  Existing quantum algorithms for quantum chemistry work well near the
equilibrium geometry of molecules, but the results can become unstable when the
chemical bonds are broken at large atomic distances. For any adiabatic
approach, this usually leads to serious problems, such as level crossing and/or
energy gap closing along the adiabatic evolution path. In this work, we propose
a quantum algorithm based on adiabatic evolution to obtain molecular
eigenstates and eigenenergies in quantum chemistry, which exploits a smooth
geometric deformation by changing bond lengths and bond angles. Even with a
simple uniform stretching of chemical bonds, this algorithm performs more
stably and achieves better accuracy than our previous adiabatic method [Phys.
Rev. Research 3, 013104 (2021)]. It solves the problems related to energy gap
closing and level crossing along the adiabatic evolution path at large atomic
distances. We demonstrate its utility in several examples, including H${}_2$O,
CH${}_2$, and a chemical reaction of H${}_2$+D${}_2\rightarrow$ 2HD.
Furthermore, our fidelity analysis demonstrates that even with finite bond
length changes, our algorithm still achieves high fidelity with the ground
state.
