Conformational Impact on Amino Acid-Surface π−π Interactions on a(7,7) Single-Walled Carbon Nanotube: A Molecular MechanicsApproachLinda Grabill†,† and Andreas Riemann*,‡

†Department of Chemistry and ‡Department of Physics & Astronomy, Western Washington University, 516 High Street, Bellingham,Washington 98225, United States

*S Supporting Information

ABSTRACT: A study of π−π interactions between a (7,7)single-walled carbon nanotube (SWNT) and three differentaromatic amino acids (AAA), namely L‑tyrosine (Tyr), L-tryptophan (Trp), and L-phenylalanine (Phe) was conductedwith a molecular mechanics (MM) approach. For each of theamino acids we investigated the behavior of six differentconformers. We examined the impact of the so-called edgeeffects by testing the parameters of the built-in switchingfunction in MM. We found the optimal SWNT length to beapproximately 80 Å for the size of the molecules in ourconformational studies. The positional effect of electronwithdrawing groups with respect to the aromatic tail wasstudied to understand the influence of this interaction specificto adsorption strength and geometry. We decomposed the aromatic amino acid−surface interactions into three components:overall energy, aromatic ring, and amino acid head adsorption energies. We found that the ability of the amino acid’s head tointeract with the surface π-densities had a greater impact on the overall energy than the amino acid head interaction with itssubstituent’s aromatic ring’s π-electrons.

■ INTRODUCTION

The interactions of certain biomolecules with carbon-basedsubstrates, single-walled carbon nanotubes (SWNT), graphene,and graphite, hold the attention of researchers for theirpotential uses in electronics, chemical sensors, medicinedelivery systems, and many more applications.1−9 Hydrophobicbiomolecules, such as aromatic amino acids, have the potentialof allowing researchers to modify substrates to obtain desirableproperties. These interactions have been explored with physicalexperiments and an array of theoretical modeling.10−13 Whileunderstanding the nature of these interactions is a criticalcomponent for engineering them for their desired character-istics, the sheer size of the systems is computationally veryexpensive, and therefore, it is practically prohibitive to samplemultiple molecular conformers in order to theoretically studythese systems.14 Previous work, in this regard, has beenaccomplished with either the use of analogues when modelingamino acids (AA) or with using only the conformer with thelowest energy.15,16

Some of the more common methods to model molecule−surface interactions includes the use of Hartree−Fock (HF)methods, density functional theory (DFT), density functionaltight binding (DFTB), and molecular mechanics (MM)/molecular dynamics (MD). Each of these approaches can beevaluated according to accuracy, applicability to specific systems

of molecules and substrates, computational requirements, costs,and time.The optimal configuration of molecules and substrates can be

found by determining the minimum total energy of the system.DFT and MP2 require the generation of energy maps fordetermination of molecular interaction distances and energies.Molecules are brought within a given distance of the substrateand moved by a predesignated step size, or rotated by givenangles, generating energy maps by either a single point(energy) calculation or after geometry optimization of themolecule followed by a single point calculation. This time-consuming approach leads to the determination of the system’senergy minima and, therefore, an optimal molecule−surfaceadsorption geometry.Ab initio HF methods, such as second-order Møller−Plesset

perturbation theory (MP2) can be used for these calculations.However, these are computationally expensive and prohibitivefor larger systems. MP2 without a counterpoise correction andsufficient basis set can overestimate the energy of π−π aromaticinteractions with the carbon substrates by as much as 100%.17

An additional and more computationally expensive calculation,

Received: November 28, 2017Revised: January 11, 2018Published: January 12, 2018

Article

pubs.acs.org/JPCACite This: J. Phys. Chem. A 2018, 122, 1713−1726

© 2018 American Chemical Society 1713 DOI: 10.1021/acs.jpca.7b11716J. Phys. Chem. A 2018, 122, 1713−1726

similar to those carried out by Morgado et al., can address the

issue.18

DFT is used to circumvent the computational costs,

including memory issues of MP2, and is one of the more

common approaches to electronic structure calculations.

Dispersion-corrected functionals such as M06,19 B97D,20

ωB97X-D21 and Grimme’s DFT with dispersion correction(DFT-D3)22,23 can be added to increase accuracy. BothMarianski et al.24 and Kabanda et al.25 provide a comprehensiveoverview over the advantages and disadvantages of the various

Table 1. 6 L-Tyrosine Conformers for Ab Initio, B3LYP/6-31+G*(QM), and Molecular Mechanics after Optimization withAMBER f f 03 (MM) and Best Charge Scheme

Table 2. Interatomic and Torsion Angles for the Various Tyrosine Conformers Optimized with DFT and MM AMBER f f 03Force Fielda

tyrosine conformer method ∠CCC ∠CCH ∠CCN ∠HCH ∠CCOH ∠CCNH

A-2 QM 114.53 110.06 116.98 107.80 179.04 64.15AMBER f f 03 115.23 108.20 111.16 107.05 173.19 80.89

B-2 QM 113.47 109.81 109.89 107.02 3.22 31.71AMBER f f 03 114.27 108.84 110.18 106.90 3.59 35.59

C-2 QM 114.37 110.56 111.51 107.24 179.62 67.65AMBER f f 03 110.28 109.48 110.35 108.89 177.53 65.22

D-2 QM 114.84 109.96 113.44 107.56 178.39 67.01AMBER f f 03 115.61 108.02 109.39 107.38 167.82 110.06

E-2 QM 112.70 110.03 108.43 107.38 176.52 47.05AMBER f f 03 114.81 109.81 110.22 107.26 173.90 21.08

X-1 QM 114.32 110.53 109.10 107.27 2.78 30.91AMBER f f 03 115.35 108.12 112.30 106.79 3.36 42.92

reference valuea 114.24 110.22 109.96 106.06 N/A N/AaReference value from Wang et al.16

Figure 1. Labeling of interatomic and torsion angles from Table 2.

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DFT functionals and present comparative results betweenDFT, MP2, and another higher order HF method, coupledcluster single double (triple) (CCSD(T)).All of the above methods including electronic structures and

charge distributions come with size limitations. Therefore,DFTB becomes one of the only suitable resources for higherlevel calculations. While Yang et al. found DFTB-D whichincorporated Lennard-Jones 6−12 potentials and vdWparameters tended to overestimate interaction energiesbetween stacked benzene ring dimers by 6%, other groupshave shown that dispersion-corrected DFTB is a viable optionfor weakly bound systems.15,16,23,26

DFTB-D, a semiempirical approach, is considerably lesscomputational expensive than ab initio methods, but dependingon both the size of the molecular system and availablecomputer resources, single step calculations can still range onthe order of hours. Even if a particular DFTB-D calculationwere to only take minutes, plotting a potential energy surfacewith the intent of modeling dimer type interaction when tens ofthousands of points are required would make DFTB-D tootime demanding to use. Molecular mechanics (MM) canovercome the issues of time and computer resources, but hasstruggled with overestimating interaction energies whilesimultaneously maintaining monomer stability during geometryoptimizations.The body of this work is multifaceted. One goal was to find

and test time-efficient methods to investigate adsorptionbehavior of amino acids on a single-walled carbon nanotube.A second goal was to find new physical insights into theadsorption behavior of these molecules by determining thevarious contributions of components of the amino acid to thebonding on the substrate. We used molecular mechanics tomodel the six lowest energy conformers for the aromatic aminoacids tyrosine (Tyr), phenylalanine (Phe), and tryptophan(Trp) interacting with SWNTs to better understand the impactof conformation on these interactions. To accomplish this goal,the fundamentals of MM needed to be analyzed. Therefore, asecondary effort in understanding nonbonding interactions, theso-called ”edge-effect” and the atomic charge schemes formodeling the SWNT was undertaken.Initial studies were carried out in order to clearly establish

the cause for the overestimation of energy when studying AA-substrate interactions using MM. As the work of Yang et al.eliminated the lack of polarization as the cause for energyoverestimations, we began with a larger study which entailedtesting multiple levels of theory and basis sets to generate anatomic charge scheme for each of the six L-tyrosine conformers.All conformers were then geometry optimized using theAMBER (Assisted Model Building and Energy Refinement)and CHARMM (Chemistry at HARvard MacromolecularMechanics) force fields ( f f), and the results were comparedwith structures which had been optimized using B3LYP/6-31+G*. The atomic charge methods that were ultimately usedfor the L-tyrosine conformers are listed in Table 1, with Table 2summarizing interatomic and torsion angles defined in Figure 1.While these molecules were used for the remainder of our tests,we concluded the level of theory or atomic charge approachwas not the culprit for energy overestimation, therefore, bothL‑tryptophan and L-phenylalanine were treated with thestandard approach for atomic charge generation (restrainedelectrostatic potential using molecular electrostatic potentialsgenerated with HF/6-31G). AMBER f f 03 was determined to

be the most consistent force field in these preliminary tests andwas therefore used for the remainder of our experiments.With molecular stability addressed, the next step was looking

at potential issues caused by the so-called ”edge effect”.Exploring the edge effect was a 2-fold process. First, we test theimpact of changing the switching factors specific to thesubstrate only to probe for distances which may reflect theimpact of the hydrogen terminated atoms. Second, weincreased the length of the substrates to determine whichlength would minimize or eliminate the edge atoms from theenergy calculations. It is important to stress here, we did notalter the switching factors for the amino acid itself, only for thesubstrate. This approach is akin to mixing two force fields in anoptimization with one key difference. Once the switchingfactors surpassed the standard switching factors (more details inthe sections to follow) used for atom typing, the energy for thesystem was the same whether the substrate only was altered orboth the substrate and amino acid were altered. Once theappropriate length substrate was found, this was the substrateused for our conformational studies.In the first part, we are carefully describing the edge effect

studies and further discuss MM switching functions with theSupporting Information providing additional results. Thesecond part discusses our adsorption studies, results, anddiscussions.

■ METHODS

Computational Details. Ab initio (optimizations, vibra-tional frequencies, and partial charge calculations) andmolecular mechanics frequency calculations were carried outwith Gaussian 09 and ORCA.27,28 DFTB-D calculations werecarried out with DFTB+.28−30 L-Tyrosine molecules wereoptimized at the B3LYP/6-31+G* level of theory. Vibrationalfrequencies, carried out at the same level of theory, werecompared to Inokuchi et al.’s results and all amino acidconformers were labeled in accordance with their namingscheme.31 L-Tryptophan (Trp) conformers were optimized andfrequency checked at the B3LYP/6-311G* level of theory.32 L-Phenylalanine (Phe) conformers were optimized and frequencychecked at the B3LYP/6-31+G** level of theory.33

HyperChem includes atomic charge templates for terminaland embedded residues. For monomers atomic charges areindependently calculated. The creators of AMBER used theGaussian computational chemistry software27 with HF/6-31G*and Merz−Kollman (MK)34,35 method to generate MEP andapplied the results to the RESP method. Atomic charges forboth Trp and Phe were generated using the same process.RESP charges were calculated using AmberTools1436 and ESPfiles generated by Gaussian 09.

Figure 2. Tyrosine X-1 conformer on a (7,7) SWNT. The angle θ wasmeasured between the long axis of the nanotube and the principal axisof the tyrosine molecule.

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The carbon nanotubes used as templates were generatedusing Nanotube modeler,37 then optimized with Gaussian 09using DFTBA, Gauss’s analytical approach to DFTB. We testedthree levels of theory for Mulliken atomic charge generation ofthe substrate; DFTBA, B3LYP/6-31G (DFT/6-31G), and HF/6-31G.The SWNTs used as substrates for our calculations are (7,7)

SWNT with a diameter of 9.5 Å and a mean bond length of1.43 Å. We modeled various lengths: 19 Å with 252 atoms,22 Å with 350 atoms, 32 Å with 406 atoms, 52 Å with630 atoms, and 80 Å with 952 atoms.Our conformers were brought to within 6 Å of the substrate

with the aromatic tail starting parallel to the surface. It shouldbe noted that this process was carried out for the sake ofconsistency rather than necessity. In preliminary testing, oncemolecular stability was accomplished, the molecule wouldreorient itself with the ring parallel to the surface regardless ofstarting position. For the geometry optimizations, thesubstrates were held static while the AA was optimized. Thegeometry optimization moves the molecule around the surfaceover the various binding geometries (AB, SP, hollow) until theenergy gradient was minimized to 0.01 kcal/mol. To find thelowest energy interaction, the substrate was rotated three timesat 15 degrees per rotation and the AA was optimized after eachrotation. All optimizations took place in vacuo.The angle of rotation was measured between the long axes of

the SWNT and the principal axis of the AAA. The principal axisof rotation for each AAA was taken to be the primary inertial

axis parallel to the substrate plane (the line between the AAbackbone and adjacent benzene ring carbon; see Figure 2).Rotation angles were measured with Screen Protractor.38

Cut-Offs/Switching Values for Long-Range Interac-tions. Cut offs or switching functions are generallyincorporated into systems of larger sizes to decrease computa-tional time.39 These functions either terminate nonbondedinteractions at a specified distance (cut-offs) or have a set innerand outer radius for which interactions slowly decrease to zero(switching). Since it has been shown that molecular mechanicscan have problems with nonbonded interactions, we exploredthe impact of these parameters for long-range nonbondinginteractions. HyperChem uses default switching values of 10 Å(for the inner radius) and 14 Å (for the outer radius). Theswitching function in this investigation is applied in Hyper-Chem using the following:

= ‐ ×

= − + −−

< <

E E R R R

x a bb x b x a

b aa x b

(non switch) switch( , , )

with switch( , , )( ) ( 2 3 )

( )for

ijswitch2

inner2

outer2

2

3

(1)

These functions allow for a smooth transition of thenonbonded interactions from the inner radius to zero at theouter radius. As nonbonded interactions play an integral role inintermolecular and adsorption behavior, these switchingfunctions can have a significant influence on the overallbehavior of the system.

Substrate Models. Since size limitations and therefore theedges of the nanotubes play a considerable role in computa-tional adsorption studies, we investigated the atomic chargegeneration of these nanotubes with an eye toward consistentvalues. These tests incorporated three different levels of theoryused to generate Mulliken atomic charges for the substrates:HF, DFT, and DFTBA. We consider stable regions of charge(SRC) for areas where the fluctuations in atomic chargesremain minimal.In general, fluctuations begin to disappear at about two to

two and half unit cells from the edge of the SWNT. Measuringthe distance of the SRC, along the long axis, we findapproximately 8.64 Å of total length for the 19 Å nanotube

Figure 3. 19 Å SWNT with the stable region of charge (SRC) atomsselected. The total length of the shaded region is about 8.64 Å.

Figure 4. L-Tyr X-1 conformer adsorbed on the (7,7) 19 Å nanotubes. Three substrates are compared: DFTBA, DFT and HF. The highlightedregion indicates the set of switching values that produced molecular stability for all substrates.

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which increases to 12.34 Å, 22.22 Å, 39.40 Å, and 70.65 Å forthe 22 Å, 32 Å, 52 and 80 Å SWNT’s, respectively. Figure 3visualizes an example of these results by highlighting the atomsin the SRC with consistent charge values.Edge-Effect. While DFTB-D can overestimate aromatic

interaction energies, results from these studies can still providea barometer of reasonably expected energies and geometricbehavior. Here, we used Wang et al.’s results specific to Tyradsorbed on a (7,7) SWNT to determine the acceptability ofour MM calculations. Wang et al. determined the adsorption

energy for the X-1 conformer to be −16.02 kcal/mol, and theangle between the long axis of the nanotube and the principalaxis of the molecule was 42°.16

Using the 19 Å (the same number of unit cells as Wang etal.) nanotube with three different charge calculations, wealtered the switching values and compared the results from eachSWNT (see the Supporting Information for details). Thesecalculations found the best parameters for the inner radiusswitching value are between 5 and 8 Å, and for the outer radiusswitching values between 10 and 14 Å. There was only one setof switching values which produced molecular stability, 5−11.We calculated adsorption energies of −14.07, − 14.76 and−17.09 kcal/mol and rotation angles of 22°, 5°, and 38° for theDFTBA, DFT and HF substrates, respectively. The results fromthese initial tests can be seen in Figure 4.The DFTBA substrate had a 12% underestimation of energy

compared to the DFT substrate’s 8% underestimation, and theHF substrate’s overestimation of 6% on the 19 Å nanotube,

Figure 5. Energy and rotation for the L-tyrosine X-1 conformer adsorbed on the HF and DFT 80 Å substrates.

Table 3. Comparison of Tyr Conformers Optimized with theMM AMBER ( f f 03) Force Field on the 52 Å DFT SWNTUsing Switching Values of 22−26 and on the 80 Å HFSWNT with Switching Values 27−30 and 31−34a

Tyr conformerSWNT length

(switching values)ring

energyheadenergy total calculated

%ring

%head

A-252 Å (22−26) −11.97 −3.76 −15.73 −15.68 76 2480 Å (31−34) −11.89 −2.97 −14.86 −14.81 80 2080 Å (27−30) −11.82 −2.99 −14.82 −14.77 80 20B-252 Å (22−26) −11.30 −5.71 −17.01 −16.52 66 3480 Å (31−34) −11.28 −5.16 −16.45 −16.03 69 3180 Å (27−30) −11.34 −5.07 −16.41 −16.01 69 31C-252 Å (22−26) −11.79 −3.65 −15.44 −15.38 76 2480 Å (31−34) −11.54 −3.57 −15.11 −15.02 76 2480 Å (27−30) −11.56 −3.52 −15.09 −15.00 72 28D-252 Å (22−26) −12.76 −2.69 −15.45 −15.33 83 1780 Å (31−34) −14.25 −2.64 −16.89 −16.64 84 1680 Å (27−30) −12.11 −2.63 −14.74 −14.69 82 18E-252 Å (22−26) −11.66 −5.09 −16.74 −16.91 70 3080 Å (31−34) −12.09 −5.07 −17.16 −14.30 70 3080 Å (27−30) −11.91 −4.78 −16.69 −13.82 71 29X-152 Å (22−26) −13.17 −3.82 −16.98 −16.70 78 2280 Å (31−34) −13.89 −2.60 −16.49 −16.34 84 1680 Å (27−30) −11.90 −2.99 −14.89 −14.85 80 20

aEnergy is in kcal/mol.

Table 4. X-1 L-Tyrosine Conformer Lowest EnergyConfigurations for Both the DFT and HF Substrates

27−30 28−31 29−32 30−33 31−34

HFenergy [kcal/mol] −14.85 −14.85 −14.86 −16.39 −16.34rotation [degrees] 8 10 9 45 45DFTenergy [kcal/mol] −14.85 −14.86 −14.84 −14.86 −14.84rotation [degrees] 8 8 12 9 9

Table 5. X-1 L-Tyrosine Conformer Lowest Energy [kcal/mol] Configurations for Both the DFT and HF Substrates onDifferent Diameter SWNTsa

SWNT (n,n) HF DFT ref. value

(4,4) −14.66 −14.07 −14.57(5,5) −15.70 −14.27 −15.15(6,6) −16.49 −14.32 −15.61(7,7) −17.09 −14.76 −16.05(8,8) −19.64 −15.80 −16.48(9,9) −20.38 −16.23 −16.86(10,10) −20.98 −16.54 −17.16

aReference values are from Wang et al.16

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therefore, the nanotubes where the charges were calculatedusing DFT and HF are the focus of the remainder of the tests.Other Tyr conformers were tested on the DFT and HFsubstrates to establish a baseline of energy and stability. Thecalculations were repeated on the 22 Å, 32 and 52 Å SWNTs.A couple of patterns emerge from the initial calculations: As

the length of the nanotubes was increased, so too did thenumber of suitable switching values. Molecules optimized atlower switching values (i.e., 5−10) had a consistently lowerenergy and a larger energy difference between the twosubstrates, than those at higher switching values (i.e., 7−11).To ascertain if these differences were a reflection of theinclusion of additional nonbonded interactions or an indicationof the impact of the edge-effect, the 80 Å nanotube wasincluded in the final stages of calculations.Differences in HF and DFT substrate adsorption energies

diminished as the length of the nanotubes increased. On the52 Å-long nanotube energy differences between the twosubstrates were found to be as small as hundredths of kcal/moluntil the 22−26 switching factors were included (all results canbe seen in the Supporting Information). Measurements of atomdistances to the SWNT edge atom region (outside of the SRC),found that the most electronegative atoms were within a rangeto be impacted by the increase in atomic charges influenced bythe terminal hydrogens, which accounted for these differencesin energy.Calculations using the 80 Å substrate was limited to the X-1

conformer alone (see Figure 5). This was done for two primaryreasons. First, the results of all conformers were included tocheck for molecular stability with more than one molecularconfiguration. The second reason was to track the impact ofenergy over the range of switching values to probe for the edgeeffect. Molecular stability only became an issue once theswitching values were increased beyond half of the SWNTlength, 41 Å. There was a 1 kcal/mol difference between thelowest switching values, 5−10, and the default switching valuesof 10−14. Including longer range nonbonded interactions, outto 30−34, only increased the energy by 0.05 kcal/mol. Largervariations in energy and geometric orientation between themolecule and the substrate only became significant when theedge atoms influenced adsorption behavior. The X-1 conformerwas molecularly and energetically stable, which eliminated thenecessity for expanded testing.The 22−26 switching values were included on the 80 Å

substrates for comparison to the 52 Å SWNT, but the bulk ofour switching tests began with an outer radius of 30 Å andconcluded with an outer radius of 44 Å and an inner radius of(outer radius−3, 4, and 5 Å). We determined the SRC to be70.65 Å and therefore, expected switching values of less than35 Å for an outer radius to be the most likely to limit theimpact of the edge-effect. We began to see a divergence in thesubstrate energy at switching values of 31−34 (Table 3).This was originally a surprising result as the substrates had

been consistent for switching values of 31−34 and 30−34. Wereturned to the outer radius of 30 Å and rotated the substrate tosearch for the lowest energy interactions with both substratesup to an outer radius of 34 Å. The divergence in energy androtation began at 30−33 (results can be seen in Table 4). Inboth cases, the phenol hydroxyl group was outside of the SRCand therefore influenced by the edge atoms. The HF substratehas charge symmetry about the short axis while the DFTsubstrate has symmetry about the long axis. While watchingeach optimization, as the molecule rotates on the HF substrate

the ring moves between the charge symmetry regions morereadily than it does on the DFT substrate. It appears that this iswhat leads to the edge atom interactions and increased energy.Because molecular stability was an issue at longer range

interactions on the 52 Å substrate, the behavior above was notmanifested. In all cases, when an increase in energy wasobserved, the phenol hydroxyl group was exposed to the edgeatoms and a greater extent of autorotation was observed,though AB ring stacking was the result with and without theedge-effect.When the edge atoms are included in the long-range

nonbonded interactions, the X-1 conformer matched Wanget al.’s results.16 Differences on the 52 Å (DFT, 22−26) and 80Å (HF, 31−34) nanotubes were within 4.1% and 1.9%,respectively. The ring height for the 80 Å substrate was 3.19 Åin both instances and 2.88 Å on the 52 Å substrate. With theexception of the ring height, both substrates which included theedge atoms behaved similarly. The overall trend in decreasingenergy was consistent with the limiting impact of the edgeatoms between the two substrates. Both the phenol hydroxylgroup and the amine group were within range of the SWNT’sterminal atoms on the 52 Å SWNT. The phenol hydrogen waswithin 26 Å of the negatively charged carbons while 26 Åplaced the phenol oxygen 1/2 a unit cell away from the edgecarbons. The amine group has one hydrogen and its nitrogenless than 26 Å of most of the SWNT terminal hydrogens.On the 80 Å nanotube (31−34), the amino acid head was

several unit cells away from the terminal atoms while thephenol ring was similarly positioned as it was on the 52 ÅSWNT. This lead to a decrease of energy by 0.26 kcal/mol,while the elimination of the phenol ring interaction lead to adecrease of nearly 1.5 kcal/mol.The D-2 conformer experienced a similar circumstance,

although it is the carboxylic group rather than the amine groupthat participates in the edge interactions. On the 52 Ånanotube, both the phenol hydroxyl group and the carboxylicgroup were within range of the terminal atoms, that is within26 Å of the terminal atoms. This gave a decrease of energyrelative to both attractive and repulsive forces. When themolecule was placed on the 80 Å SWNT there was an increaseof 1.31 kcal/mol in energy and the amino acid head, andrepulsive electrostatics, were back in the SRC while the phenolhydrogen was interacting with the terminal carbons. There is adecrease of nearly 2 kcal/mol when the phenol ring can nolonger be impacted by the edge atoms, as was with case on the80 Å nanotube at switching values (27−30).The A-2 conformer maintains the same pattern seen with

both X-1 and D-2. Both the carboxylic and the amine group caninteract with the terminal atoms. An amine hydrogenexperienced some repulsive forces from the few terminalhydrogens within the 26 Å range while being influenced by theterminal carbons. The carboxylic, carbonyl oxygen can interactwith the non-hydrogen-terminated carbons, and the phenolhydroxyl group is impacted by both terminal carbons andhydrogens, with more terminal carbons in range than hydrogen.When placed on the 80 Å nanotube (31−34), there is a declineof 0.87 kcal/mol, the phenol group is within one unit cell fromthe edge of the nanotube and the amino acid head is within twounit cells. These distances explain a decrease of only 0.04 kcal/mol when the switching factors are decreased to 27−30.B-2 and C-2 conformers show the least amount of impact

from the edge atoms, with energy differences of only 0.51 and0.38 kcal/mol, respectively, between the 52 Å and the 80 Å

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SWNTs. C-2’s entire amino acid head and B-2’s carboxylicoxygens were all nearly equidistant from the edge atoms. Theseinteractions provide a near balance of attractive and repulsiveforces that minimizes the impact of the increased SWNTlength.We have forgone discussions on the E-2 conformer, as it is

our belief that this conformer demonstrates a limit of molecularmechanics to properly model weakly bonded interactions. Thecarboxylic group consistently rotated below the height of theamino acid ring interacting strongly with the surface atomschanging the torsion angle between the carboxylic oxygen andamine nitrogen by 43°. The carboxylic carbonyl oxygen rotatesto within 2 Å of the amine hydrogen from 2.42 Å prior tooptimization. The attractive nature between these two elementsappears to drive the overall surface−molecule interaction.The examination of position of the electronegative groups

with respect to the terminal atoms clearly demonstrates theimpact of the edge-effect. The increase in energy and match in

geometric behavior to DFTB-D results is an artifact ofunbalanced electrostatic interactions. The impact of this canbe best seen with the D-2 conformer. When the balance ofrepulsive and attractive electrostatics is disrupted, the D-2conformer’s energy is increased, making it appear to be thelowest energy interaction.While we have shown that the elimination of the edge effect

by using shorter range switching factors on shorter SWNTs canallow MM to replicate DFTB-D results for the (7,7) SWNT, itis important to know if this holds true for other substrates. Totest this, we studied the same Tyr conformer as Wang et al., X-1, and the remaining (n,n) SWNTs used in their study. Theresults for these nanotubes can be found in Table 5. Consistentwith the (7,7) substrate, the HF substrate overestimated whilethe DFT substrate underestimated interaction energy whencompared to the DFTB-D results. We used the 5−11 switchingfactors for (7,7) SWNTs and below [(4,4), (5,5), and (6,6)]and the 5−10 switching factors for (8,8) SWNTs and above

Table 6. Six Tyrosine Conformers Optimized with AMBER ( f f 03) (MM) on the 52 Å DFT and 80 Å HF Substrates

Table 7. AMBER ( f f 03) (MM) Electrostatic Potential Maps of Five Tyrosine Conformers Optimized on the 80 Å, HFSubstrate, Using 27−30 Switching Valuesa

aPurple regions indicate electronegative; green regions indicate more electropositive.

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[(9,9) and (10,10)] consistent with our work done testing forthe edge-effect.Using both HF and DFT, the substrates followed the trend

of increasing energy with increasing diameter, but the HFsubstrate adhered to the pattern better for the substrates (7,7)and lower while the DFT substrates performed better for the(8,8) SWNTs and larger. This finding was consistent with theincreased-length nanotubes from our edge-effect tests. Thesubstrates used by Wang et al. were shorter for the (7,7)configuration and lower diameter tubes and our modelsincluded the same amount of unit cells as those used byWang et al. In all, the largest underestimations for the DFTsubstrates were 8.26% and 8.03% for the (8,8) and (7,7)substrates, respectively, with an average error of 5.29% overall.The HF substrate had only a 0.64% difference in energy on the(4,4) SWNT, but this increased to 22.24% on the (10,10)substrate.Regarding the stacking geometry, AB or SP, both substrates

led to different results in only one instance with respect to theDFTB-D geometry calculated by Yang et al., namely AB

stacking was calculated for the (4,4) DFT SWNT and the (5,5)HF SWNT.As comparison, DFTB-D calculations by Yang et al. yielded a

6% overestimation of energy when comparing benzene dimerpair interaction energies with CCSD(T) results. Ourcalculations are comparable with an average 5% under-estimation of energy (when compared to DFTB-D).

■ RESULTS AND DISCUSSION

Adsorption of L-Tyrosine Conformers on SWNTs. Ring-Surface Interaction. To explore the impact of the amino acidconformation on the ring-surface interaction, after moleculeswere optimized with MM, the AAA was broken down into twocomponents: head and ring. The energy of the individualcomponents is calculated by comparing the energy on thesubstrate to the energy in vacuo. While this does lead to anoverestimation of energy due to the unbalanced charge (withone exception), we found the sum of the two energies differfrom the whole AAA by only about 0.30 kcal/mol. In the caseof the Tyr E-2 conformer on the 52 Å substrate, the sum of the

Table 8. Six Phenylalanine Conformers for Ab Initio, B3LYP/6-31+G*(QM), and Molecular Mechanics after Optimization withAMBER ( f f 03) (MM)a

aAll atomic charges generated by HF/6-31G MK(RESP).

Table 9. Interatomic and Torsion Angles for the Various Phenylalanine Conformers Optimized with DFT and MM AMBER( f f 03) Force Fielda

Phe conformer method ∠CCC ∠CCH ∠CCN ∠HCH ∠CCOH ∠CCNH

A QM 114.49 110.06 116.92 107.94 179.30 65.45AMBER ( f f 03) 115.22 107.39 107.91 107.57 153.27 102.76

B QM 113.19 109.90 109.26 107.11 3.25 33.03AMBER ( f f 03) 115.12 110.08 109.29 106.60 3.16 63.76

C QM 114.28 110.01 111.79 107.38 179.70 68.80AMBER ( f f 03) 113.34 108.93 106.33 108.49 162.89 28.74

D QM 115.11 109.67 113.01 107.47 178.08 69.10AMBER ( f f 03) 115.62 107.84 108.93 107.62 161.88 111.62

E QM 112.52 110.03 108.19 107.46 176.63 48.53AMBER ( f f 03) 115.90 110.88 108.20 106.32 164.38 14.54

X QM 114.25 110.45 109.18 107.43 2.80 30.46AMBER ( f f 03) 115.27 108.39 112.16 106.86 3.19 49.63reference valuea 114.15 110.20 109.94 106.13 N/A N/A

aReference value from Wang et al.16

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two components was 0.17 kcal/mol lower than the calculatedenergy. Electrostatic repulsion specific to the ring atoms closestto surface atoms with like charges appeared to result in a lowerenergy calculated for the ring-surface interaction compared tothe other substrates.Table 3 summarizes the energies for all Tyrosine conformers

and Table 6 shows all of the conformers with their lowestenergy surface interactions. The lowest to highest energyinteractions were B-2, C-2, X-1, A-2 and D-2. There was a 1.72,2.44, and 0.77 kcal/mol difference in overall, head-surface, andring-surface adsorption energies between the lowest to highest.The percentage of head and ring contributions to overalladsorption energy ranged from 31% and 69% to 20% and 80%,respectively. Only the A-2 conformer adopted an SP orientationbetween the phenol ring and substrate, all others were ABstacked. The results show enough of a discrepancy that the useof a charged methyl group in substitution of the actual AA headis likely to introduce errors, as is the case in studies whereanalogues are used as substitutes for amino acids.Incorporating the results from Tables 3 and 7, a clearer

picture of the relationship between conformation and

interaction energy emerges. The electrostatic potential energymaps in Table 7 show two views: the bottom view to elucidatethe interactions between the AAA and substrate, and the topview to understand the interactions between the AA head andaromatic ring. The B-2 conformer has the lowest head-surfaceinteraction energy; it also has the largest amount of electrostaticpotential concentrated closest to the substrate. This patternfollows through with the C-2, X-1, A-2, and D-2 conformers.Likewise, hydrogen interactions with oxygen, nitrogen, and πdensities are seen. The B-2, C-2, and X-2 conformers allow forthree different hydrogen interactions; the A-2 and D-2conformers do not. The aromatic ring-surface interaction isthe strongest when the electrostatic potential resides closest tothe ring itself allowing for a H−π ring interaction. This is bestillustrated for both the D-2 and X-1 conformers. These twoconformers vary by only 0.21 kcal/mol, where D-2 has thelowest energy.

L-Phenylalanine and L-Tryptophan Conformers. Toexpand our model of amino acid adsorption on carbonnanotubes, we are investigating two additional amino acids, L-tryptophan and L-Phenylalanine. As with L-tyrosine, we are

Table 10. Six Tryptophan Conformers for Ab Initio, B3LYP/6-311G*(QM), and Molecular Mechanics after Optimization withAMBER ( f f 03) (MM)a

aAll atomic charges generated by HF/6-31G MK(RESP).

Table 11. Interatomic and Torsion Angles for the Various Tryptophan Conformers Optimized with DFT and MM AMBER( f f 03) Force Fielda

Trp conformer method ∠CCC ∠CCH ∠CCN ∠HCH ∠CCOH ∠CCNH

A QM 114.66 109.70 116.64 107.29 177.96 63.45AMBER ( f f 03) 116.90 107.60 107.67 107.15 165.92 17.19

B QM 113.27 110.09 109.04 105.69 3.10 36.80AMBER ( f f 03) 116.18 109.95 109.54 106.51 8.58 55.38

C QM 115.94 110.69 112.23 106.28 176.26 72.42AMBER ( f f 03) 115.18 108.50 106.37 107.82 162.90 84.56

D QM 115.13 109.71 113.25 107.03 178.19 66.48AMBER ( f f 03) 117.18 108.19 108.50 107.08 174.15 22.93

E QM 112.80 110.12 108.48 106.84 176.40 45.00AMBER ( f f 03) 116.40 109.94 108.75 106.98 167.52 17.10

X QM 113.68 110.33 108.58 106.68 4.46 34.86AMBER ( f f 03) 115.82 107.76 112.20 106.97 1.87 38.37reference valuea 114.08 109.84 109.80 106.17 N/A N/A

aReference value from Wang et al.16

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optimizing the various conformers using DFT-B3LYP/6-31+G* and comparing them to suitable MM optimizationwith the AMBER ( f f 03) force field. These conformers wereconsistent with previous laser adsorption spectroscopy data andtheoretical studies.40−42 The results of our optimizations,

including molecular configurations and measured angles, aresummarized in Tables 8 and 9 for L-Phe, and Tables 10 and 11for L-Trp. Torsion angles are included as they best demonstratethe propensity of MM to rotate the hydrogens about thenitrogen center. The reference angle refers to the anglesmeasured by Wang et al., who used molecular dynamics todetermine the lowest energy conformer.16

Wang et al. investigated Phe and Trp X-conformers andfound adsorption energies of −15.31 kcal/mol and −19.06kcal/mol and rotation angles of 52° and 16°, respectively. Wecalculated adsorption energies of −15.74 kcal/mol and −18.25kcal/mol and rotations of 39° and 18° with the 6−10 switchingfactors on the 19 Å SWNT. We again use the 80 and 52 ÅSWNTs to further explore the edge-effects and conformationalbehavior of each molecule.

Adsorption of L-Phenylalanine Conformers on SWNT. Theresults for the energies and configuration of the L-phenylalanineconformers are summarized in Tables 12 and 13. The impacton interaction energy resulting from the edge-effect is similar inmagnitude for the A and B conformers, increased for C and Dbut decreased for the X conformer. The Tyr C conformer has amore balanced exposure of electronegativity toward the edgeatoms on the 52 Å SWNT. Both amine hydrogens andcarboxylic oxygens are nearly in the same plane facing the edgeof the nanotube, this is not the case for the Phe C conformer.This lack of balance between the repulsive and attractive forcesleads to a larger decrease in energy when the edge atoms areremoved from the calculation. The Phe D conformer rotates insuch a way that the amino group was exposed to edge atoms onboth sides of the SWNT.While the L-tyrosine X-1 conformer experienced a significant

decrease in autorotation when the edge effect was mitigated,autorotation did occur with the Phe X conformer. This rotationoccurred even though the molecule did not experience ahorizontal translation along the SWNT’s long axis. Therefore,while autorotation can be a symptom of an attractive andrepulsive equilibrium between electronegative substituents andthe edge atoms, this balance is not the only cause of thegeometric molecule−substrate adsorption behavior.

Table 12. Comparison of Phe Conformers Optimized withMM AMBER ( f f 03) Force Field on the 52 Å (7,7) DFTSubstrate at the 22−26 Switching Factors and on the 80 ÅSWNT, Switching Factors of 31−34 and 27−30a

Phe conformerSWNT length

(switching value)ring

energyheadenergy total calculated

%ring

%head

A52 Å (22−26) −11.79 −2.26 −14.05 −14.37 84 1680 Å (31−34) −10.88 −2.40 −13.27 −13.25 82 1880 Å (27−30) −10.82 −2.48 −13.30 −13.27 81 19B52 Å (22−26) −11.12 −4.01 −15.14 −14.78 73 2780 Å (31−34) −10.73 −4.66 −15.39 −14.65 70 3080 Å (27−30) −10.59 −4.66 −15.24 −14.47 70 30C52 Å (22−26) −11.18 −3.64 −14.82 −14.63 75 2580 Å (31−34) −10.99 −3.04 −14.03 −13.98 78 2280 Å (27−30) −10.50 −3.25 −13.75 −13.65 76 24D52 Å (22−26) −11.93 −2.99 −14.92 −14.85 80 2080 Å (31−34) −10.83 −2.50 −13.33 −13.31 81 1980 Å (27−30) −10.78 −2.58 −13.36 −13.34 81 19E52 Å (22−26) −10.97 −5.18 −16.16 −17.22 70 3080 Å (31−34) −10.60 −5.58 −16.18 −15.27 66 3480 Å (27−30) −10.68 −4.88 −15.56 −15.26 69 31X52 Å (22−26) −11.16 −3.82 −14.99 −14.88 75 2580 Å (31−34) −11.51 −3.18 −14.68 −14.63 78 2280 Å (27−30) −10.32 −3.58 −13.90 −13.82 74 26

aEnergy in kcal/mol.

Table 13. Six Phenylalanine Conformers Optimized with AMBER ( f f 03) (MM) on the 52 Å DFT SWNT and the 80 Å HFSubstrates

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There is an 8% difference in adsorption energy betweenconformers B (the lowest) and A (the highest). This is again alarge enough discrepancy in energy that simulating the AA headwill likely introduce differences in energy and geometry.The electrostatic potential energy maps, seen in Table 14,

show a build-up in potential at the center of the rings on

conformers A, C, and D. This behavior reflects the electro-negative regions located next to the rings on each conformerand explains the increase in surface-ring interaction energies forthe A and B conformers. The C conformer, however, lacks asymmetrical distribution of electronegative and positivepotential areas. Rather than an increase in interaction energy,the larger electronegative region produced the second highestring-surface energy. The AA head energy, with the exception ofthe C conformer, was consistent with what was observed withthe Tyr conformers.The pattern of lowest to highest energy surface interactions

for Phe was very similar to that observed for Tyr: B, X, C, D,and A. While the order of (X and C) and (D and A)conformers are transposed between the two AAs, themagnitude of difference in energy was similar between thetwo: the difference between the C and X conformers was 0.15for Tyr and 0.17 kcal/mol for Phe, and the difference betweenthe A and D conformers was 0.08 for Tyr and 0.07 kcal/mol forPhe. These differences are small enough, approximately 1%,that the differences in conformer energy ranking becomesinsignificant.

L-Tryptophan. The Trp conformers followed the samepattern as Tyr and Phe. The impact of the edge atoms wasobserved varying only by the magnitude of the change inenergy (see Table 15). Perhaps a reflection of the amount ofSWNT surface area covered by Trp, surface-molecule geometryremained constant (with the exception of the X conformer),even as energy decreased.The surface−head interaction strength followed in the same

pattern as Tyr and Phe (electrostatic potential maps can beseen in Table 16). The conformer with the greatest surface areaof electrostatic potential, unhindered by the ring, and directedat the surface of the SWNT had the lowest surface-AAinteraction energy. Accordingly, the B conformer had thelowest adsorption and head-surface energy.For all conformers, there is a potential energy gradient

centered in the indole’s benzene ring. The A conformer also hasa region of electronegativity located in the center of the pyrrolering. This yielded the lowest ring-surface energy interaction ofall five conformers. Following the A conformer, the Dconformer has the largest electrostatic potential centered

Table 14. AMBER ( f f 03) (MM) Electrostatic Potential Maps of Five Phenylalanine Conformers Optimized on the 80 Å, HFSubstrate, Using Switching Values of 27−30a

aPurple regions indicate electronegative; green regions indicate more electropositive.

Table 15. Comparison of Trp Conformers Optimized withMM AMBER ( f f 03) Force Field on the 52 Å (7,7) DFTSubstrates at the 22−26 Switching Factors and on the 80 ÅSWNT at the 31−34 and 27−30 Switching Factorsa

Trp conformerRingEnergy

HeadEnergy Total Calculated

%Ring

%Head

SWNT length(switching value)

A52 Å (22−26) −17.02 −2.18 −19.20 −19.08 89 1180 Å (31−34) −15.45 −2.70 −18.15 −18.09 85 1580 Å (27−30) −15.35 −2.72 −18.07 −18.02 85 15

B52 Å (22−26) −15.55 −6.04 −21.59 −21.20 72 2880 Å (31−34) −14.80 −4.73 −19.53 −19.24 76 2480 Å (27−30) −14.74 −4.71 −19.45 −19.17 76 24

C52 Å (22−26) −14.81 −3.85 −18.66 −18.57 79 2180 Å (31−34) −14.66 −3.84 −18.50 −18.38 79 2180 Å (27−30) −14.70 −3.26 −17.97 −17.93 82 18

D52 Å (22−26) −15.89 −3.21 −19.10 −19.04 83 1780 Å (31−34) −15.43 −2.93 −18.36 −18.28 84 1680 Å (27−30) −15.28 −2.94 −18.23 −18.15 84 16

E52 Å (22−26) −15.76 −4.81 −20.57 −20.32 77 2380 Å (31−34) −15.06 −5.10 −20.15 −19.83 75 2580 Å (27−30) −14.78 −5.09 −19.87 −19.54 74 26

bf X52 Å (22−26) −16.18 −3.42 −19.60 −19.39 83 1780 Å (31−34) −15.58 −2.99 −18.58 −18.45 84 1680 Å (27−30) −15.22 −2.96 −18.18 −18.08 84 16

aEnergy in kcal/mol.

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nearest its pyrrole ring and the second lowest surface-ringenergy. The A conformer has the hydroxyl oxygen in closestproximity to the pyrrole ring with the hydroxyl hydrogenpointed away from the AA backbone. For the D conformer it isthe carbonyl oxygen closest to the ring. The X conformer hasthe same circumstance as the A conformer except the hydroxylhydrogen is pointed toward the backbone of the AA and theamine hydrogens are directed away from the indole ringcompletely. When the amine and carboxylic hydrogens are bestpositioned to interact with the electron densities of the indolering the overall energy is increased. Table 15 has a comparisonof all of the head and ring interaction energies, and Table 17shows the lowest energy interactions for all conformers.

■ CONCLUSIONIn our studies we have shown that molecular mechanics canindeed model interactions between aromatic amino acids andsingle-walled carbon nanotubes with sufficient precision

regarding geometry and adsorption energy. The best resultswere obtained by using a long enough SWNT (in our case 80 Ålength), with a large enough SRC, in order to avoid edge effectsinfluencing the results.For our three molecules (Tyr, Phe, and Trp), we found

switching factors of 27−30 to be effective on the long SWNT;however, this is dependent on the size of the molecule to bestudied. Our results show that shorter switching factors, i.e.,10−14, produced similar energies to that found for longerSWNT and larger values. This shows that so long as the impactof the edge atoms are sufficiently far away, increasing theamount of surface area included in energy calculations for theseweakly bound systems has a minimal impact.The difference in adsorption energy resulting from the edge

effect was mitigated by the degree of electrostatic potentialexposed to the edge atoms and therefore the ability forattractive and repulsive energy to balance out. Autorotation ofthe aromatic ring is not an artifact of the edge-effect, as a large

Table 16. AMBER ( f f 03) (MM) Electrostatic Potential Maps of Five Tryptophan Conformers Optimized on the 80 Å, HFSubstrate, Using 27−30 Switching Valuesa

aPurple regions indicate electronegative; green regions indicate more electropositive.

Table 17. Six Tryptophan Conformers Optimized with AMBER ( f f 03) (MM) on the 52 Å DFT SWNT and the 80 Å HFSubstrates

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autorotation was found with the Phe conformers, but the extentof rotation can indeed be exacerbated by the edge atoms.In agreement with Inokuchi and Baek et al.’s work, it was

found that the B and X conformers consistently had the lowestsurface−AA energy interactions.31,41 We have found that theability for the B conformer’s hydrogens to interact with thesubstrates π-electrons had a larger impact on the strength of theoverall interaction than the X conformer’s H−π AA ringinteraction did. There was a difference in interaction energybetween the highest and lowest energy conformer of 1.25 kcal/mol on average. A larger percentage of this difference wasrelated to the AA head-surface interaction rather than anincrease in the ring-surface strength. This fact furtheremphasizes the importance of incorporating the completeamino acid in the calculations (with an actual AA “head”) ratherthan either disregarding it or approximating it with a chargedmethyl group (analogue). The B conformer produced energiesof 19.45, 16.01, and 14.47 kcal/mol for Trp, Tyr, and Phe,respectively.Our results are consistent with Yang et al.’s findings that

DFTB-D, which incorporated Lennard-Jones 6−12 potentialand vdW parameters tended to overestimate interactionenergies.16 The DFTB-D calculations carried out by Yang etal. yielded a 6% overestimation of energy when comparingbenzene dimer pair interaction energies with CCSD(T) results.Our calculations are clearly in line with these by resulting inonly a 5% underestimation of energy on average (whencompared to DFTB-D). In a possible follow-up study, we areinterested in comparing the results from DFTB-D and MMoptimizations with a localized energy surface calculated using adispersion corrected DFT approach and expand our MMtesting to an 80 Å-long substrate with (4,4) through (10,10)configurations for the SWNTs in order to check the impact ofdiameter on all conformers and AAs.

■ ASSOCIATED CONTENT

*S Supporting InformationThe Supporting Information is available free of charge on theACS Publications website at DOI: 10.1021/acs.jpca.7b11716.

Additional information about methodology and adsorp-tion data for various length SWNTs (PDF)

■ AUTHOR INFORMATION

Corresponding Author*E-mail: andreas.riemann@wwu.edu; Phone: 360.650.3659.

ORCIDAndreas Riemann: 0000-0001-9867-8626NotesThe authors declare no competing financial interest.

■ ACKNOWLEDGMENTS

The authors thank Tobias Schwabe (Universitat Hamburg) forfruitful discussions regarding the quantum mechanical andtight-binding calculations.

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The Journal of Physical Chemistry A Article

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