Modeling non-adiabatic phenomena and materials at extremes has been a long-standing challenge for computational chemistry and materials science, particularly for systems that undergo irreversible phase transformations due to significant electronic excitations. Ab ini- tio and existing quantum mechanics approximations to the Schrödinger equation have been limited to ground-state descriptions or few excited electronic states, less than 100 atoms, and sub-picosecond timescales of dynamics evolution. Recently, the electron force field (eFF) introduced by Su and Goddard (2007) presented a cost-efficient alternative to describe the dynamics of electronic and nuclear degrees of freedom. eFF describes an N-electron wave function as a Hartree product of one-electron floating spherical Gaussian wave packets propagating via the time-dependent Schrödinger equation under a mixed quantum– classical Hamiltonian evaluated as sum of self- and pairwise potential interactions. Local Pauli potential corrections replace the need for explicit anti-symmetrization of total electronic wavefunction, a wavefunction kinetic energy term accounts for Heisenberg’s uncertainty, and classical electrostatics complete the total eFF energy expression. However, due to the spherical symmetry of the underlying Gaussian basis functions, the original eFF formulation is limited to low-Z numbers with electrons of predominant s-character. To overcome this, we introduce here a formal set of potential form extensions that enable accurate description of p-block elements in the periodic table. The extensions consist of a model representing the core electrons of an atom together with the nucleus as a single pseudo particle with wave-like behavior, interacting with valence electrons, nuclei, and other cores through effective core pseudopotentials (ECPs). We demonstrate and validate the ECP extensions for complex bonding structures, geometries and energetics of systems with p-block character (containing silicon, oxygen, carbon, or aluminum atoms and combination thereof) and apply them to study materials under extreme mechanical loading conditions.