A new approach to electron dynamics in molecular system is developed, which combines ab initio molecular orbital (MO) scheme and Gaussian wave packet dynamics. The time-dependent electronic wavefunction is described by the linear combination of atomic orbitals (LCAO) using frozen-width floating Gaussian wave packet basis functions. The equations of motion for the time-dependent variables, such as the LCAO coefficients, the Gaussian centers, and their phase factors of the respective basis functions, are determined based on time-dependent variational principle. This technique is demonstrated for the attosecond propagation of electronic wavefunction of hydrogen and helium atoms in response to electrostatic field. (c) 2006 Elsevier B.V. All rights reserved.