Table S1. 
Structure of the Cs conformer of H2SO4 calculated at the MP2/V(Q+d)Z level of theory. For atom numbering, see figure 2. Distances in A and angles in degrees.

S-O1              1.581
S-O1Õ             1.581
S=O2Õ             1.427
S=O2              1.410
O1-H1             0.966
O1Õ-H1Õ           0.966
O1-S-O1Õ         102.09
O1-S-O2Õ         108.00
O1-S-O2          106.28
O1Õ-S-O2Õ        108.00
O1Õ-S-O2         106.28
O2Õ-S-O2         124.08
S-O1-H1          108.18
S-O1Õ-H1Õ        108.18
O1Õ-S-O1-H1      -97.56
O2Õ-S-O1-H1       16.14
O2-S-O1-H1       151.27
O1-S-O1Õ-H1Õ      97.56
O2Õ-S-O1Õ-H1Õ    -16.14
O2-S-O1Õ-H1Õ    -151.27

CARTESIAN COORDINATES PRINCIPAL AXIS SYSTEM (in A)
ATOM     A [A]        B [A]        C [A]
S        0.0000       0.0289       0.1275
O1       1.2293      -0.0745      -0.8610
O1'     -1.2293      -0.0748      -0.8610
H1       1.5397      -0.9890      -0.8613
H1'     -1.5394      -0.9895      -0.8613
O2'      0.0002      -1.1337       0.9544
O2      -0.0002       1.3500       0.6213

S, O2, and O2' are located in the b,c-plane, while O1-H1 and O1'-H1' are Cs-symmetric with respect to the b,c-plane. 
The conformer is very nearly a symmetric top:  
ROTATIONAL CONSTANTS A, B, C [MHZ]
      5138.010744     5074.245312     4812.759788


Structure of the transition state (top of the barrier) calculated at the MP2/VTZ level of theory. Distances in A and angles in degrees.

S-O1              1.612
S-O1Õ             1.598
S=O2Õ             1.435
S=O2              1.427
O1-H1             0.968
O1Õ-H1Õ           0.965
O1-S-O1Õ          98.91
O1-S-O2Õ         107.88
O1-S-O2          108.47
O1Õ-S-O2Õ        108.96
O1Õ-S-O2         107.83
O2Õ-S-O2         122.29
S-O1-H1          106.05
S-O1Õ-H1Õ        108.61
O1Õ-S-O1-H1     -113.45
O2Õ-S-O1-H1       -0.12
O2-S-O1-H1       134.27
O1-S-O1Õ-H1Õ       2.01
O2Õ-S-O1Õ-H1Õ   -110.48
O2-S-O1Õ-H1Õ     114.79