12.T: Correlation Tables
- Page ID
- 433854
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\(\newcommand{\avec}{\mathbf a}\) \(\newcommand{\bvec}{\mathbf b}\) \(\newcommand{\cvec}{\mathbf c}\) \(\newcommand{\dvec}{\mathbf d}\) \(\newcommand{\dtil}{\widetilde{\mathbf d}}\) \(\newcommand{\evec}{\mathbf e}\) \(\newcommand{\fvec}{\mathbf f}\) \(\newcommand{\nvec}{\mathbf n}\) \(\newcommand{\pvec}{\mathbf p}\) \(\newcommand{\qvec}{\mathbf q}\) \(\newcommand{\svec}{\mathbf s}\) \(\newcommand{\tvec}{\mathbf t}\) \(\newcommand{\uvec}{\mathbf u}\) \(\newcommand{\vvec}{\mathbf v}\) \(\newcommand{\wvec}{\mathbf w}\) \(\newcommand{\xvec}{\mathbf x}\) \(\newcommand{\yvec}{\mathbf y}\) \(\newcommand{\zvec}{\mathbf z}\) \(\newcommand{\rvec}{\mathbf r}\) \(\newcommand{\mvec}{\mathbf m}\) \(\newcommand{\zerovec}{\mathbf 0}\) \(\newcommand{\onevec}{\mathbf 1}\) \(\newcommand{\real}{\mathbb R}\) \(\newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]}\) \(\newcommand{\laspan}[1]{\text{Span}\{#1\}}\) \(\newcommand{\bcal}{\cal B}\) \(\newcommand{\ccal}{\cal C}\) \(\newcommand{\scal}{\cal S}\) \(\newcommand{\wcal}{\cal W}\) \(\newcommand{\ecal}{\cal E}\) \(\newcommand{\coords}[2]{\left\{#1\right\}_{#2}}\) \(\newcommand{\gray}[1]{\color{gray}{#1}}\) \(\newcommand{\lgray}[1]{\color{lightgray}{#1}}\) \(\newcommand{\rank}{\operatorname{rank}}\) \(\newcommand{\row}{\text{Row}}\) \(\newcommand{\col}{\text{Col}}\) \(\renewcommand{\row}{\text{Row}}\) \(\newcommand{\nul}{\text{Nul}}\) \(\newcommand{\var}{\text{Var}}\) \(\newcommand{\corr}{\text{corr}}\) \(\newcommand{\len}[1]{\left|#1\right|}\) \(\newcommand{\bbar}{\overline{\bvec}}\) \(\newcommand{\bhat}{\widehat{\bvec}}\) \(\newcommand{\bperp}{\bvec^\perp}\) \(\newcommand{\xhat}{\widehat{\xvec}}\) \(\newcommand{\vhat}{\widehat{\vvec}}\) \(\newcommand{\uhat}{\widehat{\uvec}}\) \(\newcommand{\what}{\widehat{\wvec}}\) \(\newcommand{\Sighat}{\widehat{\Sigma}}\) \(\newcommand{\lt}{<}\) \(\newcommand{\gt}{>}\) \(\newcommand{\amp}{&}\) \(\definecolor{fillinmathshade}{gray}{0.9}\)| \(C_{2v}\) | \(C_{2}\) | \(C_{s}\sigma(xz)\) | \(C_{s}\sigma(yz)\) |
|---|---|---|---|
| \(A_1\) | \(A\) | \(A'\) | \(A'\) |
| \(A_2\) | \(A\) | \(A"\) | \(A"\) |
| \(B_1\) | \(B\) | \(A'\) | \(A"\) |
| \(B_2\) | \(B\) | \(A"\) | \(A'\) |
| \(C_{3v}\) | \(C_{3}\) | \(C_{s}\) |
|---|---|---|
| \(A_1\) | \(A\) | \(A'\) |
| \(A_2\) | \(A\) | \(A"\) |
| \(E\) | \(E\) | \(A'+A"\) |
| \(C_{4v}\) | \(C_{4}\) | \(C_{2v}\;\sigma_v\) | \(C_{2v}\;\sigma_d\) | \(C_{2}\) | \(C_{s}\;\sigma_v\) | \(C_{s}\;\sigma_d\) |
|---|---|---|---|---|---|---|
| \(A_1\) | \(A\) | \(A_1\) | \(A_1\) | \(A\) | \(A'\) | \(A'\) |
| \(A_2\) | \(A\) | \(A_2\) | \(A_2\) | \(A\) | \(A"\) | \(A"\) |
| \(B_1\) | \(B\) | \(A_1\) | \(A_2\) | \(A\) | \(A'\) | \(A"\) |
| \(B_2\) | \(B\) | \(A_2\) | \(A_1'\) | \(A\) | \(A"\) | \(A'\) |
| \(E\) | \(E\) | \(B_1+B_2\) | \(B_1+B_2\) | \(2B\) | \(A'+A"\) | \(A'+A"\) |
| \(C_{5v}\) | \(C_{5}\) | \(C_{s}\) |
|---|---|---|
| \(A_1\) | \(A\) | \(A'\) |
| \(A_2\) | \(A\) | \(A"\) |
| \(E_1\) | \(\{E_1\}\) | \(A'+A"\) |
| \(E_2\) | \(\{E_2\}\) | \(A'+A"\) |
| \(C_{6v}\) | \(C_{6}\) | \(C_{3v}\;\sigma_v\) | \(C_{3v}\;\sigma_d\) | \(C_{2v}\;\sigma_v\rightarrow \sigma(xz)\) | \(C_{3}\) | \(C_{2}\) | \(C_{s}\;\sigma_v\) | \(C_{s}\;\sigma_d\) |
|---|---|---|---|---|---|---|---|---|
| \(A_1\) | \(A\) | \(A_1\) | \(A_1\) | \(A_1\) | \(A\) | \(A\) | \(A'\) | \(A'\) |
| \(A_2\) | \(A\) | \(A_2\) | \(A_2\) | \(A_2\) | \(A\) | \(A\) | \(A"\) | \(A"\) |
| \(B_1\) | \(B\) | \(A_1\) | \(A_2\) | \(B_1\) | \(A\) | \(B\) | \(A'\) | \(A"\) |
| \(B_2\) | \(B\) | \(A_2\) | \(A_1'\) | \(B_2\) | \(A'\) | \(B\) | \(A"\) | \(A'\) |
| \(E_1\) | \(\{E_1\}\) | \(E\) | \(E\) | \(B_1+B_2\) | \(\{E\}\) | \(2B\) | \(A'+A"\) | \(A'+A"\) |
| \(E_2\) | \(\{E_2\}\) | \(E\) | \(E\) | \(A_1+A_2\) | \(\{E\}\) | \(2A\) | \(A'+A"\) | \(A'+A"\) |
| \(C_{\infty v}\) | \(C_{2v}\) |
|---|---|
| \(\Sigma^+\) | \(A_1\) |
| \(\Sigma^-\) | \(A_2\) |
| \(\Pi\) | \(B_1 + B_2\) |
| \(\Delta\) | \(A_1 + A_2\) |
| \(D_{\infty h}\) | \(D_{2h}\) |
|---|---|
| \(\Sigma^+_g\) | \(A_g\) |
| \(\Sigma^-_g\) | \(B_{1g}\) |
| \(\Pi_g\) | \(B_{2g} + B_{3g}\) |
| \(\Delta_g\) | \(A_g + B_{1g}\) |
| \(\Sigma^+_u\) | \(B_{1u}\) |
| \(\Sigma^-_u\) | \(A_{u}\) |
| \(\Pi_u\) | \(B_{2u} + B_{3u}\) |
| \(\Delta_u\) | \(A_u + B_{1u}\) |