Using a variational method with an explicitly correlated Gaussian basis, we study the e þ -Li and e þ -Be complexes in the ground and lowest excited states with higher spin multiplicity. Our calculations provide rigorous theoretical confirmation that a positron can be attached to the excited states: 1s2s2p 4 P o and 1s 2 2s2p 3 P o for e þ -Li and e þ -Be, respectively. The result is particularly notable for the e þ -Be complex, as the excited 3 P o state lies below the autoionization threshold. We report accurate binding energies, annihilation rates and structural properties of these positron-atom systems. The existence of the ground and metastable excited states with bound positron opens up a new route to the presently lacking experimental verification of stability of a positron binding to any neutral atom. DOI: 10.1103/PhysRevLett.111.193401 PACS numbers: 36.10.Àk, 31.15.ac, 31.15.xt Understanding the mechanisms of the interaction of low energy positrons with matter is one of the main tasks of positron physics and chemistry. In particular, of great interest is the question whether atoms and molecules can capture positrons and form bound states stable against dissociation [1][2][3][4][5][6][7][8][9]. Since 1997, when the first conclusive and rigorous theoretical confirmation of a possibility of attaching a positron to a neutral lithium was given [1], there have been a number of investigations claiming the dynamical stability of positron-atom complexes. At present, at least a dozen atoms are believed to be capable of binding a positron. In contrast, on the experimental side no evidence has been collected as of yet to demonstrate the existence of positronic atoms. While different experimental approaches to study positron binding to atoms have been proposed, e.g., by measuring resonant positron-atom annihilation [10,11] or by laser-assisted photorecombination [12], the existence of excited states is of crucial importance for detecting positron-atom complexes as it should allow spectroscopic measurements. Just recently such an approach has been used by Cassidy et al. [13] to confirm the production of a positronium molecule (Ps 2 ). The technique employed in Ref.[13] was based on observing small yet detectable changes in the annihilation yield of dense Ps over a narrow range of wavelengths corresponding to a transition between the ground and excited states of Ps 2 . The existence of a bound excited state of Ps 2 , in turn, had been previously predicted by numerical calculations [14].Only a handful of theoretical studies so far have dealt with the investigation of excited states of positronic atoms. The simplest multielectron atom, helium, has been known to attach a positron in its 1s2s 3 S state for more than a decade [15] (here and below the term symbol refers to electrons only). Recently, it has also been shown that positron attachment is possible in three doubly excited states [16][17][18]. Nevertheless, in its ground singlet state He does not form a bound positron-atom complex. There was also an indication...