. Author manuscript; available in PMC: 2009 Apr 6.

Published in final edited form as: J Chem Theory Comput. 2008;4(12):2067–2084. doi: 10.1021/ct800330d

Table 7.

Benchmark results for SCC-DFTB for the 19 Phosphate Reactions from the QCRNA Database^a

		Error Analysis^b
State	Property^c
		MAXE	RMSE	MUE	MSE
Overall	Energy SP (2^nd-order)^e	−24.6	10.3	8.2	−6.0
Overall	Energy SP (SCC-DFTBPR)	14.4	5.6	4.8	−0.2

Stable States	Energy SP (2^nd-order)	−23.9	9.9	7.9	−4.6
	Energy SP (SCC-DFTBPR)	14.4	5.3	4.3	1.0
	Energy OPT (2^nd-order)	−27.2	11.8	9.1	−6.1
	Energy OPT (SCC-DFTBPR)	14.8	5.3	4.5	−0.8
	P-O (Å) OPT (SCC-DFTBPR)^d	0.45/0.19	0.07/0.035	0.03/0.02	0.00/0.00
	O-P-O (°) OPT (SCC-DFTBPR)^e	−9.3	2.2	1.5	0.0

Transition states	Energy SP (2^nd -order)	−24.6	10.6	8.7	−7.5
Transition states	Energy SP (SCC -DFTBPR)	12.8	6.0	5.4	−1.6

Dipole Moment ^f	2^nd -order)	−1.2/−1.2	0.6/0.6	0.5/0.5	−0.4/−0.4
Dipole Moment ^f	SCC-DFTBPR	0.8/1.1	0.3/0.5	0.2/0.3	0.1/0.1

^a)

The reference values are from the B3LYP calculations included in the QCRNA database (http://theory.chem.umn.edu/QCRNA/). The energies are in kcal/mol and dipole moments in Debye. For specific values, see Supporting Materials.

^b)

The errors are defined in the same manner as in Table 3.

^c)

“Energy” refers to reaction energy (energy relative to the reactant state); “SP” represents single point calculation at the QCRNA structures; “OPT” indicates full geometry optimization at the relevant SCC-DFTB level with the B3LYP reference structure as the initial guess.

^d)

The number before the slash is the performance including all the P-O distances (in total, 327 P-O distances are studied); the number after the slash excludes one parameter from C6H5OH…P(O)(O)(-O-sugar-O-)_min2, (CH3)2CHOH…P(O)(O)(-O-sugar-O-)_min3, CH3OH…P(O)(O)(-O-CH2CH2-O-)_min3, CH3OH…P(O)(O)(-O-sugar-O-)_min3, HOH…P(O)(O)(-O-2'methyl-sugar-O-)_min3a, HOH…P(O)(O)(-O-CH2CH2-O-)_min3; the notation scheme follows the QCRNA convention (http://theory.chem.umn.edu/QCRNA/Nomenclature.html).

^e)

In total, 568 O-P-O angles are analyzed.

^f)

Numbers before slashes are from single point calculations at the DFT geometries from the QCRNA database; those after the slashes are after geometry optimization at the respective SCC-DFTB levels. The reference values are from QCRNA database at the level of B3LYP/6-311++G(3df,2p)//B3LYP/6-31++G(d,p).