Microsoft Excel (LiH)

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1 J. Comput. Chem. Jpn., 2010 Society of Computer Chemistry, Japan Microsoft Excel (2), a*, b c a, b, c, * nagaoka@ehime-u.ac.jp (Received: July 12, 2010; Accepted for publication: November 5, 2010; Advance publication: December 18, 2010) Microsoft Excel (LiH) (H + 2 ) [J. Comput. Chem. Jpn., 9, 177 (2010)] Excel :,,,,,,, Microsoft Excel 1 (PC) [1] Microsoft Excel 2007 (H + 2 ) (3D) [2] Excel (LiH) (ionic character) (H + 2 ) ( polarization function) LiH LiH 2s 1s 2s 3 s 2s 3 s [3] DOI: /jccj.H2211 H2211-1

(b) 3D-contour representation of f Li (2s) presented as an Excel graph.

(d) Real 2s orbital deduced from the experimental dipole moment of LiH.

y(2s) = C 1 f Li (2s) + C 2 f H (1s) = C 1 R 2,0 (r Li )Y 0,0 (q Li, j Li ) + C 2 R 1,0 (r H )Y 0,0 (q H, j H ) (1) y (3s) = C 2 f Li

2 Figure 1. (a) The first few columns of the worksheet applied to the calculation of amplitude of 2s atomic orbital in lithium atom (f Li (2s)). (b) 3D-contour representation of f Li (2s) presented as an Excel graph. (c) 2s bonding orbital in LiH when the bonding electrons are assumed to be shared equally between the two atoms. (d) Real 2s orbital deduced from the experimental dipole moment of LiH. (e) Ordinary contour representation of electron density difference between the molecular orbitals given in Figures 1c and 1d. y(2s) = C 1 f Li (2s) + C 2 f H (1s) = C 1 R 2,0 (r Li )Y 0,0 (q Li, j Li ) + C 2 R 1,0 (r H )Y 0,0 (q H, j H ) (1) y (3s) = C 2 f Li (2s) - C 1 f H (1s) = C 2 R 2,0 (r Li )Y 0,0 (q Li, j Li ) - C 1 R 1,0 (r H )Y 0,0 (q H, j H ) (2) f y Li H f y C 1 C 2 R n,l (r) Y l,m (q, j) n l m r q j zx ( z x y = 0) (z = 0 x = 0) 2s f Li (2s) = R 2,0 (r Li )Y 0,0 (q Li, j Li ) 3D r Li = (z 2 + x 2 ) 1/2 a 0 a 0 (au) a 0 = 1 3 2s (Slater) [4] 1.30 Excel 1 B1 0.2 au z = -8 ~ 8 au A 2 A2 0.2 au x = -4 ~ 4 au B2 2s B42 CD42 (Figure 1a) B2 ~ CD42 H J. Comput. Chem. Jpn.,

3 Figure 2. Schematic representation of composition of 2s and 3s orbitals in LiH. The radius of the circle denotes the magnitude of the atomic orbital coefficient in the molecular orbital. 3D (Figure 1b) x A B2 x A A $ z 1 Figure 1b -1 2s 2s 1s [5] z R LiH = 3.01 au ([6] 16.1) 1s r H {( z - R LiH ) 2 + x 2 } 1/2 Li H LiH 2s 3s 3D C 1 = -2-1/2, C 2 = 2-1/2 2s 2s 1s -1 C 1 LiH 2s 1s 3s 2s 2s 3s (Figure 2) 2s 1s 3s 2s ( C 1 < C 2 ) LiH m er LiH (C C 2 2 ) [3] R LiH m (5.882 D, [6] ) C 1 C 2 C 1 = , C 2 = [7] C 1 C 1 C 2 C 1 C 2 [3] C 1 C 2 R LiH z LiH 2s 3D 3s 3 s f Li (2s) f H (1s) 2s ( 1 2) 2s 3D 2s 2 2 s 2 2s 1s 2.2 H 2 + H 2 + ( ) ( ) 2 ( ) DOI: /jccj.H2211 H2211-3

4 Figure 3. Schematic representation of 1s g orbital in H + 2 [8]. The broken curve shows the orbital formed by a simple linear combination of two 1s orbitals (f A (1s) and f B (1s)). The solid curve shows the real orbital including polarization functions (y(1s g )). Figure 4. Schematic representation of composition of 1s g orbital in H 2 + [8]. The bond length in this Figure is larger than that in Figure 3. The broken curves show 1s orbitals (f A (1s) and f B (1s)) and polarization functions (C 4 f A (2p) and C 4 f B (2p)). The solid curves show the real orbitals including the polarization functions (Eqs. (3) and (4)). (Figure 3) Figure 3 A 1s B [8] A 1s B B 1s A Figure 4 2p 1s [8] f A (1s+ ) = C 3 {f A (1s) + C 4 f A (2p)} = C 3 {R 1,0 (r A )Y 0,0 (q A, j A ) + C 4 R 2,1 (r A )Y 1,0 (q A, j A )} (3) f B (1s+ ) = C 3 {f B (1s) - C 4 f B (2p)} = C 3 {R 1,0 (r B )Y 0,0 (q B, j B ) - C 4 R 2,1 (r B )Y 1,0 (q B, j B )} (4) y(1s g ) = 2-1/2 {f A (1s+ ) + f B (1s+ )} (5) y(1s u ) = 2-1/2 {f A (1s+ ) - f B (1s+ )}(6) A B C 4 1s 2p C 3 f A (1s+ ) f B (1s+ ) C 3 C 4 y(1s g ) y(1s u ) 2-1/2 f A (1s+ ) f B (1s+ ) f A (1s+ ) f B (1s+ ) 2p Figure 4 2p Dickinson H + 2 C 4 = p Z ( Z 2p ) 1s Z ( Z 1s 1 ) (Z 2p /2)/Z 1s = 1.15 [8,9] C 4 f A (1s) f A (2p) f A (1s+ ) C 3 C 3 = zx ( z x y = 0) (z = 0, x = 0) f A (1s+ ) Figure 4 C 3, C 4, (Z 2p /2)/Z 1s Z 1s = 1 f B (1s+ ) f A (1s+ ) f B (1s+ ) H + 2 y(1s g ) 3D z = -1, x = 0 z = 1, x = 0 (2 au) 1s g (C 3 = 1, C 4 = 0) 3D 1s u Dickinson H + 2 C 2 = Z 1s = Z 2p /2 = ( (Z 2p /2)/Z 1s = 1.15) [8,9] C 2 Z 1s Z 2p /2 y(1s g ) 3D C 2 = Z 1s = 1 (Z 2p /2)/Z 1s = 1.15 H J. Comput. Chem. Jpn.,

5 2.3 1s 2s 2p 2s 2p +2e 1s +2e - e ( ) 2s 1s 1s 2p 1s 2s 2p 2s 2s, 2p (2s < 2p) [10] 2s 2p 3s < 3p < 3d 4s < 3d 1s, 2s, 2p 2s < 2p 3s, 3p, 3d 3p, 4s, 3d 3 [2] ( ) [1] Excel PC PC ( Figure 1a 1b) PC PC Excel Excel Excel [2] LiH 2s 3D Figure 1b Li H LiH 2s 3D Figure 1c LiH 2s 3D Figure 1d DOI: /jccj.H2211 H2211-5

Figure 1e LiH 2s (Figure 1d) 3 s Figure 2 2 s (Figure 1e) 4.

4 z H 2 + 1 s g y(1s g ) (Figure 5b) Figure 3 H 2 + 1 s g (Figure 5c) Figure 3 2 (Figure 5d) 1s u [2,11] Figure 5b 5d

(b) 3D-contour representation of amplitude of real y(1s g ) with C 3 = 0.990 and C 4 = 0.145 in H 2 +.

6 Figure 1e LiH 2s (Figure 1d) 3 s Figure 2 2 s (Figure 1e) 4.2 H 2 + f A (1s+ ) Figure 5a H s g y(1s g ) 3D Figure 5b 1 s g Figure 5c Figure 5d f A (1s+ ) (Figure 5a) Figure 4 z H s g y(1s g ) (Figure 5b) Figure 3 H s g (Figure 5c) Figure 3 2 (Figure 5d) 1s u [2,11] Figure 5b 5d 4.3 Figure 5. (a) Ordinary contour representation of Eq. 3. (b) 3D-contour representation of amplitude of real y(1s g ) with C 3 = and C 4 = in H 2 +. (c) y(1s g ) with C 3 = 1 and C 4 = 0 (Figure 2a of Ref. 2). (d) Ordinary contour representation of amplitude difference between the molecular orbitals given in Figures 5b and 5c. 1s, 2s, 2p Figure 6a 2s 1s 2p 1s 2s 2p 1s H J. Comput. Chem. Jpn.,

7 ) (22 ) (23 ) 3d 4s [12] Figure 6b 4s 3d 4s 5 Figure 6. (a) Radial distribution functions for 1s, 2s, and 2p atomic orbitals in hydrogen atom. (b) 3p, 4s, and 3d orbitals. Figure 6a 2s 2p 2s 2p 2p 2s 3s < 3p < 3d 3p, 4s, 3d Figure 6b 1s, 2s, 2p 3d 4s 4s ( 19 ) (20 ) 3d 4s ( 21 Excel LiH H Excel Excel [1],, 40, 600 (1992). [2],,, J. Comput. Chem. Jpn., 9, 177 (2010). doi: /jccj.h2139 [3],, (1980), 8.4. [4] J. A. Pople, D. L. Beveridge, Approximate Molecular Orbital Theory, McGraw-Hill, New York, 1970, p. 29. [5] G. C. Pimentel, R. D. Sprateley,, (1974), p. 85. [6], 5, (2004). [7] 6 R LiH m C 1 C 2 3 DOI: /jccj.H2211 H2211-7

8 [8],, (1990), 8.1. [9] B. N. Dickinson, J. Chem. Phys., 1, 317 (1933). doi: / [10] P. Atkins, T. Overton, J. Rourke, M. Weller, F. Armstrong, ( ) 4, (2008), pp [11],, , 1. [12] E. Clementi, C. Roetti, Atomic Data and Nuclear Data Tables, 14, 177 (1974) doi: /s x(74) ;,, (1980), p [13],, (2004). Practice in Graphing Molecular-Orbitals by Using Microsoft Excel (2) Ionic Character, Polarization Function, and Penetration Shin-ichi NAGAOKA, a* Hiroyuki TERAMAE b and 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@ehime-u.ac.jp By using Microsoft Excel in university courses, we present some practical studies on showing the effects of ionic character in LiH and of polarization function in H + 2 by drawing the three-dimensional contour plots of their molecular-orbitals. Furthermore, drawing the graph of the radical distribution function on penetration has been added to the practice reported in our previous paper [J. Comput. Chem. Jpn., 9, 177 (2010)]. The practices have a large educational impact on understanding of molecular orbitals under various restraints such as time limitation. Keywords: Molecular Orbital, Ionic Bond, Covalent Bond, Polarization Function, Three-Dimensional Contour Representation, Radial Distribution Function, Penetration, Microsoft Excel H J. Comput. Chem. Jpn.,

GHW#3 Louisiana Tech University, Chemistry 281. POGIL exercise on Chapter 2. Covalent Bonding: VSEPR, VB and MO Theories. How and Why?

GHW#3 Louisiana Tech University, Chemistry 281. POGIL exercise on Chapter 2. Covalent Bonding: VSEPR, VB and MO Theories. How and Why? How is Valence Shell Electron Pair Repulsion Theory developed from