This paper introduces a practical phase-space electronic Hamiltonian that depends on both nuclear position and momentum, enabling the conservation of total linear and angular momentum in ab initio dynamics. The Born-Oppenheimer approximation, which separates nuclear and electronic motions, is insufficient for conserving total momentum, as it fails to account for nonadiabatic effects. To address this, the authors propose a phase-space Hamiltonian that incorporates nuclear momentum and electronic couplings, allowing for more accurate descriptions of both nuclear and electronic properties. The phase-space Hamiltonian is constructed using electron translation and rotation factors, which are derived from the theory of electron translation and rotation factors. These factors ensure that the Hamiltonian satisfies the necessary conditions for linear and angular momentum conservation. The authors demonstrate that by using these factors, the phase-space Hamiltonian can recover the correct electronic momentum, as shown by Nafie's expression for electronic momentum. The paper also discusses the challenges of implementing the phase-space Hamiltonian, including computational costs and numerical stability. However, the authors argue that the phase-space approach is more efficient and accurate than traditional methods, particularly for systems with electronic degeneracy or spin-orbit coupling. Numerical results are presented to validate the effectiveness of the phase-space Hamiltonian in recovering correct linear and angular momentum. The results show that the phase-space approach converges to the finite-difference values for larger basis sets, demonstrating its accuracy and efficiency. The paper concludes that the phase-space Hamiltonian provides a promising alternative for ab initio dynamics, enabling the conservation of total momentum and improving the accuracy of electronic property calculations.This paper introduces a practical phase-space electronic Hamiltonian that depends on both nuclear position and momentum, enabling the conservation of total linear and angular momentum in ab initio dynamics. The Born-Oppenheimer approximation, which separates nuclear and electronic motions, is insufficient for conserving total momentum, as it fails to account for nonadiabatic effects. To address this, the authors propose a phase-space Hamiltonian that incorporates nuclear momentum and electronic couplings, allowing for more accurate descriptions of both nuclear and electronic properties. The phase-space Hamiltonian is constructed using electron translation and rotation factors, which are derived from the theory of electron translation and rotation factors. These factors ensure that the Hamiltonian satisfies the necessary conditions for linear and angular momentum conservation. The authors demonstrate that by using these factors, the phase-space Hamiltonian can recover the correct electronic momentum, as shown by Nafie's expression for electronic momentum. The paper also discusses the challenges of implementing the phase-space Hamiltonian, including computational costs and numerical stability. However, the authors argue that the phase-space approach is more efficient and accurate than traditional methods, particularly for systems with electronic degeneracy or spin-orbit coupling. Numerical results are presented to validate the effectiveness of the phase-space Hamiltonian in recovering correct linear and angular momentum. The results show that the phase-space approach converges to the finite-difference values for larger basis sets, demonstrating its accuracy and efficiency. The paper concludes that the phase-space Hamiltonian provides a promising alternative for ab initio dynamics, enabling the conservation of total momentum and improving the accuracy of electronic property calculations.