V. G. Zakrzewski

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.

Accurate Ionization Potentials and Electron Affinities of Acceptor Molecules IV: Electron-Propagator Methods

Comparison of ab initio electron-propagator predictions of vertical ionization potentials and electron affinities of organic, acceptor molecules with benchmark calculations based on the basis set-extrapolated, coupled cluster single, double, and perturbative triple substitution method has enabled identification of self-energy approximations with mean, unsigned errors between 0.1 and 0.2 eV. Among the self-energy approximations that neglect off-diagonal elements in the canonical, Hartree-Fock orbital basis, the P3 method for electron affinities, and the P3+ method for ionization potentials provide the best combination of accuracy and computational efficiency. For approximations that consider the full self-energy matrix, the NR2 methods offer the best performance. The P3+ and NR2 methods successfully identify the correct symmetry label of the lowest cationic state in two cases, naphthalenedione and benzoquinone, where some other methods fail.

Ab initio Electron Propagator Calculations on Electron Detachment Energies of Fullerenes, Macrocyclic Molecules, and Nucleotide Fragments

Abstract Transition energies for electron attachment or detachment of closed-shell molecules that are large by contemporary standards of quantum chemistry calculations may be calculated ab initio with various electron propagator methods. Quasiparticle approximations that produce perturbative relaxation and correlation corrections to the results of Koopmanss theorem and renormalized self-energy approximations that retain their validity when the one-electron picture of electron binding energies is questionable have been implemented in efficient computer codes. In the former case, a simplified form of the Dyson equation is easily solved by evaluating diagonal matrix elements of the self-energy operator. In the latter case, strategies for solving eigenvalue problems of large dimension are reviewed. A study of the vertical ionization energies of the C 60 and C 70 fullerenes reveals the presence of many closely coinciding cationic states, some of which exhibit strong correlation effects. Vertical ionization energies for C 96 and C 144 are reported as well. Calculations on porphyrins and phthalocyanines reveal a nearly complete breakdown of the one-electron picture of electron binding energies. Calculations on the electron detachment energies of an anionic dinucleotide containing two guanine fragments produce many final states and indicate that the final state hole resides on a single guanine moiety.

NR2 and P3+: Accurate, Efficient Electron-Propagator Methods for Calculating Valence, Vertical Ionization Energies of Closed-Shell Molecules.

Two accurate and computationally efficient electron-propagator (EP) methods for calculating the valence, vertical ionization energies (VIEs) of closed-shell molecules have been identified through comparisons with related approximations. VIEs of a representative set of closed-shell molecules were calculated with EP methods using 10 basis sets. The most easily executed method, the diagonal, second-order (D2) EP approximation, produces results that steadily rise as basis sets are improved toward values based on extrapolated coupled-cluster singles and doubles plus perturbative triples calculations, but its mean errors remain unacceptably large. The outer valence Green function, partial third-order and renormalized partial third-order methods (P3+), which employ the diagonal self-energy approximation, produce markedly better results but have a greater tendency to overestimate VIEs with larger basis sets. The best combination of accuracy and efficiency with a diagonal self-energy matrix is the P3+ approximation, which exhibits the best trends with respect to basis-set saturation. Several renormalized methods with more flexible nondiagonal self-energies also have been examined: the two-particle, one-hole Tamm-Dancoff approximation (2ph-TDA), the third-order algebraic diagrammatic construction or ADC(3), the renormalized third-order (3+) method, and the nondiagonal second-order renormalized (NR2) approximation. Like D2, 2ph-TDA produces steady improvements with basis set augmentation, but its average errors are too large. Errors obtained with 3+ and ADC(3) are smaller on average than those of 2ph-TDA. These methods also have a greater tendency to overestimate VIEs with larger basis sets. The smallest average errors occur for the NR2 approximation; these errors decrease steadily with basis augmentations. As basis sets approach saturation, NR2 becomes the most accurate and efficient method with a nondiagonal self-energy.

Electron propagator calculations on the ground and excited states of C60(

Electron propagator calculations in two approximations—the third-order algebraic, diagrammatic construction and the outer valence Green’s function (OVGF)—have been performed on the vertical electron affinities of C60 and the vertical electron detachment energies of several states of C60(–) with a variety of basis sets. These calculations predict bound (2)T1u and (2)T1g anions, but fail to produce (2)T2u or (2)Hg anionic states that are more stable than ground-state C60. The electron affinity for the (2)Ag state is close to zero, but no definitive result on its sign has been obtained. This state may be a resonance or marginally bound anion. The OVGF prediction for the vertical electron detachment energy of (2)T1u C60(–), 2.63 eV, is in excellent agreement with recent anion photoelectron spectra.

Vertical Ionization Energies of Adenine and 9-Methyl Adenine†

Vertical ionization energies of 9-H adenine and 9-methyl adenine have been calculated with the following, ab initio, electron propagator methods: the outer valence Greens function (OVGF), partial third-order theory (P3), and the third-order algebraic diagrammatic construction, or ADC(3). Basis set effects have been systematically examined. All methods predict near degeneracy in the pi(2)-n(1) and pi(3)-n(2) pairs of cationic, adenine final states and larger splittings of the corresponding, cationic states of 9-methyl adenine. P3 results for adenine predict the following order of the first six final states: pi(1), n(1), pi(2), n(2), pi(3), n(3). Coupled-cluster calculations on the first three cationic states of adenine confirm these predictions. OVGF and ADC(3) calculations reverse the order of the second and third states and of the fourth and fifth states. All results confirm previous interpretations of experiments in which the second and third spectral bands correspond to the aforementioned pairs of final states and disagree with a recent reassignment based on time-resolved photoelectron spectra. Lower ionization energies and larger splittings in the methylated molecule are interpreted in terms of phase relationships in the Dyson orbitals. ADC(3) results confirm the qualitative validity of the one-electron approximation for the first six final states of both molecules and disclose its inadequacies for higher ionization energies.

Chapter 6 - Ab Initio Electron Propagator Methods: Applications to Fullerenes and Nucleic Acid Fragments

Abstract Energies of electron attachment or detachment for closed-shell molecules and ions that are large by the standards of ab initio quantum chemistry may be calculated accurately and efficiently with electron propagator methods. Low-order, quasiparticle approximations and their renormalized extensions are compared. A procedure for reducing the dimension of the virtual orbital space introduces low errors with respect to ordinary calculations. A study of the vertical ionization energies of the C 60 fullerene reveals the presence of many closely coinciding cationic states, some of which exhibit strong correlation effects. Calculations on the electron detachment energies of anionic fragments of nucleic acids produce many final states and indicate that corrections to Hartree–Fock orbital energies are necessary to obtain the correct order.

Electron propagator and coupled-cluster calculations on the photoelectron spectra of thiouracil and dithiouracil anions

Electron affinities, vertical electron detachment energies, and isomerization energies of 4-thiouracil, 2-thiouracil, and 2,4-dithiouracil and their valence anions have been calculated with ab initio electron propagator and other many-body methods. Anions in which protons have been transferred to the C5 from the N1 or N3 ring positions have been considered, but the canonical forms are most stable for the 4-thiouracil and 2,4-dithiouracil anions. Electron affinities of 0.61, 0.26, and 0.87 eV have been determined for 4-thiouracil, 2-thiouracil, and 2,4-dithiouracil, respectively. Electron propagator calculations on the canonical anions yield vertical electron detachment energies that are in close agreement with experimental peaks at 1.05, 3.21, and 3.32 eV for 4-thiouracil and at 1.4 eV for 2,4-dithiouracil.

Electron propagator calculations on C60 and C70 photoelectron spectra.

Vertical ionization energies of C(60) and C(70) fullerenes are calculated with semidirect implementations of electron propagator methods and a triple-zeta plus polarization basis set. These predictions are in close agreement with photoelectron spectra for final states in which the Koopmans description is qualitatively valid. Many correlation states, where the latter description fails, are predicted by methods with nondiagonal self-energies.

Delocalized water and fluoride contributions to Dyson orbitals for electron detachment from the hydrated fluoride anion

The experimental vertical electron detachment energy (VEDE) of aqueous fluoride, [F(-)(H(2)O)], is approximately 9.8 eV, but spectral assignment is complicated by interference between F(-) 2p and H(2)O 1b(1) orbitals. The electronic structure of [F(-)(H(2)O)] is analyzed with Monte Carlo and ab initio quantum-mechanical calculations. Electron-propagator calculations in the partial third-order approximation yield a VEDE of 9.4 eV. None of the Dyson orbitals corresponding to valence VEDEs consists primarily of F 2p functions. These results and ground-state atomic charges indicate that the final, neutral state is more appropriately described as [F(-)(H(2)O)(+)] than as [F(H(2)O)].