The origin of beam disparity in emittance and betatron oscillation orbits, in and out of the polarization plane of the drive laser of laser-plasma accelerators, is explained in terms of betatron oscillations driven by the laser field. As trapped electrons accelerate, they move forward and interact with the laser pulse. For the bubble regime, a simple model is presented to describe this interaction in terms of a harmonic oscillator with a driving force from the laser and a restoring force from the plasma wake field. The resulting beam oscillations in the polarization plane, with period approximately the wavelength of the driving laser, increase emittance in that plane and cause microbunching of the beam. These effects are observed directly in 3D particle-in-cell simulations.

An approach has been developed for calculating the vibrational spectra of linear methine-bridged tetrapyrroles constituting the chromophoric sites of various photoreceptor proteins. Using Pulay's scaling procedure (Pulay, P.; Fogarasi, G.; Pongor, G.; Boggs, J. E.; Vargha, A. J. Am. Chem. Soc. 1983, 105, 7037), scaling factors were determined for a set of 10 training molecules which mimic structural elements of the tetrapyrrole target molecules. Geometries and force fields were calculated at three theoretical levels, i.e., by the Hartree−Fock (HF), second-order Møller−Plesset perturbation (MP2), and B3LYP density functional theory methods using 6-31G* basis sets. A global optimization yielded sets of 14, 11, and 10 scaling factors for HF, MP2, and B3LYP, respectively. B3LYP provided the best results both with regard to the geometries and the vibrational frequencies. The root-mean-square deviation for the calculated frequencies was 11 cm-1 for B3LYP as compared to 13 and 17 cm-1 for HF and MP2, respectively. On the basis of the Morse model for an anharmonic oscillator, an expression was derived for correcting scaling factors for the anharmonicity changes in (deuterio) isotopomers. The effects of hydrogen bonding interactions via N−H···OC bonds on the structures and vibrational spectra were studied in the case of maleimide. For the N−H stretching, deformation, and out-of-plane wagging vibrations, modifications of the scaling factors are required in order to reproduce the vibrational spectra of the hydrogen bonded dimer. The IR and Raman intensities calculated by the B3LYP method were found to agree well with experimental spectra. For the Raman intensities, a fourth-order differentiation formula was derived for the numerically accurate calculation of polarizability derivatives with respect to Cartesian displacements, by using the finite field method.

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The electronic properties of thiophene oligomers (nT, n=2–8) have been investigated in the lowest excited triplet state. Theoretical calculations of the zero field splitting parameters and of the π-electron spin density have been performed and compared with previous experimental EPR results. The calculations are based on a simple π-electron (one-electron-per-site) model including electron–electron interaction at the extended Hubbard level. Optimized bond lengths result from making them self-consistent to the corresponding bond orders via Coulson’s relationship. The calculated D values decrease from D=0.0959 cm−1 for n=2 to D=0.0597 cm−1 for n=8, in agreement with EPR data. The measured as well as the calculated E values are rather small. Furthermore, we found that ZFS parameters are affected by the torsion angles between the thiophene rings. The chain length dependence of D can be rationalized comparing π-electron spin density calculations and computed bond length distortions. These clearly indicate that the triplet excitation reaches a finite extension over about four thiophene rings.

This paper presents a new approach to the linear scaling evaluation of density matrices in electronic structure theory. The new approach is based on the iterative computation of a special matrix function, the sign of the matrix and its performance is compared to that of some other methods developed for similar purpose. One particular variant of the sign approach turned out to be very competitive with other linear scaling density matrix evaluation algorithms, in terms of computational time and accuracy. It is also shown that a special damping technique greatly improves the stability of self-consistent field (SCF) calculations when using density matrix purification and sign methods.

The resonance Raman (RR) spectra of monomeric 3,3‘,4,4‘,5,5‘-hexamethylpyrromethene (HMPM) were measured upon excitation in resonance with the strong 436 nm absorption band. The experimental spectra were analyzed by comparison with calculated RR spectra that were obtained on the basis of scaled quantum chemical force fields in combination with the transform theory. The ground-state structure and force field of HMPM were calculated by density functional theory (DFT) using the B3LYP exchange functional and the 6-31G* basis set. The monomeric HMPM adopts a planar structure in contrast to HMPM dimers in which the intermolecular hydrogen-bonding interactions induce a slight torsion of the methine bridges as revealed by both the experimental and the calculated structures. The force fields were scaled by using a global set of scaling factors determined previously (Magdó, I.; Németh, K.; Mark, F.; Hildebrandt, P.; Schaffner, K. J. Phys. Chem. A 1999, 103, 289). To account for the effect of the intramolecular hydrogen bond between the pyrrolic N−H group and the pyrroleninic nitrogen in the monomeric HMPM, only the scaling factor for the N−H in-plane bending force constant required a slight adjustment. Electronic transitions were calculated by means of CNDO/S, Hartree−Fock single configuration interaction (HF-CIS), and time-dependent DFT, which all predict one strong and one or two adjacent weak transitions for the lowest electronic excitations. This pattern is in line with band fitting analyses of the 436 nm absorption band. The best agreement in excitation energies was obtained by time-dependent DFT calculations. Excited-state displacements as required for evaluating RR intensities were determined for the lowest excited singlet state S1 using the equilibrium geometries optimized for the ground and excited states by means of the HF and HF-CIS methods, respectively. For the second lowest excited state (S2), only an approximate equilibrium geometry could be used for determining the excited-state displacements as the S2 state became quasi-isoenergetic with the S1 state during the geometry optimization. Employing the transform theory, RR spectra were calculated for resonance enhancement via the S1 and S2 states. The experimental RR spectrum of HMPM excited at 413 nm agrees well with the calculated S1-RR spectrum, allowing a plausible and consistent vibrational assignment for most of the observed bands of HMPM and its isotopomer deuterated at the pyrrolic nitrogen. The root-mean-square deviations between the experimental and calculated frequencies are 7 and 5 cm-1 for nondeuterated and deuterated HMPM, respectively. Experimental RR intensities and their dependence on the excitation wavelength are reproduced in a semiquantitative manner. The only significant exceptions refer to the CC stretching and CH rocking modes of the methine bridge, ν21 and ν49. On one hand, these discrepancies may reflect intrinsic deficiencies of the HF/HF-CIS method in calculating excited-state displacements. On the other hand, the unique deviation o...

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The structure and vibrational spectra of hexamethylpyrromethene (HMPM) have been investigated by X-ray crystallography, IR and Raman spectroscopies, and density functional theory calculations. HMPM crystallizes in the form of dimers, which are held together by bifurcated N-H(...N)(2) hydrogen bonds, involving one intramolecular and one intermolecular N-H...N interaction. The monomers are essentially planar, and the mean planes of the monomers lie approximately perpendicular to one another, so that the four N atoms in the dimer form a distorted tetrahedron. The structure of the HMPM dimer is well-reproduced by B3LYP/6-31G calculations. A comparison of the calculated geometry of the dimer with that of the monomer reveals only small changes in the N-H...N entity and the methine bridge angles upon dimerization. These are a result of weakening of the intramolecular N-H...N hydrogen bond and the formation of a more linear N-H...N intermolecular hydrogen bond. Using an empirical relation between the shift of the N-H stretching frequency of pyrrole and the enthalpy of adduct formation with bases [Nozari, M. S.; Drago, R. S. J. Am. Chem. Soc. 1970, 92, 7086-7090], estimates of the strength of the intra- and intermolecular hydrogen bonds are obtained. IR and Raman spectroscopies of HMPM and its isotopomers deuterated at the pyrrolic nitrogen atom and at the methine bridge reveal that the molecule is monomeric in nonpolar organic solvents but dimeric in a solid Ar matrix and in KBr pellets. The matrix IR spectra show a splitting of vibrational modes for the dimer, particularly those involving the N-H coordinates. Due to intrinsic deficiencies of the B3LYP/6-31G approximation, a satisfactory reproduction of these modes of the monomeric and dimeric HMPM requires specific adjustments of the NH scaling factors for the calculated force constants and, in the case of the NH out-of-plane modes of HMPM dimers, also of intra- and intermolecular coupling constants. This parametrization does not significantly affect the other calculated modes, which in general reveal a very good agreement with the experimental data.