Molecular frame photoelectron angular distributions for H2 ionization by single and trains of attosecond XUV laser pulses

The delayed autoionization of H₂ doubly excited states into channels of different inversion symmetry gerade and ungerade is investigated by using pulses of attosecond duration (isolated or packed in trains), linearly polarized along the molecular axis. It has been shown in previous work, by using XUV laser pulses with durations of 4 fs or longer, that the molecular frame photoelectron angular distributions (MFPAD) associated with the dissociative channel H⁺ + H(n?) are not symmetric with respect to the inversion center of the molecule. In contrast, the MFPADs become symmetric for shorter fs pulses. Here we show that, although this is still the case for pulses of attosecond duration, the combination of two of these pulses with a controlled time delay may still lead to asymmetric MFPADs. From the analysis of the time evolution of the calculated MFPADs, we propose a way to elucidate autoionization lifetimes of molecular resonant states. © 2010 Wiley Periodicals, Inc. Int J Quantum Chem 110:2462–2471, 2010     

Molecular frame and recoil frame photoelectron angular distributions from dissociative photoionization of NO2

The authors report measured and computed molecular frame photoelectron angular distributions (MFPADs) and recoil frame photoelectron angular distributions (RFPADs) for the single photon ionization of the nonlinear molecule NO2 leading to the (1a2)-1 b 3A2 and (4a1)-1 3A1 states of NO2+. Experimentally, the RFPADs were obtained using the vector correlation approach applied to the dissociative photoionization (DPI) involving these molecular ionic states. The polar and azimuthal angle dependences of the photoelectron angular distributions are measured relative to the reference frame provided by the ion recoil axis and direction of polarization of the linearly polarized light. Experimental results are reported for the photon excitation energies hnu=14.4 and 22.0 eV. Theoretically the authors give expressions for both the MFPAD and the RFPAD. They show that the functional form in the recoil frame, where an average over the azimuthal dependence of the molecular fragments about the recoil direction is made, is identical to that they have earlier found for the DPI experiments performed on linear molecules. MFPADs were then computed using single-center expansion techniques within the fixed-nuclei frozen-core Hartree-Fock approximation. The computed cross sections for ionization to the (1a2)-1 b 3A2 state show a strong propensity for ionization with the polarization of the light perpendicular to the plane of the molecule, whereas the ionization to the (4a1)-1 3A1 state of the ion is of similar intensity for all orientations of the polarization of the light in the molecular frame. These qualitative features of the MFPAD are also evident in the RFPAD. The RFPAD for ionization leading to the (1a2)-1 b 3A2 state is strongly peaked in the perpendicular orientation, whereas the RFPAD for ionization leading to the (4a2)-1 3A1 state is much more nearly isotropic. Comparison between experimental and theoretical RFPADs indicates that the recoil angle for NO+ fragments is approximately 50 degrees relative to the symmetry axis of the initial C2v symmetry of the NO2 molecule in the ionization leading to the (1a2)-1 b 3A2 state and the recoil angle is approximately 120 degrees for the O+ fragment for ionization leading to the (4a1)-1 3A1 state.     

Valence and inner-valence shell dissociative photoionization of CO in the 26-33 eV range. II. Molecular-frame and recoil-frame photoelectron angular distributions

Experimental and theoretical results for molecular-frame photoemission are presented for inner-valence shell photoionization of the CO molecule induced by linearly and circularly polarized light. The experimental recoil frame photoelectron angular distributions (RFPADs) obtained from dissociative photoionization measurements where the velocities of the ionic fragment and photoelectron were detected in coincidence, are compared to RFPADs computed using the multichannel Schwinger configuration interaction method. The formalism for including a finite lifetime of the predissociative ion state is presented for the case of general elliptically polarized light, to obtain the RFPAD rather than the molecular frame photoelectron angular distribution (MFPAD), which would be obtained with the assumption of instantaneous dissociation. We have considered photoionization of CO for the photon energies of 26.0 eV, 29.5 eV, and 32.5 eV. A comparison of experimental and theoretical RFPADs allows us to identify the ionic states detected in the experimental studies. In addition to previously identified states, we found evidence for the 2 (2)Δ state with an ionization potential of 25.3 eV and (2)Σ(+) states with ionization potentials near 32.5 eV. A comparison of the experimental and theoretical RFPADs permits us to estimate predissociative lifetimes of 0.25-1 ps for some of the ion states. Consideration of the MFPADs of a series of (2)Π ion states indicates the importance of inter-channel coupling at low photoelectron kinetic energy and the limitations of a single-channel analysis based on the corresponding Dyson orbitals.     

Molecular Frame Photoemission： Probe of the Photoionization Dynamics for Molecules in the Gas Phase

Molecular frame photoemission is a very sensitive probe of the photoionization （PI） dynamics of molecules. This paper reports a comparative study of non-resonant and resonant photoionization of D2 induced by VUV circularly polarized synchrotron radiation at SOLEIL at the level of the molecular frame photoelectron angular distributions （MFPADs）. We use the vector correlation method which combines imaging and time-of-flight resolved electron-ion coincidence techniques, and a generalized formalism for the expression of the Ⅰ（χ, θe, Фe） MFPADs, where χ is the orientation of the molecular axis with respect to the light quantization axis and （θe, Фe） the electron emission direction in the molecular frame. Selected MFPADs for a molecule aligned parallel or perpendicular to linearly polarized light, or perpendicular to the propagation axis of circularly polarized light, are presented for dissociative photoionization （DPI） of D2 at two photon excitation energies, hv=19 eV, where direct PI is the only channel opened, and hv=32.5 eV, i.e. in the region involving resonant excitation of Q1 and Q2 doubly excited state series. We discuss in particular the properties of the circular dichroism characterizing photoemission in the molecular frame for direct and resonant PI. In the latter case, a remarkable behavior is observed which may be attributed to the interference occurring between undistinguishable autoionization decay channels.     

Dissociative photoionization of N(2)O in the region of the N(2)O(+)(B (2)Pi) state studied by ion-electron velocity vector correlation

Dissociative direct photoionization of the N2O(X 1Sigma+) linear molecule via the N2O+(B 2Pi) ionic state induced by linearly polarized synchrotron radiation P in the 18-22 eV photon energy range is investigated using the (VA+,Ve,P) vector correlation method, where VA+ is the nascent velocity vector of the NO+, N2+, or O+ ionic fragment and Ve that of the photoelectron. The DPI processes are identified by the ion-electron kinetic energy correlation, and the IchiA+(thetae,phie) molecular frame photoelectron angular distributions (MFPADs) are reported for the dominant reaction leading to NO+ (X 1Sigma+,v) + N(2D)+ e. The measured MFPADs are found in satisfactory agreement with the reported multichannel Schwinger configuration interaction calculations, when bending of the N2O+(B 2Pi) molecular ion prior to dissociation is taken into account. A significant evolution of the electron scattering anisotropies is observed, in particular in the azimuthal dependence of the MFPADs, characteristic of a photoionization transition between a neutral state of Sigma symmetry and an ionic state of Pi symmetry. This interpretation is supported by a simple model describing the photoionization transition by the coherent superposition of two ssigma and ddelta partial waves and the associated Coulomb phases.     

Cartesian coupled coherent states simulations: Ne(n)Br2 dissociation as a test case

In this article, we describe coupled coherent states (CCS) simulations of vibrational predissociation of weakly bounded complexes. The CCS method is implemented in the Cartesian frame in a manner that is similar to classical molecular dynamics. The calculated lifetimes of the vibrationally excited Ne-Br(2)(ν) complexes agree with experiment and previous calculations. Although the CCS method is, in principle, a fully quantum approach, in practice it typically becomes a semiclassical technique at long times. This is especially true following dissociation events. Consequently, it is very difficult to converge the quantum calculations of the final Br(2) vibrational distributions after predissociation and of the autocorrelation functions. However, the main advantage of the method is that it can be applied with relative ease to determine the lifetimes of larger complexes and, in order to demonstrate this, preliminary results for tetra- and penta-atomic clusters are reported.     

Transition state spectroscopy of open shell systems: Angle-resolved photodetachment spectra for the adiabatic singlet states of OHF

In this work three-dimensional potential energy surfaces of the first five singlet states of OHF are developed based on fits of more than 10,000 highly accurate ab initio points. An approximate treatment is presented for the calculation of the anisotropy parameter describing the electron angular distribution photodetached from a molecular anion. This method is used to calculate the angle-resolved photoelectron spectra in the photodetachment of OHF⁻. The wave packet formed in the neutral OHF system is placed at the transition state region, and yields the formation of OH + F and HF + O products. The results are compared with the recent experimental measurements published by Neumark [D.M. Neumark, Phys. Chem. Chem. Phys. 7 (2005) 433]. The intensity found at low electron kinetic energy including these five states and the three lower triplet states is found to be low. To analyze the effect of higher electronic states more excited ¹Σ⁻, ³Σ⁺ and ³Δ states are calculated at collinear geometry. The agreement with the experimental data improves, thus demonstrating that the correct simulation of the photodetachment spectrum at 213 nm involves at least 12 electronic states. All the structures of the experimental spectra are semiquantitatively reproduced finding an overall good agreement. It is concluded that the main problem of the simulation is in the intensity and anisotropy parameters. An alternative to their calculation would be to fit their values to reproduce the experimental results, but this would require to separate the contribution arising from different final electronic states.     

Slice imaging of quantum state-to-state photodissociation dynamics of OCS

Slice imaging experiments are reported for the quantum state-to-state photodissociation dynamics of OCS. Both one-laser and two-laser experiments are presented detecting CO(J) or S((1)D(2)) photofragments from the dissociation of hexapole state-selected OCS(v(2) = 0,1,2 / J = 1,2) molecules. We present data using our recently developed large frame CCD centroiding detector and have implemented a new high speed MCP high voltage pulser with an effective slice width of only 6 ns. Slice images are presented for quantum state-to-state photolysis, near 230 nm, of vibrationally excited OCS(v(2) = 0,1,2). Two-laser pump-probe experiments detecting CO(J = 63 or 64) show a dramatic change in the beta parameter for the same final state of CO(J) when the photolysis energy is reduced by about 1000 cm(-1). We attribute the observed change from large positive to large negative beta to a large increase of the molecular frame deflection angle at very slow recoil velocity, due to a breakdown of the axial recoil. Two-laser experiments on the S((1)D(2)) fragment reveal single well-separated rings in the slice images correlating with individual CO(J) states. Strong polarization effects of the probe laser are observed, both in the angular distribution of the intensity of single S((1)D(2)) rings and in the resolution of the radial velocity distribution. It is shown how the broadening of the velocity distribution can be reduced by a directed ejection of the electron in the ionization process perpendicular to the slice imaging plane. The dissociation energy of OCS(v(2) = 0, J = 0) --> CO(J = 0) + S((1)D(2)) is determined with high accuracy D(0) = (34 608 +/- 24) cm(-1).     

The influence of vibronic interactions on the chiroptical spectra of dissymmetric pseudo tetragonal metal complexes

The influence of vibronic interactions on the chiroptical spectra associated with a threesome of nearly degenerate electronic excited states in a dissymmetric molecular system is examined on a formal theoretical model. The model considers two vibrational modes to be effective in promoting pseudo Jahn-Teller (PJT) type interactions between the three closely spaced electronic excited states. Formal expressions are developed for the rotatory strengths of individual vibronic levels derived from the coupled electronic states. Two mode (vibrational)-three state (electronic) vibronic Hamiltonians are constructed (basis set size, 63–108, depending upon interaction parameters used) and diagonalized for a large number of different parameter sets representative of various vibronic coupling strengths, electronic energy level spacings, oscillator (vibrational mode) frequencies, and electronic rotatory strengths. Diagonalization of these vibronic Hamiltonians yields vibronic wave functions and energies which are then used to calculate rotatory strength spectra for the model system. The calculated results demonstrate the profound influence which vibronic interactions of the PJT type may have on the sign patterns and intensity distributions within the rotatory strength spectrum associated with a set of nearly degenerate electronic states. The implication of these results for the interpretation of circular dichroism spectra of chiral transition metal complexes with pseudo tetragonal symmetry are discussed.     

Time-resolved photoelectron spectroscopy: from wavepackets to observables

Time-resolved photoelectron spectroscopy (TRPES) is a powerful tool for the study of intramolecular dynamics, particularly excited state non-adiabatic dynamics in polyatomic molecules. Depending on the problem at hand, different levels of TRPES measurements can be performed: time-resolved photoelectron yield; time- and energy-resolved photoelectron yield; time-, energy-, and angle-resolved photoelectron yield. In this pedagogical overview, a conceptual framework for time-resolved photoionization measurements is presented, together with discussion of relevant theory for the different aspects of TRPES. Simple models are used to illustrate the theory, and key concepts are further amplified by experimental examples. These examples are chosen to show the application of TRPES to the investigation of a range of problems in the excited state dynamics of molecules: from the simplest vibrational wavepacket on a single potential energy surface; to disentangling intrinsically coupled electronic and nuclear motions; to identifying the electronic character of the intermediate states involved in non-adiabatic dynamics by angle-resolved measurements in the molecular frame, the most complete measurement.     

Exciton states of dynamic DNA double helices: alternating dCdG sequences

The present communication deals with the excited states of the alternating DNA oligomer (dCdG)5.(dCdG)5 which correspond to the UV absorption band around 260 nm. Their properties are studied in the frame of the exciton theory, combining molecular dynamics simulations and quantum chemistry data. It is shown that the dipolar coupling undergoes important variations with the site and the helix geometry. In contrast, the energy of the monomer transitions within the double helix is not sensitive to the local environment. It is thus considered to be distributed over Gaussian curves whose maximum and width are derived from the experimental absorption spectra of nucleosides in aqueous solution. The influence of the spectral width on the excited state delocalization and the absorption spectra is much stronger than that of the oligomer plasticity. About half of the excited states are delocalized over at least two bases. Many of them result from the mixing of different monomer states and extend on both strands. The trends found in the simulated spectra, when going from non-interacting monomers to the duplex, are in agreement with experimental observations. Conformational changes enhance the diversity of the states which can be populated upon excitation at a given energy. The states with larger spatial extent are located close to the maximum of the absorption spectrum.     

Evaluating First-Order Molecular Properties of Delocalized Ionic or Excited States in Molecular Aggregates by Renormalized Excitonic Method

In the past few years, the renormalized excitonic model (REM) approach was developed as an efficient low-scaling ab initio excited state method, which assumes the low-lying excited states of the whole system are a linear combination of various single monomer excitations and utilizes the effective Hamiltonian theory to derive their couplings. In this work, we further extend the REM calculations for the evaluations of first-order molecular properties (e.g. charge population and transition dipole moment) of delocalized ionic or excited states in molecular aggregates, through generalizing the effective Hamiltonian theory to effective operator representation. Results from the test calculations for four different kinds of one dimensional (1D) molecular aggregates (ammonia, formaldehyde, ethylene and pyrrole) indicate that our new scheme can efficiently describe not only the energies but also wavefunction properties of the low-lying delocalized electronic states in large systems.     

A Density Matrix Renormalization Group Study of the Low-Lying Excited States of a Molybdenum Carbonyl-Nitrosyl Complex

A density matrix renormalization group-self consistent field (DMRG-SCF) study has been carried out to calculate the low-lying excited states of CpMo(CO)₂NO, a molybdenum complex containing NO and CO ligands. In order to automatically select an appropriate active space, a novel procedure employing the maximum single-orbital entropy for several states has been introduced and shown to be efficient and easy-to-implement when several electronic states are simultaneously considered. The analysis of the resulting natural transition orbitals and charge-transfer numbers shows that the lowest five excited electronic states are excitation into metal-NO antibonding orbitals, which offer the possibility for nitric oxide (NO) photorelease after excitation with visible light. Higher excited states are metal-centered excitations with contributions of metal-CO antibonding orbitals, which may serve as a gateway for carbon monoxide (CO) delivery. Time-dependent density functional theory calculations done for comparison, show that the state characters agree remarkably well with those from DMRG-SCF, while excitation energies are 0.4–1.0 eV red-shifted with respect to the DMRG-SCF ones.     

Electron-phonon interactions in photoinduced excited electronic states in fluoroacenes

The electron-phonon coupling constants [l(B1u(HOMO-->LUMO))] in the photoinduced excited electronic states in fluoroacenes are estimated and compared with those in the monoanions (l(LUMO)) and cations (l(HOMO)). The l(B1u(HOMO-->LUMO)) values are much larger than the l(LUMO) and l(HOMO) values in fluoroacenes. Furthermore, the Coulomb pseudopotential mu* values for the excited electronic states are estimated to be smaller than those for the monoanions and cations. The complete phase patterns difference between the highest occupied molecular orbitals (HOMOs) and the lowest unoccupied molecular orbitals (LUMOs) is the main reason why the electron-phonon coupling constants and the mu* values are larger and smaller, respectively, in the photoinduced excited electronic states than in the monoanions and cations. The possible electron pairing and Bose-Einstein condensation in the excited electronic states of fluoroacenes are discussed. Because of larger electron-phonon coupling constants and smaller mu* values in the excited electronic states than in the charged states, the conditions under which the electron-electron interactions become attractive can be more easily realized, in principle, in the excited electronic states than in the charged states in fluoroacenes. The l(B1u(HOMO-->LUMO)) values hardly change by H-F substitution, even though the l(LUMO) and l(HOMO) values significantly increase by H-F substitution in acenes. Antibonding interactions between carbon and fluorine atoms in the HOMO and LUMO are the main reason why the l(B1u(HOMO-->LUMO)) values hardly change by H-F substitution in acenes.     

Implementation of renormalized excitonic method at ab initio level

The renormalized excitonic method [Hajj et al., Phys Rev B 2005, 72, 224412], in which the excited state of the whole system may be described as a linear combination of local excitations, has been implemented at ab initio level. Its performance is tested on the ionization potential and the energy gap between singlet ground state and lowest triplet for linear molecular hydrogen chains and more realistic systems, such as polyenes and polysilenes, using full configuration interaction (FCI) wave functions with a minimal basis set. The influence of different block sizes and the extent of interblock interactions are investigated. It has been demonstrated that satisfactory results can be obtained if the near degeneracies between the model space and the outer space are avoided and if interactions between the next-nearest neighbor blocks are considered. The method can be used with larger basis sets and other accurate enough ab initio evaluations (instead of FCI) of local excited states, from blocks, or from dimers or trimers of blocks. It provides a new possibility to accurately and economically describe the low-lying delocalized excited states of large systems, even inhomogeneous ones.     

The influence of ultrashort excitations on the vibrational dynamics in a diatomic molecule

The problem of vibrational wave packet dynamics in the system of two electronic states of a diatomic molecule, where the states are coupled by infinitely short light pulses, is solved. The electronic states were modeled by shifted harmonic oscillators with different frequencies. Exact expressions for the probability densities of the wave packets in the ground and excited states were derived. The spatial, spectral, and temporal characteristics of the wave packets, namely, the range of motion, spatial width, mean energy, spectral width (the mean number of vibrational states in a wave packet), and the autocorrelation function, were calculated as functions of the molecular parameters (the frequency ratio and the distance between the potential minima) and of the delay time between the light pulses. The possibility of controlling the mean energy and spectral width of the wave packets in the ground electronic state by varying the delay time is considered. It was shown that "squeezed" wave packets can be prepared in the ground electronic state if the upper electronic state is shallow.     

Identification of unavoided crossings in nonadiabatic photoexcited dynamics involving multiple electronic states in polyatomic conjugated molecules

Radiationless transitions between electronic excited states in polyatomic molecules take place through unavoided crossings of the potential energy surfaces with substantial non-adiabatic coupling between the respective adiabatic states. While the extent in time of these couplings are large enough, these transitions can be reasonably well simulated through quantum transitions using trajectory surface hopping-like methods. In addition, complex molecular systems may have multiple "trivial" unavoided crossings between noninteracting states. In these cases, the non-adiabatic couplings are described as sharp peaks strongly localized in time. Therefore, their modeling is commonly subjected to the identification of regions close to the particular instantaneous nuclear configurations for which the energy surfaces actually cross each other. Here, we present a novel procedure to identify and treat these regions of unavoided crossings between non-interacting states using the so-called Min-Cost algorithm. The method differentiates between unavoided crossings between interacting states (simulated by quantum hops), and trivial unavoided crossings between non-interacting states (detected by tracking the states in time with Min-Cost procedure). We discuss its implementation within our recently developed non-adiabatic excited state molecular dynamics framework. Fragments of two- and four-ring linear polyphenylene ethynylene chromophore units at various separations have been used as a representative molecular system to test the algorithm. Our results enable us to distinguish and analyze the main features of these different types of radiationless transitions the molecular system undertakes during internal conversion.     

Analytical time-dependent density functional derivative methods within the RI-J approximation, an approach to excited states of large molecules

Time-dependent density functional theory (TDDFT) is now well established as an efficient method for molecular excited state treatments. In this work, we introduce the resolution of the identity approximation for the Coulomb energy (RI-J) to excited state gradient calculations. In combination with nonhybrid functionals, the RI-J approximation leads to speed ups in total timings of an order of magnitude compared to the conventional method; this is demonstrated for oligothiophenes with up to 40 monomeric units and adamantane clusters. We assess the accuracy of the computed adiabatic excitation energies, excited state structures, and vibrational frequencies on a set of 36 excited states. The error introduced by the RI-J approximation is found to be negligible compared to deficiencies of standard basis sets and functionals. Auxiliary basis sets optimized for ground states are suitable for excited state calculations with small modifications. In conclusion, the RI-J approximation significantly extends the scope of applications of analytical TDDFT derivative methods in photophysics and photochemistry.     

Fully state-resolved photodissociation of formaldehyde, H2CO --> H + HCO:K conservation and a rigorous test of statistical theories

The photodissociation dynamics of the reaction H2CO+hnu --> H + HCO have been investigated in the range 60-400 cm(-1) above the reaction threshold. Supersonically cooled formaldehyde was excited into 15 specific J, K(a), K, rotational states i n two vibrational lev el s 2(1) 4(1) 6(1) and 2(2) 4(1) in the A(1A2) state. The laser-induced fluorescence spectra of the nascent HCO fragment provided detailed product state distributions (PSDs), resolved by N, K(a), K(c), and J. When just the overall molecular rotation N is considered the PSDs are in remarkable agreement with calculations based on phase space theory (PST). However, when the projection of N onto the molecular frame (K(a),K(c)) is included the distributions show consistent deviations from PST. In particular, there is a tendency to preserve the initial parent rotational motion about the a and b axes. The effect is that states with higher initial K(a) in H2CO produce higher final K(a) in the HCO fragment. There is also a tendency for the upper/lower members of the asymmetry doublets in H2CO to map onto the same upper/lower set of product state asymmetry doublets. Finally, there are oscillations in some of the detailed PSDs that remain unexplained.