Optimized geometries of Mg-containing species, at the B3-LYP/6-311+G** level of theory:

MgO:
----------------------------------------
Mg      0.000000    0.000000    0.706899
O       0.000000    0.000000   -1.060349
----------------------------------------

MgOH:
----------------------------------------
Mg      0.000000    0.000000    0.816394
O       0.000000    0.000000   -0.982843
H       0.000000    0.000000   -1.933980
----------------------------------------

HOMgOH:
----------------------------------------
Mg      0.000000    0.000000    0.000524
O       0.000000    1.799102    0.046012
H      -0.460319    2.522587   -0.371244
O       0.000000   -1.799102    0.046012
H       0.460319   -2.522587   -0.371244
----------------------------------------

MgH2+:
----------------------------------------
Mg      0.000000    0.000000    0.364343
H       0.000000    0.376199   -2.186057
H       0.000000   -0.376199   -2.186057
----------------------------------------

MgN2+:
----------------------------------------
Mg      0.000000    0.000000    1.628480
N       0.000000    0.000000   -0.848294
N       0.000000    0.000000   -1.943386
----------------------------------------

MgNO+:
----------------------------------------
Mg     -0.731238   -1.387722    0.000000
N       0.000000    0.968023    0.000000
O       1.096857    1.234562    0.000000
----------------------------------------

MgCO2+:
----------------------------------------
Mg      0.000000    0.000000    2.139756
O       0.000000    0.000000   -0.000162
C       0.000000    0.000000   -1.182395
O       0.000000    0.000000   -2.322676
----------------------------------------

MgO3+:
----------------------------------------
Mg      0.000000    0.000000    1.255267
O       0.000000    0.000000   -1.139175
O       0.000000    1.117760   -0.371863
O       0.000000   -1.117760   -0.371863
----------------------------------------

MgOH2+:
----------------------------------------
Mg      0.000000    0.000000    0.998870
O       0.000000    0.000000   -1.082907
H       0.000000    0.778504   -1.661595
H       0.000000   -0.778504   -1.661595
----------------------------------------

MgHOOH+:
----------------------------------------
Mg     -1.327800    0.000000    0.000000
O       0.817896   -0.721591   -0.106562
O       0.817896    0.721591    0.106562
H       1.423634   -1.057433    0.581738
H       1.423634    1.057433   -0.581738
----------------------------------------
 
HOMg+:
----------------------------------------
H      -0.610862    1.689457    0.000000
O       0.030543    0.974985    0.000000
Mg      0.030543   -0.790778    0.000000
----------------------------------------

MgOOH+:
----------------------------------------
Mg     -1.042316   -0.134054    0.016890
O       0.852066   -0.610891   -0.078139
O       0.504827    0.898201   -0.004982
H       1.652643   -0.689835    0.462295
----------------------------------------

HOMgH2+:
----------------------------------------
H       0.000000    0.000000   -2.143921
O       0.000000    0.000000   -1.190055
Mg      0.000000    0.000000    0.537857
H       0.000000    0.381505    2.605038
H       0.000000   -0.381505    2.605038
----------------------------------------

HOMgN2+:
----------------------------------------
H       0.000000    0.000000    3.300484
O       0.000000    0.000000    2.347174
Mg      0.000000    0.000000    0.616007
N       0.000000    0.000000   -1.557603
N       0.000000    0.000000   -2.652391
----------------------------------------

HOMgNO+:
----------------------------------------
H      -0.035837    3.351894    0.000000
O      -0.190922    2.410491    0.000000
Mg      0.000000    0.682898    0.000000
N      -0.184850   -1.524754    0.000000
O       0.357145   -2.519665    0.000000
----------------------------------------

HOMgCO2+:
----------------------------------------
H       0.000000   -3.918953    0.000000
O       0.000000   -2.966208    0.000000
Mg      0.000000   -1.232573    0.000000
O       0.000000    0.761578    0.000000
C       0.000000    1.947135    0.000000
O       0.000000    3.083009    0.000000
----------------------------------------

HOMgO3+:
----------------------------------------
H       0.000000    0.000000    3.504406
O       0.000000    0.000000    2.546919
Mg      0.000000    0.000000    0.774176
O       0.000000    0.000000   -1.848849
O       0.000000    1.068497   -1.148692
O       0.000000   -1.068497   -1.148692
----------------------------------------

HOMgOH2+:
----------------------------------------
Mg      0.000000    0.000000    0.146409
O       0.000000    0.000000    1.883220
H       0.000000    0.000000    2.835885
O       0.000000    0.000000   -1.849911
H       0.000000    0.778370   -2.429635
H       0.000000   -0.778370   -2.429635
----------------------------------------

HOMgHOOH+:
----------------------------------------
H       0.000000    0.000000    3.217645
O       0.000000    0.000000    2.265302
Mg      0.000000    0.000000    0.527270
O       0.000000    0.732363   -1.468310
O       0.000000   -0.732363   -1.468310
H      -0.715659    0.981199   -2.087168
H       0.715659   -0.981199   -2.087168
----------------------------------------