Variational wavefunctions for low-lying excited states

The multiconfiguration method based on the generalized Brillouin theorem is well suited to optimize orbitals in variational wavefunctions for low-lying excited states of a given symmetry. Such wavefunctions are constrained to be orthogonal to and noninteracting with the wavefunctions for all lower states of the same symmetry. Test calculations were performed on the lowest excited ¹S state of Be. For a Hartree-Fock ground state wavefunction, singly excited configurations were insufficient to describe the lowest excited state, and triply excited configurations had to be added. For multiconfiguration ground state wavefunctions, however, singly excited configurations gave good results.     

All-electron first principles calculations of the ground and some low-lying excited states of BaI

The electronic structure of the heavy diatomic molecule BaI has been examined for the first time by ab initio multiconfigurational configuration interaction (MRCI) and coupled cluster (RCCSD(T)) methods. The effects of special relativity have been taken into account through the second-order Douglas-Kroll-Hess approximation. The construction of Omega(omega,omega) potential energy curves allows for the estimation of "experimental" dissociation energies (De) of the first few excited states by exploiting the accurately known De experimental value of the X2Sigma+ ground state. All states examined are of ionic character with a Mulliken charge transfer of 0.5 e- from Ba to I, and this is reflected to large dipole moments ranging from 6 to 11 D. Despite the inherent difficulties of a heavy system like BaI, our results are encouraging. With the exception of bond distances that on the average are calculated 0.05 A longer than the experimental ones, common spectroscopic parameters are in fair agreement with experiment, whereas De values are on the average 10 kcal/mol smaller.     

The electronic structure of low-lying excited states of two model systems of retinal

2,4-pentadienal and 2,4,6,8-nonatetraenal were studied as simple model systems of retinal. Four kinds of CI were performed on low-lying excited states of 2,4-pentadienal by using a split valence basis set. The results show that MR SD π CI is not adequate for the π–π* state and the single excitation σπ CI is a good compromise between cost and effectiveness as far as singly excited states are concerned. This CI was applied to the bigger model system. All-trans and 11-cis forms of aldehyde, Schiff base, and protonated Schiff base of the model system were studied. A fairly large energy lowering of about 1 eV of the first allowed excited state (π → π*) occurs when the Schiff base is protonated for both all-trans and 11-cis forms.     

Table of Feynman diagrams of the interacting Fermion Green's function

The Feynman diagrams of the Green's function expansion of fermions interacting with a nonrelativistic 2‐body interaction are displayed in first, second, and third perturbative order of the interaction as 2, 10, and 74 diagrams, respectively. A name convention for the diagrams is proposed and then used to tabulate the diagrams of fourth to seventh order. The Hartree–Fock approximation summons up 2, 8, 40, and 224 of them in first through fourth order. © 2007 Wiley Periodicals, Inc. Int J Quantum Chem, 2007     

Optimized effective potential method for individual low-lying excited states

This paper presents an optimized effective potential (OEP) approach based on density functional theory (DFT) for individual excited states that implements a simple method of taking the necessary orthogonality constraints into account. The amended Kohn-Sham (KS) equations for orbitals of excited states having the same symmetry as the ground one are proposed. Using a variational principle with some orthogonality constraints, the OEP equations determining a local exchange potential for excited states are derived. Specifically, local potentials are derived whose KS determinants minimize the total energies and are simultaneously orthogonal to the determinants for states of lower energies. The parametrized form of an effective DFT potential expressed as a direct mapping of the external potential is used to simplify the OEP integral equations. A performance of the presented method is examined by exchange-only calculations of excited state energies for simple atoms and molecules.     

Theoretical description of the low-lying excited states of CuCl

The low-lying excited states of CuCl have been investigated theoretically in the Hartree-Fock approximation. Spin-orbit interactions have been included semi-empirically using an atoms-in-molecules technique. All six excited states that were previously characterized experimentally are found to arise from fine structure sublevels of the Cu⁺(3d⁹4s ^1,3D)Cl⁻(3p⁶¹S) configuration.     

The low-lying electronic excited states of NiCO

Highly correlated coupled cluster methods with single and double excitations (CSSD) and CCSD with perturbative triple excitations were used to predict molecular structures and harmonic vibrational frequencies for the electronic ground state X 1Sigma+, and for the 3Delta, 3Sigma+, 3Phi, 1 3Pi, 2 3Pi, 1Sigma+, 1Delta, and 1Pi excited states of NiCO. The X 1Sigma+ ground state's geometry is for the first time compared with the recently determined experimental structure. The adiabatic excitation energies, vertical excitation energies, and dissociation energies of these excited states are predicted. The importance of pi and sigma bonding for the Ni-C bond is discussed based on the structures of excited states.     

On the low-lying excited states of sym-triazine-based herbicides.

We report a joint computational and luminescence study on the low-lying excited states of sym-triazines, namely, 1,3,5-triazine (1) and the ubiquitous herbicides atrazine [6-chloro-N2-ethyl-N4-isopropyl-1,3,5-triazine-2,4-diamine (2)] and ametryn [6-methylthio-N2-ethyl-N4-isopropyl-1,3,5-triazine-2,4-diamine (3)]. Geometrical structures, energetics, and transition and state properties of I and 2 were computed at the TD-DFT, CASSCF, and CASPT2 levels of theory. The fluorescence and phosphorescence emission spectra, lifetimes, and fluorescence quantum yields were measured for the three compounds, and from these, the energies of the lowest excited states and their corresponding radiative rates were determined. The predictions from CASPT2 calculations are in good agreement with the experimental results obtained from the luminescence studies and allow the interpretation of different absorption and emission features.     

Semiempirical calculation of photoionization cross sections for the first excited levels of F I

Radial matrix elements and photoionization cross sections have been calculated for all levels of the first excited configuration 2p ⁴(³ P) 3s of neutral fluorine as an example for the application of the Scaled Thomas-Fermi method. The extrapolation of empirical data on energy levels to positive electron energies and the reliability of the method are discussed.     

No fluorescence decay from low-lying electronic states excited into single vibronic levels with synchrotron radiation

Fluorescence decay of NO has been studied by single photon counting using the synchrotron radiation from the Orsay Electron Storage Ring (ACO) as a source of excitation. Emissions from A²Σ⁺(υ = 0,1,2,3), B²Π(υ = 5), C²Π(υ = 0, 1) and D²Σ⁺(υ = 0, 1, 2, 3) levels have been observed in function of NO gas pressure in the 0.02–4 torr range. Collision-free lifetimes and self-quenching rate constants have been derived from these measurements for all these levels and compared to previous data. Particular attention has been paid to the C²Π(υ = 0) level decay properties. By narrow-band (≈ 45 cm^?1) excitation inside the rotational envelope of this level we show that the decay is non-exponential with a short-living component (≈ 3 ns) a long-living one (≈ 20 ns). We develop a number of arguments in order to prove the short-living levels (J > 5 or 7) are weakly predissociated.     

Spectroscopy of the ground and low-lying excited states of ThO+

The ThO(+) cation is of interest as it is a useful prototype for experimental and theoretical studies of bonding in a simple actinide compound. Formally the ground state of ThO(+) has the configuration Th(3+)(7s)O(2-), where there is a single unpaired electron associated with a closed-shell Th(4+)-ion core. The first tier of excited states above the X (2)Sigma(+) ground state is expected to be 1 (2)Delta, 1 (2)Pi, and 2 (2)Sigma(+) derived from the Th(3+)(6d)O(2-) configuration. Spectroscopic observations of ThO(+) using the pulsed field ionization-zero kinetic-energy photoelectron technique are reported here. Rotationally resolved spectra were recorded for the X (2)Sigma(+), 1 (2)Delta, and 1 (2)Pi states. Extensive vibrational progressions were observed. Surprisingly, it was found that ionization of ThO decreases the dissociation energy, while increasing the vibrational frequency and decreasing the bond length. Accurate values for the ionization energies of ThO [53 253.8(2) cm(-1)] and Th [50 868.71(8) cm(-1)] were determined as part of this investigation.     

Interaction independent π bond orders for certain excited states

Particular solutions of the bond order equations are shown for certain excited states, common to different conjugated systems and interaction-independent. The P matrix for these states has: 1 in the principal diagonal (charges), ± 1 in the secondary one, zero otherwise.Consejo Nacional de Investigaciones Cientificas y Técnicas.     

Calculation of the ground states of molecules with closed shells via Feynman diagrams

A Feynman-diagram calculation is performed for the ground-state energies of molecules of the XY_p type with closed electron shells. The first two orders in perturbation theory are considered.We are indebted to Dr. V. V. Tolmachev for proposing the topic and for substantial assistance in deriving the results, and also to Dr. U. I. Safronova for constant interest.     

Interpreting nonlinear vibrational spectroscopy with the classical mechanical analogs of double-sided Feynman diagrams

Observables in coherent, multiple-pulse infrared spectroscopy may be computed from a vibrational nonlinear response function. This response function is conventionally calculated quantum-mechanically, but the challenges in applying quantum mechanics to large, anharmonic systems motivate the examination of classical mechanical vibrational nonlinear response functions. We present an approximate formulation of the classical mechanical third-order vibrational response function for an anharmonic solute oscillator interacting with a harmonic solvent, which establishes a clear connection between classical and quantum mechanical treatments. This formalism permits the identification of the classical mechanical analog of the pure dephasing of a quantum mechanical degree of freedom, and suggests the construction of classical mechanical analogs of the double-sided Feynman diagrams of quantum mechanics, which are widely applied to nonlinear spectroscopy. Application of a rotating wave approximation permits the analytic extraction of signals obeying particular spatial phase matching conditions from a classical-mechanical response function. Calculations of the third-order response function for an anharmonic oscillator coupled to a harmonic solvent are compared to numerically correct classical mechanical results.     

Calculations of the low-lying excited states of the TiO(2) molecule

We present calculations of the lowest excited electronic states of the TiO(2) molecule. These are computed using several correlated wavefunction response based methods, as well as time-dependent density functional response theory using a range of functionals. Surprisingly lower cost wavefunction based methods, in particular the second-order CC2 and CIS(D) methods, completely fail to describe the lowest (1)B(2) and (1)A(2) states of the molecule. Density functional methods fare better but still show considerable variation amongst functionals. Thus TiO(2) provides a strenuous test for correlated excited state methods.     

On the ordering of the first two excited electronic states in all-trans linear polyenes

Reported experimental evidence of the relative position of the first two excited electronic states in linear polyenes was carefully examined and compared with that derived from time dependent density functional theory (TDDFT) theoretical calculations performed at the B3LYP level on optimized geometries. The energy values for the first two triplet states 3Bu and 3Ag, obtained from TDDFT calculations, were found to be highly strongly correlated with the experimental values. Also, the theoretical calculations for the electronic transition 1 1Ag --> 1 1Bu were also extremely well correlated with their experimental counterparts; even more important, the three reported experimental data for 1 1Ag --> 2 1Ag transitions in these systems conformed to the correlation for the TDDFT 1 1Ag --> 1 1Bu transition. The first excited electronic state in the linear polyenes studied (from ethene to the compound consisting of 40 ethene units, P40) was found to be 1Bu. The energy gap between the excited states 2 1Ag and 1 1Bu decreased with increasing length of the polyene chain, but not to the extent required to cause inversion, at least up to P40. In the all-trans linear polyenes studied, the widely analyzed energy gap from the ground electronic state to the first excited singlet state for infinitely long chains may be meaningless as, even in P40, it is uncertain whether the ground electronic state continues to be a singlet.     

Electronic structures of permethyloligosilane radical cations at the ground and low-lying excited states

The electronic structures at the ground and low-lying excited states of permethyloligosilane radical cations, Si_n(CH₃)_2n+2⁺ (n = 4-7), have been investigated using DFT and ab initio calculations. The calculations showed that positive charge (hole) is delocalized along the Si-Si main chain at the ground and first excited states. On the other hand, the hole is transferred to the methyl side-chain at the second and higher excited states. From these results, it was concluded that hole can move along the Si-Si main chain at thermal conditions. Also, it was predicted that intermolecular hole hopping takes place by photo-irradiation to the permethyloligosilane radical cation. The mechanism of hole transfer was discussed on the basis of the results.