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Atomic charge superposition calculations of STM images of glycine and alanine adsorbed on graphite
Ultramicroscopy 42-44 (1992) 1031-1036 North-Holland
Atomic charge superposition calculations of STM images of glycine and alanine adsorbed on graphite W.S. Yang, Y a n f a n g Li, J i a n x u n M o u a n d J u n j u e Y a n Department of Physics, Peking University, Beijing 100871, China Received 12 August 1991
Glycine and alanine molcules adsorbed on a graphite substrate and covered with a glycerol-water solution have been studied with STM. A variety of 2D crystalline structures with atomic-scale features can be observed in the STM images. The atomic charge superposition approach was employed to compute images from the possible models of the 2D structures. Many of the calculated images matched the experimental ones very well, thus indicating the general validity of the approach to amino acid adsorbates on graphite. Origin of the atomic resolution, proper tip-sample distance, and motivation of the 2D-ordered aggregation are discussed.
I. Introduction It is well known that STM images with atomic resolution can be obtained from a variety of samples in virtually any environment such as vacuum [1], air [2], as well as water [3]. Now, even individual hydrogen atoms are likely to be seen from the STM images of glycine molecules [3]. However, up to now, only a handful fo STM studies have interpreted the atomic-scale features with image calculations [4-8]. The reason for this is that on the one hand the theoretical methods used are all very time-consuming [4-8], and on the other hand to interpret an STM image a great deal of calculation is needed for many plausible models or structures. Fortunately, a very simple method, the atomic charge superposition (ACS) approach, has b~en suggested by Tersoff and Hamann [9], and employed to interpret the S i ( l l l ) 7 x 7 image by Tromp and co-workers [10]. As Tersoff and Hamann have also pointed out that the approach is not valid for some materials, such as semiconductors, the goal of the present work is to explore the validity of the ACS approach to 2D-ordered structures of organic (amino acid) molecules adsorbed on graphite (HOPG). The results indicate that the approach is valid for the cases tested
here. As amino acids are building blocks of proteins, the success of the present work exhibits the great potential of using the STM to study organic and biological molecules as well as interpreting, with confidence, the atomic-scale features in their STM images.
2. Experiment The experimental STM images of glycine molecules we use are from a previous study of Yang et al. [3], while those of alanine molecules are from Mou et al. [11]. The samples were prepared simply by spreading onto the freshly cleaved H O P G surface a droplet of solution of the amino acid to be studied. After air-drying, the sample surfaces were immediately covered with a very thin layer of 50% glycerol-water solution [12]. Electrochemically etched tungsten tips were used. STM images were collected in the constantcurrent mode with a slow scanning rate of about 75 ,~/s. The sample bias voltage was around 20 mV and the tunneling current was 1-2 nA. These conditions were crucial to the image quality [11].
0304-3991/92/$05.00 © 1992 - Elsevier Science Publishers B.V. All rights reserved
W.S. Yang et al. / A t o m i c charge superposition calculations
1032
3. Models
4. ACS calculations
As Yang et al. [3] have proposed the structural models to interpret the 2D-ordered atomic-scale features appearing in the STM images of glycine molecules, in the part on glycine of the present work we just verified the models by the ACS calculations. In the part on alanine of this work, we made a thorough search for all of the possible aggregation structures that can form linear chains or 2D nets of hydrogen bonds between the molecules and satisfy the van der Waals' radii as in crystals of the molecules. The criterion for the formation of the hydrogen bond was the bond length ( N - O distance: 2.7-3.2 A) and bond angles ( H - N - O : 00-40 ° and N - O - C : 111°-137 °) [13].
According to Tersoff and Hamann [9], in the ACS approach an exponentially decaying, spherically symmetric charge density distribution is assigned to each atom of the model, and at any point the charge density can be calculated by summing the charge densities of the atoms sufficiently close by to contribute. As shown by these authors, the corrugations measured in a STM experiment should be closely related to that of a surface of constant charge density. The charge density is defined as
D ( r ) = ~_,A i e x p [ - k i l r - r i l i
]
where r is the tip position and r i are atom
H2
HN( 1~ H3 H4~01 d Fig. 1. (a) Raw STM images (60,4 x 60 ,~, Vb = 20 mV, I t = 2 nA) of glycine molecules adsorbed on HOPG and covered with 50% glycerol-water solution, showing short-range ordering of the molecules [3]. (b) A zoom of the upper central portion ( 1 5 , 4 x 15 ,~) of (a), after local-contrast enhancement and smoothing, showing the 2D crystalline arrangement of some dozen of the molecules. (c) Averaged image of a glycine molecule, based on (b). (d) SChematic top-view of a glycine molecule lying on HOPG, showing the adsorbing geometry of the molecules in (b) and (c). (e) Theoretical image calculated with the ACS approach, corresponding to (b). (f) Same as (e), corresponding to (c).
W.S. Yang et al. / Atomic charge superposition calculations
1033
H2
Fig. 2. (a) Experimental STM image from the same sample as fig. la, similarly processed as figs. lb and lc [3]. (b) Theoretical image calculated from (c) with the ACS approach, corresponding to (a). (c) Schematic view of a glycine molecule, showing the adsorbing geometry of (a) and (b).
Fig. 3. (a) Experimental STM image (9 .~ x 9 ,~ Vb = 20 mV, I t = 1 nA) of alanine molecules adsorbed on H O P G and covered with 50% glycerol-water solution, similarly processed as figs. lb and lc [11]. (b) Theoretical image calculated from (c) with the ACS approach, corresponding to (a). (c) Schematic view of a 2D crystalline arrangement of alanine molecules. Dashed lines represent hydrogen bonds.
Fig. 4. Same as fig. 3, for a different adsorbing geometry.
1034
W.S. Yang et al. / Atomic charge superposition calculations
Fig. 5. S a m e as fig. 3, for a different adsorbing geometry.
positions. In our case, four different elements are involved in the calculations, i.e. H, C, N, and O. We determined the values of A i, k i, and D as follows. First, we calculated the free-atom charge density of the elements from the wave functions given by Herman and Skillman [14]. Then, we fit the charge density at radial distances ranging from 0.8 to 2 A with exponentially decaying curves to determine the A i and di values. The charge density at the nucleus of the tip atom was selected to be such that the experimental resolution was reached in the calculated images. The corresponding nominal tip-sample distance was about
1.3 A, which is indeed small but, as will be discussed later, quite reasonable.
5. Results
Some of the calculated STM images and their experimental counterparts of the glycine and alanine samples as well as the correspondent schematic views of the molecules are shown in figs. 1-6. The match of the calculated and experimental images is good in most cases, thus indicating that the ACS approach is suitable for inter-
Fig. 6. S a m e as fig. 3, for a different adsorbing geometry.
W..S. Yang et al. / Atomic charge superposition calculations
preting 2D-ordered atomic-scale features in STM images of amino acid molecules.
6. Discussion
(i) In the alanine case, a high resolution of about 2 ,~ was achieved in almost every image, while in the glycine case the resolution was even better: two hydrogen atoms separated by a distance less than 2 ,~ were resolved (fig. 2a). The atomic resolution is yet somewhat difficult to understand [9]; Baratoff [15] suggested that it may arise from a localized surface state of the tip, i.e. a dangling bond protruding from it. Very recently, Chen [16] discussed in detail the role of the tip material and the origin of atomic resolution in STM, pointing out that tungsten has a strong tendency to form highly localized metallic dzz dangling bonds on its surfaces, and that the derivative enhancement of atomic corrugation due to these d~2 tip states is probably the prime origin of atomic resolution by STM. (ii) As mentioned earlier, in the ACS calculations to make the calculated images reach the resolution of the experimental ones the nominal tip-sample distance (nucleus-nucleus) had to be about 1.3 A. This is equivalent to an experimental distance of 3.3 ,~. The reason is the following: As discussed above, in our experiments there was, very likely, a dz2 state at the tip, instead of an s state. However, in the ACS calculations, one calculates the local density of states at the tip, which is a logical consequence of the assumption of having an s state at the tip [9]. As pointed out by Chen [16], because of the derivative enhancement of STM corrugation, to obtain the same corrugation or resolution from the same sample, in the dz2-tip case the tip-sample distance must be about 2.0 .~ larger than that in the s-tip case. Applying this conclusion to our circumstances, the real tipg-sample distance must be 1.3 plus 2.0 .~, i.e. 3.3 A. This is a reasonable value [16] and in good agreement with the experiment [17], even though it is quite small. As this is only about 1 larger than the mechanical touching separation, it is no wonder in the experiment that the tunnel resistance was so crucial for getting the high
1035
resolution (close enough to the sample) and at the same time the high tip stability (avoiding touching the sample). (iii) The success of applying the ACS approach to the case of amino acids was not unexpected, because the ab initio calculations by Hagler and co-workers [18] have shown the general validity of the hard-sphere model, which is equivalent to the ACS. It seems to us that the underlying reason is that the deviations of the valence electrons from the free atom superposition case are small (less than 0.5 ,~ [18,19]), compared either to the lateral resolutions of STM images or to the dimensions of the molecules or the atomic groups consisting of the molecules. (iv) As mentioned above, in the searching process for the possible aggregation patterns of the molecules, the criterion used was the same as those for their 3D crystals, i.e. hydrogen bond formation and van der Waals' radius requirements [20]. Consequently, the fact that the models of the kind can interpret the experimental STM images indicates that hydrogen bonds can form between amino acid molecules in the aqueous environment at room temperature. This is reasonable, as the hydrogen bond energy is only about 2-10 kcal/mol and the activation energy of its formation is also very low [20]. (v) In this study we neglected the influences of the substrate to the aggregation structures and to the images. The good agreement between the calculated and the experimental images tells us that the interaction of the molecules with the substrates was indeed negligible in our work, although very often the axes of the 2D crystalline structures of the molecules lay along the axes of the substrate. 7. Conclusions
(i) With the use of a tungsten tip, STM images with atomic resolution can very often be obtained from amino acids adsorbed on H O P G , while the origin of the high resolution should be attributed to the existence of a dz2 state at the tip. (ii) To get atomic resolution, in addition to having a dz2 tip state, it is crucial that the t i p sample separation should be around 3.3 A. o
1036
W..S. Yang et al. / A t o m i c charge superposition calculations
(iii) Atomic-scale features in STM images of amino acids (organic molecules) adsorbed on H O P G can very often be interpreted satisfactorily with the ACS approach. (iv) Amino acid molecules can form (shortrange) 2D crystalline structures. The motivation of the ordering is hydrogen bond formation and van der Waals' radius requirement.
Acknowledgement This work was supported by the Natural Science Foundation of China and the Doctoral Program Foundation of Institute of Higher Education.
References [1] G. Binnig, H. Rohrer, Ch. Gerber and E. Weibel, Phys. Rev. Lett. 49 (1982) 57. [2] B.C. Schardt, S.L. Yan and F. Rinaldi, Science 243 (1989) 1050. [3] W.S. Yang, W. Sun, J. Mou and J. Yan, in: The Structure of Surfaces III, Eds. S.Y. Tong et al. (Springer, Berlin, 1991) in press; and in: Surface Physics and Related Topics, Eds. F.-J. Yang et al. (World Scientific, Singapore, 1991) p. 361. [4] D.M. Eigler, P.S. Weiss, E.K. Schweizer and N.D. Lang, Phys. Rev. Lett. 66 (1991) 1189.
[5] F. Wu, R.S. Han, W.S. Yang and Q.Q. Zheng, in: Surface Physics, Ed. X. Xie (World Scientific, Singapore, 1987) p. 203. [6] T. Sleater and R. Tycko, Phys. Rev. Lett. 60 (1988) 1418. [7] H. Ohtani, R.J. Wilson, S. Chaing and C.M. Mate, Phys. Rev. Lett. 60 (1988) 2398. [8] P.H. Lippel, R.J. Wilson, M.D. Miler, Ch. Woll and S. Chiang, Phys. Rev. Lett. 62 (1989) 171. [9] J. Tersoff and D.R. Hamann, Phys. Rev. B 31 (1985) 805. [10] M. Tromp, R.J. Hamers and J.E. Demuth, Phys. Rev. B 34 (1985) 1388. [11] J. Mou and W.S. Yang, Ultramicroscopy 42-44 (1992) 1024. [12] J. Mou, W. Sun, J. Yan, W.S. Yang, C. Liu, Z. Zhai, Q. Xu and Y. Xie, J. Vac. Sci. Technol. B 9 (1991) 1566. [13] W.S. Yang, Y. Li, J. Mou and J. Yan, to be published. [14] F. Herman and S. Skillman, Atomic Structure Calculations (Prentice-Hall, Englewood Cliffs, 1963). [15] A. Baratoff, Physica B + C 127B (1984) 143. [16] C.J. Chen, Phys. Rev. Lett. 65 (1990) 448; Mater. Res. Soc. Symp. Proc. 159 (1990) 289; J. Vac. Sci. Technol. A 6 (1988) 319; Phys. Rev. B 42 (1991) 8841. [17] U. Durig, J.K. Gimzewski and D.W. Pohl, Phys. Rev. Lett. 57 (1986) 2403; U. Durig, O. Zuger and D.W. Pohl, J. Microscopy 152 (1988) 259. [18] B. Robson and J. Garrier, Introduction to Proteins and Protein Engineering (Elsevier, Amsterdam, 1986) p. 468. [19] J. Almlof, A. Kvick and J.O. Thomas, J. Chem. Phys. 59 (1975) 3901. [20] L. Pauling, The Nature of the Chemical Bond (Cornell Univ. Press. Ithaca, NY, 1960).
Atomic charge superposition calculations of STM images of glycine and alanine adsorbed on graphite W.S. Yang, Y a n f a n g Li, J i a n x u n M o u a n d J u n j u e Y a n Department of Physics, Peking University, Beijing 100871, China Received 12 August 1991
Glycine and alanine molcules adsorbed on a graphite substrate and covered with a glycerol-water solution have been studied with STM. A variety of 2D crystalline structures with atomic-scale features can be observed in the STM images. The atomic charge superposition approach was employed to compute images from the possible models of the 2D structures. Many of the calculated images matched the experimental ones very well, thus indicating the general validity of the approach to amino acid adsorbates on graphite. Origin of the atomic resolution, proper tip-sample distance, and motivation of the 2D-ordered aggregation are discussed.
I. Introduction It is well known that STM images with atomic resolution can be obtained from a variety of samples in virtually any environment such as vacuum [1], air [2], as well as water [3]. Now, even individual hydrogen atoms are likely to be seen from the STM images of glycine molecules [3]. However, up to now, only a handful fo STM studies have interpreted the atomic-scale features with image calculations [4-8]. The reason for this is that on the one hand the theoretical methods used are all very time-consuming [4-8], and on the other hand to interpret an STM image a great deal of calculation is needed for many plausible models or structures. Fortunately, a very simple method, the atomic charge superposition (ACS) approach, has b~en suggested by Tersoff and Hamann [9], and employed to interpret the S i ( l l l ) 7 x 7 image by Tromp and co-workers [10]. As Tersoff and Hamann have also pointed out that the approach is not valid for some materials, such as semiconductors, the goal of the present work is to explore the validity of the ACS approach to 2D-ordered structures of organic (amino acid) molecules adsorbed on graphite (HOPG). The results indicate that the approach is valid for the cases tested
here. As amino acids are building blocks of proteins, the success of the present work exhibits the great potential of using the STM to study organic and biological molecules as well as interpreting, with confidence, the atomic-scale features in their STM images.
2. Experiment The experimental STM images of glycine molecules we use are from a previous study of Yang et al. [3], while those of alanine molecules are from Mou et al. [11]. The samples were prepared simply by spreading onto the freshly cleaved H O P G surface a droplet of solution of the amino acid to be studied. After air-drying, the sample surfaces were immediately covered with a very thin layer of 50% glycerol-water solution [12]. Electrochemically etched tungsten tips were used. STM images were collected in the constantcurrent mode with a slow scanning rate of about 75 ,~/s. The sample bias voltage was around 20 mV and the tunneling current was 1-2 nA. These conditions were crucial to the image quality [11].
0304-3991/92/$05.00 © 1992 - Elsevier Science Publishers B.V. All rights reserved
W.S. Yang et al. / A t o m i c charge superposition calculations
1032
3. Models
4. ACS calculations
As Yang et al. [3] have proposed the structural models to interpret the 2D-ordered atomic-scale features appearing in the STM images of glycine molecules, in the part on glycine of the present work we just verified the models by the ACS calculations. In the part on alanine of this work, we made a thorough search for all of the possible aggregation structures that can form linear chains or 2D nets of hydrogen bonds between the molecules and satisfy the van der Waals' radii as in crystals of the molecules. The criterion for the formation of the hydrogen bond was the bond length ( N - O distance: 2.7-3.2 A) and bond angles ( H - N - O : 00-40 ° and N - O - C : 111°-137 °) [13].
According to Tersoff and Hamann [9], in the ACS approach an exponentially decaying, spherically symmetric charge density distribution is assigned to each atom of the model, and at any point the charge density can be calculated by summing the charge densities of the atoms sufficiently close by to contribute. As shown by these authors, the corrugations measured in a STM experiment should be closely related to that of a surface of constant charge density. The charge density is defined as
D ( r ) = ~_,A i e x p [ - k i l r - r i l i
]
where r is the tip position and r i are atom
H2
HN( 1~ H3 H4~01 d Fig. 1. (a) Raw STM images (60,4 x 60 ,~, Vb = 20 mV, I t = 2 nA) of glycine molecules adsorbed on HOPG and covered with 50% glycerol-water solution, showing short-range ordering of the molecules [3]. (b) A zoom of the upper central portion ( 1 5 , 4 x 15 ,~) of (a), after local-contrast enhancement and smoothing, showing the 2D crystalline arrangement of some dozen of the molecules. (c) Averaged image of a glycine molecule, based on (b). (d) SChematic top-view of a glycine molecule lying on HOPG, showing the adsorbing geometry of the molecules in (b) and (c). (e) Theoretical image calculated with the ACS approach, corresponding to (b). (f) Same as (e), corresponding to (c).
W.S. Yang et al. / Atomic charge superposition calculations
1033
H2
Fig. 2. (a) Experimental STM image from the same sample as fig. la, similarly processed as figs. lb and lc [3]. (b) Theoretical image calculated from (c) with the ACS approach, corresponding to (a). (c) Schematic view of a glycine molecule, showing the adsorbing geometry of (a) and (b).
Fig. 3. (a) Experimental STM image (9 .~ x 9 ,~ Vb = 20 mV, I t = 1 nA) of alanine molecules adsorbed on H O P G and covered with 50% glycerol-water solution, similarly processed as figs. lb and lc [11]. (b) Theoretical image calculated from (c) with the ACS approach, corresponding to (a). (c) Schematic view of a 2D crystalline arrangement of alanine molecules. Dashed lines represent hydrogen bonds.
Fig. 4. Same as fig. 3, for a different adsorbing geometry.
1034
W.S. Yang et al. / Atomic charge superposition calculations
Fig. 5. S a m e as fig. 3, for a different adsorbing geometry.
positions. In our case, four different elements are involved in the calculations, i.e. H, C, N, and O. We determined the values of A i, k i, and D as follows. First, we calculated the free-atom charge density of the elements from the wave functions given by Herman and Skillman [14]. Then, we fit the charge density at radial distances ranging from 0.8 to 2 A with exponentially decaying curves to determine the A i and di values. The charge density at the nucleus of the tip atom was selected to be such that the experimental resolution was reached in the calculated images. The corresponding nominal tip-sample distance was about
1.3 A, which is indeed small but, as will be discussed later, quite reasonable.
5. Results
Some of the calculated STM images and their experimental counterparts of the glycine and alanine samples as well as the correspondent schematic views of the molecules are shown in figs. 1-6. The match of the calculated and experimental images is good in most cases, thus indicating that the ACS approach is suitable for inter-
Fig. 6. S a m e as fig. 3, for a different adsorbing geometry.
W..S. Yang et al. / Atomic charge superposition calculations
preting 2D-ordered atomic-scale features in STM images of amino acid molecules.
6. Discussion
(i) In the alanine case, a high resolution of about 2 ,~ was achieved in almost every image, while in the glycine case the resolution was even better: two hydrogen atoms separated by a distance less than 2 ,~ were resolved (fig. 2a). The atomic resolution is yet somewhat difficult to understand [9]; Baratoff [15] suggested that it may arise from a localized surface state of the tip, i.e. a dangling bond protruding from it. Very recently, Chen [16] discussed in detail the role of the tip material and the origin of atomic resolution in STM, pointing out that tungsten has a strong tendency to form highly localized metallic dzz dangling bonds on its surfaces, and that the derivative enhancement of atomic corrugation due to these d~2 tip states is probably the prime origin of atomic resolution by STM. (ii) As mentioned earlier, in the ACS calculations to make the calculated images reach the resolution of the experimental ones the nominal tip-sample distance (nucleus-nucleus) had to be about 1.3 A. This is equivalent to an experimental distance of 3.3 ,~. The reason is the following: As discussed above, in our experiments there was, very likely, a dz2 state at the tip, instead of an s state. However, in the ACS calculations, one calculates the local density of states at the tip, which is a logical consequence of the assumption of having an s state at the tip [9]. As pointed out by Chen [16], because of the derivative enhancement of STM corrugation, to obtain the same corrugation or resolution from the same sample, in the dz2-tip case the tip-sample distance must be about 2.0 .~ larger than that in the s-tip case. Applying this conclusion to our circumstances, the real tipg-sample distance must be 1.3 plus 2.0 .~, i.e. 3.3 A. This is a reasonable value [16] and in good agreement with the experiment [17], even though it is quite small. As this is only about 1 larger than the mechanical touching separation, it is no wonder in the experiment that the tunnel resistance was so crucial for getting the high
1035
resolution (close enough to the sample) and at the same time the high tip stability (avoiding touching the sample). (iii) The success of applying the ACS approach to the case of amino acids was not unexpected, because the ab initio calculations by Hagler and co-workers [18] have shown the general validity of the hard-sphere model, which is equivalent to the ACS. It seems to us that the underlying reason is that the deviations of the valence electrons from the free atom superposition case are small (less than 0.5 ,~ [18,19]), compared either to the lateral resolutions of STM images or to the dimensions of the molecules or the atomic groups consisting of the molecules. (iv) As mentioned above, in the searching process for the possible aggregation patterns of the molecules, the criterion used was the same as those for their 3D crystals, i.e. hydrogen bond formation and van der Waals' radius requirements [20]. Consequently, the fact that the models of the kind can interpret the experimental STM images indicates that hydrogen bonds can form between amino acid molecules in the aqueous environment at room temperature. This is reasonable, as the hydrogen bond energy is only about 2-10 kcal/mol and the activation energy of its formation is also very low [20]. (v) In this study we neglected the influences of the substrate to the aggregation structures and to the images. The good agreement between the calculated and the experimental images tells us that the interaction of the molecules with the substrates was indeed negligible in our work, although very often the axes of the 2D crystalline structures of the molecules lay along the axes of the substrate. 7. Conclusions
(i) With the use of a tungsten tip, STM images with atomic resolution can very often be obtained from amino acids adsorbed on H O P G , while the origin of the high resolution should be attributed to the existence of a dz2 state at the tip. (ii) To get atomic resolution, in addition to having a dz2 tip state, it is crucial that the t i p sample separation should be around 3.3 A. o
1036
W..S. Yang et al. / A t o m i c charge superposition calculations
(iii) Atomic-scale features in STM images of amino acids (organic molecules) adsorbed on H O P G can very often be interpreted satisfactorily with the ACS approach. (iv) Amino acid molecules can form (shortrange) 2D crystalline structures. The motivation of the ordering is hydrogen bond formation and van der Waals' radius requirement.
Acknowledgement This work was supported by the Natural Science Foundation of China and the Doctoral Program Foundation of Institute of Higher Education.
References [1] G. Binnig, H. Rohrer, Ch. Gerber and E. Weibel, Phys. Rev. Lett. 49 (1982) 57. [2] B.C. Schardt, S.L. Yan and F. Rinaldi, Science 243 (1989) 1050. [3] W.S. Yang, W. Sun, J. Mou and J. Yan, in: The Structure of Surfaces III, Eds. S.Y. Tong et al. (Springer, Berlin, 1991) in press; and in: Surface Physics and Related Topics, Eds. F.-J. Yang et al. (World Scientific, Singapore, 1991) p. 361. [4] D.M. Eigler, P.S. Weiss, E.K. Schweizer and N.D. Lang, Phys. Rev. Lett. 66 (1991) 1189.
[5] F. Wu, R.S. Han, W.S. Yang and Q.Q. Zheng, in: Surface Physics, Ed. X. Xie (World Scientific, Singapore, 1987) p. 203. [6] T. Sleater and R. Tycko, Phys. Rev. Lett. 60 (1988) 1418. [7] H. Ohtani, R.J. Wilson, S. Chaing and C.M. Mate, Phys. Rev. Lett. 60 (1988) 2398. [8] P.H. Lippel, R.J. Wilson, M.D. Miler, Ch. Woll and S. Chiang, Phys. Rev. Lett. 62 (1989) 171. [9] J. Tersoff and D.R. Hamann, Phys. Rev. B 31 (1985) 805. [10] M. Tromp, R.J. Hamers and J.E. Demuth, Phys. Rev. B 34 (1985) 1388. [11] J. Mou and W.S. Yang, Ultramicroscopy 42-44 (1992) 1024. [12] J. Mou, W. Sun, J. Yan, W.S. Yang, C. Liu, Z. Zhai, Q. Xu and Y. Xie, J. Vac. Sci. Technol. B 9 (1991) 1566. [13] W.S. Yang, Y. Li, J. Mou and J. Yan, to be published. [14] F. Herman and S. Skillman, Atomic Structure Calculations (Prentice-Hall, Englewood Cliffs, 1963). [15] A. Baratoff, Physica B + C 127B (1984) 143. [16] C.J. Chen, Phys. Rev. Lett. 65 (1990) 448; Mater. Res. Soc. Symp. Proc. 159 (1990) 289; J. Vac. Sci. Technol. A 6 (1988) 319; Phys. Rev. B 42 (1991) 8841. [17] U. Durig, J.K. Gimzewski and D.W. Pohl, Phys. Rev. Lett. 57 (1986) 2403; U. Durig, O. Zuger and D.W. Pohl, J. Microscopy 152 (1988) 259. [18] B. Robson and J. Garrier, Introduction to Proteins and Protein Engineering (Elsevier, Amsterdam, 1986) p. 468. [19] J. Almlof, A. Kvick and J.O. Thomas, J. Chem. Phys. 59 (1975) 3901. [20] L. Pauling, The Nature of the Chemical Bond (Cornell Univ. Press. Ithaca, NY, 1960).