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These orbital images are based on calculations done using the GAMESS¹ ab initio quantum mechanics package. These images are generated on the fly by JSmol/Jmol from the GAMESS.log file of a restricted Hartree-Fock (RHF) single point energy calculation on a ground state Ne using the aug-CC-pVDZ basis set. The computations were done on computer resources and using software maintained by chemcompute.org.² The orbitals are calculated as:³ $$\begin{array}{rl}{\mathrm{sp}}_{\mathrm{+}}& =\frac{1}{\sqrt{2}}\left[{\mathrm{2s}}_{}+{\mathrm{2p}}_{\mathrm{x}}\right]\\ {\mathrm{sp}}_{\mathrm{-}}& =\frac{1}{\sqrt{2}}\left[{\mathrm{2s}}_{}-{\mathrm{2p}}_{\mathrm{x}}\right]\\ \\ {\mathrm{sp}}_{\mathrm{a}}^2& =\frac{1}{\sqrt{3}}\left[\mathrm{2s}-\sqrt{2}({\mathrm{2p}}_{\mathrm{x}})\right]\\ {\mathrm{sp}}_{\mathrm{b}}^2& =\frac{1}{\sqrt{6}}\left[\sqrt{2}(\mathrm{2s})+{\mathrm{2p}}_{\mathrm{x}}+\sqrt{3}({\mathrm{2p}}_{\mathrm{y}})\right]\\ {\mathrm{sp}}_{\mathrm{c}}^2& =\frac{1}{\sqrt{6}}\left[\sqrt{2}(\mathrm{2s})+{\mathrm{2p}}_{\mathrm{x}}-\sqrt{3}({\mathrm{2p}}_{\mathrm{y}})\right]\\ \\ {\mathrm{sp}}_{\mathrm{i}}^3& =\frac{1}{2}[\mathrm{2s}+{\mathrm{2p}}_{\mathrm{x}}+{\mathrm{2p}}_{\mathrm{y}}+{\mathrm{2p}}_{\mathrm{z}}]\\ {\mathrm{sp}}_{\mathrm{j}}^3& =\frac{1}{2}[\mathrm{2s}-{\mathrm{2p}}_{\mathrm{x}}-{\mathrm{2p}}_{\mathrm{y}}+{\mathrm{2p}}_{\mathrm{z}}]\\ {\mathrm{sp}}_{\mathrm{k}}^3& =\frac{1}{2}[\mathrm{2s}+{\mathrm{2p}}_{\mathrm{x}}-{\mathrm{2p}}_{\mathrm{y}}-{\mathrm{2p}}_{\mathrm{z}}]\\ {\mathrm{sp}}_{\mathrm{m}}^3& =\frac{1}{2}[\mathrm{2s}-{\mathrm{2p}}_{\mathrm{x}}+{\mathrm{2p}}_{\mathrm{y}}-{\mathrm{2p}}_{\mathrm{z}}]\end{array}$$

1. M.W.Schmidt, K.K.Baldridge, J.A.Boatz, S.T.Elbert, M.S.Gordon, J.H.Jensen, S.Koseki, N.Matsunaga, K.A.Nguyen, S.Su, T.L.Windus, M.Dupuis, J.A.Montgomery J. Comput. Chem., 14, 1347-1363(1993).
2. Perri, M. J. and S. H. Weber (2014). "Web-Based Job Submission Interface for the GAMESS Computational Chemistry Program." Journal of Chemical Education 91(12): 2206-2208. (doi: 10.1021/ed5004228). These resources have been supported by the NSF through grants 2417553 (chemcompute.org) and ACI-1548562 (XSEDE).
3. LibreTexts Physical Chemistry: Hybrid Orbitals.