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ab initio algorithm atoms AUHF axial band basis functions basis set brakets calculations Cartesian chain channel axis charged solitons Chem classes computed consider contracted coordinates corresponding Coulomb D.M. Bishop deﬁned deﬁnition density matrix dipole discussed effect electron correlation equation equilibrium euclidean distances evaluation experimental ﬁeld Figure ﬁnal ﬁnds ﬁrst Fock force constants formula frequency Gaussian Gaussian functions Hamiltonian harmonic helical hyperpolarizabilities initio interaction ionic J.A. Pople Ladik Lett matrix elements membrane surface method molecular molecules Morse potential nearly free ion non-linear optics obtained odor optimization overlap matrix overlap-like parameters Phys plane Point-Molecule representation polaron polyenes polymethine possible potential energy function PRISM probe Quantum Chem quantum chemistry Section shell-pair similarity measure soliton spin density static structure Table theory trans-butadiene transform tunneling two-electron vector vibrational wall sources wavefunctions width