Microsoft Excelを用いた分子軌道の描画の実習

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1 J. Comput. Chem. Jpn.,Vol.9, No.4, pp (2010) 2010 Society of Computer Chemistry, Japan Microsoft Excel a*, b, c a, b, c, * nagaoka@ehimegw.dpc.ehime-u.ac.jp (Received: October 26, 2009; Accepted for publication: February 8, 2010; Advance publication: July 21, 2010) Microsoft Excel (H + 2 ).,. :,,,,, Microsoft Excel 1 [1,2], Schrödinger.,.,,,,.,,,.,,., (PC) [3].,. (1992 ), PC. PC, PC, PC Microsoft Office.,, PC. Microsoft Office Excel,,., Microsoft Excel 2007 (H + 2 ) (3D).,. Excel. [4,5],. DOI: /jccj.H

2 , r, 1s, 2s, 2p, 3s, 3p, 3d R n,l (r) [6]., n, l. a 0, a 0 (au), a 0 = 1. 1s A1 r A2 0.5 au r = 0~8 au. B1 R(r), B2 B18, A B, (Figure 1a)., Excel. Excel, 7. R n,l (r) 2, R n,l (r) 2 r 1, r., D(r) = 4pr 2 R n,l (r) 2. 8, Mathematica., Excel,,,. 2.2 H 2 +, zx (z, x, y = 0) (z = 0, x = 0) R n,l (r) Y l,m (q,j) 3D. Y l,m (q,j), m, q j, r = (z 2 + x 2 ) 1/2., 1 B1 0.2 au z = -8~8 au, A 2 A2 0.2 au x = -4~4 au. B2 B42, CD42, B2 Figure 1. (a) Radial function, R(r), for 1s atomic orbital in hydrogen atom presented as an Excel graph, constructed as described in the text. (b) Its radial distribution function, D(r). ~CD42, 3D., 1/4p 1/4*PI() 1/(4*PI())., x A, B2 x A., A $. z 1.,, H + 2 3D,. z = -1, x = 0 z = 1, x = 0, (2 au). z = -1, x = 0 r {(z + 1) 2 + x 2 } 1/2., [9],. 178 J. Comput. Chem. Jpn.,Vol.9, No.4, (2010)

2.3 zx (z, x, y = 0) z = -2~2 au, x = -2~2 au 0.05 au, 1 sp 3D, 2 sp 3D, 2 sp 3D, 3 sp 2 3D,. 6, 2s, 2p ( 6 p. 18) 3.25. 3 3.1, 1s R(r) Figure 1a, D(r) Figure 1b., D(r) r,, 1s 1 au a 0 (Figure 1b).. 3.2 H 2 + 1s 2 H + 2 1s g 3D Figure 2a, 1s u 3D Figure 2b.

3 2.3 zx (z, x, y = 0) z = -2~2 au, x = -2~2 au 0.05 au, 1 sp 3D, 2 sp 3D, 2 sp 3D, 3 sp 2 3D,. 6, 2s, 2p ( 6 p. 18) , 1s R(r) Figure 1a, D(r) Figure 1b., D(r) r,, 1s 1 au a 0 (Figure 1b) H 2 + 1s 2 H + 2 1s g 3D Figure 2a, 1s u 3D Figure 2b., (Figure 2a),,, (Figure 2b),,. +, H 2 2s g, 2s u, 3s g, 3s u, 1p u, 1p g 3D., 2p 2 s (3s g ) 3D Figure 3a, s (3s u ) 3D Figure 3b. 3s u 2s g, 2s u, 3s g, 1p u, 1p g,, 3s u (Figure 3b) Figure 2. (a) 3D-contour representation of amplitude of 1s g bonding orbital in H 2 + in a plane containing two nuclei at an interatomic distance of 2 au (b) 1s u antibonding orbital. Figure 3. (a) 3D-contour representation of amplitude of 3s g bonding orbital in H 2 + in a plane containing two nuclei at an interatomic distance of 2 au (b) 3s u antibonding orbital. DOI: /jccj.H

Figure 4. Schematic representation of composition of 3s u antibonding orbital adopted in a lot of textbooks.

(b) Its ordinary contour representation. Figure 6.

(b) 3D-contour representation of electron density of two sp hybrid orbitals in carbon.

4 Figure 4. Schematic representation of composition of 3s u antibonding orbital adopted in a lot of textbooks. Figure 5. (a) 3D-contour representation of amplitude of an sp hybrid orbital in carbon. (b) Its ordinary contour representation. Figure 6. (a) 3D-contour representation of amplitude of two sp hybrid orbitals in carbon. (b) 3D-contour representation of electron density of two sp hybrid orbitals in carbon. (c) Ordinary contour representation of Figure 6b.. 3s u Figure , Figure 3b + -, - +., + -, [4]., H + 2 3s u Figure 4,. 3.3 Figure 5a 1 sp 3D., + - 2s (z > 0) + (z < 0) - 2p. 3D (Figure 5b), +,., sp ( ) 2s -, CH 2 Figure J. Comput. Chem. Jpn.,Vol.9, No.4, (2010)

Figure 7. (a) Schematic representation of sp hybrid orbital adopted in a lot of textbooks. (b) sp 2 hybrid orbital. Figure 9. Overlap of three sp 2 hybrid orbitals. Figure 8.

5 Figure 7. (a) Schematic representation of sp hybrid orbital adopted in a lot of textbooks. (b) sp 2 hybrid orbital. Figure 9. Overlap of three sp 2 hybrid orbitals. Figure 8. 3D-contour representation of electron density of three sp 2 hybrid orbitals in carbon. H, 2s 2p -. 1 sp 2, sp 3. 2 sp 2 sp [10] 2s 2 [11], 3D Figure 6a., 2 sp 3D Figure 6b. 1 2s 1 2p 1. Figure 6b Figure 6c. sp (Figure 7a) + -, Figure 6a Figure 6b 6c,., 3 sp 2 3D (Figure 8), (Figure 7b) [5]., 2 p ( 2 Figure 6.13)., (Figure 7),, 1 1, (Figure 9).. sp 3,., 1s 2 2s 2 2p 2, 2s 2p 1s 2 2s 1 2p 1 x 2p 1 y 2p 1 z. 4 Excel + H 2 3D.,.., 12., Excel ( 6 2 ), DOI: /jccj.H

6 [4].. [1],, (1990). [2] I. N. Levine, Quantum Chemistry, 6th ed., Pearson, Upper Saddle River NJ (2009). [3],, 40, 600 (1992). [4],, , 1. [5], MaLS Forum, 4, 2 (2006); saitama-u.ac.jp/modules/xoonips/detail.php?id=ky- AA ( ). [6] C. M. Quinn, Computational Quantum Chemistry, Academic Press, London (2002). [7] &part=7 _ ( ) ( ). [8],,, (2005), 7 [8][9]. [9] V. Walters, J. de Paula., P. Atkins., Explorations in Physical Chemistry, 2nd ed., Oxford University Press, Oxford (2007). [10] -1 2 sp. [11] 2 sp 3 3p R. D. Miller, J. Michl, Chem. Rev., 89, 1359 (1989), Figure 6. doi: /cr00096a006 [12],, (2004). Practice in Graphing Molecular-Orbitals by Using Microsoft Excel Shin-ichi NAGAOKA a*, Hiroyuki TERAMAE b, Umpei NAGASHIMA c a Department of Chemistry, Faculty of Science, Ehime University, Matsuyama , Japan b Faculty of Science, Josai University, Keyakidai 1-1, Sakado , Japan c Nanosystem Research Institute (NRI), National Institute of Advanced Industrial Science and Technology (AIST), Umezono, Tsukuba , Japan * nagaoka@ehimegw.dpc.ehime-u.ac.jp We present some practical studies of drawing the graphs of the radial functions and the distribution functions for the hydrogen-like atom and of drawing the three-dimensional contour plots of H + 2 molecular-orbitals and hybrid orbitals by using Microsoft Excel in university courses. Some of the three-dimensional contour representations thus obtained are not consistent with figures given in various textbooks of quantum chemistry, and the usual explanations are liable to cause misunderstandings. Keywords: Radial Function, Radial Distribution Function, Molecular Orbital, Hybrid Orbital, Three-Dimensional Contour Representation, Microsoft Excel 182 J. Comput. Chem. Jpn.,Vol.9, No.4, (2010)

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D:/cssj/jcs/v7n2/a5tex/TX2.dvi J. Chem. Software, Vol. 7, No. 2, p. 87 98 (2001) *,, 338-8570 255 *e-mail: tokita@apc.saitama-u.ac.jp (Received: September 13, 2000; Accepted for publication: September 27, 2000; Published on Web: November