The dissertation is devoted to the development of the basics of theoretical cooperative spectroscopy and nonlinear quantum dynamics of molecular systems in the free state and in an intense external electromagnetic field, taking into account the effects of correlation, chaos and cooperative transitions. A new cooperative theoretical approach to the calculation of the electronic structure, energy and spectral parameters, vibrational structure in the photoelectron spectra of molecules is developed, which is based on the standard formalism of the Green's function method and the quasiparticle Fermi-liquid density functional theory with sequential calculation, exchange-correlation effects, including the effects of polarization interaction, shielding of valence quasiparticles, energy dependence of the mass operator of quasiparticles, etc. A new version of many-body perturbation theory has been developed with an optimized quasiparticle density functional zeroth approximation under the condition of maximum observance of fundamental gauge invariance principle and minimization of the contribution of gauge-noninvariant exchange-polarization diagrams. The results of calculations of bond energies, spectroscopic factors, vertical ionization potentials, coupling constants and vibrational structure of photoelectron spectra for series of diatomic molecules C2, N2, O2,F2, CO, CH, HF, as well as dimers of inert gases Ar, Kr, Xe are listed. Analysis of the obtained data indicates the presence of strong correlation effects, in particular, the possible collectivization of shells, the presence of "shadow" states in molecules with which there is strong mixing and which transmits the initial level force, "part of the spectrofactor". A new approach in the spectroscopy of cooperative e-γ-vibrational-rotational-nuclear transitions in spectra of molecules is developed and based on an optimized density functional theory. New data for cooperative transitions probabilities for HI, HBr, RbCs, OsO4, IrO4 are presented. A new non-empirical approach to calculation of polarization parameters of diatomic molecules in an intense electromagnetic field is developed. It is adapted a quantum-dynamic formalism to model chaotic dynamics of molecules in the field using such methods as Gottwald-Melbourne test, method of correlation integral, algorithms for average mutual information, false nearest neighbors, the Lyapunov’s exponents & Kolmogorov entropy analysis, algorithms of optimized trajectories, B-spline, etc. There are listed new data on spectral parameters, dynamic, topological invariants (correlation dimension, Kaplan-York dimension, Lyapunov’s exponents, Kolmogorov entropy, etc.) for GeO, ZrO, PbO molecules in a linearly polarized field of intensity up to 28 GW /cm2 and phenomenon of optical chaos is discovered for the first time.
