A critical investigation of proposed electrostatic corrections to quantum mechanical volumes: the importance of variation and the irrelevance of imbalance

Figures & data

Figure 1. The electron density isosurface for compound 1 with the B3LYP functional. The illustration was produced with the GaussView 4.1 software [29].

Table 1. Model prediction errors (RMSEP). All volumes are given in units of cm³/mol.

	Isosurface	Π	σ		Θ
B3LYP	7.40	6.27	6.04	6.59	7.63
M05	7.49	6.39	6.16	6.75	7.72

Table 2. Listed are the B3LYP/6-31G(d) enclosed volumes V_encl in our study, and the B3LYP/6-31G(d,p) enclosed volumes obtained by Rice et al. [5,8] using the geometry in the crystal as the initial guess. All values are given in cm³/mol.

Structure	Formula	Compound	Vencl
	C3H5N7O5	1	126.0	125.1
	C12H11NO3	26	151.6	152.3
	C6H4N2O5	33	108.1	108.2
	CH2N6O2	40	74.2	73.7

Table 3. Fitted parameters for the enclosed volume estimates and the models including Π and σ corrections. The AICc values are listed with respect to the model the lowest value. The unit of β is cm³/(mol Hartree) and the unit of γ is cm³/mol.

		β	γ	AICc − AICcmin
B3LYP/6-31G(d)	Enclosed (14(14) )	–	2.332	15.8
	Π (15a(15a) )	−703.735	18.380	1.9
	σ (15b(15b) )	−720.314	22.296	0.0

Figure 2. Error distributions of the models. The M05 distributions are illustrated in dark grey, while those of B3LYP are light grey. The errors are given in cm³/mol.

Figure 3. The error of the enclosed volume estimates V_encl plotted against σ. Non-CHNO compounds are shown in dark grey, and CHNO compounds in light grey. The values of σ and V_encl were computed with the M05 functional and are given in units of Hartree and cm^3/mol, respectively.

Figure 4. The values of plotted against the variation quantities σ² (top) and (bottom). All values are given in Hartree².

R. Dennington, T. Keith, and J. Millam, Gaussview Version 4.1 (Semichem Inc. Shawnee Mission KS, 2007).

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B.M. Rice, J.J. Hare, and E.F.C. Byrd, J. Phys. Chem. A 111 (42), 10874–10879 (2007).

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B.M. Rice and E.F.C. Byrd, J. Comput. Chem. 34 (25), 2146–2151 (2013).

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