Ground and Electronic Excited States from Pairing Matrix Fluctuation and Particle-Particle Random Phase Approximation

The accurate description of ground and electronic excited states is an important and challenging topic in quantum chemistry. The pairing matrix fluctuation, as a counterpart of the density fluctuation, is applied to this topic. From the pairing matrix fluctuation, the exact electron correlation energy as well as two electron addition/removal energies can be extracted. Therefore, both ground state and excited states energies can be obtained and they are in principle exact with a complete knowledge of the pairing matrix fluctuation. In practice, considering the exact pairing matrix fluctuation is unknown, we adopt its simple approximation --- the particle-particle random phase approximation (pp-RPA) --- for ground and excited states calculations. The algorithms for accelerating the pp-RPA calculation, including spin separation, spin adaptation, as well as an iterative Davidson method, are developed. For ground states correlation descriptions, the results obtained from pp-RPA are usually comparable to and can be more accurate than those from traditional particle-hole random phase approximation (ph-RPA). For excited states, the pp-RPA is able to describe double, Rydberg, and charge transfer excitations, which are challenging for conventional time-dependent density functional theory (TDDFT). Although the pp-RPA intrinsically cannot describe those excitations excited from the orbitals below the highest occupied molecular orbital (HOMO), its performances on those single excitations that can be captured are comparable to TDDFT. The pp-RPA for excitation calculation is further applied to challenging diradical problems and is used to unveil the nature of the ground and electronic excited states of higher acenes. The pp-RPA and the corresponding Tamm-Dancoff approximation (pp-TDA) are also applied to conical intersections, an important concept in nonadiabatic dynamics. Their good description of the double-cone feature of conical intersections is in sharp contrast to the failure of TDDFT. All in all, the pairing matrix fluctuation opens up new channel of thinking for quantum chemistry, and the pp-RPA is a promising method in describing ground and electronic excited states.

Energy transfer rates and population inversion investigation of sup(1)Gsub(4) and sup(1)Dsub(2) excited states of Tmsup(3+) in Yb:Tm:Nd:KYsub(3)Fsub(10) crystals

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Population inversion between the sup(3)Hsub(4) and the sup(3)Fsub(4) excited states of Tmsup(3+) investigated by means of numerical solutions of the rate equations system in Tmsup(3+)-doped and Tmsup(3+), Hosup(3+)-codoped fluoride glasses

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Relativistic photoionization cross sections for atomic Mg

The photoionization cross sections of the ground level (3s(2) S-1(0)) of atomic Mg have been studied theoretically in the energy region between the Mg+(3s) and Mg+(3p) threshold using the fully relativistic R-matrix method. The positions and widths of resonances have also been obtained and compared with a recent experiment (Wehlitz et al 2007 J. Phys. B 40 2385). Excellent agreement is shown between our theoretical calculations and experimental measurements. In the present calculations, five Rydberg series of doubly excited states have been exhibited, i.e. 3pns P-1, 3pnd P-1, 3pns P-3, 3pnd D-3 and 3pnd P-3, where 3pnd P-3 are confirmed as the fifth series in contrast to the previous theoretical results.

Energy levels, wavefunction compositions and electric dipole transitions in neutral Ca

A configuration-interaction approach, based on the use of B-spline basis sets combined with a model potential including monoelectronic and dielectronic core polarization effects, is employed to calculate term energies and wavefunctions for neutral Ca. Results are reported for singlet and triplet bound states, and some quasi-bound states above the lowest ionization limit, with angular momentum up to L = 4. Comparison with experiment and with other theoretical results shows that this method yields the most accurate energy values for neutral Ca obtained to date. Wavefunction compositions, necessary for labelling the levels, and the effects of semi-empirical polarization potentials on the wavefunctions are discussed, as are some recent identifications of doubly-excited states. It is shown that taking into account dielectronic core polarization changes the energies of the lowest terms in Ca significantly, in general by a few hundred cm(-1), the effect decreasing rapidly for the higher bound states. For Rydberg states with n approximate to 7 the accuracy of the results is often better than a few cm(-1). For series members (or perturbers) with a pronounced 3d character the error can reach 150 cm(-1). The wavefunctions are used to calculate oscillator strengths and lifetimes for a number of terms and these are compared with existing measurements. The agreement is good but points to a need for improved measurements.

Photoionization of Kr near the 4s threshold: I. Experiment and LS coupling theory

Absolute cross sections for the transitions of the Kr atom into the 4s^1 and 4p^4nl states of the Kr^+ ion were measured in the 4s-electron threshold region by photon-induced fluorescence spectroscopy (PIFS). The cross sections for the transitions of the Kr atom into the 4s^1 and 4p^4nl states were also calculated, as well as the 4p^4nln'l' doubly excited states, in the frame of LS-coupling many-body technique. The cross sections of the doubly-excited atomic states were used to illustrate the pronounced contributions of the latter to the photoionization process, evident from the measurements. The comparison of theory and experiment led to conclusions about the origin of the main features observed in the experiment.

On the production of N-2(+) ions at the N 1s edge of the nitrogen molecule

The N+2 ion yield of the N2 molecule has been measured at the N 1s → Rydberg excitations. It displays Fano-type line shapes due to interference between direct outer-valence photoionization and participator decay of the core-excited Rydberg states. The N+2 ion yield is compared with the total intensity of the outer-valence photoelectron lines obtained recently with electron spectroscopy (Kivimäki et al 2012 Phys. Rev. A 86 012516). The increasing difference between the two curves at the higher core-to-Rydberg excitations is most likely due to soft x-ray emission processes that are followed by autoionization. The results also suggest that resonant Auger decay from the core–valence doubly excited states contributes to the N+2 ion yield at the photon energies that are located on both sides of the N 1s ionization limit.

Spin and spatial dynamics in electron-impact scattering off S-wave He using R-matrix with Time-Dependence theory

R-matrix with time-dependence theory is applied to electron-impact ionisation processes for He in the S-wave model. Cross sections for electron-impact excitation, ionisation and ionisation with excitation for impact energies between 25 and 225 eV are in excellent agreement with benchmark cross sections. Ultra-fast dynamics induced by a scattering event is observed through time-dependent signatures associated with autoionisation from doubly excited states. Further insight into dynamics can be obtained through examination of the spin components of the time-dependent wavefunction.

Time-Dependent Density Functional Molecular Orbital and Excited State Calculations on Bis(porphyrinyl)butadiynes in the Monocationic, Neutral, Monoanionic, and Dianionic Oxidation States

We report a theoretical study of the multiple oxidation states (1+, 0, 1−, and 2−) of a meso,meso-linked diporphyrin, namely bis[10,15,20-triphenylporphyrinatozinc(II)-5-yl]butadiyne (4), using Time-Dependent Density Functional Theory (TDDFT). The origin of electronic transitions of singlet excited states is discussed in comparison to experimental spectra for the corresponding oxidation states of the close analogue bis{10,15,20-tris[3‘,5‘-di-tert-butylphenyl]porphyrinatozinc(II)-5-yl}butadiyne (3). The latter were measured in previous work under in situ spectroelectrochemical conditions. Excitation energies and orbital compositions of the excited states were obtained for these large delocalized aromatic radicals, which are unique examples of organic mixed-valence systems. The radical cations and anions of butadiyne-bridged diporphyrins such as 3 display characteristic electronic absorption bands in the near-IR region, which have been successfully predicted with use of these computational methods. The radicals are clearly of the “fully delocalized” or Class III type. The key spectral features of the neutral and dianionic states were also reproduced, although due to the large size of these molecules, quantitative agreement of energies with observations is not as good in the blue end of the visible region. The TDDFT calculations are largely in accord with a previous empirical model for the spectra, which was based simplistically on one-electron transitions among the eight key frontier orbitals of the C4 (1,4-butadiyne) linked diporphyrins.

Excited-state structures of molecules with nearby electronic states

Vibronic coupling among the nearby excited electronic states via the in-plane and the out-of-plane nuclear motions is examined in benzene, pyrazine, formaldehyde and thioformaldehyde. Results reveal that in benzene the structure distorts via the most active nuclear bending (planar) motion while in the other molecules the structures distort through an out-of-plane bending motion in their respective lowest excited states.

Direct Observation of Thermal Equilibrium of Excited Triplet States of 9,10-Phenanthrenequinone. A Time-Resolved Resonance Raman Study

The photochemistry of aromatic ketones plays a key role in various physicochemical and biological processes, and solvent polarity can be used to tune their triplet state properties. Therefore, a comprehensive analysis of the conformational structure and the solvent polarity induced energy level reordering of the two lowest triplet states of 9,10-phenanthrenequinone (PQ) was carried out using nanosecond-time-resolved absorption (ns-TRA), time-resolved resonance Raman (TR3) spectroscopy, and time dependent-density functional theory (TD-DFT) studies. The ns-TRA of PQ in acetonitrile displays two bands in the visible range, and these two bands decay with similar lifetime at least at longer time scales (mu s). Interestingly, TR3 spectra of these two bands indicate that the kinetics are different at shorter time scales (ns), while at longer time scales they followed the kinetics of ns-TRA spectra. Therefore, we report a real-time observation of the thermal equilibrium between the two lowest triplet excited states of PQ assigned to n pi* and pi pi* of which the pi pi* triplet state is formed first through intersystem crossing. Despite the fact that these two states are energetically close and have a similar conformational structure supported by TD-DFT studies, the slow internal conversion (similar to 2 ns) between the T-2(1(3)n pi*) and T-1(1(3)pi pi*) triplet states indicates a barrier. Insights from the singlet excited states of PQ in protic solvents J. Chem. Phys. 2015, 142, 24305] suggest that the lowest n pi* and pi pi* triplet states should undergo hydrogen bond weakening and strengthening, respectively, relative to the ground state, and these mechanisms are substantiated by TD-DFT calculations. We also hypothesize that the different hydrogen bonding mechanisms exhibited by the two lowest singlet and triplet excited states of PQ could influence its ISC mechanism.

TIME-RESOLVED RESONANCE RAMAN-SPECTROSCOPY OF EXCITED SINGLET AND TRIPLET-STATES OF FREE-BASE MESO-TETRAPHENYLPORPHYRIN

Two-color time-resolved resonance Raman spectroscopy has been used to probe the lowest excited singlet (S1) and triplet (T1) states of free-base meso-tetraphenylporphyrin and meso-tetrakis(4-sulphonatophenyl)porphyrin in solution at room temperature. The spectra were recorded using 532-nm excitation pulses and time-delayed probe pulses (DELTAT = 0-30 ns, 447 and 460 nm) near lambda(max) of the S1 and T1 states. Significant shifts in frequency of the porphyrin core vibrations were observed upon excitation to either the S1 or T1 state. Several of the strongest polarized bands in the spectra of both excited states, including nu1, nu2, nu4, nu6, and phi4, are assigned, and the information they give on the differences in electron distribution in the ground, S1, and T1 states is discussed.

A multiconfigurational time-dependent Hartree-Fock method for excited electronic states. I. General formalism and application to open-shell states

The solution of the time-dependent Schrodinger equation for systems of interacting electrons is generally a prohibitive task, for which approximate methods are necessary. Popular approaches, such as the time-dependent Hartree-Fock (TDHF) approximation and time-dependent density functional theory (TDDFT), are essentially single-configurational schemes. TDHF is by construction incapable of fully accounting for the excited character of the electronic states involved in many physical processes of interest; TDDFT, although exact in principle, is limited by the currently available exchange-correlation functionals. On the other hand, multiconfigurational methods, such as the multiconfigurational time-dependent Hartree-Fock (MCTDHF) approach, provide an accurate description of the excited states and can be systematically improved. However, the computational cost becomes prohibitive as the number of degrees of freedom increases, and thus, at present, the MCTDHF method is only practical for few-electron systems. In this work, we propose an alternative approach which effectively establishes a compromise between efficiency and accuracy, by retaining the smallest possible number of configurations that catches the essential features of the electronic wavefunction. Based on a time-dependent variational principle, we derive the MCTDHF working equation for a multiconfigurational expansion with fixed coefficients and specialise to the case of general open-shell states, which are relevant for many physical processes of interest. (C) 2011 American Institute of Physics. [doi: 10.1063/1.3600397]

A multiconfigurational time-dependent Hartree-Fock method for excited electronic states. II. Coulomb interaction effects in single conjugated polymer chains

Conjugated polymers have attracted considerable attention in the last few decades due to their potential for optoelectronic applications. A key step that needs optimisation is charge carrier separation following photoexcitation. To understand better the dynamics of the exciton prior to charge separation, we have performed simulations of the formation and dynamics of localised excitations in single conjugated polymer strands. We use a nonadiabatic molecular dynamics method which allows for the coupled evolution of the nuclear degrees of freedom and of multiconfigurational electronic wavefunctions. We show the relaxation of electron-hole pairs to form excitons and oppositely charged polaron pairs and discuss the modifications to the relaxation process predicted by the inclusion of the Coulomb interaction between the carriers. The issue of charge photogeneration in conjugated polymers in dilute solution is also addressed. (C) 2011 American Institute of Physics. [doi: 10.1063/1.3600404]

Spectroscopy of highly excited vibrational states of HCN in its ground electronic state

An experimental technique based on a scheme of vibrationally mediated photodissociation has been developed and applied to the spectroscopic study of highly excited vibrational states in HCN, with energies between 29 000 and 30 000 cm(-1). The technique consists of four sequential steps: in the first one, a high power laser is used to vibrationally excite the sample to an intermediate state, typically (0,0,4), the nu(3) mode being approximately equivalent to the C-H stretching vibration. Then a second laser is used to search for transitions between this intermediate state and highly vibrationally excited states. When one of these transitions is found, HCN molecules are transferred to a highly excited vibrational state. Third, a ultraviolet laser photodissociates the highly excited molecules to produce H and CN radicals in its A (2)Pi electronic state. Finally, a fourth laser (probe) detects the presence of the CN(A) photofragments by means of an A-->B-->X laser induced fluorescence scheme. The spectra obtained with this technique, consisting of several rotationally resolved vibrational bands, have been analyzed. The positions and rotational parameters of the states observed are presented and compared with the results of a state-of-the-art variational calculation. (C) 2004 American Institute of Physics.