Ab initio molecular electronic structure theory has been
employed in order to investigate systematically the X ^{
3}B_{1}, a ^{1}A_{1}, b ^{
1}B_{1}, and c ^{
1}Sigma_{g}^{+} states of
NH_{2}^{+}, with emphasis placed on the b
^{1}B_{1} and c ^{
1}Sigma_{g}^{+} states. The
self-consistent-field (SCF), configuration interaction with
single and double excitations (CISD), complete active space
(CAS) SCF, and CASSCF second-order configuration
interaction (SOCI) wave functions with nine basis sets, the
largest being a triple-zeta basis set with three sets of
polarization functions and two additional sets of higher
angular momentum and diffuse functions [TZ3P(2f,2d)+2diff],
were used to determine equilibrium geometries, harmonic
vibrational frequencies, infrared (IR) intensities, and
dipole moments. The ground, first, and second excited
states are confirmed to be bent, while the third excited
state is predicted to be linear. The bond angles of
NH_{2}^{+} are shown to be larger than
those of the corresponding isoelectronic CH_{2}
molecule. At the highest level of theory, TZ3P(2f,2d)+2diff
CASSCF-SOCI, the triplet-singlet splitting is predicted to
be 29.4 kcal/mol (1.28 eV, 10 300 cm^{-1}), which
is in good agreement with the experimental observation of
30.1 kcal/mol (1.305 eV, 10 530 cm^{-1}). With the
same method, the second excited state (b ^{
1}B_{1}) lies 43.7 kcal/mol (1.89 eV, 15 300
cm^{-1}) above the ground state, which is
significantly lower than the experimentally proposed value
of 2.54 eV. The third excited state (c ^{
1}Sigma_{g}^{+}) is predicted to lie
77.0 kcal/mol (3.34 eV, 26 900 cm^{-1}) above the
ground state. The equilibrium geometry of this c ^{
1}Sigma_{g}^{+} state is determined to
be r_{e} = 1.030 Angstrom at the TCSCF-CISD level
with the largest basis set. Since the IR intensities of all
active vibrational modes are predicted to be substantial,
IR spectroscopic studies of the four states are feasible.
However, of the six fundamentals experimentally assigned to
date, two appear to be incorrect. The energy separations
among the four lowest-lying states of
NH_{2}^{+} are found to be larger than the
corresponding states of CH_{2}.