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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 25, 2000) QTVR (QuickTime Virtual Reality) 19 : Atomic Orbital Wavefunction, Interactive Animation, QTVR, Virtual Reality 1 Cu 2 O d [1] [2, 3a, b] [4] [4a, b] Web site [4c, d] [5, 6] QTVR (QuickTime Virtual Reality) [7] [8] QTVR [9] QTVR 2 [8] X Y Z (isosurface) http://cssjweb.chem.eng.himeji-tech.ac.jp/jcs/content.html 87

QTVR X 0 90 Y 0 360 X Y X Y [8] 3d 5 4d 5 2p 3p 4p 3 (1) - (19) χ2p z =, 1=4 p 2π exp(,r=2)z (1) χ2p x =, 1=4 p 2π exp(,r=2)x (2) χ2p y =, 1=4 p 2π exp(,r=2)y (3) χ3p z =, 2=81 p 2π (6,r)exp(,r=3)z (4) χ3p x =, 2=81 p 2π (6,r)exp(,r=3)x (5) χ3p y =, 2=81 p 2π (6,r)exp(,r=3)y (6) χ3d 3z 2,r 2 =, 1=81 p 6π exp(,r=3)(3z 2, r 2 ) (7) χ3d yz =, 2=81 p 2π exp(,r=3)yz (8) χ3d zx =, 2=81 p 2π exp(,r=3)zx (9) χ3d xy =, 2=81 p 2π exp(,r=3)xy (10) χ3d x 2,y 2 =, 1=81 p 2π exp(,r=3)(x 2, y 2 ) (11) χ4p z =, 1=512 p 5π (80,20r + r 2 )exp(,r=4)z (12) χ4p x =, 1=512 p 5π (80,20r + r 2 )exp(,r=4)x (13) χ4p y =, 1=512 p 5π (80,20r + r 2 )exp(,r=4)y (14) χ4d 3z 2,r 2 =, 1=3072 p π (12,r)exp(,r=4)(3z 2, r 2 ) (15) χ4d yz =, 1=512 p 3π (12,r)exp(,r=4)yz (16) χ4d zx =, 1=512 p 3π (12,r)exp(,r=4)zx (17) χ4d xy =, 1=512 p 3π (12,r)exp(,r=4)xy (18) χ4d x 2,y 2 =, 1=1024 p 3π (12,r)exp(,r=4)(x 2, y 2 ) (19) 88 J. Chem. Software, Vol. 7, No. 2 (2001)

60 Figures 1-1, 1-2 (1) - (19) 12 Figure 2 [10] 3 3.1 1. n 1, 2, 3,, l 0, m 0 1s, 2s, 3s, 2. n 2, 3, 4,, l 1, m 0, 1, n 3, 4, 5,, l 2, 3,, n-1, m 0 (x, y z) (1) Z (2) X 2p, 3p, 4p, 3d 3z 2,r 2,4d 3z 2,r 2,5d 3z 2,r 2, 4f 5z 3,3zr 2,5f 5z 3,3zr 2,6f 5z 3,3zr 2, 5g 35z 4,30z 2 r 2 +3r 4,6g 35z 4,30z 2 r 2 +3r 4,7g 35z 4,30z 2 r 2 +3r 4, 3. n 3, 4, 5,, l 2, 3, 4,, n-1, m 1, l (8) - (11) (yz, zx, xy, x 2 -y 2 ) http://cssjweb.chem.eng.himeji-tech.ac.jp/jcs/content.html 89

Figure 1-1. Isosurfaces of hydrogen atomic orbitals 90 J. Chem. Software, Vol. 7, No. 2 (2001)

Figure 1-2. Isosurfaces of hydrogen atomic orbitals http://cssjweb.chem.eng.himeji-tech.ac.jp/jcs/content.html 91

Figure 2. Cross sections of hydrogen atomic orbitals 3d yz,3d zx,3d xy,3d x 2,y 2, 4d yz,4d zx,4d xy,4d x 2,y 2, 4f 5xz 2,xr 2,4f 5yz 2,yr 2,4f x 3,3xy 2,4f 3yx 2,y 3, 4. n 4, 5, 6,, l 3, 4, 5,, n-1, m 2,, (l -1) xyz 4f xyz,4f zx 2,zy 2,5f xyz,5f zx 2,zy 2, 2. 3. 3.2 QTVR 92 J. Chem. Software, Vol. 7, No. 2 (2001)

3.3 3.3.1 Table 1. Percentage of correct answer for the superposition of two different atomic orbitals with the aid of animated or still pictures No. atomic orbitals correct answer % still pictures animated pictures 1 2p z, 2p x 70 100 2 3p z, 3p x 68 100 3 3d x 2,y 2, 3d yz 57 96 4 4p z, 4p x 14 52 5 4d x 2,y 2, 4d yz 18 45 Figures 1-1, 1-2) (1)-(19) Figure 2 2p (Table 1 No. 1 70 %) 4p Table 1 No. 4 14 % 2p 3p Table 1 No. 2 68 % 2p 3p 4p 3d Table 1 No. 3 57 % 4d Table 1 No. 5 18 % (1)-(19) Figure 2 2p, 3p, 3d Table 1 No. 1 - No. 3 100 % 4p, 4d Table 1 No. 4, No. 5 http://cssjweb.chem.eng.himeji-tech.ac.jp/jcs/content.html 93

2p Figure 1-1 (1) - (3) x, y, z x, y, z 3p, 4p Figure 1-1 (4) - (6), Figure 1-1 (12) - (14) 1/3 4p (12) - (14) x, y, z 21 % 32 % 4p 2p 3.3.2 Table 2. Percentage of correct answer for the node of atomic orbitals with the aid of animated or still pictures No. atomic orbital node correct answer % still pictures animated pictures 1 2p z plane 38 100 2 3p z plane 43 100 3 sphere 30 86 4 3d x 2,y 2 plane 21 100 5 4p z plane 14 50 6 sphere 14 50 7 4d x 2,y 2 plane 17 57 8 sphere 17 54 9 4d 3z 2,r 2 sphere 0 25 10 cone 0 14 0 n n-1 Table 2 Figures 1-1, 1-2) (1)-(19) Figure 2 Table 2 No. 1 (38 %) - No. 2 (43 %)) Table 2 No. 10 (0 %)) 94 J. Chem. Software, Vol. 7, No. 2 (2001)

(1)-(19) Figure 2 Table 2 No. 1 - No. 4 Table 2 No. 5 - No. 8 Table 2 No. 9, No. 10 1 Table 2 No. 1 2 Table 2 No. 2 - No. 4 3 Table 2 No. 5 - No. 8 3 Table 2 No. 2 - No. 3 Table 2 No. 10 4d 3z 2,r 2 Table 2 No. 9 4p x 4d 3z 2,r 2 (13) (15) 0 (13) 0 0 0 0 (20) 80,20r + r 2 = 0 (20) r (21) r = 102 p 5 (21) r = 5.53 au, r = 14.47 au 5.53 au 14.47 au (1 au = 0.5292Å = 52.92 pm) Figure 2 Figure 1-1 (13) (22) x = 0 (22) YZ Figure 2 Figure 1-1 4d 3z 2,r 2 Table 2, No. 10 4d 3z 2,r 2 Figure 3 3d 3z 2,r 2 Figure 3 http://cssjweb.chem.eng.himeji-tech.ac.jp/jcs/content.html 95

Figure 3. Isosurfaces of 3d 3z 2,r 2 (left) and 4d 3z 2,r 2 (right) hydrogen atomic orbitals 3d 3z 2,r 2 (7) 3 0 (23) 3z 2, r 2 = 0 (23) (24) z = r cosθ (24) θ 3r 2 cos 2 θ,r 2 = 0 (25) cosθ = 1=,p 3 (26) θ 54.7 Z 4d 3z 2,r 2 (15) 3d 3z 2,r 2 12 au 0% 25 % ( ), 14 % ( ) Table 2, No. 9, No. 10 Figures 1-1, 1-2 [8] 3.4 0 96 J. Chem. Software, Vol. 7, No. 2 (2001)

[11] 4 [1] J. M. Zuo, M. Kim, M. O Keeffe, J. C. H. Spence, Direct observation of d-orbital holes and Cu-Cu bonding in Cu 2 O, Nature, 401, 49-52 (1999). [2] M. Jacoby, Picture-perfect orbitals, Chem. Eng. News, 77, No. 36, 9 (1999). [3a],,, No. 345, 11-12 (1999). [3b],,,, No. 352, 32-40 (2000). [4] URL : a) Orbital Viewer, A program for drawing orbitals. This has many features, and comes in both a Windows version and a command-line interface version. url = (http://www.orbitals.com/orb/ov.htm) b) Atom in a Box, Real-Time Visualization of the Quantum Mechanical Atomic Orbitals url = (http://www.physics.ucla.edu/ dauger/orbitals/) c) VRML(Virtual Reality Modeling Language) url = (http://quanta0.nihs.go.jp/vrml/) d) QuickTime Movie url = (http://www-wilson.ucsd.edu/education/qm/orbitals.html) [5],, (1988). [6],,,,,, J. Chem. Software, 3, 37-48 (1996). url = (http://cssjweb.chem.eng.himeji-tech.ac.jp/jcs/v3n1/a5/abst.html) http://cssjweb.chem.eng.himeji-tech.ac.jp/jcs/content.html 97

[7] QuickTime VR Web site, url = (http://www.apple.co.jp/quicktime/qtvr/) url = (http://www.apple.com/quicktime/qtvr/) [8],,,, QTVR, J. Chem. Software, 5, 129-136 (1999). url = (http://cssjweb.chem.eng.himeji-tech.ac.jp/jcs/v5n3/a4/abst.html) url = (http://www.apc.saitama-u.ac.jp/ ygosei/atomic orbital.htm) [9] R. M. Whitnell, Multimedia Chemistry Lectures, J. Chem. Educ., 71, 721-725 (1994). [10],,, 42, 377 (1991). [11],,, J. Computer Aided Chemistry, 1, 68-75 (2000). Interactive Animation to Facilitate Understanding of the Visual Characteristics of Atomic Orbital Wavefunctions Sumio TOKITA* and Takao SUGIYAMA Department of Applied Chemistry, Faculty of Engineering, Saitama University 255 Shimo-Ohkubo, Urawa, Saitama, 338-8570 JAPAN *e-mail: tokita@apc.saitama-u.ac.jp Multimedia have been thought to be most successful in illustrating concepts, and least successful when applied to the derivation of equations. We have developed interactive animation of hydrogen atomic orbitals using a software called QuickTime Virtual Reality (QTVR). The use of these pictures was shown to increase student interest and participation in the process to understand the mutual relation of the shapes with the mathematical functions of atomic orbitals. Keywords: Atomic Orbital Wavefunction, Interactive Animation, QTVR, Virtual Reality 98 J. Chem. Software, Vol. 7, No. 2 (2001)

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