# 12.T: Correlation Tables

$$\newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} }$$

$$\newcommand{\vecd}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash {#1}}}$$

$$\newcommand{\id}{\mathrm{id}}$$ $$\newcommand{\Span}{\mathrm{span}}$$

( \newcommand{\kernel}{\mathrm{null}\,}\) $$\newcommand{\range}{\mathrm{range}\,}$$

$$\newcommand{\RealPart}{\mathrm{Re}}$$ $$\newcommand{\ImaginaryPart}{\mathrm{Im}}$$

$$\newcommand{\Argument}{\mathrm{Arg}}$$ $$\newcommand{\norm}[1]{\| #1 \|}$$

$$\newcommand{\inner}[2]{\langle #1, #2 \rangle}$$

$$\newcommand{\Span}{\mathrm{span}}$$

$$\newcommand{\id}{\mathrm{id}}$$

$$\newcommand{\Span}{\mathrm{span}}$$

$$\newcommand{\kernel}{\mathrm{null}\,}$$

$$\newcommand{\range}{\mathrm{range}\,}$$

$$\newcommand{\RealPart}{\mathrm{Re}}$$

$$\newcommand{\ImaginaryPart}{\mathrm{Im}}$$

$$\newcommand{\Argument}{\mathrm{Arg}}$$

$$\newcommand{\norm}[1]{\| #1 \|}$$

$$\newcommand{\inner}[2]{\langle #1, #2 \rangle}$$

$$\newcommand{\Span}{\mathrm{span}}$$ $$\newcommand{\AA}{\unicode[.8,0]{x212B}}$$

$$\newcommand{\vectorA}[1]{\vec{#1}} % arrow$$

$$\newcommand{\vectorAt}[1]{\vec{\text{#1}}} % arrow$$

$$\newcommand{\vectorB}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} }$$

$$\newcommand{\vectorC}[1]{\textbf{#1}}$$

$$\newcommand{\vectorD}[1]{\overrightarrow{#1}}$$

$$\newcommand{\vectorDt}[1]{\overrightarrow{\text{#1}}}$$

$$\newcommand{\vectE}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash{\mathbf {#1}}}}$$

$$\newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} }$$

$$\newcommand{\vecd}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash {#1}}}$$

$$\newcommand{\avec}{\mathbf a}$$ $$\newcommand{\bvec}{\mathbf b}$$ $$\newcommand{\cvec}{\mathbf c}$$ $$\newcommand{\dvec}{\mathbf d}$$ $$\newcommand{\dtil}{\widetilde{\mathbf d}}$$ $$\newcommand{\evec}{\mathbf e}$$ $$\newcommand{\fvec}{\mathbf f}$$ $$\newcommand{\nvec}{\mathbf n}$$ $$\newcommand{\pvec}{\mathbf p}$$ $$\newcommand{\qvec}{\mathbf q}$$ $$\newcommand{\svec}{\mathbf s}$$ $$\newcommand{\tvec}{\mathbf t}$$ $$\newcommand{\uvec}{\mathbf u}$$ $$\newcommand{\vvec}{\mathbf v}$$ $$\newcommand{\wvec}{\mathbf w}$$ $$\newcommand{\xvec}{\mathbf x}$$ $$\newcommand{\yvec}{\mathbf y}$$ $$\newcommand{\zvec}{\mathbf z}$$ $$\newcommand{\rvec}{\mathbf r}$$ $$\newcommand{\mvec}{\mathbf m}$$ $$\newcommand{\zerovec}{\mathbf 0}$$ $$\newcommand{\onevec}{\mathbf 1}$$ $$\newcommand{\real}{\mathbb R}$$ $$\newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]}$$ $$\newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]}$$ $$\newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]}$$ $$\newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]}$$ $$\newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}$$ $$\newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}$$ $$\newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}$$ $$\newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}$$ $$\newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]}$$ $$\newcommand{\laspan}[1]{\text{Span}\{#1\}}$$ $$\newcommand{\bcal}{\cal B}$$ $$\newcommand{\ccal}{\cal C}$$ $$\newcommand{\scal}{\cal S}$$ $$\newcommand{\wcal}{\cal W}$$ $$\newcommand{\ecal}{\cal E}$$ $$\newcommand{\coords}[2]{\left\{#1\right\}_{#2}}$$ $$\newcommand{\gray}[1]{\color{gray}{#1}}$$ $$\newcommand{\lgray}[1]{\color{lightgray}{#1}}$$ $$\newcommand{\rank}{\operatorname{rank}}$$ $$\newcommand{\row}{\text{Row}}$$ $$\newcommand{\col}{\text{Col}}$$ $$\renewcommand{\row}{\text{Row}}$$ $$\newcommand{\nul}{\text{Nul}}$$ $$\newcommand{\var}{\text{Var}}$$ $$\newcommand{\corr}{\text{corr}}$$ $$\newcommand{\len}[1]{\left|#1\right|}$$ $$\newcommand{\bbar}{\overline{\bvec}}$$ $$\newcommand{\bhat}{\widehat{\bvec}}$$ $$\newcommand{\bperp}{\bvec^\perp}$$ $$\newcommand{\xhat}{\widehat{\xvec}}$$ $$\newcommand{\vhat}{\widehat{\vvec}}$$ $$\newcommand{\uhat}{\widehat{\uvec}}$$ $$\newcommand{\what}{\widehat{\wvec}}$$ $$\newcommand{\Sighat}{\widehat{\Sigma}}$$ $$\newcommand{\lt}{<}$$ $$\newcommand{\gt}{>}$$ $$\newcommand{\amp}{&}$$ $$\definecolor{fillinmathshade}{gray}{0.9}$$
$$C_{2v}$$ $$C_{2}$$ $$C_{s}\sigma(xz)$$ $$C_{s}\sigma(yz)$$
$$A_1$$ $$A$$ $$A'$$ $$A'$$
$$A_2$$ $$A$$ $$A"$$ $$A"$$
$$B_1$$ $$B$$ $$A'$$ $$A"$$
$$B_2$$ $$B$$ $$A"$$ $$A'$$

$$C_{3v}$$ $$C_{3}$$ $$C_{s}$$
$$A_1$$ $$A$$ $$A'$$
$$A_2$$ $$A$$ $$A"$$
$$E$$ $$E$$ $$A'+A"$$

$$C_{4v}$$ $$C_{4}$$ $$C_{2v}\;\sigma_v$$ $$C_{2v}\;\sigma_d$$ $$C_{2}$$ $$C_{s}\;\sigma_v$$ $$C_{s}\;\sigma_d$$
$$A_1$$ $$A$$ $$A_1$$ $$A_1$$ $$A$$ $$A'$$ $$A'$$
$$A_2$$ $$A$$ $$A_2$$ $$A_2$$ $$A$$ $$A"$$ $$A"$$
$$B_1$$ $$B$$ $$A_1$$ $$A_2$$ $$A$$ $$A'$$ $$A"$$
$$B_2$$ $$B$$ $$A_2$$ $$A_1'$$ $$A$$ $$A"$$ $$A'$$
$$E$$ $$E$$ $$B_1+B_2$$ $$B_1+B_2$$ $$2B$$ $$A'+A"$$ $$A'+A"$$

$$C_{5v}$$ $$C_{5}$$ $$C_{s}$$
$$A_1$$ $$A$$ $$A'$$
$$A_2$$ $$A$$ $$A"$$
$$E_1$$ $$\{E_1\}$$ $$A'+A"$$
$$E_2$$ $$\{E_2\}$$ $$A'+A"$$

$$C_{6v}$$ $$C_{6}$$ $$C_{3v}\;\sigma_v$$ $$C_{3v}\;\sigma_d$$ $$C_{2v}\;\sigma_v\rightarrow \sigma(xz)$$ $$C_{3}$$ $$C_{2}$$ $$C_{s}\;\sigma_v$$ $$C_{s}\;\sigma_d$$
$$A_1$$ $$A$$ $$A_1$$ $$A_1$$ $$A_1$$ $$A$$ $$A$$ $$A'$$ $$A'$$
$$A_2$$ $$A$$ $$A_2$$ $$A_2$$ $$A_2$$ $$A$$ $$A$$ $$A"$$ $$A"$$
$$B_1$$ $$B$$ $$A_1$$ $$A_2$$ $$B_1$$ $$A$$ $$B$$ $$A'$$ $$A"$$
$$B_2$$ $$B$$ $$A_2$$ $$A_1'$$ $$B_2$$ $$A'$$ $$B$$ $$A"$$ $$A'$$
$$E_1$$ $$\{E_1\}$$ $$E$$ $$E$$ $$B_1+B_2$$ $$\{E\}$$ $$2B$$ $$A'+A"$$ $$A'+A"$$
$$E_2$$ $$\{E_2\}$$ $$E$$ $$E$$ $$A_1+A_2$$ $$\{E\}$$ $$2A$$ $$A'+A"$$ $$A'+A"$$

$$C_{\infty v}$$ $$C_{2v}$$
$$\Sigma^+$$ $$A_1$$
$$\Sigma^-$$ $$A_2$$
$$\Pi$$ $$B_1 + B_2$$
$$\Delta$$ $$A_1 + A_2$$

$$D_{\infty h}$$ $$D_{2h}$$
$$\Sigma^+_g$$ $$A_g$$
$$\Sigma^-_g$$ $$B_{1g}$$
$$\Pi_g$$ $$B_{2g} + B_{3g}$$
$$\Delta_g$$ $$A_g + B_{1g}$$
$$\Sigma^+_u$$ $$B_{1u}$$
$$\Sigma^-_u$$ $$A_{u}$$
$$\Pi_u$$ $$B_{2u} + B_{3u}$$
$$\Delta_u$$ $$A_u + B_{1u}$$

12.T: Correlation Tables is shared under a not declared license and was authored, remixed, and/or curated by LibreTexts.