Monte Carlo determination of the oscillator strength and excited state lifetime for the Li 22S → 22P transition

A recently developed Monte Carlo method is used to compute the 2²S → 2²P transition dipole moment of Li. This approach employs a guided Metropolis random walk with quantum Monte Carlo “side” walks to sample the required probability distributions. The transition dipole moment is employed to obtain the oscillator strength and excited-state lifetime. Our most accurately converged calculations yield an oscillator strength of 0.742(7) and excited-state lifetime of 27.41(35) ns. These results are in excellent agreement with precise experimental measurements of 0.742(1) and 27.29(4) ns, respectively. In addition, single-state expectation values are computed for both states. Monte Carlo parameters, such as the time step size and the convergence time, are varied in order to study their effect on computed results.     

A nondiagonal quasidegenerate fourth-order perturbation theory

A canonical quasidegenerate Rayleigh-Schrödinger perturbation theory, correct through fourth order in the energy, is explored for a block-diagonal unperturbed Hamiltonian. The theory is developed completely within a Lie Algebra in Hilbert space. Explicit equations forn-particle transition elements in terms of solutions of simultaneous linear equations are presented. A two-dimensional anisotropic anharmonic oscillator is used to provide numerical results. The perturbation theory is shown to be stable under small separation of model and complement spaces. An iterative variant of the fourth order perturbation theory is introduced; the iterative variant is related to the non-iterative one in much the same way as nondegenerate coupled cluster theories are related to nondegenerate perturbation theory. The quasidegenerate coupled cluster theory appears to be stable in the presence of multiple intruder states.     

Dipole moments,transition moments,oscillator strengths,radiative lifetimes,and overtone intensities for CH and CH+ as computed by quasi-degenerate many-body perturbation theory

The correlated, size-consistent, ab initio effective valence-shell dipole operator (μ^v) method is used to calculate dipole moments and transition dipole moments of the CH molecule and transition dipole moments of the CH⁺ ion as a function of internuclear distance. The dipole and transition dipole moments computed here compare well with those of other accurate ab initio methods. The transition dipole moments are then used to calculate oscillator strengths and radiative lifetimes for the A → X and B → A transitions of the CH⁺ ion and the A → X transition of the CH molecule. Comparisons are made with the best available theoretical and experimental lifetimes. Finally, the CH ground-state dipole moment function is used to evaluate overtone intensities and to examine simple models of the CH overtone intensities in polyatomic molecules.     

Allowed transitions in silicon isoelectronic ions

Dipole‐allowed transitions have been studied for the first few members of the Si isoelectronic sequence. Transition energies, oscillator strengths, transition probabilities and quantum defect values have been estimated for the low‐ and high‐lying excited states of s and d symmetries up to the principal quantum number n=7 for these 3p open shell ions from P⁺ to Cr¹⁰⁺. Time‐dependent coupled Hartree–Fock (TDCHF) theory has been utilized to calculate such transition properties. Most of the results for transition energies, oscillator strengths, and transition probabilities for higher excited states are new. The transition energies for low‐lying excited states agree well with experimental data wherever available. © 2001 John Wiley & Sons, Inc. Int J Quantum Chem, 2001     

Comparisons of the RPA,SCRPA, Tamm–Dancoff,and full CI methods by analysis of their transition density matrices,oscillator strengths,and energy moments of oscillator strengths for the electric dipole transitions from the ground state of the B+ ion (frozen K-shell model)

The RPA, SCRPA , Tamm–Dancoff, and full CI methods are compared by analyzing their transition density matrices, oscillator strengths, and energy moments of oscillator strengths for the ¹S_ground – ¹P_odd transitions of the 4-electron B⁺ ion in the frozen K-shell approximation. It is found that the RPA gives transition density matrices that are aligned nearly as well as possible along those of the full CI , but have vector lengths that are significantly too long. The corresponding transition energies are significantly too small. These errors compensate to give oscillator strengths for the dominant transition that, for all forms of the oscillator strength, are within 1.6% of the corresponding full CI values. The SCRPA gives better transition density matrices than the RPA , but poorer oscillator strengths. The Tamm-Dancoff approximation gives very good values for the mixed length-velocity form of the oscillator strength. The RPA gives a static electric dipole polarizability that is nearly 20% larger than that of the full CI . The SCRPA gives a value 15% smaller than—and the Tamm-Dancoff approximation gives a mixed length-velocity value that is 11% larger than—that of the full CI . Other energy moments of oscillator strengths are also reported. Certain other approximations related to the RPA and the SCRPA are reported as well.     

Effective utilization of off-diagonal hypervirial relations considering diagonal hypervirial relation: Harmonic oscillator case

The effective utilization of hypervirial relations is scrutinized to improve the approximate excited-state functions in the harmonic oscillator system. A new method is presented which simultaneously employs the off-diagonal hypervirial relations with the diagonal hypervirial relation. In order to use these relations effectively, the following points are pointed out: (i) the presented method is useful to get better reasonable results for the excitation energies and the state functions; (ii) the ground state given must satisfy the virial theorem; (iii) in the hypervirial operator used here as x^m, the smaller integers of m's present better results; and (iv) the employment of the comparatively small number of trial basis functions of the type exp (?γ|x|) is sufficient for reproducing the exact excited state. Especially among them, condition (ii) plays an important role. Applying all the proposals to the first and the second excited states, one gets a highly improved excitation energy, state function, and other physical quantities (e.g., transition moment and oscillator strength). The presented method is also found to be more effective than the employment of only the off-diagonal hypervirial relations or the method of the scaling operation.     

On the linearly driven parametric oscillator

The time-dependent Schrouml;dinger equation for the oscillator H = α(t)p² + β(t)x² + γ(t)x is exactly solved. The time evolution operator is easily obtained by means of an operator algebra and the quantum-mechanical equations of motion. The problem is reduced to solving the classical equations of motion. The method is shown to apply to multidimensional oscillators.     

Triplet-triplet transitions in zinc-like ions

Theoretical oscillator strengths are reported for the lines of the 4s4p ³ P-4s4d ³ D transition in some ions of the zinc isoelectronic sequence, which are of interest in fusion plasma research. The calculations have been performed with the relativistic quantum defect orbital (RQDO) method. A core-polarization to the dipole transitions moment has also been included in the formalism. A comparative study with other theoretical results and the scarce experimental measurements has also been carried out. Systematic trends of individual oscillator strengths along the isoelectronic sequence are also shown in a graphical form.     

Electric field induced transition in the charge-transfer exciton band of anthracene-PMDA

A second, electric field induced zero-phonon transition has been observed in single crystals of anthracene-PMDA (pyromellitic acid dianhydride). The second transition is 10 cm^?1 above the lowest zero-phonon absorption; its intensity increases with increasing field strength under conservation of oscillator strength for the two transitions. The measured splitting of 10 cm^?1 is interpreted in terms of the charge-transfer exciton bandwidth. The measured field-shift gives an approximate value Δμ for the change in dipole moment which characterizes the creation of an ionic charge-transfer state.     

Toward assessment of density functionals for vibronic coupling in two‐photon absorption: A case study of 4‐nitroaniline

In this study, we predict vibronic two‐photon absorption (TPA) spectra for 4‐nitroaniline in vacuo. The simulations are performed using density functional theory and the approximate second‐order coupled‐cluster singles and doubles model CC2. Thereby we also demonstrate the possibility of simulations of vibronic TPA spectra with ab initio wavefunction methods that include electron correlation for medium‐sized systems. A special focus is put on the geometric derivatives of the second‐order transition moment and the dipole moment difference between the charge‐transfer excited state and the ground state. The results of CC2 calculations bring new insight into the vibronic coupling mechanism in TPA spectra of 4‐nitroniline and demonstrate that the mixed term is quite large and that it also exhibits a negative interference with the Franck‐Condon contribution. © 2015 Wiley Periodicals, Inc.     

Analytic energy derivatives for the equation-of-motion coupled-cluster method: Algebraic expressions,implementation and application to theS 1 state of HFCO

Summary The general theory of analytic derivatives for the equation-of-motion coupled cluster (EOM-CC) method is reviewed. Special attention is paid to the EOM-CC singles and doubles (EOM-CCSD) approximation, which has the same computational scaling properties as the coupled-cluster singles doubles (CCSD) ground state method and is therefore applicable to a wide range of molecular systems. The detailed spin orbital equations that must be solved in EOM-CCSD gradient calculations are presented for the first time, and some guidelines are discussed regarding their computational implementation. Finally, use of the EOM-CCSD gradient method is illustrated by determining the structure, dipole moment components, harmonic frequencies and infrared intensities of formyl fluoride (HFCO) in its singlet excited (n, *) state.     

The radiative lifetime of the A1II state of BH

Second-order polarization propagator calculations of the X¹Σ⁺ → A¹II transition moment as well as the radiative lifetime of the A¹II state of BH are reported. The calculated vibrational lifetimes are τ(v′ = 0) = 121 ns, τ(v′ = 1) = 129 ns, and τ(v′ = 2) = 137 ns. The τ(v′ = 0 lifetime agrees with the most recent experiment of τ(v′ = 0) = 125 ± 5 ns. We show that the electronic oscillator strength computed at the ground state equilibrium is rather different from the band absorption oscillator strength f₀₀, which demonstrates that theoretical electronic oscillator strengths should not be expected to agree with experimentally determined band oscillator strengths.     

Conformation-transitional rate in protein folding

Based on the conformation dynamics of macromolecules, the rate of conformational transition is deduced from the nonadiabaticity operator method which can be used to explain the time scale of milliseconds for protein folding. It is proved that (1) the dependence of the transition rate on inertial moment I of the atomic group obeys the I^?2.5 law; (2) its dependence on numbers n of torsional angles participating in the transition obeys the n^1.5 law; and (3) the temperature dependence of the transitional rate shows an abnormal character in the high- temperature region. © 1995 John Wiley & Sons, Inc.     

Full configuration interaction benchmark calculations for transition moments

Full configuration-interaction (FCI) calculations have been performed for the ã ¹A₁–b¹B₁and ã ¹A₁–(2)¹A₁transitions in CH₂ and for selected dipole and quadrupole transitions in BeO. The FCI transition moments are compared to those obtained from correlation treatments that truncate the n-particle expansion. The state-averaged MCSCF/SOCI and FCI results agree well, even for BeO, where the CASSCF level nonorthogonal transition moment differs from the state-averaged CASSCF transition moment.     

Polarization of fluorescent light from a uniaxially oriented rubber

The polarization of fluorescence from a polymer characterizes two segment orientation functions, f_s⁽²⁾ and f_s⁽⁴⁾. These may be calculated as a function of elongation using the kinetic theory of rubber elasticity. Three cases are considered: (a) the transition moment direction lies parallel to the segment axis and does not change its orientation during the lifetime of the excited state, (b) the transition moment direction lies at an angle γ to the segment axis, and (c) the transition moment changes its orientation during the lifetime of the excited state.     

The Absorption Spectrum of 3B2u-1Ag Transition of Crystalline Anthracene

The absorption spectrum of ³B_2u-¹A_g transition of anthracene is observed in pure crystal at low temperature. The oscillator strength, polarization, and Davydov plittings of this transition are accurately measured. The significance of these data and their relationship with the radiative and radiationless properties of this molecule are discussed.     

Illuminating the origins of two-photon absorption properties in fluorescent protein chromophores

We provide here a structural impact on two-photon absorption cross-section (σ^TPA) for 22 distinct fluorescent protein (FP) chromophores. By employing time-dependent density functional theory, we gain insight into two-photon absorption (TPA) process by investigating relationship between σ^TPA and one-photon electronic transition dipole moment and permanent dipole moment change (Δμ) upon transition. Our results reveal that for the S₁ excited state, σ^TPA is proportional to (Δμ)² in agreement with two-state model of TPA process. On the contrary, the TPA spectroscopy of higher excited states (S _n, n > 1) is much more complex. We do not find a main driving force of large σ^TPA that would be common for investigated chromophores. Instead, it seems that channel interference between one-photon transition dipole moment vectors is responsible for enhancement or diminishment of σ^TPA. Our in vacuo results may serve as a benchmark to investigate a role of chromophore-protein interaction in shaping TPA spectra of FPs.     

Charge exchange in C6+ + H (1s) collisions at low energies

The low‐energy single electron capture cross‐sections by C⁶⁺ from H atoms have been evaluated employing the semiclassical, impact parameter, close‐coupling method based on a molecular expansion augmented with the plane‐wave translation factor. Using the method of Bates and Carson, the exact Born–Oppenheimer eigenfunctions and eigenvalues are calculated. Eight‐state coupled equations are solved to obtain transition probabilities and thereby evaluate capture cross‐sections. Our calculated capture cross‐sections agree well with other theoretical and experimental results. At these energies it is found that the capture into the n = 4 manifold of the C⁵⁺ remains the main contributor to the charge exchange process. © 2003 Wiley Periodicals, Inc. Int J Quantum Chem, 2003     

Theory of phase transition kinetics with growth site impingement. I. Homogeneous nucleation

The nonlinear integral equations governing phase transition kinetics with homogeneous nucleation and growth site impingement are developed and solved to the first order for the two-dimensional case. It is shown that the fractional transformed area at time t is given approximately by a(t) = Kt³/(1 + Kt³). The iteration method used to get the solution is applicable to certain other nonlinear differential and integral equations. It is shown that the theory predicts the total number of growth sites formed, and that the nucleation rate and growth constants can be deduced from this and the gross kinetic data. The extension of the method of three-dimensional growth is indicated.     

Trial introduction of a complex potential function for perturbation that causes quantum mechanical transition in a one‐dimensional harmonic oscillator

Some results of computer simulation of the behavior of a one‐dimensional quantum mechanical oscillator are reported in this article. This harmonic oscillator comprises a particle trapped within a hyperbolic potential V(x) = x². Further, a perturbation potential function V′(x, t) was superposed upon the hyperbolic potential in order to induce a quantum mechanical transition. This perturbation function V′(x, t) is a function of both of space and time variables, and is set to represent a wave packet that is enveloped by a Gaussian bell‐shaped curve. A wave that probably has an appropriate wave number and angular frequency was inputted into the expression for the wave packet. In the initial phase, while the harmonic oscillator was allowed to oscillate almost freely, the wave packet was allowed to approach the harmonic oscillator. In the middle phase, the wave packet passes through the harmonic oscillator, affecting the shape of the quantum mechanical wave that represents the physical state of the system. In the last phase, when the wave packet left the system of the harmonic oscillator, the system settled onto an energetically stable state. The main objective of the simulation was to simulate the instance of a quantum mechanical transition from one eigenstate to another. After several trials, it was found that the perturbation function consisting of a complex function was, at least superficially, able to cause one desired transition, that is, a transition from one eigenstate to another eigenstate. By using such a complex perturbation function, a transition from the first excited state to the ground state was observed to occur. © 2004 Wiley Periodicals, Inc. Int J Quantum Chem, 2004