Probing Rapidly‐Ionizing Super‐Atom Molecular Orbitals in C60: A Computational and Femtosecond Photoelectron Spectroscopy Study

Super‐atom molecular orbitals (SAMOs) are diffuse hydrogen‐like orbitals defined by the shallow potential at the centre of hollow molecules such as fullerenes. The SAMO excited states differ from the Rydberg states by the significant electronic density present inside the carbon cage. We provide a detailed computational study of SAMO and Rydberg states and an experimental characterization of SAMO excited electronic states for gas‐phase C₆₀ molecules by photoelectron spectroscopy. A large band of 500 excited states was computed using time‐dependent density functional theory. We show that due to their diffuse character, the photoionization widths of the SAMO and Rydberg states are orders of magnitude larger than those of the isoenergetic non‐SAMO excited states. Moreover, in the range of kinetic energies experimentally measured, only the SAMO states photoionize significantly on the timescale of the femtosecond laser experiments. Single photon ionization of the SAMO states dominates the photoelectron spectrum for relatively low laser intensities. The computed photoelectron spectra and photoelectron angular distributions are in good agreement with the experimental results.     

Explicitly time-dependent coupled cluster singles doubles calculations of laser-driven many-electron dynamics

We report explicitly time-dependent coupled cluster singles doubles (TD-CCSD) calculations, which simulate the laser-driven correlated many-electron dynamics in molecular systems. Small molecules, i.e., HF, H(2)O, NH(3), and CH(4), are treated mostly with polarized valence double zeta basis sets. We determine the coupled cluster ground states by imaginary time propagation for these molecules. Excited state energies are obtained from the Fourier transform of the time-dependent dipole moment after an ultrashort, broadband laser excitation. The time-dependent expectation values are calculated from the complex cluster amplitudes using the corresponding configuration interaction singles doubles wave functions. Also resonant laser excitations of these excited states are simulated, in order to explore the limits for the numerical stability of our current TD-CCSD implementation, which uses time-independent molecular orbitals to form excited configurations.     

Rydberg character of the higher excited states of free-base porphin

 The Rydberg character of the excited states of free-base porphin (FBP) has been investigated by the ab initio configuration interaction singles (CIS) method and the state-averaged complete-active-space self-consistent-field method. Double-zeta basis sets augmented with s, p, and d Rydberg functions and d polarization functions have been employed. Two types of molecular orbitals sets, the restricted Hartree–Fock molecular orbitals obtained for the ground state (¹A _g ) and for the cation state (²A _u ), have been used in the CIS calculations. All the calculations show that Rydberg-type excitations play important roles especially in the N bands. In this article we propose applying the model of a perturbed Rydberg series to interpret the excited states of FBP. By using this model, we have succeeded in analyzing the characteristics of the excited states as well as the experimental oscillator strengths, which have considerable magnitude even in the higher excited states. Received: 27 November 2000 / Accepted: 11 April 2001 / Published online: 27 June 2001     

Delayed Doublet Emission in a Cerium(III) Complex

Doublet emission from open-shell molecules has demonstrated its research and application value in recent years. However, understandings of the photoluminescence mechanism of open-shell molecules are far less than that of closed-shell molecules, leading to challenges in molecular design of efficient doublet emission systems. Here we report a cerium(III) 4-(9H-carbozol-9-yl)phenyl-tris(pyrazolyl)borate complex Ce(CzPhTp)₃ with a new luminescence mechanism of delayed doublet emission, which also represents the first example with metal-centered delayed photoluminescence. The energy gap between the doublet and triplet excited states of Ce(CzPhTp)₃ is reduced by the management of the inner and outer coordination spheres, thereby promoting efficient energy transfer between the two excited states and activating the delayed emission. The photoluminescence mechanism discovered may provide a new way for the design of efficient doublet emission and bring insights into rational molecular design and energy level regulation in open-shell molecules.     

Excited states of antiaromatic systems1

SINDO1 studies were performed to optimize the geometry of excited states of some antiaromatic molecules. It is discussed how such states can exhibit aromatic character upon suitable electronic excitation. The nodal pattern of the molecular orbitals involved in the electronic excitation are used to invoke bond equilization in excited states. We have investigated singlet and triplet excited states of five-membered rings C₄H₅B, C₅H₅⁺ and C₅H₄O containing four π electrons and bicyclic systems bicyclo-(1,1,0)-butadiene, bicyclo-(2,2,0)-hexatriene and benzocylobutadiene. It is seen that in bicyclo-(2,2,0)-hexatriene, both the bicylic structure and the 1,4-diradical structure determine the equilibrium geometry.     

On the calculation of the satellite peaks observed in the high energy photoelectron spectra of small molecules

The shake-up peaks which are observed to high binding energy of the main photoionization peak in the high energy photoeletron spectra of CO (carbon and oxygen core holes), H₂O and NH₃ have been interpreted by an extension of the singly excited configuration interaction method used previously in the study of the low-lying excited states of these molecules. The results obtained provide a good interpretation of the experimental spectra of these molecules in terms of many shake-up states. It is concluded that relaxed orbitals and an extensive basis set, including diffuse functions, should be used in the calculations in order to obtain good results.     

Explicitly correlated multireference configuration interaction with multiple reference functions: avoided crossings and conical intersections

We develop an explicitly correlated multireference configuration interaction method (MRCI-F12) with multiple reference functions. It can be routinely applied to nearly degenerate molecular electronic structures near conical intersections and avoided crossings, where the reference functions are strongly mixed in the correlated wave function. This work is a generalization of the MRCI-F12 method for electronic ground states, reported earlier by Shiozaki et al. [J. Chem. Phys. 134, 034113 (2011)]. The so-called F12b approximation is used to arrive at computationally efficient formulas. The doubly external part of the wave function is expanded in terms of internally contracted configurations generated from all the reference functions. In addition, we introduce a singles correction to the CASSCF reference energies, which is applicable to multi-state calculations. As examples, we present numerical results for the avoided crossing of LiF, excited states of ozone, and the H(2)?+?OH (A(2)Σ(+)) reaction.     

Ab initio computations of spin-orbit interactions in polyatomic molecules. Splitting of sulfur LII,III states and singlet–triplet transitions in SO2

Spin-orbit interactions among the ground and the first few excited electronic states of SO₂, are computed with ab initio molecular wave functions and Gaussian atomic orbitals. All spin-other orbits contributions to the matrix elements are included. The computed intensity of the first singlet–triplet transition is found to be in broad agreement with experiment and sensitive to an extension of the configuration interaction expansion of molecular wave functions. Also, the splitting of sulfur L_{II ,III} states in SO₂ is derived as an example of large spin-orbit interactions among electronic states.     

Chemical bonding in excited states: Energy transfer and charge redistribution from a real space perspective

This work provides a novel interpretation of elementary processes of photophysical relevance from the standpoint of the electron density using simple model reactions. These include excited states of H₂ taken as a prototype for a covalent bond, excimer formation of He₂ to analyze non‐covalent interactions, charge transfer by an avoided crossing of electronic states in LiF and conical interesections involved in the intramolecular scrambling in C₂H₄. The changes of the atomic and interaction energy components along the potential energy profiles are described by the interacting quantum atoms approach and the quantum theory of atoms in molecules. Additionally, the topological analysis of one‐ and two‐electron density functions is used to explore basic reaction mechanisms involving excited and degenerate states in connection with the virial theorem. This real space approach allows to describe these processes in a unified way, showing its versatility and utility in the study of chemical systems in excited states. © 2017 Wiley Periodicals, Inc.     

The INDO/2-AHP (average hole potential) method for excited states: Comparison with the simple INDO/2-HP (hole potential) method

The INDO/2 version of the average hole potential (AHP) model is analyzed. The model is applied to study the geometric features, molecular inversion barriers, singlet-triplet splittings, etc., of a few small carbonyl molecules (H₂CO, HFCO, F₂CO) in the ^1,3nπ* states with partial as well as complete optimization of all geometric parameters in the excited states. The results are compared with those obtained by a simple hole-potential (HP) model.     

Thermoemission of singlet oxygen and chemical structure of copper oxides

Thermal treatment of copper oxides (CuO, Cu₂O) is accompanied by large-scale emission of singlet oxygen molecules (¹Σ⁺ _g ). Electron spectroscopy for chemical analysis (ESCA) and electronic and IR spectroscopy were used to show that the thermoemission of electronically excited molecules results from dark generation of electronically excited states which contain in their structure isolated metal-metal bonds and oxygen associates. The anomalous diamagnetic response of the samples and reduced thermoemission activity (Cu₂O) are associated with cooperative interaction of electronically excited states.     

Correlation effects in EOM-CCSD for the excited states: evaluated by AIM localization index (LI) and delocalization index (DI)

We have extended the evaluation and interpretation of QTAIM (quantum theory of atoms in molecules) localization and delocalization indices lambda (LI) and delta (DI) to electronic excited states by studying ground states (at HF and CCSD levels) and excited states (at CIS and EOM-CCSD) of H2C=CH2, HCCH, H2C=O, H2C=S, CO2, CS2, and SO2. These molecules undergo extensive geometrical changes upon the excitation to the valence adiabatic excited singlet state. The importance of Coulomb correlation effects was demonstrated by comparing the LIs and DIs at none-correlated levels (HF and CIS) and those at correlated levels (CCSD and EOM-CCSD). In interpreting the changes in the magnitudes of the LIs and DIs, we made use of simple molecular orbital and Walsh-diagram analyses. Coulomb correlation is important in determining the magnitude of the LIs and DIs and obtaining geometries that are close to experiment.     

Molecular structure calculations: a unified quantum mechanical description of electrons and nuclei using explicitly correlated Gaussian functions and the global vector representation

We elaborate on the theory for the variational solution of the Schro?dinger equation of small atomic and molecular systems without relying on the Born-Oppenheimer paradigm. The all-particle Schro?dinger equation is solved in a numerical procedure using the variational principle, Cartesian coordinates, parameterized explicitly correlated Gaussian functions with polynomial prefactors, and the global vector representation. As a result, non-relativistic energy levels and wave functions of few-particle systems can be obtained for various angular momentum, parity, and spin quantum numbers. A stochastic variational optimization of the basis function parameters facilitates the calculation of accurate energies and wave functions for the ground and some excited rotational-(vibrational-)electronic states of H(2) (+) and H(2), three bound states of the positronium molecule, Ps(2), and the ground and two excited states of the (7)Li atom.     

Properties of atoms in electronically excited molecules within the formalism of TDDFT

The topological analysis of the electron density for electronic excited states under the formalism of the quantum theory of atoms in molecules using time‐dependent density functional theory (TDDFT) is presented. Relaxed electron densities for electronic excited states are computed by solving a Z‐vector equation which is obtained by means of the Sternheimer interchange method. This is in contrast to previous work in which the electron density for excited states is obtained using DFT instead of TDDFT, that is, through the imposition of molecular occupancies in accordance with the electron configuration of the excited state under consideration. Once the electron density of the excited state is computed, its topological characterization and the properties of the atoms in molecules are obtained in the same manner that for the ground state. The analysis of the low‐lying singlet and triplet vertical excitations of CO and C₆H₆ are used as representative examples of the application of this methodology. Altogether, it is shown how this procedure provides insights on the changes of the electron density following photoexcitation and it is our hope that it will be useful in the study of different photophysical and photochemical processes. © 2014 Wiley Periodicals, Inc.     

Geometries, electronic structures, and excited states of UN2, NUO+, and UO 2 2+ : a combined CCSD(T), RAS/CASPT2 and TDDFT study

The ground- and excited-state geometries and electronic structures of the isoelectronic series of molecules UN₂, NUO⁺, and UO ₂ ²⁺ are investigated by using relativistic density functional theory (DFT) and ab initio wavefunction theory (WFT). Scalar relativistic and spin?Corbit-coupled quantum chemical methods at the CASPT2, RASPT2, CCSD(T), DFT and TDDFT levels are applied. Relativistic effects as elucidated by Pekka Pyykk? play an important role in these uranium compounds, in particular for the excited states. The three molecular species exhibit significantly different spectroscopic properties, concerning their excitation energies, bond lengths and vibrations. Density functional approaches yield qualitatively correct results for the ground states and the valence????U.7s,6d excited states. However, the performance of TDDFT for valence????U.5f type excitations (in particular of UN₂ and NUO⁺) is less satisfactory, indicating the importance of the self-interaction correction for such excitations.     

Excited state dynamics of Michler's ketone: a laser flash photolysis study

Steady state absorption and fluorescence as well as the time resolved absorption studies in the pico and subpicosecond time domain have been performed to characterize the excited singlet and triplet states of Michler's ketone (MK). The nature of the lowest excited singlet (S₁) and triplet (T₁) states depends on the polarity of the solvent - in nonpolar solvents they have either pure nπ * character or mixed character of nπ * and ππ * states but in more polar solvents the states have CT character. Concentration dependence of the shapes of the fluorescence as well the excited singlet and triplet absorption spectra provide the evidence for the association of the MK molecules in the ground state.     

Electronic and photophysical properties of selected organic boron-containing molecules: Insight into effects of heteroatom substitution and aggregation

The density functional theory (DFT) and time-dependent DFT methods were used to investigate the electronic and optoelectronic properties of several main group atom-doped polycyclic aromatic hydrocarbons, such as oxygen-substituted PHO1 and PHO2, and sulfur-substituted PHS1 and PHS2. The ground-state structures of these molecules generally have an open-shell singlet configuration with a certain diradical character. In comparison with PHO1 and PHO2, PHS1 and PHS2 own larger diradical character indices due to their increased anti-aromaticity. Although the substitution of sulfur for the peripheral oxygen has a significant effect on the molecular geometry, the adiabatic excitation energy levels of the corresponding low-lying excited states of these molecules are less changed. Calculations reveal that here the intersystem crossing (ISC) and reverse intersystem crossing processes in CH₂Cl₂ mainly occur between the S₁ and T₂ states, and the cis molecules PHO2 and PHS2 have better charge transportation performance. Furthermore, the electronic and photophysical properties of these B-containing molecules are predicted to be tuned by the peripheral atom substitution and the structural and aggregation changes.     

Ab initio excited-state dynamics of the photoactive yellow protein chromophore

The photoisomerization mechanism of the neutral form of the photoactive yellow protein (PYP) chromophore is investigated using ab initio quantum chemistry and first-principles nonadiabatic molecular dynamics (ab initio multiple spawning or AIMS). We identify the nature of the two lowest-lying excited states, characterize the short-time behavior of molecules excited directly to S2, and explain the origin of the experimentally observed wavelength-dependent photoisomerization quantum yield.