  We investigate the effect of selected N and Ti point defects in $B$1 TiN on N
1s and Ti 2p$_{3/2}$ binding energies (BE) by experiments and ab initio
calculations. X-ray photoelectron spectroscopy (XPS) measurements of
Ti-deficient TiN films reveal additional N 1s spectral components at lower
binding energies. Ab initio calculations predict that these components are
caused by either Ti vacancies, which induce a N 1s BE shift of $-0.53$ eV in
its first N neighbors, and/or N tetrahedral interstitials, which have their N
1s BE shifted by $-1.18$ eV and also shift BE of their first N neighbors by
$-0.53$ eV. However, the {\it ab initio} calculations also reveal that the
tetrahedral N interstitial is unstable at room temperature. We, therefore,
unambiguously attribute the detected signal to Ti vacancies. Furthermore, the
vacancy concentration in Ti-deficient TiN was quantified with XPS supported by
ab initio calculations. The largest BE shifts of $-1.53$, $-1.80$ and $-2.28$
eV for Ti 2p$_{3/2}$ electrons are predicted for the Ti tetrahedral, split
(10$\overline{1}$)-aligned and split (111)-aligned interstitial atoms,
respectively, and we, therefore, propose XPS could detect them. Other defects
such as N vacancy or N split (10$\overline{1}$)-aligned interstitial introduce
smaller N 1s and Ti 2p$_{3/2}$ BE shifts and are unlikely to be detectable
experimentally. Our work highlights the potential of ab initio-guided XPS
measurements in detecting and quantifying point defects in $B$1 TiN.
