Within the resolution of the identity (RI) method, the convergence of the Hartree-Fock (HF) total molecular energy and the multipole moments in the course of the combined regular expansion of the molecular and auxiliary (RI) basis sets is studied. Dunning's cc-pVXZ series is used for both the molecular and the RI basis sets. The results show the calculated quantities converge to the HF limit when both the molecular and the RI basis sets are expanded from correlation-consistent polarized valence double zeta to correlation-consistent polarized valence sextuple zeta. Combinations of molecular/RI basis sets sufficient for convergence of the total energy and of the multipole moments at various accuracy levels have been determined. A measure of the RI basis set incompleteness is suggested and discussed. As it is significantly faster than the standard HF algorithm for small and midsize molecules, the RI-HF method, together with appropriate expanding series of both molecular and RI basis sets, provide an efficient tool to estimate and control the error of the Hartree-Fock calculations due to the finite basis set.

Free-electron lasers exploiting media with periodically modulated refractive indices are studied. The regime of large modulation is considered, and the conditions of its realization are discussed. Two types of media with periodically modulated refractive indices are analyzed: a gas-plasma medium with a periodically varying degree of ionization and a superlattice-like medium. The gain, saturation field, and efficiency of these free-electron lasers are found. For any given frequency, the gain is optimized with respect to the choice of electron energy, direction of motion, and other parameters. Its relationship with other types of free-electron lasers (e.g., the Cherenkov laser) is discussed.

Excitation of induced coherent Smith-Purcell (SP) radiation by relativistic magnetized electron beam in the absence of the resonator is considered within the framework of the dispersion equation. We have found that the dispersion equation for the SP instability is a quadratic equation for frequency. The first-step approximation for solution of the dispersion equation, giving the SP-spectrum of frequency, corresponds to the mirror boundary case, when the electron beam propagates above a plane metal surface (mirror). It was found that the conditions for both the Thompson and the Raman regimes of excitation do not depend on beam current and depend on the height of the beam above the grating surface. The growth rate of the instability in both cases is proportional to the square root of the electron beam current. No feedback is needed to provide the coherent emission.

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Amplification in free-electron lasers exploiting media with periodically modulated refractive indices is studied in the regime of a large modulation. The conditions for realization of the large-modulation regime in a superlattice-like medium are established. The maximized gain, the corresponding saturation field and efficiency, as well as the optimal electron energy and propagation direction are determined. It is shown that the large-modulation regime makes it possible to extend significantly the operation frequency domain of the FEL employing a low-relativistic electron beam. Relationship with the Cherenkov and stimulated resonance-transition-radiation FELs is discussed. This research is partially supported by RFBR grant 97-02-17783.