals, an approximate MCSCF reference state with the same CAS choice is obtained for use in standard MCSTEP calculations that, in general, gives more reliable vertical MCSTEP IPs. © 2007 Wiley Periodicals, Inc. J Quantum Chem, 2008

Modification of optimal complete active space choices for the multiconfigurational spin‐tensor electron propagator method for ionization potentials

AbstractThe multiconfigurational spin tensor electron propagator (MCSTEP) method was developed as an implementation of electron propagator/single particle Green's function methods. MCSTEP was specifically designed for open‐shell and highly correlated (nondynamically correlated) initial states. Ionization or electron attachment is always from a state of pure spin symmetry to a state of pure spin symmetry even if the initial state is open shell. MCSTEP can be used as well for molecules with initial states that can be accurately described by a single determinant‐based theory. The initial state that is used in MCSTEP is typically a small complete active space (CAS) multiconfigurational self‐consistent field (MCSCF) state. We previously examined different small CAS choices for MCSTEP initial states and have developed a generally workable scheme. This article further examines some different ways to choose the CAS for MCSTEP. With several logical CAS choices, we have calculated the low‐lying vertical MCSTEP ionization potentials (IPs) of C2, N2, linear H2O, O2, CH2, and NH2, comparing them with large multireference configuration interaction (MRCI) calculations. We conclude that generally a small modification and extension of our previous schemes for choosing the MCSTEP CAS gives IPs that most effectively mimics the results of large scale MRCI IPs in general. © 2006 Wiley Periodicals, Inc. Int J Quantum Chem, 2007

The determination of low lying ionization potentials of BN, BN+ and B2N and photodetachment energies of BN− and B2N− using the multiconfigurational spin tensor electron propagator method

The multiconfigurational spin tensor electron propagator method (MCSTEP) is a Green's function based approach for directly calculating accurately the low lying ionization potentials (IPs) and electron affinities (EAs) of highly correlated closed and open shell molecules. The MCSTEP method has been employed to determine the vertical ionization potentials and adiabatic ionization potentials of BN, BN+ and B2N and the photodetachment energies (PDEs) of BN− and B2N−. These systems have had wide industrial applications and have recently been the focus of considerable attention. For BN, the lowest few MCSTEP vertical and adiabatic ionization potentials are in good agreement with other theoretical values previously reported. For BN− the MCSTEP PDEs are in good agreement with the experimental values and previous theoretical results. MCSTEP vertical and adiabatic IPs for BN+ differ for some states compared with other previously reported theoretical values. This is believed to be the first time that the vertical and adiabatic IPs of B2N have been reported. The MCSTEP PDEs of B2N are in very good agreement with the experimental values.

The direct determination of the ionization potentials of CH and CH 3 using the electron propagator method with a multiconfigurational second-order perturbation theory wavefunction as the initial state (EPCASPT2)

We directly determine the first two vertical ionization potentials (IPs) of two small organic radicals, CH and CH 3, using a new method, the electron propagator method with a multiconfigurational second-order perturbation theory wavefunction (EPCASPT2) and using the multiconfigurational spin tensor electron propagator method (MCSTEP). Our IPs using EPCASPT2 are in excellent agreement compared to full configuration interaction ( ΔFCI). For CH MCSTEP and EPCASPT2 give very accurate IPs to the lowest two cation states. For CH 3, the lowest MCSTEP IP is inaccurate while the EPCASPT2 IPs effectively mimics ΔFCI IPs for all the IPs determined.

Electron propagator method with a multiconfigurational second-order perturbation theory wave function as the initial state in the fermion operator block

We have developed an electron propagator method using a multiconfigurational second-order perturbation theory (CASPT2) wave function as the initial state [electron propagator CASPT2 (EPCASPT2)] in the fermion operator block (block 1). In the other blocks a multiconfigurational self-consistent field wave function is the initial state. We apply our new method to directly determine the low-lying vertical ionization potentials of Be, CH2, NH2, and H2O. We compare our results with the results of the calculations using multiconfigurational spin tensor electron propagator (MCSTEP), full configuration interaction (FCI), and multireference configuration interaction (MRCI) methods with the same geometries and basis sets. The calculations are performed using complete active space (CAS) choices that are usually excellent for MCSTEP ionization potential (IP) calculations and also for CAS choices that are inadequate for MCSTEP IP calculations. We show that EPCASPT2 generally improves MCSTEP IPs compared to ΔFCI when the MCSTEP IPs are in very good to excellent agreement with ΔFCI IPs and that EPCASPT2 can effectively mimic ΔFCI even when the CAS choice for the initial state is inadequate for MCSTEP.

Purely theoretical electron-impact ionization cross-sections of silicon hydrides and silicon fluorides obtained from explicitly correlated methods

Electron impact total ionization cross-sections of small silicon hydrides, SiHn(n=1–4), and fluorides, SiFn(n=1–3), have been calculated by the application of a recently developed theoretical model. The binary-encounter-Bethe (BEB) model has a simple structure and requires information from calculations on the parent ground-state molecule only (binding energies, orbital kinetic energies, and occupation numbers). Previous applications of the BEB theory to the silicon hydrides and fluorides have employed a combination of experimental and Koopman’s theorem binding energies. In the current work binding energies have been calculated using the explicitly correlated multiconfigurational spin tensor electron propagator (MCSTEP) method which gives highly accurate ionization potentials for closed- and open-shell systems. Calculations have been performed using cc-pVDZ and cc-pVTZ basis sets with multiconfigurational self-consistent field (MCSCF) reference wave functions. Comparisons are made between our MCSCF/MCSTEP and previous Hartree–Fock (HF)/Koopman’s theorem results and available experimental data. The use of improved theoretical data does not have a significant effect on the resultant cross-sections; however, our new technique is a viable method for calculating electron impact ionization cross-sections for systems where Koopman’s theorem is known to be unreliable or no experimental data is available.

Resolving the controversy over the second ionization potential of the nitrate free radical NO3

Two experimental studies determining the ionization potentials (IPs) of a nitrate free radical have recently been done. The first study performed using discharge flow-photoionization mass spectroscopy (PIMS) determined the adiabatic ionization potential at 12.57 eV. The second study using the HeI photoelectron spectroscopy (PES) observed five bands with the five lowest vertical ionization potentials of NO3 at 12.55, 13.18, 13.62, 14.05, and 15.54 eV. The second IP determined using PES (at 13.18 eV) has been questioned due to its absence in the spectrum obtained using the PIMS experiment. We use our theoretical method, the multiconfigurational spin tensor electron propagator method (MCSTEP), to help resolve the controversy over the ionization potential of NO3. We perform MCSTEP calculations on NO3 using the standard cc-pVDZ and cc-pVTZ basis sets at D3h and C2v geometries. Our results at both of these two symmetries support the experimental results obtained using PES.

Complete basis set limit ionization potentials of O 3 and NO 2 using the multiconfigurational spin tensor electron propagator method (MCSTEP)

We have calculated low-lying principal vertical ionization potentials (IPs) of O 3 and NO 2 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 NO 2 and highly correlated molecules such as O 3. Our results confirm previous assignments of photoelectron peaks based on calculations made using less accurate methods.

A small optimal complete active space (CAS) for multiconfigurational spin tensor electron propagator method (MCSTEP) ionization potentials: Application to methane, acetylene, ethylene, and ethane

The multiconfigurational spin tensor electron propagator method (MCSTEP) is specifically designed to provide accurate determination of the low-lying principal vertical ionization potentials (IP’s) and electron affinities (EA’s) of atoms and molecules. In this paper we modify and extend our definition of an “optimal” small complete active space (CAS) for MCSTEP calculations. We then use MCSTEP to determine the vertical principal ionization potentials (IP’s) below 19 eV of the small organic molecules methane, acetylene, ethylene, and ethane. The calculations are done using the standard Dunning-core-valence pVDZ and pVTZ basis sets. The results are compared with experiments as well as with some other forefront theoretical methods. The MCSTEP IP’s are in very good to excellent agreement with experimental IP’s.

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.

Accurate vertical ionization potentials of CH2, NH2, and H2O using the multiconfigurational spin tensor electron propagator method (MCSTEP)

The multiconfigurational spin tensor electron propagator method (MCSTEP) is used to determine accurate low-lying vertical principal ionization potentials (IPs) for the free radicals CH2 and NH2 and the closed shell molecule H2O. In previous MCSTEP calculations we had compared MCSTEP IPs with full configuration interaction (FCI) values for CH2 using a double zeta with polarization (DZP) basis set. Those MCSTEP results were in very good agreement with ΔFCI. An alternative complete active space (CAS) choice used in this paper gives even better agreement—differing from ΔFCI values by 0.03 eV and 0.01 eV for the lowest two vertical principal IPs from the 3B1 neutral ground state. These MCSTEP results are extended by also using pVDZ, pVTZ, and pVQZ basis sets at both the previous (FCI) geometry and the experimental geometry. Choosing the CAS in the same manner for NH2 yields very good principal vertical IPs compared with experiment. Comparisons are again made using pVDZ, pVTZ, and pVQZ basis sets. Low-lying principal vertical MCSTEP IPs are obtained for H2O and compared with recent ΔFCI values using the same basis set and geometry as the FCI calculations. Low-lying principal vertical MCSTEP IPs are also obtained using pVDZ, pVTZ, and pVQZ basis sets at the experimental geometry.

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 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 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. © 1996 John Wiley & Sons, Inc.

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.

The multiconfigurational spin tensor electron propagator method (MCSTEP): Comparison with extended Koopmans' theorem results

We applied the multiconfigurational spin tensor electron propagator method (MCSTEP) for determining the lowest few (in energy) vertical ionization potentials (IPs) of HF, H2O, NH3, CH4, N2, CO, HNC, HCN, C2H2, H2CO, and B2H6. We chose these molecules so that we could compare MCSTEP IPs with recently reported extended Koopmans' theorem (EKT) IPs on the same molecules. Using standard Dunning core-valence basis sets with relatively small complete active spaces, MCSTEP results are in very good to excellent agreement with experiment. These MCSTEP IPs are obtained using matrices no larger than 400 × 400. EKT matrices are even smaller; however, to obtain similar but generally slightly worse agreement with experiment, fairly large active spaces are required with EKT.

The multiconfigurational spin tensor electron propagator method (MCSTEP): Comparison with extended Koopmans’ theorem results

The multiconfigurational spin tensor electron propagator method (MCSTEP): Comparison with extended Koopmans’ theorem results