12.T: Correlation Tables

Last updated
Save as PDF

Page ID: 433854

\( \newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} } \) \( \newcommand{\vecd}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash {#1}}} \)\(\newcommand{\id}{\mathrm{id}}\) \( \newcommand{\Span}{\mathrm{span}}\) \( \newcommand{\kernel}{\mathrm{null}\,}\) \( \newcommand{\range}{\mathrm{range}\,}\) \( \newcommand{\RealPart}{\mathrm{Re}}\) \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\) \( \newcommand{\Argument}{\mathrm{Arg}}\) \( \newcommand{\norm}[1]{\| #1 \|}\) \( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\) \( \newcommand{\Span}{\mathrm{span}}\) \(\newcommand{\id}{\mathrm{id}}\) \( \newcommand{\Span}{\mathrm{span}}\) \( \newcommand{\kernel}{\mathrm{null}\,}\) \( \newcommand{\range}{\mathrm{range}\,}\) \( \newcommand{\RealPart}{\mathrm{Re}}\) \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\) \( \newcommand{\Argument}{\mathrm{Arg}}\) \( \newcommand{\norm}[1]{\| #1 \|}\) \( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\) \( \newcommand{\Span}{\mathrm{span}}\)\(\newcommand{\AA}{\unicode[.8,0]{x212B}}\)

\(C_{2v}\)	\(C_{2}\)	\(C_{s}\sigma(xz)\)	\(C_{s}\sigma(yz)\)
\(A_1\)	\(A\)	\(A'\)	\(A'\)
\(A_2\)	\(A\)	\(A"\)	\(A"\)
\(B_1\)	\(B\)	\(A'\)	\(A"\)
\(B_2\)	\(B\)	\(A"\)	\(A'\)

\(C_{3v}\)	\(C_{3}\)	\(C_{s}\)
\(A_1\)	\(A\)	\(A'\)
\(A_2\)	\(A\)	\(A"\)
\(E\)	\(E\)	\(A'+A"\)

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

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

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

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

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