Semiquantal Valence-Bond Wave Packet Description of Chemical Bonding

A semiquantal wave packet modeling of electrons in chemical bonding is presented. It is based on the valence bond (VB) theory with non-orthogonal floating and breathing spherical Gaussian orbitals, simplified to treat many electrons by decoupled electron pair approximations (DPA) and core pseudopotentials (CPP). The extended Hamiltonian formalism offers pictorial interpretation and analysis in the extended phase space of the wave packet center and width coordinates. The numerical calculations are demonstrated on the ground state potential energy surfaces of H-2, LiH, and BeH2. For LiH, the perfect-pairing VB (VB-PP) calculation with the minimal orbitals gives an accurate potential energy curve of comparable quality with a correlated ab initio calculation. The two-electron VB calculation with a CPP underestimates the binding energy but gives qualitatively correct potential energy curves. For BeH2, the VB-PP with CPP gives reasonably accurate potential energy surface along both the stretching and bending coordinates. A few versions of DPA are developed and assessed, aiming toward large scale dynamic simulations. A scaling ansatz is introduced and examined on the bonding potential energy surfaces. The efficacy of the theory for studying linear and nonlinear electronic polarizations is also illustrated via an analysis of potential energy surfaces in the extended phase space.