Assessment of transition operator reference states in electron propagator calculations

The transition operator method combined with second-order, self-energy corrections to the electron propagator (TOEP2) may be used to calculate valence and core-electron binding energies. This method is tested on a set of molecules to assess its predictive quality. For valence ionization energies, well known methods that include third-order terms achieve somewhat higher accuracy, but only with much higher demands for memory and arithmetic operations. Therefore, we propose the use of the TOEP2 method for the calculation of valence electron binding energies in large molecules where third-order methods are infeasible. For core-electron binding energies, TOEP2 results exhibit superior accuracy and efficiency and are relatively insensitive to the fractional occupation numbers that are assigned to the transition orbital.     

Vertical ionization potential in hydrogen molecule with many-body Green's function method

The many-body Green's function method is applied to the vertical ionization potential of the hydrogen molecule. The ionization potential is calculated iteratively by expanding the self-energy part up to third order. The effects of higher-order correlation corrections and nondiagonal self-energy elements on the solutions of the Dyson equation are examined with some techniques and approximations, by means of which a Koopmans' defect of 97.7% of the accurate value is obtained.     

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

The 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     

Second-order shakeup terms in electron propagator calculations on F2 and H2O2

A new approximation of the electron propagator includes second-order terms in the superoperator Hamiltonian matrix that are not present in the nondiagonal, renormalized method (NR2) of J. Chem. Phys. 108 , 1008 (1998). These terms are not difficult to calculate and resemble expressions obtained with various propagator and coupled-cluster formalisms. Their inclusion produces larger, more accurate vertical ionization energies of F₂ and H₂O₂. Cancellations between the second-order terms considered here and the first-order terms present in the NR2 method reduce the importance of shakeup operators in describing the first few cationic states of these molecules. Dyson orbitals for ²A final states of H₂O₂ exhibit qualitatively important mixings between canonical orbitals. © 1998 John Wiley & Sons, Inc. Int J Quant Chem 69: 175–182, 1998     

Investigation into the valence electronic structure of norbornene using electron momentum spectroscopy, Green's function, and density functional theories

Results of a study of the valence electronic structure of norbornene (C(7)H(10)), up to binding energies of 30 eV, are reported. Experimental electron momentum spectroscopy (EMS) and theoretical Green's function and density functional theory approaches were utilized in this investigation. A stringent comparison between the electron momentum spectroscopy and theoretical orbital momentum distributions found that, among the tested models, the combination of the Becke-Perdew functional and a polarized valence basis set of triple-zeta quality provides the best representation of the electron momentum distributions for all 19 valence orbitals of norbornene. This experimentally validated model was then used to extract other molecular properties of norbornene (geometry, infrared spectrum). When these calculated properties are compared to corresponding results from independent measurements, reasonable agreement is typically found. Due to the improved energy resolution, EMS is now at a stage to very finely image the effective topology of molecular orbitals at varying distances from the molecular center, and the way the individual atomic components interact with each other, often in excellent agreement with theory. This will be demonstrated here. Green's Function calculations employing the third-order algebraic diagrammatic construction scheme indicate that the orbital picture of ionization breaks down at binding energies larger than about 22 eV. Despite this complication, they enable insights within 0.2 eV accuracy into the available ultraviolet emission and newly presented (e,2e) ionization spectra. Finally, limitations inherent to calculations of momentum distributions based on Kohn-Sham orbitals and employing the vertical depiction of ionization processes are emphasized, in a formal discussion of EMS cross sections employing Dyson orbitals.     

Electron propagator calculations show that alkyl substituents alter porphyrin ionization energies

The effect of alkyl substituents on the four lowest vertical ionization energies of porphyrins is determined with ab initio electron propagator calculations on porphine and octamethylporphyrin. With the use of the partial third-order approximation, predicted ionization energies are in close agreement with recent photoelectron spectra. These data and the associated Dyson orbitals, which describe changes in electronic structure that accompany photoionization, enable assignment of photoelectron spectra and determination of alkyl-induced shifts. Hyperconjugation is most evident in the Dyson orbitals associated with the third and fourth ionization energies of octamethylporphyrin and is least prominent in the Dyson orbital of the second ionization energy. There is a positive correlation between the shift in an ionization energy produced by alkyl substitution and the degree of hyperconjugation in the associated Dyson orbital. Alkyl substitutions, therefore, may be employed to adjust the ionization energies of porphyrins and, consequently, their reactivity patterns that depend on charge-transfer capabilities and disposition to electrophilic attack.     

Ionization energies of the nucleotides

The vertical ionization energies of the four nucleotides have been computed. Geometries have been chosen to mimic orientations as they appear in B-DNA. The negative charge on the phosphate was neutralized by protonation, and also by the inclusion of counterions. Calculations have been performed with electron propagator methods (P3), M?ller-Plesset second-order perturbation theory, and density functional theory to determine the nature of the orbitals associated with the highest lying ionization energies. Calculations at the MP2/6-311G(d,p)//P3/6-311G(d,p) level of theory yield vertical ionization energies for 5'-dTMP 9.05 eV, for 5'-dCMP 8.40 eV, for 5'-dAMP 8.16 eV and for 5'-dGMP 7.96 eV. In all cases the highest occupied molecular orbital resides on the base moieties.     

Norbornane: an investigation into its valence electronic structure using electron momentum spectroscopy, and density functional and Green's function theories

We report on the results of an exhaustive study of the valence electronic structure of norbornane (C(7)H(12)), up to binding energies of 29 eV. Experimental electron momentum spectroscopy and theoretical Green's function and density functional theory approaches were all utilized in this investigation. A stringent comparison between the electron momentum spectroscopy and theoretical orbital momentum distributions found that, among all the tested models, the combination of the Becke-Perdew functional and a polarized valence basis set of triple-zeta quality provides the best representation of the electron momentum distributions for all of the 20 valence orbitals of norbornane. This experimentally validated quantum chemistry model was then used to extract some chemically important properties of norbornane. When these calculated properties are compared to corresponding results from other independent measurements, generally good agreement is found. Green's function calculations with the aid of the third-order algebraic diagrammatic construction scheme indicate that the orbital picture of ionization breaks down at binding energies larger than 22.5 eV. Despite this complication, they enable insights within 0.2 eV accuracy into the available ultraviolet photoemission and newly presented (e,2e) ionization spectra, except for the band associated with the 1a(2) (-1) one-hole state, which is probably subject to rather significant vibronic coupling effects, and a band at approximately 25 eV characterized by a momentum distribution of "s-type" symmetry, which Green's function calculations fail to reproduce. We note the vicinity of the vertical double ionization threshold at approximately 26 eV.     

Semidirect algorithms for third-order electron propagator calculations

An efficient procedure for third-order electron propagator calculations of ionization energies and electron affinities is reported. Diagonal self-energy expressions that are suitable for large molecules are empolyed. The outer-valence Green's function method also is implemented. An integral transformation program for direct and semidirect algorithms is modified to store only nonzero integrals according to Abelian point group symmetry. Contributions to self-energy matrix elements that depend on electron repulsion integrals with four virtual orbital indices are computed in a direct way. Intermediate batches of integrals are created by sort procedures while avoiding storage of transformed integrals in the main memory. This method permits calculation of electron binding energies for C with a 231 atomic orbital basis and for Zn(C₅H₅)₂ with a 220 atomic orbital basis on an IBM RISC/6000 Model 550. During these calculations, the CPU is engaged approximately 90% of the time. © 1995 John Wiley & Sons, Inc.     

Electronic properties of liquid ammonia: a sequential molecular dynamics/quantum mechanics approach

The electronic properties of liquid ammonia are investigated by a sequential molecular dynamics/quantum mechanics approach. Quantum mechanics calculations for the liquid phase are based on a reparametrized hybrid exchange-correlation functional that reproduces the electronic properties of ammonia clusters [(NH3)n; n=1-5]. For these small clusters, electron binding energies based on Green's function or electron propagator theory, coupled cluster with single, double, and perturbative triple excitations, and density functional theory (DFT) are compared. Reparametrized DFT results for the dipole moment, electron binding energies, and electronic density of states of liquid ammonia are reported. The calculated average dipole moment of liquid ammonia (2.05+/-0.09 D) corresponds to an increase of 27% compared to the gas phase value and it is 0.23 D above a prediction based on a polarizable model of liquid ammonia [Deng et al., J. Chem. Phys. 100, 7590 (1994)]. Our estimate for the ionization potential of liquid ammonia is 9.74+/-0.73 eV, which is approximately 1.0 eV below the gas phase value for the isolated molecule. The theoretical vertical electron affinity of liquid ammonia is predicted as 0.16+/-0.22 eV, in good agreement with the experimental result for the location of the bottom of the conduction band (-V 0=0.2 eV). Vertical ionization potentials and electron affinities correlate with the total dipole moment of ammonia aggregates.     

Quasiparticle virtual orbitals in electron propagator calculations

The computational limits of accurate electron propagator methods for the calculation of electron binding energies of large molecules are usually determined by the rank of the virtual orbital space. Electron density difference matrices that correspond to these transition energies in the second-order quasiparticle approximation may be used to obtain a virtual orbital space of reduced rank that introduces only minor deviations with respect to the results produced with the full, original set of virtual orbitals. Numerical tests show the superior accuracy and efficiency of this approach compared to the usual practice of omission of virtual orbitals with the highest energies.     

Partial third-order quasiparticle theory: An application to the photoelectron spectrum of S-tetrazine

An alternative choice of reference state averages in electron propagator theory and retention of all self-energy terms through third-order gives rise to the partial third-order self-energy approximation, P3. Quasiparticle P3 calculations avoid the chief computational bottlenecks of third-order theory and the outer valence Green's function (OVGF). P3 requires no multiplicative factors for scaling self-energy terms and produces better accuracy than OVGF. An application to the photoelectron spectrum of s-tetrazine illustrates the ability of the P3 method to predict correct final state orderings. © 1997 John Wiley & Sons, Inc.     

Electron propagator theory calculations of molecular photoionization cross sections: the first-row hydrides

Together with ionization potentials, cross sections provide valuable information for the interpretation of photoelectron spectra. We have developed a program to perform ab initio calculations of photoionization cross sections within the electric dipole approximation using electron propagator theory. Applications to the first-row hydrides CH(4), NH(3), H(2)O, and HF, using several approximations for the propagator self-energy and the plane-wave and orthogonalized-plane-wave approximations to represent the photoelectron, as well as comparison to experimental data, are presented. This program is implemented within the quantum chemistry package GAUSSIAN.     

Molecular ionization energies and ground- and ionic-state properties using a non-Dyson electron propagator approach

An earlier proposed propagator method for the treatment of molecular ionization is tested in first applications. The method referred to as the non-Dyson third-order algebraic-diagrammatic construction [nD-ADC(3)] approximation for the electron propagator represents a computationally promising alternative to the existing Dyson ADC(3) method. The advantage of the nD-ADC(3) scheme is that the (N+/-1)-electronic parts of the one-particle Green's function are decoupled from each other and the corresponding equations can be solved separately. For a test of the method the nD-ADC(3) results for the vertical ionization transitions in C(2)H(4), CO, CS, F(2), H(2)CO, H(2)O, HF, N(2), and Ne are compared with available experimental and theoretical data including results of full configuration interaction (FCI) and coupled cluster computations. The mean error of the nD-ADC(3) ionization energies relative to the experimental and FCI results is about 0.2 eV. The nD-ADC(3) method, scaling as n(5) with the number of orbitals, requires the solution of a relatively simple Hermitian eigenvalue problem. The method renders access to ground-state properties such as dipole moments. Moreover, also one-electron properties of (N+/-1) electron states can now be studied as a consequence of a specific intermediate-state representation (ISR) formulation of the nD-ADC approach. Corresponding second-order ISR equations are presented.     

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     

Application of the independent electron pair approach to the calculation of excitation energies,ionization potentials,and electron affinities of first row atoms

Excitation energies, first ionization potentials and electron affinities of first row atoms are calculated with a spin-adapted independent electron pair approximation (IEPA) combined with the direct determination of pair natural orbitals (PNOs). To enable comparison with molecular calculations Gaussian basis sets are used which are small enough to be also applicable to molecules. IEPA results for the above mentioned properties are accurate to 0.1–0.3 eV which is almost one order of magnitude better than the corresponding SCF-results. The same accuracy can be expected for molecules in which a localization of the doubly and singly occupied orbitals is possible, for instance for small hydrides. This is supported by the results of calculations on carbon hydrides.     

Calculated vertical ionization energies of the common α-amino acids in the gas phase and in solution

The vertical ionization energies of the low-lying conformers of the α-amino acids found in proteins have been calculated. Geometry optimizations were first performed at the B3LYP/6-311G(d,p) level of theory, and then reoptimized at the MP2/6-311G(d,p) level of theory. Vertical ionization energies were then computed by three methods, electron propagator in the partial third-order (P3) approximation, Outer-Valence-Green's Functions, and by evaluating the difference in the total energy between the cation radical and the neutral amino acid in the geometry of the neutral species. When available, the results are compared to the experimental vertical ionization energies. The vertical ionization energies calculated using the MP2/P3 method gave the best overall agreement with the experimental results. Next, the ionization energies in solution are calculated for the zwitterionic forms of the α-amino acids by using IEFPCM methods. To obtain the vertical ionization energy in solution, it is necessary to use the nonequilibrium polarizable continuum model (NEPCM), the results of which are reported here for the α-amino acids.     

Tautomeric forms of adenine: Vertical ionization energies and Dyson orbitals

For the MP2/6‐311++g(2df,p) optimized geometry of all the 14 adenine tautomers, the first three vertical ionization energies have been calculated using several electron propagator decouplings. The corresponding Dyson orbitals provide detailed insight into the role of structural variations in different adenine tautomers. Changes in the electron binding energies and the corresponding Dyson orbital amplitudes have been correlated with tautomeric proton shifts and changes in conjugation patterns. © 2009 Wiley Periodicals, Inc. Int J Quantum Chem, 2010     

Study of the photoelectron and electron momentum spectra of cyclopentene using benchmark Dyson orbital theories

A complete study of the valence electronic structure and related electronic excitation properties of cyclopentene in its C(s) ground state geometry is presented. Ionization spectra obtained from this compound by means of photoelectron spectroscopy (He I and He II) and electron momentum spectroscopy have been analyzed in details up to electron binding energies of 30 eV using one-particle Green's function (1p-GF) theory along with the outer-valence (OVGF) and the third-order algebraic diagrammatic construction [ADC(3)] schemes. The employed geometries derive from DFT/B3LYP calculations in conjunction with the aug-cc-pVTZ basis set, and closely approach the structures inferred from experiments employing microwave spectroscopy or electron diffraction in the gas phase. The 1p-GF/ADC(3) calculations indicate that the orbital picture of ionization breaks down at electron binding energies larger than approximately 17 eV in the inner-valence region, and that the outer-valence 7a' orbital is also subject to a significant dispersion of the ionization intensity over shake-up states. This study confirms further the rule that OVGF pole strengths smaller than 0.85 foretell a breakdown of the orbital picture of ionization at the ADC(3) level. Spherically averaged (e, 2e) electron momentum distributions at an electron impact energy of 1200 eV that were experimentally inferred from an angular analysis of EMS intensities have been interpreted by comparison with accurate simulations employing ADC(3) Dyson orbitals. Very significant discrepancies were observed with momentum distributions obtained from several outer-valence ionization bands using standard Kohn-Sham orbitals.     

Full configuration interaction calculation of the low lying valence and Rydberg states of BeH

The all-electron full configuration interaction (FCI) vertical excitation energies for some low lying valence and Rydberg excited states of BeH are presented in this article. A basis set of valence atomic natural orbitals has been augmented with a series of Rydberg orbitals that have been generated as centered onto the Be atom. The resulting basis set can be described as 4s2p1d/2s1p (Be/H) + 4s4p3d. It allows to calculate Rydberg states up to n= {3,4,5} of the s, p, and d series of Rydberg states. The FCI vertical ionization potential for the same basis set and geometry amounts to 8.298 eV. Other properties such as FCI electric dipole and quadrupole moments and FCI transition dipole and quadrupole moments have also been calculated. The results provide a set of benchmark values for energies, wave functions, properties, and transition properties for the five electron BeH molecule. Most of the states have large multiconfigurational character in spite of their essentially single excited nature and a number of them present an important Rydberg-valence mixing that is achieved through the mixed nature of the particle MO of the single excitations.