A. B. Trofimov

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).

Photoelectron spectra of the nucleobases cytosine, thymine and adenine

The complete valence shell photoelectron spectra of cytosine, thymine and adenine have been investigated experimentally and theoretically. Vertical ionization energies and spectral intensities have been evaluated using the many-body Greens function method, thereby enabling theoretical photoelectron spectra to be derived. In cytosine, the influence of tautomers and rotational conformers has been investigated. The calculated spectra display a satisfactory agreement with the experimental data and this has allowed most of the photoelectron bands to be assigned. Photoelectron asymmetry parameters have been determined from angle resolved spectra recorded with synchrotron radiation. The experimental data show that the electronic configuration of the five outer orbitals in cytosine, thymine and adenine is π, σ, π, σ, π. Vertical ionization energies have been measured for all the outer-valence orbitals even though some of the associated bands overlap significantly.

Electron excitation energies using a consistent third-order propagator approach: Comparison with full configuration interaction and coupled cluster results

A recently developed consistent third-order propagator method for the treatment of electronic excitation in molecules is tested in first applications. The method referred to as third-order algebraic-diagrammatic construction [ADC(3)] extends the existing second-order approximation and aims at a more accurate computation of excitation energies and transition moments than afforded at the second-order level. For a stringent test of the method we compare the ADC(3) energies for over 40 singlet and triplet vertical transitions in H2O, HF, N2, and Ne with the results of recent full configuration interaction (FCI) and coupled cluster (CC) computations. The ADC(3) results reflect a substantial and uniform improvement with respect to the second-order description. The mean absolute deviation of the single excitation energies from the FCI results is below 0.2 eV. Although this does not equal the accuracy of the third-order CC3 model, the ADC(3) method, scaling as N6 with the number of orbitals, may be viewed as a go...

Valence one-electron and shake-up ionization bands of polycyclic aromatic hydrocarbons. I. Benzene, naphthalene, anthracene, naphthacene, and pentacene

The valence ionization bands of benzene and of polyacenes ranging from naphthalene to pentacene have been entirely assigned by means of one-particle Green’s function calculations, performed using the third-order algebraic-diagrammatic construction [ADC(3)] scheme and series of basis sets of improving quality. For the sake of consistency, the computations are based on correlated (DFT/B3LYP) rather than uncorrelated geometries. Ionization bands pertaining to π-orbitals are subject to a severe shake-up contamination at already quite low binding energies (e.g., down to 8.0 eV in the case of pentacene). In sharp contrast, the orbital picture of ionization holds to a much greater extent within the σ-band system (e.g., for pentacene, up to binding energies of 14.6 eV). Despite the intricacy of ionization bands, and, possibly, vibrational complications, ADC(3) spectra consistently match photoionization measurements up to the inner-valence region, where the orbital picture completely breaks down.

An experimental and theoretical study of the valence shell photoelectron spectra of purine and pyrimidine molecules

The valence shell photoelectron spectrum of purine has been studied experimentally and theoretically. Synchrotron radiation has been used to record spectra at photon energies of 45 and 85 eV. Photoelectron angular distributions have been determined and these provide an experimental means of distinguishing between σ-and π-type orbitals. Vertical ionization energies and photoelectron spectral intensities have been evaluated using the many-body Green function method. The calculated spectra agree well with the experimental results in the outer valence region and have proved to be indispensable for interpreting the structure at higher binding energies where the single particle model of ionization breaks down. The photoelectron spectrum of pyrimidine has also been studied and is compared to that of purine.

Theoretical study of the low-lying excited singlet states of furan

2 (V), 1 A 1 (V8), respectively, at the C 2v ground-state molecular configuration# have been studied using the equation-of-motion coupled-cluster singles and doubles method ~EOM-CCSD!. Full geometry optimizations with subsequent computation of harmonic vibrational frequencies have been performed in order to locate and characterize stationary points on the potential energy surfaces ~PES!. The latter optimization work was enabled by the availability of analytic energy gradient techniques for the EOM-CCSD approach. A major new finding is that both the 1 B2(V) and 1 A1(V8) valence states are unstable with respect to non-totally symmetric distortions at the C2v configuration. The symmetry breaking in the 1 B2(V) state involves an in-plane coordinate of b2 symmetry. The relaxation process begins on the S2 adiabatic PES and, after passing through a conical intersection of the S2 and S1 PES, continues on the S1 surface, taking the system finally to the adiabatic minimum ofS1 ( 1 A2 state!. The 1 A1(V8) valence state is found to be unstable with respect to the out-of-plane bending coordinates of b1 and a2 symmetry. The resulting relaxed molecular structures have Cs and C2 symmetry, respectively. The present findings are analyzed in terms of a linear vibronic coupling model and spectroscopic implications are discussed.

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 Greens 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.

Theoretical study of excitations in furan: Spectra and molecular dynamics

The excitation spectra and molecular dynamics of furan associated with its low-lying excited singlet states 1A2(3s), 1B2(V), 1A1(V), and 1B1(3p) are investigated using an ab initio quantum-dynamical approach. The ab initio results of our previous work [J. Chem. Phys. 119, 737 (2003)] on the potential energy surfaces (PES) of these states indicate that they are vibronically coupled with each other and subject to conical intersections. This should give rise to complex nonadiabatic nuclear dynamics. In the present work the dynamical problem is treated using adequate vibronic coupling models accounting for up to four coupled PES and thirteen vibrational degrees of freedom. The calculations were performed using the multiconfiguration time-dependent Hartree method for wave-packet propagation. It is found that in the low-energy region the nuclear dynamics of furan is governed mainly by vibronic coupling of the 1A2(3s) and 1B2(V) states, involving also the 1A1(V) state. These interactions are responsible for the ultrafast internal conversion from the 1B2(V) state, characterized by a transfer of the electronic population to the 1A2(3s) state on a time scale of approximately 25 fs. The calculated photoabsorption spectrum of furan is in good qualitative agreement with experimental data. Some assignments of the measured spectrum are proposed.

Theoretical study of photoinduced ring-opening in furan

The potential energy surfaces (PESs) of the two lowest excited singlet states of furan [correlating with the Rydberg (1)A(2)(3s) and valence (1)B(2)(V) states at the C(2v) ground-state molecular configuration] have been studied in some detail with regard to the photoinduced ring-opening reaction. The surfaces have been characterized in terms of their stationary points and points of minimum energy conical intersections along the ring-opening pathway. The optimization of the geometrical parameters has been performed with the equation of motion coupled cluster singles and doubles method. The ab initio PESs have been modeled by energy grids and Taylor series. The resulting 11-dimensional PESs reproduce the ab initio results to a good accuracy and can be used in dynamical calculations.

Valence electron momentum spectroscopy of n-butane

The valence electronic structure and momentum-space electron density distributions of n-butane have been studied by means of high-resolution (e,2e) electron momentum spectroscopy based on noncoplanar symmetric kinematics. Ionization spectra for the range of binding energies 6 to 32 eV and momenta described by azimuthal angles φ=0°, 2°, 4°, 6°, 8°, and 10° have been recorded and compared to the results of one-particle Green’s function calculations, performed using the third-order algebraic–diagrammatic construction [ADC(3)] approximation and series of basis sets of improving quality. Experimental electron momentum profiles have been determined from a set of 11 measurements and compared to theoretical results. It has been shown that despite the complex structure of the spectral bands and the conformational versatility of n-butane, the experimental electron momentum distributions are accurately described by the momentum-space form of orbital densities obtained from Becke three-parameter Lee–Yang–Parr (B3LYP)...