  Electronic wave-functions in the adiabatic representation acquire nontrivial
geometric phases (GPs) when corresponding potential energy surfaces undergo
conical intersection (CI). These GPs have profound effects on the nuclear
quantum dynamics and cannot be eliminated in the adiabatic representation
without changing the physics of the system. To define dynamical effects arising
from the GP presence the nuclear quantum dynamics of the CI containing system
is compared with that of the system with artificially removed GP. We explore a
new construction of the system with removed GP via a modification of the
diabatic representation for the original CI containing system. Using an
absolute value function of diabatic couplings we remove the GP while preserving
adiabatic potential energy surfaces and CI. We assess GP effects in dynamics of
a two-dimensional linear vibronic coupling model both for ground and excited
state dynamics. Results are compared with those obtained with a conventional
removal of the GP by ignoring double-valued boundary conditions of the real
electronic wave-functions. Interestingly, GP effects appear similar in two
approaches only for the low energy dynamics. In contrast with the conventional
approach, a new approach does not have substantial GP effects in the ultra-fast
excited state dynamics.
