J. Schirmer

An efficient polarization propagator approach to valence electron excitation spectra

A practical polarization propagator method devised for the treatment of valence electron excitations in atoms and molecules is presented. This method, referred to as (second-order) algebraic-diagrammatic construction (ADC(2)), allows for a theoretical description of single and double excitations consistently through second and first order, respectively, of perturbation theory. The computational scheme is essentially an eigenvalue problem of a Hermitian secular matrix defined with respect to the space of singly and doubly excited configurations. The configuration space is smaller (more compact) than that of comparable configuration interaction (CI) expansions and the method leads to size-consistent results. The performance of the ADC(2) method is tested in exemplary applications to Ne, Ar and CO, where detailed comparison can be made with experiment and previous theoretical results. While the accuracy of the absolute excitation energies is only moderate, a very satisfactory description is obtained for the relative energies and, in particular, for the spectral intensities. Aspects related to the Thomas-Reiche-Kuhn sum rule and the equivalence of the dipole-length and dipole-velocity forms of the transition moments are discussed. Due to the relatively small computational expense and the possibility of a direct ADC(2) formulation this method should prove particularly useful in applications to large molecules.

Correlation effects in the ionization of hydrocarbons

The spectral intensity for ionization as a function of binding energy for the valence electrons of ethylene, allene, butatriene, trans‐butadiene, acetylene, benzene, methane, ethane, and cyclopropane is computed by a many‐body Green’s function method. The results are used to interpret unidentified structures in experimental ionization spectra. For the ionization out of the inner valence orbitals of the unsaturated molecules the spectral intensity is found to be distributed over several lines, in sharp contrast to the ionization out of the inner valence orbitals of the saturated molecules where the greater part of the intensity appears in one main line. The reasons for this behavior are discussed. It is also found that there is a correspondence between the behavior of the spectral intensity in the inner valence region and the satellite structure in the outer valence region. For C6H6, C4H4, and C4H6 interesting satellite lines of considerable intensity are predicted to be situated in the outer valence regio...

Strong Correlation Effects in inner Valence Ionization of N2 AND CO

Abstract The results of many-body calculations of the valence and inner-valence ionization potentials and their intensities are reported for N2 and CO. For N2 we find that the 2σg line is smashed to several pieces of roughly equal intensity. It is not possible to identify any of these lines as the ǒmainǒ line representing the ionization of a 2Ug electron and the remaining ones as satellite lines. For CO there survives a line which carries about half of the 3e intensity and which can be interpreted to represent the ionization of an electron out of the 3σ orbital. The results explain the peculiar shape of the broad innervalence peaks of N2 and CO. For both N2 and CO rich satellite structure is found in qualitative agreement with experimental X-ray photoelectron spectra.

The two-particle-hole Tamm-Dancoff approximation (2ph-TDA) equations for closed-shell atoms and molecules

An approximation scheme for the one-particle Greens function referred to as the two-particle-hole Tamm-Dancoff approximation (2ph-TDA) is introduced by means of a well defined infinite partial summation of the perturbation expansion for the so-called self-energy part. A spin-free formulation of the working equations is presented for molecular applications. It is demonstrated that the 2ph-TDA is a useful tool for a theoretical treatment of inner valence ionisation processes. A discussion of the physical content and the relationship to other approaches shows the central role of this approximation.

On Green’s function calculations of the static self‐energy part, the ground state energy and expectation values

The necessity to determine the static self‐energy part Σ(∞) in many‐body Green’s function studies of atomic and molecular ionization introduces difficulties affecting both the accuracy and the efficiency of the method. We show how this bottleneck can be overcome under an approximation obtained by truncating the Dyson expansion for the one‐particle Green’s function G(ω). Here the essential computational step consists of an inversion or a Lanczos diagonalization of constant Hermitian secular matrices associated with the dynamical self‐energy part M(ω). Both methods are very practical and efficient as is demonstrated in an exemplary application to the CO molecule. The same approximation and numerical techniques apply also to the problem of extracting ground state information from G(ω), i.e., correlation energy and expectation values of single‐particle operators.

Theoretical studies of inner-valence-shell photoionization cross sections in N2 and CO

Abstract Theoretical studies in the intensity-borrowing sudden approximation are reported of inner-valence-shell photoionization cross sections in N2 and CO. The required ionic-state energies and spectroscopic amplitudes are obtained from appropriate Greens-function and configuration-interaction calculations, and previously devised Stieltjes-Tchebycheff moment-theory techniques are employed in determinations of corresponding continuum dipole transition moments in the static-exchange approximation. Comparisons are made of the Greens-function calculations in the two-particle-hole Tamm-Dancoff approximation with wavefunction results obtained from single-excitation and polarization configuration-interaction calculations. Detailed descriptions are given of the calculated spectroscopic intensity distributions and of the hole-particle configurational compositions of the corresponding inner-valence-shell ionic states. and comparisons are made with previously reported wavefunction studies in N2+ and CO+. Spectroscopic assignments are suggested on basis of the present calculations for the strong features observed recently in higher-resolution inner-valence-shell photoelectron spectra. The corresponding calculated partial-channel photoionization cross sections for the designated C2Σg+, F2Σg+, G2Σg+, and (2σg−1)2Σg+ bands in N2 and C2Σ+, D2Π, F2Σ+, G2Σ+, and (3σ−1)2Σ+ bands in CO are found to be in good quantitative accord with dipole (e, 2e), (e, e + ion), and synchrotron-radiation studies.

Experimental and theoretical investigation of the complete valence shell ionization spectra of CO2and N2O

Abstract The valence electron ionization spectra of CO 2 , and N 2 O are studied by dipole (e—2e) spectroscopy and 2ph-TDA many-body Green function calculations. Intense satellite structure in the (e—2e) spectra between ≈ 20 eV and ≈ 30 eV binding energy is assigned with the help of the calculations. While for CO 2 , only satellite lines of 2 Π u symmetry appear with significant intensity, intense satellite lines of both 2 Π and 2 γ symmetry are found for N 2 O in the 20–30 eV energy range. The theory predicts a complete breakdown of the molecular orbital picture of ionization to occur for the two innermost valence electrons of CO 2 and N 2 O. The inner valence part of the ionization spectra of CO 2 and N 2 0 is found to be considerably more complex than has hitherto been assumed. The experimental spectra confirm the main features of the theoretical results.

Intermediate state representation approach to physical properties of electronically excited molecules

Propagator methods provide a direct approach to energies and transition moments for (generalized) electronic excitations from the ground state, but they do not usually allow one to determine excited state wave functions and properties. Using a specific intermediate state representation (ISR) concept, we here show how this restriction can be overcome in the case of the algebraic-diagrammatic construction (ADC) propagator approach. In the ISR reformulation of the theory the basic ADC secular matrix is written as a representation of the Hamiltonian (or the shifted Hamiltonian) in terms of explicitly constructable states, referred to as intermediate (or ADC) states. Similar intermediate state representations can be derived for operators other than the Hamiltonian. Together with the ADC eigenvectors, the intermediate states give rise to an explicit formulation of the excited wave functions and allow one to calculate physical properties of excited states as well as transition moments for transitions between different excited states. As for the ground-state excitation energies and transition moments, the ADC excited state properties are size consistent so that the theory is suitable for applications to large systems. The established hierarchy of higher-order [ADC(n)] approximations, corresponding to systematic truncations of the IS configuration space and the perturbation-theoretical expansions of the ISR matrix elements, can readily be extended to the excited state properties. Explicit ISR matrix elements for arbitrary one-particle operators have been derived and coded at the second-order [ADC(2)] level of theory. As a first computational test of the method we have carried out ADC(2) calculations for singlet and triplet excited state dipole moments in H(2)O and HF, where comparison to full CI results can be made. The potential of the ADC(2) method is further demonstrated in an exploratory study of the excitation energies and dipole moments of the low-lying excited states of paranitroaniline. We find that four triplet states, T1-T4, and two singlet states, S1 and S2, lie (vertically) below the prominent charge transfer (CT) excitation, S3. The dipole moment of the S3 state (17.0D) is distinctly larger than that of the corresponding T3 triplet state (11.7D).

Higher-order approximations for the particle-particle propagator

A new type of approximations for many-body Greens functions proposed recently is applied to the particle-particle (pp) propagator for anN-particle fermion system. The new approach which is referred to as the algebraic diagrammatic construction (ADC) is based on an exact resummation of the perturbation series for the pp-propagator in terms of a simple algebraic form introducing energy-independent effective interaction matrix elements and transition amplitudes. These effective quantities are represented by perturbation expansions and can be determined consistently through a given ordern of perturbation theory by comparing the algebraic form with the diagrammatic perturbation series of the pp-propagator through ordern. By this procedure one obtaines a systematic set of approximation schemes (ADC(n)) that represent infinite partial summations for the pp-propagator being complete throughnth order of perturbation theory. The explicit ADC equations forn=1 and 2 are presented and discussed. Comparison is made with the particle-particle random phase approximation (RPA). It is demonstrated that the second-order ADC scheme constitutes an essential step beyond the RPA which is consistent only through first order.

Tautomerism in cytosine and uracil: an experimental and theoretical core level spectroscopic study

The O, N, and C 1s core level photoemission spectra of the nucleobases cytosine and uracil have been measured in the vapor phase, and the results have been interpreted via theoretical calculations. Our calculations accurately predict the relative binding energies of the core level features observed in the experimental photoemission results and provide a full assignment. In agreement with previous work, a single tautomer of uracil is populated at 405 K, giving rise to relatively simple spectra. At 450 K, three tautomers of cytosine, one of which may consist of two rotamers, are identified, and their populations are determined. This resolves inconsistencies between recent laser studies of this molecule in which the rare imino-oxo tautomer was not observed and older microwave spectra in which it was reported.