Table 3.

Statistical Analysis for Application of 10 Density Functionals to Ubiquitin.

DensityaFunctional	Rb	SDc (ppm)	Ca-rmsdd (ppm)	CPU Timee (s)
OPBE	0.902	2.04 (1.72)	2.12	3475.97
O3LYP	0.905	2.01 (1.69)	2.16	6587.23
OPW91	0.903	2.03 (1.69)	2.12	3488.24
BPW91	0.908	1.99 (1.60)	2.30	3624.62
OB98	0.908	1.98 (1.62)	2.19	3559.61
BPBE	0.907	1.99 (1.59)	2.30	3605.91
B971	0.905	2.02 (1.80)	2.22	6531.22
OLYP	0.906	2.00 (1.60)	2.18	3668.72
PBE1PBE	0.902	2.04 (1.84)	2.21	6767.88
B3LYP	0.905	2.01 (1.70)	2.34	6686.93

^aThis column contains the list of the 10 functionals tested in this work. The best result for each functional (in terms of these parameters) is high-lighted in bold face in Columns 2–4.

^bThe correlation coefficient, R, (or Pearson coefficient) between the observed and the conformational-averaged ¹³C^α chemical shifts, computed with eq. (2), for each of the functionals listed in Column 1.

^cStandard deviation of the computed conformational-averaged ¹³C^α chemical shifts from a linear regression. The standard deviation (σ) of the Normal (or Gaussian) curve that fits the frequency of the error distribution computed by using an effective TMS value as given by Table 2 (see “Materials and Methods” section) is shown in parentheses.

^dCa-rmsd was computed by using eq. (3), as described in the “Materials and Methods” section. For each functional, the ca-rmsd was computed by using the effective TMS value listed in Table 1.

^eAveraged-CPU time computed by using eq. (5) from conformation 1 out of 10 conformations of 1D3Z. The CPU times that, on average, require ^~1 h are set in bold face.