Trials of Refining Multiple Lennard-Jones Parameters

Trials of refining multiple Lennard-Jones parameters

Initially, we looked for a set of Lennard-Jones (LJ) parameters that could predict the dimensions of the unit cells of the four allomorphs with good accuracy. The partial atomic charges were unchanged from the native GROMOS 53a6. Each optimization of the LJ parameters involved four independent simulations: in each simulation, three allomorphs of cellulose out of the four were selected for the refinement and the remaining one was used to test the optimized parameters.

Figure S1: Occurrence density (occurrence divided by distance2and by the step size of the histogram)as a function of distance between non-bonded carbon atoms linked to different neighbor atom types in crystal structures compiled in Cambridge Structural Database. Top: atom type CH1, bottom atom type CH2.

In the GROMOS 53a6 force field, the glucose residue is defined by four types of LJ atoms: CH1, CH2, OA and H. However, the distribution of the non-bonded CH1 to CH1 distances observed in crystal structures from the Cambridge database strongly depends on the type of other atoms attached to the carbon atom (Fig.S1 top) contrary to the CH2- CH2 which has a peak at about 4Å irrespective of the neighbor atoms (Fig. S1 bottom). Carbon atoms having more oxygen as neighbors have a clear tendency to be closer to each other. In cellulose, the anomeric carbon bears two oxygen atoms whereas all the other CH1 atoms are bound to two carbon atoms and one oxygen atom. We thus defined a supplementary carbon atom type, C1, specific to the anomeric carbon. Similarly, the alcohol and ether oxygen atoms would have different steric volume, so we introduced the atom type Or for the ring oxygen and the glycosidic oxygen. The bonded parameters and the partial atomic charges of C1 and Or where those of CH1 and OA atom types as defined in the original force field. Neglecting the hydrogen, this makes a total of 5 atom types requiring 10 LJ parameters to be optimized.

We could find sets of these 10 LJ parameters that significantly improve the prediction of unit cell parameters, as indicated by the decreased values of the target function, between 3 and 11 compared to the 200-300 using the original parameters (table S1). However, the optimized LJ parameters of the Or atom type varied considerably, leading to values of the energy minimum, ε, ranging from 2.19 to 60.61 kJ mol-1(table S1b) which were obviously unrealistic. Hence, the ether oxygen atoms, O1 and O5, were no longer treated separately from the hydroxyl oxygen atoms.

When all oxygen atoms in the glucose residue were set to OA atom type, 8 LJ parameters of 4 different atom types have to be optimized. Under such conditions, we could also find sets of parameters that give reasonable agreement for unit cell parameters of three allomorphs, with a minimal value of the target function of 9.5 (tables S2). However, some of these sets of parameters, for instance, the one excluding Iβ and the one excluding II, were not able to improve the agreement with the unit cell of the fourth allomorph, which was left out from the optimization process. Furthermore, the optimized set of LJ parameters for which the target function is minimal gives unrealistic optimal separation for the C1 and CH2 atom types, when compared to the original parameter. Further decreasing the number of parameters by merging the type CH1 and C1 did not improve this situation(tables s3) Thus we concluded that the optimization of the LJ parameters of GROMOS 53a6, without modifying the partial charges on the atoms, cannot give a robust parameter set for modeling crystalline cellulose.

Tables S1: Optimizing the LJ parameters of the 5 types of atom: CH1, CH2, C1, OA and Or.

TableS1a: Parameters: C61/2 (kJ mol-1 nm6 )1/2 and C121/2 (kJ mol-1 nm12 )1/2 optimized against unit cell parameters of three allomorphs as target and correspondingvalues of target function Fmin.

Target allomorphs / CH1 / CH2 / C1 / OA / Or / Finit / Fmin
C61/2
x1e4 / C121/2
x1e5 / C61/2
x1e4 / C121/2
x1e5 / C61/2
x1e4 / C121/2
x1e5 / C61/2
x1e4 / C121/2
x1e5 / C61/2
x1e4 / C121/2
x1e5
Initial / 779 / 985 / 864 / 583 / 779 / 985 / 476 / 110 / 476 / 110 / 336a
Excl. III / 1685 / 925 / 635 / 595 / 782 / 1693 / 178 / 98 / 468 / 74 / 214 / 11.6
Excl. II / 895 / 578 / 925 / 845 / 882 / 1214 / 404 / 126 / 607 / 63 / 297 / 5.1
Excl. Iβ / 1346 / 864 / 725 / 498 / 2754 / 2375 / 157 / 93 / 189 / 4 / 257 / 2.9
Excl. Iα / 811 / 761 / 420 / 595 / 1405 / 1303 / 478 / 112 / 688 / 30 / 239 / 6.6

a value including all allomorphs

Table S1b:Distanceσ (nm) and energy ε(kJ mol-1) at the minimum of Lennard-Jones energy between identical atom types corresponding to the optimized parameters in table S1a.

Target allomorphs / CH1 / CH2 / C1 / OA / Or
σ / ε / σ / ε / σ / ε / σ / ε / σ / ε
Initial / 0.50 / 0.09 / 0.41 / 0.41 / 0.50 / 0.09 / 0.28 / 1.06 / 0.28 / 1.06
Excl. III / 0.38 / 2.36 / 0.45 / 0.11 / 0.60 / 0.03 / 0.38 / 0.03 / 0.25 / 2.19
Excl. II / 0.40 / 0.48 / 0.45 / 0.26 / 0.52 / 0.10 / 0.31 / 0.42 / 0.22 / 8.59
Excl. Iβ / 0.40 / 1.10 / 0.41 / 0.28 / 0.44 / 2.55 / 0.39 / 0.02 / 0.13 / 16.1
Excl. Iα / 0.45 / 0.19 / 0.52 / 0.02 / 0.45 / 0.57 / 0.29 / 1.05 / 0.16 / 60.6

Table S1c:Predicted unit cell parameters of four allomorphs using the optimized L-J parameters of table S1a.

Allomorph / a (Å) / b (Å) / c (Å) / α (°) / β (°) / γ (°)
Cellulose Iβ / Excl. III / 7.918 / 8.098 / 10.40 / 90.01 / 90.01 / 97.37
Excl. II / 7.828 / 8.241 / 10.38 / 90.11 / 89.95 / 97.59
Excl. Iβ / 7.865 / 8.092 / 10.20 / 90.08 / 89.97 / 97.50
Excl. Iα / 7.846 / 8.128 / 10.16 / 90.00 / 89.99 / 96.64
Cellulose Iα / Excl. III / 6.81 / 5.965 / 10.41 / 117.2 / 114.7 / 80.31
Excl. II / 6.657 / 5.978 / 10.38 / 117.3 / 114.6 / 81.62
Excl. Iβ / 6.673 / 5.917 / 10.22 / 117.4 / 114.6 / 80.32
Excl. Iα / 6.691 / 5.884 / 10.17 / 117.1 / 114.1 / 81.21
Cellulose II / Excl. III / 8.144 / 8.951 / 10.32 / 90.03 / 90.00 / 117.9
Excl. II / 8.434 / 8.767 / 10.31 / 90.03 / 90.01 / 118.0
Excl. Iβ / 8.069 / 8.967 / 10.21 / 90.03 / 90.01 / 117.7
Excl. Iα / 8.158 / 8.927 / 10.20 / 90.01 / 90.00 / 117.0
Cellulose III / Excl. III / 4.475 / 7.918 / 10.29 / 90.00 / 90.02 / 104.4
Excl. II / 4.394 / 7.908 / 10.33 / 90.15 / 90.04 / 104.4
Excl. Iβ / 4.464 / 7.901 / 10.21 / 89.99 / 90.00 / 105.2
Excl. Iα / 4.494 / 7.751 / 10.19 / 90.73 / 89.74 / 105.1

TableS1d: Deviation (%) between the predicted unit cell parameters and the experimental ones.

Allomorph / a / b / c / α / β / γ
Cellulose Iβ / Excl. III / 1.72 / -1.26 / 0.19 / 0.01 / 0.01 / 0.85
Excl. II / 0.57 / 0.49 / 0.00 / 0.12 / -0.06 / 1.08
Excl.Iβ / 1.04 / -1.33 / -1.73 / 0.09 / -0.03 / 0.98
Excl.Iα / 0.80 / -0.89 / -2.12 / 0.00 / -0.01 / 0.09
Cellulose Iα / Excl. III / 1.38 / 0.05 / 0.10 / -0.77 / -0.10 / -0.07
Excl. II / -0.89 / 0.27 / -0.19 / -0.68 / -0.17 / 1.56
Excl.Iβ / -0.66 / -0.75 / -1.73 / -0.60 / -0.16 / -0.06
Excl.Iα / -0.39 / -1.31 / -2.21 / -0.84 / -0.63 / 1.05
Cellulose II / Excl. III / 1.67 / -0.87 / 0.10 / 0.03 / 0.00 / 0.73
Excl. II / 5.29 / -2.91 / 0.00 / 0.03 / 0.01 / 0.79
Excl.Iβ / 0.74 / -0.70 / -0.97 / 0.03 / 0.01 / 0.50
Excl.Iα / 1.85 / -1.14 / -1.07 / 0.01 / 0.00 / -0.09
Cellulose III / Excl. III / 0.56 / 0.87 / -0.19 / 0.00 / 0.02 / -0.69
Excl. II / -1.26 / 0.74 / 0.19 / 0.17 / 0.04 / -0.69
Excl.Iβ / 0.31 / 0.65 / -0.97 / -0.01 / 0.00 / 0.06
Excl.Iα / 0.99 / -1.26 / -1.16 / 0.81 / -0.29 / 0.04

Tables S2: Optimizing the LJ parameters of the 4 types of atom: CH1, CH2, C1 and OA.

Table S2a: ParametersC61/2 (kJ mol-1 nm6 )1/2 and C121/2 (kJ mol-1 nm12 )1/2 optimized against unit cell parameters of three allomorphs as target and the corresponding value of target function Fmin

Target allomorphs / CH1 / CH2 / C1 / OA
C61/2
x1e4 / C121/2
x1e5 / C61/2
x1e4 / C121/2
x1e5 / C61/2
x1e4 / C121/2
x1e5 / C61/2
x1e4 / C121/2
x1e5 / Finit / Fmin
Initial / 779 / 985 / 864 / 583 / 779 / 985 / 476 / 110 / 336
Excl. III / 1195 / 536 / 731 / 8224 / 724 / 1403 / 261 / 95 / 214 / 18.8
Excl. II / 762 / 334 / 1129 / 900 / 847 / 1305 / 400 / 115 / 297 / 22.0
Excl. Iβ / 1691 / 887 / 681 / 141 / 360 / 1395 / 354 / 82 / 257 / 9.55
Excl. Iα / 864 / 609 / 869 / 1106 / 847 / 1040 / 495 / 94 / 239 / 24.1

Table S2b:Distanceσ (Å) and energy ε(kJ mol-1) at the minimum ofLennard-Jones energy between two identical atom types corresponding to the optimized parameters in table S2a.

Target allomorphs / CH1 / CH2 / C1 / OA
σ / ε / σ / ε / σ / ε / σ / ε
Initial / 5.0 / 0.09 / 4.1 / 0.41 / 5.0 / 0.10 / 2.8 / 1.06
Excl. III / 3.6 / 1.77 / 10.4 / 0.00 / 5.8 / 0.03 / 3.3 / 0.22
Excl. II / 3.5 / 0.76 / 4.3 / 0.50 / 5.4 / 0.08 / 3.1 / 0.46
Excl. Iβ / 3.7 / 2.60 / 2.7 / 2.71 / 7.3 / 0.00 / 2.8 / 0.56
Excl. Iα / 4.1 / 0.37 / 5.0 / 0.12 / 5.0 / 0.12 / 2.7 / 0.32

Table S2c:Predicted unit cell parameters of four allomorphs using the optimized L-J parameters in table s2a.

Allomorph / a (Å) / b (Å) / c (Å) / α (°) / β (°) / γ (°)
Cellulose Iβ / Excl. III / 8.006 / 8.110 / 10.46 / 90.11 / 89.88 / 96.55
Excl. II / 7.939 / 8.168 / 10.47 / 89.89 / 90.17 / 96.16
Excl.Iβ / 7.143 / 7.674 / 10.23 / 89.46 / 90.42 / 90.86
Excl.Iα / 7.949 / 8.024 / 10.42 / 89.98 / 90.00 / 94.45
Cellulose Iα / Excl. III / 6.590 / 5.972 / 10.47 / 116.3 / 113.9 / 80.33
Excl. II / 6.492 / 6.031 / 10.47 / 116.6 / 114.8 / 80.40
Excl.Iβ / 6.656 / 5.991 / 10.43 / 116.4 / 113.7 / 79.68
Excl.Iα / 6.594 / 5.852 / 10.41 / 116.6 / 113.1 / 80.07
Cellulose II / Excl. III / 8.157 / 8.741 / 10.37 / 90.03 / 90.02 / 116.2
Excl. II / 8.031 / 8.002 / 10.19 / 90.01 / 89.99 / 118.5
Excl.Iβ / 8.120 / 8.984 / 10.37 / 90.05 / 90.02 / 118.3
Excl.Iα / 8.065 / 8.785 / 10.36 / 90.02 / 89.99 / 116.7
Cellulose III / Excl. III / 4.498 / 7.791 / 10.34 / 89.93 / 90.26 / 103.2
Excl. II / 4.497 / 7.778 / 10.33 / 90.03 / 89.87 / 103.4
Excl.Iβ / 4.475 / 7.858 / 10.31 / 89.94 / 90.26 / 103.3
Excl.Iα / 4.489 / 7.772 / 10.31 / 90.01 / 89.98 / 103.8

Table S2d: Deviation (%) between the predicted unit cell parameters and the experimental ones.

Allomorph / a / b / c / α / β / γ
Cellulose Iβ / Excl. III / 2.85 / -1.11 / 0.75 / 0.12 / -0.13 / 0.00
Excl. II / 1.99 / -0.40 / 0.84 / -0.12 / 0.19 / -0.40
Excl.Iβ / -8.23 / -6.43 / -1.43 / -0.60 / 0.47 / -5.89
Excl.Iα / 2.12 / -2.16 / 0.36 / -0.03 / 0.00 / -2.17
Cellulose Iα / Excl. III / -1.89 / 0.17 / 0.62 / -1.50 / -0.83 / -0.05
Excl. II / -3.35 / 1.16 / 0.67 / -1.26 / 0.02 / 0.04
Excl.Iβ / -0.91 / 0.49 / 0.28 / -1.42 / -0.97 / -0.86
Excl.Iα / -1.83 / -1.85 / 0.11 / -1.23 / -1.45 / -0.37
Cellulose II / Excl. III / 1.84 / -3.20 / 0.59 / 0.03 / 0.02 / -0.74
Excl. II / 0.26 / -11.4 / -1.13 / 0.01 / -0.01 / 1.19
Excl.Iβ / 1.37 / -0.51 / 0.56 / 0.06 / 0.02 / 1.02
Excl.Iα / 0.69 / -2.71 / 0.46 / 0.02 / -0.01 / -0.35
Cellulose III / Excl. III / 1.08 / -0.75 / 0.27 / -0.08 / 0.29 / -1.79
Excl. II / 1.06 / -0.92 / 0.19 / 0.03 / -0.14 / -1.61
Excl.Iβ / 0.56 / 0.10 / 0.01 / -0.07 / 0.29 / -1.72
Excl.Iα / 0.88 / -0.99 / -0.01 / 0.01 / -0.02 / -1.27

Tables S3: Optimizing the LJ parameters of the 3 types of atom: CH1, C1 and OA.

Table S3a: Optimized parameters: C61/2 (kJ mol-1 nm6 )1/2 and C121/2 (kJ mol-1 nm12 )1/2, corresponding values of target function Fmin.

Target allomorphs / CH1 / C1 / OA / Fmin
C61/2
x1e4 / C121/2
x1e5 / C61/2
x1e4 / C121/2
x1e5 / C61/2
x1e4 / C121/2
x1e5 / Finit
Initial / 779 / 9850 / 779 / 985 / 476 / 110 / 336
excl. III / 1392 / 6599 / 1213 / 1359 / 91 / 94 / 214 / 20.29
excl. II / 1314 / 5869 / 982 / 1335 / 269 / 132 / 297 / 19.84
excl. Iβ / 1382 / 6302 / 1012 / 1384 / 67 / 87 / 257 / 13.1
excl. Iα / 1051 / 7443 / 767 / 1071 / 503 / 120 / 239 / 13.6
All / 1337 / 6570 / 1202 / 1109 / 80 / 90 / 336 / 27.38

Table S3b:Distanceσ (Å) and energy ε(kJ mol-1 ) at the minimum of Lennard-Jones energy between two identical atom types corresponding to the optimized LJ parameters in table s3a.

Target allomorphs / CH1 / C1 / OA
σ / ε / σ / ε / σ / ε
Initial / 5.0 / 0.09 / 5.0 / 0.09 / 2.8 / 1.06
excl. III / 3.6 / 2.16 / 4.8 / 0.29 / 4.7 / 0.00
excl. II / 3.5 / 2.16 / 5.1 / 0.13 / 3.7 / 0.08
excl. Iβ / 3.6 / 2.30 / 5.2 / 0.14 / 5.1 / 0.00
excl. Iα / 4.4 / 0.33 / 5.2 / 0.07 / 2.9 / 1.21
All / 3.7 / 1.85 / 4.5 / 0.42 / 4.8 / 0.00

Table S3c:Predicted unit cell parameters of four allomorphs using the optimized L-J parameters in table s3a.

Allomorphs / a (Å) / b (Å) / c (Å) / α (°) / β (°) / γ (°)
Cellulose Iβ / excl. Iα / 7.754 / 8.152 / 10.48 / 90.02 / 89.99 / 94.28
excl.Iβ / 8.009 / 8.035 / 10.44 / 90.19 / 89.78 / 95.57
excl.II / 7.805 / 8.264 / 10.49 / 90.01 / 89.99 / 94.94
excl. III / 7.943 / 8.076 / 10.46 / 90.10 / 89.82 / 95.67
All / 7.925 / 8.043 / 10.44 / 90.07 / 89.93 / 95.30
Cellulose Iα / excl. Iα / 6.428 / 6.040 / 10.49 / 116.5 / 114.8 / 81.65
excl.Iβ / 6.532 / 5.971 / 10.46 / 116.1 / 113.9 / 79.93
excl.II / 6.553 / 6.111 / 10.51 / 117.2 / 115.8 / 81.53
excl. III / 6.538 / 5.962 / 10.47 / 116.2 / 113.9 / 80.45
All / 6.510 / 5.925 / 10.46 / 116.0 / 113.6 / 80.53
Cellulose II / excl. Iα / 8.123 / 8.873 / 10.36 / 90.01 / 90.01 / 116.0
excl.Iβ / 8.063 / 8.942 / 10.36 / 90.02 / 90.01 / 117.3
excl.II / 8.405 / 8.752 / 10.37 / 90.01 / 90.01 / 117.8
excl. III / 8.133 / 8.914 / 10.37 / 90.02 / 90.00 / 117.5
All / 8.125 / 8.919 / 10.36 / 90.02 / 90.01 / 117.9
Cellulose III / excl. Iα / 4.511 / 7.756 / 10.35 / 89.81 / 90.01 / 105.9
excl.Iβ / 4.458 / 7.834 / 10.34 / 90.00 / 90.02 / 104.2
excl.II / 4.350 / 8.036 / 10.38 / 89.95 / 90.18 / 103.7
excl. III / 4.446 / 7.884 / 10.33 / 90.01 / 90.02 / 104.1
All / 4.423 / 7.865 / 10.33 / 90.01 / 90.01 / 103.9

Table S4d: Deviation (in %) between the predicted unit cell parameters and the experimental ones.

Allomorphs / a / b / c / α / β / γ
Cellulose Iβ / excl. Iα / -0.39 / -0.60 / 0.92 / 0.02 / -0.01 / -2.35
excl. Iβ / 2.89 / -2.02 / 0.59 / 0.21 / -0.25 / -1.01
excl. II / 0.27 / 0.77 / 1.01 / 0.01 / -0.01 / -1.67
excl. III / 2.04 / -1.52 / 0.72 / 0.11 / -0.20 / -0.91
All / 1.81 / -1.93 / 0.59 / 0.08 / -0.08 / -1.30
Cellulose Iα / excl. Iα / -4.30 / 1.31 / 0.86 / -1.34 / -0.02 / 1.59
excl. Iβ / -2.75 / 0.15 / 0.54 / -1.67 / -0.75 / -0.54
excl. II / -2.44 / 2.50 / 1.03 / -0.76 / 0.87 / 1.44
excl. III / -2.66 / 0.00 / 0.66 / -1.62 / -0.75 / 0.10
All / -3.08 / -0.62 / 0.54 / -1.75 / -1.03 / 0.20
Cellulose II / excl. Iα / 1.41 / -1.74 / 0.51 / 0.01 / 0.01 / -0.92
excl. Iβ / 0.66 / -0.97 / 0.50 / 0.02 / 0.01 / 0.16
excl. II / 4.93 / -3.08 / 0.60 / 0.01 / 0.01 / 0.57
excl. III / 1.54 / -1.28 / 0.55 / 0.02 / 0.00 / 0.33
All / 1.44 / -1.23 / 0.52 / 0.02 / 0.01 / 0.66
Cellulose III / excl. Iα / 1.37 / -1.20 / 0.36 / -0.21 / 0.01 / 0.75
excl. Iβ / 0.18 / -0.20 / 0.26 / 0.00 / 0.02 / -0.85
excl. II / -2.25 / 2.37 / 0.69 / -0.06 / 0.20 / -1.34
excl. III / -0.09 / 0.43 / 0.23 / 0.01 / 0.02 / -0.94
All / -0.61 / 0.19 / 0.18 / 0.01 / 0.01 / -1.12

Table S4. Predicted unit cell parameters of the different allomorphs of cellulose by transferring the partial atomic charges of different force fields into GROMOS 53a6.

Force fields / a (Å) / b (Å) / c (Å) / α (°) / β (°) / γ (°) / RDγ(%)
Iβ / CHARMM C35 / 8.399(7) / 8.165(2) / 10.518(1) / 90.01(3) / 89.98(3) / 93.27(8) / -3.4
GLYCAM 06 / 8.319(5) / 8.126(2) / 10.510(1) / 90.00(3) / 89.99(2) / 92.74(2) / -3.9
GROMOS 53a6 / 8.384(6) / 8.159(2) / 10.515(1) / 90.00(4) / 90.00(4) / 90.82(7) / -5.9
GROMOS 56Acarbo / 8.379(8) / 8.178(2) / 10.503(1) / 89.99(4) / 90.01(4) / 93.09(7) / -3.6
GROMOS 87 / 8.513(5) / 8.247(3) / 10.503(1) / 90.05(4) / 89.95(5) / 93.28(9) / -3.4
Experiments / 7.784(8) / 8.201(8) / 10.38(1) / 90.00 / 90.00 / 96.55
Iα / CHARMM C35 / 6.614(2) / 6.288(3) / 10.527(1) / 115.34(3) / 114.04(3) / 78.49(3) / -2.3
GLYCAM 06 / 6.574(2) / 6.280(4) / 10.526(1) / 115.47(2) / 114.38(3) / 78.50(3) / -2.3
GROMOS 53a6 / 6.470(3) / 6.387(4) / 10.531(1) / 114.47(4) / 114.31(4) / 78.82(3) / -1.9
GROMOS 56Acarbo / 6.647(4) / 6.291(4) / 10.515(1) / 115.57(3) / 114.25(3) / 78.42(3) / -2.4
GROMOS 87 / 6.653(9) / 6.361(13) / 10.508(1) / 114.85(6) / 113.78(9) / 78.66(4) / -2.1
Experiments / 6.717(7) / 5.962(6) / 10.400(1) / 118.08(5) / 114.80(5) / 80.37(5)
II / CHARMM C35 / 8.028(1) / 9.439(3) / 10.455(1) / 90.03(1) / 90.02(1) / 113.10(1) / -3.4
GLYCAM 06 / 8.046(1) / 9.252(2) / 10.436(1) / 90.01(1) / 90.00(1) / 112.54(1) / -3.9
GROMOS 53a6 / 8.023(1) / 9.477(2) / 10.462(1) / 90.01(1) / 90.01(1) / 113.03(1) / -3.5
GROMOS 56Acarbo / 8.045(1) / 9.441(2) / 10.445(1) / 90.021(1) / 90.01(1) / 113.13(1) / -3.4
GROMOS 87 / 8.087(1) / 9.584(2) / 10.463(1) / 90.2(1) / 90.00(1) / 113.29(1) / -3.3
Experiments / 8.01(3) / 9.03(3) / 10.31(5) / 90 / 90 / 117.10(5)
IIII / CHARMM C35 / 4.918(1) / 7.777(1) / 10.446(1) / 89.99(1) / 90.03(1) / 105.94(1) / 0.8
GLYCAM 06 / 4.901(1) / 7.728(1) / 10.425(1) / 89.64(5) / 88.66(15) / 105.98(1) / 0.8
GROMOS 53a6 / 4.935(1) / 7.786(1) / 10.438(1) / 89.99(1) / 90.03(1) / 105.85(1) / 0.7
GROMOS 56Acarbo / 4.933(1) / 7.805(1) / 10.430(1) / 90.00(1) / 90.03(1) / 106.10(2) / 1.0
GROMOS 87 / 4.888(4) / 7.956(5) / 10.463(1) / 90.37(4) / 91.96(13) / 110.81(12) / 5.4
Experiments / 4.450(4) / 7.850(8) / 10.310(10) / 90 / 90 / 105.10(5)

Tables S5: Optimization of the repulsive LJ parameter of the CH1 atom type, using the charge distribution of Charmm C35.

Table S5a: Repulsion parameter: C121/2 (kJ mol-1 nm12 )1/2 optimiezed against one or all allomorphs of cellulose and the corresponding distanceσ (nm) and energy ε(kJ mol-1) at the minimum of Lennard-Jones energy between CH1, deviations (%) between the optimized parameter and its original valueandcorresponding values of target function Fmin.

Target structures / C61/2
x1e4 / C121/2
x1e5 / σ / ε / Δ(C121/2)% / Fint / Fmin
Initial / 779 / 985 / 0.50 / 0.09 / 269
Iα / 779 / 659 / 0.44 / 0.21 / -33.1 / 96 / 11
Iβ / 779 / 757 / 0.46 / 0.16 / -23.1 / 79 / 2.2
II / 779 / 726 / 0.45 / 0.17 / -26.3 / 38 / 3.4
III / 779 / 584 / 0.42 / 0.27 / -40.7 / 121 / 0.91
Four allomorphs / 779 / 697 / 0.45 / 0.19 / -31.7 / 269 / 30.38

Table S5b:predicted unit cell parameters of four allomorphs using the optimized L-J parameters in table s5a.

allomorph / target / a (Å) / b (Å) / c (Å) / α (°) / β (°) / γ (°)
Cellulose Iβ / Iα / 7.962 / 8.162 / 10.45 / 89.97 / 89.97 / 94.90
Iβ / 7.778 / 8.146 / 10.43 / 90.07 / 89.92 / 95.27
II / 7.914 / 8.154 / 10.45 / 90.03 / 89.94 / 95.07
III / 7.613 / 8.131 / 10.42 / 89.99 / 89.97 / 95.54
all / 7.803 / 8.149 / 10.44 / 89.98 / 90.03 / 95.27
Cellulose Iα / Iα / 6.551 / 6.050 / 10.46 / 116.1 / 114.1 / 80.66
Iβ / 6.493 / 5.945 / 10.44 / 116.4 / 113.9 / 81.69
II / 6.533 / 6.013 / 10.46 / 116.2 / 114.0 / 81.00
III / 6.460 / 5.855 / 10.43 / 116.7 / 113.9 / 82.50
all / 6.505 / 5.958 / 10.45 / 116.5 / 114.0 / 81.52
Cellulose II / Iα / 8.106 / 9.120 / 10.36 / 90.02 / 90.02 / 115.4
Iβ / 8.149 / 8.877 / 10.33 / 90.02 / 90.01 / 116.3
II / 8.123 / 9.037 / 10.35 / 90.03 / 90.01 / 115.7
III / 8.148 / 8.709 / 10.33 / 90.02 / 90.00 / 117.2
all / 8.147 / 8.923 / 10.34 / 90.01 / 90.01 / 116.1
Cellulose III / Iα / 4.664 / 7.841 / 10.34 / 90.00 / 90.01 / 105.1
Iβ / 4.566 / 7.836 / 10.31 / 90.00 / 90.00 / 104.5
II / 4.631 / 7.837 / 10.33 / 90.00 / 90.01 / 104.9
III / 4.480 / 7.839 / 10.28 / 89.99 / 90.01 / 104.0
all / 4.580 / 7.835 / 10.31 / 90.00 / 90.01 / 104.6

Table S5c: Deviation (%) between the predicted unit cell parameters and the experimental ones.

Allomorph / target / a / b / c / α / β / γ
Cellulose Iβ / Iα / 2.29 / -0.48 / 0.70 / -0.04 / -0.03 / -1.71
Iβ / -0.08 / -0.67 / 0.50 / 0.08 / -0.09 / -1.32
II / 1.67 / -0.57 / 0.65 / 0.03 / -0.07 / -1.53
III / -2.20 / -0.85 / 0.38 / -0.01 / -0.03 / -1.04
all / 0.24 / -0.63 / 0.54 / -0.02 / 0.03 / -1.32
Cellulose Iα / Iα / -2.47 / 1.48 / 0.62 / -1.67 / -0.65 / 0.36
Iβ / -3.33 / -0.29 / 0.41 / -1.39 / -0.75 / 1.64
II / -2.74 / 0.86 / 0.53 / -1.59 / -0.72 / 0.79
III / -3.83 / -1.79 / 0.28 / -1.15 / -0.80 / 2.65
all / -3.16 / -0.07 / 0.44 / -1.38 / -0.67 / 1.43
Cellulose II / Iα / 1.20 / 1.00 / 0.47 / 0.02 / 0.02 / -1.42
Iβ / 1.74 / -1.69 / 0.22 / 0.02 / 0.02 / -0.68
II / 1.41 / 0.08 / 0.37 / 0.03 / 0.01 / -1.20
III / 1.72 / -3.55 / 0.16 / 0.02 / 0.00 / 0.06
all / 1.71 / -1.18 / 0.25 / 0.01 / 0.01 / -0.82
Cellulose III / Iα / 4.81 / -0.11 / 0.27 / 0.00 / 0.01 / 0.00
Iβ / 2.61 / -0.18 / -0.05 / 0.00 / 0.00 / -0.56
II / 4.07 / -0.17 / 0.16 / 0.00 / 0.01 / -0.18
III / 0.67 / -0.14 / -0.29 / -0.01 / 0.01 / -1.01
all / 2.92 / -0.19 / 0.00 / 0.00 / 0.01 / -0.47

Table S5d: Comparison of unit cell parameters predicted by original L-J parameters and optimized repulsive parameter of CH1.

allomorph / a (Å) / b (Å) / c (Å) / α (°) / β (°) / γ (°)
Cellulose Iβ Exp. / 7.784 / 8.201 / 10.38 / 90 / 90 / 96.55
Opt. / 7.789 / 8.114 / 10.45 / 89.99 / 90 / 94.27
Ori. / 8.384 / 8.159 / 10.51 / 90 / 90 / 90.82
Cellulose Iα Exp. / 6.717 / 5.962 / 10.40 / 118.1 / 114.8 / 80.37
Opt. / 6.452 / 6.014 / 10.47 / 116.5 / 114.6 / 81.16
Ori. / 6.470 / 6.387 / 10.53 / 114.5 / 114.3 / 78.82
Cellulose II Exp. / 8.010 / 9.03 / 10.31 / 90 / 90 / 117.1
Opt. / 8.162 / 8.741 / 10.35 / 90.03 / 90.01 / 114.5
Ori. / 8.023 / 9.477 / 10.46 / 90.02 / 90.01 / 113.0
Cellulose III Exp. / 4.450 / 7.85 / 10.31 / 90 / 90 / 105.1
Opt. / 4.637 / 7.721 / 10.32 / 89.81 / 90.62 / 103.5
Ori. / 4.935 / 7.786 / 10.44 / 89.99 / 90.03 / 105.9

Table S5f: Deviation (%) between the predicted unit cell parameters and the experimental ones.

Allomorph / a / b / c / α / β / γ
Cellulose Iβ / Opt. / 0.06 / -1.06 / 0.72 / -0.01 / 0.00 / -2.36
Ori. / 7.71 / -0.51 / 1.30 / 0.00 / 0.00 / -5.93
Cellulose Iα / Opt. / -3.95 / 0.87 / 0.63 / -1.31 / -0.18 / 0.98
Ori. / -3.68 / 7.13 / 1.26 / -3.06 / -0.43 / -1.93
Cellulose II / Opt. / 1.90 / -3.20 / 0.42 / 0.03 / 0.02 / -2.19
Ori. / 0.16 / 4.95 / 1.47 / 0.02 / 0.01 / -3.47
Cellulose III / Opt. / 4.20 / -1.64 / 0.09 / -0.21 / 0.69 / -1.54
Ori. / 10.90 / -0.82 / 1.24 / -0.01 / 0.03 / 0.71

Tables S6: Optimizing only the repulsive LJ parameter of the CH1r atom type for GROMOS 56Acarbo, using the partial atomic charge distribution of Charmm C35.

Table S6a: Optimized parameter: C121/2 in (kJ mol-1 nm12 )1/2, distanceσ (Å) and energy ε(kJ mol-1) at the minimum, deviations (in %) between the optimized parameter and its original value, final values of target function Fmin.

C61/2
x1e4 / C121/2
x1e5 / σ / ε / Δ(C121/2)% / Finit / Fmin
Initial / 779 / 985 / 5.0 / 0.09
Four allomorphs / 779 / 673 / 4.4 / 0.20 / -32.7 / 62.9

Table S6b: Comparison of unit cell parameters predicted by original L-J parameters and optimized repulsive parameter of CH1.

allomorph / a (Å) / b (Å) / c (Å) / α (°) / β (°) / γ (°)
Cellulose Iβ Exp. / 7.784 / 8.201 / 10.38 / 90.00 / 90.00 / 96.55
Opt. / 7.799 / 8.089 / 10.44 / 89.99 / 90.00 / 94.17
Ori. / 8.426 / 8.137 / 10.43 / 89.99 / 90.01 / 92.87
Cellulose Iα Exp. / 6.717 / 5.962 / 10.40 / 118.1 / 114.8 / 80.37
Opt. / 6.481 / 5.954 / 10.48 / 116.3 / 114.0 / 81.43
Ori. / 6.661 / 6.241 / 10.47 / 114.9 / 113.3 / 78.66
Cellulose II Exp. / 8.010 / 9.030 / 10.31 / 90.00 / 90.00 / 117.1
Opt. / 8.146 / 8.628 / 10.39 / 90.02 / 90.01 / 114.0
Ori. / 8.058 / 9.380 / 10.41 / 90.10 / 90.05 / 112.7
Cellulose III Exp. / 4.450 / 7.850 / 10.31 / 90.00 / 90.00 / 105.1
Opt. / 4.715 / 8.203 / 10.00 / 90.00 / 89.97 / 111.9
Ori. / 5.008 / 8.192 / 10.06 / 89.99 / 89.99 / 111.9

Table S6c: Deviation (%) between the predicted unit cell parameters and the experimental ones.

Allomorph / a / b / c / α / β / γ
Cellulose Iβ / Opt / 0.19 / -1.37 / 0.53 / -0.01 / 0.00 / -2.47
Ori. / 8.25 / -0.78 / 0.48 / -0.01 / 0.01 / -3.81
Cellulose Iα / Opt / -3.51 / -0.13 / 0.81 / -1.55 / -0.67 / 1.31
Ori. / -0.83 / 4.68 / 0.69 / -2.69 / -1.28 / -2.13
Cellulose II / Opt / 1.70 / -4.45 / 0.78 / 0.02 / 0.01 / -2.65
Ori. / 0.60 / 3.88 / 0.94 / 0.11 / 0.05 / -3.72
Cellulose III / Opt / 5.96 / 4.50 / -2.99 / 0.00 / -0.03 / 6.43
Ori. / 12.54 / 4.36 / -2.42 / -0.01 / -0.01 / 6.47