Moment Matrix Elements Research Articles

Multireference configuration interaction based electronic Floquet states for molecules in an intense radiation field: Theory and application to Li2+

A multireference configuration interaction (CI) method which includes single and double excitations based description of adiabatic Floquet states for the electronic structure of a molecule in an intense laser field is introduced. Using a variant of a recently introduced configuration state function (CSF) based Table-CI methodology, it is shown that the multiple states of several irreducible representations required for a good description of low-lying Floquet states can be obtained using modifications of computational molecular electronic structure techniques. In particular, formulas for all components of the transition dipole moment matrix elements within the CSF-based Table-CI method are derived and presented. Moreover, the flexibility of the recently introduced macroconfiguration description of model and external configuration spaces is shown to lead to multiple potential energy surfaces of sufficiently uniform quality to allow construction of useful Floquet states. The formalism and computer programs developed are demonstrated on Li(2) (+) in a 0.9 x 10(12) W/cm(2) field. In analogy with Na(2) (+), the 1,2 (2)Sigma(g) (+), 1,2 (2)Sigma(u) (+), 1 (2)Pi(g), and 1 (2)Pi(u) states are of relevance, although the pattern of couplings is shown to be more complex. A hitherto unnoticed metastable state, which correlates asymptotically with 2 (2)Sigma(u) (+), is described.

Error analysis of 2-D MoM for MFIE/EFIE/CFIE based on the circular cylinder

We analyze the error in typical moment method scattering solutions for smooth cylindrical geometries and TM-polarized fields. We consider the magnetic field integral equation (MFIE), electric field integral equation (EFIE), and combined field integral equation. To quantify the impact of mesh element size, approximate integration of moment matrix elements, and geometrical discretization error on the accuracy of computed surface currents and scattering amplitudes, we derive error estimates analytically for the circular cylinder. For pulse functions and point testing, current and scattering amplitude errors are generally second order in the mesh element width. The convergence rate worsens to first order if low-order numerical quadrature is used to evaluate moment matrix elements with the EFIE formulation, or if a flat-facet mesh is employed with the MFIE formulation. Third-order convergence is also possible in some special cases. These results for the circular cylinder are empirically compared to computed error values for other smooth scatterer geometries. Convergence rates with respect to mesh refinement agree, but scatterers with regions of high curvature exhibit increased absolute error.

Nucleon properties at finite volume: the [formula omitted]-regime

We study the properties of the nucleon in highly asymmetric volumes where the spatial dimensions are small but the time dimension is large in comparison to the inverse pion mass. To facilitate power-counting at the level of Feynman diagrams, we introduce ε′-power-counting which is a special case of Leutwyler's δ-power-counting. Pion zero-modes enter the ε′-counting perturbatively, in contrast to both the ε- and δ-power-countings, since mq〈qq¯〉V remains large. However, these modes are enhanced over those with non-zero momenta and enter at lower orders in the ε′-expansion than they would in large volume chiral perturbation theory. We discuss an application of ε′-counting by determining the nucleon mass, magnetic moment and axial matrix element at the first non-trivial order in the ε′-expansion.

Understanding Substituent Effects on29Si Chemical Shifts and Bonding in Disilenes. A Quantum Chemical Analysis

The 29Si chemical shift tensors in both symmetrically and unsymmetrically substituted disilenes have been analyzed by quantum chemical calculations. A detailed breakdown of the paramagnetic contributions to nuclear shielding into individual sum-over-states terms allows new insights into the interrelations between bonding and chemical shifts in these unsaturated compounds. While the substituent effects in symmetrically substituted systems may be understood to a large extent from the energy denominators of the perturbation expression, the very different shifts for the two silicon nuclei in unsymmetrically substituted systems are mainly due to the spatial extent and orientation of the occupied and unoccupied molecular orbitals, as sampled by the matrix elements of nuclear magnetic moments at both silicon sites. The unequal shifts may thus be understood and could serve as a diagnostic tool to distinguish between symmetrically and unsymmetrically substituted disilenes. Furthermore, unequal charge transfer and an alternating charge distribution can rationalize unexpectedly larger pyramidalization of the silyl-substituted silicon center in unsymmetrically substituted systems.

Bounds on neutrino magnetic moment tensor from solar neutrinos

Solar neutrinos with nonzero magnetic moments will contribute to the electron scattering rates in the Super-Kamiokande experiment. The magnetic moment scattering events in Super-K can be accommodated in the standard vacuum oscillation or Mikheyev-Smirnov-Wolfenstein solutions by a change of the parameter space of mass square difference and mixing angle, but the shifted neutrino parameters obtained from Super-K will (for some values of neutrino magnetic moments) become incompatible with the fits from SNO, gallium, and chlorine experiments. We compute the upper bounds on the Dirac and Majorana magnetic moments of solar neutrinos by simultaneously fitting all the observed solar neutrino rates. The bounds of the magnetic moment matrix elements are of the order of ${10}^{\ensuremath{-}10}{\ensuremath{\mu}}_{B}.$

Line intensities of the: ν3, 4 ν2, ν1+ ν3, 3 ν1 and 2 ν1+2 ν2 bands of 16O 12C 32S molecule

The line intensities of the ν 3 band of OCS used for atmospheric retrievals, has been measured. The spectra have been recorded with the Reims Fourier transform spectrometer. Other bands of OCS 4ν 2, ν 1+ν 3, 3ν 1 and 2 ν 1+2 ν 2 were recorded to obtain the line intensities. The results are compared to usual databanks (HITRAN or GEISA). From the measured line intensities, it has been possible to estimate the square of the vibrational dipole moment matrix element ( in debye 2) , equal to 0.1313 1, 7.840 9×10 −4, 1.158 1×10 −3, 1.218 3×10 −5, 1.192 3×10 −5 , respectively, for ν 3, 4ν 2, ν 1+ν 3, 3ν 1 and 2 ν 1+2 ν 2.

Direct Investigation of the Validity of Vertical Approximation in the Calculation of Transition Moment Matrix Elements: n → π* Transition in Methyl Formate

The absolute optical oscillator strength for the n → π* transition in methyl formate is calculated, within a procedure that has recently been used by our group to determine the optical oscillator strength of symmetry-forbidden transitions and which consists of expanding the (squared) transition moment along the normal coordinates of vibration. In the present work, we extend its application to a symmetry-allowed transition and discuss the applicability of the vertical approximation. To validate the present results, the UV photoabsorption cross-section was measured, and the result is compared with the one previously reported.

Rovibrational matrix elements of the multipole moments and of the polarizability of the H2 molecule in the solid phase: Effect of intermolecular potential

Rovibrational matrix elements of the multiple moments Q l up to rank 10 and of the linear polarizability of the H2 molecule in the condensed phase have been computed taking into account the effect of the intermolecular potential. Comparison with gas phase matrix elements shows that the effect of solid state interactions is marginal.

Ab initio zero electron kinetic energy spectroscopy of the ArCl− and KrCl− anions

The theory for calculating the energies and relative intensities of the photodetachment transitions of the weakly bound diatomic anions is implemented for simulations of the zero electron kinetic energy spectra of the ArCl− and KrCl− anions using high-quality ab initio potentials. Its key features are the reduction of the molecular electronic photodetachment transition dipole moment matrix elements to the combination of atomic ones within the atoms-in-molecule model and estimation of the latter by well-developed approaches to the atomic photodetachment processes. The difference in the electronic photodetachment transition dipole moments for distinct electronic states of the neutral, importance of vibrational–rotational coupling, and rotational structure of vibronic bands are analyzed. It is shown that ab initio simulations provide almost the same level of agreement with measured spectra as did the empirical potentials adjusted to reproduce the experimental data. The predictive power of the theory is demonstrated by the discovery of the hidden transitions to the I3/2 state of KrCl which strongy overlap with those to X1/2 state.

Rovibrational matrix elements of multipole moments of the HD, HT and DT molecules

Rovibrational matrix elements of the multipole moments Q ℓ of HD, HT and DT for ranks 2 ≤ ℓ ≤ 11 have been computed. Since the present calculations have been performed with the nuclear centre of mass (rather than the geometric centre) as the origin, the computations had to include even as well as odd values of ℓ. The results are used to correlate the absorption intensities of the zero-phonon single transitions in solid HD to theory.

Electric dipole moment function of H 79Br

An anharmonic potential function with 11 parameters was used in numerically solving the radial Schrödinger wave equation to obtain potential constants of hydrogen bromide molecule, H 79Br. Vibration–rotation energy states up to the vibrational level v=8 and the corresponding wavefunctions were generated. The dipole moment matrix elements, M 0 v′(m) , were evaluated using the experimentally determined line strengths. The dipole moment coefficients, M 0, M 1,…, M 8, were then calculated from these matrix elements and wavefunctions.

Electric dipole moment function of H 35Cl

The radial Schrödinger wave equation was solved numerically using an anharmonic potential function with 11 parameters to generate wavefunctions and vibration–rotation energy levels of the hydrogen chloride molecule H 35Cl. Measured line strengths available in the literature cover transitions up to v=7. Using the measured values of the line strengths along with the computed wavefunctions, a set of 135 dipole moment matrix elements M 0 v′(m) were calculated. Finally, the dipole moment coefficients, M 0, M 1,…, M 7, were evaluated from the matrix elements.

Quantum dynamics simulation of the ultrafast photoionization of Li2

The Li2 species offers an ideal system to compare experimental pump/probe ultrafast photoionization with quantum dynamical calculations on well characterized potential energy surfaces. The present work utilizes the best available potential energy surfaces and appropriate quantum dynamical methods to analyze the photoionization and dynamics of a wave packet prepared in the E 1Σg+ shelf state of lithium dimer. A direct comparison between calculated (ab initio) and measured quantum dynamics is made for signals obtained with different laser pulse shapes, intensities, and chirps, and the validity of the theoretical model is considered, as well as the applicability and failure of perturbation theory. The results illustrate the high sensitivity of the time-dependent pump/probe ionization transient signals to the detailed modeling of both the pump and probe stages. They also show some of the inadequacies of the current potential surfaces and dipole moment matrix elements of lithium dimer.

Perturbations of radiative lifetimes of rovibrational levels of the I1 Π g - and J1 Δ g - states of H2

Adiabatic and nonadiabatic values of radiative lifetimes of rovibrational levels of the electronic states I1 Πg- and J1 Δg- of the H2 molecule are calculated by using data of ab initio calculations of matrix elements of dipole moments of transitions on vibrational wave functions. In comparing our results to those of semiempirical determination of these quantities that we obtained earlier, the two sets on average differed by 25% for rovibronic levels of the I1 Πg- state and by 30% for rovibronic levels of the J1 Δg- state. The inclusion of electronic–rotational interaction is shown to result in surprisingly small (<10%) variations of radiative lifetimes in spite of the considerable perturbations of probabilities of rovibronic transitions of the system of bands I1 Πg-,J1 Δg- → B1Σu+, C1Πu±. Thus, strong mutual perturbations of the upper levels lead only to the redistribution of flows of various channels of spontaneous decay and do not considerably vary the total decay rate of these levels.

RESEARCH NOTE Rovibrational matrix elements of multipole moments of the D2 and T2 molecules

Rovibrational matrix elements of the multipole moments Ql of D2 and T2 up to rank 10 have been computed. The results are used to correlate the absorption intensities of the zero-phonon transitions in solid D2 to theory.

Electric dipole moment function of 12C 16O

Vibration–rotation energy states and corresponding wave functions of carbon monoxide molecule 12C 16O are generated by numerically solving the radial Schrödinger wave equation using an anharmonic potential function with eight parameters. With these wave functions and the measured line strengths that are available for the first five vibrational levels, 183 dipole moment matrix elements M 0 v′(m) are evaluated. Finally, the dipole moment coefficients, M 0, M 1,…, M 4, are extracted from the matrix elements.

Relativistic expressions for current electric moments of nuclei

Relativistic expressions for the operators of current electric moments caused by electromagnetic spin-orbit interaction are obtained. Formulas for the matrix elements of the current electric moments of nuclei are derived. The contributions of the current electric moments to the quadrupole moment of the deuteron and to its root-mean-square radius are calculated with allowance for relativistic effects.

Selective vibrational excitations in the OX (X=F, Cl, Br, I) molecules

Using ab initio calculated potential energy and electric dipole moment functions for the X2Π states of OF, OCl, OBr and OI, two models have been tested to selectively populate their vibrational modes by ultrashort coherent light pulses. For a given form of the pulses either a perturbative approach using discrete vibrational eigenstates and electric dipole transition moment matrix elements or a wavepacket propagation technique were used. The optimisation of the pulse parameters and the mechanisms of the multiphoton processes are discussed. For the target level v=10 populations of more than 60% have been achieved in all four molecules. For OCl it was possible to populate selectively all target levels between v=2 and v=15 using chirped pulses.

Accuracy of the method of moments for scattering by a cylinder

We study the accuracy and convergence of the method of moments for numerical scattering computations for an important benchmark geometry: the finite circular cylinder. From the spectral decomposition of the electric-field integral equation for this scatterer, we determine the condition number of the moment matrix and the dependence of solution error on the choice of basis functions, discretization density, polarization of the incident field, and the numerical quadrature rule used to evaluate moment-matrix elements. The analysis is carried out for both the TM polarization (weakly singular kernel) and TE polarization (hypersingular kernel). These results provide insights into empirical observations of the convergence behavior of numerical methods in computational electromagnetics.

On the control of the populations of atomic states through the use of a static electric field, pulsed lasers, and competing two-photon excitation mechanisms

The control of excited state atomic populations, through the use of a combination of a static electric field, two pulsed lasers, and competitions involving two different two-photon excitation mechanisms, and different excitation pathways, from the ground state is discussed. One of the mechanisms requires non-zero diagonal dipole moment matrix element differences between the `ground' and the `final' excited states, which for atoms generally requires the application of a static electric field; the other mechanism requires a virtual state. Analytical and numerical results for a three-level atomic model, the minimal model for such a study, are used to help discuss the control of the final state atomic population via changes in the relative phase, or the angle between the polarization vectors, or the frequencies, of the two lasers. While many aspects of the atomic control scenarios are analogous to those discussed recently for dipolar molecules (in the absence of a static field), the populations of the final atomic states possess time-dependent oscillations (quantum beats) after the laser–atom interactions have ceased due to the presence of the static electric field.