Ab initio study on NH+: Transition dipole moments,transition probabilities,and radiative lifetimes

The transition electric dipole moments between low-lying valence states of NH⁺ are calculated by an ab initio effective valence-shell Hamiltonian (H^v) method. The H^v calculated transition moments are found to be in good agreement with those by other accurate ab initio methods. The spontaneous emission probabilities for the A²− → X²Π, B²Δ → X²Π, and C²−⁺ → X²Π transitions of NH⁺ are computed. Also, radiative lifetimes for A²∑⁻, B²Δ, and C²∑⁺ states are all theoretically determined using the potential energy functions by H^v. Also, the H^v results are well compared with those computed using the Morse potentials and the rkr potentials which are obtained from experimental data. © 1996 John Wiley & Sons, Inc.     

Theoretical and experimental studies of radiative lifetimes of excited electronic states in CO

The electronic dipole transition moment functions of the A ²Π-X ²Σ⁺, B ²Σ⁺-X ²Σ⁺ and B ²Σ⁺-A ²Π transitions and the dipole moment function of the X ²Σ⁺ state of CO⁺ have been calculated using large contracted CI wavefunctions. The computed transition moment functions together with experimental potential energy curves were used to obtain radiative lifetimes of the excited electronic states B ²Σ⁺ and A ²Π. Radiative lifetimes of vibrational levels of the X ²Σ⁺ state were derived from the calculated dipole moment function. The high-frequency deflection technique was used to obtain radiative lifetimes of the ν′ = 0, 1,2 and 3 vibrational levels of the B ²Σ⁺ state and also radiative lifetimes of individual rotational levels of ν′ =0. The calculated radiative lifetimes are shorter than the measured ones by about 10%. The experimental ν′ dependence is reproduced by theoretical calculation. The calculated radiative lifetimes for the A ²Π state are in excellent agreement with lifetimes measured with an ion trap technique.     

A theoretical study of the excited states of CrH: potential energies, transition moments, and lifetimes

Ab initio calculations of low-lying electronic states of CrH are presented, including potential energies, dipole and transition dipole moment (TDM) functions, and radiative lifetimes for X (6)Sigma(+), A (6)Sigma(+), 3 (6)Sigma(+), 1 (6)Pi, 2 (6)Pi, 3 (6)Pi, and (6)Delta. Calculation of dynamic correlation effects was performed using the multistate complete active space second-order perturbation method, based on state-averaged complete active space self-consistent-field reference wave functions obtained with seven active electrons in an active space of 16 molecular orbitals. A relativistic atomic natural orbital-type basis set from the MOLCAS library was used for Cr. Good agreement is found between the current calculations and experiment for the lowest two (6)Sigma(+) states, the only states for which spectroscopic data are available. Potential curves for the 3 (6)Sigma(+) and 2 (6)Pi states are complicated by avoided crossings with higher states of the same symmetry, thus resulting in double-well structures for these two states. The measured bandhead T(0)=27 181 cm(-1), previously assigned to a (6)Pi<--X (6)Sigma(+) transition, is close to our value of T(0)=28 434 cm(-1) for the 2 (6)Pi state. We tentatively assign the ultraviolet band found experimentally at 30 386 cm(-1) to the 3 (6)Pi<--X (6)Sigma(+) transition for which the computed value is 29 660 cm(-1). The A (6)Sigma(+)<--X (6)Sigma(+) TDM and A (6)Sigma(+) lifetimes are found to be in reasonable agreement with previous calculations.     

Excited states and electronic spectra of annulated dinuclear free-base phthalocyanines: a theoretical study on near-infrared-absorbing dyes

The electronic excited states and electronic absorption spectra of annulated dinuclear free-base phthalocyanine (C(58)H(30)N(16)) are studied through quantum chemical calculations using the symmetry-adapted cluster-configuration interaction (SAC-CI) method. Three tautomers are possible with respect to the position of the pyrrole protons; therefore, the SAC-CI calculations for these tautomers were performed. The structures of the Q-band states are discussed based on the character of their molecular orbitals. The lower energy shift of the Q-bands because of dimerization is explained by the decrease in the HOMO-LUMO gaps resulting from the bonding and antibonding interactions between the monomer units. The electronic dipole moments of the nonsymmetric tautomer were calculated, and the possibility of charge-separated excited states is discussed. The relative energies of these tautomers are examined using density functional theory (DFT) calculations for several peripheral substituents. The relative energies of these tautomers significantly depend on the substituents, and therefore, the abundance ratios of the three tautomers were affected by the substituents. The absorption spectra were simulated from the SAC-CI results weighted by the Boltzmann factors obtained from the DFT calculations. The SAC-CI spectra reproduce the experimental findings well. The thermal-averaged SAC-CI spectra could explain the observed substituent effect on the structure of the Q-bands in terms of the relative stabilities and the abundance ratios of the tautomers. The SAC-CI and time-dependent density functional theory calculations are also compared. The CAM-B3LYP results agreed with the trends of the SAC-CI results; however, the CAM-B3LYP calculation overestimated the excitation energies in comparison with the SAC-CI and experimental results.     

Ab initio transition probabilities,band strengths and lifetimes for the lowest-lying vibrational states of Li+3

By calculating the dipole moments at 65 discrete points on a dipole moment hypersurface and by fitting a power series analytical function to these points, we have determined the ab initio transition probabilities, band strengths and lifetimes for the ten lowest-lying states of ⁷Li⁺₃ (⁶Li⁺₃). Of these, the fourth and tenth states were found to have long lifetimes of the order 4907 s(3344 s) and 1648 s(1093 s) respectively which is in accordance with the fact that transitions from these states to the ground state are dipole forbidden.     

Experimental and theoretical investigation of radiative lifetimes in neutral gallium

Using laser spectroscopic techniques the natural radiative lifetimes of 4s ² n ₁ s ² S and 4s ² n ₂ d ² D states of neutral gallium have been measured forn ₁ = 6 to 11 andn ₂ = 4 to 9. These states, as well as previously measured4s ² np ² P states, have been investigated theoretically using multi-configuration Hartree-Fock calculations. Oscillator strengths to all lower-lying states have been calculated and theoretical lifetimes of the investigated states evaluated. The² D sequence is strongly influenced by the 4s4p ^{2 2} D perturber, and strong cancellation effects in the radiative decay are observed both theoretically and experimentally.     

Excited electronic states of a hydrogen bond: Bifluoride ion

We report here a summary of a limited CI calculation carried out on the C_∞v and D_∞h electronically excited states of bifluoride ion. This species is interesting as the prototype of a hydrogen-bonded system. It is determined that the lowest-lying excited states of the system are dissociative and/or autoionizing.     

Excited states and electronic spectrum of ferrocene

The excited states of ferrocene have been calculated using the ab-initio singly excited configuration interaction and self-consistent field methods. The results obtained are used to assign the bands of the electronic absorption spectrum of the molecule.     

Excited states and electronic spectra of extended tetraazaporphyrins

Electronic excited states, electronic absorption, and magnetic circular dichroism (MCD) spectra of free-base tetraazaporphyrin (TAP), phthalocyanine (Pc), naphthalocyanine (Nc), and anthracocyanine (Ac) were studied by quantum chemical calculations using the symmetry-adapted cluster-configuration interaction (SAC-CI) method. Not only optically allowed states including the Q- and B-bands but also optically forbidden states were calculated for transitions whose excitation energies were lower than 4.5 eV. The present SAC-CI calculations consistently assigned the absorption and MCD peaks as optically allowed π→π(?) excitations, although these calculations using double-zeta basis limit quantitative agreement and discussion. For Nc and Ac, excited states beyond the four-orbital model appeared in the low-energy region. The low-energy shifts of the Q-bands with the extension of molecular size were explained by the orbital energies. The splitting of the Q-bands decreases with extension of the molecular size. This feature was reproduced by the SAC-CI calculations but the configuration interaction with single excitations and time-dependent density functional theory calculations failed to reproduce this trend. Electron correlation in the excited states is important in reproducing this splitting of the Q-bands and in describing the energy difference between the B(2u) and B(3u) states of free-base porphyrins.     

Wavelengths,transition probabilities and lifetimes in the quartet spectra of O VI and F VII

A model-potential method is employed to describe core-excited 1s2snl ⁴ L and 1s2pnl ⁴ L levels of the ions O VI and F VII. Wavelength, transition probability and lifetime data are predicted. The calculated wavelengths and lifetimes are compared with the available experimental measurements.     

Ab initio calculations of infrared transition probabilities in the electronic ground states of AlF and AlF+

Electric dipole moment functions and radiative transition probabilities have been calculated for the electronic ground states of AlF and AlF⁺ from highly correlated CEPA electronic wavefunctions. The dipole moments inv = 0 are calculated to be 1.56 D (experimental value is 1.53 ±0.1 D) for AlF and 5.49 D for AlF⁺. Intense transitions in the microwave and infrared spectral region are predicted for both species.     

Theory of projected probabilities on non-orthogonal states: Application to electronic populations in molecules

Often it is important to consider the expansion of a quantum state ) in terms of physically meaningful basis states. For example, molecular orbitals can be expressed as linear combinations of atomic orbitals, or vibrational states can be expressed as super positions of local or normal mode eigenstates. In such expansions, it then becomes desirable to determine how much character a quantum state has in one of these basis states. One way of accimplishing this task is to calculate the projected probability of |) on basis state |j). In this paper, we consider this general quantum mechanical problem. If the basis states are orthonormal, then the projected probability of|) on |j) is of course |<|j>|². However, if the basis states are not orthogonal, then this result is no longer valid and one must develop a more general theory to calculate these projected probabilities. An earlier paper used one-dimensional projection operators to initiate this theory and gave closed form results for the case of two non-orthogonal basis states [1]. One- and many-dimensional projection operators, together with linear algebraic techniques, are used to extend this theory to the n non-orthogonal basis state case. Explicit closed form results are given for the two- and three-state cases, and a general algorithm is developed for the case of four or more basis states. Application of the theory is made to atomic populations in three- to six-atom molecules, and comparisons are made to the related work of Mulliken.     

Energies,fine structures,and radiative lifetimes for the multiexcited quartet states of B‐like oxygen

Energies for the multiexcited states 1s²2s2pnl and 1s²2p²nl ⁴P^e,o (n ≥ 2) of B‐like oxygen are calculated using Rayleigh–Ritz variation method with configuration interaction. The mass polarization and relativistic corrections are obtained with first‐order perturbation theory. Configuration structures of the high‐lying multiexcited series are identified by energies and contribution to normalization of angular‐spin components. These structures are further checked by calculations of relativistic corrections and fine structure splittings. Hyperfine parameters and hyperfine coupling constants are calculated for the first time. Wavelengths including quantum electrodynamic effect and higher‐order relativistic corrections and lifetimes are also calculated. These results are compared with available results in the literature. © 2011 Wiley Periodicals, Inc. Int J Quantum Chem, 2012     

Excited electronic states and photophysics of uracil–water complexes

The electronically excited singlet states of complexes of uracil with one water molecule have been studied theoretically using ab initio multireference configuration interaction methods. In agreement with previous theoretical and experimental results, four cyclic isomers of uracil forming hydrogen bonds with the water molecule have been located with energies within 0.2 eV from the lowest energy isomer. Focus has been given on the mechanism for radiationless decay to the ground state after initial UV absorption and on the effect of complexation with water on previously reported radiationless decay pathways. Features on the excited state potential energy surfaces, such as minima, transition states and conical intersections, have been located for all isomers and compared with those of free uracil. The hydrogen-bonded water molecule changes the relative energies of these features and may lead to different excited state dynamics and lifetimes, in agreement with experimental observations.     

The 3d states of23Na and7Li: determination of unresolved hyperfine splittings and radiative lifetimes

The electronic transitions from the ground state to the 3d states have been studied for²³Na and⁷Li atoms by two-photon Doppler-free laser spectroscopy. The positions of the resonances are used to determine the unresolved hyperfine structure of the 3d states from which the magnetic-dipole hyperfine interaction constantsA are derived. The results for theA factors are:A(3d ² D _3/2;²³Na)=+527(25) kHz;A(3d ² D _5/2;²³Na)=+108.5(2.4) kHz;A(3d ² D _3/2;⁷Li)=+843(41) kHz;A(3d ² D _5/2;⁷Li)=+343.6(1.0) kHz. For the fine structure intervals fs of the 3d doublets we obtain: fs(3d Na)=-1 494 444(44) kHz and fs(3d Li)=+1 083 936(60) kHz. The linewidths of the resonances are evaluated with respect to the natural lifetimes of the 3d states. For Na the result is τ(3d Na)=19.27(23) ns.     

One‐electron pseudopotential study of the alkali hydride cation NaH+: Structure,spectroscopy, transition dipole moments,and radiative lifetimes

The structure and spectroscopic properties of the ground and the lowest excited electronic states of the alkali hydride cation NaH⁺ have been investigated using an ab initio approach. In this approach, a nonempirical pseudopotential for the Na⁺ core has been used and a core–core and a core‐valence correlation corrections have been added. The adiabatic potential energy curves and the molecular spectroscopic constants for numerous electronic states of ²Σ⁺, ²Π, and ²Δ symmetries, dissociating up to Na (4d) + H⁺ and Na⁺ + H (3d), have been calculated. As no experimental data are available, we discuss our results by comparing with the available theoretical calculations. A satisfying agreement has been found for the ground state with previous works. However, a clear disagreement between this study and the model potential work of Magnier (Magnier, J. Phys. Chem. A 2005, 109, 5411) has been observed for several excited states. Numerous avoided crossings between electronic states of ²Σ⁺ and ²Π symmetries have been found and analysed. They are related to the interaction between the potential energy curves and to the charge transfer process between the two ionic systems Na⁺H and NaH⁺. Furthermore, we provide an extensive set of data concerning the transition dipole moments from X²Σ⁺ and the 2²Σ⁺ states to higher excited states of ²Σ⁺ and ²Π symmetries. Finally, the adiabatic potential energy curves of the ground (X²Σ⁺) and the first (2²Σ⁺) excited states and the transition dipole moments between these states are used to evaluate the radiative lifetimes for the vibrational levels of the 2²∑⁺ state for the first time. In addition to the bound–bound contribution, the bound‐free term has been evaluated and added to the total radiative lifetime. © 2012 Wiley Periodicals, Inc.     

The low-lying electronic states of nickel cyanide and isocyanide: A theoretical investigation

At different levels of coupled cluster theory optimum structures, energetics, and harmonic vibrational frequencies for several low-lying doublet and quartet electronic states of linear NiCN and NiNC were studied using four contracted Gaussian basis sets, ranging from Ni[6s5p4d2f], CN[4s3p2d] to Ni[8s7p5d3f2g1h], CN[5s4p3d2f1g]. The most reliable predictions were obtained with a relativistic Douglas-Kroll restricted open-shell-based coupled cluster method including singles, doubles, and perturbative triple excitations [DK-R/UCCSD(T)]. This level of theory was used in conjunction with correlation-consistent polarized valence Douglas-Kroll recontracted quadruple-zeta basis sets (cc-pVQZDK). The energetic ordering of the electronic states of NiCN is predicted to be 2delta < 2sigma+ < 2pi < 4delta < 4pi and that of NiNC is 2delta approximately 2sigma+ < 2pi < 4delta < 4pi < 4sigma-. Our theoretical investigation supports the assignment of the ground-state term symbol, the Ni-C stretching frequency, and the bending frequency for the ground electronic state of NiCN by Kingston et al. [J. Mol. Spectrosc. 215, 106 (2002)] and by Sheridan and Ziurys [J. Chem. Phys. 118, 6370 (2003)]. The predicted structure of the 2delta ground state of NiCN, r(e)(Ni-C) = 1.822 angstroms and r(e)(C-N) = 1.167 angstroms, at DK-R/UCCSD(T)/cc-pVQZDK shows excellent agreement with the experimentally determined Ni-C bond length of 1.826 A and less satisfactory agreement for the C-N bond length of 1.153 angstroms [J. Chem. Phys. 118, 6370 (2003)]. It is also concluded that the metal-to-ligand pi back donation is weak or negligible. Additionally, we found that on the 2delta surface the linear cyanide isomer lies lower in energy than the linear isocyanide isomer by 12.2 kcal mol(-1).     

Excited electronic states of the cyclic isomers of O2 and SO2

The low-lying electronic states of O3 and SO2 in their bent and cyclic isomers up to about 10 eV are calculated using the multireference configuration interaction (MRCI) method with a standard Gaussian correlation consistent polarized triple-zeta (cc-pVTZ) basis set. The vertical excitation energies, electron configurations, and oscillator strengths of these states are reported. The molecular orbital structures and excited states of the cyclic isomers are discussed in relation to the bent ones. Coherent anti-Stokes Raman spectroscopy (CARS) schemes for detecting the synthesis of the cyclic isomers are suggested.     

Photophysics and spectroscopy of the higher electronic states of zinc metalloporphyrins: a theoretical and experimental study

The photophysics of the S2 and S1 excited states of zinc porphyrin (ZnP) and five of its derivatives (ZnOEP, ZnTBP, ZnTPP, ZnTFPP, ZnTCl8PP) have been investigated by measuring their steady-state absorption and fluorescence spectra, quantum yields and excited state lifetimes at room temperature in several solvents. The radiative and radiationless decay constants of the fluorescent excited states accessible in the visible and near UV regions of the spectrum have been obtained. Despite the similarities in the Soret spectra of these compounds, their S2 excited state radiationless decay rates differ markedly. Although the S2-S1 electronic energies of a given zinc porphyrin vary linearly with the Lippert (refractive index) function of the solvent, the S2 radiationless decay rates of the set of compounds do not follow the energy gap law of radiationless transition theory. Calculations, using time-dependent density functional theory (TDDFT), of the energies and symmetries of the complete set of excited states accessible by 1- or 2-photon absorption in the near UV-visible have also been carried out. Substitution on the porphyrin macrocycle framework affects the ground state geometry and alters the electron density distributions, the orbital energies and the relative order of the excited electronic states accessible in the near UV-blue regions of the spectrum. The results are used to help interpret both the nature of the electronic transitions in the Soret region, and the relative magnitudes of the radiationless transition rates of the excited states involved.     

Excited states and electronic spectra of monosubstituted benzenes. An AM1 study

Excited singlet and triplet states of fluorobenzene, aniline, nitrobenzene, toluene, phenol, and phenoxide ion have been calculated using the AM1 semi-empirical method. Electronic transitions have been predicted and compared with experimental values when available.