  The Zak phase $\gamma$, the generalization of the Berry phase to Bloch wave
functions in solids, is often used to characterize inversion-symmetric 1D
topological insulators; however, since its value can depend on the choice of
real-space origin and unit cell, only the difference between the Zak phase of
two regions is believed to be relevant. Here, we show that one can extract an
origin-independent part of $\gamma$, the so-called inter-cellular Zak phase
$\gamma^{\mathrm{inter}}$, which can be used as a bulk quantity to predict the
number of surface modes as follows: a neutral finite 1D tight-binding system
has $n_s = \gamma^{\mathrm{inter}}/\pi$ (mod 2) number of in-gap surface modes
below the Fermi level if there exists a commensurate bulk unit cell that
respects inversion symmetry. We demonstrate this by first verifying that $\pm
e\gamma^{\mathrm{inter}}/2\pi$ (mod $e$) is equal to the extra charge
accumulation in the surface region for a general translationally invariant 1D
insulator, while the remnant part of $\gamma$, the intra-cellular Zak phase
$\gamma^{\mathrm{intra}}$, corresponds to the electronic part of the dipole
moment of the bulk's unit cell. Second, we show that the extra charge
accumulation can be related to the number of surface modes when the unit cell
is inversion symmetric. This bulk-boundary correspondence using
$\gamma^{\mathrm{inter}}$ reduces to the conventional one using $\gamma$ when
the real-space origin is at the inversion center. Our work thereby clarifies
the usage of $\gamma$ in the bulk-boundary correspondence. We study several
tight binding models to quantitatively check the relation between the extra
charge accumulation and the inter-cellular Zak phase as well as the
bulk-boundary correspondence using the inter-cellular Zak phase.
