We present an approach based on a dimer expansion that describes low-energy singlet excitations (singlons) in spin-12 Heisenberg antiferromagnet (HAM) on simple square lattice. An operator ("effective Hamiltonian") is constructed whose eigenvalues give the singlon spectrum. In the case of simple square lattice the "effective Hamiltonian" looks like a Hamiltonian of a spin-1/2 magnet in strong external magnetic field and it has a gapped spectrum. It is found that singlet states lie above triplet ones (magnons) in the whole Brillouin zone except in the vicinity of the point (π,0), where their energies are slightly smaller. Based on this finding, we suggest that a magnon decay is possible near (π,0) into another magnon and a singlon which may contribute to the dip of the magnon spectrum near (π,0) and reduce the magnon lifetime. It is pointed out that the singlon-magnon continuum may contribute to the continuum of excitations observed recently near (π,0). In the second part, we study singlet low-energy spectrum of HAM on square lattice with nearest- and frustrating next-nearest-neighbor exchange couplings J1 and J2. It is well known that a non-magnetic phase arises in this model at 0.4≲J2/J1≲0.6 sandwiched by two N'eel ordered phases. In agreement with previous results, we observe a first-order quantum phase transition (QPT) at J2≈0.64J1 from the non- magnetic phase to the N'eel one. Large gap (≳0.4J1) is found in the singlet spectrum at J2
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