Single Excited State Research Articles

Calculation of third-order signals via driven Schrödinger equations: General results and application to electronic 2D photon echo spectroscopy

We present the wavefunction (WF) version of the equation-of-motion phase-matching approach (EOM-PMA) for the calculation of four-wave-mixing (4WM) optical signals. For the material system, we consider a general electronic-vibrational Hamiltonian, comprising the electronic ground state, a manifold of singly-excited electronic states, and a manifold of doubly-excited electronic states. We show that the calculation of the third-order polarization for particular values of the pulse delay times and in a specific phase-matching direction requires 6 independent WF propagations within the rotating wave approximation. For material systems without optical transitions to doubly-excited electronic states, the number of WF propagations is reduced to 5. The WF EOM-PMA automatically accounts for pulse-overlap effects and allows the efficient numerical calculation of 4WM signals for vibronically coupled multimode material systems. The application of the method is illustrated for model systems with strong electron-vibrational and electronic inter-state couplings.

Динамічні електричні стани неоднорідних популяцій іонних каналів у мембранах збудливих клітин

In computer models, we studied instantaneous (time-varying) current-voltage relationships (iIVs) of populations of ion channels characteristic of the membrane of different type excitable cells, of which the responses to electrical stimuli essentially differ: giant squid axon (Hodgkin-Huxley model), cardiomyocyte, dendrites of CA3 hippocampal pyramidal neurons and Purkinje neurons of the cerebellum. The membrane potential was stepped from the rest level to a certain depolarization test level that was clamped for a certain time, and the total current was measured at different moments after the step onset. For each iIV zero-current points (potentials) were determined. A set of such points, which were situated on the limb of iIV positive slop and corresponded to the state of high membrane depolarization (excitation state, upstate) at different time moments, were used to characterize the dynamics of the excitation state in time. With these indicators the axon membrane was characterized by a single excitation state that rapidly occurred (0.25 ms) and was short-lasting (decayed from -45 to 40 mV during life-time of 5.5 ms). There were two such states of the membrane of cardiomyocyte. The first one was early, rapidly occurring and short-living (rapidly relaxing). It occurred shortly after the depolarization start and lasted for 14.5 ms. The second one was late, slowly rising and long-lasting (occurred with a 7.5-ms delay, increased from 11 to 46 mV in 39 ms and then relaxed lasting for 623 ms in total). The dendritic membrane ofCA3 neurons had one long-lasting excitation state that occurred shortly after the depolarization shift, first rapidly relaxed during 3 ms from initial 30 mV level to -10 mV and then slowly, in 80 ms, stabilized at the level of -20 mV. In the Purkinje neuron membrane two short-lasting and one very long-lasting excitation states were revealed. The first state of very high (>100 mV) depolarization relaxed to 4 mV in 0.8 ms. Shortly before its vanishing, at 0.7 ms, the second short-lasting state emerged, which relaxed in 1 ms from -22 mV to -48 mV. At 1.8 ms a new excitation state emerged, which after a transient relaxation stabilized at -29.65 mV starting from 88 ms. Thus, iIVs allowed disclosing a fine organization of the states of electrical excitation of the membrane and revealing, in populations of ion channels of different content, existence of different number of the mentioned states, which differ from each other in occurrence time and life-time.

Dynamics of Solvent-Mediated Electron Localization in Electronically Excited Hexacyanoferrate(III)

We have used polarization-resolved UV pump-mid-IR probe spectroscopy to investigate the dynamics of electron hole localization for excited-state ligand-to-metal charge-transfer (LMCT) excitation in Fe(CN)(6)(3-). The initially generated LMCT excited state has a single CN-stretch absorption band with no anisotropy. This provides strong evidence that this initial excited state preserves the octahedral symmetry of the electronic ground state by delocalizing the ligand hole in the LMCT excited state on all six cyanide ligands. This delocalized LMCT excited state decays to a second excited state with two CN-stretch absorption bands. We attribute both peaks to a single excited state because the formation time for both peaks matches the decay time for the delocalized LMCT excited state. The presence of two CN-stretch absorption bands demonstrates that this secondary excited state has lower symmetry. This observation, in conjunction with the solvent-dependent time constant for the formation of the secondary excited state, leads us to conclude that the secondary excited state corresponds to a LMCT state with a localized ligand hole.

Progress in Time-Dependent Density-Functional Theory

The classic density-functional theory (DFT) formalism introduced by Hohenberg, Kohn, and Sham in the mid-1960s is based on the idea that the complicated N-electron wave function can be replaced with the mathematically simpler 1-electron charge density in electronic structure calculations of the ground stationary state. As such, ordinary DFT cannot treat time-dependent (TD) problems nor describe excited electronic states. In 1984, Runge and Gross proved a theorem making TD-DFT formally exact. Information about electronic excited states may be obtained from this theory through the linear response (LR) theory formalism. Beginning in the mid-1990s, LR-TD-DFT became increasingly popular for calculating absorption and other spectra of medium- and large-sized molecules. Its ease of use and relatively good accuracy has now brought LR-TD-DFT to the forefront for this type of application. As the number and the diversity of applications of TD-DFT have grown, so too has our understanding of the strengths and weaknesses of the approximate functionals commonly used for TD-DFT. The objective of this article is to continue where a previous review of TD-DFT in Volume 55 of the Annual Review of Physical Chemistry left off and highlight some of the problems and solutions from the point of view of applied physical chemistry. Because doubly-excited states have a particularly important role to play in bond dissociation and formation in both thermal and photochemistry, particular emphasis is placed on the problem of going beyond or around the TD-DFT adiabatic approximation, which limits TD-DFT calculations to nominally singly-excited states.

A general route to make non-conjugated linear polymers luminescent

Photoluminescent polymer dots (PDs) were prepared by a moderate hydrothermal treatment of poly(vinyl alcohol) (PVA). A single excited state was established in the PL mechanism by ultrafast spectroscopy. Moreover, the applied method be used to prepare fluorescent polymer dots from other non-conjugated polymers, and shows general universality.

Preparation of subradiant states using local qubit control in circuit QED

Transitions between quantum states by photon absorption or emission are intimately related to the symmetries of the system which lead to selection rules and the formation of dark states. In a circuit quantum electrodynamics setup, in which two resonant superconducting qubits are coupled through an on-chip cavity and driven via the common cavity field, one single-excitation state remains dark. Here, we demonstrate that this dark state can be excited using local phase control of individual qubit drives to change the symmetry of the excitation field. We observe that the dark state decay via spontaneous emission into the cavity is suppressed, a characteristic signature of subradiance. This local control technique could be used to prepare and study highly correlated quantum states of cavity-coupled qubits.

Strong-field effects in Rabi oscillations between a single state and a superposition of states

Rabi oscillations of quantum population are known to occur in two-level systems driven by spectrally narrow laser fields. In this work we study Rabi oscillations induced by shaped broadband femtosecond laser pulses. Due to the broad spectral width of the driving field, the oscillations are initiated between a ground state and a coherent superposition of excited states, or a "wavepacket", rather than a single excited state. Our experiments reveal an intricate dependence of the wavepacket phase on the intensity of laser field. We confirm numerically that the effect is associated with the strong-field nature of the interaction, and provide a qualitative picture by invoking a simple theoretical model.

The effects of quantum interference between direct and resonant photorecombination of H-like Ar17+ ions

The multiconfiguration Dirac–Fock method has been used to study interference effects between direct and resonant photorecombination (i.e. radiative and dielectronic recombination) from the ground state 1s2S1/2 of H-like Ar17+ ions via doubly excited 2s21S0, 2s2p 3P0, 1, 2, 1P1 and 2p23P0, 1, 2, 1D2, 1S0 resonances of He-like Ar16+ ions combined with the Fano parameterization technique. In order to produce total photorecombination spectra, it is necessary to calculate the energy levels of the 1s of H-like Ar17+ ions, 1s2, 1s2l and 2l2l′ (l,l′ =0, 1) of He-like Ar16+ ions, the radiative and nonradiative properties of the doubly excited states of He-like Ar16+ ions, and the direct and resonant photorecombination cross sections from the 1s state of H-like Ar17+ ions into the ground state 1s2 and the single excited states of 1s2l (l=0, 1) of He-like Ar16+ ions, in detail. Based on good agreement between the present calculations and other available experimental and theoretical results, the interference profile determined by the so-called Fano parameters q and ρ2 is also shown. The results indicate that interference effects are remarkable at some resonances, especially near the doubly excited 2s2p 1P1 state of He-like Ar16+ ions, and strongly influence the intensity of the wing of the nonresonant background in the photorecombination of H-like Ar17+ ions through comparison between the final Fano and total radiative recombination to dielectronic recombination spectra.

Interelectronic angles: Rounding out a geometric picture of the helium atom

Multi-configuration Hartree–Fock expectation values of the inner 〈r<〉 and outer 〈r>〉 electron radii and the interelectronic angle 〈θ12〉 are reported for the ground and 54 singly-excited states of helium. These mean values can be visualized as defining a nearly right-angled triangle. Expressions connecting these expectation values with the mean value of the interelectronic distance 〈r12〉 are found to be quite accurate. Some observations are made on singlet–triplet differences of 〈θ12〉.

Radiative rates and electron impact excitation rate coefficients for Ne-like selenium, Se XXV

In this article we report calculations of energy levels, radiative rates, electron impact collision strengths, and effective collision strengths for transitions among the 241 fine-structure levels arising from 2 l 8 and 2 l 7 n ′ l ′ ( n ′ ≤ 6 and l ′ ≤ n ′ − 1 ) configurations of Ne-like Se XXV using the Flexible Atomic Code. Energy levels and radiative rates are calculated within the relativistic configuration-interaction method. Direct excitation collision strengths are calculated using the relativistic distorted-wave approximation and high-energy collision strengths are obtained in the relativistic plane-wave approximation. Resonance contributions through the relevant Na-like doubly-excited configurations 2 l 7 n ′ l ′ n ″ l ″ ( 3 ≤ n ′ ≤ 7 , l ′ ≤ n ′ − 1 , n ′ ≤ n ″ ≤ 50 , and l ″ ≤ 8 ) are explicitly taken into account via the independent-process and isolated-resonance approximation using distorted waves. Resonant stabilizing transitions and possibly important radiative decays from the resonances toward low-lying autoionizing levels are considered. In addition, the resonance contributions from Na-like 2 l 6 3 l ′ 3 l ″ n ‴ l ‴ ( n ‴ = 3 − 6 ) configurations are included and found to be predominant for many transitions among the singly-excited states in Ne-like Se XXV. We present the radiative rates, oscillator strengths, and line strengths for all electric dipole, magnetic dipole, electric quadrupole, magnetic quadrupole, electric octopole, and magnetic octopole transitions among the 241 levels. The effective collision strengths are reported for all 28920 transitions among the 241 levels over a wide temperature range up to 10 keV. To assess the reliability and accuracy of the present collisional data, we have performed a 27-state close-coupling calculation, employing the Dirac R-matrix theory. The results from the close-coupling calculation and the independent-process calculation for the identical target states are found to be in good agreement.

Characterizing the Deformational Isomers of Bimetallic Ir2(dimen)42+ (dimen = 1,8-diisocyano-p-menthane) with Vibrational Wavepacket Dynamics

We studied the Ir(2)(dimen)(4)(2+) complex with ultrafast transient absorption spectroscopy and density functional theory and concluded that it possesses two singlet ground state isomers in room temperature solution. The molecule can adopt either a paddle wheel or a propeller conformation in solution, where the paddle wheel structure possesses a metal-metal bond of 4.4 Å and a dihedral angle between the quasi-C(4v) planes of 0° and the propeller structure has a metal-metal bond of 3.6 Å and a dihedral angle of 17° when crystallized. Each conformation has a distinct absorption in the visible attributed to a (1)(dσ(z)* → pσ(z)) excitation, with the long eclipsed structure absorbing at 475 nm and the short twisted structure absorbing at 585 nm. We independently pumped at each of these visible transitions to form vibrational wavepackets on the ground and excited state potential energy surfaces, which modulated the ground state bleach and stimulated emission signals, respectively. We found that the ground state wavepacket oscillates with a frequency of 48 cm(-1) when pumping the red peak and 11 cm(-1) when pumping the blue peak. We assign these frequencies to the Ir-Ir symmetric stretch, with the variation in frequency reflecting the variation in metal-metal bond strength in support of our assignment of the blue peak to the longer Ir-Ir bond length conformer and the red peak to the shorter Ir-Ir bond length conformer. When pumping the red peak, we found two modes with frequencies of 80 and 119 cm(-1) in the stimulated emission and only one mode at 75 cm(-1) when pumping the blue peak. We assign the 75-80 cm(-1) frequency to the Ir-Ir stretch and the 119 cm(-1) vibration to the dihedral angle twist in the excited state. The variation in the excited state dynamics does not result from the excitation of different electronic states, but rather from excitation to different Franck-Condon regions of the same electronic excited state potential energy surface. This occurs because of the large difference in ground state molecular structure. DFT calculations support the existence of a single electronic excited state being accessed from two distinct structural isomers with conformations similar to those observed with X-ray crystallography.

Quantum communication and state transfer in spin chains

We investigate the time evolution of a single spin excitation state in certain linear spin chains, as a model for quantum communication. We consider first the simplest possible spin chain, where the spin chain data (the nearest neighbour interaction strengths and the magnetic field strengths) are constant throughout the chain. The time evolution of a single spin state is determined, and this time evolution is illustrated by means of an animation. Some years ago it was discovered that when the spin chain data are of a special form so-called perfect state transfer takes place. These special spin chain data can be linked to the Jacobi matrix entries of Krawtchouk polynomials or dual Hahn polynomials. We discuss here the case related to Krawtchouk polynomials, and illustrate the possibility of perfect state transfer by an animation showing the time evolution of the spin chain from an initial single spin state. Very recently, these ideas were extended to discrete orthogonal polynomials of q-hypergeometric type. Here, a remarkable result is a new analytic model where perfect state transfer is achieved: this is when the spin chain data are related to the Jacobi matrix of q-Krawtchouk polynomials. This case is discussed here, and again illustrated by means of an animation.

Correlated n 1,3 S states for coulomb three-body systems

n1,3S (n = 1 − 4) states for atomic three-body systems are studied with the Angular Correlated Configuration Interaction method. A recently proposed angularly correlated basis set is used to construct, simultaneously and with a single diagonalization, ground and excited states wave functions which: (i) satisfy exactly Kato cusp conditions at the two-body coalescence points; (ii) involve only linear parameters; (iii) show a fast convergency rate for the energy; and (iv) form an orthogonal set. The efficiency of the method is illustrated by the study a variety of three-body atomic systems [mmm] with two negatively charged light particles, with diverse masses m and m, and a heavy positively charged nucleus m. The calculated ground 11S and excited n1,3S (n = 2 − 4) state energies are compared with those given in the literature, when available. © 2011 Wiley Periodicals, Inc. Int J Quantum Chem, 2011

Inclusion complex formation of sanguinarinealkaloid with cucurbit[7]uril: inhibition of nucleophilic attack and photooxidation

The inclusion of sanguinarine, a biologically active natural benzophenanthridine alkaloid, in cucurbit[7]uril (CB7) was studied by NMR and ground-state absorption spectroscopy, as well as steady-state and time-resolved fluorescence measurements in aqueous solution. The iminium form of sanguinarine (SA(+)) produces very stable 1 : 1 inclusion complex with CB7 (K = 1.0 × 10(6) M(-1)), whereas the equilibrium constant for the binding of the second CB7 is about 3 orders of magnitude smaller. Marked fluorescence quantum yield and fluorescence lifetime enhancements are found upon encapsulation of SA(+) due to the deceleration of the radiationless deactivation from the single-excited state, but the fluorescent properties of 1 : 1 and 1 : 2 complexes barely differ. The equilibrium between the iminium and alkanolamine forms is shifted 3.69 pK unit upon addition of CB7 as a consequence of the preferential encapsulation of the iminium form and the protection of the 6 position of sanguinarine against the nucleophilic attack by hydroxide anion. On the basis of thermodynamic cycle, about 225 M(-1) is estimated for the equilibrium constant of the complexation between the alkanolamine form of sanguinarine (SAOH) and CB7. The confinement in the CB7 macrocycle can be used to impede the nucleophilic addition of OH(-) to SA(+) and to hinder the photooxidation of SAOH.

The efficiency limit of solar cells with molecular absorbers: A master equation approach

A master equation approach to the limiting efficiencies of solar cells with molecular absorbers is presented. A number of model absorbers are analyzed that possess identical absorption spectra, but with differing numbers of electronic excited states. The Shockley–Queisser limit is reproduced for a molecule resembling a semiconductor, with an infinity of electronic levels in the excited state manifold. However, when only a few electronic states contribute to the absorption spectrum, the limiting efficiency is reduced. In the extreme case, where only a single electronic excited state participates in the absorption spectrum, the efficiency limit is 28.9%. At high energy thresholds, built-in thermal up-conversion results in solar cells with efficiencies exceeding the Shockley–Queisser curve. The analysis is applicable to any single threshold photovoltaic device, including those based on semiconductor, polymer, and small molecule absorbers.

Sturmian expansions for two-electron atomic systems: Singly and doubly excited states

We present a configuration interaction (CI) method based on the Sturmian expansion for bound states of a two-electron atomic system. These Sturmian functions are solutions of one-electron quantum mechanical problems, where the eigenvalue is the magnitude of a short-range potential. Also, they fulfill the long-range boundary conditions of Coulomb potentials. We choose to expand the Sturmians of the CI basis using ${L}^{2}$ Laguerre-type functions. We compute ground and single-excited states energies for He and ${\mathrm{H}}^{\ensuremath{-}}$. Moreover, we are able to obtain energies and widths of double excited states of He, using a Sturmian basis with outgoing boundary conditions. In all cases, our ansatz outperforms other CI calculations, for similar basis size.

Three-dimensional sliced fluorescence imaging in bulbs

To study dynamic behaviors of molecular photodissociation processes and photoinitiated inelastic and reactive collisions in a bulb environment, a three-dimensional sliced fluorescence imaging method has been developed. This experimental method combines the sliced fluorescence imaging techniques and a double resonance spectroscopic detection scheme to acquire the central slice of state-selected Newton spheres of scattering products. To illustrate the essence and simplicity of the present method, experimental images of state-selected CN photofragments from the ICN photodissociation are presented. For other chemically significant product species with a single fluorescent excited state, an infrared-optical double resonance detection scheme warrants the present technique a general method in the study of dynamic processes in bulbs.

Quantum state transfer in spin chains with q-deformed interaction terms

We study the time evolution of a single spin excitation state in certain linear spin chains, as a model for quantum communication. Some years ago it was discovered that when the spin chain data (the nearest-neighbour interaction strengths and the magnetic field strengths) are related to the Jacobi matrix entries of Krawtchouk polynomials or dual Hahn polynomials the so-called perfect state transfer takes place. The extension of these ideas to other types of discrete orthogonal polynomials did not lead to new models with perfect state transfer, but did allow more insight in the general computation of the correlation function. In this paper, we extend the study to discrete orthogonal polynomials of q-hypergeometric type. A remarkable result is a new analytic model where perfect state transfer is achieved: this is when the spin chain data are related to the Jacobi matrix of q-Krawtchouk polynomials. The other cases studied here (affine q-Krawtchouk polynomials, quantum q-Krawtchouk polynomials, dual q-Krawtchouk polynomials, q-Hahn polynomials, dual q-Hahn polynomials and q-Racah polynomials) do not give rise to models with perfect state transfer. However, the computation of the correlation function itself is quite interesting, leading to advanced q-series manipulations.

Electron-pair radial sum and difference moments in atoms

Discussed are physical implications of two sets of moments 〈 s n 〉 and 〈 t n 〉 associated with the electron-pair radial sum S ( s ) and difference T ( t ) densities. The first moments 〈 s 〉 and 〈 | t | 〉 are equivalent to the sum 〈 r > 〉 + 〈 r < 〉 and the difference 〈 r > 〉 - 〈 r < 〉 of the inner 〈 r < 〉 and outer 〈 r > 〉 radii, respectively. The variances σ s 2 = 〈 s 2 〉 - 〈 s 〉 2 and σ t 2 = 〈 t 2 〉 - 〈 t 〉 2 of S ( s ) and T ( t ) are found to be connected with the statistical radial correlation coefficient τ [ r ] in a straightforward manner. For the 53 atoms He through Xe in their ground states and for some singly-excited states of the He atom, the first and second moments as well as the radial correlation coefficient are systematically studied at the Hartree–Fock limit level. The effect of electron correlations is also examined for the He atom and its isoelectronic ions.

Quantum communication through a spin chain with interaction determined by a Jacobi matrix

We obtain the time-dependent correlation function describing the evolution of a single spin excitation state in a linear spin chain with isotropic nearest-neighbour XY coupling, where the Hamiltonian is related to the Jacobi matrix of a set of orthogonal polynomials. For the Krawtchouk polynomial case, an arbitrary element of the correlation function is expressed in a simple closed form. Its asymptotic limit corresponds to the Jacobi matrix of the Charlier polynomial, and may be understood as a unitary evolution resulting from a Heisenberg group element. Correlation functions for Hamiltonians corresponding to Jacobi matrices for the Hahn, dual Hahn and Racah polynomials are also studied. For the Hahn polynomials we obtain the general correlation function, some of its special cases and the limit related to the Meixner polynomials, where the su(1, 1) algebra describes the underlying symmetry. For the cases of dual Hahn and Racah polynomials, the general expressions of the correlation functions contain summations which are not of hypergeometric type. Simplifications, however, occur in special cases.