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Gaussian

# Gaussian - Gaussian Basis Sets Gaussian Primitives(use...

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Gaussian Basis Sets Gaussian Primitives (use because integrals with r n are well known closed form functions) g s ( α ,r) = 2 α π 3 / 4 e - α r 2 g x ( α ,r) = 128 α 5 π 3 1 / 4 x e - α r 2 Atomic Orbitals (linear combination of Gaussian Primitives) φ μ = i=1 n d μ i g i ( α ,r) 3-21G basis set: core 1s orbital is sum of 3 gaussians valence shell 2s and 2p orbitals are split into two parts: inner part is sum of 2 gaussians outer part is 1 gaussian Lithium 3-21G basis set as listed in Gaussian94. α i d si d xi S 3 1.00 0.3683820000D+02 0.6966860000D-01 0.5481720000D+01 0.3813460000D+00 0.1113270000D+01 0.6817020000D+00 SP 2 1.00 0.5402050000D+00 -0.2631270000D+00 0.1615460000D+00 0.1022550000D+00 0.1143390000D+01 0.9156630000D+00 SP 1 1.00 0.2856450000D-01 0.1000000000D+01 0.1000000000D+01 Ψ 1s = 0.0697 g s ( 36.8 ,r) + 0.381 g s ( 5.48 ,r) + 0.682 g s ( 1.11 ,r) = 0.0697 2 . 36.8 π 3 / 4 e -36.8r 2 + 0.381 2 . 5.48 π 3 / 4 e -5.48r 2 + 0.682 2 . 1.11 π 3 / 4 e -1.11r 2 Ψ 2s (inner) = –0.263 g s ( 0.540 ,r) + 1.14 g s ( 0.102 ,r) Ψ 2s (outer) = 1.00 g s ( 0.0286 ,r) Ψ 2s = a Ψ 2s (inner) + b Ψ 2s (outer) Ψ 2px (inner) = 0.162 g x ( 0.540 ,r) + 0.916 g x ( 0.102 ,r) Ψ 2px (outer) = 1.00 g x ( 0.0286 ,r) E(Li,3-21G)=-200.78 eV E(exp.)=-IP 1 - IP 2 - IP 3 = -202.42eV

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6-311G basis set: core 1s orbital is sum of 6 gaussians valence shell 2s and 2p orbitals are split into three parts:
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