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. 2013 Nov 8;139(18):184103. doi: 10.1063/1.4826261

Table 2.

Raw and corrected charging free energies. For each system (Table 1) and box edge length L, the following quantities are reported: the number NS of freely moving water molecules in the computational box; the discrete solvent correction terms ΔΔGDSI (infinite system limit) and ΔΔGDSF (finite-system adjustment), see Eq. 31; the finite-size correction terms ΔΔGNUM (numerical estimate) or ΔΔGANA (analytical estimate), see Eqs. 12, 14; the difference ΔΔGANA-NUM between these two quantities; the raw ligand charging free energy ΔΔGMD,PBC based on the MD simulations; the corresponding corrected ligand charging free energies ΔΔGMD,NBC,NUM or ΔΔGMD,NBC,ANA, see Eqs. 10, 11; the estimated statistical uncertainty σ[ΔGMD] on the raw MD results, calculated as described in Sec. 3A. The quantity ΔΔGMD,PBC is calculated from Eq. 6. The corresponding raw data can be found in Table S1 of the supplementary material.154 The terms ΔΔGDSI and ΔΔGDSF are calculated from Eqs. 31, 32, 35 using the indicated NS along with MS = 18.015 g mol−1, γS = 0.0764 e nm2 and ρS = 997 kg m−3. The term ΔΔGNUM is interpolated to the indicated L based on the results of Table 4 using a polynomial fit of the form of Eq. 38. The corresponding coefficients can be found in Table S3 of the supplementary material.154 The term ΔΔGANA is calculated using the parameters reported in Table 3. For both ΔΔGNUM and ΔΔGANA, the correction relies on PB calculations with a probe-contact solvent-accessible surface based on a probe radius RS = 0.14 nm (CTC(0.14)). The data are displayed graphically in Figure 4 (see also Figure S1 of the supplementary material154 for a corresponding graph with CTC(0.10)). Additional results concerning the systems with counter-ions can be found in Table S2 of the supplementary material.154

    ΔΔGDSI ΔΔGDSF ΔΔGNUM ΔΔGANA ΔΔGANA-NUM ΔGMD,PBC ΔGMD,NBC,NUM ΔGMD,NBC,ANA σ[ΔGMD]
L (nm) NS (kJ mol−1) (kJ mol−1) (kJ mol−1) (kJ mol−1) (kJ mol−1) (kJ mol−1) (kJ mol−1) (kJ mol−1) (kJ mol−1)
lig
3.05 928 −74.10 1.39 0.80 0.78 −0.02 −198.67 −270.59 −270.60 0.25
3.48 1380 −74.10 1.26 0.67 0.66 −0.01 −198.73 −270.91 −270.92 0.25
3.87 1904 −74.10 1.18 0.59 0.58 −0.01 −198.10 −270.43 −270.44 0.26
4.28 2572 −74.10 1.11 0.52 0.52 0.00 −198.10 −270.57 −270.58 0.26
4.68 3362 −74.10 1.08 0.47 0.47 0.00 −198.21 −270.76 −270.76 0.26
4.99 4088 −74.10 1.08 0.44 0.43 −0.01 −197.98 −270.57 −270.57 0.26
5.49 5423 −74.10 1.04 0.39 0.39 0.00 −198.04 −270.72 −270.72 0.28
6.29 8174 −74.10 1.02 0.34 0.34 0.00 −197.62 −270.37 −270.37 0.27
7.07 11 638 −74.10 1.00 0.30 0.30 0.00 −197.75 −270.55 −270.55 0.27
7.86 15 948 −74.10 1.00 0.27 0.27 0.00 −197.74 −270.58 −270.58 0.27
8.69 21 472 −74.10 1.33 0.24 0.24 0.00 −197.57 −270.10 −270.10 0.27
9.50 28 248 −74.10 0.94 0.22 0.22 0.00 −197.75 −270.70 −270.70 0.27
10.32 36 184 −74.10 0.93 0.20 0.20 0.00 −197.96 −270.94 −270.94 0.27
11.08 44 761 −74.10 0.91 0.19 0.19 0.00 −197.54 −270.55 −270.55 0.27
11.91 55 685 −74.10 0.90 0.17 0.17 0.00 −197.60 −270.63 −270.63 0.26
12.72 67 804 −74.10 0.89 0.16 0.16 0.00 −197.85 −270.90 −270.90 0.27
13.49 80 897 −74.10 0.88 0.15 0.15 0.00 −197.69 −270.76 −270.76 0.28
net-5
7.42 12 077 −74.10 8.33 −11.66 −11.77 −0.11 −200.76 −278.20 −278.30 0.31
7.82 14 377 −74.10 7.22 −10.22 −10.30 −0.08 −201.03 −278.14 −278.22 0.28
8.22 16 875 −74.10 6.51 −9.03 −9.09 −0.06 −200.69 −277.32 −277.38 0.33
8.62 19 798 −74.10 5.34 −8.04 −8.08 −0.04 −201.50 −278.30 −278.34 0.27
9.02 22 999 −74.10 4.39 −7.20 −7.23 −0.03 −201.43 −278.35 −278.38 0.29
9.42 26 492 −74.10 3.60 −6.49 −6.52 −0.03 −201.80 −278.80 −278.82 0.30
9.82 30 296 −74.10 2.93 −5.89 −5.90 −0.01 −201.30 −278.36 −278.37 0.36
10.22 34 748 −74.10 1.69 −5.37 −5.38 −0.01 −200.54 −278.32 −278.33 0.33
10.62 38 852 −74.10 1.95 −4.91 −4.92 −0.01 −201.36 −278.43 −278.44 0.30
11.02 43 591 −74.10 1.65 −4.52 −4.52 0.00 −201.72 −278.70 −278.70 0.33
net0
7.42 12 077 −74.10 8.33 −0.22 −0.17 0.05 −193.97 −259.96 −259.91 0.12
7.82 14 377 −74.10 7.22 −0.16 −0.12 0.04 −193.05 −260.10 −260.05 0.17
8.22 16 875 −74.10 6.51 −0.11 −0.08 0.03 −192.48 −260.18 −260.15 0.12
8.62 19 798 −74.10 5.34 −0.07 −0.04 0.03 −191.45 −260.28 −260.26 0.15
9.02 22 999 −74.10 4.39 −0.04 −0.02 0.02 −191.62 −261.38 −261.36 0.57
9.42 26 492 −74.10 3.60 −0.01 0.00 0.01 −190.53 −261.04 −261.03 0.48
9.82 30 296 −74.10 2.93 0.01 0.02 0.01 −189.59 −260.75 −260.74 0.19
10.22 34 748 −74.10 1.69 0.03 0.03 0.00 −188.85 −261.24 −261.23 0.18
10.62 38 852 −74.10 1.95 0.04 0.04 0.00 −188.86 −260.97 −260.97 0.19
11.02 43 591 −74.10 1.65 0.05 0.05 0.00 −188.87 −261.28 −261.28 0.33
11.42 49 170 −74.10 0.67 0.06 0.06 0.00 −187.93 −261.31 −261.31 0.20
11.82 53 925 −74.10 1.47 0.07 0.06 −0.01 −188.45 −261.02 −261.02 0.04
12.22 60 146 −74.10 0.79 0.07 0.07 0.00 −187.91 −261.15 −261.16 0.08
12.62 66 411 −74.10 0.61 0.08 0.07 −0.01 −188.04 −261.46 −261.46 0.25
13.02 72 810 −74.10 0.73 0.08 0.08 0.00 −187.98 −261.27 −261.28 0.38
net3
7.42 12 077 −74.10 8.33 6.96 7.17 0.21 −197.07 −255.88 −255.68 0.22
7.82 14 377 −74.10 7.22 6.15 6.32 0.17 −195.11 −255.85 −255.68 0.23
8.22
 16 875
 −74.10
 6.51
 5.48
 5.61
 0.13
 −193.48
 −255.60
 −255.47
 0.21
8.62 19 798 −74.10 5.34 4.91 5.02 0.11 −192.03 −255.88 −255.77 0.22
9.02 22 999 −74.10 4.39 4.44 4.52 0.08 −190.89 −256.18 −256.09 0.21
9.42 26 492 −74.10 3.60 4.03 4.10 0.07 −190.50 −256.97 −256.90 0.27
9.82 30 296 −74.10 2.93 3.68 3.74 0.06 −189.19 −256.68 −256.62 0.24
10.22 34 748 −74.10 1.69 3.38 3.42 0.04 −188.34 −257.37 −257.33 0.24
10.62 38 852 −74.10 1.95 3.11 3.15 0.04 −187.61 −256.65 −256.62 0.24
11.02 43 591 −74.10 1.65 2.88 2.91 0.03 −187.65 −257.23 −257.20 0.22
net9
7.42 12 077 −74.10 8.33 20.06 20.65 0.59 −205.70 −251.41 −250.83 0.21
7.82 14 377 −74.10 7.22 17.69 18.16 0.47 −202.22 −251.42 −250.95 0.19
8.22 16 875 −74.10 6.51 15.72 16.10 0.38 −199.97 −251.84 −251.46 0.22
8.62 19 798 −74.10 5.34 14.08 14.38 0.30 −197.18 −251.87 −251.57 0.22
9.02 22 999 −74.10 4.39 12.69 12.93 0.24 −195.58 −252.60 −252.36 0.22
9.42 26 492 −74.10 3.60 11.51 11.70 0.19 −193.28 −252.27 −252.08 0.21
9.82 30 296 −74.10 2.93 10.49 10.65 0.16 −192.09 −252.76 −252.61 0.24
10.22 34 748 −74.10 1.69 9.62 9.74 0.12 −191.46 −254.25 −254.13 0.35
10.62 38 852 −74.10 1.95 8.85 8.95 0.10 −189.59 −252.89 −252.79 0.23
11.02 43 591 −74.10 1.65 8.19 8.27 0.08 −188.59 −252.86 −252.78 0.24
net9quad
7.42 12 077 −74.10 8.33 −18.39 −17.82 0.57 −190.11 −274.27 −273.70 0.21
7.82 14 377 −74.10 7.22 −15.16 −14.70 0.46 −192.76 −274.81 −274.35 0.21
8.22 16 875 −74.10 6.51 −12.56 −12.19 0.37 −194.10 −274.26 −273.88 0.25
8.62 19 798 −74.10 5.34 −10.45 −10.15 0.30 −195.46 −274.67 −274.38 0.26
9.02 22 999 −74.10 4.39 −8.72 −8.48 0.24 −195.51 −273.94 −273.70 0.24
9.42 26 492 −74.10 3.60 −7.29 −7.09 0.20 −195.89 −273.68 −273.49 0.25
9.82 30 296 −74.10 2.93 −6.10 −5.94 0.16 −198.43 −275.69 −275.54 0.23
10.22 34 748 −74.10 1.69 −5.10 −4.98 0.12 −197.67 −275.18 −275.06 0.28
10.62 38 852 −74.10 1.95 −4.26 −4.16 0.10 −199.01 −275.43 −275.33 0.22
11.02 43 591 −74.10 1.65 −3.56 −3.47 0.09 −198.69 −274.71 −274.62 0.27
net-5ion
7.42 12 022 −74.10 8.63 −0.31 −0.71 −0.40 −207.89 −273.68 −274.08 0.31
7.82 14 314 −74.10 7.51 −0.23 −0.58 −0.35 −206.93 −273.76 −274.11 0.19
8.22 16 804 −74.10 6.79 −0.17 −0.48 −0.31 −205.73 −273.21 −273.52 0.40
8.62 19 715 −74.10 5.63 −0.13 −0.39 −0.26 −205.91 −274.51 −274.78 0.53
9.02 22 906 −74.10 4.67 −0.09 −0.32 −0.23 −204.83 −274.36 −274.59 0.21
9.42 26 387 −74.10 3.88 −0.06 −0.26 −0.20 −204.60 −274.88 −275.09 0.45
9.82 30 177 −74.10 3.21 −0.03 −0.22 −0.19 −204.19 −275.11 −275.30 0.16
10.22 34 615 −74.10 1.97 −0.01 −0.18 −0.17 −202.71 −274.86 −275.02 0.50
10.62 38 703 −74.10 2.23 0.01 −0.14 −0.15 −203.10 −274.97 −275.12 0.22
11.02 43 424 −74.10 1.93 0.03 −0.11 −0.14 −202.52 −274.68 −274.82 0.32
net9ion
7.42 12 017 −74.10 8.66 1.15 0.76 −0.39 −190.27 −254.56 −254.95 0.34
7.82 14 309 −74.10 7.53 1.02 0.68 −0.34 −188.59 −254.14 −254.48 0.30
8.22 16 799 −74.10 6.81 0.91 0.61 −0.30 −188.09 −254.48 −254.77 0.28
8.62 19 710 −74.10 5.64 0.81 0.55 −0.26 −188.36 −256.01 −256.27 0.43
9.02 22 901 −74.10 4.68 0.73 0.50 −0.23 −186.51 −255.20 −255.44 0.21
9.42 26 382 −74.10 3.89 0.66 0.46 −0.20 −185.97 −255.52 −255.73 0.28
9.82 30 172 −74.10 3.23 0.61 0.42 −0.19 −185.75 −256.02 −256.21 0.11
10.22 34 610 −74.10 1.98 0.56 0.39 −0.17 −184.31 −255.88 −256.05 0.41
10.62 38 698 −74.10 2.23 0.51 0.36 −0.15 −183.80 −255.16 −255.31 0.26
11.02 43 419 −74.10 1.93 0.47 0.34 −0.13 −183.27 −254.97 −255.10 0.28