Supplemental Material for the paper entitled “Amino Acid Analogues Bind to
Carbon Nanotube via π-π interactions: Comparison of Molecular Mechanical and
Quantum Mechanical Calculations” by Zaixing Yang, Zhigang Wang, Xingling Tian,
Peng Xiu, and Ruhong Zhou
1. Analysis of Interaction Energies of Benzene Dimer with Different
Configurations for OPLSAA and CHARMM Force Fields.
As mentioned in the Introduction section of the main text, the standard Molecular
Mechanical (MM) force fields can properly model the π-π interactions of benzene
dimer (see also Table S2). Table S1 summarizes the data available in the literature1,2
of OPLSAA and CHARMM Force Fields, which demonstrates the electrostatic and
van der Waals (vdW) contributions to total interaction energies of benzene dimer with
different configurations. It is shown that the electrostatic component is important for
the total energy, so the success of the standard MM force fields in modeling benzene
dimer is partly due to the proper treatment of the electrostatic interactions between
benzene dimer.
Table S1. Contributions to Interaction Energies (kcal/mol) of Benzene Dimer with
Different Configurations for OPLSAA and CHARMM Force Fields.a
Configuration
a
OPLSAA
CHARMM
Etotal
Eelec
EvdW
Etotal
Eelec
EvdW
PD
-
-
-
-2.09
0.82
-2.91
TT
-2.31
-0.45
-1.86
-
-
-
S
-1.70
1.37
-3.07
-1.78
1.38
-3.16
T
-
-
-
-2.10
-0.52
-1.58
The data in this table derive from ref. 1 and ref. 2, for OPLSAA and CHARMM
force fields, respectively. Etotal, Eelec, and EvdW denote the total, electrostatic, vdW
1
interaction energies, respectively. PD, TT, S, and T denote different configurations of
benzene dimer, see Fig. 1 in the main text for details.
2. Complete List of Interaction Energies of Benzene Dimer Obtained by
Different Quantum Mechanical (QM) Methods.
To assess the reliability of DFTB-D method for π-π interactions, we have compared
the DFTB-D results against those of other QM methods [CCSD(T), QCISD(T), MP2,
DFT-D, and another version of DFTB-D (denoted by DFTB-D*, see footnote of Table
S2)] and MM force fields, as displayed in Table S2.
Table S2. Interaction Energies (kcal/mol) of Benzene Dimer Obtained by Different
QM Methods.
a
Methods
PD
TT
S
T
CCSD(T)a
-2.70
-2.78
-1.64
-2.69
CCSD(T)*b
-2.78
-
-1.81
-2.74
QCISD(T)/CBSc
-2.659
-
-1.653
-2.683
DFTB-Dd
-3.19
-2.36
-3.13
-2.08
DFTB-D*e
-4.37
-2.83
-4.38
-2.53
DFT-D-BLYPf
-2.00
-
-1.04
-2.03
DFT-D-PBEg
-1.82
-
-1.02
-2.18
MP2/aug-cc-PVTZh
-4.25
-2.83
-2.87
-3.22
MP2/aug-cc-pVQZi
-4.73
-
-3.35
-3.48
MP2/CBSj
-4.95
-
-
-3.62
OPLSAAk
-2.11
-2.31
-1.70
-2.15
AMBERl
-
-
-1.30
-2.27
CHARMMm
-2.09
-
-1.78
-2.10
Polarizable force fieldn
-3.14
-
-
-
Interaction energies calculated as SCF|X + corr MP2|X + dCCSD(T)OVOS|(X-1),
where X stands for Q, 5 and X - 1 for T, Q; see ref. 3 for details.
2
b
Estimated
interaction energies of CCSD(T)/CBS (complete basis set) limit, see ref. 4.
QCISD(T) interaction energies extrapolated to infinite basis, see ref. 5.
d
c
DFTB-D
energies with the standard approach to treat dispersion correction (using R-6 term).
e
DFTB-D* energies calculated with another version of DFTB-D method whose
dispersion correction adopts the Lennard-Jones 6-12 potential (with short-range
repulsion term corrected by a polynomial function) and vdW parameters of UFF force
field (see ref. 6). f Interaction energies calculated at the DFT-D-BLYP/QZV(2df,2pd)
level
of
theory,
see
ref.
7.
g
Interaction
energies
DFT-D-PBE/QZV(2df,2pd) level of theory, see ref. 7.
h
calculated
at
the
Energies calculated by us
using Gaussian8 at MP2/aug-cc-PVTZ level with basis set superposition error (BSSE)
correction, based on the MP2/6-31g**(0.25, 0.15) optimized geometry [previous
report9 showed that MP2/6-31g**(0.25) can give reasonably optimized structure; to
better describe the stacking and CH-π interaction, we have added a p-polarization
function for the hydrogen atoms10].
i
MP2 energies with a modified aug-cc-pVQZ
basis, see ref. 4. j MP2 CBS limit energies for S22 set, see ref. 11.
k-m
See refs. 1, 2,
and 12. j Polarizable force field developed by Friesner et al., see ref. 13.
3. Complete List of Equilibrium Distances of Benzene Dimer Obtained by
Different Methods.
To test the reliability of DFTB-D method for geometry prediction, we have
compared equilibrium distances of benzene dimer with different configurations
predicted by DFTB-D against those of other QM methods, standard MM force fields,
and experiment (see Table S3).
Table S3. Equilibrium Distances (Å) of Benzene Dimer with Different
Configurations Obtained by Experiment and Different QM Methods.a
Methods
PD
TT
S
T
Experimentb
-
-
-
4.96
CCSD(T)c
3.6
-
3.9
5.0
3
QCISD(T)/aug-cc-pVTZd
3.533
-
3.919
4.989
DFTB-D
3.35
4.71
3.43
4.83
3.47
4.99
3.55
5.16
3.16
4.81
3.52
4.71
MP2/aug-cc-pVQZ
3.4
-
3.7
4.9
MP2/TZ-CPg
3.36
-
-
4.91
OPLSAAh
-
4.99
3.77
5.19
AMBERi
-
-
3.7
5.1
CHARMMj
3.619
-
3.764
5.150
DFTB-D*
**
e
MP2/6-31g (0.25, 0.15)
f
a
The distance is defined as the vertical distance between geometrical centers of
benzene dimer.
b
See ref. 14.
c
High-quality estimates of CCSD(T) results with a
modified aug-cc-pVQZ basis, see ref. 15.
d
QCISD(T)/aug-cc-pVTZ optimized
geometries, see ref. 5. e Distances calculated by us at MP2/6-31g**(0.25, 0.15) level,
see the footnote of Table S2 (for “MP2/aug-cc-PVTZ” method).
f
See ref. 15.
g
Distances calculated by us using the geometry which is obtained by Hobza et al. at
MP2/cc-pVTZ level with the counterpoise corrected gradient optimization (see ref.
11). h-j See refs. 1, 2, and 12, respectively.
4. Nonbonded Parameters for Aromatic Amino Acid Analogues in MM
Calculations.
Three analogues were used to represent the corresponding aromatic amino acids,
with their backbones replaced by methyl groups. Some modifications of nonbonded
parameters of amino acids in protein force fields were necessary for the amino acid
analogues. Except for the terminated methyl groups, the nonbonded parameters for
analogues are identical to those of amino acids. For the terminated methyl groups, the
Lennard-Jones parameters were taken from those of standard methyl groups in force
fields; when the OPLSAA and CHARMM force fields were used, the atomic charges
for methyl group are obtained in a similar way. However, when the AMBER force
field was used, the situation is slightly more complicated, since the atomic charges in
4
AMBER force field have been derived with the RESP method for the entire amino
acid, including the backbone.16 Here, we followed a similar approach used by Shirt et
al.17 and Hess et al.18 previously, which is to “borrow” the atomic charges of
α-hydrogens of each amino acid to assign the atomic charges for the hydrogens in the
added methyl group, and then adjust the atomic charge of the methyl carbon to make
the entire molecule charge-neutral.
5. Snapshots of Equilibrium Binding Structures Predicted by QM Calculations.
We find that in the equilibrium structures predicted by both QM and MM
calculations, the aromatic rings of molecules remains nearly parallel and
perpendicular to CNT, for the “Flat” and “Edge” configurations, respectively, as
shown in Figure S1.
Fig. S1. QM predicted equilibrium structures of molecular complexes for both
“Flat” and “Edge” configurations, shown in side view. (A-D) Cases for Phe, Tyr, Trp,
and benzene, respectively.
6. Comparison of Equilibrium Binding Structures Predicted by QM and MM
Calculations for “Edge” Configuration.
We have compared the equilibrium binding structures for “Edge” configuration
predicted by QM and MM calculations, shown in Table S4. We use the equilibrium
ring-CNT distance, dequ, and the angle between long axes of the aromatic ring and the
CNT,  (see Scheme S1) to characterize the geometrical difference between QM and
MM predicted structures We find that all MM predicted dequ are larger than the
5
corresponding QM predicted ones by a value of about 0.1~0.3 Å, but most of MM
predicted are similar to the corresponding QM predicted ones (with the exception of
OPLSAA Trp analogue, which differs significantly from the corresponding QM
predicted structure).
Table S4. Geometrical Parameters of Equilibrium Binding Structures for “Edge”
configuration.a
Geometry
DFTB-D
OPLSAA
AMBER
CHARMM
dequ
4.68
4.84
4.79
4.84
θ
0
2
10
15
dequ
4.52
4.72
4.74
4.78
θ
2
3
3
4
dequ
4.64
4.79
4.93
4.74
θ
0
50
8
2
dequ
4.51
4.71
4.76
4.72
θ
0
0
1
3
Phe
Tyr
Trp
Benzene
a
dequ (in Å) and  (in degree) are defined as the distance between geometrical
centers of molecule’s aromatic ring and CNT surface, and the angle between long
axes of the aromatic ring and the CNT (see Scheme S1) in equilibrium structures,
respectively.
Scheme S1. Schematic representation of  used in Table S4, using the equilibrium
structure of tryptophan analogue predicted by OPLSAA force field for illustration.
6
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