Discrimination of Bond Order in Organic Molecules Using Noncontact

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Discrimination of Bond Order in Organic Molecules Using Noncontact Atomic Force Microscopy Dingxin Fan, Yuki Sakai, and James R. Chelikowsky Nano Lett., Just Accepted Manuscript • DOI: 10.1021/acs.nanolett.9b02097 • Publication Date (Web): 25 Jul 2019 Downloaded from pubs.acs.org on July 27, 2019

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Discrimination of Bond Order in Organic Molecules Using Noncontact Atomic Force Microscopy Dingxin Fan,† Yuki Sakai,‡ and James R. Chelikowsky*,†,‡,§ McKetta Department of Chemical Engineering, ‡ Center for Computational Materials, Oden Institute for Computational Engineering and Sciences, § Department of Physics, The University of Texas at Austin, Austin, Texas 78712, United States †

AUTHOR INFORMATION Corresponding Author *E-mail: [email protected]. Phone: 512-232-9083.

Abstract: Non-contact atomic force microscopy (nc-AFM) with a CO-functionalized tip can image submolecular structures through high resolution images with the possibility of discriminating

bond order. We employ real-space pseudopotential calculations to

simulate nc-AFM images of molecules containing double (dibenzo(cd,n)naphtho(3,2,1,8pqra)perylene (DBNP), hexabenzo(bc,ef,hi,kl,no,qr)coronene (HBC)) and triple (1,2bis[2-(2-ethynylphenyl)ethynyl]-benzene (BEEB), 6-phenylhexa-1,3,5-triynylbenzene (PHTB)) bonds. We find (1) triple bonds can be unambiguously distinguished from other interatomic interactions based on a characteristic image and (2) the degree of double bond character can be directly determined from the image. We propose that large lateral forces acting on the tip may induce specific image distortions in the cases of DBNP and BEEB. Key words: Atomic Force Microscopy, Density Functional Theory, Real Space, Frozen Density Theory, CO tip, Organic Chemistry

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Introduction Atomic force microscopy (AFM) is a

extremely low temperature allows one to reach ultrahigh resolution.5 Numerous experimental

popular analytical scanning probe technique used and

theoretical

studies

have

shown

that

to image systems at the atomic and even submolecular resolution nc-AFM images can be submolecular limit. AFM senses the sample obtained by employing a carbon monoxide (CO)surface through a probe tip that detects forces functionalized

tip.6-23

Specifically,

nc-AFM

between the tip and sample. Three common experiments with a CO tip are able to distinguish operating modes are employed in AFM: contact, bond orders.14-18 Direct imaging of chemical tapping and non-contact mode. In the first two bonds at submolecular resolution provides a new modes, the tip directly interacts with the perspective for characterization of molecular specimen. Contact mode can be operated under systems. ambient condition and usually has a high scan We employ a simulation method based speed. A major drawback of this mode is that on the ab initio real-space pseudopotentials to both the probe tip and the sample can be simulate nc-AFM images. Our previous work damaged during the scanning process owing to has successively simulated some features of nclarge lateral forces.1-2 The tapping mode is also AFM images, including contrast inversion,7-8 frequently used under ambient conditions as it image distortion7 and possibly hydrogen bond.8 usually generates higher signal than the nonWe simulate nc-AFM images generated with a contact mode and tapping prevents the probe tip CO

tip

for

dibenzo(cd,n)naphtho(3,2,1,8-

from getting trapped or contaminated by a thin pqra)perylene

(DBNP),

liquid layer formed on top of the specimen. For hexabenzo(bc,ef,hi,kl,no,qr)coronene

(HBC),

example, when the surface of a biomolecular 1,2-bis[2-(2-ethynylphenyl)ethynyl]-benzene complex and the mica surface are exposed to air, (BEEB) and 6-phenylhexa-1,3,5-triynylbenzene a thin water layer can be easily formed as both (PHTB). For DBNP and HBC, which contain surfaces are hydrophilic.3 The non-contact mode multiple double bonds, we employ the concept of keeps the probe tip active for a long time and Pauling bond order,14, 24-25 which was originally prevents the sample from degradation.1-2,

4

established to describe the amount of double Operating constant height non-contact AFM (ncbond character in a carbon-carbon bond. This AFM) mode in ultrahigh vacuum and at

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empirical scheme is based on an experimentally

polarization)

for

the

exchange-correlation

determined correlation between bond length and

functional.36-37 The choice of the exchange-

bond order. Pauling bond order can take values

correlation functional does not affect qualitative

from 0 (single bond) to 1 (double bond).

features of the AFM image.38-40 Our eigensolver

Computational Method We employ real-space pseudopotentials

is based on Chebyshev subspace filtering41-42 which solves the Kohn-Sham equation on real-

constructed within density functional theory space cubic grid. Subspace filtering can save (DFT)26-27 to compute the required interatomic order of magnitude of computational time.41-42 forces. We generate 2D uniform grids over the To further reduce the computational cost, we sample molecule at three different tip heights and employ the frozen density embedding theory compute the total energy of the tip-sample (FDET).43-44 Within FDET, we divide the total system (Ets) at each grid point. In previous work,

charge density of a system into two subsystems –

we verified that the tip-sample force gradient can the tip and sample: ntot(𝐫) = nt(𝐫) + ns(𝐫). The

be taken to be constant within an oscillation

total energy functional Etot[nt, ns] is given by: cycle.7-11

The relative frequency shift (∆𝑓) can be t

computed from total energy calculations using a

Etot =

three-point central finite difference method7, 28: ∆𝑓 =

∂2𝐸𝑡𝑠 ∂𝑧2

=

𝐸 ―1 ― 2𝐸0 + 𝐸1 ℎ2

∬ +

(1)

{nt(𝐫) + ns(𝐫)}{n (𝐫′) + ns(𝐫′)} 2|𝐫 ― 𝐫′|

∫ {V

t nuc(𝐫)

d𝐫d𝐫′

+ Vsnuc(𝐫)}{nt(𝐫) + ns(𝐫)}d𝐫

[nt,ns] + Ts[nt] + Ts[ns] + Tnadd s + Exc[nt + ns] + Enuc

where 𝐸 ―1,𝐸0 and 𝐸1 correspond to the total

(2)

energy of the tip-sample system at three different

where Vnuc, Ts, Exc and Enuc represent the nuclear

heights for each grid point, h is the separation

potential, kinetic energy functional, exchange-

distance between the planes.

correlation energy functional, and nuclearreal-space

nuclear interaction energy respectively. We fix

pseudopotential DFT code – PARSEC to

Vsnuc(𝐫) and ns(𝐫) during the FDET calculations.

calculate the total electronic energies.29-34 We

The nonadditive kinetic energy functional (Tnadd ) s

incorporate Troullier-Martin norm-conserving

is defined by:

We

pseudopotentials35

employ

and

a

the

local

density

[nt,ns] = Ts[nt,ns] ― Ts[nt] ― Ts[ns] (3) Tnadd s

approximation by Ceperley-Alder (without spin

3


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We approximate this nonadditive term by

HBC and BEEB. The grid spacings of the real-

adopting the analytic form of the kinetic energy

space cubic grid (for electronic structure

functional proposed by Tran and Wesołowski

calculations) are 0.25 a.u. for DBNP and 0.30 a.u.

(PBE-TW)45, which is known to give reasonable

for HBC and BEEB. The step size in the image

results.43 The Schrödinger-like equation in FDET

plane (𝑥,𝑦) is set to be an integer multiple of the

for a set of Kohn-Sham eigenvalues and wave

grid spacing. We also use a tip tilting correction

functions {ϵti, ψti(𝐫)} is given by

for lateral force developed by Guo et al.38-39

[

― ∇2 2

+ Vteff(𝐫) + Vemb(𝐫) ψti(𝐫) = ϵtiψti(𝐫) (4)

With this correction, we first compute the lateral

𝑉𝑡eff(𝐫)

forces in x and y directions, 𝐹𝑙𝑎𝑡(𝑥,𝑦), using the

]

→

where

is a Kohn-Sham potential of the tip

total energies in the middle plane by a finite

and 𝑉emb(𝐫) is the embedded potential which is

difference

given by Vemb(𝐫) =

―

δExc[n] δn

ns(𝐫′)

∫|𝐫 ― 𝐫 |d𝐫 +

| n = nt +

′

′

δTs[n] δn

Vsnuc(𝐫)

|n = ntot ―

+

δExc[n] δn

δTs[n] δn

method.

We

compute

the →

displacement of O atom in x and y directions,∆𝑙𝑎𝑡

|n = ntot

(𝑥,𝑦), by assuming a linear relationship between | n = nt

(5)

the lateral force and the lateral displacement:

FDET calculations for the tip were performed

1

→

∆𝑙𝑎𝑡(𝑥,𝑦) =

→

(6)

𝑘𝐶𝑂 ∙ 𝐹𝑙𝑎𝑡(𝑥,𝑦)

following a full DFT run of the sample system and using the Hartree potential, nuclear potential

where 𝑘𝐶𝑂 is the lateral spring constant of the

and the charge density of the sample system as

CO tip. For HBC and PHTB, we set 𝑘𝐶𝑂 to be

input. Our previous studies have shown the

0.40 N/m. This value is slightly larger than the

assumption that the tip does not have a

experimental value of 0.24 N/m as a linear

significant effect on the structural and electronic

relationship is assumed in Eq. 6.39,46 For DBNP,

properties of the sample is valid for the systems examined

we set 𝑘𝐶𝑂 to be 0.12 N/m to achieve a better

here.7-8, 43

agreement with the experimental nc-AFM

We use a confined boundary condition,

image.14 For BEEB, we generate nc-AFM

which assumes the electron wavefunctions go to

images using varies values of 𝑘𝐶𝑂 (0.40 N/m,

zero outside a spherical domain. The boundary

0.24 N/m and 0.12 N/m) to test its correlation

sphere radii are 23 a.u. for DBNP and 36 a.u. for

with submolecular features.

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We model the functionalized CO tip with

a

single

CO

molecule,

which

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deviates from the theoretical model (Fig. 1(a))

is

considerably when compared with the right half.

perpendicular to the sample (O atom facing the

From Fig. 2, the observed distortion in the

molecule). Previous studies using CO bonded to

experimental nc-AFM image of DBNP is not

metal clusters have shown that this simplification

reduced compared to that in the HBC image

gives accurate results.7-9 The optimized C=O

owing to the symmetric geometry of HBC

bond length (2.14 a.u.7) is held constant. The tip

molecule.

height is defined as the distance between the O

In Fig. 3(a), we illustrate how the

atom of the tip and the sample molecule.

apparent bond lengths can be determined. Fig.

Results and Discussion

3(b) shows a strong correlation between the

Figures. 1 and 2 show the Kekulé apparent bond lengths of the bonds (in Figs. 2(a) structures for the simulated nc-AFM, interatomic and 3(a)) and their Pauling bond orders. The forces

and the corresponding experimental values from our simulation are smaller than the

images for the molecules DBNP and HBC. For experimentally measured apparent bond lengths. DBNP, our simulation (Fig. 1(b)) agrees with However, a linear relationship exists between experiment (Fig. 1(c)) in terms of the image apparent bond length and Pauling bond order. distortion when using a relatively small 𝑘𝐶𝑂

This allows one to predict the amount of double

(0.12 N/m) which is half of the experimental determined

value.46

bond character (Pauling bond order) from the

We attribute the large

observed nc-AFM image.

distortion in nc-AFM image for DBNP to the For the BEEB molecule which contains

large lateral force. From Fig. 1(d) shows that the

four triple bonds as illustrated in Fig. 4(a), we

global maximum (ring II) and a local minimum

first generate the charge density map on an

(ring I) for the forces occur at the center of the

isosurface that is 0.8 a.u. above BEEB (Fig. 4(b)).

six-fold rings. The large difference of the forces

The simulated nc-AFM images are calculated at

acting on the tip at these two hollow sites

a tip height of 6.3 a.u. Without tip tilting

induces a stronger tip tilting effect during

correction, the apparent triple bond exhibits a

scanning. As a result, for the distortion in nc-

“spheroidal” feature. In Fig. 4(d)-(f), we vary the

AFM image of DBNP, the left half of the image

lateral force constant, 𝑘𝐶𝑂, to study the its

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correlation with the nc-AFM image. As the

the PHTB molecule (Fig. 5(a)) at a tip height of

lateral force increases, we find (1) the spheroidal

6.6 a.u. Fig. 5(b)-(c) illustrates a similar trend as

feature of the C≡C bond becomes ellipsoidal and

we find in BEEB. The spheroidal feature of the

is oriented with the major axis perpendicular to

C≡C bond transforms to ellipsoidal in the same

the bonding direction; (2) the size of the rings

direction as the lateral force increases. The

also become larger. As expected, we find that the

agreement

charge density within the triple bonds is larger

experiment is not as good as for other molecules

than their neighbor C-C bonds. Specifically, the

and can be attributed to the twisted nature of the

charge density of bond 1 (Fig. 4(a)) is about 1.4

PHTB molecule.47

times higher than the charge density of bond 2 (3

Summary

between

this

simulation

and

In brief, we find a constant height nc-

or 4) which is conjugated C-C bond independent

AFM with a CO-functionalized probe tip can

of the height above the molecule. As a result, the

identify C≡C bonds based on submolecular

triple bond regions repel the CO tip more so that

features. As the lateral force increases, the shape

the spheroidal feature becomes the ellipsoidal

of the triple bond changes from a spheroidal

feature. As Fig. 4(b) shows, the hollow sites

feature to ellipsoidal. For the BEEB molecule,

have very small charge densities so that the CO

we also find the size of the ring structure

tip does not tilt much at the hollow sites

becomes larger as the lateral force increases. For

compared with the surrounding sites. Therefore,

systems containing C=C bonds (DBNP and

the size of the rings becomes larger as the lateral

HBC), the amount of double bond character can

force increases. The bright feature observed

be directly calculated based on the nc-AFM

experimentally for the conjugated rings are

images. In addition, large lateral force can induce

rather weak in the simulation. This is likely

specific image distortion for DBNP owing to the

caused by the displacement of H atoms away

asymmetrical structure.

from Ag (100) substrate.47

ACKNOWLEDGMENTS In

order

to

confirm

the

shape

We acknowledge support from the Welch Foundation under grant F-1837 and the U.S. Department of Energy under DOE/DEFG02-06ER46286. The National Energy Research Scientific Computing (NERSC) and the Texas Advanced Computing Center (TACC) provided computational resources.

transformation of the triple bond as the lateral force changes in spatially complex systems, i.e., nonplanar, we also simulate nc-AFM images for

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Figure 1. (a) Kekulé structure of DBNP, five selected carbon-carbon bonds are labeled as a, b, c, d and e. (b) Simulated nc-AFM image of DBNP. Tip height is 6.3 a.u. and the lateral spring constant of CO tip is 0.12 N/m. (c) Experimental nc-AFM image of DBNP on bilayer NaCl on Cu(111) surface. Tip height is 6.8 a.u. (c) is adapted with permission from Gross, L. et al. Science 2012, 337, 1326-1329. Copyright (2012) The American Association for the Advancement of Science. (d) Semi-transparent simulated nc-AFM image of DBNP. The black curve corresponds to the vertical forces acting on O atom of the tip across the dashed line in the direction as the arrow indicates. For example, on the black solid line, the black dot on the curve correspond to the vertical force acting on O atom of the tip where the tip is on top of the specimen at the position as the black dot on the dashed line indicates. Force is in pN/103 and the direction of the force points from O atom toward C atom. The scale bars correspond to 5 a.u. in (b) and (d) and correspond to 9.45 a.u. in (c).

Figure 2. (a) Kekulé structure of HBC, two selected carbon-carbon bonds are labeled as f and g. (b) Simulated nc-AFM image of HBC. Tip height is 6.3 a.u. and the lateral spring constant of CO tip is 0.40 N/m. (c) Experimental nc-AFM image of HBC on Cu(111) surface. Tip height is 7.0 a.u. (c) is adapted with

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permission from Gross, L. et al. Science 2012, 337, 1326-1329. Copyright (2012) The American Association for the Advancement of Science. The scale bars correspond to 5 a.u. in (b) and correspond to 9.45 a.u. in (c).

Figure 3. (Color online) (a) Labeled nc-AFM image for DBNP for apparent bond length measurement. The red dot indicates one point we take to measure apparent bond length for b, c or d. The inset is a magnified image of the area around the red dot. (b) Apparent bond length as a function of Pauling bond order for the selected bonds in Figures. 2 and 3. The data points of bond a are not included when computing the linear regression lines as they are clearly outliers. For bond f and bond g in HBC, we take the average bond lengths of the six bonds of ring III and ring IV. The circular data points and the dashed trend line (y=2.39x+3.47) is from our simulation. The triangular data points and the solid trend line (y=-2.33x+3.81) is adapted from Gross, L. et al. Science 2012, 337, 1326-1329. Copyright (2012) The American Association for the Advancement of Science.

Figure 4. (Color online) (a) Kekulé structure of BEEB. (b) Charge density map of BEEB. The plane is 0.8 a.u. above the sample. Charge density from high to low: red – green – blue. The ball-and-stick model indicates the positions of the atoms. Blue ball: C atom; white ball: H atom. (c)-(f) Simulated nc-AFM

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images of BEEB. Tip height is 6.3 a.u. The lateral spring constant of CO tip is (c) infinity (no tip tilting correction applied), (d) 0.40 N/m, (e) 0.24 N/m, and (f) 0.12 N/m respectively. (g) Experimental nc-AFM image of BEEB on Ag (100) surface. Tip height is not reported. (g) is adapted with permission from de Oteyza, D. G. et al. Science 2013, 340, 1434-1437. Copyright (2013) The American Association for the Advancement of Science. The black scale bar corresponds to 5 a.u. in (c) - (f), the white scale bar corresponds to 5.67 a.u. in (g).

Figure 5. (Color online) (a) Kekulé structure of PHTB. (b)-(c) Simulated nc-AFM image of PHTB. Tip height is 6.6 a.u. (b) No tip tilting correction applied; (c) the lateral spring constant of CO tip is 0.40 N/m. (d) Experimental nc-AFM image of PHTB on bilayer NaCl on Cu(111) surface. (d) is adapted with permission from Pavliček, N et al. Nature Chem. 2018, 10, 853-858. Copyright (2018) Springer Nature. The white scale bars correspond to 5 a.u.

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Discrimination of Bond Order in Organic Molecules Using Noncontact

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